-x²-22x - 121 = 0 quadratic

The probability of drawing purple and green marbles will be 1/80.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Number of purple marble = 5

Number of green marble = 1

Total marble = 5 + 6 + 8 + 1 = 20

Probability drawing a purple marble = 5/20

Probability of drawing a green marble = 1/20 (because the number of marble remain the same)

Probability of drawing a purple and green = 5/20 x 1/20 = 1/80

Hence "There is a 1/80 chance of drawing purple and green marbles.".

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785.4 cubic feet

Step 1: Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.

Step 2: For Emma’s cylindrical storage tank, the radius of the base is 5 feet. Substitute this value in the formula and calculate the area of the base, which is equal to: A = π*5² = 78.54 square feet.

Step 3: Now we need to calculate the volume of the cylindrical storage tank. The volume of a cylinder is calculated by: V = π*r²*h, where r is the radius of the circle and h is the height of the cylinder. For Emma’s tank, the height is 10 feet. Substitute these values in the formula and calculate the volume, which is equal to: V = π*5²*10 = 785.4 cubic feet.

Step 4: Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.

If you have any additional questions or need further assistance, please let me know.

Answer:

You need to multiple

Step-by-step explanation:

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^{0.0475\cdot 16} \implies \cfrac{6500}{e^{0.0475\cdot 16}}=P\implies 3039.83\approx P[/tex]

Answer:

Not possible with given

Step-by-step explanation:

The measures are  NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.

What is the perimeter of the triangle?

A triangle's perimeter is measured in the same unit as its side lengths. If the lengths of its sides are measured in a different unit, first convert them to that unit.

We have,

OA = (4x + 3)  .............(1)

NE = (2.5x)     .............(2)

RN = 4.5         .............(3)

ER = (2x)         .............(4)

Mid-point segment of the triangle

EN = 1/2(OA)         .............(5)

from equations (1), (2), and (5)

2.5x = 1/2(4x + 3)

5x = 4x + 3

x = 3           .............(6)

OA = 4x + 3 = 15

NE = (2.5x) = 7.5

ER = (2x) = 6

RN = 1/2(GO)

GO = 2 * RN = 2 * (4.5)

GO = 9

ER = 2x = 2*3 = 6

AG = 2(ER) = 2 * 6 = 12

The perimeter of the OAG is OA + AG + GO = 15 + 12 + 9

= 36 units.

Hence, the asked measures are  NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.

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Answer:

he paid 20.20 for the patch

Answer:

The equation could you use to find the price of one tire patch select all that apply 4x + 1.9 = 22.2 and 22.2-4x= 1.9

The mid point of the line segment is (1,9)

The general formula to calculate the midpoint is written as

(x, y) = (x1+x2/2) , (y1 + y2)/2

Where (x1, y1) and (x2, y2) refers the end points.

Here we have given that line segment with endpoints a (-3, 7) and b (1, 11).

And we need to find the midpoint.

While we looking into the given question we have the end point of the line segment

Then the values of (x1, y1) is (-3, 7) and the value of (x2, y2) is (1, 11),

Then the midpoint is calculated by apply the values on the formula, then we get,

=> (1 - 3)/2 , (11 + 7)/2

When we do the appropriate mathematical operation, then we get

=> 2/2 , 18/2

Therefore, the midpoint is (1, 9).

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Choices B, C and D are required answer choices.

What is an isosceles triangle?

Any triangle with two equal sides and angles with equal measures on opposite sides is said to be an isosceles.

Based on the given diagram,

BD is perpendicular to AC because the given angle D is 90 degrees.

And, AD = DC (Given)

or, 4x = x + 9

or, 4x -x = 9

or, 3x = 9

or, x = 3

Then, AD = 4x = 4*3 = 12

And, AB = BC

So, the two sides of a given triangle are equal to each other.

Then, triangle ABC is an isosceles triangle.

Based on the above calculation and data, we can conclude that

Hence, Choices B, C and D are required answer choices.

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Complete Question,

The required given function is a translation of the parent function by 8 units left and  3 units up.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function, g(x) = (x − 8)³+ 3

Parent function, f(x) = x³

From observation, it is seen that,
The given function is translated function of the parent function as,
As the parent function is translated left on the x-axis by 8 units, and 3 units up on the y-axis.

Thus, the required given function is a translation of the parent function by 8 units left and  3 units up.

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We can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, the quantity of mixed nuts we need is x pounds.

There are 0.70 pounds of peanuts in this mixture.

3 pounds of peanuts make up the 20% mix, or 0.20*15.

We got the equation:

0.70 x + 3 = 0.40(x + 15)

Now, solve this equation as follows:

0.70 x + 3 = 0.40(x + 15)

0.70 x + 3 = 0.40(x + 15)

0.70x + 3 = 0.40x + 6

0.70x - 0.40x = 6 - 3

0.30x = 3

x = 10 pounds

Therefore, we can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

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The monomial that completes the expression is x²

From the question, we have the following parameters that can be used in our computation:

36 - 12x + ...

Complete the expression with a variable

So, we have

36 - 12x + y

Rewrite as

y - 12x + 36

The given terms of the expression are factors of 6

By trial and error, we make use the following representation

y - 12x + 36 = (x - 6)²

Expand the expression

y - 12x + 36 = x² - 12x + 16

Evaluate the like terms

y = x²

Hence, the monomial is x²

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Using simple mathematical operations, we know that a-b can be -1, -2, and 0.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).

So, we have: 2 < a < 5, 3 < b < 7

Now, a - b will be:

the values of a can be 3 and 4

Similarly, the value of b can be 4 and 5.

So there are 4 possibilities as shown:

3 - 4 = -1

3 - 5 = -2

4 - 4 = 0

4 - 5 = -1

Therefore, using simple mathematical operations, we know that a-b can be -1, -2, and 0.

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Using the distance formula, [tex]JP=\sqrt{(0-4)^2+(1-(-2))^2}=\boxed{5}[/tex]

Answer:

y=2/3x-2

Step-by-step explanation:

The equation is y = mx + b and m is the slope. You were already given the slope and you were even given a point. All you have to do is graph the point and use the slope until it intercepts the y-axis.

1. Plot the point (9,-8)

2. Go up 2, left 3 spots until the line hits the y-axis (the vertical one)

3. That point is what b will be equal to in y = mx + b

OR you can convert a point-slope equation into slope intercept

1. The formula for point slope is y – y1 = m(x – x1)

2. Plug in the given numbers and it will look like this: y+8=2/3(x+8)

3. Do the math and get a solution of y=2/3x-2

Answer:

B

Step-by-step explanation:

x -5 ≥ 0

x ≥ 5

the function exists only in the interval [5, +oo) and it keeps growing

Answer:

if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2

the area of a rectangle = length * width

thus, area = x*(7-x^2)= 7x-x^3

in order to maximize the area, you would need to take the derivative of the area and set it equal to 0

Area = 7x-x^3Area' = 7 - 3x^2

7-3x^2 = 0thus, x = 1.5275

this x represents the x needed to create the largest possible area with the given parameters.

Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

The number that twice the sum of it and negative seven is eight is 11.

Twice the sum of the number and negative seven is eight. The number can be found as follows:

let

the number  = x

According to the word expression, twice the value of  the addition of x and minus seven is equals to 8. Hence, we will find the value of x in the equation formed from the words expression.

The variable x is the required number.

Therefore,

2(x + (-7)) = 8

2(x - 7) = 8

open the brackets

2(x - 7) = 8

2x  - 14 = 8

add 14 to both sides of the equation

2x  - 14 = 8

2x  - 14 + 14 = 8 + 14

2x = 22

divide both sides by 2

x = 22 / 2

x = 11

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Answer:

30

Step-by-step explanation:

get the x by itself on one side to solve

x-6/2=10

multiply both sides by 2 and divide by 6 which cancels out s x is by itself

x=10*6/2

simplify

x=60/2

x=30

Answer:

x = 13

Step-by-step explanation:

Given equation,

→ x - (6/2) = 10

Now the value of x will be,

→ x - (6/2) = 10

→ x = 10 + (6/2)

→ x = 10 + 3

→ [ x = 13 ]

Hence, the value of x is 13.

Answer:

200 b/c she will use 50cm² by Wall :)

The required value of the given function f(-1) is 2.

What is a function?

Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.

For the given graph,

For x = -1, the exact y value will be 2.

So, f(-1) = 2

Hence, the required value of the given function f(-1) is 2.

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Answer:

A. No

B. Yes

C. No

Step-by-step explanation: To determine if each pair is a solution to the equation, substitute the x and y variables in the pairs for the corresponding variables in the equation. If the left and right sides are equal once you solve, you will know that the pair is a solution,

(9,1)   2(9)+7(1)=16    18+7=16    25=16    No

(8,0)    2(8)+7(0)=16    16+0=16    16=16    Yes

(0,0)    2(0)+7(0)=16    0+0=16    0=16    No

The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.

Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;

y = m·x + c

Where x is the height  in inches

Given that the maximum height allowable is 70 inches, when x = 0 we have;

y = m·0 + c = 70

Therefore, c = 70

Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1

The equation becomes;

y ≤ x + 70

Also when x > 70, we have y ≤ -x + 70   with a slope of -1

In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.

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The ball will rise 15 cm height on the right-hand incline when friction is discounted.

The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.

Given that,

The height of the ball  = 15 cm

Since, the friction force is not counted here, this implies that there will be no friction force to stop the object.

The rise of the height on the right-hand incline will be same to the initial height.

Therefore, the ball will rise 15 cm height on the right-hand incline.

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The given expression in simplified radical form is  2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

Define Radicals.

The term "radical" is used to represent the square root or nth roots.

Expression with a square root is referred to as a radical expression.

Radicand: The value or phrase contained within the radical symbol.

Given expression is,

[tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]

Rewrite this expression,

we know, 2⁵ = 32

[tex]\sqrt[4]{(2x^4.y^3)^4 .y^3 .2}[/tex]

You see this expression is equal to given expression i.e, [tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]

Take out the term from under the radical,

2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

Hence, the given expression in simplified radical form is  2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

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0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ[tex]\sqrt{n}[/tex]}/σ])

                        = P (z > [{12.7 - 10[tex]\sqrt{120}[/tex]}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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When the number of machines increased by factor 2 the order would have been finished in 11 hours,

Given that,
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Number of hours as of the current number of working machines = 22
The number of machinery now doubled so working hours = 22 / 2 = 11 hours.

Thus, When the number of machines increased by factor 2 the order would have been finished in 11 hours,

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Answer:  D. A'(-5,10)   B'(-1,10)   C'(-1,7)   D'(-5,6)

Step-by-step explanation:

A(-5,5)  B(-1,5)  C(-1,2)  D(-5,1)

A'(-5,5+5)   B'(-1,5+5)   C'(-1,2+5)   D'(-5,1+5)

A'(-5,10)   B'(-1,10)   C'(-1,7)   D'(-5,6)

When Bobby takes out a mortgage for $30 years at 4% interest with $835.48 in monthly payments, the total principal loan amount is $255644.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

The interest paid per month=$835.48

Interest paid in 30 years=835.48*12*30

Rate of interest=4%=0.04

Time=30 years

Principal=I/RT

=(835.48*30*12)/(0.04*30)

=$250644

The principal loan amount is $250644 when Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48.

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