6^3 * 7^3 = 42^3 is this correct

Answer:

w=333.33

Step-by-step explanation:

w3=1,000 divide by 3 on both sides

w=333.33333 rounded to the nearest hundredth

w=333.33

For the sample space s = {0, 1, 2} and the event a = {0}, the event a is a non-empty set that contains the element 0, and therefore, a ≠ ∅.

In probability theory, the sample space refers to the set of all possible outcomes of a random experiment, while an event is a subset of the sample space. In this case, the sample space s consists of the numbers 0, 1, and 2, while the event a consists of the number 0.

An empty set, denoted by the symbol ∅, is a set that contains no elements. In contrast, the event a contains the element 0, and therefore, a is not an empty set.

While it may be confuse the event a with the empty set, it is important to note that even a singleton set, such as a set containing only one element, is not the same as the empty set. In this case, the event a contains a single element, which is 0. Therefore, the event a is not empty and cannot be considered equivalent to the empty set.

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The average rate of change of the function f(x) over the interval 5 ≤ x ≤ 8 is 81.

The average rate of change of a function f(x) over an interval [a, b] is given by:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, we want to find the average rate of change of the function f(x) = 5x^2 + 7x + 9 over the interval 5 ≤ x ≤ 8.

So, we need to evaluate f(8) and f(5) and then plug the values into the formula:

f(8) = 5(8)² + 7(8) + 9 = 389

f(5) = 5(5)² + 7(5) + 9 = 144

Now we can plug these values into the formula for the average rate of change:

average rate of change = (f(8) - f(5)) / (8 - 5)

= (389 - 144) / 3

= 81

Therefore, the average rate of change of the function f(x) over the interval 5 ≤ x ≤ 8 is 81.

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Answer:

I am not sure what the values needed to add in / etc, but here is the height of the box: 5

Step-by-step explanation:

A cube is a kind of rectangle where all the sides are the same. So to find volume, cube the length of any side. To find height, calculate the cube root of a cube's volume. For this example, the cube has a volume of 125. The cube root of 125 is 5. The height of the cube is 5.

(hopefully this is correct, have a nice day!)

The shortest distance between the skew lines with parametric equations is |−74s/17 + 23/17|.

To find the distance between the skew lines, we need to find the shortest distance between any two points on the two lines. Let P be a point on the first line with coordinates (1t, 36t, 2t) and let Q be a point on the second line with coordinates (12s, 414s, −35s).

Let's call the vector connecting these two points as v:

v = PQ = <1−2s, 3−10s, 2+5s>

Now we need to find a vector that is orthogonal (perpendicular) to both lines. To do this, we can take the cross product of the direction vectors of the two lines.

The direction vector of the first line is <1, 6, 0> and the direction vector of the second line is <2, 14, −5>. So,

d = <1, 6, 0> × <2, 14, −5>

d = <−84, 5, 14>

We can normalize d to get a unit vector in the direction of d:

u = d / ||d|| = <−84/85, 5/85, 14/85>

Finally, we can find the distance between the two lines by projecting v onto u:

distance = |v · u| = |(1−2s)(−84/85) + (3−10s)(5/85) + (2+5s)(14/85)|

Simplifying this expression yields:

distance = |−74s/17 + 23/17|

Therefore, the distance between the two skew lines is |−74s/17 + 23/17|. Note that the distance is not constant and depends on the parameter s.

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Answer:

Angle 1 and angle 2

x=9

Step-by-step explanation:

The angle pair is complementary since it makes a right angle, so you could technically name it anything like angle 1 and angle 2. You make the equation 4x+8+5x+1=90. Then, you combine like terms and get 9x+9=90. Then, subtract the 9 from 90, 81. 9x=81. Then, divide the 9 from 81. X=9.

The volume of a right circular cone is 4.5 m³ that has height of 7.8 m and base diameter is 2.3 m.

The volume of a right circular cone is given by the formula

V = (1/3) * π * r^2 * h

where r is the radius of the circular base and h is the height of the cone.

Since the diameter of the base is 2.3 m, the radius is half of that, or 1.15 m. The height of the cone is given as 7.8 m.

Substituting these values in the formula, we get

V = (1/3) × π × (1.15 m)² × 7.8 m

V ≈ 4.501 m³

Rounding to the nearest tenth of a cubic meter, we get the final answer as

V ≈ 4.5 m³

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Null hypothesis, \(H_{0}\) P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,\(H_{0}\)  P1\(\neq\)P2 (The proportion of tablets owned by men and women are not equal.)

Sample proportion for men who own tablets  ≈0.433

Sample proportion for women who own tablets ≈0.466

p value of the test  is 0.3320.

Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.

Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.

Null hypothesis, \(H_{0}\) P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,\(H_{0}\)  P1\(\neq\)P2 (The proportion of tablets owned by men and women are not equal.)

The notations for the sample statistic are  p p1 p2

Pooled proportion p = \(\frac{x_{1}+x_{2} }{n_{1}+n_{2} }\)= 197+235/455+504

                                               ≈ 0.45

Sample proportion for men who own tablets,

                               p1 = \(\frac{x_{1} }{n_{1} }\)= 197/455

                                           ≈0.433

Sample proportion for women who own tablets,

                              p2 = \(\frac{x_{2} }{n_{2} }\) = 235/506

                                          ≈0.466

Since p1<p2  women group has higher tablet ownership.

Sample statistic, p1-p2

                          = 0.433-0.466

p value of the test  is 0.3320.

In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.

In probability and statistics, the null hypothesis is the general statement or default state that  zero  or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until  other evidence is presented to disprove the hypothesis.

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Answer:

10 kg

1kg for each back = 1kg×10 bags = 10kg

The measure of the angle coterminal to - 118° is equal to 242°. (Correct choice: A)

Two angles are coterminal when they have different measures and the same direction in the terminal side. Two consecutive coterminal angles differ their measures in 360°. Then, we can determine the value of the coterminal angle by using the following formula:

θ' = θ + 360°

Where:

If we know that θ = - 118°, then the coterminal angle between 0° and 360° is:

θ' = - 118° + 360°

θ' = 242°

The measure of the coterminal angle is 242°.

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Answer:

-21z-35t+21g

Step-by-step explanation:

-7x3z=-21z

-7x5t=-35t

-7x-3g=21g

Answer:

87

Step-by-step explanation:

the number sequence is upside down

Answer:

f(-4) = 56

Step-by-step explanation:

f(x) = 3x² - 2x

To find f(-4), substitute -4 for all the values of x in f(x).

f(-4) = 3(-4)² - 2(-4)

Square -4.

f(-4) = 3(16) - 2(-4)

Multiply 3 and 16.

f(-4) = 48 - 2(-4)

Multiply -2 and -4.

48 + 8

Add.

56

You had the right idea! :)

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

Answer:

X is 12 Y is 124

Step-by-step explanation:

left and right side have equal degrees of 56

so x would be 12 because you would multiply 4×12

since in total it will be 360 degrees

you add 56 and 56 together to get 112

then just subtract 112 from 360 and you get 248 then divide 248 by 2 and you have your bottom and top value of 124

Answer:

The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.

Step-by-step explanation:

Answer: No

f(x) = x³ + 2x − 5

Step-by-step explanation:

No

f(x) = x³ + 2x − 5

The solutions to the equations are

1. x = 4

2. x = -12

3. x = 0 and x = 4

The solutions to the inequalities are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

From the question, we have the following equations

1. 4x + 6 = 8x - 10

2. -3/4x - 2 = -1/2x + 1

3. |4 - 2x| + 5 = 9

Next, we split the equations to 2

So, we have

1. y = 4x + 6 and y = 8x - 10

2. y = -3/4x - 2 and y = -1/2x + 1

3. y = |4 - 2x| + 5 and y = 9

Next, we plot the system of equations (see attachment) and write out the solutions

The solutions are

1. x = 4

2. x = -12

3. x = 0 and x = 4

From the question, we have the following inequalities

4. x² + 4x - 5 < 0

5. x² - x - 12 ≥ 0

Next, we plot the system of inequalities (see attachment) and write out the solutions

The solutions are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

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P(B|A) = 0.04. We can use Bayes' theorem to find P(B|A) given the probabilities P(A), P(B), and P(AUB).

Bayes' theorem is a fundamental concept in probability theory that allows us to calculate the probability of an event given some other related information. In this case, we are given the probabilities of two events, A and B, as well as the probability of their union, AUB. We want to find the conditional probability of B given that A has occurred, which is denoted as P(B|A).

