A local hotel wants to estimate the average age of its guests that are from out-of-state. Preliminary estimates are that standard deviation of population of guests from out-of-state is 30. How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence? a. 12 b. 11 c. 139 d. 138

The length of CD  to 3 significant figures is 12.7

What is the  length of CD ?

Given that;

AB=6cm AC=12cm.

Using Pythagoras in triangle ABC

[tex](AC)^{2} =(AB)^{2}+(BC)^{2}[/tex]

[tex](12)^{2} =(6)^{2}+(BC)^{2}[/tex]

[tex]144 - 36 = (BC)^{2}[/tex]

[tex](BC)^{2} =108[/tex]

[tex](BC)=\sqrt{108}[/tex]

We can then use Law of sine as;

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

[tex]\frac{CD}{sin90} =\frac{ \sqrt{108} }{sin55}[/tex]

[tex]\frac{CD}{1} = \frac{\sqrt{50} }{sin55}[/tex]

[tex]CD=12.6866[/tex]

Answer:

[tex]1/6[/tex]

Step-by-step explanation:

When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.

Case 1: The difference of scores is 4.

The possible outcomes can be [tex](1,5), (5,1), (2,6) \text{ and }(6,2).[/tex] i.e. 4 number of cases are possible.

Case 2: The difference of scores is 5.

The possible outcomes can be [tex](1,6) \text{ and } (6,1)[/tex]. i.e. 2 number of cases.

Here, total number of favorable cases are 4 + 2 = 6.

Total number of cases, when two fair dice are rolled, are 36.

These cases are:

[tex][(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\..\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]}[/tex]

Formula:

[tex]\text{Probability of an event = } \frac{Number\ of\ favorable\ cases}{Total\ number\ of\ cases}[/tex]

Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is [tex]\frac{6}{36}[/tex] i.e. [tex]\frac{1}{6}[/tex].

Hence, the required probability is [tex]\frac{1}{6}[/tex].

9514 1404 393

Answer:

  8 inches

Step-by-step explanation:

The product of length, width, and height is the volume.

  V = LWH

  H = V/(LW) = 64/(2·4) = 8

The height of the new box should be 8 inches.

To create a box that is 2 inches wide, 4 inches long, and has a volume of 64 cubic inches, the box should be made 8 inches tall.

The question asks how tall a new box should be if it is 2 inches wide, has a length of 4 inches, and must have a volume of 64 cubic inches. To find the height of the box, we use the formula for the volume of a rectangular prism (box), which is Volume = length × width × height.

Given the volume (V) is 64 cubic inches, the width (w) is 2 inches, and the length (l) is 4 inches, we can rearrange the formula to solve for the height (h):

h = V / (l × w)
= 64 / (4 × 2)
= 64 / 8
= 8 inches

Therefore, to create a new box with the specified dimensions and volume, Vector should make the box 8 inches tall.

The dot product of u = 9i+4j and v = 3i- j is 23.

The dot product of two vectors can be calculated by multiplying their corresponding components and then summing them up. In this case, the dot product of u = 9i+4j and v = 3i- j is:

u · v = (9)(3) + (4)(-1) = 27 - 4 = 23

So, the dot product of u and v is 23.

Answer:

Step-by-step explanation:

The question is incomplete since they do not give information about the Car type 3.

We will do it in a generic way, we will say that the Car type 3 has a mean of M and a standard deviation SD.

We would be:

P (CT3 <550) = P [z <(550 - X) / SD]

Now if we give it values, for example that X = 600 and SD = 120

It would remain:

P (CT3 <550) = P [z <(550 - 600) / 120]

P (CT3 <550) = P [z <-0.42]

We look for this value in the normal distribution table (attached) and it shows us that the probability is approximately 0.3372, that is, 33.72%

What you need to do is replace the X and SD values of theCar type 3 in the equation above how I just did and you will get the result.

Answer:

18

Step-by-step explanation:

3(2)+2(4)+4=

6+8+4=18

The solution to the equation 3x + 2y + 4 when x = 2 and y = 4 is 18.

In the equation given, we are asked to find the value of 3x + 2y + 4 when x = 2 and y = 4.

First, let's substitute these values into the equation. We get 3×2 + 2×4 + 4, which simplifies to 6 + 8 + 4.

Adding these together gives us a total of 18. Therefore, the solution to the following equation is 18.

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#SPJ2

Answer:

  see below

Step-by-step explanation:

The component form of the polar coordinate pair (r, θ) is ...

  (r, θ)  ⇔  (r·cos(θ), r·sin(θ))

Then your point (2, 60°) translates to ...

  (2, 60°) ⇔ (2·cos(60°), 2·sin(60°)) = (2(1/2), 2(√3)/2) = (1, √3)

Answer:

(x/4) +1 OR (4/x)+1

Step-by-step explanation:

Answer:

x2 - 15 = 2x

x2 - 2x -15 = 0

(x - 5)(x + 3) = 0

X-5 = 0 or x + 3 = 0

Potential solutions are -3 and 5

Answer:

2

5

1

4

3

p-by-step explanation:

did the assignment

Answer:

a) The interest is compounded monthly, so should use the compound interest formula.

b) [tex]A(t) = 3000(1.0067)^{12t}[/tex]

c) Linda would have $14898.33 in her account after 20 years.

Step-by-step explanation:

Compound Interest Formula:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years for which the money is invested.

Continuous Interest Formula:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial amount invested and r is the interest rate, as a decimal.

For Linda: a. State which formula should be used to solve this problem.

The interest is compounded monthly, so should use the compound interest formula.

b. Write the function for Linda.

Invests 3000, so [tex]P = 3000[/tex]

8% interest, so [tex]r = 0.08[/tex]

Compounded monthly. An year has 12 months, so [tex]n = 12[/tex]

Then

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A = 3000(1 + \frac{0.08}{12})^{12t}[/tex]

[tex]A = 3000(1.0067)^{12t}[/tex]

c. Determine how much Linda would have in her account after 20 years

This is A(20)

[tex]A = 3000(1.0067)^{12*20} = 14898.33[/tex]

Linda would have $14898.33 in her account after 20 years.

For Linda the formula that would be used to solve this problem is:   FV = A (1 + r)^nm

For Linda, the function is: $3000(1.0067)^12n.

The amount Linda would have in her account after 20 years is $14,780.41.

The formula for determining the future value of an amount of money is:  FV = A (1 + r)^nm

Where:

Value after 20 years $3000(1.0067)^(12 x 20) =   $14,780.41.

A similar question was answered here: https://brainly.com/question/16035671

Step-by-step explanation:

In order to find the area, we need to find the radius. In order to find the radius, we need to divide 10 by 2 because the radius is half of the diameter.

10 ÷ 2 = 5

[tex]A=r^2\pi[/tex]

[tex]A=(5)^2\pi[/tex]

[tex]A=25\pi[/tex]

[tex]A=78.5[/tex]

So, the area of the circle (given that the diameter is 10) is 78.50 in².

Answer:

The 95% confidence interval for the mean is (3.249, 4.324).

We can predict with 95% confidence that the next trial of the paint will be within 3.249 and 4.324.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

As the population standard deviation is not known, we will use the sample standard deviation as an estimation.

The sample mean is:

[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4+5.2+3+4.8)\\\\\\ M=\dfrac{56.8}{15}=3.787[/tex]

The sample standard deviation is:

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(3.4-(3.787))^2+(2.5-(3.787))^2+(4.8-(3.787))^2+...+(4.8-(3.787))^2]}\\\\\\[/tex][tex]s=\sqrt{\dfrac{1}{14}\cdot [(0.15)+(1.66)+(1.03)+...+(1.03)]}[/tex]

[tex]s=\sqrt{\dfrac{13.197}{14}}=\sqrt{0.9427}\\\\\\s=0.971[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=3.787.

The sample size is N=15.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.971}{\sqrt{15}}=\dfrac{0.971}{3.873}=0.2507[/tex]

The t-value for a 95% confidence interval is t=2.145.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.145 \cdot 0.2507=0.538[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 3.787-0.538=3.249\\\\UL=M+t \cdot s_M = 3.787+0.538=4.324[/tex]

The 95% confidence interval for the mean is (3.249, 4.324).

To estimate a 95% prediction interval, calculate the sample mean and standard deviation, then use the t-distribution to apply the formula that includes the t-value for 95% confidence level and the sample size.

To find a 95% prediction interval for the drying time for the next trial of latex paint, we need to use the measurements provided with the assumption that they represent a random sample from a normally distributed population.

However, before we can provide the prediction interval, we must first calculate the sample mean and the sample standard deviation from the given data. With those, we can then use the t-distribution to find the prediction interval, which will take the form of:

Sample Mean ± (t-value * Sample Standard Deviation * √(1 + 1/n))

Where 'n' is the number of observations and the t-value is determined from the t-distribution table for (n-1) degrees of freedom at the 95% confidence level.

Once calculated, this interval estimates the range within which we can expect the drying time for the next trial of paint to fall, with 95% confidence.

Answer:

Step-by-step explanation:

Given that,

The reference angle is 35°

It lies in the fourth quadrant.

The reference angle is the positive acute angle that can represent an angle of any measure.

The reference angle  must be < 90∘.

In radian measure, the reference angle  must be < π/ 2.

Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

Since the reference angle is less than 35°, then, the reference angle is positive,

The negative angle is 360 - 35 = 325°

So, the positive reference angle is 35° and the negative reference angle is 325°

This question is based on concept of reference angle.Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

Given:

The reference angle is 35º and its terminal side lies in [tex]\bold{4^{th}}[/tex] Quadrant .

By the definition of reference angle,

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

Thus, positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle.Therefore, it must be < 90°.

In radian measure, it must be less than  [tex]\bold{\dfrac{\pi }{2}}[/tex].

Therefore, the reference angle is less than 35°. So, reference angle is positive.And the negative angle is 360 - 35 = 325°.

Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

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Answer:

Lacrosse = 62 students

Swimming = 62 students

Soccer = 124 students

Football = 186 students

Step-by-step explanation:

Based on the information, we can draw some equations

1.    Lacrosse = Swimming

2.   Soccer = 2 * Lacrosse

3.   Football = 3 * Swimming

4.   Football + Soccer + Swimming + Lacrosse = 434

Lets solve for once sport at a time, I will start with Football.

I will put equation 1, 2 and 3 into equation 4

3Sw + 2L + L + L = 434

We can now again put equation 1 into the new equation 4

3L + 2L + L + L = 434

Simplify

7L = 434

L = 434 ÷ 7

L = 62 students

Since L = Sw, 62 students did swimming also

We can put L into equation 2 to solve for So

So = 2 * 62

So = 124 students

And now we can put Sw into equation 3 to solve for F

F = 3 * 62

F = 186 students

Answer:

112

Step-by-step explanation:

A supplementary angle is 1 or more angles that add up to 180 degrees. So, the 2 angles we have are 2x and 3x + 10, and those add up to 180.

In order to make an equation for this, we need to add 2x and 3x + 10 and equal it to 180.

5x + 10 = 180

Now that we have our equation, the goal is to isolate the variable. The most immediate step I see is to subtract 10 from both sides so 5x will be alone on one side of the equation.

5x = 170

Now, to ultimately isolate the variable, we must divide both sides by 5 so that x will be alone.

170 / 5 is 34

5x / 5 is x

x = 34

Now, we plug in our value of x into 3x + 10 to find out what the measurement is equal to.

3(34) + 10 = y

102 + 10 = y

112 = y

3x + 10 is equal to 112.

Answer:

The 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).

Step-by-step explanation:

The (1 - α)% confidence interval for the population standard deviation is:

[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]

The information provided is:

n = 26

s = 4.8 minutes

Confidence level = 90%

Compute the critical values of Chi-square as follows:

[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652[/tex]

[tex]\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611[/tex]

*Use a Chi-square table.

Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:

[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]

     [tex]=\sqrt{\frac{(26-1)\times 4.8^{2}}{37.652}}\leq \sigma\leq \sqrt{\frac{(26-1)\times 4.8^{2}}{14.611}}\\\\=3.9113\leq \sigma\leq 6.2787\\\\\approx 3.9 \leq \sigma\leq6.3[/tex]

Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).

Answer:

91.2

Step-by-step explanation:

use formula v=1/3 by pie r squared  then the hieght

Final answer:

To calculate the volume of a cone given its height and the circumference of its base, first find the radius using the circumference formula, then apply the volume formula for a cone. In this case, the volume is approximately 92.4 cubic inches.

Explanation:

To find the volume of a right circular cone with a height of 11.1 inches and a base circumference of 17.6 inches, we first need to calculate the radius of the base. The formula for the circumference of a circle is C = 2πr. We can solve for r (radius) by rearranging the formula: r = C / (2π). Plugging in the given circumference, we get r = 17.6 / (2π) ≈ 2.8 inches.

Next, we use the formula for the volume of a cone, which is V = (1/3)πr²h. Substituting in our values for r (2.8 inches) and h (11.1 inches), we obtain V = (1/3)π(2.8)²(11.1) ≈ 92.4 cubic inches.

Therefore, the volume of the right circular cone is approximately 92.4 cubic inches, rounding to the nearest tenth.

Answer:

0.2 Cup per serving

Step-by-step explanation:

Mia used 4.5 cups of orange juice in a punch that serve 6 people.

Mia's Serving of orange juice per serving=4.5/6=0.75 cup per serving

Isaac used 2.75 cups of orange juice in a punch that serves 5 people.

Isaac's Serving of orange juice per serving=2.75/5=0.55 cup per serving

Difference of orange juice in cup per serving=0.75-0.55=0.2 cup per serving

There was 0.2 cup more orange juice in one serving of Mia's punch.

Answer:

0.2 is the correct answer

Step-by-step explanation:

Answer:

Slope is 2

Step-by-step explanation:

The number before x is the slope value.

[tex]\dotfill[/tex]

We want to find the slope for the following line:

[tex]\bf y=2x-9[/tex]

First, notice the form of the given  equation is in slope intercept (y=mx+b) form. In this formula, m is the slope and b is the y-intercept. So to find the value of m, compare the equation to the slope int. formula.

[tex]\sf y=mx+b[/tex] ← formula

[tex]\sf y=2x-9[/tex] ← the slope is 2

>>> Therefore, the slope is 2.

Answer:

b.) -2= -2

Step-by-step explanation:

i got it correct

Answer:

-2=-2

Step-by-step explanation:

Answer:

This is what it looks like and also so Regretfulderey can get brainliest

Answer:

Step

[tex] \frac{1}{2} \times (4 + 12) \times 5[/tex]

there

Answer:

Yes, they form a partition

Step-by-step explanation:

For a group of sets to be considered a partition of set A (currently enrolled students), all of the elements in set A must be contained in the subsets that form the partition and no individual element can be present in more than one subset.

In this situation, take set A0 for instance, all students whose ID numbers begin with 0 will be in this set and in this set alone. The same can be said for Ai  where i ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Since no other possible value can be assigned for the first digit of an student ID, it is correct to affirm that sets A0, …, A9 form a partition of the set of currently enrolled students.

Final answer:

The sets A0, A1, ..., A9, where each set consists of students whose ID starts with a specific digit, form a partition of the set of all currently enrolled students because each set is non-empty, the sets are mutually exclusive, and their union represents the entire set of students.

Explanation:

To understand if the sets A0, A1, ..., A9, form a partition of the set of currently enrolled university students based on their 8-digit ID numbers starting with digits 0 through 9, three conditions must be met: each set must be non-empty, the sets must be mutually exclusive, and their union must form the entire set of currently enrolled students.

Thus, the sets A0 through A9 form a partition of the set of all currently enrolled students.

Answer:

  5 miles

Step-by-step explanation:

The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.

  d^2 = 3^2 + 4^2 = 9 +16 = 25

  d = √25 = 5

Deborah ends 5 miles from her start.

Answer:

11-5 = 6

Step-by-step explanation:

Answer:

Maricopa Success invested $55,000 in stocks

Maricopa Success invested $80,000 in bonds

Maricopa Success invested $50,000 in CDs

Step-by-step explanation:

Let S denotes stocks, B denotes bonds and C denotes CDs.

Maricopa's Success scholarship fund receives a gift of $185,000 which she invests in stocks. bonds, and CDs.

Mathematically,

S + B + C = 185,000      eq. 1

Money is invested in stocks at interest = 11.3% = 0.113

Money is invested in bonds at interest = 5.5% = 0.055

Money is invested in CDs at interest = 5% = 0.05

Annual income from the investments is $13,115

Mathematically,

0.113S + 0.055B + 0.05C = 13,115      eq. 2

Maricopa Success invests $30,000 more in bonds than in CDs.

Mathematically,

B = C + 30,000       eq. 3

Substitute the eq. 3 into eq. 1

S + B + C = 185,000

S + (C + 30,000) + C = 185,000

S + 2C + 30,000 = 185,000

S + 2C = 185,000 - 30,000

S + 2C = 155000      eq. 4

Substitute the eq. 3 into eq. 2

0.113S + 0.055B + 0.05C = 13,115

0.113S + 0.055(C + 30,000) + 0.05C = 13,115

0.113S + 0.055C + 1650 + 0.05C = 13,115

0.113S + 0.105C + 1650 = 13,115

0.113S + 0.105C = 13,115 - 1650

0.113S + 0.105C = 11,465      eq. 5

Now we have to equations and two unknowns

S + 2C = 155,000      eq. 4

0.113S + 0.105C = 11,465      eq. 5

Multiply eq. 4 by 0.113 and subract it from eq. 5

0.113S + 0.226C = 17,515

subtract it from eq. 5

0.113S + 0.105C = 11,465      eq. 5

0.113S + 0.226C = 17,515

-0.121C = -6050

0.121C = 6050

C = 6050/0.121

C = 50,000

Substitute the value of C into eq. 3

B = C + 30,000

B = 50,000 + 30,000

B = 80,000

Substitute the value of B and C into eq. 1

S + B + C = 185,000

S + 80,000 + 50,000 = 185,000

S = 185,000 - 80,000 - 50,000

S = 55,000

Therefore,

Maricopa Success invested $55,000 in stocks

Maricopa Success invested $80,000 in bonds

Maricopa Success invested $50,000 in CDs

Verification:

S + B + C = 185,000       eq. 1

55,000 + 80,000 + 50,000 = 185,000

185,000 = 185,000  (satisfied)

0.113S + 0.055B + 0.05C = 13,115      eq. 2

0.113(55,000) + 0.055(80,000) + 0.05(50,000) = 13,115

6215 + 4400 + 2500 = 13,115

13,115 = 13,115  (satisfied)

B = C + 30,000       eq. 3

80,000 = 50,000 + 30,000

80,000 = 80,000  (satisfied)

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.