In a certain trail mix, 65% of the total weight is made up of nuts. Of that 65%, 3/5 of the nuts are cashews. If the total weight of the trail mix is 200 grams, how many grams are cashews?​

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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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:

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

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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Answer:

The answer is Zack garden

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

Answer:

3n+15

Step-by-step explanation:

18, 21, 24

+3. +3

3n

18-3=15

3n+15

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 linear regression model from a set of data is y =5.2956+4.0946*X.

A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.

The regression line is determined using the formula:

y = bo + b1 X

Now, using the table we have:

sum of (x) = ∑x = 103

sum of (y) = ∑y = 480

Calculating the squares we have:

sum of (x^2)= ∑x² = 1073

sum of (y^2)= ∑y² = 22868

Multiplying the variables we have:

sum of (x*y)= ∑x*y = 4939

mean(x)= ∑x/n = 9.3636

mean(y)= ∑y/n = 43.6364

Now, the intercept is given as:

intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²

Substituting the values we have:

intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2

intercept (bo) = (515040-508717) / (11803-10609)

intercept (bo) = 5.2956

The slope is given as:

slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²

Substituting the values we have:

slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2

slope (b1) = (54329-49440)/(11803-10609)

slope (b1) = 4.0946

regression equation is, y = bo + b1 X

Substituting the values we have:

y =5.2956+4.0946*X

Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.

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The complete question is:

According to the question the volume formula to find the height of the pyramid is 9 units.

Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.

The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h

108 = (1/3) × 36 × h

108 = 12 × h

h = 9 units

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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-

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:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

[tex] \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 [/tex]

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

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:

1/4 of the pot is left.

Step-by-step explanation:

Let x be the total amount of pasta in the pot.

Then the amount of pasta her mother got= 1x/12

The amount of pasta her brother got=  1x/6

The total amount of pasta he serve= 1x/12 + 1x/6

First, convert them into like fractions, then

The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4

Hence, 1/4 of the pot is left over.

Step-by-step explanation:

Mom: 1/12

Brother: 1/6

1/6 × 2/2 = 2/12

2/12 + 1/12 = 3/12

12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left

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

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:

K = √-6k

i did the math and got this answer and it was right

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:

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.

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:

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

Answer:

yes it is pretty hard but I believe I. you

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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Let's say you're trying to decide whether or not to invest in a certain stock. You've analyzed the company's financial reports and economic indicators, but you're still uncertain about the stock's future performance. Based on your intuition and experience with the stock market, you estimate that there is a 70% chance that the stock's value will rise in the next six months.

You decide to invest based on that probability, and six months later the stock has actually gone up in value. Your decision turned out to be a good one, but that doesn't necessarily mean your probability estimate was accurate. The stock could have gone down in value just as easily, despite your assessment of its likelihood of going up.

Therefore, even when we make decisions based on probability, there is always a level of uncertainty involved and the outcome may not always line up with our initial estimates. However, taking the time to consider the likelihood of different outcomes can help us make more informed decisions and better manage risk.

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Answer:

124

Step-by-step explanation:

You'll need a calculator for this one

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.

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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