The sum of two numbers is 21.
The second number is six times the first number.
Work out the two numbers.

Answers

Answer 1

Answer:

Pretend that x and y represents the 2 numbers that we need to find.

According to the information, we know that:

x + y = 21

6x = y

Replace y in the first equation with 6x (because they are equal to each other according to the second equation):

x + y = 21

x + 6x = 21

7x = 21

x = 21/7 = 3

Now have two ways to find y, both will give us the same result:

3 + y = 21 ⇔ y = 21 - 3 = 18

6 · 3 = y ⇔ y = 18

So the numbers that we need to find are 3 and 18.

Answer 2

Answer:

3 and 18.

Step-by-step explanation:

If one number is x then the other is 6x.

So, x + 6x = 21

7x = 21

x = 3.

The other number is 21 - 3 = 18.


Related Questions

The ordinate is twice the abscissa

Answers

We can construct the function:

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

Where [tex]f(x)[/tex] or [tex]y[/tex] is ordinate and [tex]x[/tex] is abscissa.

The function actually represents a line. Since it can have linear form.

[tex]f(x)=2x+0[/tex]

Hope this helps.

r3t40

whats the answer anyone​

Answers

Answer:

Middle Answer.

Step-by-step explanation:

Given that Micah intends to spend less than $150 on paint and brushes

Hence

Cost of brushes+ cost of paint ≤ 150

150 ≥ Cost of brushes+ cost of paint

150 ≥ Cost of brushes+ (price of paint per gal) · (number of gallons)

Given that he buys x gal of paint,

For middle answer:

150 ≥ 42.21 + 21.64x (which matches the inequality in the question, so this is the right answer)

The 42.21 would represent the money spent on paintbrushes. This because the amount of money spent on paintbrushes doesn't change (it's a set amount). You can tell this by the fact that 42.21 is not being multiplied by anything (the 42.21 cannot change at all)

The 21.64x  is the cost of paint per gallon.

Cost of paint per gallon means that the cost changes depending on many gallons you are getting.

The 21.64 represents the cost of 1 gallon of paint, and the 'x' represents the number of gallons.

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

So the Answer is option 2:

$42.21 on paintbrushes

Paint costs $21.64 per gallon

What is the sum of the terms in the sequence
3, 6, 9, …, 99?

Answers

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\\d=3\\a_n=99\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=3+(n-1)\cdot 3\\3n-3=96\\3n=99\\n=33\\\\S_{33}=\dfrac{3+99}{2}\cdot33=51\cdot33=1683[/tex]

You decide to put $5000 in a savings account to save $6000 down payment on a new car. If the account has an interest rate of 7% per year and is compounded monthly, how long does it take until you have $6000 without depositing any additional funds?

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$6000\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]

[tex]\bf 6000=5000\left(1+\frac{0.07}{12}\right)^{12\cdot t}\implies \cfrac{6000}{5000}\approx (1.0058)^{12t}\implies \cfrac{6}{5}\approx(1.0058)^{12t} \\\\\\ \log\left( \cfrac{6}{5} \right)\approx \log[(1.0058)^{12t}]\implies \log\left( \cfrac{6}{5} \right)\approx 12t\log(1.0058) \\\\\\ \cfrac{\log\left( \frac{6}{5} \right)}{12\log(1.0058)}\approx t\implies 2.63\approx t\impliedby \textit{about 2 years, 7 months and 16 days}[/tex]

It takes 2 years to have $6000 without depositing additional funds.

Given that,
Amount = $6000
Principal amount = $5000
rate = 7 % compounded monthly
Time = ?

What is arithmetic?

In mathematics it deals with numbers of operations according to the statements.

What is interest explain?

It is defined as the fee you pay to borrow money or the fee you levy to lend money. Interest is considerable and frequently recalled as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

[tex]6000/5000 = (1 + 0.07/12)^{12t}\\6/5 = (1.005)^{12t}\\[/tex]
[tex]1.20 = (1.005)^t\\1.20/ = (1.005)^{12t}[/tex]
taking ln both side
ln 1.13 = 12t ln(1.005)
t = ln 13/12 ln 1.005
t = 2.04 year

Thus, it takes 2 years to have $6000 without depositing additional funds.

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What is logs(4.7)+logs 2 written as a single log?
HP
O logg21
o log5 26
o logg30
o log 56

Answers

ANSWER

[tex]log_{s}(56)[/tex]

EXPLANATION

The given logarithmic expression is:

[tex] log_{s}(4 \times 7) + log_{s}(2) [/tex]

Recall and use the product rule of logarithm

[tex] log_{a}(b) + log_{a}(c) = log_{s}(bc) [/tex]

We apply this rule to obtain,

[tex]log_{s}(4 \times 7) + log_{s}(2) = log_{s}(4 \times 7 \times 2) [/tex]

We multiply out the argument to get;

[tex]log_{s}(4 \times 7) + log_{s}(2) = log_{s}(56) [/tex]

The correct answer is

[tex]log_{s}(56)[/tex]

When the expression Log₅ (4•7) + Log₅ 2 is express as a single logarithm, the result obtained is Log₅ 56

Data obtained from the question Log₅ (4•7) + Log₅ 2Single Log =? How to express as single logarithm

Log₅ (4•7) + Log₅ 2

Log₅ (4 × 7) + Log₅ 2

Log₅ 28 + Log₅ 2

Recall

Log M + Log N = Log MN

Thus,

Log₅ 28 + Log₅ 2 = Log₅ (28 × 2)

Log₅ 28 + Log₅ 2 = Log₅ 56

Thus,

Log₅ (4•7) + Log₅ 2 = Log₅ 56

From the above illustration,

We can conclude that when Log₅ (4•7) + Log₅ 2 is written as a single log, the result is Log₅ 56

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Which of the following descriptions matches the tree diagram below?

Answers

Answer:

Its the first option.

Step-by-step explanation:

Game 1 - you win or lose.

Game 2 - you win or lose

So that makes 4 possible branches  along the tree.

WW, WL LW and LL.

how do you factor x squared minus 100

Answers

Rewrite 100  as  10 ^2 .  x^ 2  −  10 ^2

Since both terms are perfect squares, factor using the difference of squares formula,  a^2 -b^2= (a + b) (a - b) where a = x and b = 10.

(x + 10) (x - 10)


Recipe ingredients remain in a constant ratio no matter how many servings are prepared. Which table shows a possible
ratio table for ingredients X and Y for the given number of servings?

Answers

Answer:

Table N 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Verify the table 4

For x=1, y=2

so

y/x=2/1=2

For x=2, y=4

so

y/x=4/2=2

For x=3, y=6

so

y/x=6/3=2

therefore

The constant of proportionality k is equal to 2 and the equation is equal to

y=2x

The table 4 represent a direct variation, therefore is a possible ratio table for ingredients X and Y

Answer:

The correct option is 4.

Step-by-step explanation:

It given that recipe ingredients remain in a constant ratio no matter how many servings are prepared.

It means the relation between x and y is

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where k is constant of proportionality.

We need to find a possible ratio table for ingredients X and Y for the given number of servings.

In table 1,

[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]

[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]

Option 1 is incorrect.

In table 2,

[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]

[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]

[tex]\frac{y_3}{x_3}=\frac{8}{3}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_3}{x_3}[/tex]

Option 2 is incorrect.

In table 3,

[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]

[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]

Option 3 is incorrect.

In table 4,

[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]

[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]

[tex]\frac{y_3}{x_3}=\frac{6}{3}=2[/tex]

[tex]\frac{y_}{x_1}=\frac{y_2}{x_2}=\frac{y_3}{x_3}[/tex]

Option 4 shows a possible  ratio table for ingredients X and Y for the given number of servings.

Therefore the correct option is 4.

˘30 points

Solve this

Answers

Answer:

53.13

Step-by-step explanation:

Answer:

i got a whole bunch of numbers so you can try them all and see if its right

3279

2764800

30720

Step-by-step explanation:

A line passes through the points (–3, –4) and (6, 2). What number is the x-intercept?

