Each square on a grid represents 1 unit on each side. Match the numbers with the slopes of the lines.

Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.

For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.

In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):

P(x ≤ 21) = 50%

P(x ≤ 21) = 50/100

P(x ≤ 21) = 0.5.

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Answer:

the value of pi is 3.14159

A. Addition

Explanation

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete

Step 1

so, firts calculate the parenthesis

the operation in parenthesis is an addition

i hope this helps you

The reminder of 2 to the 100th power divided by 5 is 1

2 to the 100th power is:

[tex]2^{100}[/tex]  = 1,267,650,600,228,229,401,496,703,205,376

Then dividing 2 to the 100th power by 5:

1,267,650,600,228,229,401,496,703,205,376 / 5 = 253,530,120,045,645,880,299,340,641,075  (without considering the decimal value)

This tells us how many times 5 can divide 2 to the 100th power.

Next, we need to multiply the answer obtained from the division by 5 (since we used 5 to divide):

253,530,120,045,645,880,299,340,641,075 x 5 = 1,267,650,600,228,229,401,496,703,205,375

Lastly, subtracting our last answer from the value of 2 to the 100th power will give us the reminder:

1,267,650,600,228,229,401,496,703,205,376 - 1,267,650,600,228,229,401,496,703,205,375 = 1

Therefore, the reminder when 2 raised to the power of 100 is divided by 5 is  1.

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We are given a set of coordinates which are;

And the slope which is;

The equation of a line in slope-intercept form is;

Note that in this equation, the variable m is the slope (that is, the coefficient of x). we can now substitute for x, y and m into the equation above and we'll have;

We now have the values of the slope and the y-intercept as

The equation now can be written as;

ANSWER:

Answer:

-29.8

Step-by-step explanation:

4 (-1.2-4-4.75) +1+(-3)²

4 (-1.2-4-4.75) +1+(-3)²

4 (-9.95) +1+9

4 (-9.95) +1+9

-39.8 +1+9 = -29.8

The multiplication expression is given as L × w

The expression is given as N = r+ g + w + b

The final product of the expression is 200 boxes

Note that the formula determining the area of a rectangle is expressed as;

Area = lw

Where;

The area of the figure can be calculated by multiplying the length and the width and then addition of the number of boxes.

This is given as;

10( 4 + 5 + 4 + 7)

Also

L × w =  r + g + w + b

The expression L×w is a multiplication expression.

Total number of boxes vertically is the length = 20

Total number of boxes horizontally is the width = 10

Total area = L×w = 20 × 10 = 200

Then,

N= r + g + w + b

We have;

L×B =  3r + w

Hence, a multiplication expression is expression having variables that are multiplied.

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The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:

i⁰ = 1 (any number with the exponent 0 equals 1)

i¹ = i (any number with the exponent 1 is the number itself)

i² = -1 (this follows from the definition of the imaginary number, the square root of -1)

i³ = i² * i = -1 * i = -i

Now, the results start to repeat from 1 to -i:

i⁴= i² * i² = (-1) * (-1) = 1

i⁵ = i⁴ * i = 1 * i = i

i⁶ = i * i⁵ = i * i = i² = -1

i⁷ = i⁶ * i = -1 * i = -i

From that, we can follow the steps below to find the value of a power of i:

• divide the exponent by 4;

• if the rest of the division is 0, then the power equals ,i⁰ = 1,;

• if the rest of the division is 1, then the power equals ,i¹ = i,;

• if the rest of the division is 2, then the power equals ,i² = -1,;

• if the rest of the division is 3, then the power equals ,i³ = -i,.

So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:

• 649/4, has a quotient of 162 and the, rest 1,. Therefore:

i⁶⁴⁹ = i¹ = i

Thus, i⁶⁴⁹ equals i.

In linear equation, 3 number of cups will be needed to marinade 4 pounds of chicken for grill.

What are a definition and an example of a linear equation?

Here we have the data from the question:-

Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.

Marcy plans to grill 4 pounds of chicken.

So total marinade required will be:-

Total marinade  =6x4=24 ounces

Now we know that the conversion:-

1 fluid Ounce = 0.125 Cup

24 fluid ounce =0.125 Cup

Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.

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g( x ) = 2x² + 12x + 22 is the standard form of the the function g( x ) = 2( x + 3 )² + 4.

Polynomials in standard forms are written in a way that arrange the terms in descending order.

Given the data in the question.

g( x ) = 2( x + 3 )² + 4

First, we expand; ( x + 3 )² → ( x + 3 )( x + 3 )

g( x ) = 2( ( x + 3 )( x + 3 ) ) + 4

Using FOIL Method

g( x ) = 2( x² + 3x + 3x + 9 ) + 4

g( x ) = 2( x² + 6x + 9 ) + 4

Apply distributive property

g( x ) = 2( x² + 6x + 9 ) + 4

g( x ) = ( 2x² + 12x + 18 ) + 4

Add 18 and 4

g( x ) = 2x² + 12x + 18 + 4

g( x ) = 2x² + 12x + 22

Therefore, the function in standard form is g( x ) = 2x² + 12x + 22

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The most appropriate choice for perimeter of a shape will be given by-

UT = 19 ft

ST = 19 ft

RS = 19 ft

UR = 19 ft

What is perimeter of a shape?

Perimeter of a shape is the length of the boundary of the shape.

It is obtained by taking the sum of all the length of the boundary.

Here,

UT = (25 - x) ft

ST = (3x + 1) ft

RS = (13 + x) ft

UR = (4x - 5) ft

Perimeter = UT + ST + RS + UR

                = (25 - x + 3x + 1  + 13 + x +4x -5) ft

                = (7x + 34) ft

By the problem,

[tex]7x +34 =76\\7x = 76 -34\\7x = 42\\x = \frac{42}{7}\\x =6[/tex]

UT = [tex]25 - 6[/tex] = [tex]19[/tex] ft

ST = [tex]3 \times 6 + 1[/tex] = [tex]19[/tex] ft

RS = [tex]13 + 6 = 19[/tex] ft

UR = [tex]4\times 6 - 5[/tex] = 19 ft

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The volume of the cube with the shortest possible side lengths is 216 cubic inches.

If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.

side length of cube = diameter of sphere

side length of cube = 2 x radius of sphere

side length of cube = 2 x 3 inches

side length of cube = 6 inches

The volume of the cube can be calculated using the formula below.

V = s³

where V = volume and s = side length of cube

V = (6 inches)³

V = 216 cubic inches

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The chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings are very low.

In radio transmission, a radio transmitter's antenna couples electromagnetic energy into the atmosphere or other open space. Electromagnetic radio waves are caught by a receiving antenna during radio reception and coupled into a receiver for detection.

Radio waves have a low frequency, which limits their ability to deliver large amounts of data at once.

There are extremely slim odds that radio signals from Earth or messages placed on far-off space probes will ever be received by living things, it is acceptable to the state. Remember that some scientists have held this belief about the existence of extraterrestrial life for years without any convincing evidence.

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The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the Cost of the small greeting card = is $1.25 .

The Cost of the large greeting card =$4.50.

We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.

The Cost of 5 small greeting cards = 6.25

The Cost of 4 large greeting cards = 18

Then the Total cost = $6.25+ $18 =$24.25

Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.

Now, the total cost of x small and y large greeting cards will be;

Cost of x small greeting cards = 1.25x

Cost of y large greeting cards = 4.50y

Total cost = 1.25x + 4.50y

Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

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A.  P(BB) = P( GG) ,P(BG), P(GB) .1/4 the sample space and probability measure that describes the genders of the two children in the order in which they are born.

B.    = 1/2 is the probability that the other child is a boy.

C.   1/2 is the probability that the older child we have not yet seen is a boy.

A. sample space s. {BB,GG,BG,GB}

    P(BB) = P( GG) ,P(BG), P(GB) .1/4

B. P(other child is boy / at least one girl

therefore P(A/B) = P(A∩B)/P(B)      ( Additional probe)

P(B) = P (at least one girl)

      = P (GG)+P(BG)+P(GB)

      = 1/4+1/4+1/4

      = 3/4

P (A∩B) = P (One boy and one girl)

             = P (BG)+P(GB)

             = 1/4+ 1/4

            = 1/2

Therefore, P(A/B) = [tex]\frac{\frac{1}{2} }{\frac{3}{4} }[/tex] = 2/3

C. P (older child is a boy/ younger child is a girl)

   P [tex]\frac{older child\ is a\ boy}{youngerchild is a girl}[/tex]

P(BG)/P (BG)+ P (GG) = 1/4/1/4+1/4 = 1/2

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The highest cut-off interest rate is 2.66%

Given that,

Standard deviation (sigma) = 0.37

Mean percentage (Mu) = 2.28 %

P(Z > 1.04) = 0.15

z = 1.04

Using the z-score formula,

x = (z × sigma) + mu

x =  (1.04 × 0.37 )+ 2.28 = 2.66 %

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Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

f(-9) = 8(-9) + 7

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

Answer:

x+1/3

Step-by-step explanation:

Add the terms together (3x+1), then divide by how many terms there are (3), to get the average of the expressions

The error term, which refers to the sum of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

Y=αX+βρ+ϵ

where:

α,β=Constant parameters

X,ρ=Independent variables

ϵ=Error term

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Answer:

70

Step-by-step explanation:

Proportional means in a ratio.

Picking any L/W from the table works. Set that equal to 42/W.

[tex]\frac{6}{10} =\frac{42}{W}[/tex]

Solve for W.

6W = 42 * 10

6W=420

W=70

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

[tex]P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320[/tex]

where ! stands for factorial.

Always that we have an integer, let's say 2, we can rewrite it like:

This will help us when multiplying fractions. To multiply two fractions, we simply multiply the numerator with the numerator and denominator with denominator. In this case:

And then solve:

Now we can further simplify this fraction, because 14 and 4 are divisible by 2, then:

14 = 2 x 7

4 = 2 x 2

Then the final answer is:

The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 140.9 cm and a standard deviation of 1 cm, and they are regularly distributed. 22 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.

mean is N (M) (109,1.6)

Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation

P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.

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If Katerina completes a 15-mile run in 2 1/2 hours. She will complete a mile in an average of five minutes. Option B is correct.

It is described as a single number that indicates either the closed value for each entry in the set of data or the mean value for the entire set of data.

It is given that, In 2 1/2 hours, Katerina completes a 15-mile run.

We have to find the average number of minutes it takes her to run 1 mile.

15 miles = 2 1/2 hours

15 miles=5/2 hours

The unitary approach allows us to calculate the value of a single unit and then use that value to calculate the value of the required number of units.

1 miles= 5 /30 hours

1 miles = 1/6 hours

As we know that 1 hour consists of 60 minutes.

1 hours = 60 minute

1 mile = 60 / 6 minutes

1 miles = 10 minute

Thus, the average number of minutes it takes her to run 1 mile will be 10 minutes. Option B is correct.

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Answer:

994

Step-by-step explanation:

work inside the parenthesis first. 8+2 = 10 then raise 10 to the power of 3 which is 1000. subtract 6 from 1000 & you get 994

Answer:

994

Step-by-step explanation:

PEDMAS

Do the math inside the parentheses first

8+2 = 10         Now do the exponent    10^3 = 1000   Now subtract 6  = 994

In order to calculate the total spending in the town each year, first, multiply by the 70% that is spent within the town,

Also, multiply by 70% of the amount people will spend after they receive it in town,

Answer:

The total spending in the town each year is $1,960,000

The graph of the equation y = –12x – 6 is attached in the solution.

We can find the x and y intercept of the line to find make the graph.

Putting x = 0 in the given equation, we get:-

y = -12(0) - 6 = 0 - 6 = -6

Hence, the x -intercept is (0,-6).

Putting y = 0 in the given equation, we get:-

0 = -12x - 6

6 = -12x

x = 6/(-12)

x = -1/2

Hence, the y -intercept is (-1/2,0).

We can find another point on the line.

Putting x = -1 in the given equation, we get:-

y = -12(-1) - 6

y = 12 - 6 = 6

y = 6

Hence, another point on the line is (-1,6).  

Plotting these points we can graph the equation of the line.

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