The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between zero and six minutes find the probability that a randomly selected passenger has a waiting time less than 0. 75 minutes

Answer:

68.54

Step-by-step explanation:

In conclusion, ∠RPQ is 21.0°, and the perpendicular distance from R to PQ is approximately 47.36 feet.

To find ∠RPQ, we can use the concept of complementary angles. Since the angle of elevation to the top of the tower is 69°, the angle between the ground and the line RP is its complement, which is 90° - 69° = 21°.

Now, let's calculate the perpendicular distance from R to PQ. We can use trigonometry and create a right triangle with R as the right angle vertex. Let's call the perpendicular distance x.

In the triangle RPQ, we have the opposite side (RP) and the adjacent side (RQ) to the angle ∠RPQ. We know that tan(∠RPQ) = opposite/adjacent.

tan(21°) = x/125

x = 125 * tan(21°)

x ≈ 47.36 feet

Therefore, the perpendicular distance from R to PQ is approximately 47.36 feet.

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Answer:

x = √143

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify

We are given a right triangle

Step 2: Define variables

Leg a = 1

Leg b = x

Hypotenuse c = 12

Step 3: Solve for x

If the seventh number is 21 and the ninth number is 55; Provided the group of numbers constitute n arithmetic progression; the tenth number is; 72

According to the question:

If assumed that the group of numbers constitute an arithmetic progression;

Hence, there are 2. terms between the seventh and ninth term;

Therefore, 2d = 55-21

On this note, the tenth term is just one term away from the ninth term;

Ultimately, the tenth term is; 55 + 17 = 72

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Answer:

a; d = 20n

Step-by-step explanation:

you can use the process of elimination and an example problem to help!

so if mason mowed 2 lawns, he'd make $40, right? now you could try each equation to see which one equals $40

a. d = 20(2) ⇒ d = 40

b. n = 20d ⇒ 2 = 20d ⇒ d = 0.1

c. d = 20 ÷ n ⇒ d = 10

d. n = 20 + d ⇒ 2 = 20 + d ⇒ d = -18

therefore, your answer would be A!

The two given triangles are congruent because of SAS.

In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other.  Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.

The given triangles are RTP and STP

P is the midpoint of RS and TP is the altitude of triangle RTS.

In the triangles RTP and STP

TP = TP (common)

∠RPT = ∠ SPT (90°)

RP = SP (median divides the side equally)

So, both triangles are congruent using SAS property.

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To estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples, with 95% confidence and a margin of error of 1.5%.

We need to use the following formula to calculate the required sample size:n = (Z^2 * p * (1-p)) / E^2
Where:
- Z is the standard normal value corresponding to the desired level of confidence, which is 1.96 for 95% confidence.
- p is the estimated population proportion, which we don't know yet.
- E is the desired margin of error, which is 0.015 (1.5%).

Let's assume that p is 0.6, which means that we expect 60% of U.S. adults to support recognizing civil unions between gay or lesbian couples.

Plugging in the values:

n = (1.96^2 * 0.5 * (1-0.5)) / 0.015^2
n = (3.8416 * 0.5 * 0.5) / 0.000225
n = 1.9208 / 0.000225
n = 8531.55556


Rounding up to the nearest integer, we need a sample size of 4,445 to be 95% confident that the obtained sample proportion will be within 1.5% of the population proportion. Therefore, the correct answer is 4,445.

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Parabola A and parabola B are similar in that they are both vertically oriented parabolas with the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix, which means they have different equations and open in different directions.

Both parabola A and parabola B are examples of vertically oriented parabolas that have the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix.

Parabola A has its vertex at (0, 0) and its focus at (0, 4). The directrix is the line y = -4, which is a horizontal line 4 units below the vertex. This means that any point on parabola A is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.

Parabola B has its vertex at (0, 0) and its focus at (0, -6). The directrix is the line y = 6, which is a horizontal line 6 units above the vertex. This means that any point on parabola B is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.

In terms of their equations, the equation of parabola A is y^2 = 16x, while the equation of parabola B is y^2 = -24x. Notice that parabola B has a negative coefficient of x, which means it opens to the left instead of the right like parabola A.

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Answer:

Step-by-step explanation:

Oh then you just multiply it

Answer:

The y-intercept is -1

The slope is -4 so you will go down 4 and over 1 to the right.

The line is negative

So it will be pointing Northwest and Southeast \ that way.

Step-by-step explanation:

Did you understand this??

Answer:

16 units²

Step-by-step explanation:

Volume:

v = s³

64 = s³

Take the cube root of both sides

4 = s

Area:

a = s²

a = 4²

a = 16 units²

Answer:

(0, -3) and (3, -5)

Step-by-step explanation:

To graph the line of the equation f(x) = -2/3x - 3, we can choose any two points on the line. One way to do this is to find the y-intercept and another point using the slope of the line.

1. To find the y-intercept, let x = 0 and solve for y:

f(0) = -2/3(0) - 3 = -3

So the y-intercept is (0, -3).

2. To find another point, we can use the slope of the line, which is -2/3. We can start from the y-intercept (0, -3) and move down 2 units (since the slope is negative) and to the right 3 units (since the denominator of the slope is 3) to get another point on the line:

(3, -5)

So the two points we can use to graph the line are (0, -3) and (3, -5).

The domain of the function y = 2 - √(-3x+2) is (-∞ , 2/3] and the range of the function is (-∞ , 2]  .

In the question ,

it is given that , the function is ⇒ y = 2- √(-3x+2) .

For Domain ,

we know that the square root function is defined only when the number inside the root is non negative .

that means ,

-3x \(+\) 2 ≥ 0

Subtracting 2 from both the sides ,

we get ,

-3x ≥ -2

x ≤ 2/3

the Domain is (-∞ , 2/3] .

For range , we know that the root function value in always non negative .

√(-3x + 2) ≥ 0

Multiply by -1 on both sides

we get ,

-√(-3x + 2) ≤ 0

Adding 2 to both the sides

2 - √(-3x + 2) ≤ 2

y ≤ 2

the range is (-∞ , 2] .

Therefore , the domain is (-∞ , 2/3]   and the range is (-∞ , 2] .

How do we find the domain and range of the function y = 2- √(-3x+2) ?

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The number of students should be invited to a party to make sure that ap least two of them have the same initials are equals to the 677 (students).

The solution of this problem is obtained by using the pigeonhole principle, which states if there are N boxes and N+1 pigeons, at least two pigeons must be in the same box. We have to determine the number of students invited in party to make make sure that at least two of them have the same initials. Now, first we figure out what N is to solve the problem. Here, box for this problem is labelled by first and last initials. If we are using the A-Z alphabet, then there are 26×26 = 676 possible sets of initials.

As soon as there are N+ 1 or 677 people, at least two must have the same first and last initials. Hence, required value is 677.

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Answer: x=6

Step-by-step explanation:

Step 1: Remove parentheses.

4(2x-5)-6=6+9+2x-54(2x−5)−6=6+9+2x−5

Step 2: Simplify  6+9+2x-56+9+2x−5  to  2x+102x+10.

4(2x-5)-6=2x+104(2x−5)−6=2x+10

Step 3: Expand.

8x-20-6=2x+108x−20−6=2x+10

Step 4: Simplify  8x-20-68x−20−6  to  8x-268x−26.

8x-26=2x+108x−26=2x+10

Step 5: Add 26 to both sides.

8x=2x+10+268x=2x+10+26

Step 6: Simplify  2x+10+262x+10+26  to  2x+362x+36.

8x=2x+368x=2x+36

Step 7: Subtract 2x2x from both sides.

8x-2x=368x−2x=36

Step 8: Simplify  8x-2x8x−2x  to  6x.

6x=36

Step 9: Divide both sides by 6.

x= 36/6 as a fraction

Step 10: Simplify  \frac{36}{6} to 6.

x= 6x

\( \bold{4(2x - 5) -6 = 6+9) + (2x - 5)}\)

\( \bold{4(2x−5)−6=6+9+2x−5}\)

\( \bold{4(2x−5)−6=2x+10}\)

\( \bold{8x−20−6=2x+10}\)

\( \bold{8x=2x+10+26}\)

\( \bold{8x=2x+36}\)

\( \bold{8x−2x=36}\)

\( \bold{6x=36}\)

\( \bold{x = \cfrac{36}{6}} \)

\( \bold{x = 6}\)

Note: The Parentheses must be eliminated to then use the law of signs, then we must expand the numbers, then simplify (that is, subtract) Now in the next step is to Add 26 on both sides then we must subtract and then add until we get the result of 6, so that ultimately we can take out a fraction and give us the correct answer, which is \(\bold{x=6}\)

Answer:

21

Step-by-step explanation:

when x=3

4x + 9

substitute x with 3

4(3) + 9

12 + 9

= 21

Answer:

B.

3x less than 12.

12/3= 4. so x is any number less than 4.

The probability of x being equal o 19.62 is d) 0.

It is given that x is normally distributed with a mean of 12 and a standard deviation of 3.

Now, Normal distribution is a continuous distribution.

This implies that the probability is measured over an interval, taking an infinite number of points in between.

If we plot a continuous distribution, the probability here at a point is not the value of the y coordinate at that point. Instead, it is seen as an area under the curve of the distribution, between the two intervals, say a and b.

Therefore, if we take up a single point say c, then the probability will be the area under the curve from c to c, which will obviously be 0.

Hence, the probability that x = 19.62 will be 0.

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Answer:

bx-3=2x+a

comparing the coefficient of x^1

b=2

comparing the coefficient of x^0

a= -3

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

By squaring the sum of two variables identity ~

\(\qquad \sf  \dashrightarrow \:(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab\)

Now, plug in the given values ~

\(\qquad \sf  \dashrightarrow \:( - 6) {}^{2} = 20 + 2ab\)

\(\qquad \sf  \dashrightarrow \:36 = 2(10 + ab)\)

\(\qquad \sf  \dashrightarrow \:10 + ab = 36 \div 2\)

\(\qquad \sf  \dashrightarrow \:10 + ab = 18\)

\(\qquad \sf  \dashrightarrow \:ab = 18 - 10\)

\(\qquad \sf  \dashrightarrow \:ab = 8\)

I hope it was clear through my steps ~

Answer:

8

Step-by-step explanation:

(a+b)^2 = (-6)^2

a^2 + 2ab + b^2 = 36

a^2 + b^2 = 36 - 2ab

Equating 36 - 2ab with 20

36 - 2ab = 20

2ab = 16

ab = 8

Hope this helps out, feel free to mark this answer as brainliest :)

The probability of having a girl in the family is also 1/2 since there are only two potential outcomes.

The probability that a family with two children has a boy and a girl is 1/2 because there are two potential birth orders: boy then girl or girl then boy.

Since the order does not matter in this case, the probability is 1/2 + 1/2 = 1.

However, since the question specifies that the family has at least one boy, we can eliminate the girl-boy birth order and conclude that the probability that the family has a boy and a girl is 1/2.

Therefore, the probability of having a girl in the family is also 1/2 since there are only two potential outcomes.

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We solved a problem after several missteps. One thing we are not certain of. We should:

When we are unsure about a part of a calculation, it is a good idea to check for hints that address that part of the calculation. This can help us confirm or correct your understanding of the problem. In addition, speaking with an instructor or classmate can provide valuable insight and help clarify any confusion.

Finally, if we still feel unsure, submitting our answer and then adjusting it based on feedback can help us improve our understanding and knowledge of the material. All of these options can help ensure that we have the most accurate and complete understanding of the problem.

This question should be provided with answer choices, which are:

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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The horizontal distance between the boat and the shark is approximately 82.24 feet.

Let's call the horizontal distance between the boat and the shark "x". We can use the tangent function to find the value of x, since we have the angle of depression and the vertical distance between the boat and the shark.

We know that:

tan(19) = (28) / x

So, we can solve for x by dividing both sides of the equation by the tangent of 19:

x = (28) / tan(19)

The value of x can be found using a calculator or a table of trigonometric values.

Using a calculator, we can get an estimate of x:

x = 28 / tan(19) ≈ 28 / 0.340339

x ≈ 82.24 feet

Therefore, the horizontal distance between the boat and the shark is approximately 82.24 feet.

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Answer:

Step-by-step explanation:

\( \sf \cfrac{8(x + 3)^{2} }{2(x + 3)} \)

Cancel out 2(x+3) in both numerator and denominator:

\(\sf 4(x + 3)\)

Use the distributive property to multiply 4 by x+3:

\(\sf 4x + 12\)

》》》》》》》》》》》》》》

Hope this helps!!

Have a nice day

Answer:

5

Step-by-step explanation:

To calculate a 95% confidence interval for the mean weight of all Utah County Fair pigs, we use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

Sample Mean (x) = 195

Standard Deviation (σ) = 18

Sample Size (n) = 100

The margin of error can be calculated using the formula:

Margin of Error = (Z * σ) / √n

For a 95% confidence level, the Z-value for a two-tailed test is approximately 1.96.

Margin of Error = (1.96 * 18) / √100

= 3.528

Therefore, the confidence interval is:

(195 - 3.528, 195 + 3.528)

(191.472, 198.528)

The correct answer is (191, 199).

Question 4: If the sample size is increased from 100 to 200, the margin of error will decrease in size. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the margin of error becomes smaller, resulting in a more precise estimate.

Question 5: To find out how many pigs must be sampled to have 90% confidence in the results with a margin of error of 6.8, we can use the formula:

Sample Size (n) = (Z^2 * σ^2) / E^2

Given:

Confidence Level (1 - α) = 90% (or 0.9)

Margin of Error (E) = 6.8

Standard Deviation (σ) = 18

For a 90% confidence level, the Z-value for a two-tailed test is approximately 1.645.

Sample Size (n) = (1.645^2 * 18^2) / 6.8^2

= 3.379

Therefore, the minimum number of pigs that must be sampled is approximately 4 (rounded up to the nearest whole number).

The correct answer is 5.

To start, write a paragraph:

Describe your position as a common man. Your name should be in the first sentence of your self-introduction.

Please describe your professional background and major achievements.

Finish with a transition into the following discussion point.

Then with the topic, you as a citizen want to raise your voice on or on specific problems you see on a daily basis.

Do not be misled; a good citizen is someone who fulfils all of her obligations to her city or county. duties such as making sure their nation or city is tidy and clean; everyone who lives there is happy and problem-free, etc.

A nice neighbour usually makes sure that their neighbourhood is kept tidy and clean. So they can live happily and disease-free if their neighbourhood is clean. Due to the fact that people do not always check to see if a place is clean. Several diseases entered their home as a result of the rubbish. due to the stench and bugs that emanated from the waste. When flies sit on food, bacteria from the food attach to their legs and cause a variety of illnesses in us.

Hence, it is our responsibility as decent citizens to maintain the cleanliness of the city in which we reside. If we begin at home, other people will think about it as well. And after all, is said and done, everyone considers how to keep their home cleaner and more orderly than the city or county. And after viewing the entire state, possibly the entire world!

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Answer:

2/6 - 1/6 = k

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

0 (104) is equal to 0, so let's cross that out. 103 times 102 is definitely not equal to 105. The third one is 105. The fourth one is not 105. The last one is not 105 either.