A careless university student leaves her iclicker device behind with probability 1/4 each time she attends a class. She sets out with her iclicker device to attend 5 different classes (each class is in a different lecture theatre).

Answer:

[tex]\sf{Choice \;B.\;\; (x-9)^2 + (y-2)^2 = 25[/tex]

Step-by-step explanation:

The standard form equation of a circle with center (a, b) and radius r is

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

where (a, b) is the center of the circle.

Here we are given that the circle has center (9, 2)

So the equation becomes

[tex](x-9)^2 + (y-2)^2 = r^2\cdots(1)[/tex]

All we have to do is find the radius and we are done

Circumference of a circle with radius r
[tex]= 2 \pi r\\[/tex]

Given circumference [tex]= 10\pi[/tex]

[tex]10\pi = 2\pi r\\\implies r = 10/2 = 5[/tex]

Substitute this into equation (1):
[tex](x-9)^2 + (y-2)^2 = 5^2\\\\(x-9)^2 + (y-2)^2 = 25\\[/tex]

This corresponds to option B.

The equation of a circle is (x - 9) + (y - 2) = 25.

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

The equation of a circle is (x - h) + (y - k) = r² _____(A)

Where (h, k) is the center and r is the radius.

Now,

Centre = (9, 2)

This means,

(h, k) = (9, 2) _____(1)

Circumference = 10π

This means,

2πr = 10π

2r = 10

r = 5 in ____(2)

Now,

Substituting (1) and (2) in (A).

(x - h) + (y - k) = r²

(x - 9) + (y - 2) = 5²

(x - 9) + (y - 2) = 25

Thus,

The equation of a circle is (x - 9) + (y - 2) = 25.

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The probability that Louis takes two green counters is 1/9, since there is only one green counter in the box.

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If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. The rules to show this include SSS, SAS, ASA.

Side-Side-Side (SSS) Rule The SSS rule states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent

The SAS rule states that if two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

The ASA rule states that if two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.

An overview was given due to the incomplete information.

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Answer: x = 1

Step-by-step explanation:

5(3x-1) = 10

Use distributive property and multiply 5 times 3x and 5 times -1.

15x-5 = 10

Move -5 to the right of the equal sign making it positive.

15x = 10+5

Solve.

15x = 15

Divide both sides of the equal side by 15.

15x÷15 = 15÷15

Solve.

x=1

Hope this helps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(3x - 1) = 10}[/tex]

[tex]\mathsf{5(3x) + 5(-1) = 10}[/tex]

[tex]\mathsf{15x - 5 = 10}[/tex]

[tex]\textbf{ADD 5 to BOTH SIDES}[/tex]

[tex]\mathsf{15x - 5 + 5 = 10 + 5}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{15x = 10 + 5}[/tex]

[tex]\mathsf{15x = 15}[/tex]

[tex]\textbf{DIVIDE 15 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{15x}{15} = \dfrac{15}{15}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{x = \dfrac{15}{15}}[/tex]

[tex]\mathsf{x = 1}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 1}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The true statement is that blood pressure increases by 1 mm HG per year.

In geometry, we have seen the lines drawn on the coordinate plane. To predict whether the lines are parallel or perpendicular or at any angle without using any geometrical tool, the best way to find this is by measuring the slope. In this article, we are going to discuss what a slope is, slope formula for parallel lines, perpendicular lines, slope for collinearity with many solved examples in detail.

What is a Slope?

The equation that represents the linear model is:

y =x+95

Linear regression is represented as:

y=mx+b

Where:

m represents the slope

b represents the y-intercept

By comparison, we have: m=1

This means that:

The blood pressure increases by 1 mm HG per year.

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Answer: X=9

180 -108=72

72/8=9

Answer:

x = 9° (or) 8x = 72°

Step-by-step explanation:

Now we have to,

→ find the required value of x.

We know that,

→ Straight line is always 180°.

Forming the equation,

→ 8x + 108° = 180°

Then the value of x will be,

→ 8x + 108° = 180°

→ 8x = 180° - 108°

→ 8x = 72°

→ x = 72° ÷ 8

→ [ x = 9° ]

Hence, the value of x is 9°.

A pound of apples and a pound of oranges each cost $2.50.

Pound is a unit of weight or mass commonly used in the imperial system of measurement. It is equal to 0.453 kilograms and 16 ounces. It is also known as the avoirdupois pound, which is the most commonly used today. In some contexts, the term "pound" may also refer to a unit of currency, the British Pound Sterling (GBP).

This can be determined by subtracting Gina's total cost from Tom's total cost.
Tom's cost was $8.00, and Gina's cost was $5.00, so 8.00 - 5.00 = 3.00. Since Tom bought 3 pounds of apples more than Gina and the same amount of oranges, the cost of the extra apples is $3.00.
Since each pound of apples and oranges costs the same amount,
then $3.00 divided by 3 pounds is $1.00,
so each pound of apples and oranges costs $2.50.

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Step 1: Find some points on the exponential f(x). The more points we plot the better the graph will look.

Step 2: Switch the x and y values to obtain points on the inverse.

Step 3: Determine the asymptote.

Graph the following logarithmic functions. State the domain and range.

A logarithmic scale (or log scale) is a way of displaying numerical facts over a completely extensive range of values in a compact manner—typically the biggest numbers inside the data are loads or even lots of times large than the smallest numbers.

Logarithmic scales are useful for quantifying the relative alternate of a fee in place of its absolute distinction. moreover, because the logarithmic feature log(x) grows very slowly for huge x, logarithmic scales are used to compress massive-scale scientific statistics.

A logarithm is an exponent or power to which a base need to be raised to yield a given quantity. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. for example, 23 = 8; therefore, 3 is the logarithm of eight to base 2, or 3 = log2 eight.

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Jazz Band Makes $785 in Profit.

31 huge boxes and 74 little boxes of fruit are sold by the jazz band.

The cost is $x and the price is $20 for each huge fruit box.

Price minus Cost is referred to as profit.

Profit therefore equals 20 - x for one large fruit box.

31 huge fruit boxes at a profit (20 - x)

Each little fruit box costs $10 and costs $10 per small fruit box.

Each tiny fruit box has a profit of 10–y.

74 little fruit boxes worth of profit (10 - y)

For 74 small boxes and 31 large boxes, the overall profit will be:

Profit overall equals 31 (20-x) + 74. (10 - y)

We can reduce the problem above by using the distributive property as follows:

Total profit is equal to 31(20)-31x + 74(10)-74y.

Profit total = 1360 - 31 x - 74 y

Part B)

Each large package is estimated to cost $9.

Accordingly, x = 9.

Each tiny box is stated to cost $4.

Therefore, y = 4.

We can determine the Jazz Band's profit by using the x and y numbers from the profit equation.

Profit of Jazz Band = 1360 - 31(9) - 74. (4)

Jazz Band Makes $785 in Profit

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mc008-1 jpg 3456 has a degree of 3840.

A degree is a unit of measurement for angles. It is not a SI unit because radians are the SI unit for measuring angles. In general, we measure angles in degrees with a protractor in geometry.

A degree is a unit of measurement for expressing the measurement of an angle. Angles are typically measured in two different units: radians and degrees. Angles are always measured in degrees in practical geometry.

A degree is denoted by the symbol °. (degree symbol). A complete angle in degrees is 360 degrees (sometimes written as 360°), which equals one complete rotation.

As a result, 3456/0.9 = 3840

As a result, mc008-1 jpg 3456 has a degree of 3840.

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Rina has been visiting the coffee shop every day for 7 days and he spent an average of $1 each day he visited the coffee shop during the week.

He started on Monday, spending $1, and each day he spent a dollar more than he did the day before. By the end of the week, he had spent $7. To calculate the average amount he spent each day, add up the total amount of money he spent that week and divide it by 7 (the total number of days he visited the shop).

7/7=1

In this case, the total amount of money spent was $7, so when divided by 7, the average amount spent each day is $1. Therefore, Rina spent an average of $1 each day he visited the coffee shop during the week.

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Answer:

function-function relation

Step-by-step explanation:

To determine if the inverse of a function is a function, we can use the horizontal line test.

A function is a set of ordered pairs (x, y) where each x value corresponds to one and only one y value. The inverse of a function is a set of ordered pairs (y, x) where each y value corresponds to one and only one x value.

To use the horizontal line test, we draw a horizontal line on a graph of the original function. If the line intersects the graph in more than one point in any vertical section, the inverse is not a function. But if the horizontal line intersects the graph in at most one point in any vertical section, the inverse is a function.

