3. In triangle ABC, 4A is a right angle, and m<B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form.

A. 18 ft.
B. 18√2
C. 18√3
D. 36
what is the answer? thank you​

The average rate of change of P between t = 3 and t = 5 is -18 people/hour.

A possible value of people in line at t = 6, given the average rate of change would be 50.

To find the average rate of change of P between t = 3 and t = 5, we can use the formula:

Average rate of change = (P(5) - P(3)) / (5 - 3)

From the table, we know P(3) = 85 and P(5) = 49.

Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour

To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:

(P(6) - P(3)) / (6 - 3) = (x - 85) / 3

This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:

(P(6) - P(5)) / (6 - 5) = (x - 49) / 1

This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.

So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.

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If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.

a) Yοu will have  yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.

b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.

The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.

Let's first calculate the tοtal number οf mοnths in 20 years:

20 years x 12 mοnths/year = 240 mοnths

a. we can use the fοrmula fοr the future value οf an annuity:

[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]

where:

PMT = the mοnthly payment ($150)

r = the annual interest rate (2.4% οr 0.024)

n = the number οf times the interest is cοmpοunded per year (12)

t = the tοtal number οf years (20)

FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))

FV ≈ $59,073.95

Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.

b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:

Interest = FV - Tοtal amοunt invested

Interest = $59,073.95 - ($150 x 12 x 8 x 12)

Interest ≈ $26,673.95

Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.

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now, if we take a looksie at the denominators on all sides, hmmm 2 and 3, so we can get an LCD of 6, so let's multiply both sides by 6 to do away with the denominators.

[tex]4-\cfrac{x-2}{2}=x+\cfrac{1-2x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( 4-\cfrac{x-2}{2} \right)~~ = ~~6\left( x+\cfrac{1-2x}{3} \right)} \\\\\\ 24-3(x-2)~~ = ~~6x+2(1-2x)\implies 24-3x+6~~ = ~~6x+2-4x \\\\\\ 30-3x=2x+2\implies 30=5x+2\implies 28=5x\implies \cfrac{28}{5}=x\implies 5\frac{3}{5}=x[/tex]

The polynomial expression that represents the area of the given square is: 4x² + 28x + 49

The formula for the area of a square is expressed as:

Area = side * side

Now, we are given the dimensions of the square and we have:

Side length = x + 7 + x = 2x + 7

Thus:

Area of square = (2x + 7) * (2x + 7)

= 4x² + 14x + 14x + 49

= 4x² + 28x + 49

Thus, we conclude that expression represents the area of the square.

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Short Answers:

a)N*tan(Θ)

b)arctan(h/N)

c)N*tan(A)

Let * stand for multiplication

Hope this is helpful to someone:)

The radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

Radius is a line segment that extends from the center of a circle or sphere to its circumference. It is the distance from the center to the edge of the circle or sphere. It is also used to measure the length of an arc of a circle. Radius is a necessary measure when calculating the area of a circle or sphere, as well as the volume of a sphere.

The arc length of a semicircle is given by the formula s = πr,
where r is the radius of the semicircle. In this case,
we are given the radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

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The arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

What is an arc?

An arc is part of a circle's circumference. It is a segment of a curved line that is formed when a straight line intersects a circle or a curved shape. Arcs can be measured in length, angle, or radius, depending on the context.

To find the arc length of a semicircle, we need to know the radius of the circle and the angle subtended by the arc at the center of the circle.

Let's assume the radius of the semicircle is 'r'. Since it is a semicircle, the angle subtended by the arc at the center of the circle is 180 degrees or π radians.

The formula for arc length is given by:

arc length = radius x angle in radians

In this case, the angle is π radians and the radius is 'r'. Therefore, the arc length of the semicircle is:

arc length = r x π

We can leave the answer in terms of π or substitute the value of π to get a numerical answer. For example, if the radius of the semicircle is 4 units, the arc length will be:

arc length = 4 x π

arc length ≈ 12.57 units (using π ≈ 3.14)

Therefore, the arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

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Answer: 36 inches

Step-by-step explanation:

The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.

The range of resting heart rates is 70 beats per minute. Subtracting the lowest value from the highest value will give us the range.

It is a set of data which is the difference between the highest and lowest values.

The range of resting heart rates, in beats per minute, is calculated by subtracting the minimum value of the data set from the maximum value. In this case, the minimum value = 35

and the maximum value = 105,

so the range of resting heart rates = 105 - 35

= 70 beats per minute

The other answers cannot be the range of the resting heart rates because they are not calculated correctly.

The answer 16 beats per minute (105 - 89 = 16) is the difference between the maximum and the 90th percentile, and the answer 31 beats per minute (85 - 54 = 31) is the difference between the 85th percentile and the median.

The answer 62 beats per minute (95 - 33 = 62) is the difference between the 95th percentile and the minimum.

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Question:

Answer:

Step-by-step explanation:

first graph

y = 5x + 2

2 = y-intercept

5 = slope

the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1

second graph:

y = 2x + 3

third graph:

y = 3x + 3

Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.

If each bird house requires 1/4 pounds of nails and Rieko has 15 pounds of nails, we can use the following equation to determine the number of bird houses she can make:

number of bird houses = amount of nails / amount of nails per bird house

Plugging in the given values, we get:

number of bird houses = 15 / (1/4)

Simplifying the right-hand side by dividing 15 by 1/4, we get:

number of bird houses = 60

Therefore, Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.

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The value of k for this line is equal to -6.

In Mathematics and Geometry, the gradient of any straight line is also referred to as slope and it can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

2 = (-14 - k)/(k + 2)

-14 - k = 2(k + 2)

-14 - k = 2k + 4

-14 - 4= 2k + k

3k = -18

k= -18/3

k = -6

In this context, we can reasonably infer and logically deduce that the value of k is equal to -6.

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Complete Question:

The gradient of the line joining the points (-2,k) and (k, -14) is 2 . Calculate the value of k.

Answer:

a

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n[/tex]  a₁ + (n - 1)d

here a₁ = [tex]\frac{3}{5}[/tex] and d = - [tex]\frac{1}{3}[/tex] , then

a₂₁ = [tex]\frac{3}{5}[/tex] + (20 × - [tex]\frac{1}{3}[/tex] )

    = [tex]\frac{3}{5}[/tex] - [tex]\frac{20}{3}[/tex]

    = 0.6 - 6.67

   = - 6.07 ( to 2 decimal places )

We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.

A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.

The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:

ln(W) = ln(2.4) + 1.84h

We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.

First, we need tο calculate the weight at h = 1 m and h = 1.1 m.

At h = 1 m, we have:

ln(W1) = ln(2.4) + 1.84(1)

ln(W1) = ln(2.4) + 1.84

ln(W1) ≈ 2.684

Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.

Similarly, at h = 1.1 m, we have:

ln(W2) = ln(2.4) + 1.84(1.1)

ln(W2) = ln(2.4) + 2.024

ln(W2) ≈ 2.807

Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.

Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:

dln(W) = 1.84dh

Using differentials, we can apprοximate the change in weight as:

dW ≈ W2 - W1

dW ≈ e².807 - e².684

dW ≈ 1.93 kg

Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.

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Answer:

Spinning Swings

10 more riders

Step-by-step explanation:

To find which ride will have more riders each hour, we need to first convert an hour into minutes.

[tex]\text{1 hour = 60 minutes}[/tex]

Now we let's first find how many riders there will be in the race cars.

So there are 25 riders every 30 minutes.

in 60 minutes there will be:

[tex]25 \times 2 = 50 \ \text{Riders}[/tex]

Now for the spinning swings there are 20 riders every 20 minutes.

In 60 minutes there will be:

[tex]20 \times 3 = 60 \ \text{Riders}[/tex]

Therefore, the spinning swings will have more riders as [tex]60 > 50[/tex].

Now to find how many more riders there will be in the spinning swings.

We simply subtract the total number of riders of each ride from each other.

[tex]\text{Race Cars = 50}[/tex]

[tex]\text{Spinning Swings = 60}[/tex]

[tex]60 - 50 = 10[/tex]

There will be 10 more riders in the spinning cups than the race cars.

The inventory cost under:

a. First-in, first-out (FIFO) - $326.

b. Last-in, first-out (LIFO) - $289.

c. Weighted average cost - $308.

a. Calculation of inventory cost using the First-in, First-out (FIFO) method:

There are 11 units of the item in the physical inventory on December 31. Under FIF7 units will be from items purchased on Nov 30 and 4 units will be from items purchased on Aug 13.

( 7 units * 30) + (4 units *29)

= 210 + 116 = $326

b. Calculation of inventory cost using the Last-in, First-out (LIFO) method:

There are 11 units of the item in the physical inventory on December 31. Under LIFO Method, 10 units will be from items purchased on Jan 1 and 1 unit will be from items purchased on Aug 13.

10 units * 26 + (1 unit * 29)

= $289

c. Calculation of Weighted Average cost per unit:

$644/23 units

=$28 per unit

Calculation of inventory cost using the Weighted Average Cost method:

11 units * 28

= $308

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Step-by-step explanation:

First = x

second = x + 2

third = x + 4

3 * x   =  2 ( x+4)

3x = 2x+ 8

x = 8              8   10  and 12

The ratio of the shaded area to the unshaded area in the figure is 1 : 5.5 which can be calculated by adding the areas of the two squares and triangle EDH.

Area is the amount of two-dimensional space taken up by a shape or object. It is measured in square units, such as square centimeters, square meters, or square miles.

The ratio of the shaded area to the unshaded area in the figure can be calculated by adding the areas of the two squares and triangle EDH, and then subtracting the shaded area.

First, calculate the total area of the figure:

Area of the two squares = (BC)²

= (CD)²

= (4)²

= 16

Area of triangle EDH = ½ x BC x DH

= ½ x 4 x 5

= 10

Total area = 16 + 10

= 26

Next, calculate the shaded area:

Shaded area of square CDEF = 25% x 16

= 4

Total shaded area = 4

Finally, calculate the ratio of the shaded area to the unshaded area in the figure:

Unshaded area = 26 - 4

= 22

Ratio of the shaded area to the unshaded area = 4 : 22

= 1 : 5.5

Therefore, the ratio of the shaded area to the unshaded area in the figure is 1 : 5.5.

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Question:

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

In the figure, the proportion of shaded to unshaded region is 1:5.5.

The area of the shaded region is the difference between the area of the entire polygon as well as the area of the polygon's unshaded part. In polygons, the area of the shaded portion can occur in two ways. The shaded area can be found in the centre of a polygon or on its sides.

As previously stated, the area of the shaded region is determined by subtracting the area of a complete polygon from the area of the unshaded region.

outer shape region – area of the interior unshaded shape = The shaded area

To begin, compute the entire area of the figure:

Area of the two squares [tex]=(BC)^2[/tex]

[tex]=(CD)^2\\\\=(4)^2\\\\=16[/tex]

Area of the EDH triangular [tex]=\frac{1}{2} \times BC\times DH[/tex]

Substitute values in the above equation

[tex]=\frac{1}{2} \times 4\times 5\\\\=10[/tex]

Total area = 16 + 10

                 = 26

The shaded region is then calculated as follows:

CDEF square shaded region = 25% x 16

                                                = 4

Total shaded area = 4

Finally, compute the shaded-to-unshaded area ratio in the figure:

Unshaded area = 26 - 4

= 22

Shaded to unshaded region ratio = 4 : 22

= 1 : 5.5

As a result, the shaded area to unshaded area ratio in the image is 1: 5.5.

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The complete question is,

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

Answer:

Approx. 4.47

Step-by-step explanation:

To calculate the standard deviation for the data, we need to follow these steps:

1. Calculate the mean (average) of the data:

mean = (13 + 17 + 9 + 21) / 4 = 15

2. Calculate the difference between each data point and the mean:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

3. Square each difference:

(-2)^2 = 4

2^2 = 4

(-6)^2 = 36

6^2 = 36

4. Calculate the variance by taking the average of the squared differences:

variance = (4 + 4 + 36 + 36) / 4 = 20

5. Calculate the standard deviation by taking the square root of the variance:

standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47

Therefore, the standard deviation for the data is approximately 4.47.

Answer:

4.5 cm.

Step-by-step explanation:

Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.

HOPE IT HELP YOU

The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.

The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.

The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.

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The correct answers are: To determine the consumer's eligibility for credit and  To set pricing for credit lines.

what is pricing?

"Pricing" refers to the process of determining the value or cost of a product or service and setting a specific price for it. Pricing decisions involve taking into account various factors such as production costs, market demand, competition, and profit margins, among others. Pricing can also involve setting

In the given question,

Based on section 1.3.2, Credit scores, on page 22 of the report, the two purposes for which credit card issuers use credit scores are:

To determine the consumer's eligibility for credit.

To set pricing for credit lines.

Therefore, the correct answers are:

To determine the consumer's eligibility for credit

To set pricing for credit lines

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Answer:  y = x + 6

Step-by-step explanation: "y = m x + b" is the format used to find the equation of a line on a graph.

Y and X remain the same in the equation, however you replace "m" with the value of the slope. In this problem, the slope is "1" because the rise is 1 and the run is 1, making it 1/1 or 1. Because the slope is "1", we do not need to include the number "1" in our equation.

Finally, "b" is the y-intercept (in other words, the place where the line crosses the y-axis). In this problem, the line crosses at "6"; therefore, 6 will replace b in the equation completing it.

The sum of the digits of the product p×q is 8

A positive integer bigger than one that can be divided only by itself and by one is referred to as a prime number.

Given that: p³ - pq² = 42024

p (p² - q²) = 42024

Since factors, 42024 = 2³ x 3 x 17 x 103, and p and q are prime numbers, we can see that p must be 3, 17 or 103, We can try each case:

If p = 3 then we have:

3 (9 - q²) = 42024

q² = -13,999

This equation has no real solutions for q, so p cannot be 3.

If p = 17, then we have:

17 (289 - q²) = 42024

q² = -2183

This equation also has no real solutions for q, so p cannot be 17 either.

If p = 103, then we have:

103 (10609 - q²) = 42024

10609 - q² = 408

q² = 10201

q = 101

This equation also has a solution for q = 101, so p = 103

Product of pq = 103×101 = 10403

So, the sum of the digits of the product pq = 1+0+4+0+3 = 8

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Answer:

1)$15000

2)0.55%

3)0.55

4)3

5)24.75

Step-by-step explanation:

5)1500×0.55×3/100

An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]

In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

Generally speaking, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number, we have the following:

[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]

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Solving the quadratic equation, we get the maximum profit is 2451 thousand dollars.

A second-degree algebraic equation in x is known as a quadratic equation. The quadratic equation is written as Ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

For an equation to be categorised as a quadratic equation, the coefficient of x2 must be a non-zero term (a 0).

The function is given as

P(q) = -0.01q2 +5q-39

We have

P(q) = -0.01q2 +5q-39

Differentiate

So, we have

P'(q) = -0.01q + 5

Set to 0

So, we have

-0.01q + 5

This gives:

-0.01q = -5

Evaluate

q = 500

Hence, 500 thousand pairs of sunglasses should be sold to maximize profits.

What is the maximum profit?

In (a), we have

q = 500

This gives:

P (500) = (-0.01)500×2 +5×500-39

Evaluating:

P (500) = -10 + 2500 -39

= 2451

Hence, the maximum profit is 2451 thousand dollars.

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When we solve the quadratic equation, we discover that the utmost profit is $2451 thousand dollars.

A quadratic equation is an x-dependent second-degree algebraic problem. [tex]ax^{2} +bx+c=0[/tex], where x is the variable, a and b are the coefficients, and c is the constant element, is how the quadratic equation is expressed.

The coefficient of [tex]x^{2}[/tex] must not be negative for an equation to be categorized as a quadratic equation (a, 0).

The function is given as

P(q) = [tex]-0.01q^2[/tex] +5q-39

We have

P(q) = [tex]-0.01q^2[/tex] +5q-39

Differentiate

So, we have

P'(q) = -0.01q + 5

Set to 0

So, we have

-0.01q + 5

This gives:

-0.01q = -5

Evaluate

q = 500

So, in order to make the most money 500 000 sets of sunglasses should be sold.

In (a), we have

q = 500

This gives:

P (500) = (-0.01)500×2 +5×500-39

Evaluating:

P (500) = -10 + 2500 -39

= 2451

Therefore, the highest profit is $2451 thousand dollars.

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The complete table that shows the proportional relationship is:

x                                 y

0.8                             4

3.2                             16

12.8                            64

The ratio of the given y-value and x-value is calculated as:

y/x = 4/0.8 = 5

Thus, the ratio of the next terms must all be 5.

The second x coordinate is 3.2. Thus:

y/3.2 = 5

y = 3.2 * 5

y = 16

Difference of the first 2 x-values = 3.2 - 0.8 = 2.4

Thus, the third value of x will be:

3.2 + 2.4 = 5.6

Thus, the third y-coordinate = 5.6 * 5 = 28

Similarly, the fourth value of x will be:

5.6 + 2.4 = 8.0

Thus, the fourth y-coordinate = 8 * 5 = 40

The sixth value of x will be:

8 + 2.4 + 2.4 = 12.8

Sixth value of y = 12.8 * 5 = 64

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Complete question is:

Drag numbers to the table so it shows a proportional relationship between x and y.

Tiles : 8.8 , 12.8 , 5.6 , 64 , 6.4 , 16

X axis Y axis

0.8.      4

3.2       ?

?           ?

he is literally hitting the gritty