A face of a solid is

Answer:

[tex]\cos{B} = -\frac{12}{13}[/tex]

Step-by-step explanation:

For any angle B, we have the following trigonometric identity:

[tex]\sin^{2}{B} + \cos^{2}{B} = 1[/tex]

In this problem, we have that:

[tex]\sin{B} = \frac{5}{13}[/tex]

So, applying the trigonometric identity:

[tex]\sin^{2}{B} + \cos^{2}{B} = 1[/tex]

[tex](\frac{5}{13})^{2}) + \cos^{2}{B} = 1[/tex]

[tex]\cos^{2}{B} = 1 - (\frac{5}{13})^{2})[/tex]

[tex]\cos^{2}{B} = 1 - \frac{25}{169}[/tex]

[tex]\cos^{2}{B} = \frac{169}{169} - \frac{25}{169}[/tex]

[tex]\cos^{2}{B} = \frac{144}{169}[/tex]

[tex]\cos{B} = \pm \sqrt{\frac{144}{169}}[/tex]

[tex]\cos{B} = \pm \frac{12}{13}[/tex]

In the second quadrant, the cosine is negative. So

[tex]\cos{B} = -\frac{12}{13}[/tex]

Final answer:

The cosine in the second quadrant is negative, giving cos(B) = -12/13.

Explanation:

To find the value of cos(B) when an angle B is in standard position with its terminal ray in the second quadrant and given that sin(B) = 5/13, we can use the Pythagorean identity:

sin²(B) + cos²(B) = 1.

First, we square the sine value to get sin²(B):
sin²(B) = (5/13)² = 25/169.

Now we use the Pythagorean identity to find cos²(B):
cos²(B) = 1 - sin²(B) = 1 - 25/169 = 144/169.

Since angle B is in the second quadrant, the cosine value must be negative.

Therefore, cos(B) = -√(cos²(B)) = -√(144/169).

The square root of 144/169 is 12/13, and thus:
cos(B) = -12/13.

Answer:

8. 11 packets

Step-by-step explanation:

8. If the machine makes 88 pieces in 1 minute and puts 8 pieces in each snack packet 88÷8=11 so, 11 packets are filled each minute.

I cannot read 9. as it is cut off, so i can't answer it :)

Final answer:

In an economy with 100 workers who can produce either four cakes or three shirts, they can make 400 cakes or 300 shirts, respectively, when all are dedicated to one task.

Explanation:

Calculating Production Output

If an economy has 100 identical workers with each one capable of producing either four cakes or three shirts, we can calculate the total production of each good. When all workers are cooking, the number of cakes that can be produced in this economy is 400 cakes (100 workers × 4 cakes per worker).

Conversely, if all workers are sewing shirts, then the total number of shirts produced is 300 shirts (100 workers   ×3 shirts per worker).

Answer:

a) 58.32% probability that his weight will be greater than 164 pounds.

b) 76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 171, \sigma = 34[/tex]

a. find the probability that if a person is randomly selected, his weight will be greater than 164 pounds.

This is 1 subtracted by the pvalue of Z when X = 164. So

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

[tex]Z = \frac{164 - 171}{34}[/tex]

[tex]Z = -0.21[/tex]

[tex]Z = -0.21[/tex] has a pvalue of 0.4168

1 - 0.4168 = 0.5832

58.32% probability that his weight will be greater than 164 pounds.

b. Find the probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

Now [tex]n = 12, s = \frac{34}{\sqrt{12}} = 9.81[/tex]

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

By the Central Limit Theorem

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

[tex]Z = \frac{164 - 171}{9.81}[/tex]

[tex]Z = -0.71[/tex]

[tex]Z = -0.71[/tex] has a pvalue of 0.2389

1 - 0.2389 = 0.7611

76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

Answer:

The Correct answer is C

Step-by-step explanation:

because i just took it.

