Chelsea
Enter in the missing numbers to create equivalent ratios.
5
2
4
25
20
Enter in the missing numbers

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores So option C is correct.

What is standard normal distribution ?

The standard normal distribution is a special case of the normal distribution in which the mean is 0 and the standard deviation is 1. It is also known as the "Z-distribution" because the scores are expressed in terms of their z-scores, which are the number of standard deviations above or below the mean.

The standard normal distribution is a bell-shaped curve that is symmetric around the mean of 0. It is used in statistics as a reference distribution for calculating probabilities and making statistical inferences.

To convert a normal distribution with a given mean and standard deviation to a standard normal distribution, we use the formula:

z = (x - μ) / σ

According to the question:
To find the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4%, we need to find the z-scores that correspond to the 4th and 96th percentiles of the standard normal distribution.

Using a standard normal table, we find that the z-score corresponding to the 4th percentile is approximately -1.75, and the z-score corresponding to the 96th percentile is approximately 1.75.

Therefore, the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4% are approximately -1.75 and 1.75, respectively.

To sketch the region containing the lowest 4% and highest 4%, we need to shade the area under the normal curve to the left of -1.75 and to the right of 1.75.

The shaded regions represent the lowest 4% and highest 4% of bone density test scores, respectively. The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores.


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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Given the function:

The parent function to the given function is f(x) = x³

To get the function p(x) from f(x), we will perform the following translations:

1) Horizontal stretch with a factor of 1/3

2) Shift downward 3 units

The graph of f(x) and p(x) will be as shown in the following picture:

Answer:

n=6

Step-by-step explanation:

\(\frac{1}{2} n=3\)

Multiply both sides by 2

2*1/2n=3*2

Simplify;

n=6

Answer: n=6

Step-by-step explanation:

6*1/2=3 so this is y n=6.

Answer:

Dylan is 10 years old, and Genesis is 11.

Step-by-step explanation:

If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:

Dylan's age: x

Genesis' age: x+1

This would mean Genesis is a year older than Dylan.

The product of their ages is 110.

We can write an equation:

x×(x+1)=110

x²+x=110 (Distribute x)

x²+x-110=0 (Move 110 to the other side)

You can solve this by the quadratic equation, by factoring or by completing the square

I'll solve it by the quadratic equation:

We must first find the coefficients a, b and c, and then plug it into the formula.

\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)

Since we have a ± symbol, we get 2 real solutions, x1 and x2.

x=-1±21/2

x1=-1+21/2

x1=20/2

x1=10

x2=-1-21/2

x2=-22/2

x2=-11

Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.

Hope this helps, and let me know if you need help with another method to solve this problem!

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

D=E (Base angle of isosceles triangle are equal)

D+E+F= 180° (sum of angles of a triangle️)

(4x+7)+(4x+7)+(5x+10) = 180

13x = 180- 24

x= 156/13 = 12°

so, E= 4x+7 = 4×12+7 = 55

Hope this helps:)

Answer:

r = 50 degrees.

Step-by-step explanation:

r = 50 degrees ( vertical angles are congruent).

Step-by-step explanation:

We define 3 events

A = event that driver is above speed limit

B = event that driver is below limit

T = event that the gun detected him

At 95%

P(A) = 1-0.95 = 0.05

P(B) = 0.95

P(T|A) = 0.98

P(A|T) = 0.02

P(T|B) = 1-0.99 = 0.01

P(B|T) = 0.99

1. For answer a

P(TnA) = P(A) x P(T|A)

= 0.05 x 0.98

= 0.049 is the probability gun detected speeding and the driver was speeding

2. For answer b

P(TnB) = P(B) x P(T|B)

= 0.95x0.01

= 0.0095 is probability that gun deects speeding and driver was not speeding

3. For answer c

We solve this using bayes theorem

P(B|T) = P(B) x P(T|B) / (P(B)*P(T|B)) + (P(A) +P(T|A))

= 0.095x0.01 divided by (0.95x0.01)+(0.05*0.98)

= 0.0095 divided by 0.0585

= 0.16239

= 0.1624 to 4 decimal places.

The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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Answer:

30% increase

Step-by-step explanation:

percentage increase is calculated as

\(\frac{increase}{original}\) × 100%

increase = $35.10 - $27 = $8.10 , then

percentage increase = \(\frac{8.10}{27}\) × 100% = 0.3 × 100% = 30%

Answer:

Step-by-step explanation:

step 1:       35.10-27 =8.1

step 2:       8.1/27 x 100 = 30%

so therefore = 30% increase

Answer:

Please Co me he re tiyvynoqtu

The seven ordered pairs that fit on the axes of the graph include the following:

In order to use the given polynomial function to complete the table, we would have to substitute each of the values of x (x-values) into the polynomial function and then evaluate as follows;

When the value of x = -3, the output value of this polynomial function is given by;

y = x³ + 6

y = (-3)³ + 6

y = -27 + 6

y = -21

By observing critically the graph (see attachment), we can logically deduce that it represents a polynomial function.

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The result of the system of equation is given by x = -18/ 49 and

y = 17/49

The equals sign is a symbol used in fine formulas to denote the equivalency of two expressions.

The veritably primary step in resolving a variable equation is to precisely identify the values of the variables that lead to a equivalency. The equation's results are the values of the unknown variables that satisfy the equivalency, which are frequently appertained to as the variables for which the equation must be answered.

We'll break the equations by elimination system

2x 5y = 1

9x- 2y = - 4

Multiplying the first equation by 2 and the alternate equation by 5 and adding we get

4x 10y = 2

45x- 10y = -20

49x = -18

or, x = -18/ 49

Now substituting the value of x in the equation we get

2x 5y = 1

y = 17/49

Hence the results of the equations is given by

x = -18/ 49 and y = 17/49

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a. The number of ways that this is done, if the order of the choices is relevant is 12 ways.

b. The number of ways that this be done, if the order of the choices is irrelevant is 6 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

= n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

When the orders are relevant, this will be:

= 4! / (4 - 2!)

= 4! / 2!

= 12

When orders are irrelevant, this will be:

= 4! / (4 - 2!)2!

= 6 ways

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The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

1/2 (1q) = 4

insert extra text here

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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According to the given question we can conclude that the probability that a student who majors in science is a female is approximately 0.375 and the probability that a student is male or majors in art is 0.78.

Probability is the research of probabilities, which also are based on the ratio of favourable events to likely circumstances. One of the areas of probability theory is the estimation of the chance of experiments occurring. With a probability, we can calculate any number of things, from the probability of obtaining a head or a tail when flipping a coin towards the likelihood of generating a research error, for example.

A.) To find the probability that a student who majors in science is a female, we need to use Bayes' theorem. Let F be the event that a randomly selected student is female, and S be the event that the student majors in science. Then we have:

P(F|S) = P(S|F) * P(F) / P(S)

We know that P(F) = 0.6 (since 60% of students are female), and P(S|F) = 0.1 (since 10% of female students major in science). To find P(S), we need to use the law of total probability:

P(S) = P(S|F) * P(F) + P(S|M) * P(M)

We know that P(S|M) = 0.4 (since 40% of male students major in science), and P(M) = 0.4 (since 40% of students are male). Therefore:

P(S) = 0.1 * 0.6 + 0.4 * 0.4 = 0.16

Now we can calculate P(F|S):

P(F|S) = 0.1 * 0.6 / 0.16 ≈ 0.375

Therefore, the probability that a student who majors in science is a female is approximately 0.375.

B.) To find the probability that a student is male or majors in art, we need to use the law of total probability again:

P(Male or Art) = P(Male) + P(Art) - P(Male and Art)

We know that P(Male) = 0.4 (since 40% of students are male), and P(Art|Male) = 0.5 (since 50% of male students major in art). We also know that P(Female) = 0.6 (since 60% of students are female), and P(Art|Female) = 0.7 (since 70% of female students major in art). Therefore:

P(Art) = P(Art|Male) * P(Male) + P(Art|Female) * P(Female)

= 0.5*0.4+0.7*0.6

= 0.58

To find P(Male and Art), we can multiply the probabilities of being male and majoring in art:

P(Male and Art) = P(Male) * P(Art|Male)

= 0.4 * 0.5

= 0.2

Now we can calculate P(Male or Art):

P(Male or Art) = 0.4 + 0.58 - 0.2

= 0.78

Therefore, the probability that a student is male or majors in art is 0.78.

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Answer:

x = 52/6

Step-by-step explanation:

The equation is given as;

\(\frac{4 + 2x}{6x} = \frac{12}{5x} + \frac{2}{15}\)

Multiply all through by 30x. This gives;

5(4+2x) = 6(12) + 2x(2)

Expanding the expression;

20 + 10x = 72 + 4x

Taking like terms;

10x - 4x = 72 - 20

6x = 52

x = 52/6

Answer:

a) 90th percentile

b) X = 51.43 ( Sophia's height ) , Amy's height = 50.92

c)  0.2394

d)  46.44 inches

Step-by-step explanation:

mean value( u ) = 47.7 inches

std ( σ )= 2.4 inches

Amy height = 1.34 std above mean value

Sophia height = 94th percentile of height distribution

A ) what percentile is Amy's height

To Calculate the percentile of Amy's height

P( X ≤  50.916   ) = P( (X-µ)/σ )  ≤  (50.916-47.7) /2.4)  

=P(Z ≤  1.340  ) = 0.9099  = 90th percentile

B) How Amy's height compare to Sophia's

The proportion given based on Sophia's height = 0.94

z -value at the proportion ( 0.94 ) = 1.55 ( from excel )

note z-value can be calculated using  =  ( x - µ ) / σ                      

therefore: X (Sophia's height )  = zσ + µ=   (1.55 * 2.4)  +  47.7  

 X = 51.43 ( Sophia's height ) , Amy's height = 50.92

C) percentage expected to be taller than 49.4 inches

P ( X ≥ 49.40  ) = P( (X-µ)/σ)  ≥ (49.4-47.7) / 2.4)              

= P(Z ≥ 0.708 )

= P( Z <  -0.708   )

= 0.2394

D) Below what height are the shortest 30% of 7-year old girls

( u ) = 47.7 inches

std ( σ )= 2.4 inches

given proportion = 30% = 0.3

The z value at 0.3 = -0.52 ( from excel )

to calculate for X ( height ) we have to apply the formula used to determine z value

z= (x-µ) /σ

hence : X = (Z * σ)  + u = (-0.52 * 2.4 ) + 47.7

            X = 46.44

below 46.44 inches lies about 30% of 7 year old girls height

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The surface area of the triangular prism is 608 cm².

Given,

base of triangle = 12 cm

height of triangle = 8 cm

length of triangle = 10 + 10 + 12 = 32 cm

Width of the triangle = 16 cm

Area of the rectangle = l x b = 32 x 16 = 512 cm²

Area of triangle = 1/2 x 12 x 8 = 48 cm²

There are 2 triangle, so 48 + 48 = 96 cm²

Add all these values, 512 + 96 = 608 cm²

∴The surface area of triangular prism = 608 cm²

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The sum of the surfaces of the five faces of a triangular prism is its surface area.

Having two triangular bases and three rectangular sides, a triangular prism is a type of polyhedron. It is a three-dimensional object with two base faces and three side faces that are joined by edges.

There are 6 vertices, 5 edges, and 5 faces on it. The other 3 faces have a rectangle-like shape, while the 2 bases are structured like a triangle. Camping tents, chocolate candies, roofs, etc. are a few instances of triangular prisms in the real world.

A solid object called a prism has plane faces enclosing each of its four sides. Faces in a prism come in two different varieties. Bases are used to describe the top and bottom faces, which are identical.

12 cm is the triangle's base.

triangle's height is 8 cm.

Triangle's length is 32 cm (10 + 10 + 10 cm).

Triangle width is 16 cm.

The rectangle's area is 512 cm2 (l x b = 32 x 16).

Triangle area equals 1/2 x 12 x 8 = 48 cm2.

Two triangles are present, therefore 48 + 48 = 96 cm2.

512 + 96 = 608 cm2 after adding all these values.

The triangular prism's surface area is 608 cm2.

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Answer:

#8 - substitution property of equality

hop this helps! <3

Answer:

8

7

6

Step-by-step explanation:

Plato/Edmentum

Could be wrong so take my answer with a grain of salt