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Answer each part. If necessary, round your answers to the nearest hundredth.

Answer:

x = 6.5

Step-by-step explanation:

Reference angle = 54°

Length of Side opposite to 54° = x

Hypotenuse = 8 cm

Recall: SOHCAHTOA.

Apply SOH:

Sin 54 = Opp/Hyp

Sin 54 = x/8

x = 8*sin 54

x = 6.47213595 ≈ 6.5 cm (nearest tenth)

9514 1404 393

Answer:

  1.3

Step-by-step explanation:

The two points are on the same vertical line, so the distance between them is the distance between their y-coordinates:

  2.5 -1.2 = 1.3

The distance between the two points is 1.3 units.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A

we have to solve the associated equation

4a^2 - 20a + 25 = 0

first of all we have to find the delta/4

Δ/4 = (b/2)^2 - ac  where a is the term that multiply a^2, b is the term that multiply a and c is the therm without the variable

Δ/4 = (-10)^2 -100 = 100-100 = 0

the delta is equal to 0 that is mean that the equation has two coincident solutions, that can be find thanks to this formula

a1,a2 = -b/2/a = 10/4 = 5/2

now we can factorize the trinomial in this way:

4(a-5/2)(a-5/2)

4[(2a-5)/2][(2a-5)/2]

(2a-5)(2a-5)

the side of the square is 2a-5

Part B

the area of the rectangle is expressed as difference by two squares, so it can be rewritten as

(3a+4b)(3a-4b)

so the dimension of the rectangle are

3a+4b and 3a-4b

Answer:

The answer should be -12

Answer:

hammood habbi knows

Step-by-step explanation:

32 or 16

Answer:

Translated down 8 units or C

Step-by-step explanation:

Answer:

x = -1/2y+2

Step-by-step explanation:

4x+2y=8

Step 1: Add -2y to both sides.

4x+2y+−2y=8+−2y

4x=−2y+8

Step 2: Divide both sides by 4.

4x/4 = -2y+8/4

x = -1/2y+2

Hope this helps!

Answer:

hi can i fu k u

Step-by-step explanation:

The answer is:

-0.5, -1.5

Answer:

angle 1 = 108°

Step-by-step explanation:

because angle 1 and angle 2 are vertical angles and vertical angles are equal.

Answer:

Volume=3418.1 ft²

Step-by-step explanation:

Volume:π r² h

r=8 ft

h=17ft

π×8²×17

=3418.052 ft³

=3418.1 ft³

hope it helps...

Answer:

let's say coconut trees is X is there from mango trees will be 2X

Step-by-step explanation:

2x+x=1320

3x=1320

divide both sides by three

3x/3=1320/3

x=440(coconut)

2x=880(mango)

Answer:

392 ft²

Step-by-step explanation:

The composite figure can be divided into a rectangle, 2 triangles and a square

Area of rectangle = Length * width

Area of rectangle = 21 feets * 14 feets = 294 feet²

Area of triangle = 0.5 * base * height

Area of triangle = 0.5 * 7 * 7 = 24.5

AREA of square = a² = 7² = 49 feets²

Total area :

294 feets + (2 * 24.5) feets² + 49 feets²

294 + 49 + 49 = 392 ft²

Answer:

he has 46.1538462% left

Step-by-step explanation:

7/13 = 0.538461538

1 - 0.538461538 = 0.461538462

Answer:

D.82.8°

Step-by-step explanation:

Hope it helps

Have a great day

Answer:

CI 99% = (  0,022  ;  0,126 )

Step-by-step explanation:

First sample  

n₁  = 500

x₁  = 48

p₁ = x₁ / n₁   =  48 / 500      p₁  =  0,096      p₁  = 9,6 %

Second sample

n₂  = 400

x₂  = 68

p₂ = x₂ / n₂   =  68 / 400      p₂  =  0,17       p₂  = 17 %

CI = 99 %    significance level α = 1 %     α  = 0,01

z(c)  for α = 0,01  is from z- table    z(c) = 2,325

CI  =  ( p₂ - p₁ ) ±  z(c) *√ p*q* ( 1/n₁  +  1 / n₂ )

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

p = ( x₁ + x₂ )  / n₁ + n₂

p =  ( 48  +  68  ) /( 500 + 400)

p = 116/ 900     p = 0,1288     and   q = 1 - p     q  = 0,8712

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 2,325 * √ 0,1288*0,8712 ( 1 / 500 + 1/ 400)

2,235 * 0,02247

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 0,052

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

The difference between the groups shows that the proportion in the second group was bigger than in the first group.

