Noj is 5 years older than Jacob. The product of their ages is 84. How old is Noj?

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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Answer:

Calculate the value of x. Give your answer ... Hyp. 5.8 m. Opp. 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... the value of x. Give your answer correct to 1 decimal place. ... a. Diagram NOT accumtely drawn. 9,6 cm. 6.4 cm. A. Hyp. To. Aaj. LMN is a right-angled triangle. MN = 9.6 cm. ... x = ton​-14.5.

Step-by-step explanation:

please be right

Answer:

50 classmates

Step-by-step explanation:

80 x 0,62 = 49,6

49,6 ≈ 50

w ≤ 250

This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, the weight, w, must be less than or equal to 250 pounds.

The weight, w, must be less than or equal to 250 pounds. This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, if the weight of the object being placed on the stepladder is greater than 250 pounds, it is not safe to use the stepladder. This inequality helps to ensure the safety of the person using the stepladder, as it limits the amount of weight that can be placed upon it. Furthermore, it also helps to protect the stepladder itself, as it prevents it from being overloaded with too much weight, which could cause it to break or malfunction. In conclusion, the inequality w ≤ 250 represents the maximum weight that a stepladder can safely hold.

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Answer:

230000.

Step-by-step explanation:

8 square unit to find the area of the parallelogram with vertices A(-4, 2), B(-2, 5), C(2, 3), and D(0, 0), follow these steps:

Step 1: Find the base and height vectors of the parallelogram. Let's use AB and AD as the base and height vectors, respectively.
AB = B - A = (-2 - (-4), 5 - 2) = (2, 3)
AD = D - A = (0 - (-4), 0 - 2) = (4, -2)

Step 2: Calculate the cross-product of the base and height vectors.
Cross product = AB_x * AD_y - AB_y * AD_x = (2 * -2) - (3 * 4) = -4 - 12 = -16

Step 3: Find the area by taking the absolute value of the cross product divided by 2.
Area = |Cross product| / 2 = |-16| / 2 = 8

The area of the parallelogram with vertices A(-4, 2), B(-2, 5), C(2, 3), and D(0, 0) is 8 square units.

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a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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Answer:

x = 3

Step-by-step explanation:

3x + 2 = 11

      -2     -2

3x = 9

÷3    ÷3

x = 3

Answer:

x=3

Step-by-step explanation:

3x+2=11

3x=11-2

3x=9

x=9/3

x=3

Answer:

okkkkk

Step-by-step explanation:

limx→0sinaxcosbxsincx=limx→0(cosbx⋅sinaxax⋅cxsincx⋅ac)=ac

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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The given statement is false.

You can compare two marginal distributions to see if the corresponding two variables are related - False.

Comparing marginal distributions can only disclose information about the distribution of each variable individually, not whether the variables are connected or not.

To see if two variables are connected, we must look at their joint distribution or conditional distribution. To examine the degree and direction of a link between two variables, statistical approaches such as correlation analysis or regression analysis can be utilised.

As a result, comparing marginal distributions is insufficient to tell whether two variables are connected or not.

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Answer

5/48, 3/16, 0.5, 0.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

6,000 units3

Step-by-step explanation:

got it rt

Answer:

\(y=11\)

Step-by-step explanation:

So we have the function:

\(g(x)=|x-4|+8\)

First, note that this is an absolute value function.

The standard form of an absolute value function is:

\(y=|mx-b|+c\)

Where m is the slope and the vertex point is (b/m, c).

Let's determine our vertex first. B is 4, m is 1, and c is 8. So:

\((4/1,8)=(4,8)\)

So, our vertex is at (4,8).

Also, note that there is no negative in front of our absolute value, so this is going upwards.

Now, recall that an absolute value function has the general shape of a V. Since this is a positive absolute value, all x-values to the left of the vertex will be decreasing, while all x-values to the right of the vertex will be increasing.

In other words, from negative infinity to 4, the function will be decreasing.

And from 4 until positive infinity, the function will be increasing.

We want to find the minimum value of the function between [-2,1].

Since [-2,1] is to the left of the vertex, this means that the function is decreasing.

So, to find the minimum value, we just need to use the x-value closest to the vertex, in this case, x=1.

So, to find the minimum value, we just need to substitute 1 into g(x). So:

\(g(1)=|1-4|+8\)

Subtract:

\(g(1)=|-3|+8\)

Absolute Value:

\(g(1)=3+8\)

Add:

\(g(1)=11\)

Therefore, our minimum value of the g(x) on the interval [-2,1] is y=11.

We can graph the function to verify our answer. As we can see, the minimum value on the interval [-2,1] (black line) is indeed y=11.

The two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is -4.08 (rounded to two decimal places).

To calculate the two-sample z-test statistic, we need to compare the proportions of students who support capital punishment in 1970 and 2005. The null hypothesis states that the percentage of students who support capital punishment did not change.

Let p1 be the proportion of students who support capital punishment in 1970, and p2 be the proportion in 2005. We can calculate the sample proportions as p1 = 590/1000 = 0.59 and p2 = 350/1000 = 0.35.

The formula for the two-sample z-test statistic is given by z = (p1 - p2) / sqrt((p(1 - p)(1/n1 + 1/n2))), where p is the pooled proportion and n1 and n2 are the sample sizes.

To calculate p, we compute the pooled proportion as p = (p1n1 + p2n2) / (n1 + n2) = (0.591000 + 0.351000) / (1000 + 1000) = 0.47.

Substituting the values into the formula, we have z = (0.59 - 0.35) / sqrt((0.47*(1 - 0.47)(1/1000 + 1/1000))) = -4.08.

Therefore, the two-sample z-test statistic for evaluating the null hypothesis is -4.08 (rounded to two decimal places).

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Answer:

Length of the rectangle is 18 ft when its width is 4ft

Step-by-step explanation:

Let us assume that the length is represented by l.

Let us assume that the width is represented by w.

As given

The length of the rectangle varies inversely with its width.

Thus

L x 1/w

l=k/w

Where k is the constant of proportionality .

As given

If the

length of the rectangle is 6 feet when the width is 12 feet,

l=6, w=12

putting the values in l = k/w

6 = k/12

k = 12 x 6

k=72

As given

width is 4ft

k= 72, w = 4

Putting the values in, L = k/w

                                   L= 72/4

                                    L=18 ft

Therefore the  length of the rectangle is 18 ft when its width is 4ft

Hope this helps You

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

The bottleneck time is the longest time it takes to complete any task in the assembly line. In this case, the longest time needed is 10, which is the last station. This means that all the other tasks must be completed within 10 seconds in order for the entire assembly line to proceed.

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

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Answer:

7

Step-by-step explanation:

as a fraction it would be 7/1 but it is a half so it goes in evenly

Answer:

7

Step-by-step explanation:

Lets turn 3 1/2 to an improper fraction.

3*2=6

6 + 1 = 7

7/2

Because dividing by 1/2 means multiplying by 2, the answer is 7.

Answer:

24/68 inches

Step-by-step explanation:

Multiply 3 times 8 to get 24. The denominator was multiplied by 8 so you have to do the same thing to the numerator.

Hope This Helps :)

The equivalent of the quantity \(\frac{3}{8}\) inch is \(\frac{24}{64}\) inch.

The given quantity is \(\frac{3}{8}\) inch.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

Here, in equivalent given fraction denominator is 64.

Let the numerator be x.

Now, \(\frac{3}{8}\) inch = \(\frac{x}{64}\) inch

3×64=x×8

x=3×8

x=24

So, the numerator of the fraction is 24.

Hence, the equivalent of the quantity \(\frac{3}{8}\) inch is \(\frac{24}{64}\) inch.

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A sentence which describe the given ratio in the context of the situation chosen include the following:

Ratio can be defined as a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

A sentence which describe the given ratio in the context of the situation chosen include the following:

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Complete Question:

Choose a situation that could be described by the following ratios, and write a sentence to describe the ratio in the context of the situation you chose.

For example:

3:2 When making pink paint, the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs to use 2 cups of red paint.

a. 1 to 2

b. 29 to 30

c. 52:12

where the above conditions are given

2.2.1 To calculate the electrical rating of the small front plate of the stove in kilowatt (kW), we need to divide the wattage by 1000:

1900 W / 1000 = 1.9 kW

From the log table, we can see that the geyser uses the most electricity, with a total of 336 kWh used for the week.

To reduce consumption in this area, Mr Thorn could consider using the geyser less frequently or reducing the temperature setting.

the cost of electricity of the refrigerator with freezer is;

total kWh x cost per kWh:

13.9 kWh x R0.945/kWh = R13.13

the total kWh Mr Thorn used when boiling his kettle for the week, we need to convert the time used in minutes to hours:

40 minutes = 40/60 hours = 0.67 hours

Calculating  the total kWh:

1.4 kW x 0.67 hours = 0.938 kWh

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Answer: (-11,0) (Please make sure this answer is correct, as I am not a master...)

Step-by-step explanation:

We can solve this a super simple way.

The midpoint is (-6,-3/2) and the coordinate B is (-1,3)

We notice that we change y by positive 5 and we change our x by negative 3/2, from M to B. So to get to A from M, we change y by -5 and change our x by positive 3/2...

So we have:

(-6-5,-3/2+3/2)

(-11,0)

So the coordinate of A is:

(-11,0) (Please make sure this answer is correct, as I am not a master...)

Answer:

The total profit made when a person buys an item for $2.25 and then sells the item for $2.25.

Step-by-step explanation:

The item is bought for $2.25 and sold for the same rate. There is no profit.

        Final value is 0.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

p = k / sqrt(q)

The first job is to find k.

p = 12

q = 36

Solution for k

12 = k / sqrt(36)

sqrt(36) = +/- 6

Multiply both sides by +/-6

12 * +/- 6 = k

k = +/- 72

Solution for q = 16

p = +/-72/ sqrt(16)

p  = +/- 72 / sqrt(16)

p = +/- 72 / +/-4

p = 18

The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

\(FV = P(1 + r/n)^{nt}\)

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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