Suppose that given x-bar = 35 and Z 0.01 =+/- 2.58, one established confidence limits for mu of 30 and 40. this means that a/the probability that mu = 35 is 0.99 b/ the probability that mu = 35 is 0.01 c/ 99% of the calculated intervals will contain mu d/ 1% of the calculated intervals contain mu explain answer choice please

Answer:

9749

Step-by-step explanation:

45000·(1+4%)5-45000

9749.38061

rounded to the nearest penny

9749

The integral of sin^4(8q)cos(8q) with respect to q is (1/40)sin^5(8q) + C or (3/8)cos(32q) - (1/64)cos(16q) + C, where C is the constant of integration.

Using the product-to-sum identity for cosine, we can rewrite the integrand as sin(2x+2x+2x+2x)cos(2x+2x) = [sin(2x+2x)cos(2x+2x) + sin(2x)cos(2x+2x+2x)]cos(2x+2x).

We can then use the double angle formula for sine and cosine to simplify the integrand to (3/8)sin(16x) - (1/8)sin(8x) + C. Therefore, the integral of sin4(8q)cos(8q) is (3/8)cos(16q) - (1/64)cos(8q) + C.

To evaluate the integral ∫sin4(8q)cos(8q)dq, we start by using the product-to-sum identity for cosine:

cos(a)sin(b) = 1/2[sin(a+b) + sin(a-b)]

We can rewrite the integrand as:

sin(8q)cos(8q)sin(8q)cos(8q) = [sin(8q+8q)cos(8q+8q) + sin(8q)cos(8q+8q+8q)]cos(8q+8q)

Using the double angle formula for sine and cosine, we can simplify the first term as:

sin(16q)cos(16q) = (1/2)sin(2*16q) = (1/2)sin(32q)

For the second term, we can apply the product-to-sum identity for sine:

sin(a)cos(b) = 1/2[sin(a+b) - sin(a-b)]

sin(8q)cos(8q+8q+8q) = 1/2[sin(8q+24q) - sin(8q-16q)] = 1/2[sin(32q) + sin(8q)]

Putting everything together, we have:

∫sin4(8q)cos(8q)dq = ∫[sin(16q)/2 + sin(32q)/2 + sin(8q)/2]cos(16q)dq

Using the substitution u = 16q, we have:

(1/16)∫[sin(u)/2 + sin(2u)/2 + sin(u/2)/2]cos(u)du

We can then integrate each term separately:

∫sin(u)cos(u)du = (1/2)sin^2(u) + C1

∫sin(2u)cos(u)du = (1/2)[(1/2)sin(3u)] + C2

∫sin(u/2)cos(u)du = -2cos(u/2) + C3

Substituting back, we get:

(1/16)[(1/2)sin^2(16q) + (1/4)sin^2(32q) - 2cos(8q) + C4]

Simplifying, we get:

(3/8)sin^2(16q) - (1/8)sin^2(8q) + C5

Using the identity sin^2(x) = (1-cos(2x))/2, we can rewrite this as:

(3/8)(1-cos(32q))/2 - (1/8)(1-cos(16q))/2 + C6

= (3/8)

To learn more about double angle formula click here: brainly.com/question/30402422

#SPJ11

The expression that is equivalent to (2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) is (D) (x - 1)/(x + 1)

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

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3)

When the expressions are factored, we have:

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) = (2x - 3)(x + 5)/(3x + 1)(x + 5) * (3x + 1)(x - 1)/(x + 1)(2x - 3)

Cancelling out the common factors, we have

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) = (x - 1)/(x + 1)

This means that the equivalent expression is (D) (x - 1)/(x + 1)

Read more about equivalent expression at

https://brainly.com/question/15775046

#SPJ1

The data provided in the question represents annual sales of a product introduced 10 years ago. To analyze the data, the researcher first prepared a scatter plot to understand the relation between X and Y. It is observed that the relation is not completely linear but there is a positive correlation between X and Y.

To find an appropriate power transformation of Y, the Box-Cox procedure is used. The procedure evaluates SSE for different values of λ, including .3, .4, .5, .6, and .7. Standardization is applied to the data to obtain more accurate results. After evaluating SSE for all values of λ, it is suggested that the appropriate power transformation of Y is Y^0.5 (square root transformation).

Using the suggested transformation Y' = √Y, the researcher obtains the estimated linear regression function for the transformed data. The function is given by Y' = 7.58 + 0.221X.

In conclusion, the researcher used scatter plot analysis, Box-Cox procedure, and transformation techniques to analyze the annual sales data of the product introduced 10 years ago. The square root transformation of Y is found to be appropriate and the estimated linear regression function for the transformed data is obtained.

Learn more about positive correlation here:

https://brainly.com/question/27886995

#SPJ11

It can be deduced as the final answer that about 45.23% of the time headways are less than 6 seconds and about 4.06% of the time headways are 10 seconds or greater.


Using the Poisson distribution with the mean rate λ, we can solve for the probability of no cars arriving in 20 seconds, which is:

P(X = 0) = e^(-λ) = 18/120

Solving for λ, we get:

λ = -ln(18/120) = 0.6052

Then we can use the Poisson distribution again to solve for the probability of exactly three cars arriving in 20 seconds, which is:

P(X = 3) = (λ^3 / 3!) * e^(-λ) ≈ 0.1097

Finally, we can multiply this probability by the total number of 20-second intervals to estimate the number of intervals in which exactly three cars arrive:

0.1097 * 120 ≈ 13.16

Therefore, we can approximate that 13 of the 120 intervals will have exactly three cars arrive.

The headway between vehicles is the time gap between the arrivals of two consecutive vehicles. We can estimate the percentage of time headways that are 10 seconds or greater and those that are less than 6 seconds by using the exponential distribution with the same mean rate λ as in problem 5.9.

For a headway X, the probability density function of the exponential distribution is given by:

f(x) = λ * e^(-λx)

Therefore, the probability of a headway being less than 6 seconds is:

P(X < 6) = ∫[0,6] λ * e^(-λx) dx = 1 - e^(-6λ)

Similarly, the probability of a headway being 10 seconds or greater is:

P(X ≥ 10) = ∫[10,∞) λ * e^(-λx) dx = e^(-10λ)

Using the value of λ obtained in problem 5.9, we can estimate these probabilities as:

P(X < 6) ≈ 0.4523 or 45.23%

P(X ≥ 10) ≈ 0.0406 or 4.06%

Therefore, we estimate that about 45.23% of the time headways are less than 6 seconds and about 4.06% of the time headways are 10 seconds or greater.

Learn more about poisson's distribution here:-brainly.com/question/30388228

#SPJ11

The probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

We can use the central limit theorem to approximate the distribution of the sample mean baking time. Since the sample size is large enough (20 pies) and the population standard deviation is known, we can use the normal distribution to approximate the distribution of the sample mean.

The mean of the sample mean baking time is the same as the population mean, which is 45 minutes.

To find the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes, we can standardize the sample mean using the formula:

[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

= (48-45)/(5/√20)

= 2.68

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being greater than 2.68 is approximately 0.0037. Therefore, the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

Learn more about Central limit theorem here

https://brainly.com/question/30115013

#SPJ4

Therefore, The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C. We can check the answer by differentiating F(x) which will give us g(x) = cos(x) - 8sin(x).

The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C, where C is the constant of integration.
Explanation: To find the antiderivative of g(x), we use the formulae of integration of trigonometric functions. ∫cos(x) dx = sin(x) + C and ∫sin(x) dx = -cos(x) + C. Therefore, ∫cos(x) − 8sin(x) dx = ∫cos(x) dx − 8∫sin(x) dx = sin(x) + 8cos(x) + C. To check our answer, we differentiate F(x) with respect to x, we get g(x) = cos(x) - 8sin(x).

Therefore, The most general antiderivative of the function g(x) = cos(x) - 8sin(x) is F(x) = sin(x) + 8cos(x) + C. We can check the answer by differentiating F(x) which will give us g(x) = cos(x) - 8sin(x).

To know more about trigonometric equations visit :

https://brainly.com/question/30710281

#SPJ11

Answer:

16

Step-by-step explanation:

7 feet x 12 inches/foot = 84 inches

Then we divide the total length of the string (84 inches) by the length of each piece (5 inches) to get the total number of pieces:

84 inches / 5 inches per piece = 16.8 pieces

Since we cannot have a fractional number of pieces, we round down to the nearest whole number to get the final answer:

16 pieces

The cooling rate of the turkey is 0.45°F per minute. This means that every minute, the temperature of the turkey decreases by 0.45°F.

The cooling rate of a roasted turkey can be determined by the rate at which it loses heat to its surroundings. In this case, the temperature of the turkey was 191°F when it was taken out of the oven and placed on a table in a room with a temperature of 75°F. After half an hour, the temperature of the turkey had decreased to 155°F.

To calculate the cooling rate, we can use Newton's law of cooling, which states that the rate of heat loss of an object is proportional to the difference in temperature between the object and its surroundings. The equation for Newton's law of cooling is:

dT/dt = -k (T - Ts)

where dT/dt is the rate of change of temperature with respect to time, T is the temperature of the turkey at time t, Ts is the temperature of the surroundings (75°F), and k is a constant that depends on the specific heat of the turkey, its surface area, and other factors.

To solve for k, we can use the data given:

dT/dt = -k (T - Ts)

-36 = -k (155 - 75)

-36 = -k (80)

k = 0.45

To learn more about cooling rate

https://brainly.com/question/31367701

#SPJ4

After considering all the data we conclude that the area of the region enclosed by the astroid is (3/8) π a⁴, under the condition that  x = a cos3θ, y = a sin3θ.

The astroid curve is given by x = a cos³θ, y = a sin³θ. The area enclosed by the astroid curve is given by the integral of ½ y dx from θ = 0 to θ = 2π ².

Staging x = a cos³θ and y = a sin³θ in ½ y dx, we get:

½ y dx = ½ a sin³θ (−3a sin²θ dθ) = −3/2 a⁴ cos⁶θ sin⁴θ dθ

Applying Integration to this expression from θ = 0 to θ = 2π provides us the area enclosed by the astroid curve:

A = ∫₀²π −3/2 a⁴ cos⁶θ sin⁴θ dθ

A = (3/8) π a⁴

Therefore, the area enclosed by the astroid curve is (3/8) π a⁴.
To learn more about integration
https://brainly.com/question/30215870
#SPJ1

The rejection region is t > 1.761.

To test the hypothesis that the mean fee for car washers (including tips) is greater than $12, we can perform a one-sample t-test.

Sample mean [tex]\bar{x}[/tex]  = $14.9

Sample standard deviation (s) = $6.75

Sample size (n) = 15

Significance level (α) = 0.05 (5%)

Since the sample size is small (n < 30) and the population standard deviation is unknown, we will use the t-distribution for inference.

Define the null and alternative hypotheses:

Null hypothesis (H₀): μ ≤ $12 (Mean fee for car washers is less than or equal to $12)

Alternative hypothesis (H₁): μ > $12 (Mean fee for car washers is greater than $12)

Determine the critical value (rejection region) based on the significance level and degrees of freedom.

The degrees of freedom (df) for a one-sample t-test is calculated as df = n - 1 = 15 - 1 = 14.

Using a t-table or statistical software, we find the critical t-value for a one-tailed test with α = 0.05 and df = 14 to be approximately 1.761.

Calculate the test statistic:

The test statistic for a one-sample t-test is given by:

t = ([tex]\bar{x}[/tex]  - μ) / (s / √n)

Plugging in the values:

t = ($14.9 - $12) / ($6.75 / √15) ≈ 2.034

Make a decision:

If the test statistic t is greater than the critical t-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value (2.034) is greater than the critical t-value (1.761), indicating that it falls in the rejection region.

State the conclusion:

Based on the test results, at the 5% significance level, we have enough evidence to reject the null hypothesis.

We can infer that the mean fee for car washers (including tips) is greater than $12.

For similar question on rejection region.

https://brainly.com/question/27963477

#SPJ11

Answer:

it will take 9 hours to empty the pool.

Step-by-step explanation:

Answer:  10

Step-by-step explanation: if you add all of them together you get 50 the oly one that can go into 50 without passing is 10

The minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

The Taylor series for cos x centred at O is given by:

cos x = 1 - x^2/2! + x^4/4! - x^6/6! + ...

The nth-order Taylor polynomial for cos x centred at O is given by the first n terms of the Taylor series. We want to find the minimum n such that the absolute error between cos (-0.85) and the nth-order Taylor polynomial is no greater than 10-4.

The error term for the nth-order Taylor polynomial is given by:

Rn(x) = cos (c) * xn+1 / (n+1)!

where c is some value between 0 and x.

To find the minimum n, we need to find the value of n such that the error term is no greater than 10-4 for x = -0.85.

Substituting x = -0.85 into the error term and using the fact that |cos (c)| <= 1, we have:

|Rn(-0.85)| <= |(-0.85)^(n+1) / (n+1)!|

We want to find the minimum n such that the right-hand side is no greater than 10-4.

We can use a computer or calculator to find that n = 5 is the smallest integer that satisfies this condition. Therefore, the minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

Learn more about Taylor series, here:

brainly.com/question/2254439

#SPJ11

The correlation coefficient between x and y is 0.61. The formula for the correlation coefficient (r) between two variables x and y is:

r = covariance(x, y) / (standard deviation(x) * standard deviation(y))

We are given that the covariance between x and y is 1225, the variance of x is 1600, and the variance of y is 2500. Since variance is the square of standard deviation, we can calculate the standard deviations of x and y as:

standard deviation(x) = sqrt(variance(x)) = √(1600) = 40

standard deviation(y) = sqrt(variance(y)) = √(2500) = 50

Plugging in these values into the formula for the correlation coefficient, we get:

r = 1225 / (40 * 50) = 0.61

r = 1225/(2000) = 0.61

Therefore, the correlation coefficient between x and y is 0.61.

Learn more about Covariance:

https://brainly.com/question/30651852

#SPJ1

The function f(x) appears to be a polynomial function.

Based on the description of the graph, the function f(x) does not appear to be exponential, logarithmic, or rational.

Exponential functions typically exhibit a constant rate of change as x increases or decreases, resulting in a curve that either exponentially increases or decreases. The graph described does not match this pattern, as it increases in some areas and decreases in others.

Logarithmic functions have a characteristic shape with a vertical asymptote and a slow growth or decay. The given graph does not exhibit this behavior.

Rational functions are defined as the ratio of two polynomials, and their graphs often have vertical and horizontal asymptotes. However, the description does not mention any asymptotes, suggesting that the function is not rational.

The most suitable choice based on the given information is polynomial. Polynomial functions are characterized by having non-negative integer exponents and can exhibit various shapes, including increasing or decreasing trends. The description mentions that the graph is increasing in quadrant 3 and quadrant 4, indicating that the function could be a polynomial.

Without additional information or the specific equation of the function, it is challenging to determine the exact degree or form of the polynomial function.

for more such questions on polynomial functions

https://brainly.com/question/2833285

#SPJ8

A random variable is a numerical outcome that is generated by a probability experiment. It is a function that assigns a unique numerical value to each outcome of the experiment.

Random variables can be either discrete or continuous. Discrete random variables take on a countable number of distinct values, while continuous random variables can take on any value within a specified range. In statistical analysis, random variables are used to model the behavior of a system or population of interest. They are often used to describe the distribution of a population or the probability of different outcomes occurring in a given scenario. Random variables are an essential tool in probability theory, statistics, and other areas of mathematics and science.

Learn more random variable about here: /rainly.com/question/13733697

#SPJ11

There are 96 different possible combos.

The principle used to calculate the number of possible combos is called the multiplication principle.

We have,

(a)

The number of possible combos, when you select a popcorn, a candy, and a soda.

= 8 (choices of candy) x 6 (choices of soda) x 2 (choices of popcorn)

= 96

(b)

The principle used to calculate the number of possible combos is called the multiplication principle.

Thus,

There are 96 different possible combos.

The principle used to calculate the number of possible combos is called the multiplication principle.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The length of the hypotenuse of this triangle is approximately 15.03 inches (rounded to the nearest tenth).

To find the length of the hypotenuse in a right triangle, we can use the trigonometric function cosine.

Given:

Leg length (adjacent side) = 7 in

Angle opposite the leg = 62°

We can use the cosine function, which relates the adjacent side and the hypotenuse of a right triangle:

cos(angle) = adjacent/hypotenuse

Let's substitute the known values into the equation:

cos(62°) = 7/hypotenuse

To solve for the hypotenuse, we rearrange the equation:

hypotenuse = 7/cos(62°)

Using a calculator, we find:

cos(62°) ≈ 0.4663

Now we can substitute this value into the equation:

hypotenuse = 7/0.4663

Calculating this, we get:

hypotenuse ≈ 15.03

Therefore, the length of the hypotenuse of this triangle is approximately 15.03 inches (rounded to the nearest tenth).

for such more question on right triangle

https://brainly.com/question/2217700

#SPJ11

If x = x1(t) and y = y1(t) and x = x2(t) and y = y2(t) are any two solutions of the linear nonhomogeneous system given by x' = p11(t)x + p12(t)y + g1(t), y' = p21(t)x + p22(t)y + g2(t), then x = x1(t) - x2(t) and y = y1(t) - y2(t) is a solution of the corresponding homogeneous system given by x' = p11(t)x + p12(t)y, y' = p21(t)x + p22(t)y.

To show that x = x1(t) - x2(t) and y = y1(t) - y2(t) is a solution of the corresponding homogeneous system, we need to verify that it satisfies the differential equations x' = p11(t)x + p12(t)y and y' = p21(t)x + p22(t)y with g1(t) = g2(t) = 0. Using the properties of derivatives, we can calculate that x' = x1'(t) - x2'(t) and y' = y1'(t) - y2'(t). Substituting these expressions and the expressions for x and y into the differential equations, we get:

x' = p11(t)x + p12(t)y

==> x1'(t) - x2'(t) = p11(t)(x1(t) - x2(t)) + p12(t)(y1(t) - y2(t))

==> p11(t)x1(t) + p12(t)y1(t) = p11(t)x2(t) + p12(t)y2(t)

y' = p21(t)x + p22(t)y

==> y1'(t) - y2'(t) = p21(t)(x1(t) - x2(t)) + p22(t)(y1(t) - y2(t))

==> p21(t)x1(t) + p22(t)y1(t) = p21(t)x2(t) + p22(t)y2(t)

Since x1(t), y1(t), x2(t), and y2(t) all satisfy the original nonhomogeneous system, we know that the expressions on the right-hand sides of the above equations are equal to g1(t) and g2(t), which are both zero in the corresponding homogeneous system. Therefore, x = x1(t) - x2(t) and y = y1(t) - y2(t) satisfy the differential equations x' = p11(t)x + p12(t)y and y' = p21(t)x + p22(t)y with g1(t) = g2(t) = 0, and hence they are a solution of the corresponding homogeneous system.

Learn more about homogeneous system here

https://brainly.com/question/14778174

#SPJ11

The equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

To find the equation of the line tangent to the curve at the point corresponding to t = π/4, we need to find the first derivatives of x and y with respect to t, evaluate them at t = π/4, and then use these values to find the slope of the tangent line.

The first derivative of x with respect to t is:

dx/dt = -sint + tcost

The first derivative of y with respect to t is:

dy/dt = cost + tsint

Evaluating these at t = π/4, we get:

dx/dt|t=π/4 = -sqrt(2)/2

dy/dt|t=π/4 = (sqrt(2)/2) + (π/4)(sqrt(2)/2)

The slope of the tangent line is the ratio of the change in y to the change in x. So, the slope of the tangent line at t = π/4 is:

m = dy/dt|t=π/4 / dx/dt|t=π/4 = -1 - π/2

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line. Using the point (x(π/4), y(π/4)) = (sqrt(2)/2, sqrt(2)/2), we get:

y - (sqrt(2)/2) = (m)(x - sqrt(2)/2)

Substituting the value of m, we get:

y - (sqrt(2)/2) = (-1 - π/2)(x - sqrt(2)/2)

Expanding and simplifying, we get the equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

Learn more about :

tangent line : brainly.com/question/30162653

#SPJ11

The given order of integration is dx first, then dy, and finally dz. To change the order of integration to dz first, then dx, and finally dy, we need to identify the new limits of integration. We can do this by using the given limits of integration and setting up the new integrals. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by looking at the given limits of integration and setting up the new integrals. First, we need to integrate with respect to z, so we set the limits of integration for z from 0 to 1 - 2x.

Next, we integrate with respect to x, so we set the limits of integration for x from 0 to 2y. Finally, we integrate with respect to y, so we set the limits of integration for y from 0 to 1/4.

Putting it all together, we get the equivalent integral with the new order of integration: ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by setting up the new integrals based on the given limits of integration. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To know more about integration visit:

https://brainly.com/question/31744185

#SPJ11

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

Learn more about perimeter on

https://brainly.com/question/19819849

#SPJ1

To draw a line and measure it to the nearest quarter inch, you will need a ruler or tape measure marked in inches.

Place the ruler or tape measure at one end of the line and align it so that the 0 mark lines up with the beginning of the line. Then, count the number of quarter inches to the end of the line and record the measurement.

Measuring to the nearest quarter inch means that you are rounding the measurement to the nearest multiple of 0.25 inches. For example, if the line measures between 3 and 3.24 inches, it would be rounded down to 3 inches; if it measures between 3.25 and 3.49 inches, it would be rounded up to 3.5 inches. This level of precision is commonly used in construction, woodworking, and other fields where precise measurements are important.

Learn more about Measurements here: brainly.com/question/28913275

#SPJ11

Thus, we can find nonzero matrices a, b, and c such that ac = bc and a is not equal to b by using the distributive property of matrix multiplication. One example of such matrices is provided above.

The problem statement requires us to find three matrices - a, b, and c, such that their product ac is equal to bc but a is not equal to b. To solve this problem, we need to use the properties of matrix multiplication. One such property is the distributive property, which states that a(b + c) = ab + ac, where a, b, and c are matrices.

Let's assume that a, b, and c are all 2x2 matrices. One example of such matrices could be:

a = [1 0]
   [0 2]

b = [2 0]
   [0 1]

c = [1 2]
   [3 4]

Using these matrices, we can verify that ac = bc, as follows:

ac = [1 0]  [1 2] = [1 2]
    [0 2]  [3 4]   [6 8]

bc = [2 0]  [1 2] = [2 4]
    [0 1]  [3 4]   [3 4]

As we can see, both products result in the same matrix. However, a and b are not equal, as a(1,1) = 1 and b(1,1) = 2. Therefore, we have found an example of three nonzero matrices such that ac = bc but a is not equal to b.

know more about the nonzero matrices

https://brainly.com/question/30881847

#SPJ11

The p-value for the given t-statistic falls between 0.005 and 0.01.

o find the p-value for the given t statistic of -2.63 with degrees of freedom of 24, we need to consult the t-distribution table or use statistical software.

Since the alternative hypothesis is μ < 100, we are conducting a one-tailed test in the left tail of the t-distribution. We want to find the area under the t-distribution curve to the left of -2.63.

Using the t-distribution table or software, we can determine that the p-value falls between 0.005 and 0.01. This means that the p-value for the statistic falls between 0.005 and 0.01.

Therefore, the p-value for the given t-statistic falls between 0.005 and 0.01.

Visit here to learn more about hypothesis:

brainly.com/question/31319397

#SPJ11

The differential of the function z = x^6 ln(y^4) is dz = 6x^5 ln(y^4) dx + 4x^6 (1/y) dy.

To find the differential of the function z = x^6 ln(y^4), we use the rules of partial differentiation.

Taking the partial derivative of z with respect to x, we get ∂z/∂x = 6x^5 ln(y^4).

Taking the partial derivative of z with respect to y, we get ∂z/∂y = (4x^6/y) ln(y^4).

Then, using the differential notation, we can write dz = (∂z/∂x) dx + (∂z/∂y) dy.

Substituting the values we calculated for ∂z/∂x and ∂z/∂y, we get dz = 6x^5 ln(y^4) dx + 4x^6 (1/y) dy.

This represents the differential of the function z = x^6 ln(y^4).

To learn more about partial differentiation : brainly.com/question/31383100

#SPJ11

Answer:

X= 95 Y=55

Step-by-step explanation:

95X5= 475

2X55= 110

475+110= 585

I hope this helps! : )

The first partial derivatives with respect to x, y, and z of the given function f(x, y, z) = 2x^2y − 9xyz/10yz^2 are:

fx = 4xy - (9yz/10z^2) = 4xy - (9/10z)

fy = 2x^2 - (9xz/10z^2) = 2x^2 - (9x/10z)

fz = (-9xy/5yz^2) - (18xyz/5yz^3) = (-9x/5z) - (18x/5y)

The partial derivative of a multivariable function with respect to a particular variable is calculated by considering all other variables as constants and differentiating with respect to the chosen variable. In this case, the partial derivative with respect to x involves differentiating the function with respect to x while treating y and z as constants, and similarly for y and z. The obtained partial derivatives are then used to find critical points, which are the points where all partial derivatives are zero.

To learn more about partial derivatives click here: brainly.com/question/28751547

#SPJ11