lf A is equal to 0.5 (a+bh) express h in terms of A, and b​

The numbers when decomposed using their prime factors are 72: 2³ × 3², 204: 2² × 3 × 17, 1800: 2³ × 3² × 5² and  42336: 2⁵ × 3 × 11² × 17

To decompose a number into its prime factors, we need to find the prime numbers that multiply together to give the original number.

The numbers are given as  72, 204, 1800, and 42336

So, we have

Let's decompose each of the given numbers:

72 = 2 × 2 × 2 × 3 × 3

Prime factorization: 2³ × 3²

204 = 2 × 2 × 3 × 17

Prime factorization: 2² × 3 × 17

1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

Prime factorization: 2³ × 3² × 5²

42336 = 2 × 2 × 2 × 2 × 2 × 3 × 11 × 11 × 17

Prime factorization: 2⁵ × 3 × 11² × 17

Therefore, the prime factorization of each number is:

72: 2³ × 3²

204: 2² × 3 × 17

1800: 2³ × 3² × 5²

42336: 2⁵ × 3 × 11² × 17

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By using the graph, the key features of the function include the following:

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or {x|x ∈ R}.

Range = {-1, ∞}.

Based on the graph, the x-intercept and y-intercept of the function both occur at the origin (0, 0).

When x = -2, the y-value is given by:

f(-2) = 3.

When x = 2, the y-value is given by:

f(2) = -1.

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There is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

The amount of drug in a given volume of a medication can be calculated using the following formula: Amount of drug (mg) = Volume (mL) x Concentration (mg/mL). In this case, we have 30 mL of a 60 mg/5 mL elixir, so the amount of drug in 30 mL can be calculated as follows: Amount of drug (mg) = 30 mL x 60 mg/5 mL = 360 mg. Therefore, there is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

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Answer:

  4.0 feet

Step-by-step explanation:

You want the diameter of a rubber ball that costs $1, if that cost is $0.02 per square foot.

The surface area of a sphere is given by ...

  A = 4πr²

In terms of diameter, this is ...

  A = 4π(d/2)² = πd²

The cost will be ...

  Cost = (cost/square foot)(area)

  1.00 = 0.02(πd²)

Solving for d, we have ...

  d² = 1.00/(0.02π) ≈ 15.915

  d ≈ √15.915 ≈ 3.989 ≈ 4.0 . . . . feet

The diameter of the ball is about 4.0 feet.

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Therefore the total cost for 18 months of membership is[tex]$742.50[/tex].The equation to find the cost of initiation and x months of membership is y + 59x = 742.50

The equation to find the cost of initiation and x months of membership is y + 59x = 742.50. Since the cost for one year of membership is known, the cost for initiation can be found by subtracting 59x from both sides of the equation, resulting in y = 742.50 - 59x. To find the total cost for 18 months of membership, we plug x = 18 into the equation, resulting in y + 59(18) = 742.50. This can be simplified to y + 1062 = 742.50, which means that y = -319.50. Therefore, the total cost for 18 months of membership is[tex]$742.50 - $319.50[/tex], which equals [tex]$423.00[/tex]. This calculation can be represented by the equation y + 59x = 742.50, where y is the cost of initiation and x is the number of months of membership. Plugging in the number of months of membership (x = 18) gives us the total cost for 18 months of membership (y + 1062 = 742.50). Simplifying this equation yields y = -319.50, and therefore the total cost for 18 months of membership is[tex]$742.50.[/tex]

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The volume of the right circular cone is approximately 1819.1 cubic centimeters.

Volume is the measure of the amount of space occupied by a three-dimensional object or shape. It is expressed in cubic units, such as cubic centimeters, cubic meters, or cubic inches, depending on the system of measurement being used. The formula for volume varies depending on the shape of the object, but for many common three-dimensional shapes, such as cubes, spheres, cylinders, and cones, there are well-known formulas for calculating their volumes.

According to the given information :

The formula for the volume of a right circular cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(9.6 cm)²(19.9 cm)

V ≈ 1819.1 cubic centimeters (rounded to the nearest tenth)

Therefore, the volume of the right circular cone is approximately 1819.1 cubic centimeters.

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Answer and Explanation:

1. corresponding: bottom right graph

         → the angles are in the same place in relation to the parallel lines

2. alternate interior: bottom left graph

         → the interior angles are on opposite sides of the transversal

3. alternate exterior: top left graph

         → the exterior angles are on opposite sides of the transversal

4. none of these: top middle graph

         → there are no parallel lines

Answer:

To find out which expression must be added to 3x - 7 to equal 0, we need to solve the equation:

3x - 7 + a = 0

where "a" is the expression to be added.

To solve for "a", we can isolate "a" on one side of the equation by adding 7 to both sides:

3x - 7 + a + 7 = 0 + 7

Simplifying the left side, we get:

3x + a = 7

Therefore, the expression that must be added to 3x - 7 to equal 0 is:

a = -3x + 7

We can check that this is correct by substituting -3x + 7 for "a" in the original equation:

3x - 7 + (-3x + 7) = 0

Simplifying the left side, we get:

3x - 3x - 7 + 7 = 0

0 = 0

The equation is true, which confirms that the expression -3x + 7 must be added to 3x - 7 to equal 0.

