A marriage counselor is interested in the proportion of clients she counsels who stay married. Define the following in terms of the study. Give examples where appropriate. Part (a) The population A. The population is a group of clients of this counselor. B. The population is all of the clients of this counselor. C. The population is all of the clients of this counselor who stay married. D. The population is all couples in marriage counseling.

The correct answer is:

scatter plot with points at (1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2), with a line passing through the coordinates (1, 6) and (5, 4).

What is the scatter plot?

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

We have given,

scatter plot with points at

(1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2),

The first option shows a line passing through the coordinates (1, 6) and (5, 4) which appears to fit the data.

Therefore, the correct answer is:

scatter plot with points at (1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2), with a line passing through the coordinates (1, 6) and (5, 4).

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The fractional probability of rolling different numbers is 5/6 or approximately 0.8333.

What is probablity?

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

To find the probability of rolling different numbers on the two rolls, we need to count the number of outcomes where the numbers are different.

If we roll the first die, there are 6 possible outcomes. For each of these outcomes, there are 5 possible outcomes on the second roll where the number is different from the first roll. Therefore, the total number of outcomes where the numbers are different is:

6 x 5 = 30

So, the probability of rolling different numbers is:

30/36

Simplifying this fraction, we get:

5/6

Therefore, the fractional probability of rolling different numbers is 5/6 or approximately 0.8333.

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1. The probability that no Independents are selected is 0.0304.2.  2. The probability that the sample has one Democrat, one Republican and one Independent is 0.0015.

1. To find out the probability that no Independents are selected, the following will be done. Let’s say that A is the event that a voter is a Democrat, B is the event that a voter is a Republican, and C is the event that a voter is an Independent. The probability of no Independent being selected is P (A and B).

The total number of combinations of 3 voters that can be selected is 40C3. This will be the denominator.The numerator will be 20C1 (15C1). This is because only one Democrat and one Republican can be selected from a total of 20 Democrats and 15 Republicans. Therefore,

P(A and B) = (20C1 * 15C1) / 40C3P (A and B) = 300/9880= 0.03042.

To four decimal places, the answer is 0.0304.2.

2. To find out the probability that the sample has one Democrat, one Republican and one Independent, the following will be done. A, B, and C have the same meaning as above. Let’s assume that the probability of the sample having one Democrat, one Republican, and one Independent is P (A and B and C).

The denominator will be 40C3. There are two ways to find the numerator. One Democrat, one Republican, and one Independent must be chosen. The probability of choosing one Democrat, one Republican, and one Independent is (20C1 * 15C1 * 5C1).

Therefore, the probability that the sample has one Democrat, one Republican, and one Independent is (20C1 * 15C1 * 5C1)/40C3P(A and B and C) = (20C1 * 15C1 * 5C1) / 40C3= 0.00153.

To four decimal places, the answer is 0.0015.

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Therefore , the solution of the given problem of expressions comes out to be  -1/x = 4

There is a need for calculations involving joining, random subdivision, varying multiplier, equation and elimination. If they came together, they could do the following: A mathematical problem, some data, and an algorithm. A statement of truth contains formulas, variables, and arithmetic procedures like additions, subtractions, errors, and groupings. It is possible to assess and analyse words and sentences.

Here,

We must simplify each equation and substitute x = -1/4 to arrange the expressions from least to greatest:

=> x = -1/4

=> 1 - x = 1 - (-1/4) = 5/4

=>x - 1 = (-1/4) - 1 = -5/4

=> -1/x = -1/(-1/4) = 4

As a result, the following phrases are listed from least to greatest:

=> x - 1 = -5/4

=> x = -1/4

=> 1 - x = 5/4

=> -1/x = 4

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If f(x) =

[tex]2tan`x+`sine(2x/1+x^2),[/tex]

then f(√2) is 4.491

To find f(√2), we need to substitute √2 for x in the expression for f(x):

f(√2) = 2tan(√2) + sin(2√2 / 1 + √2^2)

[tex]2tan`x+`sine(2x/1+x^2),[/tex]

Simplifying, we get:

f(√2) = 2tan(√2) + sin(2√2 / 3)

Now, we need to evaluate tan(√2) and sin(2√2 / 3) to get the final answer. We can use a calculator to do this:

tan(√2) ≈ 1.763

sin(2√2 / 3) ≈ 0.965

Substituting these values into the expression for f(√2), we get:

f(√2) ≈ 2(1.763) + 0.965

f(√2) ≈ 4.491

Therefore, f(√2) is approximately equal to 4.491.

