A stationery shop orders a batch of pens from a factory. The factory could make the batch of pens in 20 days using 12 machines. Due to a fault, only 9 machines were used for the first 8 days. All 12 machines were used from day 9 onwards. Work out the total number of days taken to make the batch of pens.
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Answer:

The number will be x

Step-by-step explanation:

2(x + 4) = 3(x - 2)

2x + 8 = 3x - 6

14 = x

When two random variables X and Y are considered to be independent, it means that neither X's distribution nor Y's values have any bearing on the other.

A random variable is a variable used in an experiment, such as the number of coin tosses or card draws. An independent random variable is a random variable in your experiment that doesn't affect the other random variables. In other words, it has no impact on the likelihood that another event will occur. For illustration, suppose you randomly selected 50 bags of sugar from various grocery stores in order to determine the average weight of a bag of sugar. The factors are independent since you wouldn't anticipate the weight of one bag having an impact on another. A dependent random variable, on the other hand, does have an impact on the probability of other random variables.

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Answer: 7

Step-by-step explanation:

(fg)(-1/3)=

f(g(-1/3))=

f(3(-1/3) + 1)=

f(-1 + 1)=

f(0)=

0²- 7=7

The square root of 255 is approximately 15.969.

Given,

Root 255, [tex]\sqrt{255}[/tex]

We have to find the square root of the number:

Square root of a number:

A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.

Now,

√255 = 15.9687194227

Which is approximately equals to 15.969

That is,

The square root of 255 is approximately 15.969

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Answer:

d:1

Step-by-step explanation:

the answers will always be negative and the other side will always be positive

Answer:

k = 4.33

Step-by-step explanation:

Cos 30 = 0.8660

Tan 60 = 1.732

2 Tan 60 = 2 (Tan 60)

2 Tan 60 = 2 (1.732)

2 Tan 60 = 3.464

Cos 30 + Tan 60  = 0.8660 + 3.464 = 4.33

k = 4.33

Answer:

(25,20) , (45,36)

Step-by-step explanation:

I THINK??

The information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

The Side-Angle-Side (SAS) is a triangle congruence theorem that is used to prove that two triangles are congruent to each other if they have two pairs of corresponding congruent sides and a pair of included congruent angles.

The diagram given gives us the following information:

A pair of congruent sides - BD ≅ BD

A pair of congruent angles - <ADB ≅ CDB.

Thus, the information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

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Answer:

Fe2 is elemental iron and Fe2O3 is a compound

Answer:

Step-by-step explanation:

Fe2 is elemental iron and Fe2O3 is a compound of iron and oxygen.

x(5) is approximately equal to 1.466.

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The volume of the sphere is 2144.7cm³.

Given that a sphere with radius 8 cm.

As we all know that the volume of sphere is 4/3πr³.

We will find the volume of sphere by substituting the value of radius in the formula, we get

Volume=4/3 πr³

Now, we will substitute r=8 cm in above formula, we get

V=(4/3)π(8 cm)³

V=(4/3)π(512)cm³

Now, we will simplify this by multiply by 4, we get

V=(2048/3)πcm³

Now, we will simplify it by dividing it with 3, we get

V=682.66π cm³.

As we know, the value of π is 3.14.

So, we will substitute this value and simplify it, we get

V=682.66×3.14

V=2144.66 cm³

Hence, the volume of the sphere when the radius is 8cm is 2144.7 cm³.

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Step-by-step explanation:

2x + 3x = -25

5x = -25

x = -25 / 5

x = -5

Answer:

put 244 add 7e8ue

Step-by-step explanation:

i53838 divede 73838

The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.

EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.

Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.

OM/2 = 6/EP

OM = 6/EP x 2

OM = [tex]6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}[/tex]

The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

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The statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

The statement is given as:

In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.

As a general rule;

If any two angles are congruent in a triangle, then it means that the sides that opposite the two congruent angles are congruent sides.

The above is an illustration of the base angle theorem

The base angle theorem goes hand-in-hand with the isosceles triangle theorem which is illustrated by the given statement

Hence, the statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

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Answer:

-7 i + 43

Step-by-step explanation:

Simplify the following:

(-4 i + 3) (6 i + 7) - (-3 i + 2)

(3 - 4 i) (7 + 6 i) = 3×7 + 3×6 i - 4 i×7 - 4 i×6 i = 21 + 18 i - 28 i + 24 = 45 - 10 i:

(-10 i + 45) - (-3 i + 2)

-(-3 i + 2) = 3 i - 2:

45 - 10 i + (3 i - 2)

45 - 10 i - 2 + 3 i = (45 - 2) + (-10 i + 3 i) = 43 - 7 i:

Answer:  -7 i + 43

Four numbers has a sum of 1764 and the value of one of those numbers is 1029.

Use algebraic expressions to solve for the value of n.

Algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc).

One of the four numbers is already denoted as variable n. Let m be the sum of the three other numbers.

If the sum of the four numbers is 1,764, then:

n + m = 1764

If n is 40% more than the sum of the other three numbers, then:

n = 40% m + m

n = 1.4 m

Substitute n from the 2nd equation to the 1st equation.

n + m = 1764

1.4 m + m = 1764

2.4 m = 1764

m = 735

Recall that n = 1.4 m.

n = 1.4 (735)

n = 1029

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Answer: an acute angle so it bout 55

Step-by-step explanation:

The ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

An ordered pair is defined as a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses.

Ordered Pair = (x, y)

Where;

x = abscissa, the distance measure of a point from the primary axis “x”

y = ordinate, the distance measure of a point from the secondary axis “y”

Thus the ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

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The fence is 33 feet long when measured in yards.

Here,

In order to erect a fence around a rectangular flower garden on his property, Craig has 72 feet of material.

If the fence must be 3 feet in width, then, assuming he uses the entire 72 feet of material, we must determine the fence's length in yards.

What is the rectangle's perimeter?

The rectangle's perimeter is 2 (l + b). l being the length. b=breadth (width).

Now,

A rectangular flower bed should be x feet long.

(Length + Width)2 = the perimeter of a rectangular flowerbed.

72 = 2 (x + 3)

36 = x + 3

x = 33 feet

Hence, The fence is 33 feet long when measured in yards.

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a)

[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]

b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.

c) The confidence interval at 90% would be shown (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

a)

1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.

Since the problem specifies that majority  α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)

Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)

P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.

2) Useful concepts and formulas

The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :

Alternative Hypothesis: p[tex]\geq[/tex] 0.5

Null Hypothesis: p[tex]\leq[/tex] 0.5

The proportion is thought to have a normal distribution.

This test for the percentage of union membership has one tail higher.

Verify whether the sample conforms to the presumptions required for the test to be applied.

a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.

b) The sample size must be sufficient.

[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]

3. Determine the statistic.

The formula used to calculate the statistic is as follows:

[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

According to the alternative hypothesis, the following would be the p value:

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

Using this formula, the confidence interval would be determined.

p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]

With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.

[tex]z_{\frac{\alpha }{2} }=2.58[/tex]

adding the following to the formula for the confidence interval:

[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]

Also provided would be the 90% confidence interval (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.

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Answer:

Step-by-step explanation:

Answer: x=64/7 Step-by-step explanation: 4x+3=64 7x=64

4x=−64

Divide both sides by 4.

x=

4

−64

​

Divide −64 by 4 to get −16.

x=−16

The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

The statement is given as:

5x+3 is greater than or equal to x-9

Express as an inequality

5x + 3 >= x - 9

Collect the like terms

5x - x >= -9 - 3

Evaluate the like terms

4x > = -12

Divide both sides by 4

x >= -3

Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

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Answer:

Step-by-step explanation:

if * means multiplication

the equivalent expression will be :

[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]

If the * means power :

then equivalent expression will be

[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]