bvement of the progress bor moy be uneven becouse questions can be worth more or less Rewrite ((1)/(3))^(-4)=81 as a logarithmic equation.

The following are the correct convertion for the units of mass:

8000 mg converted to gram is 8 g

80 g converted to kilogram is 0.08 kg

0.8 kg converted to g is 800 g.

Gram (g) is the base unit of mass in the metric system. The milligrams (mg) and kilograms (kg) are derived units.

1 gram = 1000 milligrams (mg)

1000 grams = 1 kilogram (kg)

8000 mg = (8000/1000) g

8000 mg = 8 g

80 g = (80/1000) kg

80 g = 0.08 kg

0.8 kg = (0.8 × 1000) g

0.8 kg = 800 g.

In conclusion, 8000 mg converted to gram is 8 g, 80 g converted to kilogram is 0.08 kg, and 0.8 kg converted to g is 800 g.

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The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.

Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.

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--The given question is incomplete, the complete question is

"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--

(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.

An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.

(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.

(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.

(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.

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The length of the rectangular prism is 13 centimetres.

The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:

Therefore,

volume of a rectangular prism = lwh

where

Hence, let's find the length

volume of a rectangular prism = lwh

208 = 16 × l

16l = 208

divide both sides by 16

l = 208 / 16

l = 13 cm

Therefore,

length of the prism = 13 cm

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Lowering interest rate by a government's central bank can have a significant impact on the economy, as it affects the cost of borrowing money for businesses and individuals, as well as the return on savings and investments.

Lowering interest rate reduces the cost of borrowing money, making it easier for businesses and individuals to access credit. It can also encourage consumers to spend more money, as they may have more disposable income due to lower borrowing costs or higher investment returns.

It can also lead to increased inflation, as businesses and individuals have more money to spend and demand for goods and services increases and reduced returns on savings and investments, which can discourage people from saving and lead to more spending

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Answer: 207.1875

Step-by-step explanation:

side length a = 19.5 cm

side length b = 21.25 cm

diagonal p = q = 28.841159824112 cm

perimeter P = 81.5 cm

area of rectangle A = 414.375 cm2

area of rectangle divided into a triangle = 207.1875

hope this helps

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:

Where r = radius of the base and h = height of the cylinder.

Here we have

Diameter of the cylinder = 2.8 cm

Radius of the cylinder = 2.8/2 = 1.4 cm

Height of the cylinder = 3.7 cm  

Using the formula,

The surface area of a cylinder SA= 2πr² + 2πrh

The surface area of the cylinder

= 2π(1.4)² + 2π(1.4)(3.7)

= 2π(1.4)² + 2.8π(3.7)

Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder

Therefore,

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

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hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)

The size of angle ACB is approximately 50.66°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

We are given that;

Angle ABC= Angle ACD + 31°

Now,

Since angle ABC is twice angle BAC, we can write:

angle BAC = x

angle ABC = 2x

angle ACB = 180° - (angle BAC + angle ABC)

Substituting these values into the equation for angle ACD, we get:

angle ACD = angle ABC + 31° = 2x + 31°

Since angles ACB and ACD form a straight line, we can write:

angle ACB + angle ACD = 180°

Substituting the values we know, we get:

(angle BAC + angle ABC) + (angle ABC + 31°) = 180°

3x + 31° = 180°

3x = 149°

x = 49.67°

Therefore, the angle of triangles answer will be 50.66°.

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The length of the enlargement of the cube, given the scale factor and the length, would be 12 cm.

When a shape is enlarged by a scale factor of k, all its dimensions are multiplied by k. In this case, the scale factor is 1 1/2, which can be written as 3/2 in fraction form. Therefore, the length of the enlargement is:

Length of enlargement = Scale factor x Original length

Length of enlargement = (3/2) x 8 cm

Length of enlargement = 12 cm

So, the length of the enlargement is 12 cm.

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The value of the expression −16 + 12 is −4.  

