Suppose Event A is taking 15 or more minutes to get to work tomorrow and Event B is taking less than 15 minutes to get to work tomorrow. Events A and B are said to be complementary events.

a. True
b. False

Answer:

They are equal

Step-by-step explanation:

4.5% is 0.045 in decimal form

Answer: They are equal

Step-by-step explanation:

I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent  (move it two spots to the right).

Answer:

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

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 - 0.98}{2} = 0.01[/tex]

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

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error 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.

[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

Supplementary angles are those angles which make a sum of 180°.

Complementary angles are those angles which make a sum of 90°.

The supplementary angles are given by the straight lines making angles of 180°.

There are two straight lines CB and DE

The angles DAF and FAE are the two angles making a straight line DE

The angles CAF and FAB are the two angles making a straight line CB

The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.

Angle BAF is formed by angle BAE and angle AEF

Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.

Complementary Angle BAF is formed by angle BAE and angle AEF.

https://brainly.com/question/12919120

Answer:

Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]

Step-by-step explanation:

Given that,  

Point estimate = sample mean = [tex]\bar x[/tex] = 88.34  

sample standard deviation = s = 19.22  

sample size = n = 14  

Degrees of freedom = df = n - 1 = 13  

Critical value =[tex]t\alpha /2,[/tex] df = 1.771

Margin of error

[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]  

Margin of error = E = 9.10  

The 90% confidence interval estimate of the population mean is,  

[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]

Answer:

We can construct a 90º angle either by bisecting a straight angle or using the following steps.

Step 1: Draw the arm PA.

Step 2: Place the point of the compass at P and draw an arc that cuts the arm at Q.

Step 3: Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.

Step-by-step explanation:

Answer:

13.5% is the increase in percentage

Answer:

74%

Step-by-step explanation:

To get the answer, divide 800 by 1080, and you will get a decimal. That decimal is 0.74074074074. Then, move the decimal point two times two the right, so you should have 074.074074074. Ignore everything after the decimal point as well as the 0 before the decimal point, and if done correctly, it should be 74%.

So, the final answer would be 74%.

Hope this helped!

Answer:

f(x) is compressed horizontally

Step-by-step explanation:

Given

[tex]f(x) = \log(4x)[/tex]

[tex]g(x) = f(13x)[/tex]

Required

The effect on f(x)

[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.

So, we have:

[tex]f(13) = \log(4 * 13x)[/tex]

[tex]f(13) = \log(52x)[/tex]

So:

[tex]g(13) = \log(52x)[/tex]

Answer:

A. -510

Step-by-step explanation:

We are given the variable values:

Geometric series formula:

[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]

Plugging in values we have:

[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]

Simplifying the equation we are left with:

[tex] \frac{ - 2(255)}{1} = - 510[/tex]

Answer:

-243

Step-by-step explanation:

(-3) (-3) (-3) (-3) (-3) = - 243

[tex]\frac{1}{-243 }[/tex]

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Answer:

6

Step-by-step explanation:

You have 2 conditions.

1. The digits must be different.

2. The digits must add to 7.

There aren't very many

124

142

214

241

412

421

That's it. That's your answer. There are 6 of them

Answer: the numbers are 10 and 5

Step-by-step explanation:

10 times 5 is 50

10 plus 5 is 15

Step-by-step explanation:

Given, x = 5

y = 5

= 6(5)^2 +7(5)(5) +3(5)

= 6(25)+7(25) +15

= 150+175 + 15

= 150 + 190

=340

Answer:

x = 12 y = 7

Step-by-step explanation:

6x^2 + 7xy + 3y

6(5)^2+ 7(5) + 7(8)y

6(5+5)+25+35 + 7(8)-7y

60+25+35+ 56-7y

y - 5 = 120 + 35 - 5 (+49y)

sqrt 150 + sqrt 49

x = 12 y = 7

Answer:

x=12

Step-by-step explanation:

each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle

ex: 8*4=32 and 17*4=68

so we can assume that 15*4= 4x+12

60=4x+12

48=4x

x=12

Answer:

x = 12

Step-by-step explanation:

The triangles are similar so we can use ratios

4x+12      32

-------  = ------------

15             8

Using cross products

(4x+12) *8 = 15 * 32

(4x+12) *8 = 480

Divide each side by 8

(4x+12) *8/8 = 480/8

4x+12 = 60

Subtract 12 from each side

4x+12 -12 = 60-12

4x = 48

Divide by 4

4x/4 = 48/4

x = 12

Answer:

28

Step-by-step explanation:

78

Answer:

Answered March 20, 2021

This is a right angle triangle where the hypotenuse a^2 = b^2 + c^2

= 15^2 + 8^2 = 225+64= 289

289= 17^2

17 = hypotenuse

The sine of an angle is the ratio of the shortest side to the hypotenuse

= 8/17= 0.4705

sine^-1 0.4705 = 28°

Terminal point for 4π/3

(cos4π/3 ,sin4π/3)

{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)

or ,(- 1/2, -√3/2)

OPTION C

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on

Given:

The function is:

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

To find:

The graph of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

It can be written as:

[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]

[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]

[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]

Putting [tex]x=0[/tex] to find the y-intercept.

[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]

[tex]f(0)=\dfrac{-5}{3}[/tex]

So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].

Putting [tex]f(x)=0[/tex] to find the x-intercept.

[tex]0=\dfrac{-2x-5}{x+3}[/tex]

[tex]0=-2x-5[/tex]

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

[tex]x=\dfrac{-5}{2}[/tex]

[tex]x=-2.5[/tex]

So, the x-intercept is [tex]-2.5[/tex].

For vertical asymptote, equate the denominator and 0.

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

So, the vertical asymptote is [tex]x=-3[/tex].

The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.

[tex]y=\dfrac{-2}{1}[/tex]

[tex]y=-2[/tex]

So, the horizontal asymptote is [tex]y=-2[/tex].

End behavior of the given function:

[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]

[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]

Using all these key features, draw the graph of given function as shown below.

Answer:

The Answer Is A.

Step-by-step explanation:

Answer: 1865

Step-by-step explanation:

Given

Claimed strains of virus is 1700

If it is increased by 9.7%

Estimated value can be given by

[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]

Thus, the estimated number is [tex]1865[/tex]

Answer:

76 degrees

Step-by-step explanation:

First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.

The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that

55 feet/ sin(29 degrees) = 110 / sin(largest angle).

If we say that the largest angle is equal to x, we can say

55 / sin(29°) = 110/sin(x)

multiply both sides by x to remove a denominator

55 * sin(x)/ sin(29°) = 110

multiply both sides by sin(29°) to remove the other denominator

55 * sin(x) = 110 * sin(29°)

divide both sides by 55 to isolate the sin(x)

sin(x) = 110 * sin(29°) / 55

For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say

x = arcsin(110 * sin(29°)/55)

x ≈ 76 degrees

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Answer:

one solution.. your answer is correct

Step-by-step explanation:

discriminate = 900 - (4*9*25)  = 0

thus only one solution

Answer:

Step-by-step explanation:

Step-by-step explanation:

I think something went wrong with the answer options you provided. and maybe with the problem statement itself.

I see 3 function definitions.

I can tell you what they are and use the provided option phrasing as closely as possible :

h(x) = 0 is a horizontal line (in fact the x-axis)

k(x) = 4x² + 312 is a parabola with the opening upwards

f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)

Answer:

Hari saves $ 10,320 in a year.

Step-by-step explanation:

Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:

100 - 80 = 20

4300 x 0.20 x 12 = X

860 x 12 = X

10320 = X

Therefore, Hari saves $ 10,320 in a year.

The shapes are the same size. Match the sides.

3x -1 = 17

Add 1 to both sides:

3x = 18

Divide both sides by 3:

X = 6

2y = 16

Divide both sides by 2

Y = 8

Answer: x = 6, y = 8

Answer:

12.9 miles

Step-by-step explanation:

Formula: (x/360)×dπ(circumference)

90/360=1/4

1/4×16.4π

1/4×51.496

12.874

Answer:

[tex]m JM=90 =\Theta[/tex]

[tex]Radius=dimeter/2=16.4/2[/tex]

[tex]\longrightarrowr=8.2[/tex]

The length of arc JM=

[tex]=\frac{\Theta }{360} \times\pi r[/tex]

[tex]=\frac{90}{360} \times2\times\ 3.14\times 8.2[/tex]

[tex]=12.874[/tex]

[tex]\approx 12.9 \; miles[/tex]

[tex]OAmalOHopeO[/tex]