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A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.

To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.

There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.

For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.

Therefore, the total number of different hats that can be made, disregarding size, is:

16 (style and stitch combinations) x 7 (yarn choices) = 112

This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.

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Complete question is:

A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?

The value of the expression is 5193.

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

From the notation, we have the following values:

The first term, a = 400

The common ratio, r = 0.93

The number of terms, n = 34 - 1 = 33

The sum of the geometric progression is represented as:

Sum = a(1-rⁿ)/(1-r)

Sum = 400(1-0.93³³)/(1-0.93)

Sum = 5193

Therefore, the value of the expression is 5193

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The solution is, the situation can be modeled as y = 52 - 8x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.

So, the total area to be painted is (28 + 3 × 8) = 52 square meters.

Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as

y = 52 - 8x ................ (1) (Answer)

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Answer:

Step-by-step explanation:

Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.

Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.

Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:

5x + 27 = 11x + 15

Solving for x, we can find the length of each shorter piece:

6x = -12

x = -2

This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.

Answer:

Below

Step-by-step explanation:

The y-axis intercept occurs when x = 0

  so the first one is y = 21    ( this is the value when x = 0 from table)

the second one shows every 4 increase causes a 3 decrease in y

   so every 4 DECREASE in x causes a +3 INCREASE in y

     decrease x = 4 to   x = 0     increase y = 6 to y = 9

The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208,  less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.

We can use the standard normal distribution and z-scores to answer these questions:

P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099

Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.

P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208

Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.

P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228

Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.

P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314

Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.

P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436

Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.

P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464

Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.

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____The given question is incomplete, the complete question is given below:

Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?

Answer:

900

Step-by-step explanation:

5% of 18,000

The Area of Rhombus is 97.5 cm².

The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.

Given:

As, diagonals of rhombus bisect perpendicularly.

so, In triangle OAD using Pythagoras theorem

AD² = OD² + OA²

10² = 7.8² + OD²

OD= 6.25 cm

So, length of BD = 2 x 6.25 = 12.5 cm

Now, area of Rhombus = 1/2 x a x b

                                       = 1/2 x 15.6 x 12.5

                                       = 97.5 cm².

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Answer:

25 minutes

Step-by-step explanation:

Subtract the two times to find the duration.

Answer:  Yes, it's wrong.

Step-by-step explanation:

In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.

r = d/2 = 3/2 = 1.5 ft

[tex]A=\pi r^{2}\\[/tex]

   ≈ 3.14 x 1.5

   = 4.71

The greatest whole number that divides both 372 and 324 without a remainder is 4.

To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).

One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.

372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]

The greatest common divisor is [tex]2^2[/tex], which is equal to 4.

So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.

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The average rate of change of f(x) over the interval 3≤x≤4 is 15

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

The table of values

On the table, we have

f(3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(3)]/[4 - 3]

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

Average rate = (11 + 4)/(4 - 3)

Evaluate

Average rate = 15

Hence, the average rate is 15

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Complete question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.

X f(x)

3 -4

4 11

5 8

6 10

7 11

8 14

The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

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Answer:

Step-by-step explanation:

Answer:

$19

Step-by-step explanation:

calculate 94-18/4 = 19

Answer:

Step-by-step explanation:

c

a

Answer:

$0.22.

Step-by-step explanation:

To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:

7.04 ÷ 32 ounces = 0.22 per ounce

So, the cost per ounce of juice is approximately $0.22.

Answer:

0.22

Step-by-step explanation:

The number of panels that Plant B produced is; 11000 panels

We are told that Plant A produced 4000 fewer panels than Plant B did.

Thus;

A = B - 4000    -----(1)

Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;

0.04A + 0.02B = 500   ------(2)

Put eq 1 in eq 2 to get;

0.04(B - 4000) + 0.02B = 500

0.04B - 160 + 0.02B = 500

0.06B = 660

B = 660/0.06

B = 11000 panels

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Step-by-step explanation:

this is very simple, we only have to divide each side by four to single out our unknown.

[tex]-7=r[/tex]

Answer:

the solution to the equation -28r = 4r is r = 0.

Step-by-step explanation:

To solve the equation -28r = 4r, we can isolate the variable "r" on one side of the equation and find its value. To do this, we can start by subtracting 4r from both sides of the equation:

-28r - 4r = 4r - 4r

-32r = 0

Next, we can divide both sides of the equation by -32 to find the value of "r":

(-32r) / -32 = 0 / -32

r = 0

So the solution to the equation -28r = 4r is r = 0.

The height of the tree to the nearest foot is 27 feet.

The height of the tree can be found as follows:

The height of the tree can be found using trigonometric ratios. Therefore,

let

tan ∅ = opposite / adjacent

Therefore,

opposite side = adjacent tan ∅

Hence,

height of the tree = 20 + x tan 45° = x tan 75°

20 + x tan 45° = x tan 75°

20 tan 45 + x tan 45° = x tan 75°

20 tan 45 =  x tan 75° -  x tan 45°

20 tan 45 =  x(tan 75 - tan 45)

20 tan 45 = x(3.73205080757 - 1)

2.73205x = 20

x = 20 / 2.73

x  = 7.32600732601

x = 7.34

Therefore,

height of the tree = x tan 75°

height of the tree = 7.34 × tan 75°

height of the tree = 27.3186119114

height of the tree = 27 ft

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It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.

Answer: knvsvvs

Step-by-step explanation:

The Kansas City Chiefs has a better chance of winning the super bowl 2023.

In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.

The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.

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The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To fill in the blanks, we need to use the given information to complete the probability distribution table.

We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

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Answer:

9

Step-by-step explanation:

72/24 = 3

72 is 3 times 24, so you need 3 times as many garbage trucks.

Answer: 9

Answer: 61 1/10

Step-by-step explanation:

9 2/5 x 6 1/2

The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

What is the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.

Let W be the total work to be done, which is installing a new deck.

Given Ted alone can complete the work W  in 15 hours.

Using unitary method,

So in one hour, work done by Ted = W/15

Also given Jimmy alone can complete the work W in 16 hours.

So in one hour, work done by Jimmy = W/16

Using unitary method,

In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240

ie 31W/240 = 1 hour

 So W = 240/31 = 7.7 hours

Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

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The linear function giving the amount remaining after buying x cups of coffee is given as follows:

A(x) = -3x + 15.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Each cup of coffee costs $3, hence the slope m is given as follows:

m = -3.

(for each cup purchased, the balance decays by $3).

Hence:

A(x) = -3x + b.

Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:

3 = -3(4) + b

b = 15.

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The correct value of the expression is,

⇒ (2²)³ - (8 - 4)² × 4 = 0

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (2²)³ - (8 - 4)² × 4

Now, We can solve as;

⇒ (2²)³ - (8 - 4)² × 4

⇒ (4)³ - (4)² × 4

⇒ 4³ - 4³

⇒ 64 - 64

⇒ 0

Thus, We get;

⇒ (2²)³ - (8 - 4)² × 4 = 0

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The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45

quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The equation of a quadratic is given as :

x²-(alpha+beta)x + alpha×beta = 0

where alpha and beta are the roots of the quadratic equation.

alpha+beta = 5-9 = -4

alpha × beta = -9× 5 = -45

therefore the equation will be;

x²-(-4)x + ( -45) = 0

x² + 4x -45 = 0

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