after a bride has interviewed 8 djs to play at her wedding, her fiance tells her she needs to narrow it down to 3 djs. in how many ways can she rank the 3 djs?

Answer:

51t^3

Step-by-step explanation:

64+3=67

67 +(-16)=51

t^2 +t= t^3

now you just add them up but they cant be combined because one is a number and the other a variable w an exponent so we just get 51t^3

Answer:

red,because The probability of choosing red is 5/12 but this probability for purple and blue is 2/12=1/6,and also for green marbles is 3/12=1/4

5/12>3/12>2/12

f(x) = (x + (5 - 3i) / 2)(x + (5 + 3i) / 2) these are complex conjugate pairs, which means that the polynomial has real coefficients.

To find the complex zeros of the polynomial function f(x) = x^2 + 5x + 4, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = 5, and c = 4, so:
x = (-5 ± sqrt(5^2 - 4(1)(4))) / 2(1)
x = (-5 ± sqrt(9)) / 2
x = (-5 ± 3) / 2
So the complex zeros of f(x) are:
x = (-5 + 3i) / 2 and x = (-5 - 3i) / 2
To write f in factored form, we can use the zeros we just found:
f(x) = (x - (-5 + 3i) / 2)(x - (-5 - 3i) / 2)
f(x) = (x + (5 - 3i) / 2)(x + (5 + 3i) / 2)
Note that these are complex conjugate pairs, which means that the polynomial has real coefficients.

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1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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No, statistics and quantitative data are not necessarily more valid and objective than qualitative research.

While quantitative data can provide precise numerical measurements, it may not capture the full complexity of a particular phenomenon or experience. Qualitative research, on the other hand, can offer rich and nuanced insights into human behavior and attitudes. It allows for a deeper understanding of the context and meaning behind the data.

Ultimately, the choice between quantitative and qualitative research depends on the research question and the goals of the study. Both methods have their strengths and limitations, and it is important to consider them carefully when designing a study.

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The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

18 square centimeters

Step-by-step explanation:

To find the area of a rectangle follow the formula, A=lw. Where A is the area, l is the length, and w is the width. So to find the area plug the dimensions into the formula. This would be A=6 x 3, which equals 18. Therefore the answer is 18 centimeters squared.

Answer:

9 cm

Step-by-step explanation:

Area is length x width

3 cm x 3 cm = 9 cm

But if you are doing the problem from the picture it is

A = 6 cm x 3 cm

= 18 cm

Answer:

The answer is y=3x+2

Step-by-step explanation:

y-y=m(x-x¹)

y-5=3(x-1)

y-5=3x-3

+5 +5

y=3x+2

Answer: 16870

Step-by-step explanation:

The money that should be invested to the nearest ten dollars, would be in the account after 13 years is $16,870.

Since the invested amount is $8,400

The rate of interest is 5.4%

In quartely it should be \(= 5.4\% \div 4\) = 1.35%

The time period is \(= 13 \times 4\) = 52

So, here the future value be like

\(= \$8,400 \times (1 + 1.35\%)^{52}\)

= $16,870

Hence, The money that should be invested to the nearest ten dollars, would be in the account after 13 years is $16,870.

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Answer:

1

Step-by-step explanation:

Answer:

y-9=0(x-1)

Step-by-step explanation:

first, find the slope with m=y2-y1/x2-x1

11-9=2

1-1=0

2/0 is undefined so i think you have to use 0

sorry if im wrong

i find it difficult when there is no slope

Answer:

Step-by-step explanation:

In order to see whether or not a point lies on the line, we need to plug in the x-coordinate (instead of x) and plug the y-coordinate instead of y.

In this case, the x-coordinate is:-

\(\mathrm{1}\)

and the y-coordinate is:-

\(\mathrm{-1}\)

Plug in the values:-

\(\mathbf{-10(1)+5(-1)=-8}\)

\(\mathbf{-10-5=-8}\)

\(\mathbf{-15=-8}\)

Huh?!

As you can see, we ended up with a false statement.

Hence, the answer is:-

\(\bigstar{\boxed{\pmb{The~point~(1,-1)~doesn't~lie~on~the~line}}}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

the point (1, -1) doesn’t  lie on the line (-10x + 5y = -8)

Step-by-step explanation:

Generaly , a point A(x₀ , y₀)  lies on the line of equation ax + by = c

If its coordinates verify the equation which means

When we replace x by x₀ and y by y₀ in our equation we get ax₀ + by₀ = c

Then

just replace x by 1 and y by -1 in the equation: -10x + 5y = -8

We get , -10(1) + 5(-1) = -10 - 5 = -15

Since -15 ≠ -8 then (1 , -1) don’t verify the equation

Hence ,  the point (1, -1) doesn’t  lie on the line (-10x + 5y = -8)

Answer:

ss

Step-by-step explanation:

s

Answer:

y=7

Step-by-step explanation:

you would divide each term by 8 to get y=7 (8/8 and 66/8) :) hope this helps!!

The linear distance traveled in one revolution of a wheel can be calculated using the formula:

Circumference = π * Diameter

Given that the diameter of the wheel is 36 inches, we can substitute the value into the formula:

Circumference = π * 36 inches

Using an approximate value of π as 3.14159, we can calculate the circumference:

Circumference ≈ 3.14159 * 36 inches

Circumference ≈ 113.09724 inches

Therefore, the linear distance traveled in one revolution of a 36-inch diameter wheel is approximately 113.09724 inches.

The required result of the sliding filament model given below.

The mechanism by which muscles contract is described by the sliding filament model. Actin and myosin myofilaments move over one another as a result of a cycle of repeated occurrences, constricting the sarcomere and creating tension in the muscle.

The A band is the middle, darkly pigmented area of the sarcomere that runs the entire length of the thick filaments. The portion of the thin filaments that cross over the thick filaments is also included. The I band is formed by the remaining thin filaments within the sarcomere but not by any thick filaments. Each A band has a narrow region in the middle called the H zone, which is made up entirely of dense filaments.

Myosin heads pull the thin filaments in the direction of the M line during muscle contraction. Because of this, the thin filaments glide inward, allowing their ends to overlap and connect at the sarcomere's core. The I band and H zone become smaller as a result.

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Answer:

the answer to the question is -2

Step-by-step explanation:

a certain number=x

therefore,x+9=5-x

x+x=5-9

2x= -4

you the divide both sides by2 to gain x

The cost of the mp3 player after the discount is $27.98.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100.

Given

An mp3 player is on sale for 30% off the regular price of $39. 98.

The price of the mp3 player after the 30% is given

\(\rm Cost \ of \ player \ after \ discount = Cost \ of \ player \times discount\\\\\rm Cost \ of \ player \ after \ discount = 39.98\times 0.30\\\\\rm Cost \ of \ player \ after \ discount = 11.99\)

The cost of mp3 player after 30% discount is;

= $39.98 - $11.99 = $27.98

Hence, the cost of the mp3 player after the discount is $27.98.

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The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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Answer:

The answer is -194.7

Step-by-step explanation:

The mathematical proof is given below. Then the claims are correct.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is a right-angle triangle. And line CD is perpendicular to line AB.

In triangles ΔABC, ΔACD, and ΔCDB, we have

∠ACB = ∠ADC = ∠BDC                     (Right angle)

∠ABC = ∠ACD = ∠CBD                     (Corresponding angles)

Then the triangles ΔABC, ΔACD, and ΔCDB will be similar to each other. And in triangle ΔABC by the Pythagoras theorem is written as,

AB² = AC² + BC²

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Answer:

5:4

Step-by-step explanation:

40:32

20:16

10:8

5:4

Answer:

Step-by-step explanation:

5:4 For  every 5 dogs there are 4 cats

40/8 =5

32/8= 4

Answer:

89

Step-by-step explanation:

Answer:

I think it's x=4

Step-by-step explanation:

i forgot how I got it

Answer: x = -4

Step-by-step explanation: Got it right

Answer:

Step-by-step explanation:

All in the Attachments

Answer:

Look below

Step-by-step explanation:

There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:

Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.

Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.

Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.

Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.

Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.

To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.

To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).

The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:

(f(x + h) - f(x))/h

where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.

Answer:

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

Step-by-step explanation:

Given

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

Required

Spot the error in the viewer's calculation

The viewer represents the correct answers with x and the incorrect ones with y.

This implies that

\(x + y = 20\)

Also, for every correct answers, she gets 2 points;

This can be represented by 2x

and for every incorrect answers, she gets -1 point

This can be represented by -y

This implies that

\(2x - y = 28\)

This is where the viewer made a mistake

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

Solving further

\(2x - y = 28\)

\(x + y = 20\)

Add both equations together

\(2x + x + y - y = 28 + 20\)

\(3x = 48\)

Divide both sides by 3

\(\frac{3x}{3} = \frac{48}{3}\)

\(x = \frac{48}{3}\)

\(x = 16\)

Substitute \(x = 16\) in \(x + y = 20\)

\(16 + y = 20\)

Subtract 16 from both sides

\(16 - 16 + y = 20 - 16\)

\(y = 20 - 16\)

\(y = 4\)

This implies that the contestant answered 16 questions correctly and 4 questions incorrectly

Answer: A

Step-by-step explanation:

(a) Null hypothesis (H₀): The population mean time for under 16's to complete the triathlon is 59.5 minutes.

Alternative hypothesis (H₁): The population mean time for under 16's to complete the triathlon is not equal to 59.5 minutes.

(b) Conducting a one-sample t-test using the data from under16.mwx, we can calculate the estimated standard error, the test statistic, and the p-value or critical values (CV5 and CV1). Based on these results, conclusions can be drawn regarding the hypotheses.

(c) By hand, calculate the 95% confidence interval for the population mean time taken for under 16s to complete the triathlon based on the t-test. Show working.

(d) A 90% confidence interval for the population mean time taken for under 16s to complete the triathlon would be narrower than the 95% confidence interval calculated in part (c).

(a) The null hypothesis (H₀) states that the population mean time for under 16's to complete the triathlon is 59.5 minutes. The alternative hypothesis (H₁) states that the population mean time for under 16's to complete the triathlon is not equal to 59.5 minutes. In symbols:

H₀: μ = 59.5 (where μ represents the population mean time)

H₁: μ ≠ 59.5

(b) To test the hypotheses, a one-sample t-test is conducted using the data from the under16.mwx file. The estimated standard error measures the variability of the sample mean around the hypothesized population mean. The test statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the estimated standard error. The p-value or critical values (CV5 and CV1) are used to determine the significance of the test. Based on the calculated test statistic and p-value or critical values, conclusions can be drawn about the hypotheses.

(c) To calculate the 95% confidence interval for the population mean time taken for under 16s to complete the triathlon, the t-test is used. The formula for the confidence interval is:

Confidence interval = sample mean ± (t-value * standard error)

The t-value is obtained from the t-distribution table or calculated using software, and it corresponds to the desired confidence level and degrees of freedom. The standard error is the estimated standard error from the t-test. By substituting these values into the formula, the lower and upper bounds of the confidence interval can be determined.

(d) A 90% confidence interval for the population mean time taken for under 16s to complete the triathlon would be narrower than the 95% confidence interval calculated in part (c). This is because a higher confidence level requires a wider interval to capture a higher percentage of the population. In contrast, a lower confidence level allows for a narrower interval as it needs to capture a smaller percentage of the population.

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