Evaluate the infinite sum

Answer:

1. The correct answer is D) 1/36

Step-by-step explanation:

WE can tell this because the chance of rolling either is 1/6. To find the total probability we multiply those together.

1/6 * 1/6 = 1/36

[tex]g(x)=x^3+5x^2-12x-36\\\\y-intercept\ for\ x=0:\\\\g(0)=0^3+5(0)^2-12(0)-36=-36\\\\\text{First or fourth graph.}\\\\\text{If the answer is 4th graph, then g(-2)=0}\\\\g(-2)=(-2)^3+5(-2)^2-12(-2)-36=-8+5(4)+24-36\\\\=-8+20+24-36=0[/tex]

The polynomial function utilizes only non-negative integers powers or positive integer exponent of the variable in a solution, like the quadratic equation, cubic equation, and so on, further calculation can be defined as follows:

Given:

[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]

To find:

Graph the polynomial function=?

Solution:

[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]

putting the value "1,2, -1, -2" into the above given function and calculate its value:

[tex]\to \bold{g(1)=1^3+5(1)^2-12(1)-36= 1+5-12-36= -42}\\\\\to \bold{g(-1)=(-1)^3+5(-1)^2-12(-1)-36= -1+5+12-36= 17-37=-20}\\\\\to \bold{g(2)=(2)^3+5(2)^2-12(2)-36= 8+5(4)-24-36= 8+20-24-36=-32}\\\\\to \bold{g(-2)=(-2)^3+5(-2)^2-12(-2)-36= -8+5(4)+24-36= -8+20+24-36=0}\\\\[/tex]Therefore, the answer is "4 choice".

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Answer:

4 miles to the nearest mile.

Step-by-step explanation:

Circumference of the track = 2 pi r

= 2*pi*0.2 = 1.257  miles

Ellie ran 3 times around the track so

the distance she ran is 3* 1.257

=  4 miles

PPEERRPPEENNDDIICCUULLAARR

Answer:

6.25

Step-by-step explanation:

Because to know the answer we have to divide 75 by 12 which is 6.25

Answer:

Problem One: D

Problem Two: B

Step-by-step explanation:

Problem One

A and B are both wrong for the same reason. The graph for both of them will increase. Any time you raise a base greater than 1 to a power, the graph goes up. See below. The red graph is y = 12*1.1^2

The question is giving you a big hint by showing you which point to look at. When x = 1, y = 8. What will do that?

Is it 12 * 1/2 or is it 12 * 2/3

I think you will find it is 12*2/3 So the answer is D

Part B

This one is just the opposite, only now you have to figure out which graph you are getting. A is the only one that is obviously wrong. When x = 1, A will give

40* 1.5 which is 60 which is not enough.

C is too large. 40 * 3.25 = 130 so that does not describe the graph when x = 1.

So B and D are your only choices. D is still a little too big. See if you can get D to be 100 when D = 1

That leaves you with b

y = 40 * 2.25 = 90 which is just what you want.

Answer

Tara puts 4 pennies if Sam puts 1 but Sam put 10 pennies in all so you multiply 10 by 4 and that gives you 40

Step-by-step explanation:

Answer:

[tex]\frac{7}{64}\approx 0.11[/tex]

Step-by-step explanation:

We have been given that there are 4 red marbles and 7 blue marbles and 5 yellow marbles in a bag. Monica will randomly pick two marbles out of the bag replacing the first marble before picking the second marble.

Since Monica will replace the first marble before picking the second marble, therefore, probability of both events will be independent and probability of occurring one event will not affect the probability of second event's occurring.          

Since the probability of two independent compound events is always the product of probabilities of both events.

[tex]P(\text{A and B})=P(A)*P(B)[/tex]

Now let us find probability of picking a red marble out of 16 (4+7+5) marbles.

[tex]P(Red)=\frac{\text{Total red marbles}}{\text{Total marbles}}[/tex]

[tex]P(Red)=\frac{4}{16}[/tex]

Probability of picking blue ball out of 16 (4+7+5) marbles:

[tex]P(Blue)=\frac{\text{Total blue marbles}}{\text{Total marbles}}[/tex]

[tex]P(Blue)=\frac{7}{16}[/tex]

Now let us find probability of Monica picking a red and then a blue marble.

[tex]P(\text{Red and Blue})=\frac{4}{16}\times \frac{7}{16}[/tex]

[tex]P(\text{Red and Blue})=\frac{1}{4}\times \frac{7}{16}[/tex]

[tex]P(\text{Red and Blue})=\frac{7}{4*16}[/tex]

[tex]P(\text{Red and Blue})=\frac{7}{64}[/tex]

[tex]P(\text{Red and Blue})=0.109375\approx 0.11[/tex]

Therefore, the probability of picking a red and then blue marble is [tex]\frac{7}{64}\approx 0.11[/tex].  

Answer:

16m

Step-by-step explanation:

Since the length of the park is 7m, then the other side is also 7m so 46-14 is 32. So 32/2 is 16.

Answer:

A/C and B/D and C/E

Step-by-step explanation:

given the order of 2 matrices

(m × n)(p × q)

For the matrices to be conformable for multiplication

The number of columns in the first must equal the number of rows in the second

That is n = p and the resulting product has order m × q

From the order of matrices given

A and C, B and D, C and E can be multiplied

The matrices that can be multiplied are A*C, C*A, B*D, and E*D, as the number of columns in the first matrix equals the number of rows in the second.

In matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Therefore, given the order of the matrices A = 3x2, B = 3x5, C = 2x3, D = 5x7, and E = 3x5, the possible matrix multiplications are: A*C, C*A, B*D, and E*D. For instance, you can multiply A (which is 3x2) with C (which is 2x3) because the number of columns in matrix A is equal to the number of rows in matrix C.

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1. The slope of the line is 3.

2. The direct variation equation is y = 3x

3. The equation in slope-intercept form is:y = 4

4. The equation in slope-intercept form is y = 2/3x + 1.

5. The equation = −2/3 − 1

6. The equation of the parallel line is y = 5x - 11.

1. Slope of the line:

The slope (m) of the line passing through (-1, 2) and (0, 5) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (5 - 2) / (0 - (-1))

m = 3 / 1

m = 3

Therefore, the slope of the line is 3.

2. Direct variation equation:

Since y varies directly with x, we can write their relationship as y = kx, where k is the constant of proportionality. We can find k using the given information:

y = 15 when x = 5

15 = k * 5

k = 3

Therefore, the direct variation equation is y = 3x

When x = 9, y = 3 * 9 = 27.

3. Equation in slope-intercept form: First, calculate the slope using the same formula as in question 1:

m = (4 - 4) / (1 - (-3))

m = 0 / 4

m = 0

Since the slope is 0, the line is horizontal. The equation in slope-intercept form is:

y = 4 (constant y-intercept because it passes through (1, 4))

4. Equation in slope-intercept form using point-slope form:

The point-slope form equation is:

y - y1 = m(x - x1)

Plug in the given values:

y - (-1) = 2/3(x - (-3))

y + 1 = 2/3(x + 3)

3y + 3 = 2x + 6

3y = 2x + 3 (subtract 3 from both sides)

y = 2/3x + 1 (divide both sides by 3)

Therefore, the equation in slope-intercept form is y = 2/3x + 1.

5. Writing the equation in standard form:

The equation = −2/3 − 1 is already in standard form (ax + by = c), where a = -2/3, b = 0, and c = -1.

6. Equation of the parallel line:

Since the parallel line has the same slope (5) as the given line, its equation will be of the form y = 5x + b. To find b, plug the point (2, -1) into this equation:

-1 = 5(2) + b

-1 = 10 + b

b = -11

Therefore, the equation of the parallel line is y = 5x - 11.

Answer: statue of liberty

Step-by-step explanation:

Answer:

when it says music its kinda a metaphor to peace when it says a flame that does burn it means the torch shes holding. She is over 40 years old shes 143 years old and she doesn't have any birth date she is the statue of liberty

The solution to the inequality is [tex]\(x > -17\).[/tex]

To solve the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex], let's first find a common denominator and then combine the fractions:

[tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex]

Multiply each term by -3 to clear the fraction:

[tex]\(5 - 2x + 12 < -3x\)[/tex]

Combine like terms:

[tex]\(-2x + 17 < -3x\)[/tex]

Add [tex]\(2x\)[/tex] to each side:

[tex]\(17 < -x\)[/tex]

Multiply each side by -1 (remember to reverse the inequality when multiplying by a negative number):

[tex]\(-17 > x\)[/tex]

So, [tex]\(x > -17\).[/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

Step 1: Start with the given inequality:

[tex]\[\frac{5-2x}{-3} - 4 < -x\][/tex]

Step 2: Multiply both sides of the inequality by -3 to clear the fraction:

[tex]\[5-2x + (-3) \cdot 4 > -3 \cdot (-x)\][/tex]

[tex]\[5-2x -12 > 3x\][/tex]

Step 3: Combine like terms:

[tex]\[-7-2x > 3x\][/tex]

Step 4: Add 2x to both sides:

[tex]\[-7 > 5x\][/tex]

Step 5: Divide both sides by 5 (remembering to reverse the inequality when dividing by a negative number):

[tex]\[\frac{-7}{5} < x\][/tex]

So, the solution to the inequality is:

[tex]\[x \in \left(-\infty, -\frac{7}{5}\right)\][/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

Multiply the amount of money he had by the percent of the game:

200 x 0.22 = 44

The game cost $44

Answer:

The probability is 17.36%

Step-by-step explanation:

In order to find this, we first need to find the probability of pulling one green marble. You can do this by dividing the number of marbles by the amount of marbles in the bag.

10/24 = 41.67%

Now in order to find the likelihood of doing this twice, you multiply that number by itself.

41.67% *41.67% = 17.36%

Answer:

y=-4x-3

Step-by-step explanation:

Answer:

Price $0.75 per ounce of confetti

Step-by-step explanation:

Given the statement: Yuki bought a pound of confetti for $12.

⇒[tex]1 pound = \$ 12[/tex]                 ......[1]

Also, it is given that there are 16 ounces in 1 pound.

⇒ 16 ounces = 1 pound                       .....[2]

To calculate the price, in dollars per ounce of confetti.

From [1] and [2] we have;

[tex]16 ounces = \$12[/tex]

then;

1 ounces =  [tex]\frac{12}{16} = \frac{3}{4} = \$0.75[/tex]

Therefore, the price, in dollars per ounce of confetti is, $0.75  per ounce.

Answer:

(11,9)

Step-by-step explanation:

If a circle is given by its equation [tex](x-a)^2+(y-b)^2=r^2,[/tex] then coordinates of the center are [tex](a,b)[/tex] and radius is r.

In your case, for the circle with equation [tex](x-11)^2+(y-9)^2=225,[/tex] you can state that coordinates of the center are (11,9) and radius is 15.

Answer:

The center of the circle is (11,9)

Answer:

Buffalo mild wings offers the lowest price per wing ($0.83).

Step-by-step explanation:  

Let us find unit price per buffalo wing of each restaurant.

[tex]\text{Unit rate for buffalo bills}=\frac{\$7}{8\text{ wings}}[/tex]

[tex]\text{Unit rate for buffalo bills}=\frac{\$0.875}{\text{ wing}}[/tex]

Upon rounding our answer to nearest cent we will get,

[tex]\text{Unit rate for buffalo bills}=\frac{\$0.88}{\text{ wing}}[/tex]

Therefore, buffalo bills offers each wing for $0.88.

[tex]\text{Unit rate for buffalo mild wings}=\frac{\$10}{12\text{ wings}}[/tex]

[tex]\text{Unit rate for buffalo mild wings}=\frac{\$0.83333}{\text{ wing}}[/tex]

Upon rounding our answer to nearest cent we will get,  

[tex]\text{Unit rate for buffalo mild wings}=\frac{\$0.83}{\text{ wing}}[/tex]

Therefore, buffalo mild wings offers each wing for $0.83.

[tex]\text{Unit rate for wingers}=\frac{\$17}{20\text{ wings}}[/tex]

[tex]\text{Unit rate for wingers}=\frac{\$0.85}{\text{ wing}}[/tex]

Therefore, wingers offers each wing for $0.85.

We can see that buffalo mild wings offers the lowest price per wing that is $0.83 per wing.

Answer:

Vectors can be used in sports to define how a baseball player moves to catch a high fly baseball they can also be used with aircrafts.

Remember that science uses vectors to describe anything that has both a direction and a magnitude (size or quantity). These are drawn as pointed arrows, which length represents the magnitude. They are very used to locate persons or objects as the final direction can be predicted using a reference point, an stimated speed and direction. Vectors are also usefull to predict what would happen if two objects come into contact, an example would be predicting the movement of billiard balls, or calculating the trajectory of a golf ball.  

The equation of the line that passes through the point (-1,5) and has a slope of -7 is y = -7x - 2. This can be determined by substituting the given values into the equation y = mx + b and solving for 'b'.

In mathematics, the equation of a line is commonly represented as y = mx + b, where 'm' represents the slope and 'b' is the y-intercept. In this equation, the slope '-7' is the rate at which 'y' changes for a unit change in 'x'. The y-intercept is the 'y' value when 'x' is zero.

It's given that the line passes through the point (-1,5). We can substitute these values into the equation to find 'b':

5 = -7(-1) + b, which simplifies to 5 = 7 + b. Therefore, 'b' equals to -2 after rearranging.

So, the equation of the line that passes through the point (-1,5) and has a slope of -7 is y = -7x - 2.

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Answer:

Hey There so i saw your question. Solving it is very easy so i'm gonna help you step by step.

Step-by-step explanation:

(-3,4) (5,6) the slope formula y2-y1 over x2-x1  

so its 6-4/5-(-3)  which you gonna get 2/8 which is 1/4 so thats your slope.

*just know that your slope will flip since it's perpendicular and not parallel

so now you gonna find "b" on the equation Y=mx=b so out of your 2 points, choose one. I choose (5,6) all you gotta do is plug it into y=mx+b

so it's gonna be 6= 4 (the flipped slope)*5+b    {1.4*5 = 1.25}

so you gonna take 6 - 20 = -14 whcih is your b

so your new equation + the answer is Y= 4x-14

Answer:

hello : here is a solution

Answer:

A) Infinite and f(6) does not exist

Step-by-step explanation:

The three types of discontinuities are:

1. Removable or Hole: When the left hand limit is same as right hand limit but they are not equal to the value of function at x = 6.

Graphically if there exist a hole at the point x = 6, removable discontinuity occurs. But, it is not the case in the given graph.

2. Jump: When the left hand limit is not same as right hand limit.

But graphically, we see that both left and right limit at x=6 are tending to infinity i.e. both limits are same.

3. Infinite: It occurs when there exists vertical or horizontal asymptotes between the function and both limits tend to infinity.

Graphically, we see that the function has infinite discontinuity as there exist vertical asymptote and the value of function does not exist at x = 6.

Answer:

5 hours

Step-by-step explanation:

given :

Distance between the cities = 540 miles

Speed of motorcycle =48 mph

TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :

[tex]\frac{DISTANCE}{SPEED}[/tex]

By putting given values in the formula we get :

[tex]\frac{540}{48}[/tex]

= 11.25 hours

Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle

⇒ 11.25 hours - 2.25 hours

⇒ 9 hours

Thus , Time taken by car to cover the same distance is 9 hours .

Now to calculate speed of car by using formula:

[tex]\frac{distance}{time}[/tex]

[tex]\frac{540}{9}[/tex]

= 60 mph

Let t be the time taken to meet if they start moving towards each other.

So distance covered by motorcycle in t hours is

speed\times time

= 48t miles

Distance covered by car in t hours is

speed\times time

= 60t miles

⇒ 60t + 48t =540

⇒ 108t = 540

⇒ t= 5 hours

Therefore, time taken to meet if they start moving towards each other is 5 hours.

Answer: 2500 meters²

Step-by-step explanation:

Perimeter: 200 = 4w  

             ⇒    50 = w

Area = w²

        = (50)²

        = 2500

The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The perimeter of the rectangle = 2( length + Width)

                                             200 = 2( length + Width)

                                         100 - w = L

The area of the rectangle = length × Width

                                            = w(100 - w)

                                            = (-w)²+ 100w

So,  (-w)²+ 100w where, a = -1 and b = 100

w = -100/2(-1)

w = 50

The area of the rectangle = (-w)²+ 100w

                                            = (-50)²+ 100(50)

                                           = 2500

Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

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