I wish to accumulate $100 000 over 20 years at 10% p.a. compounded annually. What should be the amount of my annual payments?

The missing length KL in ΔLKJ is x = 22.

Similar triangles are two triangles that have the same shape but may have different sizes.

Corresponding angles are equal and corresponding sides are proportional to each other. 

Since the triangles are similar, the corresponding sides are in proportion.

We can set up the proportion:

LJ/RP = KJ/QP

Substituting the given values, we get:

28/42 = x/33

Cross-multiplying and simplifying, we get:

42x = 28 × 33

42x = 924

x = 924/42

x = 22

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The evaluated expression  [tex]\frac{4^{x} }{2^{x} }[/tex] for x = 3 is 4.

An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication and division.

Therefore, to evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Hence, let's evaluate the expression as follows:

[tex]\frac{4^{x} }{2^{x} }[/tex] for x = 3

Therefore,

[tex]\frac{4^{3} }{2^{3} } = \frac{64}{16}[/tex]

Therefore,

64 / 16 = 4

Hence, the evaluated expression is 16.

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The missing side of a right triangle, from the figure, is 33.1 meters long.

A right triangle has three sides, what are they?

An "opposite" side in a right triangle is the one that is across from a specific angle, while an "adjacent" side is the one that is next to a specific angle. The hypotenuse seems to be the longest side in a right triangle. The sides in right triangles are described with particular terminology.

We can apply the tangent function in order to calculate the length of the missing side if we assume that it is opposite the 43-degree angle that is provided:

tan(43°) = x/34

When we multiply all sides with 34, we get:

x = 34 tan(43°)

Using just a calculator, we determine:

x ≈ 33.1

Rounded to the nearest tenth, we obtain:

x ≈ 33.1

Hence, the missing side of the given triangle is x = 33.1.

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The complete question is in the attached figure.

Answer:

The numbers are 0 and 1

MARK ME AS BRAINLIEST

The probability of completion is the same for Drug A and Drug B, The test statistic is 3.1234, with 1 degree of freedom, and the p-value is 0.0762. The 90% confidence interval for the estimated odds ratio is 2.4444, and the interval is (0.5957, 14.1111). Based on the study design, the most appropriate sampling model for describing the data in this problem is the multiple hypergeometric model,

To test the hypothesis that the probability of completion is the same for Drug A and Drug B, we can use a two-sample test of proportions. We can use a normal approximation to the binomial distribution to calculate the test statistic and p-value. Specifically, we can use the following R code:

# Set up the data

n1 <- 20

n2 <- 19

x1 <- 19

x2 <- 12

# Calculate the test statistic and p-value

p1 <- x1/n1

p2 <- x2/n2

pooled_p <- (x1 + x2) / (n1 + n2)

se <- sqrt(pooled_p * (1 - pooled_p) * (1/n1 + 1/n2))

z <- (p1 - p2) / se

p_value <- 2 * pnorm(abs(z), lower.tail = FALSE)

# Print the results

cat("Test statistic:", round(z, 2), "\n")

cat("p-value:", p_value, "\n")

# Draw a conclusion

if (p_value < 0.05) {

 cat("There is significant evidence to suggest that the completion rates differ between Drug A and Drug B.")

} else {

 cat("There is not enough evidence to suggest that the completion rates differ between Drug A and Drug B.")

}

The sampling model appropriate for this test is the multinomial model.

To compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B, we can use the following R code:

# Calculate the odds ratio and its standard error

odds1 <- (n1 - x1) / x1

odds2 <- (n2 - x2) / x2

odds_ratio <- odds1 / odds2

log_odds_ratio <- log(odds_ratio)

se_log_odds_ratio <- sqrt(1/x1 + 1/(n1 - x1) + 1/x2 + 1/(n2 - x2))

# Calculate the confidence interval

alpha <- 0.1

z_alpha <- qnorm(1 - alpha/2)

lower <- exp(log_odds_ratio - z_alpha * se_log_odds_ratio)

upper <- exp(log_odds_ratio + z_alpha * se_log_odds_ratio)

# Print the results

cat("Odds ratio:", round(odds_ratio, 2), "\n")

cat("90% confidence interval:", round(lower, 2), "-", round(upper, 2), "\n")

# Interpret the results

cat("We are 90% confident that the true odds ratio of not completing the study for Drug A versus Drug B lies between", round(lower, 2), "and", round(upper, 2), ".\n")

In this case, we can use an asymptotic interval since both sample sizes are greater than 10 and the sample proportions are not too close to 0 or 1.

The sampling model appropriate for this analysis is the multiple hypergeometric model.

Based on the study design, the appropriate sampling model for describing the data in this problem is the repeated measures model. Inferences in parts (I) and (II) are based on the multinomial model and the multiple hypergeometric model, respectively, since they are appropriate for comparing proportions and odds ratios between two groups with binary outcomes.

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--The given question is incomplete, the complete question is given

"A clinical trial to compare the effectiveness of two treatments for schizophrenia was conducted involving 39 patients, twenty of whom were randomly assigned to receive Drug A, with the other 19 receiving Drug B. The design of the study called for each patient’s severity of symptoms to be assessed at baseline (before randomization and the onset of treatment) and at 4 follow-up occasions. Although all 39 patients were assessed at baseline, some patients did not return for one or more of the scheduled follow-up measurements, and investigators were concerned that attrition rates (the proportion of subjects dropping out of the study) may not be the same in each treatment and that failure to account for such differences in the analysis could bias the results of such an analysis. Among the 20 patients assigned to Drug A, complete data (observations at all follow-up occasions) were obtained on 19 subjects. Among the 19 subjects assigned to Drug B, complete data were obtained on 12 subjects. Use R coding to help answer the questions.

I. Test the hypothesis that the probability of completion is the same for Drug A and Drug B using the most appropriate method for this task. Be sure to identify clearly what method you use and draw an appropriate conclusion in the context of the problem.

II. Compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B. Use an exact p-value based interval, an exact mid-p-value based interval, or an asymptotic interval, whichever you think is most appropriate, and justify your choice. Be sure to interpret the estimated odds ratio and the interval you obtain for it in the context of the problem.

III. Based on the study design, what sampling model is most appropriate for describing the data in this problem: the Poisson, multinomial, product multinomial, or multiple hypergeometric model? What sampling model are your inferences in parts (I) and (II) based on?"--

The equation to represent the number of cookies sold and profit earned is p=0.25c

In mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.

From the given graph;

The graph represents the straight line passing through origin.

Let Number of cookies sold=c

and profit earned be p.

The linear equation is p=mc+b

Taking the value;

c=2

p=0.5

0.5=2m+b....... Equation1

Taking another value,

c=4

p=1

1=4m+b....... Equation2

Subtracting Equation 1 from 2, we get

0.5=2m

m=.25

Putting the value of m=0.25 in the equation1, we get

.5=.25×2+b

b=0

Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.

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The exact value of the volume of the sphere is V = 1.333π cm³ and the exact value is V = 3.14 cm³

A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.

The formula for the volume of a sphere is:

V = ⁴/₃πr³

where:

V = volume

r = radius

The radius of a sphere is half its diameter.

We are given diameter = 2 cm

Thus: r = 2/2 = 1 cm

V = ⁴/₃π * 1³

V = 1.333π cm³

V = 3.14 cm³

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Answer: 90ft

Step-by-step explanation:

To solve, you have to use similar triangles. the ratios of the lengths of the sides of the triangles are the same (because the sun makes the same angle with the objects.

[tex]\frac{6.2ft}{2.5ft}[/tex] = [tex]\frac{height of tree}{36.2ft}[/tex]

(2.48)(36.2ft) = 89.776ft

=90ft

Answer:

Step-by-step explanation:

The expression (6)(2)^(n-1) means to multiply 6 by 2 raised to the power of n-1. For example, when n = 3, we have:

(6)(2)^(n-1) = (6)(2)^(3-1)

= (6)(2)^2

= (6)(4)

= 24

On the other hand, the expression 12^(n-1) means to raise 12 to the power of n-1. For example, when n = 3, we have:

12^(n-1) = 12^(3-1)

= 12^2

= 144

Step-by-step explanation:

Area of a trapezoid =

     height  ( 9 m)   times the average of the bases (10+14)/2 m

          9 x (10+14)/2 = 108 m^2

Answer:

p=18

Step-by-step explanation:

if 4(p-7) = 44,

Then you can use distributive property to solve

4p-28=44

add 28 to both sides. So,

4p=72

Divide 4 from both sides.

p= 18.

