d) an undeclared major thinks that the time it takes for a freshmen to pick their major has a standard deviation of 1 year. to find the average he surveys 10 freshmen and finds out how long it took them to pick a major. he does a confidence interval to find the average time it takes.

Answer:

B) 24

Step-by-step explanation:

f(x)=2x+4

g(x)=3x+1

----------------

g(3)=3(3)+1=9+1=10

f(g(3))=f(10)=2(10)+4=20+4=24

Composite functions are function into another function. The value of the composite function f(g(3)) is 24

Composite functions are function into another function. Given the following functions:

f (x) = 2x + 4 and;

g(x) = 3x + 1,

Determine the composite function f(g(3))

f(g(x)) = f(3x + 1)

f(3x+1) = 2(3x + 1) + 4

Substitute x = 3 into the result

f(g(3)) = 2(3(3)+1) + 4

f(g(3) = 2(10) + 4

f(g(3)) = 24

Hence the value of the composite function f(g(3)) is 24

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The area of 36 tiles with side length x is ,36x².

The domain of this function is: Domain = {2, 3, 4, 5, 6}.

The meaning of x = 3 in this context implies that the area is 600 inches².

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The function for the area of a single tile with side length x is:

Area of a single tile = x²

Therefore, the area of 36 tiles with side length x is:

Area = 36x²

The domain of this function is limited to whole-number side lengths from 2 to 6 inches, as stated in the problem. Therefore, the domain of this function is:

Domain = {2, 3, 4, 5, 6}

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You are an interior designer and plan to have part of a floor tiled with a pattern that requires 36 square tiles. The tiles come in whole-number side lengths from 2 to 6 inches. You need to decide which size would be most appropriate, so you utilize some of your mathematics know-how.

1. Write a function for the area, where x is the side length of the tile. (2 points)

Area =

Hint: Multiply the area of each tile by the total number of tiles.

2. Identify the domain of this function.

Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer. So Rational numbers are decimals and fractions.

Step-by-step explanation:

A- True

B-FALSE

C-FALSE

D- True

SO not 100% sure but its B or C.- sorry for not being more help

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The rug covers 42 feet of space. We calculate the area of a rectangle to determine it. A rug is woven fabric or animal skin used as a floor covering.

It is a shape with four straight sides and four right angles that is not square, especially if the sides next to it are uneven.

When a 2-D enclosed shape has four sides, four corners, and four right angles (90°), it is referred to as a rectangle. When opposing sides of a diagram are equal and parallel, the shape is referred to as a rectangle.

Area of rectangle = L × B

So, Area of rug =  7 × 6

                         = 42 feet

Therefore the required answer is 42 Feet.

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Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

Answer:

x = 7

Step-by-step explanation:

-12 - (-4) = x - 15

-12 + 4 = x - 15

-8 = x - 15

x = 7

a. The monthly contribution from a friend's company is $120 minus 0.5, or $60.

b. The total monthly contribution to the fund is $180.

The computation of FV in Excel is shown in the attachment below:

Using the current number as a starting point, subtract the prior value to determine the growth rate. To calculate the growth rate in percentage terms, divide the difference by the previous amount and multiply the result by 100. Growth Rate equals (Ending Value - Beginning Value) - 1. The year-over-year (YoY) growth rate of a business, for instance, would be 20% if its revenue increased from $100 million in 2020 to $120 million in 2021.

GDP, turnover, wages, etc., all have growth rates that reflect how much they have changed over time (month, quarter, year). Percentages are a pretty common way to communicate it.

20 years is the age.

20 times 12 periods equals 240.

3% growth rate

The computation of FV in Excel is shown in the attachment below:

So, FV= $7,223,115.77

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Cara's first error was not 7 - 13, leading to an incorrect result of -32.

Cara's first error was that she did not evaluate (Negative 4) squared.

The expression in question is not provided, so let's assume it is "6 - 2 × (-4)² + 7 - 13".

According to the order of operations (PEMDAS/BODMAS), we evaluate operations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

To evaluate the expression correctly, we follow the order of operations:

Evaluate the exponent (-4)².

Since (-4) squared is positive, (-4)² = 16.

Multiply 2 and 16.

2 × 16 = 32.

Evaluate the addition and subtraction from left to right.

6 - 32 + 7 - 13.

At this point, we see that Cara did not evaluate 7 - 13.

Therefore, her first error was not evaluating the subtraction correctly.

Continuing the evaluation:

6 - 32 + 7 - 13 = -32.

So, Cara's first error was not evaluating 7 - 13, leading to an incorrect result of -32.

It's important to carefully follow the order of operations to ensure accurate evaluations of mathematical expressions.

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Answer:

0.15

Step-by-step explanation:

I just put the fraction in decimal form since there is no photo.

Answer: 0.10299,0.1037  ,0.1038 ,0.9

Step-by-step explanation:

In all the numbers we could see that 0.9 is the greatest because it has the greatest tenth value. The rest three have the same tenth value which is one and the same hundredth value which is 0 so we will compare the numbers using  their thousandth values.

In the numbers 0.1038,0.10299, 0.1037   The first one has a thousandth value of 3, the second one has a thousandth value of 2, and the third one has a thousandth value of 3. Which means the first and the second have the same thousandths value so using their last numbers which is 8  and 7 , 8 is greater than 7  so  0.1038  is greater than 0.1037 and 0.10299.  The same way 0.1037 is greater than 0.10299.

So to order them from least to greatest,

0.10299 will be first

0.1037  will be second  

0.1038  will be the third  

0.9  will be the last.

Answer:

\({ \boxed{ \tt{trig \: identity : { \bf{ { \cos}^{2} A + { \sin }^{2} A = 1}}}}} \\ \therefore \: { \green{ \tt{ \sin A = \sqrt{1 - { \cos }^{2}A } }}} \\ \sin A = \sqrt{1 - {( \frac{3}{4}) }^{2} } \\ \sin A = \frac{ \sqrt{7} }{4} = 0.661 \\ \\ { \green{ \tt{ \tan A = \frac{ \sin A }{ \cos A} }}} \\ \tan(A ) = \frac{ \frac{ \sqrt{7} }{4} }{ \frac{3}{4} } = \frac{ \sqrt{7} }{3} = 0.882 \\ \\ { \underline{ \blue{ \tt{ becker \: jnr}}}}\)

The exact values of sin (A) and tan ( A)​ are 0.661 and 0.882 respectively.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given that 270º < AS 360° and cos(A)= 3/4.

We are required the exact values of sin (A) and tan ( A)​

Since, cos(A)= 3/4.

cos ²A + sin² A = 1

sin A = √ 1- cos ²A

sin A = √ 1-  (3/4) ²

Sin A = 0.661

Tan A = sin A / Cos A

Tan A = 0.661/ 3/4 = 0.882

Hence, the exact values of sin (A) and tan ( A)​ are 0.661 and 0.882 respectively.

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The expression 5z + 5 - 6z is equivalent to the expression 5 - z.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 5z + 5 - 6z

Simplify the expression, then we have

⇒ 5z + 5 - 6z

⇒ 5 - z

The expression 5z + 5 - 6z is equivalent to the expression 5 - z.

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Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

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Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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Amount Included in Cost of Equipment:

Invoice price of machine = $10,300

Less: Discount received = $103

Net purchase price = $10,300 - $103 = $10,197

Additional costs incurred:

Transportation costs = $233

Mounting and power connections = $712

Assembling cost = $336

Materials cost = $40

Repair cost = $250

Total additional costs = $233 + $712 + $336 + $40 + $250 = $1,571

Cost recorded for this machine:

Net purchase price + Total additional costs = $10,197 + $1,571 = $11,768

Therefore, the cost recorded for this machine is $11,768.

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

The monthly payment and total price paid by Antony at interest rate of 6.8% for vehicle is $362.59 and $21204.4 respectively.

Cost price of the car Antony decided to purchase = $19,000

Down payment =  20% of purchase value

Interest rate of amount to be finance = 6.8%

Time period of finance amount = 4 years

Down payment = 0.2 × $19,000

                         = $3,800

Amount that Anthony needs to finance,

Amount to finance = $19,000 - $3,800

                               = $15,200

The monthly payment , use the formula for the monthly payment on a loan,

M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1)

where M is the monthly payment,

P is the principal the amount to finance

r is the monthly interest rate

n is the total number of payments which is the number of years multiplied by 12

The monthly interest rate is 6.8% / 12 = 0.00567,

and the total number of payments is 4 × 12 = 48.

Substituting these values into the formula, we get,

⇒M = $15,200 × 0.00567 × (1 + 0.00567)⁴⁸ / ((1 + 0.00567)⁴⁸ - 1)

⇒M = $15,200 × 0.00567 × 1.3118 / (1.3118 -1)

⇒M = $15,200 × 0.00567 × 1.3118 / 0.3118

⇒M = 113.056 / 0.3118

⇒M ≈ $362.59

Anthony's monthly payment will be about $362.59

Total price that Anthony paid for his vehicle,

add up the down payment and the total amount of payments over the 4-year period.

Total price = $3,800 + ( $362.59 × 48)

                  = $21204.4

Therefore, the monthly payment and the total price at interest rate of 6.8% that Anthony paid for vehicle is $362.59 and $21204.4 respectively.

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Answer:

a)

Null hypothesis : H₀:μ = $43,500

Alternative Hypothesis : H₁ : μ ≠ $43,500

b)

The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance

Null hypothesis is accepted

c)

The calculated value t = 2.2975 < 1.7709

The residents of Wilmington, Delaware, have more income than the national average

Step-by-step explanation:

Step(i):-

Given mean of the Population = $43,500,

Given mean of the sample  = $50,500

Given standard deviation of the sample  = $11,400.

level of significance = 0.01

Step(ii):-

a)

Null hypothesis : H₀:μ = $43,500

Alternative Hypothesis : H₁ : μ ≠ $43,500

b)

Test statistic

\(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

\(t = \frac{50,500 -43,500}{\frac{11400}{\sqrt{14} } }= 2.2975\)

Degrees of freedom

                           ν =n-1 = 14-1 =13

The critical value

\(Z_{\frac{0.01}{2} } = Z_{0.05} = 1.7709\)

c)

The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance

Null hypothesis is accepted

Conclusion:-

The residents of Wilmington, Delaware, have more income than the national average

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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