Abc is an isosceles triangle. Ab is the longest side with the length 8x+5. Bc= 4x+4 and ca = 3x+9. Find ab

Answer:

Step-by-step explanation: 160$

The largest number of members such a subset can have is 60.

Let's consider the numbers in the subset that are multiples of 5. If we have one of these multiples in the subset, then we cannot have any other multiple of that number in the subset, otherwise, one of them would be 5 times another.

So we can choose at most one number from each set of multiples of 5: either 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, or 100.

This gives us a maximum of 20 numbers that we can choose from these sets.

Now we consider the remaining numbers from 1 to 100 that are not multiples of 5. Each of these numbers can be expressed as a product of a power of 2 and an odd number. For example, 33 = 2^0 x 33, 72 = 2^3 x 9.

If we choose any number that has a power of 2 greater than or equal to 3, then we cannot choose any other number that has the same odd factor, otherwise, one of them would be 5 times another. This is because any number with a power of 2 greater than or equal to 3 is a multiple of 8, and any multiple of 8 has a factor of 5.

So we can choose at most two numbers from each set of numbers that have the same odd factor: either 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, or 99.

This gives us a maximum of 2 x 20 = 40 numbers that we can choose from these sets.

Therefore, the largest number of members such a subset can have is 20 + 40 = 60.

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Answer:

19

Step-by-step explanation:

r = 32.5 cm

C = 2πr = 2(3.14159)(32.5 cm) = 204.20 cm

40 m = 40 m × (100 cm)/m = 4000 cm

4000 cm / 204.2 cm = 19.588

Answer: 19

Using derivative of the function  dy/dt = 6.

Differentiation involves finding the derivative of a function, which is a new function that describes the rate of change of the original function at each point.

Since we have x term and we are differentiating with respect to t, we need to apply the chain rule. This means we first differentiate with respect to x and then multiply by dx/dt. That is:

dy/dt = d[x² + 3]/dt

dy/dt = (2x) dx/dt

dy/dt = 2(1) + 4    (Since x=1 and dx/dt= 4)

dy/dt = 2 + 4

dy/dt = 6

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There are 90 possible combinations of marble color and die number that are possible from a bag of 15 different colored marbles and rolling one six-sided die.

This can be determined using the multiplication principle of counting.

The multiplication principle of counting can be used to find the number of ways two or more tasks can be performed together. The principle states that if there are m ways to perform task A and n ways to perform task B, then there are m × n ways to perform both tasks A and B.

To apply the multiplication principle of counting to this problem, we need to determine the number of ways the die can land and the number of ways a marble can be chosen. There are six possible outcomes of rolling a six-sided die, and there are 15 different colored marbles to choose from. Thus, the number of possible combinations of marble color and die number is: 15 different colored marbles × 6 possible die numbers= 90 possible combinations.

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Answer:

False. A correlation coefficient of -1 indicates a perfect negative correlation between two variables.

The measure of angle M in triangle KLM is approximately 47.3 degrees, to the nearest 10th of a degree.

Solving for nearest 10th of degree:

To find the measure of angle M in triangle KLM, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. The Law of Cosines states that:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c: length of the side opposite angle C, and a & b are the lengths of the other two sides.

In this case, we wish to find the measure of angle M, which will be opposite the side of length m. We are aware that the lengths of the other two sides, k and l, and measure of angle L. To find l, we use the Law of Cosines:

[tex]l^2 = k^2 + m^2 - 2km cos(L)[/tex]

Substituting:

[tex]l^2 = 8.3^2 + 5.2^2 - 2(8.3)(5.2) cos(162 degree)[/tex]

Solve for the l, we get:

l = 10.038 cm

We will use Law of Cosines again to find the measure of angle M:

cos(M) = [tex](k^2 + l^2 - m^2) / (2kl)[/tex]

Substituting:

cos(M) = [tex]([/tex][tex]8.3^2 + 10.038^2 - 5.2^2)[/tex] [tex]/ (2(8.3)(10.038))[/tex]

Simplifying:

cos(M) = 0.665

To get the measure of angle M, we take the inverse cosine:

M = 47.3°

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The value of the system determinant is -2.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. Or, applying a tool called determinant. Here, for solving this exercise you should apply the determinant since the question asks about its value. The example below shows the steps that you should do.

Example:

2x+y=10

-x-y=25

Firstly, you should identify the coefficients of the system.  The coefficients are the previous numbers before the each variable. Therefore, for the example, the coefficients are: 2, 1 ,-1 and -1.

After that, you should write these coefficients to form a matrix. See: [tex]\left[\begin{array}{ccc}2&1\\-1&-1\\\end{array}\right][/tex].

Finally, you have a matrix and you should calculate the determinant. The determinant is calculated as shown below.

[tex]|D|=\left[\begin{array}{ccc}a&b\\c&e\\\end{array}\right]\\ \\ |D|=a*e-b*c[/tex]

Now, you can get to solve the given exercise.

         1,1,1,-1

         [tex]\left[\begin{array}{ccc}1&1\\1&-1\\\end{array}\right][/tex]

       D= 1*(-1)-(1)*(1)

       D= -1-(1)

       D= -1-1=-2

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The answer is: g(x) increases by a factor of 9.

What is change in interval?

In mathematics, the term "interval" refers to a range of values between two endpoints. A change in interval refers to a shift or movement of this range along the number line.

There are two types of changes that can occur in an interval: a shift or a stretch.

A shift occurs when the interval is moved left or right along the number line. For example, if we start with the interval [0, 5] and shift it to the right by 2 units, we get the new interval [2, 7]. Similarly, if we shift it to the left by 3 units, we get the new interval [-3, 2].

A stretch occurs when the interval is expanded or compressed. For example, if we start with the interval [0, 5] and stretch it by a factor of 2, we get the new interval [0, 10]. If we compress it by a factor of 1/3, we get the new interval [0, 5/3].

Changes in interval are important in many areas of mathematics, including calculus, where they are used to describe the domain and range of functions, and in geometry, where they are used to define the length and area of shapes.

The function g(x) = 3ˣ represents exponential growth.

To determine how g(x) changes over the interval from x=8 to x=10, we can evaluate g(10) and g(8) and compare the ratios:

g(10) = 3¹⁰ = 59,049

g(8) = 3⁸ = 6,561

The ratio of g(10) to g(8) is:

g(10)/g(8) = 59,049/6,561 = 9

Therefore, g(x) increases by a factor of 9 over the interval from x=8 to x=10.

The answer is: g(x) increases by a factor of 9.

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Keep in mind that the numbers used in the example are arbitrary, and you will need to use the actual premium amounts to calculate the deductions

Hi! To find the annual premium deductions and weekly deductions for each insurance plan, follow these steps:

1. Calculate the annual deduction for each plan by multiplying the total annual premium by 30% (your contribution).
2. Calculate the weekly deduction by dividing the annual deduction by 52 (number of weeks in a year).

For example, if AAA+ annual premium is $1,000, Health Today annual premium is $1,200, and Best Insurance annual premium is $800:

AAA+ Annual Deduction = 30% of $1,000 = $300
Weekly Deduction = $300/52 ≈ $5.77

Health Today Annual Deduction = 30% of $1,200 = $360
Weekly Deduction = $360/52 ≈ $6.92

Best Insurance Annual Deduction = 30% of $800 = $240
Weekly Deduction = $240/52 ≈ $4.62

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Answer:

Step-by-step explanation:

$250,000 per depositor per insured bank *fire emoji*

Answer:

8.4

Step-by-step explanation:

8+8+8+9+9/5=

42/5=

=8.4

The company's average yearly profit, in millions of dollars, was $8.4 million.

The total profit earned by the company in the first 3 years is $8.0 million x 3 = $24.0 million.

In the following two years, the business will make a total profit of $9.0 million multiplied by two, or $18.0 million.

Therefore, the total profit earned by the company in the 5-year period is $24.0 million + $18.0 million = $42.0 million.

To find the average yearly profit, we divide the total profit by the number of years: $42.0 million / 5 = $8.4 million.

Therefore, the company's average yearly profit, in millions of dollars, was $8.4 million. The answer is (H) 8.4.

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The numerical value of x is 23.

Vertical angles are simply angles that are opposite of each other when two straight lines crosses.

They are congruent, hence, they have the same angle measure.

From the diagram:

Since the angles that are opposite of each other, they are vertical angles, meaning they are congruent.

Hence:

Angle A = Angle B

( 6x - 100 ) = ( x + 15 )

Solve for x

6x - x = 15 + 100

5x = 115

x = 115/5

x = 23

Therefore, x has a value of 23.

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Answer:

b

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the five interior angles and equate to 540

148 + 3x + 10 + x + 112 + 90 = 540

4x + 360 = 540 ( subtract 360 from both sides )

4x = 180 ( divide both sides by 4 )

x = 45

Then

∠ B = 3x + 10 = 3(45) + 10 = 135 + 10 = 145°

The possible function f(x) is C. [tex]f(x) = (x + 6)/(x - 6)[/tex] because C   satisfy the limit conditions as well.

To determine which function could be function f, we need to check if it satisfies the given domain and limit conditions.

First, let's check the domain.

Option A: The function is undefined at x = 6, but is defined for all other values of x. Therefore, the domain of f is (-∞, 6) U (6, ∞), as required.

Option B: The function is undefined at x = ±6, but is defined for all other values of x. Therefore, the domain of f is (-∞, -6) U (-6, 6) U (6, ∞), which is not the required domain.

Option C: The function is undefined at x = 6, but is defined for all other values of x. Therefore, the domain of f is (-∞, 6) U (6, ∞), as required.

Option D: The function is undefined at x = -6, but is defined for all other values of x. Therefore, the domain of f is (-∞, -6) U (-6, 6) U (6, ∞), which is not the required domain.

Therefore, options A and C are the only ones that satisfy the domain condition. Now let's check the limit conditions.

Option A:

[tex]\lim_{x \to -\infty} [(x^2 -36)/(x - 6)] = \lim_{x \to -\infty} [(x+6)(x-6)/(x-6)] \\= \lim_{x \to -\infty} [x+6] = -\infty[/tex]

[tex]\lim_{x \to \infty} [(x^2 -36)/(x - 6)] = \lim_{x \to \infty} [(x+6)(x-6)/(x-6)] \\= \lim_{x \to \infty} [x+6] = \infty[/tex]

Option C:

[tex]\lim_{x \to -\infty} [(x+6)/(x - 6)] = \lim_{x \to -\infty} [x/x] = -\infty[/tex]

[tex]\lim_{x \to \infty} [(x+6)/(x - 6)] = \lim_{x \to \infty} [x/x] = \infty[/tex]

Therefore, both options A and C satisfy the limit conditions as well.

Therefore, the possible function f is either A or C.

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The complete question is :

The domain of function f is (-∞, 6) U (6, ∞). The value of the function -∞ approaches as x approaches -∞ , and the value of the function approaches ∞ as x approaches ∞ . Which function could be function f?

A. [tex]f(x) = (x^2 -36)/(x - 6)[/tex]

B.[tex]f(x) = (x -6)/(x^2 - 36)[/tex]

C. [tex]f(x) = (x + 6)/(x - 6)[/tex]

D. [tex]f(x) = (x - 6)/(x + 6)[/tex]

Given:

Robert gets a loan from his bank he agrees to borrow £6000 at a fixed annual simple interest rate of 7% he also agrees to pay the money back over a 10 year period.

To Find:

How much money in total will he have paid back at the end of the 10 years?

Solution:

We know that,

[tex]\text{Simple interest}=\dfrac{\text{P}\times\text{R}\times\text{T}}{100}[/tex]

Here, we have

[tex]\text{Principle}=\£6000[/tex]

[tex]\text{Rate}=7\%[/tex]

[tex]\text{Time}=10\ \text{years}[/tex]

Substituting these values, we get

[tex]\text{SI} = \dfrac{6000\times7\times10}{100}[/tex]

  [tex]= \dfrac{420000}{100}[/tex]

  [tex]= 4200[/tex]

[tex]\text{Amount = Principal + Simple Interest}[/tex]

              [tex]= 6000 + 4200[/tex]

              [tex]= \£10200[/tex]

Hence, Robert would have paid back £10200 at the end of the 10 years.

By formula:-

SI= PTR/100

A=I+P

Answer:

y = x + 3

Step-by-step explanation:

The question is y is 3 more than x.

We know that "more" means addition.

and since y is the greater number here, the answer would be y = x + 3!

Simple!

:)

The two-digit number with a ones digit that is 3 more than its tens digit is 58.

We know that a number is a two-digit number and the sum of its two digits is 13. Based on this, some possible numbers that fit this description are:

Moreover, we know that the ones digit is 3 more than the tens digit. Based on this principle, the number that fits the description is 58.

5 (3 more than 8 ) + 8 = 13

Note: This question is incomplete; here is the complete question:

I am 2 digit number. My ones digit is 3 more than my tens and the sum of my digit is 13. Who am I?

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The average number of samples (out of 20) that will contain the pollutant is 2.

a. Probability that 2 of the next 20 samples contain the pollutantTo calculate the probability that 2 of the next 20 samples contain the pollutant, we use the binomial distribution. We can use the formula below:P(X=k) = (nCk) pk(1-p)n-kwhere:n = 20, the number of samples; k = 2, the number of samples containing the pollutant; p = 0.10, the probability that a sample contains the pollutant; q = 1 - p = 0.90, the probability that a sample does not contain the pollutant.Using the above formula, we get:P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979Therefore, the probability that 2 of the next 20 samples contain the pollutant is approximately 0.3979.

b. Probability that at least four of the next 20 samples contain the pollutantTo calculate the probability that at least four of the next 20 samples contain the pollutant, we need to calculate the probability of P(X ≥ 4).We can use the complement of P(X < 4) and use the binomial distribution formula to calculate this. We get:P(X ≥ 4) = 1 - P(X < 4)P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)P(X=0) = (20C0) (0.10)0(0.90)20= (1) (1) (0.1216)≈ 0.1216P(X=1) = (20C1) (0.10)1(0.90)19= (20) (0.10) (0.2296)≈ 0.4593P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059Therefore, P(X < 4) ≈ 0.1216 + 0.4593 + 0.3979 + 0.2059 ≈ 1.185P(X ≥ 4) = 1 - P(X < 4)≈ 1 - 1.185= -0.185This is not a valid probability. Therefore, we have made an error in our calculations, and the probability cannot be calculated using this method.

c. Probability that more than 2 and less than 7 of the next 20 samples contain the pollutant. To calculate the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant, we can use the binomial distribution formula again. We need to calculate P(3 ≤ X ≤ 6).We can use the formula:P(3 ≤ X ≤ 6) = P(X=3) + P(X=4) + P(X=5) + P(X=6)P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059P(X=4) = (20C4) (0.10)4(0.90)16= (4845) (0.0001) (0.3112)≈ 0.1516P(X=5) = (20C5) (0.10)5(0.90)15= (15504) (0.00001) (0.3544)≈ 0.0583P(X=6) = (20C6) (0.10)6(0.90)14= (38760) (0.000001) (0.3919)≈ 0.0121Therefore,P(3 ≤ X ≤ 6) ≈ 0.2059 + 0.1516 + 0.0583 + 0.0121 ≈ 0.4279Therefore, the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant is approximately 0.4279.

d. Average number of samples (out of 20) that will contain the pollutantThe expected value or average number of samples that will contain the pollutant can be calculated using the following formula:E(X) = npwhere:n = 20, the number of samples; p = 0.10, the probability that a sample contains the pollutant.Using the above formula,E(X) = np= 20 (0.10)= 2.

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Daniel

Step-by-step explanation:

student of account

Answer:

$5.69

Step-by-step explanation:

To find the unit price (price per pair) of the gloves, we need to divide the total cost by the number of pairs:

Unit price = Total cost / Number of pairs

In this case, the total cost is $34.14 and the number of pairs is 6, so:

Unit price = $34.14 / 6

Unit price = $5.69 (rounded to the nearest cent)

Therefore, the unit price of the pairs of insulated gloves is $5.69.

Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

The time it takes to coat a donut hole is directly proportional to the surface area of the donut hole.

The surface area of a sphere is given by the formula:

Surface Area = 4πr²

Here, r is the radius of the sphere.

Comparing the surface areas of the donut holes:

Niraek's donut hole: Surface Area = 4π(6²)

Theo's donut hole: Surface Area = 4π(8²)

Akshaj's donut hole: Surface Area = 4π(10²)

Now, let's find the LCM of the surface areas to determine the time it takes for all workers to finish:

LCM(144π, 256π, 400π) = 57600π mm²

This means that it will take the same amount of time for all three workers to finish their current donut holes when they have covered a total surface area of 57600π mm².

Number of donut holes = (Total surface area) / (Surface area of Niraek's donut hole)

= (57600π mm²) / (144π mm²)

= 57600 / 144

= 400

Therefore, Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

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By finding a common denominator, we can rewrite the sum as:

3/8 + 7/12 = 9/24 + 14/24 = 23/24

Here we want to find the sum between two fractions that have different denominators.

To sum them, we need to find a common denominator, so we need to find a common multiple between 8 and 12.

We know that:

8*3 = 24

12*2 = 24

Then we can multiply and divide the first fraction by 3:

3/8*(3/3) = 9/24

7/12*(2/2) = 14/24

Then the sum will give:

9/24 + 14/24 = 23/24

That is the outcome.

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Answer:

[tex]y = -2x + 15[/tex]

Step-by-step explanation:

center of the circle C is at (0, 0).

let P be the point (6, 3),

There is a property of a circle,

line drawn from center of a circle to a point P (x, y) is perpendicular to the tangent at P.

see the attached figure

so basically we have to find the equation of line perpendicular to the line passing through (6, 3).

slope of line CP = 1/2

therefore the slope of perpendicular line = -2 (tangent at P)

It passes through (6, 3) (the point of tangency),

using the equation,

[tex]y_2 - y_1 = m(x_2 - x_1)[/tex]

[tex]y - 3 = -2(x - 6)[/tex]

[tex]y = -2x + 15[/tex]

Hopefully, this answer will help you!

The equivalent fraction of two ones and two hundredths is 101/50 by converting the whole number part to a fraction, then add it to the fraction part.

Two ones and two hundredths can be represented as a mixed number, which is [tex]2 \frac{2}{100}[/tex].

To convert this mixed number to an equivalent fraction, we need to first convert the whole number part to a fraction by multiplying it by the denominator of the fraction part, and then adding the numerator of the fraction part. So, we have:

2 + 2/100 = (2 * 100 + 2) / 100 = 202/100

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

202/100 = (2 * 101) / (2 * 50) = 101/50

Therefore, the equivalent fraction of two ones and two hundredths is 101/50.

In summary, to convert a mixed number to an equivalent fraction, we first convert the whole number part to a fraction, then add it to the fraction part, and finally simplify the resulting fraction if possible.

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Answer:

To find the percentage decrease, we need to calculate the difference between the initial and final values, divide that by the initial value, and then multiply by 100.

The initial use of electricity was 12,000 kilowatt-hours per month, and the final use was 7,000 kilowatt-hours per month. The difference is:

12,000 - 7,000 = 5,000

To find the percentage decrease, we divide the difference by the initial value:

5,000 / 12,000 = 0.4167

Finally, we multiply by 100 to get the percentage:

0.4167 * 100 = 41.67%

Therefore, the percentage decrease in electricity usage is 41.67%.

To find the volume of a sphere with a circumference of 20π, we first need to find its radius.

The formula for the circumference of a sphere is C = 2πr, where C is the circumference and r is the radius.

Therefore, we can rearrange this formula to solve for the radius:

r = C/(2π) = 20π/(2π) = 10

Now that we know the radius is 10, we can find the volume of the sphere using the formula:

V = (4/3)πr^3

Substituting r = 10 into this formula, we get:

V = (4/3)π(10)^3 = (4/3)π(1000) = 4000π/3

So, the volume of the sphere is 4000π/3, which is approximately equal to 4188.79 cubic units.

Answer: x = 2, y = 6

Step-by-step explanation:

For the rectangle:
x + 4y + x + 4y = 52

2x + 8y = 52

2x = 52 - 8y

x = (52 - 8y)/2

For the triangle:
3y + 3y + 2x = 40

6y + 2((52 - 8y)/2) = 40

6y + (52 - 8y) = 40

-2y = -12

y = 6

x = (52 - 8y)/2

x = (52 - 8(6))/2

x = (52 - 48)/2

x = 4/2

x = 2

Answer:

The surface area of rectangular prism is 390 in²

Step-by-step explanation:

As per given question we have provided that :

Here's the required formula to find the surface area of rectangular prism :

[tex]\star\boxed{\text{Area}=2(\text{lw}+\text{wh}+\text{lh})}[/tex]

Substituting all the given values in the formula to find the surface area of rectangular prism :

[tex]\implies \text{Area}=2(\text{lw}+\text{wh}+\text{lh})[/tex]

[tex]\implies \text{Area}=2[(9\times3)+(3\times14)+(14\times9)][/tex]

[tex]\implies \text{Area}=2[(27)+(42)+(126)][/tex]

[tex]\implies \text{Area}=2[27+42+126][/tex]

[tex]\implies \text{Area}=2[69+126][/tex]

[tex]\implies \text{Area}=2[195][/tex]

[tex]\implies \text{Area}=2\times195[/tex]

[tex]\implies \text{Area}=390[/tex]

[tex]\star\boxed{\text{Area}=390 \ \text{in}^2}[/tex]

Hence, the surface area of rectangular prism is 390 in².

[tex]\rule{300}{1.5}[/tex]

Answer:  it's T

Step-by-step explanation: