find the value of a and b. ​

Answer:

41.4 in

Step-by-step explanation:

(sin 80) opposite      =    x

          hypotenuse        42

x = 42 * sin (80)  = 41.4 in

To interpolate a cubic spline between the points (0, 1), (2, 2), and (4, 0), we can use the concept of spline interpolation. A cubic spline is a piecewise-defined function consisting of cubic polynomials, which smoothly connects the given points.

In order to construct a cubic spline, we need to determine the coefficients of the cubic polynomials for each interval between the given points. The spline should satisfy three conditions: it must pass through each of the given points, it should have continuous first and second derivatives at the interior points, and it should have zero second derivatives at the endpoints to ensure a smooth connection.

We start by dividing the interval into three subintervals: [0, 2], [2, 4]. For each subinterval, we construct a cubic polynomial that satisfies the interpolation conditions. By imposing the continuity and smoothness conditions at the interior point (2, 2), we can obtain a system of equations. Solving this system gives us the coefficients of the cubic polynomials.

Once we have the coefficients, we can express the cubic spline as a piecewise function. The resulting cubic spline will smoothly connect the given points (0, 1), (2, 2), and (4, 0) and provide an interpolation function between them. This interpolation technique ensures a smooth and continuous curve, which can be useful for approximating values between the given data points.

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Answer:

90 toys

Step-by-step explanation:

We should use the same unit for time.  Rewrite 20 minutes as 1/3 hour.

The unit rate is then:

    3 toys         9 toys

----------------- = -----------

 1/3 hour          hour

Multiply this unit rate by 10 hours, obtaining 90 toys

The time spent by Noah exercising is 130 minutes

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

using the above as a guide, we have the following:

Vera = 60% * Noah

So, we have

60% * Noah = 78

Divide both sides by 60%

Noah = 130

Hence, Noah exercised for 130 minutes

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Answer:

12

Step-by-step explanation:

If you cut them into halves then there will be twice as many pieces.

so you do:

6 x 2

= 12

Answer: nice

Step-by-step explanation:

Sounds like a Scam though ngl

Answer:

−1+1.732051i

Step-by-step explanation:

Answer:

$20.60

Step-by-step explanation:

You find how much it costs for the total amount of basketballs (10.40×20=208), then you subtract that number from the total cost of everything to get the cost of all the uniforms (620-208=412), then you divide the total costs for all uniforms by 20 to find the cost for a single uniform (412÷20=20.6). Always make sure that the decimals go until the hundredths place for USD.

Hope this helps!

The chi-square goodness-of-fit test requires that all anticipated counts be at least five and observations be drawn from random sample in order to be valid. The correct statements are I and III only. Correct option is C.

I. The chi-square goodness-of-fit test requires that all anticipated counts be at least five and that observations be drawn from a random sample in order to be valid. This statement is correct. The chi-square goodness-of-fit test is based on the chi-square distribution, which approximates the sampling distribution of the test statistic.

To ensure the validity of the test, it is generally recommended that all expected counts in the cells of the contingency table have a minimum expected count of five. This guideline helps to ensure that the chi-square test statistic follows the chi-square distribution, which is approximately valid under this condition.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom. This statement is incorrect. The number of categories being assessed determines the degrees of freedom for the chi-square goodness-of-fit test. It is equal to the total categories less one. So, if there are n categories, the degrees of freedom for the test would be n - 1, not 1 - n.

III. A condition for using the chi-square goodness-of-fit test is that the observations are based on a random sample. This statement is correct. The chi-square goodness-of-fit test assumes that the observations are obtained from a random sample or represent a random selection from a population.

This assumption is important to ensure that the test results are generalizable to the population from which the sample is drawn. If the observations are not based on a random sample, the test results may not be valid or may be biased. Therefore, random sampling is a condition for using the chi-square goodness-of-fit test.

The correct statements are I and III only. Correct option is C.

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Complete question is:

Which of the statements are correct?

I. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom.

III. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.

a) I only

b) II only

c) I and III only

d) II and III only

e) I, II, and III

Answer:

1.25/4 = 5/16

1.75/5 = 7/20

Determine which one of these fractions is bigger.

Both milkshakes have the same thickness.

Given that,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milkshake is thicker is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
According to the question,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.
Ratio of the milk = 1.25 / 4 = 0.35
A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.
Ratio of the milke = 1.75 / 5 = 0.35
comparing the ratio both are equal,

Thus, Both milkshakes have the same thickness.

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Answer: -1/9 * x.

Step-by-step explanation:

To simplify the expression (5x^2) / (-45x), we can divide the coefficients and subtract the exponents:

(5 / -45) * (x^2 / x)

Simplifying the coefficient:

-1/9 * (x^2 / x)

Now, simplify the variables:

-1/9 * x^(2-1) = -1/9 * x

Therefore, the simplified expression is -1/9 * x.

Using normal approximation, the probability that exactly 29 out of 108 eligible voters voted is approximately 0.2346, or 23.46%.

To find the probability that exactly 29 out of 108 eligible voters voted, we can use a normal approximation.

First, we need to calculate the mean (μ) and standard deviation (σ) for the binomial distribution, which can be approximated using the formula:

μ = n * p

σ = √(n * p * (1 - p))

where n is the number of trials (108 in this case) and p is the probability of success (22% or 0.22).

μ = 108 * 0.22 = 23.76

σ = √(108 * 0.22 * (1 - 0.22)) = 4.3

Next, we use the normal distribution to approximate the probability of exactly 29 voters. We will use the continuity correction by considering the interval between 28.5 and 29.5.

P(28.5 < X < 29.5) ≈ P(28.5 - 0.5 < X < 29.5 + 0.5) ≈ P(28 < X < 30)

To find this probability, we calculate the z-scores for 28 and 30 using the mean and standard deviation:

z₁ = (28 - μ) / σ

z₂ = (30 - μ) / σ

Then, we use a standard normal distribution table or calculator to find the probability associated with each z-score:

P(28 < X < 30) ≈ P(z₁ < Z < z₂)

Let's calculate the z-scores and find the corresponding probabilities:

z₁ = (28 - 23.76) / 4.61 ≈ 0.92

z₂ = (30 - 23.76) / 4.61 ≈ 1.35

Using the standard normal distribution table or calculator, we find the probabilities associated with these z-scores:

P(0.92 < Z < 1.35) ≈ 0.4082 - 0.1736 = 0.2346

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Answer:

x = 2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + x² = (2[tex]\sqrt{2}[/tex] )² , that is

2x² = 8 ( divide both sides by 2 )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

Answer:

Reminder to eat drink and take care. :)

Step-by-step explanation:

Answer:

8,255 reminder to eat today

Answer:

(a) 25

(b) 9.27

Step-by-step explanation:

Step 1

We have to rearrange the given days set from least to highest

35, 40, 45, 55, 60

(a) the range

Range = The highest number - The least number

= 60 - 35

= 25

(b) the standard deviation of the data set

35, 40, 45, 55, 60.

We find the Mean

Mean = Sum of values/Number of values

= 35+40+45+55+60/5

= 235/5

= 47

We can find the standard deviation now.

The formula =

√(x - Mean)²/n

= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5

= √144 + 49 + 4 + 64 +169/5

= √430/5

= √86

= 9.273618495

Approximately = 9.27

Answer:

m = 18/4 = 9/2 = 4.5

Step-by-step explanation:

Notice that the line passes through (0, 0) and (4, 18).  Thus, its 'rise' is 18 - 0, or 18, and its 'run' is 4 - 0, or 4, and the slope (which is the desired constant of proportionality) is m = 18/4 = 9/2 = 4.5             This is Answer B

Answer:

hi

Step-by-step explanation:

sorry

Answer:

0

Step-by-step explanation:

The sine function of 0 is 0.

We got 0 because you multiplied -9 by 0 divided by -3. DIviding by 0 really doesn't have an answer, but it'd most logically be 0.

Answer:

r = 7

Step-by-step explanation:

Volume of a cylinder:

V = πr²h

Given:

V = 2000

h = 13

Work:

V = πr²h

r² = V/(πh)

r² = 2000/(3.14 * 13)

r² = 2000/40.82

r² ≈ 49

[tex]\sqrt{r^2} =\sqrt{49}[/tex]

r = 7

Answer:

11 11/12 lb

Step-by-step explanation:

"3 2/3 times more than the small bag" comes out to:

(3 2/3)*(3 1/4) lb.

Convert both mixed numbers to improper fractions:

11     13       143

--- * ---- = ----------- = 11.917

3      4         12

The large bag weighs 11.917 lb, which may be converted to the mixed number 11 11/12 lb

Answer:

10cm

Step-by-step explanation:

pretty sure the diameter is measured by multiplying the radius twice :)

Answer:

Diameter = 10 cm

Circumference = 31.43 cm

Area = 78.57 cm²

Answer:hi there!that same guy did that w my question too :( i’m reporting his answers. i will help u out tho ahah. the answer is 470(32-n). i hope this helps :). have a good dayyy

Step-by-step explanation:

Answer:

arc BC = 132°

Step-by-step explanation:

The central angle is equal to the arc that subtends it , then

arc BC = ∠ BOC = 132°

Answer:

your answer should be 48 degrees

Answer: $1,800

Step-by-step explanation:

600x3=1,800

Answer:

1800 is the cost.

Step-by-step explanation:

Each hoop costs 600 dollars and their are 3 hoops so multiply 600 times 3 or you can do 6 times 3 and add the zeros at the end which is 1800 dollars and btw you got this!!! don't give up. I believe in you :)

Answer:Using the slope-intercept form, the y-intercept is 1

Answer:

A v=2.25   H=1

b. 5.625

Step-by-step explanation:

Answer:

V = 3.90625 cm³

Step-by-step explanation:

Given that V varies directly as h³ then the equation relating them is

V = kh³ ← k is the constant of variation

To find k use the condition

V = 6.75 when h = 3 , then

6.75 = k × 3³ = 27k ( divide both sides by 27 )

0.25 = k

V = 0.25h³ ← equation of variation

(b)

When h = 2.5 , then

V = 0.25 × 2.5³ = 3.90625 cm³

The probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.1587. The z-score corresponding to 60 minutes is 2. The probability of completing the job in more than 60 minutes is 15.87%.

To find the probability that the worker will finish assembling the racing car in more than 60 minutes, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the given time (60 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).

z = (60 - 50) / 5

z = 2

Next, we look up the probability corresponding to a z-score of 2 in Table A (standard normal distribution table). The value in the table represents the probability of a random variable being less than the given z-score. To find the probability of the worker finishing in more than 60 minutes, we subtract this value from 1.

From Table A, the probability corresponding to a z-score of 2 is approximately 0.9772.

Probability = 1 - 0.9772

Probability ≈ 0.0228

Therefore, the probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.0228 or 2.28% (rounded to two decimal places).

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Answer:

[tex]62^{o}[/tex]

Step-by-step explanation:

All the angles in a triangle add up to [tex]180^{o}[/tex]

Every right angle triangle has a right angle in it which is [tex]90^{o}[/tex]

So to find the remaining angle, you do [tex]180^{o}[/tex] - [tex]90^{o}[/tex] - [tex]28^{o}[/tex] = [tex]62^{o}[/tex]