Find two consecutive numbers if the square root of the smaller number is 3 less than the bigger number.

Answer:

a. P

b. C

c. C

d. C

e. P

Step-by-step explanation:

When order matters, the count is of permutations. When order doesn't matter, then you count combinations.

_____

a. Order matters: It makes a difference to the three people chosen which one gets what color ribbon. (permutations)

__

b. Order doesn't matter. Bob and Charlie and Alice are effectively the same as Alice and Bob and Charlie. (combinations)

__

c. Order doesn't matter. (combinations)

__

d. Assuming the representative positions all have the same duties, order doesn't matter. (combinations)

__

e. The order of sprinters on a relay team matters. (permutations)

Try suggested solution, note, the answers are marked with green colour.

The probability for drawing marbles without replacement varies with each draw as both the available and desired outcomes decrease. By applying this rule, the probabilities can be calculated for drawing 5 marbles with all, exactly two, or none being red.

To answer these questions, we first need to know the total number of marbles in the bag. The bag contains 5 red, 8 white, and 10 blue marbles, yielding a total of 23 marbles. When answering probability questions when drawing without replacement, the denominator (total possible outcomes) decreases with each draw, while the numerator (desired outcomes) remains constant if the kind of object drawn remains the same and decreases otherwise.

For the first question, we're drawing 5 marbles all of which are red. The probability is calculated as follows: (5/23) * (4/22) * (3/21) * (2/20) * (1/19). This is because with each draw, both the total number of marbles and the number of red marbles decrease by 1.

For the second question, we're drawing 5 marbles, 2 of which are red. This can happen in various ways (e.g., red, red, not red, not red, not red, etc.). Each of these sequences has a probability and we sum these probabilities. Assuming we draw 2 red then 3 not red, the probability is: (5/23) * (4/22) * (18/21) * (17/20) * (16/19). The 18 in the third fraction is derived from the total number of non-red marbles (8 white + 10 blue).

For the last question, we're drawing 5 marbles, none of which are red. The probability is: (18/23) * (17/22) * (16/21) * (15/20) * (14/19), similar to the previous example, we only consider non-red marbles.

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The probable question may be:

A bag contains 5 red marbles, 8 white marbles, and 10 blue marbles. You draw 5 marbles out at random, without

replacement. What is the probability that all the marbles are red?

The probability that all the marbles are red is _____

What is the probability that exactly two of the marbles are red?

The probability that exactly two of the marbles are red is _______

What is the probability that none of the marbles are red?

The probability of picking no red marbles is __________

Answer:

see attachment for answers and correction

Step-by-step explanation:

Your answer is correct for Wyatt.

The missing blanks for Abigail are filled with the integer part and the fractional part of the mixed number Abigail started with.

___

Beware signs. In this problem -6 + 1/4 is not the same as -6 1/4.

Answer:

A) The y-coordinates have the same value.

Step-by-step explanation:

Answer:

D) Both points are 4 units above the y-axis.

Step-by-step explanation:

Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE?

A) The y-coordinates have the same value. TRUE. The y-coordinates have the value 4.

B) The x-coordinates have the same absolute value. TRUE. 3 and -3 have the same absolute value, |-3| = |3| = 3.

C) The x-coordinates are opposite numbers. TRUE. 3 and -3 are opposite numbers.

D) Both points are 4 units above the y-axis. NOT TRUE. Both points are 4 units above the x-axis.

Answer:

f(x) = 3(x -4)^2 +1

Step-by-step explanation:

Usually you start by factoring the leading coefficient from the first two terms:

f(x) = 3(x^2 -8x) +49

Now, you add the square of half the x-coefficient inside parentheses, and subtract the same quantity outside.

f(x) = 3(x^2 -8x +(-4)^2) -3(-4)^2 +49

= 3(x -4)^2 -48 +49

f(x) = 3(x -4)^2 +1 . . . . . . . . the vertex form you desire

Answer:

  465.988 mph

Step-by-step explanation:

The two speed vectors form two sides of a triangle. Their included angle is 45°, so the law of cosines can be used to find the resultant magnitude x.

  x^2 = 500^2 +50^2 -2·500·50·cos(45°) ≈ 217,144.66

  x ≈ √217,144.66 ≈ 465.988 . . . . miles per hour

_____

You may find you need to round the answer to the nearest whole number.

Answer:  [tex]\bold{x=\dfrac{1\pm \sqrt5}{2}}[/tex]

                both zeros are irrational numbers

Step-by-step explanation:

Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.

[tex]\dfrac{1}{x}=x-1\qquad \text{Restriction: }x\neq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=\dfrac{-(-1)\pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}\\\\\\x=\dfrac{1\pm \sqrt5}{2}[/tex]

Answer:  The side length of the inner square is 17.3 ft.

Step-by-step explanation:  Given that a community is building a square garden with a walkway around the perimeter with the design shown at the right.

We are to find the area of the inner square equal to 75% of the total area of the garden.

The step-wise solutions area s follows:

(1) From the figure, we note that

The side length of the inner square is x ft.

We know that the area of a square is equal to (side)².

So, the area of the inner square will be

[tex]A_i=x\times x\\\\\Rightarrow A_i=x^2~\textup{sq. ft}.[/tex]

(2) The whole garden is in the form of a square with side length 20 ft.

Therefore, the area of the entire garden is given by

[tex]A_g=20\times 320\\\\\Rightarrow A_g=400~\textup{sq. ft}.[/tex]

(3) The area of the entire garden is 400 sq. ft.

So, 75% of the area of the entire garden will be

[tex]75\%\times 400\\\\=\dfrac{75}{100}\times 400\\\\=\dfrac{3}{4}\times 400\\\\=3\times 100\\\\=300~\textup{sq. ft}.[/tex]

(4) Since the area of the inner square is equal to 75% of the area of the entire garden, so we must have

[tex]x^2=300.[/tex]

(5) The solution of the quadratic equation is as follows:

[tex]x^2=300\\\\\Rightarrow x=\pm\sqrt{300}\\\\\Rightarrow x=\pm10\sqrt{3}.\\\\\Rightarrow x=\pm10\times 1.732\\\\\Rightarrow x=\pm17.32\\\\\Rightarrow x=17.32,~-17.32.[/tex]

So, the required solution is x = 17.32, - 17.32.

Rounding to nearest tenth, we get

x=17.3, - 17.3.

(6) Since the length of the side of a square cannot be negative, so the solution that best describes the side length of the inner square will be

x = 17.3.

Thus, all the questions are answered.

And, the side length of the inner square is 17.3 ft.

Answer: Y=-13/4 + 4

Hope this helps! :)

Answer:

252 square inches

Step-by-step explanation:

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches. The area of a triangle is ...

A = (1/2)bh

so one face of Georgia's pyramid will have an area of ...

A = (1/2)(9 in)(14 in) = 63 in^2

Then all four faces will have a total area of ...

(63 in^2) · 4 = 252 in^2

_____

Comment on the pattern

The pattern shown includes the base of the pyramid. The problem text says the base is not included. We have assumed that the base is not included. (For Georgia's pyramid, a different pattern would be more to the point: see attachment.)

252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The square pyramid will not have a bottom.

We have to find the lateral surface area as the base area is not included.

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches.

The area of lateral face is A = (1/2)bh

A = (1/2)(9 in)(14 in)

= 63 square inches

There are four faces so, 4×63 = 252 square inches

Lateral surface area is  252 square inches

Hence, 252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

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In analyzing the data set and the corresponding box plot, we can determine the accuracy of several statements. It is true that 25 percent of the data are at most five. However, it is false to say that there is the same amount of data from 4-5 as there is from 5-7. Additionally, there are data values of three, but it is false to say that 50 percent of the data are four.

A. True – the first quartile (Q1) is equal to the 25th percentile, which means that 25 percent of the data fall at or below Q1. If Q1 is at most five, then at least 25 percent of the data is at most five.

B. False – the second quartile (Q2) is equal to the median, which separates the data into two halves. If there is the same amount of data from 4-5 as there is from 5-7, then the median would not be in the middle of the data.

C. False – there are data values of three, as shown by the lower whisker in the box plot.

D. False – the second quartile (Q2) is equal to the median, which is the value that separates the data into two halves. If 50 percent of the data are four or less, then the median would be four or less.

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Answer:

  D.  N = w² + 8w + 12

Step-by-step explanation:

The current size is w by w+4, so the area is ...

  A = w(w+4)

When each dimension is increased by 2, the new size is (w+2) by (w+4+2). The latter dimension can be simplified to (w+6). Now, the new area is ...

  N = (w+2)(w+6) = w² +8w +12 . . . . . . . matches choice D

Answer: 132 Square Feet

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

Answer:

  0.01000188

Step-by-step explanation:

The third term is ...

  8C2·x^6·y^2 = 28 x^6 y^2

Putting in the given values for x and y, we get ...

  28·3^6·7^2·10^-8 = 1000188×10^-8 = 0.01000188

_____

8C2 = 8!/(2!·(8-2)!) = 8·7/(2·1) = 28

➷ The rule is:

The inscribed angle would be half the measure of the intercepted arc

If the arc was 48, the inscribed angle = 48/2 = 24 degrees

If the arc was 57, the inscribed angle = 57/2 = 28.5 degrees

If the arc was 90, the inscribed angle = 90/2 = 45 degrees

If the arc was 124, the inscribed angle = 124/2 = 62 degrees

If the arc was 180, the inscribed angle = 180/2 = 90 degrees

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

I hope you understand it well :)

The measure of an inscribed angle is half the measure intercepted arc.

With that rule

Hope this helps :)

If you have a doubt just reply over here, I would be happy to help you further :)

Answer:

30°

Step-by-step explanation:

If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.

If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.

Thus, the measure of the angle ELM is 180°-42.5°=137.5°.

Consider triangle EML. In this triangle,

m∠MEL=180°-137.5°-12.5°=30°.

Thus, m∠MEJ=30°.

Answer:

30°

Step-by-step explanation:

x=(a-b)/2 because of secants exterior angles

x=(85-25)/2 Substitution

x=60/2 Algebra

x=30° Answer

Answer:

Step-by-step explanation:

Exponential decay describes a situation in which the dependent variable is reduced by the same factor when the independent variable is increased by the same amount.

A — the population is increasing, not being reduced

B — the amount is cut in half when time increases by 15 years (exp. decay)

C — the number of teams is cut in half when the number of rounds increases by 1 (exp. decay)

D — the amount is cut in half when time increases by 3 hours (exp. decay)

E — the population is increasing, not being reduced

Answer:

  (a) reduction

  (b) 1/2

Step-by-step explanation:

The image figure A'B'C'D' is smaller than the original figure ABCD, so the dilation is a reduction.

Each of the points A'B'C'D' is half as far from the origin as the original points ABCD, so the scale factor is 1/2.

_____

Draw lines C'C and D'D. You will see they meet at the origin, which is the center of dilation. Then look at how far the points are along those lines. C' is one grid square diagonal along the line; C is 2 grid square diagonals along that line, so is twice as far from the origin. That is, C' is 1/2 the distance of C, so represents a reduction by a scale factor of 1/2.

The same distance considerations are observed along the line D'D. The point D' is the diagonal of a 2x1 rectangle from the origin (A distance of √5.) The point D is the diagonal of a 4x2 rectangle from the origin, so is twice as far. Once again D' is 1/2 the distance of D, so represents a reduction by a factor of 1/2.

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The lateral area of a cone is equal to

[tex]LA=\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=5\ cm[/tex]

[tex]l=6\ cm[/tex]

assume [tex]\pi =3.14[/tex]

substitute the values

[tex]LA=(3.14)(5)(6)=94.2\ cm^{2}[/tex]

This value is an underestimate, because the assumed pi value is less than the real value

assumed value [tex]\pi =3.14[/tex]

real value [tex]\pi =3.1415926536...[/tex]

Answer:

  A.  The dilated line lies on the original line.

Step-by-step explanation:

Dilation changes sizes, but not slopes or angles. The dilated line is guaranteed to have the same slope as the original.

The center of dilation is "invariant" (doesn't move) as a result of the dilation. Here, the point (3, 0) is the center of dilation. It is the x-intercept of the original line, so will also be on the dilated line.

The dilated line has the same slope as the original and goes through a point that the original line goes through. Hence it lies on the original line.

_____

How do you do this question?

1. make use of the properties of dilation, as we have done above.

2. plot some points on the original line—(0, 3) and (3, 0) are the intercepts—apply the dilation, and see where the line goes. (You will find (0, 3) ⇒ (-6, 9), and (3, 0) ⇒ (3, 0). Both are on the original line.)

Answer:

Step-by-step explanation:

The function to be analyzed is:

[tex]y = \frac{4}{x-1}+5[/tex]

This function has a vertical and a horizontal asymptote. The vertical asymptote is located where discontinuity exist. That is:

[tex]x = 1[/tex]

Besides, the horizontal asymptote coincides with the limit of function, which is:

[tex]\lim_{x \to \pm \infty} \left(\frac{4}{x-1} + 5\right)[/tex]

[tex]\lim_{x \to \infty} \frac{4}{x-1} + \lim_{x \to \infty} 5[/tex]

[tex]L = 0 + 5[/tex]

[tex]L = 5[/tex]

The horizontal asymptote is:

[tex]y = 5[/tex]

The function and the asymptotes are presented in the image attached below.

Answer:

4.25 Liters

Step-by-step explanation:

Edge of Cubical tank

= 20 cm

= 20 (0.01 m)……………..1 meter = 100 cm

= 0.2 m

Volume of Tank

= ( Edge ) ^ 3

= ( 0.2 m ) ^3

= 0.008 m^3

= 8 liters…………….. 1 m^3 = 1000 Liters

Volume required to fill the tank

= 8 - 3.75

= 4.25 Liters

Answer:

65

Step-by-step explanation:

Let "a" represent the number of adult tickets sold. Then the number of child tickets sold is 151-a and the total revenue for the day is ...

9.10·a + 5.10·(151-a) = 1030.10

4a = 260 . . . . . . subtract 770.10

a = 65 . . . . . . . . . divide by 4

The number of adult tickets sold on Monday was 65.

_____

Check

65 adult tickets and 86 child tickets will produce a revenue of ...

65·9.10 + 86·5.10 = 591.50 + 438.60 = 1030.10 . . . . answer checks OK

Answer: 65 adult tickets were sold that day

Step-by-step explanation:

Let's call:

c: number of child tickets sold on Monday.

a: number of adult tickets sold on Monday.

Set up the following system of equations:

[tex]\left \{ {{c+a=151} \atop {5.10c+9.10a=1030.10}} \right.[/tex]

You can solve it by Substitution method, as following:

- Multiply the first equation by -5.10

- Add both equations.

- Solve for a.

Then:

[tex]\left \{ {{-5.10c-5.10a=-770.1} \atop {5.10c+9.10a=1030.10}} \right.\\---------\\4a=260\\a=65[/tex]

To find the initial value of a linear function from its graph, examine the y-intercept where x=0, and use the slope to verify the linearity. The initial value is the y value at x=0.

Identifying the initial value of a linear function from its graph involves examining the y-intercept, where x=0. The steps to find it include:

The notion that the initial value corresponds to the y value when x = 1 is incorrect for linear functions. The initial value or y-intercept is always found where x = 0. Adjustments or predictions for other values of x, such as x = 1, 2, 6, 7, or 8, involve using the line's slope or rate of change but do not directly determine the initial value.

Answer:

its a, c, e

hope this helps!!

