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1 year ago

10

Eric created a rectangular patio using 1 foot square paving stones which are sold in batches by the Dozen the patio measures 7 f

eet by 8 feet how many batches of paving stones did Eric need

1 answer:

Verdich [7]1 year ago

6 0

Eric need 5 batches of paving stones to created his patio.

You might be interested in

Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage ea

garik1379 [7]

Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.26.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328$

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

3 0

2 years ago

1) Proiectiile catetelor unui triunghi dreptunghic pe ipotenuza au lungimile 9 cm si 25 cm. Aflati lungimea inaltimii din varful

Flauer [41]

Answer:

1) 15cm

2) left projection/h = h/right projection

Step-by-step explanation:

Question:

1) The projections of the legs of a right triangle on the hypotenuse have lengths of 9 cm and 25 cm. Find the length of the height at the top of the right angle.

2) In a right triangle the length of the hypotenuse is 34 cm, and the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75. Calculate the length of the height corresponding to the hypotenuse.

Solution

1) The length of the height of a right angle triangle is also called the altitude.

Since there are no diagrams in the question, I sent a diagram of the right angle as an attachment to the solution.

The projections of the legs are 25cm and 9cm.

Hence, the longer projection length AD = 25cm and the shorter projection length DB = 9cm

In a right triangle, the altitude (height) drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the

geometric mean of these two segments (the two projections) and it's given by:

left projection/h = h/right projection

AD/h = h/DB

25/h = h/9

Cross multiply

h^2 = 25×9

h =√225 = 15cm

The length of the height at the top of the triangle = 15cm

2) Length of hypotenuse = 34

From the question, the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75.

There is an error with the figures because the sum of the length of the projection of the legs should be equal to the hypotenuse but it isn't in this case.

To calculate the length of the height corresponding to the hypotenuse, we would use the same formula above.

left projection/h = h/right projection

To find each leg using question 1 above, each leg of the triangle is the mean proportional between the hypotenuse and the part of the hypotenuse directly below the leg.

Hypotenuse =34cm

Hyp/leg = leg/part

To find leg y, part for leg y = 25cm

34/y = y/25

y^2 = 34×25 = 850

y = √850 = 29.2cm

To find leg x, part for leg x = 9cm

34/y = y/9

y^2 = 34×9 = 306

y = √306 = 17.5cm

8 0

2 years ago

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each s

emmainna [20.7K]

Answer:

Triangle QRS is an isosceles triangle because QR = RS.

Step-by-step explanation:

option D for Edgu hope this helps :)

9 0

2 years ago

Read 2 more answers

Repeated student samples. Of all freshman at a large college, 16% made the dean’s list in the current year. As part of a class p

Dima020 [189]

Answer:

a) p-hat (sampling distribution of sample proportions)

b) Symmetric

c) σ=0.058

d) Standard error

e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Step-by-step explanation:

a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.

b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.

This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.

c) The variability of this distribution, represented by the standard error, is:

$\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058$

d) The formal name is Standard error.

e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:

$\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667$

If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

0 0

2 years ago

What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

GalinKa [24]

Options

A. UV = 14 ft and m∠TUV = 45°

B. TU = 26 ft

C. m∠STU = 37° and m∠VTU = 37°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

E. m∠UST = 98° and m ∠TUV = 45°

Answer:

A. UV = 14 ft and m∠TUV = 45°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

Step-by-step explanation:

Given

See attachment for triangle

Required

What proves that: ΔSTU ≅ ΔVTU using SAS

To prove their similarity, we must check the corresponding sides and angles of both triangles

First:

$\angle UST$ must equal $\angle UVT$

So:

$\angle UST = \angle UVT = 98$

Next:

UV must equal US.

So:

$UV = US = 14$

Also:

ST must equal VT

So:

$ST = VT = 20$

Lastly

$\angle TUV$ must equal $\angle TUS$

So:

$\angle TUV = \angle TUS = 45$

Hence: Options A and D are correct

4 0

2 years ago