Tomas works as an underwater photographer. He starts at a depth of 20 feet, ascends 9 feet, descends 12 feet, and then descends 15 feet more. What is the diver's final depth?

Answer:

The answer is 72.

Step-by-step explanation:

You have to put in the values of a and b into the expressions :

[tex] {a}^{2} {b}^{3} - {(ab)}^{2} [/tex]

[tex]let \: a \: = - 2 \\ let \: b = 3[/tex]

[tex] {( - 2)}^{2} \times {(3)}^{3} - {( - 2 \times 3)}^{2} [/tex]

[tex] = 4 \times 27 - { (- 6)}^{2} [/tex]

[tex] = 108 - 36[/tex]

[tex] = 72[/tex]

Answer:

x = ±11

Step-by-step explanation:

x^2 = 121

Take the square root of each side

sqrt(x^2) = ±sqrt(121)

x = ±11

Answer:

Vertical: 2 units down

Horizontal: 1 unit left

Step-by-step explanation:

X +/- numbers: means it will go up or down

If its parentheses then it is the opposite

Answer:

150=2x5x5x3, or 150=2x5^2x3

Step-by-step explanation:

150=50x3

50=5x10

10=2x5

150=2x5x5x3

Answer: 4:5

Step-by-step explanation:

Subtract like terms:

3 -4 = -1

8i - 2i = 6i

The answer is -1+6i

Answer:

a) n = 3

b) every 9 cm represents 175,000 km

Step-by-step explanation:

a) 20 min : 1 hour

Let's convert it into same units

⇒20 min : 60 min

÷ 20        ÷ 20

⇒ 1 : 3

So n = 3

b) 1 : 25,000

Which means every 1 cm on the map represents 25,000 km

And,

1 cm = 25,000 km

So,

9 cm = 25,000 × 9

9 cm = 175,000 km

So every 9 cm represents 175,000 km

Answer:

a) 3

b) 2.25 km

Step-by-step explanation:

a) 20 min : 1 hour = 1 : n

20 min : 60 min= 1 :3

n=3

b) 1: 25000 scale

1 mm : 25000 mm

9 cm = 90 mm

90 mm : 90*25000 mm

9 cm : 2250000 mm

9 cm : 2.25 km

Answer:

100 : 20 : 60 Making the total number of cookies 180

Step-by-step explanation:

Looking at the basic information given we know:

If there are 5 oatmeal cookies, there will be: 1 raisin cookie and 3 butter cookies. This is a base value.

So, we have equations like this:

[tex]r = 1/3b[/tex] and [tex]o = 5/3b[/tex]

So, if we plug in 60 for butter cookies we will have something like this:

[tex]o : r : 60[/tex] or [tex](5/3b) : (1/3b) : b[/tex] where b=60

Solving:

[tex](5/3b) : (1/3b) : b[/tex]

[tex](5/3b) : (1/3b) : 60\\100 : 20 : 60[/tex]

Then add the amounts of together to get 180.

I hope this helps! It's a bit difficult to explain, where I do most of this in my head, but I hope this will be able to provide some understanding to you.

Answer:

4(-2) + 8(4) / 7 - (-2)²

-8 + 32 / 7 - 4

24 / 3

= 8

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

[tex]\frac{99}{660} =\\\\\frac{3}{20} =\\\\\frac{15}{100}[/tex]

99 is 15% of 660

Answer:

-22, 4, -27, 2

Step-by-step explanation:

-10 + (-12) = -10 - 12 = -22

-3 + 7 = 4

-11 - 16 = -27

-13 - (-15) = -13 + 15 = 2

Answer:

-22 4 -27 2

Step-by-step explanation:

-10 + (-12) = -22

-3 + 7 = 4

-11 - 16 = -27

-13 -(-15) = 2

Answer:

Step-by-step explanation:

Using set notation to answer the question. let:

n(U) be the total people in a sport centre =130

n(G) be number of people that use the gym.  = 76

n(P) be number of people that use the swimming pool. = 60

n(T) be number of people that use the track = 32

n(G∩P) be number of people that uses the gym and the pool = 23

n(P∩T) be number of people that uses the  pool and the track = 8

n(G∩T) be number of people that uses the gym and the track = 320

n(G∩P∩T) be number of people that uses all three facilities = 6

Using the relationship below;

n(U)= n(GUPUT)+n(GUPUT)'

where n(GUPUT)' is the number of people that doesn't use any facility.

Before we can get that, we need to know n(GUPUT) using the formula;

n(GUPUT) = n(G) + n(P)+n(T)-n(G∩P)-n(P∩T)-n(G∩T)+n(G∩P∩T)

n(GUPUT) = 76+60+32-23-8-20+6

n(GUPUT) = 123

n(GUPUT)' = n(U)- n(GUPUT)

n(GUPUT)' = 130 - 123

n(GUPUT)' = 7

This means that 7 person doesn't use any facility.

Probability that a person selected at random doesn't use any facility = n(GUPUT)' /n(U) = 7/130

Answer:

8 i think

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

2x^2-4x+1=0

This is written in the form

ax^2 +bx+c =0

a=2   b = -4  c =1

The discriminant is

b^2 -4ac

(-4)^2 -4(2)(1)

16 - 8

8

The discriminant is 8

Answer:

$68.40

Step-by-step explanation:

Let x represent the required cost.

Since the number of toys is directly proportional to the cost:

x : $20.52 = 120 : 36

i.e.  x/$20.52 = 120/36

      x = ([tex]\frac{120 * $20.52}[/tex])/36

      x = $2462.40/36

      x = $68.40

Hope this helps!!!

Answer:

2

180 and 360

Step-by-step explanation:

We conclude that the angle of rotational symmetry is 180°.

For any regular shape that has internal angles measuring θ, the angles of rotational symmetry of that figure are:

A = n*θ

Where n is an integer number (different than zero, because that is the trivial case).

For the case of the rectangle not all the sides measure the same thing, we have internal angles of 90° and opposite sides measure the same.

So we only have rotational symmetry for each two internal angles (2*90° = 180°).

So we conclude that the angle of rotational symmetry is 180°.

If you want to learn more about rotational symmetry:

https://brainly.com/question/15178808

#SPJ2

Answer:

3 1/7 units

Step-by-step explanation:

(im assuming that 22/7 is what it's being converted here lol) basically what you would do is turn this in to a mixed fraction. You look at how many sevens can go into 22. In this case, three "sevens" would go into 22 (7x3=21). Since we have one left over, it would go over the 7! So that final answer would be 3 1/7!

Answer:

The test is left - tailed

We cannot reject the organization's claim ( its cheapest screens will truly last less than 2.8 years)

Step-by-step explanation:

Sample size, n = 61

Sample mean, [tex]\bar{X} = 2.4[/tex]

Standard deviation, [tex]\sigma = 0.88[/tex]

Significance level,  α=0.02

Null hypothesis, [tex]H_{o} : \mu = 2.8[/tex]

Alternative hypothesis, [tex]H_{a} : \mu < 2.8[/tex]

It is clearly seen from the alternative hypothesis, that it is a left tailed test. It is not tailed towards the two directions.

Calculate the test statistic:

[tex]Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n} } \\Z = \frac{2.4 - 2.8}{0.88/\sqrt{61} }\\Z = - 3.55[/tex]

Calculate the P-value:

P(Z < -3.35) = 0.0002

Since (p-value = 0.0002) < (α=0.02), the null hypothesis is rejected.

It can therefore be concluded that the mean of the cheapest screen is less than 2.8 years. i.e. the cheapest screen will last less than 2.8 years

Answer:

The null and alternative hypotheses:

H0: u = 2.8

H1: u < 2.8

This is a left - tailed test.

For test statistics, use the formula:

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

Where,

Mean, u = 2.8

Sample mean,x' = 2.4

Sample size, n = 61

Standard deviation [tex] \sigma [/tex] = 0.88

Significance level = 0.02

[tex] Z = \frac{2.4 - 0.02}{0.88/ \sqrt{61}} =-3.55[/tex]

Test statistics, Z = -3.55

Pvalue:

Pvalue of Z = -3.55 using standard normal table,

NORMSTID(-3.55) = 0.00019

Pvalue = 0.0002

Critical value:

Since this is a left tailed test, the critical value at 0.02 level of significance is:

[tex] Z_\alpha = Z_0_._0_2 = -2.05 [/tex]

Decision: If pvalue is less than level of significance reject null hypothesis H0.

Conclusion:

Since pvalue, 0.00019 is less than level of significance, 0.02, reject null hypothesis, H0.

We conclude that the mean life of the cheapest screen is less than 2.8 years

Answer:

A

Step-by-step explanation:

Since the two polygons are similar, corresponding sides will have a constant ratio. So, the ratio between ST and FG will be the same as the scale factor between the two shapes.

[tex]\dfrac{FG}{ST}=\dfrac{15}{36}=\dfrac{5}{12}[/tex]

Therefore, the correct answer is choice A. Hope this helps!

Answer:

rotation then translation

Based on the information given regarding the triangle, the transformations that can be used to map △RST onto △VWX is D. rotation, then translation.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

Since Triangle RST can be rotated about point S and then shifted down and to the left to form triangle VWX, the transformations that can be used to map △RST onto △VWX is rotation, then translation.

Learn more about triangles on:

https://brainly.com/question/2644832

Answer: P ≤ $10

Step-by-step explanation:

You have $18

You want to buy a belt that cost $8, so the money that you have tou buy a pair of jeans is $18 - $8 = $10

This means that we the range of prices P that you can afford is:

P ≤ $10

This means that the price of the jeans can be, at maximum, 10 dollars.

Answer:

C

Step-by-step explanation:

If 30% of the entire population of students are seniors, then this will apply to the female population as well. This means that the probability of being a female senior is 30% * 54%=0.3*0.54=0.162=16.2%, or answer choice C. Hope this helps!

Answer:

9/22

Step-by-step explanation:

They are 30 25-fils coins, 25 10-fils coins, 40  5-fils coins and 15 1-fils coins.

The total number of fils coins = 30 + 25 + 40 + 15 = 110 coins

The probability of picking n-fils coin = number of n fils coin /  total number of fils coins.

Therefore:

The probability of picking 25-fils coin = number of 25 fils coin /  total number of fils coins = 30/110 = 3/11

The probability of picking 10-fils coin = number of 10 fils coin /  total number of fils coins = 25/110 = 5/22

The probability of picking 5-fils coin = number of 5 fils coin /  total number of fils coins = 40/110 = 4/11

The probability of picking 1-fils coin = number of 1 fils coin /  total number of fils coins = 15/110 = 3/22

The probability that the first coin  he picks is a 25-fils coin or a 1-fils coin = The probability of picking 25-fils coin + The probability of picking 1-fils coin = 3/11 + 3/22 = 9/22

The cube root of a number is the number which when multiplied by itself three times give you the original number. ... The square root of a number is the number which when multiplied by itself twice give you the original number. As an example, the square root of 9 is 3 because 3×3 = 9

Answer:

302.5

Step-by-step explanation:

30 x 8

5/8

I hope this helps I'm like 90 percent sure this is right. There is no other answer I could think of so I hope Hope helpa

Answer:

Buying 5 packs of bread rolls and 3 packs of burger meat

Step-by-step explanation:

Sara needs to find the least common multiple between 6 bread rolls and 10  pieces of burger meat:

[tex]LCM:\\10\ 6\ |2\\5\ \ 3\ |3\\5\ \ 1\ |5\\1\ \ 1\ |1\\\\LCM = 2*3*5=30[/tex]

Sara will get the same amount of burger to bread rolls when she buys 30 units of each. The numbers of packs of each product that she must buy are:

[tex]B=\frac{30}{6}=5\ packs\\ M=\frac{30}{10}=3\ packs[/tex]

Sara should buy 5 packs of bread rolls and 3 packs of burger meat.

Answer:

a) [tex]\sqrt[3]{4096} = 16[/tex]

b) 4096/ 4 = 1024

Step-by-step explanation:

Answer:

[tex]-3\frac{2}{3}[/tex]

Step-by-step explanation: