ITUTUS
Every day a school bus driver passes the same traffic light twice, once before school and once after.
Each time he passes the light, he records if it is red, green, or yellow.
Here is a summary of the data he got after 150 days.
Traffic light
before school
Traffic light
after school
Number of days
red
red
13
red
green
17
red
yellow
23
green
red I
11
green
green
10
green
yellow
17
yellow
red
24
yellow
green
21
yellow
yellow
14
Suppose the driver will continue recording the colors for 50 more days.
In how many of these 50 days will the light be yellow at least once? Use the data to make a prediction.
Х
$
?​

Answer:

13/3

Step-by-step explanation:

To find the mean of a data set, you must add all the given numbers and then divide the numbers by how many numbers there are.

3+5+4+3+5+6=26/6=4.3333...

When we convert the answer from a decimal to a fraction, we get 13/3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

x=3

Step-by-step explanation:

f(x) = 2^x

Let f(x) =8

8 = 2^x

Rewriting 8 as 2^3

2^3 = 2^x

The bases are the same so the exponents are the same

3=x

Answer:

A. 3

Step-by-step explanation:

y = 2^x

y = 8

Plug y as 8 in the first equation.

8 = 2^x

Make the left side of the equation with a base of 2.

2^3 = 2^x

Cancel bases.

3 = x

Answer:

x² - 2x - 8

Step-by-step explanation:

Algebra tiles are tiles used to represent variables or numbers and are rectangular or square shaped.

1 is labeled + x squared, this gives x²

2 are labeled + x, this gives +x × 2 = +2x

4 tiles below + x squared are labeled negative x, this gives - x × 4 = - 4x

8 tiles below the + x tiles are labeled negative, this gives -1 × 8 = -8

Therefore to get the polynomial that was factored, we add all the terms. This gives :

+x² + (+ 2x) + (-4x) + (-8) = x² + 2x - 4x - 8 = x² - 2x - 8

Answer:

The answer is A, and if edge is being weird the answer is x^2-2x-8, Have fun dreamers!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The term 2013 in this context refers to the amount invested.

Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;

V = P(1+r)^t

Such as in the case of amount obtained in a compound interest formula

Where P is the present value or principal or amount invested

V is the future value

r is the rate of investment

with t being the time taken

Answer:

|6n+7|=8=  n=1/6,-5/2

|3x–1|=4  x=5/3,-1

Step-by-step explanation:

Answer: 15π m³

Step-by-step explanation:

Volume of a cone = 1/3πr²h

where,

r = radius = 3 meters

h = height = 5 meters

Volume = 1/3πr²h

Volume = 1/3 × π × 3² × 5

Volume = 1/3 × π × 9 × 5

Volume = 1/3 × π × 45

Volume = 45π/3

Volume = 15π m³

Answer:

6n(n³ - 4n² + 3)

Step-by-step explanation:

Given

6[tex]n^{4}[/tex] - 24n³ + 18n ← factor out 6n from each term

= 6n(n³ - 4n² + 3) ← which may be factored further if required

6n(n³ - 4n² + 3)  is the factored form.

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given that,

⇒6n⁴ - 24n³ + 18n

factor out 6n from each term

⇒6n(n³ - 4n² + 3)

There are two factors 6n and (n³ - 4n² + 3) of given expression.

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Answer:

The answer is A) 4.84 cm :P

Step-by-step explanation:

Gwen wants to create a congruent shape, so, all the sides have to be the same size. And if its a pentagon like in your situation , a pentagon has 5 sides so you have to divide 24.2 cm because it's your regular pentagon by 5 (sides) (24.2 cm ÷ 5 sides = 4.84 cm )

I hope I helped you :P

Answer:

The answer is A.

Step-by-step explanation:

Answer:

Use a graphing calc.

Step-by-step explanation:

Answer:

7 1/8

57/8

Hope this helps :)

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  [tex]6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}[/tex]

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

Comment on the solution

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

Answer:

1

2

6

Step-by-step explanation:

1/2 +1/2 =1

length 1/2 ×4=2

wide 1/2 ×3 =1 1/2

height 1/2×3= 1 1/2

Answer:

$4,523.40

Step-by-step explanation:

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

Answer:

HEY!

your answer is

it would be best to use litres

this is because a litre is 1000 millilitres and a swimming pool is a large amount of water.

Step-by-step explanation:

hope this helps

pls put brainliest

Answer:

36°

Step-by-step explanation:

Let m∠8 = x°

Therefore, m∠7 = 4x°

Since, ∠7 and ∠8 are linear angles.

Therefore,

m∠7 + m∠8= 180°

4x° + x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

x = 36

Hence,

m∠8 = 36°

Answer:

5x - 9 = 2x + 23

Step-by-step explanation:

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

The equation is 5x - 9 = 2x + 23.

The answer is option A.

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

An equation is a mathematical announcement this is made up of expressions related to the same signal. For instance, 3x – 5 = 16 is an equation. Fixing this equation, we get the price of the variable x as x = 7.

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Answer:

a) Use a ruler for the measurement.

b) convert to centimetres then use a ruler to draw the unit on the diagram.

c) measure the angle between K and L from K

See explanations below

A complete question related to this found on brainly (ID:15577387) is stated below.

Towns K and L are shown on a map.

a) Work out the actual distance

between towns K and L.

b) A third town, M, is 150 km due

South of town K.

Mark M on the map with X.

c) Measure the bearing of town L

from town K.​

Scale: 1cm represent 50km

Step-by-step explanation:

Scale: 1cm represent 50km

a) To find the actual distance between towns K and L use a ruler to measure the distance between K and L.

Your answer would be in centimetres (cm).

The answer obtained would be multiplied by 50km because from the scale given 1cm represent 50km.

Therefore you'll get the actual distance in km.

b) Here we are told M is 150 km due

South of town K.

Since the length of the initial diagram is in centimeters, we have to find how many centimeters equals 150km.

50km = 1cm

150km = (150km × 1cm)/50km = 150cm/50

150km = 3cm

Now we can represent the distance between K and M on the diagram.

Measure 3cm from K using a ruler in the direction of south (straight line downwards). The distance of M from K would be 3cm on the south of k.

c) Draw a cross on the position of K. Also draw a cross on the position of L. Connect the distance and measure the angle from K to L. The unit would be in degrees.

From the diagram, the angle is greater than 090° but less than 180°

Find attached the diagram.

Answer:

a) 100 km

b) check the photo of my work

c) 117 degrees

Step-by-step explanation:

To get full marks take a look at the photo of my work.

Question (b) use a compass and make sure it’s 3cm aiming down {South} as u can see in the photo, then draw a line aiming {South} with a ruler. On the end of the line you put the (x) point there to get the mark.

Thank you

Answer:

It's pretty easy! You can manipulate the numbers to match the equation.

For example,

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

The other equivalent expressions that are equal to 7x - y​ could be; x + 8y + 6x - 9y = 7x - y, 5x + 2x - 2y + y = 7x - y and 10x + 7y - 3x - 8y = 7x - y

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; that can also be used to indicate the logical syntax's order of operations and other features.

We have been given the expression as;

6x + 7y + x-8y = 7x - y

When someone asks to solve an equation, then it usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

The other equivalent expressions that are equal to 7x - y​ could be;

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

To know more about an expression follow;

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Answer:

yes

Step-by-step explanation:

Answer:

Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Step-by-step explanation:

I took the K12 test :)

Answer:

r=8

Step-by-step explanation:

Using the formula they gave us you could plug in the area (64) and divide it by pi which cancels out the pi so taking the square root of 64 gives you 8FT

Hope this helps :)

Answer:

8 ft

Step-by-step explanation:

[tex] \because \: r = \sqrt{ \frac{Area}{\pi} } \\ \\ \therefore \: r = \sqrt{ \frac{64\pi}{\pi} } \\ \\ \therefore \:r = \sqrt{64} \\ \\ \therefore r = 8 \: ft[/tex]

Answer:

715

Step-by-step explanation:

The total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division,and  multiplication by a conversion factor.

We have:

A birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

1/2 liters = 0.5 liters

We know,

1 lter = 1000 ml

0.5 liters = 0.5×1000 = 500 ml

Total water = 215 ml + 500 ml = 715 ml

Thus. the total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

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Answer:

A

Step-by-step explanation:

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

Hey there! :)

Answer:

a) 24 cm²

b) 40.04 cm²

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

Use the formula A = l × w to solve for each rectangle's area:

a)

8 × 3 = 24 cm².

b)

5.2 × 7.7 = 40.04 cm²

Answer:

a) 24

b) 40.04

Step-by-step explanation:

a) Area of a rectangle: length x width

length = 8

width = 3

Plug these values into the equation above:

8 x 3 = 24

b) Same steps as above except with different values for length and width

5.2 x 7.7 = 40.04

Answer:

x=1.

Step-by-step explanation:

2x + 1 = -x + 4

+x - 1 = +x - 1

3x. = 3

3/3. = x

1. = x

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Plug in the coordinates given:

[tex](\frac{10-3}{2}, \frac{8-10}{2})[/tex]

Simplify:

[tex](\frac{7}{2}, \frac{-2}{2})[/tex]

Therefore, the coordinates of the mid-point are:

(3.5, -1).

Answer:

See picture.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To get the value f x, we need to use SOH, CAH, TOA identity on ΔAEB but first we need to know any of the sides EB or AB.

From ΔBED, sum of the the angle in the triangle is 180° i.e ∠BED+∠EDB+∠EBD = 180°

65+55+∠EBD  = 180

∠EBD  = 180-120

∠EBD  = 60

Also ∠DBC = 90- ∠EBD

∠DBC = 90- 60

∠DBC = 30°

Applying sine rule on ΔBCD;

52/sin∠DBC = DB/sin115

52/sin30 = DB/sin115

DB = 52sin115/sin30

DB = 52sin115/0.5

DB = 104sin115

DB = 114.75 m

Also applying sine rule on ΔBED to get side BE;

BE/sin55 = 114.75/sin65

BEsin65 = 114.75sin55

BE =  114.75sin55/sin65

BE = 93.998/0.906

BE = 103.75m

Finally, applying the trigonometry identity SOH on  ΔABE

sinΔEAB = opp/hyp

sin70° = BE/AE

Since AE = x;

sin70° = 103.75/x

x = 103.75/sin70°

x = 110.41m

Hence, the value of x missing is approximately 110.41m

Answer:

(a) Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

(b) The correct option is (A).

(c) The correct option is (C).

Step-by-step explanation:

The 95% confidence interval for the difference between the two population​ mean hemoglobin level is:

CI = (-1.76 < μ₁ - μ₂ < -1.62)

(a)

The hypothesis to test the equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men is:

H₀: The two population means are equal, i.e. μ₁ = μ₂.

Hₐ: The two population means are not equal, i.e. μ₁ ≠ μ₂.

The (1 - α)% confidence interval can be used to draw conclusion about the hypothesis test.

Decision rule:

If the (1 - α)% confidence interval does not consist of the null value then the null hypothesis will be rejected and vice-versa.

The 95% confidence interval for the difference between the two population​ means is:

CI = (-1.76, -1.62)

The 95% confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

"Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men."

(b)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

So, the 95% confidence interval (-1.76, -1.62) implies that there is a 95% confidence that the above interval actually contains the value of the difference between the two population means, (μ₁ - μ₂).

The correct option is (A).

(c)

Now it is provided that the measures from men is denoted as population  1 and measures from women is denoted as population  2.

The confidence interval for the difference between two mean is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm MOE[/tex]

According to the information:

[tex]\bar x_{1}=\bar x_{2}\\\\\bar x_{2}=\bar x_{1}[/tex]

So, the new confidence interval will be:

[tex]CI=-(\bar x_{2}-\bar x_{1})\pm MOE[/tex]

Then the confidence interval with measures from men being population

1 and measures from women being population  2 is:

[tex]CI=(1.62<\mu_{1}-\mu_{2}<1.76)[/tex]

The correct option is (C).

Answer: 2398.72

Step-by-step explanation:

Simply do 3100*0.95*0.95*0.95*0.95*0.95 ≈ 2398.72

Hope it helps <3

Answer:

$2398.72( I cannot use your dollar sign).

Step-by-step explanation:

If it decreases by 5% every year, then 3100*0.95=2945. Then 2945*0.95=2797.75. Then the 3rd year is 2797.75*0.95=2657.8625. Then 2,657.8625*0.95=2524.96938. Lastly, in the fifth year, it is 2524.96938*0.95=2398.72091. Then, I round off to the nearest penny(hundredths). The answer I get is $2398.72!

Answer:

The amount Sam invested the first year = $2000

The amount Sally invested the last year = $1900

Complete question related to this was found at brainly (ID 4527784):

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Step-by-step explanation:

First we would represent the information given with mathematical expressions.

Sam investment for 3 consecutive years:

Year 1 = x dollars

Year 2 = $2,000 less than 5/2 times the amount he invested the first year

Year 2 = (5/2)(x) - 2000

Year 3 = $1,000 more than 1/5 of the amount he invested the first year

Year 3 = (1/5)(x) + 1000

Sally investment for 3 consecutive years:

Year 1 = $1,000 less than 3/2 times the amount Sam invested the first year

Year 1 = (3/2)(x) - 1000

Year 2 = $1,500 less than 2 times the amount Sam invested the first year

Year 2 = 2x - 1500

Year 3 = $1,400 more than 1/4 of the amount Sam invested the first year.

Year 3 = (1/4)(x) + 1400

Since Sam and Sally invested the same total amount at the end of three years, we would equate their sum:

Sum of Sam investment for the 3years = x + (5/2)(x) - 2000 + (1/5)(x) + 1000

= x + 5x/2 -2000 + x/5 + 1000

= (10x+25x+2x)/10 - 1000

= 37x/10 - 1000

Sum of Sally investment for the 3years = (3/2)(x) - 1000 + 2x - 1500 + (1/4)(x) + 1400

= 3x/2 - 1000 + 2x -1500 + x/4 + 1400

= (6x+8x+x)/4 - 1100

= 15x/4 - 1100

37x/10 - 1000 = 15x/4 - 1100

37x/10 - 15x/4 = -100

(148x - 150x)/40 = -100

-2x = -4000

x = 2000

Therefore the amount Sam invested the first year = x = $2000

The amount Sally invested the last year (3rd year) = (1/4)(x) + 1400

(1/4)(2000) + 1400 = 500+1400 = 1900

The amount Sally invested the last year = $1900