ILL BRAINLIEST YOU AND GIVE U TEN EXTRA POINT IF YOU GET IT RIGHT

PLEASE HELP SOLVE THIS WITH EXPLANATION PLEASE

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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a) The integral ∫\(x^3 √(x^2 + 1) dx\) evaluates to (1/5)\((x^2 + 1)^(5/2) - (1/3) (x^2 + 1)^(3/2) + C.\)  b) The integral ∫(0 to 1) \((3t - 2)^{50\)dt evaluates to 1/51. c) The integral ∫(0 to 1)\(1 / (1 + √x)^4 dx\) evaluates to -2 / (3 \((1 + √x)^3) + C.\)

Certainly! Let's go through each integral step by step.

a) To evaluate the integral ∫ \(x^3 √(x^2 + 1) dx:\)

Let's use the substitution method.

Let \(u = x^2 + 1.\)

Then, du = 2x dx, which implies dx = du / (2x).

Substituting these values, we have:

∫ \(x^3 √(x^2 + 1) dx\) = ∫ (1/2) (u - 1) √u du

Expanding the integrand, we get:

∫ (1/2) \((u^{(3/2)} - √u) du\)

Now we can integrate each term separately:

∫ (1/2) \((u^(3/2) - √u) du\) = (1/2) * (2/5) * \(u^{(5/2)} - (1/2) * (2/3) * u^(3/2) + C\)

Simplifying further, we obtain:

(1/5) \(u^{(5/2)} - (1/3) u^{(3/2)} + C\)

Replacing u with x^2 + 1, the final result is:

\((1/5) (x^2 + 1)^(5/2) - (1/3) (x^2 + 1)^{(3/2)} + C\)

b) To evaluate the integral ∫(0 to 1) (3t - 2) dt:

Using the power rule for integration, we can directly integrate the given expression:

\(∫(0 to 1) (3t - 2)^50 dt = (1/51) * (3t - 2)^51\) evaluated from 0 to 1

Plugging in the upper limit, we have:

\((1/51) * (3(1) - 2)^51\)

Simplifying further, we obtain:

\((1/51) * (1)^51 = 1/51\)

So, the value of the integral is 1/51.

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Answer:

-9

Step-by-step explanation:

The parametric inferential statistical test for a single sample with a known population variance is the one-sample z-test.The null hypothesis in this test is that the sample mean is equal to the population mean.

The one-sample z-test is a parametric test used to determine whether a sample mean is significantly different from a known population mean when the population variance is also known. This test assumes that the data are normally distributed and the sample is a random sample from the population.

The one-sample z-test is a statistical test used to test a hypothesis about a population mean when the population variance is known. It is a parametric test, which means that it makes assumptions about the population distribution and sample size. Specifically, it assumes that the data are normally distributed and that the sample is a random sample from the population. The test is called a z-test because it uses the standard normal distribution to calculate the test statistic. The test statistic is calculated by taking the difference between the sample mean and the population mean, and dividing it by the standard error of the mean. The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size.

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The sum of the tension in each rope will be equal to 50 N.

When an object is in equilibrium, the sum of the forces acting on it is zero. In this case, the lantern is in equilibrium as it is not accelerating vertically.

If we consider the tension in each rope, they act in opposite directions and have equal magnitudes. Let's denote the tension in one rope as T1 and the tension in the other rope as T2.

Since the lantern is not accelerating vertically, the sum of the vertical forces must be zero. Therefore, the sum of the tension in each rope (T1 + T2) must be equal to the weight of the lantern, which is 50 N.

T1 + T2 = 50 N

The sum of the tension in each rope will be equal to 50 N, which is the weight of the lantern.

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Answer:

29/80

Step-by-step explanation: It would be 29/80 because you cannot simplify that fraction. 29 is a prime number.

Answer:

\(3(2x + 4y - 15z) \\ 6x + 12y - 45z\)

Step-by-step explanation:

y=-8x + 89​

Slope m= 8

y- intercept = +89. For x= 0

Q27: The periodic monthly rate is 0.0074, Q28: The equivalent effective semiannual rate is 0.0299.

Q27: To calculate the periodic monthly rate, we divide the APR by the number of compounding periods in a year. Since the loan has monthly compounding, there are 12 compounding periods in a year.

Periodic monthly rate = APR / Number of compounding periods per year

= 0.0888 / 12

= 0.0074

Q28: To find the equivalent effective semiannual rate, we need to consider the compounding period and adjust the periodic rate accordingly. In this case, the loan has monthly compounding, so we need to calculate the effective rate over a semiannual period.

Effective semiannual rate = (1 + periodic rate)^Number of compounding periods per semiannual period - 1

= (1 + 0.0074)^6 - 1

= 1.0299 - 1

= 0.0299

The periodic monthly rate for the loan is 0.0074, and the equivalent effective semiannual rate is 0.0299. These calculations take into account the APR and the frequency of compounding to determine the rates for the loan.

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Answer:

The answer is 35 yards

Step-by-step explanation:

25-19.05 = 5.95

5.95/0.17 = 35 yards

Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

40

Step-by-step explanation:

Cohen's conventions for interpreting d, this effect is small. Therefore, the correct answer is a. small.

According to Cohen's conventions for interpreting the effect size (d), the effect described in the study is considered "small." Cohen's conventions provide a general guideline for categorizing the magnitude of an effect size.

In this case, the effect size (d) is calculated to be 0.02. Cohen's conventions typically classify effect sizes as follows:

Small effect: d = 0.2

Medium effect: d = 0.5

Large effect: d = 0.8

Since the effect size of 0.02 is significantly smaller than the threshold for a small effect (0.2), it falls into the "small" category. This means that the difference in the number of words uttered per day between men and women, as reported in the study, is relatively small or negligible in practical terms.

Therefore, the correct answer is a. small.

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The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Answer:

i think it`s the first one

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The player runs 5 meters forward, and then runs 5 meters in the opposite direction.

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Density of water (ρ) = 1 g/cm³ Pressure at the tank (P1) = 1 atm (gauge) = 1 + 1 = 2 atm = 2 * 101.325 kPa Pressure at the surface of the lake (P2) = 1 atm (gauge) fric tion losses and Height difference between the lake and the tank (h) = 50 m Power delivered to the pump (P) = 2.5 hp = 2.5 * 745.7 W = 1864.25 WLet's solve the problem step by step.

Step 1: Calculate the pressure at the lake surface:Pressure at the lake surface = P2 + ρghHere, h = 50 m∴ Pressure at the lake surface (P2) = 1 atm (gauge) + 1 g/cm³ × 9.8 m/s² × 50 m = 601.8 kPa

Step 2: Determine the volume flow rate of water:Volume flow rate = Power / (ρgΔh)Here, Δh = h = 50 m∴ Volume flow rate = 1864.25 W / (1 g/cm³ × 9.8 m/s² × 50 m) = 3.784 m³/s

Step 3: Convert volume flow rate to mass flow rate:Mass flow rate = ρ × Volume flow rate= 1 g/cm³ × 3.784 m³/s= 3784 kg/s Therefore, the mass flow rate of water (in kg/s) is 3784.

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The requried each side of the square is 17 cm.

The formula for the area of a square is:

Area = side²

We know that the area of the square is 289 cm², so we can write:

289 = side²

To solve for the length of each side, we need to take the square root of both sides of the equation:

√289 = √(side²)

17 = side

Therefore, each side of the square is 17 cm.

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Answer:

40

Step-by-step explanation:

40 divided by 1/4 = 10

25% = 1/4

Answer:

40

Step-by-step explanation:

We Know

25% of x is 10

Find x

We Take

10 x 4 = 40

So, 25% of 40 is 10

The probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

The given problem can be solved using the Poisson distribution. Let \($\lambda$\) be the average rate of cars passing through the section per hour. Then, since the probability of no cars passing in one hour is 0.4, we have:

Solving for \($\lambda$\), we get \($\lambda= -ln(0.4) \approx 0.916$\). Therefore, the probability of no cars passing in three hours (two hours have already passed) is:

The probability of waiting at least 1 more hour for the next car is the same as the probability of having no cars pass in the next hour, given that no cars have passed in the last 2 hours. This can be calculated using the conditional Poisson distribution:

\($= \frac{\frac{(0.916\cdot1)^0e^{-0.916\cdot1}}{0!}\cdot \frac{(0.916\cdot2)^0e^{-0.916\cdot2}}{0!}}{0.148} \approx 0.631$\)

Therefore, the probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

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Answer: the value of n = 1.5

Step by Step Solution: to figure this out, you can just substitute the number in for the variable and solve. hope this helps

Answer:

Alternative Interior Angles: ∠d and ∠e

Step-by-step explanation:

Answer:

Can't see the rest

Step-by-step explanation:

\(7^{2+5+2} =7^{9}\)

\(x^{5-8} y^{12-9}z^{0} =x^{-3} y^{3}\)

\(x^{3+5}=x^{8}\)

\(5^{1} +5^{0} ,(5^{1})^{1},5^{2}/5\)

\(\sqrt[3]{7} ,\frac{7}{7^{2/3} } ,7^{1/6}*7^{1/6}\)

\(625 = 5*5*5*5, 5^{4}\)

\(2^{10} =2*2*2*2*2*2*2*2*2*2=1024\)

Answer:

1.875

Step-by-step explanation:

Answer:

1.875 is the answer I got

Answer & Step-by-step explanation:

In the problem, we are asked to find the quotient. The quotient is the number that we get once we divide two numbers.

We are asked to find the quotient of 9⁵ ÷ 9⁵.

When a number is divided by itself, then the answer is always going to be 1.

So, the quotient of 9⁵ ÷ 9⁵ is going to be 1.

Answer/Step-by-step explanation:

a. Since both cones, as shown in the figure attached below, are similar, 11/8 = l/4

Cross multiply to find l

4*11 = 8*l

44 = 8l

l = 44/8

l = 5.5cm

b. Given the slant height and diameter of cone, volume of cone can be calculated using the formula ⅓πr²*√(l² - r²)

Where, r = diameter ÷ 2 = 4/2 = 2cm

l = 5.5cm

Volume of smaller cone = ⅓*3.142*2²*√(5.5² - 2²)

= ⅓*3.142*4*√30.25 - 4)

= ⅓*12.568*√26.25

= ⅓*12.568*5.124

= 64.40/3

Volume of small cone ≈ 21.5 cm³

The independent variable of interest in an ANOVA procedure is called a factor. Hence (d).

The independent variable of interest in an ANOVA procedure is referred to as the factor. The factor represents the different categories or levels being compared to assess their impact on a dependent variable. It is the variable that is manipulated or controlled by the researcher to determine its effect on the outcome. In the context of ANOVA, the factor is typically a categorical variable that divides the data into distinct groups or treatments. These groups are compared to evaluate if there are statistically significant differences in the means of the dependent variable across the different levels of the factor. Therefore, the correct answer is factor(d).

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Answer:

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

I'm not sure

sorry

Answer:

yes , sure ... i think it should be non linear