find the area of the compound shape. use 3.14 for pi.

1. 26.1cm square 2
2. 125.1cm square 2
3. 68.5cm square 2
4. 28.3cm square 2

Answer:

-11

Step-by-step explanation:

[tex]3( - 2) + 5( - 1)[/tex]

[tex] - 6 + ( - 5)[/tex]

[tex] - 11[/tex]

Answer:

9.32millimetres

10. 7inches

Step-by-step explanation:

9. r=½diameter

r=½×64

r=32

10. volume=length×width×height

336=6×8×h

336=48h

h=336/48

h=7

Answer:

4

Step-by-step explanation:

Answer:

6 times

Step-by-step explanation:

y = −3.5x + 20 ; x = 4

y = -3.5(4) + 20

y = -14 + 20

y = 6

Answer:

It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration

Step by Step Solution:

The given data are;

Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80

Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65

Using the functions of Microsoft Excel, we get;

The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25

The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478

The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625

The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649

The significance level, α = 5%

The null hypothesis, H₀:  [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ:  [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The pooled variance, [tex]S_p^2[/tex], is given as follows;

[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]

Therefore, we have;

[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]

The test statistic is given as follows;

[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]

Therefore, we have;

[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]

The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14

At 5% significance level, the critical t = 2.145

Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration

Answer:

The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]

Step-by-step explanation:

At the null hypothesis, we test that the mean is equal to a certain value.

At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.

The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 238[/tex]

A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.

This means that the alternate hypothesis is:

[tex]H_{a}: \mu > 238[/tex]

Answer:

C. AB/BC=FE/ED

Step-by-step explanation:

Answer:

Total Depth: 64.28m

Step-by-step explanation:

Assuming that the submarine is travelling at a constant rate, then we can use the information provided and apply a Rule of Three since it is basically a ratio problem. In this rule, you simply need to multiply the diagonal values of the ratio and divide by the last value to get the variable, which would be the depth after 110m

70min  <=======>  25 m

110min  <=======>  x m

(110 * 25) / 70 = x

2750 / 70 = x

39.28 = x

We can see that at 110min the depth would be 39.28 m but since this is an additional period of time that the submarine travelled we need to add this distance to the initial 25 m to get the total depth of the submarine.

39.28m + 25m = 64.28m

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

brainly.com/question/8708520

Answer:

[tex](-2,\, 0)[/tex].

Step-by-step explanation:

Dilate a point [tex](x,\, y)[/tex] by a scale factor of [tex]r[/tex] with [tex](a,\, b)[/tex] as the center, and the resultant point would be at [tex](a + r\, (x - a),\, b + r\, (y - a))[/tex].

In this question:

Point to dilate: [tex](x,\, y) = (-8,\, 0)[/tex].

Scale factor: [tex]r = 0.25[/tex].

Center of dilation: [tex](a,\, b) = (0,\, 0)[/tex].

The resultant point would be:

[tex](0 + 0.25\, (-8 - 0),\, 0 + 0.25\, (0 - 0))[/tex], which simplifies to [tex](-2,\, 0)[/tex].

Answer:

1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Step-by-step explanation:

1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:

C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Answer (assuming it can be in slope-intercept form):

[tex]y = -2x +10[/tex]    

Step-by-step explanation:

1) First, we need to find the slope of the given equation. To do that easily, convert it to slope-intercept form, represented by the formula  [tex]y = mx + b[/tex]. Isolate y:

[tex]2x + y = 3\\y = -2x + 3[/tex]

The number in place of [tex]m[/tex], or the coefficient of the x-term, represents the slope of the equation. So, the slope of the given equation is -2.

Lines that are parallel share the same slope. So, the slope of the new equation will be -2 as well.  

2) Now, remember that the slope-intercept form is represented by the formula [tex]y = mx + b[/tex]. In order to write an equation of a line using that formula, we need to substitute values for [tex]m[/tex] and [tex]b[/tex]. We know [tex]m[/tex] is the slope, so we already know what that equals. Now, we just need to find [tex]b[/tex].

To do that, substitute -2 for [tex]m[/tex] in the slope-intercept formula. Additionally, substitute the x and y values of the point (2,6) for the x and y in the formula as well. This sets up the equation so that we can isolate [tex]b[/tex] and find its values:  

[tex]y = mx +b\\6 = (-2)(2)+b\\6 = -4 + b\\10 = b[/tex]

So, [tex]b[/tex] = 10.

3) Substitute values for [tex]b[/tex] and [tex]m[/tex] into the slope-intercept formula to write the slope-intercept form of the line:

[tex]y = -2x +10[/tex]

Equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6) is y+2x=10

Lines which does not intersect each other at any point is said to be Parallel.

