Duane always uses 3/10 of money he earns mowing lawns to buy lawn supplies for the work. He puts the rest of the money in the bank. If Duane earned $80 last month mowing lawns, how much money did he put in the bank?​

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

B

Step-by-step explanation:

Basically you are dividing X by 4, meaning the number of boxes, if you took all the mugs out of the boxes there are 55 mugs.

The sale price of the coat is $45.

The percentage is the representation of a value with respect to a base value when the base value is taken as 100.

For example. If we need to calculate 20 as a percentage of 40. The ratio is 20/40 and the percentage is 20/40*100 which is 50%.

Given,

The normal price of the coat is $75

The sale price of the coat = $75 - $30 = $45

The coat is discounted by (30 / 75 *100 ) percent or 40%.

The sale price of the coat is the normal price -  discount = 75 - (75*40%)= 75-30 = $45

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4 oz is equivalent to 118.29 mL (milliliters).

The conversion factor for ounces to milliliters is that 1 oz is equal to 29.5735 mL. To convert ounces to milliliters, you can multiply the number of ounces by 29.5735. In this case, 4 x 29.5735 = 118.29 mL.It is important to note that milliliters and ounces are both units of measurement for volume.

Ounces are widely used in the United States and the United Kingdom, while milliliters are used in most of the countries worldwide. The milliliter is the base unit of volume in the International System of Units (SI) and it is defined as the volume of a cube that is 1cm x 1cm x 1cm. The ounce is a unit of volume in the imperial system and the avoirdupois system.

The avoirdupois system is a weight system that is based on a pound that is divided into 16 ounces and it is used in most of the countries worldwide.When working with volume measurements, it's important to be aware of the units of measurement being used, as well as the conversion factors between different units, in order to ensure accurate conversions and measurements.  

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Answer:

G = (y-x)/2

Step-by-step explanation:

Here, we want to find the value of the angle marked G

To do this, we are going to use one of the important circle angle-arc relationships

Thus, we have it that;

G = 1/2 (mFE - mJH)

G = 1/2 (y-x)

Which is simply

G = (y-x)/2

Answer: D. Subtracting 9 from each side

Step-by-step explanation:

Always start with numbers without variables first before doing anything with x. And make sure one side must not equal 0 unless you're doing polynomials.

Answer:

19x23 = 437

437-23 = 414

414-9 = 405

Step-by-step explanation:

I believe this is what the question is asking. if not please let me know and tell me how the question works.

Answer:

\( \frac{1}{3} \times x = 14 \\ \\ x = 14 \times 3 \\ \\ { \underline{ \: \: x = 42 \: \: }}\)

The value of x in 1/3 of x is 14 will be 42.

Given,

1/3 of x is 14

Now,

Expression : 1/3 of x is 14

Rewriting the expression in the simplified form,

1/3 of x = 14

Now to get the value of x cross multiply,

x = 14 * 3

x = 42

The value of x is 42.

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Answer:

1.50 $

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

2.b=90

1.30

Answer:

Step-by-step explanation:

6. You're gonna use Cos to find Y

Cos = adj/hyp

Cos 27 = 10/y

10/cos27 = y

11.2 = y

7. It'll help immensily if you draw this one out.

You're gonna use Sin to find the angle.

Sin = opp/hyp

Sin 65 = 14/x

14/sin65 = x

15.4 = x

The vector z = [2 + 4i, -2i] can be written as a linear combination of z₁ and z₂ as,(z,z₁)z₁ + (z,z₂)z₂= (5 + 3i) [1 + i/2, 1 - i/2] + (-3√2 + i√2) [i/√2, -1/√2].

(a) Here, {z₁, z₂} is an orthonormal set in C².

We have given,

z₁ = [1 + i/2, 1 - i/2],z₂ = [i/√2, -1/√2].

Now, we need to show that {z₁, z₂} is an orthonormal set in C².As we know that, the inner product of two complex vectors v and w of dimension n is defined by the following formula:

(v,w) = ∑i=1nviwi^* where vi and wi are the i-th components of v and w, respectively, and wi^* is the complex conjugate of the i-th component of w.

