Two numbers have a sum of 23 and a difference of 9. Find the two numbers

Answer:

[tex]z=\frac{13725-13960}{\frac{2345}{\sqrt{500}}}=-2.24[/tex]    

[tex]p_v =2*P(z<-2.24)=0.0251[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 13960 at 10% of signficance.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=13275[/tex] represent the sample mean

[tex]\sigma=2345[/tex] represent the sample standard deviation

[tex]n=500[/tex] sample size  

[tex]\mu_o =68[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is 13960, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 13690[/tex]  

Alternative hypothesis:[tex]\mu \neq 13690[/tex]  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z=\frac{13725-13960}{\frac{2345}{\sqrt{500}}}=-2.24[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(z<-2.24)=0.0251[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 13960 at 10% of signficance.

Answer:

Step-by-step explanation:

Hello!

Given the regression equation

Credit= 17.9 - 0.09 Work

That was estimated from a sample of n= 21 statistic students.

Y: number of college credits taken

X: number of hours worked per week at an outside job

a)

The estimation for the slope is -0.09

As you see the estimated slope is negative, this means that the association between the two variables is indirect or inverse. Meaning, when the number of Work increases, the number of Credit decreases. (negative regression)

The correct option is: "An increase in the number of hours worked per week decreases the expected number of credits."

b)

The estimation for the intercept is 17.9

In general, the intercept is the estimated average of Y when X=0. You can interpret the intercept of this equation as "the value of Credits earned by a student that does not work outside of school"

The correct option is: " The intercept is meaningful as a student may not have a job outside of school. "

c)

If Work=0, then Credit= 17.9 (As explained in item b)

By replacing the value in the equation: Credit= 17.9 - 0.09 * 0= 17.9

If Work=60, you replace it in the equation and:

Credit= 17.9 - 0.09 Work= 17.9-0.09*60= 12.5

If the student works 60 hs outside of school it is expected that he takes 12.5 college credits.

I hope this helps!

The correct answers are that an increase in work hours decreases the number of expected credits, the intercept is meaningful as it represents the credits for a student not working, and credits equal to 17.9 when work hours are zero and 12.5 when work hours are 60.

The regression equation given is Credits = 17.9 - 0.09 Work, where Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job.

(a) From this equation, we can see that for an increase in the number of hours worked (Work), the number of expected credits (Credits) decreases because the coefficient of Work is negative (-0.09). So, the correct statement is: An increase in the number of hours worked per week decreases the expected number of credits.

(b) Regarding the intercept, it is meaningful since it represents the expected number of credits a student would take if they did not work at all (Work = 0). Therefore, the correct option is: The intercept is meaningful as a student may not have a job outside of school.

(c) If Work = 0, then Credits = 17.9. If Work = 60, then Credits = 17.9 - 0.09(60) = 17.9 - 5.4 = 12.5.

Only the volume is given, so you can already assume the rectangular prism is a cube, which in that case you can divide by 3 to get the answer.

Answer:

1.  [tex]l \leq 45[/tex] ( in this inequality, the time can be less than or equal to 45, but no more than 45)

2. [tex]m > 60[/tex]  (Mario's height is more than 60.)

3. [tex]f > 8000[/tex] (More than 8000 fans attended.)

Answer:

True

Step-by-step explanation:

Use the unit circle

tan(x) = 0 only when x is 0 or a multiple of 180 (in degrees)

Answer:

true

Step-by-step explanation:

Answer:

D (1,1)

Step-by-step explanation:

Answer:

D. (1,1)

Hope it works!

Step-by-step explanation:

Answer:

it would be A. -25

Step-by-step explanation:

`for example if she sold 0 dollars worth of necklaces and she spent 25 dollars on supplies she would have lost 25 dollars so it would be -25.

Answer:A,-$25

Step-by-step explanation:

She bought the necklace. When she sold it, she sold it for $25 less than what she bought it for. Therefore, she lost $25, the same as -$25.

Answer:

- pentagon area= 6.9

-hexagon area=10.4

Answer:

Pentagons: 6.9 square inches

Hexagons: 10.4 square inches

Step-by-step explanation: i got it right on edge

Answer:

14

Step-by-step explanation:

M = (13+8+12+10+27)/5

= 70/5

= 70 : 5

= 14

Answer:

-1/6

Step-by-step explanation:

The slope of the line can be found by

m = (y2-y1)/(x2-x1)

    = (7-9)/(8 - -4)

    -2 /(8+4)

     -2/(12)

     -1/6

Answer: 2.18

Step-by-step explanation:

log(11)/log(3)=2.18

Answer:

2.18

Step-by-step explanation:

I just did it and got it right

Answer:

False

Step-by-step explanation:

Substitute 13 in for c

c - 12 > 30

13 - 12 > 30

1 > 30

This is false, because 1 is not greater than 30

The solution:

c - 12 > 30

Add 12 to both sides

c  > 42

Answer: C

Step-by-step explanation:

Answer:

It might be C

Step-by-step explanation:

I am so sorry if it is the wrong answer. I didn't have a test about this.... :(

a. Salt flows into tank A at a rate of

(y(t)/500 lb/gal) * (50 gal/min) = y(t)/10 lb/gal

and out at a rate of

(x(t)/500 lb/gal) * (50 gal/min) = x(t)/10 lb/gal

so the net rate of change of the amount of salt in tank A is

[tex]x'(t)=\dfrac{y(t)}{10}-\dfrac{x(t)}{10}[/tex]

Similarly, you would find

[tex]y'(t)=\dfrac{x(t)}{10}-\dfrac{y(t)}{10}[/tex]

b. We have

[tex]x'=-\dfrac x{10}+\dfrac y{10}\implies x''=-\dfrac{x'}{10}+\dfrac{y'}{10}[/tex]

Notice that x' = -y', so

[tex]x''=-{2x'}{10}\implies 5x''+x'=0[/tex]

Solve for x: the characteristic equation

[tex]5r^2+r=r(5r+1)=0[/tex]

has roots [tex]r=0[/tex] and [tex]r=-\frac15[/tex], so

[tex]x(t)=C_1+C_2e^{-t/5}[/tex]

Again using the fact that y' = -x', we then find

[tex]x'(t)=-\dfrac{C_2}5e^{-t/5}\implies y'(t)=\dfrac{C_2}5e^{-t/5}\implies y(t)=C_1-C_2e^{-t/5}[/tex]

Given that x(0) = 0 and y(0) = 10, we find

[tex]\begin{cases}0=C_1+C_2\\10=C_1-C_2\end{cases}\implies C_1=5,C_2=-5[/tex]

Answer:

We can see the details in the pic.

Step-by-step explanation:

We can see the details in the pic shown.

Answer:

We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to​ 10%.

Step-by-step explanation:

We want to use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%.

We set up our hypothesis to get:

[tex]H_0:p=0.10[/tex]------->null hypothesis

[tex]H_1:p\ne0.10[/tex]------>alternate hypothesis

This means that: [tex]p_0=0.10[/tex]

Also, we have that, one restaurant had 36 orders that were not accurate among 324 orders observed.

This implies that: [tex]\hat p=\frac{36}{324}=0.11[/tex]

The test statistics is given by:

[tex]z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]

We substitute to obtain:

[tex]z=\frac{0.11-0.1}{\sqrt{\frac{0.1(1-0.1)}{324} } }[/tex]

This simplifies to:

[tex]z=0.6[/tex]

We need to calculate our p-value.

P(z>0.6)=0.2743

Since this is a two tailed test, we multiply the probability by:

The p-value is 2(0.2723)=0.5486

Since the significance level is less than the p-value, we fail to reject the null hypothesis.

We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to​ 10%.

