Help please, I could not figure this problem because the answer was -108 but I only solved it to -244. The problem is “Find coefficient of x in expansion of (x-3)^4”

If Mary needs to have $9,000 in 9 years at 4% interest compounded quarterly, she should deposit $208.93 in a sinking fund at the end of each quarter.

Compound interest refers to the system that charges interest on both the accumulated interest and the principal at the end of each period.

The compounding period may vary from annual, quarter, and monthly to daily.

N (# of periods) = 36 quarters (9 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $9,000

Results:

Periodic (Quarterly) Deposit (PMT) = $208.93

The sum of all periodic payments = $7,521.44

Total Interest = $1,478.56

Thus, Mary needs to deposit $208.93 each quarter.

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Analysis, a form of horizontal analysis, is a method used to identify patterns in data across different periods. It involves calculating the ratio of the analysis period amount to the base period amount, multiplied by 100. This calculation helps to assess the changes and trends in the data over time.

Analysis, as a form of horizontal analysis, provides insights into the changes and trends in data over multiple periods. It involves comparing the amounts or values of a specific variable or item in different periods. The purpose is to identify patterns, variations, and trends in the data.
To calculate the analysis, we take the amount or value of the variable in the analysis period and divide it by the amount or value of the same variable in the base period. This ratio is then multiplied by 100 to express the result as a percentage. The resulting percentage indicates the change or growth in the variable between the analysis period and the base period.
By performing this analysis for various items or variables, we can identify significant changes or trends that have occurred over time. This information is useful for evaluating the performance, financial health, and progress of a business or organization. It allows stakeholders to assess the direction and magnitude of changes and make informed decisions based on the patterns revealed by the analysis.

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Answer:

hlo buddy

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 πr³.

Calculate the sample size needed to estimate the population mean within a given range with a given confidence level and standard deviation and we get a.136, b.657, c.193, and d.83.

a. To estimate the sample size required to estimate a population mean to within 10 units, we can use the formula:

\(n = (z*σ/E)^2\)

where:

z = the z-score corresponding to the desired confidence level (90% confidence level corresponds to z = 1.645)

σ = the population standard deviation (50)

E = the desired margin of error (10)

Plugging in the values, we get:

\(n = (1.645*50/10)^2 = 135.61\)

Therefore, a sample size of at least 136 is required.

b. Using the same formula, but changing the standard deviation to 100, we get:

\(n = (1.645*100/10)^2 = 656.10\)

Therefore, a sample size of at least 657 is required.

c. Using a 95% confidence level, the corresponding z-score is 1.96. Plugging the values into the formula, we get:

\(n = (1.96*50/10)^2 = 192.08\)

Therefore, a sample size of at least 193 is required.

d. To estimate the sample size required to estimate a population mean to within 20 units, we can use the same formula as in part (a):

n = (z*σ/E)^2

Plugging in the values, we get:

n = (1.645*50/20)^2 = 85.90

Therefore, a sample size of at least 86 is required.

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Answer:

its 2b+30 bc you can't find b in this case

Step-by-step explanation:

Answer:

40 years old.

Step-by-step explanation:

\(x - \frac{2}{5} x = 24 \\ \frac{3}{5} x = 24 \\ x = 24 \div \frac{3}{5} = 40\)

Answer:

\(x=44.5ft\)

Step-by-step explanation:

From the question we are told that:

Height \(h=42ft\)

Angle of depression \(\theta=27\textdegree\)

Angle of Elevation \(\alpha=23 \textdegree\)

Generally the equation for the vertical distance between Emery's distance x and the bottom of the building  is mathematically given by

Since the angle of depression and elevation are given as

27 and 23 respectively

Therefore

Emery's view of the 42 ft building is

\(\gamma=23+27\)

\(\gamma=50 \textdegree\)

Therefore Emery's distance x to the base of the building h' is

\(h'=\frac{27}{50}*42\)

\(h'=22.68ft\)

Generally the Trigonometric equation for Emery's distance x is mathematically given by

\(x=\frac{h'}{tan\theta}\)

\(x=\frac{22.68}{tan 27}\)

\(x=44.5ft\)

An expression for which subtracting 5 from an expression would isolate the variable is -9x + 5 = x + 2

Algebraic expressions are described as expressions that consists of coefficients, terms, variables, factors and constants.

These expressions are also known to consist of arithmetic operators, which includes;

From the information given, we have to subtract five from an expression to isolate the variable

Now, let's us the algebraic expression;

-9x + 5 = x + 2

Let's subtract 5 from both sides of the equation, we get;

-9x + 5 - 5 = x + 2 - 5

add and subtract the like terms

-9x + x = -3

-8x = -3

x = 3/8

Hence, the expression is -9x + 5 = x + 2

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Answer:

-1

Step-by-step explanation:

3x^2-2x-5=0

(use the quadratic equation)

or

3(-1)^2-2(-1)-5=0

3+2-5=0

Answer:

Its an example  Unit rate becuase theres the #1 in it and its constant

Step-by-step explanation:

A rate is more like a ratio of 2 different number

3:6

or

9:18

When these are simplified you’ll get 1 in one of the 2 numbers but then it would be a unit rate

Rate= no #1

Unit rate= Defined as a number 1

Answer:

7,040

Step-by-step explanation:

2 miles is half of 4 miles so you would multiply 3,520 yards by 2.

Given:

Aim:

We need to find the trigonometric function and the quadrant of the angle.

Explanation:

Take inverse trigonometry on both sides of the equation.

Final answer:

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

Step-by-step explanation: I don’t know if this is what your asking for but 26, 37, 48.

Formular for total surface area of a cylinder

S = 1231.5 sq ft

In order to determine which of the given sets is a subspace of \( \mathbf{P}_{3} \), it is required to verify if it meets the following three requirements:It must contain the zero vector.It must be closed under vector addition.It must be closed under scalar multiplication.

\((a) \( \mathbf{S}=\left\{f \mid f \in \mathbf{P}_{3}, f^{\prime \prime}(0)=2\right\} \)\).

This is a subspace of\(\( \mathbf{P}_{3} \)\).It contains the zero vector since it is a polynomial and therefore, \(\( f^{\prime \prime}(0)=0 \).\)

It is closed under vector addition:\(Let \( f(x)=a_{3} x^{3}+a_{2} x^{2}+a_{1} x+a_{0} \) and \( g(x)=b_{3} x^{3}+b_{2} x^{2}+b_{1} x+b_{0} \)\)be two polynomials in\(\( \mathbf{S} \)\),

then we have:\(\( (f+g)^{\prime \prime}(x)=f^{\prime \prime}(x)+g^{\prime \prime}(x) \)\( (f+g)^{\prime \prime}(0)=f^{\prime \prime}(0)+g^{\prime \prime}(0)=2+2=4 \)\)

Therefore, \(\( f+g \in \mathbf{S} \)\)and is closed under vector addition.

It is also closed under scalar multiplication:Let \(\( f(x)=a_{3} x^{3}+a_{2} x^{2}+a_{1} x+a_{0} \)\) be a polynomial in \(\( \mathbf{S} \)\), and let c be a scalar, then we have:\(\( (cf)^{\prime \prime}(x)=c f^{\prime \prime}(x) \)\( (cf)^{\prime \prime}(0)=c f^{\prime \prime}(0)=2c \)\)

Therefore, \(\( cf \in \mathbf{S} \)\)and is closed under scalar multiplication.

Thus, (a) is a subspace of \(\( \mathbf{P}_{3} \)\).Hence, option a is the correct answer.Note:Option b cannot be the answer because it is not possible for more than one set to be a subspace of\(\( \mathbf{P}_{3} \)\).Option c is incorrect because option a is a subspace of \(\( \mathbf{P}_{3} \)\).

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The consumer testing group has confirmed that the samples were randomly selected and independent, and the populations have normal distribution and the population variances are equal and test Statistic for this example is 8.90b and the P-value for this example is 0.011

The null hypothesis and alternative hypothesis are:H0: μ1 = μ2 = μ3HA: At least one μi differs from the rest of the means.The level of significance is α = 0.05The test statistic used for this example is the F distribution (ANOVA).a. Calculation of the Test Statistic:

Test Statistic = MSR / MSEWhere,MSR = mean square due to regression = SSTR / 2 = 190.66MSE = mean square due to error = SSE / 12 = 21.43Therefore, the test statistic F = MSR / MSE = 8.90b.

Calculation of the P-value:P-value = P(F > 8.90)The degrees of freedom for numerator is k-1 = 3 - 1 = 2 and the degrees of freedom for the denominator is N-k = 15 - 3 = 12.The p-value of the F distribution with 2 and 12 degrees of freedom at 5% level of significance is 0.011. Therefore, P-value < α.

Thus, we reject the null hypothesis. We conclude that at least one μi differs from the rest of the means. Therefore, the average battery lifetimes are not statistically the same for the three brands.

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Answer:

D. 14.7 m

Step-by-step explanation:

7 times 2 equals 14

7 times .1 equals .7

7 times 2.1 equals 14.7

Answer:

What do you need help with?

Answer

n = 5

Explanation

We need to solve for n in the equation given

7n - 4 = 31

Add 4 to both sides

7n - 4 + 4 = 31 + 4

7n = 35

Divide both sides by 7

(7n/7) = (35/7)

n = 5

Hope this Helps!!!

The points that lies on the same line are (-3, 12), and, (-1, 4).

Here, we have,

The given coordinate points are (-2, 8) and (5,-20).

Here, slope (m)= 8+20/-2-5

= 28/-7

=-4

Substitute m= -4 and (x, y)=(-2,8) in y=mx+c, we get

8 = 8+c

or, c = 0

So, the equation of a line is y= -4 x

Now,

(-6, -2) in the given equation is -2=-4 (-6)

-2≠ 24

(-3, 12)  in the given equation is y= -4 x

12 = 12

(4, 16) in the given equation is y= -4 x

16 ≠ -16

(0, 6) in the given equation is y= -4 x

6 ≠ 0

(-1, 4) in the given equation is y= -4 x

4 = 4

(7,5) in the given equation is y= -4 x

5 ≠ -28

Therefore, the points that lies on the same line are (-3, 12), and, (-1, 4).

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Answer:

32,52,96

Step-by-step explanation:

Replace all occurrences of x with y + 3 in each equation.

Replace all occurences of x in 6x - 5y = 15 with y + 3.

6 (y+3) -5y = 15

x = y + 3

Simplify 6 (y + 3) - 5y.

Simplify each term.

Apply the distributive property.

6y + 6 · 3 - 5y = 15

x = y + 3

Multiply 6 by 3.

6y + 18 - 5y = 15

x = y + 3

Subtract 5y from 6y.

y + 18 = 15

x = y + 3

Move all terms not containing y to the right side of the equation.

Subtract 18 from both sides of the equation.

y = 15 - 18

x = y + 3

Subtract 18 from 15.

y = -3

x = y + 3

Replace all occurences with y with -3 in each equation.

Replace all occurences of y in x = y + 3 with -3.

x = (-3) + 3

y = -3

Add -3 and 3.

x = 0

y = -3

The solution to the system is the complete set of ordered pairs that are valid solutions.

(0,-3)

The result can be shown in multiple forms.

Point Form:

(0,-3)

Equation Form:

x = 0, y = -3

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The required values are :

Refer to the attachment for solution ~

The equations are solved to w = 0 and z = -2. Option B

From the information given, we have the simultaneous equations as

3w-4z=8

2w+3z=-6

Make w the subject from equation 1

w = 8 + 4z/3

Substitute the value into equation 2, we have that;

2(8 + 4z/3) + 3z = -6

expand the bracket, we get;

16 + 8z/3 + 3z = -6

find the LCM, we have;

16 + 8z + 9z/3 = -6

cross multiply

16 + 17z = - 18

add the values

19z = -34

Make 'z' the subject

z =-2

Substitute the value

3w - 4z = 8

3w = 8 - 8

w = 0

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the acceleration at any given time t is given by the function a(t) = 24t.

To find the velocity of the particle at time t, we need to take the derivative of the position function with respect to time. Let's calculate the velocity function:

(a) Velocity function:

v(t) = f'(t)

To find the derivative of f(t) = 4t^3 + 7t + 9, we differentiate each term separately:

f'(t) = d/dt (4t^3) + d/dt (7t) + d/dt (9)

Differentiating each term:

f'(t) = 12t^2 + 7 + 0

Simplifying:

v(t) = 12t^2 + 7

(b) Velocity at t = 3 seconds:

To find the velocity at t = 3 seconds, substitute t = 3 into the velocity function:

v(3) = 12(3)^2 + 7

    = 12(9) + 7

    = 108 + 7

    = 115 m/s

Therefore, the velocity at t = 3 seconds is 115 m/s.

(c) Acceleration at time t:

Acceleration is the derivative of velocity with respect to time. We can differentiate the velocity function obtained in part (a) to find the acceleration function:

a(t) = v'(t)

Differentiating v(t) = 12t^2 + 7:

a(t) = d/dt (12t^2 + 7)

Differentiating each term:

a(t) = 24t + 0

Simplifying:

a(t) = 24t

the acceleration at any given time t is given by the function a(t) = 24t.

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Answer:

r = 7 cm

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( where r is the radius )

Given A = 154 , then

πr² = 154 , that is

\(\frac{22}{7}\) r² = 154 ( multiply both sides by 7 to clear the fraction )

22r² = 1078 ( divide both sides by 22 )

r² = 49 ( take square root of both sides )

r = \(\sqrt{49}\) = 7 cm

Answer:

A. About 1/3 of the people prefer pie without ice cream

Step-by-step explanation:

We know there were 80 people surveyed, so that's our denominator. Pie without ice cream is the bottom row. 15 + 12 = 27. 27/80 = 0.3375, which is 33.75% (multiply 0.3375 by 100), which is about 1/3.

B is wrong, because the blueberry pie numbers are not double the cherry pie numbers

C is wrong because cherry with ice cream is 24, blueberry without is 15

D is wrong because the ratio of blueberry to cherry is 44:36, and with ice cream to without is 53:27

Step-by-step explanation:

speed = distance/time

we know the speed and the time (11:45am to 1:45pm = 2 hours).

distance = speed × time = 56 m/h × 2 h = 112 miles

Answer:

21 ÷ -10x

Step-by-step explanation: