which probability is equal to 4/5?

Answer:

mean: 101 (add all the numbers then divide by 7)

mode: 102 (the most frequent number in the set)

median: 102 (the number in the middle of the set)

range: 20 (the difference between the largest and smallest number)

Mean = 101

Mode = 102

Median = 102

Range = 20

MEAN: Add up all the numbers, then divide by how many numbers there are.

102 + 107 + 99 + 102 + 111 + 95 + 91 = 707

707 ÷ 7 = 101

MODE: Arrange all numbers in order from lowest to highest or highest to lowest and then count how many times each number appears in the set. The one that appears the most is the mode.

91,95,99,102,102,107,111

MEDIAN: Arrange the numbers from smallest to largest. If the amount of numbers is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers in the list.

91,95,99,102,102,107,111

RANGE: Subtract the lowest number from the highest number

111 - 91 = 20

The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606

The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).

To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula

z = (x - μ) / (σ / √n)

where

x is the sample mean

μ is the population mean (believed to be 80 months)

σ is the population standard deviation (8 months)

n is the sample size (77)

Plugging in the values, we get

z = (82.59 - 80) / (8 / √77) ≈ 1.55

To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.

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The equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.

A ratio is a comparison of two or more quantities that are related to each other in some way. It is expressed as a fraction or using the "colon" notation.

If Mike pays 12 dollars for one pizza, the ratio of dollars to pizza is:

12 : 1

To find the equivalent ratio for 4 pizzas, we need to keep the ratio of dollars to pizza constant. We can do this by multiplying both the numerator and denominator of the ratio by 4, since we are now dealing with 4 pizzas instead of 1. This gives us:

12 x 4 : 1 x 4

Simplifying this ratio gives us:

48 : 4

We can further simplify this ratio by dividing both the numerator and denominator by 4, which gives us:

12 : 1

Therefore, the equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.

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Answer:

Same equation just using the assocaitive property

Step-by-step explanation:

For example, 8 + (2 + 3) = (8 + 2) + 3 = 13

Hope this helps! =D

The statement which  is true for the quadrilateral is B.

To dilate a figure by a scale factor of 2, each point of the original figure is multiplied by 2.

So the coordinates of each vertex of A'B'C'D' are twice the coordinates of the corresponding vertex of ABCD.

The coordinates of A' are (4,10), B' are (4,4), C' are (8,6), and D' are (8,12).

To determine which statements are true, we can compare the angles and side lengths of the two quadrilaterals:

A) None of the answers apply. This may be a valid answer, but we should check the other options before concluding that none of them apply.

B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. This is true because dilation does not change angles. The corresponding angles of the two quadrilaterals are congruent.

C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are not the same. We can see this by calculating the length of each side of both quadrilaterals.

Therefore, the correct answer is B.

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The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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Answer:

The perimeter of this trapezoid is

7 + 5 + 3 + 7 + 4 = 26 cm

rectangle, A = lw, 4 × 7 = 28 square cm

triangle, A = (1/2)bh, (1/2) × 3 × 4 =

6 square cm

(1/2)(4)(7 + 10) = (1/2)(4)(17) = 34 square cm = 28 square cm + 6 square cm

The probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

Probability is a measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event that will not occur, and 1 represents a certain event that will always occur.

According to the given information:

There are 5 balls numbered 1 through 5 in the bowl. The total number of possible outcomes, when Josh chooses a ball, is 5, as there are 5 balls in the bowl.

Now let's consider the probability of choosing a ball with an even number. There are 3 even numbers (2, 4, and 5) out of the 5 possible numbers, so the probability of choosing a ball with an even number is 3/5.

Next, let's consider the probability of choosing a ball with a number greater than 2. There are 3 numbers (3, 4, and 5) greater than 2 out of the 5 possible numbers, so the probability of choosing a ball with a number greater than 2 is also 3/5.

To find the probability that the product of the two chosen numbers will be even and greater than 2, we need to multiply the probabilities of choosing an even number and choosing a number greater than 2.

Probability of choosing an even number: 3/5

Probability of choosing a number greater than 2: 3/5

Multiplying these probabilities, we get:

(3/5) * (3/5) = 9/25

So, the probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

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Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]

From inspection of the given right triangle RST:

Substitute the values into the formulas:

[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]

[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]

[tex]\implies 80=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]

[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]

[tex]\implies x=4\sqrt{5}[/tex]

Solve the equation for y:

[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]

[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]

[tex]\implies 320=y^2[/tex]

[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]

[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]

[tex]\implies y=8\sqrt{5}[/tex]

Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

Answer:

5 1/4

Step-by-step explanation:

A number of

convergence tests

can be used to examine a Taylor series' convergence, but the Ratio Test is one that is frequently employed. According to the

ratio test, the series converges absolutely if the limit of the

absolute value

of the ratio of the (n+1)th term to the nth term is smaller than 1. In mathematics, this is expressed as:

lim┬(n→∞)⁡〖|a_(n+1)/a_n |<1〗

where a n is the

series' nth term. The series

diverges

if the limit is bigger than 1, and extra tests must be employed if the limit is equal to 1.

Although the

Ratio Test

is a frequently used test for

Taylor series

convergence, it is not always appropriate and other tests can be required based on the unique characteristics of the series.

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Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

The probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day is approximately 0.2676

To find the probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day, we need to compare the distribution of their running times.

Let X be the running time of Alyse and Y be the running time of Jocelyn. Then, we have

X ~ N(13.5, 2.5^2)

Y ~ N(12, 1.5^2)

We want to find P(X < Y). We can start by standardizing the variables:

Zx = (X - 13.5) / 2.5

Zy = (Y - 12) / 1.5

Then, we have

P(X < Y) = P(X - Y < 0)

Substituting the standardized variables, we get

P(X - Y < 0) = P((Zx - Zy) < (0 - (13.5-12)/sqrt(2.5^2 + 1.5^2)))

Using the standard Normal distribution table or calculator, we find that the probability of Zx - Zy being less than -0.624 is approximately 0.2676.

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(13) Angle A, angle B and angle C are collinear and are proved.

(14) Based on corresponding angles theorem, X is bisector of angle A.

The sum of the measures of collinear angles is always 180 degrees, as they together form a straight angle.

If we consider triangle PCQ;

Since line CP = line CQ; then angle P = angle Q = x

m∠PCQ = 180 - 2x

If we consider triangle PBQ;

Since line PB = line BQ; then angle P = angle Q = x

m∠PBQ = 180 - 2x

If we consider triangle PAQ;

Since line AP = line AQ; then angle P = angle Q = x

m∠PAQ = 180 - 2x

Thus, angle A, angle B and angle C are collinear.

14. To prove that X is a bisector A;

Draw a line parallel to AN from point B to opposite side, call this point Y

Angle formed from line M to line BY, is a corresponding angle to angle formed from line M to line AN.

If X is the bisector of angle B, then it is also a bisector angle A since both angles are equal.

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The analysis of the bank statement thus, given below. Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

1. If we put withdrawals and deposits in the same column, they can be represented as positive and negative values in a single column. Deposits would be represented with positive values, and withdrawals would be represented with negative values.

2. Andre's new balance would be $16.37. We can calculate this by subtracting $40 (the withdrawal) from his previous balance of $56.37:

$56.37 - $40 = $16.37

3. If Andre deposits $100 in this account, he will no longer be in debt. We can calculate his new balance by adding his previous balance and the deposit, and then subtracting any withdrawals:

$56.37 + $100 = $156.37 (balance after the deposit)

$156.37 - $28.50 - $37.91 - $16.43 - $42.00 - $72.50 - $45.00 - $50.00 - $10.03 - $62.47 = -$49.47

Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

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Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3

The probability that Neta is chosen first and Jinita is chosen second is:

1/56(or approximately 0.018.)

There are 8 students in class, so there are 8 choices for first person and 7 choices for second person.

Since we want to calculate probability that Neta is chosen first and Jinita is chosen second, we need to consider the number of ways in which these two students can be chosen in that order.

There is only one way for Neta to be chosen first and Jinita to be chosen second, so the total number of possible outcomes is:

8 x 7 = 56

Therefore, the probability that Neta is chosen first and Jinita is chosen second is: 1/56 or approximately 0.018.

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fraction wise, a whole is always simplified to 1, so

[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]

so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot,  and we also know that 3/4 of that is 12, the guys who chose the bottle of water

[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]

This supports the analyst's hypothesis that betas are higher in  down markets.

In algebra, the definition of an equation, in its simplest form, is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the equation.

To test the hypothesis that stock betas are higher in bear markets, we use the following regression equation:

Ri = αi + βi(Rm) + εi

where,

Ri = return on ith stock

Rm = market return

αi = intercept (constant term) of the regression equation of the ith stock.

βi = slope of the market return of the ith stock (regression coefficient).

εi = error period of the ith stock

To test the hypothesis, we  include an additional variable in the regression equation that describes the effect of the market return when it is negative. This variable would be a dummy variable that takes the value  1 if the market return is negative and 0 otherwise. Let's call this variable D. So the modified regression equation would be:

Ri = αi + βi(Rm) + γiD + εi

where,

γi = the excess regression coefficient of the ith stock that describes the effect of the market return when it is negative

The coefficient γi measures the difference between the  beta value of a stock between a falling market and a non-falling market. If γi is significantly greater than 0, this supports the analyst's hypothesis that betas are higher in  down markets.

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Answer:

r = 2

center: ( -7,0 )

Step-by-step explanation:

Answer:

Set your calculator to degree mode.

[tex] \tan(39) = \frac{12}{x} [/tex]

[tex]x \tan(39) = 12[/tex]

[tex]x = \frac{12}{ \tan(39) } = 14.818766[/tex]

So the area of this triangle is

(1/2)(14.818766)(12) = 88.91 (B)

Answer:

The answer that you're looking for is approximately 9202.77 and in terms of π it is 2929.33π

Step-by-step explanation:

Using the equation [tex]\frac{4}{3}\pi r^{3}[/tex] you can replace r with 13 to get [tex]\frac{4}{3} \pi 13^{3}[/tex] you then multiply them all to get 9202.77 and divide by π to find the terms of pi which is 2929.33π.

I hope this was helpful!

When x is 2, the value of the expression is 9.

An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.

Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.

Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.

When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:

12/4 + 3(8 - 2) - 12

= 3 + 3(6) - 12

= 3 + 18 - 12

= 9

Therefore, when x is 2, the value of the expression is 9.

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The complete question is :

When x is 2, what is the value of the expression 12/4+3(8−x)-12?

Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

Step-by-step explanation:

Given:

The damage to the parked car was

$4,300and the damage to the store

was

$50,400.

Objective:

The objective is to determine the

amount will the insurance company pay

for Susan's car accident.

Explanation:

Having a 100/300/50 insurance policy

means you have $100,000 in coverage

for bodily injury liability per person,

$300,000 for bodily injury liability per

accident, and $50,000 for property

damage liability.

The anmount insurance company

will pay $4,300 for car damage and

$50,000 for property damage.

So total amount that must be paid is

$50000+$4300=$54300

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Arun is not correct - he has just under $5 in total, not just over.

Let's start by finding out how many 5-cent and 10-cent coins Arun has.

Let the number of 5-cent coins be 5x and the number of 10-cent coins be 3x (since the coins are in the ratio 5:3).

Then the total value of the 5-cent coins is 5x0.05 = 0.25x dollars, and the total value of the 10-cent coins is 3x0.1 = 0.3x dollars.

So the total value of all the coins is 0.25x + 0.3x = 0.55x dollars.

Since Arun has 72 coins, we know that 5x + 3x = 72, or 8x = 72, or x = 9.

Therefore, Arun has 5x = 59 = 45 5-cent coins and 3x = 39 = 27 10-cent coins.

The total value of these coins is 450.05 + 270.1 = 2.25 + 2.7 = 4.95 dollars.

So Arun is not correct - he has just under $5 in total, not just over.

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The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)

To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.

Amplitude:

The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.

Period:

The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.

From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.

Phase shift:

The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).

In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.

With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:

d(t) = 5.3 sin(2π/15 * t)

where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.

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The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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The margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .

A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiment's outcomes.

A proportion is an equation in which two ratios are set equal to each other.

The margin of error for estimating the true population proportion can be calculated using the formula:

Margin of Error = Critical Value * Standard Deviation

where the Critical Value is determined based on the desired confidence level and the Standard Deviation is an estimate of the variability of the population proportion.

Given that the sample size is large (n = 1200) and we are using a 95% confidence level, we can use the standard normal distribution (Z-distribution) for the Critical Value. The critical value for a 95% confidence level in a standard normal distribution is approximately 1.96.

The Standard Deviation can be estimated using the sample proportion, which is given as 32% or 0.32 in this case. The sample proportion is a point estimate of the population proportion.

Using these values, we can calculate the margin of error as follows:

Margin of Error = 1.96 * √( (0.32 * (1 - 0.32)) / 1200 )

= 1.96 * √( 0.2176 / 1200 )

= 1.96 * √( 0.00018133333 )

= 1.96 * 0.01345451543

= 0.02633 (rounded to 5 decimal places)

So, the margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .

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