The value of the expression 3x + 4y² when x = -3 and y = 5 is 91.
What is the value of the given expression?Given the expression in the question;
3x + 4y²
x = -3y = 5To determine the value of the expression when x = -3 and y = 5, plug in x = -3 and y = 5 for every x and values in the expression and simplify.
3x + 4y²
3( -3 ) + 4( 5 )²
Simplify
Take the square of 5
3( -3 ) + 4( 25 )
Multiply 3 and -3
-9 + 4( 25 )
Multiply 4 and 25
-9 + 100
Add -9 and 100
91
Therefore, the value of the expression is 91.
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If a plane can travel 490 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the plane in still air.
Answer:
460
Step-by-step explanation:
Let b = base speed and w = wind power.
Here's what we know:
b + w = 490
b - w = 430
From here, we can use the elimination method. If we treat each variable and constant as columns, we do the following:
b + b = 2b
w - w = 0
490 + 430 = 920
Leaving us with:
2b = 920
Divide by 2:
2b / 2 = b
920 / 2 = 460
So b = 460 mph
(a) Suppose that to provide additional funds for higher education, the federal government adopts a new income tax plan that consists of the 2010 income tax plus an additional 200 dollars per taxpayer. Let gg be the function such that g(x)g(x) is the 2010 federal income tax for a single person with taxable income xx dollars, and let hh be the corresponding function for the new income tax plan.
Write a formula for h(x)h(x) in terms of g(x)g(x):
h(x)=
⋅g(=
)+=
(b) Suppose that in order to pump more money into the economy during a recession, the federal government adopts a new income tax plan that makes income taxes 95 percent of the 2010 income tax. Let gg be the function such that g(x)g(x) is the 2010 federal income tax for a single person with taxable income xx dollars, and let hh be the corresponding function for the new income tax plan.
Write a formula for h(x)h(x) in terms of g(x)g(x):
h(xh(x)=
⋅g(=
)+=
h(x) = g(x) + 200, which means the average new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.
h(x) = g(x) + 200
h(x) is the new income tax for a single person with taxable income x dollars.
g(x) is the 2010 federal income tax for a single person with taxable income x dollars.
Therefore, h(x) = g(x) + 200, which means the new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.
The new income tax plan consists of the 2010 income tax plus an additional 200 dollars per taxpayer. To represent this mathematically, we let g(x) be the function such that g(x) is the 2010 federal income tax for a single person with taxable income x dollars, and let h(x) be the corresponding function for the new income tax plan. By examining the new income tax plan, we can see that the new income tax is the sum of the original income tax plus an additional flat fee of 200 dollars per taxpayer. Thus, h(x) = g(x) + 200, which is a concise formula that captures the essence of the new income tax plan. This formula shows that the new income tax is simply the original income tax increased by a fixed amount of 200 dollars.
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The sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7: 6. The store donates 24 soccer balls. How many basketballs does the store donate?
The number of basketballs that were donated is equal to 28 basketballs.
How to determine the number of basketballs that were donated?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;
7:6 = x:24
7/6 = x/24
Cross-multiplying, we have the following:
6x = 7 × 24
6x = 168
x = 168/6
x = 28 basketballs.
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80 items to ship full case and 7 items per case
Answer: You want to ship 80 items, and each case holds 7 items. To find the number of cases needed to ship the 80 items, you can use the formula:
Number of cases = (Number of items) / (Items per case)
So in this case, the number of cases needed to ship 80 items is:
Number of cases = 80 / 7
Which simplifies to 11.428571428571429, so you will need 12 cases to ship 80 items.
Step-by-step explanation:
Find the measure of the numbered angles.
The measure of the numbered angles of the quadrilaterals in the question are presented as follows;
14. m∠1 = 54°, m∠2 = 36°, m∠3 = 54° m∠4 = 108°, m∠5 = 72°
15. m∠1 = 90°, m∠2 = 45°, m∠3 = 45°, m∠4 = 45°, m∠5 = 45°
16. m∠1 = 64°, m∠2 = 64°, m∠3 = 26°, m∠4 = 90°, m∠5 = 64°
What is a quadrilateral?A quadrilateral is a four sided polygon.
