From the top of a canyon, the angle of depression to the far side of the river is 52°, and the angle of depression to the near side of the river is 71°. The depth of the canyon is 230 feet. What is the width of the river at the bottom of the canyon? Round to the nearest foot.
Trig question

If we generate the multiple datasets from a distribution with a given mean and variance , then mean and variance of from generated data will not be same .

The sample mean and the variance are random variables that vary from sample to sample, even if the samples are drawn from the same population.

When we generate a sample from a distribution with a known mean and variance, the sample mean and variance will be estimates of the population mean and variance ;

So , because of sampling variability, the estimates obtained from different samples may differ from one another and from the true population parameters.

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Answer:

[tex]\boxed{\checkmark}\;\;52 = 8n + 4[/tex]

[tex]\boxed{\checkmark}\;\;4(2n + 1) = 52[/tex]

[tex]\boxed{\checkmark}\;\;4 = 52 - 8n[/tex]

[tex]\boxed{\phantom{\checkmark}}\;\;4n = 48[/tex]

[tex]\boxed{\checkmark}\;\;n = 6[/tex]

Step-by-step explanation:

To determine if the equations are equivalent, solve the equations for n.

Option 1

[tex]\begin{aligned}\implies 52&=8n+4\\52-4&=8n+4-4\\48&=8n\\48\div 8&=8n \div 8\\6&=n\\n&=6\end{aligned}[/tex]

Option 2

[tex]\begin{aligned}\implies 4(2n+1)&=52\\8n+4&=52\\8n+4-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 3

[tex]\begin{aligned}\implies 4&=52-8n\\4+8n&=52-8n+8n\\4+8n&=52\\4+8n-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 4

[tex]\begin{aligned}\implies 4n&=48\\4n \div 4&=48 \div 4\\n&=12\end{aligned}[/tex]

Option 5

[tex]n=6[/tex]

Therefore, the equations that are equivalent are:

The number of multiplications for the power₁ is 3 multiplication power₂ is one multiplication and power₃ is 5 multiplications and the number of recursive calls will power2 and power3 make when computing 332 and  319 is 5.

First, let's look at power₁. This function can compute the power of a number by repeated multiplication. For example, to compute 3 to the 4th power, power₁ would perform three multiplications: 3 x 3 x 3 x 3 = 81.

Using this approach, we can see that to compute 3 to the 32nd power, power₁ would perform 31 multiplications (3 x 3 x 3... repeated 31 times). Similarly, to compute 3 to the 19th power, power₁ would perform 18 multiplications.

Next, let's consider power₂. This function uses a different strategy for computing powers. It relies on the fact that any number can be expressed as a power of 2

To compute 3 to the 32nd power using power₂, we would first express 32 as a sum of powers of 2:

=> 32 = 2⁵ + 2⁴ + 2³.

Then, we would use the fact that 3 raised to a power of 2 can be computed with just one multiplication: 3² = 9.

Using this fact repeatedly, we can compute 3 to the 32nd power with only 5 multiplications:

=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

For 3 to the 19th power, power2 would express 19 as 2⁴ + 2¹ and then use 4 multiplications:

=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

Finally, let's look at power3. This function is similar to power2 but uses a more efficient algorithm called exponentiation by squaring. This algorithm works by repeatedly squaring the base and halving the exponent until the exponent is 1.

To compute 3 to the 32nd power using power₃, we would start with the binary representation of 32 (100000 in binary).

we can see that power₃ will only perform 5 multiplications to compute 3 to the 32nd power.

Similarly, to compute 3 to the 19th power, power₃ would start with the binary representation of 19 (10011 in binary) and use the exponentiation by squaring algorithm to perform only 6 multiplications.

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Complete Question:

How many multiplications will each of the functions power₁, power₂, and power₃ perform when computing 332? 319?

The number of adults in the museum, using the fractional value of girls and boys, is 75.

A fractional value refers to a portion of the total value.

A fractional value can be depicted in fractions, decimals, or percentages.

A fractional value can also be represented as a ratio or proportion.

In this situation, the fractional number of adults is determined using subtraction.

The total number of people in a museum = 250

The fraction of girls in the museum = 2/5

2/5 of 250 = 100 girls

The fraction of boys in the museum = 3/10

3/10 of 250 = 75

Alternatively:

2/5 + 3/10 = 7/10

7/10 of 250 = 175

Therefore, the number of adults = 75 [250 - (100 + 75)]

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There are 250 people in the museum.

2/5 of the 250 people are girls.

3/10 out of the 250 people are boys.

The rest of the 250 people are adults.

Work out the number of adults in the museum.

The graph of the piecewise function is given by the image presented at the end of the answer.

A piecewise function is a function that has multiple definitions, according to it's input values.

The two definitions for this problem are given as follows:

For the values until x = 1, we have an increasing linear function, with intercept of y = -2, and finishes at the point (1,-1).

For the values greater than x = 1, the function is a linear function, starting at the point (1,-1), and decaying.

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In a case whereby the distance between Dallas and Houston is about 364 kilometers the approximately measurement is closest to the number of miles between these two towns is A 227.5 miles.

The concept that will be used here is unit conversion. It should be noted that 1 Mile = 1.609344 kilometres.

Then                                 Xmile  = 364 kilometers

We can cross multiply to have

 Xmile  =364 kilometers/1.609344 kilometres.

=226.179

Hence the  closest to the number of miles is A 227.5 miles

Therefore, option A is correct.

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According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...

To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.

On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:

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Answer:

4

Step-by-step explanation:

Rate of change forumla

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

We have our X points, -7 and -2. Now to find the Y value at those places.

For -7, Y is 5

For -2, Y is 25

Now we plug this into the equation

[tex] = \frac{25 - 5}{ - 2 - ( - 7)} = \frac{20}{5} = 4[/tex]

Solution of the system of equations y - x²- 14x = 54 and 43 = y - 6x are

x = -4 ± √5 and y = ± 6√5 + 19

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given equations

y - x²- 14x = 54

y = x² + 14x + 54            -------------(1)

43 = y - 6x

y = 6x + 43                     ------------(2)

By equation (1) and (2)

6x + 43 = x² + 14x + 54

x² + 14x + 54 - 6x -43 = 0

x² + 8x + 11 = 0

a = 1, b = 8, c = 11

x = (-b ± √(b² - 4ac))/2a

x  = (-8 ± √(64 - 4.11))/2

x  = -4 ± √16-11

x = -4 ± √5

Putting value of x in equation (2)

y = 6(-4 ± √5) + 43

y = -24 ± 6√5 + 43

y = ± 6√5 + 19

Hence, x = -4 ± √5 and y = ± 6√5 + 19 are the solutions of equations

y - x²- 14x = 54 and 43 = y - 6x.

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The value of x in the triangle is equal to: A. 21.

In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).

Note: x is the side opposite to the 60° angle.

The side opposite to the 60° angle, x = 7√3 × √3

The side opposite to the 60° angle, x = 7 × 3

The side opposite to the 60° angle, x = 21 units.

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Answer:

5/12

Step-by-step explanation:

4/6 - 1/4  The common denominator would be 12

8/12 - 3/12 = 5/12

Answer:

5/12

Step-by-step explanation:

mark me please

The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.

To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

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The percent of change is the change in value in percent from 90 to 18 that is an 80% decrease.

To calculate the percent change from 90 to 18, we first need to find the difference between the two values:

Change = Final Value - Initial Value

Change = 18 - 90

Change = -72

The negative sign indicates that there has been a decrease in value.

To find the percent change, we can use the following formula:

Percent Change = (Change / Initial Value) x 100%

Percent Change = (-72 / 90) x 100%

Percent Change = -80%

So there is decrease in percent from 90 to 18 that is by 80%.

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if a t test yields p > 0.05 the null hypothesis would normally be option (A) accepted

The null hypothesis defined as the types of hypothesis that do not have any statistical significance exist in the given set of observation.

The p value is defined as the measurement that is used to validate the hypothesis using the observed data. The range of the p value varies from zero to one.  Zero means no chance and 1 means absolute certainty  

If a t test yields a p-value greater than 0.05, it means that there is insufficient evidence to reject the null hypothesis, and the results are not statistically significant. Therefore, the null hypothesis is accepted.

Therefore, the correct option is (A) accepted

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The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.

To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.

Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:

11 = [tex]a * b^0[/tex]

Since [tex]b^0[/tex] = 1 for any value of b, we have:

11 = a * 1

So a = 11.

Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:

1375 = [tex]11 * b^3[/tex]

Dividing both sides of the equation by 11, we have:

125 = [tex]b^3[/tex]

By combining the cube roots of the two sides, we obtain:

b = 5

So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].

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The complete question is:

an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?

Answer:70% chance they vote yes

Step-by-step explanation:

Answer:

3/10 for red people and 7/10 for blue people.

Step-by-step explanation:

Step-by-step explanation:

use the pythagors theorm b square = h2 -p2

then the 10 cm is parallel so use area of right angled triange =1/2 b×p

The number of decimeters in  3.6 millimeters is 0. 0036 decimeters. Option D

Conversion of units is simply defined as the conversion that is between different units of measurement for a particular quantity.

it is carried out mostly through multiplicative conversion factors.

It may involve multiple steps of multiplication or division by  a conversion factor.

From the information given, we have that;

1 decimeter = 1000 millimeters

Then, x decimeter = 3.6 millimeters

Cross multiply the values

x = 3.6/1000

divide the values

x  = 0. 0036 decimeters

Hence, the value is  0. 0036 decimeters

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The power in a significance test is the probability of detecting a true effect, while the probability of making a type II error is the complementary probability of power.

A significance test is a statistical method used to determine whether an observed difference or effect is statistically significant or simply due to chance.

Power is defined as the probability of detecting an effect in a significance test if an effect truly exists. In other words, it is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. The null hypothesis assumes that there is no significant difference between two groups, while the alternative hypothesis states that there is a significant difference.

Mathematically, power is calculated using the following formula:

Power = 1 - β

Where β is the probability of making a type II error, which is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. In other words, it is the probability of not detecting an effect when an effect truly exists.

Therefore, power and β are complementary probabilities. If power is high, β is low, and vice versa. A significance test with a low power has a higher chance of making a type II error, meaning that it can fail to detect a real effect. Conversely, a test with a high power has a lower chance of making a type II error, meaning that it can detect a real effect more accurately.

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By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.

Let x = number of seats on the main-floor

y = number of balcony seats

We know that if all the seats are sold, then the total income is $4,200, we can write the equation:

x*8 + y*5 = $4,200

And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:

0.25*x*8 + 0.4*y*5 = $1,200

x*2 + y*2 = $1,200

2(x + y) = $1200

x + y = $600

x = 600 - y

putting the value of x in equation1)

8(600-y) + 5y = 4200

4800 - 8y + 5y = 4200

3y = 600

y = 200

and x = 600 - 200 = 400

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Answer:

the answer according to your question is that " b" is = -0.3

Step-by-step explanation:

this is a 14.4 in × 10.2 in rectangle, were 2 identical half-circles (= 1 full circle) are removed.

so, in other words, the shaded area is

rectangle area - circle area

the rectangle area is length × width.

the circle area is pi×r². with r (radius) being half the diameter. the diameter is 10.2 in, so, r = 10.2/2 = 5.1 in.

so, the shaded area is

14.4 × 10.2 - pi × 5.1² = 146.88 - 3.14 × 26.01 =

= 146.88 - 81.6714 = 65.2086 ≈ 65.21 in²

remember, an area is always expressed in square units. a volume in cubic units. and a length in simple units.

The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.

It follows from the task content that the relationship between y and x is to be.

By comparison with the slope-intercept equation; y = mx + c.

Since, slope, m is the rate of change; m = 12$ per hour.

Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.

Therefore, the required equation is;

y = 12x + 5.

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Answer:36x^13

Step-by-step explanation:

We can solve this problem using the rule of exponents: (am)n = amn.

First, let's simplify the exponent on the first term:

(-3x^5)^2 = (-3x^5) × (-3x^5)

Next, let's multiply this by 4x^3:

(-3x^5)^2 × 4x^3 = (-3x^5) × (-3x^5) × 4x^3

Now, let's multiply the coefficients and combine the exponents:

(-3 × -3)x^(5 + 5 + 3) = 36x^13

Therefore, the answer is 36x^13.

The length of the ramp that must cover the horizontal distance is 13.13 feet.

Given the data in the question, this forms a right-triangle.

To solve for the length of the ramp, we use  trigonometric ratio

Cosine = Adjacent / Hypotenuse

Plug in the values

cos( 8° ) = 13ft / hypotenuse

Hypotenuse = 13ft / cos( 8° )

Hypotenuse = 13.13 ft

Therefore, the ramp's length is 13.13 ft.

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The measure of angle ABC from the given circle D is 34°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Given that, circle with the center D and measure of arc AC is 34°.

The measure of arc = m∠ABC

m∠ABC =34°

Therefore, the measure of m∠ABC is 34°.

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Answer:

Step-by-step explanation:

chicken

Bob needs to buy 500 kg of sand.

What is the ratio?

A ratio is a quantitative relationship between two numbers, quantities, or values that expresses how many times one is contained in the other. Ratios are typically expressed in the form of "a to b" or "a:b" and can be represented as fractions or decimals.

Since the ratio of cement to sand to stone is 1:2:3 by weight, the total weight of the ingredients needed to make one bag of dry concrete is:

Cement: 1/6 of 30 kg = 5 kg

Sand: 2/6 of 30 kg = 10 kg

Stone: 3/6 of 30 kg = 15 kg

To make 50 bags of dry concrete, Bob will need 50 times these amounts:

Cement: 5 kg x 50 = 250 kg

Sand: 10 kg x 50 = 500 kg

Stone: 15 kg x 50 = 750 kg

Hence, Bob needs to buy 500 kg of sand.

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Answer:

A

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1

= 3x + 2 - 2x + 2 ← collect like terms

= x + 4