Bayes' theorem states: P(B|A) = P(A ∩ B) / P(A)

where P(A ∩ B) is the probability of both A and B occurring, and P(A) is the probability of A occurring. We can rearrange the equation to solve for P(A ∩ B): P(A ∩ B) = P(B|A) * P(A)

We know that P(A) = 0.50, P(B) = 0.40, and P(AUB) = 0.88. To find P(A ∩ B), we can use the formula: P(A ∩ B) = P(A) + P(B) - P(AUB)

Substituting in the given values, we get: P(A ∩ B) = 0.50 + 0.40 - 0.88 = 0.02

Now we can use Bayes' theorem to find P(B|A): P(B|A) = P(A ∩ B) / P(A)

= 0.02 / 0.50

= 0.04

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Answer:  906 in^3.

Step-by-step explanation:

The volume of a triangular pyramid is the area of the base multiplied by the height divided by 3.

First, we can start by finding the area of the base.

The area of the base is equal to 19*13/2

= 123.5 in^2

Next, we plug in the formula.

So the volume = 123.5*22/3 in^3

= 905.666 repeated in ^3

Rounded to the nearest whole number is 906 in^3.

Check the picture below.

so the base of the pyramid is just a triangle with a base of 19 and an altitude of 13, and the pyramid has a height of 22.

\(\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(19)(13)\\\\ h=22 \end{cases}\implies \begin{array}{llll} V=\cfrac{1}{3}\left[ \cfrac{1}{2}(19)(13) \right](22) \\\\\\ V=\cfrac{2717}{3}\implies V\approx 906~in^3 \end{array}\)

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Miguel served 23 orders, Ahmad served 46 orders, and Jane served 15 orders at the school cafeteria on Monday.

To solve this problem, let's assign variables to represent the number of orders served by each person. Let's say Miguel served x orders.
According to the information given, Ahmad served 2 times as many orders as Miguel, so Ahmad served 2x orders.
Jane served 8 fewer orders than Miguel, so Jane served (x - 8) orders.
The total number of orders served by all three is 84, so we can set up the equation:
x + 2x + (x - 8) = 84
Simplifying the equation, we have:
4x - 8 = 84
Adding 8 to both sides of the equation:
4x = 92
Dividing both sides by 4:
x = 23

Now we can find the number of orders served by each person:

Miguel served 23 orders.
Ahmad served 2 * 23 = 46 orders.
Jane served 23 - 8 = 15 orders.

In conclusion, Miguel served 23 orders, Ahmad served 46 orders, and Jane served 15 orders at the school cafeteria on Monday.

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None of the sides are congruent, as they have different side lengths.

When we have two points of the coordinate plane, the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem, as the distance is the hypotenuse:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The vertices of the quadrilateral in this problem are given as follows:

D(-2,-1), E(3, 13), F(15, 5), G(13, -11).

Hence the side lengths are given as follows:

Hence none of the sides are congruent, as they have different side lengths.

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The coefficient of x²y⁴ in the expansion of (x + 2y)⁶ can be found using the binomial theorem. The coefficient is 15.

To find the coefficient of x²y⁴, we need to determine the term in the expansion of (x + 2y)⁶ that contains x²y⁴. According to the binomial theorem, the term in the expansion of (x + 2y)⁶ with x²y⁴ can be calculated using the formula: C(n, k) * a^(n-k) * b^k, where n is the exponent of the binomial, k is the power of the variable in question (in this case, y), and C(n, k) represents the binomial coefficient.

In this case, n = 6, k = 4, a = x, and b = 2y. Plugging these values into the formula, we get: C(6, 4) * x² * (2y)⁴. Evaluating C(6, 4) gives us 15. Therefore, the coefficient of x²y⁴ in the expansion is 15.

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The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  \(\bar x\) = σ/\(\sqrt{(n)\)  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P((\(\bar x\) - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

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Answer:

Step-by-step explanation:

"or" means sum, that is all x≤-2 plus all x≥3

≤-2  mens all numbers less than -2 and the -2

≥3  mens all numbers greater than 3 and the 3

Answer: Either use a calculator or do mental math/ practice more often.

Answer:

look t it like multiplication then the answer is divided by one of the numbers

Step-by-step explanation:

hope this was helpful lol