what expression is equivalent to 2m (32m + 1) + 3 (53 - 2)

If z is a standard normal random variable , then the value of z for which P(Z≤z)=0.2580 is -0.65 .

A standard normal random variable is a continuous random variable that follows a normal distribution with a mean of 0 and a standard deviation of 1.

We can use a standard normal distribution table to find the value of z for which P(Z ≤ z) = 0.2580.

By using the standard normal distribution table, we can find the value that is closest to 0.2580, which is 0.2580 itself, and locate the corresponding z-value in the table,

Which is approximately z = -0.649523 ,

⇒ z ≈ -0.65 .

Therefore , the required value of z is -0.65 .

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The given question is incomplete , the complete question is

Given that z is a standard normal random variable, the value z for which P(Z≤z)=0.2580 is

b) 'The probability of success remains the same from trial to trial' is true for a binomial distribution.

A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where the probability of success remains constant from trial to trial.

The Poisson distribution, on the other hand, is a discrete probability distribution that describes the number of events occurring in a fixed interval of time or space, where the events are rare and random, and the mean number of events per interval is constant.

The number of possible outcomes in a binomial distribution depends on the number of trials and the number of possible outcomes in each trial, and there is no specific requirement for a minimum number of outcomes.

The value of T is not relevant or defined in the context of a binomial distribution.

Correct Question :

Which is true for a binomial distribution?

a) It approximates the Poisson distribution

b) The probability of success remains the same from trial to trial

c) There are ten or more possible outcomes

d) The value of T Is equal to 1.50,

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When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer:

-2.5 , -1 , 15.03 , 15.32

-10 , -6 1/2 , -1 , 0

0.02 , 0.2 , 2.02 , 2.2

Step-by-step explanation:

Answer:

-2.5 , -1 , 15.03 , 15.32

-10 , -6 1/2 , -1 , 0

0.02 , 0.2 , 2.02 , 2.2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Revenues and expenses are closed every year so that the profit or loss can be determined for the yearly period.

Answer:

A. Third quartile – First quartile

Step-by-step explanation:

The interquartile range is found by taking the third quartile minus the first quartile.  It is also found by taking the right side of the box in a box  and whisker plot and subtracting the left side of the box  in a box  and whisker plot

53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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Check the picture below.

50 minutes later, well, each cat has been running for 50 minutes, so same time for each.  Let's say the rate of A is slower so is "r" and the rate of B is twice that much or "2r".  Now, by the time 50 minutes passed, they're 750 meters apart, that means if cat A has covered "d" meters then cat B has covered that much plus 750 meters, as you see in the picture.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{meters}{distance}&\stackrel{m/min}{rate}&\stackrel{minutes}{time}\\ \cline{2-4}&\\ A&d&r&50\\ B&d+750&2r&50 \end{array}\hspace{5em} \begin{cases} d=(r)(50)\\\\ d+750=(2r)(50) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{we know that}}{d=50r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{(50r)~~ + ~~750=(2r)(50)} \\\\\\ 50r+750=100r\implies 750=50r\implies \cfrac{750}{50}=r\implies \stackrel{ \textit{\LARGE A} }{\boxed{15=r}}~\hfill~\stackrel{ \textit{\LARGE B} }{\boxed{2r=30}}\)

The likelihood that the CD rack will be organized alphabetically is 1 in 28.

The first step is to count all conceivable arrangements.

Use combinations if you want to organize 6 of the 8 CDs. Combinations can be calculated using the formula C(n, r) = n! / [r!(n - r)!!], where n denotes the total number of items and r denotes the number of items being selected. Here, n = 8 and r = 6, respectively.

C(8, 6) = 8! / [6!(8 - 6)!] = 8! / [6!2!] = 28

The six CDs can therefore be organized in 28 different ways.

Step 2: Count how many configurations lead to an alphabetical order.

When they are placed precisely in that sequence, there is only one configuration in which the CDs are organized alphabetically.

3. Determine the likelihood.

Probability equals the product of the number of successful outcomes and the total number of conceivable outcomes.

Probability equals 1/28

You want to put 6 of the 8 CDs you have in this issue in a CD rack. We discover that there are 28 different possible arrangements using combinations. Only one of these configurations causes the CDs to be arranged alphabetically. As a result, there is a 1/28 chance that the CD rack will be organized alphabetically.

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John sold 30U

Rick sold 25U

So, Rick sold 5 fewer units than John.

Hope that helps.

6000FT, is the shortest length of fence that the rancher can use.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Let the rectangular field's length be x.

rectangle field width = y

square feet of a rectangular field's area

Because length is always positive, it is always positive.

Once more, discriminate with respect to x

replace x=1500

Therefore, at x=1 500, fencing is minimal.

Change x to 1 500.

the rectangular field is 1500 feet long.

rectangle field's width is 1000 feet.

Replace the values

shortest used fence length =6000ft

Hence, 6000FT, is the shortest length of fence that the rancher can use.

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Answer:

 14 boys

Step-by-step explanation:

We know

The ratio of girls to boys is 5:2, which means for every 7 kids, there are 5 girls and 2 boys

So, 49 kids there are

2 x 7 = 14 boys

So, there are 14 boys

Answer:

A. 33 and 23

Step-by-step explanation:

33 and 23 have a sum of 56 and a difference of 10, so the answer is A. 33 and 23

Answer:

C

Step-by-step explanation:

With the same point estimate, Matthew's estimate will have a smaller margin of error due to the larger sample size and wider confidence interval.

The margin of error is influenced by the sample size and the chosen confidence level. Generally, a larger sample size leads to a smaller margin of error, and a higher confidence level leads to a larger margin of error.

Matthew's sample size is four times larger than Katrina's sample size (400 vs. 100). Assuming they obtained the same point estimate, Matthew's estimate will have a smaller margin of error compared to Katrina's estimate. This is because a larger sample size allows for more precise estimation and reduces the variability in the estimate.

Additionally, Katrina constructed a 95% confidence interval, while Matthew constructed a 99% confidence interval. A higher confidence level requires a wider interval to capture the true population parameter with a higher degree of certainty. Therefore, Matthew's estimate will have a smaller margin of error compared to Katrina's estimate.

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The statement that is true is:

Statements 1 and 3

Let's examine each statement individually:

If n is a multiple of 8, then n is a multiple of 4. This statement is true because every number that is divisible by 8 is also divisible by 4. Since 8 is a multiple of 4, any multiple of 8 will have factors of both 8 and 4. If n is a multiple of 18, then n is a multiple of 2.

This statement is also true. Any number that is divisible by 18 is also divisible by 2 because 18 contains a factor of 2. Every multiple of 18 will have at least one factor of 2.

Statement 2 is not true. If n is a multiple of 18, then n is a multiple of 9.

This statement is false because there are numbers that are multiples of 18 but not multiples of 9. For example, 18 itself is a multiple of 18 but not a multiple of 9, as 18 divided by 9 is equal to 2.

Therefore, the correct answer is c) Statements 1 and 3.

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Answer:

The value of x is 1

Step-by-step explanation:

Let us solve the question

∵ Δ PQR ≈ Δ FGH

→ From similarity, then their corresponding sides have an equal ratio

∴ \(\frac{PQ}{FG}\) = \(\frac{QR}{GH}\) = \(\frac{PR}{FH}\)

∵ PQ = 3, QR = x + 3, PR = 2

∵ FG = 6, GH = 6x + 2, FH = 4

→ Substitute them in the ratios above

∴ \(\frac{3}{6}\) = \(\frac{x+3}{6x+2}\) = \(\frac{2}{4}\)

→ By using cross multiplication between the first two ratios

∵ 3 × (6x + 2) = 6 × (x + 3)

∴ 3(6x + 2) = 6(x + 3)

∴ 3(6x) + 3(2) = 6(x) + 6(3)

∴ 18x + 6 = 6x + 18

→ Subtract 6x from both sides

∵ 18x - 6x + 6 = 6x - 6x + 18

∴ 12x + 6 = 18

→ Subtract 6 from both sides

∵ 12x + 6 - 6 = 18 - 6

∴ 12x = 12

→ Divide both sides by 12

∴ x = 1

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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Answer:

x=75

Step-by-step explanation:

Knowing that

a=72 and that

b=33 you add both to get 105

and because triangles entire angle is 180 you subtract 180 to 105

A gumball machine contains 8 blue gumballs and 8 red gumballs. two gumballs are purchased, one after the other, without replacement. The probability that the second gumball is red is 2/15.

Unravel the issue, we are able to utilize the conditional likelihood equation, which says that the likelihood of an occasion A given that occasion B has happened is rise to the likelihood of both A and B happening isolated by the likelihood of B happening:

P(A|B) = P(A and B) / P(B)

P(A|B) = P(A and B) / P(B)

where:  P(A and B) = (8/16) * (8/15) = 32/240

P(B) is the likelihood that the primary gumball isn't ruddy, which is break even with to the likelihood of selecting a blue gumball on the to begin-with draw, i.e., P(B) = 8/16

Substituting these values into the equation, we get:

P(A|B) = P(A and B) / P(B) = (32/240) / (8/16) = 2/15

thus, the likelihood that the moment gumball is ruddy, given that the primary gumball isn't ruddy, is 2/15.

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Answer: m=3

Step-by-step explanation:

3+4m+5+m=23

3+5+4m+m=23

5m+8=23

5m=15

m=3

Answer:

Step-by-step explanation:

3 + 4m + 5 + m = 23

4m + m = 23 - 3 - 5

5m = 15

m = 15 : 5

m = 3

--------------

check        (remember PEMDAS)

3 + 4 * 3 + 5 + 3 = 23

23 = 23

the answer is good

Answer:

36 cm^3

Step-by-step explanation:

Area of right triangle ends    1/2 b * h = 1/2 * 3 * 4  = 6 cm^2

area * height = volume

6 x 6 = 36 cm^3

Answer:

You can apply the formula of prism
\(= > Base * height\)
The 6 cm is the height here
You can find the base here by using the right triangle area formula
\(= > Length*width *0.5\)
which is
\(\frac{3*4}{2} *6\)

The answer is
36
make sure to apply unit
\(36cm^3\)

Answer:

It is C

Step-by-step explanation:

Answer:

\( \boxed{\sf Mass \ (M) \ of \ the \ round \ ball = 10 \ grams} \)

Given:

Volume (V) = 10 millilitres

Density (\( \sf \rho \)) = 1 gram/millilitre

To Find:

Mass (M) of the round ball

Step-by-step explanation:

Formula:

\( \boxed{ \bold{Density \: ( \rho) = \frac{Mass \ (M)}{Volume \ (V)} }}\)

\( \sf \implies Mass \ (M) = Density \ (\rho) \times Volume \ (V)\)

Substituting value of density (\( \sf \rho \)) & volume (V) in the equation:

\( \sf \implies M = 1 \times 10 \\ \\ \sf \implies M = 10 \: grams\)

\( \therefore\)

Mass (M) of the round ball = 10 grams

The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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Answer:

7%

Step-by-step explanation:

1 yr interest

2576 ÷ 4 = 644

1 yr interest rate

644 ÷ 9200 = 7

check

7% x 9200 x 4yrs = 2576