5. In the figure, . Solve for . Show your work.

Answer:

We conclude that the board's length is equal to 2564.0 millimeters.

Step-by-step explanation:

We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.

Let [tex]\mu[/tex] = population mean length of the board.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2564.0 millimeters    {means that the board's length is equal to 2564.0 millimeters}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 2564.0 millimeters      {means that the boards are either too long or too short}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean length of boards = 2559.5 millimeters

            s = sample standard deviation = 15.0 millimeters

             n = sample of boards = 26

So, the test statistics =  [tex]\frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }[/tex]  ~   [tex]t_2_5[/tex]

                                     =  -1.529    

The value of t-test statistics is -1.529.

Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the board's length is equal to 2564.0 millimeters.

Answer:

1

Step-by-step explanation:

Answer:

the anser is 9.5+1.5n and the second ansr is 48x+16

Answer:

a

Step-by-step explanation:

Answer:

Standard form:

Simplify the words.

6,090,036

Expanded form:

Take the standard number and expand it.

6000000 + 90000 + 30 + 6

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

As we know that 1 mile=1.6km

then,

62 miles=62*1.6km

=99.2km/hour

so, yes we are driving under the speed limit.

Answer:

Yes

Step-by-step explanation:

Convert 62 mph to kph by multiplying it by 1.6

62(1.6)

= 99.2

Yes, you are driving under the speed limit

Answer:

Step-by-step explanation:

2x+3x+4x=180 degrees

9x=180 fdegrees

x=180/9

x=20

2x=40

3x=60

4x=80

Answer:

18

Step-by-step explanation:

The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.

We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.

2x+3x+4x=180

(2+3+4)x=180

(9)x=180

x=180/9

x=20

So one interior angle measures 2x=2(20)=40.

Another measures 3x=3(20)=60.

The last measuring 4x=4(20)=80.

The exterior angles of this triangle therefore measure the following:

180-40=140

180-60=120

180-80=100

So the un-simplified ratio of the measures of the exterior angles is as follows:

140:120:100.

Let's simplify that.

It is easy to see each number is divisible by 10.

Let's reduce it by dividing each by 10:

14:12:10

Let's simplify more (as we want the most simplified ratio).

Each number is divisible by 2 since they are all even.

Let's reduce again but not by dividing by 2:

7:6:5

So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.

Answer is 18.

Answer:

X=2

Step-by-step explanation:

First, distribute the 3 to get

3x+3-2=x+5

Solve for 3-2 to get

3x+1=x+5

subtract 1 from both sides to get

3x=x+4

subtract x from both sides to get

2x=4

divide both sides by 2 to finalily get

x=2

Answer: 3 people ordered soup.

Step-by-step explanation:

Let x be the number of people ordered salad and y  be the number of people ordered soup.

As per given,

x=2y           (i)

7.50x+6.25y= 63.75          (ii)

Substitute value of c =2y in (ii) , we get

7.50(2y)+6.25y= 63.75

⇒ 15y+6.25y =  63.75

⇒21.25y =  63.75

⇒ y= 3   [divide both sides by 21.25]

Then, x= 2(3) =6

So 6 people ordered salad and 3 people ordered soup.

Answer:

Total number of votes- 145,000

Votes secured by winning candidate- 76,850

Step-by-step explanation:

Candidate A- 47%

Candidate B- 53%

6% difference or 8700 votes so

6%=8700

1%=1450

100%=145,000

53%= 76,850

Answer:8,2,0,2,8; Graph A

Step-by-step explanation:

The graph of the given equation best represents a parabola.

A graph represents the nature of the equation graphically by plotting the points of it.

Given, y = 2x²

For x = - 2, y = 2(- 2)² = 8

For x = - 1, y = 2(- 1)² = 2

For x = 0, y = 2(0)² = 0

For x = 1, y = 2(1)² = 2

For x = 2, y = 2(2)² = 8

Therefore, the given table will be:

x  - 2   - 1   0   1   2

y    8     2   0  2   8

By plotting the graph, it is clear that, the graph best represents a parabola.

Learn more about the graph of an equation here: https://brainly.com/question/4047677

#SPJ2

Answer:

Step-by-step explanation:

1. binomial polynomial

2. 2 terms

3. 4 is the constant term

4. - 1/10 x^3 is the leading term

5. -1/10 is the leading coefficient.

Answer:

[tex]\huge\boxed{\rho=1.6125\dfrac{g}{cm^3}}[/tex]

Step-by-step explanation:

The formula of a density:

[tex]\text{density}=\dfrac{mass}{volume}\Rightarrow\rho=\dfrac{m}{V}[/tex]

We have

[tex]\text{mass}\ m=12.9g\\\\\text{volume}\ V=8cm^3[/tex]

Substitute:

[tex]\rho=\dfrac{12.9g}{8cm^3}=\dfrac{12.9\cdot10}{8\cdot10}\dfrac{g}{cm^3}=\dfrac{129}{80}\dfrac{g}{cm^3}=1.6125\dfrac{g}{cm^3}[/tex]

The the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

Given the following data:

To find the density of the brown sugar;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, the density of a substance is given by the formula;

[tex]Density = \frac{Mass}{Volume}[/tex]

Substituting the values into the formula, we have;

[tex]Density = \frac{12.9}{8}[/tex]

Density =  [tex]1.6125 \;g/cm^3[/tex]

Therefore, the the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

Find more information: brainly.com/question/5995838

Answer: Try to use socratic

Step-by-step explanation:

Answer:

0.00387

To convert from meters to kilometers, you must divide the number pf meters by 1000.

