Fractions that are not equivalent to 1/5

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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Ms. Losch can cut the original piece of rope into as many pieces as she wants, provided that each piece is the same length as the original.

If the original piece of rope is 12 inches long, she can cut it into 12 one-inch long pieces, 6 two-inch long pieces, 4 three-inch long pieces, 3 four-inch long pieces, 2 six-inch long pieces, or 1 twelve-inch long piece.

It is important to note that the pieces of rope must all be the same length, so if she wants to make any combination of the lengths, she must make sure that the total length of the pieces of rope adds up to the original length.

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The expression as a perfect square trinomial is \(\rm x^2+4x+4\\\).

The expression as a perfect square trinomial is \(\rm x^2-20x+100\\\)

The expression as a perfect square trinomial is \(\rm x^2+4x+\dfrac{25}{4}\\\).

The given equations are as follows;

\(\rm x^2 + 2x + \\\\ x^2 -20x +\\\\ x^2 + 5x +\\\\\)

What values are needed to make each expression a perfect square trinomial?

According to the question

To know more about the values are needed to make a perfect square trinomial following all the steps given below.

A perfect square trinomial is equal to;

\(\rm (x+a)^2 = x^2+a^2+2ax\)

1. The given equation is,

\(\rm x^2 + 2x +\)

Then,

Compare with the formula of a perfect square trinomial.

\(\rm x^2+2ax+a^2= x^2+4x\\ \\ 4x=2ax\\ \\ a = \dfrac{4x}{2x}\\ \\ a=2\)

Substitute the value of a

\(\rm x^2+2ax+a^2= x^2+4x+(2)^2\\ \\ x^2+2ax+a^2= x^2+4x+4\\\)

The expression as a perfect square trinomial is \(\rm x^2+4x+4\\\).

2. The given equation is,

\(\rm x^2 - 20x +\)

Then,

Compare with the formula of a perfect square trinomial.

\(\rm x^2+2ax+a^2= x^2-20x\\ \\ -20x=2ax\\ \\ a = \dfrac{-20x}{2x}\\ \\ a=-10\)

Substitute the value of a

\(\rm x^2+2ax+a^2= x^2 -20x+(-10)^2\\ \\ x^2+2ax+a^2= x^2-20x+100\\\)

The expression as a perfect square trinomial is \(\rm x^2-20x+100\\\).

3. The given equation is,

\(\rm x^2 + 5x +\)

Then,

Compare with the formula of a perfect square trinomial.

\(\rm x^2+2ax+a^2= x^2+5x\\ \\ 5x=2ax\\ \\ a = \dfrac{5x}{2x}\\ \\ a=\dfrac{5}{2}\)

Substitute the value of a

\(\rm x^2+2ax+a^2= x^2+4x+(\dfrac{5}{2})^2\\ \\ x^2+2ax+a^2= x^2+4x+\dfrac{25}{4}\\\)

The expression as a perfect square trinomial is \(\rm x^2+4x+\dfrac{25}{4}\\\).

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Answer:

2022

Step-by-step explanation:

1

100

25/4

on edge

The physiological responses that occur in response to low blood levels of calcium are bones release calcium into the blood, the kidneys retain more calcium, intestines absorb more calcium

Calcium is a chemical element which plays an important role in building and maintaining strong bones. It also plays other significant roles in blood clotting, muscles contraction, and normal heart rhythms regulation, and nerve functions. Calcium ions are essential in several cellular processes and the body tightly regulates calcium levels within a narrow physiological range as relatively small changes can have dramatic effects, including heart failure, muscle and brain dysfunction, and even death. Blood calcium levels are regulated by parathyroid hormone (PTH), produced by the parathyroid glands. PTH is released in response to low blood calcium levels and improves calcium levels by targeting the skeleton, the kidneys, and the intestine. The physiological responses that occur in response to low blood levels of calcium are bones release calcium into the blood, the kidneys retain more calcium, intestines absorb more calcium

Note: The question is incomplete as it is missing options which are a) liver releases calcium into the blood. b) bones release calcium into the blood. c) kidneys retain more calcium. d) intestines absorb more calcium.

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Answer:

well it is b

Step-by-step explanation:

well I tried my best

When a figure or a shape is dilated, the size of its image will either be enlarged or compressed.

The scale of dilation from A to B is 1.5

See attachment for the image that completes the question.

Using a ruler, we have the following measurements

\(\mathbf{A = 1\ inch}\)

\(\mathbf{B = 1.5\ inches}\)

The scale factor (k) from A to B is:

\(\mathbf{k = \frac BA}\)

This gives

\(\mathbf{k = \frac {1.5\ inches}{1\ inch}}\)

\(\mathbf{k = \frac {1.5}{1}}\)

\(\mathbf{k = 1.5}\)

Hence, the scale factor (k) from A to B is 1.5

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

  (c)  (15, -30)

Step-by-step explanation:

A proportional relationship has the equation ...

  y = kx

The value of the constant of proportionality is the ratio of y to x:

  k = y/x = 40/-20 = -2

__

The point that is on the line y = -2x is the point (15, -30).

Answer:

160

Step-by-step explanation:

360-170-30=160 subtract all angles from 360

Answer:

140°

Step-by-step explanation:

oh, come on, this is like "you have 8 apples as a mixture of red and green apples. 5 apples are red, how many are green ?".

it is the same here.

the total angle is 170°.

now we know a part of it is 30°.

how large is the rest ?

well, it is 170 - 30 = 140°

Given:

The total 5 yards of thread on the spool.

Convert yard into meters.

For 5 yards to meters is,

Allison uses 3.5 meters of the thread, the thread remains is,

Answer: The thread left will be approximately 1.072 meters.

Answer:

5, 9,13,17

Step-by-step explanation:

5 +4 +4+4

One of k , k + 2 , k + 4 is divisible by 3 .

Given,

Positive integer(K) .

Here,

To prove this statement by cases, we can consider the three different cases: k is divisible by 3, k+2 is divisible by 3, and k+4 is divisible by 3.

Case 1: k is divisible by 3

If k is divisible by 3, then k is already a positive integer that is divisible by 3. Therefore, this case satisfies the statement that "at least one of k, k+2, or k+4 is divisible by 3."

Case 2: k+2 is divisible by 3

If k+2 is divisible by 3, then we can write k+2 = 3n for some positive integer n. Then, k = 3n-2 is a positive integer that is divisible by 3. Therefore, this case also satisfies the statement.

Case 3: k+4 is divisible by 3

If k+4 is divisible by 3, then we can write k+4 = 3n for some positive integer n. Then, k = 3n-4 is a positive integer that is divisible by 3. Therefore, this case also satisfies the statement.

Hence from cases we can justify our statement .

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the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

7

Step-by-step explanation:

The angles that we are sure about is 33 and 90. The angles of a triangle add up to 180. 33 + 90 = 123. 180 - 123 = 57. 57 = 7x+8, 49 = 7x, x = 7.

Answer:

x = 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Set Up Equation

33° + 90° + (7x + 8)° = 180°

Step 2: Solve for x

Answer:

1. Angle forming a linear pair sum to 180°

2. Transitive property of equality

3. Algebra

4. Definition of congruency

Step-by-step explanation:

The given statement and reasons are presented as follows;

Statement      \({}\)                          Reason

1. m∠GKH + m∠HKI = 180°    \({}\) 1. Angle forming a linear pair sum to 180°

m∠HKI + m∠IKJ = 180°

2. m∠GKH + m∠HKI = m∠HKI + m∠IKJ \({}\)2. Transitive property of equality

3. m∠GKH = m∠IKJ  \({}\)              3. Algebra

4. m∠GKH ≅ m∠IKJ               4. Definition of congruency

The explanation are;

1. The sum of angles on a straight line is 180°

2. The transitive property of equality can be written as follows;

Given a = c and b = c, therefore, a = b

3. The addition property of equality states that given a + b = c + b, therefore a = c

4. Two geometric figures are said to be congruent when they are equal.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

B. $330

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

180 = 60+40+4x+20

60 = 4x

15 = x

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

A fraction is a value representing a part of a whole.

We have,

Supporters for the Home team = 4/9

Supporting for the away team = 1 - 4/9 = 5/9

Now,

Male supporters from the away team = 3/5 x 5/9 = 1/3

So,

Female supporters from the away team = (1 - 3/5) x  5/9 = 2/5 x 5/9 = 2/9

Thus,

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

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1. A graph of two similar, but not equal, right triangles using segments of line AB as the hypotenuse of each triangle is shown below.

2. The three pair of corresponding angles and sets of proportionate sides include:

ΔACE ≅ ΔBDF, ΔAEC ≅ ΔBFD, and ΔCAE ≅ ΔDBF.

AC = BD, EC = FD, and AE = BF

3. Yes, the slope of line is the same between any two points on the line.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Part 1.

In this exercise, we would use an online graphing tool to create two similar, but not equal, right triangles by using line segments AB as the hypotenuse of each triangle.

Part 2.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent (similar) triangles and sets of proportionate sides:

Part 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using this formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope AC = (0 + 1)/(-3 + 5)

Slope AC = 1/2.

Slope BD = (3.5 - 2)/(4 - 1)

Slope BD = 1/2.

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Answer:

I think the first one is power ( if not then coefficient) and the second is definitely expression

Step-by-step explanation:

Answer:

The value of x=3

Step-by-step explanation:

We are given that

AE is parallel to BD.

BC=12 units

CD=16 units

DE=4 units

AB=x

We have to find the value of x.

Triangle proportionality theorem:

When a line  is parallel to  one side  of a triangle and intersect the other two sides of triangle, then the line divides the sides proportionally.

Using triangle proportionality theorem

\(\frac{BC}{AB}=\frac{CD}{DE}\)

\(\frac{12}{x}=\frac{16}{4}\)

\(x=\frac{12\times 4}{16}\)

\(x=3\)units

Hence, the value of x=3

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Therefore, a sailfish would travel 51 miles in 45 minutes if it maintained a speed of 68 miles per hour in the equation.

To calculate the distance traveled in a given time, we can use the formula distance = rate x time, where rate refers to the speed of travel and time refers to the duration of travel. In this scenario, we are given a rate of 68 miles per hour and a time of 45 minutes.

To use the formula, we first need to convert the time to hours since the rate is given in miles per hour. We do this by dividing the time by 60, since there are 60 minutes in an hour. In this case, 45 minutes divided by 60 minutes per hour gives us 0.75 hours.

Now, we can plug in the values for rate and time into the formula and solve for distance. Multiplying 68 miles per hour by 0.75 hours gives us a distance of 51 miles.

45 minutes / 60 minutes per hour = 0.75 hours

Then, we can use the formula: distance = rate x time

distance = 68 miles per hour x 0.75 hours

distance = 51 miles

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When performing one-dimensional graphical vector addition, the proper starting position for each of the two arrows representing the two vectors being combined depends on the specific scenario.

In general, when adding two vectors in one dimension, you can start both arrows at the same point, such as the origin of a coordinate system. This is commonly done when the vectors are acting in the same direction.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the right with a magnitude of 2 units, you can start both arrows at the same point and draw them to the right, one after the other, with a total length of 5 units.

However, if the two vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the left with a magnitude of 2 units, you can start the arrow for vector A at the origin and draw it to the right for 3 units.

Then, you can start the arrow for vector B at the endpoint of vector A and draw it to the left for 2 units. The resulting vector sum would be the vector connecting the starting point of vector A to the endpoint of vector B.

Therefore, the proper starting position for each of the two arrows representing the two vectors being combined in one-dimensional graphical vector addition depends on their directions. If the vectors are acting in the same direction, you can start both arrows at the same point.

If the vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

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Answer: I’ll explain it in simpler terms for you. A proportional relationship is one in which two quantities vary directly with each other. Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional. An example of a proportional relationship is simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Hope this helps! :D

Answer:3400

Step-by-step explanation:

Answer:

3240

Step-by-step explanation:

3.24

×

10

3

=

3.24

×

1000

This means you move the decimal spot 3 digit spaces to the right.

Count 3 spaces:

3.2.4.0 →

3240

So then your number becomes

3240

Answer:

Given data:

Arrange the numbers in the ascending order:

Identify the minimum and the maximum values:

Identify the median of the data set.

Since the number of data is even, the median is the average of the middle two numbers:

Identify the medians of the lower and upper regions.

For the lower region, the median- the first quartile is 14, for the upper region, the median - the third quartile is 83

We have all required numbers:

Attached is the example of the plot, this may be horizontal or vertical

Answer:

1:yes it is

2:no- an integer cannot have a decimal or fraction

3:yes it is

4: true

5: false- integers can be negative or positive

6: false- irrational numbers can be negative, have decimals or fractions

7: true