Select the correct answer.
What is the end behavior of this radical function?
f(x) = 3√x-4
As x approaches positive infinity, f(x) approaches positive infinity.
As x approaches negative infinity, f(x) approaches positive infinity.
As x approaches positive infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches 0.

Answer:

C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.

Answer:

C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.

Step-by-step explanation:

Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will  will hold your money until you want to deposit it out of your account.

Answer:

x = -6

Step-by-step explanation:

-4 + 2x = 4x+8

-4-8 = 4x - 2x

-12 = 2x

x = -6

Answer:

x = - 6

Step-by-step explanation:

Hope this helps! <33

Answer:

Let's start by using algebra to solve the problem.

Let x be the total number of entries at the fair.

Given that 60% of the entries are livestock, we can write:

0.6x = number of livestock entries

Of those livestock entries, 70% are sold at the auction, which means:

0.7(0.6x) = 130

Simplifying the second equation, we get:

0.42x = 130

Solving for x, we can divide both sides by 0.42:

x = 309.52

Since we can't have a fractional number of entries, we can round up to the nearest whole number, giving us:

x = 310

Therefore, there were a total of 310 entries at the fair.

Step-by-step explanation:

Answer: why do u need help again? this is easy boy

Step-by-step explanation:

The sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

Rotation is a physical phenomenon where an object spins around an axis. It is a type of circular motion where an object moves in a circular path around a central point.

To accomplish this transformation, first, the point representing the letter D is rotated 90 degrees clockwise around the origin so that it is now pointing in the same direction as the letter O. After that, the point representing the letter D is translated 5 units to the right, resulting in the final transformation of DOG to D'O'G'.

Thus, the sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

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The theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

If each sectiοn has 14 red seats, then there are a tοtal οf 4 x 14 = <<4 × 14=56>>56 red seats in the theater.

Tο find οut hοw many blue seats are in each sectiοn, we need tο subtract the number οf red seats frοm the tοtal number οf seats in each sectiοn:

88 tοtal seats / 4 sectiοns = 22 seats per sectiοn

22 seats per sectiοn - 14 red seats per sectiοn = 8 blue seats per sectiοn

Therefοre, each sectiοn has 8 blue seats, and the theater has a tοtal οf 4 x 8 = <<4 × 8=32>>32 blue seats.

Sο, the theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

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The interval that contains a local minimum for this function is (0,2).

A local maximum is present on the graph of the function y = f(x) at the location where the graph shifts from increasing towards decreasing.

Thus, over the span, a local minimum happens (0,2)

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The table for the function is given:

The solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

To solve the inequality 6x + 9 ≥ −(x − 9), we need to first distribute the negative sign on the right side of the inequality. This gives us:

6x + 9 ≥ -x + 9

Next, we need to isolate the variable on one side of the inequality. We can do this by adding x to both sides and subtracting 9 from both sides:

7x ≥ 0

Finally, we can divide both sides by 7 to solve for x:

x ≥ 0

Now, we can write the solution set in interval notation. Since x is greater than or equal to 0, the solution set is [0, ∞).

So, the solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

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The values of x and y that satisfy the given equation are x = 2 and y = 1.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Since a and b span R², any vector in R² can be expressed as a linear combination of a and b.

Let's call the coefficients of this linear combination c₁ and c₂ so that any vector v in R² can be expressed as:

v = c₁a + c₂b

Now let's use this fact to solve the given equation:

(2-x)a + b = ya + (x-3)b

We can rearrange this equation to get all the terms with an on one side and all the terms with b on the other side:

(2-x)a - ya = (3-x)b

Now we can write both sides of the equation as linear combinations of a and b:

(2-x)a - ya = 2a - xa - ya = (2-x)a - (x-2)a - ya = (2-x - x + 2)a - ya = (4 - 2x)a - ya

(3-x)b = 3b - xb = 3b - xb + 3b - 3b = (6 - x)b - 3b = (6 - x - 3)b = (3 - x)b

So now we have:

(4 - 2x)a - ya = (3 - x)b

Since a and b span R², we know that any vector in R² can be expressed as a linear combination of a and b. Therefore, we can write:

(4 - 2x)a - ya = c₁a + c₂b

(3 - x)b = c₁a + c₂b

Now we can set the coefficients of a and b equal to each other and solve for x and y:

4 - 2x = c₁

-y = c₂

3 - x = c₂

Substituting the third equation into the second equation, we get:

-y = 3 - x

Solving for x and y, we get

x = 2

y = 1

Therefore, the values are x = 2 and y = 1.

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It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.

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To determine the average rate of the speed's increase or decrease from t=2 to t=5, we need to find the slope of the line connecting the points (2,s(2)) and (5,s(5)) on the graph of the equation s(t)=T^2-6T+35. The slope of a line is given by the formula:
slope = (y2-y1)/(x2-x1)

In this case, x1=2, x2=5, y1=s(2), and y2=s(5).
Plugging in the values of x1 and x2 into the equation s(t)=T^2-6T+35, we get:
y1=s(2)=2^2-6(2)+35=4-12+35=27
y2=s(5)=5^2-6(5)+35=25-30+35=30
Now we can plug in the values of x1, x2, y1, and y2 into the slope formula:
slope = (30-27)/(5-2) = 3/3 = 1

Therefore, the average rate of the speed's increase or decrease from t=2 to t=5 is 1. This means that the speed is increasing at a constant rate of 1 unit per unit of time from t=2 to t=5.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.

Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.

Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.

My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.

The number of bacteria or the number of all the other animals in the table put together is 7.8 x 10⁶.

To compare the number of bacteria to the number of all other animals in the world, we need to use some mathematical estimates. It's important to note that it's almost impossible to count the exact number of bacteria and animals in the world since they are found in vast numbers and diverse environments.

According to some scientific estimates, the number of bacteria on Earth is around 5 x 10³⁰, which is a massive number. In comparison, the total number of all other animals, including insects, birds, and mammals, is estimated to be around 7.8 x 10⁶.

In conclusion, the number of bacteria is much greater than the number of all other animals in the world. Although bacteria are tiny microorganisms, they are present in vast numbers and can be found in almost every environment.

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Answer:

I CAN NOT SEE THAT OML

Step-by-step explanation:

The velocity of the pendulum is approximately -2.45 inches/second.

The acceleration of the pendulum is approximately 5.13 inches/second².

To find the velocity and acceleration of the pendulum, we need to find the first and second derivatives of the function d(t).

a. The velocity of the pendulum is given by the first derivative of the function d(t):

v(t) = d'(t) = 7 * (π/3) * cos(πt/3 - 2)

To find the velocity at t = 6 seconds, we simply plug in 6 for t:

v(6) = 7 * (π/3) * cos(π(6)/3 - 2) = 7 * (π/3) * cos(4) ≈ -2.45 inches/second

So the velocity of the pendulum at 6 seconds is approximately -2.45 inches/second.

b. The acceleration of the pendulum is given by the second derivative of the function d(t):

a(t) = d''(t) = -7 * (π/3)² * sin(πt/3 - 2)

To find the acceleration at t = 6 seconds, we simply plug in 6 for t:

a(6) = -7 * (π/3)² * sin(π(6)/3 - 2) = -7 * (π/3)² * sin(4) ≈ 5.13 inches/second²

So the acceleration of the pendulum at 6 seconds is approximately 5.13 inches/second².

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The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. The 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is option c. 4650±70.84.

To find the 98% confidence interval for the population mean salary, we will use the formula:

CI = X ± Z* (σ/√n)

Where:
CI = Confidence Interval
X = Sample mean
Z = Z-score for the given confidence level
σ = Population standard deviation
n = Sample size

Plugging in the given values, we get:

CI = 4650 ± 2.33* (165/√36)

CI = 4650 ± 70.84

Therefore, the 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is C.

