You roll a six sided die and toss a coin. What is the probability of rolling an odd number and then getting heads?

Answers

Answer 1
P(O,T)=(3/6)(1/2)

P(O,T)=1/4
Answer 2
Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering your question, and will teach you how to tackle it on your own in the future.

So, let's take a look at our question.
"You roll a six sided die and toss a coin. What is the probability of rolling an odd number and then getting heads?"

First, we need to understand what we're dealing with, and how to handle it.
Let's tackle these individually, rather than doing it all at once and getting confused/stuck.
We roll a six sided die, which is numbered from 1 to 6. "What is the probability of rolling an odd number?"
Well, let's count how many odd numbers there are from 1 to 6.
1, 3, 5; We have three odd numbers on our six sided die.
Let's set that up as a fraction, [tex] \frac{3}{6} [/tex]
However, we can simplify it into simpler terms - divide both numbers by 3.
3/3 = 1
6/3 = 2
We now have our simplified fraction, [tex] \frac{1}{2} [/tex]

Now, let's focus on the other half of the problem.
"You flip a coin. What's the probability of landing on heads?"
Well, a coin only has two sides - heads and tails - which means we have 1/2 chances of landing on heads or tails generally.

Since the question asks for the probability of an odd number and landing on heads, we need to multiply our fractions.

We have these two fractions:
[tex] \frac{1}{2} [/tex] * [tex] \frac{1}{2} [/tex]
Multiply them.
[tex] \frac{1}{2} [/tex] * [tex] \frac{1}{2} [/tex] = [tex] \frac{1}{4} [/tex]

Your answer is [tex] \frac{1}{4} [/tex]

I hope this helps!

Related Questions

Human iq scores are approximately normally distributed with mean 100 and standard deviation 15. determine the minimum iq scores for the top 5% of the population.

Answers

To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645

Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):

x = z s + u

x = 1.645 (15) + 100

x = 24.675 + 100

x = 124.675

 

Therefore the minimum iq score for the top 5% of the population is around 124.675

The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.

To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.

To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:

IQ Score = Mean + (Z-score * Standard Deviation)

Plugging the values in:

IQ Score = 100 + (1.645 * 15)

IQ Score = 100 + 24.675

IQ Score = 124.675

Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).

Which of the following are vertical asymptotes of the function y = 2cot(3x) + 4? Check all that apply. A.x = pi/3 B.x = +/- pi/2 C.x = 2pi D.x = 0

Answers

The vertical asymptotes of the function y = 2cot(3x) + 4 are  A.x = π/3  C. x = 2π D.x = 0

How to determine the vertical asymptote?

The function is given as:

y = 2cot(3x) + 4

The above function is a cotangent function, represented as:

y = Acot(Bx +C) + D

By comparison, we have:

B = 3

The vertical asymptotes are then calculated using:

[tex]x = \frac{\pi}{B}n[/tex], where n are integers

Substitute 3 for B

[tex]x = \frac{\pi}{3}n[/tex]

Using the above format, the vertical asymptotes in the options are  A.x = π/3  C. x = 2π D.x = 0

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HELP! Will give Brainliest! Using dimensional analysis, convert 293 cm into m. (1 m= 100 cm)
(and this is also a Chemistry Question)
I get how to work out the other question, but I'm confused on this one

Answers

To convert from one unit to another unit, a conversion factor is needed. This is a value that would relate the original unit to the desired unit. We either multiply or divide this value depending on what is being asked in the problem. For this problem, the conversion factor would be 1/100 which means that in 1 m there is 100 cm. We do the conversion as follows:

293 cm ( 1 m / 100 cm ) = 2.93 m 

Find the length of an arc that subtends a central angle of 135° in a circle of radius 2 mi

Answers

arc length = (πrθ)/180        [r=radius, θ=central angle, π≈3.14]

arc length = (3.14 * 2 * 135)/180 = 4.71 

Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed

Answers

Answer:

6 to the tenth power over 7 to the sixth power

Step-by-step explanation:

Given phrase,

6 to the fifth power over 7 cubed all raised to the second power,

[tex]\implies (\frac{6^5}{7^3})^2[/tex]

By using [tex](a^m)^n=a^{mn}[/tex]

[tex]=\frac{6^{5\times 2}}{7^{3\times 2}}[/tex]

[tex]=\frac{6^{10}}{7^6}[/tex]

= 6 to the tenth power over 7 to the sixth power

Simplify the expressions

(6⁵/7³)² = 2143588816/117649

(6⁷/7¹⁰) = 279936/282475249

(6¹⁰/7⁶) = 60466176/117649

(6³/7) = 216/7

(12⁵/14³) = 90855/1001

To simplify the given expressions, we can calculate the numerical values and perform the necessary operations. Let's evaluate each expression:

(6⁵/7³)²:

First, calculate the numerator and denominator:

Numerator: 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776

Denominator: 7³ = 7 × 7 × 7 = 343

Now, substitute the values into the expression and square the result:

(7776/343)² = (7776/343) × (7776/343) = 2143588816/117649

The simplified form is 2143588816/117649.

(6⁷/7¹⁰):

Calculate the numerator and denominator:

Numerator: 6⁷ = 6 × 6 × 6 × 6 × 6 × 6 × 6 = 279936

Denominator: 7¹⁰ = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 282475249

Substitute the values into the expression:

279936/282475249

This expression cannot be simplified further.

(6¹⁰/7⁶):

Calculate the numerator and denominator:

Numerator: 6¹⁰ = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60466176

Denominator: 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 117649

Substitute the values into the expression:

60466176/117649

This expression cannot be simplified further.

(6³/7):

Calculate the numerator and denominator:

Numerator: 6³ = 6 × 6 × 6 = 216

Denominator: 7

Substitute the values into the expression:

216/7

This expression cannot be simplified further.

(12⁵/14³):

Calculate the numerator and denominator:

Numerator: 12⁵ = 12 × 12 × 12 × 12 × 12 = 248832

Denominator: 14³ = 14 × 14 × 14 = 2744

Substitute the values into the expression:

248832/2744 = 90855/1001

The simplified form is 90855/1001.

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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed

(6⁵/7³)²

(6⁷/7¹⁰)

(6¹⁰/7⁶)

(6³/7)

(12⁵/14³)

the old price for school lunches is $5. The new price is $5.25. What is the percent increase in the cost if school lunches? Write answer as percent. The formula is p=b-a/a. b =new price for lunch. a=old price for lunch. P=percent increase

Answers

p=(5.25-5.00)/5.00

p=0.25/5.00

p=0.05

p = 5% increase

What is the probability of getting exactly 2 heads, given that the first toss is a head?

Answers

there is a 1/2 probability of getting heads on any one flip

 since the first one landed on heads you have a 1/2 probability f getting a 2nd one


Probability = 1/2

When constructing a circle circumscribed about a triangle, what is the purpose of constructing perpendicular bisectors?

Answers

Their point of intersection will be the center of the circle.

determine the slope of y=3x^2-8 at (x,y)

Answers

By definition, the slope of a curve is the rate of change of the independent and dependent variables. When graphed in a Cartesian plane, the slope between any two point on the curve is equal to Δy/Δx. However, we should not that only a linear function has a constant slope. For this problem, the equation is quadratic. Hence, you must specify the point where we should get the slope.

In calculus, the slope is the first derivative of the equation:

y=3x²-8
dy/dx = slope = 6x - 0

Thus, the slope at any point of the curve is 6x. For instance, you want to find the slope of the curve at point (1,1), then the slope is equal to 6(1) = 6 units.

What is the length of the hypotenuse, x, if (12, 35, x) is a Pythagorean triple?

Answers

a^2 + b^2 = c^2...where a and b are the legs and c is the hypotenuse
12^2 + 35^2 = c^2
144 + 1225 = c^2
1369 = c^2
sqrt 1369 = c
37 = c <=== ur hypotenuse is 37

so ur pythagorean triple is (12,35,37)

Answer:37

Step-by-step explanation:

12•12=144

35•35=1225

1225+144=1369

Square root 1369=37

please i need help....the question is.........

Answers

area = H/2*(b1+b2)

8.1 = 1.5/2*(6.7 +b2)

8.1=0.75*(6.7+b2)

10.8=6.7+b2

b2=10.8-6.7

b2=4.1m

What is the solution to the system of linear equations graphed below?

A. (3.5, -4)
B. (-4, 3.5)
C. (0,3)
D. (0,-4)

Answers

Look at the picture.

Answer: A. (3.5, -4)

Graph y < 1/3x + 1/2

Answers

the answer is in the picture.

(02.03 LC)

Read the following statement:

Line segment AB is congruent to line segment CD.

Which of the following is an equivalent statement?

AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar

Answers

Answer:

AB overbar congruent to CD overbar

Explanation:

The question is asking whether Line segment AB is CONGRUENT to line segment CD.

The meaning of congruent is having the same shape and size.

Congruent ≅

Element ∈

Equal =

Similar ~

In conclusion, you could say:

AB ≅ CD

I cannot type the lines over the top AB and CD but they are there.

(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)

If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.

What is congruence?

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.

So, congruent lines are lines whose lengths are the same.

The sign of congruency is ≅ so AB ≅ CD.

Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".

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Does arkansas lie south of 40 degrees latitude

Answers

All of Arkansas is between 33 degrees and 36.5 degrees lol

Candis took out a payday loan with an effective interest rate of 15,400%. if she had 220 to invest for a year at this interest rate, how much would make in interest?
A. 3,388,000
B 338,800
C.. 3388
D 33,880

Answers

The formula is
I=prt
I interest?
P 220
R 15400/100=154
T time 1 year
I=220×154×1
I=33,880

It's d
Final answer:

To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.

Explanation:

The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.

Converting 15,400% to a decimal, we get 154. Then, apply the formula:

I = $220 × 154 × 1

This gives us:

I = $33,880

Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.

A rectangle is placed around a semicircle as shown below. the width of the rectangle is 6ft . find the area of the shaded region. use the value 3.14 for π , and do not round your answer. be sure to include the correct unit in your answer.

Answers

As the figure is missing, I will do the most logical assumptions and explain the way to solve the problem.

Assumptions:

1) radius of the semicircle = width of the rectangle = 6ft

2) length of the rectangle = 2*radius of the semicircle = 12 ft

3) Area of the shaded region = area of the rectangle - area of the semicircle

Solution

area of the rectangle = width * length = 6 ft * 12 ft = 72 ft^2

area of the semicircle = [1/2]*π*(r^2) = [1/2]*3.14*(6ft)^2 = 56.52 ft^2

area of the shaded region = 72 ft^2 - 56.52 ft^2 = 15.48ft^2

Answer: 15.48 ft^2

The shaded region is by assumption the region which is not covered by the semicircle in in given rectangles.

The area of the shaded region is given by 15.48 sq. ft.

What is a semicircle?


A semicircle is a circle cut in half. Thus, one circle produces two semicircle.

How to find the area of the shaded region?

Firstly we will find the area of the rectangle and then subtract the area of the semicircle to find the are of the shaded region.

Since the radius of the semicircle is equal to width of the rectangle(6 ft), thus the length of the diameter of the circle( twice the radius which is 12 ft) serves as length of the considered rectangle.

Thus, we have:

[tex]\text{Area of the given rectangle\:} = 6 \times 12 = 72 \: \rm ft^2[/tex]


Since the semicircle is having radius of 6 ft, thus:

[tex]\text{Area of semicircle} = \dfrac{\pi r^2}{2} = \dfrac{3.14 \times 6^2}{2} = 56.52 \: \rm ft^2[/tex]

Thus, area of the shaded region will be equal to area of rectangle - area of semicircle = 72 - 56.52 = 15.48 sq. ft.

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How to find the volume of a parallelepiped with 8 vertices?

Answers

The volume would be the same as a rectangular prism on the same base and between parallel planes.
So the volume = area of the base * altitude.


The volume of parallelepiped with 8 vertices is 75 units.

What is Volume of Parallelepiped?

A parallelepiped's volume is determined by multiplying its surface area by its height.

The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.

Given:

let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).

so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]

                    = |0( 0- 0) - 3(25- 0) + 2(0 - 0)|

                    = |0 - 75 + 0|

                    = |- 75|

                    = 75 units

Hence, the volume of parallelepiped with 8 vertices is 75 units.

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A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.07 inches per second, and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t, and find the volume when t = 400 seconds.

Answers

The increase of the radius is a linear increase since we have the constant rate of 0.07 inches per second

The equation for a linear growth/decay is given by the form [tex]y=mx+c[/tex] where [tex]m[/tex] is the rate of increase and [tex]c[/tex] is the value of [tex]y[/tex] when [tex]x=0[/tex]

We have 
[tex]m = 0.07[/tex] 
[tex]c=36[/tex] when [tex]t=0[/tex]

So the equation is [tex]r=0.07t+36[/tex]

The length of the radius when [tex]t=400 [/tex] seconds is
[tex]r=0.07(400)+36[/tex]
[tex]r=64[/tex] inches

Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Approximately what percent of the adult male population is taller than the average basketball player? 0.135% 0.875% 49.875% 99.875%

Answers

z = (x - mean) / SD = (79 - 70) / 3 = 3 
P (Z > 3)? = 1 - F (z) = 1 - F (3) = 0.00135

Answer:

A. 0.135%

Step-by-step explanation:

We have been given that adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall.  

We need to find the area of normal curve above the raw score 79.

First of all let us find the z-score corresponding to our given raw score.

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

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Raw-score}[/tex],

[tex]\mu=\text{Mean}[/tex],

[tex]\sigma=\text{Standard deviation}[/tex].

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{79-70}{3}[/tex]

[tex]z=\frac{9}{3}[/tex]

[tex]z=3[/tex]

Now we will find the P(z>3) using formula:

[tex]P(z>a)=1-P(z<a)[/tex]

[tex]P(z>3)=1-P(z<3)[/tex]

Using normal distribution table we will get,

[tex]P(z>3)=1-0.99865 [/tex]

[tex]P(z>3)=0.00135[/tex]

Let us convert our answer into percentage by multiplying 0.00135 by 100.

[tex]0.00135\times 100=0.135%[/tex]

Therefore, approximately 0.135% of the adult male population is taller than the average basketball player and option A is the correct choice.

Find the sum of the first 100 terms in the series
[tex] \frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + . . . \frac{1}{n*(n+1)} [/tex]

Answers

Hello,

[tex] \dfrac{1}{n} - \dfrac{1}{n+1} = \dfrac{1}{n(n+1)} \\ \dfrac{1}{1*2} = \dfrac{1}{1} - \dfrac{1}{2} \\ \dfrac{1}{2*3} = \dfrac{1}{2} - \dfrac{1}{3} \\ \dfrac{1}{3*4} = \dfrac{1}{3} - \frac{1}{4} \\ ...\\ \dfrac{1}{n*(n+1)} = \dfrac{1}{n} - \dfrac{1}{n+1} \\ [/tex]

Adding member by member, we have

[tex] \dfrac{1}{1*2} + \dfrac{1}{2*3} +\dfrac{1}{3*4} +...\dfrac{1}{n*(n+1)}=\\ \dfrac{1}{1} - \dfrac{1}{n+1} \\ = \dfrac{n}{n+1} \\ [/tex]

if n=100 sum [tex]\boxed{= \dfrac{100}{101} }[/tex]


factors of 3x^2y^2+6x^2+12y^2+24

Answers

look for  the GCF

GCF = 3

so we have 

3 (x^2y^2 + 2x^2 + 4y^2 + 8)      Factor by grouping:-

= 3[ x^2(y^2 + 2) + 4(y^2 + 2)]

= 3(x^2 + 4)(y^2 + 2)

In the figure, if AB ≅ CD, then

A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.

Answers

Answer:

D. arc AB ≅ arc CD.

Step-by-step explanation:

To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".

Applying this theorem, we have

[tex]AE \times EB = CE \times ED[/tex]

Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means

[tex]AE+EB=CE+ED[/tex]

However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is

[tex]arc(AB) \cong arc(CD)[/tex]

Because an arc is defined by its chord basically, and in this case they are congruent.

Part A: Solve -vp + 30 < 45 for v .. show your work.
Part B: Solve 3w - 6r = 30 for r .. show your work.

Answers

-vp + 30 < 45....for v
-vp < 45 - 30
-vp < 15
-v < 15/p
v > -15/p <==
============
3w - 6r = 30 ...for r
-6r = 30 - 3w
r = (30 - 3w) / -6
r = -5 + 1/2w...or r = 1/2w - 5 <==
Part A: v > -15/p

Part B: r = 1/2w - 5

Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. The answer key says that the answer is x + 4y = 22, but I'm confused on how to get there

Answers

The gradient of the original line is 4. For a perpendicular gradient, you use the negative reciprocal, which is -1/4. Using y - y1 = m(x - x1), you can solve that y - 5 = -(1/4)(x - 2).
Multiply through by -4, you get -4y + 20 = x - 2, which can be rearranged as x + 4y = 22

To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.

To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.

The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.

Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.

A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?

Answers

Let x = length of the park
Let y = width of the park

Because the area is 392392 ft², therefore
xy = 392392          (1)
Because three sides of fencing measure 5656 ft, therefore
2x + y = 5656        (2)
That is
y = 5656 - 2x          (3)
Substitute (3) into (1).
x(5656 - 2x) = 392392
5656x - 2x² = 392392
2x² -5656x + 392392 = 0
x² - 2828x + 196196 = 0

Solve with the quadratic formula.
x = (1/2)*[2828 +/- √(2828² - 4*196196)]
   = 2756.83 or 71.17

Answer:
The possible dimensions are 2756.8 ft and 71.2 ft (nearest tenth)

A regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the octagon? 71 ft2 101 ft2 110 ft2 202 ft2

Answers

Answer:

Option B is correct.

The approximate area of regular octagon is, 101 square ft.

Step-by-step explanation:

Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.

To find the area of a regular octagon(A) of side length a is given by :

[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]

Given the length of side, a= 4.6 ft

Substitute the value of a=4.6 ft in the given formula of area:

[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or

[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or

[tex]A=(2+2.828)\cdot(21.16)[/tex]

Simplify:

[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.

therefore, the approximate area of regular octagon is, 101 square ft






how many cups of grape punch containing 10% fruit juice and berry punch containing 20% fruit juice must be added together to create 12 cups of punch with 18% fruit juice?

Answers

well, let's say we need "g" of grape punch, now how much juice is in the "g" amount? well, just 10% of it is juice or (10/100) * g, 0.1g.

let's say we need "b" of berry punch, now, is 20% juice, how much juice in "b"? well, (20/100) * b, or 0.2b.

whatever "g" and "b" are, they must add up to 12 cups, of 18%, how much juice in 12cups? well (18/100) * 12, or 2.16

[tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentrated\\ amount \end{array}\\ &-----&-----&-----\\ \textit{grape punch}&g&0.10&0.10g\\ \textit{berry punch}&b&0.20&0.20b\\ -----&-----&-----&-----\\ mixture&12&0.18&2.16 \end{array}[/tex]

[tex]\bf \begin{cases} g+b=12\implies \boxed{b}=12-g\\ 0.1g+0.2b=2.16\\ ----------\\ 0.1g+0.2\left( \boxed{12-g} \right)=2.16 \end{cases} \\\\\\ 0.1g+2.4-0.2g=2.16\implies 2.4-2.16=0.2g-0.1g \\\\\\ 0.24=0.1g\implies \cfrac{0.24}{0.1}=g\implies \boxed{2.4=g}[/tex]

and of berry will then be 12 - g

Give the degree and classify the polynomial by the number of terms- 3

A)degree 1, monomial
B)degree 1, binomial
C)degree 0, monomial
D)degree 0, binomial

Answers

The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s). Examples: 5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial. 3x4+4x2The highest exponent is the 4 so this is a 4thdegree binomial.

Answer:

Step-by-step explanation:

the answer is a

The first term of a geometric sequence is –2 and the common -1/4. What are the next three terms of the sequence?

Answers

The common ratio tells you by which factor every successive term will be with respect to the preceding term so you have:

-2(-1/4)(-1/4)(-1/4)

1/2, -1/8, 1/32
[tex]a_1=-2\\ a_2=-2\cdot\left(-\dfrac{1}{4}\right)=\dfrac{1}{2}\\ a_3=-2\cdot\left(-\dfrac{1}{4}\right)^2=-\dfrac{1}{8}\\ a_4=-2\cdot\left(-\dfrac{1}{4}\right)^3=\dfrac{1}{32}[/tex]
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