Is it

1.A

2.B

3.C

4.D

72 millimeters is equal to 2.83 inches.

Length is a measure of the distance between two points. There are different units of measurement for length, one of which is millimeters (mm) and another is inches (in). In order to convert from one unit to another, we use a conversion factor.

Here's how you convert 72 millimeters to inches:

1 inch = 25.4 millimeters

So, to convert 72 millimeters to inches, we divide by the conversion factor:

72 mm / 25.4 mm/in = 2.83 in

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The relative frequency of selecting a diamond given the number of trials is 30%.

Relative frequency = (number of diamonds picked in the trial/ total number of trials) x 100

(12/40) x 100 = 30%

Therefore, 30% is the relative frequency of the selecting a diamond.

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Complete question:

A card was selected at random from a standard deck of cards. The suit of the card was recorded, and then the card was put back in the deck. The table shows the results after 40 trials.

Outcome - Club | Diamond | Heart | Spade

Number of trials- 8 | 12 | 11 | 9

What is the relative frequency of selecting a diamond?

A. 23%

B. 25%

C. 30%

D. 42%

Answer:

you answer will be ∠JKH=129°

Step-by-step explanation:

hope it helps..

have a great day!!

Answer:

k = 3   or k = -3

Step-by-step explanation:

|4k|=12

There is a positive and a negative solution

4k =12 or 4k = -12

k = 3   or k = -3

Answer:

±3

Step-by-step explanation:

4k=12

-4k=12

k = 3

k = -3

k = ±3

Answer:

64 divided by 4=16

144 divided by 9=16

Step-by-step explanation:

No, to construct a confidence interval, the population should be is approximately normal.

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, the population is approximately normal before constructing a confidence interval.

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Answer:

15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.

Step-by-step explanation:

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

In this question, we have that:

\(\mu = 26, \sigma = 3\)

Approximately what percentage of her shots will travel less than 23 feet?

This is the pvalue of Z when X = 23. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{23 - 26}{3}\)

\(Z = -1\)

\(Z = -1\) has a pvalue of 0.1587.

15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.

Answer:

145000x2

=answer

then

answer×2

= final answer

Answer:

580,000 people

Step-by-step explanation:

First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.

48÷24=2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

145,00022=580,000

That calculation could also be written with exponents:

145,000 x 2^2=580,000

After 48 years, the population will be 580,000 people.

The amount of fertilizer Debra needs is 14 cups.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

Debra's rectangular vegetable garden measures 9 1/3 yard by 12 yard.

Area of a rectangle = Length × Width

Area of the rectangular garden = 12 × 9 1/3

                                                    = 12 × 28/3

                                                    = 112 square yard

Number of cups of fertilizer needed for 1 square yard = 1/8 cups

Number of cups of fertilizer needed for 112 square yard = (1/8) × 112

                                                                                             = 14 cups

Hence 14 cups of fertilizer are needed for the whole garden.

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The Expression that have a product greater than 4 is one hundred  and one hundredths times four , the correct option is (d).

In the question ,

four expressions are given as

(a) four times ninety-nine hundredths

= 4 × 99/100

= 4 × 0.99

= 3.96

(b) four times eight-eighths

= 4 × 8/8

= 4 × 1

= 4

(c) three-fourths times four

= 3/4 × 4

= 3

(d) one hundred  and one hundredths times four

= 1.01 × 4

= 4.04

Therefore , The Expression that have a product greater than 4 is one hundred and one hundredths times four .

The given question is incomplete , the complete question is

Which of the following expressions will have a product greater than 4?

(a) four times ninety-nine hundredths

(b) four times eight-eighths

(c) three-fourths times four

(d) one hundred and one hundredths times four

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Answer:

A = 2.5434 C = 5.652

Step-by-step explanation:

A = 0.9 times 0.9 times 3.14

C = 2 times 3.14 times 0.9

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

We know that ,

\(\qquad\underline{ Area \: of \: circle\: = \: \pi \: r^{2}}\)

\(\\\therefore \: area = \frac{22}{7} \times 0.9 \times 0.9 \\ \\ \implies \: area = \frac{17.82}{7} \\ \\ \implies \: area = 2.55 \: yards {}^{2} \: (approx.)\)

also ,

\(\qquad\underline{Circumference \:of \: circle\:=\:2 \pi \: r}\)

\(\\\therefore \: circumference = 2\pi \: r \\ \\ \implies \: circumference = 2 \times \frac{22}{7} \times 0.9 \\ \\ \implies \: circumference = \frac{39.6}{7} \\ \\ \implies \: circumference = 5.66 \: yards \: (approx.)\)

hope helpful :)

Answer: 34

Step-by-step explanation:

There are 30.48 centimeters in a foot.

This conversion factor is derived from the definition of a foot, which is a unit of length in the imperial and US customary measurement systems. One foot is equal to 12 inches, and one inch is equal to 2.54 centimeters.

Therefore, to convert feet to centimeters, we simply multiply the number of feet by 12 to get the number of inches, and then multiply the number of inches by 2.54 to get the number of centimeters. For example, 6 feet is equal to 72 inches, and 72 inches is equal to 182.88 centimeters (72 x 2.54 = 182.88).

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Answer:

y=2x+10

Step-by-step explanation:

the picture has the answer

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The required answer is Sₙ = -2 (1 - (-3)^n) / (1 + 3) = (3^(n + 1) - 1) / 2.

Explanation:-

Given a geometric sequence with g₃ = 4/3, g₇ = 108, the value of r and g₁, the specific formula for gₙ, and g₁₁ will be determined. The formula for the geometric sequence is gₙ = g₁ × rⁿ⁻¹.As a result, substituting n = 3, g₃ = 4/3, and n = 7, g₇ = 108,  g₃ = g₁ × r²⁻¹ = g₁ × r = 4/3And g₇ = g₁ × r⁶⁻¹ = g₁ × r⁵ = 108. In comparison to the first equation, this may be simplified to r = (4/3)/g₁. Again, substituting the above value of r into the second equation, g₁(4/3)/g₁⁵ = 108, g₁ = (4/3) / 2⁵⁻¹ = 2/5.

Specific formula for the geometric sequence gₙ = (2/5) × (4/3)ⁿ⁻¹.So, g₁₁ = (2/5) × (4/3)¹⁰ = 174.016. Sum of the terms of the geometric sequence -2,6,-18,..,486: -2+6-18+..+486 is requested to be written in summation notation. Since the first term is -2 and the common ratio is r = -6/2 = -3,  write this sequence in summation notation as follows:∑ (-2) × (-3)^k where k = 0 to n-1 is the general formula for a geometric sequence with first term -2 and common ratio -3.

Summing this series from k = 0 to k = n-1 gives the sum of the first n terms of the sequence. The sum of the terms is given by the  formula: Sₙ = a(1 - rⁿ) / (1 - r)Plugging in the values of a = -2 and r = -3, we get: Sₙ = -2 (1 - (-3)^n) / (1 + 3) = (3^(n + 1) - 1) / 2.

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Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

Answer:

\( \frac{3}{4} x\)

Step-by-step explanation:

because form one corner of the square to the other it goes to the right 3 and Up by 4 so the slope is 3 / 4x

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

STEP 2: Plot these points

STEP 3: Get the new points from the given function

STEP 4: Plot these new points also

Hence, the type of mapping here is One-to-One

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:

X' = AX, where X = [x y], A = [22 60; -6 -16]

The matrix exponential of A can be calculated as follows:

\(e^{(At)}\) = I + At + \(\frac{(At)^{2}}{2!}\) + \(\frac{(At)^{3}}{3!}\) + ...

where I is the identity matrix and t is the variable of integration.

We can substitute A and t = 1 into the formula to get:

\(e^{A}\)= I + A + \(\frac{(A)^{2}}{2!}\) + \(\frac{(A)^{3}}{3!}\)+ ...

= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...

