a. The hare's distance from the starting line is represented by the expression 7.5t.
b. The tortoise's distance from the starting line is represented by the expression 4.5t+820.
c. The number of meters the tortoise is ahead of the hare is represented by the expression 4.5t+820-7.5t.
In the race, the hare is running at a constant speed of 7.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to run that distance. This is represented by the expression 7.5t, where t is the time in seconds it takes the hare to run.
Similarly, the tortoise is crawling at a constant speed of 4.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to crawl that distance, plus the 820-meter head start they were given. This is represented by the expression 4.5t+820, where t is the time in seconds it takes the tortoise to crawl.
To find the number of meters the tortoise is ahead of the hare, we subtract the hare's distance from the starting line from the tortoise's distance from the starting line, which gives us the expression 4.5t+820-7.5t.
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In the box below, enter the value that is missing from the table.
Answer: 8
Step-by-step explanation:
Answer:
the value that is missing from the table is 8.
Write and graph the inequality represented: chase needs to make more than nine dollars an hour let w represent the hourly wage
Answer: I dont know im sorry
Step-by-step explanation:
By next year , 2,125 students are expected to be enrolled in a county's middle schools . This is 25 % of the total student population . What is the total student population ?
POSSIBLE POINTS: 5
Taina found the area of a table in the shape of a trapezoid. The height of the trapezoid is 10 ft, base one is 6 ft and base two is 5 ft. Taina says the area of the figure
is 110 square foot inches. What mistake did Taina make? What is the actual answer?
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Answer:
wrong formulawrong unitsStep-by-step explanation:
The formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
A = (1/2)(6 ft +5 ft)(10 ft) = 55 ft²
The numerical value of the answer would be 110 if we "forgot" to multiply by 1/2.
The area units would be "square foot inches" if inch dimensions crept into the problem somewhere.
It looks like Taina made two mistakes:
didn't correctly use the correct formuladidn't pay attention to area unitsthe volume of a rectangle prism is 8cm height 4 width.
Answer:
Step-by-step explanation:
Kayla and her children went into a restaurant and she bought $63 worth of hotdogs
and tacos. Each hotdog costs $3.50 and each taco costs $4. She bought 3 more
hotdogs than tacos. Write a system of equations that could be used to determine the
number of hotdogs and the number of tacos that Kayla bought. Define the variables
that you use to write the whats the system of equation.
Answer:
x= hotdogs
y=tacos
Step-by-step explanation:
(3.50)x+ 3x + 4y= 63
Perform the indicated operation (x-3y)(3x-11y)
Answer:
[tex]3x^{2} - 20xy + 33y^{2}[/tex]
Step-by-step explanation:
[tex](x-3y)(3x-11y)\\3x^{2} - 9xy - 11xy + 33y^{2} \\3x^{2} - 20xy + 33y^{2}[/tex]
Eric spends 4/5 of his pocket money to buy lunches. The rest of the money he will save. If the amount he saves is $2, how much does he spend buying lunch?
Answer:
Wait u want me to answer your question or the Jono question? Or both?
Step-by-step explanation:
1. $6/5
Subtract 2/3 and 1/4.
Answer:
5/12
Step-by-step explanation:
Find common denominators. Note that what you multiply to the denominator, you must multiply to the numerator as well. The common denominator is 12:
(2/3) * (4/4) = (8/12)
(1/4) * (3/3) = (3/12)
Subtract:
(8/12) - (3/12) = (8 - 3)/12 = 5/12
5/12 is your answer.
~
Convert. 7 oz. = ____ lb.
Plzzzzzzzzzzz help
Answer:
0.435 pounds
Step-by-step explanation:
There are 16 ounces in one pound. Use that conversion to find your answer.
Answer:
7oz=0.4375lb
Step-by-step explanation:
i hope this helps
have a nice night
mark brainliest please :)
Ms. Bohan drinks 3/5 of her drink from starbucks. What percent of her drink did she have?
Answer:
30%
Step-by-step explanation:
3/50 = 60/100
Answer:
u
Step-by-step explanation:
A rectangular library has a length of 54 feet and a perimeter of 172 feet.
What is the width, in feet, of the library?
Answer:
yes
Step-by-step explanation:
what is the area of the composite figure
Answer:
D) 476 ft²
Step-by-step explanation:
12x14=168
(25+31)/2=28
28x11=308
308+168=476
HELP PLEASE PLEASE ASAP
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Answer:
150 square units
Step-by-step explanation:
Each of the six squares has an area of 5×5 = 25 square units. (You can count them, if you wish.)
Then the total area is ...
6×(25 square units) = 150 square units
2. WHICH EXPRESSIONS ARE EQUIVALENT TO 6X?
SELECT ALL THAT APPLY
5X+X
3X+3
5+X
9X-3
X+X+4X
Answer:
5x+x and x+x+4x
Step-by-step explanation:
5x+x is basically 5x+1x which is 6x since x has an "invisible one" in front of it.
x+x+4x is 2x+4x which is 6x
hope this helps. :)
Answer:
4 and 5
Step-by-step explanation:
9x - 3 is 6x
5x + x can be 6x because there's is a x next to it that means it can be any number so if the number is suppose to become 6x we need to add 1 to both sides, and the a swer will be 6x.
sorry of wrong.
Consider this absolute value function.
f(3) = (+31
If function fis written as a piecewise function, which plece will it include?
A. -x- 3, x<3
B. -x + 3, x <-3
C. x+3, x >3
D. x+3, x>-3
Answer:
D
Step-by-step explanation:
f(x) = |x+3|=x+3 when x+3≥0 ⇒x≥-3
According to exit polling from the 2014 U.S. midterm elections, 36% of voters had a household income less than $50,000, while 64% had a household income of at least $50,000. Forty-three percent of voters from house-holds making less than $50,000 voted for the Republican party in the election, while 55% percent of voters from households making at least $50,000 voted Republican. What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000
Answer:
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Republican
Event B: From a household that makes at least $50,000.
Probability of Republican:
43% of 36%(makes less than $50,000).
55% of 64%(makes more than $50,000).
So
[tex]P(A) = 0.43*0.36 + 0.55*0.64 = 0.5068[/tex]
Republican and from a household that makes at least $50,000.
55% of 64%. So
[tex]P(A \cap B) = 0.55*0.64 = 0.352[/tex]
What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.352}{0.5068} = 0.6946[/tex]
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
Pleas help
Today is payday at your job at Toys R Us! You go to the bank to deposit your $150 check into your account. You receive a deposit slip. You decide to go to American Eagle. There you see a pair of jeans you like on sale for $39.99 from the usual $69.99. Wow! This is a steal! You pay the store attendant using your debit card, and you are the proud owner of a brand new pair of American Eagle jeans! With this scene in mind, Name the three uses of money and describe how each use is displayed in this scenario. Be specific.
Answer:
earning the money,depositing the money, and spending the money.
you worked all week to earn the money.
You deposit your money in your account.
You spent some money at American eagle.
Step-by-step explanation:
PLEASE HELP ME ON THIS
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Answer:
(d) $775.50
Step-by-step explanation:
The parallelogram on the left has an area of ...
A = bh = (4 yd)(2 yd) = 8 yd²
The rectangle in the middle has an area of ...
A = lw = (6 yd)(4 yd) = 24 yd²
The triangle on the right has an area of ...
A = 1/2bh = 1/2(1 yd)(2 yd) = 1 yd²
The total area of the carpet is ...
(8 + 24 + 1) yd² = 33 yd²
__
At $23.50 per square yard, the cost is ...
($23.50/yd²)(33 yd²) = $775.50 . . . . . matches the last choice
I need help with this plz
Answer:
-5.3, -5/2, 72%, sqrt52, then 49
Step-by-step explanation:
edge 2020
p.s. pls mark brainliest, and have a good day! :)
interest earned on both the principal and any previously earned interest?
a. compound interest
b. simple interest
c. interest rate
d. principal
Answer:
A. Compound Interest
Step-by-step explanation:
Compound interest is interest paid on both the principal and previously earned interest.
Compound interest earned on both the principal and any previously earned interest. Therefore, the correct answer is option A.
What is the rate of interest?An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Therefore, option A is the correct answer.
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An office building has the dimensions
shown. What is the volume of the building?
50 m
10 m
110 m
90 m
70 m
Answer:
330 the volume of building
If I said you needed to pick up a number that was less than 7 or a number greater then 5 what would be the solution
Answer:
6
Step-by-step explanation:
the only number between those to is 6
if -2x + 3 = 7 and 3x + 1 = 5 + y, the value of y is
Answer:
value of y is -10
Step-by-step explanation:
-2x+3=7 equation 1
3x+1=5+y equation 2
by eq 1
-2x=7-3
-2x=4
x=-2
put value of x in equation 2 to get value of y
3(-2)+1=5+y
-6+1=5+y
-5=5+y
-5-5=y
y=-10
PLEASE HELP| calculate measure of angle H. round answer right nearest tenth of a degree
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Answer:
28.1°
Step-by-step explanation:
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(H) = 8/17
H = arcsin(8/17)
H ≈ 28.1°
Mrs. Miller and 8 of her closest friends are taking a
Yoga class. The total cost for the class is $78.75.
Write and solve a multiplication equation to show
the cost per person for the Yoga class.
Answer:
f f f f f ff f f ff f f ff f f f f f f
Step-by-step explanation:
Samir has collected 35% of the skins on Fortnite. If there are 300 total skins, how many more does he need to collect to be at 50%? Explain or show your work.
I believe its 45.
Its hard to explain but what I can say is if you subtract the percentage with the total of the skins you would subtract what you had from there and then you would have 45.
