barnie tosses 2 fair dice. let e be the event that the sum of the two dice is 6. let f be the event that the first die shows 4. are events e and f independent?

The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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Answer:

30 people ordered apple pie

Step-by-step explanation:

one third of the total people:

180/3 = 60

subtract the people who ordered ice cream, so that we have the total people who ordered pie:

180-60= 120

divide the total people by 4 to find the people who ordered apple pie

120/4 = 30

30 people ordered apple pie

Answer:

82.97cm^2

Step-by-step explanation:

Given data

Circumference=  131.88 centimeters

We want to find the area of 6/10 part of a circle

Firstly, let us find the area of the circle

We need to get the radius

C= 2πr

131.88= 2*3.142*r

131.88=6.284r

r=  131.88/6.284

r=20.98 cm

Area= πr^2

Area= 3.142*20.98^2

Area= 3.142*440.16

Area= 1382.98cm^2

Hence 6/10 of a 1382.98

=0.06*1382.98

=82.97cm^2

As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19

The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x =  infinity, as shown in the graph.

Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .

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Answer:

Step-by-step explanation:

If XY bisects DF at point E, then DE = EF.

Given DE = 2y and EF = 8y-3

2y = 8y-3

subtract 8y from both sides

2y-8y = 8y-8y-3

-6y = -3

y = 3/6

y = 1/2

y = 0.5

DF = DE+EF

DF= 2y+8y-3

DF = 10y - 3

DF = 10(0.5)-3

DF = 5-3

DF = 2

Answer:

Geometric Sequence

Step-by-step explanation:

As you can see, the terms are of consecutive sequences.

The 3rd term ÷ The 2nd term = 3

The 4th term ÷ The 3rd term = 3

The ratio between the consecutive terms is the same. Therefore, it's a geometric sequence.

Answer:

243

Step-by-step explanation:

3^5  in standard form

3*3*3*3*3

243

The equation of the plane that contains the two lines is:3x + 9y − 12z + 6 = 0.

Given two lines r1 and r2 such that,  r1 = [x,y,z] = [1+3t,-3t,2+t] r2 = [x,y,z] = [4,s,-3s+2]The point of intersection of these two lines is (x, y, z) which is common to both lines. We can use the equation of two lines to find the values of t and s, and then the point of intersection. As given, the equation of the line r1 is: r1 = 1, 3, 0 + t 3, −3, 2 And the equation of line r2 is: r2 = 4, 0, 2 + s −3, 3, 0 To find the point of intersection, we set the x, y, and z components of the two lines equal to each other and solve for t and s. Then we substitute the values of t and s back into either equation to get the point of intersection, (x, y, z). Equating the x coordinates, we get:1 + 3t = 4 + s Equating the y coordinates, we get:−3t = 3 Solving for t, we get: t = −1 Substituting this value of t into either equation of the lines, we get: r1 = 1, 0, 1 r2 = 4, −1, 5 Therefore, the point of intersection is (1, 0, 1).

Given two lines r1 and r2 such that,  r1 = [x,y,z] = [1+3t,-3t,2+t] r2 = [x,y,z] = [4,s,-3s+2]Let's find the equation of the plane that contains these two lines. The normal vector of the plane is perpendicular to both of the lines and can be found using the cross product of the direction vectors of the two lines: n = r1 × r2= [3,9,-12]Therefore, the equation of the plane is:3(x−1) + 9(y−0) − 12(z−1) = 0Simplifying this expression, we get:3x + 9y − 12z = −6Therefore, the equation of the plane that contains the two lines is:3x + 9y − 12z + 6 = 0.

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The mean and standard deviation of the population is 19.8 and 0.004 respectively.

Mean:

The mean is the simple mathematical average of a set of two or more numbers. The mean of a given set of numbers can be calculated in several ways, including the arithmetic mean, which uses the sum of the numbers in the range, and the geometric mean, which takes the mean product of a set. However, all major methods of calculating simple averages produce the same approximate result most of the time.

Standard Deviation:

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values.  A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

Given that:

E(x) = μ = 19.8

var(x) = σ²/n = 0.2/50 = 0.004

from here can say that mean = 19.8 and

standard Deviation is 0.004.

Now,

295 -298 P(Bottle x < 295) =P(Z< ) =-1.00 =.15873

Thus, there is nearly a 16% probability that just 1 randomly selected

bottle contains < 295 ml.

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Answer:

$2,150

Step-by-step explanation:

We are given that Kesha is an hourly worker, is paid bi-weekly, and her wage is $25.

We are also told that she works 40 hours a week (derived from 8 hours a day for 5 days a week) and that she works 4 hours every other Saturday at time-and-a-half pay.

We are asked to find Kesha's gross income on her pay stub.

First, determine her weekly wage by multiplying her hourly wage by the number of hours she works each week:

\(\$25 \times 40 = \$1,000\)

Then, multiply this value by 2 since Kesha is paid bi-weekly (twice a month):

\(\$1,000 \times 2 = \$2,000\)

Then, determine her time-and-a-half pay by first multiplying her hourly wage by 1.5:

\(\$25 \times 1.5 =\$37.50\)

Then, multiply this value by 4 to represent the hours she works every other Saturday:

\(\$37.50 \times 4 = \$150\)

NOTE: Since "every other Saturday" means twice a month, this is the same definition as bi-weekly. Therefore, no adjustments need to be made to this value.

Finally, add her time-and-a-half pay to her bi-weekly pay:

\(\$2,000 + \$150 = \$2,150\)

Therefore, Kesha's gross income on her pay stub is $2,150.

Answer:

24=1,2,3,4,6,8,12,24

18=1,2,3,6,9,18

I hope this helps!

Please mark brainliest!

Answers:

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

Explanation:

A function has any given input lead to exactly one output.

Relation 1 has the input "paper" lead to more than one output, which are the values 9 and -3. Therefore, relation 1 is not a function.

Relations 2 and 4 are similar stories.

---------

In contrast, relation 3 has each input lead to exactly one output, which is why we have a function here.

Put another way: a function cannot have the x coordinates repeat, but the y coordinates can repeat.

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

we can simplify to get the answer, like this:

Therefore, the correct answer is B.

Answer:

this is just a hint

Step-by-step explanation:

the question measures 6.EE.7 because it asks the student to solve a real-world problem by writing an equation of the form px=qpx=qpx=q for a case in which p,qp,qp,q and x are all non-negative rational numbers. In this case the equation includes a division expression and shows the total cost of $13.50\$ 13.50$13.50 divided by 666, the number of spiral notebooks.

Answer:

4/5 is the slope!

(please give me brainiest if it's right!)

Answer:

4/5

Step-by-step explanation:

4/5 give me brainllist pls

the surface area of the regular pyramid is approximately  \(40sqrt(14) + 43.3 mm^2.\)To find the surface area of a regular pyramid, we need to find the area of each triangular face and add them together, then add the area of the base.

Let's start with finding the area of each triangular face. Since the pyramid is regular, all the triangular faces will be congruent, so we just need to find the area of one.

We know that the base of the triangle is 10 mm, and the height of the triangle is half the distance between the apex (the point at the top of the pyramid) and the base. Since the pyramid is regular, the apex is directly above the center of the base.

The height of the pyramid can be found using the Pythagorean theorem, where the height of the pyramid (h) is the hypotenuse of a right triangle with the base (b) and half the slant height (s) as the legs.

\(s^2 = hr^2 - (b/2)^2\)

We know the base is 10 mm and the height of the big triangle is 9 mm, so the half slant height is:

\(s = sqrt(h^2 - (b/2)^2) = sqrt(9^2 - (10/2)^2) = sqrt(81 - 25) = sqrt(56) = 2sqrt(14)\)

Now we can find the area of one triangular face using the formula:

Area = 1/2 x base x height

Area = 1/2 x 10 mm x 2sqrt(14) mm = \(10sqrt(14) mm^2\)

Since there are four triangular faces, the total area of the triangular faces is:

4 x 10sqrt(14) mm{power}2 = \(40sqrt(14) mm^2\)

Finally, we need to add the area of the base, which we know is 43.3 \(mm^2.\)

So the total surface area of the pyramid is:

\(Surface Area = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) + 43.3 mm^2\)

Therefore, the surface area of the regular pyramid is approximately \(40sqrt(14) + 43.3 mm^2.\)

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Edward drives 160.9 kilometres per month

Edward drives 12,000 miles per year

There are 12 months in a year, this means that Edward travels 12,000 miles in 12 month

The number of kilometres travelled per month can be calculated as follows

12,000= 12

x= 1

cross multiply both sides

x= 12,000/12

x= 100

The next step is to convert 100 miles to kilometres

100 × 1.609

= 160.9 kilometres

Hence Edward travelled 160.9 kilometres per month

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To find a math game on coolmath.com or another math game site, you can simply go to the site and browse through the available games. Choose a game that seems interesting to you and fits your skill level. I can recommend a popular math game called "Number Munchers" available on coolmathgames.com.

Number Munchers is an educational game where you navigate a little green character around a grid filled with numbers. Your goal is to eat the correct numbers based on the given criteria, such as multiples of a specific number or prime numbers. The game helps improve math skills while being enjoyable.

The individual experiences with games may vary, as everyone has different preferences and levels of difficulty. I suggest trying it out with a child, family member, or friend and discussing your experiences afterward.

