state whether the following statement is true and explain why or why not: a trinomial is always a higher degree than a monomial.

A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]

Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .

So it is z with a p value of 1-0.02 = 0.98, so z= 2.055

Now, find the margin M as such

[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]

In which [tex]\sigma[/tex]  is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]

Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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In the distribution system, the water  main sizes most commonly in use up to 3.65m to  tiny 12.7mm.

Water pipes come in a variety of sizes, from enormous mains with a diameter of up to 3.65 m to tiny 12.7 mm pipes used to supply individual outlets within a building.

Any pipe or tube intended to deliver drinking water to consumers is referred to as a water pipe. Depending on the situation, water may be treated either before distribution or at the point of use (POU). Water is typically treated before distribution in well-thought-out water distribution networks, and occasionally it is also chlorinated, to prevent recontamination on the way to the end user.

Polyvinyl chloride (PVC), cast iron, copper, steel, and, in older systems, concrete or fired clay are materials frequently used to build water pipes. Long runs of water pipe can be joined together using flange, nipple, compression, or soldered joints (SCOTT 2011).

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Infeasibility is the absence of a solution in the set of solutions to a linear programming models which satisfy all requirements.

If no feasible solution could be created, or if no solution exists that fulfills all of the criteria, then a linear program is infeasible.

Thus, infeasibility is the absence of a solution in the set of solutions to a linear programming models which satisfy all requirements.

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Answer:

I'm sure the answer is 125

Step-by-step explanation:

Hope it helps ; )

In this experimental design, the y variable is the testosterone levels.

A variable is defined as any symbol or letter that is used to express an unknown quantity. There are two types of variables: the dependent variable (y variable) and the independent variable ( x variable).

An independent variable (x variable) is the variable which causes the change in another variable.

A dependent variable (y variable) is the result or effect of that change in the dependent variable.

If we are interested in what happens to testosterone levels as the men age in adult men ages 18 years and older, then the x variable is the age and the y variable is the testosterone levels.

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Answer: x=-3/28

Step-by-step explanation:

isolate x alone and move all other numbers to the right

-2/3x+3/7-(3/7)=1/2-3/7

-2/3x= 1/14

-2/3(-3/2)+x=1/14*-3/2

x=-3/28

Answer:

128 4/7

Step-by-step explanation:

100%-30%=70%

90=.7X

900=7X

128 4/7=X

The value of x for the given linear equation; 3 ( −4x + 5 ) = 12 is; 1 / 4.

It follows from the task content that the value of x in the given linear equation; 3 ( −4x + 5 ) = 12 is to to be determined.

Since the given expression is;

3 ( −4x + 5 ) = 12

By the distributive property; we have;

-12x + 15 = 12

-12x = 12 - 15

-12x = -3

x = -3 / -12

x = 1/4.

Therefore, the required value of x in the given linear equation is; 1 / 4.

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Answer:

[tex]5mn^{2} (2+ 5m^{2} n)[/tex]

Step-by-step explanation:

I assumed the polynomial is [tex]10mn^{2} +25m^{3}n^{2}[/tex]

FIRST: Highlight the common factors{ 5 , m and[tex]n^{2}[/tex])

[tex]5mn^{2} (2+ 5m^{2} n)[/tex]

Answer:

60

Step-by-step explanation:

both triangles are 30 60 90, angle G is made up of 2 30 degree angles

30 plus 30 is 60

Answer:

[tex]120^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem, [tex]x=50^{\circ}+70^{\circ}=120^{\circ}[/tex].

Answer:

Step-by-step explanation:

we know the inside total angles for triangle is 180 degrees.

We are given the two internal angles as 70 and 50 degrees.

So the equation can be written as

70+50+y = 180

y= 60

Also, we know that straight line is 180 degrees.  Now we can write the second equation as follow:

60+x = 180

x = 120 degrees

Answer:

3r < = 4r - 6

3r - 4r < = -6

-r < = -6

r > = 6........it is 6 and 7

Step-by-step explanation:

Answer:

your answer would be 6, and 7.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

0 in the 0nes place but less than 12. more than 6. so it has to be 10.

Answer: A+B+C=π⇒A+B=π−C

Step-by-step explanation: I think not sure hope this helps :)

The perpendicular bisector of the line is option c)

The bisector of the angle YXZ is option B)

The perpendicular from point Z to the line XY is option G)

What is perpendicular bisector?

