Not understanding this

Answer:

cos²A - cosA - 6

Step-by-step explanation:

Given

(cosA + 2)(cosA - 3)

Each term in the second factor is multiplied by each term in the first factor, that is

cosA(cosA - 3) + 2(cosA - 3) ← distribute both parenthesis

= cos²A - 3cosA + 2cosA - 6 ← collect like terms

= cos²A - cosA - 6

Answer:

Side lengths are 2

Step-by-step explanation:

Perimeter of the rectangle would be = 4x+2+4x+2

Simplified= 8x +4

Perimeter of the square=4x+4x+4x+4x

Simplified 16x

16x=8x+4

Take away 8x

8x=4

Then divide by 8

X=0.5

The squares side lengths are 4x, so 0.5 times 4 is 2.

The side of the square will be equal to 2.

The perimeter is defined as the sum of all the sides of a given figure. For a rectangle, the perimeter will be the sum of two times the length and width of the rectangle. Similarly for a square, the perimeter is the sum of all the sides of the square.

Given that one rectangle has a length of 4x+2 and a width of 2x. A square has side lengths that are 4x. The perimeter of the rectangle and the square are equal.

The perimeter of the rectangle would be = 4x+2+4x+2

Simplified= 8x +4

The perimeter of the square.

P =4x+4x+4x+4x

P = 16x

Equate the perimeter of the rectangle and square.

16x=8x+4

Take away 8x

8x=4

Then divide by 8

X=0.5

The square's side lengths are 4x, so 0.5 times 4 is 2.

Side = 4x

Side = 4 x 0.5 = 2 units

Therefore, the side of the square will be equal to 2.

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Out of the 42 students, 22 take history, 17 take biology, and 8 take both history and biology. Therefore, there are 11 students who take neither biology nor history.

To find the number of students who take neither biology nor history, we need to subtract the number of students who take at least one of these subjects from the total number of students in the group.

Let's break down the information given:

Total number of students (n) = 42

Number of students taking history (H) = 22

Number of students taking biology (B) = 17

Number of students taking both history and biology (H ∩ B) = 8

To find the number of students who take at least one of these subjects, we can use the principle of inclusion-exclusion. The formula for the principle of inclusion-exclusion is:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

In this case, A represents the set of students taking history, and B represents the set of students taking biology.

Using the formula, we can calculate the number of students taking at least one of these subjects:

n(H ∪ B) = n(H) + n(B) - n(H ∩ B)

= 22 + 17 - 8

= 31

Therefore, there are 31 students who take either history or biology or both.

To find the number of students who take neither biology nor history, we subtract this value from the total number of students:

Number of students taking neither biology nor history = Total number of students - Number of students taking at least one of the subjects

= 42 - 31

= 11

Hence, there are 11 students who take neither biology nor history.

In summary, out of the 42 students, 22 take history, 17 take biology, and 8 take both history and biology. Therefore, there are 11 students who take neither biology nor history.

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Answer:

Simon approximately 8.7 years to repay the loan.

Step-by-step explanation:

Answer:

An explicit rule for the nth term of the sequence will be:

\(a_n=-4\cdot \:2^{n-1}\)      

Thus, option (A) is true.

Step-by-step explanation:

Given the sequence

\(-4, -8, -16, -32, ...\)

A geometric sequence has a constant ratio r and is defined by

\(a_n=a_0\cdot r^{n-1}\)

Computing the ratios of all the adjacent terms

\(\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2\)

As the ratio 'r' is the same.

so

\(r=2\)

as

\(a_1=-4\)

Hence, the nth term of the sequence will be:

\(a_n=a_0\cdot r^{n-1}\)

substituting the values \(r=2\) and \(a_1=-4\)

\(a_n=-4\cdot \:2^{n-1}\)      

Therefore, an explicit rule for the nth term of the sequence will be:

\(a_n=-4\cdot \:2^{n-1}\)      

Thus, option (A) is true.

Answer:

Answer:

Step-by-step explanation:

Maybe I can be Brainliest.

Have a nice day

Best regards

To choose a president, vice-president, and secretary are selected from the 25 club members, and a pledge chairman and pledge vice chairman are selected from the 15 pledges there are 241 500 ways

This problem is a problem of combination and not permutation as the order of selecting is not significant. Combination formula is used to determine the number of ways to choose from a given set.

The number of ways of selecting 3 positions from 25 members and 2 position from 15 members can be obtained by

= 25C3 × 15C2

= 25! / (3! × (25 - 3)!) × 15! / (2! × (15 - 2)!)

= 25*24*23/6*15*14/2

= 241 500

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Answer:

y=-1/2x-3 = slope-intercept

y+5=-1/2(x-4) = point-slope

Step-by-step explanation:

I used the slope and the point provided to get other points and eventually the y-intercept to complete the slope-intercept equation.

I plugged in the numbers provided to get the point-slope equation.

If 100 students participate in the fundraiser, each student needs to raise $137.50.If 25 students participate in the fundraiser, each student needs to raise amount $550.

Amount = (Total Amount Needed) ÷ (Number of Students)

For 60 students:

Amount = $275 ÷ 60 = $4.58

For 75 students:

Amount = $275 ÷ 75 = $3.67

For 40 students:

Amount = $275 ÷ 40 = $6.88

To solve this problem, we need to use a simple equation: Amount = (Total Amount Needed) ÷ (Number of Students). We can then plug in the given information to calculate the amount each student needs to raise. For example, if 50 students participate in the fundraiser, we can calculate that each student needs to raise $275 ÷ 50 = $5.50. We can then use this equation to calculate the amount that each student needs to raise if there are different numbers of students participating in the fundraiser. For example, if there are 100 students participating in the fundraiser, each student needs to raise $275 ÷ 100 = $2.75. Similarly, if there are 25 students participating in the fundraiser, each student needs to raise $275 ÷ 25 = $11.00.

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\(f(x) = \sqrt{3x} + 7 \\ \\ f ^{ - 1} (x) = ( \sqrt{3x} + 7) ^{ - 1} \\ \\ f ^{ - 1} (x) = \frac{1}{ \sqrt{3x} + 7} \\ \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{3(2)} + 7} \\ \\f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \times \frac{ \sqrt{6} - 7 }{ \sqrt{6} - 7 } \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{(6 - 49)} = \frac{ \sqrt{6} - 7 }{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{ - 43} = \frac{2.449 - 7}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ - 4.551}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ 4.551}{ 43} =0.10584\)

I hope I helped you^_^

The distance between two points a and b on the real line is given by the absolute difference between the two points, which is calculated as the positive difference between the values of a and b regardless of their order.

The distance function, denoted as d(a, b), is a metric that satisfies the properties of non-negativity, symmetry, and the triangle inequality. It is used to quantify the distance between two points in one-dimensional space, and is an important concept in geometry, analysis, and other fields of mathematics. The distance formula can be extended to higher dimensions and is used in various applications such as optimization, clustering, and machine learning.

The distance between two points a and b on the real line is given by the absolute difference between the two points: d(a, b) = |a - b|

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Answer:

he can get 6 shirts

Step-by-step explanation:

12.60 x 26.5

333.9 - 280

53.9 ÷ 8.6

6

Answer:

6

Step-by-step explanation:

Answer:

The average speed is 9 km per hour

Step-by-step explanation:

Average speed = total distance ÷ total time

Let us use this rule to solve the question

∵ Johnnie runs 4.5 km every day

∴ The total distance = 4.5 km

∵ It takes him 30 minutes to run his route

∴ Total time = 30 minutes

→ We need to change the time to hours to find the average speed in km/h

∵ 1 hour = 60 minutes

→ Divide the time by 60 to change it from minutes to hours

∴ Total time = 30/60 = 0.5 hour

∵ Average speed = distance ÷ time

∴ Average speed = 4.5 ÷ 0.5

∴ Average speed = 9 km/h

∴ The average speed is 9 km per hour

The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.

Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:

1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0

where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.

We can see that if we set base = 2, then the equation becomes:

1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

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The probability that the insurance company needs to pay on a claim they receive, i.e., the cost of a claim exceeds the deductible of $500, is approximately 83.33%.

In this scenario, the losses from claims on the policy are assumed to follow an exponential distribution with a mean of $3000. The exponential distribution is commonly used to model continuous random variables with a constant hazard rate. In this case, the hazard rate is determined by the mean of $3000.

To find the probability that the cost of a claim exceeds the $500 deductible, we need to calculate the cumulative probability of the exponential distribution beyond the deductible amount. Since the exponential distribution is memoryless, we can consider the deductible as a starting point and calculate the probability of the claim exceeding that amount.

Using the exponential distribution's probability density function (PDF), we can determine the probability of a claim exceeding the deductible. The PDF for an exponential distribution with rate parameter A is given by f(x) = A * exp(-A * x), where x is the claim amount.

Integrating the PDF from the deductible amount ($500) to infinity will give us the probability that the cost of a claim exceeds the deductible. However, in this case, we can simplify the calculation since we know the mean of the exponential distribution is $3000. The probability of a claim exceeding the deductible can be approximated as the ratio of the mean loss exceeding the deductible to the mean loss overall, which is (3000 - 500) / 3000 = 0.8333 or 83.33%.

Therefore, the probability that the insurance company needs to pay on a claim they receive, i.e., the cost of a claim exceeds the deductible of $500, is approximately 83.33%.

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Benjamin has 10 markers in total, consisting of 2/3 pastel, 1/3 not pastel, 3/9 bold, and the rest neon. He has 5 neon markers.

We need to start by figuring out how many markers Benjamin has in total. We know that 2/3 of the markers are pastel, which means that 1/3 of the markers are not pastel. So, if we let x be the total number of markers, we can set up the equation:
1/3x = 10 - (2/3x)
1/3x = 10 - 2/3x
1x = 30 - 2x
3x = 30
x = 10
So, Benjamin has 10 markers in total. Now we need to figure out how many of them are neon. We know that 2/3 of the markers are pastel, which means that 1/3 of them are not pastel. So, 1/3 of 10 markers is 3.33 markers, but since we can't have a fraction of a marker, we know that 3 markers are not pastel.
Now, we need to figure out how many of the remaining 7 markers are bold. We know that 3/9 of them are bold, which simplifies to 1/3. So, 1/3 of 7 markers is 2.33 markers, but again, we can't have a fraction of a marker, so we know that 2 markers are bold.
Finally, we can figure out how many markers are neon. We know that Benjamin has 10 markers in total, and we know that 3 of them are not pastel and 2 of them are bold. So, the remaining 5 markers must be neon. Therefore, Benjamin has 5 neon markers.
In summary, Benjamin has 10 markers in total, consisting of 2/3 pastel, 1/3 not pastel, 3/9 bold, and the rest neon. He has 5 neon markers.

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Answer:

slope = - \(\frac{2}{3}\)

Step-by-step explanation:

Parallel lines have equal slopes

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (3, 10)

m = \(\frac{10-6}{3-9}\) = \(\frac{4}{-6}\) = - \(\frac{2}{3}\) ← slope of parallel line

Answer:

Step-by-step explanation:

Y2-Y1÷X2-X1=slope

10-6÷3-9=M

4÷-6=M

Slope =0.67

Answer:

Step-by-step explanation:

The quotient is 0.62 and the remainder is 0.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, 2.48 divided by 4.

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.

Here,

4|2.48|0.62

  24

  24

_____

   08

   08

_____

    0

So, quotient is 0.62 and remainder is 0.

Therefore, the quotient is 0.62 and the remainder is 0.

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Answer:

The watermelon has fallen 15.53625m

Step-by-step explanation:

x=vi*t+.5*a*t^2

x=3*1.5+.5*9.81*1.5^2

x=15.53625m

the customer spent $13 if it's not 13 it's the closest answer too 13

Answer:

$0.85, or 85 cents.

Step-by-step explanation:

To find this, we first need to find out how much it costs for one square. We know it is $2 per pound, and there are twelve squares in each pound. So to find out how much one square costs, we need to divide $2 by 12. We get an answer that is never-ending when we solve this, so we will round to the hundredths place since we are working with money. What we get as a result is that one square costs $0.17.

Now we multiply the above number by five to find out how much the customer spent. This comes out to be $0.85. In total, the customer spent 85 cents for all five squares of the fudge.

If cruz purchased a large pizza for $12.75. It serves 5 people, the cost per serving of the pizza is $2.55. So, correct option is A.

To find the cost per serving of the pizza, we need to divide the total cost of the pizza by the number of servings. In this case, the pizza costs $12.75 and serves 5 people.

Therefore, the cost per serving can be calculated as:

Cost per serving = Total cost of pizza / Number of servings

Cost per serving = $12.75 / 5

Cost per serving = $2.55

So, the cost per serving of the pizza is $2.55.

When working with fractions or dividing quantities, we need to pay attention to the units involved. In this case, the units of the cost and the servings must match for the division to be meaningful.

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Answer: There are infinitely many.

For example, 5314410.5 or 93. You are probably looking for (3)^6 tho

Answer:

D

Step-by-step explanation:

Answer:

23/4

Step-by-step explanation:

5\(\frac{3}{4}\) = 5*4 + 3 / 4

= 23/4

Answer:

23/4

Step-by-step explanation:

4*5 = 20

20+3=23

keep denominator

23/4

a) The volume of the composite figure is represented by the cubic equation V = x³ + 16 · x.

b) The measure of the missing side x in the composite figure is 3 inches.

a) In the first part of the question we need to derive the volume formula of the composite figure, which is the sum of the volumes of the cube and the rectangular prism:

V = V' + V''

V = x³ + 16 · x, where x is in inches.

The volume is represented by V = x³ + 16 · x.

b) If we know that V = 25 · x, then the measure of the missing side is:

First, set the volume formula found in section a):

V = x³ + 16 · x

Second, replace the volume:

25 · x = x³ + 16 · x

Third, simplify the expression and clear x within the resulting equation by algebra properties:

25 = x² + 16

x² - 9 = 0

x² = 9

x = 3

The measure of the missing side x is 3 inches.

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