A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting​ point?

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

----------------------------------------

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

--------------------

Hope this is helpful.

Solution :

The objective is to obtain the [tex]\text{probability of a positive result}[/tex] for 2 samples combined into a [tex]\text{mixture}[/tex].

Given that the [tex]\text{probability of a single sample testing positive is 0.15}[/tex]

The probability of the positive test result is calculated as follows :

P ( positive mixture ) = P(1 or more samples positive)

                                  = 1 - P (none +ve)

                                  = 1 - P ((-ve) x (-ve))

                                  [tex]$= 1-P(-ve )^2$[/tex]

                                  [tex]$=1-[1-P(+ve)]^2$[/tex]

                                  [tex]$=1-(1-0.15)^2$[/tex]

                                  [tex]$=1-(0.85)^2$[/tex]

                                  = 1 - 0.7225

                                  = 0.2775

No, the probability is not low enough.

Answer:

[tex]( \frac{1}{3})^{3} [/tex]

Step-by-step explanation:

There are many expressions that can be equivalent to 1/27.

For example, 2/54, 3/81 etc

But I think the expression you are looking for is

[tex] \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} [/tex]

Hope this is helpful

Answer:

JAR WITH MARBLES.

There's

5 Blue Marbles

3 Red Marbles

2 Yellow Marbles

Pr = No of desired outcome/No of Possible Outcomes

No of Possible Outcomes = 10.

1. Pr(yellow) = 2/10 = 1/5.

2. Pr(Red) = 3/10

3. Pr(Blue) = 5/10 = 1/2

4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.

5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.

6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.

THE CHIPS ARE PLACED IN A JAR AND MIXED.

No of Possible Outcomes = 8.

The Numbers are 1,2,3,4,5,6,7,8.

There's

4 Even Numbers

4 Odd Numbers

1. Pr(Even) = 4/8 = 1/2

2. Pr(Odd) = 4/8 = 1/2

3. Pr(Chip with Biggest No) = 1/8.

Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.

4.Pr(Smallest Number) = 1/8 (Same concept).

5.Pr(Prime Number)

The prime Numbers above are 2,3,5,7

Pr(Prime) = 4/8 = 1/2.

Hope this helps!.

Answer:

[tex]\frac{23x-37}{x-4}[/tex]

Step-by-step explanation:

Let A be college A and let B be College B

A= 14,100

Rule: 1 Year = +1,000 students

B= 34,350

Rule: -1250 per year

1st Answer: 2017

Notice: I didn't show the formula because I'm not %100 sure I'm kind of off so if this is incorrect I'm deeply sorry. I truly am. On the bright side, I think its correct.

Answer:

0.5015 = 50.15% probability that it came from manufacturer A.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: From manufacturer A.

Probability a unit is defective:

2% of 43%(from manufacturer A)

1.5% of 57%(from manufacturer B). So

[tex]P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715[/tex]

Probability a unit is defective and from manufacturer A:

2% of 43%. So

[tex]P(A \cap B) = 0.02*0.43 = 0.0086[/tex]

What is the probability that it came from manufacturer A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015[/tex]

0.5015 = 50.15% probability that it came from manufacturer A.

Answer:

[tex]P(Negative | Yes) = 0.0486[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Yes} & {No} & {Positive} & {137} & {24} & {Negative} & {7} & {132} \ \end{array}[/tex]

Required

[tex]P(Negative | Yes)[/tex]

This is calculated as:

[tex]P(Negative | Yes) = \frac{n(Negative\ n\ Yes)}{n(Yes)}[/tex]

So, we have:

[tex]P(Negative | Yes) = \frac{7}{137+7}[/tex]

[tex]P(Negative | Yes) = \frac{7}{144}[/tex]

[tex]P(Negative | Yes) = 0.0486[/tex]

Answer:

decrease

Step-by-step explanation:

Answer:

=6

Step-by-step explanation:

(5×8)×(5-2)/(5×4)

Numerator =40×3

=120

Denominator = 5×4

=20

simplifying 120/20

=6

Answer:

6

follow the BDMAS rule

bracket ,division ,multiplication, addition and last subtraction

you won't get any maths problem wrong

Answer:

1.504

Step-by-step explanation:

0.47×100 = 47

3.2×100 = 320

47×320 = 15040

15040÷10000 = 1.504

Answer:

32°

Step-by-step explanation:

in 32° is right answer

In isosceles triangle, △HAM, m∠H is 74 degree.

A triangle in which any two sides are equal in length and angles opposite to equal side are also equal. And sum of all angles in a triangle is 180.

Given, m∠A = 32°

sum of all angles = 180°

In △HAM

∠H = ∠M

∠H+ ∠A+ ∠M = 180°

2∠H = 180 - 32

2∠H = 148

∠H = 74°

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Answer:

c. Random

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Systematic sampling.

2. Convenience sampling.

3. Stratified sampling.

4. Cluster sampling.

5. Random sampling.

Random sampling can be defined as a type of sampling in which the researcher select a sample of the population in order to determine an outcome.

Thus, the type of sampling used is random sampling.

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

[tex] W(-1, 1) = (x_1, y_1) [/tex]

[tex] X(1, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]

[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]

[tex] WX = \sqrt{4 + 1} [/tex]

[tex] WX = \sqrt{5} [/tex]

[tex] WX = 2.24 [/tex]

✔️Distance between X(1, 2) and Y(2, -4)

Let,

[tex] X(1, 2) = (x_1, y_1) [/tex]

[tex] Y(2, -4) = (x_2, y_2) [/tex]

Plug in the values

[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]

[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]

[tex] XY = \sqrt{1 + 36} [/tex]

[tex] XY = \sqrt{37} [/tex]

[tex] XY = 6.08 [/tex]

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

[tex] Y(2, -4) = (x_1, y_1) [/tex]

[tex] Z(-2, -1) = (x_2, y_2) [/tex]

Plug in the values

[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]

[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]

[tex] YZ = \sqrt{16 + 9} [/tex]

[tex] YZ = \sqrt{25} [/tex]

[tex] YZ = 5 [/tex]

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

[tex] Z(-2, -1) = (x_1, y_1) [/tex]

[tex] W(-1, 1) = (x_2, y_2) [/tex]

Plug in the values

[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]

[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]

[tex] ZW = \sqrt{1 + 4} [/tex]

[tex] ZW = \sqrt{5} [/tex]

[tex] ZW = 2.24 [/tex]

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

Answer:

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.

This means that [tex]p = 0.0746[/tex]

Random sample of 318 independent returns

This means that [tex]n = 318[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]

What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]

[tex]Z = -0.26[/tex]

[tex]Z = -0.26[/tex] has a p-value of 0.3974.

1 - 0.3974 = 0.6026

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Answer:

[tex]41\text{ [units squared]}[/tex]

Step-by-step explanation:

The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.

The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:

Formulas:

Area of triangles:

All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.

Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]

The area of all four is then [tex]2\cdot 4=8[/tex] units squared.

Area of rectangles:

The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.

The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.

Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]

Answer:

Time of flight of first rocket = 60 seconds

Time of flight of second rocket = 40 seconds

Step-by-step explanation:

Let the time of flight of first rocket be t1.

Since the second rocket is launched 20 seconds later, then it means that;

t1 = t2 + 20

Where t2 is the time of flight of the second rocket.

When destruction has occurred, it means that both of the rockets would have covered the same distance.

We know that;

Distance = speed × time

Thus;

2000t1 = 3000t2

We know that t1 = t2 + 20

Thus;

2000(t2 + 20) = 3000t2

2000t2 + 40000 = 3000t2

3000t2 - 2000t2 = 40000

1000t2 = 40000

t2 = 40000/1000

t2 = 40 seconds

Thus;

t1 = 40 + 20

t1 = 60 seconds

Answer:

The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.

In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.

When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.

9514 1404 393

Answer:

Step-by-step explanation:

1. The various goals can be met without filling the theater. This fact means there is a range of possibilities for each of the answers. However, we take the wording, "because of the demand for tickets ..." to mean demand is high and the theater will be sold out.

Since two children's tickets will be sold for each adult ticket sold, the number of children's tickets is 2/3 of the total.

  children's tickets = 2/3 × 120 = 80

__

2. The remaining 40 tickets will be adult tickets.

  40 adult tickets will be sold.

__

3. The total revenue must be at least $1800. If we allow 'd' tickets to be sold at a discount, then we can find the limits on d using the inequality ...

  24(40-d) +24(0.75)d +12(80) ≥ 1800 . . . . revenue from ticket sales

  -6d ≥ -120 . . . . . . . . . . . . . . . . . . . collect terms, subtract 1920

  d ≤ 20 . . . . . . . . . . divide by -6

  At least 10 and at most 20 adult tickets can be sold with a discount.

("At least 10" comes from the problem requirements.)

Answer:

One lamp is equal to 23 dollars

One table is equal to 42 dollars.

Step-by-step explanation:

We can solve this by first organizing what we have.

1 table (t) + 2 lamps (l) = 88.

2 tables (t) + 3 lamps (l) = 153.

_____________

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

1t + 2l = 88

2t + 3l = 153

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

-------------------------

If we multiply both sides by 2 on the first equation of

1t + 2l = 88

we could get

2t + 4l = 176.

If that is true, we can subtract the second equation of

2t + 3l = 153 from the new equation to get the price of a lamp.

    2t + 4l = 176

-    2t + 3l = 153

____________

= 0t + l = 23

One lamp is equal to 23.

We can check this by plugging it into an equation.

1 + 2(23) = 88

1t + 46 = 88

1t + 46 - 46 = 88 - 46

1t = 42

If one table equals 42, we can put this back into the second equation to check.

2 (42) + 3 (23) = 153

84 + 69 = 153

That is correct.

Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.

Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.

Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.

Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.

    2t + 3l = 153

 -  1t + 2l = 88

____________

= t + l = 65

If t + l = 65, we can rearrange that equation to be something like t = 65 - l.

That means "t" is equal to 65 bucks minus a lamp.

We put this back into the first equation of

1t + 2l = 88

and replace "t" with the previous expression.

1(65 - l) + 2l = 88

Simplify/distributive property

65 - l + 2l = 88

65 - 65 - l + 2l = 88 - 65

-l + 2l = 23

l = 23

One lamp is equal to 23 bucks.

Confirmed :)

A lamp cost $23

Let the cost of a table be represented by x

Let the cost of a lamp be represented by y.

Since one table and two lamps cost $88, this can be represented as:

x + 2y = 88 ........ equation i

Since two tables and three lamps cost $153, this can be represented as:

2x + 3y = 153 ........ equation ii

Therefore, the equations are:

x + 2y = 88 ....... i

2x + 3y = 153 ....... ii

From equation i,

x + 2y = 88

x = 88 - 2y ...... iii

Put the value of x into equation ii

2x + 3y = 153

2(88 - 2y) + 3y = 153

176 - 4y + 3y = 153

Collect like terms

-4y + 3y = 153 - 176

-y = -23

y = 23

Therefore, a lamp cost $23

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Answer:

Cuboid = width*height*length

Cuboid = 24 cm^2

9514 404 393

Answer:

  5.64

Step-by-step explanation:

The increase in price for the given items will be ...

  5% × (22.80 + 89.98) ≈ 5.64

The artist will save 5.64 by making a purchase before the price increase.

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer: A simple random sample

Step-by-step explanation:

Simple random sampling refers to the probability sampling whereby the researcher chooses selects a subset of participants from the population.

In this case, every member has an equal chance of being chosen. Since anyone could mail in a response or use the paper's Web site to respond, then it's a simple random sampling.

Answer:

Sum= 5000005

Difference= 4999995

Step-by-step explanation:

The place value of 5 in the number 35086941 is 5000000

The face value is 5

The sum between the face value and place value can be calculated as follows

°= 5000000+5

= 5000005

The difference can be calculated as follows

= 5000000-5

= 4999995

Step-by-step explanation:

there is the answer. good luck

Answer:

B)      [tex]\sqrt{\frac{v}{15\pi } } = 10[/tex]

Step-by-step explanation:

Answer:

(1/x + 1/y)k is the answer :)

Answer:

According to me its 90 degree

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

There 2 ways to interpret this problem.

From the info given:

These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.

If the triangles are similar, the side lengths form a proportion of that

[tex] \frac{3}{3} = \frac{3}{3} [/tex]

So the ratio or scale factor is 1.

The scale factor in the figure is 1.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given that two triangles, LMN and OPQ, we need to find the scale factor,

We can see triangles are congruent, and we know that

Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,

Hence, the scale factor in the figure is 1.

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