Answer:

L is parallel to n.

Step-by-step explanation:

Prove: angle 4 ≅ angle 6

1. L is parallel to n 1. Given

2. angle 2 ≅ angle 6 a. ???

3. angle 4 ≅ angle 2 b. ???

4. angle 6 ≅ angle 4 c. ???

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer: 804.25 yards3

Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3

The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is a null hypothesis?

The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.

It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.

A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.

Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.

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Answer:

To use the line of best-fit equation to estimate the cost of a collection with 1,500 cards, we can substitute 1.5 (since x represents thousands of cards) for x in the equation and solve for y:

y = 39.94x + 3.84

y = 39.94(1.5) + 3.84

y = 59.91

Therefore, based on the store owner's line of best-fit equation, she should expect to pay approximately $59.91 for a collection that has 1,500 cards.

The answer is: $59.91

Step-by-step explanation:

Answer:

[tex]x1 = \frac{ - 9 - \sqrt{33} }{4} [/tex]

[tex]x2 = \frac{ - 9 + \sqrt{33} }{4} [/tex]

Step-by-step explanation:

[tex]2 {x}^{2} + 9x + 6 = 0[/tex]

a = 2, b = 9, c = 6

[tex]d = {b}^{2} - 4 \times a \times c = {9}^{2} - 4 \times 2 \times 6 = 81 - 48 = 33 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 9 - \sqrt{33} }{4} [/tex]

[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 9 + \sqrt{33} }{4} [/tex]

The coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

An object's location, size, or shape can be altered via transformations in geometry. Translations, rotations, reflections, and dilations are only a few examples of transformations. A separate method of altering an object's location, size, or shape corresponds to each sort of transformation. For instance, a translation is the straight-line movement of an item without altering its size or shape, but a reflection is the flipping of an object over a symmetry line.

The coordinates of the triangle are S(-4, 4), R(-4, 1) and T (-2, 1).

For the given transformations the new coordinates are:

S(-4, 4) translates to (-4-1, 4-5) = (-5, -1) and reflects to (5, -1)

R(-4, 1) translates to (-4-1, 1-5) = (-5, -4) and reflects to (5, -4)

T(-2, 1) translates to (-2-1, 1-5) = (-3, -4) and reflects to (3, -4)

Hence, the coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

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Answer:

no the 85 will not be accurate percentage for math test because you don't have any previous math test scores to even get a average grade.

Leslie used 2.5 pints of blue paint to paint her bedroom walls.

Using the given information, we can calculate the number of pints of blue paint Leslie used to paint her bedroom walls by setting up a proportion. Let x = the number of pints of blue paint.

2.5/8.6 = x/8.6

Cross-multiply and solve for x.

2.5*8.6 = 8.6x

21.5 = 8.6x

Divide both sides by 8.6.

21.5/8.6 = 8.6x/8.6

2.5 = x

Therefore, Leslie used 2.5 pints of blue paint to paint her bedroom walls.

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Answer:

Step-by-step explanation:

[tex]x^3x^3x^3=x^{3+3+3}=x^9\\\\x^{3\times3\times3}=x^{27}[/tex]

These are not equivalent.

The probability that less than 10 of the entry forms will include an order is 0.0193, rounded to four decimal places.

The company has received 14 entries in the sweepstakes, and they know that the probability of receiving a magazine subscription order with an entry form is 0.5. Now, we want to find the probability that less than 10 of the entry forms will include an order.

To find the probability that less than 10 of the entry forms will include an order, we need to add up the probabilities of getting 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 orders. We can use the binomial probability formula to calculate these probabilities:

P(X = x) = (n choose x) x pˣ x (1 - p)ⁿ⁻ˣ

where P(X = x) is the probability of getting x successes, n is the number of trials, p is the probability of success, and (n choose x) is the number of ways to choose x successes from n trials.

We can also use a calculator or spreadsheet to do the calculations.

P(X = 10) = (14 choose 10) x p¹⁰ * (1 - p)¹⁴⁻¹⁰ = 0.0193

After adding up the probabilities for 0 to 9 orders, we get a probability of approximately 0.0193.

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the equation Y = 1(1-x)² - 5 represents a downward-facing parabola with vertex at (1,-5), which opens upwards, and the value of Y increases as x moves away from 1 in either direction.

What is equation?

An equation is a mathematical statement that contains an equality sign (=) between two expressions. It indicates that the expressions on either side of the equality sign are equal in value. Equations can have variables, constants, coefficients, and operators like addition, subtraction, multiplication, and division. The variables represent unknown values, and the goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.

For example, the equation 2x + 5 = 11 is an algebraic equation, where "x" is the variable, "2" and "5" are constants, and "+" and "=" are operators. The solution to this equation is x = 3, since when we substitute x = 3 into the left-hand side of the equation, we get 2(3) + 5 = 11, which satisfies the equality.

The equation given is Y = 1(1-x)² - 5.

This equation represents a parabola in vertex form, where the vertex is at (1,-5). The coefficient of the squared term is positive, which means that the parabola opens upwards.

When x = 1, the value of Y is -5, which is the minimum value of the parabola. As x moves away from 1 in either direction, the value of the expression (1-x)² increases, causing the value of Y to increase as well.

Therefore, the graph of this equation is a downward facing parabola with the vertex at (1,-5), and it opens upward. As x moves away from 1, the value of Y increases.

In summary, the equation Y = 1(1-x)² - 5 represents a downward-facing parabola with vertex at (1,-5), which opens upwards, and the value of Y increases as x moves away from 1 in either direction.

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Answer:

6√5/5

Step-by-step explanation:

6/√5 x √5/√5 is equal to 6√5/5

so thats what the answer should be but i don't know if its different for you

Answer:

1:1:1

Step-by-step explanation:

The ratio of orange to black to green cars is 1:1:1.

The product of two number is 17,20,740, When one number is 1785 and other number is 39,460.

To find the other number, we can divide the product of the two numbers by the known number:

Other number = 17,20,740 ÷ 1785

We can simplify this calculation by factoring out common factors from both numbers. First, we can factor 1785 into its prime factors:

1785 = 3 x 3 x 5 x 7 x 2

Next, we can factor 17,20,740:

17,20,740 = 2^2 x 5 x 7 x 11 x 13 x 17 x 19

We can then cancel out any common factors in the numerator and denominator. In this case, we can cancel out one factor of 5, one factor of 7, and two factors of 2:

Other number = (2 x 11 x 13 x 17 x 19) ÷ (3 x 3 x 5 x 7 x 2)

Simplifying this expression further, we get:

Other number = (2 x 11 x 13 x 17 x 19) ÷ (3^2 x 5 x 7)

Other number = 39460

Therefore, the other number is 39,460.

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The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees

Draw a diagram of the circle and label the given points and segments.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.

Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.

This implies that triangle ABD is an isosceles triangle.

Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.

We also know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle ABD is equal to (180 - 2x) degrees.

Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.

Therefore, angle BOC is equal to 2 * angle BAC.

Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.

Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.

Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.

Therefore, angle BDC is equal to angle BAC.

Substituting this value into the equation from step 6, we get (180 - 2x) degrees

= (2 * angle BDC) + angle BAC

= 2 * angle BAC + angle BAC

= 3 * angle BAC.

Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.

2 * angle BAC = 2 * (180 - 2x) / 3 degrees.

Use the chord length formula: Using the chord length formula, we can find that BC

= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.

Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]

= 2 * r * sin[(180 - 2x) / 3] .

Solve for x:

We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.

Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.

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The author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

The number of steps a runner takes in a specific length of time is referred to as stride rate and is commonly expressed in steps per second. You can figure it out by dividing the total number of steps you took during a certain amount of time by how long that time period lasted. Stride rate, which is frequently used as a gauge of running effectiveness, is impacted by a variety of variables, including running speed, terrain, and personal running form.

Hence, in the given section, the author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

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