Figure ABCDE was reflected across the line y=x to create figure A’B’C’D’E’. What are the coordinates of the pre image of E?

Answer:

that's cool . . .

\is ok everyone makes mistakes

Answer:

a. $21.50

b. $980

c. $25 and $18

Step-by-step explanation:

a. The price that generates the maximum profit is

In this question we use the vertex formula i.e shown below:

[tex](-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\[/tex]

where a = -80

b = 3440

c = 36000

hence,

P-coordinate is

[tex](-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\[/tex]

[tex]= \frac{3440}{160}[/tex]

= $21.5

b. Now The maximum profit could be determined by the following equation

[tex]f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\[/tex]

= $980

c. The price that would enable the company to break even that is

f(p) = 0

[tex]f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0[/tex]

By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come

(p - 25) = 0 or (p - 18) = 0

so we can write in this form as well which is

p = 25 or p = 18

Therefore the correct answer is $25 and $18

Answer:

2x^3-11x^2+16x-3

Step-by-step explanation:

1) multiply each term inside the parentheses with all other terms:

(x*2x^2)=2x^3

x*-5x=-5x^2

x*1=x

-3*2x^2=-6x^2

-3*-5x=15x

and

-3*1=-3

so

2x^3-5x^2+x-6x^2+15x-3

is our equation

to simplify:

2x^3-11x^2+16x-3 is the answer

Answer:

924 cm²

Step-by-step explanation:

The surface area is equal to the area of the two triangles + area of the three rectangles.

Area of two triangles:

12 × (9+5) × 1/2

= 84

84(2) = 168

Area of the three rectangles:

15 × 20 + 13 × 20 + 14 × 20

= 840

840 + 84

The surface area of the triangular prism is 924 cm².

Answer:

Sum of 2 digit = 48

Sum of 3 digit = 317

Sum of 4 digit = 3009

Total = 3374

Step-by-step explanation:

Given:

9, 8 and 7

Required

Sum of Multiples

The first step is to list out the multiples of each number

9:- 9,18,....,99,108,117,................,999

,1008

,1017....

8:- 8,16........,96,104,...............,992,1000,1008....

7:- 7,14,........,98,105,.............,994,1001,1008.....

Calculating the sum of smallest 2 digit multiple of 9, 8 and 7

The smallest positive 2 digit multiple of:

- 9 is 18

- 8 is 16

- 7 is 14

Sum = 18 + 16 + 14

Sum = 48

Calculating the sum of smallest 3 digit multiple of 9, 8 and 7

The smallest positive 3 digit multiple of:

- 9 is 108

- 8 is 104

- 7 is 105

Sum = 108 + 104 + 105

Sum = 317

Calculating the sum of smallest 4 digit multiple of 9, 8 and 7

The smallest positive 4 digit multiple of:

- 9 is 1008

- 8 is 1000

- 7 is 1001

Sum = 1008 + 1000 + 1001

Sum = 3009

Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit

Sum of All = 48 + 317 + 3009

Sum of All = 3374

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

First let's find how much Susan earns per hour.

She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:

0.004 * 90 = $0.36

Then, per hour, she will earn:

0.36 * 60 = $21.6

Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:

1000 / 21.6 = 46.3 hours.

She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.

If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:

48 * 21.6 = $1036.8

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

Answer:

Option 4

Step-by-step explanation:

=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]

Combining like terms

=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]

=> [tex]x^2+7x+5[/tex]

Answer:

For this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Step-by-step explanation:

We have the following dataset given:

[tex] X= 43[/tex] represent the households consisted of one person

[tex]n= 125[/tex] represent the sample size

[tex] \hat p= \frac{43}{125}= 0.344[/tex] estimated proportion of  households consisted of one person

We want to test the following hypothesis:

Null hypothesis: [tex]p \leq 0.27[/tex]

Alternative hypothesis: [tex]p>0.27[/tex]

And for this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Answer:

Point Q is at a distance of 4.7 units from A.

Step-by-step explanation:

From the graph, AC = 10 units and BC = 6 units. Applying the Pythagoras theorem,

[tex]AB^{2}[/tex] = [tex]AC^{2}[/tex] + [tex]BC^{2}[/tex]

      = [tex]10^{2}[/tex] + [tex]6^{2}[/tex]

      = 100 + 36

     = 136

AB = [tex]\sqrt{136}[/tex]

AB = 11.6619

AB = 11.66

     ≅ 11.7 units

But point Q divides AB into ratio 2:3. Therefore:

AQ = [tex]\frac{2}{5}[/tex] × AB

     =  [tex]\frac{2}{5}[/tex] × 11.66

     = 4.664

AQ = 4.664

AQ ≅ 4.7 units

QB = [tex]\frac{3}{5}[/tex] × AB

     =  [tex]\frac{3}{5}[/tex] × 11.66

     = 6.996

QB  ≅ 7.0 units

So that point Q is at a distance of 4.7 units from A.

Answer: Rent = 29%,  Food = 21%,    Fun = 17%

Step-by-step explanation:

Rent =     $433

Food =    $320

Fun =       $260

Other =   $487  

TOTAL = $1500

[tex]\dfrac{Rent}{Total}=\dfrac{433}{1500}\quad =0.2886\quad =\large\boxed{29\%}\\\\\\\dfrac{Food}{Total}=\dfrac{320}{1500}\quad =0.2133\quad =\large\boxed{21\%}\\\\\\\dfrac{Fun}{Total}=\dfrac{260}{1500}\quad =0.1733\quad =\large\boxed{17\%}[/tex]

Answer:

Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.

y= -3x+b

Now, we can substitute in the point given to find the intercept.

2= -3(4)+b

2= -12+b

b=14

Finally, put in everything we've found to finish the equation.

y= -3x+14

Answer:

y = -3x + 14

Step-by-step explanation:

First find the reciprocal slope since it is perpendicular.  Slope of the other line is 1/3 so the slope for our new equation is -3.  

Plug information into point-slope equation

(y - y1) = m (x-x1)

y - 2 = -3 (x-4)

Simplify if needed

y - 2 = -3x + 12

y = -3x + 14

Answer:

x+4=0,x=−4x−7=0,x=7

Answer:

Step-by-step explanation:

Hello!

You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.

                n  |  Mean |  Std. Dev.

Midsize  | 31 |  25.8   |  2.56

SUV’s     | 31 |  22.68 |  3.67

Pickups  | 14 |  21.29  |  2.76

Be the study variables :

X₁: highway gas mileage of a midsize car

X₂: highway gas mileage of an SUV

X₃: highway gas mileage of a pickup truck.

Assuming these variables have a normal distribution and are independent.

The hypotheses are:

H₀: μ₁ = μ₂ = μ₃

H₁: At least one of the population means is different.

α: 0.01

The statistic for this test is:

[tex]F= \frac{MS_{Treatment}}{MS_{Error}}[/tex]~[tex]F_{k-1;n-k}[/tex]

Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.

For the treatments:

The degrees of freedom between treatments are k-1 (k represents the amount of treatments): [tex]Df_{Tr}= k - 1= 3 - 1 = 2[/tex]

The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean, is the mean that results of all the groups together.

So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26

[tex]SS_{Tr}[/tex]= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689

[tex]MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33[/tex]

For the errors:

The degrees of freedom for the errors are: [tex]Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73[/tex]

The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:

[tex]MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52[/tex]

Now you can calculate the test statistic

[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56[/tex]

The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:

[tex]F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07[/tex]

If [tex]F_{H_0}[/tex] ≥ 4.07, reject the null hypothesis.

If [tex]F_{H_0}[/tex] < 4.07, do not reject the null hypothesis.

Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.

Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)

I hope this helps!

Answer:

Step-by-step explanation:

These come directly from my textbook, so I'm not sure if your teacher will accept this kind of work.

1. Angle construction:

Given an angle. construct an angle congruent to the given angle.

Given: Angle ABC

Construct: An angle congruent to angle ABC

Procedure:

1. Draw a ray. Label it ray RY.

2. Using B as center and any radius, draw an arc that intersects ray BA and ray BC. Label the points of intersection D and E, respectively.

3. Using R as center and the same radius as in Step 2, draw an arc intersecting ray RY. Label the arc XS, with S being the point where the arc intersects ray RY.

4. Using S as center and a radius equal to DE, draw an arc that intersects arc XS at a point Q.

5. Draw ray RQ.

Justification (for congruence): If you draw line segment DE and line segment QS, triangle DBE is congruent to triangle QRS (SSS postulate) Then angle QRS is congruent to angle ABC.

You can probably also Google videos if it's hard to imagine this. Sorry, construction is super hard to describe.

Answer:

the answer is C. y=[x-4]-2

Answer:

Step-by-step explanation:

Y=(x+4)-2

Answer:

49

Step-by-step explanation:

When Karen was born, the dad is 22 so Karen is now 27 which means the dad is 22+27= 49

Answer:

Their father is 49.

Step-by-step explanation:

Her father had her when he was 22, meaning that he is 22 years older than Karen. Karen is 27 right now, so her fathers age is (27+22) 49 years old.

Hope this helps!

Answer:

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Step-by-step explanation:

When the normal approximation is suitable?

If np > 5 and np(1-p)>5

In this question:

[tex]n = 24, p = 0.6[/tex]

So

[tex]np = 24*0.6 = 14.4[/tex]

And

[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Answer: a= 3x and b= 7

Step-by-step explanation:

^^

Answer:

2^52

Step-by-step explanation:

(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52

Answer:

Hey there!

This flower has 8 lines of symmetry.

