What is the factored form of x°-1?
(x2-1)(x2+x+1)
o (x-1)(x2-x+1)
o (x-1)(x2+x+1)
o (p-1)(x2+2x+1)

To solve this problem, we can set up an equation based on the principle of concentration. Let's assume that x represents the number of gallons of the 5% salt solution that needs to be mixed.

The amount of salt in the 5% solution is 0.05x (since 5% is equivalent to 0.05) and the amount of salt in the 9% solution is 0.09 * 30 = 2.7 gallons.

When these two solutions are mixed, the total volume of the mixture is 30 + x gallons, and the amount of salt in the mixture is 0.07 * (30 + x) gallons.

Now we can set up the equation:

0.05x + 2.7 = 0.07 * (30 + x)

Simplifying the equation:

0.05x + 2.7 = 2.1 + 0.07x

0.05x - 0.07x = 2.1 - 2.7

-0.02x = -0.6

Dividing both sides by -0.02:

x = 30

Therefore, 30 gallons of the 5% salt solution must be mixed with 30 gallons of the 9% solution to obtain a 7% solution.

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How many gallons of a 5% salt solution must be mixed with 30 gallons of a 9% solution to obtain a 7% solution ??

The perpendicular distance from point P to the line connecting stations Shore and Rock is approximately 668,389.33 feet.

To find the perpendicular distance from point P to the line connecting stations Shore and Rock, we can use the formula for the distance between a point and a line.

The equation of the line connecting stations Shore and Rock can be determined using the slope-intercept form of a straight line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's calculate the slope of the line:

slope = (Y2 - Y1) / (X2 - X1)

     = (392,133.86 - 394,087.52) / (652,531.72 - 654,127.26)

     = -1,953.66 / -1,595.54

     ≈ 1.224

Next, we can find the y-intercept (b) by substituting the coordinates of either station (e.g., Rock) into the slope-intercept form and solving for b:

392,133.86 = 1.224 * 652,531.72 + b

b ≈ 392,133.86 - 799,247.25

b ≈ -407,113.39

So, the equation of the line connecting Shore and Rock is:

y ≈ 1.224x - 407,113.39

Now, let's calculate the perpendicular distance from point P to the line using the formula:

distance = |Ax + By + C| / sqrt(\(A^2\) + \(B^2\))

where A, B, and C are the coefficients of the line equation in the form Ax + By + C = 0. In this case, the equation of the line can be rewritten as:

-1.224x + y + 407,113.39 = 0

Therefore, A = -1.224, B = 1, and C = 407,113.39. Plugging in the coordinates of point P (653,594.81, 393,436.47) into the formula, we get:

distance = |-1.224 * 653,594.81 + 1 * 393,436.47 + 407,113.39| / sqrt((-1.224)^2 + 1^2)

        = |-799,103.63 + 393,436.47 + 407,113.39| / sqrt(1.497)

        = |1,001,446.23| / 1.225

        ≈ 818,003.79 / 1.225

        ≈ 668,389.33

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Answer:

Thats what i got too :)

Step-by-step explanation:

You have the correct answer. It is 80.3 square yards.

Work Shown:

Area of parallelogram = length*width = 21.5*33.6 = 722.4 sq ft

1 yard = 3 ft

1 sq yd = 9 sq ft ... square both sides

To convert from square feet to square yards, we'll divide by 9

This is the same as multiplying by 1/9

722.4 sq ft = (722.4 sq ft)*(1 sq yd/9 sq ft)

722.4 sq ft = (722.4)*(1/9) sq yards

722.4 sq ft = 80.2667 sq yards

722.4 sq ft = 80.3 sq yards

Answer:

Rate of Return = 24.7%

Step-by-step explanation:

Given 10 shares of Stock A are purchased for $30/share:

\(\sf \implies Initial \; value = \$30 \times 10 = \$300\)

The current value, after deducting the commission:

\(\implies \sf Current \; value = \$380 - \$6 = \$374\)

A rate of return is the net gain (or loss) of an investment over a specified time period, expressed as a percentage of the investment's initial cost.

