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The sum of two consecutive integers 42 and 43  is 85.

The sum of two consecutive integers is 85. This means that we need to find two integers that are next to each other on the number line and add up to 85. We can write this as an equation:
x + (x + 1) = 85

Simplifying the equation gives us:
2x + 1 = 85

Subtracting 1 from both sides gives us:
2x = 84

Dividing both sides by 2 gives us:
x = 42

This means that the first integer is 42. Since the two integers are consecutive, the second integer is 42 + 1 = 43. Therefore, the two integers are 42 and 43.

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Answer:

The volume of a rectangular solid is given by the formula V = LWH, where L is the length, W is the width, and H is the height.

In this case, we have:

W = x + 3

L = x + 2

H = x

So the volume is:

V = (x + 2)(x + 3)(x)

V = x(x + 2)(x + 3)

V = x(x^2 + 5x + 6)

V = x^3 + 5x^2 + 6x

Therefore, the volume of the rectangular solid is given by the polynomial expression x^3 + 5x^2 + 6x.

Given the box and whiskers plot with the given data, the five number summary would be :

Arrange the numbers in order from smallest to largest:

2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15

The minimum number is therefore 2.

First Quartile Q1 = 4 :

= ( 15 + 1 ) / 4

= 4 th position

Median :

= ( 15 + 1 ) / 2

= 8 th position which is 8

Third quartile :

= ( 15 + 1 ) x 3 / 4

= 12 th position which is 13.

Maximum value is 15.

Move the box plot to correspond with these figures.

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The missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

To find the missing lengths of ΔABC, we can use the properties of a 45-45-90 triangle. A 45-45-90 triangle is a special type of right triangle in which the two legs are congruent and the angles are 45°, 45°, and 90°. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, where the hypotenuse is √2 times the length of each leg.

Since we are given that BC = 6 and ∠A and ∠B are both 45°, we can conclude that ΔABC is a 45-45-90 triangle. Therefore, the lengths of AC and AB are both equal to the length of BC, which is 6.

AC = 6
AB = 6

To find the lengths in simplest radical form, we can multiply the lengths of AC and AB by √2/√2 to get:

AC = 6 * √2/√2 = 6√2/2 = 3√2
AB = 6 * √2/√2 = 6√2/2 = 3√2

To find the approximations correct to two decimal places, we can use a calculator to find the decimal values of 3√2:

AC ≈ 3 * 1.41 = 4.23
AB ≈ 3 * 1.41 = 4.23

Therefore, the missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

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Answer: A

Step-by-step explanation:

(3x ^ 2 + 4x - 7) (2x + 9)

2x (3x ^ 2 + 4x - 7) + 9 (3x ^ 2 + 4x - 7)

6x ^ 3 + 8x ^ 2 - 14x + 27x ^ 2 + 36x - 63

6x ^ 3 + 35x ^ 2 + 22x - 63

Answer:

41.9 cubic feet

Step-by-step explanation:

V = 1/3πr^2h,

r=radius

h=height.

V = 1/3πr^2h

  = 1/3π4^2 * 2.5

  = 40π/3 cubic feet

so the answer would be 41.9 cubic feet

Answer:

The volume of a sphere with a diameter of 8.6 m = 333.0 m^3

Step-by-step explanation:

To simplify the expression (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6))), we need to use the distributive property and the laws of exponents.

First, we can distribute the 8d^((3)/(2)) and 7h^((5)/(6)) to the 7h^((3)/(2)) and 8d^((5)/(6)):
= (8d^((3)/(2))*7h^((3)/(2)))*(7h^((5)/(6))*8d^((5)/(6)))
Next, we can use the laws of exponents to simplify the expressions with the same base:
= (8^2*d^((3)/(2)+(5)/(6))*7^2*h^((5)/(6)+(3)/(2)))
= (64*d^((11)/(6))*49*h^((9)/(6)))
Finally, we can simplify the exponents and multiply the constants:
= (3136*d^((11)/(6))*h^((3)/(2)))

Therefore, the simplified expression is 3136*d^((11)/(6))*h^((3)/(2)).

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Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

To find the standard deviation of BMI for the 9 patients in the study, we need to follow these steps:
Find the mean of the BMI scores: (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24) / 9 = 29.67
Subtract the mean from each BMI score to find the deviation: -4.67, -2.67, 1.33, 3.33, -3.67, -1.67, 8.33, 11.33, -5.67
Square each deviation: 21.81, 7.13, 1.77, 11.09, 13.45, 2.79, 69.43, 128.51, 32.15
Find the mean of the squared deviations: (21.81 + 7.13 + 1.77 + 11.09 + 13.45 + 2.79 + 69.43 + 128.51 + 32.15) / 9 = 32.12
Take the square root of the mean of the squared deviations to find the standard deviation: √32.12 = 5.67

Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

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The equation that has no solution is 2x+1=5x-3.

