The length of the base of an isosceles triangle is x. The length of a leg is 3x - 2. The perimeter of the triangle is 66. Find x.

X= ?

The corporation should deposit $4,298.46 at the end of each month into the sinking fund.

The amount of interest earned over the life of the account is: $47,616.64.

The value of the fund after 2, 4, 6 are $56,243.62, $115,263.54, $178,155.28 respectively.

The interest earned during the second month of the 7th year is $317.13

To determine the amount that should be placed in the sinking fund at the end of each month, we can use the formula for present value of an annuity:

PV = R[(1-(1+i)^(-n))/i]

where:

PV = present value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

We know that the sinking fund needs to have a future value of $460,000 in 8 years. If we assume monthly deposits and monthly compounding, we have:

PV = 0

FV = $460,000

i = 6.5%/12 = 0.00541667

n = 8 years * 12 months/year = 96 months

Using the formula, we can solve for R:

R = (FV*i)/((1+i)^n - 1) = ($460,000 * 0.00541667)/((1+0.00541667)^96 - 1) = $4,298.46

Therefore, the corporation should deposit $4,298.46 at the end of each month into the sinking fund.

To determine the amount of interest earned over the life of the account, we can subtract the total amount deposited from the total amount in the sinking fund at the end of 8 years:

Total amount deposited = $4,298.46/month * 96 months = $412,383.36

Total amount in sinking fund after 8 years = $460,000

Interest earned = $460,000 - $412,383.36 = $47,616.64

To determine the value of the fund after 2, 4, and 6 years, we can use the formula for future value of an annuity:

FV = R[((1+i)^n - 1)/i]

where:

FV = future value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

After 2 years, we have:

FV = $4,298.46[((1+0.00541667)^(2*12)) - 1]/0.00541667 = $56,243.62

After 4 years, we have:

FV = $4,298.46[((1+0.00541667)^(4*12)) - 1]/0.00541667 = $115,263.54

After 6 years, we have:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

To determine the interest earned during the second month of the 7th year, we can first calculate the total amount in the sinking fund at the beginning of the 7th year:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

Then, we can calculate the amount of interest earned during the first month of the 7th year:

Interest earned = $178,155.28 * 0.00541667 = $964.11

Finally, we can calculate the amount of interest earned during the second month of the 7th year by subtracting the interest earned during the first month from the total interest earned during the 7th year:

Interest earned during second month = $47,616.64 * (0.065/12) - $964.11 = $317.13

Therefore, the interest earned during the second month of the 7th year is $317.13

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Answer:

ture,false,true,true,false,true

Step-by-step explanation:

it is very easy just read it carefuly and then add it up

The equation of the line passing through the given points S(1/2, 1), T(1/2,4) would be 2y = 3x - 1/2.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

\((y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\)

The equation of the line passes through the given points.

S(1/2, 1), T(1/2,4)

Then the equation ;

\((y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y - 1/2) = \dfrac{4 - 1}{1-1/2} (x -1/2)\\\\(y - 1/2) = \dfrac{3}{1/2} (x -1/2)\\\\2(y - 1/2) = 3(x -1/2)\\\\2y -1 = 3x - 3/2\\\\2y = 3x -1/2\)

The equation of the line passing through the given points S(1/2, 1), T(1/2,4) would be 2y = 3x - 1/2.

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Answer: 1/2 > 3p

Step-by-step explanation:

TO GET THE VALUE OF 5t YOU SHOULD FIRST SOLVE FOR t IN THE GIVEN EQUATION

\( \frac{6t}{6} = \frac{44.4}{6} \\ t = 7.4\)

THEREFORE TO GET THE VALUE OF 5t PLUG IN THE VALUE OF t AND SIMPLIFY

\( = 5(7.4) \\ = 37\)

THE ANSWER IS 37.

Answer:

To find the value of 5t, we can simply divide the given equation 6t = 44.4 by 6 to get t = 7.4. Then, we can multiply 7.4 by 5 to get 5t = <<5*7.4=37>>37.

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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x= 3

awutydyt7asd67awt67

The probability of getting between three and seven heads, inclusively, when flipping a coin 10 times is approximately 0.377 or 37.7%.

The probability of getting between three and seven heads, inclusively, when flipping a coin 10 times can be calculated using the binomial probability distribution.

The probability of getting x successes in n trials, where the probability of success in a single trial is p, is given by the formula P(x) = nCx * p^x * (1-p)^(n-x), where nCx is the number of combinations of n things taken x at a time.

In this case, the probability of getting a head on a single coin flip is 0.5, and we are flipping the coin 10 times. So the probability of getting between three and seven heads, inclusively, is:

P(3) + P(4) + P(5) + P(6) + P(7)

= (10C3 * 0.5³ * 0.5⁷) + (10C4 * 0.5⁴ * 0.5⁶) + (10C5 * 0.5⁵ * 0.5⁵) + (10C6 * 0.5⁶ * 0.5⁴) + (10C7 * 0.5⁷ * 0.5³)

= 0.376953125

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Answer: I need more evindence to answered it but I say its the third one

Step-by-step explanation:

Answer:

B.(x-3)(x+8)

Step-by-step explanation:

product of -3 and 8 is -24 and sum of -3+8 is +5

Answer:

(x+8) (x-3)

Step-by-step explanation:

x² + 5x – 24

What 2 numbers multiply to -24 and add to 5

8*-3 = -24

8+-3 = 5

(x+8) (x-3)

The x-coordinate of the vertex is 0.  the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

To find the dimensions that will create the maximum area of the prop section, we need to analyze the given equation A = -x^2 + 40. The equation represents a quadratic function in the form of A = -x^2 + 40., where A represents the area of the prop section and x represents the dimension.

The quadratic function is in the form of a downward-opening parabola since the coefficient of is negative (-1 in this case). The vertex of the parabola represents the maximum point on the graph, which corresponds to the maximum area of the prop section.

To determine the x-coordinate of the vertex, we can use the formula x = -b / (2a), where the quadratic equation is in the form Ax^2 + Bx + C and a, b, and c are the coefficients. In this case, the equation is -x^2 + 40, so a = -1 and b = 0. Plugging these values into the formula, we get x = 0 / (-2 * -1) = 0.

Therefore, the x-coordinate of the vertex is 0. To find the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation  A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

Hence, the equation that reveals the dimensions that will create the maximum area of the prop section is A = 40. This means that regardless of the dimension x, the area of the prop section will be maximized at 40 units.

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Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Answer:

1400

Step-by-step explanation:

Let x= total number of students

10% of students is also 140 students

i.e 10% of x =140

10/100*x=140

10x/100=140

10x=14000

x=14000/10

x=1400

Answer: the second, third and fifth options.

Step-by-step explanation:

When an equation is set up in a y=mx+b format, the slope is always equal to the value m.

Answer:

2

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

First find the slope (m)

m = (-1-(-3) / (6-4) = 2/2 = 1

Now find b, the y-intercept, by plugging either point into the equation.

y = mx + b

-3 = 1(4) + b

b = -7

Answer:

i would go with D to

Step-by-step explanation:

Answer:

A Graph = C ; B Graph = D ; C Graph = B ; D Graph = A

Step-by-step explanation:

Answer:

a. = C.

b. = D.

c. = B.

d. = A.

Step-by-step explanation:

The equation to find the amount of space between the end of the wall and the painting is x = 16.9 - 2 * space, where 'x' represents the length of the painting and 'space' represents the unknown space.

To find the amount of space between the end of the wall and the painting, we need to subtract the length of the painting from the length of the wall and divide it by 2.

Given that the wall is 16.9 feet long and the painting is to be centered, we can assume the painting's length is unknown. Let's represent it as 'x'.

Therefore, the equation becomes (16.9 - x) / 2 = space between the end of the wall and the painting.

To solve for x, we can multiply both sides of the equation by 2 to get rid of the fraction, resulting in 16.9 - x = 2 * (space between the end of the wall and the painting).

Next, we simplify the equation to 16.9 - x = 2 * space.

To isolate x, we subtract 2 * space from both sides, resulting in x = 16.9 - 2 * space.

