Lauren is working furiously to knit scarves and beanies for a craft fair next weekend. Yesterday she completed 3 scarves and 1 beanie, using a total of 23 yards of yarn. The day before, she used 27 yards to knit 3 scarves and 3 beanies. Assuming Lauren is using the same pattern and type of yarn for each scarf and beanie, how much yarn does each project require?​

The numerical will be equal to 159 ÷ 16 and the polynomial will be (9x +15)/x.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

In comparison to the divisor, the dividend will be 15 times greater. It seems that you are free to select any divisor. It must be more than 15 if the divisor is totally numerical.

Numerical:

Divisor = 16,

so we have,

(9×16 +15) ÷ 16

= 159 ÷ 16

Polynomial:

The simplest divisor we can have is a single variable: x.

(9x +15)/x

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Answer:

  107 meters

Step-by-step explanation:

You want Nikko's distance from a 50 m high building if the angle of elevation to the top is 25°.

The tangent relation tells you the acute angle in a right triangle is related to the sides by ...

  Tan = Opposite/Adjacent

In this problem, the relation means ...

  tan(25°) = building height / distance to building

Solving for the distance to the building, we get ...

  distance to building = (building height)/tan(25°) = (50 m)/tan(25°)

  distance to building ≈ 107.225 m

Nikko is about 107 meters from the building.

Answer:

(2x+2)=(3x-52)

2x+2=3x-52

2x-3x=-52-2

-x=-54

x=54

Answer:

1.097174699×10^²⁶

Step-by-step explanation:

100×100×325×1773×3.44554×34444×6878755×23324=

1.097174699×10^²⁶

The percentage of girls in a class are 26.67%.

What is percentage?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Given:

In a class of 45 student there are 12 girls.

We have to find the percentage of girls in the class.

Percentage of girls = (number of girls / Total number of students ) x 100

                                = (12 / 45) x 100

Percentage of girls = 26.6666

Percentage of girls ≈ 26.67

Hence, the percentage of girls in a class are 26.67%.

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The number 120 in the equation of y = 5x + 120 mean is there were 120 customers per night when the restaurant opened.

For this case, the equation of y = 5x + 120 is for linear relationship.

Which is

y represent average number of nightly customer.

x represent number of months the restaurant opened.

For example for month 0 or for the first time restaurant open the nightly customer is,

y = 5(0) + 120

y = 0 + 120

y = 120

It mean the average number of nightly customer is 120 in the first time restaurant open. After month 0, in month 1 the nightly customer is increase by 5. So, total average nightly customer is 125, and so on.

Attached graph is for visualization and to make it easier to understand the equation mean.

Thus, number 120 in the equation is to represent there were 120 customers per night when restaurant opened.

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The frictional loss will be greater for aspect ratio of 2 as friction will be more when the height of the duct is higher compared to the increase in width.

In a straight duct with constant cross sectional area , the velocity of the water is changed. The change in static pressure is the frictional loss .

In the duct the energy is constant. Therefore when water moves upwards with the increase in height the frictional loss or the pressure loss will be more more.

When width increases there will be less pressure, So frictional loss will be increased with height.

Let the width and height be a and b respectively.

now area = ab

and a\b =2

or, a = 2b

again a\b = 4 or, a = 4b

if ab is constant then the height for the aspect ratio of 4 is greater.

Therefore there will be more frictional loss for the increased height.

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The average speed of John for the whole journey is 54km/h.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Speed is the rate of movement of something at a specific time.

Average speed refers to the average speed over the course of a journey.

So, the average speed will be:

Distance = speed x time

d₁ = v₁ x t₁

d₁ = 50 x 3

d₁ = 150 km

d₂ = v₂ x t₂

d₂ = 60 x 2

d₂ = 120 km

So,

D = d₁ + d₂

D = 150 + 120

D = 270 km

Utilizing the S formula:

S = D/ T

S = 270 / 5

S = 54 km/hr

S = 54km/hr

Therefore, the average speed of John for the whole journey is 54km/h.

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The probability of no more than 8 heads given that at least one toss resulted in heads will be 511/512.

What is probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

A coin has two possibility, either head or tail.

So, there will be 2 possible outcomes when a coin is tossed.

hence, Total no. of outcomes (T) =  2^9. = 512

  Now,  Probability of getting one tail = 1/2^9 = 1/512

and, Probability of getting at most 8 heads

       = 1 - Probability of getting one tail

       = 1 - 1/512

       = 511/512.

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Answer:

[tex]5c+\frac{9-8c}{24}[/tex]

Step-by-step explanation:

Simplify

[tex]5c+\frac{1*(\frac{3}{4}-\frac{2c}{3} )}{2}[/tex]

[tex]5c+\frac{9-8c}{24}[/tex]

The volume of the cube will increase by 8 cubic centimeters per second.

Given,

The edge length of a cube is changing at a rate of 1/6 cm/sec.

We have to find the rate by which cube's volume changing when the edge length is 4 cm.

Here,

We have,

da/dt = 1/6 cm/sec

We know that, volume of cube is

V = a³

Differentiate with respect to t.

dV/dt = 3a² da/dt

Substituting da/dt = 1/6  and a = 4, we get;

dV/dt ₐ ₋ ₄ = 3 × 4² 1/6

dV/dt ₐ ₋ ₄ = 3 × 16 × 1/6

dV/dt ₐ ₋ ₄ = 16/2 = 8

Therefore,

The volume increased by 8 cubic centimeters per sec.

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Answer: 15000

Step-by-step explanation: Step by step solution for calculating 135 is 0.9 percent of what number

We already have our first value of 135 and the second value of 0.9. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1135 = 0.9% × Y

STEP 2135 =

0.9

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 0.9 we will arrive at:

STEP 3Y = 135 ×

100

0.9

STEP 4Y = 135 × 100 ÷ 0.9

STEP 5Y = 15000

Finally, we have found the value of Y which is 15000 and that is our answer.

You can easily calculate 135 is 0.9 percent of what number by using any regular calculator, simply enter 135 × 100 ÷ 0.9 and you will get your answer which is 15000

They need to put 14.4 grams of onion powder in each bottle.

Given,

The quantity of onion powder in a seasoning blend = 4%

We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Here,

Let x be the seasoning blend.

Now, 4% of 72=20% of x

⇒ 0.04×72=0.2×x

⇒ 0.2x=2.88

⇒ x=2.88/0.2

⇒ x=14.4 g

Therefore, a container should contain 14.4 grams of onion powder.

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What is it you are trying to solve with the given equation? Are you graphing it? Determining the slope and y-intercept? Finding slope? Elaborate a bit more, if you could, on what you seek and I'll see what I can do to help. Tysm!

Answer: 23

Step-by-step explanation: To evaluate the expression (2.3x6)+(2.3x4), we can first use the order of operations to simplify the expression. Since the multiplication and division have the same precedence, we can evaluate them from left to right. Therefore, we have: (2.3x6)+(2.3x4) = (2.36)+(2.34)

Next, we can evaluate the multiplication to get: (2.36)+(2.34) = 13.8 + 9.2

Finally, we can evaluate the addition to get: 13.8 + 9.2 = 23

Therefore, the value of the expression (2.3x6)+(2.3x4) is 23.

The true statement about his relationship is that the hours worked is directly proportional to the money earned.

We know that a graph could be used to show the relationship between variables. This relationship can be shown by the use of the cartesian coordinates. The cartesian coordinates is directed in the x and the y plane as shown in the image in the question.

Now, we can see that the line of best fit that was drawn through the data points is point upwards. This would show us that as the number of hours worked is increasing, the money earned is also increasing.

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the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

When there are multiple alternatives accessible, hypothesis testing is utilised. To decide whether to accept or reject the null hypothesis, the z test is performed in the mean, which determines the t value. This value is then compared with the p value. The alternate explanation in this case is mu, which is represented. For P1 and P2, the 90% confidence interval is (- 0.0765, 0.02646).

Hence, the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%

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Rate of change: 9
Initial value: 14

explanation:
9 x 4 = 36 (she adds 9 stickers every week, it's 4 weeks)
50 - 36 =  14 (subtract what she added to find initial value)

Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is =24.21

What is binomial probability?

When an experiment or survey is repeated numerous times, the likelihood that the results will be SUCCESS or FAILURE is known as the binomial distribution. The prefix "bi" implies "two" or "twice," therefore the term "binomial" refers to a distribution type with two probable outcomes. A coin flip, for instance, can only result in one of two outcomes: heads or tails, and completing a test can result in either passing or failing.

standard deviation =[tex]\sqrt{n*p(1-p)}[/tex]

p = probability of success = 6% = 0.06

1 - p = 1 - 0.06 = 0.94

Sample size, n = 10400

Substituting the values into the equation :

[tex]\sqrt{10400*0.06(1-0.04)}[/tex]

[tex]\sqrt{10400*0.06(0.94)}[/tex]

[tex]\sqrt{10400*0.0564}[/tex]

[tex]\sqrt{586.56}[/tex]

= 24.21  

Hence, the standard deviation is 24.21.

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Answer:

[tex]M=\left(-1, \dfrac{7}{2} \right)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given endpoints:

Substitute the given points in the midpoint formula:

[tex]\implies M=\left(\dfrac{x_C+x_A}{2}, \dfrac{y_C+y_A}{2} \right)[/tex]

[tex]\implies M=\left(\dfrac{-5+3}{2}, \dfrac{16+(-9)}{2} \right)[/tex]

[tex]\implies M=\left(\dfrac{-2}{2}, \dfrac{7}{2} \right)[/tex]

[tex]\implies M=\left(-1, \dfrac{7}{2} \right)[/tex]

Answer:

66 foot per second

Step-by-step explanation:

Step-by-step explanation:

H is the plan

F is the side

A is the plan

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The positive solution is 5.

given,

When 10 is subtracted from a number's square, the result is three times the number.

let x be the number

according to given statement the quadratic equation will be

[tex]x^2-10=3x\\\\x^2-3x-10\\\\x^2+2x-5x-10=0\\\\x(x+2)-5(x+2)=0\\\\(x-5)(x+2)=0\\\\x=5\ or\ -2[/tex]

Thus, the positive solution is 5.

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The probability that the sum will be an even number on the toss of two dice is  5/9 .

In the question ,

it is given that ,

the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .

the probability of getting an odd number first is = 4/6 = 2/3,

the probability of getting an even number first is = 2/6 = 1/3,

To get an even, we must get either 2 odds or 2 evens.

The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .

The probability of getting 2 evens is 2/6 × 2/6 = 4/36.

If we add them together,

we get ,

= 16/36 + 4/36

= 20/36

= 10/18 = 5/9

Therefore , the required probability is 5/9  .

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We have to use pigeonhole principle to find balls from bowl. From 75 balls at least one out of 31 balls will be of black color, out of 23 balls will be red, out of 25 will be blue, out of 27 balls will be green, out of 29 will be yellow.

out of 75 balls for each ball to be chosen at least once then we have to compute each color of ball separately,

By using the pigeonhole principle's formula n(r - 1) + 1

For red ball,

N=11, k=1, [N/2]≥3

= 11(3-1)+1

= 23

Hence, out of 23 balls from 75 balls at least one will be of red color

For, blue ball

N=12, k=1, [N/2]≥3

= 12(3-1)+1

= 25

Hence, out of 25 balls from 75 balls at least one will be of blue color

For green color,

N=13, k=1, [N/2]≥3

= 13(3-1)+1

= 27

Hence, out of 27 balls from 75 balls at least one will be of green color

For yellow ball,

N=14, k=1, [N/2]≥3

= 14(3-1)+1

= 29

Hence, out of 29 balls from 75 balls at least one will be of yellow color

For black ball,

N=15, k=1, [N/2]≥3

= 15(3-1)+1

= 31

Hence, out of 31 balls from 75 balls at least one will be of black color

The pigeonhole principle states that if n items are put into m containers, where n > m, at least one container must contain more than one item. If there are k+1 or more pigeons dispersed throughout the k pigeonholes, at least one pigeonhole will have two or more pigeons. Proof. The statement's converse is that there can only be a maximum of k pigeons if each slot can only accommodate one bird.

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Answer:

x = 3

Step-by-step explanation:

Solve for x:

35 + 6x - 2 = 13x + 12

Simplifying on the left side:

33 + 6x = 13x + 12

Subtracting 33 on both sides:

6x = 13x - 21

Subtracting 13x on both sides:

-7x = -21

Dividing by -7 on both sides:

x = 3

Answer:

y = -4x + 0 or y = -4x

Step-by-step explanation:

y = mx + b

y = -4x + b

21 = -4(0) + b

21 = 0 + b

b = 0

y = -4x + 0 or y = -4x (the 0 is unnecessary to write but you could write it both ways)

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The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

The iterated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

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The correct option for the dilation scale factor is-

By creating a right triangle with vertices just at origin, Point P as an extra point, and a leg down the x-axis, the scaling factor can be applied.

Thus, this triangle will plot a new point, the image of P, on the line with any dilation given to it.

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