The mean score of the students in Dr. Battle’s math class on the most recent quiz was 78 points with a standard deviation of 6 points. If these scores can be modeled using a normal distribution, which percentage best represents the number of students with quiz scores between 72 and 90 points?

Approximate Percentages of Data in a Normal Distribution:

• 68% of the data lie within 1 standard deviation of the mean.
• 95% of the data lie within 2 standard deviations of the mean.
• 99.7% of the data lie within 3 standard deviations of the mean.
Responses

A.68.0%
B.81.5%
C.95.0%
D.97.5%

Answer:

the height of the trapezoid is 25 yards.

Step-by-step explanation:

The area of a trapezoid is given by the formula:

Area = (1/2) * (b1 + b2) * h

where b1 and b2 are the lengths of the parallel bases and h is the height of the trapezoid.

In this problem, we are given the area of the trapezoid (600 yd^2), as well as the lengths of the two parallel bases (25 yd and 23 yd). Let's use this information to find the height of the trapezoid.

We can start by rearranging the formula for the area to solve for the height:

h = (2 * Area) / (b1 + b2)

Substituting the given values, we get:

h = (2 * 600 yd^2) / (25 yd + 23 yd)

Simplifying, we get:

h = 1200 yd^2 / 48 yd

h = 25 yd

Therefore, the height of the trapezoid is 25 yards.

The given vertices don't form parallelograms.

A parallelogram is a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and have the same length. Examples of parallelograms include rectangles, rhombuses, and squares.

Here we have

The coordinates of the vertices of quadrilateral LOVE are L (-2, -1), O(2, 1), V (5, 0), and E (-1, -3).  

Using the distance formula we can find the lengths of the sides as follows  

From L (-2, -1) and O(2, 1),

=> LO = √[ (2 + 2)² + (1 + 1)² ] = √20

From O(2, 1) and V (5, 0)

=> OV = √[ (5 - 2)² + (0 + 1)² ] = √10      d = √(x2 - x1)^2 + (y2 - y1)^2)

From V (5, 0) and E (-1, -3)

=> VE = √[(-1 - 5)² + (-3 - 0)²] = √45

From L (-2, -1) and E (-1, -3)

=> LE = √[(-1 +2 )² + (-3 + 1)²] = √5

Here LO ≠ OV ≠ VE ≠ LE

Therefore,

The given vertices don't form parallelograms.

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There are 640 juniors enrolled in Eagle Mountain High school.

Percentage can be define as the way of shown a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "by the hundred." Percentages are commonly used to represent proportions or rates, and they are denoted using the symbol "%".

Let's denote the total number of juniors in the high school as "x".

From the problem, we know that 90% of the juniors have a driver's license. We can express this as:

0.9x = 576

To solve for x, we can divide both sides by 0.9:

x = 576 / 0.9

x = 640

Therefore, there are 640 juniors enrolled in Eagle Mountain High school.

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The measures of the angles in the parallel lines is

m∠a = 97°

m∠b = 15°

m∠c = 68°

m∠d = 68°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the two parallel lines be represented as l and m

Now , the transversal line is t

The measure of m∠a = 97° ( corresponding angles )

The measure of m∠d = 180° - 112° ( angles in a straight line = 180° )

So , the measure of m∠d = 68°

The measure of m∠c = measure of m∠d ( alternate interior angles )

So , the measure of m∠c = 68°

From the triangle formed by the intersection of lines ,

The measure of m∠b = 180° - ( a + d ) ( angles of a triangle = 180° )

So , the measure of m∠b = 180° - ( 97° + 68° )

The measure of m∠b = 15°

Hence , the measures of angles are solved

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Answer:

Step-by-step explanation:

y = √24²+32² = √1600 = 40

find base angle Ф on the right:

Ф = sin⁻¹(32/40) = 53.13

find other base angle (sum of interior angles of a Δ is 180):

180 - 90 - 53.13 = 36.87

now you can use the Law of Sines to find z, x:

40/sin36.87 = z/sin53.13 = (x+24)/sin90

z = 40(sin53.13)/sin36.87 = 53.33

sin36.87(x+24) = 40(sin90)

x+24 = 40/sin36.87 = 66.66

x = 66.67 - 24 = 42.67

double check the answers:

y² + z² = (x+24)²

40² + 53.33² = (42.67 + 24)²

1600 + 2892 = 4444

4444 = 4444  answers are correct!

Answer:

h [tex]\ge[/tex] 48

Step-by-step explanation:

This inequality states that the height h, must be either equal to 48 to greater than 48.

Answer:The easiest way to do this is to just raise 10 to the negative value of the pH.  Thus, in this case hydrogen ion concentration would be 1x10-2.4.   However, one doesn't usually leave it that way, so you put it in to the more conventional form as

3.98x10-3 and this would be the hydrogen ion concentration.  If you take the negative log of this number (pH) you will get 2.4

The measure of the angle ∠ADB of the parallelogram is m∠ADB = 49°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented a ABCD

Now , the measure of ∠ACB = ( 13x - 16 )°

The measure of ∠ACB = ( 9x + 4 )°

And , the measures of the angles ∠ACB = measure of ∠ACB

On simplifying , we get

13x - 16 = 9x + 4

On simplifying , we get

4x = 20

Divide by 4 on both sides , we get

x = 5

So , the measure of m∠ACB = ( 9 ( 5 ) + 4 ) = 49°

The measure of m∠ADB = measure of m∠ACB ( alternate angles )

So , the measure of m∠ADB = 49°

Hence , the angles of the parallelogram are solved

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Answer:

0.05%

Step-by-step explanation:

The answer should be: x [tex]\geq[/tex] -10

Answer: $1.25

Step-by-step explanation:   Noah has $1.25 because since Noah has 50 cents, and you add on another 75, you get $1.50

Answer:

Noah has 50 cents initially and his mother gives him 3 quarters, which is 75 cents (3 quarters x 25 cents/quarter).

Therefore, in total, Noah has 50 cents + 75 cents = 125 cents.

In dollars, that is $1.25.

Answer: Let's define the events:

A: a proposal is judged worthy of funding by the first panel

B: the decision to fund a proposal is reversed by the second panel

We want to find the probability of the intersection of events A and B (i.e., a worthy proposal is disapproved by both panels). We can use the formula:

P(A and B) = P(B|A) * P(A)

We know that P(A) = 0.22 (the probability that a proposal is judged worthy of funding by the first panel). We also know that when a proposal is judged worthy of funding by the first panel, the probability that the decision to fund is reversed by the second panel is 0.74 (i.e., P(B|A) = 0.74).

Plugging in these values, we get:

P(A and B) = 0.74 * 0.22 = 0.1628

Therefore, the probability that a worthy proposal is disapproved by both panels is 0.1628, or approximately 16.28%.

Step-by-step explanation:

Answer:

We should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

Step-by-step explanation:

This problem can be solved using the binomial distribution, which can tell us the probability of getting a certain number of successes in a given number of trials, each with a certain probability of success. In this case, the trials are the bonds, the probability of success is 50% (the chance that a bond will not default), and we want to know how many bonds we need to buy to have at least a 97% chance of getting 5 or more successes.

Let X be the number of bonds that do not default. We want to find the smallest value of n (the total number of bonds we buy) such that P(X ≥ 5) ≥ 0.97.

Using the binomial distribution, we can calculate that the probability of getting exactly k successes out of n trials with a probability p of success is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.

To find P(X ≥ 5), we can calculate the probabilities of getting 5, 6, 7, 8, 9, or 10 successes and add them up:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

We want this probability to be at least 0.97, so we can set up the following inequality:

P(X ≥ 5) ≥ 0.97

P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) ≥ 0.97

We can then use a spreadsheet or a binomial probability table to find the smallest value of n that satisfies this inequality. For example, using Excel's BINOM.DIST function, we can enter the following formula in a cell:

=BINOM.DIST(4,n,0.5,TRUE) + BINOM.DIST(5,n,0.5,TRUE) + BINOM.DIST(6,n,0.5,TRUE) + BINOM.DIST(7,n,0.5,TRUE) + BINOM.DIST(8,n,0.5,TRUE) + BINOM.DIST(9,n,0.5,TRUE) + BINOM.DIST(10,n,0.5,TRUE)

where n is the number of bonds we want to buy, and TRUE indicates that we want to calculate the cumulative distribution function (CDF) up to the given value of k.

We can then use Excel's Goal Seek tool to find the smallest value of n that makes this formula equal to 0.97. For example, if we set the target value to 0.97 and the "Set cell" to the formula cell, and we vary the "To value" of n, Goal Seek finds that the smallest value of n that satisfies the inequality is 19. Therefore, we should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

The number of ducks in a farm are 20 and the number of pigs in a farm are 8.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, in a farm there are 28 animals and combined they have 72 legs.

Let the number of pigs be p and let the number of ducks be d.

Here, p+d=28 ------(i)

4p+2d=72 -------(ii)

From equation (i), p=28-d

Substitute p=28-d in equation (ii), we get

4(28-d)+2d=72

112-4d+2d=72

112-72=2d

d=20

Substitute d=20 in equation(i), we get

p+20=28

p=8

Therefore, the number of ducks in a farm are 20 and the number of pigs in a farm are 8.

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The answer to this question is as follows The formula for the letter C is: equation  $1.25C = $72.50

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

Let C represent the volume of vehicles that passed through the booth.

As $1.25 is the amount collected per vehicle, the following equation represents the total amount collected:

Total = $1.25 plus C

Also, we are aware that $72.50 was collected in one hour, allowing us to create another equation:

$72.50 = $1.25 × C

We may divide both sides by $1.25 to find C:

C = $72.50 ÷ $1.25

C = 58

58 vehicles passed through the booth as a result.

The formula for the letter C is:

$1.25C = $72.50

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Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

The function F: R²⇒R²

where, [tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex], is not a linear transformation, as the y-intercept of the given function is not zero, so, we can say that, given function  is not a linear transformation.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

the function is defined as, F: R²⇒R²

where,[tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]

so, here, the y-intercept of the function is,  [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]  

now, we know that,  [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex] ≠ 0

so, the y-intercept is not zero.

again, we have,

now, we know that,

A single variable function f(x)=ax+b is not a linear transformation unless its y-intercept b is zero.

we have that,

the given function doesn't have y-intercept = 0.

so, we get, given function  is not a linear transformation.

Hence, The solution is, as the y-intercept of the given function is not zero, so, we can say that, given function  is not a linear transformation.

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The weekly growth rate of these gnats is approximately 1.38%.

With discrete growth, we may observe change taking place following a particular event. We receive fresh options when we flip a coin. We pay interest once a year. After a successful mating season, young are produced. Change occurs continuously in an economy that is growing. We are unable to remark, "It changed here," in reference to an occurrence. The pattern is always changing (radioactive decay, a bacteria colony, or perfectly compounded interest).

Given that,

G(t) = 500(1.182)t

Using the growth function for 52 weeks = 1 year we have:

= 500(1 + r)⁵²ˣ

where r is the weekly growth rate.

To find the weekly growth rate, we can first rewrite the equation as:

1 + r = (1.182)⁽¹⁾⁵²

1 + r = 1.0138

r = 0.0138

The equivalent equation using the weekly growth factor is:

G(t) = 500(1.0138)⁵²ˣ

The weekly growth rate of these gnats is approximately 1.38%

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Answer:

The area of a rectangle is given by the product of its length and width. In this case, the length of the rectangle is -x + 18, and the width is x + 4. So, the area is:

Area = (length) x (width)

= (-x + 18) x (x + 4)

= -x^2 + 14x + 72

Therefore, the area of the rectangle is -x^2 + 14x + 72.

The total area of the composite figure is 107/216 square yards.

What is Area?

Area is a measure of the size of a two-dimensional shape or surface. It is the amount of space inside the boundaries of a flat object, measured in square units such as square meters, square feet, or square inches.

To find the total area of the composite figure, we need to first convert the dimensions from inches to yards, since the given scale is in inches per yards.

Since 1 yard is equal to 3 feet, which is equal to 36 inches, we have:

The height of the triangle is 6/36 = 1/6 yards.

The base of the triangle is 9 times the height, which is 9/6 = 3/2 yards.

The length of the rectangle is 7/9 yards.

The width of the rectangle is 6/9 = 2/3 yards.

The area of the triangle is:

(1/2) x (1/6) x (3/2) = 1/8 square yards.

The area of the rectangle is:

(7/9) x (2/3) = 14/27 square yards.

Therefore, the total area of the composite figure is:

1/8 + 14/27 = 107/216 square yards.

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No because it is not possible to groom 0.2 of an animal.

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, the median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.

To support this, we can also calculate the median and mode of the data set to see if they are close to the mean. The median is the middle value of the sorted data set, which is 8 in this case, and the mode is the most common value, which is also 7 and 8 in this data set. So, the mean, median, and mode are all relatively close to each other, indicating that the data is roughly symmetric around the center.

Based on the given data, the mean of 8.2 animals per day can be considered as a reasonable measure of central tendency.

Hence the answer is No because it is not possible to groom 0.2 of an animal.

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Answer:

Yes, because there is no outliers to skew the data.

Step-by-step explanation:

I did the quiz

Answer:

True

Step-by-step explanation:

Given a function:
[tex]\displaystyle{f(x)=\sin 3x + x}[/tex]

Verify that f(-x) = -f(x) by substitution -- therefore:

[tex]\displaystyle{f(-x) = -f(x)}\\\\\displaystyle{\sin 3\left(-x\right)+\left(-x\right) = -\left(\sin 3x + x\right)}\\\\\displaystyle{\sin \left(-3x\right) - x = -\sin 3x - x}\\\\\displaystyle{-\sin 3x - x = -\sin 3x - x}[/tex]

Both sides are equal, hence f(-x) = -f(x).

The slopes of the points are computed below

The slope of any two points is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Using the above as a guide, we have the following slopes in set 2

For set 3, we have the following slope values

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Answer:

B

Step-by-step explanation:

The dashed lines are problem asymptotes, where the denominator is 0. It's showing those at x = 0 and x = 4. Plug in 0 to answer B and you get

(0)(0-4) and that equals 0

Plugging in 4, you get

(4)(4-4) = 4(0) and that also equals 0

0 is what creates that space in the function and disconnects it

Answer: One possible expression that equals the target number (-2) using the given numbers (-1, -3, -5, -7, and -2) and basic arithmetic operations (+, -, *, /) is:

-3 * (-5) + (-7) - (-2) / (-1) = -2

Explanation:

-3 * (-5) = 15 (multiplication of -3 and -5 gives +15)

-7 - (-2) = -5 (subtracting a negative is the same as adding a positive, so -7 - (-2) = -7 + 2 = -5)

-2 / (-1) = 2 (dividing a negative number by a negative number gives a positive result, so -2 / (-1) = 2)

Therefore, 15 + (-5) + 2 = -2

Step-by-step explanation:

In the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

An ellipse is a geometric shape that is a type of curve. In mathematics, an ellipse is defined as a set of points in a plane, such that the sum of the distances between any point on the curve and two fixed points is a constant which is known as foci.

To identify the major and minor axes of an ellipse, you can use both the graph and the equation of the ellipse.

Identify the major and minor axes using the graph: The major axis is the longest diameter of the ellipse, which passes through the center and touches the curve at two points called the vertices. The minor axis is the shortest diameter of the ellipse, which also passes through the center and touches the curve at two points called the co-vertices. On the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

Identify the major and minor axes using the equation: The equation of an ellipse can be written in the standard form:

[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

where the ellipse's center is (h, k), the semi-major axis' length is a, and the semi-minor axis' length is b. The semi-major axis is half the length of the major axis, while the semi-minor axis is half the length of the minor axis. Therefore, you can identify the major and minor axes by looking at the denominators of the terms that contain x and y in the equation. The larger denominator corresponds to the semi-major axis, while the smaller denominator corresponds to the semi-minor axis.

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It is the last one ...................

The solutions are given below.

Gross domestic product is a monetary measure of the market value or the market value of all the final goods and services produced and sold in a specific time period by a country or countries, generally "without double counting the intermediate goods and services used up to produce them".

here, we have,

1a. We can see immediate short run aggregate supply in North vaudeville in column A. This is because the price is fixed while output increases

1b. We can see short run aggregate supply in North vaudeville in column c. This is because output increases with price increase.

1c we can see long run aggregate supply in North vaudeville in column B. This is because output is constant with price increase.

Assuming output per hour of work decreases by 25% for column C then for each price, output is:

2A. Given price P= 110, output is 285(1-0.25) = 213.75

2B. Given price P = 100, output is 260(1-0.25) = 195

2C. Given price P = 95, output is 235(1-0.25) = 176.25

2D. Given price P = 90, output is 210(1-0.25) = 157.50

3. The new data from question 2 reflects a decrease in aggregate supply.

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The length of the diagonal of the rectangle is AC = 17.69 units

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Let the rectangle be represented as ABCD

Now , the measure of side AB = 12 units

The measure of side BC = 13 units

Let the length be BC and the width be AB

where the diagonal of the rectangle is AC

Now , Diagonal of a Rectangle = √ ( Length )² + ( Width )²

On simplifying , we get

The diagonal of the rectangle AC = √ ( 12 )² + ( 13 )²

The diagonal of the rectangle AC = √ ( 144 + 169 )

The diagonal of the rectangle AC = √313

The diagonal of the rectangle AC = 17.69 units

Hence , the diagonal of the rectangle is 17.69 units

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