A teacher is randomly handing out tests. There are 2 different versions of the test, Test A and Test
B. If there are 8 tests in all and an equal number of each version, what is the probability that the
first 4 students will all receive Test A?

Answer:

∠ K = 129° , ∠ M = 93°

Step-by-step explanation:

the figure has one pair of parallel sides and is therefore a trapezoid.

• Each lower base angle is supplementary to the upper base angle on the same side , then

∠ K = 180° - 51° = 129°

∠ M = 180° - 87° - 93°

The ball reaches the skydiver at 2.81 seconds.

Height of sky diver

          h(t) = -300t + 1000

Height of ball

           h(t) = -16t² + 100t

We need to find out when the ball reach the skydiver

That is both heights are equal

              -300t + 1000 = -16t² + 100t

                16t² - 400t + 1000 = 0

                t = 22.18 s   or t = 2.81 s  

The ball reaches the skydiver at 2.81 seconds.

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The half-life of bismuth-210 is given as follows:

5 days.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

For this problem, we have that:

Hence the decay rate is obtained as follows:

\(6.64 = 122(1 - r)^{21}\)

\((1 - r)^{21} = \frac{6.64}{122}\)

\(((1 - r)^{21})^{\frac{1}{21}} = \left(\frac{6.64}{122}\right)^{\frac{1}{21}}\)

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294.

Hence the function is given as follows:

y = a(0.8706)^t.

The half-life is the value of t for which:

y = 0.5a.

Hence:

0.5a = (0.8706)^t.

(0.8706)^t = 0.5

log((0.8706)^t) = log(0.5)

tlog(0.8706) = log(0.5)

t = log(0.5)/log(0.8706)

t = 5 days.

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Answer:

0.0000002702

Step-by-step explanation:

2.702 * 10^-7

The number of spanning trees of a connected graph can be proven to be the product of the number of spanning trees of each of its blocks.

Here are the steps-

1. Consider a connected graph G with blocks B1, B2, ..., Bk. Each block is a maximal connected subgraph with no cut-vertex.

2. The number of spanning trees of G can be denoted as T(G), and the number of spanning trees of each block Bi can be denoted as T(Bi).

3. To prove the given statement, we need to show that\(T(G) = T(B1) * T(B2) * ... * T(Bk).\)

4. We can start by considering a single block B1. Since B1 is a maximal connected subgraph with no cut-vertex, it is a connected graph on its own.

5. The number of spanning trees of B1, T(B1), can be calculated using any method such as Kirchhoff's theorem or counting the number of spanning trees directly.

6. Now, consider the original graph G. We can remove block B1 from G, which leaves us with a graph G' that consists of the remaining blocks B2, B3, ..., Bk.

7. G' is still a connected graph, but it may have cut-vertices. However, the removal of B1 does not affect the connectivity between the other blocks, as each block is a maximal connected subgraph.

8. The number of spanning trees of G', denoted as T(G'), can be calculated using the same method as step 5.

9. Since G' is the remaining part of G after removing B1, the number of spanning trees of G can be expressed as T(G) = T(B1) * T(G').

10. We can repeat this process for the remaining blocks B2, B3, ..., Bk. For each block Bi, we remove it from G and calculate the number of spanning trees of the remaining graph.

11. By repeating steps 6-10 for all blocks, we can express the number of spanning trees of G as-

\(T(G) = T(B1) * T(G')\)

\(= T(B1) * T(B2) * T(G'')\)

= ...

\(= T(B1) * T(B2) * ... * T(Bk).\)

12. Therefore, we have proved that the number of spanning trees of a connected graph G is the product of the number of spanning trees of each of its blocks.

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The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Answer:

-4

Step-by-step explanation:

Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{2}{3}\) x + 8 ← is in slope- intercept form

with slope m = - \(\frac{2}{3}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{2}{3} }\) = \(\frac{3}{2}\) , then

y = \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute (- 6, 2 ) into the partial equation

2 = - 9 + c ⇒ c = 2 + 9 = 11

y = \(\frac{3}{2}\) x + 11 ← equation of perpendicular line

Answer:

I miss you

Step-by-step explanation:

Answer:

m∠CAD = 120°

m∠CBA = 30°

Answer:

Can is gonna be 120 and cba is gonna be 30

Step-by-step explanation:

Use 180 - 60 you will get 120 and the sum degree for a triangle is 180, use 180-60-90 you will get an answer for cba

Answer:

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

There are various tips or suggestions on how others can represent real-life situations using rational functions​, one of them is the application of a work problem formula.

By using the work problem formula, one can measure the time it will take different people working at different speeds to complete the work. With the formula w =r*t. Where w = work done, r = rate of work donee, and t = time

One tip or suggestion on how others can represent real life situations using rational functions is;

Modelling the density of an object by the formula; density = mass/volume

Similarly, when looking for average speed travelled by a vehicle, it is given by the formula;

speed = distance/time

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Answer: \(t^8\)

\(\mathrm{Domain\:of\:}\:t^8\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<t<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

\(\mathrm{Range\:of\:}t^8:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(t\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}\)

\(\mathrm{Axis\:interception\:points\:of}\:t^8:\quad \mathrm{X\:Intercepts}:\:\left(0,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:0\right)\)

\(\mathrm{Asymptotes\:of}\:t^8:\quad \mathrm{None}\)

\(\mathrm{Extreme\:Points\:of}\:t^8:\quad \mathrm{Minimum}\left(0,\:0\right)\)

Answer:

y = 0

Step-by-step explanation:

4(y + 3) - 8 = 2(y + 2) ← distribute parenthesis

4y + 12 - 8 = 2y + 4 , that is

4y + 4 = 2y + 4 ( subtract 2y from both sides )

2y + 4 = 4 ( subtract 4 from both sides )

2y = 0 , then

y = 0

For parts 1 and 2, you'll need to find a way to gather these data points, either by measuring them yourself or by asking your friends. Another option is to search out "Census at School", with quotes, and it will lead you to spreadsheets of data on this sort of thing (that some researchers have already done previously).

In short, the answers to parts 1 and 2 will vary depending on what the actual data values you collect. So I'm not much help here in this case.

============================================================

Part 3

Part A

In this case, we have x = 17 as the length of the person's forearm in inches. We'll plug it into the given regression equation to find an estimate of y

y = 0.860x + 3.302

y = 0.860*17 + 3.302

y = 14.62 + 3.302

y = 17.922

The person's foot is approximately 17.922 inches long

Rounding to the nearest whole number, this is approximately 18 inches

Note: 18 inches = 12 in + 6 in = 1 ft, 6 in = 1.5 ft

------------------

Part B

Unfortunately I can't help with this part either because I don't know what data set you're working with. So it all depends on how you do parts 1 and 2.  You shouldn't get the same exact values, but you should get close to the average.

The quantity of purple marbles that Leslie has would be = 32 purple marbles.

The number of bags of marbles that Leslie has = 6 bags.

The quantity of marbles that is found in each bag = 16 marbles.

Therefore the total number of marbles = 6× 16 =96 marbles.

The fraction of purple marbles that Leslie has = 1/3 of 96

Therefore the total number of purple marbles the Leslie have = 1/3× 96 = 32

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Complete question:

Leslie has 6 bags of marbles. Each bag has 16 marbles. If ⅓ of the marbles are purple, how many purple marbles does Leslie have?

Answer:

Step-by-step explanation:

See image

The actual distance between the two cities is 280 miles.

A map's key shows that every of 5 inches on the map represents 200 miles of actual distance. Suppose the distance between two cities on the map is 7 inches. What is the actual distance between the two cities? Write the rule you used to find the actual distance.

The rule used to find the actual distance between the two cities is multiplying the scale factor by the distance on the map.

The scale factor is given as 200 miles for every 5 inches, which means that for every 1 inch on the map, the actual distance is 40 miles. Hence, the actual distance for 7 inches on the map is calculated as follows:

Actual distance = Scale factor × Distance on the map Scale factor = 200 miles / 5 inches = 40 miles per inch distance on the map = 7 inches Actual distance = 40 miles per inch × 7 inches Actual distance = 280 miles

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Step-by-step explanation:

step 1. m: m is the variable, 1 is the coefficient, 1 is the degree, constant is 0.

step 2. 3t^2 +4t - 6: t is the variable, 3 and 4 are the coefficients, 2 is the degree, -6 is the constant.

step 3. 2 - h: h is the variable, -1 is the coefficient, 1 is the degree (highest variable exponent), the constant is 2.

step 4. -7a^2: a is the variable, -7 is the coefficient (before the variable), 2 is the degree, the constant is 0.

Answer:

216

Step-by-step explanation:

36 ÷ 6 x 12 x 3 you mean?

Use the bodmas method to solve this question.

If you need me to reflect on what bodmas is, comment it down.

36 ÷ 6 x 12 x 3 =

6 x 12 x 3 =

72 x 3 = 216

The answer is:

114

Explanation:

Answer:

#1

#2

#3

Given:

Base salary = $1700

Additional salary = $60 for each copy of English Pleasure she sells.

Total wage = P

Number of copies of English is Fun she sells = N

To find:

The equation relating P to N.

Step-by-step explanation:

Let P represent her total wage (in dollars), and N represent the number of copies of English is Fun she sells.

Additional salary = $60N

Base salary = $1700

Total wage = Base salary + Additional salary

\(P=1700+60N\)

Therefore, the required equation is \(P=1700+60N\).

Substitute N=26 to find the gross wage if she sells 26 copies of English is Fun.

\(P=1700+60(26)\)

\(P=1700+1560\)

\(P=3260\)

Therefore, the gross wage if she sells 26 copies of English is Fun is $3260.

Answer:

They both have q+3/2p, so that means that 2PQ=CB and that means they are parallel to each other

Step-by-step explanation:

PQ=PA+QA

PQ=1/2(2q-p)+2/5*5p=q-1/2p+2p=q+3/2p

CB=2q+3p=2(q+3/2p)

Answer:

No it is not a factor

Step-by-step explanation:

Reason for not being a factor is 3x^3-4x^2-4x. 3x3−4x2−4x 3 x 3 - 4 x 2 - 4 x. Factor x x out of 3x3−4x2−4x 3 x 3 - 4 x 2 - 4 x

When a transversal cuts two parallel lines, 8 angles are created.

When two lines do not cross one another, they are said to be parallel. In addition, parallel lines are two lines that cross each other at infinity.

A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.

Corresponding angles are those that are created when two parallel lines and a transversal intersect, also known as matching corners or corresponding corners.

∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

The pair of angles that are created on the outer side of two lines but on the other side of the transversal are known as alternate exterior angles.

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

When a transversal cuts two parallel lines, 8 angles are created.

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∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

Answer:

2 hours

Step-by-step explanation:

Answer:

About 2.5 hours

Step-by-step explanation:

divide 130 by 52 = 2.5

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

(a) Mean The mean (or average) of a dataset is calculated by summing up all the values and dividing by the total number of values.

The formula for calculating the mean is: `mean = (sum of values) / (total number of values)`For the given dataset, we have:20, 50, 22, 14, 23, 10

Sum of values = 20 + 50 + 22 + 14 + 23 + 10 = 139

Total number of values = 6Therefore, the mean is given by: `mean = 139 / 6 = 23.17`Answer: 23.17 (rounded to two decimal places)

(b) Median To find the median, we need to arrange the dataset in increasing order:10, 14, 20, 22, 23, 50The median is the middle value of the dataset. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values. Here, we have 6 values, so the median is the average of the two middle values: `median = (20 + 22) / 2 = 21` Answer: 21(e)

Sample variance s²The sample variance is calculated by finding the mean of the squared differences between each value and the mean of the dataset.

The formula for calculating the sample variance is: `s² = ∑(x - mean)² / (n - 1)`where `∑` means "sum of", `x` is each individual value in the dataset, `mean` is the mean of the dataset, and `n` is the total number of values.For the given dataset, we have already calculated the mean to be 23.17.

Now, we need to calculate the squared differences between each value and the mean:

20 - 23.17 = -3.1722 - 23.17

= -1.170 - 23.17

= -13 - 23.17

= -9.1723 - 23.17

= -0.1710 - 23.17

= -13.17

The sum of the squared differences is given by:

∑(x - mean)² = (-3.17)² + (-1.17)² + (-13.17)² + (-9.17)² + (-0.17)² + (-13.17)²

= 867.7959

Therefore, the sample variance is given by: `s² = 867.7959 / (6 - 1) = 173.5592`Answer: 173.5592 (rounded to four decimal places)

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

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Answer:

Solution given:

2:centroid=\(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\)

=\(\frac{1+3+5}{3},\frac{2+7+3}{3}=(3,4)\)

4:

Slope:\(\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{5-3}=2\)

3;

perpendicular distance =\(\frac{ax_1+by_1+c}{\sqrt{a²+b²}}\)

\((x_1,y_1)=(3,-2)\)

4x-3y+2=0

comparing above equation with ax+by+c =0 ,we get

a=4

b=-3

c=2

d=\(\frac{4*3+(-3*-2)+2}{\sqrt{4²+(-3)²}}\)

=4 units