14. The figure is a rectangle
The two diagonals of a rectangle are the same length and the diagonals of a rectangle bisect each other, therefore;
The triangles formed by the diagonals of the rectangle are isosceles triangles.
The angle at the vertex of the isosceles triangle that has 36° as the base angle of the triangle is therefore; (180° - 2 × 36°) = 108°
The angle ∠4, is a vertical angle to the angle calculated above, therefore;
m∠4 = 108°
m∠5 = (360° - 2 × 108°) = 72°
m∠5 = 72°
The similar triangles formed by the diagonals indicates that we get;
m∠2 = 36°
m∠1 = (180° - m∠5)/2
Therefore; m∠1 = (180° - 72°)/2 = 54°
m∠1 = 54°
∠1 ≅ ∠3
Therefore; m∠3 = m∠1 = 54°
m∠3 = 54°
15. The quadrilateral is a square, therefore;
The diagonals bisect each other and are perpendicular.
m∠1 = 90° (Definition of perpendicular angles)
m∠5 = (180° - 90°)/2 = 45°
m∠5 = 45°
∠3 ≅ ∠5, therefore;
m∠3 = m∠5 = 45°
m∠3 = 45°
m∠3 + m∠2 = 90° (The vertex angles of a square are 90°)
m∠2 = 90° - m∠3
m∠2 = 90° - 45° = 45° (Substitution property)
m∠2 = 45°
16. The quadrilateral is a rhombus, therefore;
The diagonals of a rhombus perpendicular
Adjacent angles are supplementary
The opposite angles of a rhombus are congruent
The opposite sides of a rhombus are parallel
Diagonals of a rhombus bisect the interior angles
The above properties indicates that we get;
90° + m∠1 + 26° = 180°
m∠1 = 180° - 26° - 90° = 64°
m∠1 = 64°
m∠4 = 90°
The angle ∠3 and the 26° angle are alternate interior angles. Alternate interior angles between parallel lines are congruent, therefore;
m∠3 = 26°
m∠1 = m∠2 (definition of bisected angle), therefore;
m∠2 = m∠1 = 64°
m∠2 = 64°
∠2 and ∠5 are alternate interior angles, therefore;
∠2 ≅ ∠5
m∠5 = m∠2 = 64°
m∠5 = 64°
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Basketball Baseball Soccer Football 6th grade 7th grade 8th grade 2 1 7 8 4 6 4 15 Explain what the ratio 8:73 represents. 5 4 10 O The ratio 8:73 represents the ratio of total athletes to 7th grade football players. OThe ratio 8:73 represents the ratio of 6th grade football players to total athletes. O The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes. OThe ratio 8:73 represents the ratio of 6th grade athletes to total athletes.
Answer:
Step-by-step explanation:
can u send the story or did you lie?
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please help !! JK is parallel to what?
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 22 by 29 ft brick patio installed.
Answer:
1,547
Step-by-step explanation:
15' x 20' = 300 square feet
2,275 / 300 = $7.583 per square foot
12 x 17 = 204 square feet
204 x 7.583 = 1,547
Rob runs at a constant speed of 3.4 meters per second for one half hour. Then, he walks at a rate of 1.5 meters per second for one half hour. How far did Rob run and walk in 60 minutes?
The total distance that rob ran and walked for 60 minutes is; 8820 meters
How to calculate the distance covered?The parameter for the constant speed is that Rob runs at a speed of 3.4 meters per second for one half hour. Thus;
V1 = 3.4 m/s
t1 = 1.5 hours =
30 * 60 = 1,800 seconds.
The distance he runs at that speed and time is;
S1 = V1 * t1
= 3.4 * 1,800
= 6,120 meters
He walks at V2 = 1.5 m/s for t2 = 1,800 seconds.
The distance he walks;
S2 = V2 * t2
= 1.5 * 1,800
= 2,700 meters
The total distance he runs and walks;
S = S1 + S2
= 6120 + 2700
= 8820 meters
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the bus has a maximum capacity of 30 passengers write as an inequality
The inequality of the statement is x ≤ 30
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
The bus has a maximum capacity of 30 passengers
Represent the bus capacity with x
This means that the value of x cannot exceed 30
The term cannot exceed implies less than or equal to
So, we have
x ≤ 30
Hence, the inequality is x ≤ 30
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Using trial and improvement, find the numbers that should replace A and B in the
rule for this sequence.
