A store has a 28% off sale on hammers. Before the discount, the price of a hammer is $49. What is the sale price?

Answer:

(0, 25) or (3, 20) or (6, 15) or (9, 10) or (15, 0)

Step-by-step explanation:

Answer: Either angle QPO or  angle OPQ

Explanation:

When naming an angle, we always have the vertex as the middle letter. That vertex is P. It's where the two rays are joined.

So we could have the name "angle QPO" or "angle OPQ" since the order of the other letters doesn't matter. All that we care about is P is in the middle.

The area of the region bounded by the given curves. y = 6x2 ln(x), y = 24 ln(x) is 2.85 sq.units.

In this question we need to find the area of the region bounded by the given curves. y = 6x^2 ln(x), y = 24 ln(x)

Equating both the equations of the curve,

6x^2 ln(x) = 24 ln(x)

24 ln(x) - 6x^2 ln(x) = 0

x = 1, 2

This means,  the curves intersect at x = 1 and x = 2.

So, the required area would be,

A = ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

First we find the indefinite integral ∫[24 ln(x) - 6x^2 ln(x)] dx

= -6  ∫[-4 ln(x) + x^2 ln(x)] dx

= -6 ∫ln(x) (x^2 - 4) dx

= -6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x

So,  ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

= [-6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x] _(x = 1 to x = 2)

= 32 ln(2) - 58/3

= 22.18 - 19.33

= 2.85 sq.units.

Therefore, the area of the region is 2.85 sq.units.

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Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

The correct option is (A) 55.8093 (approximately). i.e The value of f(5) = 55.8093

Given that a differentiable function f(1) = π, and f'x = √(x³) = 6.

To find the value of f(5).

As we know, If f(x) is differentiable at x = a, then f(x) is continuous at x = a.

And, f'(x) = (dy/dx) is the derivative of f(x) at x = a.

Then we have to integrate f'(x) to get f(x).

So we have,f'(x) = √(x³)   ------(1)

Integrating both sides with respect to x, we get,

f(x) = ∫ f'(x) dx

= ∫√(x³) dx

= ∫ x⁽³/²⁾ dx

=(2/5) x⁽⁵/²⁾ + C, where C is a constant of integration.

Using the given condition f(1) = π, we get,

π = f(1) = (2/5) * 1^(5/2) + C or

C = π - (2/5).

Therefore, f(x) = (2/5) x⁽⁵/²⁾ + π - (2/5) = (2/5) (x⁽⁵/²⁾ - 1) + π.

Now putting the value of x = 5, we get,

f(5) = (2/5) (5⁽⁵/²⁾) - 1) + π= 55.8093 (approximately).

Hence, the value of f(5) is 55.8093 (approximately).

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Answer:

1.)c=±√58

Step-by-step explanation:

According to Pythagorean theorem, square of the hypotenuse is equal to the sum of the squares of other two sides

a^2+b^2=c^2

Short sides-a and b

Long side=c

I will do number 1 for you as an example.

A=3

B=7

C=x

3^2+7^2=c^2

58=c^2

Dont forget to square 58

c=±√58

Answer:

x^2 + 2x - 1

Step-by-step explanation:

g(x)=(x+1)2−2 would be a quadratic if you'd write it like this:  g(x)=(x+1)^2−2.

This expands to g(x) = x^2 + 2x + 1 - 2  =  x^2 + 2x - 1

Answer:

12÷2=6

100÷1=100

Step-by-step explanation:

Answer: 6 and 1

Answer:

6

100

Step-by-step explanation:

in division:

12÷2=6

100÷1=100

The population will double in about 69.31 years from its size at t = 0.

Given that the population of Integration in millions at time t in years is given by the function

                               P(t) = 2.6e^0.00t, where t = 0 is the year 2000.

To find the population at time t = 0, substitute t = 0 in the given equation.

Thus,P(0) = 2.6e^0.00(0) = 2.6 × 1 = 2.6 million

To find the time it takes for the population to double, we have to solve the equation 2P(0) = P(t).

Thus, 2P(0) = P(t)2(2.6) = 2.6e^0.00t

                    ln(2) = 0.00t ln(2)/0.00 = t ≈ 69.31 years

Therefore, the population will double in about 69.31 years from its size at t = 0.

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Answer:

F (-1,5)

Step-by-step explanation:

Since the problem gives you the graph, all you have to do is see which point falls in the shaded part. F is the answer since J is on the line. If the equality was less than or equal, then it would be F and J.

Answer:

1,5

Step-by-step explanation: there may be a negitive number

The periodic transfer of a portion of the cost of an intangible asset to expense is known as amortization. This is the process of spreading the cost of an intangible asset over its useful life, similar to how depreciation is used for tangible assets like buildings and equipment.

Intangible assets, such as patents, copyrights, and trademarks, do not have a physical existence but still have value to the company. Amortization recognizes the decline in value of these assets over time and helps to accurately reflect their impact on the company's financial statements.

The amount of amortization each period is calculated by dividing the cost of the asset by its estimated useful life. It is important for companies to track and properly account for their intangible assets, including amortization, as it can have a significant impact on their financial statements and overall financial health.

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The estimated winners' prize in 2040, assuming the same rate of increase per year, is approximately $54,680,580,063,400.

The initial value is $150, and the final value is $1,163,000. The number of years between 1895 and 2007 is 2007 - 1895 = 112 years.

Using the formula for percentage increase:
Percentage Increase = [(Final Value - Initial Value) / Initial Value] * 100
= [(1,163,000 - 150) / 150] * 100
= (1,162,850 / 150) * 100
= 775,233.33%

Therefore, the winners' check increased by approximately 775,233.33% over the period from 1895 to 2007.

To estimate the winners' prize in 2040, we assume the same rate of increase per year. We can use the formula:
Future Value = Initial Value * (1 + Percentage Increase)^Number of Years

Since the initial value is $1,163,000, the percentage increase per year is 775,233.33%, and the number of years is 2040 - 2007 = 33 years, we can calculate the future value:

Calculating this expression:
Future Value = 1,163,000 * (1 + 775,233.33%)^33

Using a calculator or computer software, we can evaluate this expression to find the future value. Here's the result:

Future Value ≈ $1,163,000 * (1 + 77.523333)^33 ≈ $1,163,000 * 47,051,979.42 ≈ $54,680,580,063,400

Therefore, based on the assumed rate of increase per year, the estimated winners' prize in 2040 would be approximately $54,680,580,063,400.

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Answer:

c. 5

Step-by-step explanation:

1.5m = 1.5*100 cm = 150 cm

Divide 150 cm by 30 cm,

150/30 = 5

A sketch of the required prism is as shown below.

In this question,

Josh is building a kaleidoscope using PVC pipe, cardboard, bits of colored paper, and a 12 -inch square mirror tile.

While making a kaleidoscope, the mirror tile is to be cut into strips and arranged to form an open prism, with a base like that of an equilateral triangle.

We need to make a sketch of the prism, giving its dimensions

As the base of the prism formed is an equilateral triangle, the mirror tile must be cut into three rectangular strips of equal width.

So, the width would be 12 ÷ 3 = 4 inches

The original tile is a 12-inch square, the length of each side of the square is 12 inches.

So the each rectangular strip will be 12 inches by  4 inches.

i.e., the length = 12 inches and width = 4 inches

Therefore, a sketch of the prism is as shown below.

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The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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Answer:

145.62

Step-by-step explanation:

sin 18° = 45/z

z sin 18° = 45

z = 45/sin 18°

z = 145.62

Since Marcus looked at the clock shown above and said, 1/4 of an hour has passed. Sierra said 3/12 of an hour has passed. Ali said 15/60 of an hour has passed. They're equivalent and the teacher is right that they're all correct.

It should be noted that from the information, Marcus looked at the clock shown above and said, 1/4 of an hour has passed. Sierra said 3/12 of an hour has passed. Ali said 15/60 of an hour has passed.

In this case, their teacher said that they were all correct.

This means that:

1/4 = 3/12 = 15/60

It should be noted that they are all equivalent fractions. This implies that they are equal.

Therefore, the teacher is correct.

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Answer:

Isosceles triangle

Step-by-step explanation:

Given

Triangle ABC

Required

Reflect across BC and name the triangle according to length of its side

When the triangle is reflected across line BC, the new triangle is ACA (see new attachment)

And the sides of this ACA are:

AC, CA and AA

Such that

AC = CA

and

\(AA = 2 * AB\)

\(AA = 2AB\)

From the description above, we have two sides (AC and CA) of the triangle to be equal.

By classification of sides, when two sides of a triangle are equal; such triangle is an isosceles triangle

Triangle ACA' has two equal sides, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

Recall:

Given that triangle ABC is a right triangle, if we reflect it across line BC, we will have  mirror figure of right triangle ABC, forming triangle ACA'.

That is, two right triangles of ABC, which are reflections of each other, will form triangle ACA'. (See image attached).

Thus, this means that:

Therefore,

Also, CA = C'A (congruent sides)

This means that, triangle ACA' has two equal sides that are opposite to each other.

Therefore, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

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Answer:

17m-7

Step-by-step explanation:

product means multiplication so we multiply 17 times m.

17m

and 7 less than 17m is subtraction

17m-7

Answer:

17m-7

Step-by-step explanation:

m = The height

7 less than the product ( Multiply) 17 and m.

so 17m-7

\(-8 < -2t+1 < -1\implies -8-1 < -2t+1-1 < -1-1 \\\\\\ -9 < -2t < -2\implies \stackrel{\textit{notice, division by -2}}{\cfrac{-9}{-2}\stackrel{\downarrow }{ > }\cfrac{-2t}{-2}\stackrel{\downarrow }{ > }\cfrac{-2}{-2}}\implies \cfrac{9}{2} > t > 1\)

\(4\frac{1}{2} > t > 1\implies \begin{cases} t < 4\frac{1}{2}\\\\ t > 1 \end{cases}\hspace{5em}\stackrel{\textit{valid integers for "t"}}{2~~,~~3~~,~~4} \\\\[-0.35em] ~\dotfill\\\\ 4(2)-2\implies \text{\LARGE 6}\hspace{5em}4(3)-2\implies \text{\LARGE 10}\hspace{5em}4(4)-2\implies \text{\LARGE 14}\)

Answer:

233

Step-by-step explanation:

Number at the beginning: 137

Additional number per week: 2

Number of weeks: 48

Additional number: 2 × 48 = 96

Total number at end of 48 weeks: 137 + 96 = 233

Answer: 233

In the problem,

the given system of linear equations are 10x1 - 7x2 = 7 ...

(i)-3x1 +2.099x2 + 3x3 = 3.901 ...

(ii)5x1 - x2 +5x3 = 6 ...

(iii)Now, the solution of the system of equation using Gauss elimination with partial pivoting with five significant digits with chopping leads to the following solution:

x1 = 1.8975, x2 = 1.6677, x3 = 2.00088So, option (d) x1 = 1.8975, x2 = 1.6677, x3 = 2.00088 is the correct answer. Therefore, option (d) is the right option.

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The two lines intersect at (-3,-5) and thus a common solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here, the system of linear equations as  Y=4x+7 and 2=x-y

On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.

The two equations are plotted in the attachment below.

Hence, The two lines intersect at (-3,-5) and thus a common solution.

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The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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Using a moving average of order p = 3, a forecast for time period 6 is 46.

The moving average is a mathematical method for calculating a series of averages using various subsets of the full dataset. It is also known as a rolling average or a running average. The moving average smoothes the underlying data and lowers the noise level, allowing us to visualize the underlying patterns and patterns more readily. In other words, a moving average is a mathematical calculation that employs the average of a subset of data at various time intervals to determine trends, eliminate noise, and better forecast future outcomes. Answer: 46.

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To develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals, you can follow these steps:

1. Create a spreadsheet with columns for the team names, points scored by each team, and the difference in their point totals.
2. Assign a cell to represent the average points scored by the Iowa Wolves. Let's say it's cell A1.
3. Assign a cell to represent the standard deviation of points scored by the Iowa Wolves. Let's say it's cell A2.
4. Use the "=NORM.INV(RAND(), A1, A2)" formula in a cell to generate a random value representing the points scored by the Iowa Wolves in a particular game.
5. Repeat step 4 for each game or simulation you want to run, populating the points scored by the Iowa Wolves in the respective cells.
6. Calculate the average of the generated points scored by the Iowa Wolves by using the "=AVERAGE()" formula on the range of cells containing the simulated points.
7. Calculate the standard deviation of the generated points scored by the Iowa Wolves by using the "=STDEV()" formula on the same range of cells.

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Answer:

-7 - 28

Step-by-step explanation:

First, you do -7 - 28 and then divide the equation by 7.