A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. dan draws a marble randomly from the box, replaces it, and then draws another marble randomly. what is the probability of drawing two green marbles in a row? explain your answer.

Answer:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

Given equation: -3x + 7y = 21

Slope-Intercept Form: y = mx + b -

where:

Note: parallel lines have the same slope.

1. Rewrite the given equation in slope-intercept form:

[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]

Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.

2. Find the equation of the parallel line:

substitute the point (4, 9) into the equation to find the value of b

[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]

[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

3. Check your work:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]

[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

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Answer:

[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.

Slope intercept form

y = mx + c

Here,

m = slope

c = y-intercept

Let us write the given equation in slope-intercept form.

− 3x + 7y = 21

Add 3x to both sides.

7y = 3x + 21

Divide both sides by 7.

[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]

We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.

The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.

( 4, 9 ) → ( x , y )

m → 3/7

Let us find the value of c

[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]

And now let us write the equation of the new line.

[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Answer:

100

Step-by-step explanation:

explanation is shown in the picture

Let's set all the information into equations:

 ⇒ 3/4 of Ojo's money is €600.00 ⇒ [tex]\frac{3}{4} x = 600[/tex]

     (Where x is the total amount of money)

Let's solve the equation:

 ⇒ to find the total amount of money that Ojo has:

   [tex]\frac{3}{4}x=600\\ 3x=2400\\x=800[/tex]

 ⇒ total money is €800

Original question: what is 1/8 of this pocket money

     [tex]\frac{1}{8} *800=100[/tex]  

Answer: €100 is 1/8 of his pocket money

Hope that helps!

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Answer: 188

Step-by-step explanation: If you plug in all the values, you get 188.

So, 3(-6){squared} - 5(-6)(2) + 5(2){squared)

3(36)+60+20

3(36)+80

108 + 80 = 188

I hope this helps!

Answer:

188

Step-by-step explanation:

3x² - 5xy + 5y² for x = -6 and y = 2

3(-6)² - 5(-6)(2) + 5(2)² =

= 3(36) + 60 + 5(4)

= 108 + 60 + 20

= 188

Work Shown:

[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]

Therefore,

[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]

The solution has a positive answer (True).

Arithmetic operators are those signs such as addition, subtraction, multiplication, and division that are used to solve mathematical expressions such as fractions and linear equations.

1.

The solution to the expression:

= (-1)(1)(-1)(-1)(1)(-1)(-1)(-1)(-1)(1)(-1)(1)

= 1

Thus, the solution has a positive answer(True)

2.

The solution to the improper fraction:

[tex]\mathbf{\dfrac{5}{7}+(-\dfrac{2}{7})= \dfrac{3}{7} }[/tex]

3.

= -52.31 -(-7.44)

= -52.31 + 7.44

= -44.87

= - 4487/100

4.

The solution to the improper fraction is:

[tex]\mathbf{\dfrac{3}{5}\div -\dfrac{6}{15}=-\dfrac{3}{2} }[/tex]

5.

The given equation is:

-(-6.6) (-20) = 132  which is incorrect.

The correct solution is:

-(-6.6) (-20) = -132

Eric's mistake is that he forgot to multiply by -1 first.

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Answer:

156 cm²

Explanation:

This figure is a trapezium.

Formula of Area of Trapezium = 1/2 × (a + b)  × height

Here given:

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

Area of trapezium: 1/2  × (9 + 30)  × 8 = 156 cm²

Answer:

area of the trapezium is 156

Step-by-step explanation:

Answer:

3125

Step-by-step explanation:

And

Step-by-step explanation:

Hi There! Let me help you :)

[tex] = 6.6.6.3.3[/tex]

[tex] = 6(1 + 1 + 1).3(1 + 1)[/tex]

[tex] = 6(3).3(2)[/tex]

Answer:

I'm pretty sure it is d... .......

Answer:

Mixed Number: 11 1/5

Improper Fraction: 56/5

Step-by-step explanation:

Given:

It takes 3/7 tonnes of sand to make a tonne of concrete.

Mason has 4 4/5 tonnes of sand.

To Find:

How much concrete, in tonnes, can he make?

Give your answer as a fraction in its simplest form.

Solve:

By the given , takes 3/7 tonnes of sand = tonne of concrete.

Thus, we divide the total of tonnes of sand Mason have by how many it takes to make a tonne of concrete.

Hence, we have;

[tex]4\frac{4}{5}\div \frac{3}{7}[/tex]

Convert to improper fraction;

[tex]=\frac{24}{5}\div \frac{3}{7}[/tex]

Using the fraction rule;

[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{24}{5}\times \frac{7}{3}[/tex]

Cross-cancel common factor - 3

[tex]=\frac{8}{5}\times \frac{7}{1}[/tex]

Multiply fraction:

[tex]=\frac{56}{5}[/tex]

Convert improper to mixed number:

[tex]=11\frac{1}{5}[/tex]

Hence, the answer is [tex]\mathrm{11\frac{1}{5}\;or\;\frac{56}{5} }[/tex]

RevyBreeze

Answer:

[tex]\rm Improper \ fraction : \sf \sf \dfrac{56}{5} \ of \ concrete[/tex]

[tex]\rm Mixed \ fraction: \sf 11\dfrac{1}{5} \ of \ concrete[/tex]

Explanation:

[tex]\sf concrete = total \ tones \ of \ sand \ \div \ unit \ rate \ of \ sands \ required \ to \ make \ concrete[/tex]

Here given:

Concrete:

[tex]\sf \rightarrow 4\dfrac{4}{5} \div \dfrac{3}{7}[/tex]

[tex]\rightarrow \sf \dfrac{24}{5}\div \dfrac{3}{7}[/tex]

[tex]\rightarrow \sf \dfrac{24}{5}\times \dfrac{7}{3}[/tex]

[tex]\rightarrow \sf \dfrac{56}{5}[/tex]

[tex]\rightarrow \sf 11\dfrac{1}{5}[/tex]

Answer:

Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.

Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.

Step-by-step explanation:

Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".

Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.

Answer:

25.99

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent)

For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse

the measurement of sin (opposite / hypotenuse) relates these two measurements

we can plug in our known values into sin:

sin = opposite / hypotenuse

sin (38) = 16 / x

(note: sin 38 = 0.61566147532, which we can round to 0.61566)

0.61566 = 16 / x

· x                   ·x           {multiply both sides by x to get rid of fraction}

0.61566(x) = 16

÷ 0.61566       ÷0.61566     {divide both sides by 0.61566 to isolate 1x}

x = 25.9883702043

{round to nearest hundredth}

x = 25.99

so, the measure of x is 25.99  {rounded to the nearest hundredth}

hope this helps!! have a lovely day :)

Answer:

cosx=adjacent/hypotenuse

triangle angle =180-(90+38)

=52°

cos(52°)=16/x

x=16/cos52

x≈23.373

Answer:

300 feet

Step-by-step explanation:

The absolute value of a number is defined as that number's distance from 0 (the origin) on a number line, regardless of direction.

In this case, the origin can be represented by sea level. Since the lowest point of 300 feet is taken by reference to sea level, it can be said that the absolute value of the point is 300 feet, since this represents its vertical distance from sea level.

Hope this helps!

The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672

Here,

The formula for the percentile probability is

[tex]P=\mu+z\sigma[/tex]

P=262 + 1.2816(45)

P = 319.672

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The Arc Length BD from the given diagram is; 4.09π = 12.85 in

From the attached image, we are given;

m∠APC = 92°

Now, from the principle of vertical angles being congruent, we have;

m∠APC = m∠BPD = 92°

Thus;

Arc length BD = 2π * 8 * (92/360)

Arc Length BD = 4.09π = 12.85 in

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Answer: she would have 6 bottles left, (18/2)/6

Step-by-step explanation:

she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.

Answer:

4

Step-by-step explanation:

Proportionality between skein values

8:2=4:1

Proportionality between cost values

28:7=4:1

The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value

Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

[tex]y = \frac{1}{2} x[/tex]

The polynomial within the numerator is 9x²+45x+54.

Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.

A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let's take the polynomial within the numerator is k.

So, rewrite the given expression as

[tex]\frac{k}{3x^2+15x+18}=3[/tex]

or it also can be written as

[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]

Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire

k=3(3x²+15x+18)

Simplify the above expression,

k=9x²+45x+54

Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.

