A travel trailer is bought at the price of $35,000. The price decreases at the rate of .25 every year (t). The exponential expression is 35,000(.75)^t. Find the price of the trailer at 5 years.

Answer: 3.73

Step-by-step explanation:

Answer: BD = 108

Step-by-step explanation:

In a parallelogram, the opposite sides are congruent and the diagonals bisect each other. It means that they bisect at a midpoint that divides them equally.

Therefore,

AB = DC

AD = BC

BD = AC

Also BE = ED. This means that

7x - 2 = x^2 - 10

x^2 - 10 +2 - 7x = 0

x^2 - 7x -8 = 0

Solving the quadratic equation with factorization method,

x^2 + x - 8x -8 = 0

x(x + 1) -8(x + 1) = 0

x - 8 = 0 or x + 1 = 0

x = 8 or x = -1

Since x cannot be negative,

x = 8

BE = 7×8 - 2 = 54

ED = 8^2 - 10 = 54

BD = BE + ED = 54 +54 = 108

Answer:

The total number of tennis ball did store sell in all is 1,356  

Step-by-step explanation:

Given as :

The number of sleeves of tennis ball in each box = 4

The number of tennis ball in each sleeve = 3

So, The total tennis ball in each box = 3 × 4 = 12

Now,

The selling of boxes on Saturday = 67

The selling of boxes on Sunday = 46

So, The Total number of boxes sold = 67 + 46 = 113

∵ The total tennis ball in each box = 12

∴ The total number of tennis ball did store sell in all = 113 × 12 = 1,356

Hence The total number of tennis ball did store sell in all is 1,356  Answer

Answer:

1356 Balls

Step-by-step explanation:

We first want to find out how many balls are in each box. There are [tex]$3\cdot4=\bold{12}$[/tex]balls per box. Then we find out how many boxes they sold. They sold [tex]$46+67=113$[/tex] boxes. Now we multiply.[tex]$113\cdot12=\bold{1356}$[/tex] balls/

Answer:

Minimum number of student is 4951

Step-by-step explanation:

4950 wont work because there are 99 student in each state

99 *50 =4950

there are 100 students comes from same state. So from pigeon hole principle there are at least [ 4951/50] = 100 come from state

Answer:

Yes, those are the first triangular numbers.

There is a relation between the number and its position but isn't direct.

Step-by-step explanation:

The triangular numbers can be represented by equilateral triangles, but also can be represented by:

[tex]T_{n} = \frac{n(n+1)}{2}[/tex]

where:

n, represents the position

T represent the triangular number.

As you may see, the equation of triangular numbers is not a straight line. It is a parable. For that reason there isn't a direct variation.

Answer:

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Given information:

A group of middle management employees approximated a normal distribution.

Population mean [tex]\mu[/tex] = $37,200

Population standard deviation [tex]\sigma[/tex] = $800

About 68 percent of the incomes lie between two incomes and we need to find those two incomes.

We know that 68% data lies in the interval [tex][\mu-\sigma,\mu+\sigma][/tex].

[tex]\mu-\sigma=37,200-800=36,400[/tex]

[tex]\mu+\sigma=37,200+800=38,000[/tex]

About 68 percent of the incomes lie between what two incomes $36,400 and $38,000.

Therefore, the correct option is B.

Answer: b. $36,400 and $38,000

Answer:

288

Step-by-step explanation:

Answer: 50 children

18 women

22 men

Step-by-step explanation:

There were 90 people at a party. The persons consists of men, women and children. The men and women are adults.

Let m = number of men at the party

Let w = number of women at the party

Let c = number of children at the party

There were four more men than women. It means

w = m - 4

There were 10 more children than adults. It means

m + w + 10 = c

c = m + w + 10

Substituting w = m- 4 into the above equation, it becomes

c = m + m- 4 + 10 = 2m+ 6

Note: adults = sum of men and women

There were 90 people at a party. It means

m + w + c = 90

Substituting c = 2m+6 and w = m-4, it becomes

m + m-4 + 2m+6 = 90

4m = 90 - 18 = 88

m = 88/4= 22

w = m- 4 = 22-4

w = 18

c = 2m + 6 = 44 + 6 = 50

c = 50

The measure of PQ is 12.72

We have the right triangle ΔPQR and we want to know the measure of PQ. PQ is opposite to ∠R, so from trigonometry we know that:

[tex]sin(\alpha)=\frac{Opposite \ side}{Hypotenuse} \\ \\ \\ Here: \\ \\ \alpha=m\angle R=58^{\circ} \\ \\ Opposite \ side=\overline{PQ} \\ \\ Hypotenuse=\overline{RQ}=15 \\ \\ \\ So: \\ \\ sin(58^{\circ})=\frac{\overline{PQ}}{15} \\ \\ \\ Isolating \ \overline{PQ}: \\ \\ \overline{PQ}=15sin(58^{\circ}) \\ \\ \overline{PQ}=15(0.848)\\ \\ \boxed{\overline{PQ}=12.72}[/tex]

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Answer:

C=3

Step-by-step explanation:

12c-4=14c-10        Given

6=2c                      Add 10 and subtract 12 from both sides            

c=3                       Divide by 2 to isolate the c      

The value of c is 3 in the equation 12c−4=14c−10.

The given equation is 12c−4=14c−10

Twelve times of c minus four equal to forteen times c minus ten.

We have to find the value of c.

c is the variable in the equation.

Take the variable terms on one side and constants on other side.

12c-14c=4-10

-2c=-6

Divide both sides by 2:

c=3

Hence, the value of c is 3 in the equation 12c−4=14c−10.

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Answer:

t= 3.1 years

Step-by-step explanation:

A = A_0 e kt

Half life(1/2) = 26 yrs

1/2 = 1_0 e^k.26

ln(1/2) = ln(e^26k)

26k. ln(e) = ln(1/2)

k = 1/26* ln(1/2)

k = -0.0267

A = A_0 e^kt

0.92 = 1.e^(-0.0267)t

ln(0.92) = ln(e^(-0.0267)t

-0.0267t .ln(e) = ln(0.92)

t = ln(0.92) / -0.0267

t = 3.122

t = 3.1years (approximate to 1 d.p)

Final answer:

The half-life of a substance is used to calculate how long it will take for a certain amount of it to decay. In this case, it will take approximately 3.2 years for the sample to decay to 92% of its original amount using the given half-life of 26 years and the exponential decay model.

Explanation:

The half-life of a substance is the time it takes for half of it to decay. Given that the half-life of a certain substance is 26 years, we can use the exponential decay model A = A0ekt, where k is the decay constant. To solve for the remaining 92% of the substance, we would set A to 0.92A0. The decay constant k is related to the half-life (t1/2) by the equation k = -ln(2) / t1/2. So, let's solve for k and then use it to find the time (t) it takes for the sample to decay to 92% of its original amount.

First, find the decay constant k using the half-life:

k = -ln(2) / 26 yrs = -0.0267 per year (rounded to four decimal places)

Now, set up the equation:

0.92A0 = A0e(-0.0267)t

Divide both sides by A0 and take the natural logarithm:

ln(0.92) = -0.0267t

Solving for t gives:

t = ln(0.92) / -0.0267 ≈ 3.2 years (rounded to one decimal place)

It will take approximately 3.2 years for the sample to decay to 92% of its original amount.

Answer:

The answer is $1000.

Step-by-step explanation:

The policy was issued with a $500 deductible and a limit of four deductibles per calendar year.

As given that two claims were paid in September 2013, each incurring medical expenses in excess of the deductible.

So, the family's out-of-pocket medical expenses for 2013 will be :

[tex]500+500=1000[/tex] dollars

As the limit was up to 4 deductibles in a calendar year, and in 2013, there were 2 claims, so that sums up to be $1000.

The family's out-of-pocket medical expenses for 2013 would be $1000, as they paid the $500 deductible for each of the two claims made that year, with their health insurance policy limiting to four deductibles per year.

The subject of the question involves calculating the out-of-pocket medical expenses for a family under their health insurance policy, which includes understanding how deductibles work. In the scenario given, the family purchased a policy with a $500 deductible and a limit of four deductibles per calendar year. In 2013, they made two claims where each exceeded the deductible amount. Therefore, their out-of-pocket expenses for 2013 would be two times the deductible amount, since the policy has a limit of four deductibles per year but only two claims were filed and paid within that year.

Mathematically, this can be calculated as:

Total out-of-pocket expenses for 2013: $500 + $500 = $1000.

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65 mph means in 1 hour you drive 65 miles.

To find out how many feet you drive in 1 second you need to convert the above in terms of feet and secs

1 hour = 60 minutes and 1 minute has 60 secs

So 1 hour has 60* 60 secs = 3600 secs.

1 mile - 5280 feet

65 miles = 65*5280 feet

So in 3600 secs you are driving 65 * 5280 feet

When traveling at 65 mph and taking their eyes off the road for four seconds, the driver will cover approximately 4.33 miles in that time.

When driving at a speed of 65 mph, the driver is covering 65 miles in one hour. To find the distance traveled in four seconds, we need to convert the time from seconds to hours, as the speed is given in miles per hour.

Dimensional analysis:

Given speed: 65 miles per hour (65 mph)

Time taken: 4 seconds

Step 1: Convert seconds to hours

1 minute = 60 seconds

1 hour = 60 minutes

4 seconds = 4/60 minutes = 0.0667 hours

Step 2: Calculate the distance traveled

Distance = Speed × Time

Distance = 65 mph × 0.0667 hours

Detailed calculation:

Distance = 65 mph × 0.0667 hours

Distance ≈ 4.33455 miles

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Answer:

  y = -2sin(x) + 2

Step-by-step explanation:

The sin(x) function is zero at x=0, so you want a sine function of some sort. The slope of your graph at x=0 is negative so you want a sine function with a negative multiplier. The appropriate choice is the one shown above.

__

The cos(x) function is 1 at x=0, so any graph involving the cosine will not go through the point (0, 2) the way your graph does.

The volume of the cylindrical pipe is approximately  412 cubic feet.

Given:

- Diameter of the pipe = 5 ft

- Length of the pipe = 21 ft

First, we need to find the radius r of the cylinder. The diameter is 5 ft, so the radius is half of that, which is [tex]\( \frac{5}{2} = 2.5 \)[/tex] ft.

[tex]\[ \text{Volume} = \pi r^2 h \][/tex]

Substituting the given values:

[tex]\[ \text{Volume} = 3.14 \times (2.5)^2 \times 21 \]\[ \text{Volume} = 3.14 \times 6.25 \times 21 \]\[ \text{Volume} = 3.14 \times 131.25 \]\[ \text{Volume} \approx 412.425 \, \text{cubic feet} \][/tex]

Rounding to the nearest whole number, the volume of the cylindrical pipe is approximately  412  cubic feet.

Answer:

Step-by-step explanation:

The equation of a quadratic in vertex form is ...

  y = a(x -h)² +k

The coordinates of the vertex are (h, k), which means the axis of symmetry is x=h. All of your equations have h=5, so their axis of symmetry is x = 5.

__

For a > 0, the parabola opens upward; for a < 0, it opens downward. The first three equations have a > 0, so open upward. The last one opens downward.

A quadratic equation is a second-order polynomial with real solutions represented by the quadratic formula. When graphically represented, these equations produce a curved line, and in the context of physical data, only positive roots often matter. Furthermore, vectors can form a right angle triangle with their components.

The question pertains to understanding quadratic equations and their properties. In mathematical terms, a quadratic equation is a second-order polynomial equation in a single variable with a form of ax² + bx + c = 0, where x represents an unknown, and a, b, and c are constants. Note though a ≠ 0. If a =0, then the equation is linear, not quadratic. The constants a, b, and c are referred to as the coefficients of the equation.

The solutions of these quadratic equations are given by the quadratic formula: -b ± √(b² - 4ac) / 2a.

Furthermore, when plotting the relationship between any two properties of a system which can be represented through a quadratic equation, the graph is a two-dimensional plot with a curve, indicative of the quadratic relationship. Specifically for physical data, quadratic equations always have real roots often only positive values hold significance.

Lastly, it's true that a vector can form the shape of a right angle triangle with its x and y components. This statement doesn't directly involve a quadratic equation but still ties into the broader umbrella of mathematical functions.

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Answer: the speed of the submarine is 5miles per hour

Step-by-step explanation:

The submarine left Hawaii two hours before the aircraft carrier.

Let x = the speed of the submarine

The aircraft carrier traveled at 25 mph for nine hours.

After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours

Distance travelled = speed × time

Distance travelled by submarine will be 11 × x = 11x miles per hour

Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour

If they are 280 miles apart, this would be their total distance. Therefore,

225 + 11x = 280

11x = 280 - 225 = 55

x = 55/11 = 5miles per hour

To find the submarines speed, we can set up an equation using the given information and solve for the unknown variable. The speed of the submarine is found to be 5 mph.

To solve this problem, we need to set up an equation using the information given. Let's denote the speed of the submarine as 's'. The submarine traveled for two hours longer than the aircraft carrier, so the total time traveled by the submarine is '9 + 2 = 11' hours. The total distance between the vessels is given as 280 miles.

To find the speed of the submarine, we can use the formula: Distance = Speed * Time. Plugging in the given values, we can write the equation as: 280 = (25 mph * 9 hours) + (s mph * 11 hours).

Simplifying the equation gives us: 280 = 225 + 11s. Subtracting 225 from both sides gives us: 55 = 11s. Dividing both sides by 11 gives us: s = 5.

Therefore, the speed of the submarine is 5 mph.

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Final answer:

Upon setting up an equation with the given information, we find that the shop sold 275 hamburgers on Sunday.

Explanation:

To find out how many hamburgers were sold on Sunday when the hamburger shop sold a combined total of 498 hamburgers and cheeseburgers, we can set up an equation. Let's denote the number of hamburgers as H and cheeseburgers as C. We are given that there were 52 fewer cheeseburgers sold than hamburgers, so we can express this as C = H - 52.

Since the total number of burgers sold was 498, we can also set up the following equation: H + C = 498. Substituting for C, we get H + (H - 52) = 498. Solving this equation, we get 2H - 52 = 498. Adding 52 to both sides gives us 2H = 550, and dividing by 2 gives us H = 275.

Therefore, the shop sold 275 hamburgers on Sunday.

Answer:1.642 m

Step-by-step explanation:

Given

Initial Length of bridge [tex]L_0=3910 m[/tex]

temperature on cold day [tex]t_1=-5^{\circ}C[/tex]

temperature on hot day [tex]t_2=30^{\circ}C[/tex]

Change in temperature is [tex]\Delta T=30-(-5)=35^{\circ}C[/tex]

Coefficient of linear expansion of steel [tex]\alpha =12\times 10^{-6}/^{\circ}C[/tex]

and length after change in temperature is given by

[tex]L=L_0(1+\alpha \cdot \Delta T)[/tex]

[tex]\Delta =L_0\cdot \alpha \Delta T[/tex]

[tex]\Delta L=3910\cdot 12\times 10^{-6}\cdot 35[/tex]

[tex]\Delta L=1.642 m[/tex]

The Akashi Kaikyo Bridge in Japan will be longer during a warm summer day than on a cold winter day due to the thermal expansion of the steel. By calculating the linear thermal expansion using the formula ΔL = α * L * ΔT, with the coefficients for steel and the given temperature and length values, the change in length can be determined.

To understand how much longer the Akashi Kaikyo Bridge would be on a warm summer day compared to a cold winter day, we need to calculate the thermal expansion of the material that the bridge is made of, in this case, steel. The linear thermal expansion of a solid material can be calculated using the formula:

ΔL = α * L * ΔT,

where ΔL is the change in length of the material, α (alpha) is the coefficient of linear thermal expansion for the material, L is the original length of the material, and ΔT is the change in temperature.

For steel, the coefficient of linear thermal expansion α is typically about 12x10-6 1/°C. Given that the original length of the bridge, L, is 3910 m, and the temperature change, ΔT, is the difference between the summer and winter temperatures (30°C - (-5°C) = 35°C), we can substitute the given values into the formula to find ΔL. So:

ΔL = (12x10-6 1/°C) * (3910 m) * (35°C)

This will give you the change in length of the bridge between winter and summer. This thermal expansion across changing temperatures actually represents the bridge's natural ability to contract and expand without buckling, a key engineering aspect of all extended structures like bridges, roads and railways.

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150 different committees are possible

Given that a student dance committee is to be formed consisting of 2 boys and 4 girls

The membership is to be chosen from 5 boys and 6 girls

To find : number of different possible committees

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combination is given as:

[tex]n C_{r}=\frac{n !}{(n-r) ! r !}[/tex]

where "n" represents the total number of items, and "r" represents the number of items being chosen at a time

We have to select 2 boys from 5 boys

So here n = 5 and r = 2

[tex]\begin{aligned} 5 C_{2} &=\frac{5 !}{(5-2) ! 2 !}=\frac{5 !}{3 ! 2 !} \\\\ 5 C_{2} &=\frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1 \times 2 \times 1} \\\\ 5 C_{2} &=10 \end{aligned}[/tex]

We have to select 4 girls from 6 girls

Here n = 6 and r = 4

[tex]\begin{aligned} 6 C_{4} &=\frac{6 !}{(6-4) ! 4 !}=\frac{6 !}{2 ! 4 !} \\\\ 6 C_{4} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 4 \times 3 \times 2 \times 1}=15 \end{aligned}[/tex]

Committee is to be formed consisting of 2 boys and 4 girls:

So we have to multiply [tex]5 C_{2}[/tex] and [tex]6 C_{4}[/tex]

[tex]5 C_{2} \times 6 C_{4}=10 \times 15=150[/tex]

So 150 different committees are possible

Final answer:

The question is a combinatorial problem in mathematics, where the goal is to calculate the number of different committees that can be formed from 5 boys and 6 girls. To solve this, the combinations formula is applied separately to choose 2 boys from 5 and 4 girls from 6, and the results are multiplied.

Explanation:

The question asks about the number of different committees that can be formed from a group of boys and girls. This is a combinatorial problem involving calculations to find the different possible combinations that can be made using a subset of a larger set. To solve this, you would use the combinations formula which is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes the factorial of a number.

To determine how many different committees are possible, we calculate the number of ways to choose 2 boys from 5, and 4 girls from 6 separately, and then multiply these two results:

The number of ways to choose 2 boys from 5 is C(5, 2)

The number of ways to choose 4 girls from 6 is C(6, 4)

Therefore, the total number of different committees possible is C(5, 2) * C(6, 4).

Answer:

107,426, bigger

Step-by-step explanation:

Given that a soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in.

Margin of error = 0.05 inches

Since population std deviation is known we can use z critical value.

(a) i.e. for 99% confidence interval

Z critical = 2.58

[tex]2.58(\frac{0.20}{\sqrt{n} } )<0.05\\n>106.50\\n>107[/tex]

A minimum sample size of 107 needed.

b) [tex]2.58(\frac{0.40}{\sqrt{n} } )<0.05\\\\\\n>426[/tex]

Here minimum sample size = 426

Due to the increased variability in the population, a bigger sample size is needed to ensure the desired accuracy.

Final answer:

To determine the minimum sample size required for a 99% confidence interval for the mean circumference of soccer balls, use the formula n = (Z * σ / E) ^ 2. A standard deviation of 0.40 in requires a larger sample size than a standard deviation of 0.20 in.

Explanation:

To determine the minimum sample size required to construct a 99% confidence interval for the population mean, we can use the formula:

n = (Z * σ / E) ^ 2

Where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level (in this case, 99% confidence level)

σ is the population standard deviation

E is the desired margin of error (0.05 in)

(a) The minimum sample size required to construct a 99% confidence interval using a population standard deviation of 0.20 in. is 82 balls.

(b) The minimum sample size required to construct a 99% confidence interval using a population standard deviation of 0.40 in. is 324 balls.

A standard deviation of 0.40 in requires a larger sample size. This is because a larger standard deviation indicates more variability in the population, which necessitates a larger sample size to ensure the desired level of accuracy.

Answer:

a) False

b) True

Step-by-step explanation:

Given : The chance of A is [tex]\frac{1}{3}[/tex]; the chance of B is [tex]\frac{1}{10}[/tex]

To find : True or false, and explain ?

Solution :

a) If A and B are independent, they must also be mutually exclusive.

Two events are mutually exclusive, if the events cannot occur at the same time.

When events A and B are independent, then the chance of event B is not affected by event A occurring.

However, when events A and b are mutually exclusive, then the chance of event B needs to change to 0 when event A has occurred as B cannot occur when A occurs.

Which means the given statement is false.

(b) If A and B are mutually exclusive, they cannot be independent.

Two events are independent, if the probability that  one event occurs in no way affect the probability of the other event occurring.

When events A and B are mutually exclusive, then the chance of event B needs to change to 0 when event A has occurred as B cannot occur when A occurs.

Which means, the given statement is true.

It is false that independent events must be mutually exclusive, as independence indicates no effect on each other's occurrence, not impossibility of simultaneous occurrence. Conversely, if two events are mutually exclusive, they cannot be independent because the occurrence of one negates the possibility of the other, affecting the probabilities.

The question pertains to the concepts of independent and mutually exclusive events in probability theory. Here we are presented with two parts:

To further clarify, independence between two events A and B is defined mathematically as P(A and B) = P(A)P(B). Meanwhile, two events are mutually exclusive if P(A and B) = 0.

Answer:Shanny and her friends wanted to raise $2400

Step-by-step explanation:

Fundraising events were held by Shanika and her friends to help pay for repairs.

Let x = the total amount of money that Shanika and her friends want to raise during the fund raising events. After the first event, they raise $240,which is 10% of the total amount that they want to raise. This means that after the first event, they raised 10/100 ×x = 0.1x

This 0.1x that they raised is equal to $240. Therefore,

0.1x = 240

x = 240/0.1 = 2400

Shanny and her friends wanted to raise $2400

Answer:

$2,400 is the correct answer

Step-by-step explanation:

Answer:345

Step-by-step explanation:

Final answer:

To construct a 99% confidence interval for the calorie content of the energy bars, calculate the standard error, find the appropriate t-value, then compute the margin of error, and add and subtract it from the sample mean. The resulting 99% CI for the true mean calorie content is approximately (214.59, 245.41) calories.

Explanation:

To construct a 99% confidence interval (CI) for the true mean calorie content of the chocolate energy bars, we will use the sample mean, the sample standard deviation, and the t-distribution since the sample size is small. Given are the sample mean (×) is 230 calories, the sample standard deviation (s) is 15 calories, and the sample size (n) is 10.

Steps to follow:

Identify the appropriate t-value for the 99% CI, which corresponds to a two-tailed test with 9 degrees of freedom (n-1). From the t-distribution table, this value is approximately 3.25.

Calculate the standard error (SE) of the mean by dividing the standard deviation by the square root of the sample size: SE = s / √n = 15 / √10 ≈ 4.74.

Multiply the t-value by the SE to get the margin of error (ME): ME = t * SE ≈ 3.25 * 4.74 ≈ 15.41.

Finally, subtract and add the ME from the sample mean to get the lower and upper bounds of the CI: (× - ME, × + ME) = (230 - 15.41, 230 + 15.41) = (214.59, 245.41).

Therefore, the 99% confidence interval for the true mean calorie content is approximately (214.59, 245.41) calories.

Explanation of a 95% CI: A 95% confidence interval means that if we were to take 100 different random samples from the population and construct a CI for each using the same method, approximately 95 of these intervals would contain the true population mean.

Answer:

option A

Step-by-step explanation:

Notice that you need to emulate the series: 1 + 5 + 25 + 125 + 625 (a five total term series)

with the indicated sums.

The first term in the your series (addition) has to be "1". This fact already gets rid of two of the suggested sums (B, and D) because their first term is [tex]5^1=5[/tex].

So, now analyzing the options A and C, we notice that A has a sum from i=0 to 4 (which gives a total of five terms ao, a1, a2, a3, and a4, while option C has a total of six terms (from i = 0 to 5): a0, a1, a2, a3, a4, a5.

S, the obvious candidate is option A. So now evaluate the five terms corroborating that:

[tex]5^0 + 5^1+5^2+5^3+5^4=\\=1+5+25+125+625[/tex]

Therefore, option A is the answer

Final answer:

The number of different color groupings the rug manufacturer can use is found by calculating combinations of 7 colors taken 5 at a time, which is 42 different color combinations.

Explanation:

The question asks for the number of different color groupings using seven colors taken five at a time without repetitions. This is a problem of combinations, which is a part of mathematics. To find the number of combinations, we use the formula for combinations which is:
C(n, k) = n! / (k! * (n - k)!)

where n is the total number of items, k is the number of items to choose, n! is the factorial of n, and k! is the factorial of k. Applying this to the given problem:

n = 7 (since there are seven colors)

k = 5 (since we are selecting five colors for each rug)

Therefore, the number of ways to select 5 colors from 7 is:
C(7, 5) = 7! / (5! * (7 - 5)!) = 7! / (5! * 2!) = (7*6) / (2*1) = 42

Thus, there are 42 different color combinations that the manufacturer can advertise for the rugs.

Answer:

Step-by-step explanation:

In 9 minutes it would make 9/45 = 1/5 th of a revolution.

360(1/5) = 72 degrees

Coordinates:

(30cos72, +/- 30sin72) [+ for counterclockwise, - for clockwise)

(9.3ft, +/- 28.5ft)

https://answers.yahoo.com/question/index?qid=20100518113431AAvVZGM&guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAADh3so85ELjMHYh-Bs4EBfWYXngnX6lb_DUJTEV63qEAk8V25pxPyGr-fVlMatpwaXP-ke4TzkPe-OvBlV2WAwZ7iw3e4lBodLi1bt5txsrb6ccIGmS2tQHRymY0UsEqHUDfdNuDJKZRsnZ_gUPM1ChwoRTmeHDtRf2vrisw_B_e

The coordinates of the table after 9 minutes are approximately (9.3, 28.5).

Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.

Since the restaurant takes 45 minutes to complete a full counter clockwise rotation, its angular velocity is:

ω = (2π radians) / (45 minutes)

≈ 0.1396 radians per minute

If we let θ be the angle between the position of the table and the positive x-axis at time t, then the position of the table can be expressed as:

x = 30 cos(θ)

y = 30 sin(θ)

To find the position of the table after 9 minutes, we can use the angular velocity to determine the angle that the restaurant has rotated. After 9 minutes, the angle of rotation is:

θ = ωt = 0.1396 radians/minute x 9 minutes

≈ 1.256 radians

Using the values of θ and the radius of 30 ft, we can find the coordinates of the table:

x = 30 cos(1.256) ≈ 9.3

y = 30 sin(1.256) ≈ 28.5

Learn more about Coordinates here:

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Answer: w lesser than or equal to 4

Step-by-step explanation:

Dwight and Walt are building model cars.

Let d = the number of models built by Dwight.

Let w = the number of models built by Walt.

Dwight builds 7 fewer models than 4 times the number Walt builds. This can be expressed as

d = 4w - 7 - - - - - - - - - 1

Dwight builds at most 9 models. This is expressed as

d lesser than or equal to 9

From equation 1

d = 4w - 7

4w = d + 7

w = (d+7)/4

Assuming Dwight built 9 models

w = (9+7)/4 = 4

Therefore,

Walt builds at most 4 models. It is expressed as

w lesser than or equal to 4

It is shown in the attached photo

Answer:

lesser than or equal to 4 i think i tried my hardest sorry if its wrong

Step-by-step explanation:

Answer:

It is a function.

Step-by-step explanation:

[(-6 -2),(-2 6),(0,3),(3,5)]

Plot the points on a coordinate plain.

Draw vertical lines through the graph.

If any of the lines passes through the relation on more than one point it is not a function.

If not, it is a function.

Answer: It is a function

Step-by-step explanation: The vertical line test is used to determine if a relation is a function. If there are 2 points when you draw the line, then it is not a function, because a function is linear and cannot be vertical. You can solve this question is simply by looking at the numbers, and you can see that every input (x-value) has one output (y-value), and that there are no x-values that are repeated. So, therefore, it would be a function.

Answer: There are 2635 acres covered 24 hours later.

Step-by-step explanation:

Since we have given that

At time t = 0, number of acres forest fire covers = 2008 acres

We first consider the equation:

[tex]A=\int\limits^t_0 {8\sqrt{t}} \, dt\\\\A=8\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}+C\\\\A=\dfrac{16}{3}t^{\frac{3}{2}}+C[/tex]

At t=0, A= 2008

So, it becomes,

[tex]2008=C[/tex]

So, now it becomes,

[tex]A=\dfrac{16}{3}t^{\frac{3}{2}}+2008\\\\At\ t=24,\\\\A=\dfrac{16}{3}(24)^{\frac{3}{2}}+2008\\\\A=2635.06[/tex]

Hence, there are 2635 acres covered 24 hours later.

Answer: $15966.08

Step-by-step explanation:

The formula to calculate the compound amount is given by :-

[tex]A=P(1+r)^t[/tex]

, where P = initial deposit amount.

Time = Time period .

r= Rate of interest in decimal  (compounded once per year)

Given : P= $  12000

r= 7.4 percent =0.074

t= 4 years

Then, the compound amount after 4 years :

[tex]A=12000(1+0.074)^{4}\\\\=12000(1.074)^4=12000(1.33050688258)\\\\=15966.082591\approx15966.08[/tex]

Hence, compound amount after 4 years = $15966.08

After four years, Frank will owe approximately $16,140.

To determine the amount Frank will owe after four years, we can use the formula for compound interest:

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

Given:

-  P = $12,000  (the initial amount borrowed)

-  r = 7.4% = 0.074 (annual interest rate)

-  n = 1  (compounded once per year)

-  t = 4  years (time period in question)

Plugging these values into the compound interest formula, we get:

[tex]\[ A = \$12,000(1 + \frac{0.074}{1})^{1 \times 4} \] \[ A = \$12,000(1 + 0.074)^{4} \] \[ A = \$12,000(1.074)^{4} \][/tex]

Now, we calculate [tex]\( (1.074)^{4} \)[/tex]:

[tex]\[ A = \$12,000 \times 1.345 \] \[ A \approx \$16,140 \][/tex]

Finally, we multiply this by the principal amount to find out how much will be owed after four years:

[tex]\[ A = \$12,000 \times 1.345 \] \[ A \approx \$16,140 \][/tex]