To determine the exact amount of space between the end of the wall and the painting, we would need to know the value of 'space'. Unfortunately, it is not provided in the question.

In summary, the equation to find the amount of space between the end of the wall and the painting is x = 16.9 - 2 * space, where 'x' represents the length of the painting and 'space' represents the unknown space.

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0.80 is the expected value of wei's ticket. This can be solved by using the concept of probability.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

As, we know

E(x) = x₁. p(x₁) + x₂ . p(x₂) + ....... + x(n). p(x(n))

From the table it is shown that,

E(x) = (68% × 0) + (24% × 0) + (6% × 5) + (2% × 25)

or, E(x) = 0.80

then the expected value of Wei's ticket is: 0.80

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The evidence that would help Marisa conclude that no chemical reaction occurred in a science experiment is option d) no new substance was formed.

A reaction is termed a chemical reaction if there is a change in the reactants involved. These changed substances have properties different from that of the original. This is what segregates chemical reactions from physical ones like boiling, freezing, breaking, etc.

According to the law of conservation of mass, the number of atoms will remain the same even if the chemical reaction has occurred. It is the number of molecules that changes. A chemical reaction cannot create any new element. It creates new compounds or decomposes existing ones into different elements.

Hence, the conclusion of no reaction occurred can be supported only by the evidence of no reaction of new substances.

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Complete Question

In a science experiment, Marisa concludes that no chemical reaction has occurred. What evidence would support

this conclusion?

A. the mass and total number of atoms were conserved

B. no energy was released

C. a new element was created

D. no new substance was formed

Answer:

The greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.

Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars

Step-by-step explanation:

 The greatest common divisor (GCD) of two or more numbers is the largest number by which these numbers can be divided, that is, it is the largest number that divides them all exactly.

In other words, the greatest common divisor of two numbers a and b is the largest number that divides a and divides b.

To find the greatest common divisor of two or more numbers, you start by breaking those numbers down into prime factors. In this case:

36=2²*3²

72 = 2³*3²

108 = 2²*3

The greatest common divisor is obtained by choosing only the prime factors common to the numbers, raised to the smallest exponent. That is, you choose only the common factors and those that are repeated must be raised to the minimum exponent.

The 2 appears as a prime factor in the three decompositions, whose minimum exponent is 2.

3 also appears as a common factor, whose minimum exponent is 1.

By doing the multiplication to get the greatest common divisor, you get:

2²*3=12

So the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.

To calculate how many lunches each item will contain, you simply divide the amount you have of each item by the most lunches Tyler can pack, 12.

Sandwiches: 36÷12= 3

Apples: 72÷12= 6

Granola bars: 108÷12= 9

Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars

1.386  is the sample variance .

What does the standard deviation of the sample mean?

Step 1:Add them up:

9.0 +  7.3 +  6.0 +  8.8 +  6.8 +  8.4 + 6.6  = 52.9

Step 2: Square your answer:

52.9 × 52.9 = 2798.41

…and divide by the number of items. We have 7 items in our example so:

2798.41 / 7 = 399.773

Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:

9.0^2 +  7.3^2 +  6.0^2 +  8.8^2 +  6.8^2 +  8.4^2 + 6.6^2 = 408.09

Step 4: Subtract the amount in Step 2 from the amount in Step 3.

408.09 - 399.773 = 8.317

Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:

7 – 1 = 6

Step 6: Divide the number in Step 4 by the number in.

This gives you the variance:

8.317/ 6 = 1.386

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Prove that :

\( \sf \: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} = 4 \: \vec{A} \: . \: \vec{B}\)

\( \green{\large\underline{\sf{Solution-}}}\)

Consider, LHS

\(\rm :\longmapsto\: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} \)

We know,

\(\rm :\longmapsto\:\boxed{\tt{ |\vec{x}| ^{2} = \vec{x}.\vec{x}}}\)

So, using this, we get

\(\rm \:  =  \: (\vec{A} + \vec{B}).(\vec{A} + \vec{B}) - (\vec{A} - \vec{B}).(\vec{A} - \vec{B})\)