(i) Inner product of z₁ and z₂ is

(1 + i/2).(i/√2) + (1 - i/2).(-1/√2)= i/(2√2) - i/(2√2) = 0

(ii) Magnitude of z₁ is∣z₁∣ = √((1 + i/2)² + (1 - i/2)²)= √(1 + 1/4 + i/2 + i/2 + 1 + 1/4)= √(3 + i)√((3 - i)/(3 - i))= √(10)/2

(iii) Magnitude of z₂ is∣z₂∣ = √((i/√2)² + (-1/√2)²)= √(1/2 + 1/2)= 1

(iv) Inner product of z₁ and z₁ is(1 + i/2).(1 - i/2) + (1 - i/2).(1 + i/2)= 1/4 + 1/4 + 1/4 + 1/4= 1

Therefore, {z₁, z₂} is an orthonormal set in C².

(b) Here, we are given z = [2 + 4i, -2i]and we need to write it as a linear combination of z₁ and z₂.

As we know that, we can write any vector z as a linear combination of orthonormal vectors z₁ and z₂ as,

z = (z,z₁)z₁ + (z,z₂)z₂where (z,z₁) = Inner product of z and z₁, and (z,z₂) = Inner product of z and z₂.

Now, let's calculate these inner products:

(z,z₁) = (z,[1 + i/2, 1 - i/2])

= (2 + 4i)(1 + i/2) + (-2i)(1 - i/2)

= 1/2 + 2i + 4i + 2 + i - 2i

= 5 + 3i(z,z₂)

= (z,[i/√2, -1/√2])

= (2 + 4i)(i/√2) + (-2i)(-1/√2)

= (2i - 4)(1/√2) + (2i/√2)

= -3√2 + i√2

Now, putting these values in the equation, we have z = (5 + 3i) [1 + i/2, 1 - i/2] + (-3√2 + i√2) [i/√2, -1/√2]

Thus, the vector z = [2 + 4i, -2i] can be written as a linear combination of z₁ and z₂ as,

(z,z₁)z₁ + (z,z₂)z₂

= (5 + 3i) [1 + i/2, 1 - i/2] + (-3√2 + i√2) [i/√2, -1/√2]

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For the matrix the true statement is given by option d. Both A and B are false.

Let's analyze each statement of the matrix as follow,

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R⁵.

This statement is false.

The domain of the transformation T is not R⁵.

The domain of T is determined by the dimensionality of the vectors x that can be input into the transformation.

Here, the matrix A is a 3 times 5 matrix, which means the transformation T(x) = Ax can only accept vectors x that have 5 elements.

Therefore, the domain of T is R⁵, but rather a subspace of R⁵.

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto.

This statement is also false.

The transformation x → Ax can still be onto (surjective) even if A is a 3 times 2 matrix.

The surjectivity of a transformation depends on the rank of the matrix A and the dimensionality of the vector space it maps to.

It is possible for a 3 times 2 matrix to have a rank of 2,

and if the codomain is a vector space of dimension 3 or higher, then the transformation can be onto.

Therefore, as per the matrix both statements are false, the correct answer is d. Both A and B are false.

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The above question is incomplete, the complete question is:

Which of the following best characterizes the following statements:

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R^5

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto

a. Only A is true

b. Only B is true

c. Both A and B are true

d. Both A and B are false

From the given question,

The given angle is 60 degree.

Now,

Find the x coordinate of the point where the terminal side intersects the unit circle.

So,

We know that the x-coordinate on unit circle represent the cosine and y-coordinate represent the sine function of the given angle.

Then,

The coordinate is,

Where, angle is given 60 degree.

So,

Hence, the option B is correct.

Answer:

Domain (-1,1]

Range (-1,5]

Step-by-step explanation:

Answer:

Range: is 8

Domain 8x-13

Step 1: Count the total number of students

The total number of students in the statistics class is 8.

Step 2: Count the number of women

There are 4 women in the statistics class.

Step 3: Calculate the frequency, proportion, and percentage of women

Frequency: The frequency of women in the statistics class is 4.

Proportion: The proportion of women in the statistics class is 4/8, or 0.5.

Percentage: The percentage of women in the statistics class is 50%.

The information in the question is not significant to calculate the frequency, proportion and percentage of women.

Statistical models for calculating gender through frequency involve counting the number of individuals in a population that identify as each gender. This can be done by collecting data on gender from surveys, census data, or other sources of information. The data collected is then used to calculate the frequency, proportion, and percentage of each gender in the population. This information can be used to better understand gender dynamics in a population and inform policies and practices that promote gender equity.

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Answer:

K = ½

Equation: y = ½x

Step-by-step explanation:

✔️Constant of proportionality (k) = y/x

Using a point on the line, (2, 1),

k = ½

✔️Equation of a proportional relationship would be in the form of y = kx

To write an equation, substitute k = ½, into y = kx

Thus:

y = ½x

The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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The new tableau becomes:X1X2X3S1S2S3Z101/3 0 −2/3 1/3 0 −1/3 22/3 0 2/3 8/3 0 1/3 80 1 4/3 1 0 −1/3 70X1 = 10, X2 = 0, X3 = 14/3, S1 = 0, S2 = 0, S3 = 0, and Z = 70.


Juan tells himself that it is his own fault that he did not study more for his test.Using the given initial tableau, we need to circle the pivot and write the new tableau on a separate sheet of paper.
Continue to circle each pivot and write each tableau until the indicators are all non-negative. The given initial tableau is:X1X2X3S1S2S3Z420100220122501002802210045−3−2−400001From the given initial tableau, we need to find the pivot element for which we can perform the row operations. We choose the element 2 in row 1 and column 2 as the pivot and perform row operations to make all the indicators non-negative.
The new tableau becomes:X1X2X3S1S2S3Z23/2−1/2 0 1 0 −1/2 0 11/2 3/2 0 5/2 0 1/2 0 14−1/2 0 0 0 1/2 1 9/2We choose the element 1 in row 1 and column 1 as the pivot and perform row operations to make all the indicators non-negative.

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The x-intercept of CD is 17.

Since CD is perpendicular to AB and passes through point C(5, 12), we can find the equation of CD using the slope-intercept form.

The slope of CD can be determined using the negative reciprocal of the slope of AB.

Slope of AB = (change in y) / (change in x) = (14 - (-3)) / (7 - (-10)) = 17 / 17 = 1

The negative reciprocal of 1 is -1. Therefore, the slope of CD is -1.

Using the slope-intercept form, we can write the equation of CD as:

y - y1 = m(x - x1),

where (x1, y1) is a point on CD. Let's use point C(5, 12):

y - 12 = -1(x - 5)

Simplifying the equation, we have:

y - 12 = -x + 5

y = -x + 17

To find the x-intercept, we set y = 0 and solve for x:

0 = -x + 17

x = 17

Therefore, the x-intercept of CD is 17.

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Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.

1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.

Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.

Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:

Year 1: Interest earned is P3,000 (P150,000 x 2%).

Year 2: Interest earned is P3,000 ($150,000 x 2%).

Year 3: Interest earned is P3,000 ($150,000 x 2%).

Year 4: Interest earned is P3,000 ($150,000 x 2%).

Year 5: Interest earned is P3,000 ($150,000 x 2%).

Interest earned overall: P15,000

After five years, the total will be P150,000 plus P15,000, or P165,000.

Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:

Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.

Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.

Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.

Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.

Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.

Interest earned in whole was P15,612.12096.

2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.

  Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .

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The value of x in the triangle given the midsegment points and sections is 1.35 units

The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

The midsegments of triangle UWY are VR, VZ, ZR

To find the value of x, we use a theorem called the mid segment theorem which states that:

"The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle."

The third side of triangle UWY is WY and it measures 2.7.

Therefore, x will be 2.7 divided by 2 2.7/2 which will give us the value 1.35 i.e. x = 1.35

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\((f+g)(x)=f(x)+g(x)\\\\f(x)=2x^2+3x\\g(x)=x-2\\\\(f+g)(2)=2\cdot2^2+3\cdot2+2-2=8+6=14\)

Answer:

∠P=29°

Step-by-step explanation:

The exterior angle theorem says that the exterior angle of a triangle is equal to the sum of the two remote interior angles.

56=∠P+27

∠P=56-27

∠P=29

Answer:

angle 1 equals 55 and angle 2= equals 115

Step-by-step explanation:

the middle angle is 125 so than you add 63+__ which is 62 so than the last angle to make 180 is 55(angle 1) than angle 2 10+__=125 so ___=115 than the last angle will be 55

Answer:

1) 62°

2) 115°

Step-by-step explanation:

Angle 1)

QRP= 180°-125° (adjacent angles on a straight line)

= 55°

angle 1= 180°-63°-55° (sum of angles in a triangle)

= 62°

Angle 2)

SRT= QRP (vertically opposite angles)

= 55°

angle 2= 180°-10°-55° (sum of angles in a triangle)

= 115°

The value of 6! is 720.

The number of ways the two people can be chosen from the group of six is 30 ways.

The number of ways the group can be chosen is 20 ways.

