5. suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x

Answer:

B 3/32

Step-by-step explanation:

3/8 divided by 4

do the keep change flip method and solve

3/8 x 1/4

Answer:

Step-by-step explanation:

Based on the information given in the question, the inequality which can be used to determine x, the number of people who can go to the amusement park will be:

8 + 23(x) ≤ 100

8 + 23x ≤ 100

23x ≤ 100 - 8

23x ≤ 92

x ≤ 92/23

x ≤ 4

The number of people that can go to the amusement park will be at most 4

The x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).

Given:

Equation of Line A: y-2=-(x+1)

on finding x intercept put y = 0

0 - 2 = -x - 1

-2 = -x - 1

-x = -2 + 1

-x = -1

x = 1.

The x intercept is (1,0)

The x intercept for the line B is (-2,0).

Therefore the x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).

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a) The hypothesis are given as follows:

b) The significance level is of α = 0.1.

c) The test statistic is of: t = -2.69.

d) The p-value is of: 0.018

e) The decision is to reject the null hypothesis.

At the null hypothesis, it is tested if there is not enough evidence that SUVs sustain less damage, that is, the mean is equal or greater than zero, hence:

[tex]H_0: \mu_d \geq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the SUVs sustain less damage, that is, the mean if less than zero, hence:

[tex]H_1: \mu_d < 0[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The sample of the differences is given as follows:

447, -893, -2373, 271, -1680, -1916, -1676.

Using a calculator from the above sample, the values of these parameters are given as follows:

[tex]\overline{x} = -1117, \mu = 0, s = 1100, n = 7[/tex]

Hence the test statistic is of:

t = (-1117 - 0)/(1100/sqrt(7))

t = -2.69.

Using a t-distribution calculator, considering a left-tailed test, as we are testing if the mean is less than a value, with 7 - 1 = 6 df and t = -2.69, the p-value is of 0.018.

Since this p-value is less than the significance level of 0.1, the decision is to reject the null hypothesis.

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The slope of the line is  5/6.

From the graph:

Slope : a surface of which one end or side is at a higher level than another rising or falling surface.

Points are (-3,-2) and (3,3)

slope m = y2-y1 / x2-x1

= 3 - (-2) / 3 - (-3)

= 3 + 2 / 3 + 3

m =  5/6.

Therefore  the slope of the line is  5/6.

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A formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.

First, let us understand the arithmetic progression:

Arithmetic Progression (AP) is a number sequence in which the difference between any two consecutive numbers is a constant value.

We can find the common difference (d) by subtracting any two consecutive terms of arithmetic progression.

The nth term of an arithmetic progression is given by:

a_n = a + (n - 1)d

where

a = first term of an arithmetic progression

n = nth term of an arithmetic progression

d = common difference

We are given the following sequence;

2.3, 2.8, 3.3, 3.8, ...

We need to write a formula for the given sequence.

Let us find the common difference;

d = 2.8 - 2.3 = 0.5

a = 2.3

substitute the values in the above formula;

a_n = 2.3 + (n - 1) * 0.5

a_n = 2.3 + 0.5 n - 0.5

a_n = 1.8 + 0.5 n

So, the formula for the given sequence is a_n = 1.8 + 0.5 n.

Thus, a formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.

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It is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.

Given: 2x-9 -5 = 1

We need to prove that x = 7

2x - 9 - 5 = 1

2x - 13 = 1

2x = 14

x = 7

Therefore, it is proven that the value of x in the given expression  2x-9 -5 = 1 is 7.

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The dimensions of the window: Length = 9ft , width = 4ft

What are dimensions?

In mathematics, a dimension is the length or width of an area, region, or space in one direction.

The homes we live in and the items we use on a daily basis all have three dimensions: height, length, and width.

Here, we have

l = w + 5

Area = length × width

The linear equation of the given dimension is:

36 = (w + 5)w

w² + 5w - 36 = 0

(w + 9)(w - 4) = 0

w + 9 = 0

w = -9

We only measure positive numbers so, we disregard this value.

we take,

w - 4 = 0

w = 4

l = 4 + 5

l = 9

The length of the window is 9 ft and the width of the window is 4 ft.

Hence, the dimensions of the window: Length = 9ft , width = 4ft

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Answer:

43.2km/h

Step-by-step explanation:

1km = 1000m

1h = 3600s

1km/h to m/s

= 1 × 1000/3600

= 1000/3600

1m/s to km/h

= 1 ÷ 1000/3600

= 1 × 3600/1000

Hence, 12m/s = 12 × 3600/1000

= 43.2km/h

The c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

The three hypotheses of Rolle's theorem are:

(a) f(x) is continuous on [a,b]

(b) f(x) is differentiable on (a,b)

(c) f(a) = f(b)

i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]

ii) f(x) is differentiable on (0,81)

f '(x) = 1/(2√x) - 1/9  which exists on the open interval (0,81)

iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0

Rolle's Conclusion:

f'(c) = 0

f'(c) = 1/(2√c) -1/9 = 0

(9 - 2√c)/(18√c) = 0

√c = 9/2

c = 81/4

There is one number c = 81/4, which satisfies f '(c) = 0.

Therefore the c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

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Full question:

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

f(x) =x − 1/9 x, [0, 81].

Answer: 4,300 gallons of water

215 x 4 = 860 gallons of water using the dishwasher

215 x 6 x 4 = 5,160 gallons of water by hand

5,160 - 860 = 4,300 gallons of water saved by using the dishwasher.

- Your welcome, keep it up champ.

Answer:

Fiona would need 12 pages to hold all 212 stickers.

Step-by-step explanation:

Since each page holds 18 stickers, and Fiona has 212 stickers, we need to divide.

212 / 18 = 11.7777778 pages

Because that we cannot have .77777778 of a page, we round to the nearest page, getting us 12 pages.

Have a good night, I hope my answer helped you!

Answer:

y = 2.5

Step-by-step explanation:

To double check this, you can do 5 times (2.5), then do 16.7 minus that answer so you do, 16.7- 12.5 which does indeed equal 4.2

Answer:

y = 2.5

Step-by-step explanation:

[tex]4.2 =16.7-5y[/tex]

Subtract 16.7 from both sides of the equation you get:

[tex]-12.5=-5y[/tex]

Divide by -5:

[tex]2.5=y[/tex]

Hope this answers your question :)

The factored form of n2 + n is:  n(n+1).

Given data:

n²+n

Now let find the factored form of n²+n

n²+n

Rewrite in factored form

n(n+1)

Hence,

n²+n = n(n+1)

Therefore n(n+1) is the factored form.

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Answer:14.1099

Step-by-step explanation:

Answer:

x = 31 , y = 80

Step-by-step explanation:

∠ 3 and ∠ 7 are corresponding angles and are congruent , so

3x - 18 = 75 ( add 18 to both sides )

3x = 93 ( divide both sides by 3 )

x = 31

then

∠ 3 = 3x - 18 = 3(31) - 18 = 93 - 18 = 75°

∠ 3 and ∠ 4 are a linear pair and sum to 180° , then

75 + y + 25 = 180

y + 100 = 180 ( subtract 100 from both sides )

y = 80

The value of tan W is 5/12

From the question, we have

tan W = 15/36

= 5/12 =0.41

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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The numbers that will be chosen when Corey selects all of the numbers that are less than -5 but greater than -20 include -9, -11 and -15.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality will be expressed as:

-20 < x < -5

In this case, the numbers have to be from -6 to -19. The numbers illustrated in the options are -9, -11 and -15.

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The birth weight of elephants at the 99% confidence level is 3820 pounds

What is the standard deviation?

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

The average birth weight of elephants is 200 pounds     = 200

The deviation of 60 pounds.                                               = 1500

The birth weight of elephants is at the 85th percentile.      z = 99%= 1.645

Now from the formula of z-score:-

[tex]z=\sqrt{\frac{x-\mu}{\sigma} }[/tex]

[tex]1.64 =\sqrt{\frac{x-200}{1500} }\\[/tex]

[tex]1.645^{2} =\frac{x-200}{1500}[/tex]

2.68 = (x-200)/1500

2.68×1500=x-200

4020-200=x

3820=x

Hence the birth weight of elephants at the 99% level percentile is 3820 pounds

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Answer:

∴ The measure of the hypotenuse is 20cm (to the nearest tenth).

