A spotlight is mounted on the eaves of a house 24 feet above the ground. A flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 7 feet. How long a ladder is needed so that an electrician can reach the place where the light is mounted?

The percent of adult American males could enter this contest is 2.23%

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

We solve using z score formula

z = (x-μ)/σ,

where, x is the raw score = < 64 inches

μ is the population mean = 69

σ is the population standard deviation = 2.5

Here Participants must be less than 64 inches tall.

For x < 64 inches

z = 64 - 69/2.5

z = -2

Probability value from Z-Table:

P(x<64) = 0.02275

Converting to percentage;

= 0.02275 × 100

= 2.275%

Approximately = 2.23%

The participants must be less than 64 inches tall to participate in this limbo contest, the percent of adult American males thag could enter this contest is 2.23%

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Answer:c

Step-by-step explanation:

Answer:

48 units squared

Step-by-step explanation:

You can find the number of squares in each sector by multiplying by the width and height.

So we have 4 boxes that have 10 squares each giving us 40 squares for the 4 boxes plus the other 2 boxes that have 4 squares each.

4 * 10 + 2 * 4 = 48

We get 48 inches squared.

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Answer:

Step-by-step explanation:

\((\stackrel{x_1}{-19}~,~\stackrel{y_1}{17})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{17}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-19)}) \implies y -17 = - 1 ( x +19) \\\\\\ y-17=-x-19\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}\)

Answer:

y = -x - 2

Step-by-step explanation:

We are given that a line has a slope (m) of -1 and passes through (-19,17).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name

As we are already given the slope of the line, we can plug it into the equation.

Replace m with -1.

y = -1x + b

This can be rewritten to:

y = -x + b

Now, we need to find b.

As the equation passes through (-19,17), we can use its values to help solve for b.

Substitute -19 as x and 17 as y.

17 = -(-19) + b

17 = 19 + b

Subtract 19 from both sides.

-2 = b

Substitute -2 as b into the equation.

y = -x - 2

Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

\(\frac{14}{2}\) [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

A uniform distribution is where the different possible values occur with approximately the same frequency.

In a uniform distribution, each possible value within a given range has an equal probability of occurring. This means that the frequencies of different values are approximately the same. The uniform distribution is characterized by a constant probability density function (PDF) over the range of possible values.

For example, if we consider a fair six-sided die, each face has an equal chance of being rolled, and therefore, the distribution of outcomes is uniform. The probability of rolling any specific number from 1 to 6 is 1/6, and all these probabilities are the same.

In a uniform distribution, there are no peaks or troughs, and the distribution is characterized by a flat and constant shape. This is in contrast to other distributions such as the normal distribution or the exponential distribution, where the probabilities are not evenly distributed and certain values are more likely to occur than others.

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Answer:

x = -1 and y = 3     x = 3 and y = -1

Step-by-step explanation:

The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

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The measure of the angles 2 and 3 are 70°

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

Given, angle 1 = 40°

and, angle 2 = angle 3 = x

In a triangle, sum of angles = 180°

or, m∠1 + m∠2 + m∠3 = 180°

or, 2x = 180-40

or, 2x = 140

or, x = 140/2 = 70°

Hence, the measure of the angles 2 and 3 are 70°

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Answer:

x = 12/5

Step-by-step explanation:

take the square of both sides

(x^2+49) = (x+5)^2

x^2 + 49 = (x+5) (x+5)

x^2+49= x^2 + 10x + 25

10x + 25 = 49

10x = 24

x = 12/5

Answer:

x>10

or

5x+25>75

Step-by-step explanation:

Answer:

25 + 5x > 75

Step-by-step explanation:

Let x be the number of puzzles Francis needs to solve to advance to the next round.

25 points + (No. of rounds × Points per round) is more than 75 points.

25 points: 25

(No. of rounds × Points per round): 5x

is more than: >

75 points: 75

25 points + (No. of rounds × Points per round) is more than 75 points:

25 + 5x > 75

Answer:

12 ft

Step-by-step explanation:

Write and solve an equation of ratios:

 6 ft        4 ft

-------- = --------

 18 ft        w

Cross multiplying, we get:  6w = 72 ft^2, so w = 12 ft

Answer:

12ft

Step-by-step explanation:

Since a 4ft pole casts a 6ft long shadow that means for every 2ft of height the shadow is 3ft. Now the shadow is 18ft long so you do 18 / 3 = 6. To find the walls height you do 6 * 2 = 24.

Answer:

d.

Step-by-step explanation:

i looked at the graph!

The most efficient method to see the input area and summary statistics is to use the split command.

It should be noted that statistics is the branch of mathematics that deals with data collection, organization, and presentation.

In this case, the most efficient method to see the input area and summary statistics is to use the split command and adjust one pane to see the input section and another pane to see the summary statistics.

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Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

Answer:

I also think there is 4 terms

8x and 4x4 and 3x2 and 8

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

Given the data in the question;

A bisector divides a line or angle into two equal halves.

Hence

Segment JM = Segment MK

7x + 5 = 8x

Solve for x

8x - 7x = 5

x = 5

Now, numerical value of segment JM will be;

Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40

Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80

Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

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Answer:

I think it's 12 my bad if it's wrong

You are writing an article for your school newspaper about the Oakland Athletics.  Season tickets go on sale next week and you have been assigned to write an article to help fans determine whether they should buy season tickets or single-game tickets based on their expected attendance at the games this season.

Buying a season ticket allows you to attend all 81 home games for a single price.  Without a season ticket you have to pay for every single game that you attend.

Image result for Oakland Athletics Tickets Box Office

The table shows different ticket price options.

In this task you will answer six questions about the ticket price options and recommend which is best for fans. Be sure to show all your work for each item.

1. A season has 81 home games. If you purchase a season ticket in the bleacher section , what is the cost per game, in dollars for this ticket?

.2. Complete the table based on the single game ticket for seats in the Left field reserve section.

Step-by-step explanation:

The key role for CPS is to minimize stigma and be an ambassador for recovery. Describe a situation where you had to confront stigma

The critical points occur at x = 0, π, 2π, 3π, and so on, and the function is increasing in the intervals (0, π), (2π, 3π), and so on, and decreasing in the intervals (-∞, 0), (π, 2π), and so on.

To find the critical points of the function f(x) = -4e * cos(x), we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of f(x) with respect to x, we have:

f'(x) = -4e * (-sin(x)) = 4e * sin(x)

Setting f'(x) equal to zero, we get:

4e * sin(x) = 0

sin(x) = 0

The sine function is equal to zero at x = 0, π, 2π, 3π, and so on.

Now, let's examine the intervals between these critical points.

In the interval (-∞, 0), the sign of f'(x) is negative since sin(x) is negative in this range. This means that the function is decreasing.

In the interval (0, π), the sign of f'(x) is positive since sin(x) is positive in this range. This means that the function is increasing.

In the interval (π, 2π), the sign of f'(x) is negative again, so the function is decreasing.

We can continue this pattern for subsequent intervals.

Therefore, the critical points occur at x = 0, π, 2π, 3π, and so on, and the function is increasing in the intervals (0, π), (2π, 3π), and so on, and decreasing in the intervals (-∞, 0), (π, 2π), and so on.

Since the function alternates between increasing and decreasing at the critical points, we cannot determine whether they correspond to local minimum or maximum points using only the first derivative test. Additional information, such as the behavior of the second derivative or evaluating the function at those points, is needed to make such determinations.

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Answer:

A

Step-by-step explanation:

37 is greater than 9

In  Arithmetic Progression , 56 inches of snowfall will cause the snowplow to be immobile.

What is Arithmetic Progression in math?

Let x inches of snowfall will cause the showplow to be immobile .

By a.p. formula ,

                aₙ = a + ( n - 1) d

                 aₙ= 0 ( show plow's speed is 0 ,miles/hour )

              a = 39

              n = x inches

             d = - 2.5 mile/hour

         0 = 39 + ( n - 1 ) ( -2.5)

            ( n - 1 ) ( -2.5) = -39

              n- 1 = -39/2.5 = 15.6

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As the probabilities of random variables are negative so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.

The rules of the "numbers" game are simple: a player selects a three-digit number between 000 and 999. Anyone who picks the winning number receives a payout equal to 600 times their original wager. The winning number is decided by a publicly disclosed source. The majority of bets were for $1 or less, and frequently.

A permutation is an arrangement (or ordering) of a collection of items. (We can also arrange only some of the objects in the set.) The arrangement of the objects in a permutation depends on their order.

The random variable-0.499/1000

The random variable "winning" are $1 and $600.

and their probabilities are 999/1000 and 1/1000, respectively.

The expected "winnings" are calculated as follows:

=(999/1000)(-1)+(1/1000)(500)

=-0.499/1000

=-0.499 cents

so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

The explicit formula to represent the given  situation is

Explicit: pn = 14 + 9*n

Here we want to express the number of pizza delivered. Lets try to understand the case.

If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:

p1 = 14 + 9 = 23

If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:

p2 = 14 + 9 + 9 = 14 + 2*9 = 32

If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:

p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41

Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:

pn = 14 + 9*n

But we can separate the last equation in such a way:

pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n

But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:

pn = pn-1 + 9

We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in  9*(n-2) + 9*2,  9*(n-3) + 9*3, ...,  9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.

Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.

So, we have:

Recursive: pn = pn-1 + 9

Explicit: pn = 14 + 9*n

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Answer:

5 ( or ) - 5

Step-by-step explanation:

12/3 = 4

240/4 = 60

m² + 35 = 60

m² = 60 - 35

m² = 25

m = - 5 ( or ) 5

Because,

( - 5 )² = - 5 * - 5 = 25

5² = 5 * 5 = 25