A surveyor is surveying a street. The surveyor is standing at point Plooking down the street at a No Parking sign at point A and a stop sign at point R. Given PA=3x-4, PR=21 meters, AR=7 meters and point A is between point Rand point What is the value of x in meters?​

The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.

There are four multiples: 4,8,12,16,20,24.

6, 12, 18, and 24 are multiples of 6.

12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.

LCM of 24 and 15 is equal to 222235 = 120.

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Answer:

314 =4 Pi (r squrared)

Step-by-step explanation:

so second option is the right answer

Answer:

Yes

Step-by-step explanation:

2B+B=3b and 3b and 3b are the same.

Thus, they have the same value

Answer:

the 3rd option is the correct answer . u need to make the coefficient of x² the smallest before factorizing the equation.

Answer:

C.

Step-by-step explanation:

After these two steps, we divide the whole expression by coefficient of \(x^2\) (which is a) to both sides so that we get the \(x^2\) isolated for further solving.

Answer:

36 minutes

2 rounds for Priya

3 rounds for Ravish

Step-by-step explanation:

The answer is the LCM (least common multiple) of 12 and 18.

12 = 2^2 x 3

18 = 3^2 x 2

=>LCM of 12 and 18 = 2^2 x 3^2 = 4 x 9 = 36

=> After 36 minutes they meet again at the starting point

=> At that time, Priya has completed: 36/18 = 2 rounds

=> At that time, Ravish has completed: 36/12 = 3 rounds

After 36 minutes they meet again at the starting point.

In 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.

The least common multiple (L.C.M) of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.

Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.

According to the given question.

Time taken by Priya to complete one round = 18 minutes

Time taken by Ravish  to complete the one round = 12 minutes

Therefore,

The number of minutes taken by Priya and Ravish to meet again at the starting point when they start the race same time = L.C.M (12, 18)

Since,

Prime factorization of

\(12 = 2\times 2 \times 3\)

And \(18 = 3 \times 3 \times 2\)

⇒ L.C.M of 12 and 18  = 2 × 2 × 3 × 3 = 4 × 9 = 36

Hence, after 36 minutes they meet again at the starting point.

Now, number of round completed by Priya in 36 minutes = \(\frac{36}{18}= 2\)

And the number of rounds completed by Ravish in 36 minutes = \(\frac{36}{12}\) = 3

Hence, in 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.

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Answer:

w = 21

Step-by-step explanation:

i've done this kind of thing before a million times

a/b=5/4

a=5k

b=4k

b/c=7/3

b=7x

c=3x

b=4k

b=7x

4k=7x   =>

k=7y

x=4y

a/b/c=

=5*7*y/4*7*y/3*4*y=

=35y/28y/12y=

=35/28/12y=

=5/4/12y=

=1,25/12y=

=0.1041666666666667/ y

there may be a mistake in my answer

She will likely succeed in opening the door on her third attempt is 3/7 of the time.

The area of mathematics known as probability deals with the outcomes of random events. Probability refers to a result's chance or potential. It clarifies the likelihood that a specific occurrence will take place. We frequently say things like, "He will probably pass the test," "There is very little chance of receiving a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for every instance of chance, uncertainty, likely, etc. in these statements.

In essence, probability is the ability to anticipate an outcome based on the variety and quantity of potential possibilities or the analysis of historical data.

overall keys = 7

choosing 1 opens the door since p(1)=1/7

trying to throw out = 2/7

The likelihood that she will succeed in doing so on her third attempt is:

P= 1/7 + 2/7.

P= 3/7

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Answer:

Volume of square-based pyramid = 96 in³

Step-by-step explanation:

Given:

Base side of square = 6 inch

Height of pyramid = 8 inch

Find:

Volume of square-based pyramid

Computation:

Area of square base = Side x Side

Area of square base = 6 x 6

Area of square base = 36 in²

Volume of square-based pyramid = (1/3)(A)(h)

Volume of square-based pyramid = (1/3)(36)(8)

Volume of square-based pyramid = (1/3)(36)(8)

Volume of square-based pyramid = (12)(8)

Volume of square-based pyramid = 96 in³

Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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Answer:

Step-by-step explanation:

4/9 = 32 / x

Let x be any marble that is not red and the red ones.

