Find the function value f(-8)
f(x)=6x-1

angle QRS = 51°

The diagram for the question has been attached to this response.

From the diagram, some circle theorems can be applied.

Circle theorem:

The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any other point on the remaining part of the circle.

From the diagram, QR is the arc and therefore:

∠QSR = 2 x ∠ QTR

Since ∠QTR = 39°

=> ∠QSR = 2 x 39°

=> ∠QSR = 78°

Other theorem:

(i)The base angles of an isosceles triangle are equal.

Triangle QSR is an isosceles triangle, therefore, angles SQR and QRS are equal. i.e

∠SQR = ∠QRS

(ii) The sum of angles of a triangle is 180°. i.e

∠SQR + ∠QRS + ∠QSR = 180°

Since ∠SQR = ∠QRS and ∠QSR = 78°

=> ∠QRS + ∠QRS + 78° = 180°

=> 2(∠QRS) = 180° - 78°

=> 2(∠QRS) = 102°

Divide both sides by 2

=> ∠QRS = 51°

Therefore, angle QRS = 51°

Answer:

5 th day

Step-by-step explanation:

Given :

1st day :

Time = 30 seconds

Time increases by 20% each day :

2nd day = 20% * 30 = (1.20 * 30) = 36 seconds

3rd day = 1.20 * 36 = 43.2 seconds

4th day = 1.20 * 43.2 = 51.84 seconds

5th day = 1.20 * 51.84 = 62.208

First day Aretha hold a plank for over 1 minute is the 5th day

Answer:

1760 cm³

Step-by-step explanation:

Volume For top "trapezoidal" prism : (14 * 4)/2 * 20 = 28 * 20 = 560

Volume for bottom rectangular prism = 6 x 10 x 20 = 60 x 20 = 1200

1200 + 560 = 1760 cm³

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

perimeter of the rectangular ground floor

=2(length+width)

length=X+200

width=X

=2(X+200+X)

=4x+400

4x+400 =780

4x =780-400

4x =380

x =95

width=95 feet

length=95+200

=295 feet

Answer:

The general limit exists at x = 9 and is equal to 300.

Step-by-step explanation:

We want to find the general limit of the function:

[tex]\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))[/tex]

By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.

So, let's find each one-sided limit: the left-hand side and the right-hand side.

The left-hand limit is given by:

Since the given function is a polynomial, we can use direct substitution. This yields:

[tex]=(9)^2+2^7+(9.1\times 10)[/tex]

Evaluate:

[tex]300[/tex]

Therefore:

[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300[/tex]

The right-hand limit is given by:

[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))[/tex]

Again, since the function is a polynomial, we can use direct substitution. This yields:

[tex]=(9)^2+2^7+(9.1\times 10)[/tex]

Evaluate:

[tex]=300[/tex]

Therefore:

[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]

Thus, we can see that:

[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]

Since the two-sided limits exist and are equivalent, the general limit of the function does exist at x = 9 and is equal to 300.

Step-by-step explanation:

Hey there!

Please look your required answer in picture.

Note: In left hand limit always take a smaller near number of the approaching number. For example as in the solution I took the 8.99,8.999 as it is smaller than 9 but very near to it.

And in right hand limit always take a smaller and just greater near number than the approaching number. For example, I took 9.01,9.001 which a just greater but very near to 9.

Hope it helps!

Answer:

Step-by-step explanation:

5x + 150 = 180

5x = 30

x = 6

Hope this help!!!

Have a nice day!!!

Answer:

a. All spy novels are long. S (L)

b. Not every mystery is a spy novel S (x,M)

c. Only mysteries are long M ( L)

d. Spy novels are better than mysteries S B(x, y)

e. Only spy novels are better than mystery S B(x)

Step-by-step explanation:

Spy novels and mystery novels both are long. There is a domain function representing mystery novels is better than spy novels. The spy novel can be long and and better than mystery novels. The symbol representation for spy novel and mystery novel is given in the domain function.

Answer:

X = 11

Step-by-step explanation:

4x - 26 = 18

Add 26 on both sides to get 4x alone.

4x - 26 + 26 = 18 + 26

4x = 44

44 divided by 4 is 11.

Therefore X is 11.

Answer: x=11

Step-by-step explanation:

Add 26 to both sides

4x-26+26=18+26

4x=44

Divide by 4 and get 11

x=11

Answer:

Melissa needs to drive 325 miles for the two plans to cost the same

Step-by-step explanation:

Plan A

Initial Fee = 65

Additional cost per mile = 0.50 per mile

Plan B

Initial Fee = 0

Additional cost per mile = 0.70 per mile

Required

Mile both plans will cost the same

Let

[tex]y \to cost[/tex]

[tex]x \to miles[/tex]

So, we have:

[tex]y = Initial\ Fee + Additional * x[/tex]

For plan A

[tex]y = 65+ 0.50* x[/tex]

[tex]y = 65+ 0.50x[/tex]

For plan B

[tex]y = 0 + 0.70*x[/tex]

[tex]y = 0.70x[/tex]

So, we have:

[tex]y = 65+ 0.50x[/tex] --- plan A

[tex]y = 0.70x[/tex] --- plan B

Both plans will cost the same when

[tex]y = y[/tex]

[tex]0.70x = 65 +0.50x[/tex]

[tex]0.70x -0.50x= 65[/tex]

[tex]0.20x= 65[/tex]

Divide by 0.20

[tex]x= 325[/tex]

Answer:

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Step-by-step explanation:

Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:

[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]

[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]

[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Answer:

(a) = 60

(b) = 70

Step-by-step explanation:

(a) Sum of all the angles of a triangle is 180

This is an equilateral Triangle

which means all the sides are equal since all the sides are equal that means all the angles are equal

[tex]x + x + x = 180 \\ 3x = 180 \\ x = \frac{180}{3} \\ x = 60[/tex]

(b) this is an isosceles triangle with two equal sides that means the two opposite angles are equal

[tex]40 + x + x = 180 \\ 40 + 2x = 180 \\ 2x = 180 - 40 \\ 2x = 140 \\ x = 70[/tex]

Given:

The coordinates of point P are (-5,4).

Point P is reflected over the x-axis.

To find:

The new coordinates after the reflection.

Solution:

If a point is reflected across the x-axis, then the rule of reflection is:

[tex](x,y)\to (x,-y)[/tex]

Using this rule, we get

[tex]P(-5,4)\to P'(-5,-4)[/tex]

The new coordinates of point P after the reflection over the x-axis are (-5,-4).

Therefore, the correct option is B.

Answer:

[tex]5x -2y = -2[/tex]

Step-by-step explanation:

Given

[tex]-2x + y = 0[/tex]

[tex]-7x + 3y = 2[/tex]

Required

Subtract (2) from (1)

This gives:

[tex]-2x - -7x +y - 3y = 0 -2[/tex]

[tex]5x -2y = -2[/tex]

Answer:

111.35

Step-by-step explanation:

effective rate: .085/12= .007083333333333333

payment=x

[tex]3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35[/tex]

Step-by-step explanation:

111.35

Step-by-step explanation:

effective rate: .085/12= .007083333333333333

payment=x

\begin{gathered}3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35\end{gathered}

3000=x(

.007083333333333333

1−(1+.007083333333333333)

−30

)

x=111.35

Answer:

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Rate of 18 customers per hour.

This is [tex]\mu = 18n[/tex], in which n is the number of hours.

10 minute interval:

An hour has 60 minutes, so this means that [tex]n = \frac{10}{60} = \frac{1}{6}[/tex], and thus [tex]\mu = 18\frac{1}{6} = 3[/tex]

What is the probability that more than 4 customers arrive in a 10 minute interval?

This is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex] = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]

And

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.8152 = 0.1848[/tex]

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Answer:

0.2514 = 25.14% of women have HDL below 45 mg/dl or less.

Step-by-step explanation:

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.

Mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl.

This means that [tex]\mu = 55, \sigma = 15[/tex]

What proportion of women have HDL below 45 mg/dl or less?

This is the p-value of Z when X = 45. So

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

[tex]Z = \frac{45 - 55}{15}[/tex]

[tex]Z = -0.67[/tex]

[tex]Z = -0.67[/tex] has a p-value of 0.2514

0.2514 = 25.14% of women have HDL below 45 mg/dl or less.

Answer:

D

Step-by-step explanation:

because in standard form the first number is only up to 10 and above 10 it is decimal places e.g.6.12×10^5

hope this helps u understand :)

Step-by-step explanation:

hear is answer in attachment

Answer:

1.  5 x 47    show tree of 5  x  47 and then stop both are pf

2.  2^2 × 5 × 23   show tree of  10 x 46 and then 2 x 5 (under10) and 2x23 (under 46) and then stop  2,2,5,23 are all pf

3. 2 x 3 x 97   show tree 3 x 194 and 2 x 97 and circle pf 2,3,97

4.  3^3 x 11  show tree of 3 x 99  then 3  x 33 then 3 x 11 to show 3,3,3,11 as pf

5. 3 x 7 x 37 show tree as  777/7  = 111/37 = 3 to show 3,7,37 as pf

6. 2^4 x 3 x 13 show tree as 2 x 312  2 x 156  2 x 78  2 x 39  3 x 13 to show 2,2,2,2,3,13 all as pf

Step-by-step explanation:

Answer:

Answer:

the probability of passing the exam if a student does not use ADAPT is 0.3584

Step-by-step explanation:

Given the data in the question;

Probability a student will pass = 38% = 0.38

Probability a student have used ADAPT = 5% = 0.05

P(passed  | used ADAPT) = 79% = 0.79

Now lets use table

                          Used ADAPT                        Not use ADAPT                 Total

Passed            [0.05×0.79] = 0.0395           [0.38 - 0.0395] = 0.3405     0.38

Not Passed     [0.05-0.0395] = 0.0105        [0.62 - 0.0105] = 0.6095     0.62

Total                             0.05                                      0.95

Now, the probability of passing the exam if a student does not use ADAPT will be;

⇒ P(passed and Not used ADAPT) / P( did not use ADAPT)

⇒ 0.3405 / 0.95

⇒ 0.3584

Therefore, the probability of passing the exam if a student does not use ADAPT is 0.3584

Answer:

Answer:

1. B. (x^2 + 4x)(x)

2. A. (x^3+4x^2)

3. 9

4. 0

5. 1

Step-by-step explanation:

Answer:

Blank = 17/12

Step-by-step explanation:

Blank = 2/3 + 3/4

Blank = 8/12 + 9/12

Blank = 17/12

Let's say your data is all in column A. Furthermore, we'll say we have 21 items in this column. Make sure this data column is sorted from smallest to largest. If this isn't done, then weird things will happen when it comes to connecting the dots later on.

Column B will be used later, but for now, let's move to cell C1. In this cell, type =AVERAGE(A1:A21)

The equal sign is important to tell Excel that we have a function here, and not just plain text. As the function implies, we're finding the average (aka mean) of values A1,A2,...,A20,A21. This computes the arithmetic mean.

In cell D1, type in =STDEV(A1:A21) to compute the sample standard deviation

There's nothing special about C1 or D1. We just need something off to the side. Think of it like scratch work.

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

Now move back to column B. In cell B1, type =NORMDIST(A1,$C$1,$D$1,FALSE)

The $C$1 and $D$1 refer to cells C1 and D1 respectively. The dollar signs lock in those rows and columns so they don't change. We don't want the mean and standard deviation to alter. The "False" at the end tells Excel that we don't want a cumulative normal distribution.

The first parameter A1 is the x value. Much like the curve y = x^2, we plug in various x values to find corresponding y values. We'll plot various (x,y) points to connect them with a curve. The more points, the more accurate the curve. Instead of the x^2 function, we're using the NORMDIST function.

Once cell B1 is filled out, click on the bottom right corner of the cell. You should see a very small square at this corner. Dragging this square down until you reach cell B21 will fill in the remaining 20 cells with the formula mentioned in bold; however, the A1 will change depending on what row you're on. Everything else stays the same hence the use of the dollar signs.

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

In figure 1 below, I'm showing an example of what I've discussed so far. Figure 1 shows the formulas in each cell. This is before they are evaluated.

Figure 2 shows what the formulas evaluate to. The data in column A can be anything you want. I randomly generated the data values between 2 and 17.

Once column B is figured out, you would insert a chart of (x,y) scatter points. Make sure to connect the dots so that a curve forms. This will complete the normal distribution graph. Again, the data in column A must be sorted or else the dots won't be connected properly.

To be perfectly honest, Excel doesn't really do a good job at drawing curves like this. In my opinion, programs like GeoGebra are better suited for the task. Though spreadsheet programs like Excel are still used in a lot of settings, which is why this is good practice.

9514 1404 393

Answer:

  4

Step-by-step explanation:

In order to evaluate f(g(-1)), you first need to find g(-1).

The graph of g(x) crosses the line x = -1 at y = 1, so g(-1) = 1.

The second step is evaluating f(1). The graph of f(x) crosses the line x=1 at y=4, so f(1) = 4.

  f(g(-1)) = f(1) = 4

Given:

The solution of two equation is (3,-6).

To find:

The graphs that shows a pair of lines that represents the equations with the solution (3, −6).

Solution:

In first graph, both line intersect each other at point (-6,3). So, the solution of the pair of lines is (-6,3).

In second graph, both line intersect each other at point (-3,6). So, the solution of the pair of lines is (-3,6).

In third graph, both line intersect each other at point (3,-6). So, the solution of the pair of lines is (3,-6).

In forth graph, both line intersect each other at point (6,-3). So, the solution of the pair of lines is (6,-3).

Therefore, the correct option is C.

Answer:

cos E = 6/10

cos G = 8/10

sin E = 8/10

sin G = 6/10

tan E = 8/6

tan G = 6/8