An arc through P and Q and two arcs intersecting at R have been drawn. One arc at R has been drawn from P and the other has been drawn from Q using the same compass setting. QR⎯⎯⎯⎯⎯ and PR⎯⎯⎯⎯⎯ have also been drawn.

Determine the correct justification needed for each statement to prove ∠PAR≅∠QAR.

Answer:

Step-by-step explanation:

Multiply by the inverse of the coefficient of r², then take the square root.

  \(V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{\pi h}{3}r^2\\\\r^2=\dfrac{3V}{\pi h}\\\\\boxed{r=\sqrt{\dfrac{3V}{\pi h}}}\)

For V=50, h=15, this is ...

  \({r=\sqrt{\dfrac{3(50)}{\pi(15)}}=\sqrt{\dfrac{10}{\pi}}\approx\boxed{1.78\quad\text{cm}}\)

The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

Learn more about trigonometric ratios:https://brainly.com/question/23130410

#SPJ1

Answer:

38.4 megabytes for 16 electronic books

Step-by-step explanation:

2.4 megabytes per electronic book

2.4 megabytes x 16 electronic books = 38.4 megabytes

The probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

To determine whether it is appropriate to use the normal approximation, we need to check whether the conditions for using the normal distribution are met.

We can use the following criteria:

The sample size is large enough: n × p ≥ 10 and n × (1 − p) ≥ 10

The observations are independent

Here, we are given that the sample size is n = 66. To check the first condition, we need to find the expected number of individuals who hold multiple jobs in the sample, which is given by:

np = 0.12 × 66 = 7.92

n(1-p) = 66 - 7.92 = 58.08

Both np and n(1-p) are greater than or equal to 10. So, the sample size is large enough and the first condition is met.

Additionally, we can assume that the observations are independent since the sample is random and represents less than 10% of the population of employed adults in the United States.

Therefore, it is appropriate to use the normal approximation.

To find the probability that less than 8.4% of the individuals in the sample hold multiple jobs, we need to standardize the sample proportion using the formula:

z = (p'- p) / \(\sqrt{(p(1-p) / n)}\)

where p' is the sample proportion, p is the population proportion (0.12), n is the sample size (66), and sqrt represents the square root.

Substituting the values, we get:

z = (0.084 - 0.12) / \(\sqrt{((0.12)(1-0.12) / 66)}\) = -1.496

Using a standard normal distribution table, we can find that the probability of z being less than -1.496 is approximately 0.0681.

Therefore, the probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.

To learn more about Probability from given link.

brainly.com/question/30034780

#SPJ1

Answer:

The answer would be 6 x 10^16

The resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.

According to the given information, the current in an electrical conductor varies inversely to the resistance of the conductor. Inverse variation can be represented mathematically as follows:

Current * Resistance = Constant

Let's denote the constant as 'k'. We can use the initial values to find the value of 'k'.

When the resistance is 240 ohms and the current is 12 amperes:

12 * 240 = k

k = 2880

Now that we have the value of 'k', we can use it to find the current when the resistance is 540 ohms:

Current * 540 = 2880

Current = 2880 / 540

Current ≈ 5.33 amperes

Therefore, when the resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.

For more questions on resistance

https://brainly.com/question/30901006

#SPJ8

Answer:

The y-intercept is 0

Step-by-step explanation:

y = mx + b

b is y-intercept

There are no constants in this equation

Only the first statement is false. The rest are true statements about the Central Limit Theorem.

The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.

It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.

The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.

Learn more about Central Limit Theorem at : https://brainly.com/question/18403552

#SPJ4

Answer:

Pls give us the statements

Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Learn more about cost at https://brainly.com/question/29509552

#SPJ1

Answer:

x = -20.5

Step-by-step explanation:

Simplifying

4(3x + -5) = 7(2x + 3)

Reorder the terms:

4(-5 + 3x) = 7(2x + 3)

(-5 * 4 + 3x * 4) = 7(2x + 3)

(-20 + 12x) = 7(2x + 3)

Reorder the terms:

-20 + 12x = 7(3 + 2x)

-20 + 12x = (3 * 7 + 2x * 7)

-20 + 12x = (21 + 14x)

Solving

-20 + 12x = 21 + 14x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-14x' to each side of the equation.

-20 + 12x + -14x = 21 + 14x + -14x

Combine like terms: 12x + -14x = -2x

-20 + -2x = 21 + 14x + -14x

Combine like terms: 14x + -14x = 0

-20 + -2x = 21 + 0

-20 + -2x = 21

Add '20' to each side of the equation.

-20 + 20 + -2x = 21 + 20

Combine like terms: -20 + 20 = 0

0 + -2x = 21 + 20

-2x = 21 + 20

Combine like terms: 21 + 20 = 41

-2x = 41

Divide each side by '-2'.

x = -20.5

The simplified expression of the radical expression ∛135a¹³ is (135a¹³)¹/³

From the question, we have the following parameters that can be used in our computation:

A radical expression

The radical expression is given as

\sqrt[3]{135^{a13}}

Represent the expression properly

So, we have the following representation

∛135a¹³

Apply the exponent rule of indices

This gives

∛135a¹³ = (135a¹³)¹/³

135 and a¹³ are not perfect cube root expressions

This means that the expression cannot be further simplified

Hence, the solution is (135a¹³)¹/³

Read more about radical expression at

https://brainly.com/question/12052952

#SPJ1

The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To more on factors:
https://brainly.com/question/15824403
#SPJ8

       The equation representing the relationship between Electricity and  Gas used, and your Bill is:

      T  =  0.25 * k + 0.97 * t

        Make a plan:

We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).

T  =  0.25  *  k  +  0.97  *  t

1 - Write the Equation for the cost of Electricity:

        0.25 * k

2 - Write the Equation for the Cost of Gas:

       0.97 * t

3 - Combine the Equations to Represent the total Monthly Bill (T):

       T  =  0.25 * k + 0.97 * t

Hence,  The equation representing the relationship between Electricity and  Gas used, and your Bill is:

       T  =  0.25 * k + 0.97 * t

I hope that helps!

Answer:

Hare wins the race

Step-by-step explanation:

Length of track = 100 m

Let t represent the number of seconds in completing the race.

Speed of tortoise = 0.7 m/s

Distance covered by tortoise in t seconds = Speed \times time = 0.7t

We are given that The tortoise negotiated a 60-meter head start with the hare.

So, Distance covered by tortoise in t seconds = 60+0.7t

Speed of hare = 3.6 m/s

Distance covered by hare in t seconds = 3.6 t

Now

3.6t = 100

\(t=\frac{100}{3.6}\)

t=27.77

60+0.7t=100

\(t=\frac{100-60}{0.7}\)

t=57.14

So, Hare took less time

So, Hare wins the race

Answer:

864 square inches

Step-by-step explanation:

Surface Area = 12 x 12 x 6

Surface Area = 144 x 6 = 864

Hope that helps!

Answer:

864

Step-by-step explanation:

12*12 =144 (the surface of one side

144*6 =864 (the surface of all sides)

Answer:

Point A:  (2, 10)

Point B:  (-3, 0)

Point C:  (-5, -4)

Point D:  (-5, -32)

Step-by-step explanation:

Points A and B are the points of intersection between the two graphs.

Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:

\(\implies 2x+6=-2x^2+18\)

\(\implies 2x^2+2x-12=0\)

\(\implies 2(x^2+x-6)=0\)

\(\implies x^2+x-6=0\)

\(\implies x^2+3x-2x-6=0\)

\(\implies x(x+3)-2(x+3)=0\)

\(\implies (x-2)(x+3)=0\)

\(\implies x=2, -3\)

From inspection of the graph:

To find the y-values, substitute the found x-values into either of the equations:

\(\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}\)

\(\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}\)

Therefore, point A is (2, 10) and point B is (-3, 0).

If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

\(\textsf{Equation 1}: \quad y=2x+6\)

\(\textsf{Equation 2}: \quad y-28=-2x^2+18\)

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

\(\implies 2x+6-28=-2x^2+18\)

\(\implies 2x^2+2x-40=0\)

\(\implies 2(x^2+x-20)=0\)

\(\implies x^2+x-20=0\)

\(\implies x^2+5x-4x-20=0\)

\(\implies x(x+5)-4(x+5)=0\)

\(\implies (x-4)(x+5)=0\)

\(\implies x=4,-5\)

From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

\(\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}\)

\(\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}\)

Therefore, point C is (-5, -4) and point D is (-5, -32).

Answer:

a) A = (2, 10) and B = (-3, 0)

b) C = (-5, -4) and D = (-5, -32)

Explanation:

a) To determine the coordinates of A and B, find the intersection points of  the line "y = 2x + 6" and curve "y = -2x² + 18".

Solve the equation's simultaneously:

y = y

⇒ 2x + 6 =  -2x² + 18

⇒ 2x² + 2x + 6 - 18 = 0

⇒ 2x² + 2x - 12= 0

⇒ 2x² + 6x - 4x - 12 = 0

⇒ 2x(x + 3) - 4(x + 3) = 0

⇒ (2x - 4)(x + 3) = 0

⇒ 2x - 4 = 0, x + 3 = 0

⇒ x = 2, x = -3

Then find value of y at this x points,

at x = 2, y = 2(2) + 6 = 10

at x = -3, y = 2(-3) + 6 = 0

Intersection points: A(2, 10) and B(-3, 0)

b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.

\(2x + 6 = -2x^2 + 18 + 28\)

\(-2x^2 + 18 + 28-2x - 6 = 0\)

\(-2x^2-2x+40=0\)

\(-2x^2-10x+8x+40=0\)

\(-2(x+5)+8(x+5)=0\)

\((-2x+8)(x+5)=0\)

\(x = -5, 4\)

\(\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)\)

Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4

Find y value for Point D :  -2x² + 18 =  -2(-5)² + 18 = -32

\(\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)\)

a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

learn more about probability,

https://brainly.com/question/30034780

#SPJ4

Answer:

here you go! y = 2 x + 4. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side. 2x+4=y. 2 x + 4 = y. Subtract 4 from both sides. Subtract 4 from both sides. 2x=y-4. 2 x = y − 4

Answer:

2, 4, -2

Step-by-step explanation:

The slope is directly in the equation, the variable m in the slope-intercept form of y = mx + b. This means that the slope is 2.

The y-intercept is the variable b in standard form, so 4 in this case.

To find the x-intercept, set y equal to zero.

0 = 2x + 4

2x = -4

x = -2

Answer:

The answer is 23 chocolates

Step-by-step explanation:

You do 5 times 5 for her eating 5 chocolates a day for 5 days to get 25 and then you take 48 and subtract it by 25 and you get 23

x = 20

Using the alternate exterior angles theorem, it was stated the exterior ang

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

for such more question on fewest number

https://brainly.com/question/859564

#SPJ8

Answer

x = -3/4

Step-by-step explanation

Distributing:

Adding x and subtracting 7 at both sides of the equation:

Dividing by 4 at both sides of the equation:

Answer:

Number 1 is 17 cents

Number 2 is 164.35

Number 3 is 213

Step-by-step explanation:

Please mark brainliest

Answer:

24

Step-by-step explanation:

Remark

This can be done with a proportion which consists of 2 equal ratios. That's 4 parts total. If you know 3 of the parts, you can find the 4th.

Givens

Stars1  6

Moon1 4

Starts2 x

Moon2 16

Formula

stars1/moon1 = stars2/moon2

Solution

6/4 = x / 16         Multiply by 16

6 * 16/4 = x

Answer: 96/4 = 24

Based on the given histogram, the data is skewed with a maximum range of 49.

This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.

One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.

Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.

Learn more about histogram here:

https://brainly.com/question/30354484

#SPJ1

Answer:

z = 99

Step-by-step explanation:

\(\frac{z}{9}\) + 4 = 15 ( subtract 4 from both sides )

\(\frac{z}{9}\) = 11 ( multiply both sides by 9 to clear the fraction )

z = 99

Answer: tenths

Step-by-step explanation:

Answer:

TENTHS

Step-by-step explanation: