while traveling across flat land, you notice a mountain directly in front of you. its angle of elevation (to the peak) is 4.5°. after you drive 14 miles closer to the mountain, the angle of elevation is 8°. approximate the height of the mountain.

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

\(V = \frac{4}{3} \times {41}^{3} \pi\)

\( = \frac{275684}{3} \pi\)

= 288695.6097

We have the final answer as

Hope this helps you

The answer on deltamath is

288695.6 in³

Answer:

6.05 kg, 6050 grams

Step-by-step explanation:

The kilograms were already given in your question, so that's one half done.

1 kilogram is equivalent to 1000 grams. If we multiply 6.05 by 1000, then you get 6050, the measurement in grams.

The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).

To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.

To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.

To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.

Therefore, the turning point of the parabola is approximately (-0.5, -3.25).

From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.

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(a) The speed in feet per second is 110 feet per second.

(b) The speed in kilometers per hour is 120.75 kilometers per hour

The speed limit on certain interstate highways, s = 75 miles per hour

a) We have to find the speed in feet per second.

1 mile = 5280 feet

75 miles = 75 x 5280

75 miles = 396,000 feet

s = 396,000 feet/hour

s = 39600/3600 feet/second

s = 110 feet per second

b) We have to find the speed in kilometers per hour.

1 mile = 1.61 km

75 miles = 75 x 1.61

75 miles = 120.75 km

s = 120.75 kilometers per hour

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A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

21x + 1

Step-by-step explanation:

f[g(x)]

= f(7x + 2)

= 3(7x + 2) - 5

= 21x + 6 - 5

= 21x + 1

The value of k can be determined by setting the left-hand limit equal to the right-hand limit at each point within the specified interval.

To find the value of k that makes the function continuous on any interval, we need to ensure that the left-hand limit and the right-hand limit at each point within the interval match the value of the function at that point.

For Exercise 31, we have the function f(x) defined as follows:

f(x) = kx³ - 3x² + 2x

To find the value of k, we need to consider the interval 0 ≤ x ≤ 2. For the function to be continuous at x = 0, the left-hand limit and the right-hand limit must be equal to the value of the function at x = 0.

Taking the left-hand limit at x = 0, we have:

lim(x->0-) f(x) = lim(x->0-) (kx³ - 3x² + 2x) = 0

Taking the right-hand limit at x = 0, we have:

lim(x->0+) f(x) = lim(x->0+) (kx³- 3x² + 2x) = 0

Therefore, to make the function continuous at x = 0, we set the value of f(x) at x = 0 equal to 0:

f(0) = k(0)³ - 3(0)² + 2(0) = 0

Simplifying the equation gives us:

0 = 0

This equation is always true regardless of the value of k. So, any value of k will make the function continuous at x = 0.

For Exercise 34, we have the function g(t) defined as follows:

g(t) = { t + h, if t ≤ 5

        { kt, if t > 5

To find the value of k, we need to consider the interval t ≤ 5 and t > 5 separately.

For the function to be continuous at t = 5, the left-hand limit and the right-hand limit must be equal to the value of the function at t = 5.

Taking the left-hand limit at t = 5, we have:

lim(t->5-) g(t) = lim(t->5-) (t + h) = 5 + h

Taking the right-hand limit at t = 5, we have:

lim(t->5+) g(t) = lim(t->5+) (kt) = 5k

To make the function continuous at t = 5, we set the left-hand limit equal to the right-hand limit:

5 + h = 5k

Therefore, the value of k that makes the function continuous at t = 5 is k = (5 + h)/5.

Please note that in both exercises, the given range of values for x and t determines the intervals where continuity is required. The calculations above provide the condition for continuity within those specific intervals.

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The probability of the resistor surviving 2000 hours is approximately 0.6321 or 63.21%.

The hazard function in this case is 0.00054 or 0.054%.

To calculate the probability of a resistor surviving 2000 hours of use, we can use the exponential distribution formula:

P(X > t) = e^(-λt)

Where:

P(X > t) is the probability that the resistor survives beyond time t.

λ is the failure rate parameter of the exponential distribution.

t is the time for which we want to calculate the probability.

In this case, the mean time between failures (MTBF) is given as 1850 hours. The failure rate (λ) can be calculated as the reciprocal of the MTBF:

λ = 1 / MTBF = 1 / 1850 = 0.00054

Now we can calculate the probability of the resistor surviving 2000 hours:

P(X > 2000) = e^(-λ * 2000) = e^(-0.00054 * 2000) ≈ 0.6321

Therefore, the probability of the resistor surviving 2000 hours is approximately 0.6321 or 63.21%.

The hazard function, denoted as h(t), represents the instantaneous failure rate at time t. For the exponential distribution, the hazard function is constant and equal to the failure rate λ:

h(t) = λ = 0.00054

So, the hazard function in this case is 0.00054 or 0.054%.

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The distance between the starting point and the second obstacle is 13 meters.

And the total length of one lap is equal to the perimeter of the triangle, which measures 30 meters.

We can see that this distance is equal to the hypotenuse of the triangle on the image.

The two legs measure:

5 meters and 12 meters.

Then using the Pythagorean theorem we can write:

d^2 = 5^2 + 12^2

d = √(5^2 + 12^2) = 13

So the distance between the starting point and obstacle 2 is 13 meters.

b) This will be the perimeter of the triangle, it is:

P = 13 m + 12m + 5m = 30m

One full lap has a length of 30 meters.

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Answer:

The correct option is (B).

Step-by-step explanation:

In this case, we need to test whether the claim made by the new brand of gym shoe is correct or not.

Claim: A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps.

So, we need to test whether the average vertical leap of all the athletes increased by 2 inches or not after using the new brand of gym shoe.

The sample procedure would be to compute the average vertical leap of a group of athletes in their regular shoes (or a different pair) and the average vertical leap of a group of athletes in their new shoes.

Compare the two averages to see whether the difference is 2 inches or not.

The experimental group would be the one with the new shoes and the control group would be the one with the different pair of shoes.

Thus, the correct option is (B).

Answer:

B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.

Step-by-step explanation:

equations 1, 2, 4, and 5 are consistent and possibly true, while equation 3 is not consistent.

Let's analyze each equation to determine if they are consistent and possibly true:

1. A - B - C = 0

This equation states that the difference between A, B, and C is zero. It is consistent and possibly true if A = B + C.

2. C = -7.15m

This equation states that the value of C is equal to -7.15m. It is consistent and possibly true if C is indeed equal to -7.15m.

3. |A| - |B| = -2.9m

This equation states that the absolute value of A minus the absolute value of B is equal to -2.9m. It is not consistent because the absolute value of a number is always non-negative, so the left-hand side of the equation can never be negative.

4. (42.1m) * \(\hat{x}\) = (3.2m) * \(\hat{y}\)

This equation states that the product of 42.1m and \(\hat{x}\) (unit vector in the x-direction) is equal to the product of 3.2m and \(\hat{y}\) (unit vector in the y-direction). It is consistent and possibly true if the magnitudes of \(\hat{x}\) and \(\hat{y}\) are appropriately related to satisfy this equation.

5. Ay < 0

This equation states that the y-component of vector A is less than zero. It is consistent and possibly true if the y-component of vector A is indeed negative.

In summary, equations 1, 2, 4, and 5 are consistent and possibly true, while equation 3 is not consistent.

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Among the given equations, the consistent and possibly true equations are:

A - B - C = 0 (Equation 1)

C = -7.15m (Equation 2)

Ay < 0 (Equation 5)

Let's analyze each equation to determine which ones are consistent and possibly true:

1. A - B - C = 0:

This equation represents the sum of three variables, A, B, and C, equal to zero. Without any further information about the variables, we cannot determine its consistency or truth.

2. C = -7.15m:

This equation sets the variable C equal to -7.15m. It is consistent and true if the value of C is indeed -7.15m.

3. |A| - |B| = -2.9m:

This equation states the absolute value of A minus the absolute value of B equals -2.9m. However, the absolute value of a quantity is always positive, so it cannot be negative. Therefore, this equation is inconsistent and unlikely to be true.

4. (42.1m)x^ = (3.2m)y^:

This equation equates a scalar quantity, 42.1m, multiplied by the unit vector x^, with a scalar quantity, 3.2m, multiplied by the unit vector y^. Since x^ and y^ are perpendicular unit vectors, it is not possible for them to be equal. Therefore, this equation is inconsistent and unlikely to be true.

5. Ay < 0:

This equation states that the y-component of vector A is less than zero. It is consistent and possibly true if the y-component of A is indeed negative.

Based on the analysis above, the equations that are consistent and possibly true are equation 2 (C = -7.15m) and equation 5 (Ay < 0).

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Answer:

60 pie

Step-by-step explanation:

The degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 2x+5 has an exponent of 1.

A polynomial is not an expression with a variable that has fractional or negative exponents, divides by a variable, or is contained inside a radical.

The biggest power of the variable that occurs in the polynomial is its degree.

The term with the highest degree—i.e., the term with the largest power of the variable—is the leading term.

The leading coefficient is the leading term's coefficient.

Therefore, the degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

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there is no description:/

The question is an illustration of composite functions.

The given parameters are:

(a) Functions c(n) and n(h)

Let the number of system be n, and h be the number of hours

So, the cost function (c(n)) is:

\(\mathbf{c(n) = Fixed + Additional \times n}\)

This gives

\(\mathbf{c(n) = 5000 + 250 \times n}\)

\(\mathbf{c(n) = 5000 + 250n}\)

The function for number of systems is:

\(\mathbf{n(h) = 5 \times h}\)

\(\mathbf{n(h) = 5h}\)

(b) Function c(n(h))

In (a), we have:

\(\mathbf{c(n) = 5000 + 250n}\)

\(\mathbf{n(h) = 5h}\)

Substitute n(h) for n in \(\mathbf{c(n) = 5000 + 250n}\)

\(\mathbf{c(n(h)) = 5000 + 250n(h)}\)

Substitute \(\mathbf{n(h) = 5h}\)

\(\mathbf{c(n(h)) = 5000 + 250 \times 5h}\)

\(\mathbf{c(n(h)) = 5000 + 1250h}\)

(c) Find c(n(100))

c(n(100)) means that h = 100.

So, we have:

\(\mathbf{c(n(100)) = 5000 + 1250 \times 100}\)

\(\mathbf{c(n(100)) = 5000 + 125000}\)

\(\mathbf{c(n(100)) = 130000}\)

(d) Interpret (c)

In (c), we have: \(\mathbf{c(n(100)) = 130000}\)

It means that:

The cost of working for 100 hours is $130000

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Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

The equivalent expression 36x + 12 is the same as 24x - 48. Because the statement is identical to itself, the label 24x - 48 fits it.

This equation denotes the result of multiplying 24 by x and then subtracting 48.

The phrase is referred to as "36x + 12" since it is a duplicate of itself. This formula denotes the result of multiplying 36 by x and then adding 12.

The formulations in the two scenarios cannot be compared since they use different coefficients for x and different constant terms. The word "neither" does not apply to either phrase because they are both equal to one another.

Therefore, 36x + 12 is equal to the formula 24x - 48.

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The statement is false. If f and g are continuous on [a, b], it does not imply that ∫[a to b] (f(x) × g(x)) dx = ∫[a to b] f(x) dx × ∫[a to b] g(x) dx

In general, the integral of the product of two functions, f(x) and g(x), is not equal to the product of their individual integrals.

To counter the statement, we can provide a counterexample. Consider two continuous functions, f(x) = x and g(x) = x, defined on the interval [0, 1]. The integral of their product, ∫[0 to 1] (f(x) * g(x)) dx, is equal to ∫[0 to 1] (x × x) dx = ∫[0 to 1] \(x^{2}\) dx = 1/3.

On the other hand, the individual integrals of f(x) and g(x) are ∫[0 to 1] f(x) dx = ∫[0 to 1] x dx = 1/2 and ∫[0 to 1] g(x) dx = ∫[0 to 1] x dx = 1/2, respectively. The product of these individual integrals, (1/2) × (1/2) = 1/4, is not equal to the integral of the product.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

\(6x+6x-7=5\\12x-7=5\\12x=12\\x=1\)

Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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Answer:

larger number = 3

smaller number = -1

Step-by-step explanation:

x = larger number

y = smaller number

x+y=2

8-2y=4x-2 ---> 10 = 4x+2y

10 = 4x+2y

5=2x+y

y = 5-2x

2x=5-y

x+5-2x = 2

-x+5=2

-x=-3

x=3

3+y=2

y=-1

Answer:

Pythagorean theorem

greg ride the bicycle 10 miles each day...

Step-by-step explanation:

\(c {}^{2} = \sqrt{8 {}^{2} + 6 {}^{2} } \\ c {}^{2} = \sqrt{64 + 36} \\ c {}^{2} = \sqrt{100} \\ c = 10\)

Answer:

\(d = 8 + 2t\)

Step-by-step explanation:

Given

\(Rate = 2km/trip\)

\(Base\ Cycle = 8km\)

\(d = total\ distance\)

\(t = cycles\)

Required

Determine the expression for this scenario

The expression can be derived from:

\(Total\ Distance = Base\ Cycle + Rate * Cycles\)

Substitute d for Total Distance and t for cycles

\(d = Base\ Cycle + Rate * t\)

Substitute values for Base Cycle and Rate

\(d = 8 + 2* t\)

\(d = 8 + 2t\)

The Maclaurin series for f(x) = x cos(9x) is Σ[n=0 to ∞] ((-1)^n (9x)^(2n+1))/(2n+1)!

A function expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series. Series can be used to determine the Maclaurin series of a function f (x) up to order n. [ f , x , 0 , n ]

To obtain the Maclaurin series for the function f(x) = x cos(9x), we can use the Maclaurin series for cos(x) and substitute 9x for x:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

Substituting 9x for x, we get:

cos(9x) = 1 - (9x)^2/2! + (9x)^4/4! - (9x)^6/6! + ...

= 1 - 81x^2/2! + 6561x^4/4! - 531441x^6/6! + ...

Multiplying by x, we get:

x cos(9x) = x - 81x^3/2! + 6561x^5/4! - 531441x^7/6! + ...

Therefore, the Maclaurin series for f(x) = x cos(9x) is:

f(x) = x cos(9x) = Σ[n=0 to ∞] ((-1)^n (9x)^(2n+1))/(2n+1)!

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Answer:

First find x

70-x=4x

-x-4x=-70

-5x=-70

x=14

Angle BEC = 70°-x

=70-14

=56°

Angle AEB = 180- 56

= 124°

Angle DEA =4x

= 4× 14

= 56°

Angle CED = 180-56

=124°

The length of the base edge of the square pyramid is 6 feet.

The surface area of a square pyramid is 96 square feet. The height is two thirds of the length of the base edge.

The length of the base edge can be found as follows:

Hence,

surface area of square pyramid = a² + 2al

where

Therefore,

using Pythagoras's theorem, let find the slant height of the pyramid.

c² = a² + b²

where

Hence,

height = 2 / 3 a

Therefore,

l² = (2 / 3 a)² + (1 / 2a )²

l² = 4 / 9 a² + 1 / 4 a²

l² = 25 / 36 a²

square root both sides

l = 5 / 6 a

Hence,

surface area of square pyramid = a² + 2a(5 / 6 a)

surface area of square pyramid = a² + 10 / 6 a²

surface area of square pyramid = 16 / 6 a²

96 = 16 / 6 a²

96 = 8 / 3 a²

cross multiply

96 × 3 = 8a²

288 / 8 = a²

a² = 36

a = √36

a = 6 feet

Therefore, the base length is 6 feet.

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