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is performed by subtracting the second number from the first number.

We can subtract fractions, decimals, and negative numbers by following the same principles of subtraction.

Here we have

The numerical expression −16 + 12    

As we know

12 is 4 greater than 16 and 16 has a negative sign

Therefore,

The value of the expression −16 + 12 is −4.  

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The roots in simplest form are x=-8+6i and x=-8-6i.

The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.

To complete the square, follow the steps below:

1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2

2. Square the coefficient of the x^2 term: (5x^2/2)^2

3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2

4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140

5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140

6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10

7. Simplify:
x = -8 ± √14  / 1

Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:

1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:

-5x^(2)-80x=140

2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:

-5(x^(2)+16x)=-140

3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:

-5(x^(2)+16x+64)=-140+320

4. Simplify the right side of the equation:

-5(x+8)^(2)=180

5. Divide both sides of the equation by -5:

(x+8)^(2)=-36

6. Take the square root of both sides of the equation:

x+8=±6i

7. Solve for x:

x=-8±6i

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(a) The proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) The proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

To find the proportion of observations in a standard normal distribution that satisfies each of the statements, we need to use a standard normal distribution table or calculator.

(a) z > -1.66

We need to find the area to the right of z = -1.66 on a standard normal distribution table or calculator. This is equivalent to finding the area to the left of z = 1.66 since the standard normal distribution is symmetrical.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525. Therefore, the area to the right of z = -1.66 is:

1 - 0.9525 = 0.0475

So, the proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) -1.66 < z < 1.66

We need to find the area between z = -1.66 and z = 1.66 on a standard normal distribution table or calculator.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525 and the area to the left of z = -1.66 is 0.0475 (as calculated in part (a)). Therefore, the area between z = -1.66 and z = 1.66 is:

0.9525 - 0.0475 = 0.9050

Therefore, the proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

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Answer:

See below.

Step-by-step explanation:

We are asked to "expand", rather distribute the expression.

We can Distribute due to the Distributive Property.

The Distributive Property is a property that allows us to distribute the multiplier into numbers in the parentheses.

Let's distribute for this expression.

Distribute:

[tex]-5(-2d + 6)=(-5 \times -2d)+(-5 \times 6)= 10d -30[/tex]

Our distributed expression is 10d - 30.

The identity cos²θ/2 is (1 + cosθ)/2

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the half-angle identity for the cosine function to solve this problem:

cos²θ/2 = (1 + cosθ)/2

Therefore, to find cos²θ/2 , we need to know the value of cosθ.

If the value of cosθ is known, we can substitute it into the half-angle identity to find cos²θ/2

Hence, the identity cos²θ/2 is (1 + cosθ)/2

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Using the unitary method we found that the actual distance between Snohomish to Seattle is 32 miles.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Given,

The measured distance from Snohomish to Seattle on a road map = 3.2 inches

The scale of the map is given as:

  1 inch = 10 miles

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. The use of scale is necessary for generating an accurate map and makes it simple to establish the real size of any area on the map.

The actual distance can be found using the unitary method.

So it is given 1 inch on the map = 10 miles on the road

Then 3.2 inches on the map = 10 * 3.2 = 32 miles on the road

Therefore using the unitary method we found that the actual distance between Snohomish to Seattle is 32 miles.

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The rule for the function g(x) when completed is g(x) = -10, -15 ≤ x < -10; g(x) = -8, -10 ≤ x < -8; g(x) = -6, -8 ≤ x < -1; g(x) = 2, -1 ≤ x < 1; g(x) = 4, 1 ≤ x < 10; g(x) = 8, 10 ≤ x < 15

Given

The graph of the function g(x) such that the function g(x) is a piecewise function and each sub-function is represented by horizontal lines

To complete the function definition, we write out the y value and the domain of the functions based on the current domain

Following the above statements, we have the following function definition for g(x)

g(x) = -10, -15 ≤ x < -10

g(x) = -8, -10 ≤ x < -8

g(x) = -6, -8 ≤ x < -1

g(x) = 2, -1 ≤ x < 1

g(x) = 4, 1 ≤ x < 10

g(x) = 8, 10 ≤ x < 15

The above is the definition of the function g(x)

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The ordered pairs are the solution to the inequality as follows:

6) (-1,3) and 7) (1,4).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per the question, we have:

5) (0,-1)

No, this ordered pair is not a solution to the inequality.