Answer:

c

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Because 1/1 = 1 whole and you add 5 more 1/1 and you get 6/1 so their is 6 wholes

Answer:

30 tiles

Step-by-step explanation:

SO we need to find the area of the wall so we do

8 feet * 5 feet = 40 feet squared

then we find that area in inches

40*12=480

Now we find the area of the tiles

4*4=16

So now we divide to find how many tiles are needed

480/16=30

Our answer is 30

Answer:

35.1°

Step-by-step explanation:

sin θ = 10.3 / 17.9

θ = sin⁻¹(10.3 / 17.9)

θ = 35.1°

Answer:

157.075 and yes

Step-by-step explanation: turst me

Answer: (E) H0 : µ = 10.4 vs Ha : µ < 10.4

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

From the given situation,

The recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.4 ft. This is the null hypothesis.

The biologist sunflower thinks that the mean height is shorter than reported. This is the alternative hypothesis.

Therefore, the correct null and alternative hypotheses are

(E) H0 : µ = 10.4 vs Ha : µ < 10.4

Answer:

(a) 0.85

(b) 0.7225

Step-by-step explanation:

(a) The point estimate for the proportion of all such components that are not defective is given by the number of non-defective units in the sample divided by the sample size:

[tex]p=\frac{80-12}{80}\\p=0.85[/tex]

The proportion is 0.85.

(b) Assuming that the sample is large enough to accurately provide a point estimate for the whole population, this can be treated as a binomial model with probability of success (non-defective part) p = 0.85. Since both components must be non-defective for the system to work, the probability of two successes in two trials is:

[tex]P(x=2) = 0.85^2\\P(x=2) = 0.7225[/tex]

An estimate of 0.7225 for the proportion of all such systems that will function properly.

Answer:

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Step-by-step explanation:

Given : [tex]f(x) = \frac{(3+x)}{(x-3)}[/tex]

In order to find [tex]f(a+2)[/tex] we will substitute [tex](a+2)[/tex] for [tex]x[/tex] in the given function, that is :

[tex]f(a) = \frac{(3+a+2)}{(a+2-3)}[/tex]

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Answer:

  volume is 3 1/2 units³

Step-by-step explanation:

The question asks for area, but the answers have dimensions of volume.

__

The volume is the product of the length, height, and width dimensions:

  V = LWH = (2)(1)(1 3/4) = 2 6/4 = 3 1/2 . . . . units³

The volume is 3 1/2 cubic units.

Answer:

Step-by-step explanation:

Given that,

A rectangular prism with a volume of 8 cubic units, V = 8 cubic units

The rectangular prism is filled with a cube twice.

First one

A cube with ½ length unit, we should know that a cube have equal length

Then, L = ½ units

Volume of a cube is L³

V = L³

V1 = (½)³ = ⅛ cubic units

Second cube

A cube with ⅓ length unit, we should know that a cube have equal length

Then, L = ⅓ units

Volume of a cube is L³

V = L³

V1 = (⅓)³ = 1 / 27 cubic units

So, to know number of times cube one will filled the rectangular prism

V = nV1

Where V is the volume of rectangular prism

n is the number of times the cube will be able to matched up with the volume of the rectangular prism

Then, n_1 = V / V1

n_1 = 8 / ⅛

n_1 = 64 times

Also,

n_2 = V / V2

n_2 = 8 / 1 / 27

n_2 = 8 × 27 = 216 times

So, the we need more of ⅓units and we will need (216 - 64) = 152 times

We need 152 more of ⅓units

You need 152 more cubes with side lengths of 1/3 unit than cubes with side lengths of 1/2 unit to fill a rectangular prism with a volume of 8 cubic units.

To determine how many more cubes with side lengths of 1/3 unit are needed to fill the rectangular prism compared to cubes with side lengths of 1/2 unit, we first need to find the number of each type of cube that fits into the prism.

The volume of the rectangular prism is given as 8 cubic units.

First, let's calculate the volume of one small cube:

Next, determine how many of each type of cube are needed to fill the prism:

The difference in the number of cubes needed is:

216 (1/3-unit cubes) - 64 (1/2-unit cubes) = 152 more 1/3-unit cubes.