Here given equation of line is 2x+y=3

first we will write this equation in y=mx+c form

So y=3-2x

y= -2x+3

We know that slope of parallel lines is same

So equation of parallel line will be

y=-2x+a

Now we know that line is passing through (2,6)

So

[tex]6=-2(2)+a\\\\6+4=a\\\\a=10[/tex]

Hence equation of parallel line is y=-2x+10

or we can write it as y+2x=10

Equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6) is y+2x=10

To learn more about parallel lines visit :https://brainly.com/question/24607467

Answer:

-25-5x-5y

Step-by-step explanation:

Answer:

(i) The derivative of the function is [tex]f' = \frac{1}{10}[/tex].

(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex]

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

[tex]Dom\{f'\} = \mathbb{R}[/tex]

Step-by-step explanation:

(i) Find the derivative of the function using the definition of derivative:

The derivative is defined by the following limit:

[tex]f' = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)

If we know that [tex]f(x) = \frac{1}{10}\cdot x - \frac{1}{3}[/tex], then the definition of derivative is expanded:

[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot (x+h) - \frac{1}{3}-\frac{1}{10}\cdot x +\frac{1}{3}}{h}[/tex]

[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot h }{h}[/tex]

[tex]f' = \lim_{h \to 0} \frac{1}{10}[/tex]

[tex]f' = \frac{1}{10}[/tex]

The derivative of the function is [tex]f' = \frac{1}{10}[/tex].

(ii) State the domain of the function and the domain of its derivative:

The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex]

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

[tex]Dom\{f'\} = \mathbb{R}[/tex]

Answer:

The maximum value is (2,9) I can't really see the question well btw

Answer: v-(kx8)

Step-by-step explanation: plz mark me brainliest

The answer would be B) Awesome Ansel's Farm 1 cow for every 5 chickens.

Answer:

$225 + $75x ≤ $1500

x ≤ 17

Step-by-step explanation:

The Smith family has $1500 spending limit and no more.

The initial fee is $225 in labor so we must deduct that from the current total of money left to spend.

$1500 - $225 = $1275

Then we can simply divide the amount leftover with the hours the contractor works.

$1275 ÷ $75 = 17

The inequality is $225 + $75x (x being the amount of hours the contractor works) ≤ (equal to or less than simple identifying that $1500 can be spent but no more than that.) $1500

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

Answer:

hello! As I think it is 2p coin but not sure

Answer:

7()=11

8()=42

I could barely see the answer for number 9 sorry :(

Step-by-step explanation:

the 7() is 2(3)+5

2(3)=6

6+5=11

Question (8)

c^2+3a x b

c(6)^2+ 3(3) x 2/3

36+9 x 2/3

36+6=42

Answer:

(7)=11

(8)=42

Step-by-step explanation:

here

Answer:

r = 4.90228481 in

d = 9.80456963 in

Answer:

Total calories in 8 cup = 928 calories

Step-by-step explanation:

Given:

Calories in 3/4 cup of cereal = 87 calories

Find:

Total calories in 8 cup

Computation:

Total calories in 8 cup = 8 x 87 x [4/3]

Total calories in 8 cup = 928 calories

Answer:

y = 4

Step-by-step explanation:

use the distributive property

9y - 36 = 0

     +36  +36

9y = 36

divide by 9

y = 4

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Answer:

[tex]BA = 6.0[/tex]

[tex]BC = 13.4[/tex]

Step-by-step explanation:

Given

The attached triangle

Solving (a) BA

Considering the tangent of angle C, we have:

[tex]tan\ C = \frac{BA}{AC}\\[/tex]

This gives:

[tex]tan\ 25 = \frac{BA}{12}[/tex]

Make BA the subject

[tex]BA = 12 * tan\ 25[/tex]

[tex]BA = 12 * 0.4663[/tex]

[tex]BA = 6.0[/tex] --- approximated

Solving (a) BC

Using Pythagoras theorem

[tex]BC^2 = BA^2 + AC^2[/tex]

[tex]BC^2 = 6.0^2 + 12^2[/tex]

[tex]BC^2 = 180[/tex]

Square root of both sides

[tex]BC = \sqrt{180[/tex]

[tex]BC = 13.4[/tex]

Pen is 3 x 2 = 6

Pencils s 4 x 3 = 12

Answer:

The quartile 3 is 0.3

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

X~Exp (0.2)

This means that [tex]m= 0.2, \mu = \frac{1}{0.2} = 5[/tex]

Find the quartile 3.

The 3rd quartile is the 75th percentile, for which [tex]P(X \leq x) = 0.75[/tex], or [tex]P(X > x) = 1 - 0.75 = 0.25[/tex]

Since

[tex]P(X > x) = e^{-\mu x}[/tex]

[tex]e^{-5x} = 0.25[/tex]

[tex]\ln{e^{-5x}} = \ln{0.25}[/tex]

[tex]-5x = \ln{0.25}[/tex]

[tex]x = -\frac{\ln{0.25}}{5}[/tex]

[tex]x = 0.277[/tex]

Rounding to the nearest tenth, the quartile 3 is 0.3.

__________________________

4x + 3y = 16

x = -3 / 4 y + 4

y = -4 / 3 x + 16 / 3

___________________________

y = x + 3

x = y - 3

y = x + 3

___________________________