What is the area of the shaded region? 21 mm2 24 mm2 42 mm2 48 mm2

Answer:

2/5

Step-by-step explanation:

(7-5)/(6-1)

Answer:

The value of this expression when a = 3 and b = -2 is -1.

Step-by-step explanation:

The expression is:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

Compute the value of X for a = 3 and b = -2 as follows:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

    [tex]=\frac{3\cdot (3)^{-2}\cdot (-2)^{6}}{2\cdot (3)^{-1}\cdot (-2)^{5}}\\\\=\frac{(3^{-1})\times (-2)^{6}}{2\cdot (3^{-1})\cdot (-2)^{5}}\\\\=\frac{(-2)^{1}}{2}\\\\=-1[/tex]

Thus, the value of this expression when a = 3 and b = -2 is -1.

Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Answer:

[tex]\large \boxed{\sf \ \text{2 feet, 4 seconds, 258 feet } \ }[/tex]

Step-by-step explanation:

Hello,

To know the height of the baseball when it is hit we have to compute h(0), as t = 0 is when the baseball is hit into the air.

[tex]h(0)=-16\cdot 0^2+128 \cdot 0+2=2[/tex]

So, the answer is 2 feet.

h(x) is a parabola which can be written as [tex]ax^2+bx+c[/tex], it means that the vertex is the point (-b/2a,h(-b/2a)).

The baseball reached its maximum height after

   [tex]\dfrac{-b}{2a}=\dfrac{-128}{-2*16}=\boxed{4 \text{ seconds}}[/tex]

And the maximum height of the baseball is h(4).

[tex]h(0)=-16\cdot 4^2+128 \cdot 4+2=-256+512+2=\boxed{258 \ \text{feet}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The 90%  confidence level is  [tex]19.15< L < 20.85[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 64[/tex]

     The mean age is  [tex]\= x = 20 \ years[/tex]

      The standard deviation  is   [tex]\sigma = 4 \ years[/tex]

Generally  the degree of freedom for this data set is mathematically represented as

        [tex]df = n - 1[/tex]

substituting values

        [tex]df = 64 - 1[/tex]

        [tex]df = 63[/tex]

Given that the level of confidence is  90%  the significance level is mathematically evaluated as

          [tex]\alpha = 100 - 90[/tex]

         [tex]\alpha =[/tex]10 %  

         [tex]\alpha = 0.10[/tex]

Now   [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           [tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]

   The margin for error is mathematically represented as

          [tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values  

          [tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]

         [tex]MOE = 0.85[/tex]

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           [tex]\= x - MOE < L < \= x + E[/tex]

substituting values  

         [tex]20 - 0. 85 < L < 20 + 0.85[/tex]

         [tex]19.15< L < 20.85[/tex]

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]

Answer:

If you do not need that actual numbers, the answer is B.

Step-by-step explanation:

In order to find a fully comprehensive study, you would need many more people than just 10, not to mention these are the top 10 people in the world.

(Brainliest would be much appreciated!)

Answer:

75

Step-by-step explanation:

In this case, you just need to use the distance formula of AC and DB.

Using the distance formula, we find that AC= 15, and DB=10

Therefore, area= 150/2=75

Answer:

63%

225 buyers

Step-by-step explanation:

To find the percent take the number that liked it over the total

376/600

Change to decimal form

.62666666

Change to percent by multiplying by 100

62.66666666%

The nearest percent is 63%

37.5 % would but it then multiply by the number of shoppers

37.5 % ( 600)

Change to decimal form

.375 * 600

225

Answer:

20.8 hours

Step-by-step explanation:

2 3/5 = 2.6.The painter will take (2.6 × 8) = 20.8 hours to paint a wall.

Hope this helps and pls mark as brianliest :)

Answer:

20.8, 20 4/5, and 104/5

Answer:

The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.

Step-by-step explanation:

There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.

Answer:

A). A(t) = P(1+r/n)^(nt)

B). DA/Dt = np(1+r/n)^(t)

C). A(5) =$ 5664.0

D).t = approximately 13.5 years

Step-by-step explanation:

A(t) = P(1+r/n)^(nt)

P = $5000

n= t

r= 2.5%

After five years t = 5

A(t) = P(1+r/n)^(nt)

A(5) = 5000(1+0.025/5)^(5*5)

A(5) = 5000(1+0.005)^(25)

A(5)= 5000(1.005)^(25)

A(5) = 5000(1.132795575)

A(5) = 5663.977875

A(5) =$ 5664.0

When the balance A= $7000

A(t) = P(1+r/n)^(nt)

7000= 5000(1+0.025/n)^(nt)

But n= t

7000= 5000(1+0.025/t)^(t²)

7000/5000= (1+0.025/t)^(t²)

1.4= (1+0.025/t)^(t²)

Using trial and error

t = approximately 13.5 years

Answer:

4.2 in

Step-by-step explanation:

let us first visualize the sail as a triangular shape

the angle of the triangle from top is 40°

the height of the triangle is give as 5 in

we can apply SOH CAH TOA to solve for the base of the sail

the opposite = the base of the sail

the adjacent = the height of the sail= 5 in

therefore

Tan∅= Opp/Adj

Tan(40)= Opp/5

Opp= Tan(40)*5

Opp= 0.8390*5

Opp= 4.195 in

Hence the width of the sail is 4.2 in to the nearest tenths

Answer:

4.2

Step-by-step explanation:

We have a known hypotenuse, but unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.

sin(angle) = opposite/hypotenuse

sin(50) = x/6.5

6.5*sin(50) = x

x = 6.5*sin(50)

x = 4.97928888027336 make sure your calculator is in degree mode

x = 4.98

Answer is choice B

Answer:

b

Step-by-step explanation:

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

1,114.6 kPa

Step-by-step explanation:

P(t) = 1300 (0.95)^t

P(3) = 1300 (0.95)^3

P(3) = 1114.6

Answer:

[tex]f(x) = x^3 -sinx +Cx+D[/tex]

Step-by-step explanation:

Given that:

[tex]f ''(x)= 6x +sinx[/tex]

We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.