Answer:

Equation for the perimeter of prism's square face: 16x + 12

Step-by-step explanation:

Volume of Square prism = Length * Width * Height

                                         = 144 x^3 + 216 x^2 +81 x

taking 9x common = 9x( 16 x^2 + 24 x + 9)

                               = 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )

                                = 9x ( 4x+3)^2

so the length is 9x, width is 4x+3 and height is 4x+3

Now, Perimeter of prism's square face = 2* Width + 2 * Height

                                                                = 2* (4x+3) + 2* (4x+3)

                                                                = 8x +6 + 8x + 6

                                                                = 16x +12

Final answer:

Factoring the volume expression of the square prism reveals the square's base area. Once identified, the perimeter can be found by multiplying one side length by four.

Explanation:

The volume V of a square prism can be expressed as the product of the area A of its square base and its height h, so V = A × h. Given the polynomial expression for the volume, we can factor it to find the square base area. The given volume is 144x³ + 216x² + 81x. Factoring out the greatest common factor of 9x, we get 9x(16x² + 24x + 9). Recognizing this as a perfect square trinomial, we can further factor it to 9x(4x + 3)². Therefore, the area A of the base is (4x + 3)². To find the perimeter P of the square base, we take four times one side of the square, which is P = 4(4x + 3). Simplifying, we get P = 16x + 12.

Answer: 37.2 meters

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, to calculate the height of the light pole (x), you can apply the proccedure shown below:

-Apply [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

-Substitute values.

-Solve for the  height of the light pole (x).

Then you obtain the following result:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(60\°)=\frac{x}{43}\\\\x=43*sin(60)\\x=37.2[/tex]

Answer:

37.2 meters

Step-by-step explanation:

Since this is the right triangle, the side that is 43 m is the hypotenuse.

Note: the side opposite of 90 degree angle is hypotenuse.

Also, we want the height of the pole, which is the side that is "opposite" to the angle 60 degree given.

Now, which trigonometric ratio relates "opposite" and "hypotenuse"??

It is SINE. Now we can write and solve (let the height of the pole be h):

[tex]Sin(\theta)=\frac{Opposite}{Hypotenuse}\\Sin(60)=\frac{h}{43}\\h=Sin(60)*43\\h = 37.24[/tex]

The light pole is 37.24 meters tall, to the nearest tenth, it is 37.2 meters

Answer:

Part A) The graph in the attached figure

Part B) [tex]y=2.40x[/tex]

Step-by-step explanation:

Let

y------> the price of gas

x-----> the volume of gas purchase

we know that

The relationship between the cost of gas and the volume purchase represent a direct variation and remember that a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the constant of proportionality k is equal to

[tex]m=k=2.40\frac{\$}{gallon}[/tex]

and the y-intercept b is equal to zero because the line passes through the origin

[tex]b=0[/tex]

therefore

the linear equation is

[tex]y=2.40x+0\\y=2.40x[/tex]

using a graphing tool

see the attached figure

Answer:

A D and E are the answers

Step-by-step explanation:

The general formula is n * CD so all you do is multiply n times the original length.

A is true. 3/2 * 12  = 36/2 = 18 True.

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

B is not true 4*12 = 48 not 3

B would be true if n = 1/4

1/4 * 12 = 3

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

C is not true 8*12 = 96 not 20

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

D is true 2 * 12 = 24

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

E is true 3/4 * 12  = 36/4 = 9

A D and E are the answers

Answer:

1/3.

Step-by-step explanation:

Since there are 12 friends and 4 bread loaves, you would divide 4/12 by 4 which is 1/3.

Answer: [tex]\frac{32}{35}[/tex]

Step-by-step explanation:

We need to convert the mixed numbers into fractions.

The new numerator will be the sum of the numerator of the fractional part and the product obtained by multiplying the denominator of the fractional part by the whole number part.

The new denominator will the the same denominator of the fractional part.

Then:

[tex]2\ \frac{2}{7}=\frac{2+(2*7)}{7}=\frac{16}{7}[/tex]

[tex]2\ \frac{1}{2}=\frac{1+(2*2)}{2}=\frac{5}{2}[/tex]

Dividing the fractions, we get:

[tex]\frac{\frac{16}{7}}{\frac{5}{2}}=\frac{16*2}{7*5}=\frac{32}{35}[/tex]