FIND THE LENGTH OF MP

Answer:

Step-by-step explanation:

If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:

[tex]15=-16t^2+23t+7[/tex] and

[tex]0=-16t^2+23t-8[/tex]

Factor this however you factor a quadratic in class to get

t = .59 seconds and t = .85 seconds.

This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.

Answer:

36

Step-by-step explanation:

Total students un the contest = 84

Number of students who gave their speech yesterday:-

[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]

so 21 students gave their speech yesterday

= 63

Number of students who gave their speech today:-

[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]

Number of students who have given their speech:-

= 21 + 27

= 48

Number of students who still haven't given their speech :-

= total - 48

= 84 - 48

= 36

Answer:

The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.

The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2

Explanation:

Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.

The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.

I hope this helps!

Answer:

In LDR

In PDR

Exterior angle of a triangle is formed when one side of the triangle is extended .

Interior remote angles the angles in the triangle that do not lie on the extended side.

Answer:

n = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 30 = n / 2 sqrt(3)

2 sqrt(3) tan 30 = n

2 sqrt(3) * sqrt(3)/3 = n

2 = n

We have to find,

The required value of n.

Now we can,

Use the trigonometric functions.

→ tan(θ) = opp/adj

Let's find the required value of n,

→ tan (θ) = opp/adj

→ tan (30) = n/2√3

→ n = 2√3 × tan (30)

→ n = 2√3 × √3/3

→ n = 2√3 × 1/√3

→ [n = 2]

Thus, the value of n is 2.

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Answer:

  $562,500 per hour

Step-by-step explanation:

The cost will be a minimum where C'(x) = 0.

 C'(x) = 0.56x -0.7 = 0

  x = 0.7/0.56 = 1.25

The cost at that production point is ...

  C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625

The minimum production cost is $562,500 per hour for production of 1250 items per hour.

_____

Additional comment

This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.

Complete Question

The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad

Answer:

[tex]P(-1.72<Z<1.72)=0.9146[/tex]

Step-by-step explanation:

From the question we are told that:

Population mean \mu=91

Sample Mean \=x =2.08

Standard Deviation \sigma=10

Sample size n=68

Generally the Probability that The  sample mean  would differ from the population mean

P(|\=x-\mu|<2.08)

From Table

[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]

T Test

[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]

[tex]Z=1.72[/tex]

[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]

[tex]P(-1.72<Z<1.72)[/tex]

Therefore From Table

[tex]P(-1.72<Z<1.72)=0.9146[/tex]

Answer:

A) x = 0.

B) f is concave up for (-∞, 0).

C) f is concave down for (0, ∞).

Step-by-step explanation:

We are given the function:

[tex]f(x)=5+12x-x^3[/tex]

A)

We want to find the x-coordinates of all inflection points.

Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:

[tex]f'(x) = 12-3x^2[/tex]

And the second:

[tex]f''(x) = -6x[/tex]

Set the second derivative equal to zero:

[tex]0=-6x[/tex]

And solve for x. Hence:

[tex]x=0[/tex]

We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:

[tex]f''(-1) = 6>0[/tex]

And testing x = 1:

[tex]f''(1) = -6<0[/tex]

Since the signs change for x = 0, x = 0 is indeed an inflection point.

B)

Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.

From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:

[tex](-\infty, 0)[/tex]

C)

From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:

[tex](0, \infty)[/tex]

Answer:

[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = x^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

The equation is x + 4 = 0.

Step-by-step explanation:

Point (-4 , 8)

A line parallel to the Y axis has slope is infinite.

The equation of line is

[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]

Answer:

C) the length of DG and JL

Answer:

-11

Step-by-step explanation:

I am going to assume that it is -x^2-5y^3.

-(4^2)-5(-1^3)

-16-5(-1)

-16+5

-11

Answer:

- 11

Step-by-step explanation:

If x = 4,  y = -1

then,

        - x^2 - 5y^3 = - (4)^2 - 5(-1)^3

                            = - 16 + 5

                            = - 11

Answer:

The car will depreciate at a rate of 21.14% per year.

Step-by-step explanation:

Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:

13,500 x (1 + X) ^ 1x3 = 24,000

13,500 x (1 + 0.2114) ^ 3 = 24,000

X = 21.14%

Therefore, the car will depreciate at a rate of 21.14% per year.

Answer:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Answer:

XW = 78

Step-by-step explanation:

Both triangles are similar, therefore based on triangle similarity theorem we have the following:

XW/XZ = VW/YZ

Substitute

XW/6 = 104/8

XW/6 = 13

Cross multiply

XW = 13*6

XW = 78

Answer:

(a) 129600 J

(b) 81000 J

Step-by-step explanation:

The work done is given by the product of force and the displacement in the direction of force.

Force, F = 500 N

distance, d = 324 m

(a) friction force, f = 100 N

The work done is

W = (F - f) x d

W = (500 - 100) x 324

W = 129600 J

(b) Friction, f = 250 N

The work done is

W = (F - f) d

W = (500 - 250) x 324

W = 81000 J

Answer:

A significant negative relationship exists between the variables

Step-by-step explanation:

Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.

Answer:

[tex]f(x)=\sqrt[3]{x}[/tex]  [tex]3~units\: down[/tex]

[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]

[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]

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

Hope it helps..

Have a great day!!

Answer:

its not B that what i put and i missed it

Step-by-step explanation:

Answer:

j * .07 +j

Step-by-step explanation:

The tax on the jewelry is J* .07

Add the tax to the cost of the jewelry to get the total cost

j * .07 +j

Answer:

i think 4 4 kilograms if im wrong sorry

Step-by-step explanation:

Answer:

we need a picture...

Step-by-step explanation:

Answer:

t2 = 2.5 hours.

Step-by-step explanation:

The distance is the same.

d = r * t

The rates and times are different so

t1 = 3 hours

t2 = X

r1 = 50 mph

r2 = 60 mph

r1 * t1 = r2*t2

50 * 3 = 60 * t2

150 = 60 * t2

150 / 60 = t2

t2 = 2.5

Answer:

Answer: Travel Time is 2 hours & 30 minutes

Step-by-step explanation:

Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles

Original Distance is 150 miles, New Speed is 60 mph.

Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph

9514 1404 393

Answer:

  3

Step-by-step explanation:

AB is 1 unit long.

A'B' is 3 units long.

The scale factor is the ratio of these lengths:

  scale factor = A'B'/AB = 3/1 = 3

ABC is dilated by a factor of 3 to get A'B'C'.

Answer:

6

Step-by-step explanation:

We need to evaluate :-

[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]

Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,

[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]

Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,

[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]

Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,

[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]

Hence the required answer is 6.

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Answer:

  see attached

Step-by-step explanation:

The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).

The graph of g(x) is attached.

Answer: 90° counterclockwise

Step-by-step explanation:

9514 1404 393

Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

Answer:

The answer is A: 6√2 - 2√30 + 6 - 2√15

Believe me it right.