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Answer:a

Step-by-step explanation:

The function y = |x| - 1 is a translation of 1 unit downwards of the parent absolute value function, and its graph is the first one shown in the images.

Here we want to graph:

y = |x| - 1

Notice that if we take the parent absolute value function:

y = |x|

And we translate it one unit downwards, we will get:

y = |x| - 1

Which is the function that we want to graph.

So to select the correct graph, we need to find the one that is the parent absolute value function translated one unit downwards. It is the one with the vertex at (-1, 0), which is the graph that appears on the first image.

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The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;

x³(2x + 5) - 4(2x + 5)

2x⁴ + 5x³ - 8x - 20

Therefore,

2x⁴ + 5x³ - 8x - 20

x³(2x + 5) - 4(2x + 5)

Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:

2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)

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Answer:

the answer will be 17.

Step-by-step explanation:

if, f (x) = 3x + 2

f (5) = 3 × 5 + 2 = 17.

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The number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

Permutation is the number of ways of arrangement for a given set.

The formula for a permutation is given as P(n, r) = n! / (n-r)!

Where n = items chosen from = 5

r is the number of items = 4

Substitute values into the formula

P(5, 4) = [tex]\frac{5!}{5-4!}[/tex]

P(5,4) = [tex]\frac{5 * 4* 3*2*1}{1}[/tex]

P(5,4) = [tex]\frac{120}{1}[/tex]

P(5,4) = 120

Therefore, the number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

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Answer:

The answer is actually 120.

Step-by-step explanation:

I have the keysheet to the questions.

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = x - 1/2, (-5, -2)

we can plug in the point (-5, -2)

-2 = (-5) - 1/2

-2 = -5.5

-2 does not equal -5.5 so this point is not on the line

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Answer: (2,5)

Step-by-step explanation: Step 1: Identify key concepts for Part A

y=7x-9

Slope: 7

y int.  :  -9

y=3x-1

Slope: 3

y int.  :  -1

Since you know this information, you can plot the points and graph it.

Part B

To solve a system of equations, you need to identify the point whereby the two graphs intersect, and since you're solving it graphically, just find the point of intersection. You should get an answer of: (2,5)

(x=2) and (y=5)

Answer:

x=0

Step-by-step explanation:

[tex]4 \cos(x) = - \sin {}^{2} (x) + 1[/tex]

[tex]4 \cos(x) = 1 - \sin {}^{2} (x) [/tex]

[tex]4 \cos(x) = \cos {}^{2} (x) [/tex]

[tex]4 \cos(x) - \cos {}^{2} (x) = 0[/tex]

[tex] \cos(x) (4 - \cos(x) ) = 0[/tex]

[tex] \cos(x) = 0[/tex]

[tex]x = 0[/tex]

[tex]4 - \cos(x) = 0[/tex]

[tex] \cos(x) = 4[/tex]

There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.

We need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

The amount of each volume m = CV where

The amount of 50 % mixture, m = amount of 100 % powder + amount of 20 % powder.

M = m + m'

CV = C'V' + C"V" where

So, CV = C'V' + C"V"

0.5V = 1 × V' + 0.2 × 4

0.5V = V' + 0.8  (1)

Also, we have that the total volume V = V' + V"

V = V' + 4 (2)

Substituting equation (2)into (1), we have

0.5V = V' + 0.8

0.5(V' + 4) = V' + 0.8

0.5V' + 0.5 × 4 = V' + 0.8

0.5V' + 2 = V' + 0.8

0.5V' - V' = 0.8 - 2

-0.5V' = -1.2

V' = -1.2/-0.5

V' = 2.4 mL

So, we need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

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T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]

The inverse of the matrix is

[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]

So, the Inverse Transformation is given by

[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

So, no option is correct. And the answer is

[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

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Answer:

A

Step-by-step explanation:

f(x) = x²

f(x) becomes f(13x) + 6

the "+ 6" at the end tells us already everything, because there is only one aber option listed that contains a shift up. and that is exactly what that "+ 6" did. it adds 6 to every possible y value of the function. so, the whole function moves up by 6 units.

and yes, the 13x of f(13x) stretches the function horizontally (along the x axis).

simply said, whenever the x value for the original function increased by 1, it increases for the new function by 13.