A jet goes from City 1 to City 2 at an average speed of 600 miles per hour, and returns along the same path at an average speed if 300 miles per hour. What is the average speed, in miles per hour, for the trip

Answer:

Shop A = 113 pence

Shop B = 101 pence

Step-by-step explanation:

Given :

Shop A :

5kg for £5.65

Shop B:

2kg for £2.02

Price per kg :

weight / price

100 pence = £1

Shop A :

Price of 1kg :

5.65 / 5 = £1.13 = 113 pence

Shop B:

2.02 / 2 = £1.01 = 1.01 * 100 = 101 pence

Answer:

100

Step-by-step explanation:

Answer:

100 times greater

Step-by-step explanation:

Because the number 55 moves to the right.

The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

(a) 6 + 7(b - 1) = 5 + b

6 + 7b - 7 = 5 + b

7b - 1 = 5 + b

7b - b = 5 + 1

6b = 6

b = 1

(b) x/3 + 5 = 6 has the solution x = 3

as, 3/3 + 5 = 6

1 + 5 = 6

6 = 6

also, 9 - 3x = 0 has the solution x = 3

as, 9 - 3(3) = 0

9 - 9 = 0

0 = 0

also, 2x + 4 = 10 has the solution x = 3

as, 2(3) + 4 = 10

6 + 4 = 10

10 = 10

(c) 7x - 4 = 3x + 8

7x - 3x = 8 + 4

4x = 12

x = 3

(d) 6x - 9 = 15

6x = 15 + 9

6x = 24

x = 4

(e) 9 - x = 14/x has the solution x = 7

as, 9 - 7 = 14/7

2 = 2

also, 65 - 2x = 6x + 9 has the solution x = 7

as, 65 - 2(7) = 6(7) + 9

65 - 14 = 42 + 9

51 = 51

also, 3 + 4x = 5x - 4 has the solution x = 7

as, 3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Hence, The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

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The marginal utility is the extra satisfaction derived from the consumption of a product.

Your information isn't well written. Therefore, an overview of utility will be given. The total utility is the total amount of satisfaction that a consumer derives from a product.

The marginal utility simply means the extra satisfaction that's gotten from a product when an additional unit is consumed.

The formula for marginal utility will be:

= Total utility difference/Quantity of goods difference

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Answer:

The chord is drawn below

Step-by-step explanation:

Answer:

6.1

Step-by-step explanation:

use law of cosines

d² = e² + f² - 2ef cos D

d² = 9² + 10² - 2(9)(10) cos 37

d² = 81 + 100 - 143.75

d² = 37.25

d = 6.1

Answer:

1. Q1 = 5

2.Q2 = 9

3.Q3 = 15

4.D5 = 9

5.D7 = 14.1

6.D8 = 17.4

7.P25 = 4.5

8.P60 = 11.2

9.P75 =  15.75

10.P30  = 5.3

Answer:

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Step-by-step explanation:

The ounce is a mass unit, as we notice that the metallurgist wants to make 12 ounces of an alloy containing 45 % copper by mixing two metal with different copper proportions. We can use the following two equations:

Alloys

\(m_{R} = m_{A}+m_{B}\) (Eq. 1)

Copper

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A}+r_{B}\cdot m_{B}\) (Eq. 2)

Where:

\(m_{A}\) - Mass of the 30 % copper alloy, measured in ounces.

\(m_{B}\) - Mass of the 50 % copper alloy, measured in ounces.

\(m_{R}\) - Mass of the 45 % copper alloy, measured in ounces.

\(r_{A}\) - Proportion of copper in the 30 % copper alloy, dimensionless.

\(r_{B}\) - Proportion of copper in the 50 % copper alloy, dimensionless.

\(r_{R}\) - Proportion of copper in the 45 % copper alloy, dimensionless.

Now, the mass of the 50 % copper alloy is cleared in Eq. 1 and eliminated in Eq. 2:

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A} + r_{B}\cdot (m_{R}-m_{A})\)

\((r_{R}-r_{B})\cdot m_{R} = (r_{A}-r_{B})\cdot m_{A}\)

And we clear and calculate the mass of the 30 % copper alloy:

\(m_{A} = m_{R}\cdot \left(\frac{r_{R}-r_{B}}{r_{R}-r_{A}} \right)\)

If we know that \(m_{R} = 12\,oz\), \(r_{R} = 0.45\), \(r_{A} = 0.30\) and \(r_{B} = 0.50\), the mass of the 30 % copper alloy:

\(m_{A} = (12\,oz)\cdot \left(\frac{0.45-0.50}{0.30-0.50} \right)\)

\(m_{A} = 3\,oz\)

And the mass of the 50 % copper alloy is:

\(m_{B} = m_{R}-m_{A}\)

\(m_{B} = 12\,oz-3\,oz\)

\(m_{B} = 9\,oz\)

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Triangle in (22) have value of side z = 4, and angles x = 53°, y = 37°. The triangle in (23) have the value of it sides x = 35, z = 83, and an angle y = 65°. Using trigonometric ratios to the nearest whole numbers.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(22). by Pythagoras rule;

z = √(5² - 3²) = 4

sin x = 4/5

x = sin⁻¹(4/5) {cross multiplication}

x = 53.1301

y = 180 - (53 + 90) {sum of interior angles of a triangle}

y = 37°

(23). cos 25 = 75/z {adjacent/hypotenuse}

z = 75/cos 25 {cross multiplication}

z = 82.7533

sin 25 = x/82.7533

x = 82.7533 × sin 25 {cross multiplication}

x = 34.9731

y = 180 - (25 + 90)

y = 65°

Therefore, the triangle in (22) have value of side z = 4, and angles x = 53°, y = 37°. The triangle in (23) have the value of it sides x = 35, z = 83, and an angle y = 65°. Using trigonometric ratios to the nearest whole numbers.

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Using the box-whisker plot approach, it is computed that 50% of the data values are more than 45.

In a box-whisker plot, as seen in the illustration, The minimum, first quartile, median, third quartile, and maximum quartiles are shown by a rectangular box with two lines and a vertical mark. In descriptive statistics, it is employed.

Given the foregoing, the box-whisker plot depicts a specific collection of data. A vertical line next to the number 45 shows that it is the 50th percentile in this instance and that 45 is the median of the data.

It indicates that 50% of the values are higher than 45 and 50% of the values are higher than 45.

Using this technique, we can easily determine the proportion of data for which the value is higher or lower. Data analysis and result interpretation are aided by it. Therefore, 50% of values exceed 45.

Note: The correct question would be as

The box-and-whisker plot below represents some data sets. What percentage of the data values are greater than 45?

0

H

10

20

30 40

50 60

70 80 90 100

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Answer:29,858

Step-by-step explanation:

Iñ

Answer:

The domain of y = f(x) is [0,8]

Step-by-step explanation:

Since the straight line with negative slope begins on the y-axis at (0. 9) and exits the plane at (8, 1), we get is domain from the minimum and maximum values of x for which the function is valid.

So, the minimum value of x at which the function is valid is x = 0 and the function is y = f(0) = 9.The maximum value of x at which the function is valid is x = 8 and the function is y = f(8) = 1.

So, the domain of the function y = f(x) is [0,8]

Answer:

y = f(x) is [0,8]

Step-by-step explanation:

To be in the 90th percentile of birth weights, a baby would need to weigh approximately 8.976 lbs at birth.

The 90th percentile corresponds to the value below which 90% of the data falls.

In this case, we have a normal distribution with a known mean and standard deviation of birth weights. To find the weight at the 90th percentile, we can use the properties of the standard normal distribution.

First, we convert the percentile to a Z-score using a Z-table or calculator. For the 90th percentile, the Z-score is approximately 1.28.

Next, we can use the Z-score formula to calculate the corresponding weight:
Z = (x - mean) / standard deviation

By rearranging the formula and substituting the values:
1.28 = (x - 6.8) / 1.7

Solving for x, the weight at the 90th percentile, we have:
1.28 * 1.7 = x - 6.8
2.176 = x - 6.8
x = 2.176 + 6.8
x ≈ 8.976 lbs

Therefore, a baby would need to weigh approximately 8.976 lbs at birth to be considered in the 90th percentile of birth weights.

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James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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a. the equation of the tangent line to the curve at (3,3) is 9x + 13y = 78.

b. This is false, so (4,2) does not lie on the curve.

c. the equation of the tangent line to the curve at (1,y) is 2x - y - 1 = 0.

For the first problem, we have:

\(3x^2 + 3xy + 4y^2 = 90\)

To verify that (3,3) lies on the curve, we substitute x = 3 and y = 3 into the equation and check if it is satisfied:

\(3(3)^2 + 3(3)(3) + 4(3)^2 = 27 + 27 + 36 = 90\)

Therefore, (3,3) lies on the curve.

To determine the equation of the line tangent to the curve at (3,3), we need to find the derivative of the curve with respect to x, then evaluate it at x = 3 to find the slope of the tangent line, and use the point-slope form to write the equation of the tangent line.

Taking the derivative with respect to x, we get:

6x + 3y + 3x(dy/dx) + 8y(dy/dx) = 0

Simplifying and solving for dy/dx, we get:

dy/dx = -(6x + 3y)/(3x + 8y)

Evaluating at (3,3), we get:

\(dy/dx = -(6(3) + 3(3))/(3(3) + 8(3)) = -27/39 = -9/13\)

Using the point-slope form with the point (3,3) and slope -9/13, we get:

y - 3 = (-9/13)(x - 3)

Simplifying, we get:

9x + 13y = 78

Therefore, the equation of the tangent line to the curve at (3,3) is 9x + 13y = 78.

For the second problem, we have:

\(16(x^2 + y^2)^2 = 400xy^2\)

To verify that (4,2) lies on the curve, we substitute x = 4 and y = 2 into the equation and check if it is satisfied:

\(16(4^2 + 2^2)^2 = 400(4)(2^2)\)

\(16(16 + 4)^2 = 400(4)(4)\)

20,736 = 3,200

This is false, so (4,2) does not lie on the curve.

For the third problem, we have:

\(x + y^2 - y = 1\)

To find the equations of all lines tangent to the curve at x = 1, we need to find the derivative of the curve with respect to x, then evaluate it at x = 1 to find the slope of the tangent line, and use the point-slope form to write the equation of the tangent line.

Taking the derivative with respect to x, we get:

1 + 2y(dy/dx) - dy/dx = 0

Solving for dy/dx, we get:

dy/dx = (2y - 1)/(2x - 1)

Evaluating at x = 1, we get:

dy/dx = (2y - 1)/1 = 2y - 1

Using the point-slope form with the point (1,y) and slope 2y - 1, we get:

y - y1 = (2y - 1)(x - 1)

Simplifying, we get:

2x - y - 1 = 0

Therefore, the equation of the tangent line to the curve at (1,y) is 2x - y - 1 = 0.

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To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

In the question ,

it is given that ,

the each serving should not be larger than  8oz .

let the number of Ounces of Brand A food = x , and

let the number of ounces of brand B = y ,

So , x + y ≤ 8

Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and

Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,

So , 3x + 5y ≥ 29 ,

and 4x + 2y ≥ 20,

and x , y ≥ 0  .

given, that

cost of Brand A = 5 cents/ounce

cost of Brand B = 7 cents/ounce

So , the cost equation is c(x) = 5x + 7y ,

drawing the given inequalities on the graph ,

From the graph given below , we find that the vertices of the feasible region are ,

(2,6) , (5.5,2.5) , (3,4)

Substituting the points in the cost equation , we get

For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52

For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43

For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,

the minimum cost is at point (3,4) ,

So , 3 ounces of Brand A and 4 ounces of Brand B should be used .

Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

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Answer: It will take 8 hours to reach this temperature.

Step-by-step explanation:

Given: At a desert resort, the temperature at 7 a.m. was 3°C.

The temperature increased by an average of 3.4°C each hour until it reached 30.2°C.

Let x be the number of hours taken to reach 30.2°C..

As per given ,

Initial temperature +(average increase in temperature) (Number of hours) = 30.2

⇒3+3.4x=30.2

⇒3.4x=30.2-3

⇒3.4x=27.2

⇒ x=8    [Divide both sides by 3.4]

Hence, it will take 8 hours to reach this temperature.

Answer:

(4.75, 2.25)

Step-by-step explanation:

Given the coordinate (x,y). If this coordinate is reflected over the x axis, the resulting coordinate will be (x, -y)

Note that the y coordinate was negated.

Let the original point needed be (x, y)

If the new point is located at (4.75, -2.25)

Since the y coordinate was negated, then;

-y = -2.25

y = 2.25

x = 4,75 (x coordinate remains the same)

Hence the original point is (4.75, 2.25)

Answer:

Step-by-step explanation:

The probability is the product of the probabilities for each card. and (b) With replacement: The probability remains the same.

(a) When sampling is done without replacement, the probability of the first card being an "a" is 4/52 (since there are 4 "a" cards in a standard deck of 52 cards). After the first card is selected, there are 51 cards remaining, and the probability of the second card being an "a" is 3/51 (since there are 3 "a" cards left out of the remaining 51 cards). Therefore, the probability that the first card is an "a" and the second card is an "a" is (4/52) * (3/51) = 1/221.

(b) When sampling is done with replacement, after the first card is selected, it is placed back into the deck, and the deck is reshuffled. Each card has an equal probability of being chosen for each draw. Therefore, the probability of the first card being an "a" is 4/52, and the probability of the second card being an "a" is also 4/52. Hence, the probability that the first card is an "a" and the second card is an "a" is (4/52) * (4/52) = 1/169.

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Answer:

x=99/8

Step-by-step explanation:

Answer:

x=99/8

Step-by-step explanation:

7x+6+9x−24=180

Step 1: Simplify both sides of the equation.

7x+6+9x−24=180

7x+6+9x+−24=180

(7x+9x)+(6+−24)=180(Combine Like Terms)

16x+−18=180

16x−18=180

Step 2: Add 18 to both sides.

16x−18+18=180+18

16x=198

Step 3: Divide both sides by 16.

16x/16 = 198/16

X = 99/8  

Hope it Helps !! :)

Answer:

I got 42

Step-by-step explanation:

They should add up to 180 cause parallel lines and similar angles. (3x-5)+(2x-25)=180 then just solve

Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

Answer:

circle

Step-by-step explanation:

any point on the circumference of a circle is equidistant from the centre.

Answer:

what ur question

like not gonna lie kinda of confused

i can help u if u tell me

Step-by-step explanation:

9514 1404 393

Answer:

  22

Step-by-step explanation:

The average of the 6 even integers is the odd integer halfway between the first three and the last three. That average value is 126/6 = 21, so the 4th integer is 21+1 = 22.

_____

All 6 are {16, 18, 20, 22, 24, 26}.

Answer:

Point A:

(1, 1) -----> (-1, 1)

Step-by-step explanation:

When reflecting over the y-axis, take the opposite of the x-coordinate. That means if the coordinate is positive then it becomes negative, and if it is negative then it becomes positive.

(x, y) -------> (-x, y)

Point A:

(1, 1) -----> (-1, 1)