Another way to check if the inverse of a function is a function is to check that the original function is a one-to-one function, meaning that each x value corresponds to one and only one y value. If the original function is not one-to-one, then the inverse is not a function.

It's also possible to check if the inverse of a function is a function by analyzing the equation of the function. If the original function is a one-to-one function, its inverse is also a function

1500 Lower Level seats and 600 Upper Level seats were sold.

Linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x is a variable. In this equation, a is referred to as the coefficient of x and b is referred to as the constant. Linear equations are used to represent relationships between two variables and can be used to solve for either variable. Linear equations are used in many different fields of mathematics, including algebra, calculus, and geometry.

System of linear equations:
50x + 20y = 66000
x + y = 2100

Solving the system of equations gives:
x = 1500
y = 600

Therefore, 1500 Lower Level seats and 600 Upper Level seats were sold.

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a) The exponential function defining the monthly cell phones sold is given as follows: y = 450(1.0475)^t.

b) The predicted amounts are given as follows:

The general format of an exponential function is given as follows:

y = ab^x.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 450(1.0475)^x.

Then the amounts are given as follows:

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Poll only students in 9th and 11th grades would be the best way to get an accurate response. Thus, option A is correct.

In electoral campaigns, math is frequently used. The goal of polling is to predict how the electorate will vote overall by taking a small sample of voters and extrapolating their results to the entire population. Pollsters must ensure that their sample of respondents is representative of the entire electorate, or if it is not, they must use a variety of statistical techniques to increase the representativeness of their findings.

In essence, this means that a survey is conducted, and not only are respondents' voting intentions recorded, but also their age, gender, race, and other demographics. As a result, it is possible to make predictions about the voting intentions of various social groups.

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T = 2000/r expresses the amount of time it will take to fill the pool.

The volume of liquid that can be poured, dispensed, or eaten in an hour is measured in gallons per hour.

It gauges how quickly a liquid may travel from one location to another. The flow rate of liquids in pipes, tanks, and other vessels can be determined using the rate of r gallons per hour.

The flow rate of liquids through pumps and other mechanical devices can also be measured using this technique.

You may calculate the amount of liquid utilized or consumed in an hour using the rate of r gallons per hour.

This can be useful for estimating how much water will be consumed over a certain length of time.

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73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.

To find out how much of the 6.45-ounce bottle is not juice, we need to subtract the amount of juice in the bottle, which is 1.751 ounces, from the total volume of the bottle, which is 6.45 ounces.

6.45 ounces - 1.751 ounces = 4.699 ounces

So, 4.699 ounces of the 6.45-ounce bottle is not juice.

Alternatively, we can express the answer as a percentage of the total volume of the bottle:

(4.699 / 6.45) x 100 = 73.14 %

So, 73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.

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Answer:

Step-by-step explanation:

so if x is the money he had in the beginning, than

m=x-5(3.55)

m=x-$17.75

The substitution that should be made to rewrite the given equation 4x¹² - 5x⁶ - 14 = 0 as a quadratic equation is (c) U = x⁶ .

The Quadratic Equations can be defined as a type of polynomial equations which has the highest degree of 2 , it is a algebraic equation of the second degree in x .

The given equation is ; 4x¹² - 5x⁶ - 14 = 0 ;

we have to make this equation a quadratic equation ,

If we substitute , U = x⁶ in the given equation ,

we get ;

⇒  4(x⁶)² - 5x⁶ - 14 = 0;

⇒ 4(U)² - 5U - 14 = 0 ;

the equation becomes ⇒ 4U² - 5U - 14 = 0, which is a quadratic .

Therefore , the substitution of U = x⁶ , should be used .

The given question is incomplete , the complete question is

What substitution should be used to rewrite 4x¹² - 5x⁶ - 14 = 0 as a quadratic equation

(a)  U = x²

(b)  U = x³

(c)  U = x⁶

(d)  U = x¹²

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The numbers for the sequences are 10-n = 9, 8, 7, 6, 0, and 6-2n = 4,2, 0, -2, and -14.

A sequence is a series of numbers that follow the sample principle in terms or order. In this case, the sequence is determined by the equations given, and based on this the numbers are calculated.

10-n:

10 - 1 = 9

10 - 2 = 8

10 - 3 = 7

10 - 4 = 6

And the 10th term is

10- 10 = 0

6-2n:

6 - 2 = 4

6 - 4 = 2

6- 6 = -0

6 - 8 = -2

And the 10th term is

6 - 20 = -14

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Answer:

Step-by-step explanation:The equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y, is:

y = 50x

This equation shows that the number of words Wyatt types is directly proportional to the number of minutes he types. For every 1 minute he types, he types 50 words.

This equation can also be read as "y is equal to 50 multiplied by x" which means that for any given number of minutes, x, that Wyatt types for, the number of words he types will be 50 times that value.

Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).

Three conditions must be satisfied for a radical expression to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors.

Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.

A radical expression can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.

The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.

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The slope intercept form of a line is,

⇒ y = x - 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The equation is,

⇒ 3x - 3y = 18

Now, We know that;

The slope intercept form of the equation is,

⇒ y = mx + b

Here, The equation of line is,

⇒ 3x - 3y = 18

Take 3 as common,

⇒ 3(x - y) = 18

Divide by 3;

⇒ x - y = 18/3

⇒ x - y = 6

⇒ x - 6 = y

⇒ y = x - 6

Thus, The slope intercept form of a line is,

⇒ y = x - 6

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Answer:

y=-x+4

Step-by-step explanation:

have a good day

Answer:

y=-x+4

slope intercept form is y = mx+c

m is 1 and c is 4

y=- x +

Step-by-step explanation:

Answer:

The answer is D the second quadrant.

Step-by-step explanation:

HAVE A GREAT DAY!!!!!

Answer:

mn = 20ft is the answer (I hope it helps)

Answer:

The quotient is x^2 + 9x + 6 with a remainder of 6.

Step-by-step explanation:

I used the polynomial long division method to divide the polynomial 2x^3 + 17x^2 + 20x + 6 by 2x + 1.

So the quotient is x^2 + 8.5x + 0.25x which simplifies to x^2 + 9x + 6 and the remainder is 6.

Answer:

[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]

Step-by-step explanation:

[tex] \sf \frac{2x^ 3 +17x^ 2 +20x+6}{ 2 x + 1}[/tex]

2x³/2x = x²

[tex] \sf \frac{x^ 2 +17x^ 2 +20x+6}{ 1}[/tex]

[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]

a) X'(-6, -4), Y'(0, -6), Z'(-4, -2)

b) X'(-9, -6), Y'(0, -9), Z'(-6, -3)

Rotation and dilation in geometry

For the rotation of 180° counterclockwise about the origin, we will use the rotation formula:

(x, y) → (xcosθ - ysinθ, xsinθ + ycosθ)

Where θ is the angle of rotation.

For our 180° rotation, θ = 180°.

We calculate the new coordinates for each vertex:

X(-6, 4) → X'(-6, -4):

(-6cos180° - 4sin180°, -6sin180° + 4cos180°)

Y(0, 6) → Y'(0, -6):

(0cos180° - 6sin180°, 0sin180° + 6cos180°)

Z(-4, 2) → Z'(-4, -2):

(-4cos180° - 2sin180°, -4sin180° + 2cos180°)

For the dilation of the triangle with a scale factor of 3/2 centered at the origin, we will use the dilation formula:

(x, y) → (kx, ky)

Where k is the scale factor.

For our dilation, k = 3/2.

We calculate the new coordinates for each vertex:

X(-6, 4) → X'(-9, -6):

(-6*3/2, 4*3/2)

Y(0, 6) → Y'(0, -9):

(0*3/2, 6*3/2)

Z(-4, 2) → Z'(-6, -3):

(-4*3/2, 2*3/2)

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The domain of a function is not always all real numbers.

We know that the domain of function is the set of all possible input values for which the function is well defined.

And the range of function is the set of all possible output values for given input.

As we know the domain of a function, f(x), is all real numbers when there are no restrictions on what we can take input for x, as all real numbers would make function f(x) true.

But the domain of a function is not always all real numbers.

consider the function f(x) = 1/x

This function is not defined for x = 0

So, the domain of above function f(x) is R - {0}

Also, we know that the domain of a logarithmic function is all non-zero positive real numbers.

Thus, the domain is not always set of all real numbers.

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