Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6} if you roll the die once, calculte the following probabilities. Write you answers in fraction form and in lowest terms (e. G. 1/4) a) the probability of getting a 6 is. B) the probability of getting an even number is. C) the probability of getting a number greater than 2 is

Answer:

ray ts

Step-by-step explanation:

The two states will never have the same median house value.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The intercepts are given by the values of each home in 1950, thus:

The slopes are given by the average change over the 50 years, hence:

As the number of years must be positive, Delaware starts with the higher income and has a higher yearly increase, the two states will never have the same median house value.

Solving 35500 + 1416x = 55000 + 1508x, we would end up with a negative value of x.

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The distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The the distance can be observed to be of the side of a right triangle with the hypotenuse as the radius of the circle and the base side half of the chord, if x is used to represent the distance of the chord from the centre of the circle.

so by Pythagoras rule we can write:

12² = x² + 8²

144 = x² + 64

x² = 144 - 64 {collect like terms}

x² = 80

x = √80 {take square root of both sides}

x = 8.9443

Therefore, the distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.

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When the water cooler is completely full, there are approximately 143.52 gallons of water in it.

To calculate the number of gallons of water in the water cooler when it is completely full, we can use the formula for the volume of a cylinder, which is:

Volume = π * (radius)^2 * height

where radius is half of the diameter, and π is the constant pi.

In this case, the diameter of the water cooler is 3.5 feet, so the radius is 1.75 feet. The height of the water cooler is 2 feet. Plugging these values into the formula, we get:

Volume = 3.14 * (1.75)^2 * 2 = 19.18 cubic feet

To convert this volume to gallons, we can multiply it by the conversion factor of 7.48 gallons per cubic foot:

Volume in gallons = 19.18 * 7.48 = 143.52 gallons

In summary, to calculate the number of gallons of water in a cylindrical water cooler, we can use the formula for the volume of a cylinder and then convert the resulting volume from cubic feet to gallons using a conversion factor.

In this case, we needed to use the diameter and height of the water cooler, along with the constant pi and the conversion factor of gallons per cubic foot, to calculate the number of gallons of water in the water cooler when it is completely full.

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We can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

What is confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is an interval estimate computed from a sample of data and is used to describe the uncertainty or variability associated with a sample estimate of a population parameter.

To calculate the confidence interval, we need to first find the point estimate of the proportion of applicants accepted by Bridgeton University:

Point estimate = number of applicants accepted / total number of applicants = 392 / 1000 = 0.392

The standard error of the proportion can be calculated as:

SE = sqrt(p*(1-p)/n), where p is the point estimate and n is the sample size.

SE = sqrt(0.392*(1-0.392)/1000) = 0.0194

To find the 95% confidence interval, we can use the formula:

CI = point estimate +/- z*SE, where z is the z-score for a 95% confidence level (1.96).

CI = 0.392 +/- 1.96*0.0194

CI = (0.354, 0.430)

Therefore, we can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

To evaluate whether Bridgeton's claim seems accurate, we can compare the confidence interval with the claimed acceptance rate of 42%. We can see that the claimed acceptance rate of 42% does not fall within the confidence interval, which suggests that the claim may not be accurate. However, it is important to note that this sample may not be representative of the entire population of applicants to Bridgeton University, and further investigation may be needed to confirm the accuracy of the claim.

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Answer:

D

Step-by-step explanation:

f(x)=20 cos (pi/5x + pi/2)+25

The number of vegetable seeds Frank is going to plant is 3b + 1

From the question, we are to determine the number of vegetable seeds Frank is going to plant on the gardens

From the given information, we have that

"Frank in going to plant b vegetables in one garden"

and

"2b+1 vegetables seeds in a another"

To determine the number of vegetable seeds he would be planting in the gardens, we would find the sum of the vegetable seeds he is planting in the first garden and the second garden

That is,

b + (2b + 1)

= b + 2b + 1

= 3b + 1

Hence, the number of seeds is 3b + 1

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Answer:

A - Decrease a number by 30% is the same as multiplying by 70%.

Step-by-step explanation:

This statement is incorrect. Decreasing a number by 30% means that the number will be reduced by 30% of its original value. For example, if the original number is 100, decreasing it by 30% would give you 100 - 30% * 100 = 100 - 30 = 70. On the other hand, multiplying a number by 70% would increase it by 70% of its original value, which is a different operation.

C - Decrease a number by 0.30 is the same as multiplying by 0.70.

This statement is also incorrect. Decreasing a number by 0.30 means subtracting 0.30 from the original number, while multiplying by 0.70 means multiplying the original number by 0.70. These are two different operations that will result in different results.

The solution to all the Equations is shown below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

w = -6, x = 4, y = 3, z = -8

1. WX + YZ

= (-6) (4) + (3)(-8)

= -24 - 24

= -48

2. 2w + 3z- xy + z³

= 2(-6) + 3(-8) - (4)(3) + (-8)³

= -12 - 24 - 12 -512

= -560

3. y(z + x)

= 3(-8 + 4)

= -12

4. (w + x + y)³

= (-6 + 4 + 3)³

= 1

5. (z-w)³

= (-8 + 6)³

= -8

6. 5(w + x) + 4(y + z)

= 5(-6 + 4) + 4(3 -8)

= -10 - 20

= -30

7. W² - x² =

= (-6)² - (4)²

= 36 - 16

= 20

8. (xy) – 2wz

= (4)(3) - 2(-6)(-8)

= 12 -2 (48)

= 12 -96

= -84

9. wz - 4xy

= (-6)(-8) - 4(4)(3)

= 0

10. w+ (x+y+z)²

= -6 + 1

= -5.

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Since the diameter of this circle is 14 cm, a measurement of the circumference of this circle to the nearest tenth is 43.96 centimeters.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 14

Circumference of circle, C = 43.96 centimeters.

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Answer:

arc PN = 164°

Step-by-step explanation:

given chords PM and PN are congruent.

• if 2 chords are congruent then the corresponding arcs are congruent

then

arc PN = arc PM = 164°

Step-by-step explanation:

36 - 7p = -7(p-5)

= 36 - 7p = -7p + 35

= 36 - 35 = - 7p + 7p

= 1 = 0

am confused at the last part

I don't know if p= 1 or it 0 = 1

The next number in the series 1\325,1\176,1/88,1/44,1/22 is 1/44.

Depending on whether the sequence is finite or infinite, the series might be either infinite or finite.

To find the pattern in the series, we can look at the denominators of the fractions. We can see that the denominators are getting multiplied by 2 in each successive term.

So the next term in the series would have a denominator of 1/11 * 2 = 1/22 * 1/2 = 1/44. Therefore, the next number in the series would be 1/44.

So the complete series is:

1/325, 1/176, 1/88, 1/44, 1/22, 1/44.

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Answer:

32

Step-by-step explanation:

since 8 students are 25% of the class then 25% is also a way of saying 1/4……4/4 would represent the entirety of the class so 8 times 4 is 32 which is the total number of students in the class

i don't speak that language so i don't know what your saying. im sorry

The graph that best models the situation of the home value increasing every year is Graph A

To find the graph, use the percentage increase to find the value of the house in two different time periods and then check which graph coincides with this prediction.

After 5 years, the value of the house should be:

= 200, 000 x ( 1 + 6 % ) ⁵

= $ 267, 645

After 10 years :

= 200, 000 x ( 1 + 6 % ) ¹⁰

= $ 358, 170

The best graph for the situation is therefore Graph A which starts from $ 200, 000 and passes through the above points.

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The table is completed using this function rule y = 4x + 2 is given below.

x            -2            0             2            4

y            -8            2            10           18

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = 4x + 2

At x = - 2, the value of 'y' is given as,

y = 4 × (-2) + 2

y = - 8 + 2

y = - 6

At x = 0, the value of 'y' is given as,

y = 4 × (0) + 2

y = 0 + 2

y = 2

At x = 2, the value of 'y' is given as,

y = 4 × (2) + 2

y = 8 + 2

y = 10

At x = 4, the value of 'y' is given as,

y = 4 × (4) + 2

y = 16 + 2

y = 18

The table is completed using this function rule y = 4x + 2 is given below.

x            -2            0             2            4

y            -8            2            10           18

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Step-by-step explanation:

Please here it is.

Given y = 4x + 2

Part(a), An inequality to show the number of additional minutes required to get at least 80% battery life will be 3m + 40 ≤ 80.

Part(b) The number of minutes will be 13 minutes and 20 seconds.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that according to a survey, students often have 40% of their cell phone batteries left at the end of the school day when utilizing the newest fast charger, which charges phones at a pace of 3% per minute.

Part(a) The inequality can be written as:-

3m + 40 ≤ 80.

