The perimeter of a rectangle is 18 feet, and the area of the rectangle is 14 square feet. What is the length of the rectangle?

The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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Answer:

$10,359.73.

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the specified time

P = the principal amount (the initial amount of money)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $4,000.00

r = 15% = 0.15

n = 1 (compounded annually)

t = 6 years

Substituting into the formula, we get:

A = 4000(1 + 0.15/1)^(1*6)

A = 4000(1.15)^6

A ≈ $10,359.73

Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.

The objective function that can be used to maximize the profit is Profit = 15a + 8b

Let a is the number of units of product A and b is the number of units of product B.

Profit = 15a + 8b

This function represents the total profit earned by producing a units of product A and b units of product B

Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.

To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function

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Answer:

The length of the straw will be 5.91607 inches long in radical form.

What is Length of diagonal in cuboid?

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 5 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X= 5.91607 (in radical form)

Step-by-step explanation:

Hence, the length of the straw will be  5.91607 inches.

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4w+6.

The perimeter is just the summation of the length of all sides of a shape. In the case of a circle, the perimeters is its circumference length. So for this case, all we need to do is add up all the sides in a single expression that will represent the perimeter.

So perimeter for this triangle should be:

Side 1 + Side 2 + Side 3.

Where:

Side 1= w+4;

Side 2= 2w+2;

Side 3= w.

Then, perimeter is:

(w+4)+(2w+2)+(w)

Adding up all the like terms:

(w+2w+w)+(4+2)

(4w)+(6)

4w+6.

Answer:

[tex] \sqrt{( {3 - 2)}^{2} + {( - 2 - 6)}^{2} } [/tex]

[tex] \sqrt{ {1}^{2} + {( - 8)}^{2} } [/tex]

[tex] \sqrt{1 + 64} = \sqrt{65} [/tex]

Answer:

Step-by-step explanation:

The standard parametric equations for a circle with center (h, k) and radius r are:

x = h + r cos(theta)

y = k + r sin(theta)

Here, center is (−2, −3) and the radius is 6. Therefore, we have:

h = -2

k = -3

r = 6

Substituting these values into the standard equations, we get:

x = -2 + 6 cos(theta)

y = -3 + 6 sin(theta)

So the set of parametric equations for the circle is:

x(t) = -2 + 6 cos(t)

y(t) = -3 + 6 sin(t)

where t = theta.

The State Cash Flow Statement using the direct method.

                                                         OP                       INV                  FIN

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets                          100,000

Purchase of marketable securities                           50,000

Purchase & construction of fixed assets                  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts                                            100,000

Grants & subventions from NGO                                                     200,000

Proceeds from loan & other borrowings                                         300,000

Dividends received                                                                           100,000

                                            12,234,000             -450,000              500,000  

  Net Cash Flow for the year ended 31 December 2006: 12,284,000  

To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.

Operating Activities:

(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000

Investing Activities:

(100,000 - 50,000 - 500,000) = -450,000

Financing Activities:

(-100,000 + 200,000 + 300,000 + 100,000) = 500,000

Net Cash Flow for the year ended 31 December 2006:

12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000

The above answer is in response to the question below;

The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets  100,000

Purchase of marketable securities  50,000

Purchase & construction of fixed assets  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts      100,000

Grants & subventions from NGO               200,000

Proceeds from loan & other borrowings       300,000

Dividends received                                       100,000

You are required to:

Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)

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In the given diagram, the areas of the figures are as follows:

Area of the rectangle is 1/6 cm²

Area of the parallelogram is 12 m²

From the question, we are to calculate the areas of the given plane shapes

From the diagram, we have a rectangle and a parallelogram

The area of a rectangle is given by the formula

Area = l × w

Where l is the length

and w is the width

From the given information,

l = 1/2 cm

w = 1/3 cm

Thus,

Area = 1/2 cm × 1/3 cm

Area = 1/6 cm²

Hence, the area of the rectangle is 1/6 cm²

For the parallelogram

The area of a parallelogram is given by the formula

Area = b × h

Where b is the base length

and h is the perpendicular height

From the given information,

b = 6 m

h = 2 m

Thus,

Area = 6 m × 2 m

Area = 12 m²

Hence, the area of the parallelogram is 12 m²

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Using trigonometric ratio, the value of x in the figure is 2.61 units

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In this problem, we have the adjacent side and we need to find the opposite side.

The ratio that gives us room to find this is the tangent to the angle

tanθ = opposite / adjacent

tan 43 = x / 2.8

x = 2.8 * tan 43

x = 2.61

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The values of x and y of the given transverse lines are:

x = 44.25° and y = 7.25°

We know that there are different classification of angles such as:

Corresponding angles

Alternate angles

Opposite angles

Supplementary angles

Complementary angles

Now, we also know that sum of angles on a straight line is 180 degrees. Thus:

5x - 9y - 16 = 140

5x - 9y = 156   -----(1)

We also know that alternate angles are defined as two angles, that are formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on the opposite relative sides of the other lines. If the two lines crossed are parallel, then the alternate angles are equal.

Thus:

3x + y = 5x - 9y - 16

2x - 10y - 16 = 0

2x - 10y = 16  ----(2)

Solving simultaneously gives us:

x = 44.25° and y = 7.25°

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Answer:

Step-by-step explanation:

We can calculate the t-statistic and the p-value as follows:

If we assume that the null hypothesis is true, then the t-statistic will follow a t-distribution with 19 degrees of freedom. We can compare the calculated t-statistic with the critical t-value at the 0.05 level of significance using a t-distribution table or statistical software.

If the calculated t-statistic is greater than the critical t-value, then we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population mean reading rate is greater than 96 words per minute.

The p-value is the probability of obtaining a t-statistic as extreme or more extreme than the calculated t-statistic, assuming the null hypothesis is true. We can use the t-distribution table or statistical software to find the corresponding p-value.

If the p-value is less than the significance level of 0.05, then we can reject the null hypothesis at the 0.05 level of significance and conclude that the probability of obtaining a random sample of 20 second grade students with a mean reading rate of more than 96 words per minute is statistically significant.

The amount of grams that is equivalent to 3/10 of a kg is given as follows:

300 grams.

The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.

The amount of kg is 3/10 of a kilogram is given as follows:

3/10 = 0.3kg.

(conversion of a fraction to decimal, divide the numerator by the denominator).

Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:

0.3 x 1000 = 300 grams.

(proportion applied to obtain the conversion).

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Answer:

D.

x = 31; m∠ROS = 62°

Step-by-step explanation:

we know that a right angle is always 90 degrees, so we subtract 90° by ∠QOR:

[tex]90 - 28 = 62[/tex]

Then we insert the 62 with the (2x)

[tex]62 = 2x[/tex]

we divide both sides by 2 and we get:

[tex]31 = x[/tex]

so the answer is D

x is equal to 31 and we can multiply 31 by 2 and we can get 62°

The number of times more high school football players were there is 500.

Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.

Here, the number of times more high school football players were there

= 1×10⁶/2×10³

= 1×10³/2

= 1000/2

= 500

Therefore, the number of times more high school football players were there is 500.

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"Your question is incomplete, probably the complete question/missing part is:"

In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?​

So it would take A 10 days to do the whole job alone.

An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.

Here,

Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:

In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).

If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.

We can simplify the second equation by multiplying out the brackets and collecting like terms:

8a + 2b = 1

Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:

5(a + b) = 1

5b = 1 - 5a

b = (1/5) - a

Now we can substitute this expression for "b" into the second equation:

8a + 2b = 1

8a + 2((1/5) - a) = 1

8a + (2/5) - 2a = 1

6a = (3/5)

a = (1/10)

So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:

time = amount of work / rate

Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:

time = 1 / (1/10)

= 10 days

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The calculated measure of the angle Y is 38°

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

The angle S and angle Y are corresponding angles

This means that the angles are congruent

So, we have

Y = S

Substitute the known values in the above equation, so, we have the following representation

Y = 38°

Hence, the measure of the angle Y is 38°

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Complete question

Lines MN and GH are parallel. If mS is 38°, then what is mY?

See attachment for figure

Answer:

All lines are parallel

Step-by-step explanation:

Get each equation in Slope-Intercept form:

 1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]

 2. No change

 3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]

Notice:

a. All slopes are -4/3, AND

b. All y-intercepts are different

a)There is higher variability of Y with larger values of X.

b) There is non linear relation between X and Y.

a) Based on the given figure, we can make the following observations:

Therefore, the correct statement is There is higher variability of Y with larger values of X.

b) Based on the features, it is likely that a linear model may not be suitable for these data, and a non-linear model or other regression techniques may be more appropriate to capture the relationship between X and Y accurately.

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Answer:

So we can be 95% confident that the true proportion of people with kids in the population is between 0.044 and 0.096.

Step-by-step explanation:

To construct a confidence interval, we need to use the formula:

CI = p ± zsqrt((p(1-p))/n)

Where:

CI = confidence interval

p = sample proportion (in this case, 42/600 = 0.07)

z = the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval)

n = sample size (in this case, 600)

Plugging in the numbers, we get:

CI = 0.07 ± 1.96sqrt((0.07(1-0.07))/600)

Simplifying this, we get:

CI = 0.07 ± 0.026

Therefore, the 95% confidence interval for the true population proportion of people with kids is:

0.044 ≤ p ≤ 0.096

Answer:

how many points will you give?

Step-by-step explanation:

Answer:

A!!!!!!!!!!!!!!!!!!!!!!!!!

The meauser of center is the most appropriate answer for table two is the mean.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean

It is the mean because all of the data points are fairly close and there aren't any outliers (extreme values).

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Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.

Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.

Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.

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Answer:

Step-by-step explanation:

To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.

To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.

Now we can add -7/7 and 3/7 to get -4/7.

Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form

Answer:

Each of these functions is a transformation of the parent function f(x) = |x|. The transformations include shifting the graph up or down, stretching or compressing the graph vertically, reflecting the graph across the x-axis, and shifting the graph left or right. The vertex of each graph is located at a different point.

Step-by-step explanation:

- The function f(x) = |x| - 3 is a transformation of the parent function f(x) = |x|. The "-3" at the end of the function shifts the graph 3 units down. This means that the vertex, or lowest point, of the graph is at (0, -3) instead of (0, 0).

- The function f(x) = -|x - 4| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-4" inside the absolute value function shifts the graph 4 units to the right. This means that the vertex of the graph is at (4, 0) instead of (0, 0).

- The function f(x) = (1/3)|x| is a transformation of the parent function f(x) = |x|. The "1/3" in front of the absolute value function stretches the graph vertically by a factor of 1/3. This means that the graph is narrower and closer to the x-axis than the parent function. However, because the absolute value function is symmetrical, the graph is still centered at (0, 0).

- The function f(x) = -2|x - 1| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-1" inside the absolute value function shifts the graph 1 unit to the right. The "2" in front of the absolute value function stretches the graph vertically by a factor of 2. This means that the graph is narrower and closer to the x-axis than the parent function, and it is also reflected across the x-axis. The vertex of the graph is at (1, 0).

Answer:

Step-by-step explanation:

To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.

We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's find the length of each side of the triangle:

AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34

BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136

CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170

Now, let's check if the Pythagorean theorem is satisfied:

AC² = AB² + BC²

170 = 34 + 136

Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.

We know that,

the distance between two points=√(x2-x1)²+(y2-y1)²

∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²

                                                                         =√(9+25)

                                                                         = √(34)

∴ The length of side AB = √(34)

Again,

The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]

                                                                      = √(100+36)

                                                                      = √136

∴ The length of side BC =√136

Also,

The distance between points A and D, AC= √(-8-5)²+(3-2)²

                                                                      = √(169+1)

                                                                      = √170

∴ The length of side AC=√170

Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170

Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,

AC²=170

BC²=136

AB²=34

Clearly, 170=136+34

or, AC²=AB²+BC²

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The statement that is not true is: C. The translation of a line is a pair of parallel lines.

In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.

Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.

In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.

The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.

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