A deposit of $2,630 is placed into a retirement fund at the beginning of every 6 months for 11 years. The fund earns 3% annual interest, compounded biannually and paid at the end of the 6 months. How much is in the account right after the last deposit? Round your answer to the nearest dollar.

Answer:

[tex]\boxed{<x = 17 degrees}[/tex]

Step-by-step explanation:

<EGB = 73 degrees (Vertically Opposite angles are congruent)

=> <x = 90-<EGB (Complementary angles)

=> <x = 90-73

=> <x = 17 degrees

Answer: 1. sample mean = 97.7; sample standard deviation(s) = 9.9467; standard error (SE) = 2.2241

2. t-critical value = 2.861; margin of error (m) = 97.9 ± 6.363

3. Lower limits = 91.537; upper limit = 104.263

4. d. Sheila is 99% confident that the true population mean is between 91.537 points and 104.263 points.

Step-by-step explanation: Knowing that this sample has 20 individuals, which means n = 20:

1. Sample mean is the average of the data set:

mean = [tex]\frac{81+84+...+115+116}{20}[/tex] = 97.9

Sample standard deviation is the spread of the sample data set from the mean:

s = [tex]\sqrt{\frac{(81-97.9)^{2}+...+(116-97.9)^{2}}{20-1} }[/tex] = 9.9467

Standard Error shows how far the mean of the set is from the true popultaion mean:

SE = [tex]\frac{9.9467}{\sqrt{20} }[/tex] = 2.2241

2. The t-critical value (t) is the value you use to decide if you reject or accept the null hypothesis. It can be calculated by a calculator or found in the t-test table. To use the table:

Degrees of freedom for this set is: n - 1 = 19

Critical value (α) = 0.99. For the t-test: [tex]\frac{1-0.99}{2}[/tex] = 0.005

[tex]t_{19,0.005}[/tex] = 2.861

Margin of error (m) shows, in percentage, how different your results are from the real population value. It is calculated as:

m = 97.9 ± 2.861*2.2241 = 97.9 ± 6.363

3. Lower and Upper limits are the interval the true mean can assume with a determined certainty.

lower limit = 97.9 - 6.363 = 91.537

upper limit = 97.9 + 6.363 = 104.263

4. In this case, the statistics shows that the true population mean is between 91.537 and 104.263, 99% of the time.

Answer:

  coefficients: {-2, +9, -3}

  variables: {x}

  terms: {-2x^2, 9x, -3}

  constant: {-3}

Step-by-step explanation:

It is difficult to "label" here, so we'll list each, separated by commas.

Coefficients

Coefficients are the multiplicative factor of an expression. Depending on the expression of interest, it may consist of numbers, variables, or expressions. Here, we consider the expression of interest to be powers of x, so the coefficients are as listed. The last one (-3) is sometimes called a "constant coefficient." It multiplies x^0.

  coefficients: {-2, +9, -3}

Variables

A variable is usually a letter, symbol, or sequence of letters and symbols, that stands for something else--usually an unknown quantity. Its meaning and value will depend on the context. Generic variables are usually taken from the end of the alphabet: x, y, z. Their capitalization, font, or face may give special meaning. For example bold-face capital letters may be used to represent vectors or matrices.

  variables: {x}

Terms

A term is a product of coefficients and variables. Terms in a polynomial are separated by addition or subtraction symbols.

  terms: {-2x^2, 9x, -3}

Constant

"Constant" usually refers to a term containing no variables. It generally refers to a value that doesn't change.

  constant: {-3}

Answer:  Third option is correct

Step-by-step explanation:  The y-intercepts match the constants (b in y=mx+b format)   The y-values shaded above the line y≥2x+4 are correct. The y-values shaded in the region below the  y≤2x -2 are also correct.

x-3y= -3x +3y=9

collect like terms

-3x will go to x and it will turn to

x+3x And -3y will go to +3y and it will turn to

×+3x=+3y+3y=9

solving time.

x+3x is 4x

3y +3y =6y

4x+6y =9

remove the 4x for now.

6y divided by 9.

3 in 6 is 2 and 3 in 9 is 3.

therefore 4x =2=9

4/2=2

2x=9.

4and half is the answer

Answer:

x = 3

y = 2

Step-by-step explanation:

x - 3y = -3

x + 3y = 9

Solve for x in the second equation.

x = 9 - 3y

Pu x as 9 - 3y in the first equation and solve for y.

9 - 3y - 3y = -3

9 - 6y = -3

-6y = -12

y = 2

Put y as 2 in the second equation and solve for x.

x = 9 - 3(2)

x = 9 - 6

x = 3

Answer: 2

Step-by-step explanation:

The equation for slope is change in y / change in x, which is (-4-(-12))/(4-0) in this case. That is equal to 2.

The gradient of the line segment between the points (4,-4) and (0,-12) is 2.

We have to determine, the gradient of the line segment between the points (4,-4) and (0,-12).

The gradient and slope of the line segment between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by the following formula;

The gradient of the line segment = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Then, the gradient of the line segment between the points (4,-4) and (0,-12) is,

[tex]= \dfrac{-12-(-4)}{0-4}\\\\= \dfrac{-12+4}{-4}\\\\= \dfrac{-8}{-4}\\\\= 2[/tex]

Hence, The required gradient of the line segment between the points (4,-4) and (0,-12) is 2.

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Answer: A

Step-by-step explanation:

Answer: A.

Step-by-step explanation:

A composition of reflections over two parallel lines is equivalent to a translation.

Answer:

[tex]-14x^4+71x^3-61x^2+30x-6[/tex]

Step-by-step explanation:

All we are doing is distributing each number of the 1st equation to the 2nd equation to get our answer. Once we do so, we combine like terms and we get our answer.

Answer:

(a) There are 12 values in the data set which are greater than or equal to 10 and less than or equal to 19.

(b) There are 12 values in the data set which are greater than or equal to 30 and less than or equal to 39.

(c) There are 7 values in the data set which are greater than or equal to 40 and less than or equal to 49.

Step-by-step explanation:

We are given a set of data that is summarized by the stem and leaf plot below;

Steam Leaf

1  0 0 2 4 4 4 7 8 8 8 8 9

2  2 2 5 5 7 8

3  3 4 4 5 5 5 6 6 6 7 9 9

4  3 3 3 5 5 7 9

This shows that the data values are: 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19, 22, 22, 25, 25, 27, 28, 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39, 43, 43, 43, 45, 45, 47, 49.

(a) From the data above, the number of values in the data set which are greater than or equal to 10 and less than or equal to 19 is 12, i.e; 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19.

(b) From the data above, the number of values in the data set which are greater than or equal to 30 and less than or equal to 39 is 12, i.e; 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39.

(c) From the data above, the number of values in the data set which are greater than or equal to 40 and less than or equal to 49 is 7, i.e; 43, 43, 43, 45, 45, 47, 49.

Answer:5,9

Step-by-step explanation:

Answer:

a. P-value = 0.1589

b. P-value = 0.0016

Step-by-step explanation:

a. This is a hypothesis test for the difference between populations means.

The claim is that the two types of steel have different true average fracture toughness values.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is α=0.05.

The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1.  The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.

The difference between sample means is Md=0.2.

[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=100+100-2=198[/tex]

This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]

As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

b. As the sample size changes, the standard error and the degress of freedom change.

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=500+500-2=998[/tex]

This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]

As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

If [tex]D>0[/tex] then [tex]x_1,x_2\in\mathbb{R}[/tex].

If [tex]D=0[/tex] then [tex]x_1=x_2\wedge x_1,x_2\in\mathbb{R}[/tex].

If [tex]D<0[/tex] then [tex]x_1,x_2\in\mathbb{C}[/tex].

Hope this helps.

Answer: 2.06

Step-by-step explanation:

Remember if the number is greater than 5 round up, if it is less than 5 don't round up.

After round off the number 2.0625 to its nearest hundredth, it is 2.06.

When we round to the nearest hundredth, we follow the rule that says:

The given number is 2.0625

In this number, the thousandth digit is 2 that is less than 5.

So we round down the hundredth place. The hundredth digit is 6 which remain 6 after rounding down.

So, the rounded number will be 2.06.

Hence, when we round 2.0625 to its nearest hundredth, it will be 2.06.

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Answer:

$1,06

Step-by-step explanation:

Calculation for dividend per share of common stock for board of directors of Midwest Foods

First step is to find the amount of dividends due to the preferred shareholders

Using this formula

Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )

Let plug in the formula

Total Dividend =$3,500,000-($300,000*$2.85)

Total Dividend =$3,500,000-$855,000

Total Dividend =$2,645,000

The second step is to find Dividend per share of common stock

Using this formula

Dividend per share of common stock=Total dividend/Shares of common stock

Let plug in the formula

Dividend per share of common stock=$2,645,000/$2,500,000

Dividend per share of common stock=$1.06

Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06

Answer:

a =10% b=50% c=20% d=20%

Step-by-step explanation:

n(CuT)=n(C)+n(T)-n(CnT)

so n(CnT)=10%

for b

tea but not coffee =nonly(T)

=n(T)-n(TnC)

=50%

for c

only coffee=nonly(C)

=n(C)-n(CnT)

=20%

Answer:

The interval of increase of g(x) is [tex](-6,+\infty)[/tex].

Step-by-step explanation:

The interval of increase occurs when first derivative of given function brings positive values. Let be [tex]g(x) = 190 + 8 \cdot x^{3} + x^{4}[/tex], the first derivative of the function is:

[tex]g'(x) = 24 \cdot x ^{2} + 4\cdot x^{3}[/tex]

[tex]g'(x) = 4 \cdot x^{2}\cdot (6+x)[/tex]

The following condition must be met to define the interval of increase:

[tex]4\cdot x^{2} \cdot (x+6) > 0[/tex]

The first term is always position due to the quadratic form, the second one is a first order polynomial and it is known that positive value is a product of two positive or negative values. Then, the second form must satisfy this:

[tex]x + 6 > 0[/tex]

The solution to this inequation is:

[tex]x > - 6[/tex]

Now, the solution to this expression in interval notation is: [tex](-6,+\infty)[/tex]

Answer:

nx^(n-1)

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

To find the slope: Rise/Run

You go 2 steps down for every step you go right.

Your rise is -2 and your run is 1.

So your slope is -2.

Answer:

-2

Step-by-step explanation:

Get two points that intersect that line.

(1, 5) and (2, 3)

Find the rise and run.

As we can see to get from (1,5) to (2,3), we have to go to the right by 1 and go down by 2 (in this case the movement is -2 steps).

rise/run

-2/1 = -2

Answer:

coefficient of variation = 7.108%

Step-by-step explanation:

From the given information:

The objective is to determine the  coefficient of variation for the prices of tickets purchased 30 days in advance is ____%

The mean [tex]\overline x[/tex] = [tex]\dfrac{250+286+305+256+288+282+254}{7}[/tex]

The mean [tex]\overline x[/tex] = [tex]\dfrac{1921}{7}[/tex]

The mean [tex]\overline x[/tex] = 274.4285714

The standard deviation also can be computed as follows:

[tex]\sigma =\sqrt{ \dfrac{\sum (x_i-\mu)^2}{N}}[/tex]

[tex]\sigma =\sqrt{ \dfrac{ (250-274.43)^2+(286-274.43)^2+(305-274.43)^2+...+(254-274.43)^2}{7}}[/tex][tex]\sigma =19.507[/tex]

Finally; the coefficient of variation can be calculated with the formula:

coefficient of variation = [tex]\dfrac{\sigma}{\overline x}[/tex]

coefficient of variation = [tex]\dfrac{19.507}{274.43}[/tex]

coefficient of variation = 0.07108

coefficient of variation = 7.108%

Answer:

divided by 6

Step-by-step explanation:

Given pattern

360,60,10

would it be add 60

lets

add 60 to each term

360 +60 = 420

but next term is 60, hence it incorrect choice

divided by 6

lets divide each term by 6

360/6 = 60 which is the next term in the series as well

60/6 = 10 which is also the next term in the series as well

hence divided by 6 is the correct option.

multiply by 6

multiply by 6 to each term

360 *60 = 21600

but next term is 60, hence it incorrect choice

subtract 60 from each term

360 -300 = 60 which is the next term in the series

60 -300 = -240 which is not same the next term in the series that is 10

hence this is incorrect choice

Answer:  0.627 or 62.7 %

Step-by-step explanation:

The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.

P(rejected)= 1-P(accepted)

P(accepted) is equal to probability when all 10 watches are not defective.

The probability that 1st one randomly selected watches are not defective is 51/60  (51 watches are not defective and 9 are defective)

The probability that 2-nd one randomly selected watches are not defective is  50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)

The probability that 3rd one randomly selected watches are not defective is 49/58  (49 watches are not defective total number of watches is 58)

Similarly P(4th)= 48/57  P(5th)=47/56   P(6th)=46/55  P(7th)=45/54

P(8th)=44/53  P(9th)=43/52  P(10th)=42/51

So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=

=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=

= approx= 0.373

So P(rejected)=1-0.373=0.627

Answer:

An independent sample.

Step-by-step explanation:

In this scenario, to compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected. We can safely conclude that this study uses an independent sample design.

An independent sample design can be defined as a research method that usually involves the use of multiple experimental groups (two or more). The samples or participants are only in one group and as such each group has no relationship with the other. This simply means that, the samples in a particular group is having no relationship with the other samples in another group.

Ultimately this implies, each samples are independent and satisfies only one condition of the independent sample design during the experiment to compare the production technique used by foreign and local firms in Brazil.

Hence, the researcher would use only two variables or conditions: a random sample of 80 foreign firms and a random sample of 80 local firms are selected.

Answer:

x > -6

Step-by-step explanation:

2x + 3 > -9

Subtract 3 on both sides.

2x > -9 - 3

2x > -12

Divide 2 into both sides.

x > -12/2

x > -6

Answer: c

Step-by-step explanation:

Just helped my daughter with quiz got 100%

Answer:

0.0066

Step-by-step explanation:

The x has a distribution that is approximately normal. For normal distribution the probability of x will be,

u = 12 and 18

P (12 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 18)

P (- 2.3  [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 2.85 )

P (0.9912 - 0.9978)

= 0.0066

Answer:

n²+1

2n²

Step-by-step explanation:

We can see that 2, 5, 10, and 17 becomes 1, 4, 9, and 16 when we subtract 1.

So it adds 1. The nth will be n² + 1.

2, 8, 18, and 32 is the double of n². 1, 4, 9, and 16 are their half.

So the nth term becomes 2n².

The value of the equation is

a) The nth term of the equation is Aₙ = n² + 1

b) The nth term of the equation is Bₙ = 2n²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the nth term of the equation be represented as Aₙ

Now , the sequence is

P = { 2 , 5 , 10 , 17 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 5

So , the equation for the nth term is Aₙ = n² + 1

b)

Let the nth term of the equation be represented as Bₙ

Now , the sequence is

Q = { 2 , 8 , 18 , 32 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 8

So , the equation for the nth term is Bₙ = 2n²

Hence , the equations are solved

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Answer:

The point estimate for the mean mpg of hybrid cars is 30 mpg.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 22

Upper bound: 38

Point Estimate:

(22 + 38)/2 = 30

The point estimate for the mean mpg of hybrid cars is 30 mpg.

Answer:

B. 486

Step-by-step explanation:

3^4 = 3 × 3 × 3 × 3 = 81

2^0 = 1

6^1 = 6

Find the product.

81 × 1 × 6

= 486

Answer:

option B; 486

Step-by-step explanation: 3 raised to the power 4 can be written as 3*3*3*3, 2 raised to 0 is 1( any number raised to to the power 0 is 1), 6 raised to 1 is the number itself( means that 6 is only repeated or mentioned once).

so, 3*3*3*3*1*6=486

Your question is not complete, however, I have provided answers to it by suggesting that the question goes like this;

Twelve different video games showing drug use were observed. The duration times of drug use​ (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85​sec, what does df​ denote, and what is its​ value

Answer:

df denote degree of freedom.

degree of freedom df is 11.

Step-by-step explanation:

what does df​ denote?

df denote degree of freedom

To find it value,

we have twelve different video games showing drug use, then, it means that the sample size "n" is 12

the degree of freedom is 1 < n ( i.e, one less than sample size)

df = n -1 = 12 -1 = 11

So, degree of freedom df is 11.

Note; use your sample size to solve the question as I don't know the exact value you were given. Thanks.

Answer:

gdk

Step-by-step explanation:

Answer:

r = 982

Step-by-step explanation:

[tex]-25(r-989)=175\\-25r+24725=175\\-25r=-24,550\\25r=24,550\\r=982[/tex]