A ship's sonar locates a treasure chest at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far (to the nearest meters) does the diver need to swim along the ocean floor to get the treasure chest?

Answer: the distance from one corner of the field to the other corner is 136 m

Step-by-step explanation:

The distance from one corner to the other corner is the diagonal and it

divides the field into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The length and width of the rectangle represents the adjacent and opposite sides of the right angle triangle. To determine the length of the diagonal, d, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

d² = 110² + 80²

d² = 12100 + 6400 = 18500

d = √18500

d = 136 meters

The distance from one corner of the football field to the other corner (the diagonal) is approximately 136.08 meters.

To find the distance from one corner of the football field to the other corner (the diagonal), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the width of the football field is one side of the right triangle, the length of the football field is the other side, and the diagonal (the distance we want to find) is the hypotenuse.

According to the Pythagorean theorem:

[tex]\[ d^2 = w^2 + l^2 \][/tex]

[tex]\[ d^2 = 80^2 + 110^2 \][/tex]

[tex]\[ d^2 = 18500 \][/tex]

To find d, we take the square root of both sides:

[tex]\[ d = \sqrt{18500} \][/tex]

[tex]\[ d \approx 136.08 \][/tex]

Therefore, the distance from one corner of the football field to the other corner (the diagonal) is approximately 136.08 meters.

Answer:

3

Step-by-step explanation:

in order to be correct, it would have to be "any amount of money less than or equal to $12" because if it were less then, that makes the maximum amount he can spend $11.99.

Answer:

(- 2, 3 )

Step-by-step explanation:

Given the 2 equations

7x - 2y = - 20 → (1)

9x + 4y = - 6 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the term in y

14x - 4y = - 40 → (3)

Add (2) and (3) term by term to eliminate the term in y

23x = - 46 ( divide both sides by 23 )

x = - 2

Substitute x = - 2 into either of the 2 equations and evaluate for y

Substituting into (2)

9(- 2) + 4y = - 6

- 18 + 4y = - 6 ( add 18 to both sides )

4y = 12 ( divide both sides by 4 )

y = 3

Solution is (- 2, 3 )

The required solution of the given simultaneous equation is x = -2 and y = 3.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equations,
7x - 2y = -20 - - - - - (1)

9x + 4y = -6 - - - - - (2)

Multiply equation 1 with 2 and add both equations,
14x - 4y  + 9x + 4y = -40 - 6
23x = -46
x = -2

Now,
7(-2) - 2y = -20
-2y = -6
y = 3

Thus, the required solution of the given simultaneous equation is x = -2 and y = 3.

Learn more about simultaneous equations here:

https://brainly.com/question/16763389

#SPJ6

Answer:

4.6

Step-by-step explanation:

5x +3 = 20

5x = 23

x = 4.6

There was only one pencil in each of the 5 gift bags.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that each of 5 gift bags contains {X} pencils. Tyler add 3 more pencil to each bag. Together the gift pack contain 20 pencils.

We can write the equation as -

5x + 3(5) = 20

5x + 15 = 20

5x = 5

x = 1

Therefore, there was only one pencil in each of the 5 gift bags.

To solve more questions on functions, visit the link below-

https://brainly.com/question/30194223

#SPJ2

Answer:

106.50

Step-by-step explanation:

just did it

Final answer:

To calculate the simple interest on a $400 necklace purchase with a 21.3% interest rate after 15 months, use the simple interest formula I = PRT, resulting in an interest of $106.50.

Explanation:

To calculate the simple interest added to a $400 necklace purchase with a credit card charging 21.3% simple interest after 15 months, you can use the formula for simple interest: I = PRT, where I is the interest, P is the principal amount (initial loan balance), R is the rate of interest per year, and T is the time in years. In this question, P = $400, R = 21.3% or 0.213, and T = 15/12 years (to convert months to years).

First, convert the interest rate to a decimal by dividing by 100:

R = 21.3% \/ 100 = 0.213

Next, convert the time from months to years:

T = 15 months \/ 12 = 1.25 years

Finally, calculate the simple interest:

I = P times R times T

I = $400 times 0.213 times 1.25

I = $106.50

Therefore, the interest added after 15 months would be $106.50.

Answer: $0

Step-by-step explanation:

every six months means the game loses 25%*2 per year = 50%

2 years would be 50%*2 = 100%

Therefore, if the game loses 100% of its value in 2 years, it will be free.

Answer:

84 minutes       (1 hr and 24 mins)

Step-by-step explanation:

Let's put it together:

26 = 5 + .25[tex]x[/tex]

Subtract the 5...

21 = .25[tex]x[/tex]

Divide...

[tex]\frac{21}{.25} = 84[/tex]

Answer:

2/75

Step-by-step explanation:

6 of the 30 pens are green, so the probability of selecting a green pen is 6/30 = 1/5.

The pen is then replaced, so there are still 30 pens in the drawer.  4 of the pens are black, so the probability of selecting a black pen is 4/30 = 2/15.

The probability of both events is therefore 1/5 × 2/15 = 2/75.

Answer:

y=-2x-20

Step-by-step explanation:

y=mx+b

m=(y2-y1)/(x2-x1)

m=(-5+4)/(-6+8)

m=-1/2

y=-1/2x+b

-4=-1/2(-8)+b

-4=4+b

-8=b

y=-1/2x-8

Hope this helped! Please mark brainliest :)

Answer: it’s either -5 or 5 I just took the test

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

let this happens after t hours

so

80t + 60t = 392

140 t = 392

t = 392/140

=2.8 hours

Answer:

ok the train goes 60+80=140 in 1 hour

140+140=280 2 hours

392-280=112

112/ the 60 miles and 80 miles is .80% of the hour so

60*.80=48 and 80*.80=64

48+64=112 so the trains will be 392 miles apart in 2.8 hours

Step-by-step explanation:

Answer:

x =2 and x = 6 are the x-intercepts

Step-by-step explanation:

The x -interepts mean  the value of x when y=0

so

y = 0 = (x - 2)(x - 6)

Here if we solve for x, we solve the x-intercepts.

0 = (x - 2) or  0 = (x - 6)

x = 2   or x = 6

Answer:

Step-by-step explanation:

Enclosing something with fencing is a perimeter thing.  Since we are dealing with a circle, we need the circumference instead, which is the same thing, different formula.

[tex]C=\pi d[/tex]

Filling in with the diameter of 287 m:

[tex]C=\pi (287)[/tex]  or you could just say that the circumference is

287π.  If you have to multiply in π, then the circumference is

901.18 m

Answer:

The answer to your question is 901.2 m

Step-by-step explanation:

Data

Perimeter = ?

diameter = 287 m

Process

1.- Calculate the radius of the garden

    radius = diameter/2

-Substitution

   radius = 287/2

-Result

   radius = 143.5 m

2.- Calculate the perimeter

Perimeter = 2πr

-Substitution

Perimeter = 2(3.14)(143.5)

-Simplification and result

Perimeter = 901.18 ≈ 901.2 m  

Answer:

$13,695.98

Step-by-step explanation:

We can use the continuous compound interest formula to solve:

[tex]A = Pe^{rt}[/tex]

P = principal amount

r = interest rate (decimal)

t = time (years)

First, lets change 8% into a decimal:

8% -> [tex]\frac{8}{100}[/tex] -> 0.08

Now, lets plug in the values:

[tex]A=6,154e^{0.08(10)}[/tex]

[tex]A=13,695.98[/tex]

The account balance after 10 years will be $13,695.98

Answer:

Pears weight = 1.925 kgs

Step-by-step explanation:

Total weight of apples & pears = 7.7kg

Apples weight = 3/4th of total weight

= ( 3/4 ) x ( 7.7 )

= 5.775

So, remaining pears weight = Total weight - Apples weight

= 7.7 - 5.775

= 1.925

Final answer:

The farmer sold 1.925 kilograms of pears at the farmer's market.

Explanation:

A farmer sells 7.7 kilograms of apples and pears at the farmer's market. To find out how many kilograms of pears were sold, we need to calculate the remainder that is not apples.

Since ¾ of the weight is apples, we have:

Therefore, the farmer sold 1.925 kilograms of pears at the farmer's market.

Answer: It should be g > 9

Step-by-step explanation:

-Solve:

[tex]g-3>6[/tex]

[tex]g-3+3>6+3[/tex]

[tex]g>9[/tex]

So, Therefore, the result is g > 9

The solution to the inequality is g > 9.

Here, we have,

To solve the inequality g - 3 > 6, we will isolate the variable g.

Adding 3 to both sides of the inequality, we get:

g - 3 + 3 > 6 + 3

Simplifying, we have:

g > 9

So, the solution to the inequality is g > 9.

To graph the solution on a number line, we represent all values of g that are greater than 9. We can denote this by shading the region to the right of 9 on the number line.

Here's a graphical representation:

    ------------------------>

    -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 ...

                o

                |

                |

                |

In this representation, the open circle (o) indicates that 9 itself is not included in the solution since the inequality is strict (g > 9). The shaded region represents all values of g that are greater than 9.

Please note that the number line extends indefinitely in both directions, but only the relevant portion is shown here for clarity.

To learn more on inequality click:

https://brainly.com/question/28841069

#SPJ6

Answer:

In this instance you would do what is inside the parentheses first and then use the exponent. Therefore it would be 3^2 and your answer is 9.

Step-by-step explanation:

Final answer:

The rule for raising a product to a power does not apply to sums or differences because [tex](5 - 3)^2[/tex] correctly calculated is 4, not 16 as incorrectly applying the rule to the sum would suggest (25 – 9).

Explanation:

The rule that when a product is raised to a power, it is equal to the product of each factor raised to that power, does not apply to sums or differences. The example given is [tex](5 - 3)^2[/tex], if we incorrectly apply the rule to the sum, we might think [tex](5^2 - 3^2)[/tex] which is-

25 – 9 = 16

However, performing the operation correctly, we first do the sum inside the parentheses:

(5 – 3) = 2,

and then raise to the power:

[tex]2^2[/tex] = 4.

This clearly shows that raising a sum to a power is not the same as raising each term to the power and then summing.

Answer:

the answer is 90 i just took  the test

Step-by-step explanation:

Answer:

i think that is because, that if u order them it is going to be 3,4,5,8

and probably he has a chance of 5 or 4

Step-by-step explanation:

The probability that Allen will select a red marble and the coin will land heads up is 1/10.

To find the probability that Allen will select a red marble and the coin will land heads up, we need to consider two independent events: selecting a red marble and tossing a fair coin.

The probability of selecting a red marble is the number of red marbles (4) divided by the total number of marbles in the box (4 + 8 + 3 + 5 = 20):

Probability of selecting a red marble = 4/20 = 1/5.

The probability of the coin landing heads up is 1/2 since it's a fair coin.

Now, to find the probability of both events occurring together (selecting a red marble and getting heads up), we multiply the probabilities of each event:

Probability of selecting a red marble and getting heads up = (1/5) * (1/2) = 1/10.

So, the probability that Allen will select a red marble and the coin will land heads up is 1/10.

To know more about probability, refer here:

https://brainly.com/question/30751516

#SPJ2

Answer:

D and E

Step-by-step explanation:

StartFraction negative 5 Over 2 EndFraction minus StartFraction StartRoot 33 EndRoot Over 2 EndFraction

StartFraction negative 5 Over 2 EndFraction + StartFraction StartRoot 33 EndRoot Over 2 EndFraction

❌ A.

❌ B.

❌ C.

✔   D.

✔   E.

Answer:

1187.7

Step-by-step explanation:

V = (1/3)πr2h

Volume = 1187.67 cm³.

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base. The distance from the vertex of the cone to the base is the height of the cone. The circular base has measured value of radius. And the length of the cone from apex to any point on the circumference of the base is the slant height.

Given,

Height of the cone (h) = 12.7cm

Diameter of the circular base(d) = 18.9cm

Radius (r) = d/2 = 18.9/2 = 9.45cm

Volume of the cone

V = 1/3πr²h

V = 1/3×3.14159×9.45×9.45×12.7

V = 1187.66946

V = 1187.67 cm³

Hence the volume of the cone is 1187.67 cm³.

Learn more about cone here:

https://brainly.com/question/16394302

#SPJ5

Answer: 13,200 vehicles

Step-by-step explanation:

Hi, to answer this question, first we have to calculate the number of people that will drive to the stadium, by multiplying the total number of fans (80,000) by the percentage in decimal form (57/100).

80,000 x (57/100) = 45,600

Since an average of three fans come in each vehicle, we have to divide the result by 3 to obtain the number of vehicles:

45,600/3 =15,200

Subtract the number of cars that parked in satellite lots.

15,200-2,000 = 13,200 vehicles

Answer: 13,200 rounded up to 13,000.

Step-by-step explanation:

The turnout for a game is expected to reach 80,000 fans, out of which 57% are expected to drive. The number of fans expected to drive will be:

= 57% of 80,000

= 0.57 × 80000

= 45600

An average of three fans come in each vehicle. The number of cars will be:

= 45600 ÷ 3

= 15200 cars

2,000 vehicles park in satellite lots and the rest of the vehicles parked in the stadium lot. Since there are 15200 cars, the number of cars in the stadium lot will be:

= 15,200 - 2,000

= 13, 200

Rounding up 13,200 will give 13,000.

Answer: 0.5 and 1

Step-by-step explanation: oz. bottle will contain around 500 mL of liquid. This means that you need 2 bottles of 16.9 fl. oz. to make up 1 Liter in the US.

Answer:

d ik

Step-by-step explanation:

Answer:

Nine more than two-fifths of a number is nine.

Step-by-step explanation:

that is the only one that makes sense.

Answer:the width of the rectangle is 9 because sum of the width and one is 9

Step-by-step explanation:

The length would be 9.

The width could be 8, which would make sense, because the width plus 1 would equal nine. You can confirm these dimensions by multiplying them to get the area, 72.

Answer:

1

Step-by-step explanation:

[tex]17 = 1 \times 17 \\ 25 = 1 \times 5 \times 5 \\ common \: factor = 1 \\ gcf = 1[/tex]

Answer:

Rotation, Reflection, dilation, and translation

Step-by-step explanation:

Rotation: Just rotating the shape; spinning the shape around a point

Reflection: Your shape is either reflecting on the x axis or y axis meaning it is either side by side (y) or up and down (x)

Dilation: Your shape is either going to shrink or get bigger

Translation: Shifting all the points of the figure

Answer:

okay  so,

so do a 16 by 14 rectangle it should be good

sry if its wrong i tried but i hope it helped ;0

The problem is regarding the calculation of the area of a rectangle, which in this case is a floor plan of a mausoleum. The area is calculated by multiplying the length and the width of the rectangle, yielding an area of 1400 square meters.

The problem provided is a concept of geometry and the specific topic is calculating the area of a rectangle. The area of a rectangle is calculated by multiplying its length and width. In the given problem, the length of the rectangle is 40 m and the width is 35 m.

To find the area, we perform the multiplication: Area = length x width = 40 m x 35 m = 1400 m². Therefore, the floor area of King Kyle's mausoleum, according to the architect's drawings, is 1400 square meters.

https://brainly.com/question/32024069

#SPJ3

The area would be 78.54

Step-by-step explanation:

Here's why:

By using the area of a circle formula, you should plug in the radius and get the following of:

π5^2 = 78.539...

If you round to the nearest tenth you would get the answer of 78.54.