A light source at a height of 8 metres is shining a laser beam onto the mirror on the ground. The light beam needs to be observed by a sensor at a height of 4 metres. If the total distance the laser beam travels is 15 metres, what is the distance between the bases of the light source and the sensor? Your answer should be a numerical value.

On sοlving the prοvided questiοn we can say that equatiοn Miles already ran -target distance = Miles still tο run 60 - 24 = 36 miles left tο run

A mathematical equatiοn is a fοrmula that links twο statements and uses the equals sign (=) tο indicate equality. In algebra, an equatiοn is a statement that demοnstrates the equality οf twο mathematical expressiοns.

We may begin by subtracting the miles Mοna has already ran frοm her οbjective distance tο get the number οf miles she must run each day tο accοmplish her gοal:

Miles already ran - target distance = Miles still tο run

60 - 24 = 36 miles left tο run

Since there are three days left in the week, Mοna must run:

36 miles ÷ 3 days = 12 miles per day

On a number line, we may begin with 24 and add 12 fοr each remaining day:

24 ------ 36 ------ 48 ------ 60

Tο represent this οn a number line, we can start at 24 and add 12 fοr each remaining day:

|---|---|---|---|---|---|---|

0 5 10 15 20 25 30 35 40

^ ^ ^

Day 5 6 7

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Answer:

3.15%

Step-by-step explanation:

To find the expected return and standard deviation of a portfolio that is invested in two assets A and B, we need to know the expected returns and standard deviations of those assets, as well as the correlation between them.

Let's assume that the expected return and standard deviation of asset A are 10% and 5%, respectively, and that the expected return and standard deviation of asset B are 8% and 3%, respectively. Let's also assume that the correlation between the two assets is 0.5.

To find the expected return of the portfolio, we can use the following formula:

Expected return of portfolio = weight of A * expected return of A + weight of B * expected return of B

where the weights are the proportions of the portfolio invested in each asset:

weight of A = 40% = 0.4

weight of B = 60% = 0.6

Expected return of portfolio = 0.4 * 10% + 0.6 * 8%

Expected return of portfolio = 9.2%

Therefore, the expected return of the portfolio is 9.2%.

To find the standard deviation of the portfolio, we can use the following formula:

Standard deviation of portfolio = sqrt(weight of A^2 * variance of A + weight of B^2 * variance of B + 2 * weight of A * weight of B * correlation * standard deviation of A * standard deviation of B)

where the variances are the square of the standard deviations of each asset:

variance of A = (5%)^2 = 0.0025

variance of B = (3%)^2 = 0.0009

Standard deviation of portfolio = sqrt(0.4^2 * 0.0025 + 0.6^2 * 0.0009 + 2 * 0.4 * 0.6 * 0.5 * 0.05 * 0.03)

Standard deviation of portfolio = 0.0315 or 3.15% (rounded to two decimal places)

Therefore, the standard deviation of the portfolio is 3.15%.

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It shtbe noted that 68% of the data should fall in the interval from 616 to 756.

z score for values:

z = (X-µ)/σ = (616-686)/70 = -1

z = (X-µ)/σ = (756-686)/70 = 1

Approximately 68% of the data should fall in the interval from 616 to 756.

b) B. 71% of the data falls in the interval from 616 to 756. The estimate is very close to the value predicted by the Empirical Rule.

c) (µ - 2*σ, µ + 2*σ)

(686 - 2*70, 686 + 2*70)

(546, 826)

You expect to find about 95% of the teams between the two values 546 and 826.

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Here the correct statements can be

The y-intercept represents D) the starting amount in his savings account.

The slope represents C) the change in the dependent variable with respect to the independent variable.

What is meant by y-intercept?

The y-intercept is the point where a line intersects the y-axis on a graph. It represents the value of the dependent variable when the independent variable is zero.

What is meant by the term slope?

The slope is a measure of the steepness of a line on a graph. It is calculated by dividing the change in the y-coordinate by the change in the x-coordinate between two points on the line.

According to the information

The y-intercept of the linear model y = 200x + 500 represents the starting amount in Richard's savings account.

The slope of the linear model y = 200x + 500 represents the change in the dependent variable (y, the savings amount) with respect to the independent variable (x, the number of months). Specifically, the slope of 200 means that for every additional month, Richard's savings will increase by $200.

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The cost of an individual ticket is contingent upon the overall expenditure of the performance and the quantity of tickets purchased.

Ticket sales refer to the purchase of one or multiple admission passes to an occasion, which may be facilitated either through the Event Management System, online, mobile app, third-party voucher providers (such as Groupon), or physically, among other options.

Based on the fact that there is no much details on the ticket sales, it present ]an obstacle in knowing the number cost of individual tickets. To determine the cost of each ticket, we need to have the total expenditure or the quantity of tickets sold.

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The value of the line AC is  100. 07 inches

Trigonometric identities are equations that involve trigonometric functions such as sine, cosine, and tangent, which hold true for all values of the variables in the equation.

Note that there are six trigonometric identities. They are;

From the information given, we have;

Using the sine identity, we have;

sin 58 = Line AC/118

cross multiply the values

Line AC = 100. 07 inches

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The 18% he gets over the goods purchased exceeds Rs. 6300.

a decrease from the gross amount or value of something: for example, a(1): a reduction from the usual or list price.

Total Purchase Value = Total discount in rs * % discount

= 1520/16 x 100 = 9500

Discount on upto 3200 = 3200 x 14% = 448

Discount on upto 3201-6300 = (6300-3200) x 14% = 496

Balance discount = 1520 - 448 - 496 = 576

Above 6300 purchase amount = 9500 - 6300 = 3200

Discount % = 576/3200 x 100 = 18%

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Complete question:

A customer gets 14% discount on purchasing goods whose value is up to Rs. 3200 and gets 16% discount whose value is between Rs. 3201- Rs. 6300 and customer gets certain % discount while purchase the goods exceeds Rs. 6300. A customer gets a total discount of Rs. 1520 is 16% of the total purchase value. find the %age he gets over the goods purchased exceeds Rs. 6300 ?

We can start by isolating the secant term and then taking the inverse cosine of both sides. Remember that the inverse cosine function only gives results on the interval [0,π], so we will need to adjust our solutions accordingly:

2sec(θ) + 3 = 0

2sec(θ) = -3

sec(θ) = -3/2

cos(θ) = -2/3

θ = ±cos⁻¹(-2/3)

Using a calculator, we find:

θ ≈ 2.302, 4.981 radians

However, we need to adjust these solutions to be within the interval [0,2π). Since cos(x) = cos(2π - x), we can add 2π to the negative solution to get an equivalent positive solution:

θ ≈ 2.302, 7.438 radians

Rounding to the nearest thousandth, we get:

θ ≈ 2.302, 7.438 radians

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Answer:

y = -3x + 1

Step-by-step explanation:

We are given a couple ordered pairs from this table. Lets use the slope formula so we can find the slope of this line:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Y2, y1, x2, and x1 are constants (points on the line). To make it easy, lets take the coordinates (0,1) and (1,-2). Then we just plug these points in and evaluate.

[tex]\frac{-2-1}{1-0}[/tex]

Evaluate both sides of the fraction.

[tex]\frac{-3}{1} =-3[/tex]

Now that we have the slope, we are given the y intercept coordinate, (0,1) which means the y-intercept is 1. To write it in y = mx + b form, we just plug in our numbers and were good to go.

[tex]y=-3x+1[/tex]

According to the given data the unit rate of hamburgers per hour is 9 hamburgers per hour.

The unit rate is the rate of change of the number of hamburgers produced per hour.

To find the unit rate, we can use the formula:

Unit rate = (Number of hamburgers produced) / (Number of hours)

Using the information provided in the table, we can find the unit rate for the restaurant:

For 3 hours, the restaurant produced 27 hamburgers.

Unit rate = 27 / 3 = 9 hamburgers per hour

For 5 hours, the restaurant produced 45 hamburgers.

Unit rate = 45 / 5 = 9 hamburgers per hour

For 7 hours, the restaurant produced 63 hamburgers.

Unit rate = 63 / 7 = 9 hamburgers per hour

For 9 hours, the restaurant produced 81 hamburgers.

Unit rate = 81 / 9 = 9 hamburgers per hour

Therefore, the unit rate of hamburgers per hour for the restaurant is 9 hamburgers per hour.

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a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = [tex](1-p)^{k-1}[/tex]×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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Answer:

x = 4

Step-by-step explanation:

given 2 secants drawn from an external point to the circle, then the product of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is

x(x + 4x) = 8(8 + 2)

x(5x) = 8(10)

5x² = 80 ( divide both sides by 5 )

x² = 16 ( take square root of both sides )

x = [tex]\sqrt{16}[/tex] = 4

The regular price of the running shoes is $80.

Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.

Given that the sales price is $64, we can set up the equation:

0.8P = $64

To find the regular price P, we divide both sides of the equation by 0.8:

P = $64 / 0.8

P = $80

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Kinzang grew 0.96 meters.

We have,

To find how much Kinzang grew, we need to subtract his height at birth from his current height:

Height Kinzang grew = Current height - Height at birth

Height Kinzang grew = 1.49 m - 0.53 m = 0.96 m

Therefore,

Kinzang grew 0.96 meters.

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Step-by-step explanation:

Steve spends 20% of £200 = 0.2 * £200 = £40 on his football magazine subscription.

The remaining amount he spends on football stickers, sweets, and fizzy drinks in the ratio of 5:2:1, which means that for every 5 parts he spends on football stickers, he spends 2 parts on sweets and 1 part on fizzy drinks.

So, let's call the amount he spends on football stickers "5x". Then, the amount he spends on sweets is "2x" and the amount he spends on fizzy drinks is "x".

The total amount he spends on these items is:

5x + 2x + x = 8x

We know that he has £200 - £40 = £160 left after paying for his magazine subscription. So, we can set up an equation:

8x = £160

Solving for x, we get:

x = £20

Therefore, Steve spends:

5x = 5 * £20 = £100

on football stickers.

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Answer:

5 : 2 : 1 = 100 : 40 : 20

Step-by-step explanation:

10% = 20 (200÷10=20)

20% = 40 (double both sides)

take away £40 from £200 = £160

£160 is left over after buying the magazine subscription

______________________________

add the radio all together = 5:2:1 = 8

divide 8 by 160 = £20

That now means 1 = 20

5 : 2 : 1

we already found 1, now to find 2 and 5

you times 2

1 = 20

2 = 40

and then do the same for 5

1 = 20

5 = 100

To know this is right, 100 + 40 + 20 = 160 the original number for the money left over.

On solving the provided question we can say that As a result, set D denotes a linear function.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).

The set of ordered pairs expressing a linear function must meet the requirement that any two locations in the set have a constant rate of change (slope).

We can determine the rate of change between the two supplied positions using set D:

slope = (y2 - y1) / (x2 - x1)

slope = (1 - 2) / (2 - (-1))

slope = -1/3

We may use the slope-intercept form of a linear equation to see if the remaining points in set D fulfil the same rate of change: y = mx + b, where m is the slope and b is the y-intercept.

We can solve for b using the first point in D, (-1,2):

2 = (-1/3)(-1) + b

b = 7/3

So the linear equation for set D is: y = (-1/3)x + 7/3

Now we can check if the remaining points in set D satisfy this equation:

(2, 1): 1 = (-1/3)(2) + 7/3 (satisfies the equation)

As a result, set D denotes a linear function.

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Answer:

125

Step-by-step explanation:

60% x X = 75

X              = 75/0.6
X              = 125

The cube root function represented by the graph is h(x) = ∛(x + 3) - 2.

The parent cube root function is f(x) = ∛x

If we translate the parent cube root function 3 units to the left, this means that we replace x with (x + 3) in the function.

This results in the new function g(x) = ∛(x + 3). So, for any input value of x, the output value of g(x) is the cube root of (x + 3).

Similarly, if we translate the parent cube root function 2 units down, this means that we subtract 2 from the function.

So, the new function h(x) = ∛(x + 3) - 2.

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Note that the probability of selling at least 30 widgets is 0.0468.

Given the information provided, the problem requires us to use a binomial distribution to estimate the probability of selling at least 30 widgets.

A binomial distribution is a probability distribution that describes the number of successes in a set number of trials.

Where n = 200 (the number of people that visit the store and buy a widget each day) and

p = 0.1667 (likelihood of a client purchasing a widget)

We are looking for the probability of selling at least 30 widgets, which is equivalent to finding the probability of selling 30 or more widgets.

This can be calculated using the cumulative probability formula for a binomial distribution:

P(X >= 30) = 1 - P(X < 30) = 1 - Σ (nCx)(p^x)(1-p)^(n-x) from x=0 to 29

We can use a calculator or a software to calculate this probability. The result is 0.0468 rounded to 4 decimals.

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Answer: $10.92

Step-by-step explanation:

Since there are 16 ounces in a pound, 8 ounces would be equivalent to half a pound. Thus, 3 pounds and 8 ounces = 3.5 pounds.

Since apples cost $3.12 per pound and we have 3.5 pounds, the total cost would be $3.12*3.5 pounds = $10.92

Two quadratic functions that contains the points (5, 3) and (8, 0) are

In this problem we must find two possible quadratic functions that contains two points: (x, y) = (5, 3), (x, y) = (8, 0). The factor form of the quadratic function is now introduced:

y = a · (x - r₁) · (x - r₂)

Where:

If we know that (x₁, y₁) = (5, 3) and (x₂, y₂) = (8, 0), then the two possible quadratic functions are:

3 = a · (5 - r₁) · (5 - r₂)

3 = a · [25 - 5 · (r₁ + r₂) + r₁ · r₂]

0 = a · (8 - r₁) · (8 - r₂)

0 = 64 - 8 · (r₁ + r₂) + r₁ · r₂

0 = 64 - 8 · r₁ - 8 · r₂ + r₁ · r₂

0 = 64 - 8 · r₁ + (r₁ - 8) · r₂

Now we clear r₂:

r₂ = (8 · r₁ - 64) / (r₁ - 8)

And we eliminate r₂ in the first equation:

3 = a · [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

And variable a is now cleared:

a = 3 / [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

The function is graphed and two possible solutions are introduced below:

(r₁, a) = (6, 1), (r₁, a) = (10, 0.2)

And the values of r₂ are, respectively:

(r₁, a) = (6, 1):

r₂ = (8 · 6 - 64) / (6 - 8)

r₂ = - 16 / (- 2)

r₂ = 8

(r₁, a) = (10, 0.2):

r₂ = (8 · 10 - 64) / (10 - 8)

r₂ = 16 / 2

r₂ = 8

Finally, we complete and graph the resulting quadratic functions.

Case 1:

y = (x - 6) · (x - 8)

y = x² - 14 · x + 48

Case 2:

y = 0.2 · (x - 10) · (x - 8)

y = 0.2 · (x² - 18 · x + 80)

y = 0.2 · x² - 3.6 · x + 16

The graphs of the two quadratic functions are shown in the second image.

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Answer: To calculate the cost of the triangular lot, we need to first find the area of the triangle using the given dimensions. To do this, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:

area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, we have a = 188, b = 145, and c = 158. Substituting these values into the formula, we get:

s = (188 + 145 + 158)/2 = 245.5

area = √(245.5(245.5-188)(245.5-145)(245.5-158)) ≈ 12463.15 square feet

Now that we have the area of the lot, we can multiply it by the price per square foot to get the total cost:

cost = 12463.15 × $3 = $37,389.45

Therefore, the lot would cost approximately $37,389.45.

Step-by-step explanation:

A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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The number of more points that Owen must earn to meet his goal would be = 31 points.

The total number of point expected to be scored by Owen = 50 points

The total amount of points that Owen has earned so far = 19 point.

The amount of points that Owen should earn more to meet up with the points expected of him = 50-19= 31 points.

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Answer:

28

Step-by-step explanation:

you first do the 4x4=16 then 4x3=12 then do 16+12=28

The interval(s) for which the function is decreasing are (3, 1) and (4, ∝)

From the question, we have the following parameters that can be used in our computation:

The graph

The interval(s) for which the function is decreasing is when

As x increases, the function values decreases

Using the above as a guide and examining the graph, we have the following:

The function is decreasing at (3, 1) and (4, ∝)

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The amplitude and period of each function are calculated and listed below

The amplitude and period of each function can be determined using their standard form:

y = A sin (Bx + C) or y = A cos (Bx + C)

where |A| is the amplitude, B is the frequency (or angular frequency), and 2π/B is the period.

Let's apply this formula to each function:

y = cos(2x)

Amplitude = 1

Period = 2π/2 = π

y = -sin(2x)

Amplitude = 1

Period = 2π/2 = π

y = -3sin(3x)

Amplitude = 3

Period = 2π/3

y = (1/2)cos(4x)

Amplitude = 1/2

Period = 2π/4 = π/2

y = 10sin(1/2x)

Amplitude = 10

Period = 2π/(1/2) = 4π

y = 5cos(1/4x)

Amplitude = 5

Period = 2π/(1/4) = 8π

y = (-1/3)cos(1/3x)

Amplitude = 1/3

Period = 2π/(1/3) = 6π

y = 4sin(-2x)

Amplitude = 4

Period = 2π/(-2) = -π

y = -2sin(2πx)

Amplitude = 2

Period = 2π/(1) = 2π

y = -3sin(πx)

Amplitude = 3

Period = 2π/π = 2

y = 1 + (1/2)cos(πx)

Amplitude = 1/2

Period = 2π/π = 2

y = -2 + cos(4πx)

Amplitude = 1

Period = 2π/(4π) = 1/2

The graphs of the functions are added as attachment

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Answer: The 22% discount was calculated as R551 (rounded to the nearest rand).

Step-by-step explanation:

To calculate the discount, we need to determine what percentage of the original price R2 499 the discount of R551 represents.

The formula to calculate the percentage discount is:

Discount percentage = (Discount amount ÷ Original price) x 100%

Substituting the values given in the question, we get:

Discount percentage = (551 ÷ 2499) x 100%

Discount percentage = 0.22088 x 100%

Discount percentage = 22.088%

Therefore, the discount given was 22%.