The integral sin(x - 2) dx is transformed into 1, g(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = 1/2 sin(t-3/2) g(t) = 1/2sint-5/2) g(t) = 1/2cos (t-5/2) = cos (t-3)/ 2

Answer:

Step-by-step explanation:

so you will multiply height by length and that will give you 70 cubic cm DNT FORGET TO PUT CUBIC CM!!!!!

If I did these right, it should be 70.

Jonaz traveled a total distance of 17 km, with a displacement of 7.5 km in a direction of 31 degrees north of east. His average speed was 5.67 km/h, and his average velocity was 4.5 km/h in a direction of 31 degrees north of east.

To calculate the distance, we need to find the total length of the path that Jonaz traveled. We can do this by adding up the lengths of each leg of the journey. The first leg was 2 km, the second leg was 10 km, and the third leg was 5 km. So, the total distance is 17 km.

To calculate the displacement, we need to find the straight-line distance between Jonaz's starting point and his ending point. This is equal to the length of the hypotenuse of a right triangle with legs of 2 km and 10 km. Using the Pythagorean theorem, we can find that the displacement is 7.5 km.

To calculate the speed, we need to divide the distance by the time. Jonaz traveled for a total of 6 hours. So, his average speed was 5.67 km/h.

To calculate the velocity, we need to take into account the direction of Jonaz's motion. His average velocity was 4.5 km/h in a direction of 31 degrees north of east.

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Answer:

The surface area of the red square is 180, and the surface area of the blue square is 328. So the full answer is 508.

Step-by-step explanation:

A = 2( width times length +height times length +height times width ) = 2(6 times 3 + 8 times 3 + 8 times 6)=180

A = 2(width times length + height times length + height times width) = 2(2 times 12 + 10 times 12 + 10 times 2) = 328

And 328 + 180 = 508.

Answer:

Because e is used so commonly in math and economics, and people in these fields often need to take the logarithm with a base of e of a number to solve an equation or find a value, the natural log was created as a shortcut way to write and calculate log base e. ... So ln(x) = loge(x). As an example, ln(5) = loge(5) = 1.609.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!

Answer: D

Step-by-step explanation:

Solve for y: y (greater than or equal to) (7-9x)/5

Slope is negative (-1.8x) so it must be A or D

Choose a test point to plug in. (0,0) works. If plugging in 0 for x and y yields a true inequality, then the area with (0,0) should be shaded. Since the result for plugging in (0,0) is 0 greater than or equal to 1.4, choose the shaded area without (0,0).

Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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It is most likely that 180 soda coupons will be requested when 450 tickets are purchased.

To determine the number of soda coupons that will most likely be requested when 450 tickets are purchased, we need to analyze the data in the table and calculate the probability of requesting a soda coupon.

From the table, we can see that out of 25 randomly selected customers, 10 requested a soda coupon. Therefore, the probability of requesting a soda coupon based on this sample is 10/25 or 0.4.

To estimate the number of soda coupons that will be requested when 450 tickets are purchased, we can use the probability proportion. We multiply the probability of requesting a soda coupon (0.4) by the number of tickets purchased (450): 0.4 * 450 = 180.

Therefore, it is most likely that 180 soda coupons will be requested when 450 tickets are purchased.

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Answer:

± 1.13432%

between 23.966% and 26.234% households in the population who tuned into the final episode of ​"When Will it End question mark​"

Step-by-step explanation:

Given that:

Sample size (n). = 5613

Proportion (p) = 25.1% = 0.251

Margin of Error can be obtained using :

MOE = z * √p * (1 - p) / √n

Zscore at 95% confidence interval = 1.96

1 - p = 1 - 0.251 = 0.749

Hence,

Margin of Error :

1.96 * √0.251 * 0.749 / √5613

1.96 * (0.4335885 / 74.919957)

= 0.0113432

= ± (0.0113432) * 100%

= ± 1.13432%

B.) between (25.1 - 1.134)% = 23.966% and 25.1 + 1.134)% = 26.234% households in the population who tuned into the final episode of ​"When Will it End question mark​"

Margin of Error (MOE) is a function of the critical value. We will choose a confidential interval of 95 %.

Solution is:

a) MOE = 0,011

b) We can affirm with 95 % of confidence that the porcentage of TV households in the population watching th final  episode of " When ...

would be between  25,1 - 0,011  and  25,1 + 0,011

In our question we got:

Sample size    n = 5613

p = 25.1 %    ( positive events expressed as porcentage )

q = 1 - p     q = 1 - 0,251    q = 0,749

According to the size of the sample, and the fact that

q×n    and   p×n   are both    q×n > 10   p×n > 10

We are in condition to apply the approximation of the binomial distribution to normal distribution and use table z scores

CI   = 95 %    then  confidence level   α = 5 %    α/2 = 0,025  and fom z-table we get the critical value

z(c) = 1,96

Now to find MOE

MOE = z(c)×√(p×q/n)  ⇒ MOE = 1,96 × √ ( 0,251×0,749)5613

MOE = 1,96 × 0,005787

MOE = 0,011

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If Confidential Interval is 95%

Answer:

Step-by-step explanation:

The distance walked by three students:

Add up all three:

Answer:

The 98% confidence interval for the population proportion of purchases paid with a major credit card is (0.1786, 0.3958).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 94, \pi = \frac{27}{94} = 0.2872\)

98% confidence level

So \(\alpha = 0.02\), z is the value of Z that has a pvalue of \(1 - \frac{0.02}{2} = 0.99\), so \(Z = 2.327\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2872 - 2.327\sqrt{\frac{0.2872*0.7128}{94}} = 0.1786\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2872 + 2.327\sqrt{\frac{0.2872*0.7128}{94}} = 0.3958\)

The 98% confidence interval for the population proportion of purchases paid with a major credit card is (0.1786, 0.3958).

Step-by-step explanation:

Given that,

The dosage of Benadryl for Dog is \(11\dfrac{5}{8}\ mg\)

Weight of Joel's Dog is \(15\dfrac{1}{2}\ \text{pounds}\)

(a)  Benadryl dosage per pound for Joel’s dog is calculated as :

\(\dfrac{11\dfrac{5}{8}}{15\dfrac{1}{2}}=\dfrac{\dfrac{11\times 8+5}{8}}{\dfrac{15\times 2+1}{2}}\\\\=\dfrac{\dfrac{93}{8}}{\dfrac{31}{2}}\\\\=\dfrac{93}{8}\times \dfrac{2}{31}\\\\=0.75\ \text{dosage per pound}\)

(b) If the weight of the Dog is 12 pounds, it means

\(\dfrac{11\dfrac{5}{8}}{12}\ \text{dosage per pounds}\\\\=\dfrac{\dfrac{93}{8}}{12}\\\\=\dfrac{93}{8}\times \dfrac{1}{12}\\\\=0.968\ \text{dosage per pounds}\)

Therefore, this is the required solution.

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

not significantly more than 3 minutes.

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

1. The null hypothesis is that the population mean is equal to 3 minutes.

2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.

3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

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The failure of beta cells to function can result in a condition called diabetes mellitus.

Beta cells are specialized cells located in the pancreas that produce and release insulin. A hormone responsible for regulating blood sugar levels. When beta cells fail to function properly, it can lead to two main types of diabetes:

1. Type 1 Diabetes: In this autoimmune disease, the immune system mistakenly attacks and destroys the beta cells in the pancreas, resulting in little to no insulin production.

Without sufficient insulin, glucose (sugar) cannot enter the body's cells for energy, leading to high blood sugar levels.

2. Type 2 Diabetes: This form of diabetes is characterized by insulin resistance, where the body's cells become less responsive to the effects of insulin.

Over time, the beta cells may also fail to produce enough insulin to compensate for the increased demand. Type 2 diabetes is often associated with factors such as obesity, sedentary lifestyle, and genetic predisposition.

The failure of beta cells to function properly disrupts the normal regulation of blood sugar, leading to elevated glucose levels and potential complications associated with diabetes.

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The optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.

To use the formulas from section 6.2 of the textbook to find the optimal tableau, we need to start with the initial feasible tableau, which has the following form:

Basis x1 x2 s1 s2 RHS

s1 2 1 1 0 4

s2 1 1 0 1 2

z -1 1 0 0 0

The first step is to identify the pivot element, which is the smallest positive ratio of the right-hand side (RHS) to the coefficient of the basic variable in each row. In this case, the ratios are:

s1: 4/2 = 2

s2: 2/1 = 2

Since both ratios are equal, we choose the variable with the smallest coefficient in the objective function as the entering variable. In this case, that is x1.

The second step is to perform the pivot operation, which involves dividing the pivot row by the pivot element and subtracting a suitable multiple of the pivot row from each of the other rows to eliminate the x1 variable from them. The result is a new tableau:

Basis x1 x2 s1 s2 RHS

s1 1 0 1/2 -1 2

x1 1 1 0 1 2

z 0 2 1 1 2

The new tableau shows that x2 and s1 are the basic variables in the optimal solution, with values of 2 and 2, respectively. The optimal value of the objective function is also shown in the tableau, which is 2.

Therefore, the optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x - 2)(x + 4)

=x(x + 4) -2(x + 4)

=x^2 + 4x - 2x - 8

=x^2 + 2x - 8

(x + 1)(x + 6)

=x(x + 6) +1(x + 6)

=x^2 + 6x + x + 6

=x^2 + 7x + 6

(x - 4)(x + 2)

=x(x + 2) -4(x + 2)

=x^2 + 2x - 4x - 8

=x^2 - 2x - 8

(x + 5)(x - 3)

=x(x - 3) +5(x - 3)

=x^2 - 3x + 5x - 15

=x^2 + 2x - 15

(x - 6)(x - 2)

=x(x - 2) -6(x - 2)

=x^2 - 2x - 6x + 12

=x^2 - 8x + 12

a) The set of points satisfying the equation |z| = 2 is a circle with radius 2 and center at the origin.

b) The set of points satisfying the inequality |z - 2i| < 3 is an ellipse with center at 2i and semi-major axis 3.

a) The absolute value of a complex number is its distance from the origin. So, |z| = 2 means that all points satisfying this equation are 2 units away from the origin. This forms a circle with radius 2 and center at the origin.

b) The distance between a complex number z and the number 2i is |z - 2i|. So, |z - 2i| < 3 means that all points satisfying this inequality are less than 3 units away from 2i. This forms an ellipse with center at 2i and semi-major axis 3.

Here is a sketch of the two sets of points:

[asy]

import graph;

size(150);

real r = 2;

real a = 3;

pair O = (0,0), C = (2,0);

draw(Circle(O,r));

draw(Circle(C,a));

label("|z| = 2", (r,0), N);

label("|z - 2i| < 3", (3.1,0), N);

[/asy]

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a) The set of points satisfying the equation |z| = 2 is a circle with radius 2 and center at the origin.

b) The set of points satisfying the inequality |z - 2i| < 3 is an ellipse with center at 2i and semi-major axis 3.

a) The absolute value of a complex number is its distance from the origin. So, |z| = 2 means that all points satisfying this equation are 2 units away from the origin. This forms a circle with radius 2 and center at the origin.

b) The distance between a complex number z and the number 2i is |z - 2i|. So, |z - 2i| < 3 means that all points satisfying this inequality are less than 3 units away from 2i. This forms an ellipse with center at 2i and semi-major axis 3.

Here is a sketch of the two sets of points:

[asy]

import graph;

size(150);

real r = 2;

real a = 3;

pair O = (0,0), C = (2,0);

draw(Circle(O,r));

draw(Circle(C,a));

label("|z| = 2", (r,0), N);

label("|z - 2i| < 3", (3.1,0), N);

[/asy]

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Answer:

a = 35

Step-by-step explanation:

\(a^2+b^2=c^2\\a^2+12^2=37^2\\a^2+144=1369\\a^2=1225\\a=35\)

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

MARK AS BRAINLIEST!!!

Answer:

Step-by-step explanation:

B

Answer:

B

Step-by-step explanation:

Answer:

: L = r * θ = 15 * π/4 =

Step-by-step explanation:

Jose made $84.00 for the 4 hours of overtime that he worked.

Jose worked 44 hours, which is 4 hours more than the regular working week of 40 hours.

This means that he worked 4 hours of overtime.

To calculate the amount of pay for overtime hours, we need to first determine the overtime pay rate, which is usually 1.5 times the regular pay rate for each hour of overtime.

Therefore, the overtime pay rate for Jose is:

1.5 x $14.00 = $21.00/hour

Now calculate the total amount of pay for the overtime hours by multiplying the overtime pay rate by the number of overtime hours worked:

$21.00/hour x 4 hours = $84.00

Therefore, Jose made $84.00 for the 4 hours of overtime that he worked.

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Answer:

10.6666666667

Step-by-step explanation:

Answer:

Option (B)

Step-by-step explanation:

If A = \(\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\) and B = \(\begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}\)

Multiplication of these matrices,

A.B = \(\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\times \begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}\)

      = \(\begin{bmatrix}(1(-2)+3(3) & 1(1)+3(4)\\ (-2)(-2)+5(3) & 1(-2)+5(4)\end{bmatrix}\)

      = \(\begin{bmatrix}7 & 13\\ 19 & 18\end{bmatrix}\)

Therefore, Option (B) will be the answer.

After 44 minutes is the temperature of each piece of metal the same.

The mathematical description of two things that are equal—one on each side of a "equals" sign—is called an equation. Equations help us address problems in our daily lives. Most of the time, we seek pre algebra assistance to answer challenges in real life. The fundamentals of math are found in pre-algebra ideas.

Given,

A piece of metal at 20°C is warmed at a steady rate of 2 degrees per

the same time, another piece of metal at 240°C is cooled at a steady rate of 3 degrees per minute.

Let time be t

Equation,

20 +2t = 240 - 3t

2t + 3t = 240 - 20

5t  = 220

t = 44

After 44 minutes is the temperature of each piece of metal the same.

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Answer:

X =50                  Y is also 50 since they are vertical angles

Step-by-step explanation:

70+ 60 + X = 180  (the 3 angles form a straigh line = 180 )

130 +X =180

X = 180-130

X=50