A –3
B –2
C 2
D 3

Answers

Answer:

D. 3

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{x-intercept:}\ (x,\ 0).\\\\\text{Susbtitute the coordinates of the points to the formula of a slope}\\\\(-3,\ -4),\ (6,\ 2),\ (x,\ 0):\\\\m=\dfrac{2-(-4)}{6-(-3)}=\dfrac{2+4}{6+3}=\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\\\\m=\dfrac{0-2}{x-6}=\dfrac{-2}{x-6}\\\\\text{Therefore we have the equation:}\\\\\dfrac{-2}{x-6}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\2(x-6)=(-2)(3)\\\\2(x-6)=-6\qquad\text{divide both sides by 2}\\\\x-6=-3\qquad\text{add 6 to both sides}\\\\x=3[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Look at the picture.}[/tex]

Mark points in the coordinate system.

Lead a line through these points.

Read x-intercept.

Answer: the answer is D

Step-by-step explanation:

Three identical regular polygons fit together at one point. There is a gap of 36 °. What is the name of the polygon?

Answers

Answer:

pentagon

Step-by-step explanation:

So at this point, we have a full rotation of 360 degrees round that point. The graph accounts for 36 degrees of that 360 degrees leaving 360-36=324 degrees left to be split between the three polygons at (Around) that point. So 324/3=108.  Now we got to figure out a polygon that has all of it's angles being 108 degrees.

We can usually find that if we know the number of sides of the polygon but we don't but here is the formula 180(n-2)/n=108

Cross multiply gives

108n=180(n-2)

Distribute

108n=180n-360

subtract 180n on both sides

-72n=-360

Divide both sides by -72

giving n=5

So a 5 side polygon is a pentagon

   Three identical regular polygons fitted together at one point are regular Pentagons.

   Measure of the interior angle of a polygon is given by,

Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]

Where 'n' = number of sides of the polygon

Let the number of regular polygons fitted together at one point = x

Therefore, sum of one interior angle of all polygons at a point = [tex]\frac{x(n-2)\times 180^\circ}{n}[/tex]

It has been given in the question "36° is the gap left when 3 identical regular polygons have fitted together at a point."

Therefore, sum of interior angles of all polygons joining at a point with the gap = [tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ[/tex]

Since, sum of angles at a point is always 360°.

[tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ=360^\circ[/tex]

[tex]\frac{3(n-2)\times 180^\circ}{n}=324^\circ[/tex]

[tex]540n-1080=324n[/tex]

[tex]540n-324n=1080[/tex]

[tex]216n=1080[/tex]

[tex]n=5[/tex]

  Therefore, polygons fitted at one point are Pentagons.

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If the x and y values in each pair of a set of ordered pairs are interchanged the resulting set of ordered pairs is known as the

Inverse of a function
One to one function
Inverse of a relation
Onto function

WILL GIVE BR!!!

Answers

Answer:

Inverse of a relation

Reasoning:

the inverse of a function is a full function, this is just a set of pairs.  A set of pairs, or relation, where x and y values interchange are inverse of the relation.  A one to one function is when a function's inverse is also a function (doesn't have more than one y for each x) which can be tested for on the normal function's graph with a HORIZONTAL line test.  A normal parabola isn't one to one.  An onto function has to do with every value being used (I don't remember much about them, but once again this isn't a function, but rather a specific set of pairs/data)

Example of inverse of a relation:

Relation: {(0,5), (3,2)}

Inverse: {(5,0), (2,3)}

Example of inverse of a function:

f(x)=5x

f-1(x)=x/5

Example of a one to one function:

f(x)=x+1

Answer:

For Plato the inverse of a function

Step-by-step explanation:

what is the value of 2 5/8 ÷ 7/10​

Answers

Answer: 15/4 simplified to 3 3/4 or 3.75

Answer:

2 5/8 ÷ 7/10​  is actually

(21 / 8) * (10 / 7)

(21 / 8) * (10 / 7) = 210 / 56

= 105 / 28

= 3 (21 / 28)

= 3 (3 / 4)

Step-by-step explanation:

what is the sum of the arithmetic sequence 3,9,15..., if there are 22 terms

Answers

Answer:

The arithmetic sequence given above has a first term (a1) equal to 3 and the common difference (d) equal to 6. The sum of the first n terms of the sequence is calculated through  the equation,

                               Sn = (n/ 2) x (2a1 + (n - 1) x d)

Substituting,

                               S22 = (22 / 2) x (2x3 + (22 - 1) x 6) = 1452

Therefore, the answer is the first choice, 1452. 

