The product of two numbers is 126 . The smaller number is 5 less than the larger number. Which of the following equations can be used to solve for the larger number?

The difference between area and volume is that:

8. Area describes the space taken up by two-dimensional objects whereas volume describes the space taken up by three-dimensional objects. The area can be measured in square meters (m²) and square kilometers (km²), whereas, volume can be measured in cubic millimeters (mm³), and cubic meters (m³).

9. The volume of the cube is D. 12 cubic units.

To calculate the volume of a cube, we multiply all three sides. The formula is V = S³.

So, for the cube shape with the given three sides, we can obtain the volume by executing the following operation:

1 × 2 × 6

12 cubic units. Option D is thus correct.

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The correct box plot would have a box extending from 15 to 21, with a median line at 19, and whiskers extending from 12 to 24. So, correct option is A.

To create a box plot, we need to first find the five-number summary, which includes the minimum value, first quartile (Q₁), median, third quartile (Q₃), and maximum value.

The minimum value in the given data set is 12 and the maximum value is 24. To find the median, we need to find the middle number of the set. Since there are nine numbers in the set, the median would be the average of the fifth and sixth numbers, which is 19.

To find the first quartile (Q₁) and third quartile (Q₃), we can find the medians of the lower and upper halves of the data set, respectively. The lower half of the data set includes the numbers 12, 15, 15, 17, and 19. The median of this set is 15. The upper half of the data set includes the numbers 19, 20, 22, and 24. The median of this set is 21.

Using these values, we can create a box plot with a box extending from Q₁ to Q₃, a line in the box indicating the median, and whiskers extending from the box to the minimum and maximum values.

So, correct option is A.

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Complete question is:

The data below represents the number of runners on each cross country team in the Northern Conference. 12, 15, 15, 17, 19, 19, 20, 22, 24.

Which box plot correctly summarizes the data?

The formula for this function is y = 0.9 * cos((2π/3) x + π/2) - 1.2

From the image attached, that looks like a cosine graph with 3 periods. 2 highs and 1 low. Also, it should be noted that it is a cosine function.

Therefore to derive the formula for the graph, we use a cosine function with a phase shift and amplitude adjustment.

The general formula for a cosine function is:

f(x) = A * cos(Bx + C) + D

where

A = amplitude,

B = frequency,

C = phase shift,

D = vertical shift.

To get the Amplitude:

We want the function to oscillate between 2.1 and 0.3, which is a difference of 1.8. Since the sine function oscillates between -1 and 1, we need to multiply it by half the desired difference to get the right amplitude. Therefore,

A = 1/2 *1.8 = 0.9.

To get the Frequency:

Since there are only three periods in the interval, then

frequency =  2π/3.

Therefore B = 2π/3.

To get the Phase shift:

We want the function to peak at x = 0, so we need a phase shift of π/2.

Therefore C = π/2.

To get Vertical shift:

We want the function to have a trough at y = 0.3, which means we need to shift it down by 1.8/2 + 0.3 = 1.2. We set D = -1.2.

Putting all these parameters together, we get the following formula:

f(x) = 0.9 * cos((2π/3) x + π/2) - 1.2

This function will oscillate between 2.1 and 0.3 over three periods, with a peak at x = 0 and a trough at y = 0.3.

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The equation that describes the point estimate of the population mean is x = 35.5

From the question, we have the following parameters that can be used in our computation:

As a general rule

The point estimate of the mean equals the sample mean

This means that

Point estimate = 35.5

Hence, the equation is x = 35.5

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A polygon is a geometric object with two dimensions and an infinite number of sides.  Drawing of each regular polygon: equilateral triangle, square, and regular hexagon can be drawn in the image.

A polygon is a geometric object with two dimensions and an infinite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges.

Vertex or corners refer to the intersection of two line segments, where an angle is created. Having three sides makes a triangle a polygon.  Drawing of each regular polygon: equilateral triangle, square, and regular hexagon can be drawn in the image.

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The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

We have,

∫(√(2 + (cos x)²) / sec x - cosec x) dx:

We can simplify the expression in the integral as follows:

√(2 + (cos x)²)

= √(1 + (cos² x)) + √1

= √(sin² x + cos² x + cos² x) + 1

= √(2cos² x + 1) + 1

So the integral becomes:

∫[(√(2cos² x + 1) + 1) / (1/cos x - 1/sin x)] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x - cos x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x cos x - cos² x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) sin x / (cos x - sin x)] dx

Now we can make the substitution u = cos x - sin x, which gives us

du = (-sin x - cos x) dx, or -du = (sin x + cos x) dx.