\(\boxed{\sf Rate\;of\;return=\dfrac{Current \; value - Initial \; value}{Initial \; value} \times 100}\)

Therefore:

\(\sf \implies Rate\;of\;return=\dfrac{\$374-\$300}{\$300} \times 100\)

\(\sf \implies Rate\;of\;return=\dfrac{\$74}{\$300} \times 100\)

\(\sf \implies Rate\;of\;return=0.2466666...\times 100\)

\(\sf \implies Rate\;of\;return=24.7\%\;\;(nearest\;tenth)\)

Answer:

Yes

Step-by-step explanation:

The ratio for Danny would be 3 / 6 which simplifies to 1 / 2

For Jeff the ratio would be 2 / 4 which simplifies to 1 / 2 as well

Answer:

1200ft^3

Step-by-step explanation:

30 x 20 x 2= 1200^3

Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

The equation of the line with slope -1/7 is (y-3) = -1/7(x-3).

According to the question,

We have the following information:

Slope of the line = -1/7

Points through which line is passing = (3,3)

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x') where m is the slope of the line

In this case, we have x' = 3 and y' = 3.

(y-3) = -1/7(x-3)

This expression can be solved further by multiplying -1/7 into the bracket and then by moving 3 from the left hand side to the right hand side. Then this equation will be in slope-intercept form.

Hence, the correct option is B.

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Answer:

\(x = \sqrt{36} = 6\)

Hope it helps

Have a good day Ahead

To tell if a function is convergent or divergent, you need to check the behavior of the function as the input values get larger. Here are the steps to determine whether a function is convergent or divergent:

Step 1: Find the limit of the function. Evaluate the function as the input values get larger, approaching infinity. If the limit exists and is a finite number, the function is convergent. If the limit does not exist or approaches infinity, the function is divergent.

Step 2: Test for convergence using the divergence test. If the limit of the function as the input values approach infinity is zero or does not exist, the series may be divergent. In this case, you need to use the divergence test. If the series diverges, the function is divergent. If the series converges, the test is inconclusive.

Step 3: Test for convergence using the integral test. If the function is positive, continuous, and decreasing, you can use the integral test to determine convergence. If the integral converges, the series is convergent. If the integral diverges, the series is divergent.

Step 4: Test for convergence using comparison tests. If the function can be compared to another function, you can use comparison tests to determine convergence. If the other function is convergent, the original function is convergent. If the other function is divergent, the original function is divergent.

Step 5: Test for convergence using the ratio test. If the limit of the ratio of consecutive terms is less than 1, the series is absolutely convergent. If the limit is greater than 1, the series is divergent.

If the limit is equal to 1, the test is inconclusive.In summary, determining if a function is convergent or divergent requires checking the behavior of the function as the input values get larger and using different tests depending on the characteristics of the function.

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Answer:

390cm

Step-by-step explanation:

Answer:

GH

Step-by-step explanation:

A secant is a straight line which cuts the circle at 2 points

GH and FE both do this but FE is a special secant, that is the diameter

Then GH is a secant

As a result, the solution is shaped like a circle ( -5 , 7 ). The second half of the text has a 6 mm diameter. Three and four are FALSE. There are ten miles between points A and B.

The construction of a circle is the outcome of following a thinking object in a plane and keeping a fixed distance from a particular location. A Greek word kirkos, which means hoop or ring, is the source of the English word circle.

Here,

Typically, a circle's equation is,

( x - h )² + ( y - k ) ( y - k )

x² = r²

( y - k ) ( y - k ) = r²

6² = r²

where the radius of the ring is and the center's coordinates are (h, k).

Part 1.

We arrive to using the formula for the common circle.

The circumference of a circle's coordinate is ( -5 , 7 )

As a result, the second choice is the best.

Part 2.

We arrive to using the formula for the common circle.

The circle's diameter is six.

The initial choice is therefore the best.

Part 3.

We arrive to using the equation again for common circle.

Circle circumference coordinate: ( 2 , 3 )

False as a result.

The axis coordinates of the circle are: ( 2 , 3 )

False, then.

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Using the limit definition of partial derivatives, we can find fx(x,y) and fy(x,y) for the function f(x,y) = xy. The partial derivative with respect to x, fx(x,y), is equal to y, and the partial derivative with respect to y, fy(x,y), is equal to x.

The partial derivative of a function with respect to one of its variables is the rate at which the function changes when that variable is changed, while holding all other variables constant. In the case of f(x,y) = xy, we can use the limit definition of partial derivatives to find fx(x,y) and fy(x,y). To find fx(x,y), we first fix the value of y and let x approach a small increment h. Then, we take the limit as h approaches zero:

fx(x,y) = lim (h -> 0) [f(x+h,y) - f(x,y)] / h

= lim (h -> 0) [(x+h)y - xy] / h

= lim (h -> 0) hy / h

= y

Similarly, to find fy(x,y), we fix the value of x and let y approach a small increment k. Then, we take the limit as k approaches zero:

fy(x,y) = lim (k -> 0) [f(x,y+k) - f(x,y)] / k

= lim (k -> 0) [x(y+k) - xy] / k

= lim (k -> 0) xk / k

= x

Therefore, the partial derivative with respect to x, fx(x,y), is equal to y, and the partial derivative with respect to y, fy(x,y), is equal to x.

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Answer: A. The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%

Step-by-step explanation:

Number of red tiles = 9

Number of blue files = 10

Number of green tiles = 6

Total number of tiles = 9 + 10 + 6 = 25

Probability of drawing red tile = 9/25 = 0.36 = 36%

Probability of drawing blue tile= 10/25 = 0.40 = 40%

Probability of drawing green tile = 6/25 = 0.24 = 24%

Based on the explanation above, the correct answe is option A "The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%".

Answer:

- 1/20

Step-by-step explanation:

Step 1: Equation

4/3 ÷ - 24

Step 2: Solve/Multiply

4/3 × -1/24

Answer:

- 1/20

Hope This Helps :)

Answer:

D) 408

E) 684

F) 377

Step-by-step explanation:

In these problems, we can simplify the multiplication using these steps:

1. split each number into a tens and ones place

2. multiply each place of the bottom number by both places of the top number (but remember that a digit in the tens place has a zero after it)

3. add the resulting values

D) First, we can split each number into a tens and ones place:

17 = 10 and 7

24 = 20 and 4

Next, we can multiply each digit of the bottom number by both digits of the top number:

(4 × 7)

(4 × 10)

(20 × 7)

(20 × 10)

Finally, we can add all of these values:

(4 × 7) + (4 × 10) + (20 × 7) + (20 × 10)

= 28   +     40    +     140    +     200

= 408

E)

36 = 30 and 6

19 = 10 and 9

Multiplying the places:

(9 × 6)

(9 × 30)

(10 × 6)

(10 × 30)

Adding these values:

(9 × 6) + (9 × 30) + (10 × 6) + (10 × 30)

= 54    +    270    +    60     +    300

= 684

F)

29 = 20 and 9

13 = 10 and 3

Multiplying the places:

(3 × 9)

(3 × 20)

(10 × 9)

(10 × 20)

Adding these values:

(3 × 9) + (3 × 20) + (10 × 9) + (10 × 20)

= 27    +    60      +     90    +    200

= 377

Answer:

v=53 degrees

Step-by-step explanation:

So since 180 degrees in tri, v-23+2v+v-9=180

Plus 23 and 9: 4v=212

v=53 degrees

The total Distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them

In order to calculate the time needed, we need to consider the distances between each point.

This can be done using the Pythagorean Theorem, which states that the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides.

For this problem, we can treat each segment as the hypotenuse of a right triangle, where the other two sides are the distances between each point.Using this method,

we can calculate the distances between each point:b1 to b2: distance = sqrt((b2 - b1)^2) = sqrt((8 - 10)^2) = 2b2 to b3: distance = sqrt((b3 - b2)^2) = sqrt((15 - 8)^2) = 7b3 to a: distance = sqrt((a - b3)^2) = sqrt((15 - 15)^2) = 0b3 to b: distance = sqrt((b - b3)^2) = sqrt((10 - 15)^2) = 5b4 to b: distance = sqrt((b - b4)^2) = sqrt((10 - 9)^2) = 1

Now that we have the distances,

we can add them up to get the total distance:2 + 7 + 0 + 5 + 1 = 15

Therefore, the total distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them.

So, the answer is we should take the shortest way, not the longest way.

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Answer:

https://tex.z-dn.net/?f=%5Cunderline%7B0.1875%7D%5C%5C3%3A16%5C%5C%5Cunderline%7B0%7D%5C%5C30%5C%5C%5Cunderline%7B16%7D%5C%5C140%5C%5C%5Cunderline%7B128%7D%5C%5C.%5C%20120%5C%5C%5Cunderline%7B.%5C%20112%7D%5C%5C.%5C%20%5C%2080%5C%5C%5Cunderline%7B.%5C%20%5C%2080%7D%5C%5CR%3D0Step-by-step explanation:

Answer:

58.3°

Step-by-step explanation:

Missing Information:

In this question the diagram is missing Following are the attachment of diagram of the given question.