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The dilation that took place is a reduction with a center of dilation at (2,2) and a scale factor of 1/3.

In mathematics, a scale factor is a number that scales, or multiplies, another quantity by some constant factor. In geometry, a scale factor is the ratio of the lengths of corresponding sides of two similar figures. This means that if we have two figures that have the same shape but different sizes, the scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

To determine the dilation that took place, we can compare the coordinates of the pre-image (blue triangle) and the resulting image (red triangle). We notice that the red triangle is smaller than the blue triangle, which means that the dilation is a reduction.

The center of dilation is a point on the plane about which the dilation takes place. To find the center of dilation, we can locate the point that is equidistant from each corresponding pair of vertices. In this case, we can see that the point (2,2) is equidistant from both the first vertex of each triangle. Therefore, the center of dilation is the point (2,2).

The scale factor is the ratio of the distance between corresponding points on the image and pre-image. To find the scale factor, we can choose any corresponding pair of vertices and divide the distance between the corresponding points on the image and pre-image. For example, we can take the first vertex of each triangle:

Distance between (2,2) and (2,2) = 0

Distance between (3,2) and (5,2) = 2

The scale factor is then 2/0 = undefined or infinite, which means that the image is a point, not a triangle. However, we can also calculate the scale factor using the distance between the first and second vertices of each triangle:

Distance between (2,2) and (5,2) = 3

Distance between (2,2) and (3,2) = 1

The scale factor is then 1/3, which means that each corresponding side on the image is 1/3 the length of the corresponding side on the pre-image. Therefore, the dilation that took place is a reduction with a center of dilation at (2,2) and a scale factor of 1/3.

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n=0,1, then substitution of v=y ^1-n reduces Bernoulli's equation to a linear equation.

The given equation is a Bernoulli's equation. We are asked to show that if n=0,1, then substitution of v=y ^1-n reduces Bernoulli's equation to a linear equation. This methods of solution was found by Leibniz in 1696. y'=ry-ky2 , r>0 and k>0. This equation is important in population dynamics.

First, let's consider the case when n=0. In this case, v=y^1-0=y^1=y. Substituting this into the given equation, we get:
y'=ry-ky^2
y'=rv-kv^2
This is a linear equation in terms of v, as there are no terms with v raised to a power greater than 1.
Now, let's consider the case when n=1. In this case, v=y^1-1=y^0=1. Substituting this into the given equation, we get:
y'=ry-ky^2
1'=r-k1^2
1'=r-k
This is also a linear equation, as there are no terms with v raised to a power greater than 1.

Therefore, we have shown that if n=0,1, then substitution of v=y ^1-n reduces Bernoulli's equation to a linear equation. This methods of solution was found by Leibniz in 1696. y'=ry-ky2 , r>0 and k>0. This equation is important in population dynamics.

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One way to solve this problem is by using trial and error. Trial and error is a problem-solving strategy that involves experimenting with different methods or approaches until a successful outcome is achieved. We can try different values of a until we find one that satisfies the equation a − 1 mod 29 = 9.

First, let's try a = 1:

1 − 1 mod 29 = 0

This is not the correct answer, so let's try a different value for a. Let's try a = 2:

2 − 1 mod 29 = 1

This is also not the correct answer. Let's keep trying different values for a until we find the correct answer. Let's try a = 10:

10 − 1 mod 29 = 9

This is the correct answer! So the solution to this problem is a = 10.

In conclusion, by using trial and error, we found that the solution to the equation a − 1 mod 29 = 9 is a = 10.

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Answer:

[tex](3x^2y^3 - 4x^3y^4)(3x^2y^3 + 4x^3y^4)[/tex]

Step-by-step explanation:

in algebra we have a formula,

[tex]a^2 - b^2 = (a - b)(a + b)[/tex]

we have the equation

[tex]9x^4y^6 - 16x^6y^8 = (3x^2y^3)^2 - (4x^3y^4)^2[/tex]

Now we can use the formula to simplify in the required form,

[tex]9x^4y^6 - 16x^6y^8 = (3x^2y^3 - 4x^3y^4)(3x^2y^3 + 4x^3y^4)[/tex]

Hopefully, this answer helped you!!!

The polynomial as a product of polynomials is [tex]x^4y^6 (9 - 16x^2y^2).[/tex]

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

[tex]9x^4y^6 - 16x^6y^8[/tex] as a product of polynomials.

We need to factor out the greatest common factor of the two terms.

The GCF of  [tex]9x^4y^6 ~and ~16x^6y^8~ is ~x^4y^6[/tex]

So,

Taking common out.

[tex]= 9x^4y^6 - 16x^6y^8 \\= x^4y^6 (9 - 16x^2y^2)[/tex]

Therefore,

The polynomial as a product of polynomials is [tex]x^4y^6 (9 - 16x^2y^2).[/tex]

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Step-by-step explanation:

this is the required ans

4(x-5)=92

X+100=128

3x=84

2x=56

The volume of the solid generated by revolving the region bounded by the lines y = 0, x = 2 and the curve [tex]y = x^2[/tex] about the X-axis is [tex]$\frac{32\pi}{5}$[/tex].

To find the volume of the solid generated by revolving the region bounded by the lines y = 0, x = 2 and the curve [tex]$y = x^2$[/tex] about the X-axis, we can use the disk method.

Consider a vertical slice of the region at a distance x from the y-axis. This slice has thickness dx and its area is given by the area of the circle generated by revolving the curve [tex]$y = x^2$[/tex] about the X-axis. The radius of this circle is [tex]$y = x^2$[/tex], so the area of the circle is [tex]$\pi y^2 = \pi (x^2)^2 = \pi x^4$[/tex].

The volume of the slice is then given by:

[tex]$dV = \pi y^2 dx = \pi x^4 dx$[/tex]

Integrating this expression from x=0 to x=2, we get the total volume:

[tex]$V = \int_{0}^{2} \pi x^4 dx = \left[\frac{\pi}{5} x^5 \right]_{0}^{2} = \frac{32\pi}{5}$[/tex]

Therefore, the volume of the solid generated by revolving the region bounded by the lines y = 0, x = 2 and the curve [tex]y = x^2[/tex] about the X-axis is [tex]$\frac{32\pi}{5}$[/tex]

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Answer:

SA = 2π(1.4)^2*2 + 2.8π(4.2) square feet

the second option, but the radius shld be squared in the formula :D

Step-by-step explanation:

If the company uses the double-declining-balance method, the asset will reach its residual value in the 9th year. We can find the solution in the following manner.

Under the double-declining-balance method of depreciation, the depreciation rate is twice the straight-line rate, and the book value is multiplied by the depreciation rate each year. The formula for calculating the depreciation expense is:

Depreciation expense = (2 / Useful life) x Book value at the beginning of the year.

In this case, the construction machinery has a useful life of 8 years and a cost of $100,000 with a residual value of $20,000. Therefore, the depreciable base is $80,000 ($100,000 - $20,000).

To calculate the depreciation expense for the first year, we use the formula:

Depreciation expense = (2 / 8) x $100,000 = $25,000

The book value at the beginning of year 2 is:

Book value = Cost - Accumulated depreciation

Book value = $100,000 - $25,000 = $75,000

To calculate the depreciation expense for year 2, we use the same formula:

Depreciation expense = (2 / 8) x $75,000 = $18,750

We continue to calculate the book value and depreciation expense for each year until the book value reaches the residual value of $20,000.

Year 1:

Book value = $100,000 - $25,000 = $75,000

Year 2:

Book value = $75,000 - $18,750 = $56,250

Year 3:

Book value = $56,250 - $14,063 = $42,187

Year 4:

Book value = $42,187 - $10,547 = $31,640

Year 5:

Book value = $31,640 - $7,910 = $23,730

Year 6:

Book value = $23,730 - $5,932 = $17,798

Year 7:

Book value = $17,798 - $4,450 = $13,348

Year 8:

Book value = $13,348 - $2,337 = $11,011

Year 9:

Book value = $11,011 - $1,674 = $9,337

Therefore, the asset will reach its residual value in Year 9.

