The z- score for a mark of 56 in a test with a mean of 60 and standard deviation of 8 is​

Answer: [tex]1456\ ft^2[/tex]

Step-by-step explanation:

Given

Length of whole fence is 155 feet

If the length of rectangle is 45.5 ft

Suppose width is w

Length of whole fence is perimeter which is given by

[tex]\Rightarrow 155=2(45.5+w)\\\Rightarrow 77.5=45.5+w\\\Rightarrow w=32\ ft[/tex]

Area of the rectangle is given by the product of length and width

[tex]\Rightarrow A=lw\\\Rightarrow A=45.5\times 32\\\Rightarrow A=1456\ ft^2[/tex]

Thus, total area of pasture is [tex]1456\ ft^2[/tex]

Answer:

a=1

Step-by-step explanation:

Hopefully this helps :)

The equation of the parabola is: y = (x - 2)² - 2. Finding the value of A

The vertex of the parabola is at (2,-2). Since the parabola opens upward, the equation of the parabola will be of the form:

y = A(x - 2)² - 2

We can plug the point (3,-1) into this equation to find the value of A.

-1 = A(3 - 2)² - 2

Simplifying the right side of the equation, we get:

-1 = A - 2

Adding 2 to both sides of the equation, we get:

1 = A

Therefore, the value of A is 1.

Writing the equation of the parabola

The equation of the parabola is:

y = (x - 2)² - 2

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Answer:

A mammogram is what she would receive

Step-by-step explanation:

Answer:

- Reflected over the x-axis  

- Compressed by a factor of 0.4.

- Translated 2 units left

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x-2}[/tex]

Required

The transformation from y to y'

First, y is reflected over the x-axis.

The transformation rule is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]y = \sqrt[3]{x}[/tex] becomes

[tex]y' = -\sqrt[3]{x}[/tex]

Next, it was compressed by a scale factor of 0.4

The rule is:

[tex]y' = k * y[/tex]

Where k is the scale factor (i.e. k = 0.4)

So, we have:

[tex]y' = 0.4 * -\sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x}[/tex]

Lastly, the function is translated 2 units left;

The rule is:

[tex](x,y) \to (x-2,y)[/tex]

So, we have:

[tex]y' = -(0.4)\sqrt[3]{x - 2}[/tex]

Answers:

-reflected over the x-axis

-translated 2 units right

-compressed by a factor of 0.4

Answer:

11.26 m

Step-by-step explanation:

The height of the tree is about 11.25 meters.

When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.

Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.

Let the height of the tree be x.

Note that the scenario makes two similar triangles.

Since the ratio of the side lengths of similar triangles is proportional, it follows:

(38.15 - 32.9)/1.55 = 38.15/x

5.25/1.55 = 38.15/x

3.39 = 38.15/x

x = 38.15/3.39

x = 11.25

Hence, the height of the tree is about 11.25 meters.

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Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you

Answer:

[tex]-----------[/tex]

hope it helps...

have a great day!!

Answer:

c = 5.5

Step-by-step explanation:

2 a + 5 c = 46.50

a + c = 15

a = 15 - c

2(15-c ) +5c = 46.50

30 - 2c +5c = 46.5

3c = 16.5

c = 5.5

Answer:

Step-by-step explanation:

Total cost of plant:

Greg makes total of:

Since Greg mare than cost, he has a profit and the amount is:

Answer:

y-y1=m(x-x1)

y-4=3/4(x+4)

y=3/4x+7

Area = length x width

Fill in the given information

20 = 2 x width

Solve for width by dividing both sides by 2

Width =20/2

Width = 10 feet

Answer:

It is 10 feet wide

Step-by-step explanation:

The area of a rectangle is:

A = Length x width

So if we have the area, finding the width means diving the area by the given length.

In this case, the area of the rectangle is 20 square feet and the length is 2 feet:

20/2 = 10

Therefore the missing width is 10 feet

Answer:

8,723.27$

Step-by-step explanation:

Answer:

(f + g)(x) = 5x - 3

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x + 4 + 3x - 7 ← collect like terms

= 5x - 3

Answer:

5x - 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

= 2x + 4 + ( 3x - 7 )

= 5x - 3

Answer:

Option A

Step-by-step explanation:

Sarah took 4 days to write a paper.

She wrote 12 pages per day, so total number of pages she wrote in 4 days = 12 × 4

= 48 pages

On day 1, she wrote number of pages = 12

On day 2, she wrote number of pages = 15

On day 3, she wrote number of pages = 9

On day 4, she wrote number of pages = P

She wrote total number pages in 4 days = 12 + 15 + 9 + P

                                                                    = 36 + P

Therefore, P + 36 = 48

P = 48 - 36

P = 12

She wrote 12 pages on day 4.

Option A is the answer.

The top right quadrant is quadrant 1.

The top left quadrant is quadrant 2.

The bottom left quadrant is quadrant 3.

The bottom right quadrant is quadrant 4.

Therefore, point D is in the fourth quadrant.