We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]

[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]

Now, integrating it again to find f(x):

[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]

Answer:

A fair coin because at the end of the day it will be fun no matter where you guys go

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

58 people

Step-by-step explanation:

174 people ate lunch.

1/3 of the 74 people had dessert after lunch.

Multiplying 1/3 and 174.

1/3 × 74

= 58

58 people had desert after lunch.

Answer:

[tex]\boxed{ 58\ people}[/tex]

Step-by-step explanation:

People who ate lunch = 174 people

People among among them who had desserts = 1/3 of the total

(Remember "of" means to "multiply")

=> 1/3 * 174

=> 1 * 58

=> 58 people

Answer: n = 2401

Step-by-step explanation:

Given;

Confidence level = 2% - 99%

n = ? ( which is the sample size is unknown ).

Solution:

Where;

n = [z/E]^2*pq

Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2

Substituting the given data into the formula.

n = [1.96/0.02]^2(1/2)(1/2)

n = 2401

The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401

Answer:

50 meters

Step-by-step explanation:

The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].

Assuming the radius is r, which is 4, we can substitute the values into the equation.

[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]

This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.

Hope this helped!

Complete question is;

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:

2005 Season: 73 77 78 76 74 72 74 76

2006 Season: 70 69 74 76 84 79 70 78

​A) Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.

B) What is the primary difference in performance between 2005 and 2006? What improvement,

if any, can be seen in the 2006 scores?

Answer:

A) 2006 mean = 75

2005 mean = 75

2006 standard deviation = 5.2644

2005 standard deviation = 2.0702

B)The primary difference is that variation is higher in the 2006 season than the 2005 season.

Step-by-step explanation:

A) Mean is the sum of all scores divided by the number of scores.

Thus;

μ_2005 = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8 = 75

Similarly;

μ_2006 = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8 = 75

Now, variance is calculated by the sum of the square of mean deviations divided by (n - 1)

Thus;

2005 Variance = ((73-75)² + (77-75)² + (78-75)² + (76-75)² + (74-75)² + (72-75)² + (74-75)² + (76-75)²)/(8-1) = 4.2857

2006 Variance = ((70-75)² + (69-75)² + (74-75)² + (76-75)² + (84-75)² + (79-75)² + (70-75)² + (78-75)²)/(8 - 1) = 27.7143

Now, standard deviation is the square root of variance.

Thus;

2005 standard deviation = √4.2857 = 2.0702

2006 standard deviation = √27.7143 = 5.2644

B) The primary difference is that variation is higher in the 2006 season than the 2005 season.

Also,

Answer:

I NEED POINTS

Step-by-step explanation:

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = [tex]r_{0}[/tex] + t.v

where

[tex]r_{0}[/tex] is the position vector;

v is the vector;

For point (7,4,5):

[tex]r_{0}[/tex] = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = [tex]x_{0}[/tex] + at

y = [tex]y_{0}[/tex] + bt

z = [tex]z_{0}[/tex] + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:

36

Step-by-step explanation:

You did not attach a picture, so I just assumed where the lengths of 15 and 39 were.

Incomplete question. I've made some assumptions to provide clarity.

Answer:

a. $45,743.07

b. $44,843.07

Step-by-step explanation:

Let's assume Victor is a single filer with an income of $100,000.

Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:

- 10 percent on the first $9,325 = 10% x 9525 =$932.5

- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6

- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25

- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72

Total=  $46,643.07

Minus $900 tax credit= $46,643.07-$900= $45,743.07

Minus $900 charitable contribution = $45,743.07-$900= $44,843.07

Answer:

1). x = 2

2). x = -10

3). x = [tex]-\frac{2}{5}[/tex]

4). x = 10

Step-by-step explanation:

1). x - 6 = -4

  (x - 6) + 6 = -4 + 6 [By adding 6 to both the sides of the equation]

  x = 2

2). x + 3 = -7

  (x + 3) - 3 = -7 - 3 [By subtracting 3 to both the sides of the equation]

  x = -10

3). 5x = -2

   [tex]\frac{5x}{5}=\frac{-2}{5}[/tex] [By dividing with 5 from both the sides of the equation]

   x =  [tex]-\frac{2}{5}[/tex]

4). 0.5x = 5

   [tex]\frac{0.5x}{0.5}=\frac{5}{0.5}[/tex] [By dividing with 0.5 from both the sides of the equation]

   x = 10

Answer:

There are many combinations based on the number you chose to subtract from both sides.

Step-by-step explanation:

Let the number be x.

According to the question,

3 x+7 > 4 x

We get, 3 x+1=4 x-6, after subtracting 6 from both sides.

3 x+1=4 x-6

4 x- 3 x=6+1

x=7

You will get the same answer if you subtract 3 x or 7 or any other number from both sides.

Thank you!

Answer:

the solution to the problem is D