the NACI cafeteria wants to sell two 25 cm diameter medium size pizzas for the same price as one large pizza. what should the diameter be of the large pizza so that it contains the same amount of pizza as the two medium-size pizzas?​

The given relation is a function

Step-by-step explanation:

When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.

In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.

Given relation is:

{(2, 2), (3, 2), (4, 3), (5,4)}

As we can see that the domain of given relation is:

{2,3,4,5} i.e. every element is unique

So,

The given relation is a function

Keywords: Relations, functions

Learn more about functions at:

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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.

In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.

Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.

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Answer:

-51/21

The first step in this equation would be to add -2/3 to 1/7

-2/3 and 1/7 need to have the same denominator, which 7 and 3 both go into 21

-2/3 converted to have the denominator, you would have to times top and bottom by 7, so you then get 14/21

Then you want to get the 1/7 with a denominator of 21 also, so you would times top and bottom by 3, so you get 3/21

Now you add 14/21 to 3/21 to get 17/21

-1/3h=17/21

You want to times by the reciprocal of -1/3 which would just be -3/1 so,

17/21*-3/1= -51/21 which is already simplified

So your answer would be -51/21

To check your work you would plug in -51/21 in for h

Step-by-step explanation:

Answer:

The product is [tex]x^3+5x^2[/tex]

Step-by-step explanation:

This is because we apply the distributive property of multiplication.

Thus from [tex]x(5x+x^2)[/tex]

we get this:

[tex]x*5x+x*x^2[/tex]

[tex]x*5x[/tex] is [tex]5x^2[/tex] and [tex]x*x^2[/tex] is [tex]x^3[/tex]

Answer:

1,3,5

Step-by-step explanation:

The domain is the set of all first elements of ordered pairs (x-coordinates).

The range is the set of all second elements of ordered pairs (y-coordinates).

Answer:

Step-by-step explanation:

y = 7 - 2x

x =1; y = 7 - 2*1 = 7- 2 = 5

x = 2; y = 7 - 2*2 = 7 - 4 = 3

x = 3; y = 7 - 2*3 = 7- 6 = 1

Range = { 1,3,5}

Answer:

Step-by-step explanation:

We will first find the slope of the line from those 2 points, then write the equation of the line in slope-intercept form, solving for b, the y-intercept.

[tex]m=\frac{13-19}{6-(-3)}=-\frac{6}{9}=-\frac{2}{3}[/tex]

So the slope is -2/3.  We will choose a point now to use in the slope-intercept equation.  I'm picking the one with no negatives (cuz who likes negatives!?).

[tex]13=-\frac{2}{3}(6)+b[/tex] which simplifies down to

13 = -4 + b so

b = 17

The y-intercept of the line that goes through those 2 points is (0, 17)

Answer:

The term 'numerical' means 'involving numbers' and the term 'expression' means 'phrase'. A numerical expression is a mathematical phrase involving only numbers and one or more operational symbols.

Answer:

The term 'numerical' means 'involving numbers' and the term 'expression' means 'phrase'.  In other words, it is just a phrase/ equation with numbers not letters.

Example 2+4=6

NOT 3a+4a=7a

Happy Holidays!

Answer: 3( 5m - 1 )

Step-by-step explanation:

The expression given is ; 15m - 3

This could be factorized , the common factor is 3 , so we have

3( 5m - 1 )

Answer:

solve using long division.

75/4

what is the largest whole number smaller than 75 that 4 can go into?

72.

how many times can 4 go into 72?

18.

so then subtract 72 from 75 to get 3.

the new equation is

3/4

how many times can 3 go into 4?

0.75 times.

so add the 2 answers to get

18.75

4 can go into 75 18.75 times.

To determine how many times 4 can go into 75, you divide 75 by 4. The result is 18 with a remainder of 3. Thus, 4 can go into 75 a total of 18 full times.

To find out how many times 4 can go into 75, we need to perform a division. Specifically, we need to divide 75 by 4.

This means that 4 goes into 75 exactly 18 times with a remainder of 3. So, 4 fully fits into 75 for 18 full times.

Answer:

1

Step-by-step explanation:

4/4=1

5-1-3=4-3=1

Answer:

Below.

Step-by-step explanation:

-1 + r ≥ 4

Add 1 to both sides:

r  ≥ 5.

The  graph will have a filled circle on the number 5 and a  heavy line to the right.

The similarity ratio of the two octagons, given their areas, is 2:1. This is determined by taking the square root of the ratio of their areas.

The question is about finding the similarity ratio of two similar octagons with given areas. The area of a shape increases by the square of the scale factor (similarity ratio). Hence, in this case, where the larger octagon has four times the area of the smaller, the scale factor (similarity ratio) is the square root of 4, which is 2. So, the similarity ratio of the two octagons is 2:1.

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Answer:

10

Step-by-step explanation:

Given

[tex]x+y=8\\ \\4x-y=22[/tex]

Add these two equations:

[tex]x+y+4x-y=8+22\\ \\5x=30\\ \\x=6[/tex]

Substitute it into the first equation:

[tex]6+y=8\\ \\y=8-6\\ \\y=2[/tex]

Then

[tex]2x-y=2\cdot 6-2=12-2=10[/tex]

Answer:

28 - 7x =< 28x + 28

28 - 35x =< 28

-35x =< 0

x >= 0

the answer is the fourth one

x is greater than or equal to 0

Answer:

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

[tex]\hat p=0.849[/tex] estimated proportion of adults were no longer smoking after one month

[tex]p_o=0.80[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:  

Null hypothesis:[tex]p=0.8[/tex]  

Alternative hypothesis:[tex]p \neq 0.8[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

Answer:A

Step-by-step explanation:

no need for this you only look at the answers

Answer:13hrs

Step-by-step explanation:

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

for every hour the temperature decreases by 3°c.

What time does it take to get to 0c  = . 21(°c) / 3(°c/hr)  = . 7hr

what time does it take to get to -18c  = 18(°c) / 3(°c/hr)   = . 6hr

Total Time taken  = . 7hr + 6hr = 13hr

Alternative solution

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

(21 + 18)°c/ 3(°c/hr) . = . 13hr

To cool a freezer from 21℃ to -18℃ at a rate of 3℃ per hour, it would take 13 hours for the freezer to reach -18℃.

The question asks how long it will take for a freezer to cool down from 21℃ to -18℃ if the temperature decreases at a rate of 3℃ per hour. To find the time it takes, you'll need to calculate the total temperature change required and then divide by the rate of temperature change.

First, calculate the total temperature difference:

21℃ (starting temperature) - (-18℃ target temperature) = 39℃ total temperature change.

Next, divide the total temperature change by the rate of temperature change:

39℃ total change / 3℃ per hour = 13 hours required

for the freezer to cool from 21℃ to -18℃.

874.18

Step-by-step explanation:if you multiply 800 by1.03 it will increase by 3% then repeat step two more times

Answer:

Lack of information.

Step-by-step explanation:

We can't get the answer because this question haven't provide the information enough.

Have a nice day and hope it helps ;)

The conclusion that 40% of the students have visited a science museum based on a sample of 50 may not be accurate because the Sample Size may be too small and unrepresentative of the school population. Other factors like Response Rate and random sampling are essential for validity, and a Hypothesis Test could provide more solid evidence.

The conclusion that 40% of the students in the school have visited a science museum based on a survey of 50 students is not fully valid without considering additional factors. When conducting a survey, the concept of Sample Size is crucial. A sample size of 30 is the minimum required to start establishing statistical confidence, but larger samples are generally better to reduce sampling error. In this case, sampling only 50 students might not be representative of the entire student body, depending on the school's population. Moreover, the Response Rate and the randomness of the sample are essential in determining the validity of survey results. The survey must have a relatively high response rate and the sample must be chosen randomly from the entire population to avoid bias. This helps in better reflecting the overall characteristics of the population.

Conducting a Hypothesis Test would also help validate the findings. This statistical tool helps determine whether the observed proportion significantly deviates from the expected proportion (if known) or not. Furthermore, one important aspect is to avoid making statistics imply something they do not, which is common in cases where the sample size is small or the sample is unrepresentative. Lastly, discrepancies in survey results, like those seen in vaccination rates from two different researchers, can occur even when the right procedures are followed due to inherent variability in sampling.

Answer

given,

average rent of one bed room = $1229

sample size = n = 15

Sample mean rent = $1350

Assuming standard deviation equal to $250

the test hypothesis is

H o: µ=1229

H a: µ not equal to 1229

now we know,

[tex]t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{\$ 1350-\$ 1229}{\dfrac{250}{\sqrt{15}}}[/tex]

     t = 1.875

from t- table

a=0.05, the critical value is  |t(0.025, d f= n-1 = 14)|=2.14

since t= 1.875 which is less than 2.14 we do not reject H o.

So we can not conclude that the monthly rent outside San Francisco differs from that in the city

At a 0.05 significance level, we cannot conclude that the monthly rent outside San Francisco differs from that in the city, based on the given data and hypothesis test.

To determine if the monthly rent outside San Francisco differs from that in the city based on the sample provided, we perform a hypothesis test. Our null hypothesis (H0) states that the mean rent outside San Francisco is equal to the average rent in San Francisco, i.e., $1229. The alternative hypothesis (Ha) posits that the mean rent outside San Francisco is different from $1229.

Calculate the test statistic: We use a Z-test since the population standard deviation is known. The formula for the Z-score is:
[tex]Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
where X_bar = 1350, μ = 1229, σ = 250, and n = 15. Plugging in these values:
[tex]Z = \frac{1350 - 1229}{\frac{250}{\sqrt{15}}} = \frac{121}{64.55} \approx 1.87[/tex]

Determine the critical value: At α = 0.05, the critical values for a two-tailed test are approximately ±1.96.

Compare the test statistic to the critical value: Since 1.87 is less than 1.96, we fail to reject the null hypothesis.

Conclusively, at the 0.05 significance level, we do not have enough evidence to say that the monthly rent outside San Francisco differs from that in the city.

Complete question:

The average monthly rent for a one-bedroom home in San Francisco is $1229. A random sample of 15 one-bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standard deviation is $250. At α = 0.05, can we conclude that the monthly rent outside San Francisco differs from that in the city?

Answer:

$25.24

Step-by-step explanation:

If Tim earns $45.19 each month multiply by 3 which gives you $135.57 take $211.29 subtract $135.57, you get $75.72 which is the total amount that Tom needs to give. Divide that by 3 and get $25.64 which is the amount Tom needs in 3 months.

$45.19 x 3 = $135.57

$211.29 - $135.57 = $75.72

$75.72/3 = $25.24

Answer:

y-6=1/2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=1/2(x-4)

Answer:

130 is close to 128, so 128 is a reasonable answer.

Step-by-step explanation:

Consider the provided information.

We need to Use the estimation to check weather 128 is a reasonable answer in the example above:

p=200-72

Round to the nearest ten:             p = 200 - 70

Subtract the rounded numbers:   200-70=130

130 is close to 128, so 128 is a reasonable answer.

Answer:

The answer is larger than 3 unless d = 0

Step-by-step explanation:

Well, it says increased, which means add/multiply

However, we don't know what d equals, so it is impossible to find the answer.

Answer:

30

Step-by-step explanation:

2m+180=8m

180=8m-2m

180=6m

m=180/6

m=30

Because the two lines are not parallel, we conclude that the system will have a solution.

Remember that the solution of a system of equations is the point where the graphs of the functions intersect.

In this case we have two linear functions:

f = 2m + 180

f = 8m

Notice that the slopes are different, this means that the lines are not parallel, and because of that, we know that the lines will intersect at some point. That is enough to know that the system has a solution.

If you want to learn more about systems of equations:

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Answer:

There was 10° F change in temperature in Fairbanks, Alaska.

Step-by-step explanation:

Given:

Temperature change from = -1° F.

Temperature change to = 9° F

We need to find the change in temperature.

Change in temperature can be calculated by subtracting Temperature change from with Temperature change to.

Framing in equation form we get;

Change in temperature = Temperature change to - Temperature change from

Substituting the values we get;

Change in temperature = [tex]9-(-1)= 9+1=10\° F[/tex]

Hence There was 10° F change in temperature in Fairbanks, Alaska.

Answer:

b. Right, isosceles

Step-by-step explanation:

right because it has a right angle at the top corner

isosceles because two sides of the triangle are equal to each others

Answer: The information you are given shows that 15% = 30. Multiply 30 by 6 and 2/3 (The number of times 15 goes into 100) and you have your answer. There are 200 people on the beach.

Final answer:

To find the total number of people at the beach when 15% do not wear sunscreen and 30 people represent that 15%, we divide 30 by 0.15 to get 200, meaning there are 200 people on the beach.

Explanation:

The student asked: "If 15% of people on the beach do not wear sunscreen, and 30 people don't wear sunscreen, what is the total number of people at the beach?" To find the total number of people at the beach, we need to calculate it based on the percentage of people who do not wear sunscreen.

Therefore, the total number of people at the beach is 200.

Answer:

Time= [tex]10[/tex] years

Step-by-step explanation:

Let total time[tex]=t[/tex]

Initial Amount[tex]=5000[/tex]

Final Amount[tex]=10000[/tex]

Total interest = Final Amount - Initial Amount

                      [tex]=10000-5000\\=5000[/tex]

Simple Interest [tex]=\frac{Initial Amount\times time\times rate}{100} \\\\5000=\frac{5000\times t \times 10}{100}\\\frac{t}{10} =1\\t=10 \ years[/tex]

Answer:

Step-by-step explanation:

(8,-3),(8,4)

since both points have the same x value, this means you have a vertical line with an undefined slope...so ur equation would be x = 8....because no matter what y is, x will always be 8