\(\rm \:  =  \:[ \vec{A}.\vec{A} + \vec{A}.\vec{B} + \vec{B}.\vec{A} + \vec{B}.\vec{B}] - [\vec{A}.\vec{A} - \vec{A}.\vec{B} - \vec{B}.\vec{A} + \vec{B}.\vec{B}]\)

\(\rm \:  =  \: [ { |\vec{A}| }^{2} + \vec{A}.\vec{B} + \vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} - \vec{A}.\vec{B} - \vec{A}.\vec{B} + { |\vec{B}| }^{2}]\)

\(\red{ \bigg\{  \sf \: \because \: \vec{A}.\vec{B} = \vec{B}.\vec{A} \bigg\}}\)

\(\rm \:  =  \: [ { |\vec{A}| }^{2} + 2\vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} -2 \vec{A}.\vec{B} + { |\vec{B}| }^{2}]\)

\(\rm \:  =  \: { |\vec{A}| }^{2} + 2\vec{A}.\vec{B} + { |\vec{B}| }^{2}- [{ |\vec{A}| }^{2} + 2 \vec{A}.\vec{B} - { |\vec{B}| }^{2}\)

\(\rm \:  =  \: 4 \: \vec{A}.\vec{B}\)

Hence,

\( \sf \:\boxed{\tt{ \: \: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} = 4 \: \vec{A} \: . \: \vec{B} \: \: }}\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\(\boxed{\tt{ \vec{A}.\vec{B} = \vec{B}.\vec{A}}}\)

\(\boxed{\tt{ \vec{A}.\vec{A} = { |\vec{A}| }^{2} }}\)

\(\boxed{\tt{ \vec{A} \times \vec{B} = - \vec{B} \times \vec{A}}}\)

\(\boxed{\tt{ \vec{A} \times \vec{A} = 0}}\)

\(\boxed{\tt{ \vec{A}.\vec{B} = 0 \: \rm\implies \:\vec{A} \: \perp \: \vec{B}}}\)

\(\boxed{\tt{ \vec{A} \times \vec{B} = 0 \: \rm\implies \:\vec{A} \: \parallel \: \vec{B}}}\)

Answer:

20

Step-by-step explanation:

Let Kayla's age be k.

Let Isaac's age be a.

Kayla is 6 years older than Raoul. This means that:

k = y + 6

lsaac is 4 years younger than Raoul. This means that:

a = y - 4

y = 12

=> k = 12 + 6 = 18

and

a = 12 - 4 = 8

The sun of Raoul's age and Isaac's age is:

12 + 8 = 20

Answer: 2.11 yd³ = 1613210.750364 cm³

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert cubic yards to cubic centimeters, you can use the following conversion factors:1 yard = 91.44 centimeters

1 cubic yard = (91.44 centimeters) x (91.44 centimeters) x (91.44 centimeters) = 7,645,549.23 cubic centimetersTherefore, to convert 2.11 cubic yards to cubic centimeters, you can multiply it by the conversion factor:2.11 cubic yards x 7,645,549.23 cubic centimeters/cubic yard ≈ 16,120,247.02 cubic centimetersSo, 2.11 yards^3 is approximately equal to 16,120,247.02 cubic centimeters.

Answer:  You can use the identity THE PICTURE THAT I PUT THERE

The sign is negative because the angle is in the 3rd quadrant.  This corresponds to ...  a. -(4√17)/17

value of sin ( theta ) = -4 (square root of ) 17 / 17

Real functions which relate to an angle of a right angled triangle to ratios of two side length.

Given

tan (theta) = 4`

sin(theta) = tan (theta ) / (1 + tan ^ theta)^(1/2)

sin(theta) = 4/(1+(4)^2)^(1/2)

                = 4/ (17)^ (1/2)

                multiplying  and dividing by 17 ^ (1/2), we get

                =  -4 (17) ^ (1/2) / 17 ( negative since angle is in third quadrant and tan is negative in that quadrant )

option a) -4 (square root of ) 17 / 17

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Answer:

HAHHAHAH XD sorry jkjkjk

Step-by-step explanation: