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The sum of two numbers is 57 . The larger number is 9 more than the smaller number. What are the numbers?
Larger number:
Smaller Number:
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The equation of the linear function in slope intercept form is;

y = -0.5x + (-5)

The equation of a line in slope intercept form is expressed as;

y = mx + c

where;

m is slope

c is y-intercept

From the given table, we can see that the slope is;

m = (y2 - y1)/(x2 - x1)

m = (-4.5 - (-4))/(-1 - (-2))

m = -0.5/1

m = -0.5

At x = 0, y = -5 and so the y-intercept is -5. Thus the equation is;

y = -0.5x + (-5)

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The number of bricks that will be used for the entire job would be = 1000 bricks.

The amount of bricks which will be used by the Carmona Construction Company for brick patio can be calculated as follows;

The amount of rows that has been installed = 30 rows

The amount of bricks that makes up the installed rows = 600 bricks.

The amount of uninstalled rows = 20

The amount of bricks that would be required to install the remaining 20 rows ;

30 rows = 600

20 rows = X

Make X the subject of formula

X = 20×600/30

X = 12000/30

X= 400 bricks

Therefore, the total brick that will be required = 400+600 = 1000 bricks.

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The expression which is equivalent to 3x² - 10x - 8 is (x - 4)(3x + 2).

The correct answer option is option C

3x² - 10x - 8

check all that applies:

(3x - 2)(x - 4)

= 3x² - 12x - 2x + 8

= 3x² - 14x + 8

(3x - 4)(x - 2)

= 3x² - 6x - 4x + 8

= 3x² - 10x + 8

(x - 4)(3x + 2)

open parenthesis

= 3x² + 2x - 12x - 8

= 3x² - 10x - 8

(3x - 4)(x + 2)

= 3x² + 6x - 4x - 8.

collect like terms

= 3x² + 2x - 8

Therefore, (x - 4)(3x + 2) is equivalent to the expression 3x² - 10x - 8

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Answer:

21

Step-by-step explanation:

We can use Pythagorean theorem a^2 + b^2 = c^2

a = 20

b = x

c = 29

20^2+b^2=29^2

resulting our b value being 21

When two finite populations are connected by migration , then (b) Fst decreases to 0 .

The Fixation Index denoted as Fst ,  is a measure of population differentiation, which is used to quantify the level of genetic differentiation between two populations.

The Fst ranges from 0 to 1, where 0 indicates complete gene flow between two populations and 1 indicates complete genetic isolation.

If the migration rate is 2% per organism per generation, over time this will lead to a reduction in genetic differentiation between the populations, and the Fst value will decrease towards 0.

This is because the exchange of genetic material will reduce the amount of variation that is unique to each population, which leads to an increase in the genetic similarities between the populations.

The given question is incomplete , the complete question is

What happens to Fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection) ?

(a) Fst increases to 1

(b) Fst decreases to 0

(c) Fst stays moderate, near 0.5

(d) Fst wanders around randomly between 0 and 1 forever  .

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The expression for the perimeter of the triangle is 6x + 15 units.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, an art class is making a mural for their school which has a triangle drawn in the middle.

Let x represent the bottom of the triangle.

One side if the triangle is 12 more than four times the length of the bottom of the triangle, hence:

Length of the side = 4x + 12

The last side is 3 more than the bottom of the triangle, hence:

Length of the side = x + 3

Perimeter of the triangle = x + (4x + 12) + (x + 3)

Perimeter = 6x + 15 units

Therefore, the expression for the perimeter of the triangle is 6x + 15 units.

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The wechsler intelligence scale has a mean of 100 and a standard deviation of 15.  the z score that corresponds to an iq score of 115 is 1.

To calculate the Z score, you subtract the mean from the score and divide it by the standard deviation. In this case, 115-100=15, and 15/15=1.  A Z score of 1 indicates that the score is one standard deviation above the mean. This means that a score of 115 is higher than 84% of the population. It is in the top 16% of scores.

This score is considered to be in the high average range on the Wechsler Intelligence Scale.  The Z score can be interpreted in a variety of ways. It can be used to compare scores or to see how far a score is from the mean. It also can be used to compare scores across different tests. For example, a Z score of 1 on the Wechsler Intelligence Scale could be compared to a Z score of 1 on another test to see how the scores compare.

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The length of the rectangle in centimeters is 15.60 cm.

The correct way to report the length of the rectangle in centimeters is 15.60 cm. To calculate the length of the rectangle, we must first calculate the distance between the two edges of the rectangle. To do this we can use the formula Distance = Final Position - Initial Position. Therefore, the distance between the two edges of the rectangle is 15.600 cm - 0 cm = 15.600 cm. This is the length of the rectangle, so the correct way to report the length of the rectangle in centimeters is 15.60 cm.

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The perimeter of the playground is 92 meters

The figure is added as an attachment

To calculate the perimeter, we simply add the side lengths of the playground

i.e. Perimeter = Sum of side lengths

Using the above as a guide, we have the following:

Perimeter = 10 + 14 + 10 + 10 + 6 + 6 + 6 + 14 + 6 + 10

Evaluate the like terms

Perimeter = 92

Hence, the perimeter is 92 meters

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Answer:

The mean is 8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

add all numbers together and divide by how many numbers there are so:

8+12+4+3+14+1+9+13=64

64÷8=8

Feel free to ask me any questions if you don't understand it :)

Answer:

O up to the left, down to the right

Step-by-step explanation:

See attached graph.  As x becomes negative, x^3 will always be negative.  But the minus sign in -x^3 mean it will go in the positive direction as x gets smaller (below 0).  The same logic tells us that when x is positive, the -x^3 term will always be negative,  As x increases, the term -x^3 rapidly decreases.

The probability that none are mechanical engineering majors is 0.51.

The number of students who are not mechanical engineering majors is 100 - 49 = 51. The probability of choosing a student who is not a mechanical engineering major in one draw is 51/100. The probability of choosing five students in a row who are not mechanical engineering majors is (51/100)^5. Thus, the answer is (51/100)^5 = 0.1517816.

Probability refers to potential. From 0 to 1 is used to express the value. To determine how likely an event is to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. The complete number of possibilities that can occur should be known before calculating the likelihood that a certain event will occur.

The complete question is:-

In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?

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The probability of the sample having a average gas mileage between 27 and 29 miles per gallon will be 0.0116.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

In 2015, new cars had an average fuel efficiency of 27.9 miles per gallon with a standard deviation of 6.8 miles per gallon. a sample of 30 new cars is taken.

Then the probability the sample has a mean gas mileage between 27 and 29 miles per gallon will be

The value of the z-score at x = 27, we have average as

The value of the z-score at x = 29, we have

z= 0.16

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Stratified Random Sampling is used when dividing a population into subgroups so that a random sample from each subgroup can be collected. (option 3)

Stratified Random Sampling is a type of probability sampling where the population is divided into subgroups (or strata) based on some important characteristic. The purpose of stratifying the population is to ensure that each subgroup is represented in the sample, so that the results of the study can be more accurately generalized to the larger population.

After dividing the population into strata, a random sample is selected from each stratum. This approach is used when there is heterogeneity within the population and it is important to ensure that each subgroup is adequately represented in the sample. This method can result in a more precise estimate of population parameters compared to simple random sampling, as it ensures that each subgroup is proportionately represented in the sample.

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Complete Question:

when dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

The probability that the hand contains exactly 3 face cards is 0.1503.

Combinations of 7 cards out of a choice of 52.

52!/(45! *7!)= 52*51*50*49*48*47*46/7*6*5*4*3*2 = 133,784,560

Combinations of 3 face cards out of 12

12*11*10/3*2 = 220

Combinations of 4 non-face cards out of 40

40*39*38*37/4*3*2 = 91,390

Combinations of 5 face cards and 2 non-face cards

220 * 91,390 = 20,105,800

So the probability is 20,105,800/133,784,560 or 0.1503

Probability theory is the theory used to model uncertainty. Probability value o events show how likely it is the event will occur with an interval of values between zero up to one. However, probability theory can only used for events that have information that complete.

For events that have no information complete can be represented by imprecise probability. One model of imprecise probability is the set-valued probability. Probability worth the set is the non-empty set with every the elements are the results of the probability selector mapping.

Then a set-valued measure is constructed which is constructed by set-valued probabilities.

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To answer this question, you cannot do it all at once. Since the percentage will change every year because of how percents work, you must do seven calculations for each of the seven decades.

To decrease a number by 6%, you multiply it by 0.94, which is the same as finding 94% of that number, as you have taken 60% away.

1. 1200*0.94 = 1128

2. 1128*0.94 = 1060.32

3. 1060.32*0.94 = 996.7008

4. 996.7008*0.94 = 936.898752

5. 936.898752*0.94 = 880.68482688

6. 880.68482688*0.94 = 827.843737267

7. 827.843737267*0.94 = 778.173113031

You probably don't need 9 decimal places, so we can round to 778.17.

After seven decades, the mountain will be 778.17 meters.

The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

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The value of {x} would be 11.872.

Cosine of the angle is defined as the ratio of base and hypotenuse. Mathematically -

cosθ = (base)/(hypotenuse)

Given is a right angled triangle as shown in the figure.

We can write the value of {x} as -

cos{32} = x/14

{x} = 14 cos (32)

{x} = 14 x 0.848

{x} = 11.872

Therefore, the value of {x} would be 11.872.

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The probability that it will have distinct even digits is 6/1000.

The first digit can take on 5 values (0,2,4,6,8).

The second digit could take on 4 values (one less than 5 to be unique).

The third digit could take on 3 values (two less than 5 to be unique).

So that makes,

N=5.4.3

N=60

P= 60/1000

P=3/50

So there are 60 unique three digit even numbers.

There are 1000 possible outcomes.

Probability and statistics are two fundamental concepts in mathematics. Probability is about the probability of an event, whereas statistics are about how different techniques are used to process different data.

Probability and statistics allow us to process complex data in a very understandable way.

Probability is one of the most popular topics in statistics. The reason is that this one theory is often used when trying to predict something. For example, figuring out what comes out of a random series of events. For simplicity, probability is also called chance or probability. 

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To find the mean of the data set, we will simply take the average of the data as:  Mean= 345+340+400+625/ 4=  427.5

So we have mean as, 427.5

Now we have to calculate the variance of the data.

As we know, for variance we take the difference of each value from mean, take its square and then average of all.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Now

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

So, the variance is 13556.2

Now we have to calculate the Standard deviation (S.D) of the data.

And the Standard Deviation is just the square root of Variance, so:

σ = √13556.25

σ =116.43

So, the Standard deviation of the data is 116.4

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Graph of the equation y-4=0.75(x-1) is in the attachment.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given  equation is y-4=0.75(x-1)

y-4=0.75x-0.75

Add 4 on both sides

y=0.75x+3.25

The slope is 0.75 and y intercept is 3.25.

The graph is given in the attachment.

Hence, graph of the equation y-4=0.75(x-1) is in the attachment.

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The equation that represents the total amount of kites for a given number will be y = 2x + 20.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The rate of the kite is $2 per kite and the shipping charge is $20.

Let 'x' be the number of kites and 'y' be the total amount. Then we have

y = 2x + 20

Then the table is completed below.

Number of kites      Total amount

         0                             20

          1                             22

         4                             28

         7                             34

        10                            40

The equation that represents the total amount of kites for a given number will be y = 2x + 20.

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Answer:

19.6666666667

Step-by-step explanation:

Points G, H, and I It seems to be the vertices of a triangle, forming the triangle GHI. Triangle GHI resembles triangle ABC.

A triangle is a three-sided polygon that is also known as the trigon. Every triangle has three sides and three angles, which might be different. In geometry, a triangle is a three-sided polygon with three edges and three vertices. The sum of a triangle's internal angles equals 180 degrees, which is its most important characteristic. This is known as a triangle's angle sum property.

Here,

Point G, H, I looks like the vertices of triangle making triangle GHI. Triangle GHI is similar to triangle ABC.

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The value of x based on the information given in the triangle will be 11.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

It should be noted that based on the information given, the value of x will be calculated thus:

24 / x + 5 = 54 / 36

Cross multiply

24 / x + 5 = 3 / 2

3(x + 5) = 24 × 2

3x + 15 = 48

Collect the like terms

3x = 48 - 15

3x = 33

Divide

x = 33 / 3

x = 11

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The standard deviation of the sample proportions (i.e., the standard error of the proportion) is 10.5.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

n = 525

Population Proportion(p) = 0.3

q = 1 - 0.3

q = 0.7

σ = √npq

σ = √(525 × 0.3 × 0.7)

σ = √110.25

σ = 10.5

So The standard deviation of the sample proportions = σ/n

The standard deviation of the sample proportions = 10.5/525

The standard deviation of the sample proportions = 0.02

The standard deviation of the sample proportions = 2%

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The complete question is:

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

a.0.0004

b.0.2100

c.0.3000

d.0.0200

As percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 is 25%.

A percentage is a fraction of a whole number expressed as a fraction of 100. It is often used to describe the change in a quantity over time or between different groups.

There were 50 more full-time students enrolled in the fall of 2000 than in the fall of 1999, we can calculate the change in the number of full-time students as follows:

Change in full-time students = 50

To calculate the percentage change, we need to know the initial number of full-time students in the fall of 1999. This information is not provided, so we will use the information that the total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.

Let's call the total number of students enrolled at College T in the fall of 1999 "x". Then, the total number of students enrolled at College T in the fall of 2000 would be x + 5% of x.

x + 5% of x = x + 0.05x = 1.05x

To find the number of full-time students in the fall of 2000, we can subtract the change in full-time students from the total number of students enrolled at College T in the fall of 2000:

Number of full-time students in fall of 2000 = 1.05x - 50

To calculate the percentage change, we divide the change in full-time students by the initial number of full-time students and multiply by 100:

Percentage change = (50 / x) * 100

Where the value of x as 2000, then the percentage is

=> (50/2000) * 100 = 25%.

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Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ - 1/3 (y - x)

Now, We can expand the expression as;

⇒ - 1/3 (y - x)

⇒ - 1/3 × y - 1/3 × - x

⇒ - 1/3y + 1/3x

Thus, Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

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