the product of seven non-zero factors. of which only three are positive. is

a) positive
B) negative
c) null​

The simplified form of 13¹/3 + 2¹/3 - 10/2 is a fraction 64/6 that can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2 the final answer is 32/3.

Given

13¹/3+2¹/3-10/2​

Required simplified it =?

First, we have simplified both constants separately

13¹/3 = (3 * 13 + 1) / 3 = 40/3

2¹/3 = (3 * 2 + 1) / 3 = 7/3

now the expression become = 40/3 + 7/3 - 10/2

now taking LCM of 3 and 2 which is 6.

                                                = 80/6 + 14/6 - 30/6

 now we have to simplify this fraction by dividing by 2 = 64/6

Therefore, the simplified form of 13¹/3 + 2¹/3 - 10/2 is 32/3.

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Answer:

Linear, equation: y = -2x + 1

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

Number of cube fit in prism = 24 cubes

Step-by-step explanation:

Given:

Side of cuboid = 1cm , 2cm , 2 1/2

Find:

Number of cube fit in prism

Computation:

Number of cube fit in prism = Volume of prism / Volume of cube

Number of cube fit in prism = (1)(2)(3/2) / (1/2)³

Number of cube fit in prism = 24 cubes

Answer:40 cubes

Step-by-step explanation: i did it on khan academy :D

Answer:

Step-by-step explanation:

Answer: a. 7

Work Shown:

Given set = {6, 10, 7, 2, 9, 8, 7, 3, 5}

Sorted set = {2, 3, 5, 6, 7, 7, 8, 9, 10}

P = 15 = percentile value

n = 9 = sample size, i.e. number of values in the set

R = index rank

R = (P/100)*(n + 1)

R = (15/100)*(9+1)

R = 1.5

This rounds to R = 2 when rounding to the nearest integer.

This R value tells us to look at the 2nd slot of the sorted data set. The value "3" is in the 2nd slot.

This is why the answer is choice D

Answer:

2x-4

Step-by-step explanation:

5x-(4+3x)

5x-4-3x

5x-3x-4

2x-4

Answer:

80°

Step-by-step explanation:

Because a straight line always is equal to 180°

so 180 - 100 = 80

Your answer is 80.

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The graph of the feasible region is attached

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

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

7 : 5

Step-by-step explanation:

42 : 30

7 : 5

Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

Answer:

10

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(10 - 2)² + (2 - 8)²

√(8)² + (-6)²

√(64) + (36)

√100

= 10

Step-by-step explanation:

your question is strange.

first you tell us that 50 people like coffee, 25 like tea, and 13 like both.

and then you ask how many like coffee or tea or both.

is this a joke ? or do you rather mean how many like only coffee, or only tea, and how many don't like neither ?

since 13 people like coffee and tea, these 13 are also part of the group of 50 that like coffee, and of the group of 25 that like tea.

so, to get the number of people that like only one, we need to deduct the number of people, who like both from both groups.

the number of people that only like coffee is therefore

50 - 13 = 37

and the number of people that only like tea is

25 - 13 = 12

we know the number of people that like coffee and tea is 13.

together that are

37 + 12 + 13 = 62 people.

that means 70 - 62 = 8 people don't like neither coffee nor tea.

Answer: 62

Step-by-step explanation:

Those who like coffee only = 50 - 13 = 37. Those who like tea only = 25 - 13 = 12. Those who like either coffee, or tea, or both = 37 + 12 + 13 = 62.

In theory, the 70 people being surveyed could fall under any of the following four categories:

I have labelled the four categories 1, 2, 3 and 4 for convenient reference.

From the information provided in the question, category 1 contains 50 people, category 2 contains 25 people, while category 3 contains 13 people. We do not yet know how many people fall under category 4, but we shall calculate it.

We know from set theory that the four aforementioned categories are known formally as sets. A set is simply a group of objects or things that are similar in some way. Each of the objects in a set is called a member of that set. Two sets can intersect. The intersection of two sets is simply the collection of members that are in both of the two sets. Also, two sets can unite. The union of two sets is the collection of members that in either of the two sets.

For example, category 3 is the intersection of category 1 and 2. The question requires us to calculate the union of category 1 and 2.

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:

n = 9870

Step-by-step explanation:

To determine the required sample size, we need to use the following formula:

n = (z^2 * p * q) / E^2

where:

n is the sample size

z is the z-score associated with the desired level of confidence

p is the estimated population proportion

q is 1 - p (the complement of the population proportion)

E is the maximum error of the estimate

In this case, we want to be 90% confident that our estimate is within 0.5% of the true population proportion, so we have:

z = 1.645 (from the standard normal distribution table for a 90% confidence level)

p = 0.15

q = 1 - 0.15 = 0.85

E = 0.005

Substituting these values into the formula, we get:

n = (1.645^2 * 0.15 * 0.85) / 0.005^2

Solving for n, we get:

n = 9869.795

Since we cannot have a fractional number of individuals in our sample, we need to round up to the nearest whole number. Therefore, the required sample size is:

n = 9870

a) Where the above conditions are given, this means that we can not reject the null hypothesis since the t-value = 0.31 and is greater thand the t-value which is 2.26

b) there is 95% confidence that the true mean lenght of novels written duing the pandemic falls within the range of 338 - 352 pages.

To test the above hypothesis , we used the two tailed t -test with a 95% confidence level.

T- value is computed as follows:

t = (sample mean - population mean)/ (sample Standard deviation/ √sample size)

Using the given values, we have:

t = (345/320)/(11/√10)
t = 0.31

Hence at 95% confidence leve, we have 2.26 as critical value.

Since 0.31  is less than the critical value, we cannot reject the null hypothesis.


B) to compute the 95% confidence interval for the mean lenght of the novels written during the pendemic:

Sample  ± (t-value x standard error)

Where:
Standard Error is given as = Sample Standard Deviation / √Sample size

Thus:

Standard Error = 11/√10
SE = 3.48

The 95% confidence interval therefore is:

345 ± (2.26 x 3.48
= 339.1, 351.9
≈ 339, 352.


Hence, it is correct to state that there is 95% confidence that the true mean length of novels written during the pandemic falls within the range of 338 - 352 pages.

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The tape diagram that represents 5÷2/3 is attached.

Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)

In the second step, join the three tapes in one long one maintaining the original divisions.

In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have

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Draw a tape diagram that represents 5÷2/3

Using the z-distribution, as we have the standard deviation for the population, the margin of error is given by:

b. 0.39.

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

As for the other parameters, we have that \(\sigma = 1.8, n = 81\).

Hence, the margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(M = 1.96\frac{1.8}{\sqrt{81}}\)

\(M = 0.39\)

Hence option b is correct.

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The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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Answer:

Toni should use the operation of division to solve for T.

Answer:

john=$29.75

pam=$17

Step-by-step explanation:

total amount =$46.75

  john =(46.75/5.5)*3.5

           =$29.75

    pam=(46.75/5.5)*2

             =$17

Answer:

John and Pam are paid $8.5 for each hour worked. John's share of the money is $29.75.

Step-by-step explanation:

Let x = the hourly salary. John worked for 3.5 hrs, and Pam for two. We can represent this using the equation:

3.5x + 2x = 46.75, where the coefficients equals the amount of hours.

Let's solve for x!

5.5x=46.75

x = 46.75/5.5 = 17/2 = 8.5

John and Pam are paid 8.5 dollars per each hour worked.

To figure out John's share of the money, we will multiply the wage by the hours he worked.

8.5 x 3.5 = 29.75

Answer:

The probability that a site has no problem when the machine says that the pipe at the site has no issue is

0.905

Step-by-step explanation:

Confidence level = 95%

Error level = 5% (1 - 95%)

Since the probability that the machine says the pipe has a problem for a site that in fact has an issue = 95% and the pipe has a problem in 10% of the case, this means that the pipe has a problem in exactly 0.095 (10% * 95%).

Therefore, the probability that a site has no problem when the machine says that the pipe at the site has no issue = 0.905 (1 - 0.095).

Answer:

196

Step-by-step explanation:

(18-4)^2

14^2 or 14x14

14x14=196

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Step-by-step explanation:

Answer:

The value of z + x × y is 3.

Step-by-step explanation:

x = 3/5

y = 1/3

z= 2 4/5

z + x × y

2 4/5 + 3/5 × 1/3

If we're following PEMDAS, we will first multiply.

3/5 × 1/3

= 1/5

2 4/5 + 1/5

= 3

Answer:

The equation \(-4x^2+10x-8\) does not have any real zeroes.

Step-by-step explanation:

The given equation is \(-4x^2+10x-8\).

Let us compare it with standard quadratic equation \(ax^2+bx+c\)

a = -4

b = 10

c = -8  

The nature of zeroes is determined by Discriminant 'D'.

1. If D = 0, the quadratic equation has two equal real zeroes.

2. If D > 0, the quadratic equation has two unequal real zeroes.

3. If D < 0, the quadratic equation has two non-real or imaginary zeroes.

Formula for D is:

\(D=b^{2} -4ac\)

Putting the values of a, b and c to find D:

\(\Rightarrow 10^2 - 4(-4)(-8)\\\Rightarrow 10^2 - 4(4)(8)\\\Rightarrow 100 - 4(32)\\\Rightarrow 100 - 128\\\Rightarrow D = -28\)

Here, D is negative so the zeroes of this quadratic equation are imaginary.

Hence, no real zeroes for the given equation \(-4x^2+10x-8\).

Answer:

y = 0.5x + 5

Explanation:

The equation of a line can be calculated as:

Where m is the slope and (x1, y1) is a point in the line.

To find the slope of our line, we need to identify the slope of the given line.

Since the equation of the given line is y = -2x + 1, the slope of this line is -2, because it is the number beside the x.

Then, two lines are perpendicular if the product of their slopes is equal to -1. So, we can write the following equation:

Therefore, the slope m of our line will be:

Now, we can replace the value f m by 0.5 and the point (x1, y1) by (0, 5) and we get that the equation of the line is:

Therefore, the answer is y = 0.5x + 5