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Answer:

When you multiply two numbers with the same sign (either both positive or both negative), the rule is that the result is always positive.

For example, if you multiply +2 and +3, the result is +6 because both numbers have the same positive sign. Likewise, if you multiply -4 and -5, the result is +20 because both numbers have the same negative sign.

This rule applies to any two numbers with the same sign, regardless of their values or whether they are whole numbers, fractions, or decimals.

The length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:

11). x = 11√3 and y = 33

12). x = 4√7 and y = 8√7

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

recall that sin60° = √3/2 and cos60° = 1/2

For question 11:

sin 60° = y/22√3 {opposite/hypotenuse}

y = 22√3 × sin 60° {cross multiplication}

y = 22√3 × √3/2

y = 11 × 3

y = 33

cos 60° = x/22√3 {adjacent/hypotenuse}

x = 22√3 × cos 60° {cross multiplication}

x = 22√3 × 1/2

x = 11√3.

For question 12:

sin 60° = 4√21/y {opposite/hypotenuse}

y = 4√21/sin 60° {cross multiplication}

y = 4√21 ÷ √3/2

y = 4√21 × 2/√3

y = 4√7 × 2

y = 8√7

cos 60° = x/8√7 {adjacent/hypotenuse}

x = 8√7 × cos 60° {cross multiplication}

x = 8√7 × 1/2

x = 4√7

Therefore, the length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:

11). x = 11√3 and y = 33

12). x = 4√7 and y = 8√7

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Answer: I'd say A

Step-by-step explanation:

-1+1=0

The second largest share of the three entrepreneurs is $291,666.68.

To calculate the second largest share of the three entrepreneurs, we need to first find the total ratio by adding the three individual ratios: 3 + 4 + 5 = 12.

Next, we can find the value of one part of the ratio by dividing the total amount invested by the total ratio: $875,000 ÷ 12 = $72,916.67.

Finally, we can calculate the second largest share by multiplying the value of one part of the ratio by the second largest individual ratio, which is 4: $72,916.67 × 4 = $291,666.68.

Therefore, the amount of the second largest share is $291,666.68.

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The correct answer is "No, because for each input there is not exactly one output".

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The relation is not a function because for the input value of 1, there are two possible output values: 0 and 2. In a function, each input can have only one output value. However, in this relation, the input value of 1 is associated with two different output values, so it violates the definition of a function. Therefore, the correct answer is "No, because for each input there is not exactly one output".

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Answer: 200

Step-by-step explanation:

40% of y = 100

40/100 of y = 100

40y/100 = 100

40y = 100 multiplied by 100

40y/40 = 10000

y = 250.

40% of 2 multiplied by 250

40/100 of 500

40 multiplied by 5

answer = 200.

The solution is then:

l = 6cm

w = 2cm

h = 2cm

The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid

then, use the formula: surface area (SA)=2lw+2lh+2hw.

here, we have,

We know that the formula for the volume of a box is:

V = l*w*h

Where:

l = length

w = width

h = height

The formula of the surface area of a box is:

SA = 2(lw+lh+wh)

Based on the given we know the following:

24 =  l*w*h

and

56 =  2(lw+lh+wh)

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:

24 = 6*2*2

Let:

l = 6cm

w =2cm

h =2cm    

Now let's try this on the surface area formula:

56 = 2(6*2+6*2+2*2)

so, 56 = 56

The answer is then:

l = 6cm

w = 2cm

h = 2cm

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Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

To solve this problem, we can use a system of linear equations. Let x be the cost of each shirt, y be the cost of each pair of slacks, and z be the cost of each sports coat. Then we can write the following equations based on the information given in the problem:

3x + 2y = 18.45 (equation 1)

7x + 2y + z = 35.40 (equation 2)

4x + 2z = 23.94 (equation 3)

Now we can use the elimination method to solve for the variables. First, we can subtract equation 1 from equation 2 to eliminate the y variable:

4x + z = 16.95 (equation 4)

Next, we can multiply equation 1 by -2 and add it to equation 3 to eliminate the y variable:

-6x - 4y + 4x + 2z = -36.9 + 23.94

-2x + 2z = -12.96 (equation 5)

Now we can subtract equation 4 from equation 5 to eliminate the x variable:

2z - z = -12.96 - 16.95

z = -29.91

This value for z does not make sense, so there must be a mistake in the calculations or the original problem. Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

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The sale price of a pair of dress shoes originally at $69.98 with a 25% discount will be $52.49.

To find the sale price, you need to calculate the discount amount and subtract it from the original price.

Step 1: Find the discount amount by multiplying the original price by the discount percentage.
$69.98 x 0.25 = $17.49

Step 2: Subtract the discount amount from the original price to get the sale price.
$69.98 - $17.49 = $52.49

Therefore, the sale price of the dress shoes will be $52.49.

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Answer:

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to factor the given trinomial.}[/tex]

[tex]\large\underline{\textsf{What is a Trinomial?}}[/tex]

[tex]\textsf{A Trinomial is an expression that has 3 terms. No more, and no less.}[/tex]

[tex]\large\underline{\textsf{What is Factoring?}}[/tex]

[tex]\textsf{Factoring is a way to split a trinomial into 2 binomials. Binomials have 2 terms.}[/tex]

[tex]\textsf{Factoring helps us to find the possible values of x, setting the binomials equal to 0.}[/tex]

[tex]\textsf{We don't have to do this for our problem though.}[/tex]

[tex]\large\underline{\textsf{Factoring Looks Like;}}[/tex]

[tex]\tt x^{2} + x + 1 = (x+?)(x+?)[/tex]

[tex]\tt The \ 2 x's \ multiply \ to \ equal \ x^{2}.[/tex]

[tex]\textsf{The x's multiply with the whole numbers inside the opposite binomial.}[/tex]

[tex]\large\underline{\textsf{To Factor;}}[/tex]

[tex]\textsf{Factoring is a little tedious, we must be careful and make sure we are finding}[/tex]

[tex]\textsf{the correct factors for factoring to work out. Remember that the trinomial has to}[/tex]

[tex]\textsf{equal the 2 binomials being multiplied.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt 3x^{2} + 25x + 28[/tex]

[tex]\textsf{3x can't be split apart in 2 whole numbers, so it remains 3 in one of the binomials.}[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt (3x+?)(x+?)[/tex]

[tex]\textsf{We don't have to worry about} \ \tt 3x^{2} \ \textsf{anymore.}[/tex]

[tex]\textsf{Our goal is to find factors of 28 that multiply to get to 25x and 28.}[/tex]

[tex]\textsf{We might need to try many factor pairs before we have our factored expression.}[/tex]

[tex]\underline{\textsf{Factors of 28;}}[/tex]

[tex]\tt 28: 1, 2, 4, 7, 14, 28.[/tex]

[tex]\textsf{We should substitute the factor pairs in, then FOIL.}[/tex]

[tex]\textsf{Foiling is multiplying 2 binomials together.}[/tex]

[tex]\underline{\textsf{Substitute;}}[/tex]

[tex]\tt (3x+1)(x+28) = 3x^{2}+85x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\tt (3x+2)(x+14)=3x^{2}+44x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

[tex]\textsf{Correct Factor Pair. If these factors were flipped it would be incorrect.}[/tex]

To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

The partial fraction decomposition for the given fraction is:

(4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)) = A/x + B/x^(2) + C/(x+3) + D/(x^(2)+2x+9) + E/(x^(2)+1) + F/(x^(2)+1)^(2) + G/(x^(2)+1)^(3)

Where A, B, C, D, E, F, and G are constants that need to be determined.

To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

However, since the question only asks to set up the partial fraction decomposition, we do not need to solve for the constants at this time.

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