in the diagram, find the values of a and b.​

Answer:

A: 19

Step-by-step explanation:

For this, we can complete the square. We first look at the first 2 terms,

t^2 and -6t.

We know that [tex](t-3)^2[/tex] will include terms.

[tex](t-3)^2 = t^2 - 6t + 9[/tex]

But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:

[tex]m(t) = (t-3)^2 - 9 +28[/tex]

[tex]m(t) = (t-3)^2 +19[/tex]

Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.

Answer:

The present value is  [tex]PV = \$ 396,987[/tex]

Step-by-step explanation:

From the question we are told that

   The  interest payment per year is  [tex]C = \$ 85[/tex]

    The principal payment is  [tex]P = \$ 1000[/tex]

     The  duration is  n =  8   years

      The  interest rate is  [tex]r = 10\% = 0.10[/tex]

The present value is  mathematically represented as

      [tex]PV = [ \frac{C}{r} * [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n} ][/tex]

substituting values

      [tex]PV = [ \frac{85}{0.10} * [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8} ][/tex]

      [tex]PV = \$ 396,987[/tex]

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Answer:

2x + 5y + 15

Step-by-step explanation:

add like terms

(x+x) + (y+y)+3y+15

2x+2y+3y+15

2x + 5y + 15

i hope this helps!

Answer:

A. they are parallel because their slopes are equal.

Step-by-step explanation:

edge 2020

Answer:

its A in egde

Step-by-step explanation:

Answer:

Step-by-step explanation:

Decay of carbon - 14 is exponential in nature . It decays as follows .

[tex]N=N_0e^{-\lambda t}[/tex]  λ is called decay constant .

λ = .693 / T where T is half life .

Half life of carbon-14 is 5700 years

λ = .693 / T

= .693 / 5700

= 12.158 x 10⁻⁵ year⁻¹

[tex]N=N_0e^{-\lambda t}[/tex]

N = .71 N₀

[tex].71 N_0 =N_0e^{-\lambda t}[/tex]

[tex].71 =e^{-\lambda t}[/tex]

Taking ln on both sides

ln .71 = - λ t

ln .71 = - 12.158 x 10⁻⁵  t

-0.3425 =  - 12.158 x 10⁻⁵  t

t = .3425 / 12.158 x 10⁻⁵

2817  years .

Answer:

3 and 2

Step-by-step explanation:

I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.

Answer:

D

Step-by-step explanation:

-0.81 is a high negative correlation, which means the y is decreasing with x increasing, which means y(the number of broken glass) decreases when x(amount of paper used) increased. So we can say that the toilet paper is surely helping.

make me brainly if you find it correct

Answer:

n=1

Step-by-step explanation:

93/28=15/4n-5+4 4/7

93/28=15/4n-5+32/7

93/28=15/4n-35+32/7

93/28=15/4n-3/7

93/28+3/7=15/4n

15/4n=93*7+28*3/28*7

15/4n= 651+84/196

15/4n=735/196

15/4n*4/15=753/196*4/15

n=49/49

n=1

Answer:

5/14

Step-by-step explanation:

You multiply the recripricoal in division problems:

5/2  ÷ 7/1 =

5/2 × 1/7 =

5/14

Answer:

5 / 14

Step-by-step explanation:

will make it simple... the technique is to flip the either 5/2 or 7/1

then multiply.

5/2 x 1/7 = 5 / 14

Answer:

683,280 hours is what I caculated. Is that right?

Step-by-step explanation:

Answer:

There are (365 x 24) hours for each year.

and 365 x 24 are 8760.

and 8760 x 78 are 683,280.

so, the average person does not live at least 1 Million hours, but they live more than 500 thousand hours, or 5 x 10^5 hours.

Hope it helps!

Bye!

P.S. Please give me Brainliest...

I desperately need one more Brainliest...

Answer:

_

3.126

Step-by-step explanation:

Bar notation is a way in Mathematics to write decimal number that are repetiting or infinite.

Bar notation symbol is – is placed above the first decimal number that repeats itself. It is easier than writing the same repeating number and over again. It tells us that this particular number with the bar over it, is repeated continuously till infinity

From the above question, we were asked to write 3.126666666666... using Bar notation

_

3.126666666666... = 3.126

The bar is placed over the digit 6

Answer:

Step-by-step explanation:

answer is c just took test

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Step-by-step explanation:

Represent the bus average speed with x and the motorcycle average speed with y

Given

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

Distance covered by bus = 165 miles

Distance covered by motorcycle in same time = 155 miles

Required

Determine the speed of each

Average Speed is calculated as;

[tex]Average\ Speed = \frac{Distance}{Time}[/tex]

Since the two are measured with the same time, represent time with T

For the bus

[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes

[tex]x = \frac{165}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{165}{x}[/tex]

For the motorcycle

[tex]y = \frac{155}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{155}{y}[/tex]

Since, T = T; we have that

[tex]\frac{165}{x} = \frac{155}{y}[/tex]

Cross Multiply

[tex]165y = 155x[/tex]

Substitute [tex]x = y + 2[/tex]

[tex]165y = 155(y+2)[/tex]

Open Bracket

[tex]165y = 155y - 310[/tex]

Collect Like Terms

[tex]165y - 155y = 310[/tex]

[tex]10y = 310[/tex]

Divide both sides by 10

[tex]y = 31[/tex]

Recall that [tex]x = y + 2[/tex]

[tex]x = 31 +2[/tex]

[tex]x = 33[/tex]

Hence;

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Answer:

B

Step-by-step explanation:

Option A:

1.50÷18≈0.0833

3.00÷36≈0.0833

4.50÷54≈0.0833

Option B:

0.75÷15=0.05

Option C:

2.20÷15=0.146

Answer:

No

Step-by-step explanation:

The square root of 65 is irrational.

It is not a rational number because 65 is not a perfect square.

The square root of 65 is 8.06225775...

The square root of 65 is not a rational number.

65 is not a perfect square which means it's impossible to

find a whole number times itself to give us 65.

On a calculator if you type in the square root of 65,

you will get an infinite decimal number.

The decimal values never end and never have same repeated pattern.

Answer:

Option (1)

Step-by-step explanation:

Given question is incomplete; find the picture of the graph in the attachment.

Parent function f(x) = [tex]\frac{1}{2^x}[/tex]

When function 'f' is translated by 4 units up which is evident form the graph, the translated function obtained is,

g(x) = f(x) + 4

g(x) = [tex]\frac{1}{2^x}+4[/tex]

Therefore, Option (1). [Translation of 4 units up] is defined by the graph attached.

Answer:

Option (1)

Step-by-step explanation:

Answer: intersecting lines

Step-by-step explanation:

Answer:

The relationship of the lines would be Parallel.

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

Answer:

  -5/7

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = ( -1 -4)/(5 - -2)

   = (-1-4)/(5+2)

   -5/7

Slope formula: y2-y1/x2-x1

= -1-4/5-(-2)

= -5/7

Best of Luck!

Answer:

C. 1/4

Step-by-step explanation:

Parallel lines always have the same slope.

Answer:

  C.  1/4

Step-by-step explanation:

Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.

Answer:

The sample required is  [tex]n = 135[/tex]

Step-by-step explanation:

From the question we are told that

     The  standard deviation is  [tex]\sigma = 9[/tex]

      The margin of error is [tex]E = 2[/tex]

Given that the confidence level is  99%  then the level of  significance is mathematically evaluated as

         [tex]\alpha = 100-99[/tex]

        [tex]\alpha = 1 \%[/tex]

        [tex]\alpha = 0.01[/tex]

Next we will obtain the critical value  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference  math dot armstrong dot edu) , the value is  

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58[/tex]

The  sample size is mathematically represented as

          [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

substituting values

           [tex]n = [ \frac{ 2.58 * 9 }{2} ]^2[/tex]

            [tex]n = 135[/tex]

Answer:

150<60+30n

Step-by-step explanation:

150 is the maximum amount that she can spend on gas. (which is the total)

she already spend $60

each fill up (n) costs 30

Answer:

the answer is B)

Step-by-step explanation:

Answer:

the slope of the read line is also -2

Step-by-step explanation:

Answer:

[tex]P(Dogs) = 0.2025[/tex]

Step-by-step explanation:

Given

[tex]Proportion, p = 45\%[/tex]

Required

Probability of two people having dog

First, we have to convert the given parameter to decimal

[tex]p = \frac{45}{100}[/tex]

[tex]p = 0.45[/tex]

Let P(Dogs) represent the required probability;

This is calculated as thus;

P(Dogs) = Probability of first person having a dog * Probability of second person having a dog

[tex]P(Dogs) = p * p[/tex]

[tex]P(Dogs) = 0.45 * 0.45[/tex]

[tex]P(Dogs) = 0.45^2[/tex]

[tex]P(Dogs) = 0.2025[/tex]

Hence, the probability of 2 people having a dog is [tex]P(Dogs) = 0.2025[/tex]

Answer:

The graph which shows the line y-1=2(x+2) is shown in the attachment

Answer:

a.0.375

b.0.125

c.0.375

1.0.375

2.0.125

3.0.375

Step-by-step explanation:

a.

The total events in a sample space are n(S)=8

The events that contains exactly two boys

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.

Let A be the event that there are exactly two boys. Thus, n(A)=3.

So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.

b.

The event that contains exactly 0 girls.

Boy Boy Boy

Let B be the event that contains exactly 0 girls. Thus, n(B)=1.

So, probability of exactly 0 girls is

P(B)=n(B)/n(S)=1/8=0.125.

c.

The events that contains exactly 1 girl.

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy

Let C be the event that contains exactly 1 girl. Thus, n(C)=3.

So, probability of exactly 1 girl is

P(C)=n(C)/n(S)=3/8=0.375.

Q1 is same as part a.

Q2 is same as part b.

Q3. is same as part c

Answer:

The previous palindrome date in all formats came 909 years ago on 11/11/1111. The next will come in 101 years on 12/12/2121 and after that there will not be another until 03/03/3030.

It depends how you format the date. If you do mm/dd/yyyy format

mm = month

dd = day

yyyy = year

then the last palindromic date was September 10th, 2019 since this would be written as 9/10/2019 in the mm/dd/yyyy format

Taking out the slash symbols, we have the number 9102019 which is the same when we reverse the digits.

The answer will be different if you have the date format as dd/mm/yyyy