The correct answer is that Jenny's ball bounced 32 inches.
To solve the problem, let's denote the distance that Clark's ball bounced as [tex]\( d \)[/tex] inches. According to the problem, Jenny's ball bounced 8 times farther than Clark's ball, so the distance Jenny's ball bounced is [tex]\( 8d \)[/tex] inches.
The total distance bounced by both balls is the sum of the distances each ball bounced, which is given as 36 inches. Therefore, we can set up the following equation:
[tex]\[ d + 8d = 36 \][/tex]
Combining like terms, we get:
[tex]\[ 9d = 36 \][/tex]
To find the value of [tex]\( d \)[/tex], we divide both sides of the equation by 9:
[tex]\[ d = \frac{36}{9} \][/tex]
[tex]\[ d = 4 \][/tex]
Now that we have the distance Clark's ball bounced, which is 4 inches, we can find the distance Jenny's ball bounced by multiplying [tex]\( d \)[/tex] by 8:
[tex]\[ 8d = 8 \times 4 \][/tex]
[tex]\[ 8d = 32 \][/tex]
So, Jenny's ball bounced 32 inches.
Annabelle and Navene are multiplying (4 to the power of 2•7 to the power of 5)(4 to the power of3•7 to the power of 2).
Is either of them correct?
Perpendicular lines have slopes that are what
which of the following numbers does not belong 64,16,36,32,8,4 explain
2.1m = 25.62 solve the equation
what is the value of 0.543 and what is the value of the 4
There are 3 numbers to the right of the decimal point. The first digit is tenths, the second digit is hundredths and the third digit is thousandths.
0.543 = 543 thousandths.
The 4 is in the hundredths place so the 4 would be 4 hundredths.
What is the justification for it step in solving the inequality? 75x + 35 > 7(11x+9)+4
Frank has been driving a constant speed for 3 hours during which time he traveled 195. How long will it take for him to drive 455 miles
Write a word phrase for the algebraic expression 3x - 7.
In the number 514,482,441, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s? How is it different?
6x + 10 – 2x = 7 + 23
A cheetah can run 70 mph. What is this speed in feet per hour
NEED HELP WITH
The table shows the annual profit or loss of Famed Film Corporation for the years 2003 to 2010 and the average profit of $0.3375 million for the 8-year period.
year | profits lost/millions
2004 $3.40
2005 $2.10
2006 $?
2007 $0.60
2008 $2.10
2009 -$0.20
20010 $1.30
2011 $-$0.75
average- $1
What was the profit/loss in 2006, in millions? Round your answer to the nearest hundredth.
You own a house and land with an assessed value of $55,580. Every year, you pay a total of $2,834.58 in property taxes. What is your local property tax rate? a. 0.051 b. 0.058 c. 0.019 d. 0.066
The local property tax rate is 0.051.
Given that,
You own a house and land with an assessed value of $55,580. Every year, you pay a total of $2,834.58 in property taxes.Based on the above information, the calculation is as follows:
[tex]= \$2,834.58 \div \$55,580[/tex]
=0.051
Therefore we can conclude that The local property tax rate is 0.051.
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estimate the sum 198, 819, 918
Can anyone help, please?
-1.3 ≥ 2.9 -0.6r
Graph the solution
5(n–2)=5n–10
how many solutions does it have
since the equation on the left can be rewritten :
to be 5n-10 then both sides of the equation are equal
so any real number will work
The radius of a sphere is measured to be 3.12 cm. What is the most accurate volume of the sphere you can report?
Answer: 128
Step-by-step explanation:
Debra drew this shape on the back of her notebook. What is name of the shape Debra drew? How do you know
A vial of medicine contains 60oz of medicine. If a dose is 3oz how many ounces does the vial contain
A printer prints 28 photos in 8 minutes. a. How many minutes does it take to print 21 more photos? b. Construct a double number line diagram that represents the situation. How many minutes does it take to print 35 more photos?
It takes 6 minutes to print 21 more photos. It takes 10 minutes to print 35 more photos.
To determine the time it takes to print 21 more photos, we first need to calculate the rate at which the printer prints photos. We can do this by dividing the number of photos printed (28) by the time it takes to print them (8 minutes). This gives us a rate of 3.5 photos per minute.
Next, we can divide the number of additional photos (21) by the rate of photos per minute to find the time it takes to print them. This gives us 21 photos / 3.5 photos per minute = 6 minutes.
Therefore, it takes 6 minutes to print 21 more photos.
To construct a double number line diagram, we create two parallel number lines, one for the number of photos and one for the number of minutes. We mark the starting point on both lines as 0.
Next, we plot the point (28, 8) on the diagram, representing the fact that 28 photos are printed in 8 minutes.
To determine the time it takes to print 35 more photos, we can extend the number of photos line to the point (35 + 28, 8), which is (63, 8). This point represents the fact that 63 photos are printed in 8 minutes.
Finally, we can draw a vertical line from the point (63, 8) on the number of photos line to the number of minutes line. This line intersects the number of minutes line at the point (63, 8 + 10), which is (63, 18).
Therefore, it takes 10 minutes to print 35 more photos.
Which is the correct way to model the equation x + 8 = 7 x + (-8) using algebra tiles?
Answer:
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive tiles and 8 negative unit tiles on the right side.
Step-by-step explanation:
What is 32.043 in expanded form
Final answer:
To express 32.043 in expanded form, break it into each digit's value based on its place: 30 (tens) + 2 (ones) + 0.04 (hundredths) + 0.003 (thousandths), resulting in 30 + 2 + 0.04 + 0.003.
Explanation:
The question asks about expressing the number 32.043 in expanded form. Expanded form is a way of writing numbers to show the value of each digit. It involves breaking down the number into each of its digits, multiplied by their respective place value. For the number 32.043:
The '3' is in the tens place, so it represents 30 or 3 * 10.The '2' is in the ones place, so it represents 2 or 2 * 1.The '0' is in the tenths place, so it represents 0 or 0 * 1/10. However, since it contributes no value, it's often omitted in expanded form.The '4' is in the hundredths place, so it represents 0.04 or 4 * 1/100.The '3' is in the thousandths place, so it represents 0.003 or 3 * 1/1000.Therefore, 32.043 in expanded form is 30 + 2 + 0.04 + 0.003.
Of th 30 girls who tried out for the lacrosse team team at Euclid middle school , 12 were selected. Of the 40 boys show tried out 16 were selected . Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls ? How do you know ?
All angles in the figure below are right angles. What is the area of the figure? 14 18 28 36
The answer is D 36
I found out the hard way lol
Lines that are not in the same plane are called
if we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values wil be (or were) equal in what year? (The answer might be absurd.)
To find the year two states would theoretically have equal median house values, one could use provided growth rates and starting house values to set up an equation and solve for time. However, assuming a linear trend can lead to inaccurate results as real estate markets are affected by many fluctuating factors.
Explanation:To calculate the year in which two states would have theoretically had equal median house values, we first need to know the starting house values for each state and the annual growth rate trends. We've learned from the FRED® Economic Data that median sales price for a home in the U.S. was $122,900 in 1990 and rose to $232,000 by the end of 2016, an average growth rate of 3.1% annually. In other periods, such as the 1970s, 1980s, and 1990s, housing prices increased about 6% per year on average. During the 'housing bubble' years (2003-2005), they experienced a sharp rise and then a fall with the 2007-2008 recession.
Assuming linear trend (constant growth), we would set up an equation with these variables and solve for the year (time) where the values are equal. However, do kindly note that assuming the same trend can often lead to absurd results as housing markets are affected by a variety of economic, political, and demographic factors and do not always follow a linear trend.
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a) Home values have increased at a higher rate in New York.
b) The median home value in Arkansas in 2010 would be $82,400.
c) The two states' median house values were equal in year = 190
Let’s break down each question:
a) To determine which state’s home values have increased at a higher rate, we need to calculate the rate of change for each state. The rate of change is calculated as the difference in home values divided by the difference in years.
For Arkansas, the rate of change is (72,800 - 24,800) / (2000 - 1950) = $960 per year.
For New York, the rate of change is (148,700 - 61,500) / (2000 - 1950) = $1,744 per year.
So, home values have increased at a higher rate in New York.
b) If these trends were to continue, the median home value in Arkansas in 2010 would be the 2000 home value plus the rate of change times the number of years since 2000.
So, the median home value in Arkansas in 2010 would be 72,800 + $960 * (2010 - 2000) = $82,400.
c) If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be equal when the equation for Arkansas’s home values equals the equation for New York’s home values.
We are given that the median home value in Arkansas in 1950 was $24,800 and in 2000 it was $72,800. This gives us a rate of increase of $960 per year. So, the value of a home in Arkansas in year ‘x’ can be represented by the equation:
[tex]V_{Arkansas}(x) = 24800 + 960 * (x - 1950)[/tex]
Similarly, the median home value in New York in 1950 was $61,500 and in 2000 it was $148,700. This gives us a rate of increase of $1,744 per year. So, the value of a home in New York in year ‘x’ can be represented by the equation:
[tex]V_{NewYork}(x) = 61500 + 1744 * (x - 1950)[/tex]
The two states’ median house values will be equal when
[tex]V_{Arkansas}(x) = V_{NewYork}(x)[/tex]
Setting the two equations equal to each other and solving for ‘x’ gives us:
[tex]24800 + 960 * (x - 1950) = 61500 + 1744 * (x - 1950)[/tex]
[tex]24800+960x-1872000=61500+1744x-3400800\\784x=149100\\x=190.17[/tex]
We round it to the nearest whole number because it represents a year.
So, the two states' median house values were equal in year = 190
Complete Question:
The median home value in Arkansas and New York (adjusted for inflation) are shown below:
Year Arkansas New York
1950 24,800 61,500
2000 72,800 148,700
If we assume that the house values are changing linearly,
a) In which state have home values increased at a higher rate?
b) If these trends were to continue, what would be the median home value in Arkansas in 2010?
C) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)
Had 6 bagels and ate all but 4 of them. how many bagels were left?
Let x equal the larger outcome when a pair of fair four-sided dice is rolled. find the pmf of x, its mean, variance, and standard deviation.
Use the fact that the sum of the angles in a triangle is 180 degrees for this question. Two angles of a triangle have the same measure and the third one is 24 degrees greater than the measure of each of the other two. Find the measure of the angles in the triangle.
if the area of a garden is 11 square feet what could be the dimensions of the garden
There can be multiple possible dimensions for a garden with an area of 11 square feet depending on its shape. For example, the garden could be 1ft by 11ft, 2ft by 5.5ft, or even a square with each side measuring 3.32 ft.
Explanation:The area of a garden is calculated by multiplying its length by its width. As the area of the garden is given as 11 square feet, possible dimensions for the garden could be 1 foot by 11 feet, 2 feet by 5.5 feet, or any other combinations that, when multiplied, give the result as 11 square feet.
Another way to look at it is that if you imagine the garden as a perfect square shape, each side would be approximately 3.32 feet since 3.32 multiplied by 3.32 equals roughly 11. This is because the square root of 11 is about 3.32.
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