Jessica is in an art lesson. She decides to pick a coloured pencil from her pencil case at random for her next drawing.
She has 10 coloured pencils in her pencil case, and 8 of them are yellow. What is the probability, as a percentage (%), that she picks a yellow pencil?

Answer:

[tex] \frac{11\pi}{2 } \: ft[/tex]

Step-by-step explanation:

Given:

∠AOB = 30° (it is a central angle, which is equal to the arc on which it rests on)

r (radius) = 3 ft

Find: arc ACB - ?

If arc AB is 30°, then arc ACB is (remember, that a full circle forms an angle of 360°)

[tex]360° - 30° = 330°[/tex]

Now, we can find the length of the arc ACB:

[tex]l = \frac{2\pi \times r \times \alpha }{360°} = \frac{2\pi \times 3 \times 330°}{360°} = \frac{11\pi}{2} \: ft[/tex]

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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All other expressions are equivalent to [tex]y^6 - 16y^2[/tex]  except [tex]y^4 - 16[/tex].

An expression is a group of terms joined together with the operations

+, -, x, . An equation is a claim that two expressions have values that

are equivalent, as in 4 + 2 = 6, and is denoted by an equals sign.

[tex](y^2 + 4) (y + 2) (y - 2)[/tex]

All other expressions are equivalent to [tex]y^2 (y^4 - 16).[/tex]

For example:

[tex](y^3 + 4y)(y^3 - 4y)[/tex](This is equivalent to [tex]y^6 - 16y^2[/tex] ) because ( it is the difference of two squares.)

[tex]16y^2 - y^6[/tex] (This is equivalent to [tex]-1(y^6 - 16y^2)[/tex] .

Therefore, the expression that is not equivalent to [tex]y^6 - 16y^2[/tex] is:

[tex]y^4 - 16[/tex] (This is equivalent to [tex](y^2 + 4) (y^2 - 4)[/tex]), which simplifies to

[tex](y^2 + 4) (y + 2) (y - 2)[/tex].

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A graph shows the solution to the system of linear inequalities include the following: B. graph B.

In order to graph the solution for the given system of linear inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of linear inequalities and then check the point of intersection;

x + 5y ≥ 5          .....equation 1.

y ≤ 2x + 4         .....equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of linear inequalities is the shaded region above the solid lines, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 2).

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Answer:

B

Explanation:

Answer:

The new coordinates of point C after reflection and translation are (-2, -2).

Step-by-step explanation:

I hope it helps:)

Answer:

Null hypothesis (H0): Children with antisocial tendencies have the same difficulty recognizing the emotion of surprise as children without antisocial tendencies. Symbolically: μ = 11.80

Alternative hypothesis (H1): Children with antisocial tendencies have a harder time recognizing the emotion of surprise compared to children without antisocial tendencies. Symbolically: μ > 11.80

The critical region for α = 0.05 with the t distribution would be in the upper tail of the distribution, as this is a one-tailed test (since the alternative hypothesis is directional). The degrees of freedom (df) would need to be determined based on the sample size and specific statistical test being used, but the given information does not provide the value of df.

The estimated standard error would need to be calculated using the given sample size, sample mean, and sample standard deviation. The t statistic would then be calculated as the difference between the sample mean and the hypothesized mean (11.80), divided by the estimated standard error.

Once the t statistic is calculated, it would need to be compared to the critical value of t for the appropriate degrees of freedom and α level (0.05) to determine if it falls in the critical region, and therefore whether the null hypothesis is rejected or not. Based on the given information, the t statistic is not provided, so it is not possible to determine if the null hypothesis should be rejected or not.

Step-by-step explanation:

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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The limit of f(x) as x approaches 0 is 0.

As x approaches 0, we can see that both the numerator and denominator of the expression in the given inequality approach 0. Thus, we can use L'Hopital's rule to evaluate the limit.

Taking the derivative of the numerator and denominator separately, we get:

lim x→0 [(2x - 4x^3) / 2x] = lim x→0 [1 - 2x^2] = 1

lim x→0 [x^3 / 4] = 0

Since 0 ≤ f(x) ≤ 1/4x^3, we can conclude that as x approaches 0, f(x) approaches 0 (by the squeeze theorem).

Therefore, the limit of f(x) as x approaches 0 is 0.

