Tory is saving money to buy a new drum for his drum set. The drum costs $235. He has already saved $115, and now he has $24.50 more after mowing his grandmother’s yard. Which equation can be used to find the amount of money, n, that Tory still needs to save in order to buy the new drum?

Answer:

below

Step-by-step explanation:

basically find the line that connects JK and KL, and since its 2/3 and -2/3 which are not opposite reciprocals, the points dont form a right triangle

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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The volume of the described solid is V = 16r³/3

A solid line S should be drawn between z = a and z = b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then  A(x).

Volume of S = limₙ→∞ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^a_b {A(x)} \, dx\)

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = \(\int\limits^{r}_{-r} {A(x)} \, dx\)

Substitute A(x) from (1)

V = \(\int\limits^{r}_{-r} {4(r^{2}-x^2 )} \, dx\)

V = 4[r²x - x³/3 ]

V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

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Answer:

2

Step-by-step explanation:

Substitute 2 in for y.

2=8-3x

subtract 2 from each side and add 3x to both sides

2-2+3x=8-3x+3x

3x=8-2

3x=6

x=6/3

x=2

Answer:

Step-by-step explanation:

8-3x=2

3x=8-2

3x=6

x=2

The person that has the higher average speed is Teresa.

The average speed is the total distance travelled by the object in a particular time interval.

Average speed measures the average rate of speed over the extent of a trip.

Therefore,

average speed = distance / time

Hence, Karl drove 40 miles in 50 minutes.

Therefore,

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minute

Teresa drove 35 miles in 42 minutes.

Therefore,

average speed of Teresa = 35 / 42

average speed of Teresa  = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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The values of csc W and cos W of the angle are:

csc W =  (√85)/2

cos W = 9/√85

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

since acute angle W has sin W = 2/√85 and sec W = (√85)/9.

Recall that: csc W = 1/sinW and sec W = 1/cos W.

Therefore, if sin W = 2/√85, csc W = (√85)/2

Also, if sec W = (√85)/9, cos W = 9/√85

Therefore, the values of csc W and cos W are (√85)/2 and 9/√85 respectively

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Step-by-step explanation:

\( {b}^{2} - 4b - 21 = (b + 3)(b - 7) \\ m = 3 \\ v = 4\)

\({ \qquad{ \sf \green{Answer \downarrow}}}\)

Subtract 16  from both sides of the equation.

\({ \qquad{\longmapsto \sf \red{2x + 16 - 16 = 8 - 16}}}\)

Subtract the numbers

\({ \qquad{\longmapsto \sf \red{2x = 8}}}\)

Divide both sides of the equation by the same term.

\({ \qquad{\longmapsto \sf \green{ \frac{2x}{2} = \frac{ 8}{2} }}}\)

Cancel terms that are in both the numerator and denominator

\({ \qquad{\longmapsto \sf{ \qquad\longrightarrow\quad\sf \dfrac{\cancel{2x}}{\cancel{2} } = }}}\qquad\quad\sf\dfrac{\cancel{ 8}}{\cancel{2}}\)

\({ \qquad{\longmapsto \sf{x = {\qquad{ \sf \pink{ 4}}}}}}\)

\({ \red{ \rule{9cm}{0.1cm}}}\)

Answer:

Yes, Imogen is correct.

Step-by-step explanation:

The area for a circle is \(A=\pi r\), where A is the area, and r is the radius. The area of a semicircle with a radius two times our first is half of the area of the full circle. The area of a full circle two times the size of the first has two tiimes the area, so half of itis the same as the firsy

Answer:

123 degrees

Step-by-step explanation:

180 - 57 = 123

Answer:

33

Step-by-step explanation:

123 is not the answer, on edge

Nearly 150,000,000 cars were registered in the US as a whole in 2007. China, India, and the United States are the three nations with the largest populations on earth.

Average lifespan and child mortality rate are indeed the two key metrics that most accurately reflect a citizenry's standard of living.

The population of the globe is projected to reach about 10 billion people in 2050. Africa and Asia will see the most expansion in population if indeed the patterns in demographic persist.

Cultural practices, governmental regulations, and monetary support, as well as female employment prospects as well as education levels, all have an impact on the overall birthrate of a community.

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Step-by-step explanation:

here is the answer friend

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The bold dot on the point < 0 symbolizes that x ≤ 0

Since this does not show on the point -4 < 0 it stays as this

-4 < 0 ≤ 0

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

P and R

Step-by-step explanation:

P and R are similar because R is the same thing as P but 2 times bigger.

The shopkeeper would have saved 4756.25 - 4260 = 496.25 shillings.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept. We have a graph.

Let the cost of one panga be x and one jembe be y.

From the given information, we can form the following equations:

50x + 30y = 4260 --- Equation 1

25x/2 + (30/2 - 5)y = 2970 --- Equation 2

50(1.25)x + 30(0.85)y = total cost from wholesaler B --- Equation 3

Simplifying equation 2:

25x/2 + 10y - 5y = 2970

25x/2 + 5y = 2970

25x + 10y = 5940

Simplifying equation 3:

62.5x + 25.5y = total cost from wholesaler B

To solve for x and y, we can use any method of our choice. For simplicity, we will use elimination:

Multiplying equation 1 by 5:

250x + 150y = 21300 --- Equation 4

Multiplying equation 2 by 2:

25x + 20y = 5940 --- Equation 5

Subtracting equation 5 from equation 4:

225x + 130y = 15360

Substituting the value of y from equation 5:

225x + 130(297 - 2.5x) = 15360

225x + 38610 - 325x = 15360

-100x = -23250

x = 232.5

Substituting the value of x in equation 1:

50(232.5) + 30y = 4260

y = 85

Therefore, the cost of one panga is 232.5 shillings and the cost of one jembe is 85 shillings.

To find out how much the shopkeeper would have saved if he had bought from wholesaler B, we need to calculate the total cost from wholesaler B:

50(1.25)(232.5) + 30(0.85)(85) = 4756.25

The total cost from wholesaler A was 4260 shillings.

Therefore, the shopkeeper would have saved 4756.25 - 4260 = 496.25 shillings.

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Answer:

(- 1, 1 )

Step-by-step explanation:

x + 5y = 4 → (1)

4x + 12y = 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x - 20y = - 16 → (3)

add (2) and (3) term by term to eliminate x

0 - 8y = - 8

- 8y = - 8 ( divide both sides by - 8 )

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

x + 5(1) = 4

x + 5 = 4 ( subtract 5 from both sides )

x = - 1

As a check

substitute these values into the left side of both equations and if equal to the right side then they are the solution.

- 1 + 5(1) = - 1 + 5 = 4 = right side

4(- 1) + 12(1) = - 4 + 12 = 8 = right side

(- 1, 1 ) is the solution to the system of equations

Answer:

Andrew wins the round.

Step-by-step explanation:

Seeing as red is negative and black is positive, that would make the equations as follows, in the order of Abby, Ashley, Andrew, and Anna.

\(-9+6 = -3\\7-8 = -1\\-4+4 = 0\\-8-3 = -11\)

Meaning that Andrew wins, as his sum is the highest.

Answer:

Pretty sure its Ashley, but I'm skeptical of it.

Step-by-step explanation:

-7 + 8 = 1

while all the others are negative numbers.

Given:

In triangle DEF, \(DE = EF\) and \(m\angle 98^\circ\).

To find:

The measure of angle EFD.

Solution:

In triangle DEF,

\(DE = EF\)           (Given)

It means triangle DEF is an isosceles triangle.

\(m\angle EDF=m\angle EFD\)           (Base angles of an isosceles triangle are equal)

Using angle sum property in triangle DEF, we get

\(m\angle DE F+m\angle EFD+m\angle EDF=180^\circ\)

\(98^\circ +m\angle EFD+m\angle EFD=180^\circ\)

\(2m\angle EFD=180^\circ-98^\circ\)

\(2m\angle EFD=82^\circ\)

Divide both sides by 2.

\(m\angle EFD=\dfrac{82^\circ}{2}\)

\(m\angle EFD=41^\circ\)

Therefore, the measure of angle EFD is 41 degrees.

The perimeter of the triangle with sides of 7cm is 21cm.

We can use the knowledge that a triangle's perimeter is equal to the sum of its side lengths if each of its sides is 7 cm. The triangle has sides of 7 cm, hence the perimeter is as follows:

The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle

perimeter = 7cm + 7cm + 7cm

perimeter = 21cm

Therefore, the perimeter of the triangle is 21cm.

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Answer: The perimeter of a triangle with 7cm sides is 21cm.

Step-by-step explanation:

The perimeter of any two-dimensional figure is defined as the distance around the figure.

By summing the lengths of the sides, we can determine the perimeter of any closed shape.

The perimeter of a triangle will therefore be equal to the sum of its three sides.

Consequently, if a triangle has sides a, b, and c,

Perimeter, P = a + b +c

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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The differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

from the question, we have the following parameters that can be used in our computation:

f(x) = 2x³ + 6x - 1/x + 3eˣ - sin(x)

The derivative of the functions can be calculated using the first principle which states that

if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹

Using the above as a guide, we have the following:

f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

Hence, the differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

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The explicit function for the sequence is: \(f(n) = 3(4)^(n-1)\)

An arithmetic progression (AP) is a progression in which the difference between two consecutive terms is constant.we have to know the first term (a), the number of terms(n), and the common difference (d) between consecutive terms

To find the explicit function for the given sequence, we need to determine the values of a and b in the equation f(n) = \(a(b)^(n-1\)), given that f(1) = 3.

We can find the value of a by substituting n=1 into the equation:

f(1) =\(a(b)^(1-1)\)= a

3 = a

So, we will substitute 3 for a in the equation f(n) = \(a(b)^(n-1).\)

To find the value of b, we can use the fact that the ratio between consecutive terms in the sequence is constant. We can calculate this ratio by dividing any term by its preceding term.

The ratio between the second and first terms is:

12/3 = 4

The ratio between the third and second terms is:

48/12 = 4

The ratio between the fourth and third terms is:

192/48 = 4

The ratio between the fifth and fourth terms is:

768/192 = 4

Since the ratio is constant and equal to 4, we can write:

b = 4

Therefore, the explicit function for the sequence is:

f(n) = \(3(4)^(n-1)\)

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At a significance level of 0.01, we can confidently state that the student's claim is true.

The hypothesis in this question can be stated as follows:

Null Hypothesis: H0: μ1 = μ2 (There is no difference between the mean of four-year college enrollment and two-year college enrollment.)

Alternative Hypothesis: H1: μ1 > μ2 (Mean enrollment of four-year colleges is greater than the mean enrollment of two-year colleges in the United States.)

The significance level (α) is given as 0.01, which represents the probability of rejecting the null hypothesis when it is actually true.

To calculate the test statistic, we can use the formula:

z = ((X1 - X2) - (μ1 - μ2)) / √((σ1² / n1) + (σ2²  / n2))

Substituting the given values:

z = ((6193 - 4305) - (0)) / √((598²  / 35) + (572²  / 35))

z = 10.33

Since this is a right-tailed test, we need to compare the test statistic with the critical value. At a significance level of 0.01, the critical value is 2.33.

The calculated test statistic (10.33) is greater than the critical value (2.33). Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

In conclusion, at a significance level of 0.01, we can confidently state that the student's claim is true. The mean enrollment at four-year colleges is higher than at two-year colleges in the United States.

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Answer:

223

Step-by-step explanation:

find the area for each side.

Answer:

Original Patio:

-perimeter - 36 feet

-area - 80 square feet

New Patio:

-perimeter - 40 feet

-area - 96 square feet

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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