Understanding of Multiplying by a Fraction Name: Draw a number line model to represent each multiplication problem. Then solve the problem.2/3×1/2=how do you do this
Answers
We have following:
1.
[tex]\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}=\frac{1}{3}[/tex]2.
[tex]\frac{5}{6}\cdot\frac{3}{4}=\frac{5\cdot3}{6\cdot4}=\frac{15}{24}=\frac{5}{8}[/tex]
Related Questions
The diagonal of a square measures 12 inches. What is the length of the sides
Answers
It is given that the diagonal of a square is 12 inches.
The square is given by the diagram shown below:
In the triangle ABC by pythagorean theorem it follows:
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ 2AB^2=12^2 \\ AB^2=\frac{144}{2} \\ AB^2=72 \\ AB=\sqrt[]{72}=6\sqrt[]{2} \end{gathered}[/tex]Hence the side is given by:
[tex]s=6\sqrt[]{2}\text{ inches}[/tex]Урна содержит 10 белых и 10 черных шаров. Вынимают 5 раз по два шара (без возврата). С какой вероятностью каждый раз вынимали по 2 шара разного цвета?
An urn contains 10 white and 10 black balls. Two balls are taken out 5 times (without return). What is the probability that 2 balls of different colors were drawn each time?
Answers
Answer:
≈4,365%.
Step-by-step explanation:
1) для нахождения требуемой вероятности необходимо найти вероятность каждого из пяти выниманий, а затем перемножить их;
2) при каждом вынимании вероятности:
[tex]P_1=\frac{C^1_{10}*C^1_{10}}{C^2_{10}}=\frac{10}{19};\\P_2=\frac{C^1_9*C_9^1}{C^2_{18}}=\frac{9}{17};\\P_3=\frac{C^1_8*C_8^1}{C^2_{16}}=\frac{8}{15};\\P_4=\frac{C^1_7*C^1_7}{C^2_{14}}=\frac{7}{13};\\P_5=\frac{C^1_6*C^1_6}{C^2_{12}}=\frac{6}{11};[/tex]
3) требуемая вероятность:
P=P₁*P₂*P₃*P₄*P₅≈0,04365.
Write an algebraic expression for the sum of 3 coins and c coins.
Oc+3
Oc/3
O3c
Oc-3
Answers
Answer:
c+3
Step-by-step explanation:
The word 'sum' means addition, so the equation would be c+3
If answer is decimal should be rounded to hundredths place
Answers
A rectangular prism has a volume that can be obtained using the formula
[tex]V=A\text{ x h}[/tex]where
[tex]\begin{gathered} A=\text{base area of the prism} \\ h=\text{height of the prism} \end{gathered}[/tex]Substituting the given values of
[tex]\begin{gathered} V=150 \\ A=10 \\ \end{gathered}[/tex]Into the equation, we will obtain
[tex]150=10\times h[/tex]If we make h the subject of the formula
[tex]h=\frac{150}{10}[/tex][tex]h=15\text{ units}[/tex]Use the binomial theorem to expand the binomial.(x – 3)^5
Answers
The binomial theorem tells us how to expand an expression of the form (a + b)^2 like this:
[tex](a+b)^n=nC_0a^nb^0+nC_1a^{n-1}b^1+\cdots nC_na^0b^n[/tex]And nCr is given by the following formula:
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, for this polynomial, we can apply the binomial theorem with a = x, b = -3 and n = 5 to get:
[tex](x-3)^5=5C_0x^5(-3)^0+5C_1x^4(-3)^1+5C_2x^3(-3)^2+5C_3x^2(-3)^3+5C_4x^1(-3)^4+5C_5x^0(-3)^5[/tex][tex]\begin{gathered} 5C_0=1 \\ 5C_1=5 \\ 5C_2=10 \\ 5C_3=10 \\ 5C_4=5 \\ 5C_5=1 \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} (x-3)^5=(1)x^5(-3)^0+(5)_{}x^4(-3)^1+(10)_{}x^3(-3)^2+(10)x^2(-3)^3+(5)x^1(-3)^4+(1)x^0(-3)^5 \\ (x-3)^5=x^5+(5)_{}x^4(-3)^{}+(10)_{}x^3(9)+(10)x^2(-27)+(5)x^1(81)^{}-243 \\ (x-3)^5=x^5-15_{}x^4^{}+90_{}x^3-270x^2+405x^{}^{}-243 \end{gathered}[/tex]Then, the expanded polynomial is:
x⁵ - 15x⁴ + 90x³ - 270x² + 405x - 243
math question #12solve for the missing value x 1/2: 4 = 1/3 : x
Answers
To find the value of x we need to write the equation in another form that tells us what to do; both sides of the equations are ratios then we have:
[tex]\begin{gathered} \frac{1}{2}:4=\frac{\frac{1}{2}}{4} \\ \text{ and} \\ \frac{1}{3}:x=\frac{\frac{1}{3}}{x} \end{gathered}[/tex]Then the equation is:
[tex]\frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x} \\ \frac{1}{8}=\frac{1}{3x} \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}[/tex]Therefore, the value of x is 8/3
1) Convert the improper fraction to a mixed number. 17 3 II ») 3 3 5 3 6 6.
Answers
Solve for z. 5z - 7 = 2z + 2
Answers
Solution
[tex]5z_-7=2z+2[/tex]Collect the like terms
[tex]\begin{gathered} 5z-2z=2+7 \\ 3z=9 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3z}{3}=\frac{9}{3} \\ \\ z=3 \end{gathered}[/tex]The final answer
[tex]z=3[/tex]need help asappppppp
Answers
a.
Consider that the volume (V) of a cone with radius 'R' and height 'H' is given by,
[tex]V=\frac{1}{3}\pi R^2H[/tex]Substitute the values,
[tex]\begin{gathered} V=\frac{1}{3}\pi(4)^2(3) \\ V=16\pi \end{gathered}[/tex]Therefore, option b is the correct choice.
b.
Consider that the volume (V') of a cylinder with radius 'R' and height 'H' is given by,
[tex]V^{\prime}=\pi R^2H[/tex]Solve for the ratio of volume of cone to that of cylinder as,
[tex]\frac{V}{V^{\prime}}=\frac{(\frac{1}{3}\pi R^2H)}{(\pi R^2H)}=\frac{1}{3}[/tex]Therefore, option c is the correct choice.
Solve the systems of equations. List variables a, b, and c.
a-2b+c=8
2a+b-c=0
3a-6b+ 3c = 24
Answers
a = 2b-c+8
b = (-a-c+8)/ 2
c = -a+2b+8
variable a ,b & c for 2a+b-c=0
a = (-b+c) / 2
b=-2a+c
c = 2a+b
variable a ,b & c for 3a-6b+ 3c = 24
a=2b-c+8
b = - (-a-c+8)/ 2
C = -a+2b+8
How to find variables a,b,c ?
1) Finding variable a ,b & c for a-2b+c=8
Finding a=(a-2b+c) + (2b-c)=8+ (2b-c)
a -2b+c+2b-c=8+2b-c
a-2b+2b+c-c=2b-c+8
a = 2b-c+8
Finding b =a-2b+c=8
(a-2b+c) + (−a − c) = 8+ (-a-c)
a-2b+c-a-c=8-a-c
b = (-a-c+8)/ 2
Finding c =a-2b+c8
(a-2b+c)+(-a+2b)=8+(-a+2b)
c = -a+2b+8
2) Finding variable a ,b & c for 2a+b-c=0
Finding a=2a+b-c=0
(2a+b-c)+(-b+c) = -b+c
2a+b-c-b+c = -b+c
a = (-b+c) / 2
Finding b =2a+b-c=0
(2a + b-c) + (-2a + c) = -2a + c
b=-2a+c
Finding c =2a+b-c=0
(2a+b-c) + (-2a - b) = -2a-b
c = 2a+b
3) Finding variable a ,b & c for 3a-6b+ 3c = 24
Finding a=3a-6b+3c = 24
(3a-6b+3c) + (6b-3c) = 24 + (6b- 3c)
3a-6b+3c+6b-3c = 24 + 6b-3c
a=2b-c+8
Finding b =3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
3a-6b+3c-3a-3c-24-3a-3c
3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
b = - (-a-c+8)/ 2
Finding c =3a-6b+3c=24
(3a-6b+3c) + (-3a+6b)=24+ (-3a+6b)
3a-6b+3c-3a+6b-24-3a+6b
C = -a+2b+8
System of equations :In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.A system of equations is a set of one or more equations involving a number of variables.The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. A system of equations can be classified in a similar manner as single equations.The following set of equations is an example of system of equations,2x - y = 12
x - 2y = 48
Solving a system of equations means finding the values of the variables used in the set of equations.We compute the values of the unknown variables still balancing the equations on both sides.The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.To learn more about System of equations refer :
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Final and of the non side round your answer to the nearest 10th 18 and 4
Answers
In the right triangle, there is a relation between its sides
(hypotenuse)^2 = (leg1)^2 + (leg2)^2
The hypotenuse is the side opposite to the right angle
leg1 and leg 2 are the sides of the right angle
In the given figure
The hypotenuse = 18
leg1 = 4
(18)^2 = (4)^2 + (leg2)^2
324 = 16 + (leg2)^2
Subtract 16 from both sides
324 - 16 = 16 - 16 + (leg2)^2
308 = (leg2)^2
Take square root for both sides
17.54992877 = leg2
Round it to the nearest tenth
leg2 = 17.5
if d=3, does d+d+d =3d?
Answers
Yes, d + d + d = 3d
Explanations:d + d + d can also be written as:
1d + 1d + 1d
which equals to 3d
Therefore, no matter what the value of d is,
d + d + d = 3d
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
function of f(-5) is equal to the same value of y in an equation y= f(x).
therefore x value is -5 on x-axis and on this point it gives the value of y-axis which is -2
4. Which equation does NOT have like terms to collect?
3y - 2(y-1) + y = −42
-8(b-3) = -56 - 6
15t+19r = 2
8.5d +7.5 10d +3
Answers
Answer:
15t + 19r = 2
Step-by-step explanation:
None of the unknowns are common
I might not respond for a little while, please don’t end the session! Need help on #3 and 4
Answers
We have a right triangle with a 15m hypotenuse and a 8m leg. If we use x for the missing leg then the Pythagorean Theorem states that:
[tex]15^2=8^2+x^2[/tex]Then we have to solve that equation for x:
[tex]\begin{gathered} x^2=15^2-8^2=225-64 \\ x^2=161 \\ x=\sqrt[]{161} \end{gathered}[/tex]So the answer is the square root of 161.
Kara wants to order lunch for her friends. She'll order 8 cups of soup and a $4 child’s meal for her brother. Kara has $28. How much can she spend on each cup of soup if they are all the same price?
Choose two answers: one for the inequality that models this situation and one for the correct answer.
A.
Inequality: 4x + 8 ≥ 28
B.
Answer: $3 or less
C.
Inequality: 8x + 4 ≥ 28
D.
Inequality: 8x + 4 ≤ 28
E.
Answer: $5 or less
F.
Inequality: 4x + 8 < 28
Answers
The inequality that represents the equation is 8x+4<=28. The money spent on each cup is $3 or less. So, B and D are the correct options
Number of cups ordered by Kara = 8 cups
Money spent on the child's meal by Kara = $4
Total money with Kara = $28
Let x represent the money Kara will spend on each cup of soup
In formulation of the equation we get the following:
Number of cups*Money she can spend on each cup + Money spent on child's meal <= 28
8x + 4<=28
Solving the inequality:
8x<=24
x<= $3
So, the cost of a cup is $3 or less
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Reese is selling lemonade at the parade. He gets to keep 10% of the money he collects. A large lemonadeis $4.00 and a small lemonade is $3.00.The expression represents 10% of the money he collects.0.10(4/ +35)Use the Distributive Property to expand the expression.The simplified expression is
Answers
ANSWER
[tex]0.40l+0.30s[/tex]EXPLANATION
We want to use the distributive property to expand the expression:
[tex]0.10(4l+3s)[/tex]To do this, use the term outside the bracket to multiply each of the terms in the bracket:
[tex]\begin{gathered} (0.10\cdot4l)+(0.10\cdot3s) \\ 0.40l+0.30s \end{gathered}[/tex]That is the simplified expression.
are the events mutually exclusive?event A: rational numbersevent B: irrational numbers
Answers
Given:
There are given that the statement to find them mutually exclusive.
Explanation:
According to the concept of mutually exclusive:
Tw events A and B of any sample space are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event.
Then, twp events A and B cannot occur simultaneously.
Now,
From the given question:
Event A and events B, which means, rational numbers and irrational numbers are mutually exclusive because they have no numbers in common.
So, they span the entire set of real numbers which means both are real numbers.