Answer:

7.1

Step-by-step explanation:

We used SOHCAHTOA because it's a right angle triangle

So because we have an angle with an adjacent of 6.3 and hypotenuse of x

We will use

Cos=adjacent /hypotenuse

Answer:

slope = - [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 2)

m = [tex]\frac{2-5}{\frac{3}{2}-(-2) }[/tex]

   = [tex]\frac{-3}{\frac{3}{2}+2 }[/tex]

   = [tex]\frac{-3}{\frac{7}{2} }[/tex]

  = - 3  × [tex]\frac{2}{7}[/tex]

  = - [tex]\frac{6}{7}[/tex]

Answer:

See explanation

Step-by-step explanation:

Given:

5⁴/25 = 5²

25 = 5²

Then,

5⁴ / 25

= 5⁴/5²

Note:

• multiplication sign means addition in indices

• Division sign means subtraction in indices

Both numerator and denominator have the same base, so you'll pick one of the bases and subtract the powers

So,

5⁴/5²

= 5^(4 - 2)

= 5^(2)

= 5²

Therefore,

5⁴ / 25 = 5²

Answer:

36/5

Step-by-step explanation:

9/4×16/5

144/20

36/5

hope this is helpful

Answer:

[tex]7\frac{1}{5}[/tex]

Step-by-step explanation:

1. start by turning the fractions improper fractions:

[tex]2\frac{1}{4} =\frac{9}{4}[/tex]

[tex]3\frac{1}{5} =\frac{16}{5}[/tex]

2. then multiply them together:

[tex]\frac{9}{4}[/tex] x [tex]\frac{16}{5}[/tex] = [tex]\frac{144}{20}[/tex]

3. then simplify the fraction:

[tex]\frac{144}{20}[/tex][tex]=\frac{36}{5}[/tex]

4. turn it into a proper fraction:

[tex]\frac{36}{5} =7\frac{1}{5}[/tex]

Answer:

5

Step-by-step explanation:

xy= 6

x= 2

x + y = ?

Plug in x=2 in the first equation:

2y=6

y=3

then plug x=2 and y=3 into the one you're solving for:

2+3=5

Hope that helps!

Hello,

546=2*3*7*13

a=2, b=3,c=7,d=13

b+c=3+7=10

Answer:

16/8 + 24

Step-by-step explanation:

Answer: C. 225

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

The question asks for the probability of finding 4 or more, so first, you must add up all of the teenagers that have 4 or more shoes. Both the 4 and 5 categories fit, so add 20 and 10. Then, find the total number of people in the sample size. Overall, 100 teenagers are represented. Finally, put the number of people that have 4 or more shoes, 30, over the sample size, 100. This equals 30/100 which should be simplified to 3/10.

Answer:

Please find attached the graph of the function created with MS Excel showing the relevant points required to draw an approximate graph of the function on a graph paper

Step-by-step explanation:

The given quadratic function is f(x) = -2·x² + 7·x + 4

The range of the input (x) values = -1 ≤ x ≤ 5

The coefficient of the quadratic is negative -2, the graph is n shape

The intercept form of the function is given as follows;

-2·x² + 7·x + 4 = -1 × (2·x² - 7·x - 4)

-1 × (2·x² - 7·x - 4) = -1 × (2·x² + x - 8·x - 4)

-1 × (2·x² + x - 8·x - 4) = -1 × (x · (2·x + 1) - 4·(2·x + 1))

∴ -1 × (x · (2·x + 1) - 4·(2·x + 1)) = -1 × (2·x + 1)·(x - 4)

∴ f(x) = -2·x² + 7·x + 4 = -1 × (2·x + 1)·(x - 4)

At the x-intercepts, (2·x + 1) = 0 or (x - 4) = 0, which gives;

x = -1/2 or x = 4

Therefore, the x-intercepts are (-1/2, 0), (4, 0)

The equation in vertex form is given as follows;

f(x) = -2·x² + 7·x + 4 = -2·(x² - 7·x/2 + 2)

By applying completing the squares method, to x² - 7·x/2 - 2, we get;

Where x² - 7·x/2 - 2

x² - 7·x/2 = 2

x² - 7·x/2 + (-7/4)² = 2 + (-7/4)² = 81/15

(x - 7/4)² = 81/16

∴ (x - 7/4)² - 81/16 = 0 = x² - 7·x/2 - 2

∴ x² - 7·x/2 - 2 = (x - 7/4)² - 81/16

-2·(x² - 7·x/2 + 2) = -2·((x - 7/4)² - 81/16) = -2·(x - 7/4)² + 81/8

The vertex = (7/4, 81/8)

When x = 0, we get;

f(0) = -2 × 0² + 7 × 0 + 4 = 4

The y-intercept = (0, 4)

The sketch of the function should pass through the x-intercepts (-1/2, 0), (4, 0), the y-intercept (0, 4), and the y-intercept (0, 4), and the vertex, (7/4, 81/8) on a graph sheet

Please find attached a drawing of the function of the function created with MS Excel

Answer:

14 units

Step-by-step explanation:

A = - 2, B = 12

Therefore,

d(A, B) = 12 - (-2) = 12 + 2 = 14 units

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

-3.855

Step-by-step explanation:

Not sure if you need the weight of each screw! but you just subtract 80.955-84.81

Answer:

1

Step-by-step explanation:

itnisbbsndnfnfnfnnfnfnfncjcjccjcj

Answer:

2.39

Step-by-step explanation:

Convert everything to a decimal.  

To do that with a fraction divide the numerator by the denominator.  

185 divided by 100 = 1.85

185/100 = 1.85

To convert a percent to a decimal divide the number by 100.

50 divided by 100 = 0.5

50/100 = 0.5

4 divided by 100 = 0.04

4/100 = 0.04

Now add:

1.85 + 0.5 + 0.04 = 2.39