A man drove 14 miles directly east from his home, made a left turn at an intersection, and then traveled 7 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

The equation to find the volume of the cylinder is: V = 45π cubic inches.

The volume of things or containers is often measured in cubic inches in the United States. It is the amount of area that a cube with one inch sides takes up. A cubic inch is about equal to 16.387 millilitres or 0.016387064 litres. The displacement of an engine—a measurement of the total amount of air and fuel the engine can compress into its cylinders—is frequently discussed in terms of cubic inches.

The formula to find the volume of a cylinder is:

V = πr²h

Where V is the volume, r is the radius, and h is the height.

Substituting the values given in the problem, we get:

V = π(3²)(5)

V = π(9)(5)

V = 45π

Therefore, the equation to find the volume of the cylinder is:

V = 45π cubic inches.

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Answer:

137 yd2

Step-by-step explanation:

Answer:

To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:

11x - 6y = 2 (multiply both sides by 5)

-8x + 5y = 3 (multiply both sides by 11)

55x - 30y = 10

-88x + 55y = 33

Adding the two equations, we get:

-33x + 25y = 43

Solving for y, we get:

y = (33x + 43)/25

Substituting this expression for y into either of the original equations and simplifying, we get:

x = -1/7

Substituting this value of x into the equation for y, we get:

y = 1/35

Therefore, the coordinates of the point of intersection are (-1/7, 1/35).

The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.

We know that the circle with radius 8 and center (-2,-1) has the equation:

(x + 2)² + (y + 1)² = 8²

Substituting x = 3 and y = b, we get:

(3 + 2)² + (b + 1)² = 8²

Simplifying, we get:

25 + (b + 1)² = 64

(b + 1)² = 39

Taking the square root of both sides, we get:

b + 1 = ± √39

Therefore, the possible values of b are:

b = -1 ± √39

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The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.

We need to compare the degrees of the numerator and denominator.

The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2

Furthermore, f(x) = 3/2 + x/(2x² - 1)

This expression shows that the function has a slant asymptote given by the line: y = x/2

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An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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4Construct a function to model a linear relationship between two quantities.

The "equivalent-form" of equation "x/12 - 7 = x/4" is "x - 84 = 3x", the correct option is (a).

In order to find the equivalent form of the equation "x/12 - 7 = x/4", we first need to solve for "x",

So, we first, simplify left side of equation by finding a common denominator for the two fractions:

⇒ x/12 - 7 = x/4,

⇒ x - 84 = 3x,

⇒ -84 = 2x,

⇒ x = -42,

Now, we check the given options by substituting the value of "x",

Option (a) : x - 84 = 3x,

Substituting x = -42,

We get,

⇒ -42 - 84 = 3(-42),

⇒ -126 = -126

This equation is true, so option (a) is an equivalent form of the original equation.

Option (b) : x - 74 = 12x,

Substituting x = -42,

We get,

⇒ -42 - 74 = 12(-42),

⇒ -116 = -504,

This equation is not true, so option (b) is not an equivalent form of the original equation.

Option (c) : x - 7 = 3x,

Substituting x = -42,

We get,

⇒ -42 - 7 = 3(-42),

⇒ -49 = -126,

This equation is not true, so option (c) is not an equivalent form of the original equation.

Therefore, the correct option is (a) .

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The given question is incomplete, the complete question is

Select an equivalent form of this equation: x/12 - 7 =x/4

(a) x - 84 = 3x

(b) x - 74 = 12x

(c) x - 7 = 3x

The simplest form of log5+log6-log2​ is:  log15.

Let us simplify log5 + log6 - log2 by making use  logarithmic rules:

log a + log b = log (ab)

log a - log b = log (a/b)

So,

log5 + log6 - log2

= log (5 x 6) - log2

= log30 - log2

Now let make use of the  logarithmic rule:

log a - log b = log (a/b) = log a - log b

log30 - log2

= log (30/2)

= log15

Therefore the simplest form is log15.

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The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.

The formula for finding the force parallel to the incline:

= mass of the monolith x acceleration due to gravity x sin( slope angle )

Mass in kg :

=  57 tons x 1000

= 57, 000 kg

Force parallel to the incline:

= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )

= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )

= 32, 120.52 Newtons

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The solution to the equation x + 2(7 - x) = 12 is x = 2.

Given the equation in the question:

x + 2(7 - x ) = 12

To solve the  equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.

x + 2(7 - x) = 12

Apply distributive property

x + 2×7 + 2×-x = 12

x + 14 - 2x = 12

Combine like terms by subtracting 14 from both sides:

x - 2x = 12 - 14

-x = -2

Solve for x by dividing both sides by -1:

-x/-1 = -2/-1

x = 2

Therefore, the value of x is 2.

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If "function-g" defined for all real numbers as g(x) = x² + 6, then the value of g(-5) = 31, g(-2) = 10 and g(-1) = 7.

In mathematics, a function is generally denoted by a symbol such as "f" or "g", and its definition is given by an equation or formula that specifies the relationship between the input and output values.

The function "g" is given as : g(x) = x² + 6;, which is defined for all "real-numbers",

So, to find g(-5), g(-2), and g(-1), we simply substitute these values of x into the function "g" and simplify the resulting expressions:

⇒ g(-5) = (-5)² + 6 = 25 + 6 = 31,

⇒ g(-2) = (-2)² + 6 = 4 + 6 = 10,

⇒ g(-1) = (-1)² + 6 = 1 + 6 = 7.

Therefore, g(-5) = 31, g(-2) = 10, and g(-1) = 7.

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The given question is incomplete, the complete question is

Suppose that the function G is defined for all real numbers as g(x) = x² + 6. Find g(-5), g(-2) and g(-1).

Answer:

B

Step-by-step explanation:

Notice that all y-intercepts are the same (doesn't give a clue to the answer).

The line has a downward slant as you move from left to right, so the slope is negative (eliminating A & C as answers).

Determine the actual slope by identifying the y-intercept and x-intercept, and calculate Rise over Run:

  Rise = -6 (goes from +6 to 0)

  Run = +12

  -6/12 = -1/2

Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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Answer:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3

So, 3,280 liters of water flows from the tank between the 14 minute mark and the 34 minute mark.

In mathematics, a function is a rule or relationship that assigns a unique output or value for each input or value in its domain. In other words, a function is a mathematical object that takes an input value and produces a corresponding output value. Functions are commonly denoted by f(x), where x represents the input value, and f(x) represents the corresponding output value.

Here,

To find the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark, we need to find the difference between the amount of water at the 14 minute mark and the amount of water at the 34 minute mark. At the 14 minute mark, t = 14, so we can substitute this value into the equation to get:

R(14) = 8000 - 250(14) + 2(14)²

R(14) = 5,720 liters

At the 34 minute mark, t = 34, so we can substitute this value into the equation to get:

R(34) = 8000 - 250(34) + 2(34)²

R(34) = 2,440 liters

Therefore, the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark is:

R(14) - R(34) = 5,720 - 2,440

R(14) - R(34) = 3,280 liters

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Answer:

L * W

Step-by-step explanation:

To find the difference in volume between the original prism and the new prism, we need to calculate the volume of each prism and then subtract the volumes.

Let's assume the base of the prism is a rectangle with length L, width W, and height H.

The volume of a prism is given by V = L * W * H.

Original Prism:

Height = 3 inches

Volume = L * W * 3

New Prism:

Height = 4 inches

Volume = L * W * 4

The difference in volume between the original prism and the new prism is:

New Prism Volume - Original Prism Volume = (L * W * 4) - (L * W * 3)

= L * W * (4 - 3)

= L * W

Therefore, the difference in volume is L * W.

Since we do not have specific dimensions or values for L and W, we cannot calculate the exact difference in volume. We would need additional information to determine the values of L and W or their relationship to find the difference in volume.

Answer:

Step-by-step explanation:

The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.

In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.

Thus, we would apply direct proportion.

Note: There are 16 cups of frozen strawberries in a gallon.

By direct proportion:

16 cups = 1 gallon

X cups = 3 gallons

Cross-multiplying, we have:

X = 16 × 3

X = 48 cups of frozen strawberries.

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The distance between point (−7, 8) and point (5, 8) is 12 units (since they are on the same horizontal line). The distance between point (−7, 8) and point (−7, −5) is 13 units (using the Pythagorean theorem). Therefore, the point that is farther away is option D: Point (−7, −5), and it is 13 units away.

The storage can hold approximately 10.94 cubic meters of grain.

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.  

To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.  

Here we have

Adam’s family maintains storage that can hold 14.3 yd³ of grain.

Given that 1 yard is approximately equal to 0.9144 meters

To convert cubic yards (yd³) to cubic meters (m³),

Use the conversion factor:

1 yd³ = (0.9144 m)³

So, we can convert 14.3 cubic yards of grain to cubic meters as follows:

14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³

Rounding this answer to the nearest hundredth gives us:

10.94 m³ rounded to the nearest hundredth = 10.94 m³

Therefore,

The storage can hold approximately 10.94 cubic meters of grain.

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Answer:

C

Step-by-step explanation:

The equation is:

y = [tex]\frac{1}{4}[/tex]x - 8

If you plug in the x and y value from the table, you find they are solutions to the equation.

(36,1)

y = [tex]\frac{1}{4}[/tex]x - 8  Substitute in 36 for x and 1 for y

1 = [tex]\frac{1}{4}[/tex](36) - 8

1 = 9 - 8

1 = 1

You can do the same thing for all of the other points on the table.

Helping in the name of Jesus.

The value of the function f/g is (x - 1) / (x + 8)

Let's start by writing out the functions we are given:

f(x) = 4 / (x + 8)

g(x) = x / (x - 1)

To find f/g, we need to divide f(x) by g(x). We can do this by multiplying f(x) by the reciprocal of g(x), which is (x - 1) / x. Multiplying f(x) by this reciprocal gives us:

f(x) * (x - 1) / x = 4 / (x + 8) * (x - 1) / x

To simplify this expression, we can first find a common denominator for the two fractions on the right-hand side:

4 / (x + 8) * (x - 1) / x = 4(x - 1) / x(x + 8)

Now we can simplify this expression by canceling out any common factors in the numerator and denominator. In this case, we can cancel out a factor of 4 and a factor of (x - 1):

4(x - 1) / x(x + 8) = (x - 1) / (x + 8)

Therefore, the quotient of f(x) and g(x), or f/g, is:

f/g = (x - 1) / (x + 8)

We can interpret this expression as a new function, h(x), where h(x) = f(x) / g(x) = (x - 1) / (x + 8). This new function takes a value of x and returns the ratio of f(x) to g(x) at that value.

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The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).

Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)

Where:

(h, k) = vertex

4p = distance between the vertex and focus

Comparing this with (x + 3)² = -20(y + 1) will gives us

(x + 3)² = -20(y + 1)

= (x - (-3))² = -20(y - (-1))

The vertex of the parabola is = (-3, -1)

4p = -20

p = -20/4

p = -5

The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.

The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.

The endpoints of the latus rectum are:

(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).

Therefore, the correct option is f.

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Answer: Directly proportional.

Step-by-step explanation:

      y = -x is directly proportional for a few reasons.

➜ The graph of this equation is a straight line, so all the ratios of points are equal.

➜ The constant of proportionality (k) is equal to -1.

➜ This line intersects the graph at the origin (0, 0).

➜ See the graph below.

The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.

The area of a triangle = 1/2 * b * h, where:

h is the height of the triangle, and

b is the base length of the triangle.

Given the following:

Height of triangle = √6

Base length of the triangle = √24

Plug in the values:

Area of triangle = 1/2 * √24 * √6

= (√24 * √6) / 2

= √144 / 2

= 12/2

Area of triangle = 6 square units.

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Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

Answer:

Step-by-step explanation:
To test the null hypothesis that the proportion of red light runners is the same at both intersections, we can use a two-sample z-test for proportions.

Let p1 be the proportion of red light runners at the first intersection, and p2 be the proportion of red light runners at the second intersection. We want to test the null hypothesis:

H0: p1 = p2

against the alternative hypothesis:

Ha: p1 ≠ p2

We can use the following formula to calculate the test statistic:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of red light runners at the two intersections, and n1 and n2 are the sample sizes.

For the first intersection, we have x1 = 24 and n1 = 127. For the second intersection, we have x2 = 29 and n2 = 164.

The pooled sample proportion is:

p_hat = (x1 + x2) / (n1 + n2) = (24 + 29) / (127 + 164) = 0.167

The test statistic is:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) = (0.189 - 0.177) / sqrt(0.167 * (1 - 0.167) * (1/127 + 1/164)) = 0.99

Using a standard normal distribution table, we can find that the probability of getting a z-value of 0.99 or greater is 0.160. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the proportion of red light runners differs between the two intersections.

The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.

Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.

Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.

The number of Sophomores in Mathematics Majors = 16

The number of Sophomores in Non-Mathematics Majors = 17

The total number of Sophomores in Mrs. Burke's Mathematics Class = 33

The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)

Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors  Total

Freshmen                          19                             18                                 37

Sophomores                     16                             17                                 33

Juniors                               11                             15                                 26

Seniors                              12                             13                                25

Total                                 58                            63                                121

Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.

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Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors

Freshmen                          19                             18

Sophomores                     16                             17

Juniors                               11                             15

Seniors                              12                             13