Sophie saw a dress she liked on sale for $15 off. The original price of the dress was $96. What is the sale price of the dress?

Answer: 1022.75 kWh.

Step-by-step explanation:

Given: In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.

i.e. [tex]\mu=1050\ kWh[/tex] and [tex]\sigma=218\ kWh[/tex]

Let X denote energy consumption levels for random single-family homes and x be the energy consumption level for the 45th percentile.

Then, [tex]P(X<x)=0.45[/tex]

From z-table, [tex]P(z<-0.125)=0.45[/tex]

Also, [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]\Rightarrow\ -0.125=\dfrac{x-1050}{218}\\\\\Rightarrow\ x=-0.125\times218+1050=1022.75[/tex]

Hence, the energy consumption level for the 45th percentile is 1022.75 kWh.

Answer:

a. Normally distributed with a mean of $2700 and a standard deviation of $40

Step-by-step explanation:

Given that:

the mean daily revenue is $2700

the standard deviation is $400

sample size n is 100

According to the Central Limit Theorem, the sampling distribution of the sample mean can be computed as follows:

[tex]\mathbf{standard \ deviation =\dfrac{ \sigma}{\sqrt{n}}}[/tex]

standard deviation = [tex]\dfrac{400}{\sqrt{100}}[/tex]

standard deviation = [tex]\dfrac{400}{10}}[/tex]

standard deviation = 40

This is because the sample size n is large ( i,e n > 30) as a result of that  the sampling distribution is normally distributed.

Therefore;

the statement that  describes the sampling distribution of the sample mean is : option A.

a. Normally distributed with a mean of $2700 and a standard deviation of $40

Answer:

[tex]g(x)=4x^{2} +10[/tex]

Step-by-step explanation:

If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.

Let:

[tex]a>0,\hspace{10}a\in R[/tex]

For:

If:

[tex]f(x)=4x^{2} +6[/tex]

and is translated vertically upward by 4 units, this means:

[tex]a=4[/tex]

and:

[tex]g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10[/tex]

Therefore:

[tex]g(x)=4x^{2} +10[/tex]

I attached you the graphs, so you can verify the result easily.

Answer:

A) 64 observations

B) analytic study

Step-by-step explanation:

Given:  

There are 3 number of factors i.e. armature length, spring load, and bobbin depth.

There are 4 levels i.e. low, fair, moderate, and high

There is a single i.e. 1 observation on flow made for each combination of levels.

A)

To find:

Number of observations.

There are 4 levels so these 4 levels are to be considered for each factor.

Number of observations = 4.4.4 = 64

For example if we represent low fair moderate and high as L,F,M,H

and factors armature length, spring load, and bobbin depth as a,s,b

Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]

So resulting data set has 64 observations.  

B)

This is analytic study.

The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.

let us build equation for unknown legs

If we keep the length pf one leg as x

the other leg would be x +3

so we can build a relationship using pythagoras theorem

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

x^2 + x^2 + 6x + 9 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x+ 9-225 = 0

2x^2 + 6x - 216 = 0

x^2 + 3x - 108 = 0 dividing whole equation by 2

x^2 + 12x - 9x - 108 = 0

x ( x + 12 ) - 9 (x + 12) = 0

(x -9) ( x +12) = 0

solutions for x are

x = 9 or x = -12

as lengths cannot be negative

one side length is 9cm

and other which is( x + 3)

9 + 3

12cm

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = First Leg² + Second leg²

Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:

15² = x² + (x + 3)²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

x² + 3x - 108 = 0

x = - 12 or x = 9

Since the length cant the negative hence x= 9, x + 3 = 12

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

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Answer: C. 3.68

Step-by-step explanation:

Given that;

Sample size n = 18

degree of freedom for numerator k = 2

degree of freedom for denominator = n - k - 1 = (18-2-1) = 15

level of significance = 5% = 5/100 = 0.05

From the table values,

the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68

Therefore option C. 3.68 is the correct answer

Answer:

what we have to tell

Step-by-step explanation:

please send the correct information

Answer:

The answer on PLATO is Graph Z.

Step-by-step explanation:

I just had this question and got it right!!!

Hope this Helps!!!

