an algebra test is worth 100 points and has 25 questions. there are multiple choice questions worth 3 points each and short answers worth 8 points each. how many short answer questions are on the test?

you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common mutually exclusive events

Hence, option (b) is the correct choice.

Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot occur at the same time. The set of outcomes of a single coin toss, which can result in either heads or tails but not both, is a good example.

Events that are mutually exclusive do not occur at the same time. For example, when a coin is tossed, the outcome will be either head or tail, but we cannot obtain both. Such occurrences are also known as disjunct events since they do not occur at the same time.

Events that are mutually incompatible cannot occur at the same moment. Right and left hand turns, even and odd numbers on a dice, winning and losing a game, or running and walking are all examples.

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Answer:

[tex]\rm{ \dfrac{1250}{7776}\; or\; 0.16075\\\\}[/tex]

Step-by-step explanation:

This probability can be determined using combinatorics. The number of ways a sample of size r can be obtained from a larger set of n items is given by the formula

[tex]C(n,r) = \dfrac{n!}{( r! (n - r)! )}[/tex]

We pronounce C(n, r) as n choose r

We are rolling the die five times. So n = 5

On each roll a 2 can appear or not

We need two 2's . This is our r

The number of ways two 2's can appear is given by 5 choose 2

[tex]C(5,2)\\\\= \dfrac{5!}{( 2! (5 - 2)! )}\\\\= \dfrac{5!}{2! \times 3! }\\\\[/tex]

5! is the factorial of 5, 2! is the factorial of 2 and 3! is the factorial of 3

5! = 5 x 3 x 3 x 2 x1

3! = 3 x 2 x 1

2! = 2 x1

[tex]C(5,2) = \dfrac{5\times 4 \times 3 \times 2 \times 1}{((2 \times 1) \times (3 \times 2 \times 1)}\\\\= 10\\[/tex]

You need not go through this laborious process to find 5 choose 2 there are calculators available

So two 2's can appear 10 times.

The probability of getting a 2 on one roll is 1/6 and the probability of not getting a 2 on a single roll is 1-1/6 = 5/6

This works out to a binomial probability which can be computed by the formula

P(x) = C(n, x) pˣqⁿ⁻ˣ

Where x is the number of times the desired outcome succeeds and n the total number of trials

Here x = 2, n = 5, C(5, 2) = 10

[tex]\rm{So\:P(two\:2s\:on\:5\:throws)\: = 10 \cdot \left(\dfrac{1}{6}\right)^2\cdot \left(\dfrac{5}{6}\right)^3\\\\[/tex]

[tex]{= \dfrac{10 \cdot 1\cdot 125}{{6^5}} = \dfrac{1250}{7776} = 0.16075\\\\[/tex]

Equations -7 x+7 y = 11  and -4 x + y = 11 have answers of [tex]x=-\frac{11-7 y}{7}$$[/tex] and [tex]x=-\frac{11-y}{4}$$[/tex], respectively.

solve for [tex]$x,-7 x+7 y=11 \quad: \quad x=-\frac{11-7 y}{7}$[/tex]

-7 x+7 y = 11

-7 x = 11 - 7 y Shift 7 y to the right side and subtract 7 from both sides.

[tex]\frac{-7 x}{-7}=\frac{11}{-7}-\frac{7 y}{-7}$$[/tex]

Simplify

[tex]x=-\frac{11-7 y}{7}$$[/tex]

solve for [tex]x,-4 x+y=11: x=-\frac{11-y}{4}$[/tex]

Adjust Y to the right by -4 x=11-y.

Divide -4 from both sides.

[tex]\frac{-4 x}{-4}=\frac{11}{-4}-\frac{y}{-4}$$[/tex]

Simplify

[tex]x=-\frac{11-y}{4}$$[/tex]

Finding an equation's solutions—which are the values (numbers, functions, sets, etc.) that satisfy the equation's condition—is known as solving an equation in mathematics. An equation often consists of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

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Answer: it’s A

Step-by-step explanation:

The product of the rational expressions shown is equal to: B. 2x/(x² - 1).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = 2 × x

Product of numerator = 2x

For the denominator, we have the following:

Product of denominator = (x + 1) × (x - 1)

Product of denominator = x² - x + x - 1

Product of denominator = x² - 1

Therefor, the product of the rational expressions is given by 2x/(x² - 1).

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As per the following table, the equation of a line of fit for the data round all values to the nearest 10th is  y = -6.199 x 85+ 548.7

In math the term called equation is known as  a mathematical statement that is made up of two expressions connected by an equal sign.

Here we have the following table with the value of ticket price and the number of tickets sold.

Here the First steps is calculated by using the linear regression feature that defines the line of best fit is

=> y = -6.199x + 548.7

When we take the value of x = 85, then we get,

=> y = -6.199 x 85+ 548.7

When we simplify this one then we get

=> y = 21.785 ≈ 22

Hence here this seems a reasonable model to predict the number of tickets sold because we can see that as the ticket price increase, and the number of tickets sold decreases.

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Answer:15

Step-by-step explanation:

its the middle number

Answer: i think it's 15!!

hope this helps lol

The slope of the line in the example is 25 and the y-intercept is 10. These values can be used to write the equation of the line in slope-intercept form, y = 25x + 10.

The slope, m, represents the rate of change of the height of the giant kelp plant. In this case, the slope is 25, meaning that for every day that passes, the height of the giant kelp plant increases by 25 centimeters.

The y-intercept, b, represents the height of the giant kelp plant at time = 0. In this case, the y-intercept is 10, meaning that the giant kelp plant is 10 centimeters tall at time = 0.

So in this situation the slope represents how much the height of the kelp plant changes with respect to time and the y-intercept represents the initial height of the kelp plant at time = 0.

She should allow $4107.2 for her current assignment.

Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.

The price of kettle and toaster is same. So, we can write -

25x + 20x = 1359.55

45x = 1359.55

x = 30.2

Therefore, the total cost of 80 kettles and 56 toasters will be -

(80 x 30.2 + 56 x 30. 2)

$4107.2

Therefore, she should allow $4107.2 for her current assignment.

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1. The system of equations is given as follows:

2. The system of equations has no solutions.

The amounts are obtained solving a system of equations, for which the variables are given as follows:

On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships, hence:

4x + 2y = 96.

2x + y = 48.

Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership, hence, spending $72, hence:

2x + y = 72.

The system of equations has no solutions, as the linear functions have the same slope but different intercepts.

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Answer:

The Answer is 49

Step-by-step explanation:

4+3 =7 and 7 x 7 = 49

hope this helps

El valor de las 18 bandejas es un total de $117.000

$78,000 for 12 bandejas

18 bands:

Bandeja 1:

We must first determine the price of one bandeja in order to determine the price of 18 bandejas.

solo divide 78 ÷ 12 que te dará 6.5 después multiplicas 6.5 × 18 que te dará:117

así que la respuesta es 117 pesos

entonces...

78.000÷12= 6.500

Now we have the price for 18 bandejas.

First, split $78.000 by 12 to determine the cost of each bandeja of eggs.

The result is $6.500, which you will multiply by 18 to determine their cost. This gives us a result or answer of $117.000.

RPTA: The cost of 18 bandejas is $117,000

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The number of  teaspoons that are there in 6 milliliters is 1.21731 US  teaspoons.

The concept that will be used here is conversion of units. Unit conversion is the process of changing measurements of the same quantity between different units by multiplying or dividing them. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.

1 tsp  = 4.93 mL

Then Xtsp = 6ml

The cross multiply, Xtsp= (1 tsp *6ml)/4.93 mL

Then 6 milliliters= 1.21731 US  teaspoons

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Variability in a production process is a crucial indicator of the process's quality. A significant variance frequently represents a chance to improve the process by figuring out how to lower the variance.

It will be stated as, what machine 1's mean is.

[tex]x1= \frac{2.95+3.16+3.2+3.45+...+3.35+3.12}{25} =3.3284[/tex]

Thus, machine 1's average is 3.3284.

Following that, we'll provide the variance of machine 1.

[tex]s21= \frac{∑(x−¯x1)^{2} }{n−1 } \\ = \frac{(2.95−3.3284)2+(3.16−3.3284)2+...+(3.12−3.3284)^{2} }{24} =0.0489[/tex]

So machine 1 has a variance of 0.0489.

I'll provide the machine 2 mean as,

[tex]x2= \frac{3.22+3.38+3.30+...+3.33}{22} =3.27[/tex]

Therefore, machine 1's mean value is 3.2782.

Following that, the variance of machine 2 will be given as.

[tex]s22= \frac{∑(x−¯x2) ^{2} }{n−1} \\ [/tex]

[tex]\frac{(3.22−3.2782)2+(3.38−3.2782)2+(3.30−3.2782)2+...+(3.33−3.2782)^{2} }{21} \\ =0.0059[/tex]

Thus, machine 2's variance is 0.0059.

Here are the proposed hypotheses:

[tex]H0:σ21=σ22 \\ H1:σ21>σ22[/tex]

To verify the theory, the F-test will be applied. The test statistic is as follows:

[tex]TS= \frac{s21}{s22} × \frac{σ22}{σ21} \\ =0.04890.0059=8.29[/tex]

As will be used to calculate the p-value.

P(F24,21>8.29)=1−0.99999=0.00001.

The null hypothesis will be rejected because the p-value is less than the level of significance of 5%. This indicates that machine 1 offers a greater opportunity for quality improvements.

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Step-by-step explanation:

(3i-51)*(2-6)

(-48) (-4)

192

The sum of the fractions 1/3 and 2/5 is 11/15.

How can we add two fractional numbers?

For the addition of fractions with the same denominator, we just add the numerators of two fractions, keeping the denominator common. We can then simplify the fraction to the lowest form.

For the addition of fractions with different denominators, we first find the LCM of the denominators and rationalise them. Then we add the numerators and simplify the fraction.

Following the above rules, we can add 1/3 and 2/5.

Now they have different denominators.

LCM of 3 and 5 is 15.

So we rationalise them.

[tex]\frac{1*5}{3*5} +\frac{2*3}{5*3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}[/tex]

Therefore the sum of the given fractions is 11/15.

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The domain of the function h(x)=9x/x(x²-49) is (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

In math the term called the domain of a function is the set of its possible inputs which is the set of input values where for which the function is defined.

Here we have know the function is h(x)=9x/x(x²-49)

And we need to find the domain of the function.

Here we know that this function is defined for values where the denominator is not equal to zero.

Which is written as,

=> x(x²-49) ≠ 0

When we elaborate the equation based on the difference between the two squares property, it can be written as,

=> x(x + 7)(x - 7)  ≠ 0

Based on this we have identified that the value of x must not be

=> x  ≠ -7, 7, 0

Then the domain of the function is written as,

=> (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

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we would here like to find out the values of given trigonometric ratios . A right angled triangle is given to us with perpendicular= 3 and hypotenuse= 8

Firstly by Pythagoras theorem, we have ,

[tex]\longrightarrow h^2 = p^2 + b^2\\ [/tex]

[tex]\longrightarrow 8^2 = 3^2 + b^2 \\[/tex]

[tex]\longrightarrow 64 = 9 + b^2\\ [/tex]

[tex]\longrightarrow b^2 = 64 -9 = 55\\ [/tex]

[tex]\longrightarrow b =\sqrt{55}\approx 7.41 [/tex]

now as we know that,

[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{7.41}{8}\\ [/tex]

[tex]\longrightarrow \underline{\underline{ \cos\theta = 0.92 \approx 1}} [/tex]

And ,

[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{7.41}{3}\\[/tex]

[tex]\longrightarrow \underline{\underline{\cot\theta = 2.47 \approx 2 }} [/tex]

Finally,

[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{8}{7.41}\\[/tex]

[tex]\longrightarrow \underline{\underline{\sec\theta = 1.07 \approx 1 }} [/tex]

and we are done!

The quadratic equation we  use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0

What is Quadratic equation?

The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.

What is Rectangle?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.

Let W be the width of rectangle.

then, length of the rectangle is W + 6 .

and the Area, A = 16 inches^2

And the area of recatngle is A = L x W

Hence, A = (W+6)W

So, 16 = W^2 + 6W

Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;

W^2 + 6W - 16 = 0

By the quadratic formula we have

[tex]w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}[/tex]

[tex]w = \frac{-6 \pm \sqrt{36 + 64} }{2}[/tex]

[tex]w = \frac{-6 \pm 10 }{2}[/tex]'

Hence, we take width as a positive because width never be negative .

so,the value of width is ;

w = 2

and length o rectangle is ;

l = w + 6 = 2 + 6 = 8

l = 8

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The  correct answer is B. $60,350.00. To calculate the value of Whitney's steel house, you need to multiply the annual premium per $100 of coverage ($0.43) by the annual property insurance premium ($603.50) and then divide that by 100. This works out to $60,350.00.

To determine the annual premium per $100 of coverage, you need to look at the table provided in the question. Since Whitney's steel house is located in the country, the annual premium per $100 of coverage is $0.43. Multiplying this by the annual property insurance premium of $603.50 gives you the total value of the house, which is $60,350.00. To summarize, the value of Whitney's steel house can be calculated by multiplying the annual premium per $100 of coverage by the annual property insurance premium and then dividing that by 100. In this case, the value of the house is $60,350.00.

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Question 5 of 10 Whitney's steel house is located in the country. If her building property insurance is $603. 50 per year, how much is her house worth? Annual Premium per $100 of coverage Brick Steel Mixed Wood Area Building Contents rating City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76 Suburb 0. 45 0. 52 0. 56 0. 63 0. 74 0. 83 0. 85 Rural 0. 6 0. 69 0. 71 0. 89 0. 91 1 1. 02 0. 72 0. 8 O A. $17,350.00  B. $60,350.00  C. $171,050.00  D. $603.50

Option C is correct - X + 52 = 170.

Angle

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Straight line

A line is a geometry object characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.

According to the question,

∠POR = 170°

∠ROQ = 52°

∠POQ = x,

it is clear by the question,

on the basis of figure attached with this solution,

two angles together make the third angle,

so,

first angle is 52 degree

second angle is x degree,

∠ROQ + ∠POQ  =∠POR  

x + 52 = 170

so the answer is x + 52 = 170.

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The required amount each type of solution to make mixture are  120 ml of 25% acid and 80 ml of 50% acid.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

A liquid mixture known as an acidic solution is created when water and hydrogen ions react. The Brnsted-Lowry theory states that whereas bases "receive" hydrogen protons, acids "give" hydrogen protons. Different solutions have different levels of acidity.

Let there be (200 - x) ml of 50% acid and x ml of 25% acid.

200*0.35 = 0.25x+0.5(200-x)

0.25x +100 -0.5x = 70 

30 = 0.25x 

x=120

200 - x = 200 - 120 = 80, resulting in 120 ml of 25% acid and 80 ml of 50% acid.

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For the mixture, 120 ml of 25% acid and 80 ml of 50% acid are needed for each type of solution.

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The equation of the straight line will be -

y = x - 4.

The general formula of a straight line will be -

y = mx + c

Given is a graph of straight line as shown in the image.

We can write the equation as -

y = mx + c

Now, we can write the slope as -

m = (0 + 4)(4 - 0) = 4/4 = 1

{m} = 1

{y} - intercept = - 4

{c} = - 4

We can write the equation as -

y = x - 4

Therefore, the equation of the straight line will be -

y = x - 4.

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The length of x for the given shape is 3 cm.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given the shape, and area of the figure is  54 cm²,

the figure is of L shape,

which consist of two rectangles,

the dimensions of the first rectangle are 6 cm by 7 cm

and dimensions of the second rectangle are x cm by 4 cm (reducing 6 from 10)

Area of shape = sum of the area of both rectangles

Area of shape = 6*7 + x*4

54 = 42 + 4x

4x = 54 - 42

x = 12/4

x = 3 cm

Hence the value of x is 3 cm.

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Number of quarters and dime with Pam with the total value of $1.45 is equal to 4 and 4.5 respectively.

Let 'x' represents the number of quarters coins.

And 'y' represents the number of dimes coins.

Value of quarter and dime in dollars is :

1 quarter = $0.25

1 dime = $ 0.10

Total value of all the coins = $1.45

⇒ $0.25x + $0.10y = $1.45

⇒2.5x + y = 14.5

⇒y = 14.5 - 2.5x  __(1)

Number of coins < 9 coins

x + y < 9  

⇒ x < 9 - y  __(2)

Substitute the value of 'y' from (1) we get,

x < 9 - 14.5 + 2.5x

⇒2.5x - x > 14.5 - 9

⇒1.5x > 5.5

⇒ x > 5.5./1.5

⇒ x > 3.7

⇒ x = 4 ( next possible integer)

⇒ y = 14.5 -2.5(4)

⇒y  = 4.5

⇒ y = 4.5

Therefore, the number of quarters and dime with Pam is equal to 4 and 4.5 respectively.

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Answer: a= -9

Step-by-step explanation:

a+ (−4) = −13

a - 4 = -13 (the 4 becomes -4 as when it comes to + or - it is always -)

    a = -13 +4  (when you switch the side -4 becomes +4)

    a= -9

Answer:

$1182.65

Step-by-step explanation:

(8.5/100)×$1090

(85/1000)×1090

$1853/20

=$92.65

thus, $1090+$92.65

=$1182.65

The coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.

A coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.

coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient.

Let [tex]$x$[/tex] denote the claim sizes

[tex]& x= \begin{cases}100 & ; p=0.05 \\200 & ; p=0.2 \\300 & ; p=0.5 \\400 & ; p=0.2 \\500 & ; p=0.05\end{cases}[/tex]

[tex]& \mu_1^{\prime}=\varepsilon(x)=\sum x^0 p(x=x)=300 \\\\& \mu_2{ }^{\prime}=\sum x^2 p(x)=98000 \\\\& \mu_3^{\prime}=\sum x^3 p(x)=342 \times 10^5 \\[/tex]

[tex]& \mu_4^{\prime}=\sum x^4 p(x)=1.262 \times 10^{10} \\\\& \mu_2=\mu_2^{\prime}-\left(\mu_1^{\prime}\right)^2=8000 \\\\& \mu_3=\mu_3^{\prime}-3 \mu_2^{\prime} \\\\\mu_1^{\prime}+2\left(\mu_1^{\prime}\right)^3=0 \\\\& \mu_4=\mu_4^{\prime}-4 \mu_3^{\prime} \mu_1^{\prime}+6[/tex]

[tex]\mu_2^{\prime} \mu_1^{\prime 2}-3 \mu_1^{\prime 4} \\& \mu_4=2 \times 10^8 \\\\& \beta_1=\frac{\mu_3{ }^2}{\mu_2^3}=0 \quad \Rightarrow y_1=0 \\\\& \beta_2=\frac{\mu_4}{\mu_2{ }^2}=\frac{2 \times 10^8}{64 \times 10^6}=3.125\\ \\& y_2=\beta_2-3=0.125 \\[/tex]

Therefore, coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.

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