Final answer:
To find out how many solar toys are Disney characters, multiply the total number of toys by the fraction of toys that are Disney characters.
Explanation:
To find out how many solar toys are Disney characters, we need to multiply the total number of toys by the fraction of toys that are Disney characters. In this case, 2/7 of the toys are Disney characters. So, we can calculate:
Number of solar Disney toys = Total number of solar toys × Fraction of Disney toys
Number of solar Disney toys = 28 × 2/7 = 8
Therefore, there are 8 solar toys that are Disney characters.
The table below represents the velocity of a car as a function of time:
Time (hour) x Velocity (miles/hours) y
0 50
1 52
2 54
3 56
Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points)
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points)
Part C: What would be the domain of the function if the velocity of the car was measured until it reached 60 miles/hour and the car does not change motion? (2 points)
Answer:
Part A: The y-intercept of the function is 50. It means the initial velocity is 50 miles/hours.
Part B: The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.
Part C: If the velocity of the car is 60 miles/hour, then the domain is 5.
Step-by-step explanation:
Part A:
From the given table it is clear that at x=0 the value of y is 50.
It means the y-intercept of the function is 50. It represents that the initial velocity is 50 miles/hours.
Part B:
From the given table it is clear that at x=1 the value of y is 52 and at x=3 the value of y is 56. It means the graph passes through two points (1,52) and (3,56).
The average rate of change of the function is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{56-52}{3-1}=\frac{4}{2}=2[/tex]
The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.
Part C:
The slope intercept of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of the function is 2 and y-intercept is 50, therefore the equation of function is
[tex]y=2x+50[/tex]
Put y=60 in the above equation, to find the domain at velocity 60 miles/hours.
[tex]60=2x+50[/tex]
Subtract 50 from both the sides.
[tex]60-50=2x[/tex]
[tex]10=2x[/tex]
Divide both sides by 2.
[tex]\frac{10}{2}=x[/tex]
[tex]5=x[/tex]
Therefore the domain is 5 if velocity is 60 miles/hours.
Which coefficient in the function tells us that the parabola for the function will point downward? y = -2x2 5x - 4
bob gets 3n+2=20 as the final row of his magic number puzzle table. what was his starting number?
PLZ HELP ME
What is 3^2/3 equal to?
3 square root of 9
2swuare root of 9
3 square root of 27
2 square root of 27
Stephen wants to buy yellow tangs and clown fish for his saltwater aquarium. He wants to spend no more than $77 on fish. At the store, yellow tangs cost $15 each and clown fish cost $11 each. Write and graph a linear inequality to find the number of yellow tangs x and the number of clown fish y that Stephen could purchase. Name a solution of your inequality that is not reasonable for the situation. Explain
An interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 21 inches on the architect’s plan. What is the actual length of the room in feet if the scale of the plan is 1.75 inches to 1 foot?
Answer:
12 inches i think
Step-by-step explanation:
because 21 ft = 252 ''
1.75* 12 = 21 ft
252/21 = 12ft
but im not 100% sure, I'll let yk once
I find out..
If The length of the room is 21 inches on the architect’s plan the actual length of the room is in feet if the scale of the plan is 1.75 inches to 1 foot is 36.75 feet.
What is the scale factor?It is defined as the multiplication factor used for the design of an object with respect to some other object . the scale is generally used to design prototype designs of large objects. It is also used in interior design planning rooms.
It is multiplied by the design dimension to get the actual size of the object or product.
For the given question an interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 21 inches on the architect’s plan. the scale of the plan is 1.75 inches to 1 foot means the scale factor is 1.75
The actual length of the room = 1.75 ×21
= 36.75 feet
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Which is a table of values for y=x-6? Show all work.
A. X y
-5 1
-8 -14
-7 -13
B. X y
-5 -11
-8 -2
-7 -13
C. X Y
-5 -11
-8 -14
-7 -13
D. X Y
-5 1
-8 -2
-7 -1
The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?
the answer is A. 15.21 yd
How do u write "03 December 2015" in 5 letters without using numbers ??
Let f(x) = x2 - 81. Find f-1(x).
Question 7 options:
1) ± √x+81
2) ± 9√x
3) 1 over x^2-81
4) x^2 over 81 ...?
The inverse function of f(x) = x^2 - 81 is found by swapping x and y in the original equation and solving for y, resulting in f^-1(x) = ±√(x + 81).
Explanation:To find the inverse function f-1(x) of the function f(x) = x2 - 81, we need to swap the roles of x and y in the original function and solve for y, which represents f-1(x). Here are the steps:
Start with the original function: y = x2 - 81.Rearrange to solve for x: x = y2 - 81.Swap x and y: y = x2 - 81 becomes x = y2 - 81.Add 81 to both sides: x + 81 = y2.Take the square root of both sides: y = ±√(x + 81).The correct answer is option 1, ±√(x + 81).
a store buys a jacket for$20.00 and then sells it for 80% more what is the selling price for the jacket
Answer:
16.00
Step-by-step explanation:
80% of 20.00 is 16.00
Krispy Krunch cereal is 49% sugar. about how many ounces of sugar are in a 16 oz box of Krispy Krunch?
There are 7 people at a party. Each person must shake hands with all the other people at the party once. How many handshakes does it take to do this?
Answer:
Step-by-step explanation:
21
Justin and Pedro each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. Pedro launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Pedro’s rocket?
Answer:
Equation of Pedro's rocket
[tex]h= -16t^2+120t+2[/tex]
Equation of Pedro's rocket [tex]h= -16t^2+120t+2[/tex]
Step-by-step explanation:
[tex]h= -16t^2+60t+2[/tex]
on comparing the given equation with general equation
[tex]h= -gt^2+vt+h_{0}[/tex]
we get v = 60 feet /second which is the speed of Justin's rocket.
Speed of Pedro's rocket = double of Justin's rocket
= 2(60 ) = 120 feet second
therefore equation for Pedro will be given by
[tex]h= -16t^2+120t+2[/tex]
A rocket car on the bonneville salt flats is traveling at a rate of 640 miles per hour. How much time would it take for the car to travel 384 miles at this rate?
Answer:
0.6 hour or 36 minutes
Step-by-step explanation:
We can use proportion to solve this problem.
640 miles = 1 hour
384 miles = x
cross-multiply
640 x = 384
Divide both-side of the equation by 640
[tex]\frac{640x}{640}[/tex] = [tex]\frac{384}{640}[/tex]
(On the left-hand side of the equation 640 at the numerator will cancel-out 640 at the denominator, while on the right-hand side of the equation 384 will be divided by 640)
x = [tex]\frac{384}{640}[/tex]
x = 0.6 hour
or
x = 0.6×60 = 36 minutes
Therefore the time it would take the car to travel 384 miles is 0.6 hour or 36 minutes
How do I give a "parametrization for the curve": the ray with initial point (2,5) that passes through (-1,0)? ...?
An escalator in a department store is to carry people a vertical distance of 90 feet between floors. How long is the escalator if it makes an angle of 30° with the ground? answer in feet ...?
The length of the escalator is approximately 180 feet.
Explanation:To find the length of the escalator, we can use trigonometry. The vertical distance traveled by the escalator is given as 90 feet and the angle it makes with the ground is 30°.
Using the sine function, we can determine the length of the escalator:
Length of escalator = Vertical distance traveled / sin(angle)
Therefore, the length of the escalator is:
Length of escalator = 90 feet / sin(30°)
Calculating the above expression, the length of the escalator is approximately 180 feet.
Final answer:
The length of the escalator is found using the cosine function for a 30° angle and a vertical height of 90 feet. The calculated length is approximately 77.94 feet.
Explanation:
The question asks how long an escalator is if it covers a vertical distance of 90 feet at a 30° angle with the ground. To find the length of the escalator, we can use trigonometric functions, specifically the cosine function, which relates the adjacent side (the length of the escalator) to the hypotenuse (the vertical height) in a right-angled triangle.
Using the formula:
cos(θ) = adjacent/hypotenuse
Where:
θ is the angle
'Adjacent' is the length of the escalator
'Hypotenuse' is the vertical height, which is 90 feet
To solve for the length (L) of the escalator:
cos(30°) = L / 90 feet
L = 90 feet * cos(30°)
L = 90 feet * (√3/2)
L = 45√3 feet
Or approximately L = 45 * 1.732 = 77.94 feet
Therefore, the length of the escalator is approximately 77.94 feet.
Summer day camp is about to begin. Today there are 132 boys signed up and 219 total children signed up. How many more boys than girls are signed up for camp?
The more boys than girls are signed up for camp are 22.
We have given that
Summer day camp is about to begin. Today there are 132 boys signed up and 219 total children signed up.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign
Therefore for the girl
219-132 is the equation because the rest of the 219 comes from the girls who signed up.
219-132= 77.
To find how many more boys than girls signed up you need to subtract 77 from 132.
132-77= 55
Therefore the more boys than girls are signed up for camp are 22.
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Shannon sells handmade wallets for $12 each.
Yesterday, she sold n wallets. Today, she sold 3 less wallets than yesterday.
Over the past two days, she earned a total of $396.
Drag and drop terms and an operation to create an equation that models the situation. Then, solve for n, the number of wallets Shannon sold yesterday.
15
12n + 3
+
396
396
3n
n - 3
n - 3
n + 3
12n
what is the equation in point slope form of a line that passes through the point (–8,2) and has a slope of 1/2?
A rectangular solid has sides of 7 cm, 9 cm, and 11 cm. What is its surface area?
Answer:
Surface area is, 478 square centimeter
Step-by-step explanation:
Surface area (S)of rectangle is given by:
[tex]S = 2(lw+wh+hl)[/tex] .....[1]
where,
l is the length
w is the width
h is the height of the rectangle respectively.
As per the statement:
A rectangular solid has sides of 7 cm, 9 cm, and 11 cm
⇒ l = 7 cm , w = 9 cm and h = 11 cm
Substitute in [1] we have;
[tex]S = 2(7 \cdot 9+9 \cdot 11+11 \cdot 7)[/tex]
⇒[tex]S = 2(63+99+77) = 2 \cdot 239 = 478 cm^2[/tex]
Therefore, the surface area is, 478 square centimeter
Mr. green is putting lights around 8 windows; each window is 1 and a half metres wide and 2 metres long. how many metres of lights does he need
To find the total length of lights needed, we find the perimeter of one window and multiply that by the number of windows. Mr. Green needs 56 meters of lights for all 8 windows.
Explanation:To solve the problem, we need to find the total length of lights Mr. Green needs for all the windows. First, we need to compute the perimeter for one window, which is two times the sum of the length and the width. Therefore, for one window, that would be 2×(1.5m + 2m) = 7m. Since there are 8 windows, Mr. Green would need a total of 8×7m = 56m of lights.
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Which is the best estimate for 8,104 ÷ 37?
A.
2
B.
20
C.
200
D.
2,000
What might cause the disappearance of animals in the wild
Various factors cause the disappearance of animals in the wild, including habitat destruction, hunting, disease, and changes in predator-prey relationships.
Explanation:The disappearance of animals in the wild can be caused by various factors, including habitat destruction, hunting, disease, and changes in predator-prey relationships. One of the main factors is habitat destruction, which occurs when natural habitats are altered or destroyed by human activities such as farming, logging, and construction. This leads to a loss of biodiversity as plant and animal populations are destroyed or displaced.
Hunting is another major cause of animal disappearance. Animals are hunted for various purposes including meat, hides, and horns. Large mammals are particularly vulnerable as they are often targeted for their valuable resources. In addition, diseases can spread among animals due to human activities, such as the introduction of domestic animals, leading to population declines and even extinctions.
Changes in predator-prey relationships can also affect animal populations. For example, the decline of predators like cougars, lions, and leopards can result in an increase in the prey population. This can lead to changes in vegetation, stream paths, and overall biodiversity.
You are designing a rectangular poster to contain 50 in^2 of printing with a 4 in. margin at the top and bottom and a 2 inch margin at each side. What overall dimensions will minimize the amount of paper used? ...?
To minimize the amount of paper used for a rectangular poster with 50 square inches of printing area and specified margins, the overall dimensions should be approximately 9.59 inches in width and 16.95 inches in height.
To find the overall dimensions of the rectangular poster that minimize the amount of paper used, let's start by stating the problem mathematically. The poster must contain 50 square inches of printing area. The poster has margins of 4 inches at the top and bottom, and 2 inches on each side.
Let the dimensions of the printing area be width w and height h. Therefore, we know:
w * h = 50 square inches
Including the margins, the overall dimensions of the poster will be:
Overall width = w + 2 + 2 = w + 4Overall height = h + 4 + 4 = h + 8We aim to minimize the total area of the poster including the margins, which is given by:
A = (w + 4)(h + 8)
From the constraint w * h = 50, we can express h in terms of w as follows:
h = 50 / w
Substituting this into the total area formula:
[tex]A(w) = (w + 4)igg(rac{50}{w} + 8igg) = (w + 4)(rac{50}{w} + 8)[/tex]
To minimize A(w), we take the derivative with respect to w and set it to zero. This involves some calculus:
First, expand the equation:A(w) = 50/w + 8w + 200/w + 32Simplify to A(w) = 250/w + 8w + 32Take the derivative dA/dw and set it to zero:
dA/dw = -250/w² + 8 = 0
Solving for w:
-250/w² = -8
w² = 250/8 = 31.25
w = √31.25 ≈ 5.59 inches
Using the constraint w * h = 50:
h = 50/w = 50/5.59 ≈ 8.95 inches
Therefore, the overall dimensions of the poster are:
Width: w + 4 ≈ 5.59 + 4 ≈ 9.59 inchesHeight: h + 8 ≈ 8.95 + 8 ≈ 16.95 inchesThus, to minimize the amount of paper used, the overall dimensions should be approximately 9.59 inches by 16.95 inches.
A city has a population of 320,000 people. Suppose that each year the population grows by 3.5%. What will the population be after 12 years?
Use the calculator provided and round your answer to the nearest whole number.
Answer is 483,542
Compound Interest:
The formula for compound interest is [tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where P is the principal balance
r is the interest rate
n is the number of times interest is compounded per time period.
t is the number of time periods.
(Given),
P = 320,000
n = 1
t = 12
r = 3.5% = 3.5 / 100 = 0.035
[tex]A = 320,000 (1 + 0.035)^{12}[/tex]
[tex]A = 320000(1.035)^{12}[/tex]
A = 483,541.970 (approx)
A = 483,542 (Rounded to the nearest whole number).
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Point V lies between points U and W on .
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
After analyzing each option and testing them in the equation UW = 9x - 9, none of the provided options (5 units, 6 units, 30 units, 36 units) result in a consistent solution for the length of UW in units. Without additional information or a correct option, it is impossible to determine the length of UW in units.
Explanation:The student's question asks us to find the length of segment UW in units given that the formula for its length is UW = 9x - 9. To ascertain the correct length, we need a value for 'x'. Since the options provided are measured in units and do not contain variables, we have to assume that 'x' represents a specific value that, when substituted into the equation, will yield one of the given numerical options for UW.
Going through the provided options, we can test each number to see which, when substituted into 'x', will make UW a whole number. Starting with the smallest '5 units' and '6 units', we quickly find that none of these values, when multiplied by 9 and then decreased by 9, will yield themselves as a result. Thus, they can be dismissed as possible lengths of UW.
Moving on to '30 units' and trying x = 30 in the equation UW = 9x - 9, we get UW = 9(30) - 9 = 270 - 9 = 261, which does not match. Lastly, checking x = 36 in the equation gives us UW = 9(36) - 9 = 324 - 9 = 315, which is also not an option. None of the provided options are valid when 'x' is placed into the equation UW = 9x - 9.
Therefore, without additional information or a correct choice in the options, we cannot determine the length of UW in units.
P is 9 more than half of q
Two variables which have a constant ratio between them are said to be ___.
Answer:
Two variables which have a constant ratio between them are said to be proportional.
Step-by-step explanation:
We have been given an incomplete sentence. We are supposed to complete our given sentence.
We know that two quantities are proportional, when they share a common ratio between them.
Therefore, the missing word from our given sentence is 'proportional'.
The triangles are similar. The ratio of the lengths of their corresponding sides is 25:45, or 5:9. Find the ratio of their perimeters and the ratio of their areas.