If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the bottom left corner of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.

Answer:

D

Step-by-step explanation:

Length × Width = Area

So we'll substitute the Area of the circle having formula, πr²

Answer:

4.700

Step-by-step explanation:

Find the number in the thousandth place  0  and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

brainliesssss plssssssssssssss

Answer:

y= -3/2x+12

Step-by-step explanation:

the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.

Answer:

Step-by-step explanation:

To find the average rate of change, find the change in function value, and divide that by the length of the interval.

1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4

The average rate of change of g(x) on [-1, 1] is -4.

__

2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5

  = (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5

  = 503/12 = 41 11/12

The average rate of change of g(x) on [-2, 3] is 41 11/12.

Answer:

⬇⬇⬇⬇⬇⬇

⬇⬇⬇⬇⬇⬇

Step-by-step explanation:

1, 3, 4

proof below

(1) The area of the rectangle is 88 square inches

(3) The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.

(4) The triangle has a base of 11 inches and a height of 8 inches.

Area of a rectangle is the sum of the area of two equal right triangle.

Area of rectangle = 2(area of right triangle)

Area of rectangle = 2(44 sq inches) = 88 sq inches

Let the length = x

then the width becomes, x - 3

Area = x(x - 3) = 88

x² - 3x = 88

x² - 3x - 88 = 0

x = 11

width = 11 - 3 = 8

Thus, the statements that are true include;

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Answer: Choice C

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

3/10≠3/5*1/4

so event A and B are not independent.

Answer:

The answer is No Solution

Answer:

No solution

Step-by-step explanation:

There is no solution to this question.

Since the x is an absolute number, the answer cannot be -4. It would have to equal 4

So if that x was a -4 it would equal 4 since it is in absolute value brackets

Answer:

Radius = 13 m

Step-by-step explanation:

Formula for area of circle is given as:

[tex]A = \pi {r}^{2} \\ \\ \therefore \: 169\pi \: = \pi {r}^{2} \\ \\ \therefore \: {r}^{2} = \frac{169\pi }{\pi} \\ \\ \therefore \: {r}^{2} = 169 \\ \\ \therefore \: {r} = \pm \sqrt{169} \\ \\\therefore \: r = \pm \: 13 \: m \\ \\ \because \: radius \: of \: a \: circle \: can \: not \: be \: a \: negative \: \\quantity \\ \\ \huge \red{ \boxed{\therefore \: r = 13 \: m }}[/tex]

Answer:

[tex]y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Step-by-step explanation:

Solution:-

- Given is the 2nd order linear ODE as follows:

                      [tex]ty'' + ( 2t - 1 )*y' - 2y = 6t^2 . e^(^-^2^t^)[/tex]

- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:

                     [tex]y_1(t) = 2t - 1\\\\y_2 (t ) = e^-^2^t[/tex]

- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:

                    [tex]y_p(t) = u_1(t)*y_1(t) + u_2(t)*y_2(t)[/tex]

Where,

              [tex]u_1(t) , u_2(t)[/tex] are linearly independent functions of parameter ( t )

- To determine [  [tex]u_1(t) , u_2(t)[/tex] ], we will employ the use of wronskian ( W ).

- The functions [[tex]u_1(t) , u_2(t)[/tex] ] are defined as:

                       [tex]u_1(t) = - \int {\frac{F(t). y_2(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\\\u_2(t) = \int {\frac{F(t). y_1(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\[/tex]

Where,

      F(t): Non-homogeneous part of the ODE

      W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions

- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:

                      [tex]W [ y_1 ( t ) , y_2(t) ] = | \left[\begin{array}{cc}y_1(t)&y_2(t)\\y'_1(t)&y'_2(t)\end{array}\right] |[/tex]

                      [tex]W [ (2t-1) , (e^-^2^t) ] = | \left[\begin{array}{cc}2t - 1&e^-^2^t\\2&-2e^-^2^t\end{array}\right] |\\\\W [ (2t-1) , (e^-^2^t) ]= [ (2t - 1 ) * (-2e^-^2^t) - ( e^-^2^t ) * (2 ) ]\\\\W [ (2t-1) , (e^-^2^t) ] = [ -4t*e^-^2^t ]\\[/tex]

- Now we will evaluate function. Using the relation given for u1(t) we have:

                     [tex]u_1 (t ) = - \int {\frac{6t^2*e^(^-^2^t^) . ( e^-^2^t)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_1 (t ) = \frac{3}{2} \int [ t*e^(^-^2^t^) ] \, dt\\\\u_1 (t ) = \frac{3}{2}* [ ( -\frac{1}{2} t*e^(^-^2^t^) - \int {( -\frac{1}{2}*e^(^-^2^t^) )} \, dt] \\\\u_1 (t ) = -e^(^-^2^t^)* [ ( \frac{3}{4} t + \frac{3}{8} )] \\\\[/tex]

- Similarly for the function u2(t):

                     [tex]u_2 (t ) = \int {\frac{6t^2*e^(^-^2^t^) . ( 2t-1)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_2 (t ) = -\frac{3}{2} \int [2t^2 -t ] \, dt\\\\u_2 (t ) = -\frac{3}{2}* [\frac{2}{3}t^3 - \frac{1}{2}t^2 ] \\\\u_2 (t ) = t^2 [\frac{3}{4} - t ][/tex]

- We can now express the particular solution ( yp ) in the form expressed initially:

                    [tex]y_p(t) = -e^(^-^2^t^)* [\frac{3}{2}t^2 + \frac{3}{4}t - \frac{3}{8} ] + e^(^-^2^t^)*[\frac{3}{4}t^2 - t^3 ]\\\\y_p(t) = -e^(^-^2^t^)* [t^3 + \frac{3}{4}t^2 + \frac{3}{4}t - \frac{3}{8} ] \\[/tex]

Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.

- The general solution is the superposition of complementary and particular solution as follows:

                    [tex]y_g(t) = y_c(t) + y_p(t)\\\\y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Answer:

Step-by-step explanation:

Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 1527

σ = 291

the probability to be determined is expressed as P(x > 1207)

P(x > 1207) = 1 - P(x ≤ 1207)

For x < 1208

z = (1207 - 1527)/291 = - 1.1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

P(x > 1207) = 1 - 0.16 = 0.84

Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is

0.84 × 100 = 84%

[tex]answer \\ 13.5 \: m/s \\ given \\ initial \: velocity(u) = \: 3 \: m/s \\ acceleration(a) = 1.5 \: m/s ^2\\ time(t) = 7 \: second \\ now \\ v = u + at \\ or \: v = 3 + 1.5 \times 7 \\ \: or \: v = 3 + 10.5 \\ v = 13.5 \: m/s \\ hope \: it \: helps[/tex]

Answer:

y = -z/2 - x/2

Step-by-step explanation:

2y + 5x – z = 4y + 6x

-5x. -5x

2y - z = 4y + x

+z. +z

2y = 4y + z + x

-4y -4y

-2y = z + x

÷-2. ÷-2

y = -z/2 - x/2

Answer:

0.347% of the total tires will be rejected as underweight.

Step-by-step explanation:

For a standard normal distribution, (with mean 0 and standard deviation 1), the lower and upper quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.

And the manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires.

1.5 of the Interquartile range = 1.5 × 1.34896 = 2.02344

1.5 of the interquartile range below the lower quartile = (lower quartile) - (1.5 of Interquartile range) = -0.67448 - 2.02344 = -2.69792

The proportion of tires that will fall 1.5 of the interquartile range below the lower quartile = P(x < -2.69792) ≈ P(x < -2.70)

Using data from the normal distribution table

P(x < -2.70) = 0.00347 = 0.347% of the total tires will be rejected as underweight

Hope this Helps!!!

The proportion of the tires that would be denied for being underweight through the given process would be:

[tex]0.347[/tex]% of the total tires will be rejected as underweight.

Given that,

Interquartile Range [tex]= 1.5[/tex]

Standard Deviation [tex]= 0.76[/tex]

Considering Mean = 0

and Standard Deviation = 1

Since lower quartile = -0.67448

Upper quartile  = +0.67448

IQ range =  1.34896

To find,

The proportion of tires would be rejected due to being underweight through the process would be:  

1.5 of Interquartile Range = 1.5 × [tex]1.34896 = 2.02344[/tex]

Now,

1.5 of the IQ range below the lower quartile [tex]= (lower quartile) - (1.5 of Interquartile range)[/tex]

[tex]= -0.67448 - 2.02344[/tex]

[tex]= -2.69792[/tex]

The proportion of tires that would be under 1.5 of the interquartile range below the lower quartile:

[tex]= P(x < -2.69792)[/tex] ≈ [tex]P(x < -2.70)[/tex]

Using data through the Normal Distribution Table,

[tex]P(x < -2.70)[/tex] [tex]= 0.00347[/tex]

[tex]= 0.347[/tex]%

Thus, 0.347% of the total tires would be rejected as underweight.

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Answer:

2

Step-by-step explanation:

Set the height of the bar to 2 since there are 2 numbers between 21-40.

Answer:

2 people.

Step-by-step explanation:

34 minutes and 40 minutes were recorded.

Therefore, 2 people.

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

If [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

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

By the Central Limit Theorem

[tex]Z = \frac{19 - 22}{1}[/tex]

[tex]Z = -3[/tex]

[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.

Answer:

7/200

Step-by-step explanation:

0.035= 35/1000= 7*5/200*5=7/200

Answer:

they played the pivotal role

Answer:

D. 6.3

Step-by-step explanation:

Well you can make a triangle with the line PQ with it's height as 2 and base as 6.

Then you can use the Pythagorean Theorem to find the length of PQ.

a²+b²=c²

2²+6²=c²

4+36=c²

40=c²

c²=40

Square root both sides

c=[tex]\sqrt{40}[/tex]

c≈6.3

Our answer is D. 6.3

Answer:

The minimum score that she must earn to get admitted is 523.

Step-by-step explanation:

As the scores are normally distributed, we can calculate the probability using the z-score.

The distribution has a mean of 420 and a standard deviation of 80.

We have to calculate the z-score z* that satisfies:

[tex]P(z>z^*)=0.1[/tex]

This happens for z*=1.28155.

Then, we can calculate the score as:

[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]

Answer:

B

Step-by-step explanation:

The triangular prism must have a larger base than the cylinder

Answer:

The approximate probability that more than six students were born on Christmas day is P=0.105.

Step-by-step explanation:

This can be modeled as a binomial variable, with n=1460 and p=1/365.

The sample size n is the total amount of students and the probability of success p is the probability of each individual of being born on Christmas day.

As the sample size is too large to compute it as a binomial random variable, we approximate it to the normal distribution with the following parameters:

[tex]\mu=n\cdot p=1460\cdot (1/365)=4\\\\\sigma=\sqrt{n\cdot p(1-p)}=\sqrt{1460\cdot(1/365)\cdot(364/365)}=\sqrt{3.989}=1.997[/tex]

We want to calculate the probability that more than 6 students were born on Christmas day. Ww apply the continuity factor and we write the probability as:

[tex]P(X>6.5)[/tex]

We calculate the z-score for X=6.5 and then calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{6.5-4}{1.997}=\dfrac{2.5}{1.997}=1.252\\\\\\P(X>6.5)=P(z>1.252)=0.105[/tex]

Answer:

Let's call the amount of 90% solution x.

We can write:

45% * 525 + 90%x = 55%(x + 525)

0.45 * 525 + 0.9x = 0.55(x + 525)

Solving for x we get x = 150 so the first blank is 150 and the second blank is 525 + 150 = 675.

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

GH¢. 18098.46

Step-by-step explanation:

Let the first investment giving 12% interest per annum be Bank A

Let the 2nd investment giving 10% per annum be bank B

Let the first amount invested be

GH¢. X and let the second amount invested be GH¢. X + 580

Thus; In bank A;

Principal amount in first = GH¢. x

rate = 12 %

time = 1 year

Formula for simple interest = PRT/100

Where P is principal, R is rate and T is time.

So, interest in his investment = 12X/100 = 0.12X

while in bank B;

principal amount = GH¢. X + 580

rate = 14%

time = 1 yr

So, interest in his investment = [(X + 580) × 14]/100

= 0.14(X + 580)

So, total accumulated interest is;

0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2

Now, we are given accumulated interest = GH¢. 2,358.60

Thus;

2358.60 = (0.26X + 81.2)

2358.6 - 81.2 = 0.26X

X = 2277.4/0.26

X = 8759.23

So,

first amount invested = GH¢. 8759.23

Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23

Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46

Answer:

31 degrees

Step-by-step explanation:

Since RPS and QPR make up QPS, the sum of their angle measures must be 47. Therefore:

3x-38+7x-95=47

10x-133=47

10x=180

x=18

QPR=7(18)-95=126-95=31

Hope this helps!

Answer:

  C

Step-by-step explanation:

The function of table A can be written as ...

  y = 100x -92

__

The function of table B can be written as ...

  y = 10x +446

__

The function of table C can be written as ...

  y = (5/3)·3^x

__

The function of table D can be written as ...

  y = 2x +413

__

The exponential function of Table C will have the largest y-values for any value of x greater than 6.

_____

Comment on the functions

When trying to determine the nature of the function, it is often useful to look at the differences of the y-values for consecutive x-values. Here, the first-differences are constant for all tables except C. That means functions A, B, D are linear functions.

If the first differences are not constant, one can look at second differences and at ratios. For table C, we notice that each y-value is 3 times the previous one. That constant ratio means the function is exponential, hence will grow faster than any linear function.

Answer:

yes, what the other user  is correct i just took the quiz

Step-by-step explanation:

Answer:

y = -5(x) - 4

Step-by-step explanation:

Use the equation of a line and substitution.

Information given:

point 1: (-2,6)

x1 = -2 and y1 = 6

point 2: (0,4)

x2 = 0 and y2 = 4

Equation of a line: y = m(x) + b

m = slope

To find slope, you do the equation of a linear slope, which is:

m = [tex]\frac{rise}{run}[/tex]         in other words   m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]

plug in your values

[tex]\frac{6-(-4)}{-2-0}[/tex]

= -5

Great, we've found slope, now to find b

plug in the slope you found: y = -5(x) + b

Plug in and solve for each point given, aka (x,y) into the linear equation for both points.

FIRST POINT:

6 = -5(-2) + b

6 = 10 + b

6 - 10 = b

b = -4

SECOND POINT:

-4 = -5(0) + b

-4 = 0 + b

-4 - 0 = b

b = -4

We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.

Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.

Answer:

f(x)=-5x-4

Step-by-step explanation:

You are given two points (-2, 6) and (0, -4)

Find the slope: m=(-4-6)/[(0-(-2)]=-5

So you have y=-5x+b

next, find the y intercept b.

the y intercept is when x=0. in this case, the y intercept is -4

so the linear function is f(x)=-5x-4

Answer:

[tex]t \approx 17.690\,min[/tex]

Step-by-step explanation:

This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:

[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]

[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]

[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]

[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]

[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]

[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]

The solution of the differential equation is:

[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]

Where:

[tex]y[/tex] - Temperature, measured in °C.

[tex]t[/tex] - Time, measured in minutes.

The time when the cup of coffee has the temperature of 70 °C is:

[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]

[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]

[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]

[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]

[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]

[tex]t \approx 17.690\,min[/tex]

Answer:

D. $7.50

Step-by-step explanation:

$157.50 / 21 hours = $7.50 per hour