Jose spent 2 hours watching TV.
During that time, there were 12
minutes of commercial. What
percent of the time Jose spent
watching commercials?

Answer:

A

Step-by-step explanation:

The table represents a proportional function which has a rate of proportionality equal to 5

In fact

5:1 = 5

15 : 3 = 5

25 : 5 = 5

35 : 7 = 5

If we make 90 : 18, the result is 5, so this dates can be part of the table

Answer:

What is the answer you're looking for?

Step-by-step explanation:

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Answer:

[tex]x \leqslant \frac{18}{5} [/tex]

Step-by-step explanation:

1: Solve the inequality:

[tex] - 5x + 3 \geqslant - 15 \\ rearrange \: unknown \: terms \: to \: the \: left \: side \: of \: the \: equation \\ - 5x \geqslant - 15 - 3 \\ reduce \: the \: greatest \: common \: factor \: for \: both \: sides \: of \: the \: inequality \\ 5x \leqslant 15 + 3 \\ calculate \: the \: sum \: or \: differences \\ 5x \leqslant 18 \\ divide \: both \: side \: of \: the \: inequality \: by \: the \: coefficient \: of \: variable \\ x \leqslant 18 \div 5 \\ rewrite \: as \: a \: fraction \\ x \leqslant \frac{18}{5} [/tex]

2: Plot:

[tex]x \leqslant \frac{18}{5} \\ graph \: on \: number \: line: [/tex]

Answer:

it's what will be left when it's divided

Answer:

HG = 3

Step-by-step explanation:

HF = HG + GF

11 = HG + 8

11 - 8 = HG

3 = HG

Answer:

HG = 3

Step-by-step explanation:

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Answer:

associative property of multiplication

Step-by-step explanation:

Answer:

The answer is "Option 5"

Step-by-step explanation:

Please find the complete question in the attached file.

Throughout the above output the regression equation is:

Delivery cost [tex]=0.469\times weight +9.617[/tex]

Answer:

easy:

6*10 / 2 = 30

6*10 would be a rectangle. a right triangle is just half the area

Answer: There are 128 fluid ounces in a gallon

Step-by-step explanation:

There are 128 fluid ounces in a gallon

Answer:

16/64 and 1/4

Step-by-step explanation:

Answer:

592 Votes

Step-by-step explanation:

According to the Question,

                                 A        B       С

Candidates Votes     67      57     54

And, There are 1571 students in the school.

⇒(1571/178)×67

⇒591.33 ≈ 592 Votes(Approximately)

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 109.0 inches, and a standard deviation of 12 inches.

This means that [tex]\mu = 109, \sigma = 12[/tex]

Sample of 25.

This means that [tex]n = 25, s = \frac{12}{\sqrt{25}} = 2.4[/tex]

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{112 - 109}{2.4}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

9514 1404 393

Answer:

  6·x^6·y^12

Step-by-step explanation:

(3x^6)(2y^12) = (3)(2)x^6·y^12 = 6·x^6·y^12

Answer:

6 x ⁶ y ¹²

Step-by-step explanation:

= ( 3 x ⁶ ) ( 2 y¹² )

= ( 3 ×2 ) x ⁶ y ¹²

= 6 x⁶ y ¹²

Step-by-step explanation:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{f(x + h) - f(x)}{h}[/tex]

[tex]\:\:\:\:\:\displaystyle = \lim_{h \to 0} \dfrac{(x+h)^2 -7 -(x^2 - 7)}{h}[/tex]

[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{(x^2 +2hx + h^2 -7) - (x^2 -7)}{h}[/tex]

[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{2hx + h^2}{h}[/tex]

[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} (2x +h)[/tex]

[tex]\:\:\:\:\: \displaystyle= 2x[/tex]

Answer:

0.0954 = 9.54% probability that the combined sample tests positive for the​ virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test​ positive.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they test positive, or they do not. The probability of a person testing positive is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.005.

This means that [tex]p = 0.005[/tex]

Samples from 20 people

This means that [tex]n = 20[/tex]

What is the probability that the combined sample tests positive for the​ virus? Is it unlikely for such a combined sample to test​ positive?

Probability of at least one positive test, which is:

[tex]P(X geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.005)^{0}.(0.995)^{20} = 0.9046[/tex]

Then

[tex]P(X geq 1) = 1 - P(X = 0) = 1 - 0.9046 = 0.0954[/tex]

0.0954 = 9.54% probability that the combined sample tests positive for the​ virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test​ positive.

Answer:

a

Step-by-step explanation:

1/2x-30aaaaaaaaaaaaaaaa

Answer:

47/60

Step-by-step explanation:

Find the LCM and multiply to get there.

LCM is 60

63/60-16/60

47/60

Answer:

4th option is correct

Step-by-step explanation:

[tex]8 x - 4 = 6 - 3 x[/tex]

[tex]8x−4+3x=6[/tex]

[tex]11x−4=6[/tex]

[tex]11x=6+4[/tex]

[tex]11x=10[/tex]

Answer:

option 4 ,

x=10/11

is the answer of your question

explanation is attached below .

hope it is helpful to you

Answer:

Step-by-step explanation:

4x - 9 + 23x

Combine like terms

4x+23x  -9

27x  -9

Simplest form is combining all the like terms.

4x + 23x = 27x

Then you have -9

Simplest form = 27x -9

Answer:

10*9*8*7*6*5*4*3 = 10!/2 = 1814400 Cheers

Step-by-step explanation:

hope it works.

(i) 3 csc²(x) - 4 = 0

3 csc²(x) = 4

csc²(x) = 4/3

sin²(x) = 3/4

sin(x) = ± √3/2

x = arcsin(√3/2) + 2nπ  or   x = arcsin(-√3/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

where n is any integer. The general result follows from the fact that sin(x) is 2π-periodic.

In the interval 0 ≤ x ≤ 2π, the first family of solutions gives x = π/3 and x = 4π/3 for n = 0 and n = 1, respectively; the second family gives x = 2π/3 and x = 5π/3 for n = 1 and n = 2.

(ii) 4 cos²(x) + 2 cos(x) - 2 = 0

2 cos²(x) + cos(x) - 1 = 0

(2 cos(x) - 1) (cos(x) + 1) = 0

2 cos(x) - 1 = 0   or   cos(x) + 1 = 0

2 cos(x) = 1   or   cos(x) = -1

cos(x) = 1/2   or   cos(x) = -1

[x = arccos(1/2) + 2nπ   or   x = 2π - arccos(1/2) + 2nπ]   or   x = arccos(-1) + 2nπ

[x = π/3 + 2nπ   or   x = 5π/3 + 2nπ]   or   x = π + 2nπ

For 0 ≤ x ≤ 2π, the solutions are x = π/3, x = 5π/3, and x = π.

Answer:

Exterior angle is the sum of non-adjacent interior angles:

m∠L = 4*12 + 7 = 48 + 7 = 55°

The triangles are congruent and corresponding sides are equal:

Side lengths are:

Area: 126ft

Hope it helps...

Answer: [tex]4840\ ft/min[/tex]

Step-by-step explanation:

Given

Speed is [tex]v=55\ mi/h[/tex]

Also, 1 mile is equal to 5280 ft

1 hour is equal to 60 min

Substitutes this values

[tex]\Rightarrow 55\times \dfrac{5280}{60}\\\\\Rightarrow 55\times 88\\\Rightarrow 4840\ ft/min[/tex]

It can save time from doing number crunching and analysis because it's an easy to see visual.

Answer:

-2

Step-by-step explanation:

The integer of - 2 is - 2 only as integers can be positive and negative whole numbers