Evaluate the following integrals. a. if R is the rectangle R = [0,3] x [0,1/2). = [ xsinº y dA R b. if D is the region bounded by the y-axis, yox, and yu4 If y²er dA.

Answer: Ox²1

Ox≤23

2 3

4

5 6

X

Step-by-step explanation:

Ox²1

Ox≤2

4

Oy²-3

2 3

4

5 6

X

hehehehehehehehehehhehehehehehehe

Data given to us is as follows:

Standard Deviation, S = 8.5

Sample mean, m = 212.79

Sample size, n = 42

Significance level, a = 0.05

(a)This is a one tailed hypothesis test, specifically, this is a right tailed hypothesis test, because here the population mean is checked to be greater than the value 210.

(b)The hypotheses are:

H0: =\mu 210

Ha: \mu > 210

Standard error is calculated as:

SE = S/(n^0.5) = 8.5/(42^0.5) = 1.31

Calculate the z-statistic:

z = (m-210)/SE = (212.79-210)/1.31 = 2.129

The corresponding p-value for this z-value is:

p = 0.016

Since p < a. we have to reject the null hypothesis.

So, the new mean is significantly greater, as hypothesised.

(c)In this case:

Standard error is calculated as:

SE = S/(n^0.5) = 8.5/(20^0.5) = 1.9

Calculate the z-statistic:

z = (m-210)/SE = (212.79-210)/1.9 = 1.468

The corresponding p-value for this z-value is:

p = 0.071

Since p > a. we can't reject the null hypothesis.

So, the new mean is not significantly greater, as hypothesised.

(d)As sample size increases, the standard error of the mean also increases, which decreases the chances of the data obtained as being significant.

(e)Data given to us is as follows:

Standard Deviation, S = 1

Sample mean, m = 58.03

Sample size, n = 58

Significance level, a = 0.01

The hypotheses are:

H0: \mu = 58

Ha: \mu \neq 58

Standard error is calculated as:

SE = S/(n^0.5) = 1/(58^0.5) = 0.131

Calculate the z-statistic:

z = (m-58)/SE = (58.03-58)/0.131 = 0.229

The corresponding p-value for this two tailed test using this z-value is:

p = 0.81

Since p > a. we can't reject the null hypothesis.

So, the observed mean is not significantly different from the expected mean of 58.

What is Standard Deviation?

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The rate of change is meaning the slope. The slope of A is 8, therefore, the answer would be 7.

hope this helps :)

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer:

It is V

Step-by-step explanation:

v= 468 and that is the lowest.

Answer:

3f=5

Step-by-step explanation:

f(x) = x+4

3f=4x

x<5

5<_x<7

7<_x<_10

Answer:

The sample is not random because every other household is surveyed. This means that the sample is not representative of the entire population.

Step-by-step explanation:

This is the answer because, the entire population is not being surveyed, only every other household.

the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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Answer:

The slope of a line is given by the formula "rise over run," or (y2 - y1)/(x2 - x1). In this case, the rise is 7 - 6 = 1, and the run is 4 - p.

So the slope is equal to 1/(4 - p). We are told that this slope is equal to j, so we can set up the equation:

1/(4 - p) = j

To solve for p, we can multiply both sides of the equation by (4 - p) to get:

(4 - p) = j(4 - p)

Then we can simplify the left side and rearrange the terms on the right side to get:

4 - p = 4j - jp

Then we can add p to both sides to get:

4 = 4j - jp + p

Then we can combine like terms to get:

4 = (4 - p)j + p

Then we can rearrange the terms to solve for p:

p = 4 - (4 - p)j

p = 4 - 4j + pj

p = (1 - j)p + 4 - 4j

p(1 - j) = 4 - 4j

p = (4 - 4j)/(1 - j)

This is the value of p that will make the slope of the line with points (p, 6) and (4, 7) equal to j.

Answer:

p = -5

Step-by-step explanation:

\(\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)

Given values:

Substitute the given points and slope into the slope formula:

\(\implies \dfrac{1}{9}=\dfrac{7-6}{4-p}\)

\(\implies \dfrac{1}{9}=\dfrac{1}{4-p}\)

Cross multiply:

\(\implies 4-p=9\)

Subtract 4 from both sides:

\(\implies -p=5\)

Divide both sides by -1:

\(\implies p=-5\)

Therefore, the value of p is -5.

Answer:

if an input produces more than one output, the table does not represent a function. In this case, table D is not a function. the x value 0 has three different output values, -1, 4, and 6; the input 2 also has three different output values.

Answer:

2,114,400

Step-by-step explanation:

35,250 x 60 = 2,114,400

Answer: $4,222.50.

Step-by-step explanation:

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Given that, The 99% confidence interval of a population mean is (1,7). We need to find the 95% confidence interval.As the confidence interval becomes wider as the confidence level increases. Hence, the 95% confidence interval will have a greater range than the 99% confidence interval.Confidence interval can be calculated by the formula:Confidence Interval = $\overline{X}$ ± Zα/2 (σ/√n)Where, $\overline{X}$ is the sample mean.Zα/2 is the critical valueσ is the population standard deviationn is the sample sizeNow, Zα/2 for 99% confidence interval is 2.576 as per the normal distribution table.In the same way, Zα/2 for 95% confidence interval is 1.96.Converting the above formula for 95% confidence interval:1.96 = (1,7 - $\overline{X}$)/(σ/√n)On solving the above equation, we get: σ/√n = 0.2039σ = 0.2039 √n.....(1)Also, (1,7 - $\overline{X}$)/σ = 1.96....(2)Substituting equation (1) in equation (2), we get:(1,7 - $\overline{X}$)/ (0.2039√n) = 1.96On solving this equation, we get:$\overline{X}$ = 1.47 √n + 1.7...........(3)Now, for option (a), (b), (c) and (d), we need to verify which option satisfies the equation (3).Let's check for option (a):(2+6)/2 = 4............taking the average1.47 √n + 1.7 = 4n = 19.22 squaring both sidesn = 363.6Hence, option (a) is the correct answer.Write the answer in main part:The 95% confidence interval is (2,6).Explanation:On solving the equation, we get that the option (a) is correct. Therefore, the 95% confidence interval is (2,6).Conclusion:Therefore, option (a) (2,6) is the correct 95% confidence interval.

The 95% confidence interval for the population mean is given as follows:

c) (2,6).

The 99% confidence interval for the population mean is given as follows:

(1,7).

Hence the sample mean is given as follows:

(1 + 7)/2 = 4.

Meaning that the mean of the two bounds in the interval must be of 4.

The 95% confidence interval is narrower than the 99% confidence interval, hence, considering the mean of the bounds of 4, option c is the correct option for this problem.

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According to Descartes' Rule of Signs, the given polynomial function\(f(x) = 10x^10 + 3x^5 + 8x^6 + 14x^4 + 12\) can have at most 2 positive real zeros and either 0 or 2 negative real zeros.

To apply Descartes' Rule of Signs, we need to examine the signs of the coefficients of the polynomial function.

1. Counting the positive real zeros:

2. Counting the negative real zeros:

Based on Descartes' Rule of Signs, the possible number of positive real zeros is 0 or 2, and the possible number of negative real zeros is 0 or 2.

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Step-by-step explanation:

hope it's helpful for you

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Answer:

5 x S = M (S=Students, M = money); 5 x 25 = 100

1) 180 degrees

The sum of the three angles of any triangle is equal to 180 degrees.

we get,$$a ≈ 17.011$$Therefore, the length of side a is ≈ 17.011.Hence, option (A) is the correct answer.

The Law of Cosines states that in a triangle with sides of lengths "a," "b," and "c" and opposite angles "A," "B," and "C" respectively, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab * cos(C)\)

To find the length of side "a," you would rearrange the equation as follows:

\(a^2 = b^2 + c^2 - 2bc * cos(A)\)

Then, take the square root of both sides to isolate "a":

\(a = √(b^2 + c^2 - 2bc * cos(A))\)

Once you have the values for "b," "c," and angle "A," you can substitute them into the equation and calculate the length of side "a."

Please provide the values for "b," "c," and angle "A" in order for me to assist you further

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Answer:

x = 40

smaller angle is 80

larger angle is 100

Step-by-step explanation:

Supplementary angles add up to equal 180 degrees

Hence, x + 40 + 3x - 20 = 180

( note that we just created an equation that we can use to solve for x )

We now solve for x using the equation created

x + 40 + 3x - 20 = 180

step 1 combine like terms

x + 3x = 4x

40 - 20 = 20

we now have 4x + 20 = 180

step 2 subtract 20 from each side

180 - 20 = 160

we now have 160 = 4x

step 3 divide each side by 4

160 / 4 = 40

4x / 4 = x

we're left with x = 40

we now plug in 40 for x to find the value of each angle

x + 40

* substitute 40 for x *

40 + 40 = 80

3x - 20

* substitute 40 for x *

3 ( 40 ) - 20

3 * 40 = 120

120 - 20 = 20

so the larger angle is 100 degrees and the smaller angle is 80 degrees

Answer:

one temp that ice freezes or could exist would be 32°F and at -34°C

Step-by-step explanation:

According to the EPA Clean Water Act regulations, all of the water that day is safe to drink.

To safeguard the standard of drinking water in the United States, the Safe Drinking Water Act (SDWA) was created. This legislation applies to all waters that are now or conceivably intended for consumption, whether they originate from above-ground or subsurface sources.

The Act mandates that all owners or operators of public water systems adhere to these fundamental (health-related) criteria and gives EPA the authority to set minimum standards to safeguard tap water.

The 1996 modifications to the SDWA mandate that while setting these criteria, EPA takes into account a thorough risk and cost evaluation as well as the finest peer-reviewed science.

The attainment of secondary standards is also encouraged by state governments, which may be authorized to implement these EPA regulations.

In accordance with the Act, EPA also establishes minimum requirements for state programs to safeguard underground water sources from being endangered by fluid injection underground.

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Answer:

Solution,

⇒Total students in class A=40

⇒Class B=5%

Now,

5% of 40 students

→5/100 × 40=2 students

Again,

→Number of students in class B =40 students + 2 students

                                                    =42 students

Hence, there were 42 students in class B.

Step-by-step explanation:

There are 42 students in class B which is more than 5% of the number of students in class A.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

In Class A,

there are 40 students in total.

For class B,

we have a condition that there are 5% more students in class B.

Let n be the students in class B.

So, applying the percentage formula,

we get,

n = 40 + 40 x 5 /100

n = 40 + 200/100

n = 40 + 2

n = 42.

Therefore, the number of students in class B = 42.

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The child's body weight is 28 kg. The ampicillin dose is 25 mg/kg. To find the required dose of ampicillin for the child, you need to multiply the child's weight by the dosage. 28 kg × 25 mg/kg = 700 mg The required dosage is 700 mg. A 250 mg capsule of ampicillin is given.

Therefore, the number of capsules required is calculated as follows. Number of capsules = Required dose/Capsule dosage = 700/250 = 2.8 capsules The number of capsules to be given is 2.8. Round up to 3 capsules to be given. Therefore, 3 capsules of ampicillin should be administered to the child.6a. A bottle that contains Dilantin has a concentration of 125 mg/mL and a volume of 5.0 mL. You may use the following conversion formulae to find out how many milligrams are contained in this bottle.

Dilantin bottle: 5.0 mL × 125 mg/mL = 625 mg/mL Therefore, there are 625 milligrams of Dilantin in a bottle of 5.0 mL. The oral suspension of Dilantin has a concentration of 125 mg/mL. The bottle is 5.0 mL in volume. To find the number of milligrams in the bottle, you need to multiply the concentration and volume. Concentration = 125 mg/mL Volume = 5.0 mL125 mg/mL × 5.0 mL = 625 mg The bottle contains 625 mg of Dilantin.6b. The patient requires a dose of 100 mg of Dilantin, which has a concentration of 125 mg/mL. To determine the volume of Dilantin that should be given, you may use the following conversion formula

Dilantin dose = Volume × Concentration

Rearrange the formula to solve for the volume.

Volume = Dilantin dose/Concentration

= 100/125 = 0.8 mL Therefore, 0.8 mL of Dilantin should be administered to the patient. patient requires a dose of 100 mg of Dilantin. The concentration of Dilantin is 125 mg/mL. To calculate the volume of Dilantin to be administered, we can use the formula Dilantin dose = Volume × Concentration Rearrange the formula to solve for the volume.

Volume = Dilantin dose/Concentration

= 100/125 = 0.8 mL Therefore, 0.8 mL of Dilantin should be administered to the patient.

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Answer:

B

Step-by-step explanation:

Given

7 \(\frac{3}{4}\) - \(\frac{1}{2}\)

= 7 \(\frac{3}{4}\) + (- \(\frac{1}{2}\) ) ← equivalent expression

= \(\frac{31}{4}\) - \(\frac{2}{4}\)

= \(\frac{29}{4}\) or 7 \(\frac{1}{4}\)

Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

84

Step-by-step explanation:

Divide 48 by 4

48 / 4 = 12

Now multiply the other side by 12

12 x 7 = 84

Answer:

48/4=x/7

cross multiplying

48*7= 4*x

48*7/4=x

x=336/4

x=84

The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Answer:

775

Step-by-step explanation:

62/100 * 1250