You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.

Answer:

  [tex]\dfrac{2x-11}{x-2}[/tex]

Step-by-step explanation:

Simplify the fractions, then add.

  [tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]

_____

Note that this comes with the restriction that x ≠ 0.

Answer:

Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !

Step-by-step explanation:

evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...

The value of the expression [tex]^8P_6[/tex] is 20160.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.

The value of the expression is calculated as:-

[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]

[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]

[tex]^8P_6[/tex] = 20160

Hence, the value is 20160.

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Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

The  null hypothesis is  [tex]H_o : r < 0[/tex]

The  alternative hypothesis is  [tex]H_1 : r > 0[/tex]

Generally the standard deviation is mathematically evaluated as

       [tex]Sr = \sqrt{1- r}[/tex]

       [tex]Sr = \sqrt{1- 0.65}[/tex]

       [tex]Sr = 0.616[/tex]

The  degree of freedom for the one-tail test is

       [tex]df = n- 2[/tex]

        [tex]df = 14- 2[/tex]

        [tex]df = 12[/tex]

The standard error is evaluated as

        [tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]

        [tex]SE =0.1779[/tex]

The test statistics  is evaluated as

      [tex]t = \frac{r }{SE}[/tex]

       [tex]t = \frac{0.65 }{0.1779}[/tex]

        [tex]t = 3.654[/tex]

The p-value of of  t is obtained from the z table, the value is  

        [tex]p-value = P(t < 3.654) = 0.00012909[/tex]

Given that [tex]p-value < \alpha[/tex]  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive

Answer:

A) Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) Reject H0 is t > 2.821433

C) t = 1.79

D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Step-by-step explanation:

A) The hypotheses is given as;

Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;

t = 2.821433

Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.

Thus, if t > 2.821433, we will reject the null hypothesis H0.

C) Formula for the test statistic is;

t = (x' - μ)/(s/√n)

We have, μ = 41500, x' = 47500, s = 10600, n = 10

t = (47500 - 41500)/(10600/√10)

t = 1.79

D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Answer:

0.8989

Step-by-step explanation:

Using the Newton's Raphson approximation formula.

Xn+1 = Xn - f(Xn)/f'(Xn)

Given f(x) = x³-2x+2

f'(x) = 3x²-2

If the initial value X1 = 2

X2 = X1 - f(X1)/f'(X1)

X2 = 2 - f(2)/f'(2)

f(2) = 2³-2(2)+2

f(2) = 8-4+2

f(2) = 6

f'(2) = 3(2)²-2

f'(2) = 10

X2 = 2- 6/10

X2 = 14/10

X2 = 1.4

X3 = X2 - f(X2)/f'(X2)

X3 = 1.4 - f(1.4)/f'(1.4)

f(1.4) = 1.4³-2(1.4)+2

f(1.4) = 2.744-2.8+2

f(1.4) = 1.944

f'(1.4) = 3(1.4)²-2

f'(1.4) = 3.880

X3 = 1.4- 1.944/3.880

X3 = 1.4 - 0.5010

X3 = 0.8989

Hence the value of X3 is 0.8989

Answer:

a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Step-by-step explanation:

Formulate the null and alternative hypotheses as

a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 3.5 pounds

n= 49

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 3.5 / √49

Z= -1.80

Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) If standard deviation is 1.75 pounds

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 1.75 / √49

Z= -3.6

This value does not fall in the critical region.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) If the sample mean is 69 pounds

Z = x- x`/ s/√n

Z= 69.1- 69 / 3.5 / √49

Z= 0.2

This value falls in the critical region

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Answer:

[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Step-by-step explanation:

The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]

where:

Base stands for the larger base (in our case the dimension "B" in the attached image)

base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)

and

height stands for the distance between bases (in our case the dimension "h" in the attached image.

Therefore the formula for the area of the grassy section becomes:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Answer:

1/2 (b+b) h

here is the actual picture

Answer:

24

Step-by-step explanation:

13/3 / 2/11 = 13/3 * 11/2 = 143/6 = 23 and 5/6

23 and 5/6 is closest to 24.

Answer:

23 5/6

Step-by-step explanation:

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;

the least integer for n is 2    

The function given in this exercise corresponds to:

[tex]f(x) = ln(1+x)[/tex]

knowing that the x point will be centered on:

[tex]x=0\\Pn(0,2)\\Error < 0.01[/tex]

By rewriting the equation we have to:

[tex][[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01[/tex]

So doing the derivatives related to the first function given in the exercise we have to:

[tex]f(x) = ln(1+x)[/tex]

Following this we have to:

[tex]Max|f^{(n+1)} (c)| < n![/tex]

Thus, error is;

[tex](n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01[/tex]

[tex](1/(n + 1))* 0.2^{(n + 1)} < 0.01[/tex]  

Let's try n = 1

[tex](1/(1 + 1)) *0.2^{(1 + 1)} = 0.02[/tex]

This is greater than 0.01 and so it will not work. Let's try n = 2

[tex](1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267[/tex]

This is less than 0.01. So,the least integer for n is 2.

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1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

Answer:

The 95% confidence interval is  [tex]84.83< \mu < 90.37[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 113[/tex]

     The sample mean is  [tex]\= x = 87.6[/tex]  

      The standard deviation is  [tex]\sigma = 15[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = 100 - 95[/tex]

             [tex]\alpha = 5\%[/tex]

             [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value  is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

              [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]

=>          [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]

=>          [tex]E = 2.77[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

        [tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]

        [tex]84.83< \mu < 90.37[/tex]

Answer:

A. 30

Step-by-step explanation:

The interquartile range for a box and whiskers plot, is the value from the right side of the box minus the value of the left side of the box.