Answer:

-5

Step-by-step explanation:

when you multiply a number by -1 it becomes its opposite

Answer: I am pretty sure it is 7

Step-by-step explanation:

the smaller one is to smaller than the bigger one so you would just add two to the 5

Answer:

7.5

Step-by-step explanation:

The triangles are proportional, so 6/4=x/5

1.5=x/5

x=1.5*5=7.5

The requried x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.

To find the number of items that should be produced in each run to minimize the total costs of production and storage, we can use the following steps:

Let x be the number of items produced in each run. The total cost of production and storage (C) can be expressed as:

C(x) = (640/150,000) + (7x) + (0.75 * 150,000 / x)

The first term (640/150,000) represents the cost of preparing a production run, the second term (7x) represents the cost of producing each item, and the third term (0.75 * 150,000 / x) represents the cost of storing each item.

To minimize the total cost, we need to find the value of x that minimizes the function C(x). We can do this by taking the derivative of C(x) with respect to x and setting it equal to zero:

C'(x) = 0

Now, let's find the derivative of C(x):

C'(x) = d/dx [(640/150,000) + (7x) + (0.75 * 150,000 / x)]

C'(x) = 0 + 7 - (0.75 * 150,000 / x²)

Now, set C'(x) equal to zero and solve for x:

7 - (0.75 * 150,000 / x²) = 0

0.75 * 150,000 / x² = 7

150,000 / x² = 7 / 0.75

150,000 / x² = 9.333...

Now, solve for x:

x² = 150,000 / 9.333...

x² ≈ 16,071.43

x ≈ sqrt(16,071.43)

x ≈ 126.77

Since x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.

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Answer:

22.7

Step-by-step explanation:

To find the mean absolute deviation (MAD), first find the mean (or average).

μ = (5 + 24 + 38 + 52 + 66 + 85) / 6

μ = 45

Next, subtract the mean from each value and take the absolute value.

|5 − 45| = 40

|24 − 45| = 21

|38 − 45| = 7

|52 − 45| = 7

|66 − 45| = 21

|85 − 45| = 40

Sum the results and divide by the number of animals.

MAD = (40 + 21 + 7 + 7 + 21 + 40) / 6

MAD ≈ 22.7

Answer:

The standard error of the mean is 0.3216

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 188

Sample mean =

[tex]\bar{x}= 10.97\text{ lb}[/tex]

Sample standard deviation =

[tex]s = 4.41\text{ lb}[/tex]

We have to estimate the standard error of the mean.

Formula for standard error:

[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]

Putting values, we get,

[tex]S.E =\dfrac{4.41}{\sqrt{188}} = 0.3216[/tex]

Thus, the standard error of the mean is 0.3216

Answer:

This is a Right Triangle

Step-by-step explanation:

12=a 16=b 20=c

Now lets solve

a^2+b^2=c^2

144+b^2=c^2

144+256=c^2

144+256=400

c^2=400

The square root of 400 is 20..

This IS a Right Triangle

Yes, a triangle with sides of lengths 12ft, 16ft and 20ft is a right triangle. This is proven by using the Pythagorean theorem, which these side lengths satisfy.

To verify if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In the triangle you provided with sides of lengths 12 ft (a), 16 ft (b), and 20 ft (c, as the hypotenuse is usually the longest side), you would plug those values into the equation: 12² + 16² = 20²?

144 + 256 = 400?

400 = 400

Because the equation is true, this proves that the triangle is indeed a right triangle.

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Answer:

5 a) PMT=$1,465.60

b) Total Payments=$527,616

c) Total Interest=$331,616

6a) Interest=$1,079.93

b) Principal=$584.07

Step-by-step explanation:

a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.

-The monthly mortgage payment can be calculated as follows:

[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})[/tex]

Where:

-We substitute to solve for PMT:

[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})\\\\=196000[\frac{(0.082/12)}{1-(1+\frac{0.082}{12})^{-12\times30}}]\\\\=\$1,465.60[/tex]

Hence, the monthly mortgage payment is $1,465.60

b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:

[tex]\sum(payments)=PMT\times nt\\\\=1465.60\times 12\times 30\\\\=\$527,616.00[/tex]

Hence, the total amount of payments is $527,616

c. The amount of interest paid over the loan's term is obtained  by subtracting the principal loan amount from the total payments made:

[tex]Interest=Payments-Principal\\\\=527,616.00-196,000.00\\\\=\$331,616[/tex]

Hence, an interest amount of $331,616 is paid over the loan's term.

6 a) We first obtain the effective loan amount by subtracting the down-payment:

[tex]Loan \ Amount= Regular \ Price -Downpayment\\\\=205700-0.1(205700)\\\\=\$185,130[/tex]

The interest paid on the first mortgage payment is calculated as below:

[tex]I=\frac{r}{n}\times P\\\\I=Interest\\r=interest \ rate\\n=Payments \ per \ year\\P=Outstanding \ loan \ balance\\\\\therefore I=\frac{0.07}{12}\times 185130\\\\=\$1,079.93[/tex]

Hence, the amount of interest in the first payment is $1,079.93

b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;

[tex]Principal \ Paid=PMT-Interest\\\\PMT=A[\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}}]\\\\=185130[\frac{(0.07/12)}{1-(1+\frac{0.07}{12})^{-180}}\\\\=1664.00\\\\\\Principal \ Paid=1664.00-1079.93\\\\=\$584.07[/tex]

Hence, the amount of principal applied is $584.07

(a) The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex] (b)The estimated mean number of hours is 1.8 hours.

To analyze the data and answer the questions about the time 30 children spent on their tablets one evening, let's break it down step by step.

(a) The median is the value that separates the higher half from the lower half of the data. For 30 children, the median position will be the average of the 15th and 16th values in the ordered data set.

Given the frequencies:

- [tex]\( 0 < h \leq 1 \): 6[/tex] children

- [tex]\( 1 < h \leq 2 \):[/tex] 13 children

- [tex]\( 2 < h \leq 3 \):[/tex] 7 children

- [tex]\( 3 < h \leq 4 \): 4[/tex] children

To find the median class interval, we need to determine where the 15th and 16th values fall.

Cumulative frequency:

[tex]- \( 0 < h \leq 1 \): 6\\ - \( 1 < h \leq 2 \): 6 + 13 = 19\\ - \( 2 < h \leq 3 \): 19 + 7 = 26\\ - \( 3 < h \leq 4 \): 26 + 4 = 30[/tex]

From the cumulative frequency:

The 15th and 16th values fall within the second class interval [tex]\( 1 < h \leq 2 \),[/tex] because the cumulative frequency reaches 19 in this interval.

The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex]

(b) To estimate the mean, we'll use the midpoint of each class interval and multiply by the frequency of that interval, then divide by the total number of children.

Determine the midpoints of each class interval:

[tex]- \( 0 < h \leq 1 \): midpoint = \( \frac{0 + 1}{2} = 0.5 \)\\ - \( 1 < h \leq 2 \): midpoint = \( \frac{1 + 2}{2} = 1.5 \)\\ - \( 2 < h \leq 3 \): midpoint = \( \frac{2 + 3}{2} = 2.5 \)\\ - \( 3 < h \leq 4 \): midpoint = \( \frac{3 + 4}{2} = 3.5 \)[/tex]

Multiply each midpoint by its respective frequency:

[tex]- \( 0.5 \times 6 = 3 \)\\ - \( 1.5 \times 13 = 19.5 \)\\ - \( 2.5 \times 7 = 17.5 \)\\ - \( 3.5 \times 4 = 14 \)\\[/tex]

Sum these products:

[tex]\[ 3 + 19.5 + 17.5 + 14 = 54 \][/tex]

Divide by the total number of children to find the mean:

[tex]\[ \text{Mean} = \frac{54}{30} = 1.8 \][/tex]

The estimated mean number of hours is 1.8 hours.

The complete question is:

The table shows information about the numbers of hours 30 children spent on their tablets one evening.

Number of hours (m)          Frequency

    D<h<1                                   6

    1<h<2                                   13

    2<h<3                                   7

    3<h<4                                   4

a) Find the class interval that contains the median.

b) Work out an estimate for the mean number of hours.

Answer:

Correct

Step-by-step explanation:

1. Factors

Are whole numbers that can divide the number completely.

2. Prime number

Number of factors that can be express in form of prime factorisation.

Prime factorisation of a number can be done by repeated division by prime numbers (number is written as the product of its prime factors)

For example, 17

List of factors, 1 and 17

Prime number, 17

Prime factorisation, 1×17=17

So why prime numbers cannot be express in form of prime factorisation?

Because, a prime number can only be divided by 1 or itself, so it cannot be factored any further. Not like the other number.

Brainliest would be appreciated :)

Final answer:

The student is incorrect; 17 is a prime number, and the only prime factor of 17 is 17 itself. The number 1 is not considered a prime factor as it is not a prime number.

Explanation:

No, the student is not correct in stating that the prime factors of 17 are 1 and 17. Prime factors are numbers that are both prime and divide the original number without leaving a remainder. The definition of a prime number is a number greater than 1 that has no positive divisors other than 1 and itself. In the case of 17, it is indeed a prime number, so it cannot have any prime factors other than itself. Therefore, the only prime factor of 17 is 17.

The number 1 is not considered a prime factor, as it is not a prime number because it does not meet the basic criterion of having exactly two distinct natural number divisors: 1 and itself. Examples of prime factors can be seen in other numbers, such as 15, whose prime factors are 3 and 5, both of which are prime numbers that divide 15 without leaving a remainder. In contrast, 17 can only be divided evenly by 1 and 17, and since 1 is not a prime number, 17 is the sole prime factor of 17.

Answer:

[tex]\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}[/tex]

Step-by-step explanation:

Given

The jogger’s position: p(t)

We can express the acceleration a as follows

[tex]a=\frac{d^{2}p}{dt^{2}}[/tex]

then

[tex]\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}[/tex]

only if

 [tex]0 min\leq t\leq 1 min[/tex]

The required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].

Given information:

A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run.

During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time.

Let a be the acceleration of the jogger.

So, the expression for acceleration can be written as,

[tex]a=\dfrac{d}{dt}(\dfrac{dP(t)}{dt})\\a=\dfrac{d^2P(t)}{dt^2}[/tex]

Now, the acceleration is proportional to square root of time.

So,

[tex]a\propto \sqrt t\\a=k\sqrt t\\\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex]

Therefore, the required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].

For more details about differential equations, refer to the link:

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Answer:

Option A is the right answer choice.

Step-by-step explanation:

10 plus a negative number is the same as subtracting it as a positive

Answer:

increases

Step-by-step explanation:

Answer:

the answer is:B

Step-by-step explanation:

Answer:

a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.

[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]

b) P-value = 0.0055

c) The null hypothesis is rejected.

There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.

d) Critical value tc=-1.96.

As t=-2.55, the null hypothesis is rejected.

Step-by-step explanation:

We have to perform a hypothesis test on the mean.

The claim is that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund ($1102).

a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.

[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]

b) The sample has a size n=600, with a sample refund of $1050 and a standard deviation of $500.

We can calculate the z-statistic as:

[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1050-1102}{500/\sqrt{600}}=\dfrac{-52}{20.41}=-2.55[/tex]

The degrees of freedom are df=599

[tex]df=n-1=600-1=599[/tex]

The P-value for this test statistic is:

[tex]P-value=P(t<-2.55)=0.0055[/tex]

c) Using a significance level α=0.05, the P-value is lower than the significance level, so the effect is significant. The null hypothesis is rejected.

There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.

d) If the significance level is α=0.025, the critical value for the test statistic is  t=-1.96. If the test statistic is below t=-1.96, then the null hypothesis should be rejected.

This is the case, as the test statistic is t=-2.55 and falls in the rejection region.