HELP If there are 79 people in a hip-hip dance group and 14 are girls,
what is the probability that a person chosen at random will be a boy?
State your answer as a fraction.

The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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The Biased samples that are most likely to be biased are as follows;

The residents of every other house on her street.

The people at the computer store.

At the mall every 100th person from the town’s phone registry.

Every 10th person who walks down the main street in her town.

According to the statement

we have given that the:

Maria wants to take a survey to predict who will win the election for her town’s mayor.

So, For this purpose

Biased sample In epidemiology, a sample of a group that does not equally represent the members of the group.

The above people are selected randomly with no specific characteristics, so it is less likely to be biased.

These people are selected according to specific characteristics; Subscribing to the golf magazine (who tends to be rich and biased in politics).

So, it is more likely to be biased.

The Biased samples that are most likely to be biased are as follows

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Answer:

A: The residents of every house on her street

B: The subscribers to a golf magazine

C: The people at the computer store at the mall

a) 1. The backpack weight sample mean is 6.375 pounds.

a) 2. The backpack weight sample mean is 6.375 pounds.

a) 3. The backpack weight sample mean is 6.625 pounds.

b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.

c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.

The farther the range of the sample means is from O, the less confident they can be in their estimate.

A sample mean is a statistic computed from a sample of data or variables.

The sample mean represents the average value of the sample data.

The range describes the difference between the largest number and the smallest number.

Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.

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Answer:

-0.5, either ⅙ or ⅓

Step-by-step explanation:

slope = rise / run

3) slope = (6 - 7) / (3 - 1)

slope = -1 / 2

slope = -0.5

ur mouse is blocking 4 (I'll do 2 scenarios):

4) slope = (-4 - -5) / (2 - -4)

slope = 1 / 6

I will leave it in fractional form

4) slope = (-4 - -6) / (2 - -4)

slope = 2 / 6

slope = 1/3

slope = 0.33

The parabola represented by this graph has the following equation:

y = -16.67(x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:

(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:

y = a(x - h)² + k

y = a(x + 1)² + 2

We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:

y = a(x + 1)² + 2

-4 = a(-0.4 + 1)² + 2

a = -6/0.6²

a = -16.67

Hence the equation is:

y = -16.67(x + 1)² + 2

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Helen is currently is 8 years old.

Endeavor to understand the question, analyze it and interpret it into equation.

Given that Helen's age is multiples of 4. Next year it'll be a multiple of 3. Helen's older brother is now 19.

This means Helen current age is multiple of 4 and next year it will be a multiple of 3. Also, Helen's age is less than 19

The two available numbers that fit this analysis and less than 19 are 8 and 9. 8 is multiple of 4. 8 + 1 = 9 which is multiple of 3

Therefore, Helen is 8 years old now

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The correct answers to the sample space illustrated will be:

S = {I, L, L, M, P, T, U, Y}.

S = {g, r, b, y, o}.

S = {W, X, Y, Z}.

Flipping a fair, two-sided coin.

Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

S = {Joy, Bob, Ben, Peter, John}

A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. The sample space when choosing one marble will be S = {g, r, b, y, o}.

A four-part spinner is spun once and the spinner with four parts labeled W, X, Y, and Z. The sample space for the experiment is S = {W, X, Y, Z}.

The event will have a sample space of S = {h, t} is the flipping a fair, two-sided coin.

The correct sample space for the gumballs in her bag will be sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

My experiment with 5 or more possible outcomes will be that a teacher wants to randomly give one of his give students a pack of chocolate.

The sample space for the experiment will be based on their names. This will be S = (Joy, Bob, Ben, Peter, John).

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Answer:

90 degrees

Step-by-step explanation:

Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.

Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.

3x + 3x = 180

6x = 180

x = 30

3x = 3*30 = 90

Answer:

4

Step-by-step explanation:

10 - 6 = 4

Answer:

  (5, 1)

Step-by-step explanation:

The vertex is the turning point on the graph. Its coordinates are read from the axes labels.

The term vertex is used in several different contexts. A vertex of a polygon is a point where edges meet. A vertex of a curve is an extreme value of the curve.

When applied to an ellipse, the vertices are the ends of the major axis. The ends of the minor axis are the co-vertices.

The vertex of a parabola is the extreme value of the parabola. When it opens downward, as here, the vertex is the point where the curve is at its maximum.

As with any point on any graph, the coordinates of the vertex are read from the labels of the axes. The horizontal coordinate is customarily listed first.

The vertex is (x, y) = (5, 1).

The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex]  using L'Hospital rule is 0.

According to the given question.

We have to find the limit of ln(x)/x when x approaches to infinity.

If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].

And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.

Therefore, defferentiating numerator ln(x) and x with respect to x.

[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]

So,

[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]

[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]

As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.

Therefore,

[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]

Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.

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Answer: B

Step-by-step explanation:

Answer:

3.4 units

Step-by-step explanation:

Here is the five-number summary:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the dataset. The  minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median = 25

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Answer:

EVALUATE

false

Step-by-step explanation:

Complex number

(39+5=5a=9)

Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'

Answer:

30 degrees

Step-by-step explanation:

They are corresponding angles.

Answer: 30 degrees

Step-by-step explanation:

mangle8 and mangle 4 are corresponding angles meaning the angles are both the same.

In the analysis of variance study, if we consider 3 treatments, in which we have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. Then, the degrees of freedom associated with SSE in each case is 2, 3, and 4, respectively.

Degrees of Freedom Associated with SSE

The number of degrees of freedom in statistics refers to the quantity of values that can fluctuate in a statistic's final calculation. Various amounts of data or information can be used to estimate statistical parameters.

In order to find the degrees of freedom associated with SSE in an Analysis of Variance (ANOVA) study, we subtract 2 from the number of observations. In n is the number of observations, then (n-2) gives the degrees of freedom associated with SSE.

Thus, for the first treatment, n = 4

⇒ Degrees of freedom = 4-2

= 2

For the second treatment, n = 5

⇒ Degrees of freedom = 5-2

= 3

For the third treatment, n = 6

⇒ Degrees of freedom = 6-2

= 4

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Answer:

Step-by-step explanation:

4.5x + 40 < 75

4.5x < 35

x<7.7

Answer:

see explanation

Step-by-step explanation:

K is a constant means that K is a fixed numerical value

The number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores using combinations is computed to be 350.

The combination is a process of calculating the number of ways of selecting a smaller set, from a larger set, when the order of selection is irrelevant.

In selecting x number of items, from n number of items, when the order of selection is irrelevant, we use the combination, to calculate the number of possible ways as follows:

nCx = n!/{(x!)((n - x)!)}.

In the question, we are asked for the number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores.

The number of ways of selecting 3 freshmen from 5, using a combination is:

5C3 = 5!/{(3!)((5 - 3)!} = 120/{6*2} = 120/12 = 10.

The number of ways of selecting 3 sophomores from 7, using a combination is:

7C3 = 7!/{(3!)((7 - 3)!} = 5040/{6*24} = 5040/144 = 35.

The total number of teams possible is the product of each.

Thus, the total number of teams  possible is 5C3 * 7C3 = 10*35 = 350.

Thus, the number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores using combinations is computed to be 350.

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Answer:

3

Step-by-step explanation:

f(x)-g(x)=3-cos(x)

when u limit it

u have

3-cos180

which is 3-0

3

Answer:

Step-by-step explanation:

Midpoint a point equidistant from the ends of a line or the extremities of a figure.

To find the midpoint of the line segment with endpoint, use the midpoint formula.

Midpoint formula:

[tex]\Rightarrow: \sf{\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2} }}}[/tex]

y2=(-10)

y1=16

x2=6

x1=(-4)

Rewrite the problem down.

[tex]\sf{\left(\dfrac{6-4}{2},\:\dfrac{-10+16}{2}\right)}[/tex]

Solve.

6-4=2

2/2=1

-10+16=6

6/2=3

= (1,3)

Therefore, the correct answer is B (1,3).

I hope this helps, let me know if you have any questions.

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Answer:

The general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

For given question,

We have been given a differential equation y'' − y' − 12y = e^(4x)

We need to solve the given differential equation by undetermined coefficients.

We can write given differential equation as [tex](D^2-D-12)y=e^{4x}[/tex] where [tex]D=\frac{d}{dx}[/tex]

First solve the corresponding homogeneous differential equation:

y'' - y' - 12y = 0

The characteristic equation is:

m² - m - 12 =0

Let's find the roots of above quadratic equation by factorization.

⇒ m² - m - 12 = 0

⇒ (m - 4)(m + 3) = 0

⇒ m - 4 = 0   OR  m + 3 = 0

⇒ m = 4   OR   m = -3

Hence the complementary solution is,

[tex]y_c=C_1e^{4x}+C_2e^{-3x}[/tex]

Let the general solution of a second order homogeneous differential equation be [tex]y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}[/tex]

The unknown functions C1(x) and C2(x) can be determined from the system of two equations:

[tex]C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)[/tex]

from (1),

[tex]C'_2e^{-3x}=-C'_1e^{4x}[/tex]

Substitute this value in equation (2)

[tex]4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}[/tex]

[tex]\Rightarrow C'_1=\frac{1}{7}[/tex]  and  [tex]C'_2=-\frac{1}{7}e^{7x}[/tex]

[tex]\Rightarrow C_1=\frac{1}{7} x+c_3[/tex]     and     [tex]C_2=\frac{1}{49}e^{7x}+c_2[/tex]

Therefore, the general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

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The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1

14

6 + 8

= 14

(6 + 8)

= 14

The coefficient of (6 + 8) is 1, so, the expression remains the same.

Equivalent expressions refers to those expressions that work the same even though they look different.

The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.

Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.

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Answer:

Step-by-step explanation:

6*[4-(42-63)]=

6*[4-(-21)]=

6*[4+21]=

6*25=150.

6*[4-9÷3]=

6*[4-27]=

6*(-23)=-138.

6*[4-3]=

6*1=6.

The length of the ladder is 75ft.

The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.

The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft

Therefore, we have:

Sineα = opposite/hypotenuse

Where:

Opposite = 35

Hypotenuse = Length

α = 28°

substitute values and solve for the length, as following:

Sine(28) = 35/Length

Length = 35/Sine(28)

Length = 75ft

Therefore,

The length of the ladder is 75 ft.

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The function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x  + 16 = 9.

Given the function; f(x) = x² - 8x + 7

To rewrite by completing the square.

We simplify the function into a proper form to completing the square.

x² - 8x + 7 = 0

x² - 8x = -7

We create a trinomial square on the left side of the equation that is equal to the square of the half of b.

(b/2)² = (-4)²

Next, we add the term to both side of the equation.

x² - 8x + (-4)² = -7 + (-4)²

x² - 8x  + 16 = 9

Therefore, the function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x  + 16 = 9.

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