The CI in the context of the problem is  CI 99% = (  0,022  ;  0,126 )

Given first sample is  

n₁  = 500

x₁  = 48

  [tex]P_{1} =\dfrac{X_{1} }{n_{1} }[/tex]      [tex]P_{1} =\dfrac{48}{500}[/tex]      

p₁  =  0,096      p₁  = 9,6 %

Given second sample

n₂  = 400

x₂  = 68

[tex]P_{2} =\dfrac{X_{2} }{n_{2} }[/tex]      [tex]P_{2} =\dfrac{68}{400}[/tex]        

p₂  =  0,17       p₂  = 17 %

Since given CI = 99 %    so significance level  α = 1 %     α  = 0,01

From Z-Table  z(c)  for α= 0,01  is = 2,325

CI  =   [tex](P_{2} -P_{1}[/tex]   ±    [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

[tex]P= \dfrac{X_{1} +X_{2} }{n_{1}+n_{2} }[/tex]

[tex]P=\dfrac{48+68}{500+400}[/tex]

[tex]P=\dfrac{116}{900}[/tex]

p = 0,1288     and   q = 1 - p     q  = 0,8712

[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  [tex]2325\times\sqrt[2]{0.1288\times 0.8712} (\dfrac{1}{500_{} } +\dfrac{1}{400_{} } )[/tex]

  [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )=0.052[/tex]

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

Hence the difference between the groups shows that the proportion in the second group was bigger than in the first group.

To know more about Chi square follow

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Answer:

= p× r²

= 3,14×7×7

= 21,98×7

= 153,86

[tex]153.86 \div 3.14 = 7[/tex]

Answer:

10

Step-by-step explanation:

For this you can use the pythagorean theorem such as (a^2 + b^2) = c^2 so the answer will be ten

Answer:

Lincoln will be charged $9,600.

Step-by-step explanation:

To find the answer we will first turn 8% into a decimal.  8 ÷ 100 = 0.08.  Now multiply 0.08 by $5,000 and we get $400.  then multiply $400 by 24 and we get $9,600.  Therefore, $9,600 is our answer.

Answer:

[tex]Median= 20[/tex]

Step-by-step explanation:

Given

The attached box plot

Required

The median

The median is represented by the vertical line inside the rectangle on the box plot.

Using the description above to read the median from the given box plot.

[tex]Median = 20[/tex]

It is also the same as the second quartile

Answer:If the figure is a square with a perimeter of 16 inches, then each side of the square is 4 inchest in length.

Step-by-step explanation:

Answer:

The length of each side is 4 inches.

Step-by-step explanation:

Since the shape is a square, all sides are equal so you do 16÷4 since there are 4 sides to get your answer of 4 inches.

Answer:

The domain is [tex]D_C = [0,\infty)[/tex]

The range is: [tex]R_C = [20,\infty)[/tex]

Step-by-step explanation:

Domain and range of a function:

The domain of a function are the values that the input assumes, while the range are the values that the output assumes.

In this question:

[tex]C(m) = 0.05m + 20[/tex]

m is the input, which is the number of phone calls, which can be any number between 0 and infinite. So

The domain is [tex]D_C = [0,\infty)[/tex]

When the input is m = 0, the value of C(0) = 20. As m increases, so does C(m). This means that:

The range is: [tex]R_C = [20,\infty)[/tex]

Answer:

Option 1  because

domain: m is Greater than or equal to zero

range: C is greater than or equal to twenty

Step-by-step explanation:

The (C) cost of the bill is always going to start at twenty and be higher depending on how many (m) minutes were used.

Edg2021

The fourth option is indeed correct on Edge 2021.

The graph that represents the system of nonlinear inequalities is graph (a)

The nonlinear inequalities are given as:

[tex]y \le x^2 - 1[/tex]

[tex]x > y^2 - 6[/tex]

Rewrite the above nonlinear inequalities as:

[tex]y - x^2 \le - 1[/tex]

[tex]x -y^2 > -6[/tex]

[tex]y - x^2 \le - 1[/tex] means that the inequality has a solid line, and the outside part is shaded

[tex]x -y^2 > -6[/tex] means that the inequality has a dotted line, and the inner part is shaded

So, the graph that represents the system of nonlinear inequalities is graph (a)

Read more about the system of nonlinear inequalities at:

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Answer:

1.-Then we p-value indicates that we are in the rejection region we reject H₀

We support the claim of the garbage collector the average picking up more than 4 tn of garbage

2.- p  = 75 %

3.-3.-t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim

Step-by-step explanation:

1.- If p-value is 0,04   and significance level α = 5 %  or  α = 0,05 then p-value < α

Test hypothesis should be    ( x the average of garbage)      

Null hypothesis          H₀           x = 4 Tn

Alternative Hypothesis     Hₐ    x  > 4 Tn

Then  alternative hypothesis suggests a one tail-test to the right  and

p-value <  0,05

Then we p-value indicates that we are in the rejection region we reject H₀

We support the claim of the garbage collector the average picking up more than 4 tn of garbage

2.- As we are dealing with a normal distribution the CI  95 % is symmetrical with respect to the mean, therefore the proportion of student living in Brooklyn is:  

(0,73 + 0,77) /2

p = 0,75     p  = 75 %

Test hypothesis:

Null Hypothesis            H₀            μ    =  26

Alternative Hypothesis      Hₐ      μ   <  26

Alternative hypothesis tells us the test is a one-tail test to the left

Sample size   n = 25

Sample mean   μ  =  24,4

Sample Standard deviation  =  9,2

We assume normal distribution, and as n < 30 we use t-student table

with  24 degree of freedom

Significance level is 0,05  and df = 24  we find t (c)  in t- student table

t(c) = 1,7109      test to the left   t(c) = -1,7109

To calculate  t(s)

t(s)  =  (  24,4 - 26 ) / 9,2 / √25

t(s) =  - 1,6 * 5 / 9,2

t(s) = - 0,87

Comparing t(s)  and t(c) we have

t(s) > t(c)

t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim

Answer:

x = 42

Step-by-step explanation:

Let the length of the indicated side be represented as "x".

