a movie sells tickets for for the cost of 4$ and 6$.there is a total of 75 tickets for a total of 400$,how many tickets were sold

Answer:

33

Step-by-step explanation:

I hope this helps!

Answer:

33 pillowcases

Step-by-step explanation:

16.5 yard of fabric/ 1.5 yards of fabric = 11 yards of fabric

Multiply 11 (yards of fabric) by 3 (# of pillowcases) to get the number of pillowcases you can make with 16.5 yards of fabric.

11 * 3 = 3 pillowcases

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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the indefinite integral of (16x+3)ln(2x) is ln(2x) * (8x² + 3x) - 4x² - 3 ln |2x| + C.

To integrate ∫(16x+3)ln(2x)dx, we can use integration by parts, where we choose u = ln(2x) and dv = (16x + 3) dx:

u = ln(2x) => du/dx = 1/x

dv = (16x + 3) dx => v = 8x² + 3x

Using the integration by parts formula, we get:

∫(16x+3)ln(2x)dx = uv - ∫vdu

= ln(2x) ×(8x² + 3x) - ∫(8x² + 3x) ×(1/x) dx

= ln(2x) ×(8x² + 3x) - 8∫x dx - 3∫(1/x) dx

= ln(2x) × (8x² + 3x) - 4x² - 3 ln |2x| + C

where C is the constant of integration.

Therefore, the indefinite integral of (16x+3)ln(2x) is ln(2x) ×(8x² + 3x) - 4x² - 3 ln |2x| + C.

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Answer:

zero, because the discriminant is negative

Step-by-step explanation:

By writing the quadratic formula, we have the discriminant written in the root as;

b^2-4ac

Now, given the expression, we can see that the discriminant here is -19

What this mean is that we have a negative discriminant

Hence, we can conclude that the roots are complex and as such, none of the roots are real

Answer

To multiply integers, simply multiply the unsigned numbers and place the sign on the product by repeating the above rules.

To divide unsigned integers, we divide the unsigned numeric values and put a minus sign on the result.

Answer:

X= 2 sqrt of 7

Y=2 sqrt of 7

Step-by-step explanation:

I just know the answer srry

Answer:4.5 hours, 4 hours and 30 minutes, 4 and a half hours

Step-by-step explanation: you are averaging, so you add all of the numbers together and divide that by the number of numbers.

3+6=9, 9 divided by 2=4.5

Answer:

2hours

Step-by-step explanation:

let windows = x

Mrs. Saunders can clean one-third of the windows in an hour = x/3

daughter can clean one-sixth of the windows in an hour = x/6

so,

x/3+x/6 = 1

thus, x = 2

mother and daughter together can clean the windows in 2 hours

Answer: (0,0),(0,4), and (5,0)

Step-by-step explanation:

It is easy to find lengths of horizontal and vertical segments and distances from (0,0) so always place one vertex at the origin and one or more sides on an axis.

This answer has an x intercept and y intercept.

Answer:

,L

Step-by-step explanation:

Answer:

250 hamburgers were sold on Sunday

When α is decreased from .05 to .01, the probability of making a Type II error decreases.

a. The critical values for each of the two situations are as follows:

Situation 1: Since the test is two-tailed, the critical value is given by:

Critical value = ± zα/2

where α = 0.05/2

              = 0.025 (since it is a two-tailed test)

Therefore, from the standard normal table, zα/2 = 1.96

Critical value = ± 1.96

Situation 2: Since the test is two-tailed, the critical value is given by:

Critical value = ± zα/2

where α = 0.01/2

              = 0.005 (since it is a two-tailed test)

Therefore, from the standard normal table, zα/2 = 2.58

Critical value = ± 2.58b.

In Situation 2, there is less chance of making a Type I error. The reason is that for a given level of significance (α), the critical value is higher (further from the mean) in situation 2 than in situation 1. Since the rejection region is defined by the critical values, it means that the probability of rejecting the null hypothesis (making a Type I error) is lower in situation 2 than in situation 1.c. By changing from .05 to .01, the probability of making a Type II error decreases.

This is because, as the level of significance (α) decreases, the probability of making a Type I error decreases, but the probability of making a Type II error increases.

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The volume of air at the surface is 6.9 times larger than the volume of air at the bottom. Therefore, the depth (h) of the pool can be calculated using the following formula:Volume at surface / Volume at bottom = 6.9.

Therefore, h = (V/V_0) - 1, where V is the volume of the air bubble at the surface and V_0 is the volume of the air bubble at the bottom.

Using the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the temperature is constant, we can write:

P_0V_0 = P_fVwhere P_0 is the pressure at the bottom, P_f is the pressure at the surface, and V is the volume at the surface. Since the pressure at the surface is atmospheric pressure, we have:P_f = P_atm = 1 atm.

Therefore, we can rewrite the formula for h as:h = (P_fV/P_0V_0) - 1 = (V/P_0V_0) - 1Using the ideal gas law again, we can write:P_0V_0 = nRT_0, where T_0 is the temperature at the bottom.

Therefore, we have:V_0 = (nRT_0)/P_0Substituting this into the formula for h, we get:

h = (V/P_0(nRT_0)/P_0) - 1 = V/(nRT_0) - 1Since the number of moles and the temperature are constant, we can simplify this to:h = V/(RT_0) - 1.

Therefore, the depth of the pool at a point where an air bubble, upon reaching the surface, has 6.9 times the volume than it had at the bottom is:h = V/(RT_0) - 1A

Given: The volume of the air bubble at the surface is 6.9 times larger than the volume of the air bubble at the bottom. Air bubbles are a common sight in swimming pools, but do you ever wonder how deep the pool is at a point where the bubble has reached the surface?

To determine the depth, we need to assume that the condition is isothermal, which means that the temperature of the water is constant. We can also assume that the pressure at the bottom of the pool is equal to the pressure of the air bubble at the bottom.

To calculate the depth, we need to use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the temperature is constant, we can write:

P_0V_0 = P_fVwhere P_0 is the pressure at the bottom,

P_f is the pressure at the surface, and V is the volume at the surface.

Since the pressure at the surface is atmospheric pressure, we have:

P_f = P_atm = 1 atm.

Therefore, we can rewrite the formula for h as:h = (P_fV/P_0V_0) - 1 = (V/P_0V_0) - 1.

Using the ideal gas law again, we can write:P_0V_0 = nRT_0, where T_0 is the temperature at the bottom.

Therefore, we have:V_0 = (nRT_0)/P_0.

Substituting this into the formula for h, we get:

h = (V/P_0(nRT_0)/P_0) - 1 = V/(nRT_0) - 1.

Since the number of moles and the temperature are constant, we can simplify this to:

h = V/(RT_0) - 1.

Therefore, the depth of the pool at a point where an air bubble, upon reaching the surface, has 6.9 times the volume than it had at the bottom is:h = V/(RT_0) - 1.

The depth of the pool at a point where an air bubble, upon reaching the surface, has 6.9 times the volume than it had at the bottom can be calculated using the formula h = V/(RT_0) - 1, where V is the volume of the air bubble at the surface, R is the gas constant, and T_0 is the temperature at the bottom.

This formula assumes that the condition is isothermal and that the pressure at the bottom of the pool is equal to the pressure of the air bubble at the bottom.

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Answer:

Exact Form:

1/6

Decimal Form:

0.16 (6 repeating)

Step-by-step explanation:

Answer:

14.75 in.²

Step-by-step explanation:

A = 1.5² + ½(2.5 + 1.5)(2) + 4(2) + ½(1)(1)

14.75 in.²

Answer:

Triangle=1/2BH, 1/2(1)(1)=.5

Parallelogram=BH, (4)(2)=8

Trapezoid=((B1+B2)/2)*H, ((1.5+2.5)/2)*2-->(4/2)*2=4

Square=BH, (1.5)(1.5)=2.25

.5+8+4+2.25=14.75

Step-by-step explanation:

=======================================================

Explanation:

Define the following three events:

Notation like P(A) = 12/20 means the probability of event A (aka picking the plain biscuit) is 12/20 since there are 12 plain biscuits out of 20 total. I'll leave the fraction un-reduced so we can see where the 12 and 20 come from. Going from 12/20 to 3/5 has us lose vital information about the original values.

Notation like AB means a plain biscuit was selected first and then a chocolate biscuit is selected second in that exact order. I'm assuming the first selection is not replaced. This makes the probability of the second selection dependent on the first.

So,

P(AB) = P(A)*P(B given A) = (12/20)*(5/19) = 3/19

P(AC) = P(A)*P(C given A) = (12/20)*(3/19) = 9/95

P(BC) = P(B)*P(C given B) = (5/20)*(3/19) = 3/76

The last step is to add those results to get the probability of event AB, event BC or event AC of occurring. Addition is possible since the events are mutually exclusive.

P(AB)+P(AC)+P(BC) = 3/19 + 9/95 + 3/76 = 111/380

I've skipped a few steps, so let me know if you need to see the finer details. Also feel free to ask about any questions in general if they come up.

The answer to the different parts is 32/81, (x+4) ^4/81 - 1,0.5299, -0.41 and 32.

(a) For this function to be a probability density function, it must satisfy the following conditions:

It must be non-negative for all values of x.

The area under the curve must be equal to 1 over the entire range of x.

Thus, we have:

∫f(x)dx = ∫c(x+4)^3dx = 1

Applying integration by substitution, let u = x+4, so that du/dx = 1 and dx = du. Then:

∫c(x+4)^3dx = c∫u^3du = c(u^4/4) = c(x+4)^4/4

Setting this equal to 1 and solving for c, we get

c(x+4)^4/4 ∣∣ 0 to infinity = 1

Substituting infinity, we get:

c(infinity) = 0, so we must use a limit to evaluate the integral at infinity. Let L be a large number, then:

c∫0 to L (x+4)^3dx = c[(L+4)^4/4 - 4^4/4] → cL^4 as L approaches infinity.

Thus, we have:

cL^4 = 4/[(L+4)^4 - 4^4]

Taking the limit as L approaches infinity, we get:

c = 32/81.

Therefore, c = 32/81 makes this a legitimate probability density function.

(b) The cumulative distribution function (c.d.f.) of X is given by:

F(x) = ∫f(t)dt from 0 to x

   = ∫32/81(t+4)^3dt from 0 to x

   = 32/81 [(x+4)^4/4 - 4^4/4]

   = (x+4)^4/81 - 1

(c) To find the probability that the time to failure is between 2 and 5 years, we evaluate the c.d.f. at x = 5 and x = 2, and take the difference:

P(2 ≤ X ≤ 5) = F(5) - F(2)

            = [(5+4)^4/81 - 1] - [(2+4)^4/81 - 1]

            = 4101/6561 - 625/6561

            = 3476/6561

            ≈ 0.5299

(d) To find the 60th percentile of the failure time, we need to find the value x such that F(x) = 0.6. Solving for x in the equation F(x) = (x+4)^4/81 - 1 = 0.6, we get:

(x+4)^4/81 = 1.6

Taking the fourth root of both sides, we get:

x+4 = 3.59

x = -0.41

Since the time to failure cannot be negative, we must interpret the 60th percentile as being 3.59 - 4 = -0.41 years from now, i.e., it has already failed with 60% probability.

(e) The expected value of X is given by:

E[X] = ∫xf(x)dx from 0 to infinity

   = ∫32/81(x+4)^4dx from 0 to infinity

   = 32

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The average daily snowfall estimate for Wyoming's greatest 7-day snowfall is significantly different from the average daily snowfall estimate for South Dakota's greatest 7-day snowfall.

Wyoming and South Dakota are both known for their cold winters and heavy snowfall. However, the average daily snowfall estimate for Wyoming's greatest 7-day snowfall is likely to differ from that of South Dakota. Several factors contribute to this difference.

Firstly, Wyoming is home to the Rocky Mountains, which are known for their high elevation and heavy snowfall. This region experiences more frequent and intense winter storms, leading to higher snowfall amounts. South Dakota, on the other hand, has a relatively flatter terrain compared to Wyoming, resulting in less snow accumulation.

Secondly, geographical location plays a role. Wyoming is located further west and is influenced by Pacific weather systems, which can bring moisture-laden storms and heavy snowfall. South Dakota, being more inland and farther away from major moisture sources, may receive less precipitation overall.

Lastly, climate patterns can vary between the two states. Factors such as proximity to large bodies of water, prevailing wind patterns, and local topography can influence snowfall amounts. These variations can lead to differences in the average daily snowfall estimate for the greatest 7-day snowfall in Wyoming compared to South Dakota.

In conclusion, while both Wyoming and South Dakota experience significant snowfall, the average daily snowfall estimate for Wyoming's greatest 7-day snowfall is expected to be different from that of South Dakota. Factors such as elevation, geographical location, and climate patterns contribute to these differences in snowfall amounts between the two states.

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The radius of the given circle is 7.5 units.

So, use the Pythagorean theorem:

Now, calculate as follows:

So, the diameter is 15 units.

Then the radius is:

Therefore, the radius of the given circle is 7.5 units.

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Answer:

-2

Step-by-step explanation:

2x-1=x-3

2x=x-2

x=-2

The probability that an automobile owner purchases neither collision nor disability coverage is 0

To find the probability that an automobile owner purchases neither collision nor disability coverage, we need to determine the probability of the complement event, which is the event that the owner purchases either collision or disability coverage.

Let's denote the event of purchasing collision coverage as C and the event of purchasing disability coverage as D.

From the given information, we can conclude:

(i) P(C) = 2 * P(D)

(ii) P(C ∩ D) = 0.15

(iii) P(C) and P(D) are independent events.

Since P(C) = 2 * P(D), we can denote P(D) as x, and then P(C) becomes 2x.

Using the fact that the probability of the union of two events is given by the sum of their individual probabilities minus the probability of their intersection, we can write:

P(C ∪ D) = P(C) + P(D) - P(C ∩ D)

Since C and D are independent events, P(C ∩ D) = P(C) * P(D).

Substituting the given information:

P(C ∪ D) = 2x + x - 0.15 = 3x - 0.15

The probability of the complement event (neither collision nor disability coverage) is given by:

P(~(C ∪ D)) = 1 - P(C ∪ D)

Since an automobile owner must have either collision or disability coverage (or both), the probability of purchasing neither coverage is the complement of having either coverage:

P(~(C ∪ D)) = 1 - (3x - 0.15)

Now, we need to find the value of x to calculate the probability.

To determine the value of x, we can use the fact that the sum of probabilities in a sample space is equal to 1.

P(C) + P(D) - P(C ∩ D) = 1

2x + x - 0.15 = 1

3x - 0.15 = 1

3x = 1 + 0.15

3x = 1.15

x = 1.15 / 3

x ≈ 0.3833

Now we can calculate the probability of the complement event:

P(~(C ∪ D)) = 1 - (3x - 0.15)

P(~(C ∪ D)) = 1 - (3 * 0.3833 - 0.15)

P(~(C ∪ D)) = 1 - (1.15 - 0.15)

P(~(C ∪ D)) = 1 - 1

P(~(C ∪ D)) = 0

Therefore, the probability that an automobile owner purchases neither collision nor disability coverage is 0.

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\( \sf3m + 12 = 15 \\ \sf3m = 15 - 12 \\ \sf3m = 3 \\ \sf \: m = \frac{3}{3} \\ \sf \: m \: = \underline{ \bf \: 1}\)

-> Just move all the numbers from the left side to the right side until only the variable is left. Then you can solve the equation & find the required value.

3 m+ 12 = 15

⇔3 m=  3

⇔m=  1

Answer:

-30c

Step-by-step explanation:

now:-25

noon - 10pm +10 (got 10c hotter)

-25c-10=-35c(opposite of rise)

midnight - noon: -5c

so do the opposite which is +5

-35+5=-30c

Answer: (4, 2)

Step-by-step explanation:

Centroid of the triangle  =  (x1 +x2 + x3)/3, (y1+y2+y3)/3

 =  (8+1+3)/3, (4+3-1)/3

 =  12/3, 6/3

 =  (4, 2)

Answer:

A is correct.

Step-by-step explanation:

Plug the 12 books he bought into the equation. Then, multiply 2.25 and 12, and that's your answer. Hope this helps. Please mark Brainliest! :)

Answer:

625

Step-by-step explanation:

250/6 =41.6666666667

41.6666666667x15 = 625

The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

Given that,

An octahedron is made by connecting the centers of the faces of the right rectangular prism in the illustration below.

We have to find what is the octahedron's volume.

The Greek term "Octahedron," which means "8 faces," is the source of the English word "octahedron." Eight faces, twelve edges, six vertices, and four edges that intersect at each vertex make up an octahedron, a polyhedron. It is one of the five platonic solids with equilateral triangle-shaped faces.

Since two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid. We can compute the volume of one pyramid, then multiply it by two to obtain the volume of an octahedron.

The pyramid's volume is equal to (Base area ×Height)/3.

Since the pyramid's base is square, its base area is equal to a².

Therefore, The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Given Information:

Principle amount = P = $9,129

Interest rate = r = 4% = 0.05

Period in years = t = 5

Required Information:

Balance in 5 years = ?

Answer:

Balance in 5 years = $11,651.17

Step-by-step explanation:

Using the formula given in the question,

\(B = P(1 + r )^{t}\)

Where B is the final amount, P is the initial amount, r is the interest rate and t is the number of years

\(B = P(1 + r )^{t}\\\\B = 9,129(1 + 0.05)^{5}\\\\B = 11,651.17\)

Therefore, Zack will have $11,651.17 in 5 years by investing $9,129 in a savings account at 5% annual interest.