To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 40°. From a point that is 350 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 53°. If we assume that the street is level, use this information to estimate the height of the building. The height of the building is ____

The value of x, y, z is -18000/83, -30000/83, 297000/83 respectively.

This problem is solve by substitution method.

what is substitution method?

Substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given,

x+y+z=3000

5x−3y=0

x−10.5y−z=0

Solve x+y+z=3000 for x.

x=−y−z+3000

Substitute −y−z+3000 for x in the second and third equation.

5(−y−z+3000)−3y=0

−y−z+3000−10.5y−z=0

Solve these equations for y and z respectively.

y=1875−5/8z

z=1500-23/4y

Substitute 1875−5/8z for y in the equation z=1500−23/4y

​z=1500−23/4(1875-5/8z)

z= 297000/83

put this value in y = 1875- 5/8z

y= -30000/83

substitute the value of y and z in equation one

x= -18000/83

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e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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The product of the perpendicular lines is a negative one. Then the value of p will be negative 3.75.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Given the points K(-2,5), L(1,3) and M(-5, 2p).

If KL is perpendicular to LM. Then we have

The slope of KL will be

KL = (1+2)/(3-5)

KL = -1.5

The slope of LM will be

LM = (1+6)/(3-2p)

LM = 7/(3-2p)

We know the product of the perpendicular lines is a negative one.

        KL x ML = -1

-1.5 x 7/(3-2p) = -1

              -10.5 = -3 + 2p

                 2p = -7.5

                   p = -3.75

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In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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Step-by-step explanation:

In a one-tailed hypothesis test with a significance level of 0.05, the rejection region depends on the specific alternative hypothesis being tested.

If the alternative hypothesis is one-tailed and states a direction of effect (e.g., greater than or less than), the rejection region will be either in the upper or lower tail of the distribution, but not both.

For a one-tailed hypothesis test with a significance level of 0.05, the rejection region will be either the upper 5% of the distribution or the lower 5% of the distribution, depending on the direction of the alternative hypothesis.

So, the correct answer is:

A) the upper 5% of the distribution if the alternative hypothesis is stating a greater-than effect.

or

B) the lower 5% of the distribution if the alternative hypothesis is stating a less-than effect

Answer:

slope = -1/4

Step-by-step explanation:

(-2,5) to (-1,1)

Answer:

3.75 packs

Step-by-step explanation:

15/4=3.75 packs

Answer:

D 3^3 *3^-7

Step-by-step explanation:

1/27 = 1/3^3 = 3^-3

When multiplying with the same base, add the exponents

A 3^1 * 3^-10  = 3^-9

B 3^-1 * 3^10 = 3^9

C 3^-4 * 3^7 = 3^3

D 3^3 *3^-7 = 3^-3

Answer:

4. 7 hours   6. 8.57

Step-by-step explanation:

Step-by-step explanation:

Since, Carlos completes the work in 5 hours.

So, in one hour she will do \( =\frac{1}{5}\) part

Since, Jenny completes the work in 9 hours.

So, in one hour she will do \( =\frac{1}{9}\) part

(Carlos + Jenny)'s one hour work together

\( =\frac{1}{5}+\frac{1}{9}\\

= \frac{9+5}{5\times 9}\\

= \frac{14}{45}\\\)

Total time taken by Carlos and Jenny together \( =\frac{45}{14}= 3\frac{3}{14} \: hours\)

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.

The formula is:

r = (1 + i/n)^n - 1

Where:

r is the nominal interest rate compounded annually (we're looking for this),

i is the nominal interest rate compounded quarterly (2.50% in this case),

n is the number of compounding periods per year (4 for quarterly compounding).

Plugging in the values, we have:

r = (1 + 0.025/4)^4 - 1

Calculating this expression, we find:

r ≈ 0.025335

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

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Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

Answer: 41.86 miles/hour

Step-by-step explanation:

Use Distance = Speed*Time to find the two missing values with the data that is provided for those two cases [in brackets].

