The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.
To solve this problem, we can use the equation:
M₁V₁= M₂V₂
where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.
We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.
Plugging these values into the equation, we get:
(1.25 M)(50.0 mL) = M2(150.0 mL)
Solving for M₂, we get:
M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M
Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.
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Tim brought $40.50 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Tim had $2.00 left over after buying these items.
What was the cost of each item?
Answer:
Let x be the cost of the pass.
Then the cost of the souvenir is (2/3)x.
The cost of the burger is (1/4) of the cost of the souvenir, which is (1/4)(2/3)x = (1/6)x.
The total cost of the items is x + (2/3)x + (1/6)x = (11/6)x.
Tim had $2.00 left over after buying these items, so we can set up the equation:
(11/6)x + 2 = 40.50
Solving for x, we get:
x = 18
Therefore, the cost of the pass is $18, the cost of the souvenir is (2/3)($18) = $12, and the cost of the burger is (1/6)($18) = $3.
How many fish (angelfish and eels) are there?
Number of Animals
25
20
15
10
5
0
Science Museum Water Exhibit
Snakes Turtles Angelfish
Animal
Eels
The number of fish, including angelfish and eels that are shown by the bar graph, can be found to be 45 fish .
How to find the number of fish ?The science museum water exhibit bar graph shows the number of animals that are in the water exhibit in the museum.
We see that there are 15 snakes, 10 Turtles, 25 Angelfish, and 20 eels.
If we are to find the number of fish in the science museum water exhibit, all we need to do is to sum up the number of Angelfish and Eels. Doing this sum would add up to :
= 25 Angelfish + 20 eels
= 45 fish
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Each color of gravel comes in an 8 1/2pound bag. How many 2 pounds of gravel should Alberto have left after putting in all of the colored gravel?
Answer:
where do you live
Step-by-step explanation:
Work out the minimum number of extra squares that need to be shaded so that the pattern below has rotational symmetry of order
a) 2
b) 4
The minimum number of extra squares that need to be shaded so that the pattern has rotational symmetry of order is 3
Working out the minimum number of extra squares that need to be shadedFrom the question, we have the following parameters that can be used in our computation:
The composite figure
On the extension at the left-hand side of the figure, we can see that
The shaded shape is a rectangle while other shaded shapes are squares
This means that the other shaded squares must be extended to form a rectangle
There are three of the squares that can be extended to rectangles
Hence, the minimum number of squares is 3
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What is the median of the following Systolic Blood Pressure in mmHg: 121, 110, 114, 100 160, 130 130?
Answer:
121
Step-by-step explanation:
firstly you arrange the numbers in ascending order the number in the middle is considered to be the median
What is the value of the y-intercept of the graph of h(x)=12.3(4.9)^x ?
Record your answer in the boxes below.
The value of the y-intercept of the graph of the function h(x) = 12.3(4.9)^x is 12.3.
To determine the value of the y-intercept of the graph of the function[tex]h(x) = 12.3(4.9)^x,[/tex] we need to find the value of h(0) since the y-intercept corresponds to the point where the graph intersects the y-axis (x = 0).
Substituting x = 0 into the function, we have:
[tex]h(0) = 12.3(4.9)^0[/tex]
Since any number raised to the power of 0 is equal to 1, we have:
h(0) = 12.3(1)
Multiplying 12.3 by 1 gives us:
h(0) = 12.3
Therefore, the value of the y-intercept of the graph of [tex]h(x) = 12.3(4.9)^x[/tex] is 12.
The y-intercept represents the value of the function when x = 0, which in this case is 12.3.
It is the point where the graph crosses the y-axis.
This means that when there is no exponential growth or decay (x = 0), the value of the function is 12.3. As x increases or decreases, the function will grow or decay exponentially, but at x = 0, it starts with a value of 12.3.
The graph of this function would start at the point (0, 12.3) and then either increase or decrease exponentially depending on the value of the base (4.9 in this case).
