Given that f(x)=x^2+4x-32f(x)=x
2 +4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form.

Answer:

Height = 8

Step-by-step explanation:

Area of a triangle = [tex]\frac{Base*Height}{2}[/tex]

Say the height = x

4.5x = 36

x = 8

Answer:

a) at 5 minutes: 162 gal/min

b) at 10 minutes:  144 gal/min

c) at 20 minutes:  108 gal/min

d) at 50 minutes: 0 gal/min

Step-by-step explanation:

Considering the formula given by the volume of water remaining in the tank:

we can find the rate of water draining from the tank, (that is change in volume divided elapsed time) with the derivative of the function at the different times. Notice that this function has a decaying curvature (see attached image) of volume as a function of time, and the idea is therefore to find the slope of the tangent line at the different requested times.

So we first calculate the derivative of this function at any time 't":

[tex]V(t)=4500\,(1-\frac{1}{50} \,t)^2\\V'(t)=9000\,(1-\frac{1}{50} \,t)\,(-\frac{1}{50})\\V'(t)=-180(1-\frac{1}{50} \,t)\\V'(t)=-180+3.6\,t[/tex]

And now we estimate this derivative at the different requested points for time values:

a) at 5 minutes:  [tex]V'(5)=-180+3.6\,(5) = -162\,\,gal/min[/tex]

b) at 10 minutes:   [tex]V'(10)=-180+3.6\,(10) = -144\,\,gal/min[/tex]

c) at 20 minutes:   [tex]V'(20)=-180+3.6\,(20) = -108\,\,gal/min[/tex]

d) at 50 minutes:  [tex]V'(50)=-180+3.6\,(50) = 0\,\,gal/min[/tex]

All the negative signs preceding indicate that the remaining volume in the tank is reducing as time goes by, so the volume at which the water is draining is actually the absolute value of those numbers.

Answer:

3.29 s

Step-by-step explanation:

We are given that

Height of building=240

Initial velocity=20ft/s

The height of the ball  after t seconds is given by

[tex]h(t)=-16t^2-20t+240[/tex]

When the ball strike the ground then

h(t)=0

[tex]-16t^2-20t+240=0[/tex]

[tex]4t^2+5t-60=0[/tex]

Quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Using the quadratic formula

[tex]t=\frac{-5\pm\sqrt{25+960}}{8}[/tex]

[tex]t=\frac{-5\pm\sqrt{985}}{8}[/tex]

[tex]t=\frac{-5+31.28}{8}=3.29 s[/tex]

[tex]t=\frac{-5-31.38}{8}=-4.5[/tex]

Time cannot be negative .Therefore,

t=3.29 s

Answer:

The standard unemployment rate is of 0.0794 = 7.94%.

Step-by-step explanation:

The standard unemployment rate, as a proportion, is the number of unemployed people divided by the size of the labor force.

In this question:

Labor force: 189 million

Number of unemployed people: 15 million

What is the standard unemployment rate?

15/189 = 0.0794

The standard unemployment rate is of 0.0794 = 7.94%.

Answer:

The average number of activations per 25 minutes is 2.5.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In this question:

For 2 hours = 2*60 = 120 minutes, the mean is 16 times.

To find for 25 minutes, we use a rule of three.

120 minutes - 16 times

25 minutes - m times

[tex]120m = 12*25[/tex]

[tex]m = \frac{12*25}{120}[/tex]

[tex]m = 2.5[/tex]

The average number of activations per 25 minutes is 2.5.

Answer:

Its right and scalene.

It has a right angle and all the sides are diferent.

Answer: First 4 terms of n + 5  = 6,7,8,9

10th term = 15

Hope this is right

Step-by-step explanation:

By putting n = 1 , 2, 3 , 4 we can find first 4 terms

When n = 1

n + 5 = 1 + 5 = 6

When n = 2

n + 5 = 2 + 5 = 7

When n = 3

n + 5 = 3 + 5 = 8

When n = 4

n + 5 = 4 + 5 = 9

When n = 10

n + 5 = 10 +5 = 15

Answer:

7/8!

Step-by-step explanation:

They both can be divided by 10, so do just that. Then you are left with 7/8 which cannot be simplified.

The ratio 70:80 in its simplest form is equal to 7:8.

To simplify the ratio 70:80, we need to find the greatest common divisor (GCD) of the two numbers and then divide both numbers by the GCD.

Step 1: Find the GCD of 70 and 80:

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

The common factors of 70 and 80 are 1, 2, 5, and 10. The greatest common divisor (GCD) is 10.