MPH MILES     HOURS

 50            20      [0.4]

 [40]    70      1.75

Totals   90 miles   2.15 hours

Average = 90 miles/2.15 hours

     41.86 mph

Answer:

  78 square feet

Step-by-step explanation:

You want the surface area of a rectangular prism 1 ft high by 4 ft long and 7 ft wide.

The surface area is given by ...

  SA = 2(LW +H(L +W))

  SA = 2(4·7 +1(4 +7)) = 2(28 +11) = 78 . . . . square feet

The surface area of the prism is 78 square feet.

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The probability that a male college student gains between 0 kg and 3 kg during freshman year is 0.3047, rounded to four decimal places.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is a way of quantifying uncertainty and predicting the outcomes of random processes or experiments.

a) To find the probability that a male college student gains between 0 kg and 3 kg during freshman year, we need to find the area under the normal curve between the z-scores corresponding to these values. Then, we must use the formula to standardise the values:

z = (x - u) / a

where x is the value we are interested in, u is the mean, and a is the standard deviation.

For x = 0 kg:

z = (0 - 1.3) / 4.7 = -0.2766

For x = 3 kg:

z = (3 - 1.3) / 4.7 = 0.3617

Using a standard normal distribution table or calculator, we can find the area under the curve between these z-scores, which is:

P(-0.2766 < z < 0.3617) = 0.3047

Therefore, the probability that a male college student gains between 0 kg and 3 kg during freshman year is 0.3047, rounded to four decimal places.

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If M is the midpoint of CD, then the  is cos ABM = 8 / (235) sqrt

The Platonic solid known as the regular tetrahedron has four polyhedron vertices, six polyhedron edges, and four equal equilateral triangular faces. It is frequently referred to as "the" tetrahedron. Also included are the Wenninger model and uniform polyhedron.

1: According to a rule of trigonometry, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that much of the product of those sides and the cosine of the angle between them.

To make things easier, set the tetrahedron's side equal to 1.

A  = ( -1/2 , 0 , 0)

B  = ( 1/2, 0, 0  )

C =  (0, sqrt (3)/2, 0)

D =  (0, sqrt (3)/4 , 6/sqrt (3) )

M =  (0 , (3/8) sqrt (3) , 3/sqrt (3) )  =  (0, (3/8)sqrt (3) , sqrt (3) )

AB  = 1

AM = BM   =  sqrt   [ (-1/2)^2  + (3sqrt (3) / 8)^2  + (sqrt 3)^2   =  sqrt [ 1/4 + 27/64 + 3 ]   = sqrt (235) / 8

By the Law of Cosines

AM^2  =  AB^2 + BM^2 - 2 (AB) (BM)cos (ABM)

0 = 1 - 2 (1) (235 squared / 8) cos ABM

0 = 1 - [sqrt ( 235) / 8] since ABM

cos ABM = -1 / - [ sqrt (235) / 8]

8 / (235) sqrt = cos ABM

If M is the midpoint of CD, then the  is cos ABM = 8 / (235) sqrt

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Answer:

9:14

Step-by-step explanation:

Amount invested by Danny is R 2 700

Amount invested by Refilwe is R 4 200

Ratio of investments = 2700:4200 = 9:14

Answer:

1/5

Step-by-step explanation:

1/7 * x = 1/35    multiply both sides by 7

x = 7/35 = 1/5

Answer:      a. 8.4 meters       b. 14 wreaths

Step-by-step explanation:

The following equation shows the problem, with x representing the number of wreaths made:

12 = 9(0.4) + 0.6x

To answer a, get 0.6x alone:

12 = 9(0.4) + 0.6x

12 = 3.6 + 0.6x

8.4 = 0.6x

There were 8.4 meters available to make wreaths

To answer b, get x alone

8.4 = 0.6x

14 = x

Diego could make 14 wreaths with the available ribbon

Hope this helps!

The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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Answer:

I do not understand what are you saying

Answer:

???

Step-by-step explanation:

The episode with commercials consists of 60 minutes, and without those, it consists of 41.5minutes; therefore, 60-41.5=18.5 minutes are only commercials when the episode airs.

Divide those 18.5minutes into intervals of 0.5 minutes by calculating

Therefore, the equation is

Solving for c,

Then, the episode included 37 1/2-minute commercials.

The most appropriate statement to describe the comparison of spreads between Town A and Town B is that the IQR for Town A, 20°, is greater than the IQR for Town B, 10°. This suggests that Town A experiences a wider range of temperature fluctuations within the middle 50% of the data compared to Town B.

Based on the provided box plots, the most appropriate comparison of the spreads between Town A and Town B is that the interquartile range (IQR) for Town A, 20°, is greater than the IQR for Town B, 10°. The IQR is a measure of the spread of the middle 50% of the data.

In Town A, the box extends from approximately 15°F to 35°F, indicating that the middle 50% of the data falls within this range. The whiskers extend from the box to the minimum and maximum values, which are approximately 0°F and 45°F, respectively.

The IQR is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1), which in this case is 35°F - 15°F = 20°F.

On the other hand, in Town B, the box ranges from approximately 15°F to 30°F, representing the middle 50% of the data. The whiskers extend from the box to the minimum and maximum values, which are approximately 5°F and 58°F, respectively. The IQR for Town B is calculated as 30°F - 20°F = 10°F.

Comparing the IQRs, we observe that the IQR for Town A (20°F) is greater than the IQR for Town B (10°F). This indicates that there is more variability in the daily low temperatures in Town A compared to Town B within the middle 50% of the data.

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D: C(25, 20) - C(13,7)  represents the number of ways a total inventory of twenty batteries be distributed among the six different types.

To find the total number of ways to distribute the twenty batteries among the six different types, we need to use the stars and bars method. Using this method, the number of ways to distribute 20 batteries among 6 different types is C(20 + 6 - 1, 6 - 1) = C(25, 5).

However, since we have only 12 A7b batteries, we need to subtract the cases where we distribute more than 12 A7b batteries. To do this, we calculate the number of ways to distribute the remaining 8 batteries among the 5 types other than A7b, which is C(8+5-1, 5-1) = C(12,4). Therefore, the total number of ways to distribute 20 batteries among the six different types while keeping at least 12 A7b batteries is C(25, 5) - C(12, 4) = C(25, 20) - C(13, 7).

The correct answer is option D.

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Answer:

2in

Step-by-step explanation:

Since we are not given the type of polygon, let the polygon be an hexagon. An hexagon is a 6 sides shape. The perimeter of the shape will be the sum of all the sides of the polygon

Perimeter of the polygon = 6L

Length is the length of the side

Given

Perimeter of the polygon = 12in

Substitute and get L

P = 6L

12 = 6L

L = 12/6

L = 2in

Hence the length of side x of the polygon is 2in

The number of contractions performed before the randomized min cut algorithm terminates in a connected graph G with 100 vertices, each of degree 10, and 500 edges is not deterministic and can vary.

The randomized min cut algorithm, also known as the Karger's algorithm, works by repeatedly contracting randomly chosen edges until two super vertices remain, representing the two merged components. The algorithm terminates when there are only two vertices left in the graph. In this case, the graph G has 100 vertices, each with degree 10, which means it has a total of 500 edges. During each contraction step, an edge is chosen uniformly at random and contracted. Since there are 500 edges in the graph, the algorithm will perform a maximum of 500 contractions before terminating. However, it's important to note that the actual number of contractions performed can be much lower than the maximum. The algorithm's termination depends on the random choices made during the contraction steps, and it is possible to find the min cut with significantly fewer contractions. The expected number of contractions required to find the min cut in a connected graph is typically much smaller than the number of edges.

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When a research hypothesis does not predict the direction of a relationship, the test is typically two-tailed.

A two-tailed hypothesis is used when there is no specific prediction about

the direction of the relationship between variables.

It simply states that there is a relationship between the variables being

studied, but does not specify whether the relationship will be positive or

negative.

In contrast, a one-tailed hypothesis predicts the direction of the

relationship (i.e. positive or negative) and is used when there is a clear

expectation about the direction of the effect. A direct positive hypothesis

predicts a positive relationship between variables.

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