ayme built a box in the shape of a rectangular prism with the dimensions shown. What is the volume of the box, in cubic inches? A rectangular prism has a length of 8 inches, a width of 2 inches, and a height of 4 inches. Use the formula V = l w h, where V represents the volume, l represents the length, w represents the width, and h represents the height. Inches cubed

By definition of tangent,

tan(2θ) = sin(2θ) / cos(2θ)

Recall the double angle identities:

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1

where the latter equality follows from the Pythagorean identity, cos²(θ) + sin²(θ) = 1. From this identity we can solve for the unknown value of sin(θ):

sin(θ) = ± √(1 - cos²(θ))

and the sign of sin(θ) is determined by the quadrant in which the angle terminates.

We're given that θ belongs to the third quadrant, for which both sin(θ) and cos(θ) are negative. So if cos(θ) = -4/5, we get

sin(θ) = - √(1 - (-4/5)²) = -3/5

Then

tan(2θ) = sin(2θ) / cos(2θ)

tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)

tan(2θ) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2θ) = 24/7

Answer:

C

Step-by-step explanation:

up one over three

Step-by-step explanation:

start at 3

Answer:

H0 : μd = 0

H1 : μd ≠ 0

Test statistic = 0.6687 ;

Pvalue = 0.7482 ;

Fail to reject H0.

Step-by-step explanation:

H0 : μd = 0

H1 : μd ≠ 0

Given the data:

Before: 15 26 66 115 62 64

After: 16 24 42 80 78 73

Difference = -1 2 24 35 -18 -9

Mean difference, d ; Σd / n

d = Σx / n = ((-1) + 2 + 24 + 35 + (-18) + (-9))

d = Σx / n = 33 / 6 = 5.5

Test statistic = (d / std / sqrt(n))

std = sample standard deviation = 20.146

Test statistic = 5.5 ÷ (20.146/sqrt(6))

Test statistic = 0.6687

The Pvalue :

P(Z < 0.6687) = 0.7482

At α = 0.05

Pvalue > α ; Hence we fail to reject H0

The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that [tex]\mu = 20 + 15 + 30 = 65[/tex]

The standard deviations are 1, 2, and 1.5 min, respectively.

This means that [tex]\sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926[/tex]

What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?

Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.

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

[tex]Z = \frac{60 - 65}{2.6926}[/tex]

[tex]Z = -1.86[/tex]

[tex]Z = -1.86[/tex] has a pvalue of 0.0314

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Answer:

31 IS YOUR ANSWER!!

Step-by-step explanation:

I would not mind the brainliest please!!

Answer:

n = 6

Step-by-step explanation:

Represent the unknown number by n.  Then 8 - n/3 = 6.

Consolidate the constants on the left side:  2 - n/3 = 0, or n/3 = 2.

Multiplying both sides by 3 results in:  n = 6

Answer:

C) 84 cm²

Step-by-step explanation:

The question is asking for the surface area of the square pyramid. So we need to get the area of all the surfaces, then add them together.

6 cm × 6 cm = 36 cm²

1/2(6 cm × 4 cm) = 12 cm² (There are 4 of these sides)

12 cm² + 12 cm² + 12 cm² + 12 cm² + 36 cm² = 84 cm²

Answer:/Step-by-step explanation:

We would apply pythagorean theorem to find the variable in each triangle.

Pythagorean theorem is given as: c² = a² + b², where c is the hypotenuse length or longest leg while a and b are the two other legs.

Thus:

a. h² = (√20)² + 4²

h² = 20 + 16

h² = 36

h = √36

h = 6 units

b. t² = 9² - (√17)²

t² = 81 - 17

t² = 64

t = √64

t = 8 units

c. h² = (√8)² + (√8)²

h² = 8 + 8

h² = 64

h = √64

h = 8

Answer:

63

Step-by-step explanation:

2(5)²+3(5)-2

50+15-2

using bodmas

65-2

63

Answer:

63

Step-by-step explanation:

Answer:

3 cups

Step-by-step explanation:

Answer:

Its 3

Step-by-step explanation:

you divide the volume value by 8

24 = 3

Answer:

9 pounds and 3 ounces

Step-by-step explanation:

Althea needs 9 pounds and 3 ounces of cold cuts for her party.

To convert ounces to pounds, divide the number of ounces by 16 since there are 16 ounces in one pound.

147 divided by 16 is equal to 9.1875, which can be rounded to 9.

Then, to find the remaining ounces, multiply the decimal part of the result (0.1875) by 16.

This is equal to 3 ounces.

Therefore, 147 ounces is equal to 9 pounds and 3 ounces.

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Answer:

The value of x is 25.83.

Step-by-step explanation:

Vertical angles:

If two angles are vertical, they have the same measure.

In this question:

Angle A has measure 5x + 6

Angle B has measure 6.2x - 25

Since they are vertical:

[tex]A = B[/tex]

[tex]5x + 6 = 6.2x - 25[/tex]

[tex]1.2x = 31[/tex]

[tex]x = \frac{31}{1.2}[/tex]

[tex]x = 25.83[/tex]

The value of x is 25.83.

from the pic above, hope it helps you

Answer: Expanded Notation Form:

300 + 70 + 2 + 0.3= 372.3

Step-by-step explanation:

Answer:

x = 28°

I hope it's helps you

Answer:

X=28

Step-by-step explanation:

(4x+3)+(2x+9)=180

6x+12=180

6x=168

X=28

Answer:

C. 0.10

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Goes to the city playoffs

Event B: Goes to the state playoffs.

In Littletown, the probability that a baseball team goes to the city playoffs is 0.20.

This means that [tex]P(A) = 0.2[/tex]

The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.50.

This means that [tex]P(B|A) = 0.5[/tex]

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1[/tex]

The correct answer is given by option C.

Answer:

the area of the triangle ABC is ,then value of a is 27cm.

Solution:

Given Data:

Area of the triangle ABC is

To Find:

Value of a?

Step 1:

Step 2:

By Law of Sines

Simplify the above expression

--- eqn 1

Step 3:

Step 4:

Substitute the A, B and C value from the given Data.

Apply the Sin theta respective value.

From the above we finally got the value of "a" which is 27 cm.

Step-by-step explanation:

Answer:

Positive 233

Step-by-step explanation:

7300-3280-2620-1167(14000/12)=233.

Answer:

V=3052.1 square units.

Step-by-step explanation:

Using the formulas

V=4

3πr^3

d=2r

Solving for V

V=1

1/6πd^3=1

1/6·3.14·18^3=3052.08

round to the nearest tenth place so your volume would be 3052.1 :)

Answer:

3052.1

Step-by-step explanation:

The formula for volume of a sphere: 4/3 x pi x r^3 (4/3 x pi x radius x radius x radius).

Here, only the diameter is shown. To find the radius, we must divide the diameter (18) by 2.

18 / 2 = 9

9 is the radius.

Now, we have our final equation:

4/3 x pi x radius x radius x radius

4/3 x 3.14 x 9 x 9 x 9 = 3052.08

(3.14 is commonly used for pi)

3052.08 rounded to the nearest tenth is 3052.1

Therefore, 3052.1 is the volume of the sphere.

The magnetic flux of the following options are; 0.072, 0.062, 0.

The magnetic flux can be calculated by the given formula;

Flux = magnetic field B x area A x cos(angle between B and normal of A)

Given;

Magnetic field B = 2.25 T

The length ℓ = 0.420 m

Flux = 2.25 * 0.42^2 * cos(angle)

Flux = 0.072 * cos(angle)

a) The perpendicular to the magnetic field Wb

So, angle = 0°, flux = 0.072 Wb

b) 60.0° from the magnetic field Wb

So, angle = 30°,

flux = 0.072*cos(30) = 0.062 Wb.

c) parallel to the magnetic field Wb

So, angle = 90°, flux = 0

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Answer:

80

Step-by-step explanation:

The area of a pyramid is given by the formula 1/3Bh.

We get the B from the area of the base of the pyramid, which is 1/2(6)(8) which is 24 inches. The height given is 10.

1/3(24)(10) is 80 inches cubed.

Answer:

43.98

Step-by-step explanation:

Answer:

The regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

Step-by-step explanation:

Given:

Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε ...........(1)

Since there can be only one of spring, summer,fall, and winter at a point in time or in a season, we will have the following when there are winter rainy days:

Spring = 0

Summer = 0

Fall = 0

Rain = 1

Substituting all the relevant values into equation (1) and equating ε also to 0, a reduced form of equation (1) can be obtained as follows:

Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0

Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0

Humidity = (β0 + β5) + β1Temperature

Therefore, the regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

The regression equation for winter rainy days is  

Humidity = β0 + β5 + β1Temperature

The regression model is given as:

Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε

To determine the regression equation for winter rainy days, we consider that:

[tex]Rain = 1[/tex]

This also means that:

[tex]Spring = 0[/tex]

[tex]Summer = 0[/tex]

[tex]Fall = 0[/tex]

ε = 0

Because each of these seasons can only happen one at a time, and the current season is winter

So, the regression equation becomes

Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0

Evaluate the products

Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0

The sum of 0 is 0. So, we have:

Humidity = β0 + β1Temperature + β5

Rewrite as:

Humidity = β0 + β5 + β1Temperature

Hence, the regression equation for winter rainy days is  

Humidity = β0 + β5 + β1Temperature

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Answer:

[tex]4\frac{1}{12}[/tex] miles.

Step-by-step explanation:

The goal of the family is to hike [tex]11 \frac{2}{3}[/tex] miles in total. Converting this to an improper fraction, we need a total of  [tex]\frac{35}{3}[/tex] miles.

On Monday the family completed [tex]2 \frac{1}{12}[/tex] miles, or [tex]\frac{25}{12}[/tex] miles.

On Tuesday the family completed [tex]2 \frac{1}{3}[/tex] miles, or [tex]\frac{7}{3}[/tex] miles.

On Wednesday the family completed [tex]3 \frac{1}{6}[/tex] miles, or [tex]\frac{19}{6}[/tex] miles.

Next, we can add the total amount of hiking the family has completed from Monday-Wednesday.

[tex]distance= \frac{25}{12} + \frac{7}{3} + \frac{19}{6}[/tex]

In order to add these values, we need to convert all of the fractions so that they have the same denominator. The least common multiple (LCM) of 12, 3, and 6 is 12, so the fractions can all be converted into having a denominator of 12.

Monday's distance [tex]\frac{25}{12}[/tex] already has a denominator of 12.

Tuesday's distance is [tex]\frac{7 * 4}{3 * 4} = \frac{28}{12}[/tex].

Wednesday's distance is [tex]\frac{19 * 2}{6 * 2} = \frac{38}{12}[/tex].

Convert the total distance goal to have a denominator of 12 as well. [tex]\frac{35 * 4}{3 * 4} = \frac{140}{12}[/tex].

Sum the total distance the family has walked on Monday-Wednesday. [tex]\frac{25}{12} + \frac{28}{12} + \frac{38}{12} = \frac{91}{12}[/tex].

Subtract this value from the total hiking distance. [tex]\frac{140}{12} - \frac{91}{12} = \frac{49}{12}[/tex]. The family needs to walk [tex]\frac{49}{12}[/tex] miles, or [tex]4 \frac{1}{12}[/tex] miles on Thursday to complete their goal.

As the question told , the goal of they hiking is reaching to the 11 2/3 hours of hiking which means :

The sum of the hours they hiking during those four days must equal 11 2/3 hours .

Suppose they hiking for x hours on Thursday so we have the following equation :

2 1/12 + 2 1/3 + 3 1/6 + x = 11 2/3

To simplify the addition and subtraction of fractions, we must find a common denominator between them ;

The smallest common multiple between the numbers 3, 6, and 12 is the denominator we want, which is 12. But because day 24 is easier to understand, I consider the common denominator of fractions to be 24.

2 + 2 + 3 + 1/12 + 1/3 + 1/6 + x = 11 + 2/3

7 + 2/24 + 8/24 + 4/24 + x = 11 + 16/24

7 + ( 2 + 8 + 4 )/ 24 + x = 11 + 16/24

7 + 14/24 + x = 11 + 16/24

Subtract sides minus 14/24

7 + 14/24 - 14/24 + x = 11 + 16/24 - 14/24

7 + 0 + x = 11 + 2/24

7 + x = 11 + 2/24

subtract sides minus 7

7 - 7 + x = 11 - 7 + 2/24

0 + x = 4 + 2/24

x = 4 + 1/12

x = 4 1/12

Answer:

B

Step-by-step explanation:

Divided 20 by .50 and got this