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expeople1 [14]
3 years ago
14

What is the area of the trapezoid to the nearest tenth? PICTURE BELOW ⬇⬇⬇⬇

Mathematics
1 answer:
Nastasia [14]3 years ago
6 0

Answer:

  62.4 ft²

Step-by-step explanation:

The unmarked horizontal dimension at the bottom of the triangle is ...

  (8 ft)sin(30°) = 4 ft

The unmarked vertical dimension of the triangle (the height of the trapezoid) is ...

  (8 ft)cos(30°) ≈ 6.93 ft

Then the area of the trapezoid is given by the formula ...

  A = (1/2)(b1 +b2)h

  A = (1/2)((4 ft+7 ft) +(7 ft))(6.93 ft) ≈ 62.4 ft²

_____

The mnemonic SOH CAH TOA can remind you of the relationships between right triangle dimensions and angles.

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse×Sin = Opposite

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse×Cos = Adjacent

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Find the value of x 4x + 3 = -5x + 21​
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4x + 3 = -5x + 21

9x + 3 = 21

9x = 18

x = 2

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Step-by-step explanation:

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2 years ago
Hector is rewriting the expression 7 Superscript 11 in expanded form. How many terms will be multiplied in his rewritten express
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Answer:11

Step-by-step explanation:just took the quiz <3

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K is the midpoint of PQ, P has
Pachacha [2.7K]

Answer:

Coordinates of Q (x_2,y_2) \:are\: \mathbf{(7,16)}

Option D is correct option.

Step-by-step explanation:

We are given:

K is the midpoint of PQ

Coordinates of P = (-9,-4)

Coordinates of K = (-1,6)

We need to find coordinates of Q  (x_2,y_2)

We will use the formula of midpoint: Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

We are given midpoint K and x_1,y_1 the coordinates of P we need to find x_2,y_2 the coordinates of Q.

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\(-1,6)=(\frac{-9+x_2}{2},\frac{-4+y_2}{2})\\

Now, we can write

-1=\frac{-9+x_2}{2}, 6=\frac{-4+y_2}{2}\\Simplifying:\\-2=-9+x_2\:,\: 12=-4+y_2\\-2+9=x_2\:,\: 12+4=+y_2\\x_2=7\:,\:y_2=16

So, we get coordinates of Q (x_2,y_2) \:are\: \mathbf{(7,16)}

Option D is correct option.

6 0
3 years ago
Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The
kifflom [539]

Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Hope this Helps!!!

8 0
3 years ago
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