A door wedge is 5 cm tall. Its has 3.7 cm high triangular bases with 2 congruent 5 cm sides and a 4 cm side. What is its surface area?

Answer:

D

Step-by-step explanation:

In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:

[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]

Hope this helps!

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.

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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

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:

$61.12

Step-by-step explanation:

Price of the Video game = $69.99

Discount = 18%

Discount price = 18% of $69.99

                         = $69.99*18/100

                         = $12.6

Price after Discount = Price - Discount price

                                  = $69.99 - $12.6

                                  = $57.39

Sales tax = 6.5% applied to the discounted price

                = 6.5% of $57.39

sales tax in dollars = $57.39 * 6.5/100

                               = $3.73

The amount he pays for the game = $57.39 + $3.73

                                                          = $61.12

Answer:

Please see steps below

Step-by-step explanation:

Notice the following:

(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure)  [tex]\angle 1 \,=\,\angle 5[/tex]

(b) Angles 6 and 3 are also alternate angles  between parallel lines, so they must be congruent (equal measure)  [tex]\angle 3 \,=\,\angle 6[/tex]

Therefore, instead of expressing the addition:

[tex]\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6[/tex]

we can write:

[tex]\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3[/tex]

which in fact clearly add to [tex]180^o[/tex]

Answer: 525

Step-by-step explanation:

3 km =30 hm

35hm*15=525

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

Answer:

The system has one solution.

Step-by-step explanation:

We have two equations:

y = -2x - 4

y = 3x + 3

Equalling them:

y = y

-2x - 4 = 3x + 3

5x = -7

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

And

[tex]y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}[/tex]

Replacing in the other equation we should get the same result.

[tex]y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}[/tex]

So the system has one solution.

Answer:

The answer is "[tex]58.625 cm^3[/tex]"

Step-by-step explanation:

Consider the cube volume of x =6 cm.

Substitute x = 6 cm in the volume

[tex]V= x^3\\\\ V = (6)^3\\\\ V = 216[/tex]

Therefore, whenever the cube volume

[tex]x=6 \ cm \ is \ V= 216 \ cm^3[/tex]

Then consider the cube's volume

x = 6.5 cm.

Substitute x = 6.5 cm in the volume

[tex]V_1 = x^3\\V_1 = (6.5)^3\\V_1 = 274.625 \\[/tex]   by using the calculator.

Therefore, when another cube volume

[tex]x = 6.5 cm \\\\ V_1 = 274.625 cm^3.[/tex]

The real volume error x = 6.5 cm instead of x = 6 cm is calculated as,

[tex]dV= V_1-V\\[/tex]

     [tex]=274.625-216\\=58.625\\[/tex]

Hence, the actual error in the volume when x = 6.5 cm instead of x = 6 cm is [tex]58.625 \ cm^3.[/tex]

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:

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

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:

368

Step-by-step explanation:

Answer:

x = 0.375

Step-by-step explanation:

Step 1: Simplify both sides of the equation

8x − 3 + 14 = 24x + 5

(8x) + (−3 + 14) = 24x + 5

8x + 11 = 24x + 5

- 24

-16x + 11 = 5

-11

-16x = -6

-16x/-16 = -6/-16

x = 3/8

x = 0.375

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]

Answer:

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

The correct answer is D No, Dan should reduce his discretionary spending

Explanation:

For Dan to stay on the budget he needs to spend the amount budgeted for each expense or less than the amount budgeted. This occurred in the case of the Internet, food, and rent; for example, the amount budgeted for the internet was $35 and Dan spent this money, also, the amount budgeted for food was $100 and Dan spent $95, which means he stood in the budget. However, this did not occur with discretionary spending, which refers to other non-necessary expenses, because in this case, Dan spent $140 even when the budget limit was $100. Also, this exceeds the total income considering 35 + 95 + 500+ 140 = $770, which is above the income ($750). Thus, Dan did not stay in the budget because he spent more money than expected in discretionary spending and should reduce this.

The correct answer is D. No, Dan should reduce his discretionary spending.

Hope this helps

:)

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,

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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:

volume of rectangular prism = 30 ft³

Step-by-step explanation:

The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.

volume of rectangular prism = LWH

where

L = length

W = width

H = height

volume of rectangular prism = LWH

Length = 5 ft

width = 2 ft

Height = 3 ft

volume of rectangular prism = 5 × 2 × 3

volume of rectangular prism = 10 × 3

volume of rectangular prism = 30 ft³

Answer:

x=-1/39

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

[tex]9(4a)-9(3)[/tex]

Step-by-step explanation:

[tex]36a-27[/tex]

[tex]9(4a)-9(3)[/tex]

[tex]9(4a-3)[/tex]

Answer:

it is 9(4a-3)

Step-by-step explanation:

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:

a. 336

b. 14.01%

c. 0.2%

Step-by-step explanation:

a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:

n = 8 and r = 3

we can calculate it by means of permutation:

nPr = n! / (n-r)!

replacing:

8P3 = 8! / (8-3)!

8P3 = 336

Which means there are 336 ways.

b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:

nCr = n! / (r! * (n-r)!

We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:

8C2 * 10C2 * 12C2

8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!

28 * 45 * 66 = 83160

Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)

30C6 = 30! / (6! * (30-6)! = 593775

Thus:

83160/593775 = 0.1401

In other words, the probability is 14.01%

c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:

8C6 + 10C6 + 12C6

8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!

28 + 210 + 924 = 1162

And that divide it by the total amount that we calculated the previous point, 30C6 = 593775

Thus:

1162/593775 = 0.002

In other words, the probability 0.2%

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:

(D)9.5 Units

Step-by-step explanation:

We have two chords CD and AB intersecting at E.

Using the theorem of intersecting chords

AE X EB =CE X ED

AB=AE+EB

16=10+EB

EB=16-10=6

Therefore:

AE X EB =CE X ED

10 X 6 = 4 X ED

ED =60/4 =15

Therefore:

CD=CE+ED

=4+15

CD=19

Recall that CD is a diameter of the circle and;

Radius =Diameter/2

Therefore, radius of the circle =19/2 =9.5 Units

Answer:

A score of 1920 has a z-score of 1.27.

A score of 1290 has a z-score of -0.74.

A score of 2220 has a z-score of 2.23.

A score of 1420 has a z-score of -0.32.

The score of 2220 is more than two standard deviations from the mean, so it is unusual.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is 2 or more standard deviations from the mean, it is considered unusual.

In this question, we have that:

[tex]\mu = 1521, \sigma = 314[/tex]

Score of 1920:

X = 1920. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1920 - 1521}{314}[/tex]

[tex]Z = 1.27[/tex]

A score of 1920 has a z-score of 1.27.

Score of 1290:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1290 - 1521}{314}[/tex]

[tex]Z = -0.74[/tex]

A score of 1290 has a z-score of -0.74.

Score of 2220:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2220 - 1521}{314}[/tex]

[tex]Z = 2.23[/tex]

A score of 2220 has a z-score of 2.23.

Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.

Score of 1420:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1420 - 1521}{314}[/tex]

[tex]Z = -0.32[/tex]

A score of 1420 has a z-score of -0.32.

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: