30 points!!!!!!!
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.

Several trials are performed with the results shown in the table. What is the experimental probability of randomly drawing a red marble?

Red Blue Green
16 30 34
32%
25%
20%
16%

Answer:

Step-by-step explanation:

Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;

a+2b = 400 ....

From the equation above, a = 400 - 2b ... 2

If the product of the numbers is a maximum then;

ab = (400-2b)b

let f(b) be the product of the function.

f(b) = (400-2b)b

f(b) = 400b-2b²

For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0

f'(b)= 400-4b = 0

400-4b = 0

400 = 4b

b = 400/4

b = 100

Substituting b= 100 into the equation a = 400 - 2b to get a;

a = 400 - 2(100)

a = 400 - 200

a = 200

The two positive integers are 100 and 200.

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Answer:

(3) y+2=2(x-8)

Step-by-step explanation:

Substitute the point into the equation and see if it is true

(8,-2)

(1) y+2=2(x+8)

    -2+2 = 2(8+8)

    0 = 2(16)

False

(2) y-2=2(x-8)

  -2-2 = 2(8-8)

  -4 =2 (0)

  False

(3) y+2=2(x-8)

  -2+2 = 2( 8-8)

  0 = 2(0)

 True

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

  -2-2 = 2(8+8)

  -4 = 2(16)

False

Answer:

[tex]\boxed{y+2=2(x-8) }[/tex]

Step-by-step explanation:

[tex]x=8[/tex]

[tex]y=-2[/tex]

[tex]\sf Check \ the \ third \ option.[/tex]

[tex]-2+2=2(8-8)[/tex]

[tex]\sf Both \ sides \ must \ be \ equal.[/tex]

[tex]0=2(0)[/tex]

[tex]0=0[/tex]

Answers:

[tex]\text{Perimeter} = 14\sqrt{5}\\\\\text{Area} = 50\\\\[/tex]

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

Work Shown:

[tex]L = 2\sqrt{5} = \text{length}[/tex]

[tex]W = 5\sqrt{5} = \text{width}[/tex]

P = perimeter

[tex]P = 2*(L+W)\\\\P = 2*(2\sqrt{5}+5\sqrt{5})\\\\P = 2*(7\sqrt{5})\\\\P = 14\sqrt{5}\\\\[/tex]

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

A = area

[tex]A = L*W\\\\A = (2\sqrt{5})*(5\sqrt{5})\\\\A = (2*5)(\sqrt{5}*\sqrt{5})\\\\A = 10\sqrt{5*5}\\\\A = 10\sqrt{25}\\\\A = 10*5\\\\A = 50\\\\[/tex]

[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]

The Sum is 989100.

The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.

The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)

Given:

a1 = 200

an= 1998

So, using formula

S= n(a1 + an)/2

now,

d=2

an= a1+(n-1)d

1998= 200 + (n-1) 2

1998-200= (n-1)2

1798/2=n-1

n= 900

S900= 900( 200 + 1998)/2

        =450*2198

       = 989100

Hence, the sum is 989100.

Learn more about this concept here:

https://brainly.com/question/18837188

#SPJ2

Answer:

30

Step-by-step explanation:

5x3=p

px2 = a

5x3 = 15 x 2 = 30

Answer:

5 times 3 times 2=30

Step-by-step explanation:

5×3=15×2=30

Answer:

3 hours

Step-by-step explanation:

Downstream, the speeds add up:

It will take:

To ride 87 km.

Answer:

348 frogs

Step-by-step explanation:

ratio = 3:7

total of ratio = 10

frogs = 3/10 × 1280 = 348 frogs

Answer:

let the ratio be 3x and 7x.

3x+7x=1280

10x=1280

x=128

Now

frogs =3x=3*128=384

toads =7x=7*128=896

Answer:

x=4

Step-by-step explanation:

To solve for x, we must get x by itself on one side of the equation.

[tex]\sqrt{x} +5-3=4[/tex]

First, we can combine like terms on the left side. Subtract 3 from 5.  

[tex]\sqrt{x} +(5-3)=4[/tex]

[tex]\sqrt{x} +2=4[/tex]

2 is being added on to the square root of x. The inverse of addition is subtraction. Subtract 2 from both sides of the equation.

[tex]\sqrt{x} +2-2=4-2[/tex]

[tex]\sqrt{x} = 4-2[/tex]

[tex]\sqrt{x} =2[/tex]

The square root of x is being taken. The inverse of a square root is a square. Square both sides of the equation.

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

[tex]x=2^2[/tex]

Evaluate the exponent.

2^2= 2*2 =4

[tex]x=4[/tex]

Let's check our solution. Plug 4 in for x and solve.

[tex]\sqrt{x} +5-3=4[/tex]

[tex]\sqrt{4} +5-3=4[/tex]

[tex]2+5-3=4[/tex]

[tex]7-3=4[/tex]

[tex]4=4[/tex]

Our solution checks out, so we know x=4 is correct.

Answer:

The first and second iteration of Newton's Method are 3 and [tex]\frac{11}{6}[/tex].

Step-by-step explanation:

The Newton's Method is a multi-step numerical method for continuous diffentiable function of the form [tex]f(x) = 0[/tex] based on the following formula:

[tex]x_{i+1} = x_{i} -\frac{f(x_{i})}{f'(x_{i})}[/tex]

Where:

[tex]x_{i}[/tex] - i-th Approximation, dimensionless.

[tex]x_{i+1}[/tex] - (i+1)-th Approximation, dimensionless.

[tex]f(x_{i})[/tex] - Function evaluated at i-th Approximation, dimensionless.

[tex]f'(x_{i})[/tex] - First derivative evaluated at (i+1)-th Approximation, dimensionless.

Let be [tex]f(x) = x^{2}-8[/tex] and [tex]f'(x) = 2\cdot x[/tex], the resultant expression is:

[tex]x_{i+1} = x_{i} -\frac{x_{i}^{2}-8}{2\cdot x_{i}}[/tex]

First iteration: ([tex]x_{1} = 2[/tex])

[tex]x_{2} = 2-\frac{2^{2}-8}{2\cdot (2)}[/tex]

[tex]x_{2} = 2 + \frac{4}{4}[/tex]

[tex]x_{2} = 3[/tex]

Second iteration: ([tex]x_{2} = 3[/tex])

[tex]x_{3} = 3-\frac{3^{2}-8}{2\cdot (3)}[/tex]

[tex]x_{3} = 2 - \frac{1}{6}[/tex]

[tex]x_{3} = \frac{11}{6}[/tex]

Answer:

10 km

Step-by-step explanation:

Distance = 5 cm

4 cm = 8 km

In km, how far apart is school and home?

Cross Multiply

[tex]\frac{4cm}{8km}[/tex] · [tex]\frac{5cm}{1}[/tex]

Cancel centimeters

[tex]\frac{40(km)(cm)}{4cm}[/tex]

Divide

= [tex]\frac{40km}{4}[/tex]

= 10 km

Answer:

351.86

Step-by-step explanation:

the formula is

surface area=2πrh+2πr²

r= radius

h=height

Answer:

(9, -13.5)

Step-by-step explanation:

It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.

Rule for dilation is,

(x, y) → (kx, ky)

where 'k' is the scale factor.

If vertex R of the quadrilateral is (6, -9),

By the given rule of dilation,

R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]

           → R'(9, -13.5)

Therefore, Option given in bottom right (9, -13.5) will be the answer.

Answer:

I believe it is 12,393.86

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

To simplify the fraction [tex]\frac{24}{64}[/tex], we need to find its greatest common factor.

Both 24 and 64 are divisible by 2, but that's not the biggest.

Both 24 and 64 are divisible by 4, but that's not the biggest either.

Both 24 and 64 are divisible by 8, and that's the highest we can go.

So:

[tex]\frac{24\div8}{64\div8} = \frac{3}{8}[/tex].

Hope this helped!

The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:

When the "r" is the greatest common divisor for the two fractions.

So, we will use Euclid's algorithm:  

[tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex]

this is  [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex]

we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0.  Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.

So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]".

Learn more:

greatest rational number:brainly.com/question/16660879

Answer:

Hello,

Step-by-step explanation:

[tex]y^2-x^2+1=50\\y^2=x^2+49\\2\ functions \ :\\\\y=\sqrt{x^2+49} \\\\or\\\\y=-\sqrt{x^2+49} \\[/tex]

Using function concepts, it is found that:

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

The expression is given by:

[tex]y^2 - x^2 + 1 = 50[/tex]

In terms of x, the equation is given by:

[tex]y^2 = 50 + x^2 - 1[/tex]

[tex]y^2 = x^2 + 49[/tex]

[tex]y = \pm \sqrt{x^2 + 49}[/tex]

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

Testing the input x = 0:

[tex]y = \pm \sqrt{0^2 + 49}[/tex]

[tex]y = \pm \sqrt{49}[/tex]

[tex]y = \pm 7[/tex]

Two output values for one input, thus, it is not a function.

A similar problem is given at https://brainly.com/question/24603090

should be 2 3 andd 5

think of the - (- as a plus sign (this is what i was always taught) to add them so it would in turn be (-5) + 12 which equals 7 and choice 3 and 5 also equal this

Answer: 93-(18+30)=g

93-48=g

45=g

Step-by-step explanation: yup

The answer is 93-18-30-g=0 or 18+30+g=93

Step-by-step explanation:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Then, match each answer with the corresponding letter.

The answer to #1 was 9.  9 corresponds to the letter A.

The answer to #2 was -1.  -1 corresponds to the letter C.

The answer to #3 was 5.  5 corresponds to the letter P.

Finally, write each letter with its corresponding problem number.

So everywhere you see a 1, write A.

Everywhere you see a 2, write C.

Everywhere you see a 3, write P.

Continue until every blank has a letter and the problem is solved.

Answer:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Step-by-step explanation:

Answer:

b=70

Step-by-step explanation:

The range is the value that the output takes

In this graph, the output is constant at 70

The output value is b

b=70

opposite angles are equal

[tex]\\ \sf\longmapsto 13x+19=84[/tex]

[tex]\\ \sf\longmapsto 13x=84-19[/tex]

[tex]\\ \sf\longmapsto 13x=65[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

[tex]\boxed {\boxed {\sf x=5}}[/tex]

Step-by-step explanation:

We are asked to solve for x.

We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.

Since the 2 angles are congruent, we can set them equal to each other.

[tex](13x+19)=84[/tex]

Solve for x by isolating the variable. This is done by performing inverse operations.

19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.

[tex]13x+19-19= 84 -19[/tex]

[tex]13x= 84 -19[/tex]

[tex]13x=65[/tex]

x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.

[tex]\frac {13x}{13}= \frac{65}{13}[/tex]

[tex]x= \frac{65}{13}[/tex]

[tex]x= 5[/tex]

For this pair of vertical angles, x is equal to 5.

Answer:

Step-by-step explanation:

189² = 215² + 123² - 2(215)(123)cos x°

35,721 = 46,225 + 15,129 - 52,890 cos x°

35,721 = 61,354 - 52,890 cos x°

52,890 (cos x° ) = 25,633

cos x° = 25,633 ÷ 52,890 ≈ 0.4846

x° ≈ 61.01°

Answer:

(-5/9, 16/9)

Step-by-step explanation:

2y = -x + 3

-y = 5x + 1

To find the intersection, you need to substitute the y-value from the second equation into the first equation.  Rearrange the second equation so that it is equal to y.

-y = 5x + 1

-1(-y) = -1(5x + 1)

y = -5x - 1

Substitute this equation into the y-value of the first equation.

2y = -x + 3

2(-5x - 1) = -x + 3

-10x - 2 = -x + 3

(-10x - 2) + 2 = (-x + 3) + 2

-10x = -x + 5

(-10x) + x = (-x + 5) + x

-9x = 5

(-9x)/(-9) = (5)/(-9)

x = -5/9

Plug this x value into one of the equations and solve for y.

2y = -x + 3

2y = -(-5/9) + 3

2y = 5/9 + 3

2y = 32/9

(2y)/2 = (32/9)/2

y = 32/18 = 16/9

The ordered pair is (-5/9, 16/9).

Answer:

4/6 or 66.666...%

Step-by-step explanation:

If you want to find the probability of obtaining neither a 5 nor a 2 you find how many times they occur and add them together in this case 5 occurs once and 2 also occurs once out of 6 numbers so 1/6 + 1/6 equals 2/6, you now know that 4/6 of them won't be a 5 nor a 2 and because it is a fair die the likelihood of it falling on a number is the same for all sides so the answer is 4/6 or 66.67%.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

76.8 cm

Step-by-step explanation:

Answer:

76.8 cm

Step-by-step explanation:

38.4 cm + 38.4 cm = 76.8 cm

Answer: c = 4.97 and c = -1.97

Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex]

So, for the function f(x) = [tex]2x^{3}-9x^{2}-60x+1[/tex] on interval [-4,9]

[tex]f'(x) = 6x^{2}-18x-60[/tex]

f(-4) = [tex]2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1[/tex]

f(-4) = 113

f(9) = [tex]2.(9)^{3}-9.(9)^{2}-60.(9)+1[/tex]

f(9) = 100

Calculating average:

[tex]6c^{2}-18c-60 = \frac{100-113}{9-(-4)}[/tex]

[tex]6c^{2}-18c-60 = -1[/tex]

[tex]6c^{2}-18c-59 = 0[/tex]

Resolving through Bhaskara:

c = [tex]\frac{18+\sqrt{1740} }{12}[/tex]

c = [tex]\frac{18+41.71 }{12}[/tex] = 4.97

c = [tex]\frac{18-41.71 }{12}[/tex] = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97