Part(b), The number of minutes will be:-

3m + 40 ≤ 80.

3m ≤ 40

m ≤ 40 / 3

m ≤ 13.33

The time can also be written as 13 minutes and 20 seconds.

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Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.

There are several ways to obtain a sample in research. The most common sampling methods in research are the following:

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Answer:

$1522.5

Step-by-step explanation:

(7.25 x 15)14

(108.75)14

= 1522.5

Answer:

$13.53

Step-by-step explanation:

Let's call the cost of a pepperoni pizza x.The total cost of the cheese and pepperoni pizzas before tax and tip is 1 * $11.00 + 3 * x = $57.59 - $3.00Simplifying the expression on the right side: $54.59 - $3.00 = $51.59Now we can solve for x:1 * $11.00 + 3 * x = $51.593 * x = $51.59 - $11.003 * x = $40.59x = $13.53So each pepperoni pizza costs $13.53

The value of z in the triangle using trigonometric ratio is; z = 10.90

The three basic trigonometric ratios from which others are derived are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

From the diagram, we can easily see that z is the opposite side of the given angle and 13 is the hypotenuse. Thus;

z/13 = sin 57

z = 13 * sin 57

z = 13 * 0.83867

z = 10.90

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The statement that is true about the quadratic functions is:

g(x) > h(x) for x = -1.

Here we have the two quadratic functions:

g(x) = x^2

h(x) = -x^2

Notice that h(x) = -g(x).

Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.

g(0) = 0^2 = -0^2 = h(0)

Then the statement that is true is

g(x) > h(x) for x = -1.

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The greatest whole number that divides both 372 and 324 without a remainder is 4.

To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).

One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.

372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]

The greatest common divisor is [tex]2^2[/tex], which is equal to 4.

So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.

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The total surface area is π[(4/3)x]² + π(4/3)x². The area of the base is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

The base area =  πr²; Lateral area = πrs

substituting:

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

Hence:

SA = π[(4/3)x]² + π(4/3)x²

The area of the base is greater than the lateral area.

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Regular hexagon is a closed shape polygon having six equal sides and six equal angles.

A regular hexagon is defined as a closed 2D shape made up of six equal sides and six equal angles.

Each angle of the regular hexagon measures 120 degrees.

A hexagon has six angles and the sum of all six interior angles is 720 degrees. In a regular hexagon, each interior angle measures 120 degrees.

Polygon

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices of a polygon.

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If Uriel can crush 3 cans in 23 of a minute, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.

The problem gives us information about the number of cans Uriel can crush and the time it takes him to do so. We want to find the rate at which he crushes the cans, which is a measure of how many cans he can crush per minute.

To find this rate, we use a proportion. A proportion is a statement that two ratios are equal. In this case, we can set up a proportion that relates the number of cans Uriel crushes to the time it takes him to do so, and the rate at which he crushes the cans:

3 cans / (2/3 min) = x cans / 1 min

Here, the first ratio is the number of cans Uriel can crush in 2/3 of a minute (which is the same as saying that he can crush 3 cans in 2/3 of a minute). The second ratio is the unknown rate at which Uriel crushes cans per minute.

To solve for the unknown rate, we use cross-multiplication. This involves multiplying both sides of the proportion by the same value in order to isolate the unknown variable on one side of the equation.

In this case, we can cross-multiply by the denominators of each ratio:

3 cans × 1 min = (2/3 min) × x cans

Simplifying the left-hand side, we get:

3 cans × 1 min = 3 cans/min

Simplifying the right-hand side, we get:

(2/3 min) × x cans = 2x/3 cans/min

Putting these together, we get the equation:

3 cans/min = (2x/3) cans/min

We can now solve for x by isolating it on one side of the equation. To do this, we can multiply both sides by 3/2:

(3/2) × 3 cans/min = x cans/min

Simplifying, we get:

4.5 cans/min = x cans/min

Therefore, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.

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Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet. Jayden's percent error is 25%.

To calculate the percent error, we first need to find the difference between the measured value and the actual value, then divide that difference by the actual value, and multiply the result by 100 to express it as a percentage.

Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet.

The difference between Jayden's measurement and the actual measurement is:

4 ft - 3.2 ft = 0.8 ft

The actual value is 3.2 ft, so the percent error is:

(0.8 ft / 3.2 ft) x 100% = 25%

Therefore, Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet. Jayden's percent error is 25%.

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