On a standardized test with normal distribution, the mean is 85 and the standard deviation is 3. Within which range should approximately 95% of the scores lie?

The inequality that describes the base length of the triangle is b ≤ 28/h

From the question, we have the following parameters that can be used in our computation:

The area of a triangle can be calculated using the following formula

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * b * h

Evaluate the products

Area = 1/2bh

Recall that

Area = At most 14 square feet

This means that

Area ≤ 14

So, we have

1/2bh ≤ 14

Multiply through by 2

bh ≤ 28

Divide both sides by h

b ≤ 28/h

Hence, the inequality is b ≤ 28/h

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Answer:

14,641

Step-by-step explanation:

11^4 = 11 × 11 × 11 × 11 = 121 × 11 × 11 = 1331 × 11 = 14,641

Answer:

14,641

Step-by-step explanation:

10^4 = 10000

11^4 > 10 ^4 so A is the answer

Answer:

The axis of symmetry of a parabola is the line that divides the parabola into two mirror images. This line always passes through the vertex of the parabola. For a parabola with an axis of symmetry at x = 5/12, the vertex of the parabola is at the point (5/12, 0).

The distance between the roots of a parabola is the distance between the x-coordinates of the two points where the parabola crosses the x-axis. In this case, the distance between the roots is 13/6.

To find the equation of the parabola, we can use the vertex form of the equation, which is given by y = a(x - h)^2 + k, where (h, k) is the coordinates of the vertex and a is a constant. In this case, the coordinates of the vertex are (5/12, 0) and the constant a can be determined using the distance between the roots.

To find a, we can use the fact that the distance between the roots of a parabola is equal to the square root of the product of the coefficients of the quadratic terms in the equation. In the vertex form, the coefficient of the x^2 term is a, so we can set up the following equation to find a:

(13/6)^2 = a * (5/12)^2

Solving for a, we find that a = -1/3.

Therefore, the equation of the parabola is y = -1/3(x - 5/12)^2.

Answer: 7/8

Step-by-step explanation:

According to the given sets, A ⋂ B = {blue, green, yellow}.

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

A ⋂ B:

A set called an intersection B has components that are found in both sets A and B.

The intersection of sets A and B is shown by the symbol, which is interpreted as "An intersection B" and written as A⋂B.

The set of components shared by all sets is the intersection of two or more sets.

So, we have:

A = {red, blue, green, yellow, orange}

B = {pink, blue, purple, yellow, green}

A ⋂ B which means common elements:

A ⋂ B = {blue, green, yellow}

Therefore, according to the given sets, A ⋂ B = {blue, green, yellow}.

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Answer:

<B, <C, <A

Step-by-step explanation:

The order from smallest to largest angle is the same as the order from shortest to longest opposite side.

Sides from shortest to longest:

120, 130, 180

Angles from smallest to largest:

<B, <C, <A

When x = 10 the equations are equal and when x gets any value the two equations are equal.

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.

When x = 10 the equation becomes

6x³ + 9x² + 4x + 7

6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

Both the equations are equal when x = 10

When x = -3/2 the equation becomes

6x³ + 9x² + 4x + 7

6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

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The different combinations of 5 friends could possibly receive the tickets are 56.

What is combination?

A combination is a choice made from a set of distinct items in mathematics where the order of the choices is irrelevant.

The definition of a combination is "An arrangement of objects where the order in which the objects are chosen does not matter." A combination is a "selection of things" where the importance of the order of the things is negligible.

Given:

A group of 8 friends (5 girls and 3 boys) plans to watch a movie.

We have to find the different combinations of 5 friends could possibly receive the tickets.

Here there are total 8 friends.

We have to select 5 from 8 in 8C5 ways.

[tex]8_C_5 = \frac{8!}{5!*(8-5)!} \\8_C_5 = \frac{8!}{5!*3!} \\8_C_5 = \frac{6*7*8}{1*2*3}\\ 8_C_5 = 56[/tex]

Hence, the different combinations of 5 friends could possibly receive the tickets are 56.

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Answer:

36

Step-by-step explanation:

The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

One number is 5 more than twice another and their sum is 23.

Let the two numbers be 'x' and 'y'. Then the equations are given as,

y = 2x + 5            ...1

x + y = 23           ...2

From equations 1 and 2, then we have

x + 2x + 5 = 23

3x + 5 = 23

3x = 23 - 5

3x = 18

x = 6

Then the value of the variable 'y' will be given as,

6 + y = 23

y = 23 - 6

y = 17

The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

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After 2 hours, Zoe and Wanda will complete the same total number of shirts.

Each tailor will finish 18 shirts.

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that,

Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts.

Assume that after x hours they have finished the same total number of shirts.

The number of shirts that Zoe finished is

Z(x) = 14 + 2x ....(i)

The number of shirts that Wanda finished is

W(x) = 6 + 6x ...(ii)

When they make same number of shirts, then Z(x) = W(x)

14 + 2x = 6 + 6x

6 + 6x = 14 + 2x

Subtract 2x from both sides:

6x - 2x = 14 - 6

4x = 8

Divide both sides by 4

x = 8/4

x = 2.

Putting x = 2 in Z(x) = 14 + 2x:

Z(2) = 14 + (2×2)

Z(2) = 18

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The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

As per the given,

x² + xy + y² + 1 = 0

Take the first derivative on both sides with respect to x as,

d/dx(x² + xy + y² + 1) = d/dx(0)

2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0

2x + x(dy/dx) + y + 2y (dy/dx) = 0

2x + y + dy/dx(x + 2y) = 0

Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".

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In the unit rate between two units, the denominator is always one.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Unit rate is written in a fraction form where the denominator is always one.

Example:

6 miles in 3 minutes.

This can be written as,

6 miles = 3 minutes

Dividing 3 on both sides.

2 miles = 1 minute

= 2 miles per minute

Thus,

In the unit rate between two units, the denominator is always one.

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Answer:

I'm not to sure what the answer is

Lupe's statement seems quite fair

When multiplied by 4, any number's pair

An even product will be produced

By this rule, we are not reduced

For example, take the number 6

Multiply it by 4, and what do you get?

The answer is 24, a multiple of 2

This confirms Lupe's statement is true

In conclusion, Lupe's statement rings true

It makes perfect sense, through and through

The product of 4 and any number

Will always be an even number.

Answer:

9.16

Step-by-step explanation:

formula for Geometric mean is

b = √a × √c

a = 7 and c = 12

b = √ 7×12

b = √84

b = 9.16

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Answer:

Step-by-step explanation:

turn percentage into decimal :

60/100 = 0.6

Then times it by how many flowers there are :

0.6×25 = 15

And your answer should be 15.

27 kilometers to miles

1 kilometer = 0.621371 miles

27 kilometers * 0.621371 miles = [tex]\fbox{16.777 miles}[/tex]

The bisector of the angle TUV is attached below.

What is an angle?

In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The steps to draw a bisector of an angle:

1) Cross both rays with an arc. Place the compass point at the vertex of the angle after opening it to any width. Swing the compass so the pencil creates an arc that spans the angle's two rays.

2) Make a vertical arc inside. Place the compass such that the point is at the spot where the first ray and the first arc connect. Swing the compass to create an arc that fits inside the angle.

3) To intersect the first interior arc, draw a second interior arc. Move the point to the spot where the first arc crosses the second ray without altering the compass's breadth. Draw an internal arc by swinging the compass and intersecting it with the initial interior arc you drew.

4) From the vertex to the spot where the arcs meet, draw a line. To make sure the line is exact, use a straightedge. This line cuts the angle in half.

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Answer: S wanted points I

Step-by-step explanation:

Answer:

To find the five-number summary for a set of data, we need to find the minimum, first quartile, median, third quartile, and maximum of the data. To find the interquartile range, we subtract the first quartile from the third quartile.

The minimum temperature in the list is 50 degrees Fahrenheit. The maximum temperature is 80 degrees Fahrenheit. To find the median, we need to first find the middle value in the list. Since there are 13 temperatures in the list, the middle value is the seventh temperature, which is 64 degrees Fahrenheit.

To find the first and third quartiles, we need to divide the list into two halves at the median. The first half of the list contains the first six temperatures, and the second half contains the last six temperatures. The median of the first half of the list is the average of the third and fourth temperatures, which is 55 degrees Fahrenheit. The median of the second half of the list is the average of the sixth and seventh temperatures, which is 61.5 degrees Fahrenheit.

Therefore, the five-number summary for this data set is:

Minimum: 50

Lower quartile: 55

Median: 64

Upper quartile: 61.5

Maximum: 80

The interquartile range is the difference between the upper and lower quartiles, which is 61.5 - 55 = 6.5.

The required length of the third side should be less than the sum of the other two sides or less than 37 in.

As mentioned, Kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in.,

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the length of the third side,
The property of the triangle states that the sum of the two sides of a triangle is always greater than the length of the third side.
So
x < 15 + 22
x < 37

Thus, the required length of the third side should be less than the sum of the other two sides or less than 37.

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Answer:

See below.

Step-by-step explanation:

The given functions f(x) and g(x) are linear functions.  Therefore, their inverses are a reflection about the line y = x.

The mapping rule for reflecting a point about the line y = x is:

To determine if f(x) and g(x) are inverses of each other:

If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.

Given functions:

[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]

Ordered pair: (2, 9)

Substitute x = 2 into f(x):

[tex]\implies f(2)=2(2)+5=9[/tex]

Substitute x = 9 into g(x):

[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]

Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.

Answer:

see explanation

Step-by-step explanation:

- 1x + 4y = 12 , that is

- x + 4y = 12 ( add x to both sides )

4y = 12 + x ( divide each term by 4 )

y = 3 + [tex]\frac{1}{4}[/tex] x

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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Answer:

a) 9/5

Step-by-step explanation:

Formula we use,

→ Slope (m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-16 - 2)/(-10 - 0)

→ m = (-18)/(-10)

→ m = 18/10

→ [ m = 9/5 ]

Hence, the slope is 9/5.

The number of times that the actual flag is wider than the Reagan's model would be = 3 times.

A rectangle is defined as a type of quadrilateral that has opposite sides that are parallel and equal to each other and all four angles are right angles.

The actual length of the rectangular flag = 39 inches long.

The length of Reagan's model = 13 inches.

To find the number of times wider than the actual flag the model is, use the formula:

= Length of actual flag / Length of model

= 39/13 = 3.

Therefore, the number of times that the actual flag is wider than the Reagan's model is 3 times.

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The cost of the five-minute call will be equal to $0.72.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Ron got a cell phone rate of C(a)=0.22+0.10a. The cost of a five-minute call will be calculated as,

Cost = 0.22+0.10a

Cost = 0.22 + ( 5 x 0.10 )

Cost = 0.22 + 0.50

Cost = $0.72

The five-minute call will cost $0.72.

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