If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone

The x-intercepts of y=x2+5x−24 can be determined by solving the equation 0=x2+5x−24. Using the quadratic formula, we can find that x = 6 and x = -4 are the two x-intercepts.

The x-intercepts of y=x2−11x+10 can be determined by solving the equation 0=x2−11x+10. Using the quadratic formula, we can find that x = 5 and x = -2 are the two x-intercepts.
To determine the x-intercepts of the given functions, we need to find the values of x that make y equal to 0. We can do this by factoring the equations and setting each factor equal to 0.

2. y = x^2 + 5x - 24
0 = x^2 + 5x - 24
0 = (x + 8)(x - 3)
x + 8 = 0 or x - 3 = 0
x = -8 or x = 3

The x-intercepts are (-8, 0) and (3, 0).
3. y = x^2 - 11x + 10
0 = x^2 - 11x + 10
0 = (x - 1)(x - 10)
x - 1 = 0 or x - 10 = 0
x = 1 or x = 10

The x-intercepts are (1, 0) and (10, 0).
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The surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

What is the surface area of the cylinder?

The surface area of a cylinder can be calculated using the following formula:

SA = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi, approximately equal to 3.14159.

The surface area of a cylinder is the sum of the areas of its top and bottom circles, plus the area of its lateral surface (the curved surface that connects the two circles). The lateral surface area of a cylinder is found by multiplying the height of the cylinder by the circumference of one of its circular bases. Therefore, the correct method to calculate the surface area of the cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet is:

SA = 2π(1.6)² + 3.2π(3.8)

So, the correct answer is:

SA = 2π(1.6)² + 3.2π(3.8) square feet

Hence, the surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

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The values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

To find the values of x if the distance between the points (x, 4) & (3, x) be 131/2, we can use the distance formula:

D = √((x2 - x1)² + (y2 - y1)²)

Where D is the distance, (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the given values, we get:

131/2 = √((3 - x)² + (x - 4)²)

Squaring both sides and simplifying, we get:

169 = (3 - x)² + (x - 4)²

Expanding and rearranging, we get:

2x² - 14x - 110 = 0

Using the quadratic formula, we can find the values of x:

x = (-(-14) ± √((-14)² - 4(2)(-110))) / (2(2))

x = (14 ± √(196 + 880)) / 4

x = (14 ± √1076) / 4

x ≈ 9.39 or x ≈ -4.39

So the values of x are approximately 9.39 and -4.39.

Therefore, the values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

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The equivalent expression to the given one is:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

We start with the expression:

y⁸*y³*x⁰*x⁻²

Remember the exponent rule for products of powers with the same base, it says that we can write:

xᵃ*xᵇ = xᵃ⁺ᵇ

So we just add the two exponents.

Using exponent rules, we can rewrite the product as

y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²

That is the equivalent expression.

Then we can write:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

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Answer:

if we follow the rule using y=mx+c, we would use rise and run so the distance is 3 up and 4 run.

7 total distance i guess.....i hope this helps.

Answer:

y = (4/3)x + 2/3

The y-intercept is the value of y when x is equal to zero. So we can substitute x = 0 into the equation and solve for y:

y = (4/3)(0) + 2/3 = 2/3
The y-intercept of the line y = (4/3)x + 2/3 is 2/3.

Step-by-step explanation:

Answer:

The y-intercept is (2/3)

Step-by-step explanation:

I will assume that the equation is missing the "x," and will rewrite is as:

 y = (4/3)x + (2/3)

This is in standard form of y = mx + b, where m is the slope and b is the y-intercept.

The slope is (4/3) and the y-intercept is (2/3)

Explanation:

There are 4 white marbles out of 4+10 = 14 total

4/14 = 2/7 is the probability of randomly picking a white marble.

(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.

Use a calculator to find that 4/49 = 0.0816 approximately.

That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.

The answer to the question is that \( A_{1} \) is smaller than \( A_{2} \)

To begin, it is important to note that the terms "emalier" and "5PRECALC7" are not relevant to the question and can be ignored. Additionally, there are several typos and extraneous information that can also be ignored. The main focus of the question is to determine the relationship between \( A_{1} \) and \( A_{2} \).

From the information provided, it is clear that \( A_{1} \) is smaller than \( A_{2} \). This is because the value of \( A_{1} \) is given as 2, while the values of \( b \) and \( c \) are 27 and 33, respectively. Since \( A_{2} \) is the sum of \( b \) and \( c \), it is clear that \( A_{2} \) is larger than \( A_{1} \).

Therefore, the answer to the question is that \( A_{1} \) is smaller than \( A_{2} \).

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a. The probability that a randomly sampled individual has two copies of the C allele is 0.0169.
b. The probability that a randomly sampled individuTherefore, the answers are:
al is a homozygote is 0.7074.
c. The probability that a randomly sampled individual is AS is 0.0332.
d. The probability that a randomly sampled individual is AS or AC is 0.1411.

