a senatorial committee consists of 5 republicans and 5 democrats. in how many ways can this committee be selected from a pool of 15 republican and 10 democrat candidates?

a) The inequality that models this situation is given as follows: 24x ≤ 250.

b) The solution to the inequality is given as follows: x ≤ 10.41.

c) The number of baseballs that can be purchased is of at most 10.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

As the cost of each baseball is of $24, the constant is given as follows:

k = 24.

The equation giving the total cost of purchasing x baseballs is given as follows:

y = 24x.

The budget to spend is of $250, hence the inequality is given as follows:

24x ≤ 250.

The solution is given as follows:

x ≤ 250/24

x ≤  10.41.

As the number of baseballs is a countable amount, at most 10 baseballs can be purchased, rounding down the amount.

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In correlational and experimental study designs, a key requirement for a sample is that population whom the researchers are investigation

A sample is a portion of a larger population that is selected to represent the entire group. In both correlational and experimental study designs, a key requirement for a sample is that it should be representative of the population it is meant to represent.

In a correlational study design, the goal is to examine the relationship between two or more variables. The sample must be representative of the population to ensure that the correlation calculated from the sample is representative of the correlation that exists in the population.

If the sample is not representative, the correlation calculated from the sample may be different from the correlation that exists in the population, leading to incorrect conclusions.

In an experimental study design, the goal is to test a causal relationship between two or more variables.

The sample must be representative of the population to ensure that the results of the experiment are generalizable to the population.

If the sample is not representative, the results of the experiment may not be generalizable to the population, leading to incorrect conclusions.

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The least amount that the company would have to accept as their monthly revenue is A. $43,500.

From the amount that the streaming service is able to charge and the margin of error, we would calculate this as:

The monthly charge - margin of error

= 45 - 1.5

= 43.5 dollars

From here we have to multiply the amount by the people that signed for the service

43.5 * 1000

= A. $43,500

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139.2 cm² is the surface area, in cm², of the figure.

The surface area of a three dimensional shape is the total area of all of the faces. The surface area of a solid object is a measure of the total area that the surface of the object occupies.

here, we have,

The surface area of given figure = 3×Area of rectangle + 2×area of triangle base.

so, we get,

Surface area = 3×6×6+2×15.6

Surface area = 139.2 cm²

Hence, 139.2 cm² is the surface area, in cm², of the figure.

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Answer:

15

--- = 15

1

Step-by-step explanation:

keep change flep

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

The experimental probability that Dave works will be in a wedding in next week is 7 / 22.

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such experiments are unpredictable. The likelihood of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times.

The probability that Dave will work in a wedding is given as:

P = Working in wedding / Sum of total work

P = 14 / 44

P = 7 / 22

Hence, the experimental probability that Dave works will be in a wedding in next week is 7 / 22.

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A prime number doesn't have sequence so, it cannot be model with sequence.

Prime numbers are number that can only be divided by itself and 1.

E.g 2,3,5,7,11,13,17,19,23,29 etc.

So, note that this sequence doesn't have a pattern, it is neither Geometry Progression nor Arithmetic Progression.

Now, let take look at the model given

If n is prime, then 2n-1 is prime

Let take 5 for

n=5 is a prime number

2n-1=2(5)-1=10-1=9

9 is not a prime number so the model doesn't work

A prime number doesn't have sequence so, it cannot be model with sequence.

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Answer:

your pattern is multiply by 23 and your missing number is 322

Answer:

y = 33X^2 + 55

Step-by-step explanation:

by expanding the equation you provided, we will get the answer

be reminded, the general form of a quadratic equation us,

y =ax^2+bx+c

Answer:

? = -29

Step-by-step explanation:

-19 + x = -48

x= -48 + 19

x = -29

Answer:

? = -29

Step-by-step explanation:

To figure out the unknown value, start by adding -19 to both sides to leave the unknown by itself.  

? = -48 + 19

Negative numbers count down, so -48 + 19 = -29 

I hope this helped!! :)

Answer:

164.53125%

Step-by-step explanation:

105.3 is 164.53100% of 64

Answer:

Step-by-step explanation:

we solve with a proportion

105.3 : 64 = x : 100

x = 105.3 × 100 ÷ 64

x = 164.53125%

The mean of p , g and r is given by the equation M = 12

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of p , g and r be represented as M

Now , the mean of p and g = 13

So , ( p + g ) / 2 = 13

On simplifying the equation , we get

p + g = 26   be equation (1)

And , the mean of g and r = 16

So , ( g + r ) / 2 = 16

On simplifying the equation , we get

g + r = 32   be equation (2)

And , the mean of r and p = 7

So , ( r + p ) / 2 = 7

On simplifying the equation , we get

r + p = 14   be equation (3)

Adding equation (1) , (2) and (3) , we get

2 ( p + g + r ) = 26 + 32 + 14

And , divide both sides of the equation by 2 , we get

p + g + r = 72/2 = 36

Now , the mean of p , g and r is

M = ( p + g + r ) / 3

On simplifying the equation , we get

M = 36/3

M = 12

Hence , the mean is M = 12

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The correct answer is B) an equation of the best-fit line of data can be used to estimate untested values.

The equation of the best-fit line of data can be calculated by determining the slope (m) and the y-intercept (b) of the line. It is calculated by using the linear regression equation: y = mx + b, where m is the slope and b is the y-intercept. The slope is determined by the equation: m = (Σxy)/(Σx2). The y-intercept is determined by the equation: b = (Σy - mΣx)/n. Once these values are determined, it is possible to estimate untested values with the equation of the best-fit line. For example, if we have a graph with data points (2, 3) and (4, 7), the equation of the best-fit line would be y = 2x + 1. This equation can be used to estimate the value of y when x = 6; in this case, y = 11.

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The probability of rolling two sixes is 1/25.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given, the probability of rolling a 6 on a biased dice is 1/5.

Since the probability of rolling a six on the first roll is 1/5, then probability of not rolling a six on first roll is;

P(not 6) = 1 - 1/5

P(not 6) = 4/5

A) Please find attached the completed tree diagram

B) First Roll:

P(6) = 1/5

P(not 6) = 4/5

Second Roll:

Now,

P(6 | 6) = 1/5 × 1/5

= 1/25

P(6 | not 6) = 1/5 × 4/5

= 4/25

So, P(not 6 | 6) = 4/5 × 1/5

= 4/25

P(not 6 | not 6) = 4/5 × 4/5

= 16/25

Therefore, the probability of rolling two sixes is 1/25.

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"Your question is incomplete, probably the complete question/missing part is:"

The probability of rolling a 6 on a biased dice is 1/5

1) complete the tree diagram.

2) Work out the probability of rolling two sixes.

The required probability for the given table are as follow :

a. Probability of someone from US = 0.5089

b. Probability of someone has at least 2 children = 0.4196

c. Probability of someone from US and has one child = 0.125.

Total number of children is equal to 112

Probability = Favourable outcome / ( total number of outcome )

a. Number of children representing someone from US = 57

Probability of someone from US = 57 / 112

                                                      = 0.5089

b. Favourable outcome representing someone has at least 2 children is

= P (2) + P(3)

= ( 18 + 11 )/ 112 + (8 + 10 )/ 112

= (29 + 18) / 112

= 47/112

= 0.4196

c. From US and has one child :

Favourable outcome = 14

Probability of someone from US and has one child

= 14 / 112

= 0.125

Therefore, the probability of the different conditions are :

a. Probability from US = 0.5089

b. Probability of at least 2 children = 0.4196

c. Probability from US and one child = 0.125

The above question is incomplete, the complete question is:

For the table given below answer the following question:

Children         :   0                  1            2           3 or more            Total

From US         :  17                 14         18               8                         57

Outside US     : 15                  19         11               10                        55

Total                :  32                33         28              18                       112

a. What is the probability that someone is from the US?

b. what is the probability that someone has at least 2 children?

c. what is the probability that someone is from the US and has one child?

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Volume of sphere is 288π mm³.

Volume is defined as a capacity occupied by a three-dimensional solid shape. In any shape, it is hard to visualize but can be compared between shapes.

Given,

Radius of sphere r = 6 mm

Volume of sphere

= (4/3)πr³

= (4/3)π×6³

= (4/3)π×6×6×6

= 4π×2×6×6

= 288π mm³

Hence, 288π mm³ is volume of sphere.

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Answer:

The transformation f(x)↦f(-x) , the graph of f(x) reflects it across the y-axis

Step-by-step explanation:

El número de amigos que reciben 2/7 de la pizza es de 7 personas.

Por cierto dividimos 2 pizzas con 2/7 = 2 : 2/7 = 7 personas

Las comparaciones en matemáticas también pueden denominarse proporciones.

Entonces, ¿qué es una comparación o razón?

La comparación (razón) es una técnica o forma de comparar dos cantidades.

Escribir proporciones o comparaciones se puede escribir como a : b o a/b donde a y b son dos cantidades que tienen las mismas unidades.

A continuación se explicarán ejemplos de aplicación de comparaciones en la vida cotidiana.

Comparaciones en la vida cotidiana

Hay muchas aplicaciones de la comparación en la vida cotidiana. Escribir la escala en un mapa es una aplicación de la comparación.

Luego, cuando vamos a hacer pan suele haber una mezcla de masa de harina de trigo y harina de tapioca.

Por ejemplo, la proporción es de 2:1, lo que significa que para hacer el pan necesitas 2 partes de harina de trigo y 1 parte de harina de tapioca.

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The percentage of players weighing less than or equal to 233 pounds is 88.04%.

Percentage

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

See attachment for box plot,

From the box plot, the maximum is ,

Max = 244

the maximum is.

Min = 152

Percentage less than 233 is calculated as:

percentage = (233 - min)/ max - min

percentage = (233 - 152)/ 244 - 152

percentage = 81/92

express as percentage,

= 81/92 *100

= 8100/92

= 88.04%

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Answer: 75%

Step-by-step explanation: got it right

The surface area of the prism is 142 square in

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

The net of a rectangular prism

The surface area of the prism is the sum of the individual shapes that make up the net

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

Surface area = 2 * 7 * 3 + 2 * 5 * 3 + 2 * 5 * 7

Evaluate the sum of products

Surface area = 142

Hence, the surface area is 142 square in

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Answer:

(5x-7)(5x+7)

Step-by-step explanation:

[tex]25x^2-49\\=(5x)^2-(7)^2\\=(5x-7)(5x+7)[/tex]

Remember that the difference of squares formula is [tex]a^2-b^2=(a-b)(a+b)[/tex].

Answer:

(5x-7) x (5x+7)

Step-by-step explanation:

25x^2- 49

5^2 x 2^2 - 49

5^2 x 2^2 -7^2

(5x)^2 -7^2

(5x-7) x (5x+7)

The domain and the range of the function and its inverse is increasing.

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

When the value of x = -1, the linear function is given by;

f(x) = 3x + 2

f(-1) = 3(-1) + 2

f(-1) = -1.

When the value of x = -2/3, the linear function is given by;

f(x) = 3x + 2

f(-2/3) = 3(-2/3) + 2

f(-2/3) = 0.

When the value of x = -1/3, the linear function is given by;

f(x) = 3x + 2

f(-1/3) = 3(-1/3) + 2

f(-1/3) = 1.

When the value of x = 1/3, the linear function is given by;

f(x) = 3x + 2

f(1/3) = 3(1/3) + 2

f(1/3) = 3.

When the value of x = -1, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(-1) = 1/3(-1) - 2/3

f⁻¹(-1) = -0.9999

When the value of x = 0, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(0) = 1/3(0) - 2/3

f⁻¹(0) = -2/3.

When the value of x = 1, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(1) = 1/3(1) - 2/3

f⁻¹(1) = -1.

When the value of x = 3, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(3) = 1/3(3) - 2/3

f⁻¹(3) = 1/3.

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Answer:

The answer can be written in multiple forms

[tex]4 \left(x-2 \right)[/tex]  or   [tex]4x-8[/tex]

Step-by-step explanation:

Given "4 times the difference of x and 2​".

"Times" is multiplication and can be expressed as *

"the difference of x and y" can be expressed as (x -y)

Therefore in this example we can write

[tex]4 \left(x-2 \right)[/tex]

We can leave it as is or simplify it further.

We can simplify it by applying  the distributive property.

Distribute the 4.

[tex](4*x)-(4*2)[/tex]

[tex]4x-8[/tex]

The perimeter of the triangle is given by the equation P = 42.588 m

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the perimeter of the triangle be represented as P

Let the right triangle be represented as ABC

Now , the hypotenuse of the triangle is AC = 18m

And , the measure of ∠ACB = 30°

From the trigonometric relations ,

Let the angle be θ , such that

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin 30° = AB / 18

On simplifying the equation , we get

Multiply by 18 on both sides of the equation , we get

sin 30° = 1/2

AB = 18/2

The opposite side of the triangle AB = 9 m

Now , the base of the triangle BC is calculated from Pythagoras theorem

hypotenuse² = base² + height²

So , base BC² = ( 18 )² - ( 9 )²

The base of the triangle BC = √ ( 324 - 81 )

The base of the triangle BC = 15.588 m

Now , the perimeter of the triangle P = opposite side of the triangle AB + base of the triangle BC + hypotenuse of the triangle AC

The perimeter of the triangle P = 18 + 9 + 15.588

The perimeter of the triangle P = 42.588 m

Hence , the perimeter of the triangle is 42.588 m

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[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{11\pi }{6}\\[1em] r=18 \end{cases}\implies s=18\cdot \cfrac{11\pi }{6}\implies s=33\pi \implies s\approx 104~cm[/tex]

The probability number of times to roll the number cube to result in a prime number 12 times is 24

How to determine the number of times?

The given parameters are:

Number cube = 6 sides

Number of times= 12

The probability of obtaining a prime number in a six-sided die is:

P(Prime) = 3/6

The number of times (n) is then calculated as:

p * n = 12

Substitute known values

3/6 * n = 12

Evaluate the fraction

1/2 * n = 12

Multiply both sides by 2

n = 24

Hence, the number of times is 24

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