Answer:

Required probability is 0.2262

Step-by-step explanation:

given data

mean length = 170 millimeters

standard deviation = 10 millimeters

sample n = 299

population mean by greater than = 0.7 millimeters

solution

we consider here batch of steel rod produced = x

probability that mean length sample that differ than the population mean greater than 0.7  required probability is

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - P (  [tex]\bar {x} -\mu[/tex] ≤ 0.7 )   .................1

so we take here value

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - [  P ( -0.7 ≤  [tex]\bar {x} -\mu[/tex] ≤ 0.7 ) ]

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 -  [  P (     [tex]\frac{-0.7}{\frac{10}{\sqrt{299}}}[/tex]    ≤   [tex]\frac{\bar {x} -\mu}{\frac{\sigma }{\sqrt{n}}}[/tex]    ≤    [tex]\frac{0.7}{\frac{10}{\sqrt{299}}}[/tex]    )  

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 [ P ( - 1.21  ≤  Z  ≤ 1.21 ) ]

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 ( P ( Z ≤ 1.21 ) - P ( Z ≤ - 1.21 ) )

we use here excel function that

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - { (=NORMSDiST (1.21) - (=NORMSDiST (-1.21)  }

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - ( 0.8869 - 0.1131 )

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 0.2262

so required probability is 0.2262

To find the probability that the sample mean length of steel rods differs from the population mean by more than 0.7 millimeters, we calculate the standard error, convert 0.7 mm to a z-score, and then find the two-tailed probability using the standard normal distribution.

To calculate the probability that the mean length of a sample of steel rods will differ from the population mean by more than 0.7 millimeters, we must use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed as the sample size gets larger (which holds true in this case since we have 299 rods).

We can apply this theorem to find the standard error of the mean (SEM), which is the standard deviation of the sample mean distribution, calculated as σ/√n (population standard deviation/square root of sample size).

With σ = 10 millimeters and n = 299, the SEM is 10/√299 = 0.5787 millimeters. To find the probability that the sample mean differs from the population mean by more than 0.7 millimeters, we convert 0.7 millimeters to a z-score by dividing by the SEM: z = 0.7/0.5787 = 1.2096.

Using the standard normal distribution, we find the probability for the corresponding z-score and then calculate the two-tailed probability, as we are looking for the probability that the sample mean is either above or below the population mean by 0.7 millimeters. However, to provide the exact figure, we would need a z-table or software to get the precise probability.

Finally, we find that the distribution of the sample mean will have higher probabilities closer to the population mean, as described in the provided information.

Answer:

0.011

Step-by-step explanation:

let's see so first

first you line the numbers on the right (DO NOT ALINE DECIMAL POINTS)

second, starting from on the right multiply each digit in the top number by each digit in the bottom number just as whole numbers .

after add the products

Answer:

its 280

Step-by-step explanation:

Answer:

I.

CORRECT.

II.

CORRECT.

III.

CORRECT.

IV.

CORRECT.

V.

INCORRECT.

VI.

CORRECT

Step-by-step explanation:

To understand let us restate the comparison test in simple terms.

Comparison test :

Given     [tex]\text{Series}_A[/tex]   and [tex]\text{Series}_B[/tex] such that    [tex]\text{Series}_A < \text{Series}_B[/tex] , then

1.   If    [tex]\text{Series}_B[/tex] converges then [tex]\text{Series}_A[/tex]  converges as well.

2.  If  [tex]\text{Series}_A[/tex]  diverges then [tex]\text{Series}_B[/tex]  diverges as well.

Now to give you a more intuitive idea of what is going on, think about it like this.  When   the series on top converges it is like an "upper bound" for what you have on the bottom, therefore what you have on the bottom has to converge as well.

Similarly if what you have on the bottom explotes, then what you have on top will explote as well.

That's how I like to think about that intuitively.

Now, using those results let us examine the statements.

I.

[tex]\frac{1}{n} < \frac{ln(n)}{n}[/tex]

Since the infinite sum of 1/n  diverges in fact the infinite sum of ln(n)/n does not converge.

Therefore, CORRECT.

II.

[tex]\frac{\arctan(n)}{n^3} < \frac{\pi}{2}\frac{1}{n^3}[/tex]  

Since the infinite sum of    [tex]\frac{\pi}{2}\frac{1}{n^3}[/tex]   is in fact convergent then  [tex]\frac{\arctan(n)}{n^3}[/tex] converges as well using the comparison theorem. Therefore

CORRECT.

III.

[tex]\frac{n}{2-n^3} < \frac{1}{n^2}[/tex]

Once again   [tex]1/n^2[/tex]  does converge so what you have on the bottom converges as well. Therefore

CORRECT.

IV.

[tex]\frac{\ln(n)}{n^2} < \frac{1}{n^{1.5}}[/tex]

Once again   [tex]\frac{1}{n^{1.5}}[/tex]  converges therefore since it is on top what is on the bottom converges as well. Therefore.

CORRECT.

V.

[tex]\frac{\ln(n)}{n} < \frac{2}{n}[/tex]

Now the fact that  [tex]\frac{2}{n}[/tex]    diverges does not necessarily imply that what you have on the bottom diverges. Therefore

INCORRECT.

VI.

That is correct as well since what you have on top converges therefore what you have on the bottom converges as well.

Using the normal distribution and the central limit theorem, it is found that there is a 0.1335 = 13.35% probability that the sample proportion will be less than 0.03.

In a normal distribution 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]

In this problem:

The mean and the standard error are given by:

[tex]\mu = p = 0.04[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.04(0.96)}{469}} = 0.009[/tex]

The probability that the sample proportion will be less than 0.03 is the p-value of Z when X = 0.03, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.03 - 0.04}{0.009}[/tex]

[tex]Z = -1.11[/tex]

[tex]Z = -1.11[/tex] has a p-value of 0.1335.

0.1335 = 13.35% probability that the sample proportion will be less than 0.03.

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Answer:

The measure of m∠B = 19°.

Step-by-step explanation:

Given

As we know that an angle inscribed in a semicircle is always a right angle.

So from the given diagram,

As we know that the sum of the three interior angles is equal to 180.

so

m∠A + m∠B + m∠C = 180°

71° + m∠B + 90° = 180°

m∠B = 180° - 71° - 90°

m∠B = 19°

Therefore, the measure of m∠B = 19°.

Answer:

Step-by-step explanation: 19

Answer:

37

Step-by-step explanation:

all triangle's angle measures add up to 180

180-98-45 = x

x = 37

Answer:

Step-by-step explanation:

All triangles = 180 degrees

^ That is known.

98 + 45 = 143

     ^ These 2 angles are given (98 and 45)

180 - 143 = 37

          ^ This was the total.

37 is the final answer.

I hope I helped you!

Answer:

Adding 254 to both sides.

This is an inverse operation.

On the right side of the equation, there is a -254, which you need to get rid of in order to isolate p. (You have to isolate p to find the value)

So, since it is -254, you would do +254 on BOTH sides of the equation. Hope this helps!!

The inverse operation needed to solve for p in the equation 765 = p - 254 is addition.

To solve for p in the equation 765 = p - 254, we need to isolate p on one side of the equation. To do this, we can use the inverse operation of subtraction, which is addition. By adding 254 to both sides of the equation, we get:

765 + 254 = p - 254 + 254

Simplifying the equation gives us:

1019 = p

Therefore, the inverse operation needed to solve for p is addition.

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Answer:

The values of T which satisfies the inequality are: [tex](8.8, \infty)[/tex]

Step-by-step explanation:

In the equation [tex]P= T^4+ 5T^3 + 5T^2 + 6T[/tex]

        [tex]T^4+ 5T^3 + 5T^2 + 6T-10000>0[/tex]

[tex]T^4+ 5T^3 + 5T^2 + 6T>10000\\9^4+ 5(9)^3 + 5(9)^2 + 6(9)>10000\\10665>10000[/tex]

Since 10665 is grater than 10000, the result is reasonable.

Answer: 0.66

Step-by-step explanation:

The United States senate had 57 Democrats and 43 Republicans which makes the total numerous of senators 100.

38 Democrats had served in the military while 28 Republicans has served in the military which makes the total number of senators that had served in the military 66.

Probability of a Republican senator that had served in the military will be:

Answer:52

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

6×2=12

That is how I got the answer.

Answer:

2

Step-by-step explanation:

Answer:

504 in.

Step-by-step explanation:

6 · 12 · 7 = 504

Answer:

504in^3

Step-by-step explanation:

voluke of rectangular prism formula: LWH

where l=length(7)

w=width(12)

h=height(6)

so

7*12*6=504

504in^3

Answer:

f(x) = 1-x^2

Step-by-step explanation:

The graph of f(x) is just shifted down 3 units

A shift down is a subtraction

f(x) = g(x) -3

     = 4- x^2 -3

     =1-x^2

Answer:

1 - x^2

Step-by-step explanation:

F(x) is 3 units down. So,

G(x) - 2 = 4 - x² - 3

F(x) = 1 - x²

Answer:

-10

Step-by-step explanation:

combine like terms -5x+9=59 subtract 9 from both side and get -5x=50 so x=-10

Answer:

-10

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−t+9−4t=59

−t+9+−4t=59

(−t+−4t)+(9)=59(Combine Like Terms)

−5t+9=59

−5t+9=59

Step 2: Subtract 9 from both sides.

−5t+9−9=59−9

−5t=50

Step 3: Divide both sides by -5.

−5t −5 = 50−5

t=−10

Given:

A plane can fly 1200 miles in the same time as it takes a car to go 320 miles. The car travels 110 mph slower than the  plane.

We need to determine the speed of the plane.

Speed of the plane:

Let the speed of the plane be x.

Equating the time taken by the plane and the time taken by the car using the formula,

[tex]Time=\frac{Distance}{Speed}[/tex]

Thus, we have;

[tex]\frac{1200}{x}=\frac{320}{x-110}[/tex]

Cross multiplying, we get;

[tex]1200(x-110)=320x[/tex]

Simplifying, we get;

[tex]1200x-132000=320x[/tex]

                [tex]880x=132000[/tex]

                     [tex]x=150[/tex]

Thus, the value of the speed of the plane is 150 mph

Final answer:

The speed of the plane is found by setting up an equation based on the relationship between distance, speed, and time for both the plane and the car. After setting up the equations and equating the times, we find that the plane's speed is 150 mph.

Explanation:

To find the speed of the plane, we can set up an equation based on the relationship between distance, speed, and time. Let's denote the plane's speed as x mph. Then the car's speed would be x - 110 mph. Since they travel for the same amount of time, we can write two equations:

Time for plane = 1200 miles / x mph

Time for car = 320 miles / (x - 110) mph

These two times are equal, so we set the equations equal to each other:

1200 / x = 320 / (x - 110)

To solve for x, cross-multiply and solve the resulting quadratic equation:

1200(x - 110) = 320x

1200x - 132,000 = 320x

1200x - 320x = 132,000

880x = 132,000

x = 132,000 / 880

x = 150 mph

Therefore, the speed of the plane is 150 mph.

Answer:

the answer is 3/2

Step-by-step explanation:

because when you divide it you have to do keep change flip so you change 4/9 to 9/4 and divide it by 2/3 to get 3/2 so you put it in the equation to see if it is correct

The equation is a linear function, and the value of n that makes the 2/3 times n equals 4/9 true is 2/3

The equation in the question implies that:

2/3 of n equals 4/9

This equation can be expressed as:

2/3 * n = 4/9

Multiply both sides by 3

3 * 2/3 * n = 3 * 4/9

Evaluate the product

2 * n = 4/3

Divide both sides by 2

n = 2/3

Hence, the value of n that makes the 2/3 times n equals 4/9 true is 2/3

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Answer:

248cm

Step-by-step explanation: