What is the length of the unknown side? Hint: Pythagorean
Theorem.

The adults that attended the showing is 29.

The children that attended the showing is 16

$4.50a + $2c = $162.50 equation 1

a + c = 45 equation 2

Where:

Multiply equation 2 by 2

2a + 2b = 90 equation 3

2.50a = 72.50 equation 3

a = 29

45 - 29 = 16

Subtract equation 3 from equation 1

Here is the complete question:

Tickets to Gone With the Wind, at the Classic Movie House, cost $4.50  for adults and  $2 for children. If  people attended the Saturday matinee showing and the Classic Movie House sold $162.50 worth of tickets: a.) How many adults attended the showing? b.) How many children attended the showing?

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Answer:

Option B

Step-by-step explanation:

Here ,

The mean value is 0.62

Z value formula is

z = (x' -mean)/(sigma/sqrt (n))

Substituting the given values, we get -

sigma = Sqrt {(x'-mean)^2/n}

Sigma = sqrt { (0.58-0.62)^2/75} = 0.09

z = (0.58-0.62)/(0.09)

z = -0.433

Hence, option B is correct

Answer:

im choosing A cause my answer shows 0.238 ill let yall know what i get

Step-by-step explanation:

I got a hundred

Standard Dev: 0.05604

0.58-0.62 / 0.05604 = (Z-Score) -0.713

Answer:

options pls. or any image.......................................

The distance between two points is √29 unit.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have the points (-2, 3) and (3, 1).

Using Distance formula

= √(1-3)² + (3 - (-2))²

= √ (-2)² + (5)²

= √ 4 + 25

= √29 unit

Thus, the distance between two points is √29 unit.

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Answer:

Total: $9,789.13

Interest: $3,789.13

Step-by-step explanation:

Answer: First answer goes with second graph

Second answer goes with third graph

Third answer goes with first graph :)

Step-by-step explanation:

The equation 1 matches option (B), equation 2 matches option (C),  equation 3 matches option (A).

"An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region".

For the above situation,

The inequalities are given as

1. [tex]4x+3 > 15[/tex] or [tex]-6x > =12[/tex]

2. [tex]-8x > -24[/tex] and [tex]-10 < =2x-6[/tex]

3.[tex]-29 < =9x-2 < 16[/tex]

By finding the solution for these equations will give the points that to be plotted on the graph.

Equation 1:

[tex]4x+3 > 15[/tex]

⇒[tex]x > 3[/tex]

[tex]-6x > =12[/tex]

⇒[tex]x > =-2[/tex]

So the points are (3,-2).

Equation 2:

[tex]-8x > -24[/tex]

⇒[tex]x > 3[/tex]

[tex]-10 < =2x-6[/tex]

⇒[tex]x > =-2[/tex]

So the points are (3,-2).

Equation 3:

[tex]-29 < =9x-2[/tex]

⇒[tex]x > =-3[/tex]

[tex]9x-2 < 16[/tex]

⇒[tex]x < 2[/tex]

So the points are (-3,2).

Hence we can conclude that the equation 1 matches option (B), equation 2 matches option (C),  equation 3 matches option (A).

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Answer:

The p-value for the one-sided Hypothesis test described in this example is 0.3121.

Step-by-step explanation:

Test the hypothesis that more than 50% of people plan on voting for the levy.

At the null hypothesis, we test that the proportion is 50%, that is:

[tex]H_0: p = 0.5[/tex]

At the alternate hypothesis, we test if this proportion is above 50%, that is:

[tex]H_a: p > 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]

Of these 150 respondents, 78 people say they plan on voting for the levy.

This means that [tex]n = 150, X = \frac{78}{150} = 0.52[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.52 - 0.5}{\frac{0.5}{\sqrt{150}}}[/tex]

[tex]z = 0.49[/tex]

Pvalue of the test:

The pvalue of the test is the probability of finding a proportion above 0.52, which is 1 subtracted by the pvalue of z = 0.49.

Looking at the z-table, z = 0.49 has a pvalue of 0.6879.

1 - 0.6879 = 0.3121

The p-value for the one-sided Hypothesis test described in this example is 0.3121.

Solution :

      x                   [tex]$(x-\overline x)$[/tex]                          [tex]$(x-\overline x)^2$[/tex]

45860             -1742.8571                 3037551.0204

38860            -8742.8571                 76437551.0204

64820              17217.1429                296430008.1633

63480             15877.1429                252083665.3061

36710              -10892.8571              118654336.7347

50410             2807.1429                 7880051.0204

33080             -14522.8571            210913379.5918    

333220          0.0000                        965436542.8571

Sample size, n = 7

Mean = [tex]$\frac{\sum x}{n}=\frac{333220}{7}$[/tex]

                   = 47602.8571

Variance = [tex]$\frac{(\sum (x- \overline x))^2}{(n-1)}=\frac{965436542.8571}{7-1}$[/tex]

                                       = 160906090

Standard deviation = [tex]$\sqrt{Variance} = \sqrt{160906090}$[/tex]

                                                     = 12684.876

a). df = n - 1

        = 7 - 1

       = 6

Level of significance, α = 0.02

Critical, [tex]$t_c = 3.143$[/tex]

b). Sample mean, [tex]$\overline x = 47602.8571$[/tex]

    Sample standard deviation, s = 12684.876

Sample size, n = 7

c). 98% confidence interval = [tex]$\overline x \pm t_c \times \frac{s}{\sqrt n}$[/tex]

                                             [tex]$=47602.8571 \pm 3.143 \times \frac{12684.876}{\sqrt 7}$[/tex]

                                             [tex]$=(32533.96,62671.76)$[/tex]

The Answer Is 18

Order Of Operation laws says that you must do the parentheses first, 45x2.

45x2=90

The next thing you must do is divide 90 by 10 since division is before addition.

90/10=9

Now combine like terms.

9+9=18

Answer:

Life insurance

Step-by-step explanation:

The rest are governm taxes

Answer:

Step-by-step explanation:

the 1st and 2nd b/c they are both square the input number  

Answer: The mode is 12

Step-by-step explanation: It is the most common number in the data set.

Answer:

645 mm^3

Step-by-step explanation:

Volume of a prism = base area x height

43 x 15 = 645 mm^3

Answer:

Natalie is 13 years old, while Fred is 28 years old.

Step-by-step explanation:

Given that if you add Natalie’s age and Fred’s age, the result is 41, and if you add Fred’s age to 3 times Natalie’s age, the result is 67, to find how old Fred and Natalie are, the following calculation must be performed:

N + F = 41

3N + F = 67

(67 - 41) / 2 = N

26/2 = N

13 = N

13 x 3 + F = 67

39 + F = 67

F = 67 - 39

F = 28

28 + 13 = 41

Therefore, Natalie is 13 years old, while Fred is 28 years old.

( 5 + 8 )x^3 + ( 1 - 5 )x^2 + ( - 5 + 8 )x + 4 + 9 =

13x^3 - 4x^2 + 3x + 13

Answer:

20.5

Step-by-step explanation:

Answer: The answer is 3

Answer:

the answer should be B becaise just multiply and then round up that is what I got good luck

Answer:

The p-value is 0.1867.

Step-by-step explanation:

Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one of its competitors, which is $68,000.

At the null hypothesis we test that the salary is the same of the competitor, that is:

[tex]H_0: \mu = 68000[/tex]

At the alternate hypothesis, we test that it is more than 68000. So

[tex]H_a: \mu > 68000[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

68000 is tested at the null hypothesis:

This means that [tex]\mu = 68000[/tex]

A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the population standard deviation is $5500.

This means that [tex]n = 20, X = 66900, \sigma = 5500[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{66900 - 68000}{\frac{5500}{\sqrt{20}}}[/tex]

[tex]z = -0.89[/tex]

P-value:

The pvalue is the probability of finding a sample mean below 66900, which is the pvalue of z = -0.89.

Looking at the z-table, z = -0.89 has a pvalue of 0.1867.

The p-value is 0.1867.

Answer:

- L < 1, so by series ratio test, It is convergent

- sum of the convergent series is 49

Step-by-step explanation:

Given the data in the question;

series = 7 + 6 + 36/7 + 216/49 + .........

⇒ 7 + 7 × 6/7 + 7 × 36/49 + 7 × 216/343 +........

⇒ 7 + 7 × 6/7 + 7 × 6²/7² + 7 × 6³/7³ .....

⇒ 7( 1 + 6/7 + 6²/7² + 6³/7³ + ..... )

⇒ 7 ∞∑_[tex]_{n=0[/tex] [tex]([/tex] 6/7 [tex])^n[/tex]

⇒ ∞∑_[tex]_{n=0[/tex] ( [tex]6^n[/tex]/[tex]7^{n-1[/tex] )

So, L =  [tex]\lim_{n \to \infty} | \frac{a_{n} + 1}{a_n} |[/tex]

= [tex]\lim_{n \to \infty} | \frac{\frac{6^n+1}{7n} }{\frac{6^n}{7^n-1} } |[/tex]

= [tex]\lim_{n \to \infty} | \frac{6}{7} |[/tex]

= 6 /7

L < 1

so by series ratio test,

It is convergent

So we find the sun;

Sum of  infinite geometric series is;

⇒ a / (1-r)

here, a = first number and r = common ratio

∑ = 7( 1 + 6/7 + 6²/7² + 6³/7³ + ..... )

a = 1 and r = 6/7

so

∑ = 7( [tex]\frac{1}{1 - \frac{6}{7} }[/tex] )

= 7( [tex]\frac{1}{\frac{7-6}{7} }[/tex] )

= 7( [tex]\frac{1}{\frac{1}{7} }[/tex] )

= 7( 7 )

= 49

Therefore, sum of the convergent series is 49

The surface area of the figure will be equal to 1326 square meters.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.

Given that:-

The surface area will be calculated as:

SA = 2 { LW + LH + WH )

SA = 2 { ( 9 x 12) + (15 x 22 ) + (15 x 9 )}

SA = 1326 square meters.

Therefore the surface area of the figure will be equal to 1326 square meters.

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Answer:

The pvalue of the test is 0.0012 < 0.05, which means that the data provides convincing evidence that the pediatrician's claim is true.

Step-by-step explanation:

A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds.

This means that at the null hypothesis, we test that the mean is 25 pounds, that is:

[tex]H_0: \mu = 25[/tex]

At the alternate hypothesis, we test that it is more than 25 pounds, that is:

[tex]H_a: \mu > 25[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

25 is tested at the null hypothesis:

This means that [tex]\mu = 25[/tex]

The National Health Statistics Reports described a study in which a sample of 315 one-year-old baby boys were weighed. Their mean weight was 25.6 pounds with standard deviation 5.3 pounds.

This means that [tex]n = 315, \mu = 25.6, \sigma = 5.3[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{25.6 - 25}{\frac{5.3}{\sqrt{315}}}[/tex]

[tex]z = 3.04[/tex]

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean above 25.6 pounds, which is 1 subtracred by the pvalue of z = 3.04.

Looking at the z-table, z = 3.04 has a pvalue of 0.9988

1 - 0.9988 = 0.0012

The pvalue of the test is 0.0012 < 0.05, which means that the data provides convincing evidence that the pediatrician's claim is true.

Answer:

Area:

4 x 4 = 16

Finding area of semi circle:

4 is your diameter so half of it is your radius which is 2 since half of 4 is 2!

2^2<---your radius being squared = 4

4(radius squared) x 3.14(pi) = 12.56

12.56 divided by 2 since its a semi circle is = 6.28

6.28 + 16 = 22.28 is your area

Perimeter is:

4 + 4 + 4 (all sides of a square are equal therefore one or two given lengths will be all the sides) = 12

Circumference:

Radius is 2,

2(you just always have to multiply this number when finding circumference) x 3.14(pi) x 2(radius), 2 x 3.14 x 2 = 12.56

12.56 divided by 2 = 6.28

6.28 + 12 = 18.28 is your perimeter.

Just a refresh:

Circumference Formula:

2(always use this number when finding circumference) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x radius

Area of a Circle Formula:

Radius squared x pi(3.14 or 22/7 whatever they tell you to use for pi)

Another thing you should remember:

Whenever it gives you 1/4 of a circle or 1/3 or a semi circle or any fraction, REMEMBER TO DIVIDE BY THAT DENOMINATOR TO WHAT YOU GET FROM EITHER CIRCUMFERENCE OR AREA OF A CIRCLE!

Answer:

Average low temp. = 6.  The fourth number is 9.

Step-by-step explanation:

To find the average of 7 low temperatures, add them and divide the sum by 7.

Average low temp. = (5 + 8 + 6 + 5 + 10 + 7 + 1) / 7 = 42 / 7 = 6

The mean is the average.  Call the missing number  x.

There are four numbers, three of which are given.  Add all the number, including the unknown  x, then divide the sum by 4.  The result is 7 (given in the problem).

[tex]\frac{5+7+7+x}{4}=7\\\frac{19+x}{4}=7\\19+x=28\\x=9[/tex]

Answer:

Em matemática, costumamos usar a letra “x” para representar a quantidade desconhecida. Mas agora x está em toda parte em nossa sociedade. As pessoas usam “x” para representar algo inexplicável ou desconhecido, como raio-X, arquivo X e  i hope that helps :)