An electrical wiring job requires the following lengths of 14/2 BX cable: seven pieces each 612ft long, four pieces each 3434in. long, and nine pieces each 1938in. long. What is the total length of cable needed?

Answer:

a. 1996

Step-by-step explanation:

Let Paul's age in 2000 be P

Let Bilko's age in 2000 be B

Statement: Paul was twice as old as his brother Biko in 2000 means
P = 2B          (1)

In 2008 Paul was only four years older than his brother.

Since 2008 is 8 years from 2000, both Paul and Bilko have aged 8 years

Paul's age in 2008 = P + 8

Bilko's age in 2008 = B + 8

Statement: In 2008 Paul was only four years older than his brother means

P + 8 = B + 8 - 4

P = B + 4           (2)

Given these two equations (1) and (2)

Substitute P = 2B from (1) in (2):
2B = B + 4

==> 2B - B = 4

==> B = 4

Therefore in 2000, Paul was 8 years old and Bilko was 4 years old

Bilko's year of birth = 2000 - 4 = 1996

Answer: (-1.25, 0.41)

Step-by-step explanation:

Answer:

[tex]\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]

Step-by-step explanation:

Given Problem

[tex]\displaystyle \int {xe^{5x}} \, dx[/tex]

Make substitutions for IBP

Let [tex]u=x,\,du=dx[/tex] and [tex]v=\frac{1}{5}e^{5x},\,dv=e^{5x}dx[/tex]

Perform IBP

[tex]\displaystyle \int {u} \,dv=uv-\int {v} \, du\\\\\int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x} -\int {\frac{1}{5}e^{5x}} \, dx\\\\\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]

the value of x=17/9 and y=5 by solving the system of equations.

What is a System of Equations?

When two or more algebraic equations are solved together, they form a system of equations. A system of linear equations is a collection of equations that are all satisfied by a single set of variables. The first stage in resolving an equation system is determining the values of the variables used in the equation system. We determine the values of the unknown variables while keeping the equations' equality on both sides. The main purpose of solving an equation system is to identify a variable whose value makes the condition of each equation in the system true.

The given equation are

9x+2y = 27

y=-8x+31

9x+2y =27

16x+2y =62

7y = 62-27

7y = 35

y=5

x = 17/9

Hence the value of x=17/9 and y=5 by solving the system of equations.

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For large samples, the sample proportion is approximately normally distributed, with mean μˆP=p. and standard deviation σˆP=√pqn

Taken from stats.libretexts.org btw^^

392

8630 divided by 22. = 392.272727... cant be decimal so round down

Answer:

The $30,000 in revenue should be entered as a credit in the journal entry.

Step-by-step explanation:

In accounting, revenues are recorded as credits, which means that they increase the credit side of the accounting equation (revenues increase equity, which is a credit account). Debits, on the other hand, are used to record expenses and decreases in assets.Therefore, the journal entry to record $30,000 in revenue for the business on October 1 would be:Date

Account Account Number Debit Credit

1 - Oct Revenue 4050 30,000Since revenue is being credited, there is no debit amount entered in this entry. The credit amount of $30,000 is entered in the credit column, as shown above.

Answer:

684π

Step-by-step explanation:

It is two parts: half of a sphere and one cylinder.

Sphere volume formula: V=4/3πR³, r=12/2=6, r³=216

                                      v=4/3π216

                                      v=288π

Half of sphere:  288π/2=144π

Cylinder volume: V=πr²h, r=12/2=6, r²=36, h=15,

                           V=π*36*15=540π

So, total is 144π+540π=684π

For given function f(x) = √x + 9, the inverse function and domain are respectively, f⁻¹(x) = (y - 9)², x ≥ 0 & x ∈ (∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Given that,

A function,

⇒ f(x) = √x + 9

f⁻¹(x) = ?

the given function is defined for all the values of x,

So domain of the function is real number,

x ∈ (∞, ∞)

Now for f⁻¹(x),

Suppose, f(x) = y

y = √x + 9

y - 9 = √x

squaring both the sides,

(y - 9)² = (√x)²

x  = (y - 9)²

And value of x should be greater than zero

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The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.

The given matrix is:

| 1 0 5 |

| -2 1 -6 |

| 0 2 8 |

We must compute the matrix's determinant in order to determine if the matrix's column vectors are linearly independent or linearly dependent.

A scalar value that can be used to assess linear dependency or independence is the determinant of a matrix.

The determinant of the matrix is:

det(A) = 1(-68) - 0(18) + 5(-2*2) = -6 + 0 - 20 = -26

Since The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.

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Showing this information in a ledger is given below":

Ordinary Share Capital:

28 February 2021: 1,000,000 authorized shares * 500 cents per share (for the shares issued on 31 August 2020) = R500,000

28 February 2020: 600,000 issued shares * R35 (2,100,000 / 60) = R21,000

Retained Income:

28 February 2021: R500,000 (Ordinary Share Capital) - R21,000 (Ordinary Share Capital) + R120,000 (repurchased shares at 620 cents per share) = R599,000

28 February 2020: R737,100 (Retained Income)

Note: The R35 per share in 28 February 2020 was calculated by dividing the total ordinary share capital of R2,100,000 by the number of shares in issue (600,000).

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Answer:

The surface area of a rectangular prism can be calculated by adding the area of each of its six faces. The formula for the surface area of a rectangular prism with length l, width w, and height h is:

Surface Area = 2lw + 2lh + 2wh

So for a rectangular prism with length 29 inches, width 36 inches, and height 5 inches, the surface area can be calculated as follows:

Surface Area = 2 * 29 * 36 + 2 * 29 * 5 + 2 * 36 * 5

= 2,612 + 290 + 360

= 3,262 square inches

Therefore, the surface area of the rectangular prism is 3,262 square inches.

Answer:

It is graphed in the picture.

Step-by-step explanation:

Answer:

See the attached graph

Step-by-step explanation:

Take each inequality and isolate x for each

x+1 < 9
==> x + 1 - 1 < 9 -1  add 1 both sides

==> x < 8

4x ≤ 8

==> 4x/4 ≤ 8/4    divide by 4 both sides

==> x  ≤ 2

So we have two inequalities to satisfy

To graph,

To graph the first inequality, draw a vertical line at x = 9 parallel to the y-axis. This line should be dotted to show it is a < inequality. Everything to the left of this line satisfies x < 8

To graph the second inequality, x ≤ 2, draw a vertical line at x = 2 parallel to the y-axis. This line should be solid to show it is a ≤ inequality. Everything to the left of this line satisfies x ≤ 2

The common points for both lines are shown in dark purple in the graph where the two shaded areas overlap

If you just wanted it on the number line that would be the second image

Answer:

Salary with $3300 raise per year:

t (years)     Salary

1            $69300

5            $82600

10            $95900

15            $1092000

20            $1225000

Salary with 4% raise per year:

t (years)      Salary

1             $68640

5             $83833

10             $102219

15             $124869

20             $152947

Note: The calculations for the 4% raise are done as follows:

Year 1: 66000 * 1.04 = $68640

Year 5: 66000 * 1.04^5 = $83833

Year 10: 66000 * 1.04^10 = $102219

Year 15: 66000 * 1.04^15 = $124869

Year 20: 66000 * 1.04^20 = $152947

Step-by-step explanation:

Amount of gallons of water after 6 hours is  482 gallons.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

Initial volume of the swimming pool = 500 gallons

The change in the amount of water in the pool is -3 gallons per hour.

Each hour, the volume of the pool is decreasing by -3 gallons.

Change in the amount of water in 1 hour = -3 gallons

Change in the amount of water in 6 hours = -3 × 6 = -18 gallons

After 6 hours,

Volume of the pool = 500 - 18 = 482 gallons

Hence there will be a volume of 482 gallons of water after 6 hours.

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a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

The augmented matrix is:

[tex]\left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\-2&6&3&-4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-5&4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-1&2\end{array}\right][/tex]

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since   [tex]\left[\begin{array}{c}1\\0\\-2\end{array}\right] = 1. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right][/tex] we have that a₁ is in the W.

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a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

No, b is not in {a1, a2, a3}.

There are 3 vectors in {a1, a2, a3}.

Yes, b is in W.

There are infinitely many vectors in W.

Yes, a1 is in W because it can be expressed as a linear combination of the vectors in W. This is shown by the equation a1 = 1(a1) + 0(a2) + 0(a3).  The coefficients of the vectors in the linear combination are all integers and this equation shows that a1 is in the span of the vectors in W.

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since we have that a₁ is in the W.

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Based on the information, it can be inferred that the area of a surface with sides 23 yards and base 23 yards is 529 square yards.

To calculate the surface area of this figure we must perform the following procedure:

We know the side and the base of this figure measure 23 yards, so we must apply the following formula.

So we can infer that the area of this surface would be 534 square yards.

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Answer:

Here are some fractions and equivalent percentages.

1/4 = 1/4 x 100 = 25%
1/8 = 1/8 x 100 = 12.5$
3/8 = 3/8 x 100 = 300/8 = 37.5%
3/4 = 3/4 x 100 = 75%
1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)
54% = 54/100 = 27/50

Here are some percentages and equivalent fractions:
54% = 54/100 = 27/50
36% = 36/100
45% = 9/20
20% = 1/5
30% = 3/10

Step-by-step explanation:

To convert a fraction to a percentage, multiply by 100

To convert a percentage to a fraction, divide by 100 and reduce to lowest fractional form

Examples:

1/4 = 1/4 x 100 = 25%

1/8 = 1/8 x 100 = 12.5$

3/8 = 3/8 x 100 = 300/8 = 37.5$

3/4 = 3/4 x 100 = 75%

1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)

Similarly,

54% = 54/100 = 27/50

36% = 36/100
dividing by 4 both numerator and denominator gives
36% = 36/100 = 9/20

45% = 45/100 = 9/20  (divide by 5)

20% = 20/100 = 1/5

Answer:

Stem | Leaf

-----|-----

1    | 2 7 7 2 4

2    | 9 8 7 6 3 0 9 7

3    | 7 6 4 3 1 7

4    | 3 6

-----|-----

Step-by-step explanation:

To create a stem-and-leaf plot, we first divide each data point into two parts: the stem, which is the first digit or digits, and the leaf, which is the final digit or digits.

For this data set, the stem for each data point would be the tens digit, and the leaf would be the units digit.

Here's how the plot would look like:

Stem | Leaf

-----|-----

1    | 2 7 7 2 4

2    | 9 8 7 6 3 0 9 7

3    | 7 6 4 3 1 7

4    | 3 6

-----|-----

Note that the stems are listed in increasing order, and the leaves for each stem are listed in order within that stem. This helps to give an overall sense of the distribution of the data, such as the range and the concentration of data points in certain regions.

The change in temperature between 11.00am and 11.00pm would be = 43°F. That is option D.

Temperature is defined as the scalar quantity that shows or measure the degree of hotness or coldness of a medium.

The temperature of a medium at 11.00am = 37°F

The temperature of a medium at 11.00 pm = -6°F

The difference between the both given temperature = 37-(-6) = 37+6 = 43°F.

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[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ x = \sqrt{13^2+17^2~-~2(13)(17)\cos(98^o)} \implies x = \sqrt{ 458 - 442 \cos(98^o) } \\\\\\ x\approx\sqrt{519.51}\implies x\approx 22.8[/tex]

Make sure your calculator is in Degree mode.

1. The diagonals bisect each other.

2. The diagonals of parallelogram are perpendicular and equal to each other.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

Given:

Using the theorem a quadrilateral whose diagonal bisect each other is a parallelogram.

Then, the diagonals bisect each other then the quadrilateral is a parallelogram.

As, the diagonals of parallelogram are perpendicular and equal to each other then , the parallelogram is a square.

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Answer:

(1/x)+31

Step-by-step explanation:

To simplify the expression

5/(1/6) + 1/X + 1,

we need to first simplify the fraction 5/(1/6):

5/(1/6) = 5 * 6/1 = 30

Now we can substitute this value back into the expression:

30 + 1/X + 1

To combine the last two terms, we need to find a common denominator, which is X:

30X/X + 1/X + X/X

Simplifying the numerator:

30X + 1 + X

Combining like terms:31X + 1

so the simplified rational expression is (1/x)+31

Answer:

Option A: 4/5

Step-by-step explanation:

If y varies directly as x written as y ∝ x, this can be written as an equation:
y = kx  where k is a constant

Since y = 6 when x = 15:
6 =k · 15

6 = 15k

15k  = 6

k = 6/15  = 2/5

The equation beocmes
y = (2/5) x

Therefore when x = 2,

y = (2/5) x 2 = 4/5

Option A: 4/5

The entire length of the trip is 9/12 miles.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

After biking 5/12 miles,

Jada has traveled 2/3 of the length of her trip.

Let x be the entire length of the trip.

The equation is,

x = 1/3 + 2/3

x = 1/3 + 5/12

x = 9/12

Therefore, the distance is 9/12 miles.

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Step-by-step explanation:

a. Given a positive test result, the probability that a random patient has the disease is called the positive predictive value (PPV). The PPV can be calculated using the following formula:

PPV = Sensitivity * Prevalence / (Sensitivity * Prevalence + (1 - Specificity) * (1 - Prevalence))

Plugging in the values given in the question, we get:

PPV = 0.92 * 0.01 / (0.92 * 0.01 + (1 - 0.93) * (1 - 0.01)) = 0.087

So, the probability that a random patient has the disease given a positive test result is 0.087 or 8.7%.

b. A tree diagram for a typical sample of patients with a positive test result would look something like this:

+-----------+-----------------+

| Test Result| Positive (TP + FP) |

+-----------+-----------------+

| | TP (Disease) |

| | 0.92 * 0.01 |

| | FP (No Disease)|

| | 0.08 * 0.99 |

+-----------+-----------------+

c. If the prevalence is lower, the proportion of positive test results due to false positives (FP) increases compared to true positives (TP). This is because the positive predictive value (PPV) decreases as the prevalence decreases, meaning that a larger proportion of positive test results are due to false positives. This is why the proportion in error is larger if the prevalence is lower.

The coordinate of the other stop sign located will be (21, 3).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11).

Then the coordinate of the other stop sign located is given as,

(12, 7) = [(x₁ + 3) / 2, (y₁ + 11) / 2]

(24, 14) = [x₁ + 3, y₁ + 11)

(21, 3) = (x₁, y₁)

(x₁, y₁) = (21, 3)

The coordinate of the other stop sign located will be (21, 3).

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As a fraction, the probability of each sample point is 8/9.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

(a) The sample points in this experiment are:

V1V1, V1V2, V1V3, V2V1, V2V2, V2V3, V3V1, V3V2, V3V3

(b) Since the vendors are selected at random each day, each sample point has the same probability of occurrence. There are a total of 3 * 3 = 9 possible sample points, so each sample point has a probability of 1/9.

(c) Let A denote the event that the same vendor gets both orders, and let B denote the event that V2 gets at least one order.

P(A) is the probability that the same vendor gets both orders, so it is the sum of the probabilities of the sample points V1V1, V2V2, and V3V3. P(A) = 1/9 + 1/9 + 1/9 = 3/9.

P(B) is the probability that V2 gets at least one order, so it is the sum of the probabilities of the sample points V2V1, V2V2, and V2V3. P(B) = 1/9 + 1/9 + 1/9 = 3/9.

P(AUB) is the probability of either A or B occurring, so it is the sum of the probabilities of all 9 sample points. P(AUB) = 9/9 = 1.

P(ANB) is the probability of both A and B occurring, so it is the sum of the probabilities of the sample points V2V2. P(ANB) = 1/9.

So, P(AUB) - P(ANB) = 1 - 1/9 = 8/9.

The probability of each sample point as a fraction is 8/9.

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