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2 years ago

The variable z is directly proportional to x. When x is 11, z has the value 44. What is the value of z when x = 21?

Mathematics

1 answer:

dimulka [17.4K]2 years ago

4 0

Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..

Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller.... So

Problem:

Dirextly to X (× by X)

Inversely to Y, (÷ by Y)

Z= k X/Y

Solve, working backwards: Z =5 becomes

5 = k (X) ÷ (Y). And

X=15 and Y =9 becomes

5= k(15)/(9). Undo ÷9, ×9 both sides

45= k(15). Now undo ×15 by ÷15 both sides

45/15 = 3. So k=3, (also called your constant of variation)....and your Equation/Proportion becomes...

Z = 3X/Y

Use the new #s.... X=23, Y=14

Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals

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The positive square root of 38 is between?

Oksanka [162]

It's between 6 and 7.

4 0

3 years ago

54 ÷ (−6) A. 9 B. -9 C. -8

sp2606 [1]

Answer:

Option B, -9

Hope this helps!

6 0

2 years ago

From the side of a hill wai-kin looks up at the top of a nearby vertical cliff at an angle of elevation of 36 degrees and looks

oksano4ka [1.4K]

Answer:

881.5 meters.

Step-by-step explanation:

The horizontal plane at the level of wai-kin's eyes divide the height of the cliff into two parts. Let the upper part be represented by x and the lower part be represented by y.

The height of the cliff = x + y

Applying the appropriate trigonometry functions.

To determine the value of x;

Tan θ = $\frac{opposite}{adjacent}$

Tan $36^{o}$ = $\frac{x}{490}$

⇒ x = 490 x Tan $36^{o}$

= 490 x 0.7265

= 355.985

x = 356 meters

To determine the value of y;

Tan θ = $\frac{opposite}{adjacent}$

Tan $47^{o}$ = $\frac{y}{490}$

⇒ y = 490 x Tan $47^{o}$

= 490 x 1.0724

= 525.476

y = 525.5 meters

Therefore,

The height of the cliff = x + y

= 355.985 + 525.476

= 881.461

The height of the cliff is 881.5 meters.

3 0

3 years ago

if a sample size 40 is drawn from the population that has mean 276 and a variance of 81, what is the probability that the mean o

lapo4ka [179]

Answer:

The probability is 0.017429

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)/SD/√n

In this case;

x = 273

mean = 276

SD = √(variance) = √81 = 9

n = 40

Substituting these values into the z-score formula, we have that;

z = (273-276)/9/√40

z = -2.11

So we proceed to get the probability

the probability in this case is;

P( z < -2.11)

We can use the normal distribution table for this

Our answer will be

P( z < -2.11) = 0.017429

4 0

3 years ago

How do the 5s in 50.8 and 18.35 compare?

telo118 [61]

The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35 ⇒ 1st answer

Step-by-step explanation:

Let us revise some important notes in a number:

Every digit in a number has a place value
Place value is the value represented by a digit in a number
Ex: the place value of 2 in the number 2,345 is 1,000 because 2 is in the thousands place, the place value of 9 in 12.29 is 0.01 because 9 is in the hundredths place

∵ The number is 50.8

∵ 5 is in the tens place

∴ The place value of 5 is 10

∵ The number is 18.35

∵ 5 is in the hundredths place

∴ The place value of 5 is 0.01

Let us compare between the places value of 5 in the two numbers

Let x the number which multiplying by the hundredth digit to give the ten digit

∵ 10 = x × 0.01

∴ 10 = 0.01 x

- Divide both sides by 0.01

∴ 1,000 = x

∵ 5 × 10 = 0.05 × 1000

∴ 50 = 50

∴ The value of 5 in 50.8 = 1,000 × the value of 5 in 18.35

The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35

Learn more:

You can learn more about the place value in brainly.com/question/13174282

#LearnwithBrainly

6 0

3 years ago