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QuestionAnswerA factory uses 1/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 3/4 of a barrel of raisins. How many batches of granola bars did the factory make yesterday?3A water bottle holds 5/6 of a gallon of water. There are 5 5/6 gallons of water in a water tank. How many water bottles can be filled with the water in the tank?7Molly ran 2 laps around the track. If the total distance Molly ran was 3 3/4 miles, how long is each lap around the track?Every day, the Knox Pet Store uses 2 5/6 bags of dog food to feed the dogs. For how many days will 5 2/3 bags of dog food last?Sam grew tomatoes this summer and used them to make 1/2 of a gallon of tomato sauce. He split it into 5 equal portions to freeze for using later. How many gallons was each portion?1/10Kimberly made 2 1/2 quarts of hot chocolate. Each mug holds 1/2 of a quart. How many mugs will Kimberly be able to fill?5Rosa made fancy orange costume decorations for each of the 5 dancers in her year-end dance performance. She cut 5/6 of a yard of ribbon into equal pieces to make the decorations. How long was each piece of ribbon?1/6A factory uses 1/2 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make yesterday?3

The factory made 3 batches of granola bars yesterday.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Given that a factory uses 1/6 of a barrel of raisins in each batch of granola bars.

Let the factory make n batches of granola bars yesterday.

Yesterday, the factory used 1/2 of a barrel of raisins.

So 1/2 barrel = n batches of granola bars

The proportionality of the relationship as

⇒ 1/6 : 1 :: 1/2 : n

⇒ (1/6)n = 1/2

Multiplying both sides by 6

⇒ n = 3

Hence, the factory made 3 batches of granola bars yesterday.

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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ANSWER

36 feet

EXPLANATION

We are given that the scale of the model is 1 inch to 9 feet.

The two flagpoles are 4 inches apart in the model.

To find the distance between them when they are installed, we have to use ratio/proportion.

Let the distance between them be x.

We have that from the scale:

1 inch = 9 feet

=> 4 inches = x feet

Now, we can cross-multiply:

Therefore, the distance between them when they are installed is 36 feet.

Answer:

b

Step-by-step explanation:

put -2 on x and you will get a value of 1/4

(can use other number on table too but must got the same value of y)

example: use -1 for x and the answer must be 1/2

The following functions can be simplify as follows:

(a) f+g=x²+3x+8

(b) f-g=x²-13x-8

(c) fg=x³+3x²-40x-40

(d) f/g= (x-5)/(x+8) domain is x≠-8.

(a) To find f+g, we simply add the two functions together:

f+g=x^{2}-5x+x+8= x^{2}+3x+8

(b) To find f-g, we subtract g from f:

f-g=x^{2}-5x-(x+8)= x^{2}-6x-8= x^{2}-13x-8

(c) To find fg, we multiply the two functions together

:fg=(x^{2}-5x)(x+8)= x^{3}+3x^{2}-40x-40

(d) To find f/g, we divide f by g:

f/g= (x^{2}-5x)/(x+8)= (x-5)/(x+8)

The domain of this function is all real numbers except for -8, since dividing by zero is undefined. So the domain is x≠-8.

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Answer:Here you can enter any number with as many or as few decimal places as you want, and we will round it to the nearest one decimal place. Please enter your

Step-by-step explanation:

The total cost is represented as C = $0.50x + $4300  and the average cost as avgC = $0.50 + $4300/x

We have been given that,

The variable cost for producing the game = $0.50 per unit

The fixed cost for producing the game = $4300

Let the total cost be denoted by C.

And let x be the number of games produced.

a) Total cost = variable cost + fixed cost

          C = $0.50x + $4300

b) Average cost = total cost/number of games produced

                        = C/x

                        = ($0.50x + $4300)/x

                        = $0.50 + $4300/x

Hence the total cost is C = $0.50x + $4300 and the average cost is $0.50 + $4300/x

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Answer:

Step-by-step explanation:

Use the Pythagorean theorem a^2 +b^2 =c^2

So 15^2 + 5^2 = c^2

sqrt c = sqrt 250

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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Answer:

12  more miles

Step-by-step explanation:

she drives 50 miles an hour and the park is 10 miles away so 60 divided by 5 is 12.

Answer:

60/3=20

20/21

Step-by-step explanation:

The quadratic equation whose sum of two real roots is 31 and product is 210 will be \(x^{2} -31x+210 = 0\).

According to the question,

We have the following information:

The sum of roots of a quadratic equation = 31

The product of roots of a quadratic equation = 210

We know that the standard form of the quadratic equation is given as follows:

\(ax^{2} +bx+c = 0\)

Now, the sum of roots is -b/a and the product of roots is c/a.

So, we have the following expressions:

-b/a = 31

b = -31 and a = 1

c/a = 210

c = 210 and a = 1

So, the equation will be:

\(x^{2} -31x+210 = 0\)

Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be \(x^{2} -31x+210 = 0\).

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\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}\)

The second ladder touches the wall approximately 11 feet higher than the shorter ladder, or equivalently, around 8 feet 8 inches higher.

Let's denote the height at which the second ladder touches the wall as h. We can set up a proportion based on the similar right triangles formed by the ladders and the building:

(6 6 feet) / (h) = (9 9 feet) / (5 5 feet 9 9 inches + h)

To solve for h, we can cross-multiply and solve the resulting equation:

(6 6 feet) * (5 5 feet 9 9 inches + h) = (9 9 feet) * (h)

Converting the measurements to inches:

(66 inches) * (66 inches + h) = (99 inches) * (h)

Expanding and rearranging the equation:

4356 + 66h = 99h

33h = 4356

Solving for h:

h = 4356 / 33 = 132 inches

Converting back to feet and inches:

h ≈ 11 feet

Therefore, the second ladder touches the wall approximately 11 feet higher than the shorter ladder, or equivalently, around 8 feet 8 inches higher.

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The area of the rainforest in 9 years is 3045

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

Inital area, a = 4,100

Rate of decrease, r = 3.25%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 - r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 4100 * (1 - 3.25%)ˣ

In 9 years, we have

\(f(9) = 4100 * (1 - 3.25\%)^9\)

Evaluate

f(9) = 3045

Hence, the area is 3045

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Answer:

7.9m

Step-by-step explanation:

Area of square = length^2

62.41 = L^2

L= √62.41

so, L= 7.9m

The correct answer is C. √(s²u + s²v) is the standard deviation of W

When two independent random variables U and V are added together to form a new random variable W = U + V, the standard deviation of W is given by the square root of the sum of the variances of U and V.

In this case, the standard deviation of U is represented by su and the standard deviation of V is represented by sv. Since U and V are independent, their variances add up. Therefore, the variance of W is s²w = s²u + s²v.

To find the standard deviation of W, we take the square root of the variance: √(s²u + s²v). This is because the standard deviation is the square root of the variance.

Hence, the correct answer is C. √(s²u + s²v), which represents the standard deviation of W.

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The value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve

C is 0.

To evaluate the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C:

x = 6cost, y = 12sint (0 ≤ t ≤ 4π), we need to substitute the parametric equations for x and y into the given expression and integrate with respect to t.

Let's calculate the line integral step by step:

∫C (x+5y)dx + (4x-3y)dy

= ∫[0,4π] ((6cost + 5(12sint))(dx/dt) + (4(6cost) - 3(12sint))(dy/dt)) dt

= ∫[0,4π] ((6cost + 60sint)(-6sint) + (24cost - 36sint)(12cost)) dt

= ∫[0,4π] (-36costsint - 360sintsint + 288costcost - 432costsint) dt

= ∫[0,4π] (-360sintsint - 144costsint + 288costcost) dt

= ∫[0,4π] (-144costsint - 360sintsint + 288costcost) dt

Now we can integrate each term separately:

∫[0,4π] (-144costsint) dt = -144 ∫[0,4π] costsint dt

∫[0,4π] (288costcost) dt = 288 ∫[0,4π] costcost dt

∫[0,4π] (-360sintsint) dt = -360 ∫[0,4π] sintsint dt

The integrals of costsint and sintsint over the interval [0,4π] evaluate to zero since they are periodic functions with a period of 2π.

Therefore, the line integral simplifies to:

∫C (x+5y)dx + (4x-3y)dy = -144 ∫[0,4π] costsint dt + 288 ∫[0,4π] costcost dt - 360 ∫[0,4π] sintsint dt

= -144(0) + 288(0) - 360(0)

= 0

Hence, the value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C is 0.

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Answer:

D. 71

Step-by-step explanation:

Plug 7 into f

(7)^2 + 2(7) + 8

then solve

49 + 14 + 8

      71

"Financial" as it is not an effectiveness MIS metric.

To determine which one is not an effectiveness MIS metric, we need to understand the purpose of these metrics. Effectiveness MIS metrics measure how well a system is achieving its intended goals and objectives.

Customer satisfaction is a common metric used to assess the effectiveness of a system. It measures how satisfied customers are with the product or service provided.

Conversion rates refer to the percentage of website visitors who complete a desired action, such as making a purchase. This metric is often used to assess the effectiveness of marketing efforts.

Financial metrics, such as revenue and profit, are crucial indicators of a system's effectiveness in generating financial returns.

Response time measures the speed at which a system responds to user requests, which is an important metric for evaluating system performance.

Therefore, based on the given options, "Financial" is not a type of effectiveness MIS metric. It is a separate category of metrics that focuses on financial performance rather than the overall effectiveness of a system.

In summary, the answer is "Financial" as it is not an effectiveness MIS metric.

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Answer:

The ratio 9 to 12 is greater than 4 to 6

Step-by-step explanation:

9÷12=0.75

4÷6=0.67

0.75> 0.67

It will take approximately 27 years to accumulate $100,000 in the savings account.

To calculate the time required, we can use the future value of an ordinary annuity formula. In this case, the annuity is the annual savings of $1,300, the interest rate is 5%, and the desired future value is $100,000. By plugging these values into the formula, we can solve for the number of periods (years) it will take to reach the target amount.

The formula is:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods. Rearranging the formula to solve for n, we have:

n = log((FV * r / P) + 1) / log(1 + r)

Substituting the given values, we get:

n = log((100000 * 0.05 / 1300) + 1) / log(1 + 0.05)

Evaluating this expression, we find that n is approximately equal to 27. Therefore, it will take approximately 27 years to accumulate $100,000 in the savings account by saving $1,300 annually at an interest rate of 5%.

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Answer

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Explanation

To solve this, we need to note that √(-1) = i

So, for this simplification

√(36 - 40) = √(-4) = √[(4)(-1)] = 2i

We can now fully simplify the expression given

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Hope this Helps!!!

Answer:

c.

Step-by-step explanation:

for this peoblem, an open dot would be used to indicate >. so in this, the arrow would be moving right to indicate a positive change in the number with the open dot to insight that it is greater than the original number.

Answer:

B,C,E are right statements

The correct statements about the given quadrilateral are:

So, according to the given quadrilateral, we can conclude that the correct statements are:

Therefore, the correct statements about the given quadrilateral are:

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Answer:

955.0 ft^3 remains in A

Step-by-step explanation:

Volume of a cylnder = V = pi r^2 h

A:   pi (9)^2 *9   =  729 pi    (Note:  You are given DIAMETER...need RADIUS)

B:   pi  (5)^2 *17  = 425 pi

A - B =  pi ( 729 - 425) = 955.0 ft^3 remains

Answer:

a)  see below

b)  radius = 16.4 in (1 d.p.)

c)  18°. Yes contents will remain. No, handle will not rest on the ground.

d)  Yes contents would spill.  Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

Part a

A chord is a line segment with endpoints on the circumference of the circle.  

The diameter is a chord that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle.  Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

Part b

The tangent of a circle is always perpendicular to the radius.

The tangent to the wheel touches the wheel at point B on the diagram.  The radius is at a right angle to this tangent.  Therefore, we can model this as a right triangle and use the tan trigonometric ratio to calculate the radius of the wheel (see attached diagram 1).

\(\sf \tan(\theta)=\dfrac{O}{A}\)

where:

Given:

Substituting the given values into the tan trig ratio:

\(\implies \sf \tan(20^{\circ})=\dfrac{r}{45}\)

\(\implies \sf r=45\tan(20^{\circ})\)

\(\implies \sf r=16.37866054...\)

Therefore, the radius is 16.4 in (1 d.p.).

Part c

The measure of an angle formed by a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

\(\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}\)

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

Part d

This can be modeled as a right triangle (see diagram 3), with:

Use the sin trig ratio to find the angle the handle makes with the horizontal:

\(\implies \sf \sin (\theta)=\dfrac{O}{H}\)

\(\implies \sf \sin (\theta)=\dfrac{48-r}{48}\)

\(\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}\)

\(\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)\)

As 41.2° > 20° the contents will spill out the back.

To find the maximum height of the handle from the ground before the contents start spilling out, find the height from center of the wheel (setting the angle to its maximum of 20°):

\(\implies \sin(20^{\circ})=\dfrac{h}{48}\)

\(\implies h=48\sin(20^{\circ})\)

Then add it to the radius:

\(\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)\)

(see diagram 4)

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Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Tangent: a straight line that touches a circle at only one point.

The locus of all points from which a given segment subtends equal angles is a circle. Therefore:

so:

Divide both sides by 2:

The factors of -18 that sum to 3 are 6 and -3, therefore:

So:

The correct answer is D: If "a" is greater than 1. The value of "a" in the quadratic equation determines the degree of vertical stretching or compression. If "a" is greater than 1, the parabola will be stretched vertically by a factor of "a" compared to the standard parabola.

If "a" is between 0 and 1, the parabola will be compressed vertically by a factor of "a". If "a" is less than zero, the parabola will be reflected across the x-axis. The values of "h" and "k" determine the vertex of the parabola, but they do not affect the degree of stretching or compression. Therefore, option D is the correct answer to the question.

The characteristic of the general quadratic equation y = a(x - h)^2 + k that determines whether the corresponding graph has a vertical stretch is related to the value of "a". Specifically, the correct option is D: If "a" is greater than 1. A vertical stretch occurs when the absolute value of "a" is greater than 1, causing the parabola to become narrower. Conversely, if the absolute value of "a" is between 0 and 1, the parabola experiences a vertical compression and becomes wider. The value of "k" affects the vertical position of the parabola, but not the stretch.

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As per the divisibility rule, the number is 6552

In math, the divisibility rule states that one to check whether a number is divisible by another number without the actual method of division here if a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.

Here we have given that 655Δ i a 4-digit number with one of it digit represented by Δ. 655Δ is divisible by 3.

Here we have to find the missing digit in the given number.

Here we have given that the number is 655Δ.

And we have also given that the given number is divisible y 3.

So, here we must know the divisibility rule of 3.

The divisibility rule of 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

So, based on these rules let us consider that x be the missing digit.

Then it can be written as.

=> [6 + 5 + 5 + x]/3

=> 16 + x/3

Here we put the value of x as 2, then we get 18, that is divisible by 3.

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