The number of ways the six people can be placed in a line for a photo is calculated as;

\(= 6!\\\\= 6 \times 5 \times 4 \times 3 \times 2 \times 1\\\\= 720 \ ways\)

The number of ways the two people can be chosen from the group of six is calculated;

\(= 6P_2\\\\= \frac{6!}{(6-2)! } \\\\= \frac{6!}{4!} \\\\= \frac{6\times 5 \times 4!}{4!}\\\\= 6\times 5 \\\\= 30 \ ways\)

The number of ways the group can be chosen is calculated as;

\(= 6C_3\\\\= \frac{6!}{(6-3)! \times 3!} \\\\= \frac{6!}{3! \times 3!} \\\\=20 \ ways\)

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Answer:

The answer is 20

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

Y=2+x/2

Step-by-step explanation:

llllllllllllll

When deciding how much to sell an oil well, it's important to consider the present value of its future cash flows. In this case, the oil well will pay $12,000 per month for 12 years, with the first payment being made today.

To calculate the present value of this stream of cash flows, we can use the present value formula:PV = C * [(1 - (1 + r)^-n) / r], where: PV = present value, C = cash flow per period, r = discount rate, n = number of periods.

First, we need to find the cash flow per period. Since the well will pay $12,000 per month for 12 years, there will be a total of 12 x 12 = 144 payments. Therefore, the cash flow per period is $12,000.Next, we need to find the discount rate.

The question tells us that a fair return on the well is 7.45%, so we'll use that as our discount rate.Finally, we need to find the present value of the cash flows. Using the formula above, we get:PV = $12,000 * [(1 - (1 + 0.0745)^-144) / 0.0745]= $12,000 * (90.2518 / 0.0745)= $144,317.69.

So the present value of the cash flows is $144,317.69. This is the amount that the oil well is worth today, given the expected cash flows and the discount rate of 7.45%. Therefore, if you decide to sell the oil well, you should ask for at least $144,317.69 to receive a fair return on your investment.

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Option D: There is not enough evidence to suggest that the average percent increase of company sales after an advertising campaign is different from 17 percent.

The marketing manager wants to test the claim that the percent increase in company sales after an advertising campaign is different from 17 percent. To do this, a z-test statistic was calculated, which came out to be 2.43. The marketing manager wants to know if there is enough evidence to reject the null hypothesis. The significance level, or alpha, is given as 0.01.

To determine if there is enough evidence to reject the null hypothesis, we need to compare the test statistic to the critical value(s) and the p-value.

First, let's determine the type of test we should use. Since the alternative hypothesis is that the percent increase is different from 17 percent, we need a two-tailed test.

Next, we compare the test statistic to the critical value(s) based on the significance level. Since the significance level is 0.01, we need to find the critical value(s) that split the alpha evenly between the two tails of the distribution. In this case, the critical value(s) would be ±2.58 (which corresponds to an alpha of 0.005 for each tail).

Now, let's compare the test statistic (2.43) to the critical value(s) (±2.58). Since the test statistic falls within the range of the critical value(s), we do not have enough evidence to reject the null hypothesis.

Lastly, let's consider the p-value. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In this case, the p-value is given as 0.015. Since the p-value is greater than the significance level (0.01), we do not have enough evidence to reject the null hypothesis.

Based on these results, we can conclude that there is not enough evidence to suggest that the average percent increase of company sales after an advertising campaign is different from 17 percent.

COMPLETE QUESTION:

Understand and interpret the test-statistic and p-value Question A marketing manager would like to test the claim that the percent increase of company sales after an advertising campaign is different than 17 percent. If the z, test statistic was calculated as z = 2.43, does the marketing manager have enough evidence to reject the null hypothesis? Assume a = 0.01. Move the blue dot to choose the appropriate test (left, right, or two-tailed). Then, use the graph below to show the test statistic, p-value, and the rejection region to make a conclusion about the hypothesis test. Move the blue dot to choose the appropriate test Significance level = 0.01 a=0.01 a=0.025 a=0.05 a=0.1 Move the blue dot to choose the appropriate test Significance level = 0.01 a=0.01 a=0.025 a=0.05 a=0.1 a/2 = 0.005 a/2 = 0.005 p-value= 0.015 D Ź T Ő tes statistic = 2. test statistic = 2.43 Z= 2.58 Z= -2.58 powered by Select the correct answer below:

A.There is enough evidence to suggest the average percent increase of company sales after an advertising campaign is greater than 17 percent. B. There is not enough evidence to suggest the average percent increase of company sales after an advertising campaign is greater than 17 percent.

C. There is enough evidence to suggest the average percent increase of company sales after an advertising campaign is not 17 percent.

D. There is not enough evidence to suggest the average percent increase of company sales after an advertising campaign is not 17 percent.

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Answer:

Function

Step-by-step explanation:

Passes vertical line test