The y-intercept of the graph is located at (0, 0). So, the value of c is 0.
What is graph?
A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.
To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.
Substituting x = 0, we get:
y = -7(0) + 140y
y = 140y
Simplifying the equation, we get:
139y = 0
Dividing both sides by 139, we get:
y = 0
Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.
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Penny says that 4 x 65 = 260. Estimate to check pennys answer. Is she right? Explain
Neil and Joey share a 24-ounce box of cereal. By the end of the week, Neil has eaten 3 8 of the box, and Joey has eaten 1 4 of the box of cereal. How many ounces are left in the box?
Neil and Joey ate a total of 15 ounces of cereal from the 24-ounce box. By subtracting the amount eaten from the total amount, we find that there are 9 ounces of cereal left in the box.
Neil has eaten 3/8 of the box, which is equal to (3/8) x 24 = 9 ounces.
Joey has eaten 1/4 of the box, which is equal to (1/4) x 24 = 6 ounces.
Together, they have eaten 9 + 6 = 15 ounces.
Subtracting the amount they have eaten from the total amount, we get:
24 - 15 = 9
Therefore, there are 9 ounces of cereal left in the box.
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Edgar has $7,000 in an account that earns 15% interest compounded annually. To the nearest cent, how much interest will he earn in 3 years?
Answer:
429
Step-by-step explanation:
Answer:
Edgar will earn $3,646.30 in interest over 3 years.
Step-by-step explanation:
I'd be happy to walk you through the problem step by step!
The problem is asking how much interest Edgar will earn in 3 years on an initial deposit of $7,000 that earns 15% interest compounded annually.
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (the initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years) the money is invested
We are given that:
P = $7,000
r = 15% = 0.15 (as a decimal)
n = 1 (compounded annually)
t = 3 years
Now, we can plug these values into the formula and solve for A, which is the final amount including interest:
A = $7,000(1 + 0.15/1)^(1*3)
We simplify the expression inside the parentheses first, by dividing the annual interest rate by the number of times the interest is compounded per year:
A = $7,000(1.15)^(3)
We raise 1.15 to the power of 3 using a calculator or by multiplying 1.15 by itself 3 times:
A = $7,000(1.5209)
We multiply the initial deposit by the final amount including interest to get the total amount of interest earned:
Interest = $7,000(1.5209) - $7,000
We simplify the expression:
Interest = $10,646.30 - $7,000
Interest = $3,646.30
So, Edgar will earn $3,646.30 in interest over 3 years.
Hope this helped! If it didn't, I'm sorry! If you still need more help on this, ask me! :]
What is the range of f(x)? {x | −2 ≤ x < 4} {x | −2 < x ≤ 4} {y | −5 < y < −1} {y | −5 ≤ y ≤ −1}
Option (d) is correct i.e., y | −5 ≤ y ≤ −1 , for this we have to know the concept of range and coordinates.
What is Range?In mathematics, a function's range can refer to one of two closely related ideas: The function's codomain a representation of the action A binary relation f between two sets P and Q is a function if there is exactly one y in Q such that f connects x to y for every x in P .
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.
The range of a function is the set of all values that f can produce for all the x-axis in the domain.
If we are given the graph, in order to find the range, we project the graph into the y-axis. Informally, we draw the "shadow" of the graph into the y axis as in the FIGURE attached.
Option (d) is correct i.e., y | −5 ≤ y ≤ −1 .
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Kusum brought 50 glasses for Rs 1500 out of which 4 were broken. If she sold
the rest of the glasses for Rs 35 each, how much profit or loss precent did she bear?
Answer: 7.33%
Step by step explanation:
CP of 50 glasses = Rs. 1500
4 glasses broken
Glass remaining = 50 - 4 = 46
Selling price of 1 glass = Rs 35
SP of 46 glass = 46 x 35 = Rs 1610
Profit = SP - CP = 1610 - 1500 = 110
Profit percentage,
= Profit/CP x 100%
= 110/1500 x 100%
= 7.33%
The cost price of 50 glasses = Rs.1500
The remaining glasses = 46
The Selling price of remaining glasses = 46 × 35
=Rs. 1610
Now
Profit = 1610 - 1500
= Rs.110
Now
Profit Percent
[tex] \frac{Profit}{CP} \times 100%[/tex]
[tex] \frac{110}{1500} \times 100%[/tex]
= 7.33%
i need help please help me
According the question given above the value of n is 21.
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue. The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).
Here, we have
Given : 7 = n/3
we have to find the value οf n.
We apply simplification here and we get
7 = n/3
n = 7×3
n = 21.
Hence, the value οf n is 21.
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Please answer the both questions in the photos below ( will mark brainliest if available + 30p )
Answer:
(5,1)
(7, -5)
Step-by-step explanation:
y = mx + b
The b is the y intercept. This is where the graph crosses the y axis. Graph this first. The m is the slope. It is the rise over the run. You can make any number a fraction by putting it over 1. From the y-intercept you use the slope (rise/run) to graph the second point.
For example, if the slope is 1. then 1/1 would show your rise and run. Start when the y-intercept is and go up 1 and then 1 right. Connect the two points that you have graphed.
If the slope is 2/7, then from the y-intercept go up 2 and right 7. Graph that point and draw a line connecting that point to the point on the y-intercept.
Helping in the name of Jesus.
ANSWER OF THE FIRST TWO EQUATIONS
y = x -4
y= -x+6
both the equations represent a straight line with y intercept as -4 and 6 respectively
x-y-4 = 0. ........(equation 1)
x+y-6 = 0. .........(equation 2)
adding equation 1 and 2
2x - 10 = 0
x = 5
subtracting equation 2 from 1
-2y -2 = 0
y = 1
FINAL ANS : (5,1)
Solve for x. Round your final answer to the nearest tenth.
Law of cosines.
55 90 50
Answer: the length of side c is approximately 74.3 units.
Step-by-step explanation: In a triangle with sides a, b, and c, and opposite angles A, B, and C, respectively, the Law of Cosines states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
We are given the following information:
a = 55 (the side opposite angle A)
b = 50 (the side opposite angle B)
C = 90 degrees (the angle opposite side c)
Substituting these values into the Law of Cosines, we get:
c^2 = 55^2 + 50^2 - 2(55)(50)*cos(90)
c^2 = 3025 + 2500 - 0
c^2 = 5525
Taking the square root of both sides, we get:
c = sqrt(5525)
c ≈ 74.3
Here's what she knows:
The distance between the center of the cow pen and the center of the horse pen is 15 yards.
The distance between the center of the cow pen and the center of the pig pen is 10 yards.
All radii are whole numbers, and all are greater than 3 yards.
● The distance between the center of the cow pen and the center of the horse pen is 15 yards
No two pens are the same size.
She has labeled distances between the barn & points of tangency to the pens in her diagram.
You can help her decide which animal goes in which pen.
1. Now help her find the distance from the barn to the center of each pen! Show all of your work.
Use the page below for workspace as needed.
Distance from barn to center of...
Horse pen:
Cow pen:
Pig pen:
9.5 yds.
8.75 yds.
OX
112⁰
248°
8.75 yds.
16 yds.
This means that the distance from the barn to the center of the pig pen is 8.75 yards.
What is distance?Distance is the amount of space between two points or objects. It is commonly measured in linear units such as meters, feet, or miles. Distance is a fundamental concept in mathematics, physics, and other sciences. It is used to measure the size of objects, the speed of objects, and the time it takes for objects to move. Distance can also be used to measure the strength of a force, the intensity of a light source, or the similarities between two objects. Distance is a crucial concept for understanding the physical world, as it helps us to understand the relationships between objects and how they interact.
The difference in the distances between the center of the cow pen and the center of the horse pen compared to the center of the cow pen and the center of the pig pen is due to the different radii of the pens. Since all radii are greater than 3 yards, the distance of the cow pen and the horse pen is longer than the distance of the cow pen and the pig pen.
To calculate the distance from the barn to the center of each pen, we need to use the angle of tangency and the radii of the pens. For each pen, we need to calculate the angle of tangency, which is the angle between the hypotenuse of the triangle formed by the barn, the pen and the center of the pen and the radius of the pen. This can be calculated by either the Law of Cosines or the Law of Sines.
For the horse pen, the angle of tangency is 112 degrees and the radius is 7 yards. This means that the distance from the barn to the center of the horse pen is 9.5 yards. For the cow pen, the angle of tangency is 248 degrees and the radius is 5 yards. This means that the distance from the barn to the center of the cow pen is 8.75 yards. Finally, for the pig pen, the angle of tangency is 128 degrees and the radius is 3 yards. This means that the distance from the barn to the center of the pig pen is 8.75 yards.
Therefore, the difference in the distances between the center of the cow pen and the center of the horse pen compared to the center of the cow pen and the center of the pig pen is due to the different radii of the pens. The larger the radius of the pen, the longer the distance from the barn to the center of the pen.
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The distances from the barn to the center of the Horse pen, Cow pen, and Pig pen are 15 yards, 15 yards, and 18.35 yards respectively.
What is distance?Distance is the amount of space between two points or objects. It is commonly measured in linear units such as meters, feet, or miles. Distance is a fundamental concept in mathematics, physics, and other sciences. It is used to measure the size of objects, the speed of objects, and the time it takes for objects to move.
First, let's start with the Horse pen. To find the distance from the barn to the center of the Horse pen, we'll use the law of cosines. The law of cosines states that for a triangle ABC, with angle A being 90°, the following equation can be used to find the length of side a:
a² = b²+ c² - 2bc cosA
Therefore, for our triangle, with angle A being 90°, we have:
a²= 15² + 10² - 2(15)(10)cos90
a²= 225 + 100 - 300
a²= 25
a = √25
a = 5
Now, we can find the distance from the barn to the center of the Horse pen by adding the distance from the center of the pen to the barn, which is 10 yards, to 5 yards, which is the distance from the barn to the center of the Horse pen.
Therefore, the distance from the barn to the center of the Horse pen is 10 + 5 = 15 yards.
Now, let's find the distance from the barn to the center of the Cow pen. Again, we'll use the law of cosines. The law of cosines states that for a triangle ABC, with angle A being 90°, the following equation can be used to find the length of side a:
a² = b²+ c² - 2bc cosA
Therefore, for our triangle, with angle A being 90°, we have:
a²= 15² + 9.5² - 2(15)(9.5)cos90
a²= 225 + 90.25 - 285.75
a²= 30.25
a = √30.25
a = 5.5
Now, we can find the distance from the barn to the center of the Cow pen by adding the distance from the center of the pen to the barn, which is 9.5 yards, to 5.5 yards, which is the distance from the barn to the center of the Cow pen.
a²= b²+ c²- 2bc cosA
Therefore, for our triangle, with angle A being 90°, we have:
a²= 16² + 8.75² - 2(16)(8.75)cos90
a²= 256 + 76.5625 - 240
a² = 92.5625
a = √92.5625
a = 9.6
Now, we can find the distance from the barn to the center of the Pig pen by adding the distance from the center of the pen to the barn, which is 8.75 yards, to 9.6 yards, which is the distance from the barn to the center of the Pig pen.
Therefore, the distance from the barn to the center of the Pig pen is 8.75 + 9.6 = 18.35 yards.
In conclusion, the distances from the barn to the center of the Horse pen, Cow pen, and Pig pen are 15 yards, 15 yards, and 18.35 yards respectively.
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What is the monthly periodic rate on a loan with an APR of 20.3%
The monthly periodic rate with APR 20.3% is 1.69%
What is APR?APR is also known as Annual Payment Rate. And it is the cost of your mortgage credit as a yearly rate.
Annual Percentage Rate is typically higher than your interest rate because it includes your interest rate plus certain fees, such as lender and mortgage broker fees, based on the specific characteristics of your loan.
Monthly Interest Payment means the amount of interest paid on a Payment Date for the preceding Interest Period based on interest calculated for such preceding Interest Period at the Monthly Interest Rate.
If the Annual Percentage Rate is 20.3% and there are 12 months on a year , the monthly interest = 20.3/12 = 1.69 %
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The explicit formula of an arithmetic sequence is an=−6−4(n−1). What is the recursive formula of the sequence? ( 1 point)
A. an+1=an−4, a1=−6
B.an+1=an−6, a1=−4
C. an+1=an+4, a1=−6
D. an+1=an−4
Answer: Option A. an+1=an-4, a1=-6
Step-by-step explanation:
Games A group of friends tries to keep a beanbag from touching the ground.
On one kick, the beanbag's height can be modeled by h = -161² + 14t + 2, where h
is the height in feet above the ground and t is the time in seconds. Find the time it
takes the beanbag to reach the ground.
The time it takes for the beanbag to reach the ground is t = 1 second.
What is quadratic equation ?
A quadratic equation is a expression of the form ax^{2} + bx + c = 0, where x is the variable, and a, b, and c are constants. It is a type of second-degree polynomial equation, which can be solved using various methods, including factoring, completing the square, and using the quadratic formula
We know that the beanbag will touch the ground when its height, h, equals zero. Therefore, we can set the equation for h equal to zero and solve for t:
h = -16t² + 14t + 2
0 = -16t² + 14t + 2 (substitute h=0)
0 = -8t² + 7t + 1 (divide both sides by 2)
0 = (t-1)(-8t-1) (factor the quadratic)
So, either t - 1 = 0 or -8t - 1 = 0. Solving for t in each case, we get:
t - 1 = 0 => t = 1
-8t - 1 = 0 => t = -1/8
The negative value of t doesn't make sense in this context, since time cannot be negative. Therefore, the time it takes for the beanbag to reach the ground is t = 1 second.
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what is this question for math need help
Answer:
A
Step-by-step explanation:
The answer is 2x+2y+2 which is A
Answer: I think its B but I'm not quite sure
Step-by-step explanation:
PLEASE HELP!! ⚠️⚠️⚠️
Bernie wanted to stock up on drinks for an upcoming party. first, he spent $37 on 7 cases of juice and 8 cases of soda, which is all the store had in stock. A few days later, he returned to the store and purchased an additional 7 cases of juice and 15 cases of soda, spending a total of $51. What is the price of each drink?
The price of each drink is given as follows:
Case of juice: $3.Case of soda: $2.How to obtain the price of each drink?The price of each drink is obtained by a system of equations, for which the variables are given as follows:
Variable x: cost of a case of juice.Variable y: cost of a case of soda.He spent $37 on 7 cases of juice and 8 cases of soda, hence:
7x + 8y = 37.
Purchased an additional 7 cases of juice and 15 cases of soda, spending a total of $51, hence:
7x + 15y = 51.
Hence the system is composed by these two equations:
7x + 8y = 37.7x + 15y = 51.Subtracting the second equation by the first, the value of y is obtained as follows:
7y = 14
y = 2.
Then the value of x is obtained as follows:
7x + 15(2) = 51
7x = 21
x = 21/7
x = 3.
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The ordered pair (a,b) satisfies the inequality y
Answer:
If you add 5 to a, it will be greater than b
Step-by-step explanation:
i got it right
Identify the function in standard form. 3x 2 + 6x - 12 = 0 3x 2 + 2x + 10 = 0 5x 2 - 10x + 5 = 0 2x 2 - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.
The functions in standard form are:
3x² + 6x - 12 = 0
3x² + 2x + 10 = 0
5x² - 10x + 5 = 0
2x² - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0
where a, b, and c are constants and a ≠ 0.
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A population of 250 wild turkeys decreases by 2. 2% per year. At the end of 8 years, there will be approximately 209 turkeys in the population. Which function can be used to determine the number of turkeys, y, in this population at the end of t years?
We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878. The number of turkeys, y, in the population at the end of t years is obtained by substituting this value into the exponential decay formula and getting the following result: y = 250(0.878)t.
The equation y = 250(1 - 0.022)t, where t is the number of years, may be used to calculate the number of turkeys, y, in this population at the end of t years.
Using the exponential decay formula, A = P(1 - r)t, where A is the final amount, P is the beginning amount, r is the rate of decay in decimal notation, and t is the duration in years, we may arrive at this function.
If we substitute the values provided, we get: 209 = 250(1 - 0.022)^8
We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878.
This value may be substituted into the exponential decay formula to obtain the number of turkeys, y, in the population at the end of t years: y = 250(0.878)t.
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While trying to understand and prepare data for further analysis you find out that there are small amount missing values for a categorical variable, and you know that keeping this variable is important for the success of your project. What would be the correct way to handle the missing values?
A. Replace missing values with the mean value.
B. Although it seems like keeping this variable is important for the success of the project, due to missing values decide to exclude this variable from the analysis.
C. Replace the missing values with the most frequent category.
D. Do nothing and proceed with further analysis.
The result, doing nothing is not a sensible approach to missing data handling.
The correct way to handle the missing values is to replace the missing values with the most frequent category.What is a variable?A variable is any feature, number, or measurement that may be measured, manipulated, or controlled in an experiment. Variables in scientific investigations are classified as dependent or independent. A categorical variable is one that may take on one of several different categories or distinct groups of data. Understanding the problem statement While attempting to understand and prepare data for further analysis, you discover that there are a small number of missing values for a categorical variable.
Since you know that retaining this variable is important for the project's success, what is the appropriate method for handling the missing values?Missing values should be replaced with the most frequent category because this is the best way to handle them.
To get a complete dataset, the missing values must be filled. The variables with missing data are imputed to improve the accuracy of your analysis.Replace missing values with the mean value (option A) - This technique is only applicable to quantitative variables.
In categorical variables, it makes no sense to replace missing data with the mean value. It might produce nonsensical data, making the whole data set unusable.Although it seems like keeping this variable is important for the success of the project, due to missing values decide to exclude this variable from the analysis (option B) - This alternative may lead to the exclusion of crucial data that can help with a future examination.
Replace the missing values with the most frequent category (option C) - The most frequent category is frequently used to replace missing data. The most common category is determined and substituted for missing data. It's a reasonable method because the data is still valuable and the categorical variable is critical for the project's success.Do nothing and proceed with further analysis (option D) - The examination results would be influenced if we use the existing data without filling in the missing information. As a result, doing nothing is not a sensible approach to missing data handling.
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Give a linear equation for the total remaining oil reserves, , in terms of , the number of years since now. (Be sure to use the correct variable and Preview before you submit. ) R=
A. The linear equation is R = -18t + 1,820
B. total reserve oil 1,568 billions of barrels
C. approximately 101.11 years
To make our equation, we'll use the form R = mt + b. M represents how many billion barrels of oil are being lost each year, which we know is 18 billion. So -18 will be our m. B is how many total barrels of oil there are, which is 1,820. So 1,820 will be our b. Now the equation looks like this:
R = -18t + 1,820
We can use this equation to answer Part B.
Replace the t with 14:
R = -18(14) + 1,820
Now solve for R:
R = -18(14) + 1,820
R = -252 + 1,820
R = 1,568
14 years from now, there will be 1,568 billions of barrels left.
To solve part C, we need to find how many years it will take for all of the oil to be used up. After it's all used up, the total amount of oil will be 0, so we can replace R with 0 and then solve for t:
0 = -18t + 1,820
Subtract 1,820 from both sides to isolate -18t:
0 - 1,820 = -18t + 1,820 - 1,820
-1,820 = -18t
Divide both sides by -18 to isolate the t:
-1,820/-18 = -18t/-18
101.11 = t
After approximately 101.11 years, all of the oil will be used up.
The complete question is-
Suppose that the world's current oil reserves is R = 1820 billion barrels. If, on average, the total reserves
is decreasing by 18 billion barrels of oil each year, answer the following:
A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms of t, the
number of years since now. (Be sure to use the correct variable and Preview before you submit.)
R
B.) 14 years from now, the total oil reserves will be
billions of barrels.
C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all
used up) approximately
years from now.
(Round your answer to two decimal places.)
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Apple stock rose from $75 per share on January 1, 2013 to $109 per share on January 1, 2015. During the
same period, Microsoft stock rose from $27 to $47.
(a) What was the absolute change in dollars in the Apple stock price?
(b) What was the absolute change in dollars in the Microsoft stock price?
(c) What was the relative change in the Apple stock price, rounded to the nearest percent? $
(d) What was the relative change in the Microsoft stock price, rounded to the nearest percent?
%
(e) Suppose you invested $5,000 in Apple stock on January 1, 2013. How many whole shares would you have
been able tobuy? (Enter a whole number.)
shares
%
(f) At the end of the two years, if you sold all these shares, what would be the total amount in dollars from
the sale? $
(g) Suppose you invested $5,000 in Microsoft stock on January 1, 2013. How many whole shares would you
have been able to buy? (Enter a whole number.)
shares
(h) At the end of the two years, if you sold all these shares, what would be the total amount from the
sale? $
The stock price of corporation is [tex]45[/tex]%, [tex]34[/tex] and [tex]20[/tex] correspondingly for the absolute change in the dollar and the Ms dollar.
The price of a stock right now.It is the latest trading price for a stock or some other security. Inside an market, the place to start is the current price. It demonstrates the cost that a both parties would be willing to pay for a subsequent deal involving that security.
(a) The absolute change in dollars in the Apple stock price is:
[tex]109 - 75 = 34[/tex]
(b) The absolute change in dollars in the Microsoft stock price is:
[tex]47 - 27 = 20[/tex]
(c) The relative change in the Apple stock price, rounded to the nearest percent is: [tex]((109 - 75)/75) * 100 = 45[/tex]%
(d) The relative change in the Microsoft stock price, rounded to the nearest percent is: [tex]((47 - 27)/27) * 100 = 74[/tex]%
(e) If you invested $[tex]5,000[/tex] in Apple stock on January 1, 2013, and the price per share was $[tex]75[/tex], you could buy: [tex]5,000/75 = 66.67[/tex] shares
Rounded down to the nearest whole number, you would be able to buy [tex]66[/tex] shares.
(f) If you sold all [tex]66[/tex] shares of Apple stock at the price of $[tex]109[/tex] per share at the end of two years, the total amount from the sale would be:
[tex]66 shares * $109/share = 7,194[/tex]
(g) If you invested $[tex]5,000[/tex] in Microsoft stock on January 1, 2013, and the price per share was $[tex]27[/tex], you could buy: [tex]5,000/27 = 185.19[/tex] shares
Rounded down to the nearest whole number, you would be able to buy [tex]185[/tex] shares.
(h) If you sold all [tex]185[/tex] shares of Microsoft stock at the price of $[tex]47[/tex] per share at the end of two years, the total amount from the sale would be:
[tex]185 shares * 47/share = 8,695[/tex]
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a model rocket is 5cm tall. If it was built with a scale of 1cm: 2m, then how tall is the real rocket?
Answer:
If the model is 5cm and 1cm is equal to 2m, it means the actual rocket is 10 meters.
Step-by-step explanation:
1cm = 2m
5cm is 5 times the amount of 1cm.
10m is 5 times the amount of 2m
Answer : 10 Meters
Explanation : 2 × 5 = 10
prove that (sec theta + tan theta - 1)(sec theta - tan theta + 1) = 2tan theta
Answer:
(secΘ+tanΘ-1)(secΘ-tanΘ+1)
=sec²Θ-secΘtanΘ+secΘ+secΘtan-tan²Θ+tanΘ-secΘ+tanΘ-1
=2tanΘ+(sec²Θ-tan²Θ)-1
=2tanΘ+1-1
=2tanΘ
The angle of elevation from the spot where a basketball player is standing up to the
top of a 10ft high hoop is 25 degrees. How far is the player from the base of the hoop
(to the nearest hundredth of a foot)?
If the angle of elevation from the spot where a basketball player is standing up to the top of a 10ft high hoop is 25 degrees, the player is approximately 21.45 feet away from the base of the hoop.
To solve this problem, we can use the trigonometric function tangent, which relates the opposite side of a right triangle to its adjacent side, using the angle of elevation:
tan(25 degrees) = opposite / adjacent
where the opposite side is the height of the hoop (10 feet), and we need to find the adjacent side, which is the distance from the player to the base of the hoop.
To isolate the adjacent side, we can rearrange the equation:
adjacent = opposite / tan(25 degrees)
adjacent = 10 / tan(25 degrees)
Using a calculator, we can find that tan(25 degrees) is approximately 0.4663:
adjacent = 10 / 0.4663
adjacent ≈ 21.45 feet
We round to the nearest hundredth of a foot, which gives us the final answer of 21.45 feet.
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The area of a triangle is one fourth the area of a square. If the base of the triangle and a
side of the square are equal, what is the ratio of the side of the square to the height of the
triangle?
Answer:
see below
Step-by-step explanation:
2:1
Look at the image below.
To make cherry trail mix, Sebastián needs 4 oz of nuts for every 3 oz of dried cherries. To make sunflower trail mix, he needs 5 oz of nuts for every 2 oz of sunflower seeds. Can Sebastian make more cherry trail mix or sunflower trail mix with 20 oz of nuts? Show your work.
Answer:
Cherry Trail Mix
Step-by-step explanation:
cherry trail mix ratio = 4:3
sunflower trail mix ration = 5:2
4 goes into 20 5 times so multiply 3 by 5 to get 15. Add them together to make 35 oz
5 goes into 20 4 times so multiply w by 4 to get 8. Add them together to make 28 oz
35 > 28
Would the interval found in part c increase, decrease, or remain the same if fewer than 95 people were surveyed? justify your answer
The confidence interval would increase because with fewer people, the margin of error would be larger.
The confidence interval found in part c would increase if fewer than 95 people were surveyed. This is because the margin of error is calculated using the sample size; the smaller the sample size, the larger the margin of error. The margin of error dictates the range of values that the population parameter is likely to fall within. Therefore, if fewer people are surveyed, the margin of error would increase, resulting in a wider confidence interval. This means that the interval from part c would no longer be valid if the sample size decreased, and a new interval with a larger range would need to be calculated.
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Use the Pythagorean identity, (a²- y2)2 + (2xy)² = (x² + y²)2, to create a Pythagorean triple.
Follow these steps:
1. Choose two numbers and identify which is replacing and which is replacing y.
2. How did you know which number to use for x and for y
3. Explain how to find a Pythagorean triple using those numbers.
4. Explain why at least one leg of the triangle that the Pythagorean triple represents must have an even-numbered length.
The Pythagorean triple created by the steps are (3, 4, 5) where the hypotenuse is 5
How to create a Pythagorean triple.The numbers x and y
Let's choose 3 and 4 as our x and y, respectively.
How we chose x and y
We can choose any numbers for x and y.
However, we usually choose numbers such that x > y to avoid duplicates.
Finding the triple
To find the Pythagorean triple, we substitute x = 3 and y = 4 in the Pythagorean identity:
(x²- y²)² + (2xy)² = (x² + y²)²
(3² - 4²)² + (2(3)(4))² = (3² + 4²)²
(-7)² + (24)² = (9)² + (16)²
49 + 576 = 81 + 256
625 = 625
We can see that this equation is true, which means that (3, 4, 5) is a Pythagorean triple.
Why at least one leg must be even
At least one leg of the triangle represented by the Pythagorean triple must have an even-numbered length because if one of the legs is odd, then the other leg and the hypotenuse must be odd too.
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Q26) Suppose you are a project manager, and you estimate that the time it takes to complete a particular task on your project follows a normal distribution with a mean of 20 days and a standard deviation of 3 days. What is the probability that the task will take more than 25 days to complete?
The probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.
To find the probability of a task taking more than 25 days to complete, given that the mean and standard deviation of the normal distribution are 20 and 3 days, respectively, one can use the Z-score formula.Z = (X - μ)/σwhere Z is the standard score, X is the observed value, μ is the mean, and σ is the standard deviation. Therefore,Z = (25 - 20)/3 = 5/3 ≈ 1.67The area to the right of Z = 1.67 on a standard normal distribution table represents the probability that the task will take more than 25 days to complete. Using a standard normal distribution table or calculator, we can find that P(Z > 1.67) = 0.0475 or approximately 4.75%.Therefore, the probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.
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Find all complex zeros of the given polynomial function, and write the polynomial in completely factored form.
f(x)=4x^3+3x^2-44x-33
Find the complex zeros of f. Repeat any zeros if their multiplicity is greater than 1.
x=
From the given information, the complex zeros of the polynomial are x = -3/4, (9 + 17i)/8, (9 - 17i)/8.
To find the complex zeros of the given polynomial function, we can use the Rational Root Theorem to check for possible rational roots, and then use synthetic division or long division to factor the polynomial.
The possible rational roots of the polynomial are of the form ±a/b, where a is a factor of the constant term 33 and b is a factor of the leading coefficient 4. Therefore, the possible rational roots are:
±1/4, ±3/4, ±1/2, ±3/2, ±11/4, ±33/4, ±11/2, ±33/2.
We can check these possible roots using synthetic division, and we find that the polynomial has a rational root x = -3/4. Dividing by (x + 3/4) using synthetic division, we get:
4x³ + 3x² - 44x - 33 = (x + 3/4)(4x² - 9x - 44)
Now, we can use the quadratic formula to find the roots of the quadratic factor 4x² - 9x - 44:
x = (9 ± √(9² + 4(4)(44)))/(2(4)) = (9 ± 17i)/8.
To factor the polynomial completely, we can use the complex zeros and the linear factor we found earlier:
f(x) = 4x³ + 3x² - 44x - 33 = (x + 3/4)(x - (9 + 17i)/8)(x - (9 - 17i)/8).
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i need help with thiss
The only true statement in the following equation are B and D.
How to find true statement?A. When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.
To check this statement, we can use the formula for exponential growth:
P(t) = P0 * [tex]3^{(t/6)[/tex]
Where P(t) is the population at time t, P0 is the initial population, and t is the time in hours.
If P(t) = 900, we can solve for t:
900 = [tex]100 * 3^{(t/6)[/tex]
9 = [tex]3^{(t/6)[/tex]
ln(9) = (t/6) * ln(3)
t = 6 * ln(9) / ln(3) ≈ 12.68
So, it takes approximately 12.68 hours for the population to reach 900. Therefore, statement A is false.
B. Three hours after the colony is placed on the petri dish, there are 200 bacteria.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement B is true.
C. Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement C is false.
D. In the first hour the colony is placed on the petri dish, the population grows by a factor of [tex]$3^{\frac{1}{6}}$[/tex]
Using the formula above with t=1:
P(1) = [tex]100 * 3^(1/6)[/tex]
So, the population after 1 hour is 100 times the sixth root of 3. We can write this as:
P(1) = [tex]100 * (3^(1/6)) = 100 * 3^{\frac{1}{6}}[/tex]
Therefore, statement D is true.
E. Between 8 a.m. and 9 a.m., the population grows by a factor of [tex]$3^{\frac{2}{3}}$[/tex]
Between 7 a.m. and 8 a.m., the population grows by a factor of 3. Then, between 8 a.m. and 9 a.m., it grows by another factor of 3. So, between 7 a.m. and 9 a.m., the population grows by a factor of [tex]3^2[/tex] = 9. Taking the sixth root of 9 gives:
[tex](3^2)^(1/6) = 3^(1/3) = 3^{\frac{2}{6}} = 3^{\frac{1}{3}}[/tex]
So, the population between 8 a.m. and 9 a.m. grows by a factor of [tex]3^(1/3)[/tex]. Therefore, statement E is false.
In summary, the true statements are B and D.
We can employ the AC approach to factor the quadratic expression seen in the image. To achieve -6 * -15 = 90, we first multiply the coefficients of the first and last terms. The middle term's coefficient, which is -9, is then shown to be two factors of 90. Since -6 * -15 = 90 and -6 + (-15) = -21, which is the same as -9 when we factor out the GCF of 3, these factors are -6 and -15:
[tex]x^2 - 9x - 90 = (x - 15)(x + 6)[/tex]
As a result, the quadratic expression's factored form is (x - 15)(x + 6).
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