Hope this helps :)

Answer:

27m

Step-by-step explanation:

It's the Pythagorean Theorem.

20^2+18^2=c^2

400+324=c^2

724=c^2

take the square root of both sides

26.9m=c

to the nearest meter = 27

The Confidence Interval is 0.403 < p < 0.497

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given:

Sample proportion =  190/425

                                = 0.45

Now, [tex]\mu[/tex] = 1.96 x √[0.45 x 0.55/425]

          [tex]\mu[/tex] = 0.047

So, 95% CI:

0.45-0.047 < p < 0.45+0.047

0.403 < p < 0.497

Learn more about Confidence Interval here:

https://brainly.com/question/24131141

#SPJ5

Answer:

94 years

Step-by-step explanation:

We can approach the solution using the compound interest equation

[tex]A= P(1+r)^t[/tex]

Given data

P= $40,000

A=  $120,000

r=  1.25%= 1.25/100= 0.0125

substituting and solving for t we have

[tex]120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t[/tex]

dividing both sides by 40,000 we have

[tex](1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47[/tex]

dividing both sides by 0.005 we have

[tex]t= 0.47/0.005\\t= 94[/tex]

Answer:

Therefore, the coordinates of point Q is (2,3)

Step-by-step explanation:

Let the coordinates of Q be(a,b)

Let R be the midpoint of PQ

Coordinates of R [tex]=(\frac{4+a}{2}, \frac{3+b}{2})[/tex]

R lies on the line x + y - 6= 0, therefore:

[tex]\implies \dfrac{4+a}{2}+ \dfrac{3+b}{2}-6=0\\\implies 4+a+3+b-12=0\\\implies a+b-5=0\\\implies a+b=5[/tex]

Slope of AR X Slope of PQ = -1

[tex]-1 \times \dfrac{b-3}{a-4}=-1\\b-3=a-4\\a-b=-3+4\\a-b=-1[/tex]

Solving simultaneously

a+b=5

a-b=-1

2a=4

a=2

b=3

Therefore, the coordinates of point Q is (2,3)

Answer:

This is proved using Proof by induction method. There are two steps in this method

Let P(n) represent the given statement  ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

1. Basis Step: This step proves the given statement for n = 1

2. Induction step: The step proves that if the given statement holds for any given case n = k  then it should also be true for n = k + 1.

If the above two steps are true this means that given statement P(n) holds true for all positive n and the mathematical induction P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true.

Step-by-step explanation:

Basis Step:

For n = 1

∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] = ∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

We show that

∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]  for n = 1

Hence P(1) is true

Induction Step:

Let P(k) be true which means that we assume that:

for all k with k≥1, P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true

This is our induction hypothesis and we have to prove that P(k + 1) is also true

This means if ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] holds for n = k  then this should also hold for n = k + 1.

In simple words if P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true then ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is also true

∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex]

           ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex]                 As ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

           ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex]                 As  [tex]A_{k+1}[/tex] ⊆ [tex]B_{k+1}[/tex]

           =  ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

The whole step:

∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] =  ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

shows that the P(k+1) also holds for ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]

hence P(k+1) is true

So proof by induction method proves that P(n) is true. This means

P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true

Answer:

Approximately standard deviation= 108

Step-by-step explanation:

Let's calculate the mean of the data first.

Mean =( 330+ 274+ 492 +371 +160+ 283+ 164)/7

Mean= 2074/7

Mean= 296.3

Calculating the variance.

Variance = ((330-296.3)²+( 274-296.3)²+ (492-296.3)²+( 371-296.3)²+ (160-296.3)² (283-296.3)²+(164-296.3)²)/7

Variance= (1135.69+497.29+38298.49+5580.09+18577.69+176.89+17503.29)/7

Variance= 81769.43/7

Variance= 11681.347

Standard deviation= √variance

Standard deviation= √11681.347

Standard deviation= 108.080

Approximately 108

There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).

The second way is to plug (x,y) = (3,-2) into the given inequality to find that

[tex]y \le -x+1\\\\-2 \le -3+1\\\\-2 \le -2[/tex]

which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.

Answer:    x1=1   x2=-2  and x3=2

Step-by-step explanation:

1st   x1=1 is 1 of the roots , so

F(1)=1-1-4+4=0 - true

So lets divide x^3-x^2-4x+4 by (x-x1), i.e  (x^3-x^2-4x+4) /(x-1)=(x^2-4)

x^2-4 can be factorized as (x-2)*(x+2)

So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)

So there are 3 dofferent roots:

x1=1   x2=-2  and x3=2

Answer:

The value of x is x = 6

Step-by-step explanation:

[tex]\frac{1}{3}(12x - 24) = 16\\ 12x - 24 = 48\\12x = 48+ 24\\12x = 72\\12/12 = x\\72/12 = 6\\x=6[/tex]

Hope this helped! :)