a family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. what is the probability that

The length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

The owner of the used tire store wants to construct a fence to enclose a rectangular outdoor storage area. The side of the store is 240 feet long and there are 460 feet of fencing available for the other three sides. The formula for the area of a rectangle is A=LxW, where A is the area, L is the length, and W is the width. To find the dimensions of the outdoor enclosure with the most area, the length and width must be equal so that all of the fencing is used. Therefore, the length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

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Jesse engage in self injuries behavior every time he is denied access to the ipad and when it occurs we tally one mark on the data sheet it represents the Frequency

The frequency (f) of a specific fee is the variety of times the value takes place in the facts. The distribution of a variable is the pattern of frequencies, that means the set of all viable values and the frequencies associated with those values. Frequency distributions are portrayed as frequency tables or charts.

As a statistical device, a frequency distribution affords a visible illustration of the distribution of observations within a particular check. Analysts often use a frequency distribution to visualise or illustrate the facts accrued in a pattern

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The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ g (x) = 6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

Now, The value of function are,

At x = - 2;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (- 2) = 0

At x = 4;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x < 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (4) = - 4

Thus, The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

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Answer:

Nathan will make $20

Jackson will make $29

hope you like it

Answer:The coefficient in this expression is 3.

Step-by-step explanation:

What is a Coefficient?

By definition, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic.

What is a variable?

A variable is a symbol that represents a mathematical object. So for example, 9p + 2. In this equation, the variable would be the letter "p."

Check the picture below.

so the triangle with the 35° angle is an isosceles, namely a triangle with twin sides stemming from the center of the circle, well, twin sides make twin angles, and since the center of the circle makes a central angle, well, any arc will get its degrees from that.

The length Thebe the HCF (highest common factor) of the given dimensions that are 168mm and 196 mm. Hence, the length of each square will be equal to 28mm.

The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers. As a result, it is also known as the greatest common factor (GCF). If M is the greatest common factor of N, then M is the greatest possible number that divides N.

The length of the each square will be given by the HCF of the dimensions that are 168mm and 196mm.

[tex]168=2*2*2*3*7\\196=2*2*7*7[/tex]

So, the length of the each square paper=[tex]2*2*7=28mm.[/tex]

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Answer:

Step-by-step explanation:

You want to solve the triangle with A=35°, B=60°, and c=10.

When two angles and a side are given, the Law of Sines is useful for providing a solution. In order to use it, we need to know an angle and its opposite side. That is, we need angle C.

Using the sum of angles of a triangle, we have ...

  A +B +C = 180°

  C = 180° -A -B = 180° -35° -60° = 85°

Now, we can use ...

  a/sin(A) = b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = 10·sin(60°)/sin(85°) ≈ 8.69

  a = c·sin(A)/sin(C) = 10·sin(35°)/sin(85°) ≈ 5.76

The normal probability plot can reveal information about the population from which the data were drawn. A straight line pattern indicates normality, whereas deviations from the straight line indicate non-normality.

A normal probability plot is a graphical method for determining whether a set of data values is normally distributed. The plot depicts sample data values on the y-axis and theoretical normal deviate values on the x-axis.

If the plotted points follow a roughly straight line, the population is likely to be normally distributed. If the points plotted deviate significantly from a straight line, the population is not normally distributed.

As a result, the shape of the normal probability plot can provide insight into the normality of the population from which the data were drawn. A straight line pattern indicates that the distribution is normal, whereas deviations from the straight line indicate non-normality.

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Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. on 20th of the steps will both meet if both start jumping together. we can find it out with the help of HCM and LCM

GIVEN

Sam can jump four steps at a time and Nina can jump five steps at a time.

TO DETERMINE

On which of the steps will both meet if both start jumping together

EVALUATION

Here it is given that Sam can jump 4 steps at a time and Nina can jump 5 steps at a time.

Now we find the LCM of 4 and 5

Since 4 and 5 are prime to each other

So LCM of 4 and 5 = 4 × 5 = 20

Hence after 20 steps both meet if both start jumping together

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The fifth term of the expansion by using Binomial Expansion is +1008x¹⁵y¹⁴.

When algebraic identities cannot be employed to extend a binomial, the binomial expansion formulae are used to determine the powers of the binomials.

The expansion of (x + y)^n is given by this binomial expansion formula, where n is a natural number. There are (n + 1) terms in the expansion of (x + y)^n.

Given that:

[tex]=(\dfrac{1}{2}x^3y^2-4y)^9[/tex]

Use the binomial expansion theorem to find each term. The binomial theorem states [tex](a+b)^n = \sum \limits^n_{k=0}nCk*(a^{n-k}b^k)[/tex]

[tex]\sum \limits^9_{k=0} \dfrac{9!}{(9-k)!k!}* (\dfrac{1}{2}*(x^3y^2))^{9-k}*(-4y)^k[/tex]

Expand the summation.

[tex]=\dfrac{9!}{(9-0)!0!}*(\dfrac{1}{2}*(x^3y^2)^{9-0}*(-4y)^0+ \dfrac{9!}{(9-1)!1!}*(\dfrac{1}{2}*(x^3y^2)^{9-1}*(-4y)^1+...+\dfrac{9!}{(9-9)!9!}*(\dfrac{1}{2}*(x^3y^2)^{9-9}*(-4y)^9[/tex]

Simplify the exponents for each term of the expansion.

[tex]=1*(\dfrac{1}{2}*(x^3y^2)^{9}*(-4y)^0+ 9*(\dfrac{1}{2}*(x^3y^2)^{8}*(-4y)^1+...+1*(\dfrac{1}{2}*(x^3y^2)^{0}*(-4y)^9[/tex]

Simplify the polynomial result.

[tex]=\dfrac{x^{27}y^{18}}{512}-\dfrac{9x^{24}y^{17}}{64}+\dfrac{9x^{21}y^{16}}{2}-84x^{18}y^{15}+1008x^{15}y^{14}-8064x^{12}y^{13}+43008x^9y^{12}-147456x^6y^{11}+294912x^3y^{10}-262144y^9[/tex]

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The measurement of acute triangle ABC we can find by direct substitution of the labeled measures in the Law of Sines is,

a/ sin a = b/sin b

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sine rule for a triangle ABC is, a/sinA = b/sinB = c/sinC .

In the diagram, there are two identified sides and if you use the sine rule, you can find the opposed angles easily.

Side a, with angle A.

Side b, with angle B.

If you input these into the sine rule, it would be, a/ sin a = b/sin b

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The correct proportion to represent the triangle ABC is similar to triangle PQR is,

⇒ 4 / 9 = 12 / n

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

Triangle ABC is similar to triangle PQR.

Hence, Corresponding sides of both triangles are equal to each other.

So, We ca formulate;

⇒ Base / Hypotenuse

⇒ 4 / 9 = 12 / n

Thus, Correct proportion to represent the triangle ABC is similar to triangle PQR is,

⇒ 4 / 9 = 12 / n

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The compound inequality would be: 0 <= x <= 5 or x >= 10

From the question, we have the following parameters that can be used in our computation:

no more than 5 totts or more than 10 totts

Represent the variable with s

So, we have the following representation

x no more than 5 totts or x more than 10 totts

As an inequality, we have

0 <= x <= 5 or x >= 10

See attachment for the graph

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The graph of the inequality -3x + y ≥ 1 is given below.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality:

-3x + y ≥ 1.

The intercepts are (0, 1) and (-0.33, 0)

The graph of the inequality is given in the attached image.

Therefore, the graph is given.

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The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.

Quarts of frozen yogurt made by factory is equal to 100 quarts

Time required to make 100 quarts of frozen yogurt is equal to 5 hours

Let 'x' quarts of frozen yogurt made in 36 hours

5 hours = 100 quarts of frozen yogurt

⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt

⇒ 36 hours =  ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 20 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 720 ) quarts of frozen yogurt

Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.

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Answer:

x=-2.083

or x=-25/12

Step-by-step explanation:

Answer:

x = -25/12

Step-by-step explanation:

We can solve for x by isolating x:

[tex]((-12x-7)=18)+7\\((-12x=25)/12\\x=-25/12[/tex]

Answer:

Below

Step-by-step explanation:

Circumference = pi * d = 22/7 * d

2517 = 22/7 * d             ( are you sure 2517 is correct??)

d = 2517 * 7/22 = 800.86 inches    ( a VERY large pie)

radius = 1/2 * d = 400.43 inches

Area = pi r^2

        = 22/7   * (400.43)^2 = 503 943 in^2

The two forms of representing her hair length are (3/4)H cm and 0.75H cm.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, On Monday, Florencia's hair was H centimeters long.

Therefore, After the hair cut her hair length will be,

= (75/100)×H.

= (3/4)H cm.

Now, We can also write it in terms of decimals which is,

= (75/100)×H.

= 0.75H cm.

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Answer:

you take the perimeter and subtract 2*the length. Then you divide that answer by 2

Step-by-step explanation:

This is because a rectangle is made up of 2 pairs of heights. 2 equal sides represent the height and 2 equal sides represent the width.

When we subtract the lengths of the 2 sides that represent the height we get a number that we then have to divide by 2 to get the width of the triangle.

Hope this helps. It's a little difficult to explain but the answer is correct :)

Using the graph we will see that line q can be written as:

y = (-1/2)*x + 3

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:

a = (2 - 3)/(2 - 0) = -1/2

And the y-intercept is y = 3, then the linear equation is:

y = (-1/2)*x + 3

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(a) The markup is $3.9.

(b) The selling price of the CD is $11.70.

The markup of the CD is calculated by applying the following formula.

The markup = 50% x $7.80

The markup = ( 50 / 100 ) x $7.80

The markup = 0.5 x $7.80

The markup = $3.9

The selling price of the CD is calculated as follows;

selling price = $7.80 + $3.9

selling price = $11.7

Thus, the selling price of the CD is a function of the cost price, and mark up price. So the final selling price of the CD is $11.7 while the mark up is $3.9

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 62% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 62%. The alternative hypothesis would be that the true proportion is less than 62%. After gathering information from 110 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis. If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 62% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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In ΔJKL using the angle bisector theorem the value for x is obatined as 48.6 units.

What is angle bisector theorem?

The opposite side of a triangle is divided into two pieces by the angle bisector in proportion to the other two sides. If the interior point of a triangle is equally spaced from its two sides, that point will be on the angle bisector of the angle created by the two line segments.

The measurement for line segment JK = 54 units.

The measurement for line segment LK = x units.

The measurement for line segment LM = 36 units.

The measurement for line segment JM = 40 units.

In ΔJKL line segment KM is an angle bisector.

So, according to the angle bisector theorem -

JM / LM = JK / LK

Substitute the values in the equation -

40 / 36 = 54 / x

Simplify to find the value of x -

x = (54 × 36) / 40

x = (27 × 9) / 5

x = 48.6 units

Therefore, the value of x is 48.6 units.

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Answer: 90

Step-by-step explanation:

The number that you need to find because it is missing in the equation is 48.

Let's assume the number we're trying to find is "x."

According to the problem, one-third of the number is (1/3)x, and one-fourth of the number is (1/4)x.

We're told that the sum of one-third of the number and one-fourth of the number is 28, so we can write the equation as follows:

(1/3)x + (1/4)x = 28

To solve this equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the equation as:

(4/12)x + (3/12)x = 28

Combining the fractions, we get:

(7/12)x = 28

To isolate x, we multiply both sides of the equation by the reciprocal of (7/12), which is (12/7):

x = 28(12/7)

Simplifying the right side of the equation, we have:

x = 48

Therefore, the number we're looking for is 48.

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Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

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

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

The standard deviation of x is 3 cars. So the option A is correct.

Suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the Poisson distribution.

If the mean of x is equal to 9 cars, then we have to determine the standard deviation of x.

An indicator of how much variance from the mean there is is the standard deviation, which can be expressed as spread, dispersion, or spread. A "typical" departure from the mean is represented by the standard deviation. As a result of returning to the data set's original units of measure, it is a well-liked measure of variability.

The Mean = 9 cars

Standard Deviation = Square Root of Mean

Standard Deviation = √9

Standard Deviation = 3 cars

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The correct answer is Stratified Random Sampling

Given that,

In a study, the sample is selected by dividing the class into gender-based groups, then choosing 10 men and 10 women.

Researchers split a population into homogeneous subpopulations called strata (plural of stratum) depending on particular traits in a stratified sample (e.g., race, gender identity, location, etc.).

In order to estimate statistical measures for each subpopulation, each stratum is then sampled using a different probability sampling technique, such as cluster sampling or simple random sampling.

When a population's traits are varied and researchers want to make sure that each characteristic is accurately represented in the sample, they rely on stratified sampling. This aids in the study's validity and generalizability while preventing biases in the research process like undercoverage bias.

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