6) (-1,3)

Yes, this ordered pair is a solution to the inequality.

7) (1,4)

Yes, this ordered pair is a solution to the inequality.

8) (0,0)

No, this ordered pair is not a solution to the inequality.

9) (3,3)

No, this ordered pair is not a solution to the inequality.

10) (2, 1)

No, this ordered pair is not a solution to the inequality.

Thus, the ordered pairs are the solution to the inequality as follows:

6) (-1,3) and 7) (1,4).

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To find the missing quantity, we will plug in the given values into the formula for simple interest and solve for the unknown variable. The formula for simple interest is I = Pxrxt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given:
P = $4000
r = 8% = 0.08
t = 3 years

Plugging in the given values into the formula, we get:

I = $4000 x 0.08 x 3

Simplifying the equation, we get:

I = $960

Therefore, the missing quantity is the interest, I, which is equal to $960.

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The x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

R(x) cannot be at x=-1, -2, 2, 3 because these are the values of the function at these points. Additionally, R(x) cannot be at x=10 and x=1 because these are the holes of the function. Therefore, the x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

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The result of this synthetic division is the quotient (1 2/3 5/3)

To divide two polynomials using synthetic division, we need to write the dividend as a binomial of the form (x-r) and the divisor in its linear form. In this case, the binomial is (x+2) and the linear form is 3x2+7x+2.

Quotient:
3/3=1

2/3=2/3

Coefficients of dividend: 3 7 2

Quotient: 1 2/3

Product of quotient and binomial: (x+2)

(3x2+7x+2) - (x+2): 3x+5 2

Quotient:
3/3=1

2/3=2/3

5/3=5/3

The result of this synthetic division is the quotient (1 2/3 5/3).

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Answer: 75% of $13.50 is 10.125

Step-by-step explanation:

Answer:

10.125

Step-by-step explanation:

13.50 x .75 = 10.25

Answer:

C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.

Answer:

C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.

Step-by-step explanation:

Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will  will hold your money until you want to deposit it out of your account.

The fraction when a 100-square grid has 70 shaded squares will be 7/10.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, a 100-square grid has 70 shaded squares.

The fraction will be:

= Number it shaded square / Total square

= 70 / 100

= 7 / 10

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A 100-square grid has 70 shaded squares. Explain how you could express this model as a fraction.

Answer:

The fraction when a 100-square grid has 70 shaded squares will be 7/10.

The equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6. To find the equation of a line that passes through a given point with a given slope, we can use the point-slope formula. The point-slope formula is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point that the line passes through. In this case, the slope is -(2)/(3) and the point is (3, 4).

Plugging these values into the point-slope formula, we get:

y - 4 = -(2)/(3)(x - 3)

We can then rearrange the equation to get it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

y - 4 = -(2)/(3)x + 2
y = -(2)/(3)x + 6

So, the equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6.

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Answer:

True both each.

Step-by-step explanation:

Your teacher would probably like you to remember the Trig Identities or allow you to have a cheat sheet for the Quiz or Test.

[tex]\frac{sin(\alpha )}{sin^{2}(\alpha) +cos2\alpha } \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +[cosx^{2} (\alpha)-sinx^{2} (\alpha )]} \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +cosx^{2} (\alpha)-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{[sin^{2}(\alpha) +cosx^{2} (\alpha)]-sinx^{2} (\alpha )}[/tex]

[tex]\frac{sin(\alpha )}{1-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )*cos(\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )}*\frac{1}{cos(\alpha )} \\\\tan(\alpha )*sec(\alpha )\\\\\frac{1}{cot(\alpha )}*sec(\alpha )\\\\\frac{sec(\alpha )}{cot(\alpha )}[/tex]

Points A and Q are connected by a line. To get the length of AR, measure the distance between A and Q and multiply that value by k. To find point R, mark off the length of AR along a ray that extends from point A in the direction of Q.

In mathematics, a ray is a segment of a line with a known starting point but no known endpoint. It can go on forever in that one direction. A beam cannot be measured since it lacks a terminal. fun facts A ray is similar to the sun's rays.

In geometry, a ray is a line that, starting from a single terminal, extends indefinitely in one direction (or point of origin). A ray is represented by a beam of sunlight travelling across space; while the sun is the ray's goal, it continues to travel forever.

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Complete question -

The equation f(x) = 0 has four complex zeros: ±2i and 1 ± √2i, each with a multiplicity of 1.

To solve the equation f(x) = 0, we need to factor the polynomial f(x) into linear factors and then find the zeros of the equation.

Step 1: Factor the polynomial f(x) into linear factors.
f(x) = x ^ 4 + 2x ^ 3 + x ^ 2 + 8x - 12
= (x^2 + 4)(x^2 - 2x + 3)

Step 2: Find the zeros of the equation by setting each factor equal to zero and solving for x.
x^2 + 4 = 0
x^2 = -4
x = ±√(-4)
x = ±2i

x^2 - 2x + 3 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
x = (-(-2) ± √((-2)^2 - 4(1)(3)))/(2(1))
x = (2 ± √(-8))/2
x = (2 ± 2√2i)/2
x = 1 ± √2i

State the multiplicity of each zero.
The zeros of the equation are ±2i and 1 ± √2i. Each zero has a multiplicity of 1.

Use the table from your calculator to find any real zeros, then use synthetic division to find the remaining zeros.
There are no real zeros in this equation, as all of the zeros are complex numbers. Therefore, there is no need to use the table from the calculator or synthetic division to find the remaining zeros.

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Answer: To find the number of stamps on each page, we can divide the total number of stamps by the number of pages:

263 stamps ÷ 9 pages = 29.22 stamps per page (rounded to two decimal places)

Since we want to place the same number of stamps on each page with as few left over as possible, we can round down to the nearest whole number:

29 stamps per page

To find out how many stamps were left to put in an envelope, we can multiply the number of pages by the number of stamps per page, and then subtract from the total number of stamps:

263 stamps - (29 stamps per page x 9 pages) = 8 stamps left over to put in an envelope

Therefore, the completed sentences are:

29 stamps were placed on each page.

8 stamps were put in an envelope.

Step-by-step explanation:

The right rectangular prism's longest line segment measures around 14.79 cm in length.

We are aware that the rectangular prism's body diagonal makes up the longest line segment inside a right rectangular prism. The longest distance is that between points A and D. AD is the longest line segment as a result. To determine a line segment's length, use a scale. Straight line segments can be measured with it.

The Pythagorean theorem can be used to determine how long the space diagonal is:

a = length = 12.6 cm

b = width = 3.2 cm

c = height = 7 cm

You may determine the space diagonal (d) by using:

d = sqrt(a² + b² + c²)

Substituting the values, we get:

d = sqrt(12.6² + 3.2² + 7²) cm

d = sqrt(159.76 + 10.24 + 49) cm

d = sqrt(219) cm

d ≈ 14.79 cm

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Question:

What is the measurement of the longest line segment in a right rectangular prism that is 12.6 centimeters long, 3.2 centimeters wide, and 7 centimeters tall, and that connects two vertices that are not on the same face of the prism?

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

Bonjour !

Il faut isoler x.

3x + 4 = 2x + 9

3x - 2x = 9 - 4

x = 5