Triangle P'Q'R' (shown below) is a dilation of Triangle PQR (not shown) using center point C and a scale factor of 1.5.



What is the length, in units, of segment PQ? Explain your thinking by writing or showing math work.

Claire's is twice as tall as Zoe implies that:

The sum of their ages is 108 inches.

Thus, we have:

Therefore, Zoe's height is 36 inches while Claire's height is 72 inches

The answer of this question is found to be 0.0012.

The mean total service time is 10 minutes times lambda (the average number to turn up during the hour)

Lambda is 7, since the average rate is 7 per hour and your time window is 1 hour.

mean service time = 7 × 10 = 70 minutes.

For a poisson process, lambda is both the mean and variance of the arrivals.

So the variance = 10² × lambda = 700, since we want the variance of the service time, rather than the variance of the arrival rate.

This is because:

σ(aX) = a × σ(X).

and σ = sqrt(variance)

σ(service time) = 10 σ(arrival time)

variance(service time) = (10 × σ(arrival time))²

variance(service time) = 100 × variance(arrival time) = 100 × lambda =    100 × 7

mean(servicetime) = 70

variance(servicetime) = 700

2.5 hour = 150 min

Z = \(\frac{(S - 70)}{\sqrt{700} }\)  follow N(0,1)

P(S > 150) = P(  \(\frac{(S - 70)}{\sqrt{700} }\)>  \(\frac{(150 - 70)}{\sqrt{700} }\))

=P(Z > -2.5512)

=0.0012

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Answer: 120

Step-by-step explanation:

We can put it in an equation like this:

6 = 5%x

Then, we solve:

6 = 1/20 x

x = 20/1 *6

x=120

Therefore, 5% of 120 is 6.

Answer:

120

Step-by-step explanation:

5/100=6/x

Cross multiply

5x=100(6)

5x=600

/5. /5

x=120

Hopes this helps please mark brainliest

Answer:

1.4 x 10^6

Step-by-step explanation:

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

by changing y's value with the ten pounds until it equals 23 pounds.

Given:-

Michiko record the colors of all cars passing through an internection.

To find:-

Probability that the next car through the intersection will be red.

So to calculate the probabilty. we add all the number of cars and we divide 11 with that number and multiply with 100. To get the required solution.

So the total cars is,

So now we simplify. we get,

So the required solution is 18.3%

So the correct option is OPTION 1.

Explanation:

We're subtracting 7 from both sides to go from 4x+7 = 21 to 4x = 14.

In more general terms, the subtraction property says we can go from a = b to a-c = b-c.

Answer:

40

Step-by-step explanation:

2/10 are blue

so we need to find out 2/10's of 200

so in your calculator multiply 200 by 2/10

you get 40

Answer:

24

Step-by-step explanation:

hello

let's note x the number we are looking for

\(\dfrac{x}{12}=6\\<=> x = 6*12=72\)

so 1/3 of it equals

\(\dfrac{72}{3}=24\)

another way to see it is that 12=4*3

so 1/3 of it equals 6*4=24

hope this helps

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120

Answer:

Option (4)

Step-by-step explanation:

From the graph attached,

Local minimum → (3, -4)

Global Maximum → (-0.44, -4.3)

Maximum of the function → (1.7, 0.7)

Since, local maximum lies in the interval 2.5 ≤ x ≤ 4

Interval that contains the local minimum will be→ [2.5, 4]

Therefore, Option (4) will be the correct option.

Answer:

9%

Step-by-step explanation:

p*r*t = Interest

$6000*x*10 years = $5400

interest ÷ time ÷ principal = rate

5400 ÷ 10 ÷ 6000 = 0.09

0.09 = 9%

Answer:

\(p > 5\)

Step-by-step explanation:

\(2(p + 1) > 7 + p \\ expanding \: the \: bracket \\ 2p + 2 > 7 + p \\ collect \: like \: terms \\ 2p - p > 7 - 2 \\ p > 5\)

I hope this helps

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.

Answer:\(10n^{2}\)+180

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

There are 3 numbers fitting the rule, 1, 2, and 6. There is a 3/6 chance rolling one of them or 50%.

Answer:

50%

Step-by-step explanation:

1 value> 5 and 2 values<3, out of total of 6

P (greater than 5 or less than 3) = 3/6= 50%

Step-by-step explanation:

h=b-4

A=30ft^2

A=1/2bh

30=1/2b(b-h)

Cross Multiply

60=b(b-4)

60=b^2-4b

b^2-4b-60=0

Factorise the equation

(b^2+6) (-10b-60)

b(b+6)-10(b+6)

(b-10) (b+6)

b-10=0 or b+6=0

b=10 or b=-6

base =10 (since measurement can not be negative)

h=b-4

Sub the value of b

h = 10-4

h=6

So the height is 6ft and base is 10ft

Answer: 1, 2 and three

Step-by-step explanation:

Answer:

On the left side is "13", that is the whole number part. There are two digits on the right side, the 7 is in the "tenths" position, and the 6 is the "hundredths" position. So, 13.76 is "13 and 7 tenths and 6 hundredths".

Step-by-step explanation:

Answer:

3 x 10 x .5 - 25

Step-by-step explanation:

Is your expression

Answer:

do u go to il Texas and BTW u look nice

The following answers are obtained from HW, which it shows answers to.

Answer:

A. The Queen can state, "All the inscriptions are false."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined

(b) The Queen can state, "Exactly one of the inscriptions is true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Trunk 1 and 3

(c) The Queen can state, "Exactly two of the inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Cannot be determined

d) The Queen can state, "All the three inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined

The expected value of X is given as follows:

E(X) = 8.13.

(representing the expected Apgar score of a randomly selected newborn baby.)

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence the expected value of X is calculated as follows:

E(X) = 0 x 0.001 + 1 x 0.006 + 2 x 0.007 + 3 x 0.008 + 4 x 0.012 + 5 x 0.02 + 6 x 0.038 + 7 x 0.099 + 8 x 0.319 + 9 x 0.437 + 10 x 0.053 = 8.13.

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The required statistical parameters has been computed as follows:

Range = 15.

Standard deviation, SD = 4.4441.

Variance = 19.75.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 36 - 21

Range = 15.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 22 + 29 + 21 + 24 + 27 + 28 + 25 + 36

F(x) = 212.

Mean = 212/8

Mean = 26.5

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × ∑(22 - 26.5)² + 1/5 × ∑(29 - 26.5)² + 1/5 × ∑(21 - 26.5)² + 1/5 × ∑(24 - 26.5)² + 1/5 × ∑(27 - 26.5)² + 1/5 × ∑(28 - 26.5)² + 1/5 × ∑(25 - 26.5)² + + 1/5 × ∑(36 - 26.5)²)

Standard deviation, SD = 4.4441.

In Statistics, the standard deviation of a data sample is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 4.4441²

Variance = 19.75.

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Answer:

0.125 mm

Step-by-step explanation:

A/L=W

W=0.125

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Given:

Point k is located on the y-axis 8 units away from the origin.

To find:

The coordinates of point k​.

Solution:

Since point k is located on the y-axis, therefore it means the x-coordinate is 0.

Point k is 8 units away from the origin. So, it can be either or positive or negative side of y-axis.

If k is on the negative side of y-axis then y-coordinate of point k is -8.

If k is on the positive side of y-axis then y-coordinate of point k is 8.

Therefore, the possible coordinates of point k are either (0,-8) or (0,8).