Final answer:
Hence, the correct option is Yes-Mutually exclusive.
what is the inequality on a graph with the boundary line x+3y=-15
Answers
Solution
To graph the inequality,
we make y the subject of the formula;
[tex]\begin{gathered} x+3y\ge-15 \\ \\ \Rightarrow3y\ge-x-15 \\ \\ \Rightarrow y\ge-\frac{1}{3}x-\frac{15}{3} \\ \\ y\ge-\frac{1}{3}x-5 \end{gathered}[/tex]The inequallity is;
[tex]\begin{gathered} \ge \\ \\ That\text{ is} \\ x+3y\ge-15 \end{gathered}[/tex]how can i get an elimination out of this equation? i think its c but im not sure
Answers
We have the system of equations
[tex]\begin{cases}x+8y=2 \\ -2x+8y=20\end{cases}[/tex]We can solve it subtraction, the first equation minus the second equation
[tex]\begin{gathered} x+8y-(-2x+8y)=2-20 \\ \\ x+8y+2x-8y=-18 \\ \\ x+2x=-18 \\ \\ 3x=-18 \\ \\ x=\frac{-18}{3}=-6 \end{gathered}[/tex]Therefore x = -6, we can now find the value of y
[tex]\begin{gathered} x+8y=2\Rightarrow-6+8y=2 \\ \\ -6+8y=2 \\ \\ 8y=8 \\ \\ y=1 \end{gathered}[/tex]Therefore the solution is
[tex](-6,1)[/tex]j(x) = 2x² - 2
Find j(-1)
Answers
Your answer would be 0, hope this helps.
The test scores for the analytical writingsection of a particular standardized test canbe approximated by a normal distribution, asshown in the figure.(a) What is the maximum score that can be inthe bottom 10% of scores?(b) Between what two values does the middle80% of scores lie?
Answers
Solution:
Given:
Recall that the z-value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{where} \\ \mu\Rightarrow\operatorname{mean}\text{ value} \\ \sigma\Rightarrow s\tan dard\text{ deviation} \end{gathered}[/tex]Thus,
[tex]z=\frac{x-3.7}{0.91}\text{ ---- equation 1}[/tex]A) maximum score that can be in the bottom 10% of scores
using the table of z-values,
for the bottom 10% scores, we have
[tex]z=-1.28155156554[/tex]To evaluate x, substitute the value of z into equation 1.
Thus,
[tex]\begin{gathered} -1.28155156554=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5337895 \end{gathered}[/tex]Thus, the maximum score that can be in the bottom 10% of scores is 2.5
B) Two values for which the middle 80% of scores lie.
From the z score values shown below:
The z scores of the value are
[tex]\begin{gathered} z_1=-1.28 \\ z_2=1.28 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{when z=-1.28, we have} \\ -1.28=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5352 \\ \text{when z=1.28, we have} \\ 1.28=\frac{x-3.7}{0.91} \\ \Rightarrow x=4.8648 \end{gathered}[/tex]Thus, the two values for which the middle 80% of scores lie are 2.5 and 4.86.
find the probability of rolling a die five times and getting no threes 
Answers
Answer:
5/5
Step-by-step explanation:
since its 5 times u re rolling the dice and u have 5 chances or 5 possibilities of getting 5
Answer:
Step-by-step explanation:
1) Set an equation
Getting a three on the dice is 1/6. So the opposite is 5/6.
5/6 * 5/6 * 5/6 * 5/6 * 5/6
2) Solve
3125/7776
0.4018
40.18%
The amount Lins sister earns at her part time job is proportional to the number of hours she works. She earns 9.60 dollars per hour1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.2. is y a function of x? explain how you know.3. Write an equation describing x as a function of y
Answers
The amount Lins sister earns at her part-time job is proportional to the number of hours she works.
She earns 9.60 dollars per hour.
1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.
$9.60 per hour means that y = 9.60 and x = 1
[tex]\begin{gathered} y=kx \\ 9.60=k(1) \\ k=\frac{9.60}{1} \\ k=9.60 \end{gathered}[/tex]Since we found the value of constant k, so the relation becomes
[tex]y=9.60x[/tex]2. is y a function of x? explain how you know
y is a function of x means that the value of y depends on the value of x.
In the above function, when the value of x changes then the value of y will also change.
3. Write an equation describing x as a function of y
To write the equation describing x as a function of y, make x the subject of the equation.
This simply means to separate out the variable x.
[tex]\begin{gathered} y=9.60x \\ 9.60x=y \\ x=\frac{y}{9.60} \end{gathered}[/tex]The farm raises its own produce and meat. Will has a cow that produces milk. She gives 2.3 gallons of milk aday. How many gallons does she give in a month that has 30 days?
Answers
Cow produces:
2.3 gallons of milk per day
To obtain the number of gallons that she will give in a month of 30 days, simply multiply the amount she gives per day (2.3) by the numbe rof days (30):
2.3 g/day x 30 day
An individual's income varies with age. The table
shows the median income I of individuals of
different age groups within the United States for
a certain year. For each age group, let the class
midpoint represent the independent variable x.
For the class "65 years and older," assume that
the class midpoint is 69.5.
Complete parts (a) through (e).
Answers
Considering the relation between the two variables in the table, it is found that:
A quadratic relation with a < 0 exists between the two data-sets.The quadratic relation is given by: y = -46.359 x^2 +4385.3 x -57255.975.How to find the type of relation of the variables?We have to look at the behavior of the relation over the entire domain as follows:
If it only increases, or only decreases, it is a linear relation.If it increases and then decreases, or vice-versa, then it is a quadratic relation.In the context of this problem, the median income increases until a age group of 45-54 years, then it decreases. Since it increases then it decreases, the relation is concave down quadratic, that is, quadratic with a < 0.
To find the equation that models the relation, we insert the data-points given as follows into the calculator:
(19.5, 10963), (29.5, 32131), (39.5, 41636), (49.5, 46693), (59.5, 41477), (69.5, 22500).
Using the calculator with these points, the quadratic equation of best-fit is given as follows:
y = -46.359 x^2 +4385.3 x -57255.975
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Answer:
-46.537x^2 + 4409.695x - 57770.475
Step-by-step explanation:
Sal has invested in two different stocks over the past few years. He has 22 shares of Company A's stock, which is currently selling at $45 per share. He also has 130 shares of Company B's stock, which is currently selling at $75 per share. What is the total value of Sal's stock holdings?
Answers
Total value of Sal's stock holdings is $10740
What is stock holding?The quantity of stocks, or shares, that a person or organization owns in a corporation is referred to as their stock holdings. Along with futures, bonds, mutual funds, and other assets, these make up an element of an investment portfolio. Each of these is an investment that has the potential to appreciate in value, bringing its owner a profit.
Stock holdings can comprise securities such as stocks, bonds, futures, mutual funds, ETFs, and other types of assets.
Preferred stock and ordinary stock are the two main categories of stock holdings.
Money earned on selling stocks of company A
= 22×45
= $990
Money earned on selling stocks of company B
= 130×75
= $9750
Total money earned on selling stocks of company A and B
= 990 + 9750
= $10740
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Use the distributive property to write an equivalent expression to y(6+15)
Answers
The most appropriate choice for distributive property of algebraic expression will be given by-
21y is the required equivalent expression
What is distributive property of algebraic expression?
At first it is important to know about algebraic expression.
Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division.
Distributive property is a property which connects both addition and multiplication.
Suppose a, b and c are three numbers. Distributive property implies
a [tex]\times[/tex] (b + c) = a [tex]\times[/tex] b + a [tex]\times[/tex] c
Here,
y(6 + 15)
y [tex]\times[/tex] (6 + 15)
6 [tex]\times[/tex] y + 15 [tex]\times[/tex] y
6y + 15y
21y
This is the required equivalent expression
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3. Pentagon PENTA with P(0, 2), E(4,6), N(8,-1), T(6,-3), and A(2,-4); reflect across y-axis. /1a. What is the "arrow rule" to show this transformation? 15 b. What are the vertices of the image after the transformation?
Answers
1a) The arrow will be (-x,y) for reflection
1b)The vertices are P(-(0),2), E(-4,6), N(-8,-1), T(-6,-3), A(-2/-4) = P(0,2), E(-4,6), N(-8,-1),T(-6,-3), A(-2,-4)
15) Cost of a computer game: $4.99
Markup: 40%
Discount: 55%%
Tax: 1%
Answers
Answer:
$3.18
Step-by-step explanation:
(4.99×0.4)+4.99=6.986
6.986-(6.986×0.55)=3.1437
(3.147×0.01)+3.147=3.175137
