Find the sum of 3√3 and √2 in simplest form. Also, determine whether the result is

rational or irrational and explain your answer.

Answer:

400 cubic cm

Step-by-step explanation:

Given that base is square and is side is 10 cm

area of square is given by side^2

Thus, area of base of cuboid  = \(10^2\) square cm = 100 sq. cm

We know volume for any cuboid is area of base * height

height is 4cm

thus, volume of cuboid = area of base of cuboid * height

                                     = 100 * 4 cubic cm = 400 cubic cm

Volume of cuboid is 400 cubic cm.

Unit is cubic cm

The volume of square based cuboid is \(400cm^{3}\).

Given that, base is square and side of base is 10 cm.

Height of the square-based cuboid.is 4cm.

Area of base = \((side)^{2}=(10)^{2}=100cm^{2}\)

Volume of the cuboid is multiplication of base area and height of the cuboid.

  \(Volume=100*4=400cm^{3}\)

Hence, the volume of square based cuboid is \(400cm^{3}\).

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Answer:

2 and 4 only

Step-by-step explanation:

hope it helped!!!

The x-intercepts of the graph of the quadratic function is 1, 3.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0

Now the quadratic function is,

y = x² - 4x + 3

Now for x-intercepts, y = 0.

⇒ x² - 4x + 3 = 0

Factoring we get,

⇒ x² - 3x - x + 3 = 0

⇒ x(x - 3) - 1(x - 1) = 0

⇒ (x - 1) (x - 3) = 0

Thus we get,

x = 1, 3

this is the required x-intercepts of the graph of the quadratic function.

Thus, the x-intercepts of the graph of the quadratic function is 1, 3.

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Answer:

$6.93. Because it's 9 pounds and it lasts longer.

Step-by-step explanation:

Answer:

its b lol

Step-by-step explanation:

jus got it right

There is only one solution which is x = -370 to the given equation 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) option B is correct.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We have a linear equation in one-variable:

0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)

0.75(x + 40) = 0.7(x + 20)

75(x + 40) = 70(x + 20)

75x = 70x - 1600

x = -370

Hence, there is only one solution which is x = -370 to the given equation 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) option B is correct.

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Given function f(x) = 7x-1, x = 6; we need to find the following limit lim_{h\to 0} \frac{f(x+h) - f(x)}{h}Let's substitute the value of x in f(x) to get f(6) = 7(6) - 1 = 41Now, we need to compute the following: lim_{h\to 0} \frac{f(6+h) - f(6)}{h}Using the given function, we have f(6+h) = 7(6+h) - 1 = 42 + 7h

Therefore, we have:f(6+h) - f(6) = [42+7h]-41 = 7hHence, we can write:

lim_{h\to 0} \frac{f(6+h) - f(6)}{h} = lim_{h\to 0} \frac{7h}{h} = 7

Hence, the answer is 7. Given the function f(x) = 7x-1 and x = 6, we need to determine the following limit: lim_{h\to 0} \frac{f(x+h) - f(x)}{h}In order to do that, we need to first compute the value of f(x) when x = 6.Using the given function, we have:f(6) = 7(6) - 1 = 42 - 1 = 41Now, we need to determine f(x+h) and simplify the expression f(x+h) - f(x).Using the given function, we have:

f(x+h) = 7(x+h) - 1 = 7x + 7h - 1

Now, we can write:

f(x+h) - f(x) = [7x + 7h - 1] - [7x - 1] = 7h

Thus, we have:

lim_{h\to 0} \frac{f(x+h) - f(x)}{h} = lim_{h\to 0} \frac{7h}{h}

Since the limit is of the form 0/0, we can apply L'Hopital's Rule and differentiate the numerator and denominator with respect to h, i.e., we have:

lim_{h\to 0} \frac{7h}{h} = lim_{h\to 0} 7 = 7

Therefore, the answer is 7.

The limit of the function lim_{h\to 0} \frac{f(x+h) - f(x)}{h} for f(x) = 7x-1 and x = 6 is 7.

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The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.

The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.

To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.

Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

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Answer: 1 tablespoon

Step-by-step explanation:

Answer: 12cm.

Step-by-step explanation:

Based on the scatter plot, we can see that as the average temperature increases, the amount of grass growth also increases. The data points form a general upward trend, although there is some variability in the data.

To predict the amount of grass growth that would occur at a temperature of 55° F, we can draw a line of best fit through the data points. One possible line of best fit is shown in the scatter plot below:

scatter plot with line of best fit

Using this line of best fit, we can estimate that the amount of grass growth at a temperature of 55° F would be approximately 13 centimeters. Therefore, the best prediction for the growth that would occur if the temperature were 55° F is 12 centimeters.

Answer:

huh?

Step-by-step explanation:

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer: m = 55

n = 135

p = 45

Explanation:

Since the two lines are parallel, B = M. So, M = 55 The angle of a line is 180, so I subtracted 180 by the two angles of the triangle, 80 and 55, and I got 45. So P = 45.

P is equal to the right side of the smaller triangle. The angle of a line is 180, so I subtracted 180 by 45 to get 135. So N = 135. I am not sure if my answer is correct though because I’m still in middle school.

Answer:

\( \sf \large \: a = \frac{ - 1}{4} \)

Step-by-step explanation:

Let's solve your equation step-by-step.

3/a(−2)−4=20

−4a−6/a=20

Step 1: Multiply both sides by a.

−4a−6=20a

−4a−6−20a=20a−20a(Subtract 20a from both sides)

−24a−6=0

−24a−6+6=0+6(Add 6 to both sides)

−24a=6

−24a/−24=6/−24

(Divide both sides by -24)

a=−1/4

Check answers. (Plug them in to make sure they work.)

a=−1/4

(Works in original equation)

Number 16 fill expressions B and C to make equations correct.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

For equation B. 8(2+9)=___ + 72

8*11=x+72

x=16

For equation C. 4(7+4)=28+___

4*11=28+x

x=44-28

x=16

Hence,

         Number 16 fill expressions B and C to make equations correct.

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Answer:

Step-by-step explanation:

yuuu

Answer:

The answer is b1= -√42, b2= √42

Step-by-step explanation:

If you calculate SLE to be $25,000 and that there will be one occurrence every four years (ARO), then the ALE is $40,000.

A expected monetary decline each moment an asset is at risk is referred to as single-loss expectancy (SLE). It is a term that is most frequently used during risk analysis and attempts to assign a monetary value to each individual threat.

Quantitative risk analysis predicts the likelihood of certain risk outcomes as well as their approximate monetary cost using relevant, verifiable data.

IT professionals must consider a wide range of risks, including the following:

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There are 6 ways to buy two pieces of fruit to have for lunch.

What is combination?

From 3 fruits = first choose one

From rest 2 fruits = choose one

So,

1 + 1 = 2 fruits

3 * 2 = 6 ways

Hence, there are 6 ways to buy two pieces of fruit to have for lunch.

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Answer:

15 is the answer I think.

The amount of the periodic payment necessary for the deposit to a sinking fund is approximately $18,065.19.

To find the amount of the periodic payment necessary for the deposit to a sinking fund, we can use the formula for the future value of an ordinary annuity. The formula is:

X = A * (1 + r)^nt / [(1 + r)^nt - 1]

Where:

X is the amount needed

A is the periodic payment

r is the interest rate per period

n is the number of compounding periods per year

t is the total number of years

Given the information:

Amount Needed (X) = $85,000

Frequency: Quarterly

Rate (r) = 1.4% (or 0.014 as a decimal)

Time (t) = 5 years

Since the frequency is quarterly, the number of compounding periods per year (n) is 4.

Substituting the values into the formula:

$85,000 = A * (1 + 0.014)^(4*5) / [(1 + 0.014)^(4*5) - 1]

Simplifying the equation:

$85,000 = A * (1.014)^20 / [(1.014)^20 - 1]

To find the value of A, we can rearrange the equation:

A = $85,000 * [(1.014)^20 - 1] / (1.014)^20

Using a calculator or spreadsheet, we can calculate the value of A.

A ≈ $85,000 * 0.298 / 1.350

A ≈ $18,065.19

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Answer:

$277.75

5.50×40=220

5.50÷2=2.75

5.50+2.75=8.25×7=57.75

57.75+220=277.75

The interest rate for an investment of $2,000 to grow to $6000 in 6 years compounded continuously is 9.76%.

For the given investment of $2,000 to grow to $6,000 in 6 years, If interest is compounded continuously, we need to determine the interest rate r.

In order to determine the interest rate r, we can use the following formula for continuous compounding of interest,  A = Pe^(rt) where A is the amount we end up with (in this case, $6,000), P is the principal (in this case, $2,000), t is the time (in this case, 6 years), r is the interest rate.

Now, let's plug in the values we know and solve for r, 6000 = 2000e^(6r)

Divide both sides by 2000, 3 = e^(6r)

Take the natural logarithm of both sides, ln(3) = 6r ln(e)

By Simplifying,  ln(3) = 6r

Divide both sides by 6, r = ln(3)/6r ≈ 0.09762

Convert to a percentage and round to 2 decimal places, r ≈ 9.76%

Therefore, the exact interest rate (without using a calculator) is ln(3)/6 or approximately 9.76%.

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Answer:

Step-by-step explanation:

No of students study math = 3/5 of 50 = 30

No of students study English = 3/10 of 50 = 15

Total = 30 + 15 = 45

Remaining students = 5

No of students study geography = 5

Fraction of geography to whole class = 5/45 = 9

Answer: B) y=-3x+2.

Step-by-step explanation:

+2 is where the line touches on the y axis. and for -3. you find 2 points and you go from 1 point to the other. the points i got were. (0,2) (2,-4). i went down 6 times, and to the right 2. that’s a fraction 6/2. and then simplify. 2 can go into 6 three times, and can go into 2 once. 3/1. since there’s a 1 underneath it’s just 3. and since you went down. it’s is negative. so y=-3x+2 is your answer.

Answer:

549.5

Step-by-step explanation:

The formula for the Volume of a right cylinder is V= π r² h. First you are going to substitute the 5 with the r and the 7 with the h. V= (3.14)5²(7). 5²= 25.

3.14 (25)=78.5

78.5 (7)=549.5

Answer is 549.5

Answer:

15.55555555555556

Step-by-step explanation:

Gotta run srry

Answer: 15.5556 unless you round it up to 16

Answer:

16

35

27

29

Ecuaciones:

9)(x+10)+64=90

10) ( 2+x)+143=180

11)55=(2x+1)

12)  2x=58

Answer:

Lol

Step-by-step explanation:

The probability that a person has a positive rh factor given that he/she has type O blood is approximately 82.2 %

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

\(P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)\)

Suppose two dimensions are there, viz X and Y. Some values of X are there as \(X_1, X_2, ... , X_n\) and some values of Y are there as \(Y_1, Y_2, ... , Y_n\)

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  \(X_i\) and \(Y_j\) (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

\(\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}\)

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

The missing two-way table for this problem is given below:

\(\begin{array}{cccccc}&A&B&AB&O&\rm Total\\\text{Negative}&0.07&0.02&0.01&0.08&0.18\\\text{Positive}{&0.33&0.09&0.03&0.37&0.82\\\rm Total & 0.40&0.11&0.04&0.45&1 \end{array}\)

Instead of frequencies, it contains ratio of frequency to total count of people surveyed (thus, relative frequency).

We want the probability that a person has a positive rh factor given that he/she has type O blood.

If we take:

E = event that a random person chosen has a positive rh factor

and F = event that a random person chosen has type O blood

Then, the needed probability is written symbolically as:

P(E|F).

Using the considered two-way table and the chain rule, we get this probability as:

\(P(E|F) = \dfrac{P(E \cap F)}{P(F)} = \dfrac{n(E \cap F)/ n(Total)}{n(F)/n(Total)}\)

Since the two way table consists relative frequency with total count, so, we get:

\(n(E \cap F)/n(Total) = 0.37\\n(F)/n(Total) = 0.45\)

\(P(E|F) = \dfrac{n(E \cap F)/ n(Total)}{n(F)/n(Total)} = \dfrac{0.37}{0.45} \approx 0.822 = 82.2\%\)

Thus, the probability that a person has a positive rh factor given that he/she has type O blood is approximately 82.2 %

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Answer:

The answers will be

The probability that a person has a positive Rh factor given that he/she has type O blood is 82 percent.There is a greater probability for a person to have a positive Rh factor given type A blood than a person to have a positive Rh factor given type O blood.

Step-by-step explanation:

Hope this help!

The slope of the line passing through the points (9, 4) and (3, 9) is 5/(-6).

To find the slope of the line that passes through the points (9, 4) and (3, 9), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates of the given points into the formula:

m = (9 - 4) / (3 - 9)

Simplifying the numerator and denominator, we have:

m = 5 / (-6)

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 1:

m = 5 / -6

Therefore, the slope of the line passing through the points (9, 4) and (3, 9) is 5/(-6).

It is worth noting that the negative sign in the slope indicates that the line is sloping downwards from left to right. The magnitude of the slope, 5/6, represents the rate at which the line is ascending or descending. In this case, for every 6 units of horizontal change (from 3 to 9), there is a corresponding 5 units of vertical change (from 9 to 4), resulting in a slope of 5/6.

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Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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