What is the missing reason in the proof?

given
transitive property
alternate interior angles theorem
converse alternate interior angles theorem

Answer:

2804

Step-by-step explanation:

2504 + 140 + 160 = 2804   (hint: add the 140 + 160 first. It sums up to 300 which is easy to add to 2504)

To determine the area of the trapezoid we need to use the following expression:

Applying the dimmensions given in the problem we can calculate the area as shown below:

The area of the trapezoid is 18 square inches.

Approximately 234,314 people are lending money through Kiva.org.

To solve this problem, you can use the formula:

\(Total amount loaned = (average loan amount) x (number of loans) x\) \((number of lenders)\)

Let x be the number of lenders. Then we have:

Total amount loaned = $283,697,150

Average loan amount = $388.44

Number of loans = total amount loaned / average loan amount = $283,697,150 / $388.44 ≈ 729,464

Number of loans per lender = 8

Number of lenders = x

Using the formula, we get:

$283,697,150 = $388.44 x 729,464 x x / 8

Simplifying, we get:

x ≈ 234,314

Therefore, approximately 234,314 people are lending money through Kiva.org.

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Answer:

Saanvi is 15 and her brother is 7

Step-by-step explanation:

If Saanvi is 15 and her brother was 7 she would be 8 years older than her brother. If you add their ages together (15+7) it equals 22.

The probability that a randomly selected passenger has to wait for more than 4.25 minutes is 0.25, or 25%.

To calculate this probability, we can use the formula for the uniform distribution, which tells us that the probability density function (PDF) is given by:

f(x) = 1/(b-a)

where a and b are the endpoints of the interval (0 and 6 minutes in this case). This means that the probability of a waiting time between a and b is the area under the PDF curve between a and b, which is:

P(a < x < b) = ∫(a to b) f(x) dx = ∫(a to b) 1/(b-a) dx

In our case, we want to find the probability of a waiting time greater than 4.25 minutes, which means we need to calculate:

P(x > 4.25) = ∫(4.25 to 6) f(x) dx = ∫(4.25 to 6) 1/(6-0) dx

Simplifying this integral, we get:

P(x > 4.25) = ∫(4.25 to 6) 1/6 dx = [x/6] from 4.25 to 6

Evaluating this expression at the endpoints, we get:

P(x > 4.25) = [6/6] - [4.25/6] = 0.25

This means that there is a 1 in 4 chance that a passenger will have to wait longer than 4.25 minutes for their train to arrive.

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The amount of investment after 20 years nearest hundredth will be $21,777.72.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The rate for semiannually is given as,

r = 4.7 / (2 x 100)

r = 4.7 / 200

r = 0.0235

Then the number of years is given as,

n = 20 x 2

n = 40

Then the amount after 20 years is given as,

A = $8,600 × (1 + 0.0235)⁴⁰

A = $8,600 × (1.0235)⁴⁰

A = $8,600 × 2.53229

A = $21,777.72

The amount of investment after 20 years nearest hundredth will be $21,777.72.

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The shape of the sampling distribution of the sample wait times is approximately "normal". According to the Central Limit Theorem, the sampling distribution of the sample mean tends to be approximately normal, regardless of the shape of the underlying population distribution, as long as the sample size is large enough (usually greater than or equal to 30)

It is given that the distribution is right skewed with a mean of 11 minutes and a standard deviation of 4 minutes, we'll consider the "sampling distribution" of the sample wait times of size 49.

The shape of the sampling distribution of the sample wait times can be determined using the Central Limit Theorem, which states that if the sample size (n) is large enough, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the original distribution.

In this case, the sample size is 49, which is considered large enough (n >= 30 is a common rule of thumb). Therefore, the shape of the sampling distribution of the sample wait times is approximately normal, even though the original distribution is right skewed.

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Answer:

12

Step-by-step explanation:

I think I haven't learned this yet If I did I forgot but sorry if wrong

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Answer:

Step-by-step explanation:

9am to 5pm = 8 hours

8 x 4 =32

32 + 50 = 82 degrees Fahrenheit at 5pm

Step-by-step explanation:

Between 9am to 5pm = 8 hours.

Temperature increases 4 degrees Fahrenheit/hr

= Temperature increases 32 degrees Fahremheit in 8 hours.

50 degrees + 32 degrees = 82 degrees.

Hence the temperature at 5pm is 82 degrees Fahrenheit.

Each cutting machine cuts 105 parts every 3 minutes. There are 5 cutting machines because one cutting machine is shut down.

In order to determine how many parts the 5 cutting machines cut in 4 1/2 hours, multiply the factor 105/3 by 5 (number of cutting machines) by the factor 4 1/2 but in minutes:

4 1/2 = 4.5 hours = 4.5 (60 min) = 270 min

then,

(5)(105 parts/ 3min)(270 min) = 47,250

Hence, in 4 1/2 hours the rest of the cutting machines cut 47,250 parts

Answer:

To simplify this expression, we first need to evaluate the expression inside the parentheses:

10 - 9 + 6 = 7

Now we can substitute this value back into the original expression:

10 + 28 ÷ 7 (7) = 10 + 4(7) (since 28 ÷ 7 = 4)

= 10 + 28

= 38

Therefore, 10 + 28 divided by 7 (10-9+6) equals 38.

Answer:  41

Step-by-step explanation:

Median is the middle value.  There are two numbers in the middle: 40 & 42

Find their average: (40 + 42)/2 = 41

For N = 4, Simpson's rule approximates the integral ∫(0 to 2) dx/(x² + 5) as S_4 ≈ 0.31611.

To apply Simpson's rule, we need to divide the integration interval [a, b] into subintervals of equal width, h, where:

h = (b - a) / N,

and N is an even integer representing the number of subintervals. Then, Simpson's rule states that:

∫(a to b) f(x) dx ≈ h/3 [f(a) + 4f(a + h) + 2f(a + 2h) + 4f(a + 3h) + ... + 2f(b - h) + 4f(b - h) + f(b)]

where f(x) is the integrand function.

In this case, we have:

So, applying Simpson's rule, we get:

To evaluate S_N, we can use a computer or calculator to sum up the terms in the expression above for the given value of N. For example, for N = 4, we have:

S_4 = (2/3*4) [1 + 4/21 + 2/68 + 4/149 + 1/21] ≈ 0.31611

Therefore, for N = 4, Simpson's rule approximates the integral ∫(0 to 2) dx/(x² + 5) as S_4 ≈ 0.31611.

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Answer:

4

Step-by-step explanation:

You can use the Pythagorean theorem to find the length of the unknown side.

For that, let the unknown side be x.

Let us solve now.

2² + x² = ( 2√5)²

4 + x²  = 2√5 × 2√5

4 + x² = 2 × 2 × √5 × √5

4 + x² = 4 × 5

4 + x² = 20

x² = 20 - 4

x² = 16

x = √16

x = 4

Hope this helps you :-)

Let me know if you have any other questions :-)

Answer:

Equation of the plane is 19x - 20y - 15z - 38 = 0.

Step-by-step explanation:

We can find an equation of the plane that passes through the given three points by first finding two vectors that lie in the plane and then taking their cross product to get the normal vector of the plane. Once we have the normal vector, we can use any of the three points to write the equation of the plane in point-normal form.

Let's start by finding two vectors that lie in the plane. We can take the vectors connecting (2, −1, 3) to (7, 4, 6) and from (2, −1, 3) to (−3, −3, −2), respectively:

v1 = <7-2, 4-(-1), 6-3> = <5, 5, 3>

v2 = <-3-2, -3-(-1), -2-3> = <-5, -2, -5>

Now we can find the normal vector to the plane by taking the cross product of v1 and v2:

n = v1 x v2 = det( i j k

5 5 3

-5 -2 -5 )

= < 19, -20, -15 >

Now we can use the point-normal form of the equation of a plane, which is:

n · (r - r0) = 0

where n is the normal vector, r0 is a point on the plane, and r is a generic point on the plane. We can use any of the three given points as r0. Let's use the first point, (2, −1, 3):

n · (r - r0) = < 19, -20, -15 > · ( < x, y, z > - < 2, -1, 3 > ) = 0

Expanding the dot product, we get:

19(x - 2) - 20(y + 1) - 15(z - 3) = 0

Simplifying, we get:

19x - 20y - 15z - 38 = 0

Therefore, an equation of the plane is 19x - 20y - 15z - 38 = 0.

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Answer:

1/6

Step-by-step explanation:

sequence should be 1/6,1/3,1/2,2/3

common difference=1/3-1/6=2/6-1/6=1/6

or 1/2-1/3=(3-2)/6=1/6

or c.d.=2/3-1/2=(4-3)/6=1/6

Answer:

The answer is 1/6.

Step-by-step explanation:

I got it right when I did it.

The linear distance traveled in one revolution of a wheel can be calculated using the formula:

Circumference = π * Diameter

Given that the diameter of the wheel is 36 inches, we can substitute the value into the formula:

Circumference = π * 36 inches

Using an approximate value of π as 3.14159, we can calculate the circumference:

Circumference ≈ 3.14159 * 36 inches

Circumference ≈ 113.09724 inches

Therefore, the linear distance traveled in one revolution of a 36-inch diameter wheel is approximately 113.09724 inches.

The Half Angle Formula for Sin is an equation used to find the sine of half of an angle by using the sine of the original angle. It is written as sin(x/2) = ±√(1/2)(1 ± cosx).

The Half Angle Formula for Sin is an equation used to find the sine of half of an angle by using the sine of the original angle. It is written as sin(x/2) = ±√(1/2)(1 ± cosx). The half angle formula is a useful tool for simplifying trigonometric expressions and for finding the exact value of certain angles. The "±" symbol indicates that the sine of the angle can be either positive or negative, depending on the sign of the cosine of the original angle. The ± sign is also used to indicate that the result of the formula can be either an acute or an obtuse angle. The formula is based on the Pythagorean Identity, which states that sin2x + cos2x = 1. By plugging in the value of the original angle into the formula, we can find the sine of the angle. The half angle formula can be used to find the sine of any angle, such as the sine of a right angle or the sine of an obtuse angle. The formula is also useful for finding the sine of angles that cannot be easily measured with a protractor.

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Our equation: 33x + 10 = 5 - 2x

Step 1:

To solve for x, we need to remember to isolate the variable (that is our way to solve for x). To do that, we add 2x on the right side of the equation to cancel -2x out. Then, we add 2x on the left of the equation. The equation becomes:

\(35x+10=5\)

Step 2:

We subtract 10 from both sides (to cancel out the 10 on the left). Equation:

\(35x=-5\)

Step 3: Divide 35 on both sides to get our x value.

\(\frac{35x}{35}=x\\\\\frac{-5}{35} =\frac{-1}{7}\)

Answer: \(x=\frac{-1}{7}\) Hope this helps!

Answer:

x=66

y=-57

Step-by-step explanation:

Answer:

4.

Step-by-step explanation:

because i said so. :)

Answer:

C. 31 units

Step-by-step explanation:

Circumference of a circle is the distance around the circle and is given by C = pi•d

Your circle with a point and center given has a radius of 5 because from (2,1) to (7,1) is 5 units. Radius 5 means the diameter is 10.

C = pi•10

= 3.14•10

= 31.4 using 3.14 as an approximation for pi.

Circumference is approximately 31 units.

Answer:

3,468?

Step-by-step explanation:

I think the prompt is a little confusing, but I went with the logic of literally using the numbers and combining them.

Answer:

192.22775 Liters

Step-by-step explanation:

Answer:

a= 6

b= 7

c= 8

d= 7

e= 6

Step-by-step explanation:

The table of height versus width shows that the values represented will be 6, 7, 8, 7, and 6.

From the given information, a = 6. Therefore, the value of b will be: = a + 1 = 6 + 1 = 7

The value of c will be:

= a + 2 = 6 + 2 = 8.

The value of d is also the value of b which will be 7. Lastly, the value of e will be 6.

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A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² =  8 (y - 3)

Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The focus

F (h, k + p) = (-5,-1)

h = -5

k + p = -1

P in this problem, is the midpoint between the focus and the directrix

P = (-1 - 7) / 2 = -4

p = -4

the vertex

v(h, k)

h = -5

k + p = -1, k = 3

v(h, k) = v(-5, 3)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -5)² =  4 * 2 (y - 3)

(x + 5)² =  8 (y - 3)

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The given series \(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) is convergence and the sum of the series is 33/28.

In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.

The given series is \(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\).

Firstly we check the convergence of the given series.

When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.

We can write the series as:

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right\)

As |0.3|<1 and |0.2|<1

Then \(\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n\) is convergent.

So \(\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right\) is also convergent.

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right\)

Series \(\sum_{n=1}^{\infty}(x)^{n-1}\) converges to 1/x-1 for |x|<1.

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}\)

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}\)

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) = 10/7 - 1/4

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\) = 33/28

Hence, the sum of the given series is 33/28.

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The right question is:

Determine whether the series is convergent or divergent.

\(\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]\)

If is is convergent, find the sum. (If the quantity diverges, enter diverges.)

The explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\). B.

The explicit rule for the geometric sequence 3, 12, 48,... need to determine the common ratio, r.

We can do this by dividing any term by the previous term:

r = 12/3

= 48/12

= 4

Now that we know the common ratio can use the formula for the nth term of a geometric sequence:

\(a_n\) = \(a_1 \times r^{(n-1)\)

where:

\(a_n\) is the nth term

\(a_1\) is the first term (3 in this case)

r is the common ratio (4 in this case)

n is the term number

Substituting these values into the formula, we get:

\(a_n\) = \(3 \times 4^{(n-1)\)

So, the explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\)

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Let the common root is ‘x’

Let the common root is ‘x’x2 + ax + b = 0 ……(1)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))⇒ a + b = –1