The Theorem of proportionality can be extended and applied to find the indicated side.

Thus, based on the theorem, it is assumed that the parallel lines divides the transversals proportionally.

This implies that:

x/(77 - x) = 30/25

x/(77 - x) = 6/5

Cross multiply

x(5) = 6(77 - x)

5x = 462 - 6x

Add 6x to both sides

5x + 6x = 462

11x = 462

x = 462/11

x = 42

Answer:

c Melindas account will have about 5.40 more than olivia's account

Step-by-step explanation:

Answer:

Hello some data related to your question is missing attached below is the missing data

a) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures. since ( to > critical value )

b) ( 3.819 , 8.5226 )

Step-by-step explanation:

Applying the Given data:

The test hypothesis :

H0 : μ1 = μ2

Ha : μ1 > 2

A) since ( to > critical value ) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures

B ) construct and interpret

next calculate the SP value

[tex]S^{2} _{p}[/tex] = [tex]\frac{( n1 - 1 )S^{2} _{1} + ( n_{2}- 1 )S^{2} _{2} }{n1 + n2 - 2}[/tex]

where: S1 = 7524 , n1 = 50 , n2 = 100 , S2 = 5551   ( input values into equation above )

∴ [tex]S^{2} _{p}[/tex] = 39354491.3716

hence : [tex]S_{p}[/tex] = 6273.32

next calculate the value of test statistic

to = ( X1 - X2 - Δo ) / Sp [tex]\sqrt{\frac{1}{n1} + \frac{1}{n2} }[/tex]

where: X1 = 61234 , X2 = 54529 , Sp = 6273.32 , n1 = 50 , n2 = 100  ( input values into equation above )

to = 6705 / 1086.5702 = 6.1708

Df ( degree of freedom ) = n1 + n2 - 2 = 148

critical value at ∝ = 0.01  = ± 2.3518  ( using excel function : T.INV(0.01,148) )

hence the confidence Interval

= ( 6.1708 ± 2.3518 )

= ( 3.819 , 8.5226 )

For the table of Mrs. Toguchi the t test for two sample is not justified and the confidence interval for this two values is (6.1708, ±2.3518).

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

Mrs. Toguchi wants to determine if politicians tend to have higher salaries, on average, than first responders (specifically emergency medical technicians, EMTs).

Independent random samples from each of these two professions were selected and their salaries were recorded. The data are summarized below.

                                   Politicians        EMT's

Mean                            $61,234       $54,529

Standard deviation      $7524          $5551

n                                      50                100

The hypothesis for the test,

[tex]H_0:\mu_1=\mu_2\\H_a:\mu_1 > 2[/tex]

No it is not justifies, as the null hypothesis is rejected.

The pooled estimate of a common population standard deviation can be given as,

[tex]S_p=\sqrt{\dfrac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}}[/tex]

Put the values in the above formula from the table, we get,

[tex]S_p=\sqrt{\dfrac{(50-1)(7524)^2+(100-1)(5551)^2}{50+100-2}}\\S_p=6273.32[/tex]

Use the formula of test statistics for equal variance as,

[tex]t=\dfrac{\overline y_1-\overline y_2-0}{s_p\sqrt{\dfrac{1}{n_1}+\dfrac{1}{n_2}}}[/tex]

Put the values from the table as,

[tex]t=\dfrac{61234-54529-0}{(6263.32)\sqrt{\dfrac{1}{50}+\dfrac{1}{100}}}\\t=6.1708[/tex]

The degree of freedom can be given as,

[tex]DF=100+50-2\\DF=148[/tex]

The critical value for 99 percent interval (0.01) is ±2.3518.

Hence, the confidence interval for this two values is (6.1708, ±2.3518).

Thus, for the table of Mrs. Toguchi the t test for two sample is not justified and the confidence interval for this two values is (6.1708, ±2.3518).

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Answer:

The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

Step-by-step explanation:

Example:  "3" can be "distributed" across the "2+4" into 3 times 2 and 3 times 4.

Answer:

The first thing we need to do is to find the area bounded by:

y = x^3

y = 0

between:

x = 0 and x = 2

This is the integral of the given function between x = 0 and x = 2, written as:

[tex]\int\limits^2_0 {x^3} \, dx = \frac{2^4}{4} - \frac{0^4}{4} = 2^2 = 4[/tex]

This means that the area of the bounded region is 4 square units.

Now, if we do a full rotation around the x-axis, the volume generated will be equal to the area that we obtained times 2*pi units.

The volume is:

V = (4 square units)*(2*pi units) = 8*pi cubic units.

(Notice that no option coincides with this, there may be a mistake in the options)