The sum of the numerator and denominator of the fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.

Answer:

17) (4,7) (4,5)

18) (-4,7), (-4,5) , (4,7. ) ,( 4,5) is a rectangle solve for area

19) quadrant 2

To determine the total grade we mutiply each one by the percentage it represents of the overall grade in decimal form and add them, that is:

Therefore, the overall grade is 69

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Using the information provided, it appears that your neighbor will not save money by picking up the soil himself as its total cost is $103.86 as opposed to cost of delivery $30.

Here is a detailed breakdown of the calculations and assumptions made:

The area of the yard is estimated to be around 7,200 sq.ft. Assuming a 4 inch layer of topsoil, this requires 4 cubic yards (1 cubic yard = 27 cubic feet).

The cost of the soil delivery is $30 per truckload (up to 18 cubic yards). So the delivery cost for 4 cubic yards of soil would be $30.

The cost of topsoil per cubic yard is $18. Thus, the total cost of the topsoil is $72.

The weight of topsoil is 2000 pounds per cubic yard, so the total weight of the soil is 8,000 pounds (4 cubic yards x 2000 pounds).

The pickup truck's payload capacity is 1800 pounds, so the truck can only transport 1/4 of the total weight of the soil (1800/8000 = 0.225). Thus, it would require 4 trips to transport the soil, and the total trip distance is 36 miles (9 miles x 4 trips).

The truck gets 17 miles per gallon, so it would require 2.1 gallons of gas for each trip (36 miles/17 mpg = 2.12). The total amount of gas needed for the 4 trips is 8.4 gallons (2.1 gallons x 4 trips). The cost of gas per gallon is assumed to be $3.79, so the total cost of gas for the 4 trips is $31.86.

Thus, the total cost of picking up the soil himself is $31.86 + $72 = $103.86. This is higher than the cost of delivery which is only $30, so it would be better to pay for delivery.

To conclude, your neighbor will not save money by picking up the soil himself, and it is recommended that he pays for delivery.

Note: The question is incomplete. The complete question probably is: He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for:

Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

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Answer:

b ≤ 7

Step-by-step explanation:

Given that:

A red block and a blue block are on a scale.  The red block weights 9 ounces. The total weight of both blocks is 16 ounces.  

To Find:

Which inequality best represents b, the possible weight of the blue block in ounces?

Knowing that;

< ⇒ less than

> ⇒ Greater than

≤ ⇒ less than or equal to

≥ ⇒ greater than or equal to

Solve:

Since the total blocks is 16 ounces that means it can't be pass 16 also known as can't be greater than. As well as, it given us that the red block weight 9 ounces that means

16 - 9 = 7

which given us that it must be equal to 7 or less than 7 to make it true.

Thus,

b ≤ 7

Kavinsky

Answer:

870 cm³

Step-by-step explanation:

V= lwh

V= 15cm*5.8cm*10cm=  870 cm³

Given:

The polynomial \(x^3-1\) is divided by (x+2).

To find:

The remainder.

Solution:

Remainder theorem: If a polynomial p(x) is divided by (x-c), then the remainder is p(c).

Consider the polynomial:

\(p(x)=x^3-1\)

It is divided by (x+2). So, by the remainder theorem the remainder is p(-2).

Substituting x=-2 in the above polynomial, we get

\(p(-2)=(-2)^3-1\)

\(p(-2)=-8-1\)

\(p(-2)=-9\)

Therefore, the remainder is -9.

The remainder when x³ - 1 is divided  by (x + 2) is -9

Polynomial is an expression consisting of only the operations of addition, subtraction, multiplication of variables.

The remainder theorem states that when a polynomial f(x), is divided by a linear polynomial x - a, the remainder of that division will be equivalent to f(a).

Given the polynomial f(x) = x³ - 1.

The linear equation is x + 2, hence; x = -2

f(-2) = (-2)³ - 1 = -8 - 1 = -9

The remainder when x³ - 1 is divided  by (x + 2) is -9

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Answer:

This property is known as the associative property

Step-by-step explanation:

In the associative property, you rearrange the numbers so they make the most sense in what position they are in.

Hope this helps! :)

Answer:

associate property

:<

When we measure a ECG waveform the large boxes represents 0.2 seconds.

To determine the measurements of the big box on ECG paper, we need to consider the standard calibration of ECG paper.

In most ECG papers, the standard calibration is as follows:

These measurements allow for accurate interpretation of the ECG waveform and analysis of heart activity.

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Answer:

28 pillows

Step-by-step explanation:

\( = 10 \frac{1}{2} \div \frac{3}{8} \\ = \frac{21}{2} \div \frac{3}{8} \\ = \frac{21}{2} \times \frac{8}{3} \\ = 28\)

Answer:

Let us assume Maricopa invested X amount in CDs, then she would have invested X+30000 in bonds

We know Amount Invested in CDs + Amount invested in Bonds + Amount Invested in Stocks = 90000

As we earlier discussed Amount Invested in CDs = X, Amount Invested in X + 30000 putting these in above equation

X + X + 30000 + Amount invested in stocks = 90000

2X+ 30000 + Amount invested in stocks = 90000

Taking 2X + 30000 to right hand side of equation  

Amount invested in stocks = 90000 - 30000 - 2X

= 60000 - 2X

Now Interest on CDs = 4.25 % * Amount invested in CDs = 4.25/100 * X =  0.0425 X

Interest on bonds = 4.3/100 % * Amount invested in Bonds = 4.3/100 * (30000 + X)= 1290 + 0.043X  

Interest on stocks = 8.6/100% * Amount invested in stocks = 8.6/100 * (60000 - 2X) = 5160 - 0.172X

Total Interest = 5153

Adding all the interest calculated

0.0425X + 1290+ 0.043X + 5160 - 0.172X = 5153

(0.0425X + 0.043X - 0.172X) + (1290+5160) = 5153

-0.0865 X + 6450 = 5153

0.0865 X = 6450 - 5153

0.0865 X = 1297

X = 15000

CDs amount = $15000

Bonds amount = $45000

Stocks amount = $30000

Let "x" be the number of grams of peanuts in the mixture, then "1000 − x" is the number of grams of green peas in the mixture.

The cost of peanuts per kilogram is PHP 50.00 while the cost of green peas is PHP 80.00 per kilogram.

Now, let us set up an equation for this problem:

\(\[\frac{50x}{1000}+\frac{80(1000-x)}{1000} = 62\]\)

Simplify and solve for "x":

\(\[\frac{50x}{1000}+\frac{80000-80x}{1000} = 62\]\)

\(\[50x + 80000 - 80x = 62000\]\)

\(\[-30x=-18000\]\)

\(\[x=600\]\)

Thus, the composition of the mixture must be:

Nuts: 600 grams, Green peas: 400 grams.

Therefore, the correct answer is option B.

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Answer:

Step-by-step explanation: sowwy I dunno

AxP(x) is equivalent to Ex-P(x) because they represent the same concept of calculating the expected value of a random variable.

The expression "AxP(x)" represents the sum of the product of a random variable X and its corresponding probability P(x) over all possible values of X. On the other hand, "Ex" represents the expectation or the average value of the random variable X.

To understand why "AxP(x)" is equivalent to "Ex-P(x)", we can consider the definition of expectation. The expectation of a random variable X is calculated by multiplying each value of X by its corresponding probability and summing up these products.

For example, let's consider a discrete random variable X with the following probability distribution:

X P(x)

1 0.2

2 0.3

3 0.5

Using "AxP(x)", we can calculate:

A = (1 × 0.2) + (2 × 0.3) + (3 × 0.5) = 0.2 + 0.6 + 1.5 = 2.3

Now, let's calculate "Ex-P(x)":

Ex = (1 × 0.2) + (2 × 0.3) + (3 × 0.5) = 0.2 + 0.6 + 1.5 = 2.3

P(x) = 0.2 + 0.3 + 0.5 = 1

Ex - P(x) = 2.3 - 1 = 1.3

As we can see, both "AxP(x)" and "Ex-P(x)" in this example give us the same result, which is 1.3. This illustrates that the sum of the product of a random variable and its corresponding probability is equivalent to the expectation minus the probability itself.

Therefore, in general, "AxP(x)" is equivalent to "Ex-P(x)" because they represent the same concept of calculating the expected value of a random variable.

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Answer:

4

Step-by-step explanation:

rllly

The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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The empirical formulas in the list are "C4H," "C8," "C2H6O," "Al2Br6," and "C8H8."

In chemistry, an empirical formula represents the simplest, most reduced ratio of atoms in a compound. The empirical formula does not provide the exact number of atoms in a molecule but gives the relative proportions.

In the given list, the formulas "C4H" and "C8" are already in their empirical form because they represent the simplest ratio of carbon and hydrogen atoms. The formula "C2H6O" is also an empirical formula as it represents the simplest ratio of carbon, hydrogen, and oxygen atoms.

However, the formula "Al2Br6" is already in empirical form, as it represents the simplest ratio of aluminum and bromine atoms.

The formula "C8H8" is already in empirical form as it represents the simplest ratio of carbon and hydrogen atoms.

Therefore, the empirical formulas in the list are "C4H," "C8," "C2H6O," "Al2Br6," and "C8H8."

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Answer:

\(3x + x + 7x - 4y\)

\(4x + 7x - 4y\)

\(11x - 4y\)

Answer:

Step-by-step explanation:

\(\sf 3x + x +7x - 4y\)

\(\sf (3x+x+7x)\) \(\sf +(-4y)\)

\(\sf 11x-4y\)

Hope it helps! :)

The curve given by r = sin(10) is a polar curve with one loop.

To find the area enclosed by one loop of the curve, we can use the formula for the area of a polar region, which is given by:

A = (1/2)∫θ2θ1 [r(θ)]^2 dθ

Since the curve has one loop, we need to find the values of θ that correspond to one complete revolution around the origin. Since sin(θ) has period 2π, we have:

r = sin(10) = sin(10 + 2π) for all values of θ

So, one complete revolution occurs when θ increases from 0 to 2π. Thus, the area enclosed by one loop of the curve is:

A = (1/2)∫02π [sin(10)]^2 dθ

Using the identity sin^2(θ) = (1/2)(1 - cos(2θ)), we can simplify this integral to:

A = (1/2)∫02π (1/2)(1 - cos(20θ)) dθ

Simplifying further, we get:

A = (1/4)∫02π (1 - cos(20θ)) dθ

Evaluating this integral gives:

A = (1/4) [θ - (1/20)sin(20θ)]02π

A = (1/4) (2π)

A = π/2

Therefore, the area enclosed by one loop of the curve r = sin(10) is π/2 square units.

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Given:

There are 4 quarts in a gallon.

She wants to convert 6 quarts to a gallon.

To find:

Whether she should multiply 6 by 4 or divide 6 by 4 to find her answer.

Solution:

We have,

\(4\text{ quarts}=1\text{ gallon}\)

\(1\text{ quarts}=\dfrac{1}{4}\text{ gallon}\)

\(6\text{ quarts}=\dfrac{6}{4}\text{ gallon}\)

Here, 6 quarts is equal to \(\dfrac{6}{4}\) gallon. It means we need to multiply 6 by 4 in \(4\text{ quarts}=1\text{ gallon}\) to find the answer.

Answer: did u get it right

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x ÷ (6x² -10x) and

\(\dfrac{2x}{6x^{2}-10x}\)

Answer:

567 insects

Step-by-step explanation:

8x3=24

3x189=567

Answer: i don't really know how you want me to solve it

Use the formula x =−b/2a (b over 2a)

(1 second

to find the maximum and minimum.

6t^(2 )+ 12t + 30

which should give you this answer

6(t2+2t+5)

what i did was factor 6 out of 6t^(2 )+ 12t + 30

Answer: 1 second

Step-by-step explanation:

There are two ways to solve this:

1. Graph it. You will see an inverted parabola with time (in seconds) on the x axis and height (in feet) on the y axis. The top of the parabola is point (1, 36) which means at 1 second the ball will be at 36 feet. Since the balcony is at 30 feet, the ball only goes up 6 feet before it changes direction toward the ground.

2. Take the first derivative and set it equal to zero. The first derivative will give us the slope, or rate of change, of the parabola for any point t (on the x-axis). The rate of change when the ball reaches its maximum height will be zero, when it goes from a positive value (going up) to a negative value (going down).

-6t^2 + 12t + 30

First derivative = h'(t) = -12t + 12

Set h'(t) to zero: 0 = -12t + 12

t = 1 second

Either way works. Put 1 second into the original equation and it will return 36 feet. That's 36 feet aboove ground. 6 feet above the balcony from which it is thrown. You can throw better then that, I assume.

Hideki should use coupon 2 to get a better deal.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Hideki buys 2 sweaters for $18 each.

Coupon 1: Buy one, get one 40% off

Here, 40% of 18

= 40/100 ×18

= 0.4×18

= $7.2

So, cost of entire purchase 2(18)-7.2

= 36-7.2

= $28.8

Coupon 2: 25% off entire purchase

25% of 2(18)

= 25/100 ×36

= 0.25×36

= $9

Now, 36-9 =$27

Therefore, Hideki should use coupon 2 to get a better deal.

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The slope of the table is 5 / 4 .

The slope of a line is the change in the dependent variables with respect to the change in the independent variable.

The slope of a line is rise over run.

In other words, the slope of a line is a measure of its steepness.

Therefore, let's find the slope of the table.

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (4, 5) and (8, 10)

slope = 10 - 5 / 8 - 4

slope = 5 / 4

Therefore, the slope is 5 / 4.

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Answer:

1.25

Step-by-step explanation:

You divide five by four, and you get one and twenty-five hundredths.

Answer:

c

Step-by-step explanation:

(a) The conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 7/18.

(b) The conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 2/18 = 1/9.

(c) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 12/19.

(d) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 7/19.

(a) When the balls are selected without replacement and X₂ is known to be 1 (black), there are 12 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 12/18 = 7/18.

(b) When the balls are selected without replacement and X₂ is known to be 0 (white), there are still 7 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 7/18.

(c) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 1) = 12/19.

(d) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 0) = 12/19.

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9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.