A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)

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.

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

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 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 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

Step-by-step explanation:

V = 1/3 x π x r² x h

48 = 1/3 x π x r² x 9

48÷3π = r²

√48÷3π =r

so, r= 2.26 (3.s.f)

Answer:

Step-by-step explanation:

You want to classify the functions shown in the tables as linear, quadratic, or exponential.

We notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.

The differences have the following interpretation:

The differences of y-terms are constant at 3 -5 = -2.

The function is linear.

The differences of y-terms are constant at 5 -2 = 3.

The function is linear.

We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."

The differences of y-terms are ...

  1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20

The differences of differences are ...

  4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8

The second differences are constant.

The function is quadratic.

The first differences are ...

  3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54

The second differences are

  6 -2 = 4, 18 -6 = 12, 54 -18 = 36

We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.

The function is exponential.

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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A. The 51st note on a piano keyboard corresponds to a pitch of 440 cycles per second.

B. The pitch that is 73 notes higher on the keyboard has a frequency of about 1760 cycles per second.

A. Use the formula to find how many notes up the piano keyboard the pitch of 440 cycles per second corresponds to:

440 = 27.5 × 2⁽ⁿ⁻¹⁾/12

Dividing both sides by 27.5 and taking the logarithm with base 2 gives:

log₂(440/27.5) = (n-1)/12

n-1 = 12 × log₂(440/27.5)

n-1 = 12 × 4.1702 ≈ 50.042

n ≈ 51.042

Therefore, the pitch of 440 cycles per second is the 51st note up the piano keyboard.

B. Use the same formula to find the frequency of the pitch that is 73 notes up the keyboard:

73 = 1 + 12 log₂(f/27.5)

72 = 12 log₂(f/27.5)

6 = log₂(f/27.5)

f/27.5 = 2⁶

f = 27.5 × 2⁶

f ≈ 1760

Therefore, the frequency of the pitch that is 73 notes up the keyboard is approximately 1760 cycles per second.

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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 simplified expression of  2x multiplied by 7 with the exponent of 4 is 4,802x.

The expression is simplified by applying the rules of multiplication and exponent rules.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the resultant solution of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the simplified expression of  2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.

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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.

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.

Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Let x represent the number of candy that Reese sell and y represent the number of Skittles candies

Reese's sells for $1 and skittles for $1.50

34 candies was sold, hence:

x + y = 34      (1)

He made $41, hence:

x + 1.5y = 41    (2)

Solving both equations simultaneously:

x = 20; y = 14

Reese had 20 candy and Skittles had 14 candy.

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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:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3

Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

The practical domain of the situation is [0, ∞].

The practical range of the situation is [0, 100].

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [0, ∞] or 0 ≤ x ≤ ∞.

Range = [0, 100] or 0 ≤ y ≤ 100.

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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 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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Note that 7th grade mean = 277.86

the 5th grade mean = 254.77

So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .

To compute the means here   is what we did

7 th  grade mean = (1 × 10) + (1 × 11) +   (2 × 12) + (1 × 13) +   (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) +   (3 × 20) / 21

= 277.857142857

≈ 277.86

For the 5th grade mean

5th  grade mean = (1 × 8)   + (2 × 9) + (2 × 10) +   (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17)  +  (2 × 18) + (1 × 19) + (1   × 20) / 26 = 12.5

= 254.769230769

≈ 254.77

This means that  trully,  the relationship between the mean is that the 7  th grade mean is higher than the 5 th grade mean.

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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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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 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:

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 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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