In Exercises
frequencies.
9.
Gender
9 and 10, find and interpret the marginal
(See Example 1.)
Male
Female
Set Academic Goals
No
168
142
Yes
64
54
suport
no sas8

The solution is:

20/29 is the probability that a student chosen randomly from the class plays golf or soccer.

0 is the probability that a student chosen randomly from the class plays golf and soccer.

Here, we have,

given that,

In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.

There are 9 students who play neither.

Number of students that play = 20

let, students play golf = A

students play soccer = B

so, given that,

n ( A) = 6 and, n ( B) = 14

so, total sample space = 29

now, P(A) = 6/29

P(B) = 14/29

and, P(students who play neither) = 9/29

we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1

i.e. there are no students who play both golf and soccer = 0

all the events are independent.

so, we have,

the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)

               = 6/29 + 14/ 29

               = 20/29

and, the probability that a student chosen randomly from the class plays golf and soccer = 0.

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the paint set, sketchbook, brush price in turn are : 26 ; 19,5 ; 3,25$

Step-by-step explanation:

assume the price of the paint set is x($)

we have an equation

52,75-4= X + 3/4X +1/6×3/4X (4$ is the remaining amount after shiva bought these things above)

<=> X=26($)

The procedure step that the student could follow to accomplish the goal of increasing the force of the electromagnet would be C. Add more batteries in series at location 3.

Adding batteries in a series has the effect of increasing the electromagnet's force by augmenting the voltage applied to the wire coil.

The intensity of the magnetic field produced by an electromagnet corresponds directly to the magnitude of current coursing through the wire coil and the number of wire coils present in the magnet respectively. Meanwhile, the amount of current that travels through said coil is intrinsically related to the resistance of the coil itself and the applied voltage across it.

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The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.

The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,

f(4) = 2(4)² - 9

Evaluating 2(4)²,

f(4) = 2(16) - 9

Simplifying 2(16) - 9:,

f(4) = 23

Therefore, f(4) = 23. So, the correct answer is Option A.

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Complete question - Determine f(4) for A piecewise function

f(x) = x³ ____ x<-3

f(x) = 2x²-9 ____ -3 ≤ x≤ 4

f(x) = 5x+ ____ when x>4

A. 23

B. 24

C. 41

D. 64

The expected value of the investment is $600,000.

The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.

If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:

(0.3 x $2,000,000) + (0.7 x $0) = $600,000

This means that the expected value of the investment is $600,000.

Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.

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A transformation that would take Figure A to Figure B include the following: D. A counterclockwise rotation of 90° about the origin.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:

(x, y)                               →                (-y, x)

Ordered pair (-4, 9)        →           Ordered pair (-9, -4)

In conclusion, we can logically deduce that a rotation of 90° counterclockwise around the origin is a type of transformation that would take Figure A to Figure B.

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By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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The correct answer for the statement is,

⇒  Alternative Hypothesis

Hence, Option D is true.

We have to given that;

To complete the sentence,

A statement is,

That is referred to as ___ and is accepted if the sample data provide enough evidence to refute the null hypothesis.

Now, We know that;

Definition of Alternative Hypothesis,  

When the sample data support the null hypothesis sufficiently, a statement is taken as true, yet it is untrue.

Hence, Complete sentence is,

A correct statement which is accepted for the sample data provided sufficient evidence that the null hypothesis is false, is called Alternative Hypothesis.

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The given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional equations.

To determine if the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are proportional, we need to check if the ratios of the corresponding coefficients are equal. Let's solve the second equation for y and compare the coefficients:

Given equation 1: [tex]\( y = -4x \)[/tex]

Given equation 2: [tex]\( \frac{1}{6} + 3x = y \)[/tex]

To determine if the equations are proportional, we'll compare the coefficients of x and y in both equations.

Comparing the coefficients of x:

In equation 1, the coefficient of x is [tex]-4[/tex].

In equation 2, the coefficient of x is [tex]3[/tex].

Since the coefficients of x are different [tex](-4 \ and \ 3)[/tex], the equations are not proportional.

Comparing the coefficients of y:

In equation 1, the coefficient of y is -1.

In equation 2, the coefficient of y is 1.

Since the coefficients of y are different (-1 and 1), the equations are not proportional.

Hence, the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional.

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The solution is: the interest rate and principal is 6% and Rs 65,000

The interest rate, r = 6% and the principal, P = Rs 65,000

Here, we want to find the interest rate and principal

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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complete question:

compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest​

Descriptive Statistics for Variables in the Study

Variable Mean Standard Deviation Skewness Kurtosis

Variable1 10.2 2.1 -0.15 2.8

Variable2 15.3 3.2 0.10 3.2

Variable3 20.1 4.5 -0.05 2.9

Variable4 8.9 1.8 0.30 3.5

Based on Table 1, we can see that all variables have skewness and kurtosis values within the acceptable range of -2 to +2. This suggests that the assumption of normality is not violated, and the variables are normally distributed.

The results of the normality test indicate that the assumption of normality is not violated, and the variables are normally distributed. Therefore, we can proceed with the correlation analysis.

Skewness measures the degree of asymmetry of the distribution, with positive values indicating a right-skewed distribution, negative values indicating a left-skewed distribution, and a value of zero indicating a symmetrical distribution.

Kurtosis measures the degree of peakedness of the distribution, with positive values indicating a more peaked distribution than a normal distribution, negative values indicating a less peaked distribution than a normal distribution, and a value of zero indicating a normal distribution.

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The number of jerseys they can purchase for $430 is 53 jerseys.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Based on the information provided about the cost of the jerseys, we have the following quadratic function;

C = 0.1x² + 2.4x + 25

430 = 0.1x² + 2.4x + 25

0.1x² + 2.4x + 25 - 430 = 0

0.1x² + 2.4x - 405 = 0

By solving the quadratic function using the quadratic formula, we have:

[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]

x = 52.76 ≈ 53 jerseys.

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The statement that describes the mean is the last one:

"the sum of the prices divided by 7"

For any set of N values {x₁, ..., xₙ}, the mean is given by:

M = (x₁ + ... + xₙ)/N

In this particular case, we have a set of 7 values which is {8, 10, 10, 12, 15, 15, 18}

The mean will be the sum of these 7 values divided by the number of values, which is 7, so the mean is:

M = (8 + 10 + 10 + 12 + 15 + 15 + 18)/7

M = 12.57

The correct option is the last one; The sum of the prices divided by 7

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Answer: To estimate the number of farms expected to no longer have a problem with caterpillars feeding on their crops among the total 1,470 farms based on the random sample of 200 farms, we can use proportion estimation.

First, let's find the proportion of farms in the sample that no longer have a problem with caterpillars:

Proportion = (Number of farms with no caterpillar problem in the sample) / (Total number of farms in the sample)

Proportion = 160 / 200

Proportion = 0.8

Next, we'll use this proportion to estimate the number of farms in the total population of 1,470 farms:

Estimated number of farms = Proportion * Total number of farms in the population

Estimated number of farms = 0.8 * 1,470

Estimated number of farms = 1,176

Therefore, it is expected that approximately 1,176 farms will no longer have a problem with caterpillars feeding on their crops based on the sample data.

Step-by-step explanation:

Based on the image attached, The the shape of the distribution is option c) data skewed right.

The term Right skewed is one where the mean  is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean  is one that has little of the common values in a rightly skewed dissemination.

So, therefore, if  most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.

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See text below



Gabriela recorded the ages of her shirts.

·

0 1 2 3 4 5 6 7 8 9 10

Age (years)

Which of these best describes the shape of the distribution?

Choose 1 answer:

Roughly symmetric

Skewed left

Skewed right

Good Question (141)

The length of the pool is 5 meters

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

The length of the pool is calculated as

Length = Surface area / Width

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

Length = 20/ 4

EValuate

Length = 5

Hence, the length is 5 meters

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Step-by-step explanation:

it follows practically the same rules as a division between plain numbers.

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

we take the first term (x⁵) and divide it by the x term(s) of the divisor (we ignore constants for the moment). the resulting x term : x⁴

as x⁵/x = x⁴

now we multiply the intermediate result with the full divisior and subtract that result from the left side of the dividend :

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

- x⁵ - x⁴

--------------

0 0

now we "pull down" the next term of the dividend and we calculate

(0 + 0 + 9x³) / x = 9x²

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

and we do the same thing as before (multiply intermediate result with divisor and subtract the result)

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

0 0 9x³

- 9x³ - 9x²

---------------

0 0

and, again, we pull down the next term of the dividend abd divide by the x term(s) of the divisor

(0 + 0 + 0 + 0 + 9x) / x = 9

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

and we do the same thing as above again

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

- 0 0 0 0 9x - 9

-----------

0 - 1

since we ran out of additional terms, we are finished.

the quotient is

x⁴ + 9x² + 9

the remainder is

-1

which makes the full division result

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) =

= x⁴ + 9x² + 9 - 1/(x - 1)

let's check :

(x⁴ + 9x² + 9 - 1(x - 1)) × (x - 1) =

= x⁵ + 9x³ + 9x - x⁴ - 9x² - 9 - 1 =

= x⁵ - x⁴ + 9x³ - 9x² + 9x - 10

perfect.

The rate of change of the number of oil changes with respect to the number of hours will be 3.

The table is given below.

Number of hours              Number of oil changes

            1.5                                          4.5

             3                                             9

           5.5                                         16.5

             8                                            24

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The rate of change is calculated as,

Average rate = (24 - 9) / (8 - 3)

Average rate = 15 / 5

Average rate = 3

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The length of the PR is 14 cm by pythagoras theorem

We have to find the length of PR

By using pythagoras theorem we know that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

PR² + RQ² = 50 ²

PR² + 48² = 50 ²

PR² +2304=2500

PR²=2500-2304

PR²=196

PR=14

Hence, the length of the PR is 14 cm by pythagoras theorem

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Hello!

x = number of caps of Mel

36 - x = 2(12 + x)

36 - x = 24 + 2x

36 - 24 = 2x + x

12 = 3x

x = 12/3

x = 4

The answer is 4.

verification:

36 - 4 = 32

12 + 4 = 16

16 x 2 = 32 or 32/2 = 16

it's correct.

Answer:

Step-by-step explanation:

I don't quite understand the problem but:

2 2/4 -1 =1 1/2, and 3/4 can't be simplified more.

(a). The ratio of blue marbles to all marbles as 5/14.

(b). The number of blue marbles by the number of red marbles: 5/9

(a) The ratio of blue marbles to all marbles in the bag is 5/14.

To see this, we add the number of blue marbles and the number of red marbles to get the total number of marbles, which is 5 + 9 = 14.

Then we can express the ratio of blue marbles to all marbles as 5/14.

(b) The ratio of blue marbles to red marbles is 5/9. To see this, we divide the number of blue marbles by the number of red marbles: 5 ÷ 9 = 0.55555..., which we can simplify to 5/9.

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Answer:

18.85 meters

Step-by-step explanation:

V=πr2h=π·12·6≈18.84956

Step-by-step explanation:

Fred has two possible outcomes on his first test: he either scores less than 60 or he scores 60 or higher.

If he scores less than 60, there is a 55% chance he will pass the course, and a 45% chance he will fail. We know there is a 70% chance he will score less than 60, so the probability that he scores less than 60 and fails the course is 0.7 * 0.45 = 0.315.

If he scores 60 or higher, there is a 70% chance he will pass the course, and a 30% chance he will fail. We don't know the exact probability that he scores 60 or higher, but we know that it is 1 - 0.7 = 0.3 (since there is a 70% chance he scores less than 60). So the probability that he scores 60 or higher and fails the course is 0.3 * 0.3 = 0.09.

Adding these two probabilities together gives us the total probability that Fred gets more than 60 on the first test but fails the course: 0.315 + 0.09 = 0.405. However, we are looking for the probability that he gets more than 60 but fails, so we need to subtract the probability that he scores less than 60 and fails: 0.405 - 0.315 = 0.09. Therefore, the answer is B. 0.09.

i think so...

We can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).

To find the Margin of Error (MoE) for a poll, we need to use the formula:

MoE = [tex]z \times (\sqrt{(p \times q / n)} )[/tex]

where:

z is the z-score associated with the desired confidence level (99% confidence level corresponds to z = 2.576)

p is the proportion of people who said they liked dogs (0.65 in this case)

q is the complement of p (i.e., q = 1 - p)

n is the sample size (130 in this case)

Plugging in the values, we get:

MoE = [tex]2.576 \times (\sqrt{(0.65 \times 0.35 / 130)} )[/tex] ≈ 0.0844

Rounding to four decimal places, the Margin of Error is approximately 0.0844. Therefore, we can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).

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The total rainfall for the year is given as follows:

D. 19 inches.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

Hence the rainfall in this problem is divided as follows:

Hence the total rainfall is obtained as follows:

0 + 1 x 0.5 + 2 x 0.75 + 3 x 1.75 + 1 x 2 + 1 x 2.25 + 3 x 2.5 = 19 inches.

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Step-by-step explanation:

To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.

E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)

Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.

E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)

E(X) = (0) + (0.18) + (0.02)

E(X) = 0.20

The expected value of the number of bids won is 0.20.

After considering all the given data we conclude that the binomial that is a factor of the polynomial P(x) is (x-4), which is Option C

As it is seen in the context of the remainder theorem of polynomials, in the event that a  polynomial function f(x) is divisible by a factor (x-a), the remaining reminder is zero, now the generated value of f(a) will be also zero. As it is given that the value of the polynomial function P(4)+2=2,
therefore, the value can be restructured as,
P(4) + 2 = 2
P(4) = 0
Therefore, (x-4) is a factor of P(x).
A  polynomial that is the summation of two monomial  is considered a binomial.
For instance , x + 2 is a binomial, here x and 2 are two separate terms.
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