3.87 ÷ 1000 = 0.00387.

So, that is the answer. Hope it helps!

Answer:

  (-1, 0), (-1, -5)

Step-by-step explanation:

The initial translation transformation was ...

  (x, y) ⇒ (x +4, y)

Then the reflection across the line y=x added the transformation ...

  (x, y) ⇒ (y, x)

So, the result of the composition of transformations was ...

  (x, y) ⇒ (y, x+4)

Then the reverse transformation, the one that gets from the image back to the pre-image, will be ...

  (y, x+4) ⇒ (x, y)

  (x, y) ⇒ (y-4, x)

The points A", B", C", D" will be transformed back to pre-image points ...

  A"(-4, 5) ⇒ A(1, -4)

  B"(-1, 5) ⇒ B(1, -1)

  C"(0, 3) ⇒ C(-1, 0) . . . . . . matches an answer choice

  D"(-5, 3) ⇒ D(-1, -5) . . . . . matches an answer choice

Answer: h= 8

Step-by-step explanation:

-3h - 6(5h/3 + 7/2) + 9h = -53   Distribute on the left

-3h - 10h - 21 + 9h = -53   combine like terms  on the left side

-4h -21 = -53          Now add 21 to both sides

      +21    +21

-4h = -32               Divide both sides by -4

h = 8

Answer: 2.308 .

Step-by-step explanation:

Let X denotes the number of earthquakes in SanFernando valley region of Los Angeles in 1994.

Given: [tex]\mu=17.6[/tex]

Probability is 0.87 that there will be at least 15 earthquakes .

i.e. [tex]P(X\geq15)=0.87[/tex]

[tex]\Rightarrow\ P(\dfrac{X-\mu}{\sigma}\geq\dfrac{15-17.6}{\sigma})=0.87\\\\ \Rightarrow\ P(Z\geq\dfrac{-2.6}{\sigma})=0.87\ \ \ [Z=\dfrac{X-\mu}{\sigma}][/tex]

Z-value corresponding to p-value 0.87 is -1.1263 .

So, [tex]\dfrac{-2.6}{\sigma}=-1.1263[/tex]

[tex]\sigma= \dfrac{-2.6}{-1.1263}\approx2.308[/tex]

Hence, the required standard deviation = 2.308 .

Answer:

Length= 30 ft

Width= 18ft

Step-by-step explanation:

The perimeter of the rectangular patio is to be 96 feet.

the length is to be 6 feet less than twice the width

Perimeter=2(length+width)

But

Length= 2(width)-6

Substituting in perimeter equation

Perimeter=2(length+width)

Perimeter=2((2(width)-6)+width)

Perimeter= 96 feet

Let width= x

Perimeter=2((2(width)-6)+width

96=2((2(x)-6)+x)

96= 4x-12+2x

108= 6x

18= x

Width= 18ft

Length= 2(width)-6

Length= 2(18)-6

Length= 36-6

Length= 30 ft

Answer:

g = 4

Step-by-step explanation:

5g = 20

Divide each side by 5

5g/5 = 20/5

g = 4

Answer:

g= 4

Step-by-step explanation:

5g = 20

5g /5 = 20 /5

g =4

Answer:

x-3

Step-by-step explanation:

x²-9÷x+3=x-3

Answer:

= 274

Step-by-step explanation:

202 + 6(9 + 3)

= 202 + 9 * 12

= 202 + 72

= 274

Answer:

Its is actually 472

Step-by-step explanation:

Answer:

Please see attached picture

hope it helped you:)

Answer:

C

Step-by-step explanation:

Here we have the question,

7x+4 = -19 + 5x

Now we add 19 to both sides,

7x + 4 + 19 = -19 + 19 + 5x

7x + 23 = 5x

Now we subtract 7x from both sides,

23 = -2x

We divide -2 from both sides,

x = -23/2

Now we plug this in into 2x - 14,

2(-23/2) - 14 = -23-14 = -37

Our answer is C

Answer:

0 belongs to the set of whole number,set of rational numbers,set of real numbers and integers

Step-by-step explanation:

Answer:

6.25

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides.

For a rectangle, it's the two widths plus the two heights.

P = 2W + 2H

Plugging in values:

52 = 2(3x − 1) + 2(x + 2)

52 = 6x − 2 + 2x + 4

52 = 8x + 2

50 = 8x

x = 6.25

Find the value of x.

Perimeter of rectangle = 2 ( l + b )

We know that,

Perimeter of rectangle = 52 [ Given ]

⇒ 2 ( l + b ) = 52

⇒ 2 ( 3x - 1 + x + 2 ) = 52

⇒ 2 ( 4x + 1 ) = 52

⇒ 8x + 2 = 52

⇒8x = 52 - 2

⇒ 8x = 50

⇒ x = 50/8

⇒ x = 6.25 inches

Answer:

y= -7

Step-by-step explanation:

This line is a horizontal line.

Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).

The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.

Let's return to the form for horizontal lines.

y= k

The y-intercept is -7. Substitute -7 in for k.

y= -7

The equation of the line is y= -7

Answer:

the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.

Answer:

A

Step-by-step explanation:

Answer:

Hey there!

The correct answer would be a line from (0, 0) to (-1, 2)

Let me know if this helps :)

Step-by-step explanation:

(2) (x+2)^2 + (-15x -3)

I hope this will be helpful for you.

Answer:

[tex]2(x + 2)^{2} + (-15x - 3)[/tex]

The guy above is correct

Proof :

[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]

[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]

My workings are in the picture

My asnwer was 5/2 and -1