The sum of the angle measures of any triangle is 180°. Find the angle measures of a triangle if the second angle measures 7° less than twice the first, and the third angle measures 19° more than the second.

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

The mean of this sample distribution is

Mean = μₓ = np = 0.61 × 1600 = 976

But the sample mean according to the population mean should have been

Sample mean = population mean = nP

= 0.56 × 1600 = 896.

To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.

We will be doing the calculations in sample proportions,

We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).

Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.

Confidence interval = (Sample mean) ± (Margin of error)

Sample Mean = population mean = 0.56

The margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =

[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124

The critical value for 68% confidence interval = 0.999 (from the z-tables)

The critical value for 95% confidence interval = 1.960 (also from the z-tables)

Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)

Confidence interval for 68% confidence level

= 0.56 ± (0.999 × 0.0124)

= 0.56 ± 0.0124

= (0.5476, 0.5724)

Confidence interval for 95% confidence level

= 0.56 ± (1.960 × 0.0124)

= 0.56 ± 0.0243

= (0.5357, 0.5843)

Confidence interval for 99.7% confidence level

= 0.56 ± (3.000 × 0.0124)

= 0.56 ± 0.0372

= (0.5228, 0.5972)

Therefore,

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

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Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

In this question, Mr. Harrington wants to buy a new TV for $500

He has a 10% off coupon.

After applying this coupon, the cost of TV would be,

500 - (10 percent of $500)

= 500 -[ (10/100) * 500]

= 500 - 50

= 450

He knows the tax be 13.5%.

13.5 percent of 450 would be,

(13.5/100) * 450

= 60.75

So, the amount he will need to save to buy the TV,

$450 + $60.75 = $510.75

Therefore, Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

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The number of pieces the bakery will sell is 16 and a half. The total amount of money they will make is $82.5.

To get the number of pieces of pies that they have to sell, we need to first determine how many 1/4 pies are in 4 and 8 pieces of bread. Going by that, we can see that:

1/4x of 4 = 16.

Also, 1/4x of 1/8 = 1/2.

So, the total number of pies that they have to sell is 16 and a half.

Now if 1/4 of a pie costs $5, then 4 1/8 will be equal to 33/8 × 5 ÷ 1/4.

This is equal to 165/8 × 4 = $82.5

So, the total amount of money that the bakery will make will be $82.5.

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Answer:

Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.

The solution set for the inequality is.

-113 ≤ y ≤ 131

Here we have the following inequality:

|y - 9| ≤ 122

Any absolute value inequality can just be decomposed as follows:

|y - 9| ≤ 122

to:

-122 ≤  y - 9 ≤  122

Now we can solve this for y by adding 9 in all places:

-122 + 9 ≤ y - 9 + 9 ≤  122 + 9

-113 ≤ y ≤ 131

That is the solution set.

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There are 126 blue marbles.

Total marbles in the bag=150

There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150

21 blue marbles appear 6 times for every 4 blue marbles

So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles

∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.

Let x denote the score. Assuming x follows normal distribution with

mean m = 70 and SD = 5 ,

we first calculate P( x < or = 80)

The SNV is z = (x — m) /SD

When x = 80, Z = ( 80 — 70)/5 = 2

So, P( x < or= 80)

Given that total number of students is

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Answer:

45.47

Step-by-step explanation:

Answer:

The length = 5x + 25

Step-by-step explanation:

A = l x w

fi r e re r er e r er e re r e r er e re

Answer:

Answer is [tex](\frac{4}{-1})[/tex] option D is correct

The expression that is equivalent is 6(y + 1) and 6y + 6.

The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

3(x + 3) and 3x + 6

3x + 9 and 3x + 6

Therefore, the expressions are not equivalent.

6(y + 1) and  6y + 6

6y + 6 and 6y + 6

They are equivalent expression.

x(x + 4) and x² + 4

x² + 4x and x² + 4

They are not equivalent expression.

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The minimum cost will be 1091 units.

Define Vertex Formula.

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

Given expression is,

C = 70,000 - 120x + 0.055x²

For this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, plug in the values and find 'x'

minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )

                            = 120 / 0.11

                            = 120 / 0.11

                            = 1090.90  or 1091 units

Therefore, the minimum cost will be 1091 units.

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the required sample size for the interval estimate with a 95% level of confidence  is 385

since we are given the margin of error which is f $10 and a standard deviation which is $1,000,  and we are also given the level of confidence which is 95%

so the formula we are  referring to calculate the sample size is :

n=z(0..95)*s²/ E

here, E is the margin of error, S is the standard deviation

so z score of 0.95 is 1.96

so n = 1.96*1000^2/100

        = 384.16 ,which is almost 385

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Answer:

Step-by-step explanation:

15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4

cevaplar: 17, 19,21,23

Answer:

3

Step-by-step explanation:

[tex]4x + 5y = - 5 \\ 8 + 4x + 5y = {?} \\ 8 + - 5 \\ = 3 \\ 8 + 4x + 5y = 3[/tex]

The exponential function has an equation of f(x) = 2(3)^x

From the question, we have the following points that can be used in our computation:

(0, 2) and (1,6)

Also, we understand that

Function type = Exponential function

An exponential function is represented as

f(x) = ab^x

At point (0, 2), we have

2 = ab^0

Evaluate

a = 2

Substitute a = 2 in f(x) = ab^x

f(x) = 2b^x

At point (1, 6), we have

6 = 2b^1

This gives

2b = 6

Divide

b = 3

So, we have

f(x) = 2(3)^x

Hence, the equation of the exponential function is f(x) = 2(3)^x

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The Excel formula that Bill would use is PMT.

From Bill's situation, he has the following information:

time = NPER = number of periods = 18 years

RATE of the bank

FV = future value = cost of tuition

PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."

In conclusion, the correct option is PMT.

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Complete question

Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.

Answer:

Question 1: #3 is correct.

Question 2: #4 is correct.

Answer:

SA(surface area) of the rectangular prism is 1,510 in inches

Step-by-step explanation:

SA=2(lh+lw+hw)

2inch=24ft

lh=264

lw=336

wh=154

755*2=1,510

When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)

So, we will do 3.472 divided by 0.112

3.472/0.112 = 31

Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.

0.112 x 31 = 3.472

In conclusion,

3.472/31 = 0.122

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Answer: 3.472/31 = 0.122

Step-by-step explanation: I hope this helps:)

The number 1.41421356 is not a rational number.

What is a rational number?

A number that can be expressed as a ratio is called a rational number. This indicates that it may be expressed as a fraction, where the numerator (the number on top) and denominator (the number on the bottom) are both whole numbers.

The given number is 1.41421356

The square root of 2 has the approximate value of 1.41421356

The number is non-terminating and non-repeating decimals.

That's why the given number is not a rational number.

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Step-by-step explanation:

ratios are special fractions and follow therefore all the fraction rules.

e.g. they follow the rule that for transformations the same multiplications or divisions have to happen for the denominator and the numerator when bringing them to the same denominator.

and they follow the same division and multiplication rules.

2/3 : 1/6 : 5/2 = (2/3)×(2/2) : 1/6 : (5/2)×(3/3) =

4/6 : 1/6 : 15/6 = 4 : 1 : 15

The confidence interval for the population mean is 0.2896 , 0.3505)

The sample mean is x = 0.32

The sample standard deviation is s = 0.09

The sample size is n = 10

The population standard deviation is unknown and sample size is atleast 10.

Thus use the t distribution.

Replacing the values in the following formula, determine the 95% confidence interval.

95% C.I = x ± t₀.₉₅,ₙ₋₁ . Sm

= x ± t₀.₀₅/₂,₁₀₋₁ . s/√n

= 0.32 ± 2.03 . 0.09/√10

= (0.2896 , 0.3505)

Hence the confidence interval for the population mean is 0.2896 , 0.3505)

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The degree of the polynomial is 5, and the end behavior is:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

For any given polynomial, we define the degree as the largest exponent on the polynomial.

On this case we have:

f(x) = 2x^3 - 3x^5 - x^2 + 1

We can see that the largest exponent is 5, so the degree is 5.

Now, for the ending behavior.

If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.

If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

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The balance on the bank account at the end of the third quarter of the year is  2,630.80

How to find the compound interest?

Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Compound interest is found using the formula

A=P(1+r/n)ⁿˣ  where:

Therefore, the amount (A)=2630.80

The P=2500

interest rate is 0.17%

Number of interest applied per period is 365 periods and

number of time period is 3.

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Answer:

20

Step-by-step explanation:

do parenthesis first

1/5(3+2+ 5)² =

1/5(10)² =

then exponent

1/5(10)² =

1/5(100) =

20

The minimum amount of fence needed to enclose the lots is 120ft.

Adding areas of both fields, the combined area comes about to be 600sq ft.

The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.

g(x, y, z) = xy - 600

g(x, y, z) = 2x + 3y

∇g = ∇ (xy - 600) = (y, x)

∇f = ∇(2x + 3y) = (2, 3)

Now from the Lagrange method,

∇f = λ∇g

2 = λy

3 = λx

Now to get the value of lambda,

(2/y) = (3/x) = λ

x = 1.5y

Solving now we get,

1.5y² = 600

y = 20

x = 1.5 × 20 = 30

Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.

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