= [1 + 22 + \(\frac{44}{2!}\) - \(\frac{256}{3!}\)*60 + \(\frac{192}{2!}\) - \(\frac{768}{3!}\);

-6 + \(\frac{(-6)}{2!}\) + \(\frac{96}{3!}\) - 16 + \(\frac{(-104)}{2!}\)+ \(\frac{272}{3!}\)]

= [\(\frac{29}{3}\) \(\frac{102}{3}\);

\(\frac{-13}{3}\)  \(\frac{-4}{3}\) ]

Now we can use the initial conditions to find the constants of integration. We have:

X(0) = [x(0) y(0)] = [5 3]

So,

[\(e^{A}\)] [\(c_{1}\)] = [5]

[\(c_{2}\)] [3]

Multiplying both sides by the inverse of \(e^{A}\), we get:

[\(c_{1}\)] = [29/3 102/3]^(-1) [5]

[\(c_{2}\)] [-13/3 -4/3] [3]

Solving this system of linear equations, we get:

\(c_{1}\) = -4/3

\(c_{2}\) = 2/3

Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

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Ozone can be both harmful and beneficial to health, depending on its location in the atmosphere and the levels at which it is present.

In the stratosphere (the layer of the atmosphere that is located about 10-50 kilometers above the Earth's surface), ozone is a beneficial gas that protects life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. However, at ground level, ozone can be harmful to health, particularly for people with respiratory problems such as asthma.

Exposure to high levels of ozone can irritate the respiratory system and cause coughing, throat irritation, and chest pain. It can also worsen bronchitis, emphysema, and other lung diseases. Ozone can also reduce lung function and inflame the linings of the lungs, leading to more serious health problems.

It is important to note that ground-level ozone is not emitted directly into the air, but is formed when pollutants from sources such as vehicle exhaust, power plants, and industrial facilities react with sunlight and heat.

Therefore, Ozone can be both harmful and beneficial to health.

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Answer:

thxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Step-by-step explanation:

The probability that a randomly selected student is in music/drama is 25%

From the table, we have the following values

Music/Drama = 7 + 13 + 5 = 25

Total = (20 + 20 + 25 + 7 + 13 + 5 + 3 + 2 + 5) = 100

The probability is then calculated as:
P = Music/Drama / Total

So, we have:

P = 25/100

Express as percentage

P = 25%

Hence, the probability that a randomly selected student is in music/drama is 25%

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Answer:

z=31°

Step-by-step explanation:

32°+117°+z=180°{ sum of angle of triangle}

z=180-149

z=31°

Answer:

31 degrees = x

Step-by-step explanation:

a triangle's sum is 180 degrees

let's form an equation that allows us to work backwards and find this

add the other two angle measures to x and let the sum be 180

32+117+x=180

31 is the difference and therefore the missing angle measure

The approximate probability that the baggage limit will not be exceeded on the particular airplane is approximately 0.033, or 3.3%.

To calculate this probability, we need to use the concept of the standard normal distribution. We can convert the given mean and standard deviation of the individual passengers' checked-in baggage weight into a standard normal distribution by applying the formula:

Z = (X - μ) / σ

where Z is the standard score, X is the individual baggage weight, μ is the mean weight, and σ is the standard deviation.

In this case, the maximum allowable weight of the checked baggage for the airplane is 6,000 pounds, and the capacity of the airplane is 125 passengers. So the maximum allowable weight per passenger is 6,000 / 125 = 48 pounds.

Now, we need to find the probability that the baggage weight of a randomly selected passenger is less than or equal to 48 pounds. We can convert this value into a standard score by substituting the values into the formula:

Z = (48 - 42) / 25 = 0.24

We can then look up the probability associated with this standard score in the standard normal distribution table or use a statistical calculator to find that the probability is approximately 0.590.

Since there are 125 passengers on the plane, we need to calculate the probability that all of them have baggage weights less than or equal to 48 pounds. This is done by raising the individual probability to the power of the number of passengers:

P = 0.590^125 ≈ 0.033

Therefore, the approximate probability that the baggage limit will not be exceeded on the particular airplane is approximately 0.033, or 3.3%.

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