(x + 1)(x - 3)(x - 4)

Radical Equations

Step 1

To demonstrate how to solve a radical equation, let's use the following equation as an example:

Answer:

100 inches (using the given data)

98.43 (using exact numbers)

Step-by-step explanation:

1 inch = 2.54 centimeters

20 inches = 50.8 centimeters, but for the purpose of answering this question we will assume that 20 inches = 0.5 meters (instead of 0.58).

we must solve the following equation:

20 inches / 0.5 meters = X inches / 2.5 meters

(2.5  meters x 20 inches) / 0.5 meters = X inches

20 inches x 5 = X inches

100 inches = X inches

if we do the exact calculation, 2.5 meters in inches = 250 centimeters / 2.54 centimeters per inch = 98.43 inches

Answer:

B

Step-by-step explanation:

We're looking for a number (x) that's less than 44

We can represent it by simply using the less sign, so x < 44

we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.

Then we have the product:

P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now, notice that there is a 20 there.

Any number times 20 will end with a zero, then:

P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

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Answer:

Q’(–5, –3)

Step-by-step explanation:

This is because the pints of q are this.

Roadway offers the best deal for renting a truck, and it becomes the best deal when you need to drive more than 98 miles a day.

To determine which company offers the best deal for renting a truck, we need to compare the costs based on the daily rate and the cost per mile. Roadway charges $50.70 per day and an additional $0.25 for each mile driven, while UK-Plug-It charges $55.60 per day and an additional $0.20 per mile.

To find out when Roadway becomes the best deal, we need to calculate the point at which the total cost for Roadway is lower than that of UK-Plug-It. Let's assume the number of miles driven in a day is represented by 'm.'

For Roadway, the total cost can be calculated as:

Total cost for Roadway = $50.70 (daily rate) + $0.25 (cost per mile) * m (miles driven)

For UK-Plug-It, the total cost can be calculated as:

Total cost for UK-Plug-It = $55.60 (daily rate) + $0.20 (cost per mile) * m (miles driven)

To find the point at which Roadway becomes the best deal, we need to equate the total costs of Roadway and UK-Plug-It:

$50.70 + $0.25m = $55.60 + $0.20m

Simplifying the equation, we get:

$0.05m = $4.90

Dividing both sides by $0.05, we find:

m = 98

Therefore, if you need to drive more than 98 miles in a day, Roadway offers the best deal for renting a truck.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The amount of the total number of possible pizzas is 4083 pizzas.

The problem of finding the total number of possible pizzas with 12 toppings is basically a problem of counting the number of subsets (or combinations) of a set of 12 elements (the toppings) with the additional condition that double toppings are not allowed.

Therefore, the solution to this problem is simply the sum of the number of subsets with between 0 and 12 toppings, inclusive, but excluding those subsets that contain any repeated element (topping).

First, let's find the number of subsets with k elements. Since we cannot repeat toppings, we can select the k elements from the 12 available toppings in 12 C k ways.

Therefore, the total number of possible pizzas with exactly k toppings is 12 C k.

To find the total number of pizzas with between 0 and 12 toppings, we can use the formula for the sum of the first n binomial coefficients:

∑ k=0 n (n C k) = 2ⁿ

Hence, the total number of possible pizzas is:2¹²- (1 + 12) = 4096 - 13 = 4083 pizzas.

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Answer:

y=-2x+4

Step-by-step explanation:

y=mx+b

m is the slope so the equation looks like this:

y=-2x+b

Now we just need to find b or the y-intercept

so distribute -2 into x and 8 into y (x,y) (-2,8)

8=-2(-2)+b

Multiply -2 and -2 which is 4

8=4+b

Subtract by 4 on both sides:

b=4

So the equation is

y=-2x+4

Hope this helps!

Using the z-distribution, as we are working with a proportion, it is found that a sample size of 1701 is required.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, the parameters are:

Hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.96\sqrt{\frac{0.23(0.77)}{n}}\)

\(0.02\sqrt{n} = 1.96\sqrt{0.23(0.77)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.23(0.77)}}{0.02}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.23(0.77)}}{0.02}\right)^2\)

\(n = 1700.8\)

Rounding up, a sample size of 1701 is required.

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Answer:

A = 160 mm²

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = bh ( b is the base and h the height )

Given P = 52 and P = 2(b + h) , then

2(b + h) = 52 ( divide both sides by 2 )

b + h = 26 ( substitute b = 16 )

16 + h = 26 ( subtract 16 from both sides )

h = 10

Then

A = 16 × 10 = 160 mm²

Answer:

its: 160^{2}

Step-by-step explanation:

ps: (b=l)

we have  : P=2 [l+w]

and : P= 52mm

so: 52=2(16mm+w)

    52/2= 16mm+w

     26-16=w

   10=w

so: w=10

and we know that:  area= w*l

so:                          area=10*16

so:          area= 160 mm^{2}

The probability of at most six individuals in the sample having used a discount broker is calculated to be approximately 0.997.

To solve this problem, we need to use the binomial distribution formula. Let X be the number of individuals in the sample who have used a discount broker. Then, X follows a binomial distribution with parameters n = 9 and p = 0.3.

The probability of at most six individuals in the sample having used a discount broker can be calculated as follows:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 6)

Using a binomial probability table or calculator, we can find the individual probabilities and sum them up. Alternatively, we can use a normal approximation to the binomial distribution if the sample size is large enough (np and n(1-p) are both greater than 5).

Using the normal approximation, we have:

mean = np = 9 x 0.3 = 2.7

variance = np(1-p) = 9 x 0.3 x 0.7 = 1.89

standard deviation = √(variance) = 1.374

To standardize the distribution, we calculate the z-score:

z = (6.5 - 2.7) / 1.374 = 2.75

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than or equal to 2.75 is approximately 0.997.

Therefore, the probability of at most six individuals in the sample having used a discount broker is approximately 0.997.

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The complete question is :

What is the probability that in a random sample of nine individual investors, at most six have used a discount broker, given that the American Society of Investors survey found that 30% of individual investors have used a discount broker?

The expression -4x^2 + 16x - 24 can be factored completely as -4(x - 2)(x - 3).

To factor the given expression completely, we can first look for common factors among the terms. In this case, all the terms are divisible by -4, so we can factor out -4 as a common factor:

-4(x^2 - 4x + 6)

Now, we need to factor the quadratic expression (x^2 - 4x + 6). Since the coefficient of x^2 is 1, we can look for two numbers that multiply to give 6 and add up to -4 (the coefficient of x).

The numbers that satisfy this condition are -2 and -3. We can rewrite the expression by splitting the middle term:

-4(x^2 - 2x - 3x + 6)

Now, we group the terms:

-4((x^2 - 2x) + (-3x + 6))

We can factor out x from the first two terms and -3 from the last two terms:

-4(x(x - 2) - 3(x - 2))

Notice that we have a common factor of (x - 2). We can factor it out:

-4(x - 2)(x - 3)

Therefore, the expression -4x^2 + 16x - 24 can be factored completely as -4(x - 2)(x - 3).

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-24.5 my bro told me the answer

The product of the expression sixty-four sixty-fifths times twenty will be less than 20. The correct option is D.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

The product of the expression sixty-four sixty-fifths times twenty will be:

= 64/65 × 20

= 0.985 × 20

= 19.7

This is less than 20.

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Answer:

Step-by-step explanation:

-11

Answer:

The graph would look like this

Step-by-step explanation:

I'll do the first two to get you started.

======================================================

Problem 1

Answer:  0-7+11 = 4

-----------------------------------

Explanation:

The bottom arrow is where we start. Specifically at 0 on the number line.

Then we move 7 units to the left. This is represented by -7 on the number line. So -7 is part of the addition equation.

Then we move 11 units to the right to arrive at 4 on the number line. This is the same as adding 11 to -7 to get -7+11 = 4 and that is the same as 0-7+11 = 4

======================================================

Problem 2

Answer:  1 + (-5) + 9 = 5

-----------------------------------

Explanation:

We now start at 1 on the number line. Move 5 units to the left to get to -4

Moving 5 units to the left is the same as subtracting 5, or adding on -5

So far we have 1 + (-5) which simplifies to -4

The last thing we do is add on 9 to go from -4 to 5. In other words, we move 9 units to the right when we go from -4 to 5

In terms of an equation,  -4 + 9 = 5

So overall, that's how I got 1 + (-5) + 9 = 5

The area of this circular plate is about 36.53 square inches.

Let r be the radius of circular plate, C be the circumference of circle and A be the area of the circle.

Here,

C = 21.4 inches

We need to find the value of A

Using the formula of circumference of circle,

C = 2 * π * r

21.4 = 2πr

r = 21.4/2π

r = 3.41 inches

Using the formula of the area of the circle,

A = π * r²

A = π × (3.41)²

A = 36.53 sq. in

Therefore, the area of this circular plate is about 36.53 square inches.

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Answer:

20

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

12        ?

----- = -------

3         5

Using cross product

12*5 = 3?

60 = 3?

Divide each side by 3

60/3 = 3?/3

20 = ?

The unknown side is 20

Answer:

20

Step-by-step explanation:

Since the triangles are similar, all the side lengths can be multiplied by a scale factor,

12/3 = 4, so the scale factor is 4, which

5 x 4 = 20, so the missing side length is 20

Answer:

\(\displaystyle h'(0) = -5\)

Step-by-step explanation:

We are given the function:

\(\displaystyle h(x) = 3f(x) -2g(x) - 5\cos x - 3\)

And that f'(0) = 3 and g'(0) = 7.

And we want to determine the value of h'(0).

Find h'(x). We can take the derivative of both sides:

\(\displaystyle h'(x) = \frac{d}{dx}\left[ 3f(x) - 2g(x) - 5\cos x - 3\right]\)

Expand and simplify:

\(\begin{aligned}\displaystyle h'(x) & = \frac{d}{dx}\left[ 3f(x) - 2g(x) - 5\cos x - 3\right] \\ \\ & = \frac{d}{dx}[3f(x)] + \frac{d}{dx}[-2g(x)] + \frac{d}{dx}[-5\cos x] + \frac{d}{dx}[-3]\\ \\ & = 3f'(x) -2g'(x) +5\sin x\end{aligned}\)

Therefore:

\(\displaystyle h'(0) = 3f'(0) -2 g'(0) + 5 \sin (0)\)

Substitute and evaluate:

\(\displaystyle \begin{aligned} h'(0) & = 3(3) - 2(7) + 5(0) \\ \\ & = (9) - (14) + (0) \\ \\ & = -5\end{aligned}\)

In conclusion:

\(\displaystyle h'(0) = -5\)

A. By the given conditions, the function f has a root in the interval [a, b].

B. The given conditions provide information about the function f and its derivatives.

Let's analyze the conditions step by step:

1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.

In other words, the function changes the sign between a and b.

2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).

This indicates that the function is increasing within this interval.

3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).

This indicates that the function is concave up within this interval.

By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).

Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].

Therefore, the main answer is that the function f has a root in the interval [a, b].

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In a stratified sample of 50 students, approximately 10 Year 7 students are picked.

We have,

The total number of students in the population.

= 135 (Year 7) + 150 (Year 8) + 120 (Year 9) + 154 (Year 10) + 132 (Year 11)

= 691

The proportion of Year 7 students in the population.

= 135/691

= 0.1957

To calculate how many Year 7 students are picked in a sample of 50 students, we multiply the sample size by the proportion of Year 7 students in the population.

= 50 × 0.1957

= 9.785

Rounding to the nearest whole number.

= 10

Therefore,

In a stratified sample of 50 students, approximately 10 Year 7 students are picked.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

itsb a

Step-by-step explanation:

sorry

Answer:

I think that the answer is B

Answer:

Answer B, (-2,-4)

Step-by-step explanation:

Let's solve your system by substitution.

y=3x+2;y=−2x−8

Step: Solvey=3x+2for y:

y=3x+2

Step: Substitute3x+2foryiny=−2x−8:

y=−2x−8

3x+2=−2x−8

3x+2+2x=−2x−8+2x(Add 2x to both sides)

5x+2=−8

5x+2+−2=−8+−2(Add -2 to both sides)

5x= −10

5        5

(Divide both sides by 5)

x=−2

Step: Substitute−2 for x in y=3x+2:

y=3x+2

y=(3)(−2)+2

y=−4(Simplify both sides of the equation)

Hope this helps good luck.