Points A and B have the same x-coordinates but opposite y-coordinates. How many units away are each of the points from the y-axis?
3
4
6
7

The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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Answer:

0.5

Step-by-step explanation:

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

Length of hypotenuse = √( a² + b²)

Step-by-step explanation:

The question is incomplete and unclear. From the question, it is clear we are to determine the hypotenuse of the triangle. Hence the triangle is a right angled triangle.

Find attached the diagram used in solving the question.

From the diagram,

a = opposite

b = adjacent

c = hypotenuse

To find the hypotenuse of a right angled triangle, we apply Pythagoras theorem.

Using Pythagoras theorem

Hypotenuse² = opposite ² + adjacent²

Insert the values of each, we have:

c² = a² + b²

Then we find the Square root both sides

c = √( a² + b²)

So we can insert the values of a and b if we are given.

For instance, if b = 6

c = √( a² + 6²)

Using the diagram,

Hypotenuse: c = √( a² + b²)

Answer:

Step-by-step explanation:

Answer: 6 feet

Step-by-step explanation:

1 inch= 2 feet

so

3 inches = 6 feet

ratio

Answer: 6

Step-by-step explanation:

The green line is located is \(\frac{1}{2}\)

Fraction - A fraction is numerical value which is a part of a whole number. It is created by dividing a whole into number of parts. There are three major types of fractions. They are proper fractions, improper fractions and mixed fractions.

Ken takes 5 steps to get to the spot where the green line falls, and the line falls exactly between the 3rd and 4th steps. Therefore, the green line is \(\frac{1}{2}\) of the way between the 3rd and 4th steps. So, the fraction that represents where the green line is located is \(\frac{1}{2}\)

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The fraction that represents where the green line is located is 7/12.

A division is an approach to communicating a piece of an entire or a proportion between two amounts.

It is addressed by two numbers isolated by a level line, where the number over the line is known as the numerator and the number beneath the line is known as the denominator.

The numerator addresses the piece of the entire or the amount being thought of, while the denominator addresses the absolute number of a balance of in the entire or the reference amount.

If the rug is exactly six steps wide, and Ken takes six steps to measure it, then each step represents 1/6th of the rug's width.

Since the green line falls right where the third and fourth steps meet, it is located between the 3rd and 4th step, which means it is on the 3.5th step.

Therefore, the fraction that represents where the green line is located is:

3.5 / 6

For simplifying this fraction, we can divide both the numerator and denominator by 0.5, which gives:

7/12

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multiplication property of equality

Division property of equality

a. The number of ways that this is done, if the order of the choices is relevant is 12 ways.

b. The number of ways that this be done, if the order of the choices is irrelevant is 6 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

= n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

When the orders are relevant, this will be:

= 4! / (4 - 2!)

= 4! / 2!

= 12

When orders are irrelevant, this will be:

= 4! / (4 - 2!)2!

= 6 ways

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Answer:

22.5

Step-by-step explanation:

8 pieces is 180 calories to find the calorie of one piece :

180/8 to get 22.5

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

We have,

In set theory, a proper class is a class that is not a set.

A class is a collection of objects, and a set is a class that can be a member of other classes.

On the other hand, a proper class cannot be a member of another class.

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

This means that V cannot be an element of any other class or set within the context of the set theory being considered.

The concept of proper classes is used to prevent paradoxes and contradictions that can arise when unrestricted comprehension is allowed in set theory.

Thus,

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

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Answer:

If the radius of the pastry stamp Petra uses to stamp circles in the dough for the donuts is 4.25 inches, then the diameter is 2 * 4.25 = 8.5 inches. The area of each donut can be calculated using the formula for the area of a circle:

Area of a circle = π * radius^2

So, the area of each donut is:

π * (4.25)^2 = 56.75π square inches (rounded to two decimal places)

If the radius of the pastry stamp Petra uses to stamp out circles for the donut holes is 0.4 inches, then the diameter is 2 * 0.4 = 0.8 inches. The area of each donut hole can be calculated using the same formula:

Area of a circle = π * radius^2

So, the area of each donut hole is:

π * (0.4)^2 = 0.16π square inches (rounded to two decimal places)

Hope This Helps!

Answer:

Привет! Кто-нибудь читал Криспину крест ведущего? Если да, то может ли кто-нибудь дать мне представление о том, как он изменился в этой истории! Спасибо за ваше время!

Step-by-step explanation:

The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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The Required equilibrium solution are (400, 40) (500, 50) (600,60).

To find the equilibrium solutions and to enter answer as a list of ordered pairs (A,L), where A is the number of aphids and L the number of ladybugs.

equation is the relationship between variable and represented as y =ax+b    is example of polynomial equation.

since the equilibrium solution given by the expression

L = 10A
where A is the number of aphids and L the number of ladybugs.

And ordered pairs with equilibrium solution  of one with 400 aphids and 40 ladybugs, one with 500 aphids and 60 ladybugs and one with 600 aphids and 60 ladybugs  are (400, 40) (500, 50) (600,60).

Thus, The Required equilibrium solution are (400, 40) (500, 50) (600,60).

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Answer: See explanation

Step-by-step explanation:

The sampling methods include:

1. Simple random sampling: Here, the individuals in the population have an equal chance of being selected as the selection is done randomly and anyone can be picked from the population

2. Systematic sampling: This is when the selection of the individuals is done at regular intervals. For example from the population, every 10th person might be picked.

3. Stratified sampling: Here, the total population is first divided into a smaller group called the strata before the sampling is done.

4. Clustered sampling: Here, the sampling unit is the subgroups of the population and not the individuals.

Answer: The treatments in the study are strength training, flexibility training, aerobics, and jogging.

Step-by-step explanation:

A correct description of a feature of the study is that the treatments in the study are strength training, flexibility training, aerobics, and jogging.

It should be noted that the study has no replication. Also, the experimental units are the 40 members that participated.

Therefore, the correct option is D.

Answer:

  38°

Step-by-step explanation:

The sum of angles that make a line is 180°; the sum of angles in a triangle is 180°. So, we have the following relations:

  2x +y +A = 180

  2y +x + B = 180

  A +B +33 = 180

Adding the first two equations and subtracting the third, we get ...

  (2x +y +A) +(2y +x +B) -(A +B +33) = 180 +180 -180

  3x +3y -33 = 180

  x + y - 11 = 60

  x + y = 71

__

We know vertical angles are congruent, so in triangle QRK, we have ...

  2y +2x +∠K = 180

  ∠K = 180 -2x -2y = 180 -2(x +y) = 180 -2(71)

  ∠JKL = 38°

Answer:

38 degrees

Step-by-step explanation:

Answer:

Leena walked 5/7 miles with her friend

Step-by-step explanation:

7/7 = 1

7 +4 =11

Answer:

5/7

Step-by-step explanation:

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Therefore, the solution to the equation \((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system is z = -1.

To solve the equation\((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system, we can simplify the equation and then find the values of z that satisfy it.

Let's start by simplifying the equation:

\((z + 1)^7 + (z + 1)^7 = 0\)

We notice that both terms on the left side of the equation are identical, so we can rewrite it as:

2(z + 1)^7 = 0

Now, we can divide both sides of the equation by 2 to isolate the term\((z + 1)^7:\)

\((z + 1)^7 = 0\)

To find the solutions, we set each factor of \((z + 1)^7\)equal to zero. In other words, we set the exponent 7 to be a multiple of 2:

z + 1 = 0

From this equation, we find that z = -1.

It's important to note that complex numbers have a real and imaginary part.

In this case, since the equation simplifies to a real number, the solution is a real number (-1).

If the equation involved complex terms or the roots of unity, the solutions could include complex numbers as well.

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To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

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Answer:

Jemma: 22x + 5

Debra: 20x

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = n*25

V is the value of the quarters.

n is the number of quarters

and 25 is the value (in cents) of each quarter.

The quotient is equal to  \(x^{2} +x+1\)

Given

The provided equation is as follows:

\(\frac{x^{2}+1 }{x-1}\)

What exactly is synthetic division

The synthetic division method is a quick way to divide polynomials.

When divided by the linear factor, it is also known as the polynomial division technique of a specific instance.

Therefore,

The quotient is as follows:

\(\frac{x^{2}+1 }{x-1}\)

\(\frac{x(x^{2} +x+1)-1(x^{2} +x+1)}{x-1}\)

\(\frac{(x-1)(x^{2} +x+1)}{x-1}\)

\(x^{2} +x+1\)

As a result, the quotient is

\(x^{2} +x+1\)

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Answer: C

Step-by-step explanation:

Answer:

123 m²

Step-by-step explanation:

Surface area of the object = surface area of the bigger rectangular prism + (surface area of the smaller rectangular prism - area of the smaller rectangular prism base)

Surface area of the bigger rectangular prism:

L = 7 m

W = 3 m

H = 3 m

S.A = 2(LW + WH + LH)

S.A = 2(7*3 + 3*3 + 7*3)

S.A = 102 m²

Surface area of the smaller rectangular prism:

L = 3 m

W = 3 m

H = 1 m

S.A = 2(LW + WH + LH)

S.A = 2(3*3 + 3*1 + 3*1)

S.A = 30 m²

Area of the base of the smaller rectangular prism = L*W

L = 3 m

W = 3 m

Area = 3*3 = 9 m²

Surface area of the object = 102 + (30 - 9)

= 102 + 21

= 123 m²

You have that the red curve is:

f(x) = x²

you can notice that the blue curve is a translation of the red curve. The vertex of f(x) is (0,0). The vertex of the blue curve is (2,1).

Take into account that the general expression for a parabola is:

g(x) = (x - h)² + k

where (h,k) is the vertex. By replacing h=2 and k=1, the values of the coordinates of the blue curve, you have:

c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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The maximum amount you can finance is $896.

We are given that;

The monthly gross income = $3,200

Now,

28% of your gross monthly income on your mortgage, including taxes and insurance

The percentage = 28%

3200* 28/100

=32*28

=896

Therefore, by percentage the answer will be $896.

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