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Omar bought 1000 shares of a company's stock for $15.23/share. If he pays a broker 0.75% commission to buy and sell stock. After one year, he sold all his shares, which were worth $18.78/share. What was his rate of return? Question 38 options: 21.5% 22.4% 22.7% 23.3%
Answer:
First, let's calculate the total cost of buying the shares:
1000 shares * $15.23/share = $15,230
Next, we need to calculate the commission paid to the broker for buying the shares:
$15,230 * 0.0075 = $114.23
So, the total cost of buying the shares including the commission is:
$15,230 + $114.23 = $15,344.23
Now, let's calculate the total revenue from selling the shares:
1000 shares * $18.78/share = $18,780
We also need to calculate the commission paid to the broker for selling the shares:
$18,780 * 0.0075 = $140.85
So, the total revenue from selling the shares after the commission is:
$18,780 - $140.85 = $18,639.15
The total profit from buying and selling the shares is:
$18,639.15 - $15,344.23 = $3,294.92
The rate of return is the profit divided by the total cost, expressed as a percentage:
($3,294.92 / $15,344.23) * 100% = 21.5%
Therefore, Omar's rate of return is 21.5%.
A fruit company delivers fruit in two different size boxes: large and small A delivery of 3 large boxes and 5 small boxes has a total weight of 135kg. A delivery of 9 large boxes and 7 small boxes has a total weight of 279Kg. How much does each box weigh
The large box weighs 18.75 kg, and the small box weighs 15.75 kg.
We have,
Let's assume the weight of a large box is L kg, and the weight of a small box is S kg.
According to the given information, we can create the following equations:
Equation 1: 3L + 5S = 135 (1st delivery)
Equation 2: 9L + 7S = 279 (2nd delivery)
To solve these equations, we can use a method called "elimination" or "substitution."
Multiply Equation 1 by 3 and Equation 2 by 1, so that the coefficients of L will be the same:
Equation 1: 9L + 15S = 405
Equation 2: 9L + 7S = 279
Now, we can subtract Equation 2 from Equation 1 to eliminate L:
(9L + 15S) - (9L + 7S) = 405 - 279
Simplifying:
8S = 126
Divide both sides of the equation by 8:
S = 126/8 = 15.75
So, the weight of a small box (S) is 15.75 kg.
Now,
substitute the value of S into Equation 1 to find the weight of a large box (L):
3L + 5(15.75) = 135
3L + 78.75 = 135
3L = 135 - 78.75
3L = 56.25
Divide both sides of the equation by 3:
L = 56.25/3 = 18.75
So,
The weight of a large box (L) is 18.75 kg.
Thus,
The large box weighs 18.75 kg, and the small box weighs 15.75 kg.
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According to the NCAA 7.1% of high school women cross country runners will end up running cross country at the collegiate level. If 30 female high school cross country runners are selected at random, what is the probability that exactly 2 of them will run cross country in college. Express your answer as a probability between 0 and 1 and round your answer to three decimal places.
Answer:
Step-by-step explanation:
Find the probability of randomly choosing an ace or a club from a standard deck of cards. Remember that a standard deck consists of
52 cards, where each card is made up of a number or letter from {2, 3,4, 5, 6, 7, 8, 9, 10, J, Q, K, A} and a suit from {clubs, diamonds, hearts, spades
Answer: The probability of choosing an ace or a club is 16.
Step-by-step explanation:
Scores in golf can be 0 (also called par), a positive integer (also called above par), or a negative integer (also called below par). The bar graph shows final scores of selected golfers from a tournament. Use this graph to answer the question below Find the average of the scores for player C, player D, player E, and player F. (Hint: Here, the average is the sum of the scores divided by the number of players ).
Answer:
The answer is -4.4.
Step-by-step explanation:
First, you have to add -12 + -10 + -6 and it equals -28. Next add the positive numbers 4+ 2 equals 6. Then, put them altogether meaning -28 + 6 equals -22, then divide it by the number of players which is 5 then you get the answer of -4.4.
Have a nice day.
The number of meters a student swam this week are listed.
200, 450, 600, 650, 700, 800
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability and equals 600.
The IQR is the best measure of variability and equals 250.
The mean is the best measure of variability and equals about 567.
The median is the best measure of variability and equals 625.
The appropriate measure of variability for this data is the IQR, and its value is 250.
We have,
The range is not the best measure of variability for this data since it only takes into account the maximum and minimum values and does not consider the other values in the dataset.
The IQR (interquartile range) is a better measure of variability since it gives a measure of the spread of the middle 50% of the data.
To find the IQR, we first need to find the median:
Arranging the data in order, we get:
200, 450, 600, 650, 700, 800
The median is the middle value, which is 650.
The first quartile (Q1) is the median of the lower half of the data:
Q1 = median(200, 450, 600) = 450
The third quartile (Q3) is the median of the upper half of the data:
Q3 = median(700, 800, 650) = 700
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
= 700 - 450
= 250
Therefore,
The appropriate measure of variability for this data is the IQR, and its value is 250.
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The revenue R
from the sale of x
cameras is given by R=24x−x2.
The cost C
of producing x
cameras is given by C=30+13x.
How many cameras must be produced and sold in order to break even? If there is more than one break-even point, separate the answers with commas.
In order to break even, either 5 cameras or 6 cameras must be produced and sold.
Understanding Revenue and Break-even pointAt break-even point, revenue (R) equal is set to equal the cost (C)
Given that:
R = 24x - x².
C = 30 + 13x.
where
R is revenue and
C is the cost
Setting R equal to C:
24x - x² = 30 + 13x
Rearranging the equation:
x² - 11x + 30 = 0
Now, we can solve this quadratic equation to find the break-even point(s).
Factoring the quadratic equation:
(x - 6)(x - 5) = 0
Setting each factor equal to zero:
x - 6 = 0 ==> x = 6
x - 5 = 0 ==> x = 5
Therefore, the break-even point occurs when x = 6 or x = 5.
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given this equation, what is the value of y at the indicated point?
(6,y)
y^2 = x - 3
Please Help. am very stuck!
The value of y at the indicated point is √3.
What is a square root function?In Mathematics and Geometry, a square root function refers to a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In this scenario and exercise, we would determine the y-value by substituting the x-value into the given square root function as follows;
y² = x - 3
By taking the square root of both sides of the square root function, we have:
y = √(x - 3)
When x = 6, the y-value is given by;
y = √(6 - 3)
y = √3
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Maria’s line is represented by the equation
y
=
−
5
6
x
+
8
. Nate’s line is perpendicular to Maria’s line.
Which of the following could be an equation for Nate’s line?
A.
5
x
−
6
y
=
15
B.
5
x
+
6
y
=
15
C.
6
x
−
5
y
=
15
D.
6
x
+
5
y
=
15
The possible equation for Nate's line is C) 6x - 5y = 15.
To find the equation of the line perpendicular to Maria's line, we need to determine the slope of Maria's line first.
Maria's line is represented by the equation:
y = -5/6 x + 8
The slope of this line can be determined by comparing it to the slope-intercept form of a linear equation (y = mx + b), where m is the slope. Thus, the slope of Maria's line is -5/6.
The slope of a line perpendicular to Maria's line will be the negative reciprocal of -5/6, which is 6/5.
Therefore, the equation of Nate's line could be in the form:
y = 6/5 x + b
where b is the y-intercept of Nate's line.
To determine which of the given answer choices is the equation of Nate's line, we can substitute the equation y = 6/5 x + b into each answer choice and see which one holds true.
A) 5x - 6y = 15
Substituting y = 6/5 x + b, we get:
5x - 6(6/5 x + b) = 15
5x - 36/5 x - 6b = 15
-11/5 x - 6b = 15
This equation is not equivalent to y = 6/5 x + b, so A is not the answer.
B) 5x + 6y = 15
Substituting y = 6/5 x + b, we get:
5x + 6(6/5 x + b) = 15
5x + 36/5 x + 6b = 15
46/5 x + 6b = 15
This equation is not equivalent to y = 6/5 x + b, so B is not the answer.
C) 6x - 5y = 15
Substituting y = 6/5 x + b, we get:
6x - 5(6/5 x + b) = 15
6x - 6x - 5b = 15
-5b = 15
b = -3
This equation is equivalent to y = 6/5 x - 3, so C could be the answer.
D) 6x + 5y = 15
Substituting y = 6/5 x + b, we get:
6x + 5(6/5 x + b) = 15
6x + 6x + 5b = 15
12x + 5b = 15
This equation is not equivalent to y = 6/5 x + b, so D is not the answer.
Therefore, the possible equation for Nate's line is C) 6x - 5y = 15.
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Assume that ryan does save 10% for retirement if he allocate the remainder of his take-home pay to entertainment then what percent of the total budget will entertainment compromise how much money will the budget towards entertainment in each month
Entertainment will comprise 90% of Ryan's total budget. He will allocate 90% of his monthly income towards entertainment expenses.
How to solveAccording to the given information:
Let's assume Ryan's take-home pay is P dollars.
Assuming that Ryan puts aside 10% of his net income for his retirement plan, he will accumulate savings of 0.10P dollars.
After setting aside funds for retirement, the remaining portion of his net earnings will constitute 90% of the original amount, equating to 0.90P dollars.
Assuming that Ryan puts the remaining amount of his income towards entertainment, it is possible to determine the proportion of his overall expenses that entertainment would represent.
Percentage of entertainment budget = (Entertainment budget / Total budget) * 100
Given an overall budget of P dollars, with 0.90P dollars allotted for entertainment expenses, the proportion of the total budget that will be spent on entertainment can be calculated as a percentage.
Percentage of entertainment budget = (0.90P / P) * 100
Percentage of entertainment budget = 90%
So, entertainment will comprise 90% of Ryan's total budget.
He will allocate a monthly entertainment budget of 0.90P dollars, equivalent to 90% of his salary after taxes.
As such, the overwhelming majority of Ryan's budget will be allocated towards Entertainment. Every month, the entertainment allowance will constitute 90% of his net income as per the allocated budget.
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It takes 14 hours for a tap with a flow of 18 litres per minute to fill a reservoir with water. How long will it take if the flow is reduced to 7 litres per minute? I need formulas
If the flow rate of the tap is reduced to 7 litres per minute, it would take 36 hours to fill the reservoir.
Let's use the formula:
time = volume/flow rate
where volume is the volume of the reservoir and flow rate is the flow rate of the tap.
Let V be the volume of the reservoir.
With a flow of 18 litres per minute, we have:
14 hours = V / 18 L/min
Solving for V, we get:
V = 14 hours x 18 L/min = 252 L
Now, let's find the time it takes to fill the same reservoir with a flow of 7 litres per minute:
time = V / 7 L/min
Substituting V with 252 L, we get:
time = 252 L / 7 L/min = 36 hours
Therefore, it will take 36 hours to fill the reservoir with a flow rate of 7 litres per minute.
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5. Find the volume of the pyramid below? 4. Find the volume of the cone below.
40m
30m
52m
The volume of the rectangular pyramid is 20800 m³.
How to find the volume of a pyramid?The volume of the pyramid can be found as follows:
The pyramid is a rectangular base pyramid. Therefore,
volume of the pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
B = 52 × 30
B = 1560 m²
volume of the pyramid = 1 / 3 × 1560 × 40
volume of the pyramid = 62400 / 3
volume of the pyramid = 20800 m³
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Daisy works at an ice cream parlor. She's paid $10/hr. For first 8hrs she works in a day for every extra hr she is paid 1.5x her hourly wage if daisy works x hours in a day and x is > 8 expression giving her net earnings for the day is _. If daisy works 13 hrs she is paid _
Daisy would be paid $155 if she works 13 hours in a day.
If Daisy works for up to 8 hours in a day, she is paid a flat rate of $10 per hour, so her earnings for the day would be:
Earnings = 10 × 8 = $8
If Daisy works for more than 8 hours in a day, then her earnings for the extra hours are calculated at a rate of 1.5 times her hourly wage, which is $15 per hour.
So, if Daisy works x hours in a day, where x is greater than 8, then her net earnings for the day can be expressed as:
Earnings = 80 + (x - 8) × 15
This expression takes into account the first 8 hours of work, which are paid at a flat rate of $10 per hour, and the extra hours, which are paid at a rate of $15 per hour
If Daisy works 13 hours in a day, then her net earnings for the day would be:
Earnings = 80 + (13 - 8) × 15 = 80 + 5 × 15 = $155
So Daisy would be paid $155 if she works 13 hours in a day.
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The heat of vaporization for ethanol is 0.826 kJ/g. Calculate the heat energy in joules required to boil 75.25 g of ethanol.
The required heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.
The heat energy required to boil a substance can be calculated using the formula:
Q = m × Hv
where Q is the heat energy, m is the mass of the substance, and Hv is the heat of vaporization. From the given, we have m = 75.25 g and Hv = 0.826 kJ/g
Substituting the given values, we get:
Q = 75.25 g × 0.826 kJ/g
Q = 62.1835 kJ
Where kJ (kilojoule) is the unit of heat.
Therefore, the heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.
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What is the meaning of "when [tex] x_{1}, ..., x_{n}[/tex] are permuted in all possible ways, the number of different values of [tex]f (x_{1}, ..., x_{n})[/tex] is a divisor of n!"?
The meaning of the statement is if you take n distinct numbers, x₁, ..., xₙ, and permute them in all possible ways, the number of different values that the function f(x₁, ..., xₙ) can take on will be a divisor of n!.
How to explain the concept ?This assertion is a specific instance of a broader concept known as the Principle of Inclusion-Exclusion in the field of combinatorics. The Principle of Inclusion-Exclusion asserts that when dealing with a set comprising n elements and aiming to determine the number of possible subsets that can be selected, one can arrive at this figure by summing up the number of options for choosing 0, 1, 2, and up to n elements from the set.
Regarding the aforementioned assertion, the collection of components comprises every potential arrangement of the numerical values x₁, ..., xₙ. There is only one possible way to choose 0 elements, there are n options for choosing 1 element, selecting 2 elements can be done in n(n-1)/2 ways, and the pattern continues.
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Please help me with homework!
Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.
How to calculate the fractionHolden drinks 1/8 gallon of water every 2 miles, so after hiking 14 miles, he would have drank (14/2) * (1/8) = 7/16 gallons of water.
Melissa drinks 3/8 gallon of water every 2 miles, so after hiking 14 miles, she would have drank (14/2) * (3/8) = 21/32 gallons of water.
The difference in the amount of water they drink is:
21/32 - 7/16 = 21/32 - 14/32 = 7/32 gallons
Therefore, Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.
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00 Which transformation most likely maps figure ABCD onto figure A'B'C'D'? A Reflection across the Y-axis B Rotation 90⁰ Clockwise about the origin C Rotation 90° Counter-Clock- wise about the origin D Rotation 180° about the origin |-10-9-8-7-6 D B 10 19 8 17 6 5 3 -2 I 1 5 +6 +7 AC -8 9 10 910 A) Rotati B) Reflec C) Reflec (D) Transl
Based on the given figures, the most likely transformation that maps figure ABCD onto figure A'B'C'D' is option A, reflection across the Y-axis.
This is because the x-coordinates of the corresponding points in the two figures are opposite to each other when reflected across the Y-axis.
A rotation of 90⁰ clockwise or counter-clockwise about the origin would result in the image being in a different quadrant, and a rotation of 180° about the origin would place the image on the opposite side of the origin.
A translation would move the image to a different location without changing its orientation, but there is no indication in the question that a translation is a possible transformation. Hence it's a reflection across Y-axis.
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Correct Question
(Image Attached)
Which is the graph of linear inequality 2y > x-2?
543241
X
54321.
-2.
3
O
3 4 5 x
5432
S
25
es
4
4₁
25
n
C
The graph of the inequality is attached in the solution.
Given is an inequality, 2y > x-2, we need to graph it,
So, considering this as, 2y = x-2
Solving like a linear equation to get the points to plot,
So,
Put y = 0,
0 = x - 2
x = 2
(2, 0)
Put x = 0,
2y = 0-2
y = -1
(0, -1)
Hence the two points from which the graph will pass are (2, 0) and (0, -1).
Now, since the inequality has a > sign so the shaded area will be above the line and the line will be dotted.
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Consider a circle whose equation is x2 + y2 -2x -8 =0. Which statements are true? Select three options
The three statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
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Complete Question:
Consider a circle whose equation is x² + y² – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
C=5/9 (f -32
F= 9/5C + 32
When C = 20, F is equal to 68, and when F = 100, C is approximately 37.78.
Given the equations:
C = (5/nine) * (F - 32)
F = (9/5) * C + 32
If we replace specific values for F or C, we will locate the corresponding price for the opposite variable. Here are some examples:
Let's expect C = 20. Substituting this fee into the second equation:
F = (9/five) * 20 + 32
F = 36 + 32
F = 68
Therefore, when C = 20, F is equal to sixty-eight.
Let's expect F = a hundred. Substituting this cost into the primary equation:
C = (five/9) * (100 - 32)
C = (5/9) * 68
C = 340/9
C ≈ 37.78
So, whilst F = one hundred, C is approximately 37.78.
These examples exhibit how you may locate the values of F and C by using substituting one variable into the equations and fixing for the alternative variable. Remember, you could choose any unique values for F or C and perform the calculations consequently.
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The correct question is:
"C=5/9 (f -32)
F= 9/5C + 32
Solve for F and C"
NO LINKS!! URGENT HELP PLEASE!!
What is the surface of this problem? Please show work!!
Answer:
720 m^2
Step-by-step explanation:
Solution:
The formula for the surface area of a triangular prism is:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
where,
b is the bottom edge of the base triangle,h is the height of the base triangle,L is the length of the prism andS1, S2, and S3 are the three edges (sides) of the base triangle(bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bhGiven:
side 1 (S1) : 5 m
side 2(S2): x m
side 3(S3): 12 m
length (l)=22m
Here we need to find side 2, we can easily find it using Pythagoras' theorem.
a^2+b^2=c^2
5^2+12^2=x^2
x^2=169
x=[tex]\sqrt{169}=13 m[/tex]
therefore, side 2 is 13 m.
Substituting value in the formula
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
Surface Area=(5+13+12)*22+5*12= 720 m^2
Answer:
720 m²
Step-by-step explanation:
The given diagram shows a triangular prism.
A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.
To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:
[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]
The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:
[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]
Therefore, the total surface area of the given triangular prism is 720 m².
What is the range of this data ?
60 65 70 75 80 85 90 95 100
How many liters each of a 25% acid solution and a 65% acid solution must be used to produce 80 liters of a 40% acid solution? (round to two decimal places if necessary.)
Answer:
50
Step-by-step explanation:
To solve this problem, we can use the following formula:
(amount of solution 1) + (amount of solution 2) = total amount of mixture
We can also set up equations for the amount of acid in each of the solutions:
0.25(amount of solution 1) + 0.65(amount of solution 2) = 0.4(total amount of mixture)
We have two equations and two unknowns, so we can solve for the amounts of each solution. Let's set x to be the amount of the 25% acid solution and y to be the amount of the 65% acid solution. Then we have:
x + y = 80 (equation 1)
0.25x + 0.65y = 0.4(80) (equation 2)
We can simplify equation 2 by multiplying everything by 100, to get rid of the decimals:
25x + 65y = 3200
Now we can solve this system of equations. One way to do this is to solve equation 1 for one of the variables, and substitute it into equation 2. We get:
x = 80 - y
25(80 - y) + 65y = 3200
2000 - 25y + 65y = 3200
40y = 1200
y = 30
So we need 30 liters of the 65% acid solution. To find the amount of the 25% acid solution, we can substitute y = 30 into equation 1:
x + 30 = 80
x = 50
So we need 50 liters of the 25% acid solution. Therefore, we need 50 liters of the 25% acid solution and 30 liters of the 65% acid solution to produce 80 liters of a 40% acid solution.
The table shows the net revenue in millions of dollars of a company every three months for two years. An exponential function can be used to model the data.
Company
Time, x (months) Net Revenue, r(x) (millions of dollars)
3 274
6 389
9 467
12 560
15 960
18 1,100
21 1,320
24 1,584
Which function best models the data?
r(x)=223.06(1.09)^x
r(x)=1.09(223.06)^x
r(x)=2,232.91(0.92)^x
r(x)=0.92(2,232.91)^x
An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]
How to determine the equation of line of best fit?In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:
[tex]r(x) = 223.06(1.09)^x[/tex]
Read more on scatter plot here: brainly.com/question/28605735
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