10. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot
35 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 51°. What is the height of the tower, to the nearest meter? (show work pls)

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

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Answer: there are 118 dimes in the jar.

Step-by-step explanation: Let's use a system of equations to solve the problem:

Let d be the number of dimes and n be the number of nickels.

We know that:

d + n = 250 (Equation 1) (The total number of coins is 250)

0.1d + 0.05n = 18.4 (Equation 2) (The total value of all coins is $18.4)

To solve for d, we need to eliminate n from the equations above. We can do this by multiplying Equation 1 by -0.05 and adding it to Equation 2:

-0.05d - 0.05n = -12.5

0.1d + 0.05n = 18.4

0.05d = 5.9

Dividing both sides by 0.05, we get:

d = 118

Therefore, there are 118 dimes in the jar.

The evaluation of f(x² + y² + 3) dA over the circle of radius 2 centred at the origin yields a direct answer of 12π.

To explain further, let's consider the integral in polar coordinates. The circle of radius 2 centred at the origin can be represented by the equation r = 2. In polar coordinates, we have x = r cosθ and y = r sinθ. The area element dA can be expressed as r dr dθ. Substituting these values into the integral, we get:

∫∫ f(x² + y² + 3) dA = ∫∫ f(r² + 3) r dr dθ.

Since the function f is not specified, we cannot evaluate the integral in general. However, we can determine the value for a specific function or assume a hypothetical function for further analysis. Once the function is determined, we can integrate over the given limits of integration (θ = 0 to 2π and r = 0 to 2) to obtain the result. The direct answer of 12π can be obtained with a specific choice of f(x² + y² + 3) function and performing the integration.

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If Neptune's distance from the sun is about 4.5 billion km and Venus distance is 2×\(10^{8}\) km, then its 22.5 times farther is Neptune from the sun than Venus.

The Neptune's distance from sun = 4.5 billion km

we know

1 billion = \(10^{9}\)

The Venus's distance from sun = 2×\(10^{8}\) km

How many times farther is Neptune from the sun than Venus = The Neptune's distance from sun / The Venus's distance from sun

Substitute the values in the equation

= (4.5×\(10^{9}\))÷(2×\(10^{8}\))

= 22.5

Hence, If Neptune's distance from the sun is about 4.5 billion km and Venus distance is 2×\(10^{8}\) km, then its 22.5 times farther is Neptune from the sun than Venus.

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If a calculator displays an angle measure in radians instead of degrees, it would make you question whether the calculator is in the right mode. Radians and degrees are two different units of measuring angles, with radians being the standard unit in mathematics and degrees being more commonly used in everyday life and geography.

Because the range of values for angles in radians is between 0 and 2π, while the range for angles in degrees is between 0 and 360. So, if a calculator gives an angle measure in radians that is outside the range of 0 to 2π or gives an angle measure in degrees that is outside the range of 0 to 360, it would indicate that the calculator is not in the correct mode for the desired unit of measurement.

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The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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The above are irregular polygons. Their missing external angles are given as follows:

A) x = 30°

6) x = 105°, y = 55°

B)  x = 70°; y =

F) x =  138.33°

A)

Sum of angles in a pentagon = 540°

Missing internal angle = 540 - (95+100+110+85) = 150

Since exterior angle = 180 degre - it's liner pair

180 - 150 = 30°

so , x = 30°

6)

Sum of angles in hexagon = 720°

To get x and y we must find the missing internal angle (e) between vertex 105° and 145° and (f) between 105° and 115°

Since its' external angel = 45

e = 180-45 = 135°

So f = 720 - (135 + 105 + 115+ 125+ 145)

f = 95°
so x = 180-f = 180-95 = 105°

y = 180-125 = 55°

b) Sum of angles in  a heptagon = 900°

Lets call missing internal angles e1 and e2

Let e1 = 180-y
let e2 = 180-60°

e2 = 120°

So e1 = 900 - (160+120+115+110+125+115)

e1 = 155°

Since e1 = 180 -y
155 = 180-y

y = 180 - 155

y = 25°

x = 180-110

x = 70°

F)  Sum of angles in an Octagon is 1080°

To solve for x, we must realize all internal angles.
Let call the missing angle between x and x+25 e1; and

the one between 135° and (x-5) e2 and
the one between x+25 and 140 e3


e1 = 180-25 = 155°
e2 = 155°

e3 = 180-20=60°

to find x:

1080 = (x+25) + 60 + 140 + (x-5)+155+135+155+x)

collect like terms

1080 - 60 - 155- 155-140-25+5 -135 = x + x + x
415 = 3x
x = 415/3
x = 138.33°

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Answer:

336

Step-by-step explanation:

V=whl=8·7·6=336

Answer:  22:2, 33:3 and, 44:4

Step-by-step explanation:

Answer:

Step-by-step explanation:

22 : 2

33 : 3

44 : 4

Answer:

$48

Step-by-step explanation:

Given that:

Money spent on clothing last month = $40

Money spent this month is 120% of the spending of the last month.

To find:

A proportion to model this situation.

And the spending done this month?

Solution:

Let us have a look at 120% first.

\(120\%= \dfrac{120}{100} = \dfrac{6}{5}\)

\(\frac{6}{5}\) of \(x\) can be found by comparing \(x\) with 5, then we have to find the equivalent of 6.

Here, \(x\) is 40.

5 parts are equivalent to 40

1 part is equivalent to \(\frac{40}{5} = 8\)

6 parts are equivalent to \(8\times 6 = 48\)

OR

simply:

\(40 \times \dfrac{120}{100} = 48\)

A triangle can not have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm

We know that the triangle inequality theorem states that for any triangle the sum of any two sides of a triangle is greater than or equal to the third side.

Here, we have been given the three measurements.

Let a = 3.2 cm, b =  5.3 cm and c = 9.4 cm

Consider the sum of sides a and b,

a + b

= 3.2 + 5.3

= 8.5cm

< 9.4

= c

i.e., a + b < c

Acctording to triangle inequality theorem, a, b, c can not be the sides of triangle, as the sum of two sides that measure 3.2 cm and 5.3 cm is not greater than or equal to the third side which measures 9.4 cm

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Answer:

Step-by-step explanation:

Answer:

y=1/3x+45 I think

Step-by-step explanation:

The best predicted value of the response variable, denoted as y, for x = 9.9 is 83.42. The correct option is b.

To find the best predicted value of y for x = 9.9, we can use the given regression equation: y = 55.8 + 2.79x. Substituting x = 9.9 into the equation, we get y = 55.8 + 2.79 * 9.9. Calculating this expression gives us y ≈ 83.42. Therefore, the best predicted value of y for x = 9.9 is 83.42, which corresponds to option (b).

In regression analysis, the regression equation represents the relationship between the independent variable (x) and the dependent variable (y). The equation y = 55.8 + 2.79x indicates that for each unit increase in x, y is expected to increase by 2.79. The coefficient of determination, denoted as r², provides a measure of how well the regression equation fits the data. In this case, the coefficient of determination is given as r = 0.708.

By using the regression equation and plugging in the specific value of x = 9.9, we can estimate the corresponding value of y. The best predicted value of y for x = 9.9 is obtained by substituting the given value into the equation: y = 55.8 + 2.79 * 9.9. The resulting value is approximately 83.42, indicating that for x = 9.9, the predicted value of y is 83.42.

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Sequence is the set of rules that guide the creation of a set. The rule of the sequence is to add 5, and the next three terms are 10, 15 and 20.

The first two terms of the sequence are given i.e.

\(T_1 =0\) --- first term

\(T_2 = 5\) --- second term

Because the first term is 0, then the sequence must be arithmetic.

Calculate the common difference using:

\(d = T_2 - T_1\)

\(d = 5 - 0\)

\(d = 5\)

The nth term of an arithmetic sequence is calculated using:

\(T_n = T_1 +(n - 1)d\)

So, we have:

\(T_n = 0 +(n - 1) \times 5\)

\(T_n = 5(n - 1)\)

So, the next three terms are:

\(T_3 = 5(3 - 1) =10\)

\(T_4 = 5(4 - 1) =15\)

\(T_5 = 5(5 - 1) =20\)

Hence, the rule of the sequence is:

\(T_n = 5(n - 1)\) or Add 5

The next three terms of the sequence are: 10, 15, 20

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To construct a confidence interval for the proportion of all customers who experienced an interruption, we can use the formula:

Confidence Interval = Point Estimate ± (Critical Value) * (Standard Error)

First, let's calculate the point estimate:

Point Estimate = Number of customers who experienced an interruption / Total sample size

Point Estimate = 75 / 550 ≈ 0.136 (rounded to three decimal places)

Next, we need to determine the critical value corresponding to a 98% confidence level. Since the sample size is large (n = 550) and the data are assumed to be approximately normally distributed, we can use the z-table.

The critical value for a 98% confidence level can be found by finding the z-score that corresponds to an area of (1 - 0.98) / 2 = 0.01 in the upper tail of the standard normal distribution. Using the z-table, this critical value is approximately 2.33 (rounded to two decimal places).

Next, we need to calculate the standard error:

Standard Error = sqrt((Point Estimate * (1 - Point Estimate)) / Sample Size)

Standard Error = sqrt((0.136 * (1 - 0.136)) / 550) ≈ 0.016 (rounded to three decimal places)

Now we can construct the confidence interval:

Confidence Interval = 0.136 ± (2.33 * 0.016)

Confidence Interval ≈ 0.136 ± 0.037 (rounded to three decimal places)

So the 98% confidence interval for the proportion of all customers who experienced an interruption is approximately 0.099 < p < 0.173.

c. The company's quality control manager claims that no less than 10% of its customers experienced an interruption. We can check if this claim is contradicted by examining the confidence interval.

In the confidence interval, the lower bound is 0.099, which is greater than 0.1. Therefore, the confidence interval does not contradict the claim. It is possible that at least 10% of the customers experienced an interruption based on the provided data.

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Answer:

the answer to your question is 576 square feet

Step-by-step explanation:

Step 1: 96 ÷ 4 = 24

Step 2: 24×24 =576

the area under the standard normal curve between z1 = -1.96 and z2 = 1.96 is approximately 0.950 (rounded to four decimal places).

To find the area under the standard normal curve between z1 = -1.96 and z2 = 1.96, we need to calculate the cumulative probability associated with these z-values.

Using a standard normal distribution table or a calculator, we can find the cumulative probability to the left of z1 and z2, respectively.

The cumulative probability to the left of z1 = -1.96 is approximately 0.025 (rounded to three decimal places).

The cumulative probability to the left of z2 = 1.96 is also approximately 0.975 (rounded to three decimal places).

To find the area between z1 and z2, we subtract the cumulative probability to the left of z1 from the cumulative probability to the left of z2:

Area = 0.975 - 0.025 = 0.950

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======================================================

Explanation:

The notation <-5,2> is the same as writing the translation rule \((x,y) \to (x-5,y+2)\)

It says: move 5 units to the left and 2 units up

The point (6,2) moves to (1,2) when moving five units to the left. Then it ultimately arrives at (1, 4) after moving 2 units up. You could move 2 units up first and then 5 units to the left later on, and you'd still arrive at (1, 4). In this case, the order doesn't matter (some combinations of transformations this won't be the case and order will matter).

---------

Or you could write out the steps like so

\((x,y) \to (x-5, y+2)\\\\(6,2) \to (6-5, 2+2)\\\\(6,2) \to (1, 4)\\\\\)

We see that (6,2) moves to (1, 4)

Main Answer:The volume is \(\pi\)/6.

Supporting Question and Answer:

How can we determine the volume using the slicing method when the slices are semicircles perpendicular to the x-axis?

To determine the volume using the slicing method with semicircular slices perpendicular to the x-axis, we need to integrate the areas of the infinitesimally thin slices over the range of x-values. The radius of each semicircle depends on the x-coordinate, and we can use the formula for the area of a semicircle to calculate the area of each slice. By integrating the areas over the given range, we can obtain the total volume of the solid.

Body of the Solution:To find the volume using the slicing method, we need to integrate the areas of the infinitesimally thin slices perpendicular to the x-axis.

In this case, the slices perpendicular to the x-axis are semicircles. The radius of each semicircle depends on the x-coordinate.

Let's denote the variable of integration as x and consider a slice at a specific value of x. The corresponding semicircle's radius is given by r = 1 - x (since the triangle's height is 1 and decreases linearly with x).

The area of a semicircle is given by A = (1/2) * \(\pi\) * r^2.

Integrating the area over the range of x from 0 to 1, we get:

V = ∫[0,1] A dx = ∫[0,1] (1/2) * \(\pi\) * (1 - x)^2 dx

Simplifying and evaluating the integral, we get:

V = (\(\pi\)/2) * ∫[0,1] (1 - 2x + x^2) dx = (\(\pi\)/2) * [x - x^2/2 + x^3/3] |[0,1] = (\(\pi\)/2) * [1 - 1/2 + 1/3] = (\(\pi\)/2) * [2/6] = \(\pi\)/6

Final Answer:Therefore, the volume of the solid bounded by the triangle and the semicircles is π/6, rounded to two decimal places.

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The volume off the given triangle is π/6.

How can we determine the volume using the slicing method when the slices are semicircles perpendicular to the x-axis?

To determine the volume using the slicing method with semicircular slices perpendicular to the x-axis, we need to integrate the areas of the infinitesimally thin slices over the range of x-values. The radius of each semicircle depends on the x-coordinate, and we can use the formula for the area of a semicircle to calculate the area of each slice. By integrating the areas over the given range, we can obtain the total volume of the solid.

To find the volume using the slicing method, we need to integrate the areas of the infinitesimally thin slices perpendicular to the x-axis.

In this case, the slices perpendicular to the x-axis are semicircles. The radius of each semicircle depends on the x-coordinate.

Let's denote the variable of integration as x and consider a slice at a specific value of x. The corresponding semicircle's radius is given by r = 1 - x (since the triangle's height is 1 and decreases linearly with x).

The area of a semicircle is given by A = (1/2) *  * r^2.

Integrating the area over the range of x from 0 to 1, we get:

V = ∫[0,1] A dx = ∫[0,1] (1/2) *  * (1 - x)^2 dx

Simplifying and evaluating the integral, we get:

V = (/2) * ∫[0,1] (1 - 2x + x^2) dx = (/2) * [x - x^2/2 + x^3/3] |[0,1] = (/2) * [1 - 1/2 + 1/3] = (/2) * [2/6] = /6

Final Answer:Therefore, the volume of the solid bounded by the triangle and the semicircles is π/6, rounded to two decimal places.

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Answer:

2/3 is larger

Step-by-step explanation:

3/5 x 3/3 = 9/15

2/3 x 5/5 = 10/15

Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is:  42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.

To prove the above lets us factor and rewrite the radicand in exponential form as follows:

8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)

Rework the expression using

ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x

Simplify the expression 8x² * 5∛3x + 2x² ∛3x

Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:

(40 + 2)x² ∛3x

Calculate the sum to get 42x²∛3x

Thus the simplified version of  8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x

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Full Question:

Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0

A) 42x³

B) 42x²∛3x

C) 10x⁴∛125x

D) 10x²∛125x³

Using the binomial distribution, it is found that she should expect to roll the number cube 46 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

\(E_s(X) = \frac{q}{p}\)

In this problem:

Then:

\(E_s(X) = \frac{23}{0.5} = 46\)

She should expect to roll the number cube 46 times.

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Answer:

answer is 46.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

630

Step-by-step explanation:

630 - 594 = 36

594 - 540 = 54

630 is closest to 594

Answer:

630 is closer

Step-by-step explanation:

The number of units separating 540 and 594 is 54; that separating 594 and 630 is 36.  So 630 is closer to 594.

Considering the provided information and that the volume of a cuboid is the result of multiplying the width by the length by the height, we obtain the following:

Volume of a cuboid= Width * Length * Height

Volume of a cuboid= 3.4cm * 6.2cm * 5cm

Volume of a cuboid= 105.4 cm³

Finally we obtain that the volume of the cuboid is 105.4 cm³

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

to find the number of plants in the pond at the time t we can use the equation N(t) = 150(3)^t.

        The equation that can be used to find the number of plants in the pond at time t, given that the number of plants is growing exponentially, is:

                      N(t)=ab^t.

         The given values in the table for the function N(t) are:

                      t  N(t)0  1501  450

         We can use these values to determine the values of constants a and b in the equation

                       N(t)=ab^t:

          Substitute t = 0 and N(t) = 150 in the equation

                      N(t)=ab^t.

          Then, 150 = a × b^0 → 150

                            = a × 1 → a

                            = 150

            Substitute t = 1 and N(t) = 450 in the equation N(t)=ab^t.

             Then, 450 = 150 × b^1 → b = 3.

     Now that we have found the values of a and b, we can write the equation that can be used to find the number of plants in the pond at time t as:  N(t) = ab^t = 150(3)^t.

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