An airplane ascends from the ground at an angle
of 17°. When the airplane has traveled a
horizontal distance of 650 ft, what is its height
above the ground to the nearest foot?

If the point in question is on the line of reflection, then the point won't move. Any point on a line of reflection stays where it is.

If that same point is the center of dilation, then it also doesn't move. The center of dilation is the only point that doesn't move in a dilation.

So the two conditions are:

These two facts mean that the line of reflection must go through the center of dilation.

The probability that X equals 2 is 0.44.

We have given  cumulative distribution function for the discrete random variable X. The probability that X equals 2 can be found by taking the difference between the probability that X is less than or equal to 2 and the probability that X is less than or equal to 1.

P(X = 2) = P(X ≤ 2) - P(X ≤ 1)

Using the cumulative distribution function given in the problem, we find:

P(X ≤ 2) = 0.30 + 0.44 = 0.74

P(X ≤ 1) = 0.30

Therefore,

P(X = 2) = 0.74 - 0.30 = 0.44

So the probability that X equals 2 is 0.44.

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Step-by-step explanation:

1.

\(2d + 3 \leqslant - 11 \\ 2d \leqslant - 11 - 3 \\ 2d \leqslant - 14 \\ \frac{2d}{2} \leqslant \frac{ - 14}{2} \\ d \leqslant - 7\)

2.

\(3d - 9 > 15 \\ 3d > 15 + 9 \\ 3d > 24 \\ \frac{3d}{3} > \frac{24}{3} \\ d = 8\)

Welcome

Answer:

132.277 if this isnt the right answer i just googled how many pounds is 60 kg

Step-by-step explanation:

The geometric series that has been provided is of divergence, since r>5.

The series is given as /10 + 3/2 + 15/2 + 75/2 + 325/2 +.....

The common ratio is

3/2 ÷ 3/10

= 3/2 ×10/3

= 5

Then,

15/2 ÷ 3/2

= 15/2 × 2/3

= 5

Thus, the common ratio is greater than 5. Therefore, the series is divergence.

Hence, the given geometric series is divergence, since r>5.

A series is considered to be convergent if the partial sums tend to a particular value, also known as a limit. In contrast, a divergent series is one whose partial sums do not approach a limit. Typically, the Divergent series either reach, reach, or don't reach a particular number.

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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\(~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)\)

Answer:

C)  (-1, -4) and (4, 6)

Step-by-step explanation:

\(\textsf{Equation 1}:y=2x-2\)

\(\textsf{Equation 2}:y=x^2-x-6\)

Substitute Equation 1 into Equation 2 and solve for x:

\(\implies 2x-2=x^2-x-6\)

\(\implies x^2-3x-4=0\)

Find two numbers that multiply to -4 and sum to -3:  -4 and 1

Rewrite the middle term as the sum of these two numbers:

\(\implies x^2-4x+x-4=0\)

Factorize the first two terms and the last two terms separately:

\(\implies x(x-4)+1(x-4)=0\)

Factor out the common term \((x-4)\):

\(\implies (x+1)(x-4)=0\)

\(\implies (x+1)=0 \implies x=-1\)

\(\implies (x-4)=0 \implies x=4\)

Substitute the found values of x into Equation 1 and solve for y:

\(x=-1 \implies y=2(-1)-2=-4\)

\(x=4 \implies y=2(4)-2=6\)

Therefore, the solution to the system of equations is:

(-1, -4) and (4, 6)

Answer:

Point D is the point of dilation.

Step-by-step explanation:

If the smaller triangle A'B'C' is dilated to form a larger triangle ABC by the dilation about point D,

Ratio of the DA and DA' will be equal to the ratio of DB and DB'.

Length of DA = 3 units

Length of DA' = 1 unit

Coordinates of D → (3, 0)

Coordinates of B → (9, 3)

Coordinates of B' → (5, 1)

Use the formula of distance between the two points to find find the length of DB and DB'

Length of DB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(3-0)^2+(9-3)^2}\)

                                                                 \(=\sqrt{45}\)

                                                                 \(=3\sqrt{5}\)

Length of DB' = \(\sqrt{(5-3)^2+(1-0)^2}\)

                       \(=\sqrt{5}\)

Ratio of DB and DB' = \(\frac{3\sqrt{5} }{\sqrt{5} } =3:1\)

Ratio of DA and DA' = 3 : 1

Since, \(\frac{DA}{DA'}=\frac{DB}{DB'}\)

Therefore, smaller triangle is dilated by a scale factor of 3 to form the bigger triangle about the point D.

Answer:

y = -1/2 | x+3|

Step-by-step explanation:

y = f(x + C)  C > 0 moves it left

                 C < 0 moves it right

y = Cf(x)   C > 1 stretches it in the y-direction

                0 < C < 1 compresses it

y = −f(x)  Reflects it about x-axis

Our parent function is

f(x) = |x|

We want it 3 units left

y = f(x + 3)

y = |x+3|

Then reflected across the x axis

y = −f(x)

y = -|x+3|

Then shrink by 1/2 vertically

y = Cf(x)

y = -1/2 | x+3|

Answer:

y = -1/2 | x+3|

Step-by-step explanation:

Step-by-step explanation:

\( \sqrt[6]{5} \times \sqrt[2]{5} \)

\( = {5}^{ \frac{1}{6} } \times {5}^{ \frac{1}{2} } \)

\( = {5}^{ \frac{1}{6} + \frac{1}{2} } \)

\( = {5}^{ \frac{1 + 3}{6} } \)

\( = {5}^{ \frac{4}{6} } \)

\( = {5}^{ \frac{2}{3} } \)

\( = \sqrt[3]{ {5}^{2} } (ans)\)

It will take approximately 3.77 hours for the iceberg and the ship to collide, rounded to the nearest minute, this is 3 hours and 46 minutes.

Velocity is a term used in physics to describe the rate at which an object changes its position. It is a vector quantity, meaning that it has both a magnitude (numerical value) and a direction.

Let's call the distance between the iceberg and the ship "d" and let's use the formula:

distance = rate × time

We know that the iceberg is moving at a rate of 1 mile per hour and the ship is moving at a rate of 12 miles per hour. Since they are moving towards each other, their effective rate of approach is the sum of their individual rates, which is 1 + 12 = 13 miles per hour.

We want to find out how long it will take for the two to collide, so let's use "t" to represent the time (in hours) it will take for the collision to occur.

Using the formula distance = rate × time, we can write:

d = 13t

We also know that the initial distance between the iceberg and the ship is 98 miles. Therefore, we can write:

d = 98 - 1t - 12t

The first term, 98, represents the initial distance between the iceberg and the ship. The second term, 1t, represents the distance that the iceberg moves in "t" hours, and the third term, 12t, represents the distance that the ship moves in "t" hours.

Now we can equate the two expressions for "d" and solve for "t":

13t = 98 - 1t - 12t

13t + 12t + 1t = 98

26t = 98

t = 3.77 hours

Therefore, it will take approximately 3.77 hours for the iceberg and the ship to collide, rounded to the nearest minute, this is 3 hours and 46 minutes.

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The average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.

First step is to calculate the total cost for steaks

Total cost=400×$9.98 + 120×$6.49

Total cost=$4770.8

Second step is to calculate the total pound

Total pound=400 + 120

Total pound= 520

Third step is to calculate the average cost in dollars

Average cost=$4770.8 / 520

Average cost= 9.174615385

Average cost=9.17 per pound (Approximately)

Inconclusion the average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.

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Answer:

Regular pizza: £5

Small pizza: £4

Step-by-step explanation:

Let x = regular pizza

Let y = small pizza

6x + 12y = 78

2x + 3y = 22

I'm going to use elimination method to solve for y

6x + 12 y = 78

-3(2x + 3y = 22) = -6x -9y = -66

Eliminate the x

3y = 12

Divide both sides by 3

3y/3 = 12/3

y = 4

Substitute the y in one of the original equations

2x + 3(4) = 22

2x + 12 = 22

Subtract both side by 12

2x + 12 - 12 = 22 - 12

2x = 10

Divide both sides by 2 to solve for x

2x/2 = 10/2

x = 5

Answer:

small  $3.4   regular $6.2

Step-by-step explanation:

2r +3s = 22.6

6r *12s = 78

Multiply the first  by -3

-6r -9s = -67.8

6r +12 s = 78

Add both (6r will be cancelled)

   3s = 10.2

s = 3.4   small = 3.4   (3 small = 10.2)  

2r +10.2 = 22.6

2r =  12.4

r = 6.2

Answer:

3,2

Step-by-step explanation:

3 is equal to 3 which can be it and 2 is less than 3

Answer:

-7/3

Step-by-step explanation:

The first step is to combine like numbers. Although there are several different ways to go about doing this, I started by adding 2y to both sides which left me with -8-6y=6. I then added 8 to both sides and got 6y=14. Now divide 6 on both sides to get "y" by itself which left me with y = -14/6. When you simplify the answer you get -7/3.

Answer:

x = -6/5 and x = 2

Step-by-step explanation:

y = -10x² + 8x + 24

0 = -2(5x+6)(x-2)

5x+6 = 0         x-2 = 0

5x = -6             x = 2

x = -6/5

Answer:

0.5

Step-by-step explanation:

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Answer:

3500

Step-by-step explanation:

3.5 * 10^3 means you move the decimal 3 places to the right.

The discount rate raised to nth power.

NPV is defined as Net Present Value. It is mainly used in capital budgeting and investment planning for the purpose of analyzing the project profit. NPV is the difference between  the present value of cash inflows and the present value of cash outflows in a period of time. The occurrence of cashflows in a series at different times is termed as NPV. NPV is a measure widely used in finance and commercial real estate. It is used to help taking decisions in accounting calculation. The cashflow that is discounted can be termed as NPV.

A simple example for NPV is, If a security offers a series of cashflows with an NPV of $30,000 and an investor pays exactly $30,000 for it, then the  investor's, NPV is $0.

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"What is the total number of miles that the teacher ran last week and this week, if he ran a total of 5 3/4 miles last week and 4/5 of that distance this week?" is 10 13/20 miles.

To find the total number of miles that the teacher ran last week and this week, we need to:

Determine how many miles the teacher ran this week.

Add that number to the total number of miles the teacher ran last week.

Let's start by finding out how many miles the teacher ran this week:

The teacher ran 4/5 of the total number of miles he ran last week, which means he ran:

(4/5) x 5 3/4 miles = 4 3/5 miles

Next, we can add the number of miles the teacher ran last week to the number of miles he ran this week to find the total number of miles he ran:

5 3/4 miles + 4 3/5 miles = 10 13/20 miles

Therefore, the teacher ran a total of 10 13/20 miles last week and this week combined.

The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

See explanation below

Step-by-step explanation:

Question is incomplete. Here's the whole question:

"Two solutions of different concentrations of acid are mixed creating 40 ml of a solution that is 32% acid. one-quarter of the solution is made up of a 20% acid solution. the remaining three-quarters is made up of a solution of unknown concentration, c. equation can be used to determine c, the unknown concentration?

a) 30c + 10(0.2) = 40(0.32)

b) (c) + (0.2) = 40(0.32)

c) (c)( (0.2)) = 40(0.32)

d) 30(c)(10(0.2)) = 40(0.32)"

With this, we can now solve the question.

We have a solution that was made mixing2 different solutions of acid. In this case, we can assume the following:

Solution 1 = 40 mL 32% acid

Solution 2 = 1/4 solution 1, 20% acid

Solution 3 = 3/4 solution 1, c% acid.

Thus we can say:

Solution 1 = Solution 2 + Solution 3     (1)

Now, 1/4 of the volume of solution 1, means that we use 10 mL of a 20%acid, and the remaining 30 mL is the unknown acid.

With this, we can discart option b) and c) because these option are not considering the volume of solution 3 used. Option d is not doing any sum, only multiplications, so, this is not the option to use. We can easily say it's option a, but let's prove it.

In general terms, concentrations and volume are related, and if we have two solutions, the information of these two solutions must be conserved in the resulting solution. In other words:

M₁V₁ = M₂V₂

According to this, the concentration of the unknown acid would be:

30c + 0.2*10 = 40(0.32)

30c + 2 = 12.8

30c = 10.8

c = 0.36

Which means that the concentration of the acid is 36%

Hope this helps

Answer:

A. a) 30c + 10(0.2) = 40(0.32) !

Step-by-step explanation:

EDG

Answer: 1 solution

Step-by-step explanation:

The system of linear equations has a unique solution. Then the correct option is A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If the slopes are different then the system has one solution.

From the graph, the slope of the lines is different. Then the system of linear equations has a unique solution.

Thus, the correct option is A.

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Answer:

I believe the answer is 30.

Step-by-step explanation:

Answer:

___30_____ − 17 = 38 − 25

Step-by-step explanation:

________ − 17 = 38 − 25

Do the subtraction on the right side.

________ − 17 = 13

Add 17 to both sides.

________ = 30

Answer:

___30_____ − 17 = 38 − 25

Answer:

x = 25

Step-by-step explanation:

The mistake here is the squaring. When you square one side, you have to do the same on the other side:

\(\sqrt{3x+6}\) = 9

\((\sqrt{3x+6}) ^{2}\) = \(9^{2}\)

3x + 6 = 81

3x = 75

x = 25

\(\huge\boxed{x=25}\)

The mistake is in Step 1. The solver should have also squared \(9\) when squaring the other side of the equation.

\(\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}\)

The required present ages of the father and the son are 47 years and 7 years respectively.

Let the present age of the father and the son be x years and y years, respectively.

According to the question,

Condition I,

2 years ago, the father's age was nine times the son's age.

or,(x−2)=9(y−2)

or,x−2=9y−18

or,x=9y−18+2

or,x=9y−16 - (i)

Condition II,

3 years later, the father's age will be five times the son's age.

or,(x+3)=5(y+3)

or,x+3=5y+15 - (ii)

Put the value of x from equation (i) in equation (ii), and we get,

or,(9y−16)+3=5y+15

or,9y−16=5y+15−3

or,9y−5y=12+16

or,4y=28

or,y=284

∴y=7

Put the value of y in equation (i), and we get,

or,x=9×7−16

or,x=63−16

∴x=47

So, (x,y) = (47,7)

Therefore, the required present ages of the father and the son are 47 years and 7 years respectively.

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