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2 years ago

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Mathematics

1 answer:

Naily [24]2 years ago

4 0

Answer: 136 square feet

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Explanation:

The front face is a triangle with base 6 and height 4.

The area is 0.5*base*height = 0.5*6*4 = 12 square feet

The back face is also 12 square feet since the front and back faces are identical triangles.

So far we have 12+12 = 24 square feet of surface area.

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The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.

To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.

This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.

So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.

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Angles of triangle sand explain how u got each question and answer pls ! ((:

horsena [70]

Answer:

m∠1 = 41°

m∠2 = 85°

m∠3 = 95°

m∠4 = 85°

m∠5 = 36°

m∠6 = 49°

m∠7 = 96°

Step-by-step explanation:

Alright, so to start we have 2 quadrilaterals intersecting to form a triangle, which means that in the shapes with 4 angles, all angles will add up to 360°, while the triangle's angles will add up to 180°

Right off the bat, we can tell that ∠3 and ∠95° are going to be the same, because they're at a perpendicular intersection, which also means that ∠2 and ∠4 will be the same as well

Knowing the ∠3 = 95° means that ∠5 and ∠6 must add up to equal 85°, so that the whole of the triangle equals 180°

Considering that in the first quadrilateral we already have ∠90° and ∠144°, this means that ∠1 and ∠2 have to add up to 126°, to make an even 360° total

If ∠95° is supplementary to ∠2, this means ∠2 = 85°, and since ∠4 and ∠2 are the same, ∠4 also equals 85° - This leaves 41° left for ∠1, and now we can move on to the other quadrilateral

So since we know ∠4 = 85°, and we already have ∠38°, this means that ∠7 and the unmarked angle will add up to equal 237°, so that the entire shape has 360°

Since we know that ∠5 and ∠144° are supplementary, this means ∠5 is equal to 36°, which would make ∠6 = 39°

And lastly we have ∠7, which since ∠6 = 39° this means our unmarked supplementary angle must equal 141° - Now that means that ∠4 + ∠38° + ∠141° = 264° out of 360°, which leaves ∠7 to equal 96°

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2 years ago

The CEO of the Jen and Benny's ice cream company is concerned about the net weight of ice cream in their 50 ounce ice cream tubs

MissTica

Answer:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

We need to find the degrees of freedom given by:

$df = n-1= 26-1 = 25$

Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average is higher than 52 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=54.98$ represent the sample mean

$s=8.43$ represent the sample deviation

$n=26$ sample size

$\mu_o =52$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 52, the system of hypothesis would be:

Null hypothesis: $\mu \leq 52$

Alternative hypothesis: $\mu > 52$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

P-value

We need to find the degrees of freedom given by:

$df = n-1= 26-1 = 25$

Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

Conclusion

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3 years ago

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3 years ago

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Answer:

a) Standard Error = 0.010

b) 95% Confidence Interval = (0.0924 , 0.1316)

Step-by-step explanation:

a) The formula for Standard Error = √Sample Proportion (1 - sample proportion)/n

Standard Error = √p (1 - p)/n

We are told in the question that:

In a random sample of 400 people, 112 agree and 288 disagree. Estimate the standard error using 1000 samples

p = x/n

n = 1000 because we were told to use it instead of 400

x = number for people that agree = 112

p = 112/1000

p = 0.112

Standard Error = √p (1 - p)/n

= √0.112 (1 - 0.112)/1000

= √0.112 × 0.888/1000

= √0.099456 /1000

= √0.000099456

= 0.0099727629

Approximately to 3 decimal places = 0.010

Therefore, the standard error is 0.010

b) The Question above also asked that we solve for the 95% Confidence Interval

The formula =

p ± z × Standard Error

p = 0.112

z score for 95% confidence interval = 1.96

Standard Error = 0.010

Confidence Interval =

0.112 ± 1.96 × 0.010

= 0.112 ± 0.0196

0.112 - 0.0196

= 0.0924

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3x3=9

The fence is about 9 feet.

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3 years ago