Step 2: Divide both numbers by the GCD (10):

70 ÷ 10 = 7,

80 ÷ 10 = 8.

In summary, the ratio 70:80 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 10. After simplification, the ratio becomes 7:8. Simplifying ratios involves dividing both parts of the ratio by the greatest common factor to express the ratio in its simplest and most concise form.

This makes it easier to understand and work with the relationship between the quantities being compared. In this case, the simplified ratio tells us that for every 7 units of the first quantity, there are 8 units of the second quantity.

To learn more about ratio click on,

https://brainly.com/question/14636942

#SPJ2

Answer:

percentage change in weight ≈ 10%

Step-by-step explanation:

The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as

decrease in weight = original weight - new weight

original weight  = 48 kg

new weight = 43 kg

decrease in weight = 48 - 43 = 5 kg

Since the weight decrease their will be a percentage decrease in weight.

% decrease = decrease in weight/original weight × 100

% decrease = 5/48 × 100

% decrease = 500/48

% decrease = 10. 42666666667

percentage change in weight ≈ 10%

Answer:

B. 0.0043

Step-by-step explanation:

The null and alternative hypothesis of this one-tailed test are:

[tex]H_0: p_1-p_2=0\\\\H_a:p_1-p_2> 0[/tex]

The output of proportions_ztest method from statsmodels is a size-2 vector with the value of the test statistic and the P-value.

Then, if the output is (3.25, 0.0043), the P-value for this one-tailed test is 0.0043.

Answer:

C =81.64 cm

Step-by-step explanation:

The circumference of a circle is given by

C = 2*pi*r

C = 2 * 3.14 * 13

C =81.64 cm

_______________________________

Radius(r)=13 cm

Circumference of circle=?

Now,

Circumference of circle=2 pi r

=2*3.14*13

=81.64 cm

Hope it helps..

Good luck on your assignment

________________________________

Answer:

The population of interest for this student is the students whom are enrolled in statistics classes.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population of interest are all residents of New York State.

A simple random sample of 500 students was selected from all the students enrolled in statistics classes.

This means that the population of interest for this student is the students whom are enrolled in statistics classes.

Answer:

A = 27 cm²

Step-by-step explanation:

[tex]A = lw\\Where, l=10.8 cm , w = 2.5 cm\\[/tex]

Putting in the above formula

A = (10.8)(2.5)

A = 27 cm²

Answer:

the quotient is 9 because a negative divided by a negative is a positive

Answer: 525

Step-by-step explanation:

3 km =30 hm

35hm*15=525

Answer:

4

Step-by-step explanation:

[tex] \because \: f(4) = 2 \\ \therefore \: {f}^{ - 1} (f(4)) = {f}^{ - 1} (2) \\ \therefore \: 4 = {f}^{ - 1} (2) \\ \huge \red{ \boxed{{f}^{ - 1} (2) = 4}}[/tex]

Answer:

4 four

Step-by-step explanation:

hope it helps you

Answer:

Hello!

I believe this is what you are looking for:

x=3

33=27

32=9

S=Surface area

V=Volume

L=Length

R=Radius

I hope this helped.  If not, please let me know.  I will try my best again. :)

Step-by-step explanation:

Answer:

The equation is found to be: [tex]y = 50.6e^{0.16x}[/tex]

y(20) = 1241.34

Step-by-step explanation:

The given data is:

x:   3          7         11        14          17

y: 83      142      301     450      722

Now, we find sum summation values, relevant to the formula of exponential regression model, using calculator:

∑ ln y = 27.77305, ∑x ln y = 308.1494, ∑x = 52, ∑ x² = 664

and, n = no. of data points = 5

Now, we use formulae of exponential regression model to find out values of constant:

b = (n∑x lny - ∑x ∑ln y)/[n∑x² - (∑x)²]

b = [(5)(308.1494) - (52)(27.77305)]/[(5)(664) - (52)²]

b = 0.16

Now, for a;

a = (∑ln y - b∑x)/n

Therefore,

a = [(27.77305) - (0.16)(52)]/5

a = 3.9

For, α:

α = e^a = e^3.9

α = 50.6

So, the final equation of exponential regression model is given as:

[tex]y = \alpha e^{bx}\\ y = 50.6e^{0.16x}[/tex]

Now, we find value of y for x = 20:

y(20) = (50.6) e^(0.16*20)

y(20) = 1241.34

Complete question is:

A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%. In a random sample of 170 babies born in this hospital, 56 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the level of significance?

Answer:

Yes, there is enough evidence to reject the claim.

Step-by-step explanation:

We are given;

n = 170

x = 56

So, will use one sample proportion test to solve this.

p^ = x/n

p^ = 56/170

p^ = 0.3294

Since the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.

Thus;

Null Hypothesis H0: p ≠ 0.36

Alternative Hypothesis Ha: p = 0.36

Formula for test statistic = (p^ - p)/√(p(1 - p)/n)

This gives;

Test statistic = (0.3294 - 0.36)/√(0.36(1 - 0.36)/170)

Test statistic = -0.8311

From z-table and online z-calculator, the p - value is 0.203.

level of significance is; α = 0.05

Now, Since the p value < α, we reject the null hypothesis .

Thus, the claim is true

Answer:

Step-by-step explanation:

a) image attached

b) Lets do the analysis in R , the complete R snippet is as follows

x<- c(89,177,189,354,362,442,965)

y<- c(.4,.6,.48,.66,.61,.69,.99)

# scatterplot

plot(x,y, col="red",pch=16)

# model

fit <- lm(y~x)

summary(fit)

#equation is

#y = 0.4041 + 0.0006211*X

# beta coeffiecients are

fit$coefficients

coef(summary(fit))[, "Std. Error"]

# confidence interval of slope

confint(fit, 'x', level=0.95)

The results are

> summary(fit)

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5 6 7

-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***

x 6.211e-04 7.579e-05 8.195 0.00044 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05405 on 5 degrees of freedom

Multiple R-squared: 0.9307,   Adjusted R-squared: 0.9168 # model is able to capture 93% of the variation of the data

F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403 , p value is less than 0.05 , hence model as a whole is significant

> fit$coefficients

(Intercept) x

0.4041237853 0.0006210758

> coef(summary(fit))[, "Std. Error"]

(Intercept) x

3.458905e-02 7.579156e-05

> confint(fit, 'x', level=0.95)

2.5 % 97.5 %

x 0.0004262474 0.0008159042

c)

> x=c(89,177,189,354,362,442,965)

> y=c(0.40,0.60,0.48,0.66,0.61,0.69,0.99)

>

> ### linear model

> model=lm(y~x)

> summary(model)

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5 6 7

-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346

Coefficients:

Estimate Std. Error t value Pr(>|t|)    

(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***

x 6.211e-04 7.579e-05 8.195 0.00044 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05405 on 5 degrees of freedom

Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168

F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403

s_e is the Residual standard error from the model and its estimated value is 0.05405. s_e is the standard deviation of the model.  

d) 95% confidence interval

> confint(model, confidence=0.95)

2.5 % 97.5 %

(Intercept) 0.3152097913 0.4930377793

x 0.0004262474 0.0008159042

Comment: The estimated confidence interval of slope of x does not include zero. Hence, x has the significant effect on y at 0.05 level of significance.

 e)

> predict(model, newdata=data.frame(x=250), interval="confidence", level=0.95)

fit lwr upr

1 0.5593927 0.5020485 0.616737

f)

> predict.lm(model, newdata=data.frame(x=250), interval="prediction", level=0.95)

fit lwr upr

1 0.5593927 0.4090954 0.7096901

Answer:

The answer of top prism is 262

and down prism is 478

The upper figure is triangular prism.

so, we use bh+2ls+lb formula

B=5

h=3

s=4

l=19

Now,

surface area of triangular prism = bh+2ls+lb

= 5×3+2×19×4+19×5

= 262

The down figure is rectangular prism.

so, we use 2lw+2lh+2hw

l=5

h=6

w=19

Now,

The area of rectangular prism = 2lw+2lh+2hw

= 2×5×19+2×19×6+2×5×6

= 478

Answer:

368

Step-by-step explanation:

Answer:

7x -14 = jl

Step-by-step explanation:

Assuming a straight line

jm+ ml = jl

5x-8 + 2x-6 = jl

Combine like terms

7x -14 = jl

The value of the median is 25 from the dot plot because the middle value is 25 on the dot plot,

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

We have a dot plot shown in the picture.

As we can see in the dot plot there are a total of 9 dots.

4 dots left side and 4 dots right side.

One dot is left which is pointing to the value 25 at the number line.

Thus, the value of the median is 25 from the dot plot because the middle value is 25 on the dot plot,

Learn more about the median here:

brainly.com/question/21396105

#SPJ1

Here is the correct question.

The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:

                                           [tex]n[/tex]                     [tex]\bar x[/tex]                  [tex]S_x[/tex]

Pay attention                    20                 10,244            1,580

Do not pay attention        20                 8.,648            2,350

Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 ?

[tex](A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (B) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} - \dfrac{2350^2}{20}} \\ \\ \\ (C) \ 1596 \pm 2.576 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (D) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} + \dfrac{2350^2}{\sqrt{20}}) \\ \\ \\ (E) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} - \dfrac{2350^2}{\sqrt{20}})[/tex]

Answer:

[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]

Step-by-step explanation:

Given that :

significance level [tex]\alpha = \mathbf{0.01}[/tex]

From the Given data;

Using Excel with the function : TINV(0.01,19);

Critical value t* = 2.861

The margin of error can now be represented by the illustration:

Margin of error = [tex]t^* \sqrt{ \dfrac {s_1 ^2}{n_1} + \dfrac {s_2 ^2}{n_2}[/tex]

Lower Limit =  [tex](\bar x_1 - \bar x_2)- (Margin \ of \ error)[/tex]

Upper Limit =  [tex](\bar x_1 - \bar x_2)+ (Margin \ of \ error)[/tex]

Thus; the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:

[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]

The correct answer is False

Explanation:

A tessellation refers to a regular pattern created by using regular polygons; additionally, in a tessellation, there are no gaps or spaces between the polygons. Besides this, a tesselation is categorized as regular if there is only one type of polygon in all the pattern or as semi-regular if there are two or more polygons but these still form a regular pattern. According to this, the illustration below is not a semi-regular tessellation because this only includes one polygon (hexagons), and therefore this would be classified as a regular tessellation.

Answer:

B

Step-by-step explanation:

Answer:

The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.

The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

260 stickers

Step-by-step explanation:

Let Gareth's stickers be x.

Hence Cheryl sticker is 160+x;

If Cheryl gave 185 stickers

to Gareth, it means:

Cheryl has at the moment;

160 + x - 185 = x - 25

At this time when Gareth receives 185 he now has:

x+ 185

Also when he receives x +185, he has 3 times Cherry's meaning:

x+185 =3(x-25)

x + 185 = 3x -75

185 + 75 = 3x-2x

260= x

x = 260.

Hence Gareth has 260 stickers

Answer:

Step-by-step explanation:

Mean = (11.4 + 13.9 + 11.2 + 14.5 + 15.2 + 8.1 + 12.4 + 8.6 + 10.5 + 17.1 + 9.8 + 15.9)/12 = 12.4

Standard deviation = √(summation(x - mean)²/n

n = 12

Summation(x - mean)² = (11.4 - 12.4)^2 + (13.9 - 12.4)^2 + (11.2 - 12.4)^2+ (14.5 - 12.4)^2 + (15.2 - 12.4)^2 + (8.1 - 12.4)^2 + (12.4 - 12.4)^2 + (8.6 - 12.4)^2 + (10.5 - 12.4)^2 + (17.1 - 12.4)^2 + (9.8 - 12.4)^2 + (15.1 - 12.4)^2 = 89.62

Standard deviation = √(89.62/13) = 2.7

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

µ ≤ 15

For the alternative hypothesis,

µ > 15

This is a right tailed test

b) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 12,

Degrees of freedom, df = n - 1 = 12 - 1 = 11

t = (x - µ)/(s/√n)

Where

x = sample mean = 12.4

µ = population mean = 15

s = samples standard deviation = 2.7

t = (12.4 - 15)/(2.7/√12) = - 3.34

We would determine the p value using the t test calculator. It becomes

p = 0.0034

c) Assuming level of significance = 0.05.

Since alpha, 0.05 > than the p value, 0.0034, then we would reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the water from this source does meets the EPA standard. They are higher than 15ppb

Using the t-distribution, we have that:

a)

The null hypothesis is: [tex]H_0: \mu \geq 15[/tex]

The alternative hypothesis is: [tex]H_1: \mu < 15[/tex]

b) The p-value is of 0.0051.

c) Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

Item a:

At the null hypothesis, it is tested if the mean is of at least 15 ppb, that is:

[tex]H_0: \mu \geq 15[/tex]

At the alternative hypothesis, it is tested if the mean is of less than 15 ppb, that is:

[tex]H_1: \mu < 15[/tex]

Item b:

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

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

The parameters are:

In this problem, we have that [tex]\mu = 15, n = 12[/tex]. Additionally, using a calculator, the other parameters are: [tex]\overline{x} = 12.38, s = 2.93[/tex]

Hence, the value of the test statistic is:

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

[tex]t = \frac{12.38 - 15}{\frac{2.93}{\sqrt{12}}}[/tex]

[tex]t = -3.1[/tex]

The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.1 and 12 - 1 = 11 df.

Item c:

Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

A similar problem is given at https://brainly.com/question/16194574