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Answer:

The z-score for a sales associate from this store who earns $37,500 is 2

Step-by-step explanation:

From the given information:

mean [tex]\mu[/tex] = 32500

standard deviation = 2500

Sample mean X = 37500

From the given information;

The value for z can be computed as :

[tex]z= \dfrac{X- \mu}{\sigma}[/tex]

[tex]z= \dfrac{37500- 32500}{2500}[/tex]

[tex]z= \dfrac{5000}{2500}[/tex]

z = 2

The z-score for a sales associate from this store who earns $37,500 is 2

Answer:

Please look at the picture below!

Step-by-step explanation:

Hope this helps!

If you have any question, please feel free to ask any time.

Answer:

75%.

Step-by-step explanation:

In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.

The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.

Hope this helps!

Answer:

2/5

Step-by-step explanation:

(7-5)/(6-1)

Answer:

[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

[tex]x+8\neq 0[/tex]

Subtract 8 from both parts.

[tex]x\neq -8[/tex]

[tex]x-2\neq 0[/tex]

Add 2 on both parts.

[tex]x\neq 2[/tex]

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

[tex]x+3\geq 0[/tex]

Subtract 3 from both parts.

[tex]x\geq -3[/tex]

The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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Answer:

Step-by-step explanation:

[tex] \frac{8}{7} = \frac{x}{5} [/tex]

To find x first cross multiply

We have

7x = 8 × 5

7x = 40

Divide both sides by 7

That's

[tex] \frac{7x}{7} = \frac{40}{7} [/tex]

[tex]x = \frac{40}{7} [/tex]

x = 5.7142

We have the final answer as

Hope this helps you

Answer:

[tex]\boxed{\sf x = 5.7}[/tex]

Step-by-step explanation:

[tex]\sf \frac{8}{7} = \frac{x}{5} \\=> 1.142 = \frac{x}{5}\\ Multiplying \ both \ sides \ by \ 5\\1.142 * 5 = x\\5.7 = x\\OR\\x = 5.7[/tex]

Answer:

16. x=48 y=70

17. x=45 y=5

Step-by-step explanation:

16. This is an isosceles triangle meaning that the two angles are the same. Meaning that (x+7)=55.

55-7=48

(48+7)=55 x=48

There are 180 degrees in a triangle, so 55+55=110

180-110=70. y=70

17. This is a right angled triangle meaning that the squared part is 90 degrees. And it is also an isosceles triangle meaning that x=97.

There are 180 degrees in a triangle, and 90 is already taken, meaning that there is 90 degrees more left.

90/2=45

x=45

9✖️5=45 y=5

Hope this helps, BRAINLIEST would really help me!

Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Spinner: 50%

Die: 50%

Step-by-step explanation:

Well for the spinner it depends on the amount of numbers it has,

in this case we’ll use 6.

So The probability of landing on the even numbers in a 6 numbered spinner.

2, 4, 6

3/6

50%

Your average die has 6 sides so the odd numbers are,

1, 3, 5

3/6

50%

Answer:

16x²

Step-by-step explanation:

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

[tex]\alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]

[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]

Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:

[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{1} = -2\cdot k[/tex]

[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{2} = -3\cdot k[/tex]

It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} + \alpha_{3} = 0[/tex]

[tex]3\cdot \alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

Answer:

4 ft

7.2 ft

20 ft

Step-by-step explanation:

When the balloon is shot, x = 0.

y = -0.05(0)² + 0.8(0) + 4

y = 4

The balloon reaches the highest point at the vertex of the parabola.

x = -b / 2a

x = -0.8 / (2 × -0.05)

x = 8

y = -0.05(8)² + 0.8(8) + 4

y = 7.2

When the balloon lands, y = 0.

0 = -0.05x² + 0.8x + 4

0 = x² − 16x − 80

0 = (x + 4) (x − 20)

x = -4 or 20

Since x > 0, x = 20.

The slingshot launched the ballon from a height of 4 feet. The balloon's maximum height was 72 feet. The balloon landed 20 feet from the slingshot.

To determine the height from which the slingshot launched the balloon, we need to evaluate the function f(0) because when x is zero, it represents the starting point of the balloon's trajectory.

f(x) = -0.05x² + 0.8x + 4

f(0) = -0.05(0)² + 0.8(0) + 4

f(0) = 4

Therefore, the slingshot launched the balloon from a height of 4 feet.

To find the maximum height of the balloon, we can observe that the maximum point of the parabolic function occurs at the vertex.

The x-coordinate of the vertex can be calculated using the formula x = -b / (2a).

In our case, a = -0.05 and b = 0.8.

Let's calculate the x-coordinate of the vertex:

x = -0.8 / (2×(-0.05))

x = -0.8 / (-0.1)

x = 8

Now, substitute this x-coordinate into the function to find the maximum height:

f(x) = -0.05x² + 0.8x + 4

f(8) = -0.05(8)² + 0.8(8) + 4

f(8) = -0.05(64) + 6.4 + 4

f(8) = -3.2 + 6.4 + 4

f(8) = 7.2

Therefore, the balloon reached a maximum height of 7.2 feet.

To determine how far from the slingshot the balloon landed, we need to find the x-intercepts of the quadratic function.

These represent the points where the height is zero, indicating the balloon has landed.

Setting f(x) = 0, we can solve the quadratic equation:

-0.05x² + 0.8x + 4 = 0

x² - 16x - 80= 0

x=-4 or x=20

We take the positive value, so  the balloon landed 20 feet from the slingshot.

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Answer:

[tex]\boxed{(-\frac{\sqrt{3}}{2}, \frac{1}{2})}[/tex]

Step-by-step explanation:

Method 1: Using a calculator instead of the unit circle

The unit circle gives coordinates pairs for the cos and sin values at a certain angle. Therefore, if an angle is given, use a calculator to evaluate the functions at cos(angle) and sin(angle).

Method 2: Using the unit circle

Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.

This coordinate pair is (-√3/2, 1/2).

Answer: This coordinate pair is (-√3/2, 1/2).

Step-by-step explanation:

Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.

Answer:2/3-4

Step-by-step explanation:

Hi,

The correct answer is √ra = v or v = √ra.

The original equation is a = v^2/r.

Then we multiply r to get ra = v^2

After that we √ra = √v^2

Our final answer is then √ra = v

XD

Answer:

c. ax+b=ax+b

Step-by-step explanation:

To know what equation has infinite solutions, you first try to simplify the equations:

a.

[tex]ax=bx+c\\\\(a-b)x=c\\\\x=\frac{c}{a-b}[/tex]

In this case you have that a must be different of b, but there is no restriction to the value of c, then c can be equal to a or b.

b.

[tex]ax+b=ax+c\\\\b=c[/tex]

Here you obtain that b = c. But the statement of the question says that a, b and c are three different numbers.

c.

[tex]ax+b=ax+b\\\\0=0[/tex]

In this case you have that whichever values of a, b and are available solutions of the equation. Furthermore, when you obtain 0=0, there are infinite solutions to the equation.

Then, the answer is:

c. ax+b=ax+b

Answer:

ax + b = ax + b

Step-by-step explanation:

i just answered it

Answer:

I hope it will help you...

The value of [tex]x+y[/tex] will be equal to 185 degrees.

From figure it is observed that,

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

        [tex]y=45+60=105[/tex]

We know that, By triangle property  sum of all three angles in a triangle must be equal to 180 degrees.

  So that,             [tex]x+55+45=180[/tex]

                           [tex]x=180-100=80[/tex]

Thus,    [tex]x+y=105+80=185[/tex] degree

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Answer: Use calculations for population standard deviation.

Step-by-step explanation:

The population standard deviation is defined as

A sample standard deviation is defined as

Since, data set represents the heights of all students in the middle school with 600 students which is population here.

So, we do calculations to find population standard deviation.

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

a

   $10,151   [tex]< \mu <[/tex]  $11448.12

b

  [tex]n = 158[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  19

    The  sample mean is  [tex]\= x =[/tex]$10,800

     The  standard deviation is  [tex]\sigma =[/tex]$1095  

    The  population mean is  [tex]\mu =[/tex]$225

Given that the confidence level is 99%  the level of significance is mathematically represented as

       [tex]\alpha = 100 -99[/tex]

      [tex]\alpha = 1[/tex]%

=>    [tex]\alpha = 0.01[/tex]

Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as

        [tex]Z_{\frac{0.01}{2} } = 2.58[/tex]

The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex]  is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Now the margin of error is obtained as

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

substituting values

    [tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]

     [tex]MOE = 648.12[/tex]

The  99% confidence interval for the population mean yearly premium is mathematically represented as

    [tex]\= x -MOE < \mu < \= x +MOE[/tex]

substituting values

   [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

    [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

   $10,151   [tex]< \mu <[/tex]  $11448.12

The  largest sample needed is mathematically evaluated as

      [tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]

substituting values

       [tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]

      [tex]n = 158[/tex]

Answer:

78

Step-by-step explanation:

The measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

x = 31 + 47

x = 78