Step-by-step explanation:

The calculated vertex of the graph represented in the figure is (-3, -3)

Given that we have the graph

The curve on the graph is a quadratic function

As a general rule, the vertex of a graph is the minimum or the maximum point on a graph

From the graph, we have the minimum point to be

Minimum = (-3, -3)

This means that

Vertex = (-3, -3)

Hence, the vertex is (-3, -3)

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The correct locations for the three missing labels in the diagram are "Analyze the Situation" in the top-left corner, "Identify Options" in the bottom-left corner, and "Make a Decision" in the bottom-right corner. We need to apply the decision-making process to the three missing labels in the diagram.

The first missing label is for the top-left corner of the diagram. The correct location for this label is "Analyze the Situation." This is because the decision-making process begins with an analysis of the situation to understand the problem and identify any potential constraints.

The second missing label is for the bottom-left corner of the diagram. The correct location for this label is "Identify Options." This is because the decision-making process involves identifying all of the available options for solving the problem.

The third missing label is for the bottom-right corner of the diagram. The correct location for this label is "Make a Decision."

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A $9. 00 album is marked up 6 1/4% and then is offered for 14% off. If the sales tax is 5%. The total amount of tax that must be paid for this album is $0.41.

Let's break this problem down into steps:

Markup price = $9.00 + 6.25% of $9.00

Markup price = $9.00 + $0.56

Markup price = $9.56

Sale price = Markup price - 14% of Markup price

Sale price = $9.56 - 14% of $9.56

Sale price = $9.56 - $1.34

Sale price = $8.22

Tax amount = 5% of the Sale price

Tax amount = 5% of $8.22

Tax amount = $0.41

Therefore, the total amount of tax that must be paid for this album is $0.41.

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Answer:

3/8

Step-by-step explanation:

1/4+1/8

2/8+1/8

=

3/8

3/8

1+2 to equal 3, which is all the numerators above the least common denimonater 8

Answer:

1.)  51.515%  2.) 48.485%

Step-by-step explanation:

In this question we know 66 is 100% of the fraction, so we can start the process of converting a fraction into a percent, by figuring out how to adjust the fraction so that the denominator will be 100. First, divide 100 by the denominator.

100/66 = 1.515

Now we want to multiply denominator and numerator by 100.

34 × 1.515 = 51.515

66 × 1.515 = 100

Therefore, 34/66 as a percentage will be 51.515%

Now we want to convert 32/66. We will do the same for this equation.

100/66 = 1.515

32 × 1.515 = 48.485

66 × 1.515 = 100

Therefore 32/66 as a percentage will be 48.485

Hope this helps : )

Based on the information provided, the probability of both events happening is 0.011 or 1.1% (option A).

The probability can be described as the proportion between the desired outcome happening and the total of possible outcomes. Using this principle, let's calculate the probability:

Probability of Gypsy finishing first: 1 / 10 = 0.1

Probability of Silver Rush finishing second: 1/ 9 = 0.11

Total probability 0.1 x 0.11 = 0.011 or 1.1% (0.011 x 100)

Therefore, the answer that matches the probability is option A.

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Answer: 17.5

Step-by-step explanation:

First find the two numbers (data values) that are in the middle. Thats 15 and 20. When you have two numbers in the middle of a data set you average them. (Buy adding 15 and 20 then dividing by 2) So the answer is 17.5

Answer:

50s

Step-by-step explanation:

180cm³= 30s

300cm³=x s

Thus,

180x= 30×300

180x = 9000

x= 50s.

Hope this helps! :)

Therefore , the solution of the given problem of expression comes out to be  the response is j + 8.

Calculations like variable multiplication, splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

We must first determine the difference between 10 and 2, which is: before we can add the distinction of 10 and 2 to j.

=> 10 - 2 = 8

Now, by writing only the expression: we can add 8 to j.

=> j + 8

Consequently, the response is j Plus 8.

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The reasons for the statements supporting the proof that ∡TV ≅ ∡ XW are given as follows;

A - Given

H - Vertical Angles

F- Angles that inscribe a half circle are congruent and 90°

C - Angle-Angle-Side Triangle Congruence

E - CPCTC

D - Reflexive Property

I - Hypotenuse Leg (H-L) Triangle Congruence

G - CPCTC

B - Arcs of a congruent angles are congruent

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". It is a theorem used in geometry to prove that two triangles are congruent.

An inscribed angle is half the measure of its intercepted arc. A half circle is a semicircle, which has an intercepted arc of 180°, so the inscribed angles are 1/2(180°) = 90° and congruent.

The reflexive property is a property of equality that states that any quantity is equal to itself. In other words, a = a. This property is used in many mathematical proofs.


The Hypotenuse-Leg (H-L) Triangle Congruence is a rule used to prove that two right triangles are congruent. If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and the corresponding leg of another triangle, then the two triangles are congruent.


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Answer:

x = 114 degrees

Step-by-step explanation:

Angle x and the exterior angle form a straight line, which is 180 degrees. Because of this, we can subtract 66 from 180, equaling 114.

The minimum value of the function is 9, and the function never stops increasing.

The given function is y=(x−9)²+9.

We need to find the minimum and maximum value of the function. The given function is a quadratic function whose graph is a parabola. Since the coefficient of x² is positive, the graph of the quadratic function will be in the form of an upward parabola whose vertex is at the point (h,k).

The vertex form of the quadratic function is given byy = a(x - h)² + k, where(h,k) is the vertex of the parabola.

a is the coefficient of (x - h)².

In the given function,y = (x-9)² + 9, the vertex of this function is (9,9) and a=1.

Therefore, the minimum value of the function is 9 at x=9, which is the vertex of the parabola.

The function y=(x−9)²+9 is an upward parabola, and hence it never stops increasing, which means that the function has no maximum value.

Thus, the minimum value of the function is 9, and the function never stops increasing.

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Answer:

the third option

Step-by-step explanation:

Answer: 32+2.25(8)=50

Step-by-step explanation:

If you have $50 and waste $32 that leaves you with $18.

If each dip cost 2.25 you can have a total of 8 dips.

32+2.25(x)=50

32+2.25(8)=50

Answer:

40 and 27

Step-by-step explanation:

Answer:Let's call the two numbers x and y.

From the problem, we know that:

x + y = 67 (equation 1)

and

x - y = 13 (equation 2)

To solve for x and y, we can use the method of elimination. We can add equations 1 and 2 to eliminate y:

(x + y) + (x - y) = 67 + 13

Simplifying this equation, we get:

2x = 80

Dividing both sides by 2, we get:

x = 40

Now we can use equation 1 to solve for y:

x + y = 67

40 + y = 67

Subtracting 40 from both sides, we get:

y = 27

Therefore, the two numbers are 40 and 27.

Step-by-step explanation:

The set of sample means generated by Mark may not be representative of the population of the city.

This is because Mark's sampling method is not random and may introduce bias into the sample. By only surveying bypassers in the central street, the sample may not be representative of the whole population of the city. On the other hand, Judy's random sampling method has a higher chance of capturing a representative sample of the population.

To confirm this, we can compare the sampling distributions generated by both methods. We can calculate the mean and standard deviation of the sample means for each method and compare them. If the means and standard deviations are significantly different, it may suggest that Mark's sampling method is biased.

To calculate the standard deviation of the sampling distribution, we can use the formula:

Since the population standard deviation is not given, we can use the sample standard deviation as an estimate. Assuming the sample standard deviation is 2, we can calculate the standard deviation of the sampling distribution as follows:

For Judy's method:

For Mark's method:

Assuming that the central street has a population size of 1000, we can calculate the standard deviation as:

The standard deviation of Mark's sampling distribution is much larger than Judy's, indicating that Mark's sampling method may not be representative of the whole population of the city.

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The ordered pairs that correspond to input-output pairs of the function y=-7x+3 are  (5,32).

The input-output pairs of the function y=-7x+3 can be determined by plugging in the input value x into the function and solving for y. The formula y=-7x+3 can be used to calculate the output value corresponding to a given input value x. For example, if x=4, then y=-7(4)+3=-28+3=5, so the input-output pair is (4,5). Similarly, if x=5, then y=-7(5)+3=-35+3=32, so the input-output pair is (5,-32). The ordered pairs that correspond to input-output pairs of the function y=-7x+3  and (5,32).

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The can measure exactly 4 litres by having 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and been asked to imagine how you would solve it using math.

These word problems are interpreted into mathematical equation or expression.

If the woman wants to have the water in two containers with a good ratio, then we say;

The ratio of container 1 to container 2 is 5:7

therefore;

the amount of water in 5litres container = 5/12 × 4 5/3 = 1 2/3 litres

the amount of water in 7 litres = 7/12 × 4 = 7/3 = 2 2/3 litres

Therefore to measure it, she will have 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

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The number of sets is 128 by using the multiplication principle.

The multiplication principle states that if there are k events, and if the first event can happen in n_1 ways, the second event can happen in n_2 ways, and so on, then the k events can happen in n_1 × n_2 × ... × n_k ways.

To find the number of sets of four marbles include one of each color other than lavender, A bag contains two red marbles, four green ones, one lavender one, four yellows, and four orange marbles.

There are two red marbles.

There are four green ones.

There are four yellows.

There are four orange marbles.

So, total of 2 + 4 + 1 + 4 + 4 = 15 marbles in the bag.

To find the total number of sets of four marbles including one of each color other than lavender, use the multiplication principle.

In this question, there are 5 events (choosing one of each color).

The first event can happen in 2 ways.

The second event can happen in 4 ways.

The third event can happen in 4 ways.

The fourth event can happen in 4 ways.

Therefore, by the multiplication principle, the total number of sets of four marbles includes one of each color other than lavender

= 2 × 4 × 4 × 4 ⇒ 128 sets.

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