Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20​

Answer:

Step-by-step explanation:

8.

any number ×0=0

so b

9.

additive identity

any number+0=same number

c

1.

[tex]\frac{(3+u)^2}{8} =\frac{(3+5)^2}{8} =\frac{8^2}{8} =\frac{64}{8} =8\\where ~u=5[/tex]

2.

-2(a-7)=-2×a-2×(-7)=-2a+14

Answer:

Approximately [tex]4.75[/tex].

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of  [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] are equal.

[tex]{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}[/tex]

Since [tex]\rm CH_3COONa[/tex] is a salt soluble in water. Once in water, it would readily ionize to give [tex]\rm CH_3COO^{-}[/tex] and [tex]\rm Na^{+}[/tex] ions.

Assume that the [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] ions in this solution did not disintegrate at all. The solution would contain:

[tex]0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COOH[/tex], and

[tex]0.06\; \rm mol[/tex] of [tex]\rm CH_3COO^{-}[/tex] from [tex]0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COONa[/tex].

Accordingly, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] would be:

[tex]\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

[tex]\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

In other words, in this buffer solution, the initial concentration of the weak acid [tex]\rm CH_3COOH[/tex] is the same as that of its conjugate base, [tex]\rm CH_3COO^{-}[/tex].

Hence, once in equilibrium, the [tex]\rm pH[/tex] of this buffer solution would be the same as the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex].

Calculate the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex] from its [tex]{\rm K}_{a}[/tex]:

[tex]\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}[/tex].

Answer:

So, the initial number of apples is 7.

Step-by-step explanation:

The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)

Let the initial numbers of apples is a.

An gave 17 apples

Chi gave 19 apples

So,

x - 19 = 5 (x - 17 + x)

x - 19 = 5 (2x - 17)

x - 19 = 10 x - 85

9 x = 66

x = 7

Answer:

Step-by-step explanation:

3=$2.91

22=x

3x=64.02

x=21.34

Answer:

[tex]\frac{257357187500}{19683}[/tex]

Step-by-step explanation:

We can convert these mixed fractions to ordinary fractions.

[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]

[tex]3(1/3)=\frac{10}{3}[/tex]

[tex]3(1/2)=\frac{7}{2}[/tex]

[tex]9(3/4)=\frac{39}{4}[/tex]

Then we have:

[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]

[tex]\frac{257357187500}{19683}[/tex]

I hope it helps you!

Hello,

2 points of the line: (2,0) and (0,3)

[tex]\Delta\ y=3-0=3\\\Delta\ x=0-2=-2\\\dfrac{\Delta\ y}{\Delta\ x} =\dfrac{-3}{2} \\\\y-0=\dfrac{-3}{2}*(x-2)\\\\\boxed{y=-\dfrac{3x}{2}+3}\\[/tex]

Answer:

Step-by-step explanation:

1. Circle A and circle A', have the same circumference. (Yes)

2. The radii of circle A and circle A', have the same lengths. (Yes)

3. .... (No)

4. ... (No)

Answer:

(1/8x)-(5/6)

Step-by-step explanation:

-3/4x-1/3+7/8x-1/2

-6/8x-2/6+7/8x-3/6

-6/8x+7/8x-2/6-3/6

1/8x-5/6

Answer:

(5) we have multiple the powers

I believe your answer is D.) $900

204 + 96 = 300

300 x 3 = 900

I hope this is correct and helps!

Answer: The answer is b

Answer:

HEY THERE!

Step-by-step explanation:

the answer is:800

hope it helps and have a great day!

Ans: 800

explanation:

Answer:

L.H.S.

= (cos5a.sin2a-cos4a.sin3a)/ (sin5a.sin2a-cos4a.cos3a)

Multiply numerator and denominator by 2.

= 2(cos5a.sin2a - cos4a.sin3a) / 2(sin5a.sin2a - cos4a.cos3a)

= (2cos5a.sin2a - 2cos4a.sin3a)/

(2sin5a.sin2a - 2cos4a.cos3a) = [sin(5a+2a)-sin(5a-2a)-sin(4a+3a)

+sin(4a-3a)]/[cos(5a-2a)-cos(5a+2a)-sin(4a-3a) +cos(4a+3a)]

= (sina - sin3a)/(cso3a-cosa)

= (-2cos2a.sina)/(-2sin2a.sina)

= cos2a/sin2a

= cot2a

= R.H.S.

answer is in a picture have a look

Answer:

This Question Is From The Novel Of The Fantastic Mr.Fox

Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....

________________________________

Swift | Slay | Ginger | Rough | Fast

Thief. | Clever | Fur | Tail | Wife | Night

Cunning | Bushy | wiry | bush | Den | trick

________________________________

Complete question is;

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?

(a) A defective component will be detected only by the first inspector?

b) A defective component will be detected by exactly one of the two inspectors?

(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer:

A) 0.17

B) 0.34

C) 0

Step-by-step explanation:

a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.

This means that;

P(A) = P(B) = 83% = 0.83

We are also told that at least one inspector does not detect a defect on 34% of all defective components.

Thus;

P(A' ⋃ B') = 0.34

Also, we now that;

P(A ⋂ B) = 1 - P(A' ⋃ B')

P(A ⋂ B) = 1 - 0.34

P(A ⋂ B) = 0.66

Probability that A defective component will be detected only by the first inspector is;

P(A ⋂ B') = P(A) - P(A ⋂ B)

P(A ⋂ B') = 0.83 - 0.66

P(A ⋂ B') = 0.17

B) probability that a defective component will be detected by exactly one of the two inspectors is given as;

P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)

P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34

C) Probability that All three defective components in a batch escape detection by both inspectors is written as;

P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))

Plugging in the relevant values, we have;

0.34 - 0.34 = 0

Answer:

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Step-by-step explanation:

Let

Set A={a,b,c}

Now, define a relation R on set A is given by

R={(a,a),(a,b),(b,a),(b,b)}

For reflexive

A relation is called reflexive if (a,a)[tex]\in R[/tex] for every element a[tex]\in A[/tex]

[tex](c,c)\notin R[/tex]

Therefore, the relation R is  not reflexive.

For symmetric

If [tex](a,b)\in R[/tex] then [tex](b,a)\in R[/tex]

We have

[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]

Hence, R is symmetric.

For transitive

If (a,b)[tex]\in R[/tex] and (b,c)[tex]\in R[/tex] then (a,c)[tex]\in R[/tex]

Here,

[tex](a,a)\in R[/tex] and [tex](a,b)\in R[/tex]

[tex]\implies (a,b)\in R[/tex]

[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]

[tex]\implies (a,a)\in R[/tex]

Therefore, R is transitive.

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.

Answer:

269 and 1/16 feet total (or 269.0625 feet to be precise)

Step-by-step explanation:

20 and 1/2 = 20.5

13 and 1/8 = 13.125

20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet

Answer:

7

Step-by-step explanation:

For simple interest,

I = prt

where I = interest,

p = principal (amount deposited)

r = annual rate of interest

t = time in years

We have r = 2% = 0.02

p = $3,000

I = $420

We need to find t

I = prt

420 = 3000 * 0.02 * t

420 = 60t

t = 420/60

t = 7

Answer: 7 years

Answer:

61

Step-by-step explanation:

3x + 6 = 183

3x = 177

x = 59

(x+2) = (59+2) = 61

It is correct on khan academy

Answer:

The third number in this sequence is 63.

Step-by-step explanation:

Let the first odd number be x.

Since our sequence are consecutive odd numbers, the second term must be (x + 2) and the third (x + 4). If we only add one, we will get even numbers.

Their sum is 183. Hence:

[tex]x+(x+2)+(x+4)=183[/tex]

Solve for x. Combine like terms:

[tex]3x+6=183[/tex]

Subtract six from both sides:

[tex]3x=177[/tex]

And divide both sides by three. Hence:

[tex]x=59[/tex]

Therefore, our sequence is 59, 61, and 63.

The third number in this sequence is 63.

Note: If we do not get an odd number or if we get a fraction for x, we can conclude that no three consecutive integers sum to 183.

[tex]2(2x + 4) + 2(x - 7) = 78[/tex]

[tex]4x + 8 + 2x - 14 = 78[/tex]

[tex](4x + 2x) + (8 - 14) = 78[/tex]

[tex]6x - 6 = 78[/tex]

[tex]6x = 78 + 6[/tex]

[tex]6x = 84[/tex]

[tex]x = \frac{84}{6} [/tex]

[tex]x = 14[/tex]

Answer:

mean = 7

median = 7

range = 9

mid range = 7.5

Step-by-step explanation:

3, 5, 6, 7, 7, 9, 12

Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

12 - 3 = 9  

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

3, 5, 6, 7, 7, 9, 12

median = 7

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(6 + 12 + 5 + 7+  7 + 3 + 9) / 7 = 7

Mid range = (highest value + lowest value) / 2

(12 + 3) / 2 = 7.5

Answer:

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.

This means that [tex]p = 0.07[/tex]

Sample of 459 phone calls:

This means that [tex]n = 459[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]

What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?

Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.

Probability the proportion is below 0.04.

p-value of Z when X = 0.04. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]

[tex]Z = -2.52[/tex]

[tex]Z = -2.52[/tex] has a p-value of 0.0059

2*0.0059 = 0.0118

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

Answer:

[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]k = 2[/tex] --- scale factor

Required

Relationship between ABC and A"B"C"

[tex]k = 2[/tex] implies that the sides of A"B"C" are bigger than ABC

i.e.

[tex]A"B" = 2AB[/tex]

[tex]A"C" = 2AC[/tex]

[tex]B"C" = 2BC[/tex]

In [tex]A"B" = 2AB[/tex]

Divide both sides by A"B"

[tex]1 = \frac{2AB}{A"B"}[/tex]

Divide both sides by 2

[tex]\frac{1}{2} = \frac{AB}{A"B"}[/tex]

Rewrite as:

[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]

(a) is correct

Answer:

0.9898 = 98.98% probability that there will not be more than one failure during a particular week.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

3 failures every twenty weeks

This means that for 1 week, [tex]\mu = \frac{3}{20} = 0.15[/tex]

Calculate the probability that there will not be more than one failure during a particular week.

Probability of at most one failure, so:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607[/tex]

[tex]P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898[/tex]

0.9898 = 98.98% probability that there will not be more than one failure during a particular week.

Answer:

[tex]f(g(2)) = 2[/tex]

Step-by-step explanation:

Given

[tex]x \to f(x)[/tex]

[tex]-6 \to 1[/tex]

[tex]-3 \to 2[/tex]

[tex]g(x) = f^{-1}(x)[/tex] --- inverse

Required

[tex]f(g(2))[/tex]

For two functions f(x) and g(x) where f(x) and g(x)are inverse;

[tex]f(g(x)) = x[/tex]

So, by comparison:

[tex]f(g(2)) = 2[/tex]

Answer:

a) 0.0147 = 1.47% probability that none of them graduates from the local community college.

b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.

c) The expected number that will graduate is 2.85.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, 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.

57% of students who enter the college as freshmen go on to graduate.

This means that [tex]p = 0.57[/tex]

Five freshmen are randomly selected.

This means that [tex]n = 5[/tex]

a. What is the probability that none of them graduates from the local community college?

This is P(X = 0). So

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

[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]

0.0147 = 1.47% probability that none of them graduates from the local community college.

b. What is the probability that at most four will graduate from the local community college?

This is:

[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]

In which

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

[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]

So

[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]

0.9398 = 93.98% probability that at most four will graduate from the local community college.

c. What is the expected number that will graduate?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 5*0.57 = 2.85[/tex]

The expected number that will graduate is 2.85.

Answer:

2×(6ײ+3×-1)=18.

2×(6×3×+4)(6×4×-3)=144

2×(6×3×-2)(4×2+4×-6)=1154..

12×2=24

12×2+7×-12=60

12×2+25×-12=276

12×3+4×2-10×+12=76

12×3+4×2-26×+12=8

12×3+6×2-2=46

Answer:

10 hours

Step-by-step explanation:

ok so we know he is getting payed $20 + $7 every hour so what i would do is keep the multiply the 7 till you get 70 so thats 7x10=70 and 70+20=90 so he worked for 10 hours last week :)  i hope this helps, i tried my best to explain it

Step-by-step explanation:

3600s=1hr

so, 1hr:1hr

1:1

Based on the concept of fractions and the information in the question, the fraction form in the lowest term is 1/2.

Fraction is a term that is used to describe the portion/part of the whole thing. It represents the equal parts of the whole.

Generally, the term fraction has two parts, namely numerator and denominator.

Hence, in this case, to express the ratio as a fraction in its lowest term, convert both units to the same unit of time.

1 hour is equal to 3600 seconds so 2 hours is equal to 2 * 3600 = 7200 seconds.

Now the ratio is 3600 seconds to 7200 seconds.

To simplify this ratio we can divide both terms by their greatest common divisor which is 3600.

So the simplified ratio is 1:2.

Therefore, in this case, it is concluded that the fraction form in the lowest term is 1/2.

Learn more about fraction here: https://brainly.com/question/30154928

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