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Answer:

x^2 + 7x + 12 = 0

x^2 + 7x  = -12

(+3)(+4)=0

=−3

=−4

I also love r        o      blox

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Answer:

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

Step-by-step explanation:

Given

x² + 7x + 12 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 7x

x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

Answer:

= 5 * NORMINV(RAND(), 35, 5)

Step-by-step explanation:

From the given information:

The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.

Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.

Using the Excel Formula:

The weekly profit can be computed as:

= 5 * NORMINV(RAND(), 35, 5)

Answer:

Below in bold.

Step-by-step explanation:

Perimeter = 2*width + 2*length

So

240 = 2w + 2l

120 = w + l

l = 120 - w

(a) Area = w*l

Substituting for l:

A = w(120 - w)

A = 120w - w^2

(b)

Finding the derivative:

A = 120w - w^2

A' = 120 - 2w

For a maximum area A' = 0, so:

120 - 2w = 0

2w = 120

w = 60 yards for maximum area.

(c)

Maximum area

= 120*60 - 60^2

= 3600 yd^2.

Answer:

The height of the scale model is of 91.14 cm.

Step-by-step explanation:

Scale problems are solved by proportions, using rule of three.

A scale model of a building has a scale of 3 : 79.

This means that 3m on the drawing represent 79m of real height.

The height of the real building is 24 m.

3m - 79m

xm - 24m

Applying cross multiplication

[tex]79x = 72[/tex]

[tex]x = \frac{72}{79}[/tex]

[tex]x = 0.9114[/tex]

In centimeters:

Multiplying by 100:

0.9114*100 = 91.14 cm.

Answer:

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.

This means that [tex]\mu = 100, \sigma = 15[/tex]

Sample of 3

This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]

Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

We have to find the z-score.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]

[tex]Z = 1.73[/tex]

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Answer:

d. higher blood cholesterol causes more severe heart attacks.

Step-by-step explanation:

Two tailed tests are a method for hypothesis testing when data is distributed on the two sides. P value is determined to identify whether the hypothesis is true or false. When rs is 0.89 between blood cholesterols and severity of heart attacks then these is significant relation between them.

Answer:

The correct answer is "(11.69, 29.11)".

Step-by-step explanation:

Given:

[tex]38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4[/tex]

[tex]n=10[/tex]

As per the question,

Mean,

[tex]\bar x=20.40[/tex]

Standard deviation,

[tex]s=12.17[/tex]

or,

[tex]df=10-1[/tex]

    [tex]=9[/tex]

For 95% confidence interval,

[tex]t^*=2.262[/tex]

hence,

The 95% confidence interval will be:

= [tex]\bar x \pm \ t^*\times \frac{s}{\sqrt{10} }[/tex]

By substituting the values, we get

= [tex]20.40 \pm 2.262\times \frac{12.17}{\sqrt{10} }[/tex]

= [tex](11.69, 29.11)[/tex]

Answer:

c.the mean of each data set

Answer:

A

Step-by-step explanation:

9514 1404 393

Answer:

  6 = 6/1 = 12/2 = 18/3

Step-by-step explanation:

The simplest ratio of integers with a value of 6 is ...

  6 = 6/1

We can multiply numerator and denominator by any non-zero integer value to obtain an equivalent:

  6 = 12/2 = 18/3 = -54/-9

Answer:c

Step-by-step explanation:

The equivalent expression is 1 + In 2 - In x.

Given:

[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]

Apply log rule:

[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]

[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]

= ln (2e) - ln (x)

Apply log rule:

[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]

ln (2e) = ln (2) + ln (e)

= ln (2) + ln (e) - ln (x)

Apply log rule:

[tex]$\log _{a}(a)=1$[/tex]

= ln (2)+1-ln (x)

Therefore, the correct answer is option C. 1 + In 2 - In x.

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Answer:

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Step-by-step explanation:

Let the cost of paint set is s.

cost of sketch book = s/2

cost of brush = s/3

Money spent = $ 28 - $ 3 = $ 25

So,

s +  s/2 + s/3 = 25

6 s + 3 s + 2 s = 150

11 s = 150

s = $ 13.64

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Answer:

(h o k) (3) = 3

(k o h) (-4b) = -4b

Step-by-step explanation:

An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.

This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.

Answer:

I. Length, L = 9.552 meters

II. Width, W = 7.96 meters

Step-by-step explanation:

Let the length = L

Let the width = W

Given the following data;

Perimeter = 35 m

Translating the word problem into an algebraic equation, we have;

Length = 1.2W

To find the dimension of the room;

The perimeter of a rectangle is given by the formula;

P = 2(L + W)

Substituting into the formula, we have;

35 = 2(1.2W + W)

35 = 2(2.2W)

35 = 4.4W

Width, W = 7.96 meters

Next, we would find the length of the rectangle;

L = 1.2*W

L = 1.2 * 7.96

Length, L = 9.552 meters

Answer:

1 , -2

Step-by-step explanation:

6x^2 + 6x = 12

6x^2 + 6x - 12 = 0

using middle term break method

6x^2 + (12 - 6)x - 12 = 0

6x^2 + 12x - 6x - 12 = 0

6x(x + 2) - 6(x + 2) = 0

(x + 2)(6x - 6) = 0

either (x + 2) = 0                             OR (6x - 6) = 0

x + 2 = 0

x = 0 -2

x = -2

6x - 6 = 0

6x = 6

x = 6/6

x = 1

therefore , x = 1 , -2

Answer:

No

Not continous at x = 6

Step-by-step explanation:

When x = 6

G(6) = 1/(6 - 6) = 1/0

Dividing by 0 creates a discontinuity

Answer:

$133.20

Step-by-step explanation:

You make 7.20 an hour for 18 1/2 hours. You must multiply to know how much she made that week

7.20/hr = ?/18 1/2 hr

7.20 x 18 1/2

7.20 x 18.5=

133.20

Answer:

a) Japan =0.599

US= 0.006

b) Japan

Variance= 0.475

Standard Deviation =0.69

USA

Variance =2.4

Standard Deviation= 1.55

Step-by-step explanation:

A represents the number of defendants found guilty in Japan in 10 trials

B represents the number of defendants found guilty in US in 10 trials

A represents a binomial function such that n=10,p=0.95 and B represents a binomial function such that n=10,p=0.60

a) Japan: P(A=10)=0.95^10=0.599

US: P(B=10)=0.60^10=0.006

b) Japan:

Expected number of guilty verdicts in 10 trials in Japan =  np=10*0.95=9.5

Variance: Var(A) = np(1-p) = 10*0.95*(1-0.95) = 0.475

Standard Deviation = sd(A)=√0.475=0.69

US:

Expected number of guilty verdicts in 10 trials in USA = np=10*0.60=6

Variance: Var(B)=np(1-p)=10*0.6*0.4=2.4

Standard Deviation sd(B)=√2.4=1.55

Given:

The function is:

[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]

To find:

The values that are NOT in the domain of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]

This function is a rational function and it is defined for all real values of x except the values for which the denominator is equal to 0.

Equate the denominator and 0.

[tex]x^2-25=0[/tex]

[tex]x^2=25[/tex]

Taking square root on both sides, we get

[tex]x=\pm \sqrt{25}[/tex]

[tex]x=\pm 5[/tex]

So, the values [tex]x=-5,5[/tex] are not in the domain of the given function.

Therefore, the correct option is D.

The following statistics which would provide a good comparison between data sets is all of the above and is denoted as option A.

This refers to the branch of science which involves the collection and interpretation of data sets or variables. There are different ways or techniques which are used and they vary according to the features of the data set.

There are statistics which provide a good comparison between data sets include the following below:

This comparison is done so as to to prove that there are no differences between them and other reasons.

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Answer:

so to find the mph of the lorry for the original route we divide 66 by 55 since it 66 is 1.1 of 60

66 divided by 55=1.2

so it takes 1 minutes 12 seconds for the lorry to go a mile

now we multiply 55 by 1.15=63.25

so we divide 66 by 63.25=1.04347826087

so it takes 1 minute and 1 second for the the lorry to go a miles

1 minute 1 second is 59 miles per hour

1 minute 12 seconds is 50 miles per hour

so the lorry travels 9 mph over its expected speed

Hope This Helps!!!

=================================================

Explanation:

distance = rate*time

d = r*t

r = d/t

r = 55/1.1

r = 50

The lorry's original speed is 50 mph when going the original route.

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

Now consider the longer route, which is 15% longer compared to the original 55 mile route. So the longer route is 1.15*55 = 63.25 miles exactly. Or you could say 15% of 55 = 0.15*55 = 8.25 which adds onto the original 55 to get 55+8.25 = 53.25; either way the longer distance is 63.25 miles.

Computing the new rate or speed gets us

r = d/t

r = 63.25/1.1

r = 57.5

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

When traveling the original route, the lorry goes 50 mph. When traveling the longer route, the lorry goes 57.5 mph. This is a difference of 57.5 - 50 = 7.5 mph

Meaning that the lorry must drive 7.5 mph faster on the longer route compared to the shortest route. This is if the driver wants to make the trip in the same 1.1 hour timeframe.

Note: 1.1 hours = 1.1*60 = 66 minutes = 1 hour, 6 minutes.

Answer:

Option B

Step-by-step explanation:

In the given triangle,

Two sides of the triangle measure 2 cm and one side measures 3 cm.

Therefore, in this triangle two sides measuring 2 cm are congruent.

Option B is the correct option.

Answer:

10

Step-by-step explanation:

Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33

Number of pizzas with pepperoni = 29

Number of pizzas with pepperoni and sausage = 15

Pizza with pepperoni only = 29 - 15 = 14

Pizza with sausage only = 33 - 29 = 4

Pepperoni only than sausage only :

14 - 4 = 10

Answer:

2000 meters

Step-by-step explanation:

400 * 5

9514 1404 393

Answer:

  m∠3 = 63°

Step-by-step explanation:

Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.

Angle 1 is an obtuse angle; angle 3 is an acute angle.

  angle 3 = 180° - angle 1 = 180° -117° = 63°

The measure of angle 3 is 63°.

_____

Additional comment

There are a number of applicable theorems describing the different angle relationships. Taken together, they are summarized by the first statement above. For example, we could declare angles 1 and 4 to be "corresponding" (hence, congruent), and angles 4 and 3 to be a "linear pair", hence supplementary. The net result is that angle 1 is supplementary to angle 3, as we said above.

We could also get there via relations between alternate exterior angles, alternate interior angles, consecutive exterior or interior angles, and other ways. While that terminology is useful to understand in some problems, it is largely irrelevant here.

Answer:

Why do we need an order of operations?

Example: In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?

We know there are 14, but how do we write this calculation? If we just write

2 + 3 x 4

how does a reader know whether the answer is

2 + 3 = 5, then multiply by 4 to get 20 or

3 x 4 = 12, then 2 + 12 to get 14?

There are two steps needed to find the answer; addition and multiplication. Without an agreed upon order of when we perform each of these operations to calculate a written expression, we could get two different answers. If we want to all get the same "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.

One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this:

2 + (3 x 4)

The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.

Another example: Calculate 15- 10 ÷ 5

If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13. We need an agreed order.

[tex]\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }[/tex]

Answer:

y = 1(x - 5)² + 3

Step-by-step explanation:

The general formula of a quadratic equation is written as;

y = a(x − h)² + k

Where (h, k) are the x and y coordinates at the vertex.

Our vertex coordinate is (5, 3)

Thus;

y = a(x - 5)² + 3

Now,we are given another coordinate as (8, 12)

Thus;

12 = a(8 - 5)² + 3

12 = 9a + 3

9a = 12 - 3

9a = 9

a = 9/9

a = 1

Thus,the equation is;

y = 1(x - 5)² + 3

An inverse function is y = k/x

replace x and y with the given values:

6 = k/18

Solve for k by multiplying both sides by 18:

k = 108

1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.

[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]

Substitute the values to find k:

[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]

[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]

[tex]\sf\rightarrow{k=(6)(18)}[/tex]

[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]

[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]

[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]

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