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

1452.

Step-by-step explanation:

Sum of n terms = n/2  [2a1 + d(n - 1) ] where a1 = the first term and d = the common difference.

Here a1 = 3 and d = 9-3 = 6.

So S22 = 11 [2*3 + 6(22-1)]

=  11 * 132

=  1452

The consumer price index is

Answers

Answer: b would be the correct answer

Step-by-step explanation:

I answered those other questions but need help with this one because I have trouble so can someone answer this for me?

Answers

[tex]\bf \begin{array}{ccll} \stackrel{x}{\textit{sprayed times}}&\stackrel{f(x)}{\textit{left termites}}\\ \cline{1-2} 1&12000\left( \frac{1}{4} \right)^1\\\\ 2&12000\left( \frac{1}{4} \right)^2\\\\ 3&12000\left( \frac{1}{4} \right)^3\\\\ x&12000\left( \frac{1}{4} \right)^x\\ \end{array}[/tex]

Answer:

the answer is C

Step-by-step explanation:

What is the slope of a line that is parallel to the line shown
on the graph?
A -4
B -1/4
C 1/4
D 4

Answers

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Parallel lines have the same slope

The slope of the line shown is  [tex]\frac{1}{4}[/tex]

Therefore, the slope of the parallel line will also be [tex]\frac{1}{4}[/tex]

Find the center and the radius of the circle with the equation: x^2-2x+y^2+4y+1=0?

Answers

Answer:

Center (h,k) is (1,-2) and radius r = 2

Step-by-step explanation:

We need to find the center and radius of the circle of the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

We need to transform the above equation into standard form of circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where(h,k) is the center of circle and r is radius of circle.

Solving the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

Moving 1 to right side

[tex]x^2-2x+y^2+4y=-1[/tex]

Now making perfect square of x^2-2x and y^2+4y

Adding +1 and +4 on both sides of the equation

[tex]x^2-2x+1+y^2+4y+4=-1+1+4[/tex]

Now, x^2-2x+1 is equal to (x-1)^2 and y^2+4y+2 =(y+2)^2

[tex](x-1)^2+(y+2)^2=4[/tex]

Comparing with standard equation of circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h = 1 , k =-2 and r =2 because r^2 =4 then r=2

So, center (h,k) is (1,-2) and radius r = 2

Line CD passes through points C(3.-5) and D(6.0). What is the equation of line CD in standard form?
5x + 3y = 18
5x - 3y = 30
5x - y = 30
5x + y = 18

Answers

Answer:

5x - 3y = 30

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

=====================================

We have the points C(3, -5) and D(6, 0).

Substitute:

[tex]m=\dfrac{0-(-5)}{6-3}=\dfrac{5}{3}[/tex]

use (6, 0):

[tex]y-0=\dfrac{5}{3}(x-6)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y=\dfrac{5}{3}(x-6)[/tex]       multiply both sides by 3

[tex]3y=5(x-6)[/tex]            use the distributive property

[tex]3y=5x-30[/tex]       subtract 5x from both sides

[tex]-5x+3y=-30[/tex]          change the signs

[tex]5x-3y=30[/tex]

Answer:

5x-3y=30

Step-by-step explanation:

took the unit test yall and got it right.

What is the measure of L?

Answers

Answer:

A. 25°

Step-by-step explanation:

From the diagram, in triangle JKL, JK=KL=7 units. This means triangle JKL is isosceles triangle with base JL.

In isoscels triangle angles adjacent to the base are congruent, so

∠KJL=∠KLJ=25°

Note that ∠KLJ is ∠L, so ∠L=25°

Answer: 25

Step-by-step explanation:

6. You have $20.00 to spend. How many different food/drink combinations could you have?
List some of the combinations. Use the space on this page to show your work.
Food/Drink Item
Price
Fries
$2.75
Hot Dog
$1.75
Hamburger
$2.15
Cheeseburger
$2.25
Soda
$1.25
Ice Cream
$1.50
Cookies (3)
$1.00
Water
$1.00

Answers

You can get (7) fries
You can get (11) hot dogs
You can get (9) hamburgers
You can get (8) cheeseburgers
You can get ( 16) sodas
You can get ( 16) ice creams
You can get ( 20) cookies
You can get (20) waters

What is the slope of the line that passes through the points (–9, 2) and (0, 4)?
The slope of the line is

Answers

Let m = slope of the line

m = delta y divided by delta x

m = (4 - 2)/(0 - (-9))

m = 2/(0 + 9)

m = 2/9

The slope is 2/9.

Do you know what the answer really means?

Answer:

[tex]{\huge\boxed {\frac{2}{9}}}[/tex]

Step-by-step explanation:

Slope formula:

      ↓

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2=4\\y_1=2\\x_2=0\\x_1=(-9)\\[/tex]

[tex]\frac{4-2}{0-(-9)}=\frac{2}{9}[/tex]

The slope of the line is 2/9.

2/9 is the correct answer.

I hope this helps you, and have a wonderful day!

2w -5. when w = 16 HELP ME

Answers

Answer:

27

Step-by-step explanation:

Plug in

2(16) - 5

= 32 - 5

= 27

For this case we have the following expression:

[tex]2w-5[/tex]

We must evaluate the expression when w = 16. So, we have:

[tex]2 (16) -5 =\\32-5 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]32-5 = 27[/tex]

Thus, the value of the expression with [tex]w = 16[/tex] is 27

Answer:

[tex]32-5 = 27[/tex]

With her motorboat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1.5 hours. How fast could her motorboat go in still water? What is the rate of the current?

Answers

Answer:

Speed_still  = 12.25 mi/h

Speed_current = 1.75 mi/h

Step-by-step explanation:

In the first trip, the motorboat goes upstream

Speed_boat = Speed_still - Speed_stream

The speed is defined as

Speed = Distance / time

This means

Speed_boat  = 21 miles/ 2 h = 10.5 mi/h

Then

Speed_still - Speed_stream = 10.5 mi/h

In the second trip:

Speed_boat = Speed_still + Speed_stream

Speed_boat  = 21 miles/ 1.5 h = 14 mi/h

Speed_still + Speed_stream = 14 mi/h

Then, the ystem of equations result

Speed_still + Speed_stream = 14 mi/h

Speed_still - Speed_stream = 10.5 mi/h

If we add them together

2*Speed_still  = 24.5 mi/h

Speed_still  = 12.25 mi/h

Speed_stream  = 14 mi/h - 12.25 mi/ h = 1.75 mi/h

A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side. What is the expression for the volume of the pyramid?​

Answers

Answer:

[tex]\large\boxed{V=\dfrac{2}{9}s^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-base\ area\\H-height\\\\\text{The base of the pyramid os athe square with side length}\ s.\\\text{Therefore the base area}\ B=s^2.\\\\\text{The height of the pyramid is}\ \dfrac{2}{3}\ \text{that of it's side:}\ H=\dfrac{2}{3}s.\\\\\text{Substitute:}\\\\V=\dfrac{1}{3}(s^2)\left(\dfrac{2}{3}s\right)=\dfrac{2}{9}s^3[/tex]

Answer:

For plato users is OPTION D

Step-by-step explanation:

D. [tex]v=\frac{2}{9} s^{3}[/tex]

Suppose there are 10 five and six-year-old attending a birthday party. When a 30 year old mother walks into the room with an infant in her arms, what happens to the mean age in the room? what happens to the standard deviation of ages in the room?

A. The mean and standard deviation of both change.
B. The meaning will change, but the standard deviation will stay approximately the same.
C. I mean will stay approximately the same, but the standard deviation will change.
D. The mean and standard deviation will both stay approximately the same.

Answers

Answer:

d•

^™¢[¢™°¢¢™¢™¢|℅|®|℅``|

•€=™|℅€€

The mean and standard deviation of both change ages in the room.

What are the mean and standard deviation?

The mean of a dataset exists as the sum of all values divided by the total number of values. It's the most generally utilized measure of central tendency and exists often referred to as the “average.”

The median exists as the middle value in a list ordered from smallest to largest. The mode exists as the most frequently occurring value on the list.

The standard deviation exists as a statistic that measures the dispersion of a dataset relative to its mean and is computed as the square root of the variance. The standard deviation exists estimated as the square root of variance by determining each data point's deviation relative to the mean.

Standard deviation describes how spread out the data is. It is a measure of how far each observed value exists from the mean.

Here given that,

There are 10 five and six-year-olds attending a birthday party.When a 30-year-old mother walks into the room with an infant in her arms. what happens to the mean and standard deviation of ages in the room.

Hence, A. The mean and standard deviation of both change.

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A game store sells 2 large puzzles for $16 and 3 small puzzles for $15. The store made $128 in puzzle sales this week.

The equation 8l+5s=128 represents this week's earnings from puzzle sales, where ll represents the number of large puzzles sold and s represents the number of small puzzles sold.

Which statements are correct regarding the equation 8l+5s=128?

select all the apply.

1.The coefficient 5 in the equation gives the cost of one large puzzle.

2.The coefficient 5 in the equation gives the cost of one small puzzle.

3.The constant 128 in the equation gives the total number of puzzles sold.

4.The coefficient 8 in the equation gives the cost of one large puzzle.

5.The coefficient 8 in the equation gives the cost of one small puzzle.



Answers

Answer:

2&4

Step-by-step explanation:

The equation 8l+5s=128 represents puzzle sales earnings, where the coefficients correspond to puzzle costs correctly.

Statements 1, 2, and 4 are correct regarding the equation 8l + 5s = 128:

The coefficient 5 in the equation gives the cost of one small puzzle.The coefficient 5 in the equation gives the cost of one small puzzle.The coefficient 8 in the equation gives the cost of one large puzzle.

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Answers

Answer:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Step-by-step explanation:

We know that Aron flips a penny 9 times and gets exactly 3 heads .

Probability of getting a head or a tail is [tex] \frac { 1 } { 2 } [/tex].

Here, we need to find the probability of getting exactly 3 heads:

[tex]P(x=3)=^9C_3(\frac{1}{2})^3\times \frac{1}{2}^6\\\\P(x=3)=^9C_3(0.5)^3\times (0.5)^6\\\\P(x=3)=\frac{9!}{3!\tiems 6!}\times (0.5)^9\\\\P(x=3)=0.16[/tex]

So the expression representing this situation will be:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Final answer:

The probability of getting exactly 3 heads in 9 coin flips is calculated using the binomial probability formula, resulting in approximately 16.40625%.

Explanation:

The probability of getting exactly 3 heads when flipping a penny 9 times involves combinations and binomial probability. The probability of getting a head on any single flip is 50% (or 0.5), and the same is true for getting a tail.

To calculate the probability of getting exactly 3 heads (and therefore 6 tails), we use the binomial probability formula:

P(exactly k heads) = C(n, k) × ([tex]p^k[/tex]) × ([tex](1-p)^(n-k)[/tex])

Where:

‘C(n, k)’ is the number of combinations of n things taken k at a time   ‘p’ is the probability of getting a head on a single flip (0.5)‘n’ is the total number of flips (9)‘k’ is the number of desired heads (3)

Therefore, the probability is:

P(3 heads) = C(9, 3) × (0.5³) × (0.5⁽⁹⁻³)

Calculating C(9, 3) gives us 84 combinations. So the probability is:

P(3 heads) = 84 × (0.5³) × (0.5⁶) = 84 × (0.125) × (0.015625) = 0.1640625 or 16.40625%

Which is equivalent to 5√1,215^x

Answers

Answer:

here is the answer look at picture above

HELP!!THANKS FOR ACCURACY

Answers

[tex]\bf tan^2(x)-1=0\implies tan^2(x)=1\implies tan(x)=\pm\sqrt{1} \\\\\\ tan^{-1}[tan(x)]=tan^{-1}(\pm 1)\implies x=tan^{-1}(\pm 1)\implies x= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4}\\\\ \frac{5\pi }{4}\\\\ \frac{7\pi }{4} \end{cases}[/tex]

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