Rule:
Start at 6
Multiply by A then subtract B each time
6-8->
-36->
Using trial and improvement the numbers that should replace A and B is 20 and 34.
What is the trial and improvement process?If you are unable to solve a problem using standard algebraic techniques, try using the trial and improvement approach. If you want to get a C in math, you must comprehend this question because it typically is worth 3 marks.
According to the topic
6 = A * 2 - B = 2A - B
SZ = A - S - B = SA - B {Find the relationship}
:: 3A = 36 - 8 = 28
/ A = 28/3 = 9
; B = 2A - 8 = 18 - 8 = 10
the rule expression. 14n-10
: n = 3 , 10 . 3 - 10 = 20
n = 4 11 . 4 - 10 = 34
Using trial and improvement the numbers that should replace A and B is 20 and 34.
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at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. which of the following is closest to the proportion of orders that are processed in less than 240 seconds? following is closest to the proportion of orders that are processed in less than 240 seconds?
А
0.17
B
0.25
0.36
D
083
E
0.95
As per the interpolation method, the proportion of orders that are processed in less than 240 seconds is 0.17
The interpolation method is defined as a method of deriving a simple function from the given discrete data set such that the function passes through the provided data points.
Here we have given that at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds.
And the proportion of orders that are processed in less than 240 seconds is calculated as,
Here we know that 1 standard deviation below mean = 16% = M - d
Then we apply the value on it, then we get,
=> 276 s - 38 s = 238 s
Here we know that the mean of distribution is,
=> 50% which is equal to 276 s
And the proportion less than 240 s is consider that x%, then by using the interpolation method it can be calculated as,
=> (240 - 238) / (276 - 238) = (x - 16) / (50 - 16)
When we simplify this one then we get,
=> 1/19 = x - 16 / 34
Which can be rewritten as,
=> 19(x - 16) = 34
=> 19x - 304 = 34
=> 19x = 338
=> x = 17.78%.
Therefore the closest to the proportion of orders that are processed in less than 240 seconds is 17% that is equal to the value of 0.17.
Hence the correct option is (A).
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The land area of Statesville, NC, is 20.7 square miles. If the entire US population (currently about 322.9 million) were put inside the city limits of Statesville, determine the number of square feet that each person would have. Round your answer to two decimal places. [Hint: Remember that a mile is 5,280 feet, so a square mile is (5,280 x 5,280) square feet.]
In the land area of Statesville, NC there would be 133.54 persons per square foot.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, One mile is 5280 feet so a square mile is
(5280 × 5280) = 27878400 square feet.
Therefore, The number of persons in each square foot should be,
= 322900000/27878400 persons per square foot.
= 3229000/278784 persons per square foot.
= 133.54 persons per square foot.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, three softball players discussed their batting averages after a game.
Probability:
Player 1: 4/7 =0.57
Player 2: 5/8 =0.625
Player 3: 3/6 =0.5
Therefore, option B is the correct answer.
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GIVING 50 POINTS FOR THE RIGHT ANSWER!!!!
What is 34 + 4/9 x 1/2
Answer:
308/9
Step-by-step explanation:
Answer: 34 + 4/9 x 1/2 = 34 + 2/9 = 36/9.
Decimal Form: 34 + 4/9 x 1/2 in decimal form is 34.22222222.
Step-by-step explanation:
find the largest zero for the function below. f(x)=x^3-2x^2-3x
Answer: The zeros of the function f(x) are the values of x that make f(x) equal to zero. To find the zeros of the function, we can set f(x) equal to zero and solve for x.
f(x) = x^3 - 2x^2 - 3x = 0
One way to find the zeros of the function is to factor it:
x(x-3)(x+1)=0
Thus the zeros of the function are x=0, x=3, x=-1
The largest zero of the function is 3.
Another way to find the zeros of the function would be using synthetic division or other root-finding techniques like the Newton-Raphson method.
Step-by-step explanation:
Find the area help asap!!!
Answer:
First let 'A' stand for area.
So, there's 3 areas so we write it like this:
A1: 14 ft × 3ft = 42 ft
A2: (14 ft - 2 ft) × 2 ft = 24 ft
A3: 8 ft × 3 ft = 24 ft
So when you add all of them = 90 ft
Have a wonderful day! :-)
10 pts.!!!!!
You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
ASAPPPPPPPPP PLSSS ITS GRADED
The best prediction possible for the number of times you will pick a marble that is not orange, is 7 times.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
There are 4 pink marbles and 3 orange marbles.
The probability of not picking orange marbles,
= 4/(3 + 4)
= 4/7
If you do this 7 times,
the best prediction possible for the number of times you will pick a marble that is not orange,
= 4/7 x 7
= 4 times
Therefore, number of times is 4.
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The complete question:
There are 4 pink marbles and 3 orange marbles.
You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
Visitors to a carnival pay an admission fee and must buy a ticket for each ride they go on.
Last year the total cost for a visitor to go on n rides was modeled by the expression 4.00 +1.50n.
This year, the carnival doubled the cost of a ride ticket but kept the admission fee the same.
Which expression models the total cost for a visitor to go on n rides at the carnival this year?
The expression models the total cost for a visitor to go on n rides (c) is 4.00+1.50n
What is Expressions?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
total cost for a visitor to go on n rides (c) = 4.00+1.50n
Admission fee = 4.00
Cost of each ride = 1.50
Now the cost of each ride is doubled.
New cost of each ride = 2×1.50 = 3.00
New cost model (C') for n rides = 4.00+ 3n
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on Saturday there was a -4 change in inventory. How many phones were In inventory on Sunday?
Answer:
14
Step-by-step explanation:
First we can find Wednesdays inventory by doing 16-5, giving us 11
We can do the same thing for Saturday. Doing -2+20 because the change was positive 20, not negative. That brings Saturdays inventory to 18
They said Saturdays change was -4
So taking the 18 and subtracting 4 gets you Sundays inventory of 14
Charlie’s runs 8 miles in 74 minutes. How many minutes does he take per mile?
Answer: 9.25
For this equation you will need to use division. 74min. divided by 8mi.
To double check your answer is correct you have to multiply. 9.25min times 8mi.
Explain how a $45 Timex watch and a $10,000 Rolex watch deliver value to respective target markets? Which factors account for the dramatic difference in watch prices?
Brand and product quality are the factors account for the dramatic difference in watch prices.
What are Factors?The factors of production are resources that are the building blocks of the economy they are what people use to produce goods and services.
Given that the Timex watch is $45.
Rolex watch is $10000.
We have to find the factors account for the dramatic difference in watch prices.
The rolex watch quality is better than the Timex, so the price of Rolex watch is high compared to Timex.
The brand and product quality are the factors account for the dramatic difference in watch prices.
Hence, brand and product quality are the factors account for the dramatic difference in watch prices.
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avin was reviewing a scatterplot and noticed several negative coefficients on the scatterplot. which of the following does that tell avin about the correlation coefficients?
A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables.
A scatterplot is a graph that shows the relationship between two variables by plotting points that represent the values of the two variables. When reviewing a scatterplot, one can look for the correlation coefficient, which is a statistical measure that describes the strength of the relationship between the two variables. A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables. A scatterplot with several negative coefficients indicates that the correlation between the two variables is negative, meaning that when one variable increases, the other one decreases. The strength of the correlation is determined by how close the points on the scatterplot are to the line of best fit. A strong negative correlation means that the points are close to the line of best fit and are spread in a downward direction, while a weak negative correlation means that the points are further away from the line of best fit and are spread in a more random pattern.
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If there are 24 apples and 12 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made
Answer:
Step-by-step explanation:
for every 24 apples there is 12 bananas
so if you dived it by 2 it will be 12 apples 6 bananas
so it will always be half amount of bananas
what is the y-interpect on this graph
Answer:
16
Step-by-step explanation:
It's the number where the line crosses the y-axis
Solve the equation on the
interval [0, 2π).
2sin(x) + √3 = 0
X =
?]π
5TT
The equation on the interval [0, 2π).x is 4π / 3 ,5π / -2
How should an interval equation be written?Intervals are expressed using parentheses or rectangular brackets, and a comma is used to separate two integers. The two numbers are referred to as the interval's endpoints. The least element or lower bound is shown by the number on the left. The biggest element or upper bound is shown by the number on the right.
As a result, when x = 4 and 5 4, f (x) has its maximum value of 1, which is 1.
A range of numbers between two specified numbers that include all real numbers in that range is known as an interval.
2sinx+ [tex]\sqrt{}[/tex]3 =0
⇒sinx= [tex]\sqrt{}[/tex] 3− 2
⇒x=nπ+(−1) ^-n 4π /3 (∵sin3 4π = [tex]\sqrt{}[/tex]3/-2 )
X =?]π5TT
x = 4π / 3 ,5π / -2
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Water is flowing from a horizontal pipe 48 feet above the ground. The falling stream of water has the shape of a parabola whose vertex (0, 48) is at the end of the pipe (see figure). The stream of water strikes the ground at the point (10 sqrt3 , 0). Find the equation of the path taken by the water
The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).
The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.
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A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City. What is the range of this set of data?
The range of this set of data is 30 ≤ y ≤ 80.
What is a range?In Mathematics, a range is the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:
Domain = 0 ≤ x ≤ 24 or [0, 24].
Range = 30 ≤ y ≤ 80 or [30, 80].
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It is a cold, dark, and stormy winter morning. Your boss has called a 5 a.m. meeting before she leaves to catch a flight to the Bahamas for her vacation, and there is a power outage. Your alarm does not go off and you sit up in bed with a fright at what you guess is about 4:45 a.m. You are trying frantically to get dressed and you need to reach into your sock drawer to get two matching socks in the dark. Naturally, your mind wanders to solving probability equations. Your sock drawer contains 20 total socks which consist of 10 matched pairs of socks. All of them are only black or white and they are loose, disorganized randomly, and not bound together. This means you have 10 black socks and 10 white socks in your disorganized drawer. You do not have a light source because your phone did not charge and you cannot find a flashlight or a candle. You are completely in the dark! You have to get dressed and go! You have to math fast! 1. Think for a minute and describe your optimal strategy for solving this problem in 50 words or less. 2. Let’s say for a moment that all 20 socks are different colors meaning that none match. What is the total number of different ways they could be combined in pairs? 3. Now consider all the socks are only black and white. What is the total number of different ways they could be combined in pairs? (Suggestion: You might consider listing the sample space of all possible outcomes.) For the remaining problems, let’s go back to the assumption that there are 20 total socks, 10 white and 10 black. This makes 10 total matching pairs of 5 pair of white and 5 pair of black.
1. Optimal strategy for solving this problem would be to feel for the socks, and grab two socks of the same color at random, as they have a 50% chance of being a match.
2. The total number of different ways they could be combined in pairs, assuming all 20 socks are different colors, is calculated by using the formula (nCr) = n! / (r! * (n-r)!)
So, the total number of different ways they could be combined in pairs would be (20*19)/2 = 190.
3. The total number of different ways they could be combined in pairs would be 10, as there are 10 black and 10 white socks, and they can only be paired with one another.
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the module `math` also provides the name `e` for the base of the natural logarithm, which is roughly 2.71. compute $\sqrt{e^{2\pi} 30\pi}$, giving it the name `near twentyfive`.
The value of `near twentyfive` is approximately equal to 25.3 and is calculated by taking the square root of the product of `e` raised to the power of[tex]$2\pi$[/tex], and 30[tex]$\pi$[/tex].
The designation "e" for the natural logarithm's base, which is around 2.71, is provided by the math module. We must take the square root of the product of "e" raised to the power of $2 pi and of "30 pi" in order to determine the value of "near twentyfive." The mathematical notation for this is sqrt(e(2)pi, pi). 'near twentyfive' has a value that is roughly equivalent to 25.3. This is due to the fact that $e2pi$ is roughly equivalent to 19.7, and $30pi$ is roughly equivalent to 94.2. 1867.4 is the result of adding these two integers together, while 43.4 is the result of taking 1867.4 as its square root. Finally, when 43.4 is divided by 2, the result is 25.3
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