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Finally, we can substitute this expression for QS into our equation for the perimeter: Perimeter = [tex][(51 + x) / x] * [(x^3 + 15x^2 - 3375) / (15x)][/tex]

Perimeter is the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches, depending on the context and the units used to measure the sides of the shape. For example, the perimeter of a rectangle can be calculated by adding the length and width of the rectangle, and then multiplying that sum by two, since a rectangle has two pairs of equal sides. Similarly, the perimeter of a circle can be calculated by multiplying the diameter of the circle by pi (π), a mathematical constant that is approximately equal to 3.14.

Let's denote the length of QS as x. Then, by the angle bisector theorem:

[tex]PQ / QS = 36 / x and PS / QS = 15 / x[/tex]

We can solve for PQ and PS in terms of x by cross-multiplying:

[tex]PQ = (36 / x) * QS and PS = (15 / x) * QS[/tex]

To find the perimeter of triangle PQS, we add up the lengths of all three sides:

[tex]Perimeter = PQ + QS + PS[/tex]

[tex]= (36 / x) * QS + QS + (15 / x) * QS[/tex]

[tex]= (36 / x) * QS + QS + (15 / x) * QS[/tex]

[tex]= (51 / x) * QS + QS[/tex]

[tex]= (51 + x) / x * QS[/tex]

Now, we just need to determine the length of QS. To do this, we can use the fact that ∠Q is bisected. Let's call the point where the angle bisector intersects QS "R". Then, we have:

QR / RP = QS / PS (by the angle bisector theorem)

We can plug in the values we know:

[tex]QR / RP = x / 15 (since PS = 15)[/tex]

We also know that QR + RP = QS = x. We can use these two equations to solve for QR and RP:

[tex]QR + RP = x[/tex]

[tex]QR / RP = x / 15[/tex]

[tex]QR = (x^2 / 15) - RP[/tex]

[tex]QR = (x / 15) * (x - 15)[/tex]

[tex]RP = x - QR[/tex]

[tex]RP = (15 / x) * (x - 15)[/tex]

Now, we can plug in these values for QR and RP to find QS:

[tex]QS = QR + RP[/tex]

[tex]= (x / 15) * (x - 15) + (15 / x) * (x - 15)[/tex]

[tex]= [(x^2 - 15x) / 15] + [(15x - 225) / x][/tex]

[tex]= [(x^3 - 210x + 225x - 3375) / (15x)][/tex]

[tex]= [(x^3 + 15x^2 - 3375) / (15x)][/tex]

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The value of both the integrals is 0.

To evaluate each of the integrals, we can use the definition of the Dirac delta function. According to its definition, the Dirac delta function is zero everywhere except at the point t=0, and its integral over the entire domain is equal to 1.

Therefore, for the first integral, we have:

∫-∞∞e3tδ(t-4)dt = e3(4)δ(0-4) = e12δ(-4) = 0

Similarly, for the second integral, we have:

∫-∞∞cos(4t)δ(t-3)dt = cos(4(3))δ(0-3) = cos(12)δ(-3) = 0

Therefore, the value of both the integrals is 0.

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The graph shοws that the ball reaches a maximum height οf 52 units after 8 secοnds.

Prοjectile mοtiοn is the mοtiοn οf an οbject that is thrοwn, launched, οr οtherwise prοjected intο the air and then allοwed tο mοve under the influence οf gravity.

As instructed, we can graph the equatiοn h = -12 + 8t οver the interval 0 ≤ t ≤ 8 οn a cοοrdinate plane. Tο dο this, we can plοt a few pοints by chοοsing values οf t, and then plοtting the cοrrespοnding values οf h that we get frοm the equatiοn.

When t = 0, h = -12 + 8(0) = -12, sο the first pοint οn the graph is (0, -12).

When t = 1, h = -12 + 8(1) = -4, sο the secοnd pοint οn the graph is (1, -4).

When t = 2, h = -12 + 8(2) = 4, sο the third pοint οn the graph is (2, 4).

When t = 3, h = -12 + 8(3) = 12, sο the fοurth pοint οn the graph is (3, 12).

When t = 4, h = -12 + 8(4) = 20, sο the fifth pοint οn the graph is (4, 20).

When t = 5, h = -12 + 8(5) = 28, sο the sixth pοint οn the graph is (5, 28).

When t = 6, h = -12 + 8(6) = 36, sο the seventh pοint οn the graph is (6, 36).

When t = 7, h = -12 + 8(7) = 44, sο the eighth pοint οn the graph is (7, 44).

When t = 8, h = -12 + 8(8) = 52, sο the ninth pοint οn the graph is (8, 52).

We can nοw plοt these pοints οn a cοοrdinate plane and cοnnect them tο fοrm a smοοth curve that represents the path οf the ball.

The hοrizοntal axis represents time (t), and the vertical axis represents the height (h) οf the ball at any given time. The graph shοws that the ball reaches a maximum height οf 52 units after 8 secοnds, and lands back οn the grοund after apprοximately 1.5 secοnds (when h = 0)

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The minimum value of sin x + cos x where x E [-360:360] is √2/2.

We can approach this problem using trigonometric identities and algebra.

First, we will use the fact that:

sin(x + y) = sin x cos y + cos x sin y

We can rewrite sin x + cos x as:

sin x + cos x = √2(sin(x + 45°))

We can see that the maximum value of sin(x + 45°) is 1, so the maximum value of sin x + cos x is √2.

Next, we want to find the minimum value of sin x + cos x. To do this, we will square both sides of the equation:

(sin x + cos x)² = 2(sin²(x + 45°))

sin² x + 2 sin x cos x + cos² x = 2(sin² x + cos² x + 2sin x cos x)

sin²x - 2 sin x cos x + cos² x = 0

(sin x - cos x)² = 0

sin x = cos x

We can see that the minimum value of sin x + cos x occurs when sin x = cos x. At this point, sin x + cos x takes on the value of √2/2.

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Rounding to the nearest tenth, the answer is approximately 4,646.7 ft³, which is option (C).

The base of a cone can be any size, and the point where the sides converge is called the apex. The distance from the apex to the base along the center of the cone is called the height, and the distance from the center of the base to any point on the circumference is called the radius.

There are different types of cones, such as right cones and oblique cones. A right cone is a cone in which the apex is directly above the center of the base, and an oblique cone is a cone in which the apex is not directly above the center of the base.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where V is the volume, π is a constant (approximated as 3.14), r is the radius of the base, and h is the height.

Converting the given measurements from meters to feet, we have:

Height = 68 m = 68 * 3.2808 ft ≈ 223.10 ft

Radius = 48 m = 48 * 3.2808 ft ≈ 157.48 ft

Substituting the values into the formula, we get:

V = (1/3) * 3.14 * 157.48² * 223.10

V ≈ 4,646.7 ft³

Rounding to the nearest tenth, the answer is approximately 4,646.7 ft³, which is option (C).

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By the rational-root theorem, the roots of 12x³-8x²-3x+2=0 are  ±1, ±2, ±3,±4,±5,±6,±7,±8,±9,±10,±11,±12.

The rational root theorem tells you that if an equation has a comprehension (it doesn't need to have a comprehension), then when you write it as a reduction a/b (the reduction means that a and b n 'have no common factors), then a must be divided by the constant term of the polynomial and b must be divided by the principal term.

The constant term here is 1, so that means a must be ±1. The first term is 12; whole numbers divided by 12 are ±1, ±2, ±3, ±4, ±6 and ±12.

Once the root r has been found, we must stop and factor x−r of the polynomial, thus reducing the problem to a small extent.

According to the Question:

The given polynomial is,

f(x) = 12x³-8x²-3x+2

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number,

x = p/q

Where, p is a factor of constant term and

q is the factor of coefficient of leading term.

In the given polynomial the constant is 2 and the leading coefficient is 12.

All possible factor of 2 are ±1 and ±2

All possible factor of 12 are ±1, ±2, ±3,±4,±5,±6,±7,±8,±9,±10,±11,±12.

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Answer: -2x + 3y

Step-by-step explanation:

-(2x-3y) = -1(2x-3y), then if we multiply both of them by -1: -1(2x) -1(-3y) = -2x + 3y

The statements 1. lim f(x) = 3 and lim f(x) = 7 as x approaches 1- and x approaches 1+ respectively indicate a discontinuity at x=1, and the statements 2. (a) lim f(x) = [infinity] and 2. (b) lim f(x) = -[infinity] as x approaches -3 and 4+, respectively, indicate that the function becomes unbounded and approaches infinity or negative infinity.

1. The statement lim f(x) = 3 and lim f(x) = 7 as x approaches 1- and x approaches 1+ respectively means that the function f(x) has different limit values as x approaches 1 from the left and the right side of x=1. This indicates that there is a discontinuity at x=1, which can be a jump, infinite, or oscillatory discontinuity.

In this situation, the limit of f(x) as x approaches 1 may not exist because the limit value from the left and right are different. If the limit exists, it means that the left and right limit values are equal.

2. a) The statement lim f(x) = [infinity] as x approaches -3 means that the function f(x) becomes unbounded and approaches infinity as x approaches -3 from either side. This indicates that the function increases without bound as x approaches -3.

2. b) The statement lim f(x) = -[infinity] as x approaches 4+ means that the function f(x) becomes unbounded and approaches negative infinity as x approaches 4 from the right. This indicates that the function decreases without bound as x approaches 4.


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Therefore, the measure of angle J in rhombus JKLM is (d) (180-2x)°.

A rhombus is a quadrilateral (a four-sided polygon) in which all four sides are of equal length. In other words, a rhombus is a special type of parallelogram with two adjacent sides that are equal in length. Another way to define a rhombus is as a quadrilateral with all four sides congruent and opposite angles equal.

Here,

In a rhombus, all sides have equal length, and opposite angles are equal. Therefore, we can use the fact that the opposite angles in a rhombus are equal to find the measure of angle J. Since angles KJL and KML are opposite angles and have a measure of x degrees, we know that:

angle KJL = angle KML = x

The sum of the angles in triangle JKL is 180 degrees, so we can find the measure of angle J by subtracting the sum of angles KJL and KML from 180 degrees:

angle J = 180 - angle KJL - angle KML

angle J = 180 - x - x

angle J = 180 - 2x

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Answer:

The probability that the second child will have the disease depends on whether the parents have one or two copies of the recessive disease-causing allele. Since both parents are heterozygous carriers, they each have one copy of the disease-causing allele and one normal allele.

When they have a child, each parent randomly passes one allele to their offspring. There are four possible allele combinations that can result in the child inheriting the disease:

The child inherits the disease-causing allele from both parents (homozygous recessive)

The child inherits one disease-causing allele from one parent and one normal allele from the other parent (heterozygous carrier)

The child inherits the normal allele from both parents (homozygous dominant)

The probability of each of these combinations depends on the probabilities of the parents passing on each of their alleles. Since the parents are each heterozygous carriers, there is a 25% chance that they will both pass on the disease-causing allele, a 50% chance that they will each pass on one disease-causing allele, and a 25% chance that they will both pass on the normal allele.

Therefore, the probability that the second child will have the disease is 25%.

The probability that fewer than 135 did not use the top web browser is 0.0885 (rounded to four decimal places).

Given that the top web browser had 51.04% of the market.

Representing the probability of using top web browser P(T) = 0.5104

Probability of not using the top web browser is P(N) = 1 - 0.5104 = 0.4896

The sample size is n = 300 people.

We need to find the probability that fewer than 135 people did not use the top web browser.

Therefore, the required probability is given by;

P(X < 135)

Where X is the number of people who did not use the top web browser.

The number of people who did not use the top web browser follows a binomial distribution with parameters n = 300 and p = 0.4896.

The mean of the distribution is given by;

Mean = np= 300 × 0.4896 = 146.88

The variance of the distribution is given by;

Variance = np(1 - p)= 300 × 0.4896 × 0.5104 = 74.8473

The standard deviation of the distribution is;

Standard deviation = √variance= √74.8473= 8.6485z = (X - μ) / σ

Where μ is the mean and σ is the standard deviation of the distribution

Substitute the mean and standard deviation of the distribution; z = (X - μ) / σ = (135 - 146.88) / 8.6485= -1.3542

Using a standard normal distribution table, find the probability that Z < -1.3542P(Z < -1.3542) = 0.0885

The probability that fewer than 135 did not use the top web browser is 0.0885 (rounded to four decimal places).

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Equivalent ratios for 4 customers entering a store over 6 minutes are (4,6), (2,3), (1,1.5), and (8,12), and can be represented on a Cartesian plane to show the relationship between time and number of customers.

To create a table of equivalent ratios, you can set up a proportion between the number of customers and the time in minutes:

x customers / 6 minutes = y customers / 1 minute

Solving for y,

y = (1 minute * x customers) / 6 minutes

Simplifying,

y = x/6

Using this formula, you can fill out a table of equivalent ratios for the number of customers and time:

To plot the points on a coordinate axis, you can use a Cartesian plane with time on the x-axis and number of customers on the y-axis. For example, the point (6, 4) represents 4 customers entering the store in 6 minutes, while the point (1.5, 1) represents 1 customer entering the store in 1.5 minutes.

The table shows the relationship between the number of customers and the time. As the time increases, more customers enter the store, and the ratio between the number of customers and time remains the same. The plotted points on the coordinate axis represent each scenario where customers entered the store in a given amount of time. The data can be used to make predictions about future customer traffic and plan staffing needs accordingly.

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Answer: i think its 3

Step-by-step explanation:

The investment was worth R9,500 less than Thembeka expected at the end of six months (R2,100 × 4.5).

Amount is a word used to describe a numerical value or quantity. It can refer to a sum of money, a number of items, a measurement, or any other quantity that has a numerical value. Amounts can be expressed as a whole number, a fraction, a percentage, or a combination of these. Amounts may also be expressed in varying units such as grams, liters, or ounces.

At the end of six months, the investment was worth R9,500 less than Thembeka expected. This is because the interest rate dropped from 10.8% to 8.4% after three months and further to 7.2% after another month. This means that the investment earned less interest than Thembeka anticipated.

To calculate the difference, we need to consider the interest earned for each of the three months at each of the interest rates. For the first three months, the investment earned 10.8% per year, compounded monthly. This means that the investment earned an interest of R3,750 (10.8%/12 × R150 000) for the first three months.

For the last three months, the interest rate was 8.4% per year, compounded monthly. This means that the investment earned an interest of R2,700 (8.4%/12 × R150 000) for the last three months.

The difference between the interest earned in the first three months and the last three months is R1,050. To calculate the total difference, we need to multiply this by two, as there were two three month periods in the six month period. This means that the total difference in interest earned is R2,100 (R1,050 × 2).

Therefore, the investment was worth R9,500 less than Thembeka expected at the end of six months (R2,100 × 4.5).

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The value of x + y can be calculated by taking the square root of both equations, which gives x = 10 and y = 4, so the value of x + y is 14.

To calculate the value of x + y, we first need to solve for x and y in the two equations.

The equation x2 = 100 can be rewritten as x2 - 100 = 0, and then solved by taking the square root of both sides. This gives us x = 10.

Next, we can solve for y in the equation y2 = 16. Again, we can rewrite this as y2 - 16 = 0 and take the square root of both sides. This gives us y = 4.

Now that we have the values for x and y, we can calculate the value of x + y. Adding 10 and 4 together gives us 14, so the value of x + y is 14.

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Answer:

VOLUME = 125 cm ³

SURFACE AREA  = 125 cm ²

Step-by-step explanation:

Volume of cube is

V = s³, where s = 5 cm

V = ( 5 cm )³ = 125 cm³

Surface area of the cube is

SA = 6 * s², where s = 5 cm

SA = 6 * ( 5 cm )² = 6 * 25 cm² = 125 cm²

Yes, it is possible for a given angle θ to satisfy both cot θ > 0 and tan θ < 0. This is because cot θ = 1/tan θ, which means that for a given angle θ, when tan θ is negative, cot θ will be positive.

To explain further, let's consider an example. Let θ = 270°. The value of cot θ is cot 270° = -1/tan 270° = -1/(0) = 0. Since 0 > 0, cot θ > 0. On the other hand, the value of tan θ is tan 270° = 0. Since 0 < 0, tan θ < 0. Therefore, it is possible for a given angle θ to satisfy both cot θ > 0 and tan θ < 0.

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