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Yes , the graphing calculator can be used as a scientific calculator.

As given in the question,

Scientific calculator can not be used as a graphing calculator.

But graphing calculator can be used as a scientific calculator.

Therefore, yes the graphing calculator can be used in place of scientific calculator.

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The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The water output rate for the Tran family's sprinkler was 35 L per hour.

The water output rate for the Campbell family's sprinkler was 25 L per hour.

And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.

Now,

Let time in hours for the Tran family's sprinkler = t

And, The time in hours for the Campbell family's sprinkler = 65 - t

So, We can formulate by the given condition,

⇒ 35t + 25 (65 - t) = 1925

Solve for t as;

⇒ 35t + 25 (65 - t) = 1925

⇒ 35t + 1625 - 25t = 1925

⇒ 10t + 1625 = 1925

⇒ 10t = 1925 - 1625

⇒ 10t = 300

⇒ t = 30

Thus, The time in hours for the Tran family's sprinkler = t

                                                                                   = 30 hours

And, The time in hours for the Campbell family's sprinkler = 65 - t

                                                                                          = 65 - 30

                                                                                          = 35 hours.

Therefore, we get;

The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

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Answer:

x = 0.4

x = 2/ 5

Step-by-step explanation:

Answer:

x=0 or x=-2/5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

5x2+2x=0

Step 2: Factor left side of equation.

x(5x+2)=0

Step 3: Set factors equal to 0.

x=0 or 5x+2=0

Hope it helps ;)

Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

Answer:

Volume of a sphere can be calculated by this equation

\(v=\frac{4}{3} \pi r^3\)

=> radius is diameter divide by 2

\(v=\frac{4}{3}\:\pi \:\left(\frac{15}{2}\right)^3\)

\(v=\frac{5^3\cdot \:3^2\pi }{2}\)

\(v=\frac{1125\pi }{2}\)

or 1767.14 cm cube

The answer is C

The straw can hold 1200π cubic millimeters.

The  length of the soda straw is 30 centimetres. This can be conerted into millimeters as,

1 centimeters = 10 millimetres

⇒ 30 centimeters = 10* 30 millimeters

⇒ 30 centimeters = 300 millimeters

Thus the height of the straw is h= 300 millimeters.

The diameter of the soda straw s given as 4 milli meters.

We know,

Diameter = 2* Radius

⇒ 4 millimeters = 2* Radius

⇒ Radius = 4/2 millimeters

⇒ Radius = 2 millimeters

Thus the radius of the soda straw is r= 2 millimeters.

The amount of soda the straw can hold is equivalent to the volume of the straw.

Volume of the straw = π r² h cubic unit

=π (2)² (300) cubic millimeters

= 1200π cubic millimeters

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A rotation of 90° counter-clockwise about the origin, would map △ ABC onto △ DEC, in the given transformation.

A transformation in mathematics is a function f, typically with some geometrical foundation, that maps a set X to itself, i.e. f: X X. Examples include geometric transformations, such as projective transformations, affine transformations, and specific affine transformations like rotations, reflections, and translations, as well as linear transformations of vector spaces.

Any bijection of a set to itself (or to another set of the same kind) that has a clear geometrical foundation is known as a geometric transformation in mathematics. More specifically, it is a function that is bijective, meaning that its inverse exists, and whose domain and range are sets of points, most frequently both R2 and R3. The research of these transformations can be used to approach the study of geometry.

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Assuming you want to divide 4x^3 + 0x^2 - 3x + 4 by 2x - 5 using polynomial long division:

        2x^2 + 4x + 7

  ---------------------

2x - 5 | 4x^3 + 0x^2 - 3x + 4

       - (4x^3 - 10x^2)

       ---------------

                10x^2 - 3x

               - (10x^2 - 25x)

               ---------------

                       22x + 4

Therefore, the quotient is 2x^2 + 4x + 7 and the remainder is 22x + 4.

Thus, we can write:

4x^3 + 0x^2 - 3x + 4 = (2x - 5)(2x^2 + 4x + 7) + (22x + 4)

So the division of the polynomial 4x^3 + 0x^2 - 3x + 4 by 2x - 5 results in the quotient 2x^2 + 4x + 7 and the remainder 22x + 4.

An equation is formed of two equal expressions. The solution of the equation (5x+2)² + 15x + 6=0 is -0.4 and -1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution to the equation,

(5x+2)² + 15x + 6=0

25x² + 4 + 20x + 15x + 6 = 0

25x² + 35x + 10 = 0

Plotting the equation on the graph, the value of x is,

x = -0.4, -1

Hence, the solution of the equation (5x+2)² + 15x + 6=0 is -0.4 and -1.

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Answer:

1

Step-by-step explanation:

Answer:x+19=(6)+19=25

Step-by-step explanation: