The National Science Institute was conducting research on the speed of Cheetahs. After
concluding their research, they were able to predict the cheetahs speed or distance when given
certain times or miles that the cheetah traveled. Complete the table of values and graph the
data on the coordinate plane.
Time(min) |. Distance(mi)
0. 0
1/2. 2/3
1. ?
? 3
8. ?
Answer the following questions using the information above.
1.) Is the relationship proportional? Why or why not?
2.) What is the unit rate?
Answers
The table of values is:
Time(min) | Distance(mi)
0 0
1/2 2/3
1 4/3
9/4 3
8 32/3
1) The relationship between Distance and Time is proportional.
2) The unit rate is 4/3 miles
To complete the table, we need to find the missing values of time and distance.
We use the relation between Distance, speed and time ,to find the missing values, which is given by,
Distance = Speed x Time
Given when time = 1/2 minute, the distance = 2/3 miles
Speed = Distance/Time
= 2/3 x 2/1
= 4/3 mile per minute.
This is the constant speed of the cheetah. We use this constant speed to find the other values to complete the table.
So If we take 'y' as the distance and 'x' as the time, then the relationship between time and distance can be expressed as
y = (4/3)x [since Distance = Speed x Time ].
So this relationship is proportional because there is a constant of proportionality 4/3 in the linear equation above and hence can be graphed as well.
The graph will contain the time values on the x-axis and distance values on the y-axis.
So now we need to find the missing values on the table using the above linear equation.
When time, x = 1 minute, distance, y = (4/3) x 1 = 4/3 miles.
When distance, y = 3 miles, 3 = (4/3)x
⇒ time, x = 3 x (3/4) = 9/4 minutes.
When time, x = 8 minutes, distance, y = (4/3) x 8 = 32/3 miles.
So the table is:
Time(min) | Distance(mi)
0 0
1/2 2/3
1 4/3
9/4 3
8 32/3
The unit rate refers to the y-value when the x-value is unity(1). So the unit rate here is found when time = 1 minute.
From the table, distance when time = 1 minute is 4/3 miles.
Hence, unit rate = 4/3 miles.
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Related Questions
Help Quickly! Which survey would you expect to have fair results regarding attitudes about carnivals?
A. Do you like going to carnivals?
B. Do you like going to exciting carnivals?
C. Do you like traveling across town to go to carnivals?
D. Do you like going to noisy, overpriced carnivals?
Answers
Question A is the survey that you expect to have fair results regarding attitudes about carnivals
How to get the best survey questionThis survey question is the most neutral and fair among the options provided. It doesn't include any leading or biased language that may influence the respondent's answer.
Option B uses the adjective "exciting," which could lead people to think positively about carnivals.
Option C brings in the unrelated factor of "traveling across town," which could negatively influence the response based on travel preference rather than attitude towards carnivals. Option D uses negative descriptors "noisy" and "overpriced," which could lead people to think negatively about carnivals.
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GEOMETRY NAME THE BIGGEST SIDE OF THE GIVE TRIANGLE 15 POINTS
Answers
Answer:
AB
Step-by-step explanation:
You want the longest side of triangle ABC with angles A=71°, B=35°, C=74°.
Law of sinesThe law of sines tells you that side lengths are proportional to the sine of the opposite angle. This means the longest side is opposite the largest angle.
Longest sideThe largest angle is C = 74°, so the longest side is opposite.
The longest side is AB.
raul wants to know if reading a book or watching a movie has a lower cost per minute the book Costs $15 and takes Raul 200 minutes to read the movie costs 14 and takes Raul 2 hours and 39 minutes to watch does the book or the movie have a lower cost per minute
Answers
The book has a lower cost per minute than the movie.
To find the cost per minute of the book, we divide the cost by the number of minutes:
cost per minute of book = $15 / 200 minutes = $0.075 per minute
To find the cost per minute of the movie, we need to convert the time to minutes.
2 hours and 39 minutes is equal to:
2 hours x 60 minutes/hour = 120 minutes
39 minutes = 39 minutes
Total minutes = 120 + 39 = 159 minutes
cost per minute of movie = $14 / 159 minutes = $0.088 per minute
Therefore, the book has a lower cost per minute than the movie.
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A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
Answers
no explanation really
like dilation 2x, 2y makes the size bigger but the shapes rhe same
In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion? (a) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.095 from the true proportion. (b) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.048 from the true proportion. is ne (c) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.095 from the true proportion.
(d) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion (e) There is not enough information to calculate the standard error.
Answers
The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.
What is the best interpretation of the standard errorThe correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."
The standard error of the sample proportion can be calculated using the formula:
SE = √[p*(1-p) / n]
where p is the sample proportion and n is the sample size.
In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:
SE = sqrt[0.37*(1-0.37) / 100] = 0.048
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- 7x - 5y = 36
x = 2y + 3
Answers
Answer:
Solution
\(x = - 3,\: y = -3\)
Step-by-step explanation:
If the objective is to solve for the system of equations
- 7x - 5y = 36 [1]
x = 2y + 3 [2]
Then the process is as follows
Substitute x = 2y + 3 from eq [2] in eq [1] : -7 x- 5y = 36==> - 7(2y + 3) - 5y = 36
Expand the brackets
-7 ( 2y + 3) = -7 (2y) - 7(3) = - 14y - 21
Simplify
==> -14y - 21 - 5y = 36
==> -19y - 21 = 36
Add 21 both sides:
-19y -21 + 21 = 36 + 21
-19y = 57
Divide both sides by - 19
- 91y/-19 = 57/-19
y = - 3
Substitute y = -3 in x = 2y + 3:
x = 2(-3) + 3 = -6 + 3 = -3
x = -3
1. In the number 123,546,870, which digit
is in the hundred thousands place?
Answers
Answer:
5
Step-by-step explanation:
Suppose the function h(x) = 2x - 9 is translated up 5 units to become a new function,
Xx). What's the equation of the new function?
A) x) = 7x-4
B)(x) = 2x - 14
C)(x) = 7x-9
D) (x)=2x-4
Answers
According to the given data the equation of the new function is (D) f(x) = 2x - 4.
What is meant by equation?An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.
According to the given information:If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:
f(x) = h(x) + 5
Substituting the definition of h(x) into this equation, we get:
f(x) = 2x - 9 + 5
Simplifying, we have:
f(x) = 2x - 4
Therefore, the equation of the new function is (D) f(x) = 2x - 4.
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11 of 3011 of 30 Questions
Question
A baker makes peanut butter cookies and chocolate chip cookies.
She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?
Answers
The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.
Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."
From the given information, we can set up the following system of equations:
For the flour:
2x + 3y = 26
For the butter:
34x + y = 9
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 17 (to make the coefficients of x in both equations the same):
34x + 51y = 442
Now we have the system of equations:
34x + y = 9
34x + 51y = 442
Subtract the first equation from the second equation:
34x + 51y - (34x + y) = 442 - 9
50y = 433
Divide both sides by 50:
y = 433/50
Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.
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If the cost of my building is 85,000, my scrap value is 7,500 and the expected life is 31.5 years. What is the depreciation for one month. I'd like the answer and the formula.
205 was not the answer.
Answers
The depreciation for one month is approximately $205.03.
To calculate the depreciation for one month, we can use the straight-line depreciation method. The formula for straight-line depreciation is:
Depreciation per period = (Initial cost - Scrap value) / Expected life
Given that the cost of the building is $85,000, the scrap value is $7,500, and the expected life is 31.5 years, we can plug these values into the formula:
Depreciation per period = ($85,000 - $7,500) / 31.5
Simplifying the equation, we get:
Depreciation per period = $77,500 / 31.5
Dividing $77,500 by 31.5, the depreciation per period is approximately $2,460.32.
To find the depreciation for one month, we need to divide this amount by 12 (since there are 12 months in a year):
Depreciation per month = $2,460.32 / 12
Therefore, the formula for calculating the depreciation for one month using the straight-line method is: Depreciation per month = (Initial cost - Scrap value) / (Expected life in years * 12 months).
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A family needs a truck that has a volume of at least 850 cubic feet. Will a truck that is 17 feet long , 7 feet wide, and 7 feet tall be big enough to hold all the familys belongings?
