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Answer: Charlotte's 15 and Edgar's 7

Step-by-step explanation:

7*2=14

14+1 = 15

15 + 7 = 22

The probability that the chosen number from the list of the given number is prime number is 1.

The probability of an event E is defined as,

P(E) = Total favorable outcomes/Total possible outcomes

In this case,

The sample space is  2, 3, 5, 7, 11, 13, 17, 19.

Total possible outcomes are 8.

One number is chosen at random, the chosen number has to be a prime number,

Total prime number in the sample space are 2, 3, 5, 7, 11, 13, 17, 19.

So. total favorable outcomes are 8.

So, the probability that the chosen number is prime number,

P(E) = 8/8

P(E) = 1.

So, the probability of the chosen number to be a prime number is 1.

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\((2 + 3)(1 + x) = 25 \\ 5(1 + x) = 25 \\ 1 + x = 25 \div 5 \\ 1 + x = 5 \\ x = 5 - 1 \\ \boxed{x = 4}\)

Note :-

Image is attached.

Hope it helps!

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

4

Step-by-step explanation:

2+3=5

5*(1+4)

1+4=5

5*5=25

Answer:

3

Step-by-step explanation:

How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn’t spill a drop? Use 3.14 for pi

Number of times = volume of tank /volume of cylinder

volume of cylinder = πr²h

3.14 x 5² x 20 = 1570

4710 /  1570 = 3 times

Answer:

20 books

Step-by-step explanation:

given that the shelf can hold 25 1/2 lbs (i.e 25.5 lbs), and that each book weighs 1 1/4 ln (i.e 1.25 lbs)

number of books which the shelf can hold

= weight that the shelf can hold ÷ weight of each book

= 25.5 ÷ 1.25

= 20.4 books

because having 0.4 of a book (i.e part of a book) would not be very feasable, we have to round the number of books down to the nearest whole number)

20.4 books rounded down to nearest whole number = 20 books (answer)

Answer:

20 2/5 books

Answer:

no

Step-by-step explanation:

The statement is true as  a function f(x) is continuous at a specific point, in this case, x=3, then it implies that the function is also differentiable at that point.

The concept of continuity and differentiability are closely related in calculus. If a function is continuous at a particular point, it means that the function is "smooth" and has no abrupt changes or breaks at that point. In other words, as x approaches the specific point, the function values approach a single, well-defined value.Differentiability, on the other hand, relates to the existence of the derivative of a function at a point. If a function is differentiable at a point, it means that the slope or rate of change of the function is well-defined at that point.

In this case, since the function f(x) is given to be continuous at x=3 and f(3) is defined as 15, it implies that the function has no abrupt changes at x=3 and the function values approach 15 as x approaches 3. Consequently, the function is also differentiable at x=3, indicating that the slope or rate of change of the function is well-defined at that point.

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Answer:

\(4.97~m\)

Step-by-step explanation:

We know that the scale model of the sculpture is \(\frac{71}{3}\) times bigger than the actual model. So, the scale model has a size of \(\frac{71}{3}\cdot 21=71\cdot \frac{21}{3}=71\cdot 7=497\) cm and we're done!

But wait! The problem asks for the answer in meters, so the answer is actually \(\frac{497}{100}=\boxed{4.97~m}\) and we're(actually) done!

Answer:

1/3

Step-by-step explanation:

since number 2 card was not replaced, we have;

probability of picking a second card, 3;

let S be number of sample space

n(S)= 4

n(3)= 1

Pr(3/2)= 1/3

(because since one was already chosen and n, the sample space would reduce)

Answer:

-7/15

Step-by-step explanation:

For:

Use distributive property:

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

Let:

x = Unknown number

When the number x is increasesd by 35 the result is 38, so:

Area of the polygon 542.5ft²

A polygon is a two-dimensional geometric shape that is made up of a finite number of line segments that are connected end-to-end to form a closed shape. The line segments of a polygon are called sides, and the points where the sides meet are called vertices.

A polygon can have any number of sides, but must have at least three. Some examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and so on.

First way:

Area of the polygon=Area of small rectangular part+ area of trapezium part

=7×7 + 1/2(23+12)×26

49+455

=504ft²

Second Way

Area of the polygon= area of trapezium part-Area of rectangular par=1/2×26(30+19)-19×7=504ft

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Profit fall in one year = 116.8$

What is profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are several profit metrics that are frequently used.

Let cost price = C

And selling price before reducing = S

Profit for 1 day = S-C

Now, After reducing selling price to = S-0.32

Profit= S - 0.32 - C for 1 day

Profit fall by = (S-C)-(S - 0.32 - C)

                     = S - C - S + 0.32 + C

Profit fall by = 0.32 for 1 day

Profit fall by one year = 0.32×365

                                    = 116.8$

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The Z-transform of the sampled function f(t) = t is calculated.

The Z-transform is a mathematical tool used in signal processing and discrete-time systems analysis to transform a discrete-time signal into the complex frequency domain. In this case, we have a function f(t) = t that is sampled at regular intervals of T.

To find the Z-transform of the sampled function, we apply the definition of the Z-transform, which states that the Z-transform of a discrete-time signal x[n] is given by the sum from n = 0 to infinity of x[n] times \(Z^-^n\), where Z represents the complex variable.

In our case, the sampled function f(t) = t can be represented as a discrete-time signal x[n] = n, where n represents the sample index. Applying the definition of the Z-transform, we have:

X(Z) = Σ[n=0 to ∞] (n *\(Z^-^n\))

Now, we can simplify this expression using the formula for the sum of a geometric series. The sum of the geometric series Σ[\(r^n\)] from n = 0 to ∞ is equal to 1 / (1 - r), where |r| < 1.

In our case, r = \(Z^(^-^1^)\), so we can rewrite the Z-transform as:

X(Z) = Σ[n=0 to ∞] (n * \(Z^-^n\)) = Z / (1 - Z)²

This is the Z-transform of the sampled function f(t) = t.

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Answer:

D.

Step-by-step explanation:

AB is NOT equal to BA in matrix multiplication.

It is not commutative.

Answer: \(20,706\ m^3\)

Step-by-step explanation:

Given

The warehouse has the following dimension

Height is \(h=8\frac{1}{2}\ m\)

\(h=\dfrac{17}{2}\ m\)

Length is \(l=120\ m\)

Width is \(w=20\frac{3}{10}\ m\)

\(w=\dfrac{203}{10}\ m\)

Volume of the warehouse is the product of height, length and width

\(\Rightarrow V=h\times l\times w\\\\\Rightarrow V=\dfrac{17}{2}\times 120\times \dfrac{203}{10}\\\\\Rightarrow V=20,706\ m^3\)

Therefore, the length of the warehouse is \(20,706\ m^3\).

Answer:

10 ft

Step-by-step explanation:

Given:

Plug in the values given:

Cancel π from both sides and simplify:

Answer:

The height of the cone if the radius is 6ft is,

⇒ h = 3.18 feet

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

An orange cone has a exact volume of 120π ft³.

And, The radius = 6 feet

Now, We know that;

Volume of cone = πr²h/ 3

Hence, We get;

⇒ 120 = 3.14 × 6² × h / 3

⇒ 120 = 3.14 × 12h

⇒ 120 = 37.68h

⇒ h = 3.18 feet

Thus, The height of the cone if the radius is 6ft is,

⇒ h = 3.18 feet

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The estimated conditional probability of a family having two girls if it has at least one girl is 1/2 or 0.5.

Having one girl does not provide any information about the gender of the second child, so the probability of the second child being a girl or a boy is still 50-50.

To estimate the conditional probability of a family having two girls if it has at least one girl, we can utilize the concepts of "one_girl" and "two_girls" scenarios.

Let's define "one_girl" as the event of a family having one girl, and "two_girls" as the event of a family having two girls. We want to calculate the probability of "two_girls" occurring given that "one_girl" has occurred.

The conditional probability can be calculated using the formula:

P(two_girls | one_girl) = P(two_girls and one_girl) / P(one_girl)

To estimate this probability, we need to make certain assumptions. Assuming that the probability of having a girl or a boy is equal (50% each), we can analyze the possible outcomes for a family with at least one girl:

GG (two_girls)

GB (one_girl)

BG (one_girl)

Out of these three possibilities, two of them satisfy the condition of having at least one girl (GG and GB). The event "one_girl" occurs in two out of three possible scenarios.

Therefore, P(one_girl) = 2/3.

Among these two scenarios, only one corresponds to "two_girls" (GG). Therefore, P(two_girls and one_girl) = 1/3.

Now, we can substitute these values into the conditional probability formula:

P(two_girls | one_girl) = (1/3) / (2/3) = 1/2.

It's important to note that this estimation assumes equal probability for a girl or a boy and assumes independence between the genders of different children within a family. In reality, the probability of having a girl or a boy may vary, and the gender of siblings can be dependent in certain cases (e.g., due to genetic factors). Therefore, this estimation serves as a simplified scenario based on the assumption of equal probabilities and independence.

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Answer: GCF = 6, LCM = 72

Step-by-step explanation:

The prime factorization of 18 is 2*3^2 and the prime factorization of 24 is 2^3*3

Therefore, the gcf is 2*3 = 6.

The lcm is 2^3*3^2 = 8*9 = 72

Answer:

2nd 3rd last one

Step-by-step explanation:

Angles, lines, rays, and segments can be found in a plane. The terms shown on the diagram are: Ray KM, Line JK, and Ray MJ

A line is an unending, straight path that has no endpoints and travels in both directions along a plane. A line segment is a finitely long portion of a line with two endpoints. A line segment that goes on forever in one direction is known as a ray.

To identify the terms shown on the diagram, we need to note the following: A ray has no endpoint; it is represented with an arrow on one side line segment has two endpoints.

It is represented with dots on both sides. An angle is a space between intersecting lines, line segments, or rays. There is no connection between J and L. So, JL is not a line segment

Ray KM

KM has a dot at point K and an arrow that points in the direction of M. So, KM is a ray.

Line JK

JK has dots on both ends (at J and K). So, JK is a line.

Ray PK

PK has dots on both sides (at P and K). So, PK is a line; not a ray.

Angle LJK

There is no connection between points L, J, and K. Hence, LJK is not an angle.

Ray MJ

MJ has a dot at point M and an arrow that points in the direction of J. So, MJ is a ray.

The diagram is attached with the answer below.

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The measure of both angles is 60 and 180 degrees respectively.

In a literal sense, corresponding means pairwise angles. Like the right corner angles of two triangles etc. But usually, we take them as:

For two similar figures, the pair-by-pair similar angles of those two similar figures are called corresponding angles. They are of the same measurement.

Given that angle a is corresponding to angle b the measure of angle b is 2x+60 and the measure of angle a is x.

Since both the angles are equal then;

Angle A = Angle B

x = 2x + 60

Solving for x;

2x - x = -60

x = -60

Therefore, the measure of both angles is 60 and 180 degrees.

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The equation that does not pass through the point (3, -4) is the equation that does not satisfy the given point when we substitute it into the equation.

Thus, we can check each equation and see which one does not satisfy the given point. Therefore, the equation that does not pass through the point (3,-4) is the equation whose long answer does not give us a correct ordered pair in the form (3,-4).

The correct option is:2x - 3y - 18 To check, substitute x = 3 and y = -4 into the equation:2x - 3y - 18 = 2(3) - 3(-4) - 18= 6 + 12 - 18= 0

Thus, the ordered pair (3,-4) does satisfy the equation 2x - 3y - 18, which means the equation that does not pass through the point (3,-4) is not 2x - 3y - 18.

Therefore, the correct answer is B. y = 5x - 19. To verify, let's substitute x = 3 and y = -4:y = 5x - 19 = 5(3) - 19= -4

The ordered pair (3,-4) does not satisfy the equation y = 5x - 19. Thus, the equation y = 5x - 19 does not pass through the point (3,-4).

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The correct answer is option (D). The answer is 100 on weekdays, 80 on weekends

Given that,

Ms. Liu wants to concentrate on growing her clientele and is looking for recurring business. She is less intrigued by visitors who are new to the site. The percentage of first-time users is 20%, according to analytics.

To find : What percentage of clients return on weekdays and weekends?

Number of repeat customer on weekdays = 125 * (1 - 20%) = 100

Number of repeat customer on weekend = 100 * (1 - 20%) = 80

Therefore, option is the appropriate response (D).The answer is 80 on weekends and 100 throughout the week.

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Answer:

TOM KENNYY

Step-by-step explanation:

Tom Kenny as Spongebob Squarepants

Answer:

x = 10 ^ 5 - x

Step-by-step explanation:

You need to invest in a graphing calculator my friend.

log10(x)=5-x

10^log10(x) = 10^5-x

x = 10^5-x