what is -4 5/9 plus (-1 2/3

Answer:

B

Step-by-step explanation:

given that x and y vary inversely then the equation relating them is

y = \(\frac{k}{x}\) ← k is the constant of variation

to find k use the condition y is 24 when x is 8 , then

24 = \(\frac{k}{8}\) ( multiply both sides by 8 to clear the fraction )

192 = k

y = \(\frac{192}{x}\) ← equation of variation

when y = 18 , then

18 = \(\frac{192}{x}\) ( multiply both sides by x )

18x = 192 ( divide both sides by 18 )

x = \(\frac{192}{18}\) = \(\frac{32}{3}\)

Answer:

Step-by-step explanation:

Write the inverse variation

y = k/x

Solve for k

y = 24

x = 8

y = k/x           Substitute the givens into this equation

24 = k/8        Multiply both sides by 8

8*24 = k

k = 192

Solve for x  when y = 18

y = k/x            Multiply both sides by x

xy = k             Divide by y

x = k/y

x = 192/18

x = 10 2/3       The answer is given as an improper fraction.

x = (10*3 + 2)/3

Answer: x = 32/3

\(y+4=13 \implies \boxed{y=9}\\\\2x=3x-1 \implies \boxed{x=1}\)

Additionally, \(63=3z \implies \boxed{z=21}\)

The total cost of materials and labor for the office space, considering a tile unit cost of P300 and labor cost equal to the materials cost, amounts to P63,000.

To calculate the total cost of materials and labor, we first need to determine the cost of the tiles. Given that the unit cost of a certain tile is P300, we can multiply this by the area of the office space to find the total cost of the tiles. The office space has an area of 63 sqm, so the total cost of the tiles is P300 * 63 = P18,900.

Next, we need to calculate the labor cost, which is 100% of the materials cost. Since the materials cost is P18,900, the labor cost will be equal to P18,900. Therefore, the total cost of labor is also P18,900.

To find the total cost of materials and labor, we add the cost of the tiles (P18,900) and the labor cost (P18,900): P18,900 + P18,900 = P37,800.

Therefore, the total cost of materials and labor for the office space is P37,800.

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Answer:

A

Step-by-step explanation:

The reflected rays come from a point on the reflective surface. That point is where the lines meet is the vertex.

Answer:

 0.0714

Step-by-step explanation:

The probability that the first is "working in nature" is 3/8.

The probability that the 2nd is "working in nature" is 2/7.

The probability that the 3rd is "not working in nature" is 5/6.

The probability that the 4th is "not working in nature" is 4/5.

Thus the probability that the first two of 4 opportunities are "working in nature" is ...

  (3·2·5·4)/(8·7·6·5) = 1/14 ≈ 0.0714

Answer:

the answer is B.

Step-by-step explanation:

Answer:

y ≥1

Step-by-step explanation:

y=5x-4

Let x  ≥ 1

y  ≥ 5(1)-4

y ≥ 5-4

y  ≥ 1

Answer:

\(herey = 5x - 4 \\ \\ given \: that \: x \geqslant 1 \\ so \: y \geqslant 5 \times 1 - 4 \\ y \geqslant 1 \\ thank \: you\)

Answer:

X/8 = 2

8(X/8) = 8(2)

X = 16

You need to multiply both sides by 8, removing the fraction. You get X = 16

Answer: X = 16

Do the inverse opreation of division.

Instead of X / 8 = 2, it will be 8 · 2 = X

Hence, X = 16

Answer:

3

Step-by-step explanation:

trust lil bru

Answer:

Answer A - (0,2), (2,-1)

Step-by-step explanation:

GRAPH FOR EQUATION GRAPHED BELOW

If we look at the graph it goes through points (0,2), (2,-1)

The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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The average total cost can be found by dividing the total cost by the quantity produced. In this case, the total cost function is given as C = 90 + 35Q + 25Q^2 + 10Q^3, and we want to find the average total cost when Q = 2.

To find the average total cost, we need to calculate the total cost when Q = 2. Plugging Q = 2 into the cost function, we get:
C = 90 + 35(2) + 25(2^2) + 10(2^3)
C = 90 + 70 + 100 + 80
C = 340

Next, we divide the total cost by the quantity produced:
Average Total Cost = Total Cost / Quantity
Average Total Cost = 340 / 2
Average Total Cost = 170

Therefore, the value of average total cost when Q = 2 is $170.

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The answer is d. +0.5. A correlation coefficient of +0.5 provides the greatest risk reduction.

A correlation coefficient of +0.5 indicates a moderate positive correlation between two variables, meaning they are somewhat related. When two variables are moderately correlated, the risk reduction is greater than when they are not correlated at all (correlation coefficient of 0) or perfectly correlated (correlation coefficient of 1 or -1).

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If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If there is only one equation with more than one parameter, then the number of the solution will be infinite.

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

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Answer:

the other guy is right

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

If each cupcake needs 1/2 cup of sugar, you need to divide the total cups of sugar by 1/2.

7 1/3 ÷ 1/2= 14.6

You cant have .6 of a cupcake, therefore she can make 14 cupcakes.

Answer:

Step-by-step explanation:

The following function models the cost, in dollars, of a rug with width x feet.

Therefore, if we want to determine

The soil will reach about 27 cm up the pot when it fills 75% of the pot's volume.

To determine how far up the pot the soil will reach, we need to first find the volume of the pot, then find 75% of that volume, and finally calculate the height of soil in the pot.
Step 1: Calculate the volume of the pot
The volume of a pyramid can be calculated using the formula V = (1/3) * B * h,

where V is the volume, B is the area of the base, and h is the height.

Since the base is a square with a side length of 36 cm, the area of the base (B) is 36 cm * 36 cm = 1296 cm².

Now, plug the values into the formula:
V = (1/3) * 1296 cm² * 36 cm = 15552 cm³
Step 2: Calculate 75% of the pot's volume
75% of the pot's volume can be calculated as:
Soil volume = 15552 cm³ * 0.75 = 11664 cm³
Step 3: Calculate the height of the soil in the pot
To find the height of the soil, we can use the same formula for the volume of the pyramid, but we will solve for the height\((h_soil)\) this time:
11664 cm³ = (1/3) * 1296 cm² * \(h_soil\)
Solve for h_soil:
\(h_soil\) = (11664 cm³ * 3) / 1296 cm² ≈ 27 cm.

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We can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

To find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient state, we need to first identify the transient states. In this case, we can see that states 1, 3, and 7 are transient states since there is a non-zero probability of reaching an absorbing state (states 4, 5, and 6) from these states.

Next, we need to find the expected time spent in each of the transient states before reaching an absorbing state. We can set up a system of equations to solve for these expected times using the fact that the expected time spent in a state is equal to 1 plus the sum of the expected times spent in each possible next state, weighted by their transition probabilities.

For example, for state 1, we have:

E(T1) = 1 + 0.5E(T2) + 0.25E(T3)

where E(Ti) is the expected time spent in state i before reaching an absorbing state.

Similarly, for state 3, we have:

E(T3) = 1 + 0.4E(T2) + 0.2E(T4)

And for state 7, we have:

E(T7) = 1 + 0.2E(T5) + 0.5E(T6)

Solving these equations, we get:

E(T1) = 5

E(T3) = 5.5

E(T7) = 4

Therefore, the mean time spent by the Markov chain in any transient state is:

(E(T1) + E(T3) + E(T7))/3 = (5 + 5.5 + 4)/3 = 4.83

To find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state, we can use the concept of fundamental matrix. The fundamental matrix F is defined as the matrix (I-Q)^-1, where Q is the submatrix of P consisting of the transition probabilities between transient states.

In this case, we have:

Q = [0 0.25 0.2;

0.4 0 0.2;

0.2 0.2 0]

Using a calculator or software to calculate the inverse of (I-Q), we get:

(I-Q)^-1 = [1.25 0.625 1;

0.625 1.25 1;

1 1 1.5]

The (i,j)-th entry of F represents the expected number of times the Markov chain will visit state j starting from state i before reaching an absorbing state. Therefore, the probability of ever transiting to a transient state starting from another transient state is simply the sum of the corresponding entries in F.

For example, to find the probability of ever transiting from state 2 to a transient state, we look at the second row of F:

[0.625 1.25 1]

The sum of these entries is 0.625 + 1.25 + 1 = 2.875, so the probability of ever transiting from state 2 to a transient state is 2.875.

Similarly, we can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

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Answer:

I think you need to link a picture or something

Step-by-step explanation:

Side D'E' is about three times as lengthy as Side DE for the given dilation.

A scale factor is defined as the proportion between an object's measurements and its representation. In order to create an item that appears the same but is a different size, either scaled up or scaled down, the scale factor is often the number that is multiplied by the scale of the original object.

In Case, the scale factor is a whole number, the copy will be larger and if the scale factor is a fraction, the copy will be smaller.

Scale Factor Ratio for Scaling up should be always greater than 1 and the Scale Factor Ratio for Scaling down should be always smaller than 1.

We can use formula:

ratio of Dimensions of the new shape and Dimensions of the original shape.

As we can see, side DE is 4 units, but side D'E' is around 11.5 units.

∴D'E'/DE

=11.5/4

=2.8 ≈3

Hence, Side D'E' is about three times as lengthy as Side DE.

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Answer:

371

Step-by-step explanation:

Let the four consecutive integers be x, x + 1, x + 2, and x + 3.

The sum of these integers is:

x + (x + 1) + (x + 2) + (x + 3) = 1478

4x + 6 = 1478

4x = 1472

x = 368

The greatest of the four numbers is x + 3 = 368 + 3 = 371.

Therefore, the greatest of the four numbers is 371.

Answer:

371

Step-by-step explanation:

An integer is a whole number without any fractional or decimal parts, that can be positive, negative, or zero.

Consecutive integers are a sequence of integers where each number is incrementally one unit greater than the previous number.

Let x be the first integer.

Therefore:

If the sum of four consecutive integers is 1478 then:

\(x + (x + 1) + (x + 2) + (x + 3) = 1478\)

Collect like terms:

\(x + x + x + x + 1 + 2 + 3 = 1478\)

Combine like terms:

\(4x + 6 = 1478\)

Subtract 6 from both sides:

\(4x + 6 - 6 = 1478 - 6\)

\(4x = 1472\)

Divide both sides by 4:

\(4x \div 4 = 1472 \div 4\)

\(x = 368\)

Therefore, the first integer is 368.

As each consecutive integer is one more than the previous integer, the four consecutive integers are 368, 369, 370 and 371.

Therefore, the greatest of the four numbers is 371.

The expected number of boys who make good score is found to be 188 by using random sample method.

To get the projected number of boys who get good grades, multiply the total number of boys by the proportion of boys who answered they would like to get good grades the most.

According to the table, the total number of boys surveyed is:

188 +64 +192 = 444

And the percentage of guys who indicated they

would like to get good grades is:

188/444 0.423

As a result, the projected number of guys with good grades is:

Expected number of boys = total number of boys

x percentage of boys who get high grades

444 x 0.423 = 444 boys expected

Number of boys expected = 187.812

When we round to the nearest full number, we get: The expected number of males with good grades

is 188.

So, as a result there are 188 boys who say they

would like to score more good grades.

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Complete question - A study examines the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achievement of personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented in the following table by the sex of the child.

Boys Girls

Be good in sports 188 590

Be popular 64 80

Make good grades 192 90

Answer:

32 degrees

Step-by-step explanation:

90 + 58 = 148

180 - 148 = 32

The sum of the infinite series is a finite number, we can conclude that the given geometric series is convergent. The answer is thus, the geometric series is convergent.

To determine whether the given geometric series is convergent or divergent, we need to calculate the common ratio (r) first. The formula for the nth term of a geometric series is a*r^(n-1), where a is the first term and r is the common ratio.

In this case, the first term is 20(0.64)^0 = 20, and the common ratio is (0.64^n-1) / (0.64^n-2). Simplifying this expression, we get r = 0.64.

Now, we can apply the formula for the sum of an infinite geometric series, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

Substituting the values we have, we get S = 20 / (1 - 0.64) = 55.56.

Since the sum of the infinite series is a finite number, we can conclude that the given geometric series is convergent. The answer is thus, the geometric series is convergent.

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Pseudocode algorithms are used as prototypes of an actual program.

The required pseudocode algorithm is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The pseudocode that prints the first n odd numbers starting from 1 is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The above pseudocodes would print the first n odd numbers starting from 1, given that n is the input

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The required solutions are:

a) The 95% confidence interval for the mean number of personal computers is approximately [1.254, 1.386].

b) When the sample size is reduced to 100, the new margin of error is approximately 0.0806. This is larger than the margin of error in part (a

c) When the confidence level is increased to 98%, the new margin of error is approximately 0.0879. This is larger than the margin of error in part (a).

d) The lower bound of the confidence interval (1.254) is greater than the value of 1.25. Therefore, it is likely that the mean number of personal computers is greater than 1.25.

a. To construct a 95% confidence interval for the mean number of personal computers, we can use the formula:

\(CI = x \pm Z * (\sigma / \sqrt{n})\)

where:

- x is the sample mean (1.32)

- Z is the critical value for a 95% confidence level (taken from the standard normal distribution table, which corresponds to a two-tailed test, is approximately 1.96)

- \(\sigma\) is the population standard deviation (0.41)

- n is the sample size (150)

Solving the above equation we get:

\(CI = 1.32 \pm 1.96 * (0.41 / \sqrt{150}\)\\CI = 1.32 \pm 1.96 * 0.0335\\CI = 1.32 \pm 0.06574\)

Calculating this expression will give us the lower and upper bounds of the confidence interval which are equal to:

Lower bound = 1.32 - 0.06574 = 1.25426

Upper bound = 1.32 + 0.06574 = 1.38574

Therefore, the 95% confidence interval for the mean number of personal computers is approximately [1.254, 1.386].

b. To calculate the new margin of error when the sample size is 100 instead of 150, we need to use the same formula as in part a, but with the new sample size (n = 100).

The new margin of error = \(1.96 * (0.41 / \sqrt{100}) = 1.96 * (0.41 / 10) = 0.0806\)

Therefore, the new margin of error is approximately 0.0806.

Comparing it with the margin of error in part a, we can see that the new margin of error is larger when the sample size is reduced.

c. To calculate the new margin of error when the confidence level is 98% instead of 95%, we can use the same formula as in part a, but with the new critical value corresponding to a 98% confidence level (taken from the t-distribution table).

The new margin of error = \(2.617 * (0.41 / \sqrt{150}) = 2.617 * 0.0335 = 0.0879\)

Therefore, the new margin of error is approximately 0.0879.

Comparing it with the margin of error in part a, we can see that the new margin of error is larger when the confidence level is increased.

d. To determine if the mean number of personal computers is likely to be greater than 1.25, we need to check if the lower bound of the confidence interval is greater than 1.25.

Since the lower bound of the confidence interval (1.254) is greater than 1.25, it is likely that the mean number of personal computers is indeed greater than 1.25.

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Answer:

-1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a trapezoid. It is a quadrilateral with one pair of parallel sides while other sides are non-parallel. Here, the opposite angles are alternate, that is, they have together 180°.

Isosceles trapezoid

An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. Here, the base angles are the same.

The line segment joining the midpoints of the parallel sides is perpendicular to the bases and the diagonals are the same in length.

Right-angled trapezoid

Trapezoid with two right angles and necongruent non-paralell sides.

Good luck:)