3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45

Answer:

  (0, -5)

Step-by-step explanation:

You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).

That would be ...

  (x, f(x) -5) = (0, 0 -5) = (0, -5)

Answer:

Step-by-step explanation:

(x+yi)+4+6i=7-2i

x+yi=7-2i-4-6i

x+yi=3-8i

equating real and imaginary parts

x=3,y=-8

B.

x+yi=5+9i+(-8+11i)

x+yi=5+9i-8-11i

x+yi=-3-2i

equating real ,and imaginary parts

x=-3

y=-2

The value of x  and y for equation A is

[tex]x=3, y=-8[/tex]

The value of x  and y for equation B is

[tex]x=-3 , y=20[/tex]

Given :

[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]

find the value of x  and y in the given equation

Lets open the parenthesis and combine like terms

Equate the real and imaginary part to solve for x  and y

[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]

The value of x=3  and y=-8

Now we do the same with second equation

[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]

The value of x  and y is x=-3 and y=20

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Answer:

a. 0.67

b. 1.31

Step-by-step explanation:

We have the following information n = 20, mean (m) = 10 and standard deviation (sd) = 3

a.

SE (m) = sd / n ^ (1/2)

replacing we have:

SE (m) = 3/20 ^ (1/2) = 0.67

Therefore the standard error of the mean is 0.67

b.

the critical value is obtained as shown below:

the level of sifnificance is alfa = 1 - 0.95 = 0.05

the critical value with level of significance alfa / 2 = 0.05 / 2 = 0.025

and to this value corresponds z = 1.96 (z table)

The margin of error with 95 confidence is calculated as follows:

E = z * SE

E = 1.96 * 0.67

E = 1.31

Therefore the margin of error is 1.31

(a) The standard error will be "0.67".

(b) The margin of error will be "1.31".

According to the question,

Standard deviation,

Sample size,

(a)

As we know,

→ The Standard error,

= [tex]\frac{sd}{\sqrt{n} }[/tex]

= [tex]\frac{3}{\sqrt{20} }[/tex]

= [tex]0.67[/tex]

(b)

As we know,

→ The margin of error,

= [tex]Z_{a/2}\times \frac{sd}{\sqrt{n} }[/tex]

By substituting the values, we get

= [tex]Z_{a/2}\times \frac{3}{\sqrt{20} }[/tex]

= [tex]1.96\times 0.67[/tex]

= [tex]1.31[/tex]

Thus the above response is right.

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Answer:

,.........................................................

Answer:4541(Rounded) 4541.99779(Unrounded)

Step-by-step explanation:

A= P(1 + r)^T

A= answer

P=principle(amount of money)

r=Rate(percent / 100)

T=Time(Annually)

1030(1 + .077)^20

Brainliest would be appericiated!

Answer:

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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].

In this question:

We apply the inverse Central Limit Theorem.

The mean monthy car payment for 123 residents of the local apartment complex is $624.

So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.

Answer:

I believe it is D

Answer:

  The sum of 3 and the quotient of y and 2.

Step-by-step explanation:

The order of operations requires that you evaluate the expression ...

  3 + y ÷ 2

by first performing the division, then the addition. So, the addition gives you the sum of 3 and a quotient, because the quotient must be evaluated first.

The quotient is of y and 2 (not 2 and y), because the wording "the quotient of a and b" is always interpreted to mean a÷b.

So, the expression can be described as ...

  the sum of 3 and the quotient of y and 2.

Answer: 200 ft²

Step-by-step explanation:

The area of a rectangle is length times width

So, simply do 25 * 8 = 200

Hey there! :)

Answer:

A = 200 ft².

Step-by-step explanation:

Use the formula A = l × w to determine the area of a rectangle:

A = 25 × 8

Multiply:

A = 200 ft².

Step-by-step explanation:

he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19

Answer:

y=-1/3x-1

Step-by-step explanation:

We have the information y=3x-5, the lines are perpendicular, and the new line passes through (6,-3). The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 3, so flip it to 1/3 and multiply by -1, we get the slope of the new line as -1/3. So far we have the equation y=-1/3x+b. We are given a point on the line, (6,-3), so we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as -3=-1/3(6)+b. First you multiply to get -3=-2+b, then you add 2 to both sides to isolate the variable and you get b=-1. Then you can use b to complete your equation with y=-1/3x-1.

Answer:

yes, (0,-2) is the answer when graphing this equation.

Step-by-step explanation:

Answer:

yes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

16x^2 + 9 = 25

16x^2 = 16

x^2 = 1

x = 1, -1

Answer:

H0: p = 3.5

H1: p < 3.5

Step-by-step explanation:

We are told that past studies have indicated that the percentage of smokers is estimated to be about 35%, but with the new smoking cessation programs that have been implemented, it is believed that the percentage of smokers has been reduced, we must propose our null and alternative hypotheses, which would be the following:

Null hypothesis: H0: p = 3.5

Alternative hypothesis: H1: p < 3.5

Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

Two or more expressions with an Equal sign is called as Equation.

The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]

We need to check whether the left hand side is equal to right hand side.

These are in the form pf mixed fraction we can convert them to the improper fraction.

[tex]7\frac{1}{2}=15/2[/tex]

[tex]4\frac{2}{3}=\frac{14}{3}[/tex]

So Let us subtract 24/3 from 15/2

15/2-14/3

LCM of 2 and 3 is 6

45-28/6

17/6

This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]

Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

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Answer:

paper = $4 and stapler = $7

Step-by-step explanation:

let p represent paper and s represent stapler, then

3p + 4s = 40 → (1)

5p + 6s = 62 → (2)

Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p

15p + 20s = 200 → (3)

- 15p - 18s = - 186 → (4)

Add (3) and (4) term by term to eliminate p

2s = 14 ( divide both sides by 2 )

s = 7

Substitute s = 7 into either of the 2 equations and evaluate for p

Substituting into (1)

3p + 4(7) = 40

3p + 28 = 40 ( subtract 28 from both sides )

3p = 12 ( divide both sides by 3 )

p = 4

Thus package of paper costs $4 and stapler costs $7

Answer:

QIII

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Step 1: Find common denominators

1/2 = 4/8

2/4 = 4/8

Step 2: Evaluate

4/8 + 4/8 - 5/8

8/8 - 5/8

3/8

Alternatively, you can just plug this into a calc to evaluate and get your answer.

Answer:

3/8

Step-by-step explanation:

Look at the denominator:

2, 4, 8. The LCM (Lowest Common Multiple) is 8.

So this equation becomes

4/8+4/8-5/8=3/8

Answer: Evaluate the Function, right?

Hello!

~~~~~~~~~~~~~~~~~~

A) 4x = -4 [x=-1] =

4x = -4 =

x = -1 = x = -1

( The steps : Substitute the given value into the function and evaluate.)

B) 2(x-3) =-12 [x=3] =

2 ( x - 3) = -12 = x = -3

x = 3 = x = 3

( The steps : Substitute the given value into the function and evaluate.)

C) 8x - 4x = 24 [x = 1/2] =

8x - 4x = 24 = x = 6

x = 1/2 = x = 1/2

( The steps : Substitute the given value into the function and evaluate.)

D) 9x - 4x = 24 [x=18] =

9x - 4x = 24 = x = 24/5

x = 18 = x = 18

( The steps : Substitute the given value into the function and evaluate.)

~~~~~~~~~~~~~~~~~~

Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.

Hope this helped you!

Answer:

a) 4.8

b) 2.96

c) 4.4

d) 1.44

e) 3.76

Step-by-step explanation:

What we will do is solve point by point, knowing the following:

Fx (x) = P (X <= x) = (x - 1) / 4

a) P (X <-a) = 0.95

Fx (a) = 0.95

(a -1) / 4 = 0.95

a = 1 + 0.95 * 4

a = 4.8

b) P (X <a) = 0.49

Fx (a) = 0.49

(a -1) / 4 = 0.49

a = 1 + 0.49 * 4

a = 2.96

c) P (X <a) = 0.85

Fx (a) = 0.85

(a -1) / 4 = 0.55

a = 1 + 0.85 * 4

a = 4.4

d) P (X> a) = 0.89

P (X <a) = 1 - 0.89 = 0.11

Fx (a) = 0.11

(a -1) / 4 = 0.11

a = 1 + 0.11 * 4

a = 1.44

e) P (X> a) = 0.31

P (X <a) = 1 - 0.31 = 0.69

Fx (a) = 0.69

(a -1) / 4 = 0.69

a = 1 + 0.69 * 4

a = 3.76

Answer

1. (a) (3,4,5)--3^2 +4^2=9+16=25=5^2

2. (b) 25--172-82=50/2=25

3. (c) 5,000 kg--1,000 kg in 1 tonne

4. (a) 0.4--1-0.6=0.4

5. (d) kilometer

6. (c) hypotenuse

7. (a) grams

8. i think it is (a) 58--5+8+2=15~~8/15 =0.53~closest answer is 58

9. (c) tonne

10. (b) 15 tonnes--1000 kg in 1 tonne

11. (a) #7,600--38000*20%, or 0.20, =7,600

12. (a) 7:30 pm

13. (c) right angle

(c) metric system

Part B

1. True

2. 0.8

3. 30,000 dollars--20,000 +0+5,000+5,000=30,000

4. Planting/watering trees--20 dollars

5. Collecting/burning rubbish--0 dollars

Answer:

There are about 3.281 * 3.281 = 10.764 square feet in one square meter. Therefore, 22.5 square feet is 22.5 / 10.764 = 2.09 square meters.

Answer:

a) If interest rates go up, share prices go down : this will be assigned p→q

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r)

e) My sister wants a black and white cat. p∧q

Step-by-step explanation:

A statement  is said to be propositionally logical if the statement that can be assigned either true or false.

∧and

∨or

¬not

→implies

a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur

e) My sister wants a black and white cat. p∧q : both events can only occur together

Answer:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Step-by-step explanation:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Answer:

A sample of 385 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample:

We need a sample of n.

n is found when M = 0.05.

We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample of 385 is needed.

Hi !!

For f(x) = 3/x + 4 , B is correct.

• f(-3) = 3/(-3) + 4

f(-3) = - 1 + 4

f(-3) = 3

• f(-2) = 3/(-2) + 4

f(-2) = -1,5 + 4

f(-2) = 2,5

• f(1) = 3/(1) + 4

f(1) = 3 + 4

f(1) = 7

• f(2) = 3/(2) + 4

f(2) = 1,5 + 4

f(2) = 5,5

• f(3) = 3/(3) + 4

f(3) = 1 + 4

f(3) = 5

Answer:

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question:

[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]

What is the probability that the sample mean would be greater than 64.8 kilograms?

This is 1 subtracted by the pvalue of Z when X = 64.8.

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

By the Central Limit Theorem

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

[tex]Z = \frac{64.8 - 67}{0.86}[/tex]

[tex]Z = -2.56[/tex]

[tex]Z = -2.56[/tex] has a pvalue of 0.0052

1 - 0.0052 = 0.9948

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Answer:

a) 50S + 30C ≤ 800

b) 1) MAX = S + C

   2) Max = 0.03S + 0.05C

   3) Max = 6S + 5C

Step-by-step explanation:

Given:

Total space = 800 square feet

Each sofa = 50 square feet

Each chair = 30 square feet

At least 5 sofas and 5 chairs are to be displayed.

a) Write a mathematical model representing the store's constraints:

Let S denote number of sofas displayed and C denote number of chairs displayed.

The mathematical model will be:

50S + 30C ≤ 800

At least 5 sofas are to be dispayed: S ≥ 5

At least 5 chairs are to be displayed: C ≥ 5

b)

1) Maximize the total pieces of furniture displayed:

S + C = MAX

2) Maximize the total expected number of daily sales:

MAX = 0.03S + 0.05C

3) Maximize the total expected daily profit:

Given:

Profit on sofas = $200

Profit on chairs = $100

Max Expected daily profit =

Max = (200S * 0.03) + (100C * 0.05)

Max = 6S + 5C

Answer:

86.53

Step-by-step explanation:

Area of Triangle Formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Step 1: Draw altitude and label numbers

If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:

3² + b² = 29²

b² = 29² - 3²

b = √832 = h

Step 2: Plug in known variables into area formula:

A = 1/2(√832)(6)

A = 3√832

A = 86.5332