To find out which equation has no solution, we can use the process of elimination. First, let's look at the equation 2(x-7)=2x-14. If we simplify this equation, we get:
2x-14=2x-14
This equation is true for all values of x, so it has infinitely many solutions.

Next, let's look at the equation 15x-30=0. If we simplify this equation, we get:
15x=30
x=2
This equation has one solution, x=2.

Now, let's look at the equation 2x+1=5x-3. If we simplify this equation, we get:
-3x=-4
x=4/3
This equation has one solution, x=4/3.

Finally, let's look at the equation 3(2x+1)=6x+1. If we simplify this equation, we get:
6x+3=6x+1
3=1

This equation is never true, so it has no solution.

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The variable that satisfies the condition that the trinomial a^2 + 7a + 6 and the binomial a + 1 have the same value is a = -5 or a = -1.

Setting the trinomial and binomial equal to one another and then solving for the variable will help us identify the variable that satisfies the stated criteria. Which is:

a^2 + 7a + 6 = a + 1

By putting all the terms to one side and grouping like terms, we may make this equation simpler:

a^2 + 6a + 5 = 0

The quadratic expression on the left-hand side can now be factored:

(a + 5)(a + 1) = 0

To make each factor equal to zero, we can use the zero product property:

a + 5 = 0 or a + 1 = 0

In each equation, we can solve for a to obtain:

a = -5 or a = -1

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Answer:

7.5 inches is equal to 190.5 millimeters (mm).

To convert from inches to millimeters, we can use the conversion factor of 1 inch = 25.4 millimeters.

So, 7.5 inches x 25.4 millimeters/inch = 190.5 millimeters.

The percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

From the figure,

We can see that the total number of tiles used for flooring= 16

Out of this, 8 tiles used are white tiles.

Now it is said that the total number of white tiles is 25.

We are asked to find what percentage of 25 tiles are used on the laundry room floor.

We will use a fraction to describe the proportion of white tiles in the box to those used for the floor and then multiply it by 100 to find the percentage.

Percentage = ( white tiles used / Total number of white tiles ) * 100

            = 8/25 * 100 = 32%

Therefore the percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.

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The solution is, the measure of the, inscribed angle: 30°, and,

central angle: 60°.

The solution are,

the measure of angle C is 52°

the measure of angle B is 52°

the measure of angle BSD is 71°

the measure of angle CSE is 71°

the measure of angle E is 57°

the measure of arc BC 57°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

The central angle is double the inscribed angle for the same intercepted arc.

Since doubling the angle adds 30° to it,

the original inscribed angle must be 30°.

so, we get,

Then the central angle is 30°+30° = 2·30° = 60°.

The solution are,

the measure of angle C is 52°

the measure of angle B is 52°

the measure of angle BSD is 71°

the measure of angle CSE is 71°

the measure of angle E is 57°

the measure of arc BC 57°.

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The state income tax owed on a $40,000 per year salary is $1,500.

What is income tax?

A tax levied against people or organizations (taxpayers) in relation to their income or profits is known as an income tax. (commonly called taxable income). Tax rates multiplied by taxable income are typically used to calculate income taxes. Tax rates might change depending on the taxpayer's attributes and source of income.

To calculate the state income tax owed on a $40,000 per year salary, we need to determine which progressive tax range it falls into and apply the corresponding tax rate.

Since $40,000 falls within the range of $10,001 - $50,000, we will use the tax rate of 5% for this portion of the income.

First, we need to calculate the amount of income within this range -

$40,000 - $10,000 = $30,000

Next, we calculate the amount of tax owed on this portion of the income -

$30,000 x 0.05 = $1,500

Therefore, the value is obtained as $1,500.

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The quadratic formula is used to solve  equations of the form ax^(2) + bx + c = 0. The formula is given by:

x = (-b ± √(b^(2) - 4ac))/2a

In this case, the coefficients are a = 9, b = -3, and c = -1. Plugging these values into the formula gives:

x = (-(-3) ± √((-3)^(2) - 4(9)(-1)))/2(9)

Simplifying the expression gives:

x = (3 ± √(9 + 36))/18

x = (3 ± √45)/18

x = (3 ± 3√5)/18

Simplifying further gives:

x = (1 ± √5)/6

So the two solutions to the equation are:

x = (1 + √5)/6 ≈ 0.62

and

x = (1 - √5)/6 ≈ -0.29

Therefore, the two solutions to the equation 9x^(2)-3x-1=0 are x ≈ 0.62 and x ≈ -0.29.

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The lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years is $25,447.09.

To find the lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years, we can use the formula for compound interest;

A = P(1 + r/n)^(nt)

Where:
- A is the final amount
- P is the initial principal amount
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years

Plugging in the given values, we get:

61,000 = P(1 + 0.07/12)^(12*13)

Solving for P, we get:

P = 61,000 / (1 + 0.07/12)^(12*13)

P = 61,000 / (1.00583)^156

P = 61,000 / 2.39717

P = 25,447.09

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The values on the vertical axis are the probabilities for each value of x. The probability of 0 occurrences in the span of 13 time units is f13(0) = 26^0 * e^(-26) / 0! = e^(-26) ≈ 0.0000000000000000000000000003.

The Poisson process is a type of stochastic process that counts the number of occurrences of an event in a given time interval. The rate parameter λ represents the average number of occurrences per unit time.

i. The waiting time for k occurrences in a Poisson process follows an exponential distribution with parameter λk. The probability distributions for X1, X2, X3, and X5 are given by:

X1 ∼ Exp(λ) = Exp(2)

X2 ∼ Exp(λ*2) = Exp(4)

X3 ∼ Exp(λ*3) = Exp(6)

X5 ∼ Exp(λ*5) = Exp(10)

The expected waiting time E[Xk] is given by 1/λk, and the standard deviation σXk is also given by 1/λk. Therefore, we have:

E[X1] = 1/λ = 1/2

E[X2] = 1/(λ*2) = 1/4

E[X3] = 1/(λ*3) = 1/6

E[X5] = 1/(λ*5) = 1/10

σX1 = 1/λ = 1/2

σX2 = 1/(λ*2) = 1/4

σX3 = 1/(λ*3) = 1/6

σX5 = 1/(λ*5) = 1/10

The probability distributions for the interval 0 ≤ x ≤ 7 are shown below:

ii. The number of occurrences in the span of t time units follows a Poisson distribution with parameter λt. The probability distributions ft(x) for t = 13, t = 12, and t = 1.2 are given by:

ft(x) = (λt)^x * e^(-λt) / x!

f13(x) = (2*13)^x * e^(-2*13) / x! = 26^x * e^(-26) / x!

f12(x) = (2*12)^x * e^(-2*12) / x! = 24^x * e^(-24) / x!

f1.2(x) = (2*1.2)^x * e^(-2*1.2) / x! = 2.4^x * e^(-2.4) / x!

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In response to the aforementioned query, we may say that The right equation response is b. 25 virtual currency units (sufficient for Bloxburg purchase).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

You presently have 22 units of virtual currency, and John takes 21, according to the facts provided. You now only have 1 unit of virtual currency.

Consequently, to acquire Blox , you would require an additional 24 units of virtual currency.

The right response is b. 25 virtual currency units (sufficient for Bloxburg purchase).

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Answer:

-87.786

Step-by-step explanation:

Given:

Acceleration 1 = 3.20 m/s²

Acceleration 2 = 5.41 m/s²

Time = 28 s

To find: Acceleration before takeoff

Initial velocity = Average acceleration x time + 0.5 x acceleration 1 x time²

Initial velocity = 3.20 m/s² x 28 s + 0.5 x 3.20 m/s² x (28 s)²

Initial velocity = 2460.8 m

Acceleration before takeoff = (0 m/s - 2460.8 m/s) / 28 s

Acceleration before takeoff = -87.886 m/s²

Therefore, the acceleration before takeoff is -87.886 m/s².

On dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

Division algorithm states that -

Dividend = (Divisor x Quotient) + Remainder

Given is to find the remainder when -

(x³ + 7x² + 9x - 5) ÷ (x + 4)

We can write -

f(x) = (x³ + 7x² + 9x - 5)

g(x) = (x + 4)

So -

h(x) = f(x) ÷ g(x)

h(x) = (x³ + 7x² + 9x - 5) ÷ (x + 4)

h(x) = (x³ + 4x² + 3x² + 9x - 5)/(x + 4)

h(x) = x² + (3x² + 9x - 5)/(x + 4)

h(x) = x² + 3x + (-3x - 5)/(x + 4)

h(x) = x² + 3x - 3 + 7/(x + 4)

Therefore, on dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -

h(x) = x² + 3x - 3 + 7/(x + 4).

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To factor the trinomial 2x²+7x-4, you could rewrite it as 2x²+8x-2x-4, and then factor by grouping. The factor pairs of ac are (x+4), (2x-1).

To factor the trinomial 2x²+7x-4 by grouping, we need to find a factor pair of ac that sums to b. In this case, ac = (2)(-4) = -8 and b = 7.

The factor pair of -8 that sums to 7 is 8 and -1. Therefore, we can rewrite the trinomial as follows:

2x²+7x-4 = 2x²+8x-x-4

Next, we can group the first two terms and the last two terms:

(2x²+8x)+(-x-4)

Now, we can factor out the greatest common factor from each group:

2x(x+4)-1(x+4)

Finally, we can factor out the common factor of (x+4):

(x+4)(2x-1)

Therefore, the factored form of the trinomial 2x²+7x-4 is (x+4)(2x-1).

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The volume of the cone is approximately 94.25π cubic cm.

To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.

First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:

r = 9/2 cm

Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:

V = 1/3πr²h

V = 1/3π(9/2)²(14)

V = 1/3π(81/4)(14)

V = 1/3π(1134/4)

V = 1/3π(283.5)

V = 94.25π

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The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 4

tan 22.5° = n / 8

n = 3.3137

Then the perimeter is given as,

P = 8 x 3.3137

P = 26.51 units

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

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One leg of a right triangle measures 7 feet. If the other leg is 1 foot shorter than the hypotenuse, the dimensions of the right triangle will be 7 feet, 24 feet, and 25 feet.

To find the dimensions of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. The formula for the Pythagorean Theorem is a² + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

We are given that one leg of the triangle measures 7 feet, and the other leg is 1 foot shorter than the hypotenuse. Let's call the length of the other leg x and the length of the hypotenuse x + 1. We can plug these values into the Pythagorean Theorem to find the dimensions of the triangle:

72 + x2 = (x + 1)2

49 + x2 = x2 + 2x + 1

48 = 2x

x = 24

So the other leg of the triangle measures 24 feet, and the hypotenuse measures 24 + 1 = 25 feet. The dimensions of the right triangle are 7 feet, 24 feet, and 25 feet.

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1. (a) The probability that a randomly selected wafer is produced by machine A and not defective is 0.665 or 66.5%.
(b) The probability that a wafer is defective given that it is produced by machine B is 0.06 or 6%.
(c) The probability that a wafer is defective is 0.053 or 5.3%.
(d) The probability that a wafer is 0.947 or 94.7%.

2. (a) The probability that a car requires either a tune-up or a brake job is 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 0.392 or 39.2%.
(d) The events "car requires a tune-up" and "car requires a brake job" are independent because the probability of one event occurring does not affect the probability of the other event occurring. They are not mutually exclusive because a car can require both a tune-up and a brake job at the same time.

We can find the probability using this calculation:

The probability that a randomly selected wafer is produced by machine A and not defective is 0.7 x 0.95 = 0.665 or 66.5%.

The probability that a wafer is defective is (0.7 x 0.05) + (0.3 x 0.06) = 0.035 + 0.018 = 0.053 or 5.3%.

The probability that a wafer is not defective is 1 - 0.053 = 0.947 or 94.7%.

The probability that a car requires either a tune-up or a brake job is 0.6 + 0.02 - (0.6 x 0.02) = 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.6 x (1 - 0.02) = 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 1 - 0.608 = 0.392 or 39.2%.

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The requried distance formula to calculate the distance between points (x₁, y₁) and (x₂, y₂) is d = √((x₂ - x₁)² + (y₂ - y₁)²)

Distance is defined as the length of measure between two points on the coordinate plane.

Here,
The formula to calculate the distance between two points in a two-dimensional Cartesian coordinate system is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and sqrt represents the square root function.

This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two points represent the endpoints of the hypotenuse, and the distance between them is the length of the hypotenuse. Therefore, we can use the Pythagorean theorem to calculate the distance between the two points.

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Answer: The total height of the SUV and the box is 9 feet 1 inch.

Step-by-step explanation:

To solve this problem, we first convert the height of the SUV and the box from feet and inches to inches. The height of the SUV is 6 feet 4 inches, which is equal to 76 inches. The height of the box is 2 feet 9 inches, which is equal to 33 inches. We then add the heights of the SUV and the box to get the total height:

76 inches + 33 inches = 109 inches

To convert this back to feet and inches, we divide by 12 to get 9, with a remainder of 1. Therefore, the total height of the SUV and the box is 9 feet 1 inch.

The number of batches of the recipe Minh makes is 6

A proportion can be described as a mathematical comparison that is between two numbers.

These numbers can represent a comparison between things or people.

Also, proportions can also be written as two equivalent fractions. They are represented with the equality sign '=' or the equivalent sign ':'

From the information given, we have that;

For one recipe, one uses 1/3 cup of sesame seeds

Minh has 2 cups of sesame seeds

Then,

If 1/3 cup of sesame seeds = 1 recipe

Then 2 cups of sesame seeds = x

cross multiply

c = 2 × 3/1

c = 6 recipes

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