Find the measure of <2.

Answer: 31.8

Step-by-step explanation:

The probability that a randomly selected point within the circle falls

in the red shaded area is; 15.9%

The area of the circle is gotten from the formula;

A = πr²

A = π * 4²

A = 50.265 cm²

Area of triangle = ¹/₂ * bh

Here b = h = 4. Thus;

A = ¹/₂ * 4 * 4

A = 8 cm²

Thus;

P(randomly selected is shaded) = 8/50.265

P(randomly selected is shaded) = 0.159 = 15.9%

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Answer:

18 cm!

Step-by-step explanation:

Answer:

y = 5x +6

Step-by-step explanation:

the slope of the given equation is 5. a slope of a line parallel has the same slope. so 5

y- -4 = 5(x - -2)

y+4 = 5x +10

y = 5x +6

Answer:

lol I hope I'm right ...

Step-by-step explanation:

minimum=2, maximum=10, Q1=3, median=6, Q3=8, IQR= 5

Answer:

106.43

Step-by-step explanation:

The difference in their account balances at the end of 3 years is $24.32

To solve the compound interest for Cody

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.04/1)(1)(3)

A = 5,000.00(1 + 0.04)(3)

A = $5,624.32

To solve for the simple interest for April

P * T * R/100

5000 * 4 * 3/100

= 60,000/100

= 600.

We add the S. I of April's investment

= 5,000 + 600

= $5600.

Therefore, the difference between their account balances is $5,624.32 - $5600 = $24.32

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Answer:

60, and m = 30, and 1 min 20.

Step-by-step explanation:

For A, the 60 is the starting point meaning that the temperature was intitally 60 degrees

For B, if we divided both sides by 2 we get the answer m = 30, meaning every minute, it was up 30 degrees.

For C, we know that in one minute it will be 90 degrees, so 60 seconds = 30 degrees. So lets divided both sides by 3 to get 10 degrees. We get 20 seconds. It will take 1 min and 20 for it to be 100 degrees.

Hopefully thats right.

Answer:

here

h=4 in

r=8in

total surface area =2πr(r+h)=2π×8(8+4)=192π or 603.18in²

Answer:

then ask your teacher happy birthday to u happy birthday to u

. happy to 6

8b+4-4b+2= 4b+6

collect the like terms and add

Answer:

21❄️....................

Answer:

Step-by-step explanation:

Let the score is x. The average is:

Answer:

Yes

Step-by-step explanation:

The octopus chose the rectangles 68% of the time. From this observation you can tell that the octopus has learned there is food under the rectangular shape. Its cognitive abilities are less than a human's, but they are able to discern a rectangle from a circle with success.

Good luck ^^

Answer:

(x-1) and (x+8).

Step-by-step explanation:

The given expression is :

[tex]x^2+7x-8[/tex]

We need to find the factors of this expression.

Product of two numbers = 8 and -1 = -8

Sum of two numbers = 8 and -1 = 7

So,

[tex]x^2+7x-8=x^2+8x-x-8\\\\=x(x+8)-1(x+8)\\\\=(x-1)(x+8)[/tex]

So, the factors of this expression are (x-1) and (x+8).

The probabilities that could complete the model and maintain a total sum of 1 are options B and E.

B: P(green) = 3/8, P(yellow) = 1/8

E: P(green) = 3/7, P(yellow) = 1/14

To determine the probabilities that could complete the model, we need to consider the sum of all probabilities. In a probability model, the sum of all probabilities should equal 1.

Given the probabilities P(red) = 2/7 and P(blue) = 3/14, let's calculate the sum:

P(red) + P(blue) = 2/7 + 3/14 = 4/14 + 3/14 = 7/14 = 1/2

Since the sum of P(red) and P(blue) is 1/2, we need to find the probabilities for P(green) and P(yellow) that, when added to 1/2, give a total sum of 1.

Looking at the answer key options:

A: P(green) = 2/7, P(yellow) = 2/7

B: P(green) = 3/8, P(yellow) = 1/8

C: P(green) = 1/4, P(yellow) = 1/4

D: P(green) = 5/21, P(yellow) = 11/21

E: P(green) = 3/7, P(yellow) = 1/14

Let's check the sums:

A: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 2/7 + 2/7 = 4/14 + 3/14 + 4/14 + 4/14 = 15/14 ≠ 1 (incorrect)

B: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 3/8 + 1/8 = 4/14 + 3/14 + 6/14 + 1/14 = 14/14 = 1 (correct)

C: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 1/4 + 1/4 = 4/14 + 3/14 + 7/14 + 7/14 = 21/14 ≠ 1 (incorrect)

D: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 5/21 + 11/21 = 6/14 + 3/14 + 10/14 + 11/14 = 30/14 ≠ 1 (incorrect)

E: P(red) + P(blue) + P(green) + P(yellow) = 2/7 + 3/14 + 3/7 + 1/14 = 4/14 + 3/14 + 6/14 + 1/14 = 14/14 = 1 (correct)

Based on the calculations, the probabilities that could complete the model and maintain a total sum of 1 are options B and E. So, the correct answers are:

B: P(green) = 3/8, P(yellow) = 1/8

E: P(green) = 3/7, P(yellow) = 1/14

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Answer:

4 4/9

Step-by-step explanation:

First, you have to set it up: 5/9 times 8/1

We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.

Next, Multiply.

5/9x8/1=40/9 as an inproper fraction

As a proper fraction, it is written as 4 4/9

Answer:

$175

Step-by-step explanation:

$100/8 hours = $12.5 hourly

$12.5 * 14 hours = $175

Answer:

A!! it does not equal 180 while the others do

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

An interior triangle always is 180 degrees. A. is the only answer that doesn't add up to 180 degrees.

Answer:

width 14 perimeter 160 (l=66 cm)

Answer:

The measure of ∠DFE is 67°.

Step-by-step explanation:

Angle GFE is a straight angle, meaning that its measure is 180°, per se.

180 - 113 = m of ∠DFE

180 - 113 = 67

Answer:

The data is a random sample from the population of interest

Step-by-step explanation:

.

Answer:

a) 3

b) 3

c) because of the permutations and combinations involved

Step-by-step explanation:

a) Determine the smallest number of cars needed

The number of cars are the same as conflict free cars

hence we can group the friends without conflict into the same car

1st car we will have : ACFI  in it

2nd car we will have : GD  in it

third care we will have : BEJH  in it

∴ number of car needed = 3

b) number of conflict free cars = 3

c) Coloring is important in the question because of the permutations and combinations involved

Answer:

<1 = <8

Step-by-step explanation:

Pair of alternate exterior angles are formed when two parallel lines are cut across by abl transversal line. The two angles are found on the other side of the parallel lines but located on opposite sides along the transversal line.

Thus, <1 and <8 are exterior angles of the parallel lines that are crossed by the transversal and they are on the alternate sides along the transversal.

Therefore, <1 and <8 form a pair of alternate exterior angles.

<1 = <8

Complete Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with[tex]\sigma^2=1000[/tex]. A random sample of 12 sample specimens has a mean compressive strength of [tex]\=x=3207psi[/tex]. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.

Answer:

[tex]CI=(3189.1,3224.9)[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=12[/tex]

Standard deviation [tex]\sigma^2=1000psi^2\\\sigma=\sqrt{1000} \\\sigma=31.6[/tex]

Sample mean [tex]\=x=3207[/tex]

Confidence level =95%

[tex]\alpha=100-95\\\alpha=0.05[/tex] significance level

From table \alpha 0.05

Gives

[tex]Z_c=1.96[/tex]  

Generally the equation for confidence interval is mathematically given by

[tex]CI=(\=x-\frac{z_c*\sigma}{\sqrt{n} } ),\=X+\frac{Z_C*\sigma}{\sqrt{12} })[/tex]

[tex]CI=(3207-\frac{1.96*31.6}{\sqrt{12} } ),3207+\frac{1.96*31.6}{\sqrt{12} })[/tex]

[tex]CI=(3189.1,3224.9)[/tex]

Answer:

p is = to 3b

Step-by-step explanation:

so i did the test a

Answer:

Since p-value ( 0.4467 ) is greater than significance level ( 0.01 )

Fail to Reject Null hypothesis H₀ at 1%.

At 1% significance level, we can conclude that, population variance is maintained at historic value.

Thus, Option ((B) At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35) is the correct answer.

Step-by-step explanation:

Given the data in the question;

sample size n = 24

Sample Standard deviation S = 0.58

Let δ represent the population standard deviation

so we will test;

H₀ : δ = √0.35 ≈ 0.5916

H₁ : δ < √0.35 ≈ 0.5916

Test Statistics;

we determine our test statistics as follows;

Z = [√(2(n-1))] × [ lnS - lnδ ] ~ N(0, 1 )

Now, Under H₀, [tex]Z_{obs[/tex] = [√(2(24-1))] × [ ln (0.58 / 0.5916) ]

= 6.7823 × -0.0198026

= -0.134

From z-table;

p-value = P( z < [tex]Z_{obs[/tex] ) = p( z < -0.134 ) = 0.4467

p-value = 0.4467

Since p-value ( 0.4467 ) is greater than significance level ( 0.01 )

Fail to Reject Null hypothesis H₀ at 1%.

At 1% significance level, we can conclude that, population variance is maintained at historic value.

Thus, Option ((B) At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35) is the correct answer.