A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies. How many of each did they sell?

Answer: the speed of the commercial jet is 540 mph

the speed of the private airplane is 330 mph

Step-by-step explanation:

Let x represent the speed of the commercial jet and

Let y represent the speed of the private airplane.

It takes the commercial jet 1.1 hours for the flight from Denver to Phoenix.

Distance = speed × time

Therefore, distance covered by the commercial jet from Denver to Phoenix would be

1.1 × x = 1.1x

it takes the private airplane 1.8 hours to cover the same distance. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. It means that

y = x - 210

Distance covered by the private airplane would be

1.8(x - 210) = 1.8x - 378

Since the distance is the same, then

1.8x - 378 = 1.1x

1.8x - 1.1x = 378

0.7x = 378

x = 378/0.7 = 540

y = x - 210 = 540 - 210

y = 330

To find the speeds of a commercial jet and a private airplane, we can set up and solve an equation using the distance and time information provided in the question.

The question is about the speeds of a commercial jet and a private airplane flying from Denver to Phoenix. Let's assume the speed of the private airplane is 'x' miles per hour. According to the question, the commercial jet is 210 miles per hour faster than the private airplane. So, the speed of the commercial jet is 'x + 210' miles per hour.

Now, we have the speeds of both planes. We can use the formula 'speed = distance / time' to calculate the distance. Since the time for the commercial jet is 1.1 hours and the time for the private airplane is 1.8 hours, the distances traveled by the commercial jet and the private airplane are '1.1(x + 210)' and '1.8x' miles, respectively.

Since both planes are traveling the same distance, we can set up the equation '1.1(x + 210) = 1.8x' to find the value of 'x'. Solving this equation will give us the speed of the private airplane. Once we have the speed of the private airplane, we can calculate the speed of the commercial jet by adding 210 to it.

Answer:

Option 2: [tex]\sin(30)=\frac{1}{2}[/tex]

Step-by-step explanation:

Given:

From the triangle shown below;

A triangle QRS with angle QRS = 90°, ∠QSR = 30°.

Side QR = 5, SQ = 10 and RS = 5√3

Now, we know from trigonometric ratio that,

[tex]\sin (A) = \frac{Opposite\ side}{Hypotenuse}[/tex]

Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,

[tex]\sin(\angle QSR)=\dfrac{QR}{SQ}\\\\\\\sin(30)=\dfrac{5}{10}\\\\\\\sin(30)=\dfrac{5}{2\times 5}=\dfrac{1}{2}[/tex]

Therefore, the value of sine of 30° is one-half. So, second option is correct.

Answer:

B

Step-by-step explanation:

Answer:$2430

Step-by-step explanation:

6x45=270

270x9=2430

Answer: 16

Step-by-step explanation:

Answer:

The height of each pyramid is 1/2 h units.

Step-by-step explanation:

did it on edg 2020

Answer:

  {-4.6, -4.2, -3.8, -3.4}

Step-by-step explanation:

The length of the space Karlie is dividing is -3-(-5) = 2 units. Then the length of each of those equal 5 spaces will be 2/5 units = 0.4 units.

Each mark on the number line is 0.4 units to the right of the previous one. The first (left-most) mark is 0.4 units to the right of -5, so is at -5+0.4 = -4.6.

The marks have to be placed at -4.6, -4.2, -3.8, and -3.4.

Answer:

[tex]q=4p-14[/tex]

Step-by-step explanation:

The first step in solving

[tex]5q-4p+6=4q-8[/tex]

is to bring [tex]4q[/tex] on the right the left side to the right side by subtracting it from both sides:

[tex](5q-4p+6)-4q=(4q-8)-4q\\\\(5q-4q)-4p+6=-8\\q-4p+6=-8[/tex]

and we subtract 6 from both sides and get:

[tex]q-4p=-14[/tex]

finally we add [tex]4p[/tex] to both sides and get:

[tex]q-4p+4p=-14+4p[/tex]

[tex]\boxed{q=4p-14}[/tex]

Final answer:

Andrea's score of 76 is 2.4 standard deviations above the mean test score of 52 with a standard deviation of 10.

Explanation:

The question is how many standard deviations from the mean Andrea's score of 76 is on the mathematics test where the mean is 52 and the standard deviation is 10. To find this, you would use the formula for calculating a z-score:

Z = (X - μ) / σ

Where:

Z is the z-score

X is the value of the score

μ is the mean of the scores

σ is the standard deviation of the scores

For Andrea's score, the calculation would be:

Z = (76 - 52) / 10 = 24 / 10 = 2.4

Therefore, Andrea's score is 2.4 standard deviations above the mean. This indicates that her score was significantly higher than the average test score.

Answer: she has 16 dimes and 48 nickels

Step-by-step explanation:

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of dimes that she has in her wallet.

Let y represent the number of nickels that she has in her wallet.

she has three times as many nickels as she does dimes. This means that

y = 3x

the total value of the coins is $4.00. This means that

0.1x + 0.05y = 4 - - - - - - - - - - - 1

Substituting y = 3x into equation 1, it becomes

0.1x + 0.05 × 3x = 4

0.1x + 0.15x = 4

x = 4/0.25 = 16

y = 3x = 3 × 16

y = 48

Answer:

Step-by-step explanation:

(a) R2 does not determine the level of correlation between two variables in statistics but rather it is used to determine the level of variance in a dependent variable that is explained by an independent variable. It is also known as coefficient of determination.

Pearson's correlation coefficient (r) will better explain a direct relationship between a country's literacy rate and life expectancy and the value obtained will better explain option a

(b) The slope of the line can predict an improvement in life expectancy but cannot guarantee this improvement. And as such, the use of the word "will" suggests a form of guarantee which is wrong in interpreting slopes.

Answer:

What is the figure you are talking about?

The solution to the given system of equations, x + 5y = 11 and x - y = 5, is x = 6, y = 1. The solution matrix for this system is therefore [6, 1].

To solve the given system of linear equations, x + 5y = 11 and x - y = 5, you can use the elimination or substitution method. Let's use the elimination method:

The solution of this system of equations is x = 6 and y = 1. For the matrix format of the solution, it would be [6,1] as the solution matrix typically formats solutions in [x, y].

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The solution matrix X is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\)[/tex].

To find the solution matrix for the given system of equations [tex]\(x + 5y = 11\)[/tex] and [tex]\(x - y = 5\)[/tex], we can represent the system in matrix form \(AX = B\), where:

[tex]\[ A = \begin{bmatrix} 1 & 5 \\ 1 & -1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 11 \\ 5 \end{bmatrix} \][/tex]

The solution matrix X is given by [tex]\(X = A^{-1}B\)[/tex], where [tex]\(A^{-1}\)[/tex] is the inverse of matrix A.

1. Form the matrix equation AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

2. Compute the inverse of matrix A, denoted as [tex]\(A^{-1}\).[/tex]

3. Multiply [tex]\(A^{-1}\)[/tex]by matrix B to obtain the solution matrix X.

By following these steps, you can find that the solution matrix X for the given system is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\).[/tex]

Answer:

x= 8

Step-by-step explanation:

60/48=1.25

15/1.25= 12

12-4=8

Answer:

Angular speed of the towers top about its base is [tex]6.91\times 10^{-13}[/tex] rad per sec.

Step-by-step explanation:

Linear velocity of leaning bell tower 'v' = 1.2 mm per year

v = [tex]\frac{1.2\times 10^{-3}}{365\times 24\times 60\times 60}[/tex]

v = 3.8 × [tex]10^{-11}[/tex] meter per second

Height of the tower = 55 meter

From the formula of angular velocity,

v = rω

ω = [tex]\frac{v}{r}[/tex]

ω = [tex]\frac{3.8\times 10^{-11}}{55}[/tex]

ω = [tex]6.91\times 10^{-13}[/tex] rad per second.

Therefore, top of the tower is moving with an angular speed of [tex]6.91\times 10^{-13}[/tex] rad per second.

The probability of winning in the state lottery is 0.24%.

To calculate the probability of winning, we need to consider the total number of possible outcomes and the number of favorable outcomes. In this case, there are 10 choices for each digit, so the total number of possible outcomes is 10 x 10 x 10 x 10 = 10,000. Since any permutation of the selected integers counts as a win, we have 4! = 4 x 3 x 2 x 1 = 24 favorable outcomes.

Therefore, the probability of winning is 24/10,000 = 0.0024, or 0.24%.

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The probability of winning by selecting unique digits is 0.0024 or 24/10,000.

We first determine the total number of possible outcomes when drawing four digits. Since the digits range from 0 to 9, there are 10 possible choices for each digit.

Total outcomes = 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit * 10 choices for the fourth digit

= 10⁴ = 10,000.

Now, if you select four specific digits, we need to consider the number of ways these digits can be arranged, which is calculated using permutations. If all selected digits are unique, the number of permutations is 4! = 24.

If you select digits with repetitions, the calculation varies. For example, if you select 1, 2, 2, and 3, the permutations would be 4! / 2! = 12.

Assuming you selected four unique digits, the probability of winning is given by the number of favorable outcomes divided by the total outcomes. Thus, the probability of winning with unique digits is:

Probability = Number of favorable outcomes / Total outcomes

= 24 / 10,000

= 0.0024.

Answer: y(t) = 600(0.921)^t

Step-by-step explanation:

Given:

Percentage yearly reduction = 7.9%

Initial mass m = 600 mg

time in years = t

An exponential function with yearly decay rate to determine the final mass of the substance is given as:

y(t) = m(f)^t

y(t) = final mass in milligram

m = 600

f = final mass fraction = 1 - 0.079 = 0.921

f = 0.921

Therefore, the exponential function is given as;

y(t) = 600(0.921)^t

Final answer:

Carol has 10 green cubes in the box. After adding 12 more red cubes, she ends up with 32 red cubes.

Explanation:

To solve this problem, we can use the concept of ratios and equations. First, we know that the initial ratio of red to green cubes is 2:1. Let's represent the number of red cubes as 2x and green cubes as x. We then are told that Carol adds 12 more red cubes and the ratio becomes 4:5. If we let the number of green cubes remain as x, we have that the new number of red cubes is 2x + 12.

We can set up the following proportion to represent the new situation:

(2x + 12) / x = 4 / 5

By cross-multiplying, we can solve for x to find the quantity of green cubes:

5(2x + 12) = 4x

10x + 60 = 4x

6x = 60

x = 10

Therefore, there are 10 green cubes in the box (as x represents the number of green cubes).

To find out how many red cubes are there in the end, we add 12 to the initial amount of red cubes (2 times the number of green cubes):

Initial red cubes = 2x = 2(10) = 20

Final red cubes = 20 + 12 = 32 cubes

So, Carol has 32 red cubes in the end.

Answer:

Step-by-step explanation:

Let x represent the average speed of flight 725.

Flight 725 left New York at 10:28 a.m. flying north.

Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. This means that the speed of flight 245 is

3x - 120

At 1:06 p.m. they are 1,030 kilometers apart. This means that total distance travelled by both planes would be 1030

Between 10:28am and 1:06pm, the number of hours would be 2hr 38 minutes = 2 + 38/60 = 2.63 hours

Distance = speed × time

Total distance travelled by flight 725 = x × 2.63 = 2.63x

Between 11:18am and 1:06pm, the number of hours would be 1hr 48 minutes = 1 + 48/60 = 1.8 hours

Distance = speed × time

Total distance travelled by flight 245 = x × 1.8 = 1.8(3x - 120)

5.4x - 216 + 2.63x = 1030

8.03x = 1030 + 216 = 1246

x = 1246/8.03 = 155 kph

In order to find 30% of 75, we simply calculate 75 x 0.3.

75 x 0.3 amounts to 22.5, which is the amount we deduct.

This leaves a final price of $52.50.

A 30% discount on an item priced at $75 results in a deduction of $22.5.

The student's question is about calculating a discount on an item. Here, the discount is a 30% decrease or reduction off the original price of the item, which is $75. To calculate the discount, you multiply the original price by the percentage discount. Remember, since percentage is a proportion, you'll need to convert the percentage to a decimal first by dividing it by 100. Therefore, the formula will be:

Discount = Original Price x Percentage Discount

Substituting in the given values:

Discount = $75 x 30/100 = $22.5

So, with the 30% discount, you can deduct $22.5 from the original price of the item.

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Answer:the time for processing the payment took 58 seconds.

Step-by-step explanation:

An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. If Anna bought 31 items at the grocery store, the total time for Anna's transaction would be

(31 × 2) + 40 = 62 + 40 = 102 seconds.

The time to to process the Anna's payment took longer due to glitches. If the total time for Anna's transaction took 2 minutes = 120 seconds, then the amount of time it took to process the payment (p) would be

p = 120 - 62 = 58 seconds

Answer:

Step-by-step explanation:

The graph is sketched in the attachment. It's easy to sketch the same graph using the given information. Let's say h is the height. For time t=0 you put a dot on 3 feet since it's the lowest point of the ferris wheel (you get that by substracting the diameter of 40 feet from the highest point given (43 feet).

Second dot is your highest point 43 feet at t=4 sec since it is the half of the circle.

The third dot is your lowest point again at t=8 sec. If you connect the dots like a sine you get the sketched graph.

To find out what is the equation for the graph you need to look at the amplitude which in this case is 20 feet. Then you need to find out the frequency at which the wheel is turning. Since you are given the period (8 sec for a full cycle) you get the frequency:

[tex]f=\frac{1}{T}=\frac{1}{8}[/tex]

Now you need to find out the phase of the wave. Since we want to be at 0 feet at t=0 you need to shift the wave 90° degrees forward or [tex]\frac{\pi}{2}[/tex] in radians.

Finally it's important to shift the whole wave up. You do that by adding the appropriate amount that is in this case the half of the diameter plus the 3 feet to the ground.

The equation you get is:

[tex]h(t)=23+A\sin(2\pi f t-\phi)=23+20\sin(0.25\pi t-\frac{\pi}{2})[/tex]

where A is amplitude, [tex]\phi[/tex] is the phase shift and [tex]f[/tex] is the frequency.

Finally you can get the height at [tex]t=4.5[/tex] sec:

[tex]h(t=4.5)=23+20\sin\left(0.25\pi4.5-\frac{\pi}{2}\right)=41.478\ \text{ft}[/tex]

The student asked for the calculations of probabilities concerning a football player's passes. The answers are: (a) 21.18%, (b) 90.58%, (c) 8.68%. This involves the use of probability rules and calculations carried out to two decimal places.

The subject of this question is probability, particularly in the context of repeated independent trials. The football player has a 69.4% chance of completing a pass, so we can use this information to answer the questions.

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(a) The probability that the first pass he completes is the second pass is [tex]$\frac{3099}{10000}$[/tex].

(b) The probability that the first pass he completes is the first or second pass is [tex]$\frac{3499}{5000}$[/tex].

(c) The probability that he does not complete his first two passes is [tex]$\frac{9826}{2500}$[/tex].

To solve this problem, we will use the given completion rate of 69.4% and convert it into a fraction to make the calculations easier. The completion rate is equivalent to [tex]$\frac{694}{1000}$[/tex] or [tex]$\frac{347}{500}$[/tex].

(a) To find the probability that the first pass he completes is the second pass, we need to consider two events: he must fail the first pass and then succeed on the second pass. The probability of failing the first pass is [tex]$1[/tex] - [tex]\frac{347}{500}$[/tex], and the probability of succeeding on the second pass is [tex]$\frac{347}{500}$[/tex]. Multiplying these two probabilities gives us the desired probability:

[tex]$$ \left(1 - \frac{347}{500}\right) \times \frac{347}{500} = \frac{153}{500} \times \frac{347}{500} = \frac{3099}{25000}. $$[/tex]

Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:

[tex]$$ \frac{3099}{25000} = \frac{77475}{62500} = \frac{3099}{10000}. $$[/tex]

(b) To find the probability that the first pass he completes is the first or second pass, we need to consider the probability of completing the first pass and the probability of failing the first pass but completing the second pass. We add these two probabilities because they are mutually exclusive events. The probability of completing the first pass is [tex]$\frac{347}{500}$[/tex], and the probability of failing the first pass but completing the second pass is the same as calculated in part (a), [tex]$\frac{3099}{10000}$[/tex]. Adding these probabilities gives us:

[tex]$$ \frac{347}{500} + \frac{3099}{10000} = \frac{694}{1000} + \frac{3099}{10000} = \frac{3499}{5000}. $$[/tex]

(c) To find the probability that he does not complete his first two passes, we need to consider the probability of failing both passes. The probability of failing one pass is [tex]$1[/tex]- [tex]\frac{347}{500}$[/tex], so for two consecutive failures, we square this probability:

[tex]$$ \left(1 - \frac{347}{500}\right)^2 = \left(\frac{153}{500}\right)^2 = \frac{23409}{25000}. $$[/tex]

Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:

[tex]$$ \frac{23409}{25000} = \frac{585025}{62500} = \frac{9826}{2500}. $$[/tex]

These calculations provide the probabilities for each of the specified events.

Answer:

$3.00

Step-by-step explanation:

If you wanna buy 2 pounds, just time it by 2! $1.50*2=$3.00!

If peanuts cost $1.50 per pound, the cost of 2 pounds of peanuts would be equal to $3.0.

Given the following data:

In order to determine the cost of 2 pounds of peanuts, we would set up a direct proportion equation as follows:

1 pounds = 1.50 dollars.

2 pounds = X dollars.

Cross-multiplying, we have:

X = 2 × 1.5

X = $3.0

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Answer:

The amount invested at 3% is 300 &

The amount invested at 2% is 100.

Step-by-step explanation:

Total yearly interest for the two accounts is: $11

Let x be the amount invested at 3%

& y be the amount invested at 2%

From the question we can get 2 equations as;

x = 3y --------------------------Equation 1

0.03x + 0.02y = 11 ----------Equation 2

Substitute for x in Equation 2 we get;

0.03 (3y) + 0.02y = 11

0.09y + 0.02y = 11

0.11y = 11

Divide the above equation by 0.11, we get;

y = [tex]\frac{11}{0.11}[/tex]

y = 100

Let us substitute the value of y in Equation 1 we get;

x = 3(100)

x = 300

Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:

0.03 x 300 + 0.02 x 100

= 9 + 2

= 11

Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.

Answer:

Step-by-step explanation:

5.

y=kx

when x=4,y=5

5=4k

k=5/4

y=5/4 x

or y=1.25 x

6.

y=kx

when x=4,y=9

9=4k

k=9/4

y=9/4 x

or y=2.25 x

Final answer:

To find out how many liters of paint are needed for one door, when 3 liters were used for 1 4/5 doors, divide the total amount of paint by the number of doors. The calculation is 3 liters divided by 9/5, which results in 1.67 liters of paint for one door.

Explanation:

Maren used 3 liters of paint to cover 1 4/5 doors which implies that the amount of paint needed for 1 door can be found by dividing the total amount of paint by the number of doors painted. To calculate this:

Therefore, 1.67 liters of paint are needed for 1 door.

Answer: (1812.967, 1907.033)

Step-by-step explanation:

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm t_{df,\ \alpha} \dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = Sample mean

n= Sample size.

s = Sample standard deviation

[tex]t_{df,\ \alpha}[/tex] = Critical t-value for degree of freedom(n-1).

As per given , we have

n= 35

[tex]\overline{x}=1860[/tex]

s=102

Significance level : [tex]\alpha=0.01[/tex]

By t- distribution table , for degree of freedom 43 and [tex]\alpha=0.01[/tex] , we have

[tex]t_{df,\ \alpha}=t_{34,\ 0.005} =2.728[/tex]

Substitute all the values in the above formula , we will get

[tex]1860\pm (2.728)\dfrac{102}{\sqrt{35}}[/tex]

[tex]=1860\pm (2.728)(17.2411)[/tex]

[tex]=1860\pm47.034[/tex]

[tex]=(1860-47.033\ 1860+47.033)= (1812.967,\ 1907.033)[/tex]

Hence, the  99% confidence interval estimate of the mean of the population is  (1812.967, 1907.033).

Final answer:

To construct a 99% confidence interval for the population mean with a known standard deviation, calculate the standard error, find the appropriate z-score for 99% confidence, and apply the formula Sample mean ± z * SEM. The 99% confidence interval for the given sample data is approximately (1811.26, 1908.74).

Explanation:

A student asked how to construct a 99% confidence interval estimate for the mean of the population given that the mean of a sample of size n=35 is 1860 with a standard deviation of 102, and the population is normally distributed.

To construct a 99% confidence interval, we proceed by calculating the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size:

SEM = σ / √n = 102 / √35 ≈ 17.25

We then find the z-score that corresponds to a 99% confidence level. For a two-tailed test, which is relevant here, this value is approximately 2.576.

The confidence interval is then calculated by:

Sample mean ± z * SEM = 1860 ± 2.576 * 17.25

Lower limit: 1860 - (2.576 * 17.25) ≈ 1811.26

Upper limit: 1860 + (2.576 * 17.25) ≈ 1908.74

Hence, the 99% confidence interval estimate for the population mean is approximately (1811.26, 1908.74).

Answer:

B)temperature during the game on Saturday

Step-by-step explanation:

Answer:

Molarity is the concentration of x moles of solute in 1 L of solution. ... have different properties i.e., a low molarity acid and high molarity acid can ... For example, a 0.25 mol/L NaOH solution contains 0.25 mol of sodium hydroxide in every litre of solution ... 15.0 g of NaOH in enough water to make a total of 225 mL of solution

Step-by-step explanation:

Answer:

i dont understand

Step-by-step explanation:

1) you first add up all of the amount of ingredients you have

2)you the take the total and divide your total up by the 4 ingredients you currently have

3)that is your total

11+4++4+5=24

24/4=6

answer= 6

There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A restaurant offers a medium pizza for $8.

And, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.

Now,

Since, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.

So, We get;

The different ways for a pizza must have a topping, cheese, sauce. And crust = 11 x 4 x 4 x 5

        = 880

Thus, There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.

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