Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?

A

P will be closer to A because it

distance from A to B.

P will be closer to A because it will

the distance from A to B.

O P will be closer to B because it will be

the distance from B to A.

P will be closer to B because it will be

the distance from B to A.

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The probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times is approximately 0.972, or 97.2%.

If a success is defined as getting a three on a six-sided number cube, we can calculate the probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times.

To find this probability, we need to consider the complementary event, which is rolling a three or greater. The probability of rolling a three or greater on a single roll is 1 - P(x < 3).

The probability of rolling a three or greater on a single roll is 1 - (2/6) = 4/6 = 2/3.

Since rolling the number cube 10 times is independent, we can multiply the probabilities together. Therefore, the probability of rolling a three or greater on all 10 rolls is (2/3)^10.

To find P(x < 3), we take the complement of this probability:

P(x < 3) = 1 - P(x ≥ 3) = 1 - (2/3)^10 ≈ 1 - 0.028 ≈ 0.972.

Therefore, the probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times is approximately 0.972, or 97.2%.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

Step-by-step explanation:

C

Answer:

C.) Rich lost 20 pounds

Step-by-step explanation:

I hope you have a good rest of your day!

Answer:

x = - 2 , 0

Step-by-step explanation:

to find f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x²)

= 2x² + 1

to find g(f(x)) substitute x = f(x) into g(x)

g(f(x))

= g(2x + 1)

= (2x + 1)²

= 4x² + 4x + 1

now equate the 2 expressions

4x² + 4x + 1 = 2x² + 1 ( subtract 2x² from both sides )

2x² + 4x + 1 = 1 ( subtract 1 from both sides )

2x² + 4x = 0 ← factor out 2x from each term on the left side

2x(x + 2) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x + 2 = 0 ⇒ x = - 2

then x = - 2 , 0

Answer:

Step-by-step explanation:

the answer is c

One graph appears skewed, and one graph appears symmetrical because the interval 2 stem and leaf plots is not consistent, statement third is correct.

It is defined as the numerical data representation in the graph with the help of a bar without space. The histogram gives an idea about the data's approximate distribution.

The number line goes from 8 to 72 in incremental of 8, such as:

8, 16, 24, 32, 40, 48, 56, 64, 72

The whiskers range is from 8 to 71 and

Box ranges from 23 to 47.

The line divides the box at 38.

The mid-point of the line plot is at 40 and at first inspection, the stem and leaf plot appears to be accurate. In the stems, however, 5 is omitted entirely, giving the pattern a symmetrical rather than skewed appearance.

Thus, one graph appears skewed, and one graph appears symmetrical because the interval 2 stem and leaf plots is not consistent, statement third is correct.

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Answer:

this is answer$10,000$1o,5oo ok

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Answer:

361 tiles and $2,147.95

Step-by-step explanation:

19x19 to find tile area

361 x 5.95 to find cost

Answer:

if he leave at 2pm 45 miles in the first hr is the correct answer 3 pm

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

1.A,B,C

2.C,B,A

3.A,C,B

4.B,A,C

5.B,C,A

6.C,A,B

Answer: ~15.05267 (im not sure though i just used a calculator)

Answer:

6) 60°

7) 24.25°

8) 28°

Step-by-step explanation:

I’m not 100% sure but hope this helps.

Answer:

6. u = 60

7. 24.25°

8. 28°

Step-by-step explanation:

6. First we know that a triangle is 180 degrees. So we would do 30+90+u=180

120+u=180

-120    -120

u = 60

By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

A mathematical statement known as an equation is made up of two expressions joined by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the number of the variable x is 7.

So, calculate as follows:

Let g represent giraffes and o represent ostriches.

g + o = 70 ...(1)

4*g + 2*o = 200  ...(2)

g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:

4*g + 2*o = 200

4*(70-o) + 2*o = 200

280 - 4o + 2o = 200

-2o = 200 - 280

2o = 80

o = 80/2

o = 40

Ostriches are 40 then giraffes will be:

70 - 40 = 30

Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

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Answer:

Answer on a graph

The infant's weight is 7 pounds and 10 ounces using weight conversion.

To convert the weight of the newborn from grams to pounds, we need to divide the weight by the number of grams in one pound, which is 453.59. So, 3,459 grams divided by 453.59 grams per pound is equal to 7.628 pounds.

To find the weight in ounces, we need to multiply the decimal part of the pounds by 16 (since there are 16 ounces in one pound). So, 0.628 x 16 = 10.048 ounces.

Therefore, the infant's weight is 7 pounds and 10 ounces.

It is important to note that weight conversion is often used in the medical field to monitor the health and growth of newborns. By tracking their weight in pounds and ounces, doctors can ensure that they are gaining weight at a healthy rate and are meeting their developmental milestones.

This information can also be used to make adjustments to their feeding or treatment plans if necessary. It is crucial for healthcare professionals to accurately convert weight measurements to ensure the best possible care for their patients.

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We can solve this problem in three steps.

1) find the area of the square

\(a=lw\\\\a=(7.5)(6)\\\\a=45ft^{2}\)

2) find the area of the triangle

\(a=\frac{1}{2}bh\\\\a=\frac{1}{2} (6)(4)\\\\a=12ft^{2}\)

3) add the areas together

\(a=45+12\)

a = 57 ft²

The likelihood of the event is 1/2

Answer:

The answer is 8.

