Select the correct answer.
In the given diagram, line segment BD
bisects angle ABC
. Segment BD
is extended to E, where line segment EC
is parallel to line segment AB
. Write a two-column proof to show that AB/AD = BC/DC
.

The volume of the triangular base prims is 21.6 inches cube.

A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.

volume of a triangular prism = base area × height

Therefore,

base area = 1 / 2 bh

where

Therefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.

tan 45 = opposite / adjacent

tan 45 = x / 6

x = 6 inches

Therefore,

base area = 1 / 2 × 6 × 6

base area = 36  /2

base area = 18 inches²

Hence,

volume of the triangular base prism = 18 × 1.2

volume of the triangular base prism = 21.6 inches³

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time tables on the map mannnnn

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

The trio of sides that will make a right triangle are the ones in the first option:

5, 12, and 13.

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.

So for example, for the first option we would have:

5^2 + 12^2 = 13^2

25 + 144 = 169

169 = 169

The equation is true, thus, these sides make a right triangle.

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Answer:

12 • (17 • 23) = (12 • 17) • 23

The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s

To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.

We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:

Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)

Similarly, we can calculate the average velocities over the other intervals:

[8.7, 9]: 6.48 m/s (approx.)

[8.9, 9]: 6.60 m/s (approx.)

[8.99, 9]: 6.66 m/s (approx.)

[9, 9.01]: 6.67 m/s (approx.)

[9, 9.1]: 6.74 m/s (approx.)

[9, 9.3]: 6.87 m/s (approx.)

[9, 9.5]: 7.00 m/s (approx.)

As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.

Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).

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The radius is 5.316 cm, height is 10.362 cm and Maximum volume is  

60.583 cm³.

We have,

Surface area of sphere = 36 cm²

4πr² = 36

πr² = 9

r = 3√π

r= 5.316

Now, Volume spherical cap

= 1/3 πh² (3R- h)

= 1/3π (10.362) (3 (5.316) - 10.362)

= 1/3 π (57.882132)

= 60.583 cm³

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Answer:

16

Step-by-step explanation:

24 divided by X(3) is equal to 8, then 8+8 equals 16 (EASY)

Answer:

The answer to your problem is, 7

Step-by-step explanation:

First you can either convert;

ml to liter

liter to ml

I will use liter to ml.

1.75 liters in ml is 1750 ml

So we can then divide, 1750 / 250 = 7

Which is the answer

Thus the answer to your problem is, 7

The expected joint frequencies are

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

The table of values

Also, we have

People = 160

This means that

Male and Drama = 12.5% * 160

Male and Drama = 20

Male and Comedy = 25% * 160

Male and Comedy = 40

Female and Drama = 46.9% * 160

Female and Drama = 75

Female and Comedy = 15.6% * 160

Female and Comedy = 25

In conclusion, we have

Because the expected and the joint frequencies are not the same, gender is not independent of movie type

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The Area of Kitchen is 120 square feet.

We have,

Area of living room = 144 square feet

So, the dining room

= 1/3 (area of living room)

= 1/3 (144)

= 48 square feet

and, Area of Dining room = 2/5 x Area of kitchen

48 =  2/5 x Area of kitchen

Area of kitchen = 48 x 5/2

Area of Kitchen = 24 x 5

Area of Kitchen = 120 square feet

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The system of inequalities that represents this real-world scenario is:

x + y ≤ 450  (The total people cannot be greater than 450)

7x + 4y ≤ 1150  (total price cap of $1,150)

A group of two or more simultaneously true inequalities is referred to as a system of inequalities. A system of inequalities can be solved by finding the set of values that satisfies every one of the inequalities in the system.

Therefore, The system of inequalities that represents this real-world scenario is:

x + y ≤ 450 (The total people cannot be greater than 450)

7x + 4y ≤ 1150 (total price cap of $1,150)

Where x is the number of adults and y is the number of campers.

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Answer:

The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.

Step-by-step explanation:

The pairs of supplementary angles are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.

Thus, the pair of supplementary angles in the given diagram are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

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The equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

In a quadratic equation, an imaginary number is a complex number that can arise when trying to take the square root of a negative number.

We shall solve for x in the equation as follows:

(2x + 3)² - 2 = -6

add 2 to both sides

(2x + 3)² = 2 - 6

(2x + 3)² = -4

2x + 3 = √(-4) {taking square root of both sides}

subtract 3 from both sides

2x = 3 ± √(-4)

divide through by 2

x = [3 ± √(-4)]/2

note that: √(-4) = √(1-) × √4 where √(-1) = I, so;

x = (3 ± 2i)/2.

Therefore, the equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

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The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.

Given that,

Last year, they sold 1,080 pounds of cookie dough to 360 people.

This means that they sold an average of 3 pounds of cookie dough per person.

Number of pounds of cookie dough = 3 pounds/person × Number of people

Here, 3×460=1,380

3×500=1500

To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.

Therefore, option B is the correct answer.

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The rate of change for the cab ride is A = $3 per mile

Given data ,

Change in cost = $55 - $40 = $15

Change in distance = 15 miles - 10 miles = 5 miles

Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:

Rate of change or cost per mile = Change in cost / Change in distance

A = $15 / 5 miles

A = $3 per mile

Hence , the rate of change or cost per mile for the cab ride is $3 per mile

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If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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The values of c that satisfy Rolle's Theorem is 2.15 or -0.15.

The value of c that satisfies Roll's theorem is calculated as follows;

y = x³ - 3x² - x; [-1, 3]

Based on Roll's theorem conditions, since the function is a polynomial it is continuous.

The derivative is also a polynomial.

y' = 3x² - 6x - 1

The final condition;

y(-1) = (-1)³ - 3(-1)² - (-1)

y(-1) = -1 - 3 + 1

y(-1) = -3

y(3) = (3)³ - 3(3)² - 3

y(3) = 27 - 27 - 3

y(3) = -3

The three conditions of Rolle's theorem is statisfied,  so there exists at least one value of c in the interval (-1, 3) such that y'(c) = 0.

y' = 3x² - 6x - 1

y'(c) = 3c² - 6c - 1

3c² - 6c - 1 = 0

Solve the quadratic equation using formula method;

a = 3, b = -6, c = -1

c = 2.15 or - 0.15

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Answer:

2(5(11) + 5(2.5) + 11(2.5))

= 2(55 + 12.5 + 27.5) = 2(55 + 40) = 2(95)

= 190 square centimeters

After two years, Swathu will pay back the debt in full, which comes to Rs. 105287.27.

To find the total amount Swathu will pay back after 2 years on a loan of Rs. 90,000 with an interest rate of 8% per annum compounded half-yearly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt[/tex]

where:

A = the total amount Swathu will pay back

P = the principal amount borrowed (Rs. 90,000)

r = the annual interest rate (8%)

n = the number of times the interest is compounded per year (2 times, since it is compounded half-yearly)

t = the time period (2 years)

Substituting these values into the formula, we get:

[tex]A = 90,000(1 + 0.08/2)^{2*2}\\\\A = 90,000(1 + 0.04)^4\\\\A = 90,000(1.04)^4\\\\A = 90,000(1.16985856)\\[/tex]

A = 105287.27 (rounded to the nearest tenth)

Therefore, Swathu will pay back a total of Rs. 105287.27 after 2 years on the loan.

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The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

We have,

The formula given is incorrect.

The correct formula for Pythagorean triples with a given integer z is:

(z² - 1², 2z, z² + 1²)

Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:

z² + 1² = 29²

z² + 1 = 29²

z² = 29² - 1

z² = 840

z = √840

z = 28.98

Since z must be an integer, we can try integer values close to 28.98 to find one that works.

Trying z = 29,

a = z² - 1² = 840 - 1 = 839

b = 2z = 58

c = z² + 1² = 840 + 1 = 841

Therefore,

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

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The simplification of the given expression is equal to 192524.3.

The expression is equal to,

√2 × √6 × √110 × √120 × √450 × √520

Simplify this expression by first simplifying the square roots under the radical signs,

√2 = √(2 × 1)

     = √2 × √1

√6 = √(2 × 3)

     = √2 × √3

√110 = √(2 × 5 × 11)

        = √2 × √5 × √11

√120 = √(2 × 2 × 2 × 3 × 5)

        = 2√2 × √3 × √5

√450 = √(2 × 3² × 5²)

         = √2 × (3 × 5)²

         = 15√2

√520 = √(2³ × 5 × 13)

        = 2√2 ×√5 × √13

Substituting these simplifications back into the original expression, we have,

√2 × √6 × √110 × √120 × √450 × √520

= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2  ×  2√2 ×√5 × √13

= 2⁵ × 3² × 5²√(5 × 11  × 13)

= 7200√715

= 192524.3

Therefore, the simplification value of √2 × √6 × √110 × √120 × √450 × √520 is equal to 192524.3.

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The above question is incomplete, the complete question is:

Simplify

√2 × √6 × √110 × √120 × √450 × √520

The relationship between the distance that birds fly in relation to the time they do so, is positive.

There are about 3 outliers but for the most part, the relationship is positive.

The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.

There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.

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Answer:

60

Step-by-step explanation:

The area of a parallelogram is base x hight.

A = bh

10(b) x 6(h) = 60

The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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

5y+4= (x+3)²+12

Swap x and y in the equation

So, we have

5x + 4= (y + 3)² + 12

When we make the vairiable y the subject, we have

y = -3 ± √(5x - 8)

Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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Step-by-step explanation:

Arithmetic sequence with  d = 2    a1 = -6

a20 = -6 + 2(20-1) = 32

The measure of angle 1 is 107° suing the concepts of corresponding angles and linear pair of angles..

Given a line t which is a transversal line that cuts the two parallel lines m and n.

Here the angle which is linear pair to angle 1 and the angle 73° are corresponding angles.

By the corresponding angle theorem, the corresponding angles formed by two parallel lines cut by a transversal are equal.

So,

Measure of angle which is linear pair to 1 = 73°

Now linear pair of angles are supplementary.

∠1 + 73° = 180°

∠1 = 180° - 73°

∠1 = 107°

Hence the measure of angle 1 is 107°.

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The given shape of the distribution is not symmetric.

Given that, a box plot shows donations in dollars to charity.

We need to describe the shape of the distribution.

Donations to Charity ($) =

20 40 60 80 100 120 140 160 180 200 220

so, as we can see,

The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.

Hence, the given shape of the distribution is not symmetric.

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The time it will take the bird to travel 1.4 m is 0.5738 seconds.

In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.

In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;

Velocity = distance/time

244 cm/s to m = 244/100 = 2.44 cm/s

By making time the subject of formula, we have:

Time = distance/velocity

Time = 1.4/2.44

Time = 0.5738 seconds.

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