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

We are asked to find the perpendicular bisector on the line XY

Now this means a segment dividing segment XY in two equal parts and intersecting XY at right angle

Hence This description match with option C)

Hence The perpendicular bisector of the line is option c)

Similarly,

The bisector of Angle YXZ will be the line which divides the angle in two equal parts

This description matches with option B)

Hence the correct option is option B)

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Answer:

5 cms

Step-by-step explanation:

This is assuming that it is equilateral and that n is the length of one side

Answer:

See below

Step-by-step explanation:

This is the slope formula.  Do they give you two points?  If they give you two points like (2,3 ) and (5,7)  You subtract the y's over the subtraction of the x's

An ordered pair is in the form (x,y)  

So in the example that I give the y's are 7 and 3 and the x's are 5 and 2

[tex]\frac{7-3}{5-2}[/tex] = [tex]\frac{4}{3}[/tex]

I am thinking that they gave you two points and they want you to find the slope.

Answer:

Step-by-step explanation:

Ok so this is how to find slope of a line that passes through 2 points.

(x1,y1) and (x2,y2)

and to find the slope of the line (m) you have to do (y2-y1)/(x2-x1)

you just have to plug in the points

Answer:

9 · (x - 2)

Step-by-step explanation:

Since the problem tells us to let "a number" be the letter x, let's rewrite the sentence to include x instead of the term "a number". Doing so gives us the sentence "The product of 9 and the difference of x and 2."

Step 1: Multiplication

Now, let's work from left to right. The first word we see is "product", which refers to the operation of multiplication, as this term is used to describe the resultant quantity from multiplying 2 numbers. From the sentence, we see that the two terms we are multiplying are "9" and "the difference of x and 2". Note that we include the difference in one of our terms because of the structure of the sentence  - we usually describe a product as being a product of [one term] and [another term] as it is here.

To denote multiplication, we can use the symbol "×", but to avoid confusion between this symbol and the letter x, let's use the symbol "·". Now, we have the expression 9 · (the difference of x and 2).

Step 2: Subtraction

We still aren't done, however, because we still have some words left to "translate" into algebra. The use of the word "difference" tells us that the operation to be used is subtraction, as this term is used to describe the resultant quantity from subtracting 2 numbers. Again, the sentence tells us that the terms we are subtracting are x and 2, but which order do they go in? (This is important to consider because unlike multiplication, subtraction is not a commutative property - in other words, a - b does not necessarily equal b - a, but a · b always equals b · a.)

To answer this question, we refer again to the sentence. When dealing with a non-commutative operation, we write out the terms in the order they appear in. Therefore, "the difference of x and 2" can be represented as x - 2 (note that we use the "-" symbol as we are subtracting quantities).

Step 3: Combine the 2 Operations

Putting all of this information together, we get the algebraic expression of 9 · (x - 2). Remember to put x - 2 in parentheses, otherwise it looks like we are multiplying 9 and x and then subtracting 2 from that quantity, which is not what our original sentence was.

The probability which motor cycle owns for sample is 0.0001

What is Sample ?

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

Given,

p= 14% or 0.14

p bar = 20% or 0.20

n=500

The mean of the sample distribution of p bar is equal to the population proportion p

µp = p =0.14

The standard deviation of sample distribution of p bar is

σp = [tex]\sqrt{p(1-p}/n[/tex]

= [tex]\sqrt{0.14(1-0.14}/500[/tex]

= 0.0155177

the z score is the value decreased by the mean, divided by the standard deviation:

z =x- µ/σ

= 0.20-.014/0.0155177

=3.87

so the corresponding probability will be

P(p>20%) = P(z>3.87) = P(Z<-3.87) = 0.0001

The likelihood that a motorcycle is present in the sample is 0.0001.

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The approximate of [tex]f_{x}(3,5)[/tex] ≈ 4

We have to find an approximate of [tex]f_{x}(3,5)[/tex]  using the contour diagram, x and y, which was shown below. The slope of a second line is used to estimate the x and y direction. The curl f divides by the curl x is almost equal to the delta x. At the point of x, 13 is equal to 17 and 2 is equal to 18. The points are in a diagram. The curly f divides by curly x is equal to the delta f divided by delta x, which is 18 minus 17 divided by 2 minus 1. The value of a f is equal to 1. From here we can say that f of x 13 is equal to 1.

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The number of seconds will it take the ball to hit the ground will be 2.078 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given,

h(t)=-16t² + 14t + 40

The time when the ball hit the ground h(t) = 0

-16t² + 14t + 40 = 0

-8t² + 7t + 20 = 0

8t² - 7t - 20 = 0

t = (7 ± 26.25)16

t = 2.078 seconds

Since time can never be negative thus, 2.078 seconds will be correct.

Hence "The number of seconds will it take the ball to hit the ground will be 2.078 seconds".

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Order of Operations: BPEMDAS

Functions

Compounded Interest Rate Formula:
[tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^t[/tex]

Let's compile what we know (what we are given).

An investment of $500 means that our principle amount P equals 500.

2.8% nominal yearly interest means that our rate r equals 0.028.

Compounded quarterly means that our compounded rate n equals 4.

So, we have:

[tex]\displaystyle\begin{aligned}P & = 500 \\r & = 0.028 \\n & = 4 \\\end{aligned}[/tex]

In order to find an equation that models the final amount A in terms of t years, we can simply substitute in our known variables:

∴ our equation that models the amount A the investment is worth t years after the principle has been invested is:

[tex]\displaystyle \boxed{ A = 500(1.007)^t }[/tex]

___

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___

Topic: Algebra I

Unit: Interest Rate Formulas

There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

H0:p1=0.5,p2=0.3,p3=0.2

Ha:At least one proportion is different from the stated proportions.

Null hypothesis indicate that proportions are same as stated.

Product observed(fo) pi Expected(fe) (fo-fe)^2/fe

Whole 74 0.5 154.50 41.943

Universal 71 0.3 92.70 5.080

Annuities 164 0.2 61.80 169.010

Total 309 1 309 216.033

Expected value for the number of customers who prefer Whole Life=309*0.5=154.50

Expected value for the number of customers who prefer Universal Life=309*0.3=92.70

Test statistic:

Chi square=216.033

df=3-1=2

critical Chi square value=CHIINV(0.01,2)=9.210

Reject the null hypothesis

Therefore, There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

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The flux = 0

According to the divergence theorem, the volume integral of the divergence of a vector point function "F" taken over the volume "V" encompassed by the surface "S" is equal to the surface integral of the normal component of F taken over the closed surface "S." As a result, the divergence theorem is symbolically represented as:∬ v ∫ ▽ F → .

The sphere is presumably closed, so we can use the divergence theorem.

▽ F  =d(xy)/dx + d(yz)/dy + d(zx)/dz

▽ F =x + y + z

Now convert to spherical coordinates:

x=ρsinφcosθ,

y=ρsinφsinθ,

z=ρcosφ

The flux is then given by the volume integral for the radius 6

[tex]\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} = 36 }[/tex]   f.ds = [tex]\int\limits\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} < =36 }[/tex] (x+y+z) dv

Thus the flux = 0

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16/25 as a percentage is 64%.

The number in the denominator is the one below the fraction line, while the number in the numerator is the one above the fraction line.

When we talk about percentages, we really mean that it's a subset of 100. Since the word "percent" refers to a hundred, 50% is equivalent to expressing 50/100 or 5/10 in fractional form.

Therefore, since 25 is the denominator in 16/25, we might change the fraction so that 100 is the denominator.

To do that, we divide 100 by the denominator:

100/25 = 4

Once we have that, we can multiply both the numerator and denominator by this multiple:

[tex]\frac{16}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{64}{100}[/tex]

Now we can see that our fraction is 64/100.

Thus, 16/25 as a percentage is 64%.

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Answer: 312=(2)(2)(2)(3)(13)

Step-by-step explanation:

312  |  2

156  |  2

78   |  2

39   |  3

13    | 13

Hence, 312=(2)(2)(2)(3)(13)

The value of x and y are (11.66,5)

Given that,

3x-30=y-----------1

7y-6=3x-----------2

Now, putting the value of equation 1 in equation 2 we get

⇒7(3x-30)-6=3x

⇒21x-210=3x

⇒21x-3x=210

⇒18x=210

⇒x=11.66

now put the value of x in equation 1 we solved earlier we get

⇒3×11.66-30=y

⇒35-30=y

⇒y=35-30

⇒y=5

Therefore the value of x is 11.66 and the value of y is 5

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A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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