The probability of an individual having two copies of the C allele can be calculated using the formula for the probability of independent events: P(CC) = P(C) x P(C) = 0.13 x 0.13 = 0.0169.

The probability of an individual being a homozygote can be calculated by adding the probabilities of having two copies of each allele: P(AA) + P(SS) + P(CC) = (0.83 x 0.83) + (0.04 x 0.04) + (0.13 x 0.13) = 0.6889 + 0.0016 + 0.0169 = 0.7074.

The probability of an individual being AS can be calculated using the formula for the probability of independent events: P(AS) = P(A) x P(S) = 0.83 x 0.04 = 0.0332.

The probability of an individual being AS or AC can be calculated by adding the probabilities of each event: P(AS) + P(AC) = 0.0332 + (0.83 x 0.13) = 0.0332 + 0.1079 = 0.1411.

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Answer:

An exponential function in the form of y = a(m) x is of the form:

y = a * m^x

where "a" is a constant, "m" is a positive constant (the base of the exponential), and "x" is the independent variable.

To determine the exponential function in this form, you need to have some information about the function, such as its value at a particular point or its rate of growth.

Here are the general steps to determine the exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

Determine the value of "m" by solving for it using the given information.

For example, let's say you are given that the function passes through the point (2, 8) and has a growth rate of 3. To determine the exponential function in the form of y = a(m) x, you would follow these steps:

Plug in the values of x and y into the equation:

8 = a * m^2

Solve for "a" by isolating it on one side of the equation:

a = 8 / m^2

Use the given growth rate of 3 to find the value of "m":

m = 1 + r = 1 + 0.03 = 1.03

Plug in the value of "m" and the value of "a" you found in step 2 into the equation:

y = (8 / 1.03^2) * 1.03^x

Simplifying this equation gives:

y = 7.514 * 1.03^x

So the exponential function in the form of y = a(m) x that passes through the point (2, 8) and has a growth rate of 3 is y = 7.514 * 1.03^x.

Step-by-step explanation:

here is a more detailed explanation of the steps involved in determining an exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

In the equation y = a(m) x, "a" is a constant that represents the value of y when x is equal to 0. So to find the value of "a", we need to know the value of y for a specific value of x, other than 0.

Answer:

35

Step-by-step explanation:

(7/20) *100=35

This is why because if 20 percent is equal to 7, so 40 % will be 14, 80% 28 and 100% will be 35

Answer: 35 dolls

Step-by-step explanation:

7/x and 20/100

20 times 5 is 100

and 7 times 5 is 35. Therefore 35 dolls are in Anita’s collection

Answer:

Step-by-step explanation:

This expression isn't in simplest form. The terms 3x and 2x can be added, since they are like terms.

In simplest form, this expression would be 5x - 4.

Hope this helps!

If Jen has 72 green marbles, then she has 81 purple marbles.

If Jen has 8 green marbles for every 9 purple marbles, then the ratio of green marbles to purple marbles is 8:9.

If Jen has 72 green marbles, we can use this ratio to determine how many purple marbles she has.

Let's set up a proportion

8/9 = 72/x

where x is the number of purple marbles Jen has.

To solve for x, we can cross-multiply:

8x = 9 × 72

Multiply the terms

8x = 648

Move 8 to right hand side

x = 648 / 8

Divide the numbers

x = 81

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According to the information, it can be predicted that the number of missed shots after six weeks of practice is zero (0).

To calculate the number of lost shots after six weeks of practice, we must take into account the function that relates the weeks of practice with lost shots. In this case we must replace the value of X that corresponds to the weeks of practice and we will obtain as a result the amount of lost shots as shown below:

According to this function, we can infer that after six weeks of practice there will be 0 missed shots.

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Step-by-step explanation:

The first step is to add 6 to both sides

3x =15+6

3x=21

Divide both sides by 3

X = 7

Water turning to blood will be the first plague that will be present.

Both humans as well as mammals can contract the plague. The protozoan parasite is the bacterium that causes it. The most common ways for humans to contract the plague are through handling a plague-infected animal or by getting bitten by a rodent bug that is carrying the disease.

The 10 plagues in the correct order are:

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Answer:

Hi

Step-by-step explanation:

im pretty sure this the answer

hope this helps

good luck;)

Answer:

y≤7

Step-by-step explanation:

-8y+25≤-31

take away 25 from both sides

-8y≤-56

then divided by -8 on both sides

y≤7

The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.

The given function is f(x) = -x³ + 2x² + 3

1. End behavior:

As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:

2. X-intercepts:

To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:

-x^3 + 2x^2 + 3 = 0

x^3 - 2x^2 - 3 = 0

Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:

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

The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.