Step-by-step explanation:

If you multiply each of the measurments by 1.5 they equal the measurments on the larger trapazoid. I can't see the full question but im assuming It's asking for the measurment (2x-16). So 12 divided by 1.5 equals 8. And to get eight you replace x with 4. Hope I helped. :)

\(\\ \sf\longmapsto \dfrac{2x-16}{12}=\dfrac{12}{18}\)

\(\\ \sf\longmapsto \dfrac{x-8}{6}=\dfrac{2}{3}\)

\(\\ \sf\longmapsto 3(x-8)=12\)

\(\\ \sf\longmapsto 3x-24=12\)

\(\\ \sf\longmapsto 3x=36\)

\(\\ \sf\longmapsto x=12\)

The number of different subsets of $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$  is 13.

We are given that;

Subset = $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$

Now,

To apply the principle of inclusion-exclusion, we need to find the number of elements in each set and each intersection of sets. We have:

∣A∣=∣B∣=∣C∣=6

∣A∩B∣=∣A∩C∣=∣B∩C∣=2

∣A∩B∩C∣=1

Using the principle of inclusion-exclusion, we get:

∣A∪B∪C∣=∣A∣+∣B∣+∣C∣−∣A∩B∣−∣A∩C∣−∣B∩C∣+∣A∩B∩C∣

Plugging in the values we have found above, we get:

∣A∪B∪C∣=6+6+6−2−2−2+1=13

Therefore, by the subset the answer will be 13.

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Answer:

5.y=5x-10+5x+1

y=10x-9

6.y=2x+12+2x+6

  y=4x+18

7.y=-2x-8-2x+10

 y=-4x+2

8.y=-4x-8-4x-12

  y=-8x-20

Answer:

x = 8

y = -3

Step-by-step explanation:

Multiply the first equation with (-2)

(-2) * (x - 4y) = 20

-2x + 8y = -40 now find the sum of it with second equation

2x + 5y - 2x + 8y = 1 - 40 add like terms (2x will eliminate -2x)

13y = -39 divide both sides by 13

y = -3

Now we can use this to find the value of x

x - 4y = 20 rewrite the equation using the value we found for y

x - 4(-3) = 20 multiply (-4) and (*3) (product will be positive because we are multiplying two negatives)

x + 12 = 20 subtract 12 from both sides

x = 8

1) All the angles are,

∠ 1 = 72°

∠ 2 = 54°

∠ 3 = 54°

∠ 4 = 72°

2) All the angles are,

∠1 = 59°

∠2 = 90°

∠3 = 90°

∠ 4 = 31°

3) All the angles are,

∠ 1 = 22°

∠ 2 = 68°

∠ 3 = 68°

∠ 4 = 90° (right angle)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

1) From first figure,

⇒ ∠ 3 = 54°   (Two sides are equal hence two angles are also equal)

Hence, We get;

∠3 + ∠4 + 54° = 180°

54° + ∠4 + 54° = 180

∠4 = 180 - 108

∠4 = 72°

Hence, We get;

∠ 1 = ∠ 4

∠ 1 = 72°

And, ∠2 = ∠3 = 54°

2) From second figure,

∠ 4 = 90 - 59°

      = 31°

And, We have;

∠1 = 59°

And, Diagonal bisect each other.

Hence,

∠ 2 = ∠ 3 = 90°

3) From third figure,

∠ 2 = 68°

Hence, 2 ∠ 1 = 180 - 136°

2 ∠ 1 = 44°

∠ 1 = 22°

And, We have;

Since, ∠ 2 = 68°

Hence, ∠ 3 = 68°

And. ∠ 4 = 90° (right angle)

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To determine whether the two statement forms are equivalent, we need to create a truth table for each statement form and compare the results.

First, let's create a truth table for the statement form (p∧q)∨∼(p∨q):


 
   p
   q
   p∧q
   p∨q
   ∼(p∨q)
   (p∧q)∨∼(p∨q)
 
 
   T
   T
   T
   T
   F
   T
 
 
   T
   F
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   F
 
 
   F
   F
   F
   F
   T
   T
 

Next, let's create a truth table for the statement form (p∨∼q)∧(∼p∨q):


 
   p
   q
   ∼q
   ∼p
   p∨∼q
   ∼p∨q
   (p∨∼q)∧(∼p∨q)
 
 
   T
   T
   F
   F
   T
   T
   T
 
 
   T
   F
   T
   F
   T
   F
   F
 
 
   F
   T
   F
   T
   F
   T
   F
 
 
   F
   F
   T
   T
   T
   T
   T
 

Comparing the results of the two truth tables, we can see that the two statement forms are not equivalent. The statement form (p∧q)∨∼(p∨q) is true when both p and q are true or when both p and q are false. The statement form (p∨∼q)∧(∼p∨q) is true when both p and q are true or when both p and q are false, but it is also true when p is false and q is true. Therefore, the two statement forms are not equivalent.

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The slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

The slope of a line (m) = change in y/change in x = y2 - y1/x2 - x1 or rise/run of the line.

Given the following points on the line:

(-4, 2) = (x1, y1)

(-5, 0) = (x2, y2)

Substitute the values into m = y2 - y1/x2 - x1:

Slope (m) of the line = (0 - 2) / (-5 - (-4))

Slope (m) of the line = (-2) / (-5 + 4)

Slope (m) of the line = -2/-1

Slope (m) of the line = 2

Thus, the slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

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