The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
A.AP ≅ CP
B.BC ≅ AD
C.m∠ABC=90∘
D.∠CAD≅∠ACB

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Option B is the correct answer.

We have,

The following data set shows the values collected by the manager.

{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}

Now,

We make the stem and leaf plot as:

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Here,

3 can be written as 03 and 0 can be written as 00.

Thus,

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Learn more about stem and leaf plots here:

https://brainly.com/question/12857419

#SPJ1

The coordinates of the vertices for the image of the triangle are A(−3, 6), B(0, 10), and C(−3, 3)

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

Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0)

If the preimage is translated 3 units up, then the transformation rule is

(x, y) = (x, y + 3)

Substitute the known values in the above equation, so, we have the following representation

A(−3, 3 + 3), B(0, 7 + 3), and C(−3, 0 + 3)

Evaluate

A(−3, 6), B(0, 10), and C(−3, 3)

Hence, the coordinates of the vertices for the image are A(−3, 6), B(0, 10), and C(−3, 3)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

When an object turns 90 degrees around in a circle, it turns 1/4 of the way around in a circle. Therefore, the correct statement is: "It turns 1/4 of the way around in a circle."

To understand why an object turning 90 degrees around in a circle turns 1/4 of the way around in a circle, it's helpful to consider the relationship between angles and circles.

A circle is a geometric shape that is defined by a set of points that are equidistant from a center point.

The distance from the center point to any point on the circle is called the radius of the circle. The circumference of a circle is the distance around the circle, and it is equal to 2π times the radius.

A circle has a total angle of 360 degrees. When an object turns 90 degrees around in a circle, it covers only a quarter of the total angle.

Therefore, it turns 1/4 of the way around in a circle.

For more details regarding circle, visit:

https://brainly.com/question/29142813

#SPJ1

Your question seems incomplete, the probable complete question is:

Which statement about an object turning 90 degrees around in a circle is true?

It turns 1/4 of the way around in a circle

It turns 2/4 of the way around in a circle

It turns 3/4 of the way around in a circle

It turns 4/4 of the way around in a circle

The quadratic equation has only one solution if m = 14

For a quadratic equation:

ax² + bx + c = 0

The discriminant is:

D = b² - 4ac

If the discriminant is zero, then the quadratic has only one solution, here we have the equation:

2x² - 28x + 7m = 0

Then the discriminant is:

D = (-28)^2 - 4*2*7m

Now we need to solve:

(-28)^2 - 4*2*7m = 0

784 - 56m = 0

Solving that for m:

784/56 = m

14 = m

Learn more about quadratic equations at.

https://brainly.com/question/1214333

#SPJ1

The mean of the data set is 3.33.

The variance of the data set is 0.47.

We have,

To find the mean of the data set,

We need to add up all the numbers and divide by the total number of values:

Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9

= 3.33 (rounded to two decimal places)

To find the variance,

We need to first find the squared difference between each value and the mean:

(2 - 3.33)^2 = 1.11

(2 - 3.33)^2 = 1.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

Next, we need to find the average of these squared differences:

Average of squared differences

= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9

= 0.47 (rounded to two decimal places)

Thus,

The mean of the data set is 3.33.

The variance of the data set is 0.47.

Learn more about mean here:

https://brainly.com/question/23263573

#SPJ1

7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

Find more exercises on finding diameter and radius;

https://brainly.com/question/23891151

#SPJ1

Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

To learn more about the amount of air to fill a basketball

https://brainly.com/question/20592924?referrer=searchResults

https://brainly.com/question/16606259?referrer=searchResults

a) the   proportion of even numbers in the population is 2/3 or approximately 0.667.

b. Sample Proportions and Probability Distribution Table is attched.

c) c. The mean of the sampling distribution of the sample proportion of even numbers is approximately 0.3333.

d. The sample poportion is a biased estimator of the population proportion because   the  sample proportions do not target the proportion of even numbers in   the population.

a. The population consists of 2, 6, and 7. The proportion of even numbers in the population is 1/3 since only 6 is even.

b. We can find the proportion of even numbers in each sample as follows:

2,2:   2/2 = 1

2,6: 1/2 = 0.5

2,7: 1/2  = 0.5

6,2: 1/2 =   0.5

6,6:   2/2 = 1

6,7: 1/ 2 = 0.5

7, 2: 1/2 = 0.5

7,6: 1/2 = 0.5

 7,7: 0/2   =0

This means that

   0 ⇒     1/9

  0.5⇒    5/9

   1  ⇒    3/9 (or 1/3)

So the above is summarized onto the table attached.

C)  The mean of the sampling distribution    of the sample proportion of even numbers is the weighted average of the possible values of the sample proportion,

where the weights are the probabilities of each value. Hence,

(0 x 1/9) +   (0.5 x 6/9 ) + (1 x 2/  9)

= 1/3

Learn more about Probability at:

https://brainly.com/question/29381779

#SPJ1

Answer:

5 + 1/x = 11/5

Podemos simplificar esta ecuación multiplicando ambos lados por 5x, lo que da:

25x + 5 = 11x

Ahora, podemos resolver x aislando la variable en un lado de la ecuación:

25x - 11x = -5

14x = -5

x = -5/14

Por lo tanto, la solución a la ecuación es x = -5/14

This is correct. If M is a subset of N and N is a subset of P, then, M is a subset of P.

This follows from the transitivity of the subset relation. In set theory, the transitive property states that if a relation applies between elements A and B, and between elements B and C, then it also applies between elements A and C.

For the subset relation, if M is a subset of N (M ⊆ N), this means that every element in M is also an element of N. Similarly, if N is a subset of P (N ⊆ P), every element in N is also an element of P.

Read more on subsets here:https://brainly.com/question/13265691

#SPJ1

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

Learn more about polynomial equation at:

https://brainly.com/question/19837586

#SPJ1

Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

It is very likely that a vacuum will last between 5.5 and 7.5 years.

This is because we can use the properties of the normal distribution to calculate that about 68% of the vacuum cleaners will fall within one standard deviation of the mean, which in this case is between 6.5 - 0.5 = 6 and

6.5 + 0.5 = 7

About 95% of the vacuum cleaners will fall within two standard deviations of the mean, which in this case is between 6 - 0.5 = 5.5 and 6.5 + 0.5 = 7

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

Answer:

BFD

Step-by-step explanation:

Supplementary angles add to 180, or will form a straight line.

< AFB and angle BFD will form a straight line so they are supplementary.

The exponential function representing the lifting time on day n is given as follows:

a(n) = 2^(n - 1).

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

On the first day, the time is of one minute, while the amount doubles each day, hence the parameters a and b are given as follows:

a = 1, b = 2.

We take the day one at the reference day, not day zero, meaning that the function was shifted right one unit, hence the rule is given as follows:

a(n) = 2^(n - 1).

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Yes, this collection is a set because it has a well-defined and finite number of elements, namely {2, 3, 5, 7}.

(ii) The method of describing this collection is the roster method or tabular method, where the elements of the set are listed within curly braces and separated by commas.

(iii) {2, 3, 5, 7}

In mathematics, a set is a collection of conspicuous objects or elements, taken as an object in its own right. These elements can either be numbers, letters, symbols, or even other sets. A set is defined by listing its elements or by specifying a property that its elements satisfy.

learn more about set: https://brainly.com/question/5660357

#SPJ1

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

C

Step-by-step explanation:

given

cosΘ = [tex]\frac{9}{15}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

then to find the third side (opposite) use Pythagoras' identity

opposite² + 9² = 15²

opposite² + 81 = 225 ( subtract 81 from both sides )

opposite² = 144 ( take square root of both sides )

opposite = [tex]\sqrt{144}[/tex] = 12

then

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{9}[/tex]

The pitch of the roof is equal to 1.14

Since pitch of the roof is the angle between the roof and the horizontal line.

Pitch (slope) = V/H

Where, V represents the rising vertical distance of an object.

H represents the horizontal distance an object runs through.

Substituting the selected points into the formula, we have;

Pitch (slope) = 32/28

Pitch (slope) = 1.14

Read more on slope here: brainly.com/question/6781555

#SPJ1

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

Read more on perimeter of a rectangle here: brainly.com/question/28695033

#SPJ1

If the helicopter flies 200 mph from the station nearest, the time it will it take to reach the ship is 0.52 hours

The numerical measurement between two entities or locations is defined as the distance, recorded in units such as kilometers, feet, meters, and miles. Determining the direct geometric line from point to point requires distinct models of calculation for both 2D and 3D geometry, most notably utilizing the Pythagorean theorem or the distance formula, respectively.

Physical sciences heavily rely on this notion, as it aids with computing rates that include: displacement, velocity, and acceleration. However, multiple factors - involving speed, direction, and time - can alter measured distances traveled by an object.

Read more about distance here:

https://brainly.com/question/2854969

#SPJ1

Answer: The best estimate of the sum of the heights of the 5 mountains is between 130,000 and 135,000 ft. Therefore, option D is correct,

Step-by-step explanation: The best estimate of the sum of the heights of the five mountains listed is between 130,000 and 135,000 ft. These heights are already very high, so options A and B can be eliminated. Option C is too low, leaving option D as the best estimate.

Dhaulagiri: 26,810 ft

Nanga Parbat: 26,660 ft

Annapuma: 26,504 ft

Gasherbrum: 26,470 ft

Xixabangma: 26,286 ft

To find similar and verified answers, you can search for the "Sum of heights of five mountains" site:

https://brainly.com/question/31747557

The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

To know more about rectangle here

https://brainly.com/question/8663941

#SPJ1

The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex]  +C

If we are finding the following integral below

∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx

then

secx = 1/cosx and cscx = 1/sinx

∫ (√(2 + cos²x)) × sinx × cosx dx

givn that sin²x + cos²x = 1

sin²x = 1 - cos²x

u = cosx,

du = -sinx dx.

-∫ (√u) / (2sinxcosx) du.

-√u + C.

When you substitute the original equation into the result

1/3 (2 + cos²x)^(3/2) + C.

Find more exercises on  finding integral;

https://brainly.com/question/27745537

#SPJ1

The surface area of the right square pyramid with the given base area and slant height would be = 221cm²

To calculate the surface area of the right square pyramid, the formula that should be used would be given below as follows. That is;

Surface area = a²+ 2al

where;

a² = area of base = 169cm²

a = side length of base = √169 = 13

l = slant height = 13 cm

S.A = 169+ 2(13×13)

= 169 + 52

= 221cm²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

The information from the histogram are as follow,

Students exercised for 4 or more hours are 14.

Students exercised for 9 or fewer hours are 13.

Mean of the data = 7.3.

median of the data = 6.33.

The histogram provides information about the distribution of hours students spent exercising in a week.

The number of students who exercised 4 hours or more,

= adding up the counts in the first and second bins.

= 9 + 5

= 14 students

The number of students who exercised 9 hours or fewer,

= adding up the counts in the first and second bins

= 9 + 4

= 13 students

The mean hours of exercise is not provided by the histogram

use the formula,

Mean = Σ[tex]x_{i} y_{i}[/tex] / N

where

[tex]x_{i}[/tex] is the midpoint of the ith bin

[tex]y_{i}[/tex] is the frequency of the ith bin

N is the total sample size

Mean = [(2)(4)  + (7)(9) + (12)(5)] / 18

          = 7.3

The median hours of exercise is not provided by the histogram.

Median = L + ( (n/2 – F) / f ) × w

where

L=The lower limit of the median group

n = The total number of observations

F = The cumulative frequency up to the median group

f =The frequency of the median group

w = The width of the median group

median = 5 + ( ( 14/2 - 4 ) /9 × 4

             = 6.33

Therefore, from the histogram the number of students exercised for ,

4 hours or more are 14.

9 hours or fewer are 13.

mean = 7.3

Median = 6.33

learn more about histogram here

brainly.com/question/9696858

#SPJ1

It will take approximately 8.6 years for the population to reach 1500.

We have,

We are given that the population is growing exponentially according to the model, P(t) = 500^(0.25t),

where t is measured in years.

We need to find the value of t when the population reaches 1500.

So we can set P(t) = 1500 and solve for t:

1500 = 500^(0.25t)

Taking the natural logarithm of both sides:

ln(1500) = ln(500^(0.25t))

Using the logarithmic identity, ln(a^b) = b ln(a):

ln(1500) = 0.25t ln(500)

Solving for t:

t = ln(1500) / (0.25 ln(500))

Using a calculator, we get:

t ≈ 8.6 years

Therefore,

It will take approximately 8.6 years for the population to reach 1500.

Learn more about exponential growth here:

https://brainly.com/question/12490064

#SPJ1

The missing sides of the right triangle were obtained below.

Pythagoras' theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We have that;

1) x = √26^2 - 10^2

x = 24

2) x = √20^2 + 14 ^2

x = 24.4

3) x = √50^2 - 30^2

x = 40

4) x = √15^2 + 5^2

x = 15.8

5) x = √12^2 + 20^2

x = 23.3

These are the sides that are missing.

Learn more about Pythagoras theorem:https://brainly.com/question/343682

#SPJ1

a) The total amount that the Scotts ended up paying for the townhome (including the down payment and the monthly payments) is $445,144.80.

b) The total interest paid on the mortgage is $213,144.80.

The down payment is the advance payment made on a mortgage or loan to satisfy the lending concerning the borrower's financial capacity.

The down payment reduces the mortgage liability, including interest.

The cost of the townhome = $232,000

The down payment for the town home made by the Scotts = $48,000

The mortgage = $184,000 ($232,000 - $48,000)

Monthly payment = $1,103.18

The mortgage period = 360 months (30 years x 12)

The total payment on the mortgage over the mortgage period = $397,144.80 (1,103.18 x 360)

The total payment, including the down payment = $445,144.80 ($397,144.80 + $48,000)

The total interest paid = $213,144.80 ($445,144.80 - $232,000)

Learn more about the down payment at https://brainly.com/question/1698287.

#SPJ1

The Scotts bought a townhome for $232,000. They made a down payment of $48,000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of $1,103.18 on their mortgage until it was paid off.