Cross Multiply

4x = 9*32

4x = 288             Divide by 4

x   = 288/4

x = 72

So the whole bag contains 72 marbles.

To count the number of subsets of a set with k elements, we use the recurrence relation sk+1 = 2sk with the initial condition s0 = 1.

For your initial condition, consider a set with 0 elements, which has only one subset - the empty set. Thus, S(0) = 1. Using the recurrence relation and initial condition, you can compute the cardinality of the power set for any set of size k.

To count the number of subsets of a set with k elements, we can set up a recurrence relation.

Let sk be the cardinality of the power set of a set with k elements. When we add one more element to the set, we have two options for each subset: either include the new element or don't include it.

This means that the number of subsets of the set with k+1 elements is twice the number of subsets of the set with k elements. Therefore, we have the recurrence relation: sk+1 = 2sk.

Our initial condition is the number of subsets of an empty set, which is 1 (since the empty set itself is a subset). So s0 = 1.

In this course, when working with counting activities and sets, you can set up a recurrence relation to count the number of subsets of a set with k elements. Let S(k) represent the cardinality of the power set of a set of size k.

When you add one more element to the set, you essentially double the number of possible subsets, as each existing subset can either include or exclude the new element.

Therefore, the recurrence relation can be expressed as:

S(k) = 2 * S(k-1)

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Answer:

4

Step-by-step explanation:

a. Ashley would need to invest approximately $49,302.55 in one lump sum today. b. Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years. c. Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

a. To determine how much Ashley would need to invest today, in one lump sum, to end up with $70,000 in 6 years, we can use the future value formula:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^time

In this case, FV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values into the formula, we can solve for PV:

$70,000 = PV * \((1 + 0.07)^6\)

PV = $70,000 /\((1.07)^6\)

PV ≈ $49,302.55

Therefore, Ashley would need to invest approximately $49,302.55 in one lump sum today.

b. If Ashley is starting from scratch, we need to calculate how much she would have to put away annually to accumulate the needed capital in 6 years. This can be calculated using the present value of an ordinary annuity formula:

PV = Annual Payment * [(1 - (1 + interest rate)^(-time)) / interest rate]

In this case, PV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values, we can solve for the annual payment:

$70,000 = Annual Payment *\([(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $9,167.42

Therefore, Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years.

c. If Ashley already has $20,000 saved, we can subtract this amount from the required capital and calculate the annual payment for the remaining amount:

Remaining Amount = Required Capital - Initial Savings

Remaining Amount = $70,000 - $20,000 = $50,000

Using the same formula as in part b, we can calculate the annual payment:

$50,000 = Annual Payment\(* [(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $6,111.57

Therefore, if Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

d. Ashley can use an investment plan to help reach her objective by following these steps:

- Set a specific financial goal, such as accumulating $70,000 in 6 years.

- Determine the required investment amount, whether it's a lump sum or an annual payment.

- Consider her risk tolerance and investment options. Since she estimates a 7% return, she can explore various investment vehicles like stocks, bonds, mutual funds, or other investment instruments.

- Develop an investment plan that aligns with her financial goals and risk tolerance. This plan may involve diversifying her investments, considering different time horizons, and regularly monitoring her progress.

- Continuously track the performance of her investments and make adjustments if needed.

- Stay disciplined and committed to her investment plan, making regular contributions or adjusting investments as necessary to reach her desired capital.

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The Cartesian equation of the plane that contains the line and the point P(2, 1, 0) is -4x - 2y + 8z + 10 = 0.

To determine the Cartesian equation of the plane that contains the line and the point P(2, 1, 0), we need to find the normal vector of the plane.