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Answer: 595

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's begin by assigning variables to represent the three mixed numbers. Let a be the greatest mixed number, b be the middle mixed number, and c be the least mixed number. Then we can write:

a + b + c = 18 (the sum of the three mixed numbers is 18)

a - c = 5 1/5 (the difference between the greatest and least mixed numbers is 5 1/5)

To solve for a, b, and c, we can use substitution. From the second equation, we can solve for a in terms of c:

a = c + 5 1/5

Substituting this expression for a into the first equation, we get:

(c + 5 1/5) + b + c = 18

Simplifying, we get:

2c + b = 12 4/5

Now we need to find three mixed numbers that satisfy this equation. We can start by choosing a value for c. Let's choose c = 2 1/2, which is the smallest possible value for c that will allow the mixed numbers to be non-negative. Then we can solve for b:

2c + b = 12 4/5

2(2 1/2) + b = 12 4/5

5 + b = 12 4/5

b = 7 4/5

Finally, we can solve for a using the equation a = c + 5 1/5:

a = c + 5 1/5

a = 2 1/2 + 5 1/5

a = 7 3/5

Therefore, three mixed numbers that satisfy the conditions of the problem are:

The greatest mixed number: 7 3/5

The middle mixed number: 7 4/5

The least mixed number: 2 1/2

And indeed, their sum is 18 and the difference between the greatest and least mixed numbers is 5 1/5.

The first monthly payment is equal to $4,375.00 and its principal amount for the first payment is equal to $612.50.

Mortgage loan amount = $750,000

Rate of interest = 7%

Monthly payment amount = $4,987.50

First monthly payment is for interest

= Monthly interest rate and the portion of the payment that goes towards the principal.

Monthly interest rate = Divide annual interest rate by 12.

Substitute the value we have,

⇒ Monthly interest rate = 7% / 12

                                       = 0.583%

Principal portion of first payment

= Total payment - Interest portion

= $4,987.50 - ($750,000 x 0.583%)

= $4,987.50 - $4,375.00

= $612.50

Therefore, $4,375.00 of the first monthly payment of $4,987.50 is for interest, and $612.50 is for the principal.

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Revolutions per minute = (33π/4)/(2π) = 33/8  and this is  33/(8 x 60) = 33/480 revolutions per second

Ten revolutions will therefore take  10 / (33/480) = 4800/33 = 145.5 sec

Answer: the answer is "145.5" seconds

Step-by-step explanation: I took the test.

for example, let's find the 7.25% of "x"

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.25\% of x}}{\left( \cfrac{7.25}{100} \right)x}\implies \stackrel{ \textit{in decimal form} }{\text{\LARGE 0.0725}}\times x\implies 0.0725x[/tex]

The price for apples is cheaper at quick market.

From the question, we have

Quick market:

[tex]\dfrac{1.52}{6} = \text{0.25 per apple}[/tex]

Walmart:

[tex]\dfrac{1.32}{5} = \text{0.26 per apple}[/tex]

The price for apples is cheaper at quick market.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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Answer:

The answer would be (x+10)(x-7)

Step-by-step explanation:

The way I learned it was the numbers would multiply to get 70, but add to get 3. Multiples of 70 are 1, 2, 5, 7, 10, 14, 35, 70. Out of these the only one that works is 10 and 7. Using foil, we get x^2-7x+10x-70 which becomes x^2+3x-70

Answer: 6

Solution:

Suppose that the bag contains 2 red tokens, 4 yellow tokens, and x blue

tokens.

Then the likelihood of drawing a blue token is 2-4 ty, and the possibility of drawing a token that is not blue is 2+4+8

If the two likelihoods is equal, we can make the equation below.

X

2+4

2+4+*=2+4+*

Solve for x, = * = 6.

so, there must be 6 blue tokens in the bag.

If 107 people attend a concert, 47 adults and 60 children went to concert using substitution method.

Given,

Let A be the quantity of tickets sold to adults.

Let C be the number of tickets sold to children.

Tickets for adults cost $3.25

Tickets for children cost $2.75

Equation,

3.25A + 2.75C = 317.75

And,

107 people attend a concert.

A + C = 107

Now using the substitution method,

C = 107 - A

Substituting value of C in equation 3.25A + 2.75C = 317.75,

3.25A + 2.75(107 - A) = 317.75

3.25A + 294.25 - 2.75A = 317.75

3.25A - 2.75A = 317.75 - 294.25

0.5A = 23.5

A = [tex]\frac{23.5}{0.5}[/tex]

A = 47

Substituting the value of A in equation C = 107 - A,

C = 107 - 47

C = 60

If 107 people attend a concert, 47 adults and 60 children went to concert.

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The value of angle x as represented can be determined to 1 decimal place as required to be; 57.8°.

It follows from the task content that the given triangle can be solved for variable x using the sine rule.

Therefore;

11 / sin x = 8 / sin (38)

sin x = 11 sin (38) / 8

x = 57.8°.

Ultimately, the value of angle x as required in the task content is; 57.8°.

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Answer:

Step-by-step explanation:

The probability of getting exactly 25 heads in 50 coin flips would be higher than flipping a coin 6 times and getting exactly 3 heads.

To understand why, we can use the formula for calculating the probability of getting a specific number of heads in a given number of coin flips, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k heads, n is the total number of coin flips, p is the probability of getting heads on a single coin flip, and (n choose k) is the binomial coefficient.

For the first scenario of flipping a coin 50 times and getting exactly 25 heads, we can plug in the values and get:

P(X=25) = (50 choose 25) * 0.5^25 * 0.5^25 = 0.112

For the second scenario of flipping a coin 6 times and getting exactly 3 heads, we can similarly plug in the values and get:

P(X=3) = (6 choose 3) * 0.5^3 * 0.5^3 = 0.3125

As we can see, the probability of getting exactly 25 heads in 50 coin flips is much higher than the probability of flipping a coin 6 times and getting exactly 3 heads. This is because the probability of getting a single head on a coin flip is 0.5, and as the number of coin flips increases, the probabilities of different outcomes converge towards a bell-shaped distribution centered around 0.5. This means that the probability of getting a specific number of heads in a large number of coin flips becomes more likely as the number of coin flips increases.

Answer: The value of x is 9.

Step-by-step explanation: n a regular hexagon, all interior angles have the same measure.

Since a hexagon has six sides, the sum of its interior angles is given by the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

Since all interior angles of a regular hexagon have the same measure, we can find the measure of each angle by dividing the sum by the number of angles:

Measure of each angle = Sum of interior angles / Number of angles = 720° / 6 = 120°

We are given that one of the angles in the hexagon is (11x + 21)°. Setting this equal to 120° and solving for x, we get:

11x + 21 = 120

11x = 99

x = 9

Therefore, the value of x is 9.

For the function y=5 cos {x-(π/6)}-1

a) To find the average rate of change, evaluate the function at x = (2π)/3 and x = π/3, and then take the difference between the two values and divide by the difference between the two x-values:

Average rate of change = (y(2π/3) - y(π/3)) / ((2π/3) - (π/3))

First, find y(2π/3) and y(π/3).

y(2π/3) = 5 cos((2π/3) - (π/6)) - 1 = 5 cos(5π/6) - 1 = -5/2 - 1 = -7/2

y(π/3) = 5 cos((π/3) - (π/6)) - 1 = 5 cos(π/6) - 1 = 5/2 - 1 = 3/2

Plugging these values into the formula:

Average rate of change = ((-7/2) - (3/2)) / ((2π/3) - (π/3))

= -5 / (π/3)

= -15/π

Therefore, the average rate of change from x = π/3 to x = (2π)/3 is -15/π.

b) To find the instantaneous rate of change at x = π/2, take the derivative of the function and evaluate it at x = π/2.

y = 5 cos(x - (π/6)) - 1

y' = -5 sin(x - (π/6))

Plugging in x = π/2:

y'(π/2) = -5 sin(π/2 - (π/6)) = -5 sin(π/3) = -5 (√3)/2

Rounding this to the nearest tenth:

y'(π/2) ≈ -4.3

Therefore, the instantaneous rate of change at x = π/2 is approximately -4.3.

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Image transcribed:

4) Consider the function y=5 cos {x-(π/6)}-1

a) Find, in exact form, the average rate of change from x= π/3 to x=(2π)/3  (A-3 marks)

b) Find, to the nearest tenth, the instantaneous rate of change at x=π/2 (A-4 marks) 2

Answer:

The answer to your problem is, ∞

Step-by-step explanation:

Well there can be multiple ways to make 2/3 equivalent to another here’s how.

We know that 4/6 is equivalent to 2/3 but how exactly?

Well put it into a fraction like this:

[tex]\frac{2*2}{3*2}[/tex] Note: The denominator and the numerator needs to be multiplied by the same number in order for the fraction to be equiavalent.

= 4/6

Thus the answer to your problem is, ∞

As a result ,By using Pythagoras  each leg is the equivalent of **10 feet** and **16 feet**.

A fundamental relationship between a right triangle's three sides in Euclidean geometry is known as the Pythagorean theorem. The hypotenuse is the side that forms the right angle, and the rule says that the square of its length is equal to the sum of the squares of the lengths of the other two sides

``` a² + b² = c² ```

where the lengths of the right triangle's two legs (a and b) and the hypotenuse (c) are indicated.

Let's designate the triangle's two legs as "a" and "b," respectively. We are aware that: The length of the hypotenuse is 55 feet.

One leg of the triangle is 22 feet shorter than the other leg, which is 22 feet longer.

To find the values of "a" and "b," we can utilize the Pythagorean theorem. According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs. We thus have:

``` a² + b² = 55² ```

We also are aware of:

``` a = 2b - 22 ```

When we add this to our initial equation, we obtain:

''' (2b - 22)²+ b² = 55²

b² - 22b + 96 = 0

4b² - 88b + 384 = 0

(b - 16)(b - 6) = 0

4b² - 88b + 384 = 0

Therefore, "b" can be either "16" or "6." A = 2(16) - 22 = 10 if b = 16, otherwise b = 16.

In the event that b = 6, a = 2(6) - 22 = -10. We can disregard the negative solution because we are working with lengths.

As a result, each leg is the equivalent of **10 feet** and **16 feet**.

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Consequently, y = -2x + 1 is the equation of the slope-intercept form of the line passing.

A line can be represented using the slope-intercept form of a straight line. Typically, a linear equation in the form y=mx+c is used to represent it. It places emphasis on the slope and y-intercept of a particular line1.

m is the line's slope and c is the y-intercept in this equation. The slope of a line is the ratio of the change in y to the change in x between any two distinct places on the line. The y-intercept is the point at which the line intersects the y-axis.

x - 2y = 8 defines the given line. This equation can be expressed in slope-intercept form as follows:

y = (1/2)x - 4

This line has a slope of 1/2. A line that is perpendicular to this line will have a slope that is the negative reciprocal of 1/2, or -2.

We are aware that the line traverses the given point. (2,-3). The equation of the line can be written as follows using the point-slope form:

y - y₁= m(x - x₁)

where (x₁,y₁) is the line's passing point and m is the slope of the line.

replacing the specified values:

y - (-3) = -2(x - 2)

Simplifying:

y + 3 = -2x + 4

y = -2x + 1

So , y = -2x + 1 is the equation of the slope-intercept form of the line passing through the point (2,-3) and perpendicular to the line described by x - 2y = 8.

The work given below :

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The option that has the same variation or mean absolute deviation would be option c

Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean of that dataset.

It is a measure of how spread out the data is around the mean, and it is calculated by finding the absolute difference between each data point and the mean, adding up all of these absolute differences, and then dividing by the total number of data points.

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Therefore, the length of the third side of the right-angled triangle is 2√55.

Using the Pythagorean theorem to solve for the length of the third side of the right-angled triangle:

So, if we let the third side be x, we have:

6^2 + x^2 = 16^2

Simplifying this equation:

36 + x^2 = 256

Subtracting 36 from both sides:

x^2 = 220

Taking the square root of both sides:

x = √220

Simplifying the square root:

x = 2√55

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Volume of the water that has flowed through the pipe in 3 minutes is 36489.6

The flow of water through a pipe is determined by several factors, including the pressure difference between the two ends of the pipe, the diameter and length of the pipe, the viscosity and density of the water, and any obstructions or bends in the pipe.

The rate of flow, or the volume of water that passes through the pipe per unit of time, can be calculated using the formula:

Q = A × V

where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the water.

now area = angle / 360πr²

A= 70 / 360(3.14)(4.8)²

14.06

Now Length = Speed x time

L = 14 x 3 x 60 = 2520 cm

Now Volume = area x length

2520 x 14.06 = 36489.6

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the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

How to solve the probability?

A standard deck of 52 cards contains 12 face cards (4 Kings, 4 Queens, and 4 Jacks) and 40 non-face cards (10s, 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, and Aces). To find the probability that a 5-card poker hand contains exactly 2 face cards, we need to count the number of possible hands that satisfy this condition and divide by the total number of possible 5-card hands.

To count the number of hands with exactly 2 face cards, we can use the following steps:

Choose 2 face cards from the 12 available: 12 choose 2 = 66 ways.

Choose 3 non-face cards from the 40 available: 40 choose 3 = 91,390 ways.

Multiply the results of steps 1 and 2 to get the total number of possible hands with exactly 2 face cards: 66 x 91,390 = 6,270,540.

To count the total number of possible 5-card hands, we can use the formula for combinations: 52 choose 5 = 2,598,960.

Therefore, the probability of getting a hand with exactly 2 face cards is:

6,270,540 / 2,598,960 = 0.0241, or approximately 2.41%.

So the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

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