if g (x) = 2x + 2, find g (a + h) - g (a)

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:

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:

The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%

Step-by-step explanation:

Confidence interval for the proportion of people who own a tablet:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 150, \pi = \frac{120}{150} = 0.8[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.576[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841[/tex]

Percentage:

Multiply the proportion by 100.

0.7159*100 = 71.59%

0.8841*100 = 88.41%

The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%

Answer:

Vertex: (-1, 0)

Axis of Symmetry: x = -1

Step-by-step explanation:

Use a graphing calc.

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:

Step-by-step explanation:

Regular price  = $ 83

Discount  = 95% of 83

               = 0.95 * 83

              = $ 78.85

Price after discount = 83 - 78.85

                                = $ 4.15

Answer:

$4.15

Step-by-step explanation:

Multiply 83 by .05 to get the new price of $4.15. Additionally, multiply 83 by .95 to get the amount taken off ($78.85).

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:

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!

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

Step-by-step explanation:

Rate of growth equals 420/100 = 4.2 times per hour

So after t=three hours,

size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,

round to nearest unit 7409 bacteria after three hours (after initial size of 100).

Answer:

a) 100•4.2^t

b) P(3)= about 7409 bacteria

c) P’(3)= about 10,632 bacteria per hour

d) t= about 3.2 hours

Step-by-step explanation:

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

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:

x+4=0,x=−4x−7=0,x=7

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:

B. 4

Step-by-step explanation:

We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.

This is an identification problem. You look for the term and you determine the coefficient. It's just look, find, and answer.

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:

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:

We must use PEMDAS for this answer.

First, we must multiply 1000 and 10.

10,000-5000+23-93

Next, we must subtract 10,000 and 5,000

5000+23-93

Add 5000 and 23

5023-93

For our final step, subtract and you get your answer.

4,930

Answer:

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

Answer:

Step-by-step explanation:

Y=(x+4)-2

Answer:

a^2+4b^2+2a+4b

Step-by-step explanation:

(a +2b)2 + 4b² - a²​

=2a+4b+4b^2+a^2

=a^2+4b^2+2a+4b

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:

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:

Not perpendicular

Step-by-step explanation:

Convert it to y-intercept form first:

5x - 4y = -1

-4y = -5x - 1

y = 5/4x + 1/4

4x - y = -9

-y = -4x - 9

y = 4x + 9

y = 5/4x + 1/4

y = 4x + 9

From the slopes, they are not considered perpendicular because one of the line slope is not a negative reciprocal of the other line slope.

Answer:

The lines are not perpendicular.

Step-by-step explanation:

If the lines are perpendicular, the product of the slopes should be -1.

These equations are in standard form (Ax + By = C), so we can easily find the slopes through using equation: slope= - A / B

For line 5x−4y=−1,

slope = -A / B

= - 5 /- 4

= 5/4

For line 4x−y=−9

slope = -A / B

= - 4 / -1

= 4

Now multiply the slopes to find the product:

5 /4 x 4

= 5

Since 5 ≠ -1, the lines are not perpendicular.

Answer:

Left tailed test

Step-by-step explanation:

A two tailed test usually determined by the alternative hypothesis involves both the less than and the greater than option.

A left tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the less than option.

A right tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the greatest than option.

In this experiment, the null hypothesis is the average amount of time that spend watching television each week is ---

He introduces a campaign to encourage the students to watch less television and then performs a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. The alternative hypothesis would be: u < ---. This means that this test is a left tailed test.

Answer:

that's cool . . .

\is ok everyone makes mistakes

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:

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! :)

Answer:

Step-by-step explanation:

hello,

so we know y in terms of t and x in terms of t and we need to find y in terms of x

[tex]x=21t^2<=>\sqrt{x}=\sqrt{21}*t \ \ as \ \ t>=0 \ \ So\\t=\sqrt{\dfrac{x}{21}}[/tex]

and then

[tex]y=f(x)=3\sqrt{\dfrac{x}{21}}+5=\sqrt{\dfrac{9x}{21}}+5=\sqrt{\dfrac{3x}{7}}+5[/tex]

hope this helps

Answer: a= 3x and b= 7

Step-by-step explanation:

^^