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1 year ago

The quotient of 24 and x equals 14 minus 2 times x (into an equation don’t solve)

Mathematics

1 answer:

Katen [24]1 year ago

7 0

Answer:

24 / x = 14 - 2x

Step-by-step explanation:

Quotient means division (÷ or /)

Quotient of 24 and x = 24 ÷ x

24 ÷ x is equivalent to 24 / x

14 minus 2 times x = 14 - 2x

So, the equation is

24 / x = 14 - 2x

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In USA Today (Sept. 5, 1996), the results of a survey involving the use of sleepwear while traveling were listed as follows: Mal

Wewaii [24]

Answers:

a) 0.018.

b) 0.614.

c) 0.166.

d) 0.479

Explanations:

1) Table

----------------------Male ----------- Female ---------- Total

Underwear ----- 0.220 ---------- 0.024 ---------- 0.244

Nightgown ----- 0.002 ---------- 0.180 ------------ 0.182

Nothing --------- 0.160 ----------- 0.018 ------------ 0.178

Pajamas --------- 0.102 ---------- 0.073 ----------- 0.175

T-shirt ------------ 0.046 --------- 0.088 ------------ 0.134

Other --------------0.084 --------- 0.003 ------------ 0.087

2) Check that it is a table of relative frequencies:

total = 0.244 + 0.182 + 0.178 + 0.175 + 0.134 + 0.087 = 1 ⇒ indeed this is a table of relative frequencies.

That means that each data is a probabiilty.

3) Soluitions:

(a) What is the probability that a traveler is a female who sleeps in the nothing?

relative frequency of females that use nothing = 0.018

(b) What is the probability that a traveler is male?

Probability that a traveler is a male = relative frequency of males = 0.220 + 0.002 + 0.160 + 0.102 + 0.046 + 0.084 = 0.614

(c) Assuming the traveler is male, what is the probability that he sleeps in pajamas?

It is the relative frequency of the males that sleep in pajamas divided by the relative frequency of males = 0.102 / 0.614 = 0.166

(d) What is the probability that a traveler is male if the traveler sleeps in pajamas or a T-shirt?

It is the relative frequency of males that sleep in pajamas plus that of the males that sleep in T-shirt, divided the total relative frequency of travelers that sleep in pajamas or T-shirt

i) relative frequency of males that sleeps in pajamas plus that of the males that sleeps in T-shirt = 0.102 + 0.046 = 0.148

ii) relative frequency of travelers that sleep in pajamas or T-shirt = 0.102 + 0.046 + 0.073 + 0.088 = 0.309

iii) quotient = 0.148 / 0.309 = 0.479

5 0

2 years ago

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Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this proble

Jlenok [28]

33 in because 1056 divided by 32 is 33
hope you pass your test

3 0

1 year ago

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

If θ=0rad at t=0s, what is the blade's angular position at t=20s

babunello [35]

The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
              ω = 250 (rpm) = 250 * (2π/60) = (25/3)π    rad/s
              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰ ω dt

while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0 to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵ (0) dt   + ∫₅¹⁵ (25/3)π dt + ∫₁₅²⁰ (10/3)π dt

the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50

3 0

2 years ago

Dominique paid $15.50 to join an online music service. If

frozen [14]

Answer:

94.7

Step-by-step explanation:

6 0

2 years ago

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