In this case at the far right side of the box it is at 130, at the far left side of the box it is at 100.

130-100=30

Answer:

[tex]\huge\boxed{IQR = 30}[/tex]

Step-by-step explanation:

Q1 = 130 (Left hand edge of the box)

Q3 = 100 (Right Hand edge of the box)

Interquartile Range = Q3-Q1

IQR = 130-100

IQR = 30

Answer:

35°

Step-by-step explanation:

If BCD is 75, then BCA is 105.

105+40=145

180-145=35

So ABC is 35°

Step-by-step explanation:

A rotation about point A a reflection across the line containing AR a reflection across the line containing AQ a rotation about point R

Answer:

A rotation about point A

Step-by-step explanation:

I am taking the test if it is wrong I will add a comment

Answer:

Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.

Step-by-step explanation:

From the question we are told that

     The sample size is  n =  500

     The sample proportion is  [tex]\r p = 0.57[/tex]

     The  95% confidence interval is (0.5266, 0.6134)

Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.

Answer:

At first, we have 3 expressions that are equal.

[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]

[tex]6+21 - 63= 3+32 - 4[/tex]

[tex]-36=31[/tex]

[tex]-36\neq 31[/tex]

This is not true.

Step-by-step explanation:

Ellen - 115/23

Classmates and Ellen got = 5 each

False!

The answer is: False.

Whomever stated the answer is "true" is wrong.

Answer:

The probability of raining if the number of days is more than 23 is 0.0668.

Step-by-step explanation:

We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.

Let X = Number of days of observing rain in a particular city.

The z-score probability distribution for the normal distribution is given by;

                         Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean number of days = 20 days

           [tex]\sigma[/tex] = standard deviation = 2 days

So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])

Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)

        P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                                              = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

Answer:

70%

Step-by-step explanation:

The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.

(original price - increased price) / 10

(17 - 10) / 10 = 7/10

7/10 can be converted from its fractional form to 70% i.e.its percentage.

Hope this helps and please mark as the brainliest.

Answer:

500,000

Step-by-step explanation:

(2.1 * 10^8)/(4.2 * 10^2) =

= 2.1/4.2 * 10^8/10^2

= 0.5 * 10^6

= 500,000

The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given exponents 2.1 × 10⁸

Let's assume 2.1 × 10⁸ is x times 4.2 × 10².

2.1 × 10⁸ = x (4.2 × 10²)

x = 2.1 × 10⁸/4.2 × 10²

x = 500000

Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".

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Answer:

117 cm³

Step-by-step explanation:

To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.

Answer:

117 cubic centimeters

Step-by-step explanation:

Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:

V = LWH

For this, the L = 13cm, W = 3cm, and H = 3cm

So our volume in cubic centimeters will be:

V = LWH

V = (13cm) * (3cm) * (3cm)

V = (13cm) * (9cm^2)

V = 117 cm^3

So the volume of the stick of butter is 117 cubic centimeters.

Cheers.

Answer:

197 = 10(31-1) + a

197 = 300 + a

-103 = a

Answer:

B

Step-by-step explanation:

Let's compare the two values of 12/16 and 3/4.

Notice that 12/16 isn't a simplified fraction; both the numerator and denominator are divisible by 4. So divide the top and bottom by 4:

12 / 4 = 3

16 / 4 = 4

We are left with:

12/16 = 3/4

Now, we see that Line A and Line B are equal in length, so the answer is B.

~ an aesthetics lover

Answer:

Kelvin did not skied without falling more than twice as long as anyone else in his family.

Step-by-step explanation:

The inequality representing the event where Kelvin skied without falling more than twice as long as anyone else in his family is:

[tex]2f<223[/tex]

Here 223 is the time for Kelvin.

[tex]2f<223[/tex]

[tex]2\times 55=110<223[/tex]

Kelvin skied without falling more than twice as long as Lori.

[tex]2f<223[/tex]

[tex]2\times 265=530>223[/tex]

Kelvin skied without falling less than twice as long as Vanessa.

[tex]2f<223[/tex]

[tex]2\times 172=344>223[/tex]

Kelvin skied without falling less than twice as long as Devon.

[tex]2f<223[/tex]

[tex]2\times 112=224>223[/tex]

Kelvin skied without falling less than twice as long as Celia.

[tex]2f<223[/tex]

[tex]2\times 356=712>223[/tex]

Kelvin skied without falling less than twice as long as Arnold.

Thus, Kelvin did not skied without falling more than twice as long as anyone else in his family.

Answer:

Yes, Kevin skied 2x as long as Lori.

Step-by-step explanation:

Kevin's time was 223 seconds; Lori's time was 110 seconds.

110^2 = 220 or 110 multiplied by 2 equals 220 or 110 x 2 = 220 or

110 * 2 = 220

Thus, Kevin indeed, skied twice as long as Lori.

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The correct option is  C

Step-by-step explanation:

Generally the sample standard error  is mathematically represented as

           [tex]\sigma_{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]

Where  [tex]\sigma[/tex] is the standard deviation and  n is the sample size

  Now looking at the formula we see that

             [tex]\sigma_{\= x } \ \ \ \alpha \ \ \ \frac{1}{ \sqrt{n} }[/tex]

So  at constant [tex]\sigma[/tex] if n increases [tex]\sigma_{\= x }[/tex] decreases

So from the question if ten more urban homeowners are asked the question the samples standard error decreases

Answer:

(C) 1 and 3

Step-by-step explanation:

Corresponding angles are angles that are at the same corner at the different intersections.

We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?

That's 3.

So 1 and 3 are congruent because they are corresponding.

Hope this helped!

Answer:

-54 is a integer and rational number

Step-by-step explanation:

Answer:

50k

Step-by-step explanation: