Able has a younger sister and an older brother. - Able’s age can be represented by x. - Able’s sister is 4 years younger than him. - Able’s older brother is twice as old as he is. - The combined age of all three siblings is 32. How old is Able’s younger sister?

Probability at least one will have a defect = 1 - probability (none will have a defect) = 1 - C(7,0) (0.03)^0 (0.97)^7 = 1 - 0.808 = 0.192.

The probability that at least one product will have a defect is 0.52.

A probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

Given is a manufacturing machine has a 10% defect rate.

The binomial probability can be calculated using the formula -

P(X = x) = C(n, x) pˣ (1 - p)ⁿ ⁻ ˣ

defect rate = 10% = 10/100 = 0.1 = p

Now, the probability that at least one will not have a defect can be calculated using -

P(X = 0) = C(7, 0)(0.1)⁰(0.9)⁷ = 1 x 1 x 0.48 = 0.48

Then, the probability that at least one will have a defect = 1 - P(X = 0)

1 - P(X = 0)

1 - 0.48

0.52

Therefore, the probability that at least one will have a defect is 0.52.

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In order to simulate the amount of bullseyes that Grace will strike during her upcoming turn, we can carry out the following steps:

Within each loop cycle, generate 5 random integers between 0 and 1 to represent the likelihood of hitting a bullseye with each missile.

Accumulate the total number of bullseyes achieved for each round by adding the number of times the generated figure is less than or equal to 2/3.

After successfully running the simulation through 10,000 rounds, divide the total number of bullseyes hit by 10,000 to get the average number of bullseyes struck every round.

Finally, state the expected number of bullseyes that Grace will hit on her next turn by saying the average from step 4.

As a result, by prudently repeating numerous rounds, our algorithm can factor in the differential element instinctive throughout this process and eventually obtain a more precise tally of the predicted number of bullseyes Grace may potentially hit during her upcoming turn.

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Answer:

Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4  ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.

Hope this helps!

Step-by-step explanation:

The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.

The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.

Mathematical operations determine the results of mathematical expressions and problems.

Cost of a dress = $6.20

Cost of 3 dresses = $15.20

Cost per dress if 3 dresses were bought = $5.067

Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)

Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.

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Answer:

Draw a dashed line to represent the graph of 5x + 10y = 1500 and shade the portion below the line for positive values of x and y.

Step-by-step explanation:

This is the answer I can confirm that this is true rather than,"WhAt TyPe Of MaThEmAtIcS iS tHis?"

The exact values of the given trigonometric functions are

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{89}{39}\)

\(csc(A) =\frac{89}{80}\)

\(cot(A) =\frac{39}{80}\)

From the question, we are to determine the values of the trigonometric functions

First, we will determine the length of side c

By the Pythagorean theorem, we have that

c² = a² + b²

c² = 80² + 39²

c² = 6400 + 1521

c² = 7921

c = √7921

c = 89

Now, Using SOH CAH TOA

That is,

\(sin(A) = \frac{opposite}{hypotenuse}\)

\(cos(A) = \frac{adjacent}{hypotenuse}\)

\(tan(A) = \frac{opposite}{adjacent}\)

In the triangle,

opposite = a = 80

adjacent = b = 39

hypotenuse = c = 89

Thus,

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{1}{cos(A)} =\frac{89}{39}\)

\(csc(A) =\frac{1}{sin(A)} =\frac{89}{80}\)

\(cot(A) =\frac{1}{tan(A)} =\frac{39}{80}\)

Hence, the exact values of the given trigonometric functions are

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{89}{39}\)

\(csc(A) =\frac{89}{80}\)

\(cot(A) =\frac{39}{80}\)

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Answer:

The y-values of equivalent ratios increase at the same rate as their x-values. The vertical distance between points is constant, and the horizontal distance between points is constant. This forms a straight line.

Step-by-step explanation:

Equivalent proportions (which are, as a result, equal parts) are two proportions that express a similar connection between numbers. We can make comparable proportions by duplicating or separating both the numerator and denominator of a given proportion by a similar number.

Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.

Answer:

Here's how:-

x is the altitude or height of the triangle. To find it, we can use the Pythagoras theorem:-

\(altitude^{2} + base^{2} = hypotenuse^{2}\)

The base is 120cm and the hypotenuse is 122cm

Putting this in the equation, we get:-

\(altitude^{2} + 120^{2} = 122^{2}\)

\(altitude^{2} = 122^{2}- 120^{2}\)

\(altitude^{2} = 14884 - 14400\)

\(altitude^{2}\) = 484

altitude = \(\sqrt{484}\)

Answer:

Step-by-step explanation:

13) 8 - 6 + 4 = 2 + 4 = 6

14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5

15) 3x + 5 = 17

3x = 17 - 5

3x = 12

x = 4 ≠ 2

b. solution is incorrect

16)4y - 7 = 3y - 4

4y - 3y = -4 + 7

y = 3

a. solution is correct

17) 2m - 3 < 4

2m < 4 + 3

2m < 7

m < 3.5

2 < 2.5, so a. number is a solution

18 ) 5 + 2n ≥ 12

2n ≥ 12 - 5

2n ≥ 7

n ≥ 3.5

0 is not greater than equal to 3.5, so b. number is not a solution

By the concept of function, the value of g(x) obtained is

g(x) = 3f(x) is the required function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, from the graph, it can be seen that

g(1) = 3 and g(-1) = 3

Let g(x) = \(kx^2\)

g(1) = 3

\(k(1)^2 = 3\\k = 3\)

So g(x) = \(3x^2\) = 3f(x) is the required function

Option B is correct

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Complete Question

If f(x) = x², which equation represents function g?

A. g(x)=1/3f(x)

B. g(x)=3f(x)

C. g(x)=f(1/3x)

D. g(x)=f(3x)

The diagram has been attached here

Answer:

The answer would be 5 and -12

Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Answer:

x = 2

Step-by-step explanation:

13x - 2(8 + 5x) = 12 - 11x

13x - 16 -10x = 12 - 11x

13x - 10x + 11x = 12 +16

14x = 28

x = 28/14

x = 2

According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.

To find the wide variety of girl population, we will subtract the quantity of male population from the full population.

Total population = 88,51,84,692

Number of male = 45,40,34,570

Number of female = Total population - Number of male

= 88,51,84,692 - 45,40,34,570

= 43,11,50,122

Therefore, the number of female population is 43,11,50,122.

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The area of a outdoor carpet is 42 square feet.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

In the given figure, the outdoor carpet consist two triangles and one rectangle.

Here, rectangle measures length=11 ft and width = 3 ft, small triangle has base= 2 ft and height =3 ft and large triangle has base= 4ft and height =3 ft.

So, area of rectangle is 11×3 = 33 square ft

Area of small triangle = 1/2 ×Base×Height

= 0.5×2×3

= 3 square feet

Area of large triangle = 1/2 × 4×3

= 6 square feet

Total area = 33+3+6

= 42 square feet

Therefore, the area of a outdoor carpet is 42 square feet.

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Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

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Answer:

it's D

Step-by-step explanation:

You use distribute property, then add all like terms

Answer:

D

Step-by-step explanation:

Break it into 2 parts.

First Part

4s (5s^2 + 10s + 3)

20s^3 + 40s^2 + 12s

Second Part

2 (5s^2 + 10s + 3)

10 s^2 + 20s + 6

Now add the like terms

20s^3 + (40s^2 + 10s^2) + (12s + 20s) + 3

20s^3 + 50s^2 + 32s + 6

Solution :

a).

The different three letter initials that people have is :

= 26 x 26 x 26

= \(26^3\)

= \(17576\)

b). The first place to be fill in26 ways.

The second place to be filled in 25 ways

The third place to be filled in 24 ways.

Therefore, total number of three letter initial with no repetition is :

= 26 x 25 x 24

= \(15600\)

c). The total number of three letter initial begin with X = 1 x 26 x 26

                                                                                          = \(676\)

d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1

                                 = \(26\)

Answer:

Step-by-step explanation:

Whenever you add two number x and -x and it becomes 0 . IT is the identity property.

Ex:

-1/3 + 1/3 = 0

-1 + 1 = 0

-58 + 58 = 0

Answer: 125 I think

Step-by-step explanation:

Answer:

X + 2y = 1

3x + y = 13

Step-by-step explanation:

A and b are the coefficients of X and y

I wasn't sure about my answer so used Gauthmath

Answer:

that is alot the prob. is 20

Step-by-step explanation:

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

Explanation:

Consider a square with side length 1 unit.

Draw a diagonal and we have two congruent isosceles right triangles. Each triangle has a hypotenuse of sqrt(2) after using the pythagorean theorem.

If the person walks along the edges, then they walk 1+1 = 2 units.

If they walk along the diagonal, they walk roughly sqrt(2) = 1.4142 units.

They save roughly 2-1.4142 = 0.5858 units

which is roughly 0.5858/2 = 0.2929 = 29.29% of the walked distance along the edges. There's probably some slight rounding error going on, but it's fairly close to 30%, so that is likely the final answer.

8.6 cm

The given triangle is a right angled triangle

Using the trigonometric identity below:

The general anti derivative or indefinite integral of the function

cos2x - sec²x is 1/2 sin2x + tan x + C .

The given function is of the form : cos2x - sec²x

Now we will use the indefinite integral on the above expression:

∫cos2x - sec²x

This can be broken into :

∫cos2x -  ∫sec²x

Now we will integrate them separately:

∫cos2x, we will use u-substitution.

Let 2x = u

Differentiation both sides we get:

2 dx = du

or, dx = 1/2 du

Hence we will use this value:

∫cos2x

= ∫cos u · 1/2du

= 1/2 ∫ cos u du

=1/2 sin u + C , where C is a constant.

Again we will do the second part of the integral:

∫sec²x

= tan x + C

Hence the required integral will be:

1/2 sin2x + tan x + C .

Now we will use differentiation to check the integral

d/dx (1/2 sin2x + tan x + C )

= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)

= cos 2x + sec² x

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Answer:

D. $7.00

Step-by-step explanation:

I just did it.

In a connected weighted graph, the maximum weight edge is never in the minimum spanning tree, is a subset of A weighted undirected graph that connects all vertices together does so without cycles and with the lowest possible total edge weight.

Minimum Spanning Tree:

Given a weighted graph, we want to find the spanning tree of the graphs with the smallest total weight.

The total weight of a spanning tree is the sum of its edge weights. If T' is another spanning tree in the graph, we want to find a spanning tree T whose sum of T's weights is less than of T''s weights.

Connected Weighted Graph:

A weighted graph is a graph in which each branch is given a numerical weight. A weighted chart is therefore a special type of labeled chart in which the labels are numeric (usually considered positive).

A directed graph is a set of vertices (nodes) connected by edges, and each node has an associated direction.

Edges are usually represented by arrows pointing in the directions in which the graph can be traversed.

In the example on the right, the graph can be traversed from node A to B, but not from node B to A.

An Undirected Graph:

An undirected graph is a graph, that is, a set of interconnected objects (called vertices or nodes) in which all edges are bidirectional. Undirected graphs are sometimes called undirected networks. In contrast, a graph whose edges point in one direction is called a directed graph.

In an undirected graph, edges are bidirectional and have no associated direction. Therefore the graph can be traversed in both directions. The lack of arrows indicates that the graph is undirected.

In the left example, the graph can be traversed both from node A to B and from node B to A.

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