Step-by-step explanation:

Let the length of the hypotenuse be x cm.

 x² = 11² + 14²

∴ x = 20cm (to the nearest tenth)

Bijou made her first decimal place error in Step 4 because the answer is supposed to be 4.34, not 43,400.

The decimal place of a product of two numbers should be determined based on the number of decimal places the multiplier and the multiplicand originally have.

A decimal place error is committed when the result bears a decimal place in the wrong position.

In this situation, 0.62 of 7:

= 0.62 x 7

= 62 x 7 ... removing the two decimal places

= 434

= 4.34 ... putting back the two decimal places in the final result.

Thus, Bijou did not commit any decimal place or multiplication error in Steps 1 through 3 but in Step 4.

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Two years , is the time in which Naoh had to pay off his loan when the ammount he paid to his father was equal to $2450.

In the question we have given,

Amount borrowed by Naoh from his father

= $2000

The relationship between amount of money A in dollars with interest and elapsed time t is

A = 2000 e⁽⁰·¹⁾ᵗ

let Naoh pay $2450 after elapsing "t" years .

that is A = $2450 after time t years of borrowing.

We shall calculate the time which elapsed after borrowed by Naoh for paying $2450.

So, putting A = 2450 in above equation we get

2450 = 2000 e⁽⁰·¹⁾ᵗ

=> e⁽⁰·¹⁾ᵗ= 2450/2000 = 49/40

Taking logarithm both sides

=> ln ( e⁽⁰·¹⁾ᵗ) = ln (49/40)

=> (0.1 )t = 0.203

=> t = 2.023 ~ 2

Hence, after 2 years , Naoh will pay $2450 with including interest to his father.

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Answer:

Step-by-step explanation:

1(x1)+ (-4)x2+ (-10)x3 = -40                               Eq 1

0   +    (1)x2 +   3(x3)   = 14                               Eq 2

0  +   (-2)x2 + (-5)x3  =  -23                             Eq 3

from the 2nd equations we get

x2 + 3*x3 = 14

x2 = 14 - 3*x3

plug this into equation 3

(-2)*(14-3*x3) + (-5)x3 = -23

now solve for x3  :)

-28+6*x3-5*x3 = -23

-28 +x3 = -23

x3 = 5

nice !

now find x2

x2 = 14-3*(5)

x2 = -1

now find x1

x1 + (-4)*(-1) + (-10)*5 = -40

x1 +4 -50=-40

x1 = 6

X = [ 6 ; (-1) ; 5 ]

Answer: -19x + 10

Step-by-step explanation:

1. Remove parenthesis

-10x + 2 - 9x + 8

2. Collect like terms

(-10x - 9x) + (2 + 8)

3. Simplify

-19x + 10

By using property of logarithms, We get the answer

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

Given,

In the question:

The equation is :

In  [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1

To solve by using by using property of logarithms to expand the expression as a sum, difference, and / or constant multiple of logarithms.

Now, According to the question:

We know that:

The property of logarithms is:

[tex]log_{a}{\frac{m}{n} } = log_{a}m - log_{a}n[/tex]

The given equation is :

In  [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1

In  [tex]\frac{x^{2} -1}{x^7}[/tex] = In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex]

Again, Using the another property of logarithms.

[tex]log_am^x = nlog_am[/tex] {x∈ R}

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [tex](x^2 -1)[/tex] - 7 In x

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [ (x + 1)(x - 1)] - 7In x

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

{Log (mn) = [tex]log_{a}m - log_{a}n[/tex]}

Hence, By using property of logarithms, We get the answer

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

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Answer:

y = -12 + 4x

Step-by-step explanation:

1. Add 8x to both sides of the equation.

2y = -24 + 8x

2. Divide each term in 2y = -24 + 8x by 2, then simplify.

• Simplify left side: cancel the common factor of 2

y = -24/2 + 8x/2

• Simplify right side: 2y/2 = -24/2 + 8x

y = -12 + 4x

Check the picture below.

[tex]\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}~~ - ~~\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{2}-\sqrt{6}}{4} \end{array}}[/tex]

keeping in mind that a line with an undefined slope is a vertical line, Check the picture below.