NEED HELP ASAP PLS!!!
Jai is older than Henry. Their ages are consecutive integers. Find Jai's age if the
product of their ages is 12.

the simplified form of the given expression is 2cd³(12c + 5d²).just by using simple mathematics we are able to solve to get answer.

what is simplified form ?

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate. Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form. The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

In the given question,

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate.

Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form.

The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

The given expression is a polynomial in two variables c and d. We can simplify it by factoring out the common factors from each term:

24c² d³ + 10cd⁵ =2cd³(12c + 5d²)

Therefore, the simplified form of the given expression is 2cd³(12c + 5d²)

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what is simplified form of 24c² d³+10cd⁵ ?

Answer:

D

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (- 3, - 1 ) , then

y = a(x - (- 3) )² + (- 1)

y = a(x + 3)² - 1

to find a substitute the coordinates of any other point on the graph into the equation.

using (- 2, 0 )

0 = a(- 2 + 3)² - 1

0 = a(1)² - 1

0 = a - 1 ( ad 1 to both sides )

1 = a

then

y = (x + 3)² - 1 ← equation of graph

The probability that the average size of the fish you caught is more than 13 inches is approximately 0.0918, or about 9.18%.

We can use the Central Limit Theorem to approximate the distribution of the sample mean. According to the theorem, the sample mean of a sufficiently large sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 4, which may not be considered sufficiently large, but we can still use the approximation. Thus, the distribution of the sample mean can be approximated as:

mean = 11

standard deviation = 3 / sqrt(4) = 1.5

To find the probability that the average size of the fish you caught is more than 13 inches, we need to standardize the sample mean using the z-score formula:

z = (x - mean) / standard deviation

where x is the sample mean we want to find the probability for. Plugging in the values, we get:

z = (13 - 11) / 1.5 = 1.33

Now, we need to find the probability of getting a z-score greater than 1.33 in a standard normal distribution table or calculator. Using a calculator or statistical software, we find that this probability is approximately 0.0918.

Therefore, the probability that the average size of the fish you caught is more than 13 inches is approximately 0.0918, or about 9.18%.

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Answer: C and D

Step-by-step explanation:

To factorize the expression 2x3 + 5x2 + 6x + 15, we can look for common factors: 2x3 + 5x2 + 6x + 15 = x2(2x + 5) + 3(2x + 5) = (x2 + 3)(2x + 5)

Therefore, option C (x2 + 3)(2x + 5) is equivalent to the given expression.

To solve the problem, we need to factorize the given expression and compare it with the given options to find the equivalent expression.

The given expression is:

2x3 + 5x2 + 6x + 15

To factorize it, we can look for common factors:

2x3 + 5x2 + 6x + 15 = x2(2x + 5) + 3(2x + 5)

Now we can see that (2x + 5) is a common factor. Factoring it out, we get:

2x3 + 5x2 + 6x + 15 = (2x + 5)(x2 + 3)

Complete Question Below:

2x3 + 5x2 + 6x + 15

Which of the following is equivalent to the expression above?

A. (x + 3)(2x2 + 5)

B. (x + 5)(2x2 + 3)

C. (x2 + 3)(2x + 5)

D. (x2 + 5)(2x + 3)

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Answer: 247in

Step-by-step explanation:

Area of a circle is pi radius squared.

So that'll be 3.14 times 9 (because radius is halve if a diameter) squared.

First using Order of Operations squaring the 9, so that'll be 81.

Lastly you multiply π or 3.14.

So 81 x 3.14 is 247.  Which is rounded down to the nearest whole number.

Happy Solving.

The answer to the given question about IQR is option b Bus 14, with an IQR of 6.

To determine which bus is the most consistent, we need to look at the measure of variability for each data set. In this case, we are given the interquartile range (IQR) and the range for each bus. The IQR is a better measure of variability than the range because it is less affected by outliers.

Bus 47 has an IQR of 8, which means that the middle 50% of the data falls within a range of 8 minutes. Bus 14 has an IQR of 6, which means that the middle 50% of the data falls within a range of 6 minutes.

Since Bus 14 has a smaller IQR, it is more consistent than Bus 47. This means that the travel times for Bus 14 are more similar to each other than the travel times for Bus 47. Therefore, we can conclude that Bus 14 is the most consistent of the two buses.

Therefore, the correct answer is:

Bus 14, with an IQR of 6.

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Answer:

d.

Step-by-step explanation:

54 inches = 1 1

2

yards

Formula: divide the value in inches by 36 because 1 yard equals 36 inches.

So, 54 inches = 54

36

= 1 1

2

or 1.5 yards.

Conversion of 54 inches to other length, height & distance units

54 inches = 0.00137 kilometer

54 inches = 1.37 meters

54 inches = 137 centimeters

54 inches = 13.7 decimeters

54 inches = 1370 millimeters

54 inches = 1.372 × 1010 angstroms

54 inches = 0.000852 mile

54 inches = 3

4

fathom

54 inches = 4 1

2

feet

54 inches = 13 1

2

hands

54 inches = 12 fingers

54 inches = 0.429 bamboo

54 inches = 161 barleycorns

The height of the basketball hoop is 6 units.

Step 1: Identify similar triangles.

Similar triangles are triangles with the same shape but not necessarily the same size. They have proportional sides and equal angles.
Step 2: Determine the corresponding sides and angles
Once you have identified the similar triangles, determine which sides and angles correspond with each other. The ratio of the corresponding sides in similar triangles will be equal.
Step 3: Set up a proportion
Now, set up a proportion using the corresponding sides of the similar triangles.
(side of first triangle) / (side of second triangle) = (height of first triangle) / (height of second triangle)
Step 4: Plug in the known values
Fill in the known values from the problem into the proportion. For example:
[tex](3 / 5) = (h / 10)[/tex]
Step 5: Solve for the unknown variable
Cross-multiply to solve for the unknown variable (h). In this example:
[tex]3 * 10 = 5 * h[/tex]
[tex]30 = 5h[/tex]
h = 6
So, the height of the basketball hoop is 6 units.

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The amount of money in an account at the end of 5 years will be $14,014.40.

To calculate this, we can use the continuous compounding formula: [tex]A = Pe^(rt)[/tex] where P = 10,000, r = 6.75% (0.0675), t = 5.

Now, the amount of money in an account at the end of 5 years will be:

A = 10,000*e^(0.0675*5)

A = 10,000*e^0.3375

A = 10,000*1.40143960839

A = 14014.3960839

A = $14,014.40

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To find the weight of the puppy when it is 15 weeks old, we need to substitute 15 for x in the equation of the line of best fit:

y = 2x + 1.5

y = 2(15) + 1.5

y = 31.5

Therefore, the weight of the puppy when it is 15 weeks old is 31.5 units, where the units depend on the units used to measure weight (e.g. pounds, kilograms, etc.).

Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

In mathematics, a function is a rule or relationship that maps each input value (also known as the "argument" or "independent variable") to a corresponding output value (also known as the "value" or "dependent variable").

In other words, a function is a way to describe how one set of values (the inputs) are transformed into another set of values (the outputs). Functions are often represented using algebraic equations or graphical representations, such as graphs or charts.

For example, the function f(x) = 2x + 1 maps each input value x to the output value 2x + 1. So, if we input x=2, the output value would be f(2) = 2(2) + 1 = 5. Similarly, if we input x=3, the output value would be f (3) = 2(3) + 1 = 7.

(a) Based on the scatter plot, we can see a positive linear relationship between the hours spent on homework and the test scores. As the number of hours spent on homework increases, the test scores also tend to increase.

(b) To use Paul's function to predict the test score for 3 hours of homework, we can substitute x = 3 into the equation:

[tex]y = 8x + 40[/tex]

[tex]y = 8(3) + 40[/tex]

[tex]y = 24 + 40[/tex]

[tex]y = 64[/tex]

Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

(c) In the context of the situation, the number 40 in Paul's model represents the baseline or minimum test score that a student would get if they didn't study at all. This is the y-intercept of the line and indicates that a student who does not spend any time on homework is predicted to get a score of 40.

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...where h = -8 and k = -3.

The equivalent expression to the given equation is (2 x 10⁸)(2 x 10⁻²) and  40 x 10⁵.

What is an equivalent expression?

Equivalent expressions do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two equivalent algebraic expressions have the same value (s).

Here, we have

Given: 4 x 10⁶

We have to find the equivalent expression to the given equation.

A. (2 x 10⁸)(2 x 10⁻²)

= (2 × 2)(10⁸× 10⁻²)

= 4×10⁶

B. 40 x 10⁵

= 4×10×10⁵

= 40×10⁵

Hence,  the equivalent expression to the given equation is (2 x 10⁸)(2 x 10⁻²) and  40 x 10⁵.

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Answer: 122 cm²

Step-by-step explanation:

Answer:

a. The scale factor of the smaller cylinder to the larger cylinder is the ratio of their radii, which is 4/6 or 2/3.

b. The circumference of the base of a cylinder is given by 2πr, where r is the radius of the base. Thus, the ratio of the circumferences of the bases of the two cylinders is:

(2π)(4)/(2π)(6) = 4/6 = 2/3

c. The lateral area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height. The ratio of the lateral areas of the two cylinders is:

(2π)(4)(9)/(2π)(6)(9) = 4/6 = 2/3

d. The volume of a cylinder is given by the formula πr²h. Thus, the ratio of the volumes of the two cylinders is:

(π)(4²)(9)/ (π)(6²)(9) = 16/36 = 4/9

e. If the volume of the smaller cylinder is 144π cm³, then we can use the formula for the volume of a cylinder to solve for the height of the smaller cylinder:

144π = π(4²)h

h = 9 cm

Since the two cylinders are similar, we know that the ratio of their heights is the same as the ratio of their radii, which is 2/3. Thus, the height of the larger cylinder is:

(2/3)(9) = 6 cm

Using the formula for the volume of a cylinder, we can now calculate the volume of the larger cylinder:

V = π(6²)(6) = 216π cm³

Step-by-step explanation:

pa brainliest po.

The probability that an individual has a total cholesterol level between 200 and 250 is calculated to be approximately 0.5020 or 50.2%.

To solve this problem, we need to find the z-scores corresponding to the lower and upper bounds of the cholesterol range, and then find the area under the normal distribution curve between these z-scores.

First, we calculate the z-score for 200:

z1 = (200 - 219) / 41.6 = -0.455

Next, we calculate the z-score for 250:

z2 = (250 - 219) / 41.6 = 0.746

Now we can use a standard normal distribution table or calculator to find the area between these two z-scores:

P(-0.455 < Z < 0.746) ≈ 0.5020

This means that the probability that an individual has a total cholesterol level between 200 and 250 is approximately 0.5020 or 50.2% (rounded to one decimal place).

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This is challenging to visualize but similar to your other problem. You want to maximize x and y to maximize c.

The problem just boils down to solving the linear system.

2x + 2y = 10

3x + y = 9

I changed the less than or equal signs to equal signs because we want the largest values not the ones less than the max. I think you know how to solve this system based on the difficulty of the problem but I can give a solution. Let's use elimination. Multiplying the second equation by two and adding it to the first we have...

   -2(3x + y = 9)

+ (2x + 2y = 10)

----------------------

-4x = -8

x = 2

Then y = 9 - 3x (from eq 2) = 9 - 3(2) = 3

Then the max value of c = 4(2) + 2(3) = 14

Answer:x+y=c

Step-by-step explanation:

The correct centre measure, with a mean value of approximately 5 gallons, will be C. Coffee Ground, with a mean value of about 5 gallons, which will show which shop usually sells the most coffee per hour.

By summing up all the data points and dividing by the total number of data points, the mean is determined.

To determine which coffee shop typically sells the most amount of coffee per hour, we can compare the measures of center, specifically the mean and median, of the two datasets.

Calculating the mean for each dataset, we get:

Coffee Ground: (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.125 gallons

Wide Awake: (2.5+10+4+18+4+3+6+5+2.5)/9 = 6.0556 gallons

Therefore, Coffee Ground has a higher mean than Wide Awake, suggesting that Coffee Ground typically sells more coffee per hour.

Calculating the median for each dataset, we get:

Coffee Ground: 5 gallons

Wide Awake: 4.5 gallons

Therefore, the median for Wide Awake is lower than that of Coffee Ground, suggesting that Wide Awake typically sells less coffee per hour.

Based on these measures of center, we can conclude that the answer is: C. Coffee Ground, with a mean value of about 5 gallons.

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Answer:

10,500 grams

Step-by-step explanation:

3.5 x 3 = 10.5 kg

To convert kg to grams, multiply by 1000.  To multiply by 1,000 move the decimal right 3 places.

10,500 grams

Helping in the name of Jesus.

The probability that a randomly selected user is online less than 15 hours a week is 0.1056 (approx).