First, let's find the direction vector of the line. The direction vector is the vector that represents the direction of the line. We can subtract the coordinates of the two given points on the line to find the direction vector.

Direction vector of the line:

(2, 2, 1) - (0, 3, 4) = (2 - 0, 2 - 3, 1 - 4) = (2, -1, -3)

Next, we need to find the normal vector of the plane. The normal vector is perpendicular to the plane and is also perpendicular to the direction vector of the line.

Normal vector of the plane:

The normal vector can be obtained by taking the cross product of the direction vector of the line and another vector in the plane. Since the line is already given, we can choose any vector in the plane to find the normal vector. Let's choose the vector from the point P(2, 1, 0) to one of the points on the line, let's say (0, 3, 4).

Vector from P(2, 1, 0) to (0, 3, 4):

(0, 3, 4) - (2, 1, 0) = (0 - 2, 3 - 1, 4 - 0) = (-2, 2, 4)

Now, we can find the cross product of the direction vector and the vector from P to a point on the line to obtain the normal vector.

Cross product:

(2, -1, -3) x (-2, 2, 4) = [(2*(-3) - (-1)2), ((-3)(-2) - 22), (22 - (-1)*(-2))] = (-4, -2, 8)

The normal vector of the plane is (-4, -2, 8).

Finally, we can write the Cartesian equation of the plane using the normal vector and the coordinates of the point P(2, 1, 0).

Cartesian equation of the plane:

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

Using P(2, 1, 0) and the normal vector (-4, -2, 8), we have:

-4(x - 2) - 2(y - 1) + 8(z - 0) = 0

Simplifying the equation:

-4x + 8 - 2y + 2 + 8z = 0

-4x - 2y + 8z + 10 = 0

Therefore, the Cartesian equation of the plane that contains the line and the point P(2, 1, 0) is -4x - 2y + 8z + 10 = 0.

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Answer:

(5,-3)

Step-by-step explanation:

difference in x is 5 and in y it is .5 so add those to (0,-3.5) and you get (5,-3)

Answer:

x = 4

Step-by-step explanation:

3(2x + 1) = 18 + 4x - 7

First distribute 3 by multiplying it by 2x and 1.

= 6x + 3 = 18 + 4x - 7

Then, add any like terms.

= 6x + 3 = 11 + 4x

 -4x                -4x

= 2x + 3 = 11

         -3    -3

= 2x = 8

 /2     /2

x = 4

Answer:

Priya used cm to measure the desk while Noah used inch to measure the desk that is why they found different measurement for same desk.

Answer:Priya used cm to measure the desk while Noah used inch to measure the desk that is why they found different measurement for same desk.

Answer:

60°

140°

Step-by-step explanation:

From the given figures,

 a. we use the concept of alternate angles.

   Two parallel lines cut by a transversal will have equal alternate angles;

  So;

       6x + 12 = 7x + 4

    collect like terms and solve for x;

     6x - 7x = 4 - 12

         -x = -8

         x = 8

Now, 6x + 12 = 6(8) + 12

                     = 48 + 12

                     = 60°

b. Here we use alternate angles and angles on a line;

     4x is an alternate angle to that angle to the left of 13x + 10

And sum of angles on a line = 180

    4x + 13x + 10 = 180

        17x = 170

          x = 10

Now,  13x + 10 = 13(10) + 10 = 140°

Answer:

2

Step-by-step explanation:

5-y + x  (y=8) (x=5)

5 - 8 + 5

=2

Answer:

2

Step-by-step explanation:

I just subbed  the y and x in then got the answer 2

To calculate the required number of spins for the average loss corresponding to a certain amount of initial money, we need to consider the probability of losing on each spin.

In the game of roulette, there are 18 black slots out of 38 total slots. Therefore, the probability of losing on any given spin when betting on black is 18/38.

Let's assume the initial amount of money the gambler has is M. On each spin, the gambler bets the entire amount on black.

The expected value (average) loss per spin can be calculated as follows:

Expected loss per spin = Probability of losing * Amount bet

= (18/38) * M

= 9M/19

To calculate the average loss corresponding to the initial amount of money (M), we divide the initial amount by the expected loss per spin:

Average loss = M / (9M/19)

= 19/9

Therefore, the required number of spins for the average loss to correspond to the initial amount of money is approximately 19/9 spins.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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Answer:36

Step-by-step explanation:

Concept,

Two chords with a shared termination point on the circle make an inscribed angle in a circle. The vertex of the angle is this shared terminal point. An inscribed angle is equal to half the length of the intercepted arc.

Given,

We have been given a figure in which the line \(BD\) is the tangent to the circle at the point \(B\) and the measure of the arc \(AC\) is \(108^{\circ}}\). And also we have some options:

A. \(38^{\circ}}\)

B. \(18^{\circ}}\)

C. \(118^{\circ}}\)

D. \(72^{\circ}}\)

To find,

We have to choose the correct option which tells the measure of the angle of \(CBD\).

Solution,

In the figure, we can see that \(\angle ABC\) is an inscribed angle and we know that the inscribed angle is half of the measure of the intercepted arc.

And from the figure arc \(AC\) is the intercepted arc.

Thus, we can write

\(\angle ABC=\frac{\widehat{AC}}{2}\)

\(\angle ABC=\frac{108}{2}\)

\(\angle ABC=54^{\circ}\)

So, the measure of \(\angle ABC=54^{\circ}\).

Now given that \(BD\) is a tangent to the circle at the point \(B\).

Thus, we will get

\(\angle ABC+\angle CBD=90^{\circ}\)

\(54^{\circ}+\angle CBD=90^{\circ}\)

\(\angle CBD=90^{\circ}-54^{\circ}\)

\(\angle CBD=36^{\circ}\)

Thus, the measure of the angle \(CBD=36^{\circ}\).

So, the correct option is A. \(36^{\circ}\).

Answer:

5. 120 pages in 1 day

6. 16 inches in 1 hour

Step-by-step explanation:

Just divide the numbers to get rate. 360/3=120 and 80/5=16

Answer:

5. 120 pages in 1 day

6. 16 inches in 1 hour

Step-by-step explanation

All you have to do is divide it

Answer:

9.25

13 - 0.75t

Step-by-step explanation:

0.75 * 5 = 3.75

13 - 3.75 = 9.25

hope this helps!

The value of Volume of prism is,

⇒ Volume  = 896 feet³

Since, WE know that;

The area of 3-dimensional solid which occupy is known as its volume. And, These solids are take the form of a cube, cuboid, cone, cylinder, or sphere.

We have to given that;

Base of a prism is type of a right triangle.

And, In right triangle,

Lenght of legs are 16 feet and 4 feet.

And, the height is 14 feet,

Since, We know that;

Volume of prism = B x h

Where, B = area of base

And h = height of prism.

Hence, We get;

The value of Volume of prism is,

V = 16 x 4 x 14

V = 896 feet³

Therefore, We get;

The value of Volume of prism is,

⇒ Volume  = 896 feet³

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Answer:

5).

According to the question,

CD+DE=CE

2+13=2x-3

15=2x-3

15+3=2x

18=2x

18/2=x

8=x

6).

According to the question,

AB+BC=AC

5x-16+3x-6=2x+20

8x-22=2x+20

8x-2x=20+22

6x=44

x=44/6

x=7.33

Step-by-step explanation:

......

Step-by-step explanation:

DE = 13

2 + 2x - 3 = 13

2x - 1 = 13

2x = 12

x = 12/2

x = 6

The experimental probability that at least two heads would be gotten is 11 / 25.

The theoretical probability that at least two heads would be gotten is 1/2.

Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times at least two heads would be gotten / total number of tosses

( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25

Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes

4 / 8 = 1/2

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