Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.

The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).

Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.

The total increase in rent over 10 years is $120 per year * 10 years = $1200.

So, the monthly rent during the 11th year would be $900 + $1200 = $2100.

Therefore, the monthly rent during the 11th year would be $2100.

Step-by-step explanation:

The fraction of Mrs. Stanford's class that came late and brought notes that day was 1 / 4

To find the fraction of Mrs. Stanford's class that came late and brought notes that day, the relevant formula would be:

= Fraction of students who came late x Fraction of late students who brought notes

Fraction of students who came late = 3 / 4

Fraction of students who were late and brought notes = 1 / 3

The fraction of total students who were late and brought notes were ;

= 3 / 4 x 1 / 3

= 3 / 12

= 1 / 4

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Answer:

The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.

Step-by-step explanation:

Add  up all the sides:

-x^2+2x+3x-4+2x^2+5

x^2+5x+1

The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.

Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.

Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation

Distance = Speed × Time

to solve for the time spent in both city and highway.

For time spent in city:

35 mph × C = 995 miles

C = 995 miles/35 mph = 28.43 hours

For time spent in highway:

60 mph × H = 995 miles

H = 995 miles/60 mph = 16.58 hours

Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

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The distance between the point P and the plane through the points Q, R, and S is 60/23.

The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:

d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|

Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:

n = (Q-R) x (Q-S)

The coefficients of the normal vector can be found using the following equations:

A = n1

B = n2

C = n3

D = -(A * x2 + B * y2 + C * z2)

Substituting the values of Q, R, and S, we have:

Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)

Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)

The cross product of Q-R and Q-S is:

n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)

So,

A = -23

B = 29

C = 17

D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109

Finally, substituting the values of x1, y1, and z1:

d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|

= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|

= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|

= |60 / √(-23^2 + 29^2 + 17^2)|

= |60 / √(529)|

= 60 / 23

So the distance between the point P and the plane through the points Q, R, and S is 60/23.

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On solving the provided question, we can say that   relation between tangential speed and angular speed, v = r * w; v: tangential speed; r: radius; w: angular speed

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

relation between tangential speed and angular speed

v = r * w

v: tangential speed

r: radius

w: angular speed

the radius is

r = d/2

d is the diameter

[tex]v = (d * w)/2\\w = 2*v/d\\w = (2*9 mile/h)/(58 feet)\\w = (2*9 mile/h)/(0.011 miles) = 1636 rad/h\\w = 1636/60 = 27.2 rad/min\\[/tex]

the angular speed is in radians,

[tex]n = v/(π*d)[/tex]

n = (9 mile/h)/(π*0.011 mile) = 260 rev/h

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The value of x is 21.4.

What is right-angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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No, because each item does not have an equal chance of being selected. That is option D.

A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.

The simple random sampling method which is used by researchers has the following disadvantages such as:

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The statement made by Diego is correct.

In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.

1 ÷ 5/6

= 1 x 6/5 = 6/5

6/5 is called an improper fraction because the numerator is greater than the denominator.

6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.

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Given question is incomplete , the complete question is given below:

Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.

A cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.

A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.

A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

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Answer:

21.7% to win $3, thats ~1/5

Step-by-step explanation:

100/6 = 10.(6) % to roll for each number (let it be just ~10.7)

for rolling a 3 or a 1 u will get $3

10.7 + 10.7 = 21.7% to win $3, thats 1/5

Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

The annual interest rate on the saving account is 5%.

Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.

To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.

Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:

$200 = $1,000 * r * 4

r = $200 / ($1,000 * 4)

r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.

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Jade and Juliette 44.7days  more days to complete their trip.

To calculate how many more days Jade and Juliette need to ride, we can use the equation:

Total distance = Distance on first day + Distance on second day + Distance on remaining days

We know the first and second day distances, and the daily distance for the remaining days, so we can substitute those values in the equation:

2878 = 45.4 + 56.3 + 62x

where x is the number of remaining days they need to ride.

Simplifying the equation:

2878 - 101.7 = 62x

2776.3 = 62x

Dividing both sides of the equation by 62

x = 44.7

hence, Jade and Juliette need to ride for 44.7 more days to complete their trip.

There were a total of 95,082 students from country C.

A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.

To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

x represents the number οf students from cοuntry C.

then 122percent  of x = 116,000

122/100 * x = 116000

x = 116000 * 100/122 = 95,082 students

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Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.

Since UR = 18 and DA = 24, k = 24/18 = 4/3.

So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.

Now that we have the lengths of all sides of ABCD, we can find its perimeter:

Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC

Perimeter of RSTU = 18 + 36 + 18 + 36 = 108

So the ratio of their perimeters is:

Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108

Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:

20/18 + BC/108 = 4/3

Solving for BC:

BC = (4/3 - 20/18) * 108 = 36

Step-by-step explanation:

To determine the total energy consumption of refrigerator A in a day, we need to first convert the power usage from watts to kilowatts.

500 watts/hour * 1 kilowatt/1000 watts = 0.5 kilowatts/hour

Next, we can calculate the energy consumption in kilowatt-hours (kWh) per day:

0.5 kilowatts/hour * 12 hours/day = 6 kilowatt-hours/day

To find the daily cost of running the refrigerator, we can multiply the energy consumption by the cost per kWh:

6 kWh/day * $0.12/kWh = $0.72/day

To calculate the yearly cost of running the refrigerator, we can multiply the daily cost by 365 days:

$0.72/day * 365 days = $262.80/year

To calculate the total cost of running the refrigerator for 20 years, we can multiply the yearly cost by 20:

$262.80/year * 20 years = $5,256.00

In addition to the cost of running the refrigerator, there is also the cost of purchasing the unit itself. In this case, the cost is $1,000.

Therefore, the total cost of owning and operating Refrigerator A for 20 years is:

$5,256.00 (operating cost) + $1,000.00 (purchase cost) = $6,256.00

It's worth noting that this calculation assumes that the cost of electricity remains constant over the 20-year lifespan of the refrigerator. In reality, the cost of electricity may increase over time, which would increase the overall cost of running the refrigerator.

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To find the area of the prism we must identify the area of each of the faces of the prism and then add them. So, the surface would be: 312 ft²

To find the surface of the prism we must find the area of each of the faces and then add them as shown below:

Based on the above, the correct answer would be 312 ft² is the total area of this prism.

Note: This question is incomplete. Here is the complete information:

Image attached.

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The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.

The diameter of a circle is 2 times the radius of the circle.

The area of a circle is expressed as: A = πr²

The circumference of a circle is expressed as: 2πr

For question 1)

Radius r = 2

Diameter = 2 × radius = 2 × 2 = 4

Area = πr² = π( 2 )² = 4π

Circumference = 2πr = 2 × π × 2 = 4π

For question 2)

Radius r = 4

Diameter = 2 × radius = 2 × 4 = 8

Area = πr² = π( 4 )² = 16π

Circumference = 2πr = 2 × π × 4 = 8π

For question 3)

Diameter d = 2

Radius = diameter / 2 = 2/2 = 1

Area = πr² = π( 1 )² = 1π

Circumference = 2πr = 2 × π × 1 = 2π

For question 4)

Diameter d = 16

Radius = diameter / 2 = 16/2 = 8

Area = πr² = π( 8 )² = 64π

Circumference = 2πr = 2 × π × 8 = 16π

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The simplified expression of  K-7 ft-X-8 ft-K-20 ft is -35ft-X

An expression is combination of variables, numbers and operators.

The given expression is K-7 ft-X-8 ft-K-20 ft

We need to simplify the given expression.

Add the like terms

-7 ft-X-8 ft-20 ft

-27ft-X-8 ft

-35ft-X

Hence, -35ft-X is the simplified expression of  K-7 ft-X-8 ft-K-20 ft

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Using Chebyshev's Theorem, it is found that at least 89% of days have a high temperature between 6.6ºF and 51ºF.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

Considering k = 3, the percentage is of at least 89% and the bounds are given as follows:

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On solving the provided question, we can say that quadratic equation is 46.

A quadratic equation is x ax² +bx +c = 0, which is a quadratic polynοmial in a single variable. a 0. The Fundamental Theοrem of Algebra ensures that it has at least οne solution since this polynomial is of second οrder. Solutions may be simple or cοmplicated.

An equation that is quadratic is a quadratic equatiοn. This indicates that it has at least οne word that has to be squared. The fοrmula "ax² + bx + c = 0" is one of the often used solutions for quadratic equatiοns. where are numerical cοefficients or constants a, b, and c. where the variable "X" is unidentified.

Quadratic equatiοn is



R(d) = d³ +3d² -8

R(3) = (3)³ +3(3)² - 8

R(3) = 27 + 27 - 8

R(3) = 46

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In the function, f(x) = a(b)ˣ the value of a and b is

The function defined by f(x) = a(b)ˣ is a exponential function

Where

a is the starting function

b is the base function

The starting function from (0,24)

24 = a(b)ˣ

a = 24

using (1, 18), we solve for the base

18 = 24(b)

b = 0.75

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The another example that supports Hilary's conjecture are, 26² - 21²

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Given that,

Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.

Another example that supports Hilary's conjecture is:

= 26² - 21²

= 676 - 441

= 235

As we can see, the difference between the perfect squares of 26 and 21 is 235,

which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.

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The amount of money that would be paid for rent each year for the spa would be = $37,800

The area of the potential space for the opening of your first spa = 1,800 square feet.

The price for each square feet per year = $21

That is; = 1800× 21 = $37,800

Therefore, annual rent fees for the space which will be used for spa = $37,800.

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a. The probability that all the marbles are red is calculated as follows:

(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429

So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.

b. The probability that none of the marbles are red is calculated as follows:

(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696

So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.