What is the solution for x in the equation?

-11x − 30 + 6x = 0

Answer: Histograms can be used to exhibit the shape of distributions.

Step-by-step explanation:

Answer:

Histograms can be used to exhibit the shape of distributions.

Step-by-step explanation:

The area will be equal to Area = (28)(21) / 2 = 294 square inches.

To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:

Hypotenuse = 7 + base = 14 + height

Perimeter = 84 inches

The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,

Perimeter = height + base + hypotenuse = 84

We let x = height and y = base. We calculate area as follows:

84 = x + y + (7 + y)

77 = x + 2y

x = 77 -2y

The Hypotenuse is related to the other sides by the Pythagorean theorem.

Hypotenuse^2 = (x^2 + y^2)

(14 + x)^2 = x^2 + y^2

(14 + (77-2y))^2 = (77-2y)^2 + y^2

(91-2y)^2 = (77-2y)^2 + y^2

Solving for y and x

y = 28

x = 21

Area = (28)(21) / 2 = 294 square inches

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The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

So this is also going to stay the same, multiply first, divide, then you have your answer. Make sure if needed you need to round up your numbers.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Use power rule first:

\\(\log_{10}(5^2)+\log_{10}(2^3)-\log_{10}(2)\(

Now use product and quotient rule (if + in front inside goes on top and if - in front inside goes on bottom)

[\tex]\log_{10}(\frac{5^22^3}{2})\(

Reducing inside fraction;

[\tex]\log_{10}(5^22^2)\(

Simplifying inside:

[\tex]\log_{10}(100)\(

100 is a power of 10...that is 10^2=100 so final answer is 2.

\(\log_{10}(100)=2[\tex]

Answer:

Yes, he has enough pieces to wrap the present

Step-by-step explanation:

Given

\(Presents = 7\)

\(Cuts = 6\)

Required

Is there enough pieces to wrap all presents

As a general rule;

When a piece is cut in 1 place, you get 2 pieces

When a piece is cut in 2 places, you get 3 pieces

When a piece is cut in 3 place, you get 4 pieces

This implies that:

n cuts gives n + 1 pieces

i.e.

\(n \to n + 1\)

So, we have:

\(6\ cuts \to (6 + 1) pieces\)

\(6\ cuts \to 7\ pieces\)

Hence, there are enough pieces.

The function sin(x-y)/cosec(x+y)=sin²x-sin²y

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to prove that sin(x-y)/cosec(x+y)=sin²x-sin²y

Using the identity cosecx=1/sinx

We get sin(x-y)/cosec(x+y)=sin(x-y)sin(x+y)

We know sin(x+y)=sinxcosy+cosxsiny

sin(x-y)=sinxcosy-cosxsiny

Now sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)

=sin²xcos²y-cos²xsin²y

=sin²x(1-sin²y)-(1-sin²x)sin²y

=sin²x-sin²xsin²y-sin²y+sin²xsin²y

=sin²x-sin²y

Hence, we proved that sin(x-y)/cosec(x+y)=sin²x-sin²y

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Answer:

88 hrs

Step-by-step explanation:

1/3/4 = 7/4hr ; 7/4 = 1.75hr (the number of hours used to travel for 154km)

154/1.75 = 88 (the number of km van travels per hour)

Answer:

The chili dog would cost $3.15 after 10% off

Step-by-step explanation:

Divide

\(3.50/100=0.035\)

Subtract 10%

\(100-10=90\)

Multiply

\(0.035 * 90 = 3.15\)

To start an indirect proof of the statement PQ ⊕ ST, the assumption would be that PQ and ST are both true.

An indirect proof, also known as proof by contradiction, begins by assuming the opposite of what we want to prove and showing that it leads to a contradiction. In the case of the statement PQ ⊕ ST (which represents the exclusive disjunction or XOR between PQ and ST), we want to prove that either PQ or ST is true, but not both.

To begin the indirect proof, we assume that both PQ and ST are true. This assumption implies that either PQ is true and ST is false, or PQ is false and ST is true. However, since PQ and ST are mutually exclusive in an XOR statement, it follows that both PQ and ST cannot be simultaneously true. This creates a contradiction with our assumption, as we assumed both PQ and ST to be true.

By reaching a contradiction, we can conclude that our assumption is incorrect. Therefore, we can deduce that either PQ or ST is true, but not both. This indirect proof establishes the validity of the statement PQ ⊕ ST.

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Answer:

Step-by-step explanation:

Let the number of days is x.

Joseph tweets 13 times a day.

The number of tweets after x days would be:

t(x) - number of tweets after x days.

The surface area of the sphere to the nearest square foot is 2463 feet.

So, the surface area of the sphere:

Now, substitute the radius in the formula as follows:

Therefore, the surface area of the sphere to the nearest square foot is 2463 feet.

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Answer:

The price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

Step-by-step explanation:

David wants to make 10 servings, where each serving has 75 grams of rice. So, he needs a total of 10 * 75 = 750 grams of rice. the price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

The correct response is 503 acres. Around 503 acres with more than 190 bushels of maize per acre is what we would anticipate.

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

Let X serve as the random variable representing the yield of corn. The issue reveals that the formula for the random variable X's distribution is as follows:

\(X\)≅Nμ=185.2, σ=23.5

A sample of n=1200 acres is taken by a quality control inspector. The sample size is reflected by that.

The likelihood that the random variable X contains more than 190 bushels of maize per acre is also something we wish to calculate. Consequently, we seek to discover:

\(P(X > 190)\)

Additionally, we may use the z score this calculation produces:

z=X-μ/σ

If we substitute the provided values, we get:

\(z=190-185.2/0.2042\)

We desire the possibility that:

\(P(z > 0.2042)=1-P(z < 0.2042)=1-0.5809=0.4191\)

And to determine how many, it would be necessary to assume that each acre would produce more than 190 bushels of maize. The faction obtained can be multiplied by the sample size.

\(r=1200*0.4191=502.92=503\)acres

A 503acre crop with more than 190 bushels of maize per acre is what we would anticipate.

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Answer:

(D).

Step-by-step explanation:

\(A_{b}\) = A + \(A_{s}\)

(A). 12 + 16 > 20

(B). 10 + 18 < 30

(C). 4 + 5 < 12

(D). 8 + 16 = 24

Answer:

x=115°

y=65°

Hope it helped<3

x = 115° [corresponding angles]

y = 180° - x = 180° - 115° = 65° [linear pair]

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Answer:

a. 0.4 and 0.5

b. 0.46

Step-by-step explanation:

i don't know if this right, so lmk

Answer:

-3x-24

Step-by-step explanation:

9x - 3(4x+8)

Distribute

9x - 12x - 24

Combine like terms

-3x -24

Answer: -3x-24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Example
Find 55% of 200.

200 times 0.55 = 110

Answer: the answer is B

Step-by-step explanation:

if we want to find the percent of 700 people out of 4400 people, we would do 700/4400, which is equal to 0.16, or 16 percent.

Answer:

One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

Step-by-step explanation:

That's how I do it.

Step-by-step explanation:

I=prt

I=7400×(26.5/100)×1

I=$1961

total money 7400+1962= $9361

The measure of the central angle is equal to the measure of the subtended arc and is given by

a) A = 100°

b) B = 170°

c) C = 60°

Given data ,

Let the circle be represented as A , B and C

where the measure of the subtended arc is given by

A = 100°

B = 170°

C = 60°

Now , The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

And , The measure of the central angle is equal to the measure of the subtended arc

So , the measure of angles are

a) A = 100°

b) B = 170°

c) C = 60°

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There appears to be a positive correlation between shoe size and grade point average in Professor Walker's class, suggesting that students with larger shoe sizes tend to have higher GPAs.

The observation made by Professor Walker suggests a relationship between shoe size and grade point average. A positive correlation means that as one variable (shoe size) increases, the other variable (GPA) also tends to increase. In this case, the observation indicates that students with larger shoe sizes tend to have higher GPAs. However, it is important to note that correlation does not imply causation.

It is possible that the observed relationship is coincidental or influenced by other factors. Factors such as age, gender, or socioeconomic status could be associated with both shoe size and academic performance, leading to a spurious correlation. To establish a definitive causal relationship, further research and analysis would be required to account for confounding variables and determine the underlying mechanisms, if any, between shoe size and GPA.

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Take the 2nd term and minus the 1st term.

Now take the 3rd term and minus the 2nd term.

Notice that the differences are the same. Hence there is a common difference (difference of -0.5).

So it is an arithmetic sequence.

Answer:

y= 7

Step-by-step explanation:

3y+7=28

subtract 7 from both sides

3y=21

divide each side by 3

y/3=21/3

y=7

Answer:

y=7

Step-by-step explanation:

3y+7=28

Move the constant to the right

3y=28-7

Calculate

3y=21

divide both sides to get y=7

(2x + 7) + (2x) + (x + 18) = 180

5x + 25 = 180

5x = 155

x = 31 °

Based on the information provided, it appears that a study will be conducted to compare the mean weights of two populations of raccoons.

To do so, random samples will be selected from each population, and the mean weight of each sample will be calculated. By comparing the mean sample weights of the two populations, researchers can determine whether there is a significant difference in the mean weights between the two groups.

It is important to note that the use of random samples helps to ensure that the results are representative of the entire population and reduces the risk of bias in the study.

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The required probability for randomly selected students spend between $300 and $400 on clothing in a year is equal to 0.6730 or 67.30% (approximately ).

For a normal distribution with a mean (μ) of $340

And a standard deviation (σ) of $50.

Let X be the amount of money spent on clothing by a randomly chosen student.

Probability that a randomly chosen student will spend between $300 and $400 on clothing in a year,

P(300 < X < 400)

Standardize the distribution by converting the given values to z-scores, using the formula,

z = (X - μ) / σ

For the lower limit, we have,

z1 = (300 - 340) / 50 = -0.8

For the upper limit, we have,

z2 = (400 - 340) / 50 = 1.2

Area under the standard normal distribution curve between these two z-scores.

Standard normal distribution table

Probabilities, or use the properties of the normal distribution to calculate it as,

P(-0.8 < Z < 1.2)

= P(Z < 1.2) - P(Z < -0.8)

Using a standard normal distribution table we have,

P(Z < 1.2) ≈ 0.8849

P(Z < -0.8) ≈ 0.2119

Substituting these values in the above equation, we get,

P(-0.8 < Z < 1.2)

≈ 0.8849 - 0.2119

≈ 0.6730

Therefore, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is approximately 0.6730 or 67.30%.

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