The heights of adult men in America are normally distributed, with a mean of 69.4 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.59 inches.
a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? If a women if 5 feet 11 inches tall, what is her z-score?? (To two decimal places)

91.3 pounds of fruit are left

Jason bought = 91.5 pounds

class ate = 0.2 pounds

You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.

91.5 - 0.2 = 91.3 pounds

When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

Number is a mathematical concept used to quantify or measure a quantity. It is a symbol or group of symbols that stands for a quantity, such as 2, 4, 5, 10, and so on. Numbers are used to express amounts, to count, and to measure. They are also used to represent relationships between quantities and to compare quantities.

A place value disk can be used to represent the value of 5 times 2, which is equal to 10. The disk would have two sections, one representing the number 5 and the other representing the number 2. The number 5 would be represented by five single circles in the “ones” section, and the number 2 would be represented by two single circles in the “ones” section. When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

The place value disk is a useful visual tool to help students understand the concept of multiplication. It allows them to clearly see how the number of circles in each section are multiplied to get the final answer. This can help them better understand the concept of multiplication and how it works.

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Complete questions as follows-

The surface area of this figure is determined as 980.5 m².

The total surface area of the figure is the sum of all the area of the six faces and it is calculated as follows;

Area of top face = 12.7 m x 11 m = 139.7 m²

Area of bottom face = 9.5 m x 16 m = 152 m²

Area of far right face = 12.7 m x 14 m = 177.8 m²

Area of far left face = 9.5 m x 14 m = 133 m²

Area of front face = 16 m x 14 m = 224 m²

Area of back face = 11 m x 14 m = 154 m²

Total surface area = 139.7 m² + 152 m² + 177.8 m² + 133 m² + 224 m² + 154 m²

= 980.5 m²

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Answer:

3n+15

Step-by-step explanation:

18, 21, 24

+3. +3

3n

18-3=15

3n+15

Answer:

height= 3cm

Step-by-step explanation:

to find the base of each triangle just half the bottom to get 4cm

a^2+b^2=c^2

a^2+4^2=5^2

a^2+16=25

a^2=9

a=√9

a=3

I'm afraid you forgot to add a picture?

The vector 6v is -24j - 126.

What is vector?

In mathematics, a vector is a mathematical object that represents a quantity that has both magnitude (size) and direction. Vectors are used to describe physical quantities that have both magnitude and direction, such as velocity, force, and displacement.

Given the vector v = -4j - 21, we can find the vector 6v by multiplying each component of v by 6:

6v = 6(-4j - 21)

Distributing the 6:

6v = -24j - 126

So the vector 6v is -24j - 126.

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Complete question: Let v = - 4j- 21 Find the vector 6v.

The shaded region, the closest answer choice (B) is  20 square units.

The circumference of a circle is the length of the edge of the circle. If we cut  the circle and straighten it, the length of the border is the circumference of the circle.

 The central angle of  sector AOB is 2*35 = 70 degrees (because the central angle  is twice the circumferential angle). The remaining angle of triangle AOB is (180 - 70)/2 = 55 degrees.  Using trigonometry, we  find that the length of AB is:

AB = 2 * 8 * sin(55/2) ≈ 11.96 units

The shaded area can be divided into two parts: a sector with a central angle of 70 degrees and a triangle with base AB and height 8 units (the radius of the circle).

 The area of sector is

(70/360) * π * 8² ≈ 12.57 square units

The area of ​​the triangle is:

(1/2) * AB * 8 ≈ 47.82 square units

Therefore, the total area of ​​the shaded area is approximately:

12.57 + 47.82 ≈ 60.39 square units

Therefore, for the shaded region, the closest answer choice (B) is  20 square units.

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We can say that f(x) has a local maximum at A and a local minimum at B.

A function is a mathematical rule that assigns a unique output value to each input value. It describes the relationship between the input and output variables.

Critical numbers of a function are the values of the independent variable where the derivative is zero or undefined, indicating possible extrema or inflection points.

According to the given information:

To find the critical numbers of the function f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.

f(x) = cos(x) + √2/2

f'(x) = -sin(x)

Setting f'(x) = -sin(x) = 0, we get sin(x) = 0, which is true for x = nπ, where n is an integer. However, we only need to consider the values of x in the interval [0,2].

For n = 0, x = 0 is a critical number.

For n = 1, x = π is a critical number.

For n = 2, x = 2π is not in the interval [0,2], so we don't need to consider it.

Therefore, the critical numbers of f(x) in the interval [0,2] are A = 0 and B = π.

To find the nature of the critical points, we need to find the second derivative of f(x).

f''(x) = -cos(x)

Evaluating f''(x) at A and B, we get:

f''(A) = -cos(0) = -1, which means that f(x) has a local maximum at A.

f''(B) = -cos(π) = 1, which means that f(x) has a local minimum at B.

Therefore, we can say that f(x) has a local maximum at A and a local minimum at B.

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The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.

The set 2Z is defined as follows:

2Z = {2n | n ∈ Z, a * b = a + b}

Associative element:

There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.

Let a, b, and c be arbitrary elements of 2Z:

a = 2n₁

b = 2n₂

c = 2n₃

Then we have:

a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)

(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)

Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.

Identity element:

There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.

Let e be an arbitrary element of 2Z:

e = 2n

Then we have:

ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z

ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z

Therefore, e = 2n is an identity element in 2Z.

Inverse element:

There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.

Let a be an arbitrary element of 2Z:

a = 2n

Then we need to find an element b in 2Z such that ab = ba = e = 2.

We have:

ab = ba = 2n*b = 2

Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.

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Answer:

[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]

A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.

Answer:

124

Step-by-step explanation:

You'll need a calculator for this one

Answer:

≈ 0.153

Step-by-step explanation:

using the rules of logarithms

log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] b = 1

then

[tex]log_{c}[/tex] ( [tex]\frac{4}{c}[/tex] )

= [tex]log_{c}[/tex] 4 - [tex]log_{c}[/tex] c

= 1.153 - 1

= 0.153

Answer:

Step-by-step explanation:

There are two ways to write 4/15 as a decimal.

**Method 1: Using long division**

1. Divide 4 by 15.

2. The quotient is 0.26.

3. The remainder is 6.

4. Since the remainder is not zero, we need to bring down a zero and continue dividing.

5. We get 0.266666...

**Method 2: Using a calculator**

1. Enter 4/15 into the calculator.

2. Press the "equals" button.

3. The answer is 0.266666...

The decimal representation of 4/15 is 0.266666..., which is a repeating decimal. This means that the 6 repeats indefinitely.

Answer:

The answer is 0.2666

Step-by-step explanation:

4/15

=0.2666

Answer:

yes it is pretty hard but I believe I. you

Answer:

Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

On Thursday, she practiced for 5 minutes according to the table.

On Friday, she practiced for 9 minutes according to the table.

Adding these two times together, we get:

5 minutes + 9 minutes = 14 minutes

Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

Answer:

x = 7

Step-by-step explanation:

if A and B are parallel , then

4x + 14 and 3x + 21 are alternate angles and are congruent , that is

4x + 14 = 3x + 21 ( subtract 3x from both sides )

x + 14 = 21 ( subtract 14 from both sides )

x = 7

For A and B to be parallel then x = 7

Answer:

To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.

(a) (f◦g)(4):

To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):

g(4) = 7 - 1/2(4)^2

= 7 - 8

= -1

Now we substitute g(4) = -1 into f(x):

(f◦g)(4) = f(g(4))

= f(-1)

= 3(-1)^2 - 2

= 1

Therefore, (f◦g)(4) = 1.

(b) (g◦f)(2):

To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):

f(2) = 3(2)^2 - 2

= 10

Now we substitute f(2) = 10 into g(x):

(g◦f)(2) = g(f(2))

= g(10)

= 7 - 1/2(10)^2

= -43

Therefore, (g◦f)(2) = -43.

(c) (f◦f)(1):

To find (f◦f)(1), we need to find f(f(1)):

f(1) = 3(1)^2 - 2

= 1

Now we substitute f(1) = 1 into f(x):

(f◦f)(1) = f(f(1))

= f(1)

= 1

Therefore, (f◦f)(1) = 1.

(d) (g◦g)(0):

To find (g◦g)(0), we need to find g(g(0)):

g(0) = 7 - 1/2(0)^2

= 7

Now we substitute g(0) = 7 into g(x):

(g◦g)(0) = g(g(0))

= g(7)

= 7 - 1/2(7)^2

= -17/2

Therefore, (g◦g)(0) = -17/2.

Answer: Without the options for the vector matrices resulting from rotation, I cannot provide a specific matching. However, I can provide the general formula for rotating a vector by an angle of θ degrees counterclockwise as follows:

To rotate a vector with coordinates (x, y) counterclockwise about the origin by an angle of θ degrees, we use the following formula to find the new coordinates (x', y'):

x' = xcos(θ) - ysin(θ)

y' = xsin(θ) + ycos(θ)

Therefore, to obtain the vector matrix resulting from rotating the vector (-6, -3) by a certain angle of rotation, we plug in the values of x = -6 and y = -3 into the above formulas, and use the corresponding angle of rotation in degrees for θ.

Step-by-step explanation:

Answer:

The answer is Zack garden

The correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.

What is the quadratic function?

A quadratic function is a type of polynomial function with a degree of 2, meaning it has the form:

[tex]f(x) = ax^2 + bx + c[/tex]

The correct statements are:

Hence, the correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.

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Answer:

1

Step-by-step explanation:

1/3 + 8/12 ⬅️(factor out by common factor, 4)

= 1/3 + 2/3

=1+2/ 3

=3/3 or 1

The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.

Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary by angles

m∠4=180°-m∠3 ----> equation B

substitute the equation- B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary to angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of any of tAnswer:

Step-by-step explanation:

he interior angles that of a triangle must be equal to 180 degrees

therefore

This option is true for sure

case E) we have

m∠2+m∠3+m∠5=180°.

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The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)

It should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.

One possible substitution is to let u = x^2, so that we can write:

x^4 + 5x^2 - 8 = u^2 + 5u - 8

We can then factor this quadratic expression as:

u^2 + 5u - 8 = (u + 8)(u - 1)

Substituting back u = x^2, we get:

x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)

Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:

(x^2 + 8)(x^2 - 1)

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The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.

The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.

(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:

Projection = (A⋅B)/|B|

In this case, the scalar projection of (5,3) onto (7,-2) is:

Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
           = (35 - 6)/53
           = 29/53

Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:

Projection Vector = (A⋅B/|B|²)B

In this case, the projection vector of (5,3) onto (7,-2) is:

Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
                 = (35 - 6)/53 ⋅ (7,-2)
                 = (29/53)⋅(7,-2)
                 = (203/53, -58/53)

(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:

First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).

Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).

This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

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The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).

In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.

For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.

In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

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Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

----------------------

Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.