Answer:
I think 45
Step-by-step explanation:
An initial investment of $2,000 earns 7% interest compounded continuously. What will the investment be worth in 17 years? (Round your answer to the nearest cent.)
Answer:
Future value, A = $6,317.6
Step-by-step explanation:
Given the following data;
Principal = $2,000
Interest rate = 7%
Time = 17 years
To find the future value, we would use the compound interest formula;
[tex] A = P(1 + \frac{r}{100})^{t}[/tex]
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
t is the number of years for the compound interest.
Substituting into the equation, we have;
[tex] A = 2000*(1 + \frac{7}{100})^{17}[/tex]
[tex] A = 2000*(1 + 0.07)^{17}[/tex]
[tex] A = 2000*(1.07)^{17}[/tex]
[tex] A = 2000 * 3.1588 [/tex]
Future value, A = $6,317.6
Draw a histogram for the intervals 16-18, 19-21, 22-24, and 25-27 using the following data: 26, 16, 22, 27, 20, 24, 21, 27, 22, 21, 26, 27, 23, 20, 16, 17, 27, 19, 17, 17
Answer:
Step-by-step explanation:
Class Interval Variate Frequency
16-18 16 1
19-21 0 0
22-24 0 0
25-27 26,27 2
Answer:
A
Step-by-step explanation:
right on edge 2021
Do mice show a preference for using one paw over the other? Attempting to answer this question, a researcher tested a random sample of 48 mice and observed which forepaw (right or left) the mice used to retrieve food from a narrow tube. Eighteen of the mice used their right paw, while the rest used their left paw.
Does this data suggest that mice show a preference towards one paw over the other? Carry out the appropriate test and include all steps for full credit.
During the course of the experiment, the researcher noticed that individual mice sometimes switched which forepaw they used to retrieve the food. So she repeated this study on the same 48 mice, but measured each one 10 times and she recorded which forepaw was used each time. With her new dataset of 480 observations, would you be able to run the same analysis as in part (a)? If so, carry out the analysis and compare the results. If not, why not?
Answer:
It all depends on the food they are going for, just like humans, mice have instincts. For example, if you were falling forward, which foot would you put out? Most likely the opposite one. I hope this helps you!
Step-by-step explanation:
Using hypotheses testing,
In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.
We have,
(a)
To test whether the data suggest that mice show a preference towards one paw over the other, we can use a one-sample proportion test.
The null hypothesis (H0) is that the proportion of mice that use their right paw is 0.5 (indicating no preference towards one paw over the other).
The alternative hypothesis (Ha) is that the proportion of mice that use their right paw is different from 0.5 (indicating a preference towards one paw over the other).
We can use a significance level (alpha) of 0.05.
To conduct the test, we can calculate the test statistic using the formula:
z = (p - 0.5) / √(0.5 x 0.5 / n)
where p is the proportion of mice that use their right paw, and n is the sample size.
Using the given data, we have:
p = 18/48 = 0.375
n = 48
Plugging in the values, we get:
z = (0.375 - 0.5) / √(0.5 x 0.5 / 48) = -1.714
Using a standard normal distribution table or calculator,
We can find the p-value associated with this test statistic.
The p-value is the probability of observing a test statistic as extreme as -1.714 or more extreme, assuming the null hypothesis is true.
The p-value for this test is 0.0869.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
This means that we do not have sufficient evidence to conclude that mice show a preference towards one paw over the other, based on the given sample.
(b)
With the new dataset of 480 observations, we can still conduct a similar analysis using a one-sample proportion test.
However, since each mouse was measured 10 times, the observations are no longer independent.
Therefore, we need to use a different test that accounts for the dependency between observations, such as McNemar's test.
McNemar's test is a test of the marginal homogeneity of a two-way table, where the same subjects are measured twice on a binary outcome.
In this case, we can create a 2x2 contingency table of the number of times each mouse used their right or left paw, and conduct a McNemar's test on this table.
The null hypothesis for McNemar's test is that there is no difference in the proportions of mice that use their right or left paws.
The alternative hypothesis is that there is a difference.
To conduct the test, we can calculate the test statistic using the formula:
chi-squared = (|b-c|-1)² / (b+c)
where b is the number of mice that used their right paw more often, and c is the number of mice that used their left paw more often.
Using the given data, we have:
b = 214
c = 244
Plugging in the values, we get:
chi-squared = (|214-244|-1)² / (214 + 244) = 2.417
Using a chi-squared distribution table or calculator with 1 degree of freedom (since we have a 2x2 table), we can find the p-value associated with this test statistic.
The p-value is the probability of observing a test statistic as extreme as 2.417 or more extreme, assuming the null hypothesis is true.
The p-value for this test is 0.119.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
This means that we do not have sufficient evidence to conclude that there is a difference in the proportions of mice that use their right or left paws, based on the new dataset.
Thus,
In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.
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