As per the given statement, u.s. internet users spend an average of 18.3 hours a week online. If 95% of users spend between 13.1 and 23.5 hours a week, we need to determine the probability that a randomly selected user is online less than 15 hours a week.

To find the probability that a randomly selected user is online less than 15 hours a week, we need to use the Z-score formula, which is defined as:

Z = (X - μ) / σ

Where Z is the z-score, X is the value of the element, μ is the mean of the population, and σ is the standard deviation. Therefore, the probability of a randomly selected user being online less than 15 hours per week can be calculated as follows:Z = (15 - 18.3) / σ

We know that 95% of users spend between 13.1 and 23.5 hours per week, which means that the standard deviation is given by:

13.1 - 18.3 = 5.4 hours (lower bound)

23.5 - 18.3 = 5.2 hours (upper bound)

Therefore, σ = (5.4 + 5.2) / 4 = 2.65 hours

Hence, the z-score can be calculated as follows:Z = (15 - 18.3) / 2.65 = -1.25

Thus, the probability that a randomly selected user is online less than 15 hours a week is P(Z < -1.25). Using a standard normal distribution table, we can find that P(Z < -1.25) = 0.1056 (approx).

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By multiplication method the cargo will take up 7× 10⁷ energy.

In arithmetic, the multiplication or product of two numbers it represents the repeated addition of one number to another. It can be done in between numbers which can be whole numbers, natural numbers, integers, fractions, etc.

Dr. Nandi plans to transport  3.5×10⁵ energy prism that each take up 2 ×10² cubic feet of cargo space.

The total can be calculated by multiplication method.

Here the multiplication gives

                    3.5×10⁵ × 2 ×10²

                    = 3.5 × 2 ×10⁵⁺²

                    = 7× 10⁷ energy.

Hence, the cargo will take up 7 × 10⁷ energy.

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Answer:

Step-by-step explanation:

To find:-

Answer:-

The given coordinates of the triangle are , A(3,-4) ; B(-2,1) and C(5,0) .

To find out the coordinate of the centroid we can use the below formula ,

[tex]\longrightarrow \boxed{\rm{Centroid\ (G)}= \bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)} \\[/tex]

where ,

On substituting the respective values, we have;

[tex]\longrightarrow G =\bigg(\dfrac{3-2+5}{3},\dfrac{-4+1+0}{3}\bigg) \\[/tex]

[tex]\longrightarrow G =\bigg(\dfrac{ 6}{3},\dfrac{-3}{3}\bigg) \\[/tex]

[tex]\longrightarrow \boldsymbol{ G = (2,-1) }\\[/tex]

Hence the centroid of the given triangle is (2,-1) .

Now the given equation of the line is,

[tex]\longrightarrow x - 3y = 4 \\[/tex]

Convert this into slope intercept form of the line, which is,

Slope intercept form:-

[tex]\longrightarrow y = mx + c\\[/tex]

where, m is the slope of the line and c is the y-intercept .

So , we have;

[tex]\longrightarrow -3y = 4-x\\[/tex]

[tex]\longrightarrow 3y = x - 4 \\[/tex]

[tex]\longrightarrow y =\dfrac{x-4}{3} \\[/tex]

[tex]\longrightarrow y =\dfrac{1}{3}x-\dfrac{4}{3} \\[/tex]

On comparing it with the slope intercept form, we have;

[tex]\longrightarrow m =\dfrac{1}{3}\\[/tex]

Secondly we know that the slopes of parallel lines are equal . So the slope of the line parallel to the given line would also be ⅓ .

Now we may use point slope form of the line to find out the equation of the required line. The point slope form of the line is,

Point slope form:-

[tex]\longrightarrow y - y_1 = m(x-x_1) \\[/tex]

where the symbols have their usual meaning.

Here the line will pass through the centroid of the triangle which is (2,-1) .

On substituting the respective values, we have;

[tex]\longrightarrow y - (-1) =\dfrac{1}{3}(x-2) \\[/tex]

[tex]\longrightarrow 3( y +1) = x - 2 \\[/tex]

[tex]\longrightarrow 3y + 3 = x -2\\[/tex]

[tex]\longrightarrow x - 2 - 3 - 3y = 0 \\[/tex]

[tex]\longrightarrow\boxed{\boldsymbol{ x - 3y - 5 =0}} \\[/tex]

This is the required equation of the line.

The actual population mean is between 1.5 and 2.1 vehicles per household.