3. Positive/negative:

To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:

Putting these together, we can make the following sign chart for f(x):

x                         f(x)

x < 0                   -

0 < x < 3                  +

x > 3                  -

4. Multiplicity:

The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.

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The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into the equivalent exponential statement [tex]4^(-2)=(1)/(16)[/tex].

The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into an equivalent exponential statement by using the definition of logarithms. The definition of logarithms states that if [tex]log_(b)(a)=c[/tex], then [tex]b^c=a.[/tex]

Using this definition, we can translate the logarithmic statement[tex]log_(4)(1)/(16)=-2[/tex] into an equivalent exponential statement by rearranging the terms.

The equivalent exponential statement would be[tex]4^(-2)=(1)/(16)[/tex]. This means that 4 raised to the power of -2 is equal to 1/16.

So, the logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex]can be translated into the equivalent exponential statement[tex]4^(-2)=(1)/(16)[/tex].

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The probability for the bear visits using Poisson process of rate one visits per month is given by ,

P(X=i, Y=j) j=i                            j=2i                                        j=3i

X=i              e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i!     2/3^i× e^(-1)/i!

Bear visits form a Poisson process of rate 1 visit per month.

Number of visits in a month  = Poisson distribution with parameter λ = 1.

Let X be the number of visits in a month.

And Y be the total number of bears in the month.

Probability of X and Y is equal to ,

P(X = i, Y = j), for i = 0, 1, 2, 3 and j = i, 2i, or 3i.

Law of total probability for  P(X = i, Y = j) for each i and j.

P(X = i, Y = i)

= P(X = i) × P(Y = i | X = i)

= e^(-λ) × λ^i / i! × 1/3^i

= e^(-1) × 1^i / i! × 1/3^i

= e^(-1) (1/ i!) × 1/3^i

Now,

P(X = i, Y = 2i)

= P(X = i) × P(Y = 2i | X = i)

= e^(-λ) × ( λ^i / i!) ×  [(1/3)^i + 2(1/3)^(i-1)(2/3)]

= e^(-1) / i! × [1/3^i + 4/3^i-1]

For,

P(X = i, Y = 3i)

= P(X = i) × P(Y = 3i | X = i)

= e^(-λ) × λ^i / i! × (1/3)^i × 2

= 2e^(-1) / i! × 1/3^i

Therefore, the probability of the size of bears for given condition is equal to,

P(X=i, Y=j) j=i                            j=2i                                        j=3i

X=i              e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i!     2/3^i× e^(-1)/i!

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The given question is incomplete, I answer the question in general according to my knowledge:

A village in Alaska is sometimes visited by polar bears. In fact, bear visits form a Poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equal opportunity. Find the probability for each size.

The complete factorization of the expression 144p² - 9q² is (12p + 3q)(12p − 3q). The correct answer is B.

To factor 144p² - 9q², we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

We can see that 144p² is a perfect square, as it is the square of 12p. Similarly, 9q² is a perfect square, as it is the square of 3q. So we can write:

144p² - 9q² = (12p)² - (3q)²

Now we can use the difference of squares formula to factor:

(12p)² - (3q)² = (12p + 3q)(12p - 3q)

Simplifying, we can also write this as:

144p² - 9q² = 3²(16p² - q²)

So, the factored form of 144p² - 9q² is:

144p² - 9q² = 3²(16p² - q²) = (12p + 3q)(12p - 3q)

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The trigonometric equation [tex]\frac{2tanx}{1+tan^2x}[/tex] is equivalent to sin2x

An equation is an expression that shows how numbers and variables are related using mathematical operators like exponent, addition, multiplication, subtraction and division.

Trigonometric identity is used to show relationship between trigonometric functions. Some examples are:

1 + tan²x = 1/cos²x; tanx = cosx/sinx; sin2x = 2sinxcosx

Given:

[tex]\frac{2tanx}{1+tan^2x} \\\\but\ 1+tan^2x=\frac{1}{cos^2x};substituting:\\ \\= \frac{2tanx}{\frac{1}{cos^2x} } \\\\=2tanx*cos^2x\\\\=2*\frac{sinx}{cosx}*cos^2x\\ \\=2sinxcosx[/tex]

= sin2x

The trigonometric equation are equivalent.

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The transformation applied to the function f(x) is a translation of 4 units up.

Here we can see that:

f(x) = √(x + 3)

and g(x) is a vertical translation of k units:

g(x) = f(x) + k

To get the value of k, just look how many units the graph has been translated up ( remember that each of the smalls squares in the coordinate axis represents a single unit), we can see that it is 4 units up, then k = 4

We have a vertical translation of 4 units up.

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So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

Solving a system of linear equations by the Matrix Inversion method involves finding the inverse of the coefficient matrix, multiplying it by the constant matrix, and solving for the variables.

First, we need to write the system of equations in matrix form:

[ 2 6 2 ] [ x ] [ 8 ]
[ 6 6 3 ] [ y ] = [ -3 ]
[ 2 3 1 ] [ z ] [ 3 ]

Next, we need to find the inverse of the coefficient matrix:

A = [ 2 6 2 ]
[ 6 6 3 ]
[ 2 3 1 ]

The determinant of A is:

det(A) = 2(6-9) - 6(2-6) + 2(18-6) = -6 + 24 + 24 = 42

The adjoint of A is:

adj(A) = [ (6-3) (-2+6) (-18+6) ]
[ (-6+3) (2-4) (12-6) ]
[ (6-18) (-2+12) (2-18) ]

= [ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

The inverse of A is:

A' = (1/det(A))adj(A) = (1/42)[ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

= [ 1/14 2/21 -4/7 ]
[ -1/14 -1/21 2/7 ]
[ -4/7 5/21 -8/21 ]

Now, we can multiply the inverse of A by the constant matrix to find the solution:

[ x ] [ 1/14 2/21 -4/7 ] [ 8 ]
[ y ] = [ -1/14 -1/21 2/7 ] [ -3 ]
[ z ] [ -4/7 5/21 -8/21 ] [ 3 ]

= [ (8/14) + (16/21) + (-32/7) ]
[ (-8/14) + (-3/21) + (-6/7) ]
[ (-32/7) + (15/21) + (-24/21) ]

= [ -26/7 ]
[ -25/7 ]
[ -37/7 ]

So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

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The effective interest rate for the specified account is 6.70%.

To find the effective interest rate, we can use the following formula:
Effective Interest Rate = (1 + Nominal Yield / Number of Compounding Periods) ^ Number of Compounding Periods - 1

In this case, the nominal yield is 6.5% and the number of compounding periods is 12 (since it is compounded monthly). Plugging these values into the formula, we get:

Effective Interest Rate = (1 + 0.065 / 12) ^ 12 - 1
Effective Interest Rate = (1.0054166666666667) ^ 12 - 1
Effective Interest Rate = 1.0670171619870418 - 1
Effective Interest Rate = 0.0670171619870418

Multiplying by 100 to convert to a percentage, we get:

Effective Interest Rate = 6.70%

Therefore, the effective interest rate for the specified account is 6.70%.

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The side of figure WXYZ corresponds with QR is XY

In mathematics, mirror images are often used in the study of symmetry and geometry. A mirror image, also known as a reflection, is a transformation that flips an object over a line called the mirror line.

An image appears to be reversed from left to right. Therefore, the left side of the object appears to be on the right side of the image, and the right side of the object appears to be on the left side

Here we have

Parallelogram PQRS and WXYZ which are two mirror images

Here the corresponding side of the two figures are

=> PQ and WX

=> QR and XY

=> RS and YZ

=> PS and WZ

Therefore,

The side of figure WXYZ corresponds with QR is XY

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The the exact measurement of the height of the student is 6.279m.

A number can be expressed as a fraction of 100 using a percentage. It is frequently used, particularly in financial and statistical contexts, to depict ratios and proportions in a more practical and intelligible way. For instance, 50% denotes 50 out of 100, or half of a specified amount. It is represented by the letter "%".

Let's start by calculating the absolute error made in the measurement of the height of the pole:

Absolute error = 5% of 5.98m = 0.05 x 5.98m = 0.299m

If the actual height is 0.299m more than the measured value, then the actual height would be:

Actual height = 5.98m + 0.299m

                      = 6.279m

Therefore, the exact height is 6.279m.

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Answer:

slope = 4 , point on line (- 1, 3 )

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 3 = 4(x + 1) ← is in point- slope form

with slope m = 4 and (a, b ) = (- 1, 3 )

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

To find the total displacement vector for this walk, we can use the Pythagorean Theorem to find the magnitude of the displacement vector and the direction of the displacement vector.

First, let's find the magnitude of the displacement vector:

d = √((Δx)² + (Δy)²)

Where Δx is the change in the x-direction and Δy is the change in the y-direction.

Δx = 5 + 4cos(45°) + 0 + 3cos(225°) + 4 = 9.83 miles
Δy = 0 + 4sin(45°) + 6 + 3sin(225°) + 0 = 2.17 miles

d = √((9.83)² + (2.17)²) = √(96.58 + 4.71) = √(101.29) = 10.06 miles

So, the magnitude of the displacement vector is 10.06 miles.

Next, let's find the direction of the displacement vector:

θ = tan⁻¹(Δy/Δx) = tan⁻¹(2.17/9.83) = 12.58°

So, the direction of the displacement vector is 12.58°.

Therefore, the total displacement vector for this walk is 10.06 miles at an angle of 12.58°.

If this person walked straight home, they'd have to walk 10.06 miles.

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

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