The Music Express has $72,000 to spend on the music bundles. If it buys
more pop bundles than rock bundles, how many bundles of each type of
music can The Music Express buy while getting closest to the budget of
$72,000? Explain.

Answer:

40.07 and 40.070...

Step-by-step explanation:

(4×10)+(7×1/100)

40+0.07

40.07 or 40.070(as the extra zeros don't count)

Hope you're having a splendiferous day or night.

Answer:

The two decimals are 40.07 and 40.070 that are equivalent to (4 × 10) + (7 × 1/100)

Step-by-step explanation:

(4 × 10) + (7 × 1/100)

40 + (7 × 0.01)

40 + 0.07

40.07 or 40.070 or 40.07000..

Thus, The two decimals are 40.07 and 40.070 that are equivalent to (4 × 10) + (7 × 1/100)

-TheUnknownScientist 72

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Answer:

0,7

Step-by-step explanation:

This equation is in y=mx+b form. The b is the y intercept. As we can see b is 7. So the y-intercept is 0,7.

The y-intercept of the given equation is (0, 7). Therefore, option D is the correct answer.

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

The given equation is y=-5x+7.

In the given equation slope m is -5 and the y-intercept is 7

So, y-intercept is (0, 7)

Therefore, option D is the correct answer.

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Data:

4laps/6min

To find the time that will take to her to swim 18 laps:

Multiply 18laps per 6min/4laps

Then, Ceylon will swim 18 laps in 27 m

Answer:

The p-value falls between 0.005 and 0.01.

Step-by-step explanation:

Random sample of 30 observations, you obtain t = 2.35

This means that the pvalue is 1 subtracted by the pvalue of Z = 2.35, as we are testing that the mean is more than a value.

Looking at the z-table, z = 2.35 has a pvalue of 0.9906

1 - 0.9906 = 0.0094

So, between 0.005 and 0.01.

Answer: The p-value falls between 0.01 and 0.02.

Step-by-step explanation: I took the FLVS test.

Answer:

Proportional

Step-by-step explanation:

Proportional functions can be written as \(y=kx\), where \(k\) is some constant of proportionality. Plugging in (x,y) pair into this function will yield a constant of proportionally of \(k=\frac{3}{2}\) and since this constant is maintained through all the coordinate pairs in the table, the table is proportional.

Given:

The variable q varies inversely as the cube of v. If k is the constant of variation, which equation represents this equation?

Solution:

It says that q varies inversely as the cube of v. Inversely means the reverse or opposite.

Next, we will put the constant k.

Then, we will re arrange the expression where we can find k.

ANSWER: qv^3 = k

ANSWER: qv^3 = k.
this is the answer.

Answer:

Step-by-step explanation:

Split it into two:

Y<3x

Y<5

X = 1

Y = 3

(1,3)

X = 2

Y = 6

(2, 6)

Plot the line up to y = 4.999999999999999999999 and not higher.

Answer:

Plot the line up to y = 4.999999999999999999999 and not higher

The value of the missing entry is 4 the cell value in (d) is the mean calculated from three input rasters (a, b, and c) in a local operation option (A) is correct.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that:

The cell value in (d) is the mean calculated from three input rasters (a, b, and c) in a local operation.

a = 2

b = 7

c = 3

The mean of three numbers:

(a + b + c)/3 = (2 + 7 + 3)/3 = 4

Thus, the value of the missing entry is 4 the cell value in (d) is the mean calculated from three input rasters (a, b, and c) in a local operation option (A) is correct.

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Answer:

A) 427 × 3 = 400 × 3 + 20 × 3 + 7 × 3

Step-by-step explanation:

\(427*3=(400+20+7)*3=(400*3)+(20*3)+(7*3)\)

Therefore, the first option is correct

Answer:

secondary

Step-by-step explanation:

mixing two primary colors together always makes a secondary

Step-by-step explanation:

Step 1.  Enter the data into the lists.  

For basic entry of data, see Basic Commands.

cricket1  

Step 2.  Create a scatter plot of the data.  

cricket4

Obviously, there is some scatter to this data. This variability is the norm, rather than the exception when working with biological data sets.  Real-life data seldom creates a nice straight line.

Step 3.  Choose the Linear Regression Model.

    Press STAT, arrow right to CALC, and arrow down to 4: LinReg (ax+b).  Hit ENTER.  When LinReg appears on the home screen, type the parameters L1, L2, Y1.  The Y1 will put the equation into Y= for you.  

           (Y1 comes from VARS → YVARS, #Function, Y1)

cricket6  

cricket7Older OS form.

cricket newNewer OS form.

cricket8

The linear regression equation is

y = 3.41x + 22.85

(answer to part a)

Step 4.  Graph the Linear Regression Equation from Y1.

    ZOOM #9 ZoomStat to see the graph.

cricket9

(answer to part b)

Step 5.  Is this model a "good fit"?

    The correlation coefficient, r, is .8320424586 which just barely places the correlation into the "strong" category.  (0.8 or greater is a "strong" correlation)

    The coefficient of determination, r 2, is .6922946529 which means that 70% of the total variation in y can be explained by the relationship between x and y.  The other 30% remains unexplained.

    Yes, it is somewhat of a "good fit".

        (answer to part c)

a3

Step 6.  Extrapolate:  (beyond the data set)

     If the ground temperature reached 95º, then at what approximate rate would you expect the crickets to be chirping?

Step 7.  Interpolate: (within the data set)

    With a listening device, you discovered that on a particular morning the crickets were chirping at a rate of 18 chirps per second.  What was the approximate ground temperature that morning?

 The power equation, type 18, hit ENTER, and the answer will appear at the bottom of the screen.

cricket12

(answer to part e --  the ground

the temperature will be approx. 84.23º F)

Step 8.  If the ground temperature should drop to freezing (32º F), what happens to the cricket's chirping?

a4

The TABLE tells us that at 32º F there are 2.68 chirps per second.  So, what does this really mean?  Are the crickets cold?

These findings are a bit deceiving.  At 32º F, the crickets are dead.  The lifespan of cricket in a cold climate is very short.  The crickets spend the winter as eggs laid in the soil.  These eggs hatch in late spring or early summer and tiny immature crickets called nymphs to emerge.  Nymphs develop into adults within approximately 90 days. The adults mate and lay eggs in late summer before succumbing to old age or freezing temperatures in the fall.

Answer:

Step-by-step explanation:

Hi there,

For this problem I would use the law of sines. Start by setting yourself up to find angle C. Your set up should look like:

\(\frac{26}{sin48} = \frac{23}{sinC}\)

C= 41.102 degrees

Now, you can solve for angle B by adding angles A and C together and subtracting by 180.

m<A=48

m<B=90.898

m<C=41.102

To find side "b" I would also use law of sines, although you could do law of cosines if you want. Your setup, if using law of sines, should look like:

\(\frac{b}{sin90.898} = \frac{26}{sin48}\)

b=34.982ft

c=23ft

a=26ft

Hope this helps!

Answer:

move up by 3

Step-by-step explanation:

Graphs are quite tricky. But because they give you what f(x) all you need to do is move everything up by 3

Answer:

10

Step-by-step explanation:

first one you will see the big triangle are 1 after that there are two and three more and then start to look at four small triangles

Answer:

μ ≈ 2.33

σ ≈ 1.25

Step-by-step explanation:

Each person has equal probability of ⅓.

\(\left[\begin{array}{cc}X&P(X)\\1&\frac{1}{3}\\2&\frac{1}{3}\\4&\frac{1}{3}\end{array}\right]\)

The mean is the expected value:

μ = E(X) = ∑ X P(X)

μ = (1) (⅓) + (2) (⅓) + (4) (⅓)

μ = ⁷/₃

The standard deviation is:

σ² = ∑ (X−μ)² P(X)

σ² = (1 − ⁷/₃)² (⅓) + (2 − ⁷/₃)² (⅓) + (4 − ⁷/₃)² (⅓)

σ² = ¹⁴/₉

σ ≈ 1.25

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Answer:

11x-2

Step-by-step explanation:

4x-3+7x+1

then

4x+7x-3+1

goes to

4x+7x-2

Answer: 11x-2

The change in the temperature during these three hours will be -4.2° Celcius.

From the information, the air temperature at 9am is -5.8 degrees Celsius and the air temperature at noon is -1.6 degree.

Therefore, the change in the temperature during these three hours will be:

= -5.8 - (-1.6)

= -5.8 + 1.6

= -4.2° Celcius

Therefore, the change in the temperature during these three hours will be -4.2° Celcius.

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Answer:

Step-by-step explanation: true

Answer:

Example 5 If a force F1 = 100N is applied on the left in the hydraulic lift shown, where A1 = 0.02 m2 and. A2 = 0.08 m2, what force F2 will be.

Step-by-step explanation:

Answer: B C D

Step-by-step explanation:

Answer:

The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.

Step-by-step explanation:

Let's assume the speed of the passenger train is represented by x mph.

According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.

Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.

Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.

Since speed = distance/time, we can set up the following equation based on the distances covered by each train:

Distance covered by passenger train = Distance covered by freight train

Using the formula, distance = speed × time, we get:

x × 3 = (x - 18) × 5

Simplifying the equation:

3x = 5x - 90

90 = 5x - 3x

90 = 2x

Dividing both sides by 2:

45 = x

So, the speed of the passenger train is 45 mph.

The speed of the freight train is 45 - 18 = 27 mph.

Given:

The sequence is: 7,21,63, …

Required:

Find the sum of the first 8 terms of the given sequence. Round to the nearest hundredth if necessary.

Explanation:

The given sequence is:

7,21,63, …

The first term a = 7

Common ratio r=

The given sequence is a geometric series.

The sum of n terms of the geometric series is given by the formula:

The sum of the first 8 terms:

Final Answer:

The sum of the first 8 terms of the given sequence is 22,960.

Answer:

Sara has $144 at the beginning of the month.

Step-by-step explanation:

At the beginning of the month, x = 0 because no days have passed since the beginning of the month. When x = 0, g(0) = -4.5(0) + 144 = 144, therefore, we know that Sara has $144 on her card at the beginning of the month.

The investment with compound interest earns a greater amount of interest by $486.12 compared to the investment with simple interest.

To determine which investment earns a greater amount of interest, we need to calculate the interest earned in both scenarios and compare the results.

1. Simple Interest:

The formula for simple interest is given by: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

Using this formula, we can calculate the interest earned with simple interest:

I = 100,000 * 0.03 * 4

I = $12,000

2. Compound Interest:

The formula for compound interest is given by: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.

In this case, the interest is compounded annually, so n = 1. Let's calculate the amount earned:

A = 100,000 * (1 + 0.03/1)^(1*4)

A = 100,000 * (1.03)^4

A = $112,486.12

The interest earned in the compound interest scenario is A - P = $112,486.12 - $100,000 = $12,486.12.

The difference between the amounts of interest earned by the two investments is:

$12,486.12 - $12,000 = $486.12.

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If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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