Making this substitution and simplifying, we get:

∫[(√(2u² + 2) + 2) / u] du

= ∫[(√2(u² + 1) + √2) / u] du

= √2 ∫[(u² + 1)^(1/2) / u] du + 2 ∫(1/u) du

Using integration by substitution,

let w = u^2 + 1, then dw = 2u du, and we have:

= √2 ∫(1/w) dw + 2 ln|u|

= √2 ln|u| + 2 ln|u| + C

= 3 ln|cos x - sin x| + √2 + C

where C is the constant of integration.

And,

∫arc tan√x dx:

We can make the substitution u = √x, which gives us du = (1/2√x) dx, or 2u du = dx.

Substituting these into the integral, we get:

∫arc tan√x dx = ∫arc tan u x 2u du

Now, using integration by parts with u = arc tan u and dv = 2u du, we get:

∫arc tan u  2u du = u arc tan u - ∫(1 + u²)/(1 + u²)² du

= u arc tan u - ∫1/(1 + u²) du

= u arc tan u - ln|1 + u²| + C

Substituting back u = √x, we get:

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

where C is the constant of integration.

Thus,

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

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Answer:

C

Step-by-step explanation:

Answer:

B  x ≤ 0

Step-by-step explanation:

A solid dot on zero means that zero is included.

The line to the left of zero with an arrowhead means that all numbers less than zero are all included.

The graph represents zero and all numbers less than zero.

The correct inequality is

B  x ≤ 0

Answer:

y = − 1.3x + 10

Step-by-step explanation:

The slope-intercept form is y = mx + b

2.00x + 1.50y = 15

1.50y = -2x + 15

y = − 1.3x + 10

So, the answer to this is y = − 1.3x + 10

Answer: y= -4/3 +10

Step-by-step explanation:

given the equation 2.00x+1.50y=15

subtract 2.00x from both sides

1.50y = -2.00x +15

then divide both sides by 1.50 to isolate y

then you get your answer

y = -4/3 + 10

The experimental  probability is 1/5, or 0.20. The theoretical probability is 0.206.

Probability is represented as the number of ways for an event to happen over all possible outcomes.

a.     For the theoretical probability, there is 1 black spot and 5 total options. Therefore, the probability is 1/5, or 0.20.

b.     For experimental probability, there were 103 times it landed on black out of 500 spins. The probability is 103/500, or 0.206.

c.   Lastly, the multiple choice. The larger sample size you take, assuming a fair spinner, the more likely you are to see results similar to the theoretical probability. This is because the larger sample size taken, the less each individual spin effects the outcome.

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When h = 4, j = 5, and k = -1, the expression jkh + hj - jk equals 5.

To solve the expression we have to substitute the value of each variable in the expression. Then simplify the expression according to mathematic rule. After solving we get the solution of the expression.

An expression is a combination of numbers, variables, and/or operations that can be evaluated or simplified to obtain a numerical or algebraic result.

The given expression is:

jkh + hj - jk

Substituting the given values of h, j, and k, we get:

jkh + hj - jk = (5 x (-1) x 4) + (5 x 4) - (5 x (-1))

Now simplify the expression

jkh + hj - jk = (-20) + 20 + 5

jkh + hj - jk = 5

Therefore, the value of  jkh + hj - jk equals 5.

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The gradients for each line are given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The gradient of each line represents the slope, hence they are given as follows:

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Answer:

D

Step-by-step explanation:

The probability of guessing the correct answer to a true-false question is 1/2.

The probability of guessing the correct answer to all 8 questions is:

(1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/256

Therefore, the probability of guessing the correct answers to all 8 questions is 1/256.

The answer is D.

I hope this helps!

The median of the data set is 24 and the mean is 23.

To find the median of the data set, we need to first put the values in order from least to greatest:

3, 8, 24, 24, 31, 33, 38

There are 7 values in the data set, so the median is the middle value. Since there are an odd number of values, the median is the fourth value, which is 24.

To find the mean of the data set, we add up all the values and divide by the number of values:

Mean = (3 + 8 + 24 + 24 + 31 + 33 + 38) / 7

Mean = 161 / 7

Mean = 23

Therefore, the median of the data set is 24 and the mean is 23.

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The value of the height of the​ cylinder is,

⇒ h = 19 inches

We have to given that;

The volume of a cylinder is 171 pi cubic inches and the radius of the cylinder is 3 inches.

We know that;

Volume of cylinder = πr²h

Hence, We get;

⇒ 171π = π × 3² × h

⇒ 171 = 9h

⇒ h = 171 / 9

⇒ h = 19 inches

Thus,

The value of the height of the​ cylinder is,

⇒ h = 19 inches

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The p-value for this hypothesis test for a proportion is 0.9319.

We are given that;

Number of employees=700

Percent=400%

Now,

Plugging these values into the formula, we get:

Z=7000.40(1−0.40)​​0.4357−0.40​≈1.49

Since the alternative hypothesis is p<0.40, this is a left-tailed test. The p-value is the area to the left of 1.49 under the standard normal curve1. Using a normal table or a calculator, we find that:

p-value=P(Z<1.49)≈0.9319

Therefore, by percentage the answer will be 0.9319.

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If at the soccer game, Sue bought a pack of gum for 25¢ and a candy bar for $1.00, the average cost of the items Sue and her brother bought is 67 cents.

To find the average cost of the items, we need to add up the total cost and divide by the number of items. In this case, there are three items: gum, candy bar, and hot dog.

The total cost is 25¢ + $1.00 + 75¢ = $2.00

The number of items is 3.

So, the average cost is $2.00 / 3 = $0.67 (rounded to the nearest penny).

This means that on average, each item costs 67 cents.

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Answer:80

Step-by-step explanation: 3x+8=5x-40 so 2x=48 so x=24. 24*3+8=80 so our answer is 80.

The explanatory variable is; A. square footage.

The correct scatter diagram of the data is: B. scatter diagram.

The linear correlation coefficient between square footage and asking price is 0.91.

In this scenario, the square footage (x) would be plotted on the x-axis of the scatter plot while the selling price (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the square footage (x) and the selling price (y), an equation for the linear regression is given by:

y = 13.762782 + 0.156710276x

Correlation coefficient, r = 0.904601208 ≈ 0.91.

In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;

0.7＜|r| ≤ 1   (strong correlation)

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The measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

When a transversal line cuts a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

m∠4 + 60° + 61° = 180° {supplementary angles}

m∠4 + 121° = 180°

m∠4 = 180° - 121° {subtract 121° from both sides}

m∠4 = 59°.

Therefore, the measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

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To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

The elimination method is a useful process in solving a system of equations especially when the terms in the equations contain coefficients. By elimination method, the equations may be reduced to an equation containing only one of the unknowns and may be used to solve for the first value. The remaining unknowns are derived using the original equations and the first value.

Let x be the amount invested in stocks at 12%  interest, y be the amount invested at bonds at 3.8% interest and z be the amount invested in CD at

3% interest.

The total investment amounts to $190000

x + y + z = $190000__eq.(1)

The total interest from the three investments is $11250

0.12x + 0.038y + 0.03z = 11250 ___eq.(2)

Country Days invests $15000 more in bonds than in CDs.

y = z + $15000

y - z = $15000 ____eq.(3)

Use elimination method for the first and second equation to eliminate x.

x + y + z = $190000                [ Multiply both sides by 0.12 ]

-[0.12x + 0.038y + 0.03z = 11250]      

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

 0.12x + 0.12y + 0.12z = $ 22,800

-[0.12x + 0.038y + 0.03z = 11250]      

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

          0.082y  +   0.09z  = $11,550

Perform another elimination method for the derived equation above and Equation 3 to eliminate z.

 0.082y  +   0.09z  = $11,550

-[y - z = $15000]   [ Multiply both sides by 0.09 ]

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

0.082y  +   0.09z  = $11,550

-[0.09y - 0.09z= $1350]

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

- 0.008y = $10,200

y = - $1,275,000

Substitute the value of y to Equation 2.

y - z = $15000    [ Substitute y in Equation 3 ]

-1275000 - z = 15000

-z = 15000 + 1275000

z = -$1,290,000

Substitute the value of y and z to Equation 1.

x + y + z = $190000

x - $1,275,000 - $1,290,000 = $190000

x = $190000 + $2565000

x = $2,755,000

To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

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The required, in a reflection of triangle AB ≡ A'B' and ΔABC ≡ ΔABC are true.

AB ≡ A'B': True, because a reflection conserves length, so corresponding segments are congruent.

BC < B'C': False, in general, the length of conserves is preserved under a reflection, so BC = B'C'.

Triangle BACE = triangle B'A'C': True, because a reflection also conserves shape and size, so corresponding angles and sides are congruent.

∠BCA > ∠B'C'A': False, because the measure of an angle is not preserved under a reflection.

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Yes, its possible to have s path through the house that uses door way once and the path is BADC.

In the given graph the vertices represents the rooms.

A, B, C and D are the rooms

the edges represent doorways connecting the rooms.

Vertex represents the outdoors.

Yes, its possible to have s path through the house that uses door way once.

The path is BADC.

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The amount 6424.66 invested at 14% and amount 5221.33 invested at 8%.

We have,

Investment at 14%= $11,646

Investment at 8%= $1317.16

Let x be the amount invested at 14% and y be the amount invested at 8%.

So, x + y = 11646

0.14x + 0.08y = 1317.16

Now, solving the equation we get

x= 6424.66 and y = 5221.333

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The total price including sales tax that Brayden has to pay is $114.15

Sales tax is a tax charged to the buyer of a product based on the product's price.

From the case, we know that:

Sales tax = 6%

price = $18.70

Sales tax to be paid = Sales tax x product price

Sales tax to be paid = 6% x $18.70

Sales tax to be paid = $112.2

Total price to be paid = Product price + Sales tax to be paid

Total price to be paid = $112.2+ $1.95

Total price to be paid = $114.15

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The measure of the line segment XY is 54 units.

Since,

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Given that,

W is between X and Y, WX = 38 and WY = 16.

Here, Length of segment XY is sum of measure of line segments WX and WY, we get

XY=WX+WY

XY=38+16

XY = 54 units

Therefore, the measure of XY is 54 units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the length of XY if W is between X and Y, WX = 38 and WY = 16. XY = ?

Answer:

55,500 cm².

Given:

To find the surface area of the solid figure represented by the given net, we first have to identify the shape of the figure. By analyzing the net, we can see that the figure is a rectangular prism with a length of 65 cm, a width of 40 cm and a height of 250 cm. To find the surface area of a rectangular prism, we use the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values, we get:

Steps:

2(65)(40) + 2(65)(250) + 2(40)(250) = 13,000 + 32,500 + 10,000 = 55,500 cm²

Get:

Therefore, the surface area of the solid figure represented by the given net is 55,500 cm².

Answer:

600 cm².

Step-by-step explanation:

The net provided represents a three-dimensional solid figure. The surface area of this figure can be calculated by finding the area of each individual face and adding them together. The net includes six faces, each of which have different dimensions. The areas of these faces are: 65 cm², 250 cm², 40 cm², 90 cm², 90 cm², and 65 cm². Adding them together, we get a total surface area of 600 cm². Therefore, the surface area of the solid figure represented by the given net is 600 cm².

The delineation of A as a subset of B, and also the differentiation in assertion that A is not equivalent to B, can be attributed to A containing merely three elements (a, b, along with c) as opposed to B's countenance of five elements (including a, b, c, d, subsequently e).

As all components of A coincidentally exist within B, one may ascertrain that A is indeed a subset of B.

However, due to B enclosing two additional elements (d, then e) which are not replete within A, we can conclusively deny that A is comparable to B.

Symbolically:

A ⊆ B (A constitutes a subset of B)

A ≠ B (A isn't analogous to B)

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The value of probability that they win the next game is,

⇒ 6/13

We have to given that;

The NY Knicks won 35 games out of 65 games.

Now, We can simplify as;

The possible value of to win next game is,

⇒ 65 - 35

⇒ 30

Thus, The value of probability that they win the next game is,

⇒ 30 / 65

⇒ 6/13

So, The value of probability that they win the next game is,

⇒ 6/13

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The answer is below., the town's tax status should change within the next 3 years.

An exponential decrease can be represented by the formula:

y = ab^x

where a is the initial amount and b < 1.

Let p represent the population after t years, hence:

p = ab^t

Since the population decreases exponentially at a rate of 14.3% each year, hence:

b = 100% - 14.3% = 85.7% = 0.857

b = 0.857

Also, a = 9400 people

Therefore the equation is:

p = 9400(0.857)^t

The town's tax status will change once the population is below 6,000 people, therefore:

9400(0.857)^t < 6000

for the tax status to change.

At t = 3 years:

p = 5917

so, 5917< 6000

the town's tax status should change within the next 3 years.

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