As we seen that the vertex c is making the right angle i,e 90°  also there is an acute angle the Hypotenuse: 20 cm and the perpendicular is 10.5 cm

Now we have find the best approximation of the angle ABC used the cosx  trigonometric function.

\(cos\ x\ =\ \frac{perpendicular}{Hypotenuse} \\\)

Putting the value of perpendicular and hypotenuse in the previous formula we get

\(cos\ x\ =\ \frac{10.5\ cm}{20\ cm} \\\)

\(x\ =cos^{-1}\ 0.525\\x \ = \ 58.33\)

Answer:

58.3

Step-by-step explanation:

jus did the test review on EDGE! :)

Answer:

Both plans are correct

Step-by-step explanation:

I already did it

The probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

To find the probability that two children selected at random from Mrs. Attaway's class are girls and one is a boy, we need to calculate the number of favorable outcomes (selecting two girls and one boy) and divide it by the total number of possible outcomes.

The total number of children in the class is 5 girls + 16 boys = 21 children.

To calculate the probability, we need to determine the number of ways to select two girls from the five available girls and one boy from the 16 available boys. This can be done using combinations.

The number of ways to select two girls from five is given by the combination formula:

C(5, 2) = 5! / (2! * (5 - 2)!)

= 5! / (2! * 3!)

= (5 * 4) / (2 * 1)

= 10

Similarly, the number of ways to select one boy from 16 is given by the combination formula:

C(16, 1) = 16

The total number of favorable outcomes is the product of these two combinations: 10 * 16 = 160.

Now, let's calculate the total number of possible outcomes when selecting three children from the class:

C(21, 3) = 21! / (3! * (21 - 3)!)

= 21! / (3! * 18!)

= (21 * 20 * 19) / (3 * 2 * 1)

= 1330

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = favorable outcomes / total outcomes

= 160 / 1330

≈ 0.120 (rounded to three decimal places)

Therefore, the probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

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You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

Two functions , f(x) and g(x)

The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .

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The probability that Y=1 given X=2 and Z=3 is 1/3.

Given that X, Y, and Z have joint distribution as shown below:

\(f(x, y, z) = \frac{xy^2z}{180}, x=1,2,3;y=1,2;z=1,2,3\)

We need to find \(P(Y=1|X=2, Z=3)\).

Therefore, we can use the conditional probability formula:

\(P(Y = 1 | X = 2, Z = 3) = \frac{P(Y = 1, X = 2, Z = 3)}{P(X = 2, Z = 3)}\)

Now we find the numerator and denominator individually:

Numerator: \(P(Y = 1, X = 2, Z = 3)\)

Here, we fix X=2, Z=3 in the given probability distribution and find the value of Y=1.

\(P(Y = 1, X = 2, Z = 3) = f(2, 1, 3) = \frac{2(1)^2(3)}{180} \\= \frac{1}{15}\)

Denominator: \(P(X = 2, Z = 3)\)

We fix Z=3 in the given probability distribution and sum over all values of Y to get the probability of X=2 and Z=3.

\(P(X = 2, Z = 3) = \sum_{y=1}^{3} f(2,y,3)P(X = 2, Z = 3) = f(2,1,3) + f(2,2,3) + f(2,3,3)\\P(X = 2, Z = 3) = \frac{2(1)^2(3)}{180} + \frac{2(2)^2(3)}{180} + \frac{2(3)^2(3)}{180}\\P(X = 2, Z = 3) = \frac{1}{5}\)

Substituting these values in the conditional probability formula, we get:

\(P(Y = 1 | X = 2, Z = 3) = \frac{P(Y = 1, X = 2, Z = 3)}{P(X = 2, Z = 3)}\\P(Y = 1 | X = 2, Z = 3) = \frac{\frac{1}{15}}{\frac{1}{5}}\\P(Y = 1 | X = 2, Z = 3) = \frac{1}{3}\)

Therefore, the probability that Y=1 given X=2 and Z=3 is 1/3.

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Answer:

The value is -10

Step-by-step explanation:

Find the circumference of a circle that has a radius of 7 cm.

Use 3.14 for π

SOLUTION

The circumference of a circle = 2 π r

But Radius = 7 cm

The circumference of a circle = 2 x 3.14 x 7

= 43 .96 cm