A bag contains white, blue and red ping-pong balls in the ratio 8 : 3 : 2. There are 10 balls. If 10 white and 10 blue balls are removed from the bag, the new ratio is ?

Answer:

i think the answer is c but im not sure sorry if im wrong

Step-by-step explanation:

The approximation of the integral ∫cos(x³ + 10) dx using composite Simpson's rule with n = 3 is 0.126. When approximating the integral using Romberg integration, R₃,₃ gives an approximation of order h⁶.

To calculate the approximation using composite Simpson's rule, we divide the interval of integration into subintervals and apply Simpson's rule to each subinterval. The formula for Simpson's rule is:

S = h/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(xₙ))

where h is the step size and n is the number of subintervals. In this case, we have n = 3, so we divide the interval into three equal subintervals, and the step size is h = (b - a) / n = (π - 0) / 3 = π/3.

Evaluating the function cos(x³ + 10) at the points x₀ = 0, x₁ = π/3, x₂ = 2π/3, and x₃ = π, we get:

f(x₀) = cos((0)³ + 10) = cos(10) ≈ -0.8391

f(x₁) = cos((π/3)³ + 10) = cos(π³/27 + 10) ≈ -0.4586

f(x₂) = cos((2π/3)³ + 10) = cos(8π³/27 + 10) ≈ -0.8391

f(x₃) = cos((π)³ + 10) = cos(π³ + 10) ≈ -0.3473

Using the Simpson's rule formula, we can now calculate the approximation:

S ≈ π/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃))

 ≈ π/3 * (-0.8391 + 4(-0.4586) + 2(-0.8391) + 4(-0.3473))

 ≈ 0.126

To calculate the order of approximation using Romberg integration, we use the formula:

Rₙ,ₖ = Rₙ₋₁,ₖ₋₁ + (Rₙ₋₁,ₖ₋₁ - Rₙ,ₖ₋₁) / (4ₖ - 1)

where Rₙ,ₖ represents the Romberg approximation at level n and column k. The order of approximation is determined by the highest power of h in the error term. In this case, we have R₃,₃, so the order is h⁶.

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The null and alternative hypotheses for testing the claim that the proportion of people who own cats is significantly different from 90% at the 0.02 significance level are:

H0: p = 0.9 (proportion of cat owners is 90%)

H1: p ≠ 0.9 (proportion of cat owners is not equal to 90%)

Based on a sample of 500 people, where 82% owned cats, we can conduct a hypothesis test to determine the p-value at the 0.02 significance level. The p-value is the probability of obtaining a sample proportion as extreme as the observed proportion (82%) assuming the null hypothesis is true.

The p-value for this test is the probability of observing a sample proportion as different from 90% as 82%. Since the p-value is not provided in the question, it needs to be calculated based on the sample data and the assumed null distribution.

If the p-value is less than 0.02, we would reject the null hypothesis and conclude that the proportion of cat owners is significantly different from 90%. However, if the p-value is greater than or equal to 0.02, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the proportion of cat owners from 90%.

Without the calculated p-value, we cannot make a definitive conclusion about rejecting or failing to reject the null hypothesis.


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The 90% confidence interval estimate for the overall difference in the percentages of Democrats and Republicans who prioritize protecting the environment is between X% and Y%.

To estimate the overall difference in the percentages of Democrats and Republicans who consider protecting the environment a top priority, we can use the concept of confidence intervals.

Confidence intervals provide a range of values within which we can be reasonably confident that the true population parameter lies. In this case, we want to estimate the difference in the proportions of Democrats and Republicans who prioritize protecting the environment.

The provided information states that in a random sample of 950 Democrats, 817 consider protecting the environment a top priority, while in a random sample of 800 Republicans, 384 share the same view. To construct a 90% confidence interval, we need to calculate the margin of error, which is determined by the sample sizes and proportions.

Using the formulas for the margin of error, we find that the margin of error is 3. With this information, we can state that we are 90% confident that the difference between the percentage of Democrats and Republicans who prioritize protecting the environment lies between X% and Y%.

The confidence interval estimate gives us a range within which we can reasonably expect the true difference to fall. However, it does not provide an exact value for the difference. The range allows for some uncertainty due to the sampling variability inherent in survey data.

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Answer:

y = 2/3x - 6

Step-by-step explanation:

Use the slope intercept equation, y = mx + b

Plug in the slope and given point, then solve for b

y = mx + b

-4 = 2/3(3) + b

-4 = 2 + b

-6 = b

Plug in the slope and b into the equation

y = 2/3x - 6

So, the equation of the line is y = 2/3x - 6

Answer:

A

Step-by-step explanation:

4x+2 = 10

=> 2x+2 = 10-2x

Answer:

29 units

Step-by-step explanation:

12 + 12 + 5

29

The confidence interval for the mean at 95% confidence level with the variance known and unknown are (101.17, 102.47), (101.06, 102.58) respectively

A.)

Confidence interval is related by the formula:

Where :

μ = population mean

t = critical value for the confidence level

s = sample standard deviation

n = sample size

The critical value for a 95% confidence level is 1.96.

C.I = 101.82 ± 1.96 * 0.81 * √(1/6)

C.I = 101.82 ± 0.648

C.I = (101.172, 102.468)

Hence, the confidence interval is (101.17, 102.47)

B.)

Assuming variance is Unknown

We use the t-distribition; The critical value at 95% confidence and (6-1) degree of freedom = 2.306

CI = μ ± t * s * √(1/n)

C.I = 101.82 ± 2.306 * 0.81 * √(1/6)

C.I = 101.82 ± 0.763

C.I = 101.057, 102.583

Hence, the confidence interval is (101.06, 102.58)

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Answer:

The approximate age of the bone is approximately 11552 years.

Step-by-step explanation:

The current proportion of carbon-14 with respect to its original amount is defined by following formula:

[tex]\frac{y}{a} = e^{-0.00012\cdot t}[/tex] (1)

Where:

[tex]y[/tex] - Current amount of carbon-14, no unit.

[tex]a[/tex] - Initial amount of carbon-14, no unit.

[tex]t[/tex] - Time, in years.

If we know that [tex]\frac{y}{a} = 0.25[/tex], then the approximate age of the bone is:

[tex]t = -8333.333\cdot \ln \frac{y}{a}[/tex]

[tex]t\approx 11552.453\,yr[/tex]

The approximate age of the bone is approximately 11552 years.

Answer:

3= (87÷h)

Step-by-step explanation:

The question is to pick among the option the solutions that will be equal to 3= (87÷h)

Therefore the most suitable and correct option is

3×9= (87÷h)÷9

27= (87÷h)÷9

Divide by 9

3= (87÷h)

Hence the answer is 3=(87÷h)

Answer:

25

Step-by-step explanation:

A=1/2×b×h

A=1/2×5cm×10cm

A=25cm

Answer:

bbv

Step-by-step explanation:

Recurring decimal is decimal representation of a number whose digits are periodic and infinite. Proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330 below.

Given number in the decimal form is [tex]0. 1 \overline 7 \overline 8[/tex]

Suppose the number is equal to the x,

[tex]x=0. 1 \overline 7 \overline 8[/tex]

Recurring decimal is decimal representation of a number whose digits are periodic and infinite.

As the number 78 is the recurring number. Thus the recurring number can be written as,

[tex]x=0.1787878.....[/tex]                      .......equation 1.

Suppose this is equation number 1.

Multiply the above equation with 100 both the sides,

[tex]100\times x=100\times0. 1 787878....[/tex]

[tex]100x=100\times0.1787878...[/tex]

[tex]100x=17.87878...[/tex]

Subtract the above equation from equation number 1. Thus,

[tex]\begin{aligned}\ 100x-x&=17.87878-0.1787878\\ 99x&=17.7\\ \end[/tex]

Solve for x ,

[tex]x=\dfrac{17.7}{99} [/tex]

Multiply with 10 in both numerator and denominator,

[tex]x=\dfrac{177}{990} \\ x=\dfrac{59}{330} \\[/tex]

Hence proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330

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Answer:YOUR ANSWER IS C

Step-by-step explanation:

Answer:

y=11/2x-10

20 character minimum

Answer:

You know that the beginning salary is $32,000, and it is raised by $1,000 per year.

a) We want to find a recursive relation, let's try to find a pattern:

S₁ = salary on the first year =  $32,000

S₂ = salary on the second year = $32,000 + $1,000 = $33,000

S₃ = salary on the third year = $33,000 + $1,000 = $34,000

and so on.

We already can see that the recursive relation is: "the salary of the previous year plus $1,000", this can be written as:

Sₙ = Sₙ₋₁ + $1,000

Such that S₁ = $32,000

b) Your salary in the fifth year is S₅

Let's construct it:

S₃ = $34,000

S₄ = $34,000 + $1,000 = $35,000

S₅ = $35,000 + $1,000 = $36,000

Your salary on the fifth year is $36,000

c) When we have a recursive relation like:

Aₙ = Aₙ₋₁ + d

The sum of the first N elements is given by:

Sum(N) = N*(2*A₁ + (N - 1)*d)/2

Then the sum of your salary for the first 20 years is:

S(20) = 20*(2*$32,000 + (20 - 1)*$1,000)/2

S(20) = $830,000

Answer:

15 ÷ 17

Step-by-step explanation:

Since our hypotenuse side is 17 cm, our opposite side is 8 cm and our adjacent side is 15 cm. Since the acute angle is x degrees,

From trigonometric ratios, cosx° = adjacent/hypotenuse

= 15 cm/17 cm

= 15/17

= 15 ÷ 17

Answer: Chris's Gym pays $2.75

Step-by-step explanation:

So i was glancing at this question wondering how I was gonna figure it out then flipped it upside down in my head and figred out what I was missing

So basically we know that Tyrell pays $2.00 for court reservations

Chris on the other hand according to the table pays $52.75 for court reservation in addition to his monthly fee. Now we have to find out how much is just the court fee. So if we look at the next box I realized that a second court recomendation costs $55.5 and I realized that to find the court reservation costs I needed to subtract so 55.5-52.755= 2.75 which means Chis has a monthly costs of 50 and pays $2.75 for a court holding

Answer: C

Step-by-step explanation:

just took the quiz

The conclusion based on the statement would be option C. Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We need to Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon.

The conclusion based on the statement would be;

C. P(pass morning) = 0.48

P(pass | afternoon) = 0.82

Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.

Therefore, the correct option is C.

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The simplified ratio for 0.875 is 7:8 .

To express the ratio for 0.875, we need to convert the decimal value to a ratio form.

0.875 can be written as 875 / 1000 because the decimal value is equivalent to the fraction obtained by dividing the numerator by the denominator.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 125 in this case.

Dividing 875 and 1000 by 125, we get:

875 / 125 = 7

1000 / 125 = 8

So, the simplified ratio for 0.875 is 7:8 .

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Step-by-step explanation:

2.) -20× + 24

maaf kalo salah

Answer:

x = 93.7ft or x = 94ft

Step-by-step explanation:

Hope that helps :)

Answer:

x = 8

Step-by-step explanation:

alternate-interior angles equal 180°

17x + 14 + 4x - 2 = 180

21x + 12 = 180

21x = 168

x = 8

a )

First of all we need to find the value of x ,

because the angles are written in terms of the variable x .

______________________________________

STV angle & SUV angle have same measure because both of them are the front angle of SV arc .

[tex]STV angle \: = SUV angle \: \: = \frac{SV \: arc}{2} \\ [/tex]

So :

[tex]3x - 5 = 2x + 15[/tex]

Add sides 5

[tex]3x - 5 + 5 = 2x + 15 + 5[/tex]

[tex]3x = 2x + 20[/tex]

Subtract sides minus 2x

[tex]3x - 2x = 2x + 20 - 2x[/tex]

Collect like terms

[tex]x = 2x - 2x + 20[/tex]

[tex]x = 20[/tex]

Thus the measure of angle T equals :

[tex]measure \: of \: angle \: T = 3x - 5 \\ [/tex]

Now just need to put the value of x which we found :

[tex]measure \: of \: angle \: T \: = 3 \times (20) - 5 \\ [/tex]

[tex]measure \: of \: angle \: T \: = 60 - 5[/tex]

[tex]measure \: of \: angle \: T \: = 55°[/tex]

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b )

angle S & angle V are also have same measure because they both are the front angles to the TU arc .

And we need to find the value of x again in this part exactly like we did for a .

[tex]angle \: \: S = angle \: \: V[/tex]

As the question told :

[tex]angle \: \: S = 3x[/tex]

and ,

[tex]angle \: \: V = x + 16[/tex]

Thus :

[tex]3x = x + 16[/tex]

Subtract sides minus x

[tex]3x - x = x + 16 - x[/tex]

Collect like terms

[tex]2x = x - x + 16[/tex]

[tex]2x = 16[/tex]

Divide sides by 2

[tex] \frac{2x}{2} = \frac{16}{2} \\ [/tex]

Simplification

[tex]x = 8[/tex]

So ;

[tex]measure \: \: of \: \: angle \: \: S = 3x[/tex]

[tex]measure \: \: of \: \: angle \: \: S = 3(8)[/tex]

[tex]measure \: \: of \: \: angle \: \: S = 24°[/tex]

And we're done.

Answer: I really don’t know

Step-by-step explanation: I need help with this as well. I’m really sorry if you were looking for a real answer

Answer:

For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].

Step-by-step explanation:

To determine for which value of [tex]x[/tex], we need to apply the following identity ([tex]f(x) = g(x)[/tex]) and solve numerically the resulting expression:

[tex]2\cdot x^{2}+9 = 3^{x}[/tex]

[tex]3^{x}-2\cdot x^{2}-9=0[/tex] (1)

A quick approach is using graphic tool and looking for the value of [tex]x[/tex] such that  [tex]3^{x}-2\cdot x^{2}-9=0[/tex]. The result of the analysis is included below in the attached image. We find the following result:

[tex]x = 3[/tex]

For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].

Step-by-step explanation:

Circumference of a circle= 2πr

where r=6

and π=22/7

C=2πr

=2×22/7×6

=44/7×6

=264/7

=37.71cm