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A helicopter flies 1,500 feet over the ocean. A whale swims 150 feet below the ocean. How far apart are the helicopter and whale?

Answer:

75 number of quarters

150 number of nickels

35 number of dimes

Step-by-step explanation:

Let x, y and z be the amount of quarters, nickel and dimes respectively.

​he learns that he has 260 coins, thus;

x + y + z = 260 - - - (1)

Now, we are told that he has twice as many nickels as quarters.

Thus, number of nickels = 2x

y = 2x - - - (2)

From online research, we have the following cost;

1 quarter = $0.25

1 nickel = $0.05

1 dime = $0.1

Total cost is $29.75. Therefore;

0.25x + 0.05y + 0.1z = 29.75 - - - (3)

Put 2x for y in eq (1) and eq (3) to get;

x + 2x + z = 260

3x + z = 260 - - - (eq 4)

0.25x + 0.05(2x) + 0.1z = 29.75

0.25x + 0.10x + 0.1z = 29.75

0.35x + 0.1z = 29.75 - - - (eq 5)

From eq(4), z = 260 - 3x

Thus;

0.35x + 0.1(260 - 3x) = 29.75

0.35x + 26 - 0.3x = 29.75

0.05x = 29.75 - 26

0.05x = 3.75

x = 3.75/0.05

x = 75

So, z = 260 - 3(75)

z = 260 - 225

z = 35

Since y = 2x,

Then,y = 2(75) = 150

Thus,we have;

75 number of quarters

150 number of nickels

35 number of dimes

Answer:

\(=8\left(2a+9\right)\)

Step-by-step explanation:

\(16a+72\)

\(\mathrm{Rewrite\:}16\mathrm{\:as\:}8\cdot \:2\)

\(\mathrm{Rewrite\:}72\mathrm{\:as\:}8\cdot \:9\)

\(=8\cdot \:2a+8\cdot \:9\)

\(\mathrm{Factor\:out\:common\:term\:}8\)

\(=8\left(2a+9\right)\)

Hence, the correct answer is  \(=8\left(2a+9\right)\)

Answer:

8(2a+9)

Step-by-step explanation:

Hope this helps

Answer:

it will be a vertical line and have a undefined slope

Answer:

The equation represents a linear function.

Step-by-step explanation:

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that the expression is,

x + 20 ≤ -10

Rearrange the expression as

x≤ -10-20

x≤ -30

Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

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Answer:

Both the girls have 62 lollipops

Step-by-step explanation:

25+25=50

50+12=62

Answer:

62 lollipops

Step-by-step explanation:

If Angie has 12 more lollipops than Crystal...

25 + 12 = 37 lollipops

Angie has 37 lollipops and Crystal has 25 lollipops. In total, that is...

37 + 25 = 62 lollipops

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

USS Texas length = 573 ft

USS Texas length (picture) length = 27.7 cm

Step 02:

27.7 cm * (1 inch / 2.54 cm) = 10.91 inches

10.91 inches --------------- 573 ft

1 inch ----------------------- x

x * 10.91 inches = 1 inch * 573 ft

x = 573 / 10.91 = 52.52 ft

The answer is:

1 in = 53 ft

Answer:

(b)    a = 50 * 2^(t/4)

(c)    951

Step-by-step explanation:

After t hours

a = 50 * 2^(t/4)

After 17 hours

a = 50 * 2^(17/4)

a = 50 * 2^(4.25)

Use calculator

a = 951.3656920022

Rounded

a = 951

Answer:

231q^3

Step-by-step explanation:

Just add them together. They have the same expressions. Whenever you see a number with an ending similarly to another such as 3x and 2x, they can add together.

This is no different. If something is 6x^2 and another is 7x^2, you would add them to get 13x^2.

Answer:

6.12

Step-by-step explanation:

Six is 6

Twelve-hundredths is .12

6 + .12 = 6.12

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

Minimum=60

First Quartile(Q1)=79

Median=86

Third Quartile (Q3)=89

Interquartile range (IQR)=10

The complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

The function is given as:

f(x) = -2x^2 +5x - 3

Next, we calculate the values of the functions at the given x values

So, we have:

f(-1.4) = -2(-1.4)^2 + 5(-1.4) - 3 = -13.92

f(-0.7) = -2(-0.7)^2 + 5(-0.7) - 3 = -7.48

f(0) = -2(0)^2 + 5(0) - 3 = -3

f(0.7) = -2(0.7)^2 + 5(0.7) - 3 = -0.48

f(1.4) = -2(1.4)^2 + 5(1.4) - 3 = 0.08

Hence, the complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

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Answer:

p=45°, q=45°, s=112.5°

Step-by-step explanation:

Because the triangle is an isosceles right triangle, \(p=q=45^{\circ}\).

In the top triangle, because of the isosceles triangle, the other two angles are each 67.5°.

Therefore, because angles that add to form a straight angle add to 180°, s=112.5°.

Explanation

Using a graphing calculator, the graph of x-4y =-4 can be seen below.

Answer:

2 gallons

Step-by-step explanation:

You have to find the pattern of adding and draining water for 15 days. To get there you need to subtract 2 and add 1 but keep the negative/positives the same i.e. (this is for the 10ths of gallons)

13-2=11

11+1=10

keeping the pattern for 15 days:

+13, 11,+12,-10,+11,-9,+10,-8,+9,-7,+8,-6,+7,-5,+6 = 20 (10ths of gallons)

20/10 = 2

1. We can see that the number in the bottom box is: 13.5yd.

2. The number in the top box is: 7.5yd.

3. The area of the table = 78.75yd²

A trapezoid, also known as a trapezium in some countries, is a quadrilateral shape that has only one pair of parallel sides. The parallel sides of a trapezoid are called the bases of the trapezoid, and the non-parallel sides are called the legs.

We see here that in order to get the number in the bottom box, we discover that the number in the top box is a square which means that all the sides are equal to 7.5yd.

Thus, the number in the bottom box = 3 + 7.5 + 3 = 13.5yd.

Thus, the area of the table, a trapezoid = 1/2(a + b)h

Where a = 7.5yd

b = 13.5yd

height, h = 7.5yd.

Thus, A = 1/2(7.5 + 13.5) 7.5 = 157.5/2 = 78.75

∴ Area of the table, A = 78.75yd²

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Answer:

- 3 and 69/70

Step-by-step explanation:

3 ÷ 5(6 × 7) - 4

3 ÷ 5(40) - 4

3 ÷ 210 - 4

1/70 ÷ 4

- 3 and 69/70

Answer:

21.2

Step-by-step explanation:

3/5(42)-4

0.6(42)-4

25.20-4

21.2

Answer:

A'(-3,-7) B'(-5,-12) C'(-11,-9)

Step-by-step explanation:

A(3,2) B(1,-3) C(-5,0)

Moving 6 units left and 9 units down, assume standard axes so up and right are positive, down and left are negative.
A'(3-6,2-9) B'(1-6, -3-9) C'(-5-6,0-9)
A'(-3,-7) B'(-5,-12) C'(-11,-9)

The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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Answer:

-x + 7 / x + 1

Step-by-step explanation:

6 -(x - 1)/ x + 1

Apply distributive law: -(x - 1) = -x + 1

= 6 - x + 1 / x +1

Group like terms:

= -x + 7/ x + 1

Answer:  its 5x+7/x+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

uhh

The value of the equation f(x) = 2.5x - 10.5 and g(x) = 64(0.5x) are calculated as x = 2: f(x) = 2.5(2) - 10.5 = -5.5 and g(x) = 64(0.5(2)) = 64.

The substitution method is a quick and easy way to identify the variables' solutions to a set of linear equations. It entails, as the name implies, determining the value of the x-variable in terms of the y-variable from the first equation, and then substituting or replacing the value of the x-variable in the second equation. So, we may solve the equation and determine the value of the y-variable. Finally, we can use any of the above equations with the value of y to determine x. It is also possible to solve for x first, then for y, in the opposite order.

The given equation are f(x) = 2.5x - 10.5 and g(x) = 64(0.5x).

Substituting the value of x we have the value in the table as follows:

x = 2:

f(x) = 2.5(2) - 10.5 and g(x) = 64(0.5(2))

f(x) = -5.5                     g(x) = 64

For x = 3:

f(x) = 2.5(3) - 10.5 and g(x) = 64(0.5(3))

f(x) = -3                         g(x) = 96

For x = 4:

f(x) = 2.5(4) - 10.5 and g(x) = 64(0.5(4))

f(x) = -0.5                     g(x) = 128

For x = 5:

f(x) = 2.5(5) - 10.5 and g(x) = 64(0.5(5))

f(x) = 2                          g(x) = 160

For x = 6:

f(x) = 2.5(6) - 10.5 and g(x) = 64(0.5(6))

f(x) = 4.5                       g(x) = 192

Hence, the value of the equation f(x) = 2.5x - 10.5 and g(x) = 64(0.5x) are calculated as x = 2: f(x) = 2.5(2) - 10.5 = -5.5 and g(x) = 64(0.5(2)) = 64.

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Answer:

4

Step-by-step explanation:

Look, they are 4 spaces apart, you can also see in the x coordinates (first n umber in pair) that 0+ 4  = 4

Answer: the anwer is 3\

Step-by-step explanation:

As regards whether the p integral is convergent or divergent , A . It will diverge because of the Limits .

The p - test can be used to determine the convergence of the given improper integral .

The form of the integral is :

\(\int\limits^a_0 {1 / x ^ {p}} \, dx\)

The p - test is :

\(\int\limits^a_1 {1 / x ^ {p}} \, dx\)

If p > 1, the integral converges .

If p ≤ 1, the integral diverges .

p in this instance is 1 / 2 which is less than or equal to one and so the integral will diverge.

In conclusion, the p  integral is divergent.

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