Do the table and the equation represent the
same function?
y = 390 + 11(x)

Answer:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.635,0.082)[/tex]  

Where [tex]\mu=0.635[/tex] and [tex]\sigma=0.032[/tex]

We are interested on this probability

[tex]P(X<0.4375)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

Learn more about horizontal asymptotes here -

https://brainly.com/question/14357352

#SPJ2

Answer:

c

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

15.75

▹ Step-by-Step Explanation

3 ÷ 4 = .75

15 + .75 = 15.75

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:  m∠BAC =36.87°

It is given, but maybe difficult to see.

Step-by-step explanation: If you had to calculate it yourself, you need a scientific calculator or a conversion chart. You could figure the sine by dividing the  length of the opposite side, 6 by the length of the hypotenuse, 10. you get sine=0.6  

Then use the calculator or chart to get the angle.

input sin^-1 (0.06)

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Answer:

6 x 10⁶ or 6,000,000

Step-by-step explanation:

100 × (200 × 300)

100 x 60,000 → 6,000,000

6,000,000 → 6 x 10⁶

Hope this helps! :)

Answer:

The expected number of the people at the reception whose favorite snack will be chips is 1152

Step-by-step explanation:

Given

The data in the above table and

Reception = 3600

Required

Predict the number of the people at the reception whose favorite snack will be chips.

The first step is to determine the total number of samples;

[tex]Total = Brownies + Cookies + Chips + Other[/tex]

[tex]Total = 32 + 22 + 56 + 65[/tex]

[tex]Total = 175[/tex]

The next step is to determine the fraction of people whose favorite is chips

[tex]Fraction = \frac{Chips}{Total}[/tex]

[tex]Fraction = \frac{56}{175}[/tex]

The product of the above fraction and the expected number of people in the reception is the solution to this question;

[tex]Expected\ Number = \frac{56}{175} * 3600[/tex]

[tex]Expected\ Number = \frac{56* 3600}{175}[/tex]

[tex]Expected\ Number = \frac{201600}{175}[/tex]

[tex]Expected\ Number = 1152[/tex]

Hence, the expected number of the people at the reception whose favorite snack will be chips is 1152

Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

84%

Step-by-step explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

[tex]P_1 = 20\% * 60\% = 12\%[/tex]

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

[tex]P_2 = 80\% * 90\% = 72\%[/tex]

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

[tex]P = P_1 + P_2[/tex]

[tex]P = 12\% + 72\% = 84\%[/tex]

Answer:

Total distance= 15.055 unit

Step-by-step explanation:

Distance between the first journey i.e from her office to the supermarket is calculated as follows given the coordinates.

(-5,-7) and (4,-6)

The distance between those tow points

Is

= √((4-(-5))² +( (-6)-(-7))²)

= √(9²+1²)

= √ 81+1

= √ 82

= 9.055

Noe the distance between the second journey traveled i.e from the supermarket to her house is calculated as follows given the coordinates.

(4,-6) and (-2,-6)

Distance= √((4--2)² +( -6--6)12

Distance = √(4+2)² + 0

Distance = √ 6²

Distance = 6

Total distance= 9.055 + 6

Total distance= 15.055

Answer:

[tex]Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

Step-by-step explanation:

Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

and which in our case, we can obtain the following:

[tex]y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }[/tex]

Recall as well that [tex]0\leq x\leq 5[/tex], which gives us the limits of integration:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

If we compare it with the geometry formula:

Lateral surface of cone = [tex]\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }[/tex]

which is exactly the expression we calculated with the integral.

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Answer:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=25, p=0.85)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Answer:

Prime number

Step-by-step explanation:

A prime number has 2 factors.

A composite number has more than 2 factors.

47 has the factors 1 and 47.

47 is a prime number.

Answer:

47 is prime.

Step-by-step explanation:

Its factors are 1 and 47.

If a number has only 2 factors, then it's prime.

Answer:

all squares are quadrilaterals

Answer:

The two equations that can be used to find each of their ages are [tex]x=4 \times y[/tex] and [tex]x+y=60[/tex] .

Step-by-step explanation:

We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.

Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.

Now, according to the question;

                                     [tex]x=4 \times y[/tex]   ----------------- [equation 1]

                                 [tex]x+y=60[/tex]

                                [tex]4y + y = 60[/tex]     {using equation 1}

                                  [tex]5y=60[/tex]

                                   [tex]y=\frac{60}{5}[/tex]

                                   y = 12 years

Now, putting the value of y in equation 1 we get;

                               [tex]x=4 \times y[/tex]

                               [tex]x= 4 \times 12[/tex] = 48 years

Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.

Answer:

Mrs. Lang is 48 and her daughter is 12 years old.

Step-by-step explanation:

Answer:

z = 1.476

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.86}{2} = 0.07[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]

The answer is z = 1.476

Answer:

Q9 X=42.5

Step-by-step explanation:

let unknown angle be x

cos x=45/61

X=cos^-1 45/61

X=42.463...

X=42.5 (1 decimal place)

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

The slope greater than one would be the last image, because for every step in x, you get more than one y step.

The slope between 1 and 0 would be the second image

And the slope less than 0 would be the third image

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:  x = 4

4x - 6=10

4x = 10 + 6

4x = 16

[tex]x = \frac{16}{4}[/tex]

x = 4  ←  the missing value

Therefore the the solution is (4,-6) of the equation 4x+y=10 .

Hope this helped You!

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

Answer:

D

Step-by-step explanation:

Parallel lines are those that have the same slope, or coefficient of x.

Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):

slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6

So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.

The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.

Here, our slope is 5/6 and our given point is (12, -2). So plug these in:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-2)=(5/6)(x-12)[/tex]

[tex]y+2=\frac{5}{6} x-10[/tex]

[tex]y=\frac{5}{6} x-12[/tex]

This matches D, so we know that it's the correct answer.

~ an aesthetics lover

The answer is D I just took the test

Answer:

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Step-by-step explanation:

[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The quadratic formula is honestly the most straightforward way of solving here.

Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:

1) a=1, b=0, c=8

This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)

2) a=-9, b=4, c=-10

This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.

3) a=1, b=8, c=17

This reduces to x=(-4+i), (-4-i)

So those are the answers for each.

Please Refer to the screenshot. Hope this helps!

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.