Answer:
1/3Step-by-step explanation:
Total marbles:
5 + 10 = 15Green marbles made of glass:
10/2 = 5Required probability:
P(green glass) = 5/15 = 1/3please help. what are the x and y values here
Answer:
(6,0)
(-2,0)
2,-3
-3,-2
7,7
Step-by-step explanation:
The city is issuing bonds to raise money for a building project. You obtain a $6700 bond that pays 6% interest annually that matures in 8 years. How much interest will you earn?
The interest will earn is 3216
Interest Earned = Amount * Rate of Interest * Time
Interest Earned = 6700*6%*8 = [tex]6700*\frac{6}{100}*8[/tex]
Interest Earned = 3216
Interest Calculator
The term "interest" refers to the additional revenue received by the investor over and above the investment or the additional debt owed by the borrower over and above the amount borrowed. Simple interest and compound interest are the two different kinds of interest. The sorts of interests are covered in further detail in the interest formula. Let's explore the interest formula in further detail and go through several cases.
Interest Formula: What is it?
Simple interest and compound interest are both included in the interest formula. Interest is the cost a borrower pays a lender for a loan. This additional sum, or the interest, must be paid in addition to the loan itself. The Simple Interest Formula and the Compound Interest Formula are both discussed in the interest formula Compound Interest Formula. The interest formula for both is
Simple Interest = P × R × T
Compound Interest = [tex]P(1 + r/n)^{nt}- P[/tex]
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Two friends are both pregnant, and find out they are each expecting twins!
Let A be the event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B be the event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
A and B are independent events. What is the probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins?
Give your answer as a percent, rounded to four decimal places if necessary.
The probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins is 0.000045.
What is the probability?From the information illustrated,
Let A = event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B = event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
Therefore, the probability will be gotten by using the multiplication for two independent events. This will be:
= P(A) × P(B)
= 0.0045 × 0.01
= 0.000045
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Solve .graph the solution, state the interval notation and state the solution & set. 14x-6]
Starting with the inequality:
[tex]\lvert4x-6\rvert\le4[/tex]We have two cases:
Case 1: 4x-6≥0
Since 4x-6≥0, then |4x-6| = 4x-6. Then:
[tex]\begin{gathered} 4x-6\le4 \\ \Rightarrow4x\le10 \\ \Rightarrow x\le\frac{10}{4} \\ \therefore x\le\frac{5}{2} \end{gathered}[/tex]Case 2: 4x-6<0
Since 4x-6<0, then |4x-6| = -4x+6. Then:
[tex]\begin{gathered} -4x+6\le4 \\ \Rightarrow-4x\le-2 \\ \Rightarrow x\ge\frac{-2}{-4} \\ \Rightarrow x\ge\frac{1}{2} \end{gathered}[/tex]The solution set of the inequality is all the numbers x which are greater or equal to 1/2 AND lower or equal to 5/2:
[tex]\frac{1}{2}\le x\le\frac{5}{2}[/tex]The graph of the solution is a number line from 1/2 to 5/2 including the endpoints:
The interval notation of the solution, is:
[tex]x\in\lbrack\frac{1}{2},\frac{5}{2}\rbrack[/tex]The solution set S is:
[tex]S=\lbrace x\in\R|\frac{1}{2}\le x\le\frac{5}{2}\rbrace[/tex]what is the discriminant of the equation-x^2-9x-9=0
Given data:
The given expression is -x^2-9x-9=0.
The descriminant of the given equation is,
[tex]\begin{gathered} D=(-9)^2-4(-1)(-9) \\ =81-36 \\ =45 \end{gathered}[/tex]Thus, the descriminant of the given equation is 45.
If I am given a line with the points (1,2) and (-1,-1) how would I find out what the slope-intercept form is?
Solution:
The slope-intercept form of a line with slope m and y-intercept b is given by the following formula:
[tex]y\text{ = mx+b}[/tex]On the other hand, the slope m is given by the following equation:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:
(X1,Y1) = (1,2)
(X2,Y2) = (-1,-1)
replacing this data into the slope equation, we get:
[tex]m\text{ = }\frac{-1-2}{-1-1}\text{ = }\frac{-3}{-2}\text{ = }\frac{3}{2}[/tex]thus, the slope of the line would be:
[tex]m\text{ = }\frac{3}{2}[/tex]now, replacing this into the slope-intercept form of the line we get:
EQUATION 1
[tex]y\text{ = }\frac{3}{2}x\text{ + b}[/tex]We only need to find the y-intercept b. For that, take any point on the line, for example (x,y) = (1,2), and replace it into the previous equation:
[tex]2\text{ = }\frac{3}{2}(1)\text{ + b}[/tex]this is equivalent to:
[tex]2\text{ = }\frac{3}{2}+\text{ b}[/tex]solving for b, we get:
[tex]b\text{ = 2- }\frac{3}{2}\text{ = }\frac{1}{2}[/tex]that is:
[tex]b\text{ = }\frac{1}{2}[/tex]finally, replacing this into the EQUATION 1, we get:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]then, the slope-intercept form of a line with the points (1,2) and (-1,-1) would be:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]
some people advise that in every cold weather, you should keep the gas tank in your car more than half full. Lou's car had 5.7 gallons in the 14 gallon tank on the coldest day of the year. Lou filled the tank with gas that cost $3.60 per gallon. How much did Lou spend on gas?
The amount that Lou spent in gas is $20.52.
What is the cost?Lou's car had 5.7 gallons in the 14 gallon tank on the coldest day of the year and he filled the tank with gas that cost $3.60 per gallon.
The cost for the amount spent in gas will be:
= Gallons filled × Cost per gallon
= 5.7 × $3.60
= $20.52
The amount is $20.52.
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What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Musicologists generally define the Classical period of music as ranging from 1730 to 1820. Classical era music followed the late Baroque period of music.
Help pls
A system of equations is shown below.
y=x²-11x - 36
y = - 12x + 36
What is the largest value of y in the solution set of the system?
Utilizing differentiation, the biggest value of y=0 in the system's solution set.
What is differentiation?One of the two fundamental concepts of calculus is differentiation. Differentiation is a method for finding a function's derivative. Differentiation is a mathematical technique used to calculate the instantaneous rate of change of a function based on one of its variables. Velocity, or how quickly a distance varies in respect to time, is the most common example. Differentiation's opposite is finding an antiderivative.
Differentiating the 1st equation, we get
x=5.5
Putting back in the equation.
y = -5.75
and differentiating the 2nd equation, we get
x=3
Putting back in the equation
y= 0
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[tex]f(x)=x^{3}-3x^{2} -4x+12[/tex]
Answer:
the answer is f'(x)=3x^2-6x-4
Step-by-step explanation:
Which equations can be used to find the lengths of thelegs of the triangle? Select three options.0.5(x)(x + 2) = 24x(x + 2) = 24x2 + 2x - 24 = 0x2 + 2x - 48 = 0x2 + (x + 2)2 = 100
Triangle area is equal to
1/2 base x height x 0.5 base = x feet.Height = (x + 2) feet
= 24 square feet
24 = 0.5(x)(x+2) \s0.5(x)(x + 2) = 24
The formulas that can be used to determine the triangle's leg lengths must be equivalent to 0.5(x)(x + 2).
To elaborate on this: 0.5(x)(x + 2) = 24
0.5(x2+2x) = 24 b) x(x + 2) = 24 c) x2 + 2x - 24 = 0 0.5(x2+2x) = 24 x(x + 2) is not equal to 0.5(x2+2x)0.5(x)(x + 2) = 24 12(x)(x + 2) = 24 x2 + 2x = 2(24) x2 + 2x - 48 = 0 x2 + (x + 2) is not comparable to x2+2x- 24 = 0 or x2+2x- 48 = 0.² = 100 \sx² + x² + 4x + 4 = 1002x² + 4x = 962(x2 + 2x + 48)= 0 is equivalent to 0.5(x2 + 2x) = 24.
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Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3,0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1.
The zeros and their multiplicities are:
-2 with multiplicity 3
0 with multiplicity 1
2 with multiplicity 1
The polynomial function is therefore given as:
[tex]\begin{gathered} f(x)=(x+2)^3(x-0)^1(x-2)^1 \\ f(x)=x(x-2)(x+2)^3 \\ f(x)=(x^2-2x)(x^3+6x^2+12x+8) \\ f(x)=x^5+6x^4+12x^3+8x^2-2x^4-12x^3-24x^2-16x \\ f(x)=x^5+4x^4-16x^2-16x \end{gathered}[/tex]Therefore, the polynomial function of degree 5 is:
[tex]f(x)=x^5+4x^4-16x^2-16x[/tex]ANSWERS ASAP PLEASEEE
Graph the linear equation
y=4x-1
A line is uniquely defined by two points. So, we only need to find two points that lie on the line.
[tex]x=1 \implies y=4(1)-1=3\\\\x=2 \implies y=4(2)-1=7[/tex]
So, you can draw the line through (1, 3) and (2, 7).
Find an anti derivative for each function when C = 0
Given:
[tex]\frac{9}{8}\sqrt[8]{x}[/tex]You can find the antiderivative by integrating it:
1. Set up:
[tex]\int\frac{9}{8}\sqrt[8]{x}\text{ }dx[/tex]2. You can rewrite it in this form:
[tex]=\frac{9}{8}\int x^{\frac{1}{8}}dx[/tex]3. Apply this Integration Rule:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]Then, you get:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{x^{\frac{9}{8}}}{\frac{9}{8}})+C[/tex]4. Simplify:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{8\sqrt[8]{x^9}}{9})+C[/tex][tex]=\sqrt[8]{x^9}+C[/tex]Remember this Property for Radicals:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]You can rewrite the expression in this form:
[tex]=\sqrt[8]{x\cdot x^8}+C[/tex]Applying this Property for Radicals:
[tex]\sqrt[n]{b^n}=b[/tex]You get:
[tex]=x\sqrt[8]{x}+C[/tex]5. Knowing that:
[tex]C=0[/tex]You obtain:
[tex]=x\sqrt[8]{x}[/tex]Hence, the answer is:
[tex]=x\sqrt[8]{x}[/tex]the table below shows the rebeltonshir betweenth number of miles travledet, and the number of salle
The question is really asking for the unit rate but on a supposedly linear graph that is not to scale, so it is difficult to evaluate real rates.
HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 90 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
From the given image, we have that:
1. The distance from A to B is of 6 units.
2. The lengths are given as follows:
Vertical semgents: AB = 6, CD = 3.Horizontal segment: BC = 4.3. The length of segment AD is of 5 units.
What are the side lengths?When two points have one equal coordinate, as is the case in this problem for AB, CD and BC, the distance is given by the subtraction of the different coordinate.
Hence, considering the coordinates of the vertices on the given image, the distances are given as follows:
AB = 2 - (-4) = 2 + 4 = 6 (vertical segment as the y-coordinate is different).CD = 2 - (-1) = 2 + 1 = 3 (vertical segment as the y-coordinate is different).BC = 3 - (-1) = 3 + 1 = 4 (horizontal segment as the x-coordinate is different).The perimeter of a polygon is the sum of the lengths of all the outer sides of the polygon, hence:
P = AB + CD + BC + AD.
The perimeter in this problem is of 18 units, hence the length of AD is given as follows:
18 = 6 + 3 + 4 + AB
13 + AB = 18
AB = 5 units.
What is the missing information?The figure is missing and is given by the image at the end of the answer.
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The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.03 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 .
b. Explain the meaning of the answer to part a.
The fixed $30 unlimited calls charge for Plan 1 and the initial charge as well as a charge per call of $0.03 calls in Plan 2 gives;
a. The inequality that indicates the number of calls for which Plan 1 is more economical than Plan 2 is presented as follows;
30 > 15 + 0.03•x
Which gives;
x > 500
b. The meaning of the inequality, in part a. is that Plan 1 is more economical than Plan 2 when more than 500 calls are made
What is an inequality?An inequality makes a comparison between two values that are not equal.
The given parameters are;
The billing plan for Plan 1 is presented as follows;
Charges, C = $30
The charges of the billing plan for Plan 2 is presented as follows;
C = $15 + $0.03×xWhere;
x = The number of calls made per month
a. The inequality that can be used to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is found as follows;
At the start of registration for each plan, we have;
Cost of Plan 1 = $30
Cost of Plan 2 = $15 + $0.03 × 0 = $15
Therefore, Plan 2 is initially more economical than Plan 1
At the point (or number of calls) at which the expenses for both plans are the same, we have;
30 = 15 + 0.03 × x
Which gives;
x = (30 - 15)/0.03 = 500From the above equation, we have that after 500 calls, the expenses of both plans will be the same
The inequality that gives the number of calls for which Plan 1 is more economical than Plan 2 is therefore;
30 > 15 + 0.03•x
Which gives;
x > 500b. The meaning of the inequality, x > 500 is that Plan 1 is becomes more economical than Plan 2 when a person makes more than 500 calls in a month
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In a box there a total of four prizes: Two of them are worth $3, a single prize worth $23, and a single prize worth $190. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
Answer:
The fair price of the game is $54.75
The player is expected to win $54.75
Explanation:
Here, we want to get the fair prize of the game
From the question, there are 4 prizes
When reaching into the box, we can only pick 1
Assuming that each of the prizes have the same probability oof being picked, the probability of picking any of the prize is 1/4
Now, to get the fair price of the game (it is obviously positive as we do not know if the player has anything to lose)
We have to multiply the probability by each of the price tag, then sum
Mathematically,we have this as:
[tex]\begin{gathered} (2\times\frac{1}{4}\times\text{ \$3) + (}\frac{1}{4}\times\text{ \$23) + (}\frac{1}{4}\times\text{ \$190)} \\ \\ =\text{ \$1.5 + \$5.75 + \$47. 5 = \$54.75} \end{gathered}[/tex]What is 3/8 of 4/5??
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3}{8}\ of\ \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{3}{8}\times \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{3\times4}{8\times5}}[/tex]
[tex]\mathsf{= \dfrac{12}{40}}[/tex]
[tex]\mathsf{= \dfrac{12\div4}{40\div4}}[/tex]
[tex]\mathsf{= \dfrac{3}{10}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{3}{10}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Let y² = x² + sin(xy). Find using implicit differentiation.
By using implicit differentiation, we get dy/dx=(2x+cos(xy)y)/(-xcos(xy)+2y)
What is implicit differentiation?
Implicit differentiation is the process to finding the derivative of the implicit function.
We have given,
y^2=x^2+sin(xy)
Differentiate with respect to x, and using product rule
2y dy/dx=d/dx(x^2+sin(xy))
2y dy/dx=(dx^2)/dx+(dsin(xy))/dx
2y dy/dx=2x+cos(xy)(d(xy))/dx
2y dy/dx=2x+cos(xy)[y+x dy/dx]
2y dy/dx=2x+ycos(xy)+xcos(xy)dy/dx
2y dy/dx-xcos(xy) dy/dx=2x+ycos(xy)
On simplification, we get
dy/dx=(2x+xcos(xy))/(-xcos(xy)+2y)
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11. In how many different ways can the letters of the word MATH be rearranged to form a four-letter code word (i.e. it doesn't have to be a word in English)?
The number of letters in the word MATH IS
[tex]=4[/tex]To rearrange a letter with n letters to form a four-letter code will be
[tex]\begin{gathered} n! \\ \text{Where n=4} \end{gathered}[/tex]Hence,
The number of ways of rearranging the words will be
[tex]\begin{gathered} =4! \\ =4\times3\times2\times1 \\ =24\text{ ways} \end{gathered}[/tex]This problem is a bit different. Instead of choosing one item from each of several different
categories, we are repeatedly choosing items from the same category (the category is: the
letters of the word MATH) and each time we choose an item we do not replace it, so there is
one fewer choice at the next stage: we have 4 choices for the first letter (say we choose A),
then 3 choices for the second (M, T, and H; say we choose H), then 2 choices for the next
letter (M and T; say we choose M) and only one choice at the last stage (T). Thus, there are
4 · 3 · 2 · 1 = 24 ways to spell a code word with the letters MATH.
Hence,
The final answer = 24 ways
cual es mayor, -4 o -3
Answer:
-3
Step-by-step explanation:
question is asking, which is larger. -3 is larger than -4
Please help very confused
The correct explanations are;
2. Given
3. By definition of complementary angles.
5. ∠1 + ∠3 = 90°
6. By definition of complementary angles.
What are complementary angles?
Sum of two or more are angles are 90 degree then, angles are called Complementary angles.
Given that;
∠1 and ∠2 are complementary angles.
And, ∠2 ≅ ∠3
Now,
Statements Reasons
1. ∠1 is a complementary of ∠2. 1. Given
2. ∠2 ≅ ∠3 2. Given
3. m ∠1 + m ∠2 = 90° 3. By definition of
complementary angles.
4. m ∠2 = m ∠3 4. Definition of congruency.
5. m ∠1 + m ∠3 = 90° 5. Substitution property.
6. ∠1 is a complementary of ∠3. 6. By definition of
complementary angles.
Thus, The correct explanations are;
2. Given
3. By definition of complementary angles.
5. ∠1 + ∠3 = 90°
6. By definition of complementary angles.
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2 printing machines of a printing house can complete the printing work of the required number of Excel in Mathematics textbooks in 20 days. After printing the books for 8 days, if 1 more machine was added, in how many days would the remaining work be completed?
The remaining work can be completed in if 2 printing machines of a printing house can complete the printing work in 20 days, After printing the books for 8 days, if 1 more machine was added, is 8 days.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
2 printing machines of a printing house can complete the printing work in 20 days,
After printing the books for 8 days, if 1 more machine was added,
Assume the total work is x,
Calculate the amount of work done in 8 days by both machines as shown below,
The amount of work done in 8 days = x / 20 × 8
The amount of work done in 8 days = 2x / 5
Calculate the remaining work = x - 2x / 5
The remaining work = 3x / 5
Calculate the time taken to complete the remaining work,
Time = (3x / 5) / (3x / 40) = 8 days
Thus, the total time is 16 days.
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State the adjacent side for the angle marked as x in the picture.
Answer:
Explanation:
In
4Use algebra to solve the following equation. Round decimal to two places.400 (1.065)t = 850
We need to solve the equation
[tex]400(1.065)t=850[/tex]In order to do so, we can first divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400}{400}(1.065)t=\frac{850}{400} \\ \\ (1.065)t=2.125 \end{gathered}[/tex]Now, to isolate the variable t on the left side and find its value, we can divide both sides by 1.065:
[tex]\begin{gathered} \frac{\mleft(1.065\mright)}{1.065}t=\frac{2.125}{1.065} \\ \\ t=1.9953\ldots \\ \\ t\cong2.00 \end{gathered}[/tex]Therefore, rounding to two decimal places, the answer is 2.00.
use the graph to determine which the ordered pair is a solution of the equation y equals negative X over 3 - 1
(3, - 2)
1) As the rule of the function has been given to us. Let's find out which point fits in the Solution for:
y=-x/3 -1
As we can see, the y-intercept is b=-1
3) So, (3, - 2) is the solution. Since (3, -2) belongs to the blue line
Checking algebraically
y=-x/3 -1
-2= -3/3 -1
-2 = -2 TRUE!
-
=
help meeeeeeeeeeeeeee
Answer:
Rose.
Step-by-step explanation:
Because the number is positive, it does not symbolize a withdrawal, it shows. deposit.
I hope this helps!
P.S, Brainliest if correct, thanks!
What is the solution to the equation below? Round your answer to two
decimal places.
7x = 77
Answer:
x = 11
Step-by-step explanation:
divide both sides by 7
x = 11