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The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.

Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)

P(x > 77.83) = 1 - P(x < 77.83)

P(x > 77.83) = 1 - 0.9234

P(x > 77.83) = 0.0766

The number of different colors that Sam can use for the triangle is given as follows:

60 different colors.

The Fundamental Counting Theorem (also known as the multiplication rule) is a fundamental principle in combinatorics that describes how to count the number of possible outcomes in a sequence of events.

The theorem states that if there are m ways that one event can occur and n ways that a second event can occur, then there are m x n ways that both events can occur.

The parameters for this problem are given as follows:

Hence the number of options is obtained as follows:

5 x 4 x 3 = 60 options.

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Figure1 shows pair of corresponding angles

Figure 2 and 6 shows pair of alternate exterior angles

Figure 5 shows pair of alternate interior angle

Figure3 shows pair of consecutive exterior angles

Figure 4 shows pair of consecutive interior angles

A set of angles on the outside of each of the two lines but on the opposing sides of the transversal are known as alternate exterior angles.

When a transversal intersects two parallel lines, the angles created within are equal to the alternative pairings of those pairs.

the angles created when two parallel lines cross any other line, whether they are corresponding or matching corners with the transversal.

In the given figures

Figure1 is  showing pair of the corresponding angles

Figure 2 and 6 showing pair of the alternate exterior angles

Figure 5 is showing pair of the alternate interior angle

Figure3 is showing pair of the consecutive exterior angles

Figure 4 is showing pair of the consecutive interior angles.

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Even though the table appears to have varied shapes depending on the angle from which it is seen, Baby Mary recognizes the table as having the same shape. Shape constancy can be seen in this situation.

             Shape constancy is the ability of an object to retain its shape, size, and orientation even when viewed from different perspectives or angles. In essence, when the shape of an object is known, this allows an individual to recognize the object as a whole.

           It's an important part of perception, and it's what allows us to recognize objects even when they're partially obscured or viewed from a different angle. A child can recognize objects as having the same shape, regardless of the angle from which they are viewed. As the object is observed from a variety of angles, its proportions and the shapes of its edges and sides change. Even so, the child perceives the object as having a consistent shape, size, and orientation.

          This can be attributed to the ability of a child's brain to maintain a mental image of the object's actual shape, even when presented with an altered image.

            As a result, a child may perceive an object as having a consistent shape, even if it appears to be different from one angle to another.

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Answer:

Step-by-step explanation:

(-3m + 3d) : 3 =

(-3m + 3d) x 1/3 =

-m + d

The rate at which the water is being drained from the container is -12.56 cubic inches per second.

Given that the water is being drained from a container which has the shape of a right circular cone. The cone has a radius of 3 inches at the top and a height of 6 inches. When the water is 3 inches deep, the surface level is falling at a rate of 2 inches per second. We need to find the rate at which the water is being drained from the container.

Step 1: Calculate the volume of the cone. Consider the cone with the height h = 6 inches and radius of the base r = 3 inches. Let H be the height of the water and V be the volume of the water in the cone. Let V0 be the volume of the cone.

Cone Volume formula: $V=\frac{πr^{2}h}{3}$V0 = πr²h/3 = (3.14) (3²) (6)/3 = 56.52 cubic inches

Step 2: Find the rate at which the water level is falling. Let the rate at which the water level is falling be dh/dt. When the water is 3 inches deep, the surface level is falling at a rate of 2 inches per second. Thus, dh/dt = -2.

Step 3: Find the rate at which the water is being drained from the containerLet dv/dt be the rate at which the water is being drained from the container. To find this rate we need to differentiate the volume of water with respect to time V = (1/3)πr²H.H²dv/dt = (2/3)πr² dh/dtdv/dt = (2/3)π(3²)(-2) = -12.56 cubic inches per second.

Hence, the rate at which the water is being drained from the container is -12.56 cubic inches per second.

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Answer: 1/3

Step-by-step explanation:

4 + 8 = 12 so there's 12 marble in the bag and only 4 purple ones. so the probability is 4/12 which we can simplify to 1/3

Answer:

12+2x

Step-by-step explanation:

5×3= 15

15+ 2x - 3

collect like terms

15-3+2x

12+2x

therefore 5×3+ 2x - 3 = 12 +2x

The price of the television after the drop in its sales price would be = 1200

The percentage of money that was removed from the cost price for the television = 20%

The original price of the television = 1200

The percentage equivalent of 1200 that is 20 = 20/100×1200/1

= 24000/100

= 240

After the sales 240(20%) is added back to the sale price which show that it remains the same after sales.

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If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.

The balance can be determined using subtraction operation.

Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.

Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.

The total spending budget that Kathy has = $20

The number of gifts to buy = 3

The amount spent on Gift A = $10.07 ($10⁷/₁₀)

The amount spent on Gift B = $6.04 ($6²/₅)

The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).

Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.

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Answer:

D

Step-by-step explanation:

Because this binary function opens down, and it has an extreme point, at t=5, and you plug it in and you get 124 as the maximum.

There are $22$ valid $3$-word sentences in gnollish.

We can count the number of valid sentences by counting the number of all possible 3-word sentences and subtracting the number of invalid sentences where "splargh'' comes directly before "glumph.''

The total number of possible 3-word sentences is 3³ = 27, as there are 3 choices for each word.

To count the number of invalid sentences where splargh'' comes before glumph,'' we can fix splargh'' in the first position and then there are only 2 choices for the second position and 2 choices for the third position (since we cannot use splargh'' or glumph'' again). Thus, there are 2 * 2 = 4 invalid sentences where splargh'' comes before ``glumph.''

Therefore, the number of valid sentences is 27 - 4 = 23. However, we must also exclude the sentence where all three words are the same (i.e., ``splargh splargh splargh''), since this sentence is not valid according to the given condition. Thus, the final answer is 23 - 1 = 22.

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Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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13.4 square inches of plastic wrap will be needed to completely cover an ice cream cone that has a slant height of 4.25 inches and a diameter of 2 inches.

To completely cover an ice cream cone that has the slant height of 4.25 inches and a diameter of 2 inches, a plastic wrap of about 13.4 square inches will be needed.

How to calculate the amount of plastic wrap required to cover the ice cream cone?

To calculate the amount of plastic wrap required to cover the ice cream cone, we need to find the lateral area of the cone. This can be calculated using the following formula:

Lateral area of cone = πrℓ

where r is the radius of the base of the cone, ℓ is the slant height, and π is the constant pi, which is approximately equal to 3.14.

In this problem, the diameter of the cone is given as 2 inches, which means the radius of the cone will be half of that, i.e., 1 inch. And the slant height is given as 4.25 inches. Therefore, we can calculate the lateral area of the cone as follows: Lateral area of cone = πrℓ = π × 1 × 4.25= 13.4 square inches.

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The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.

The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.

It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.

According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:

Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.

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To determine if a system of linear equations has infinitely many solutions, you need to solve the system and check the resulting equations.

Here are the general steps:

If you obtain a valid solution for each variable, then the system has a unique solution.

If you have two or more variables and only obtain a solution for some of them, then the system has infinitely many solutions.

It's also important to note that if you have a system with fewer equations than variables, it may also have infinitely many solutions.

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The line for y=5x passes through the origin (0,0) and has a steep slope of 5, meaning it rises 5 units for every 1 unit to the right. The line for y=4x-1 intersects the y-axis at -1 and has a slope of 4, meaning it rises 4 units for every 1 unit to the right.

To graph the equations  [tex]y=5x[/tex] and [tex]y=4x–1[/tex]  , we can plot their corresponding points on a coordinate plane and connect them to form a line.

For [tex]y=5x[/tex]

        |

     6  |       .

        |     .

     5  |   .

        | .

     4  |     *

        |        .

     3  |           .

        |              .

     2  |                 .

        |                       .

     1  |                            .

        |                                    .

     0  |________________________________________

            0   1   2   3   4   5   6   7   8   9

Choose any x value, let's say x=0, and find the corresponding y value by substituting it into the equation: y=5(0) = 0. This gives us the point (0,0).

Choose another x value, let's say x=1, and find the corresponding y value: y=5(1) = 5. This gives us the point (1,5).

Therefore, A steep slope of 5 means that the line for y=5x climbs 5 units for every 1 unit to the right and passes through the origin (0,0). The line for  [tex]y=4x-1[/tex] has a slope of 4, which means it rises 4 units for every 1 unit to the right, and it meets the y-axis at -1.

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Answer:

The volume of a tetrahedron can be found using the formula:

V = (1/3) * A * h

where A is the area of one of the faces of the tetrahedron, h is the height of the tetrahedron, and V is the volume of the tetrahedron.

In this case, we are given that the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m. Substituting these values into the formula, we get:

V = (1/3) * 21 m² * 6 m

V = 42 m³

Therefore, the volume of the tetrahedron is 42 cubic meters.

The height οf the juice can is apprοximately 9.98 inches.

A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο cοngruent and parallel circular bases, and a curved lateral surface that cοnnects the twο bases. The twο bases are usually circular, but they can be any οther shape as well. The lateral surface οf a cylinder is curved, and it has the same crοss-sectiοn alοng its entire length.

The volume of a cylinder is given by the formula [tex]\rm V = \pi r^{2}h[/tex], where V is the volume, r is the radius, and h is the height.

Since the diameter of the juice can is 4 inches, the radius is half of that, or 2 inches.

We are given that the volume of the can is 125 cubic inches, so we can set up the equation:

[tex]\rm 125 = \pi (2)^{2}h[/tex]

Simplifying this equation, we get:

125 = 4πh

Dividing both sides by 4π, we get:

h = 125 / (4π)

So the height of the juice can is approximately 9.98 inches when rounded to two decimal places.

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According to the question, we are given a triangle XYZ

where,

Angle sum property states that sum of all the angles of triangle is 180°. So by adding all the three angles we will get the required value of a.

∠X + ∠Y + ∠Z = 180°

30° + 20° + 2a° = 180°

50° + 2a° = 180°

2a° = 180° - 50°

2a° = 130°

a° = 130/2

a° = 65°

Therefore, required value of a is 65°

Answer:

B

Step-by-step explanation:

remember : the sum of all angles in a triangle is always 180°.

are you sure the third angle is called ZZ ?

I am rather sure it would be called XY !

so,

180 = ZX + ZY + XY = 30 + 20 + 2a

130 = 2a

a = 130/2 = 65°

There are 11 people in your sample size and 80% of them can read.

To be 87% sure that 7 of the 11 people could read, you would need to interview eight people.

To calculate this, you need to use a binomial probability formula.

This formula will allow you to calculate the number of successes (people who can read) that must be achieved in order to have an 87% certainty that the sample size of 11 people is representative of the population.

The formula you need to use is P(x) = n! / (x! (n - x)!).

You'll want to plug in x = 7, n = 8. This will give you the probability of 8 successes in 8 trials, which is equal to 0.87. Therefore, you will need to interview 8 people in order to be 87% sure that 7 of the 11 people could read.

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In the figure of circle provided. the value of x is

In a circle, equal chords subtends equal arc length.

In the problem it was given that:

chord SU is equal to chord ST hence we have that

x + x + 38 = 360 (angle in a circle)

collecting like terms

2x + 38 = 360

2x = 360 - 38

2x = 322

Isolating x by dividing both sides by 2

2x / 2 = 322 / 2

x = 161

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The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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When the polynomial p(x)=-x^5-2x^3+4x-3, then the value of p(-1) is 3

The Remainder Theorem is a fundamental concept in algebra that relates the value of a polynomial at a certain point to the remainder of the polynomial's division by a linear factor.

The remainder theorem states that when a polynomial p(x) is divided by (x - a), the remainder is equal to p(a).

In this case, we are asked to find p(-1) when p(x) = -x^5 - 2x^3 + 4x - 3.

To use the remainder theorem, we need to divide p(x) by (x - (-1)), which is the same as (x + 1).

We can perform polynomial long division to find the quotient and remainder

The remainder is -x + 2, which means that p(-1) = -(-1) + 2 = 3.

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The two numbers that fit the description are 27 and 99.

There are two numbers that fit this description. To find them, we can solve the equation:

Difference = Number - Number’s Reverse

Difference = 72

Number - Reverse = 72

Let’s call the two-digit number “x” and its reverse “y”. So, we can rewrite the equation as:

x - y = 72

Now, we can solve the equation using algebraic methods. First, add “y” to both sides of the equation:

x - y + y = 72 + y

x = 72 + y

Next, let’s solve for “y” by subtracting “72” from both sides of the equation:

x - 72 = 72 + y - 72

x - 72 = y

Therefore, we can rewrite the equation as:

x - 72 = y

Now, we can solve for “x” and “y” by plugging in possible values for “x” and “y” and seeing which ones work. Since we’re dealing with two-digit numbers, let’s start with numbers between 10 and 99.

First, let’s try x = 10 and y = 82.

10 - 82 = -72

This doesn’t work, since the difference cannot be negative.

Next, let’s try x = 15 and y = 87.

15 - 87 = -72

Again, this doesn’t work.

Finally, let’s try x = 27 and y = 99.

27 - 99 = -72

This works! So, the two numbers that fit the description are 27 and 99.

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The distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

What is a skewed distribution?

A skewed distribution is one in which the data is not uniformly distributed but rather concentrated on one side. In simple words, a skewed distribution is one in which one tail has a greater number of observations than the other tail, with the majority of data falling in the tail with the greater number of observations.

In a symmetric distribution, the data is uniformly distributed on both sides of the median, with half of the data lying to the right and half to the left.

Thus, the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

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Based on the given circle with center Y, each of the measure include the following:

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners.

Based on the given circle with center Y and line AD is perpendicular to line DB, we can reasonably infer and logically deduce that arc AC is equal to arc BC;

mAC = mBC = 71 degrees.

mAB = mAC + mBC

mAB = 71 + 71

mAB = 142 degrees.

Since line DC is the perpendicular bisector of line AB, the measure of line AB and line BD can calculated as follows;

AD = BD = AB/2

AD = BD = 60/2

AD = BD = 30 units.

Note: YB is the radius of this circle and the hypotenuse of right-angle triangle YDB, which is equal to 34 units.

In order to determine the length of YD, we would have to apply Pythagorean's theorem as follows;

x² + y² = z²

BD² + YD² = YB²

30² + YD² = 34²

YD² = 1156 - 900

YD = √256

YD = 16 units.

DC = YB - YD

DC = 34 - 16

DC = 18 units.

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Answer:

16/5

Step-by-step explanation:

We can see that the new triangle is larger than the original triangle so we know the scale factor is greater than 1.

The scale factor can be found by calculating the ratio of the length of any two corresponding sides. The length of the bottom side of the original triangle is 5. The length of the bottom side of the new triangle is 16. We can calculate the ratio which is 16:5 or 16/5.

The statement that shows the correct definition of multicollinearity is that when several variables are related to each other, it is very likely that more than one of these variables does not account for much additional variation. That is option C.

Multicollinearity is defined as the phenomenon that shows the correlative relationship that exists between independent variables in statistics.

The occurrence of multicollinearity found between independent variables is that it will result in less reliable statistical inference and a problem because independent variables should be independent.

Also, more than one of these variables does not account for much additional variation because, changes in one variable are associated with shifts in another variable.

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