The sum of Joy's age and her brother's age is $24$ . Her brother's age is $3$ years older than twice Joy's age.

What is the difference, in years, between Joy's age and her brother's age?

In 1996, the cooperative expects approximately 40% of cranberries processed to be water-harvested.

This is a decrease of 18% from 1995. This decrease is likely due to the fact that water-harvested cranberries cost more to process than traditional dry-harvested cranberries.

Additionally, the cooperative may not be able to find enough cranberry farmers willing to switch to the water-harvesting method, which is a labor-intensive process.

Thus, the cooperative is likely to experience a decrease in the percentage of water-harvested cranberries processed in 1996.

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Answer:

volume v = base area * height

= 1/2*9*4 * 8

The probability that outdoor equipment will meet all of their demand is 0.0478.

We are given that Outdoor equipment purchased 215 hydra insulated water bottles. The demand for the hydra water bottle is normally distributed with a mean of 150 and a standard deviation of 77.The formula for calculating the probability of demand can be given by: P(X ≤ 215)P(X ≤ 215) is the probability of selling all 215 water bottles.

It means that they will sell a maximum of 215 bottles. The probability of selling less than or equal to 215 bottles is calculated as: P(X ≤ 215)=P(Z ≤ (215 - 150)/77)=P(Z ≤ 0.844).

Therefore, P(X ≤ 215) = 0.8023P(X ≤ 215) = 0.8023P(X = 215) is calculated as: P(X = 215) = P(X ≤ 215) - P(X ≤ 214). Therefore, P(X = 215) = 0.8023 - P(Z ≤ (214.5 - 150)/77)= 0.8023 - 0.7545 = 0.0478.

Therefore, the probability that outdoor equipment will meet all of their demand is 0.0478.

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Answer:

  no

Step-by-step explanation:

You want to know if a triangle with sides 54, 66, and 87 is a right triangle.

The side lengths of a right triangle will satisfy the relation given by the Pythagorean theorem. Here, that would require ...

  54² +66² = 87²

  2916 +4356 = 7569

  7272 = 7569 . . . . . . . . . false — not a right triangle

Triangle WXY is not a right triangle, so XY is not tangent to circle W.

__

Additional comments

The parity of the integer side lengths of a right triangle is always even. That is, there can be two odd side lengths, but never just one odd side length.

Side lengths 54 and 66 are even, while length 87 is odd. There is only one odd side length, so this triangle cannot be a right triangle.

A tangent always meets a radius at right angles, so XY is a tangent if and only if angle X is a right angle.

Answer:

Step-by-step explanation:

To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.

The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.

Using the formula with a = -0.75 and b = 9.75, we get:

x = -9.75 / 2(-0.75)

x = -9.75 / -1.5

x = 6.5

Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.

To determine when people stop watching the video, we need to check the values of y after this point.

When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).

Answer:

15 Full orbits per day

Step-by-step explanation:

To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.

We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:

Distance traveled in one orbit = 42,600 kilometers

Speed of the ISS = 27,576 kilometers per hour

To calculate the time taken for one orbit:

Time taken = Distance traveled / Speed

Time taken = 42,600 kilometers / 27,576 kilometers per hour

Time taken = 1.54 hours (rounded to 2 decimal places)

So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.

Now, we can calculate the number of orbits the ISS does in one day:

Number of orbits per day = 24 hours / Time taken for one orbit

Number of orbits per day = 24 hours / 1.54 hours

Number of orbits per day = 15.58 (rounded to 2 decimal places)

Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.

Answer:

[tex]26a - 10 = 2(13a - 5)[/tex]

The family-sized box requires 130 more square inches of cardboard than the regular-sized box, has an additional 228 cubic inches of cereal capacity, and costs less per cubic inch of cereal.

To calculate the additional square inches of cardboard needed for the family-sized box, we need to find the difference in surface area between the regular-sized box and the family-sized box.

The regular-sized box has a surface area of 2 x 6 + 2 x 11 + 6 x 11 = 104 square inches.

The family-sized box has a surface area of 2 x 8 + 2 x 15 + 3 x 15 + 3 x 8 + 3 x 15 = 234 square inches.

Therefore, the additional square inches of cardboard needed for the family-sized box is 234 - 104 = 130 square inches.

B. To find how many more cubic inches of cereal fit in the family-sized box than the regular-sized box, we need to calculate the difference in volume between the two boxes.

The regular-sized box has a volume of 2 x 6 x 11 = 132 cubic inches.

The family-sized box has a volume of 3 x 8 x 15 = 360 cubic inches.

Therefore, the additional cubic inches of cereal that fit in the family-sized box is 360 - 132 = 228 cubic inches.

C. To determine which cereal costs less per cubic inch of cereal, we need to divide the cost of each box by its respective volume.

The regular-sized box costs $3.99 for 132 cubic inches of cereal, which gives us a cost of $0.03 per cubic inch.

The family-sized box costs $5.69 for 360 cubic inches of cereal, which gives us a cost of $0.02 per cubic inch.

Therefore, the family-sized box costs less per cubic inch of cereal.

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the inequality that describes the problem is x ≤ 210, meaning that Simon can drive at most 210 more miles before his electric car runs out of battery.

If Simon has driven 140 miles since fully charging his car, then the amount of charge remaining in the battery can power the car for x miles. We can set up the following inequality to represent this situation:

x ≤ 350 - 140

The amount of charge left in the battery is shown on the right-hand side of the inequality and is equal to the maximum amount of charge the battery can store (350 miles) minus the amount of charge that has already been utilised (140 miles). The left-hand side of the inequality displays the number of miles Simon can travel until his battery runs out, which is either less than or equal to the battery's remaining charge.

Simplifying the inequality, we get:

x ≤ 210

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The probability that a student chosen at random likes science given that he or she likes art is 41.4%

In our case, we want to find P(Science|Art), which is the probability of a student liking science given that he or she likes art. Using Bayes' theorem, we have:

P(Science|Art) = P(Art|Science) x P(Science) / P(Art)

We know that P(Art) = 0.35 and P(Science|Art) = 0.22. To find P(Art|Science), we can use the formula:

P(Art|Science) = P(Science|Art) x P(Art) / P(Science)

We don't know P(Science) yet, but we can calculate it using the fact that:

P(Science) = P(Science|Art) x P(Art) + P(Science|Not Art) x P(Not Art)

where P(Not Art) is the probability that a student does not like art, which is 1 - P(Art) = 0.65. We are given that P(Science|Not Art) = 0.15, which is the probability that a student who does not like art likes science. Substituting these values, we get:

P(Science) = 0.22 x 0.35 + 0.15 x 0.65 = 0.1855

Now we can substitute all the values into Bayes' theorem:

P(Science|Art) = 0.22 x 0.35 / 0.1855 = 0.414 or 41.4%

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The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.

Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by [tex]D(t)= (t-10)^2[/tex]; 0. We will solve this problem by finding the answer step by step. FunctionThe function of the lesion's size over time is provided by the equation D(t)= (t-10)2, where t is the time in days and D(t) is the diameter of the lesion at the time t.

The origin of this equation is given by D(t) = f(t), where the variable t represents the independent variable, and the variable D(t) represents the dependent variable. To calculate the diameter of the lesion over time, substitute values of t into the equation D(t) = (t-10)2. When t = 0, for instance, D(0) = (0-10)2 = 100. This means that the lesion's diameter at time zero is 100cm.

The model's interpretation The mathematical model that describes the diameter of a lesion as a function of time was created by a medical researcher. The equation D(t) = (t-10)2 represents this model. The researcher's model indicates that the diameter of the lesion is equal to the square of the difference between the time and ten. The difference between the time and ten is squared, which means that the model represents a parabolic curve.

The question is, "Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as a function of time (days) is given by D(t)= (t-10)^2; answer in 200 words."
The given equation is a quadratic function, which is expressed as[tex]D(t)= (t-10)^2.[/tex]This means that the diameter (D) of the lesion is dependent upon the time (t) that has passed since the lesion's onset. Specifically, the diameter of the lesion will increase as the time since onset increases.
The graph of this equation will be a parabola with its vertex at (10, 0). This is because, when t=10, the diameter of the lesion (D) will be zero. As t increases, the graph will move up and to the right, forming a parabola with a positive slope.
In addition to describing the diameter of the lesion as a function of time, the equation also allows us to calculate the diameter of the lesion for any given time. To do this, we can plug in the desired time value for t, and calculate the resulting diameter.
For example, if the medical researcher wants to determine the diameter of the lesion when t=15 days, they can plug in 15 for t, and calculate that the diameter of the lesion at that time is 25 cm. This can be found by plugging in 15 for t and calculating [tex]D(15)=(15-10)^2[/tex]=25 cm.
In conclusion, the equation[tex]D(t)= (t-10)^2.[/tex]is a quadratic function that describes the diameter of a lesion in cm as a function of time (days). The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.

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Answer:

The television tower is 132 feet high.

Step-by-step explanation:

Let h be the height of the television tower. Set up and solve this proportion.

[tex] \frac{3}{5} = \frac{h}{220} [/tex]

[tex]5h = 660[/tex]

[tex]h = 132[/tex]

The probability of a family having two boy children is 0.25, or 25%. This probability is determined by a simple calculation. If there are two children in the family, the probability of each child being a boy is 0.5 (50%), and the probability of both children being boys is 0.5 x 0.5, or 0.25 (25%).

When it comes to probability, the likelihood of an event is determined by the number of possible outcomes. In the case of this question, there are four possible outcomes: two boys, two girls, one boy and one girl, and one girl and one boy. Since each outcome is equally likely, each has a probability of 0.25 (25%).

It is important to note that the probability of a family having two boy children is the same as the probability of a family having two girls. In each case, the probability is 0.25 (25%). This is because the gender of a child is independent of the gender of their sibling.

In conclusion, the probability of a family having two boy children is 0.25 (25%). This probability is determined by the number of possible outcomes, each of which is equally likely. It is also important to note that this probability is the same for a family having two girls.

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Answer:

Slope is -2. So, choice D is the best option.

Step-by-step explanation:

Start with one point then use the formula to get to the next point:

Rise
------

Run

Let's start at (0,5) then count down 2 points, which is the "Rise"(seems like an interesting name to pick but it works).
Next, you go to the right once. Which counts as the "Run".

Remember: The slope is like a ratio, and the "y" will always go as the numerator and the "x" as the denominator. Which is why "Rise" is on top and the "Run" is on the bottom.

So your answer would be 2/1. And that simplifies to 2. But since you went down and not up, it would be negative 2.

Hope this helps and if you have any other questions or need clarification please ask!

The correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw would depend on the weight of the people and their distance apart.

When the seesaw is in equilibrium, the height of the people will be related inversely proportional to their weight. If the weight of one person increases, the height of the other person would decrease and vice versa.

The correlation coefficient will be negative and can range from -1 to 0, with -1 being the highest correlation. The closer the correlation coefficient is to -1, the more closely related the heights of the two people will be. The correlation coefficient will be zero when the people are not in equilibrium.

This is because the height of the people is not related in any way when the seesaw is not in equilibrium. Therefore, the correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw is negative and ranges from -1 to 0.

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Answer:  72

Step-by-step explanation:

b + 108 = 180

        b = 180 - 108

        b = 72 = c

The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.

When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.

Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.

These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.

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Therefore, the 95% confidence interval for the population standard deviation is approximately (2.6, 12.3).

To construct a 95% confidence interval for the population standard deviation, we will use the chi-square distribution. Here are the steps:

Step 1: Identify the given values.
n = 5 (sample size)
s = 4.4 (sample standard deviation)
c = 0.95 (confidence level)

Step 2: Find the degrees of freedom.
df = n - 1 = 5 - 1 = 4

Step 3: Find the chi-square values.
For a 95% confidence interval, we will use the values corresponding to 2.5% and 97.5% in the chi-square distribution table. For df = 4:
Chi-square (0.025) = 11.143
Chi-square (0.975) = 0.485

Step 4: Calculate the confidence interval for the population variance.
Lower limit:[tex] (n - 1) * s^2 / Chi-square (0.025) = 4 * (4.4)^2 / 11.143 = 6.960[/tex]
Upper limit:[tex] (n - 1) * s^2 / Chi-square (0.975) = 4 * (4.4)^2 / 0.485 = 151.977[/tex]

Step 5: Calculate the confidence interval for the population standard deviation by taking the square root of the variance limits.
Lower limit: [tex]√6.960 = 2.6[/tex]
Upper limit:[tex] √151.977 = 12.3[/tex]

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Optiοn A : Side AD is οppοsite tο the angle ACD in the given triangle ADC.

Every triangle has 3 sides and thus 3 angles. Each side οf a triangle has 2 angles οf it fοrmed at the 2 endings οf the side and οne angle is the οne present οppοsite tο the side.

Thus, fοr each side, 2 angles are tοuched and 1 angle at the οppοsite is called the οppοsite angle tο that side.

Here, the triangle is ADC.

The 3 angles οf the triangle are : ADC, ACD, and CAD

Fοr side AD,

The twο angles A ( CAD ) and D( ADC ) are cοnnected with the side AD and are adjacent tο it.

The third angle C ( CAD ) is nοn-adjacent tο side AD and is οppοsite tο it. Hence, Optiοn D is cοrrect.

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Answer:B

Step-by-step explanation: x=3;x=6

Answer:

Step-by-step explanation:

Credits : sqdancefan (Brainly.com)

I changed some of it myself  :)

Answer:

A) intercept: 0 profit : Maximum(max) : max profit. increasing x <4 ; decreasing x > 4

B) average slope: ≈50, about $50 increasing profit for each $1 increasing in price.

Step-by-step explanation:

A) The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice

The higher or largest number of the chart is the maximum reach

B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about ...

(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50

The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.

______

* if we take the peak profit to be $270 we can write f(x) as ...

f(x) 16.875x(x-8)

Then f(1) = 118.15 ad average rate if changed is 50.625. For the purpose here, we judge the extra precision to be pointless

The maximum number of hours Connor can work in landscaping is 5 hours.

In mathematics, inequalities are statements that compare two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), and "!=" (not equal to).

Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:

x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)

8(12) + 12x ≥ 160 (since Connor must earn no less than $160)

Simplifying the second inequality, we get:

96 + 12x ≥ 160

12x ≥ 64

x ≥ 64/12

x ≥ 5.33

Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours. We can check that this satisfies both inequalities:

5 ≤ 15 - 12

5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160

Therefore,Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:

x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)

8(12) + 12x ≥ 160 (since Connor must earn no less than $160)

Simplifying the second inequality, we get:

96 + 12x ≥ 160

12x ≥ 64

x ≥ 64/12

x ≥ 5.33

Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours.

We can check that this satisfies both inequalities:

5 ≤ 15 - 12

5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160

Therefore, the answer is 5.

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The provided assertion states that is the answer to a inequality 4x - 5 ≥ 7 is x ≥ 3.

In mathematics, "inequality" refers to a connection between two formulas or numbers that is not identical to each other. As a result, disparity results from a lack of balance.

To solve 4x - 5 ≥ 7, we can isolate the variable x by adding 5 to both sides of the inequality:

4x - 5 + 5 ≥ 7 + 5

Simplifying:

4x ≥ 12

Next, we can isolate x by dividing both sides by 4:

4x/4 ≥ 12/4

Simplifying:

x ≥ 3

Therefore, the solution to the inequality 4x - 5 ≥ 7 is x ≥ 3.

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Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

Step-by-step explanation:

The side opposite to the 4 degree angle is 18 m

The side adjacent the 4 degree angle is x

tan(4) = opposite / adjacent

adjacent = opposite / (tan(4))

adjacent = 18 / tan(4)

adjacent = 257.41

so, x = (11 + [tex]\sqrt{-109}[/tex]) / 4 is not a real root because the square root of a negative number is not a real number. x = 9.140 and x = 1.855 are not roots of the polynomial.

The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number "x" is represented by the symbol "√x". For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25.

Given by the question.

To find the roots of the polynomial [tex]x^{2}[/tex] - 11x + 17, we can use the quadratic formula:

x = ([tex]\sqrt{b^{2}-4ac }[/tex]) / 2a

Here, a = 1, b = -11, and c = 17.

Substituting these values into the quadratic formula, we get:

x = (11 ± [tex]\sqrt{11^{2}-4(1)(17) }[/tex]) / 2(1)

Simplifying this expression, we get:

x = (11 ± [tex]\sqrt{53}[/tex]) / 2

Therefore, the two roots of the polynomial are:

x = (11 + [tex]\sqrt{53}[/tex]) / 2 and x = (11 - [tex]\sqrt{53}[/tex]) / 2

x= (11+7.280)/2 and x = (11-7.280)/2

x= 18.280/2 and x = 3.71/2

x = 9.140 and x = 1.855

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Answer:

Step-by-step explanation:

36 +55

The value of the angle x is 30 degrees

Trigonometric identities are identified as those equalities of a function holding that all of the values in the given function, equation or expression are true.

There are distinct trigonometric identities. They are enumerated thus;

Note that the sine identity is represented as;

sin θ = opposite/ hypotenuse

Opposite of angle x = 48cm

Hypotenuse = 96cm

Substitute the values

sinx =48/96

sin x = 0. 5000

Take sine inverse

x = 30 degrees

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The medians intersect at the coordinate (4, 5/3).

The medians of a triangle intersect at a point known as the centroid. The coordinate of centroid is given by:

Centroid of the triangle = ((x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3)

where (x,y) are the coordinates of the vertices

The coordinate of the vertices of the triangle are (0,0), (5,0), and (7,5). Using the formula:

Centroid of the triangle = ((x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3)

Centroid of the triangle = ((0+5+7)/3 , (0+0+5)/3)

Centroid of the triangle = (12/3, 5/3)

Centroid of the triangle = (4, 5/3)

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The most likely number of marbles in Aileen's bag is given as follows:

The most likely number of marbles is obtained applying the proportions in the context of the problem.

Out of 10 marbles, from the sample, the results are given as follows:

Aileen has 40 colored marbles inside a bag, which is four times the size of the sample, hence the most likely number of marbles in Aileen's bag is obtained as follows:

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