Answers
Answer:
No it can not
Step-by-step explanation:
What is the standard form of the following equation?
y= -3x+2
3x+y=2
y-2=-3x
y-3x=2
3x-y=2
Answers
Answer:
(a) 3x +y = 2
Step-by-step explanation:
You want the equation y = -3x +2 written in standard form.
Standard formThe standard form of a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.
To put the given equation into that form, we can add 3x to both sides:
3x +y = 3x -3x +2
3x +y = 2
Kaizen is a Japanese word that means continuous development. It says that each day we should focus on getting1% better on whatever we're trying to improve.How much better do you think we can get in a year if we start following Kaizen today?Note: You can take the value of (1.01)^365 as 37.78%Show Calculator
Answers
This is a compound interest-like problem.
The formula we can use is:
\(Improvement=P(1+r)^{365}\)P is the initial value of the skill we are trying to improve
r is the rate we are improving per day, in decimal
Then:
Let's say P = 1, that's the initial value of the skill
To convert 1% daily in to decimal:
\(r=\frac{1}{100}=0.01\)Thus:
\(Improvement=1(1+0.01)^{365}=1.01^{365}\)Using the value given by the problem:
\(Improvement=37.78\)This means that after a year of improving 1% daily, we are getting 37.78 times better at it!
To convert this to percentage, we multiply by 100:
\(37.78\cdot100=3778\%\)The answer is 3778%
Calculate the distance between the points M(6,2) and N(-1,7).
Answers
Answer: chupapi munanyo
Step-by-step explanation:chupapi munanyo
ALGEBRA
identify the terms, coefficients, and constants in the expression.
3p^2+7
Answers
sample of size n will be selected from population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal? a. Both np and n(1 P) are at least 10.b. n is greater than 30 c. p is greater than 0.5. d. The mean is equal to np e. the variance is equal to np(1-p)
Answers
True sampling distribution sample which is proportion to be approximately normal is "Both np and n(1 P) are at least 10".
For the sampling distribution of the sample proportion to be approximately normal, the sample size must be sufficiently large, and the sample proportion must be neither too small nor too large.
Specifically, the sample size multiplied by the sample proportion (np) and the sample size multiplied by one minus the sample proportion (n(1-P)) must both be at least 10. This is known as the "success-failure" condition.
Option b is not entirely accurate, as a sample size greater than 30 is a rule of thumb for the Central Limit Theorem to apply, but it is not a strict requirement for normality.
Option c is incorrect as a sample proportion greater than 0.5 means the distribution is skewed towards one end and not normal.
Option d and e are the mean and variance of the binomial distribution and are not directly related to normality.
The correct answer is option a. Both np and n(1-P) are at least 10.
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the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities
Answers
The number of months Mark can have the phone is given by the equation
A = 11.4 months
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of months be represented as = A
Now , the equation is
Now , the total amount with Mark = $ 146.43
The initial amount for the smartphone = $ 33
The amount per month for 2GB is = $ 9.95
So , the amount for A months = $ 9.95 ( A )
So , the equation will be
Initial amount for the smartphone + the amount for A months = total amount with Mark
Substituting the values in the equation , we get
33 + 9.95 ( A ) = 146.43 be equation (1)
On simplifying the equation , we get
Subtracting 33 on both sides of the equation , we get
9.95 ( A ) = 113.43
Divide by 9.95 on both sides of the equation , we get
A = 11.4 months
Therefore , the value of A is 11.4 months
Hence , the number of months is 11.4 months
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Write an expression using the distributed property to dind the product of 7x63
Answers
The product of the expression 7 x 63 is 441.
We have,
To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:
7 x 63 = 7 x (60 + 3)
Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:
7 x (60 + 3) = 7 x 60 + 7 x 3
Simplifying further:
7 x 60 + 7 x 3 = 420 + 21
Therefore,
The product of 7 x 63 is 441.
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Which of the following are consistent with the
guidelines for hitching trailers?
Trailers must be connected to the tow vehicle before loading.
Loads cannot exceed the maximum payload of 1,750 pounds.
Loads cannot exceed the maximum payload of 3,000 pounds.
Customer vehicles must have at least a frame mounted Class 3 receiver hitch
with a 2" or 2 5/6" ball.
Answers
The statement that are consistent with the guidelines for hitching trailers are:
A. Trailers must be connected to the tow vehicle before loading.
D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.
Guidelines for hitching trailers?Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.
Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.
Therefore the correct option is A and D.
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The fraction of PKR 1 is 50 paisas
Answers
The fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
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An employee plays $300 towards health insurance, while the employer pays $575. What is the ratioof the employers contribution to the employees contribution?
Answers
Employee pays toward health insurance is E= $300.
Employer pays toward health insurance is E' = $575.
Determine the ratio of employers contribution and employee contribution.
\(\begin{gathered} \frac{E^{\prime}}{E}=\frac{575}{300} \\ =\frac{115}{60} \\ =\frac{23}{12} \end{gathered}\)So ratio of employers contribution to the employees contribution is 23:12.
Answer: 23:12
A teacher bought 8 books at (p - 1500) each book and 2 pens at (p + 1000) each pen. If the teacher spent 53,000 altogether, how much money did he spend on the books?
Answers
Answer:
38400/=
Step-by-step explanation:
8(p-1500)=8p-12000
2(p+1000)= 2p+2000
8p-12000+2p+2000=53000
10p-10000=53000
10p=53000+10000
10p=63000
p=6300/=
8 books=8(6300-1500)
=38400/=
Which expression is equivalent to 9 more than the quoteint of x and 5
Answers
The equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:
x/5 + 9.
How to obtain the equivalent expression?The sentence in the context of this problem is defined as follows:
"9 more than the quotient of x and 5"
The quotient of x and 5 is given by the division of x by 5, as follows:
x/5.
9 more means that 9 is added to the quotient of x and 5, hence the equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:
x/5 + 9.
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Find the volume of the
triangular prism.
8 ft
6 ft
The volume of the triangular prism is ft³.
15 ft.
Answers
The volume of the triangular prism will be 400 cubic feet.
Given that:
Width, W = 15 feet
Height, h = 8 feet
Base length, b = 6²/₃ feet
Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.
The volume of the triangular prism is calculated as,
V = 1/2 · b · h · W
V = 0.5 · 6²/₃ · 8 · 15
V = 400 cubic feet
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Same directions as question #1
Sn = ( -1 )n + 1
Answers
The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.
How to depict the information?The formula for finding the nth term in an arithmetic sequence given as:
= a + (n - 1)d
Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:
= (-1)n + 1
= (-1)5 + 1
= (-1)6
= -6
Here is the complete question:
Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.
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If rolling a pair of dice, which result has the highest probability?
A) sum of 2
B) sum of 7
C) sum of 9
D) sum of 12
Answers
Answer:
7
Step-by-step explanation:
a woman invest a specific amount of money which earns compounded interest at a particular rate. this situation is represented by the equation : A=1000(1.023) ^(2*T) how much will she have in her account at 10 years?
Answers
We are given the following formula for interest compound:
\(A=1000(1.023)^{2t}\)Where "t" is time. We are asked to determine the value of "A" when t = 10. We replace the value of 10 in the formula, like this:
\(A=1000(1.023)^{2(10)}\)Solving the operations
\(A=1000(1.023)^{20}\)\(A=1000(1.58)=1575.8\)Therefore, in 10 years she will have $1575.8
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They
plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let x represent the number
of slushies sold.
a. Write a linear function for cost.
C(x) =
b. Write a linear function for revenue.
R(x) =
Answers
Part (a)
The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.
\(C(x)=500+1.25x\)
Part (b)
The revenue is the number of slushies sold multiplied by the amount charged per slushie.
\(R(x)=3.50x\)
Fill in the table using this function rule y= - 2x + 3
Answers
Step-by-step explanation:
you just have to put that value in place of x in the function.
don't be so lazy you a hole do it yourself
59:52
Step 1: Subtract 3 from both sides of the inequality.
Step 2:
Step 3: Divide both sides of the inequality by the
coefficient of x.
What is the missing step in solving the inequality 5;
8x < 2x + 3?
O Add 2x to both sides of the inequality.
O Subtract 8x from both sides of the inequality.
O Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.
Save and Exit
Answers
Answer:
I'm not really sure on this but I'm thinking it could be B