The median is a statistical measure that represents the middle value of a dataset. It is the value that separates the lower half of the dataset from the upper half. To find the median, the data must be arranged in order from smallest to largest, and then the middle value is identified.

If the dataset contains an odd number of values, then the median is the middle value. For example, if the dataset is {2, 4, 6, 7, 9}, then the median is 6, which is the middle value.

If the dataset contains an even number of values, then the median is the average of the two middle values. For example, if the dataset is {2, 4, 6, 7, 9, 10}, then the median is (6+7)/2 = 6.5, which is the average of the two middle values, 6 and 7.

The actual population mean is between 1.5 and 2.1 vehicles per household.

The margin of error represents the possible distance between the sample mean and the true population mean.

The lower bound is found by subtracting the margin of error from the sample mean:

1.8 - 0.3 = 1.5

The upper bound is found by adding the margin of error to the sample mean:

1.8 + 0.3 = 2.1

Therefore, we can be 95% confident that the true population mean falls between 1.5 and 2.1 vehicles per household.

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Answer:

[tex]728 \: {m}^{2} [/tex]

Step-by-step explanation:

Given:

l = 15 m (length)

w = 16 m (width)

h = 4 m (height)

Find: a (surface) - ?

First, let's find the area of the base:

a (base) = l × w

a (base) = 15 × 16 = 240 m^2

Since the rectangular prism has 2 bases, we multiply this number by 2:

240 × 2 = 480 m^2 (area of both bases)

Now, let's find the lateral surface area:

a (lateral) = 2(4 × 15) + 2(4×16) = 2 × 60 + 2 × 64 = 120 + 128 = 248 m^2

Finally, in order to find the whole surface area, we have to add the lateral surface area and both bases area together:

a (surface) = a (lateral) + a (base)

a (surface) = 248 + 480 = 728 m^2

To determine the rows where the expression (p ∧ q) ∨ (p ∧ r) is true, we can construct a truth table with columns for p, q, r, p ∧ q, p ∧ r, (p ∧ q) ∨ (p ∧ r), as shown below:

```

p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r)

----------------------------------------------

T | T | T | T | T | T

T | T | F | T | T | T

T | F | T | F | T | T

T | F | F | F | F | F

F | T | T | F | F | F

F | T | F | F | F | F

F | F | T | F | F | F

F | F | F | F | F | F

```

The rows where the expression (p ∧ q) ∨ (p ∧ r) is true are the first, second, and third rows, where the last column is true. Therefore, the rows where the expression is true are:

```

p | q | r

--------

T | T | T

T | T | F

T | F | T

```

Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

How to find distance and direction?

To find the distance and direction of Port C from Port A, we can use basic trigonometry and vector analysis.

First, we need to draw a diagram of the situation. We can assume that Port A is located at the origin (0,0) of a two-dimensional coordinate system, and that the ship sails in a straight line from A to B on a bearing of 050 degrees, which means that its direction is 40 degrees clockwise from the positive x-axis. Since Port B is 80 kilometers to the east of A, we can represent it as the point (80,0) in the coordinate system.

Next, the ship sails from B to C on a bearing of 062 degrees, which is 22 degrees clockwise from its previous direction. To calculate the distance and direction of C from A, we need to find the vector that represents the displacement of the ship from B to C, and add it to the vector that represents the displacement from A to B.

To find the vector that represents the displacement from B to C, we can use basic trigonometry. Let d be the distance from B to C, and let θ be the angle between the displacement vector and the positive x-axis. Then, we have:

cos(θ) = adjacent/hypotenuse = 80/d

sin(θ) = opposite/hypotenuse = (d*sin(22))/d = sin(22)

Solving for d, we get:

d = 80/cos(θ) = 80/cos(arctan(sin(22)/cos(22))) ≈ 92.56 km

Therefore, the vector that represents the displacement from B to C is (dcos(θ), dsin(θ)) ≈ (64.39 km, 35.77 km) in the coordinate system.

To find the vector that represents the displacement from A to C, we can add the two vectors:

(80,0) + (64.39,35.77) ≈ (144.39,35.77)

Therefore, the distance from A to C is the magnitude of this vector:

|AC| = sqrt((144.39)² + (35.77)²) ≈ 148.96 km

To find the direction of C from A, we can use the inverse tangent function:

tan⁻¹(35.77/144.39) ≈ 13.93 degrees

Therefore, Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

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