Craig has £13.40 he sees this offer in a restaurant :main courses £8.90 each.Buy one main course and get the second half price. Can he afford to buy two main courses?Show your working

Answers

Answer 1

Answer:

Yes

Step-by-step explanation:

Full price for first course:  £8.90

Half price:                           £4.45

One and one half times

 full price is then:             £13.35

Since this is less than Craig's £13.40, he can just barely afford to buy two main courses at these prices.


Related Questions

can anyone help me? I've been stuck with this problem for hours

Answers

Answer:

336.02 square centimeters

Step-by-step explanation:

The surface area is the area of all the surfaces of the prism shown.

The prism has 7 surfaces.

Top and Bottom are pentagons with side lengths of 5.

The other 5 side surfaces are rectangles with length 10 and width 5.

Note the formulas of area of pentagon and area of rectangle below:

Area of Rectangle = Length * Width

Area of Pentagon = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2[/tex] ,  where a is the side length

Lets find area of each of the surfaces:

Top Surface (Pentagon with side length 5) = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01[/tex]

Bottom Surface = same as Top Surface = 43.01

Side Surface (rectangle with length 10 and width 5) = 10 * 5 = 50

There are 5 side surfaces that are each 50 sq. cm. so area would be:

Area of 5 Side Surface = 5 * 50 = 250

Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters

After a storm damages the community center, Shanika and her friends hold fundraising events to help pay for repairs. After the first event, they raise $240, which is 10% of the total amount that they want to raise. What is the total amount of money that Shanika and her friends want to raise?

Answers

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:

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use the vertical line test to determine if the relation [(-6 -2),(-2 6),(0,3),(3,5)] is a function. explain your reason

Answers

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.

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6, 10, and 15.?Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning.

Answers

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:

A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% CI for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.

Answers

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.

Many states have banned texting while driving because it is dangerous. Suppose you are driving 65 mph and you take your eyes off the road for four seconds. How many feet will you travel in that time. What is the dimensional analysis

Answers

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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A rug manufacturer has decided to use seven compatible colors in her rugs. However, in weaving a rug, only five spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that five different colors will go into each rug—in other words, there are no repetitions of color.)A. 840B. 42C. 21D. 7

Answers

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.

A sporting good store sells tennis balls in boxes. Each box has 4 sleeves of tennis balls. Each sleeve has 3 tennis balls. The store sold 67 boxes on Saturday and 46 boxes on Sunday. How many tennis balls did the store sell in all?

Answers

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/

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
a. $30,000 and $40,000
b. $36,400 and $38,000
c. $34,800 and $39,600
d. $35,600 and $38,800

Answers

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

A local hamburger shop sold a combined total of 498 hamburger and cheeseburger on Sunday. 52 fewer cheeseburgers sold than hamburgers how many hamburgers were sold on Sunday

Answers

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.

The chance of A is 1/3; the chance of B is 1/10. True or false, and explain: (
a) If A and B are independent, they must also be mutually exclusive.
(b) If A and B are mutually exclusive, they cannot be independent.

Answers

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.

Final answer:

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.

Explanation:

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

(a) If A and B are independent, they must also be mutually exclusive. This statement is false. If events A and B are independent, this means the occurrence of A does not affect the occurrence of B and vice versa. Meanwhile, mutually exclusive events cannot happen at the same time. Therefore, independence does not imply mutual exclusivity.(b) If A and B are mutually exclusive, they cannot be independent. This statement is true. If events A and B are mutually exclusive, it means that if one occurs, the other cannot, hence they are not independent. Independence implies that the occurrence of one event does not affect the probability of the other, which contradicts mutual exclusivity.

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.

Find the area of a triangle with the given vertices.

Part I: Graph the following points on the coordinate grid below.
(1, -3), (3, -1), (5, -3)

Part II: Find the area of the triangle. Show your work.

Answers

Answer:

the area of the triangle is 4 square units.

Step-by-step explanation:

Plotting the points, we can see that the triangle is isosceles lying in the 4th quadrant of graph.

we can break the triangle in 2 similar right angled triangles,

each with base 2 and height 2  units.

area of triangle is given by the formula,

A= [tex](\frac{1}{2})(base)(height)[/tex]

thus, A= [tex](\frac{1}{2})(2)(2)[/tex]

A=2 square units.

there are 2 such triangles,

thus total area is 4 square units.

A Hospital/Surgical Expense policy was purchased for a family of four in March of 2013. The policy was issued with a $500 deductible and a limit of four deductibles per calendar year. Two claims were paid in September 2013, each incurring medical expenses in excess of the deductible. Two additional claims were filed in 2014, each in excess of the deductible amount as well. What would be this family's out-of-pocket medical expenses for 2013?

Answers

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.

Final answer:

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.

Explanation:

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:

Claim 1 in September 2013: $500 (deductible)Claim 2 in September 2013: $500 (deductible)

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

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Dwight and Walt are building model cars. Dwight builds 7 fewer models than 4 times the number Walt builds.Dwight builds at most 9 models.Which inequality could be used to find the number of models Walt builds.

Answers

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:

Which function could this graph represent?
O y=2sin x+2
O y=-2sin x+ 2
O y= 2cos x + 2
O y=-2cos x + 2

Answers

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 diameter of a cylindrical construction pipe is 5 ft. If the pipe is 21 ft long, what is its volume?
Use the value 3.14 for 7, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer

Answers

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.

A boat leaves New Orleans and travels up stream on the Mississippi River for 4 hours the return trip takes only 2.8 hours because the boat travels 3 miles per hour faster downstream due to the current. How far does the boat travel up stream?

Answers

Answer: 3.73

Step-by-step explanation:

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in.
(a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.20 in.
(b) Repeat part (a) using a standard deviation of 0.40 in. Which standard deviation requires a larger sample size? Explain.
(a) The minimum sample size required to construct a 99% confidence interval using a population standard deviation of 0.20 in. is balls. (Round up to the nearest integer.)
(b) The minimum sample size required to construct a 99% confidence interval using a standard deviation of 0.40 in. is balls. (Round up to the nearest integer.)
A population standard deviation of in. requires a larger sample size. Due to the increased variability in the population, a sample size is needed to ensure the desired accuracy.

Answers

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.

Solve for (c).

12c−4=14c−10
c= ?



Answers

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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For the quadratic equations shown here, which statement is true?

Answers

Answer:

opens upward; axis of symmetry is x = 5opens upward; axis of symmetry is x = 5opens upward; axis of symmetry is x = 5opens downward; axis of symmetry is x = 5

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.

Final answer:

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.

Explanation:

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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There were 90 people at a party. There were four more men than women and there were 10 more children than adults now many men women and children were at the party?

Answers

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

orest fire covers 2008 acres at time t equals 0. The fire is growing at a rate of 8 StartRoot t EndRoot acres per hour, where t is in hours. How many acres are covered 24 hours later? Round your answer to the nearest integer.

Answers

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.

Frank borrows 12000 dollars at 7.4 percent annual interest, compounded once per year, when he begins college. Four years later, how much will he owe? (Assume that he makes no payments during the four years.)

Answers

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]

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent

Answers

Answer: These events are dependent.

Step-by-step explanation: The probability of the second woman getting a pink rose is affected by the first woman getting a pink rose as the pink rose obtained by the first woman was not replaced. Hence there are less pink roses in the flower vase and hence lower probability that the second woman gets a pink rose. These events are thus dependent.

Answer:

Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

Step-by-step explanation:

What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?.

Answers

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

A or B or C or D which expression??​

Answers

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

PLZ HELP!!
The revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth.

A. (9.3, 28.5)
B. (28.5, 9.3)
C. (23, 19.3)
D. (11.3, 17.3)

Answers

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)

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

What are Coordinates?

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

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The​ half-life of a certain substance is 26 years. How long will it take for a sample of this substance to decay to 92​% of its original​ amount? Use the exponential decay model, A = A_0 e kt, to solve. years (Round to one decimal place as needed.)

Answers

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.

A submarine let Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier traveled at 25 mph for nine hours. After this time the vessels were 280 miles apart. Find the submarines speed.

Answers

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

Final answer:

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.

Explanation:

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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In parallelogram ABCD
What is BD

Answers

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

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