Answers
Maximum number of identical boxes with no. of supply items in each box will be:
a. 78 boxes with 1 pencil and 1 eraser in each box.
b. 195 boxes with 1 notebook and 1 folder in each box.
c. 65 boxes with 1 eraser, 1 marker and 2 folders in each box.
First Lana will make 78 boxes with 1 pencil and 1 eraser in each box. After that she'll be left with
143 - 78 = 65 erasers.
Secondly she will make 195 boxes with 1 notebook and 1 folder in each box. After that she'll be left with
330 - 195 = 135 folders.
Next she will make 65 boxes with 1 eraser, 1 maker and 2 folders in each box.
By doing this she will be able to make maximum number of identical boxes.
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Related Questions
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=3x^2+4x+2
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The quadratic formula states that the solutions x1 and x2 of a quadratic function in the form y = ax^2 + bx + c is equal to:
[tex]\begin{gathered} x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, using this formula with the values a = 3, b = 4 and c = 2, we have that:
[tex]\begin{gathered} x_1=\frac{-4+\sqrt[]{4^2-4\cdot3\cdot2}}{2\cdot3}=\frac{-4+\sqrt[]{16-24}}{6}=\frac{-4+\sqrt[]{-8}}{6} \\ x_1=\frac{-4+\sqrt[]{2^2\cdot(-2)}}{6}=\frac{-4+2\cdot\sqrt[]{-2}}{6}=\frac{-2+\sqrt[]{-2}}{3}=-\frac{2}{3}+i\cdot\frac{\sqrt[]{2}}{3} \\ x_2=\frac{-4-\sqrt[]{-8}}{6}=\frac{-2-\sqrt[]{-2}}{3}=-\frac{2}{3}-i\cdot\frac{\sqrt[]{2}}{3} \end{gathered}[/tex]Since the zeros have a complex part, the solutions are imaginary.
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart and a spade.The probability of being dealt a heart and a spade is __.(Type an integer or a simplified fraction.)
Answers
Okay, here we have this:
the probability that describe the related frequency of actual observation of an event is an experiment is which of the following
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The relative frequency is an empirical probability. So, the answer is the first option
graph the line represented by the equation 2x + 3y = 8
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Given the equation
2x + 3y = 8
The given equation represents a line
It is required at minimum two points to graph the line
So, assume two value for x and find y using the given equation
When x = -2
2 * -2 + 3y = 8
-4 + 3y = 8
3y = 8 + 4
3y = 12
y = 12/3 = 4
so, the point (-2 , 4) lie on the line
And assume x = 4
so, 2 * 4 + 3y = 8
8 + 3y = 8
3y = 0
y = 0
So, the point (4 , 0) lie on the line
so, the line is passing through the points (-2 , 4) and ( 4 , 0)
By connecting the points and extending the line we will get the graph of 2x + 3y = 8
See the following image;
Circle the value that correctly converts 6.5 cm in inches.26 in0.26 in2.6 in260 in
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2.6 inches (third option)
Explanation:Given:
To convert 6.5cm to another unit
To find:
The value of 6.5 cm inches
To determine the value in inches, we need to do a conversion from cm to inches
1 inch = 2.54 cm
let 6.5 cm in inches = y
6.5cm = y
2.54cm = 1 inch
crossmultiply:
[tex]\begin{gathered} 6.5(1)\text{ = y\lparen2.54\rparen} \\ 6.5\text{ = 2.54y} \\ divide\text{ both sides by 2.54y:} \\ \frac{6.5}{2.54}\text{ = y} \\ y\text{ = 2.559} \end{gathered}[/tex]To the nearest tenth, y = 2.6
Hence, the value of 6.5cm in inches is 2.6 inches (third option)
create a trinomial with a constant of 4 and -1 coefficient of the x term. fast help!!!
Answers
A trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
What is defined as the trinomial?A trinomial is a three-term algebraic expression. An algebraic expression is made up of one or more terms' variables and constants. A perfect square trinomial is an algebraic expression formed by squaring a binomial formation. It has the formula ax² + bx + c. Here, a, b, as well as c are all real numbers, and a ≠ 0.For the given question;
Trinomial have-
constant of 4 and -1 coefficient of the x termThe general equation of the trinomial is-
ax² + bx + c = 0
Where, a and b are the coefficients and c is the constant.
Thus,
Put b = -1 and c = 4
ax² - x + 4 = 0
Now, value of a can be any number but not zero.
Thus, suitable value of a is 1.
The trinomial becomes,
x² - x + 4 = 0
Thus, a trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
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Translate to an equation and solve: 4 is the product of 8 and b. Simplify all fractions.Provide your answer below:b=
Answers
If 4 is the product of 8 and b, 4 is the result of the multiplication of 8 and b. Then,
4 = 8b
Which is the same as:
8b = 4
To find b, let's divide both sides by 8:
[tex]\begin{gathered} \frac{8b}{8}=\frac{4}{8} \\ b=\frac{4}{8} \end{gathered}[/tex]
Dividing the numerator and the denominator by 4:
[tex]\begin{gathered} b=\frac{\frac{4}{4}}{\frac{8}{4}} \\ b=\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]b=\frac{1}{2}[/tex]Find the slope of the line passing through thepoints (-5,4) and (7,8).
Answers
We have two points and we have to calculate the slope of the line pasing through this points.
We can calculate the slope as the ratio of the difference between the y-coordinates and the difference between the x-coordinates.
This can be written as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{7-(-5)}=\frac{4}{7+5}=\frac{4}{12}=\frac{1}{3}[/tex]The slope of the line is 1/3.
solve each system of equations below by graphing, please use my graphy = 2xy = -x + 3
Answers
Given:
y= 2x ; y=-x+3
Substitute the value of x as -2,-1,0,1,2
y=2x
[tex]\text{When x=-2, y=-4}[/tex][tex]\text{When x=-1, y=-}2[/tex][tex]\text{When x=0, y=}0[/tex][tex]\text{When x=1, y=}2[/tex][tex]\text{When x=2, y=}4[/tex]y= -x+3
[tex]\text{When x=-2, y=}5[/tex][tex]\text{When x=-1, y=}4[/tex][tex]\text{When x=0, y=}3[/tex][tex]\text{When x=1, y=}2[/tex][tex]\text{When x=2, y=}1[/tex]Therefore, the solution is (1,2) .
This parabola opens to the left. P. O A. True O B. False
Answers
Answer:
True.
Explanation:
We take the analogy from the graph of y = ax^2
When y = x^2, the parabola opens upward (towards the positive y-axis). However, when the parabola is y = -x^2, it opens downward (towards the negative y-axis).
In a similar way, when we have x = ay^2, the parabola opens towards the positive x-axis ( towards the right). However, if we have x = -ay^2, then the parabola opens towards the negative x-axis ( towards the left).
Therefore, by comparison, x = - 1/8 y^2, opens to the left, and the correct option to choose is 'True'.
find (8.4x10^11)/(5.25x10^2)(8.0x10^3), expressed in a scientific notation
Answers
The simplified form of the expression, (8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3), in scientific notation is 2.0 × 10⁵
Evaluating an expression in scientific notationFrom he question, we are to evaluate the given expression in scientific notation.
The given expression is
(8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3)
First, we will write this expression properly
The expression written properly is
(8.4 x 10¹¹)/(5.25 x 10²)(8.0 x 10³)
Evaluating
(8.4 x 10¹¹)/(5.25 x 8.0)(10² x 10³)
(8.4 x 10¹¹)/(5.25 x 8.0)(10² ⁺ ³)
(8.4 x 10¹¹)/(42.0)(10⁵)
(8.4 x 10¹¹)/(42.0 × 10⁵)
(8.4/42.0) × (10¹¹ / 10⁵)
(0.20) × (10¹¹ ⁻ ⁵)
(0.20) × (10⁶)
= 0.20 × 10⁶
= 2.0 × 10⁵
Hence, the expression is 2.0 × 10⁵
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3x-8=2x+18Solve for x
Answers
x=26
Explanation
[tex]3x-8=2x+18[/tex]Step 1
subtract 2x in both sides
[tex]\begin{gathered} 3x-8=2x+18 \\ 3x-8-2x=2x+18-2x \\ x-8=18 \end{gathered}[/tex]Step 2
add 8 in both sides
[tex]\begin{gathered} x-8=18 \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]I hope this helps you
Write 1.75 % as decimal AND simplified fraction. ANS. As decimal __________. As simplified fraction. ________.
Answers
The given percentage is 1.75%.
To find the decimal expression of this percentage, we just have to divide it by 100. It's important to know that when we divide a number by 100, we just have to move the decimal point two spots to the left, as follows
[tex]\frac{1.75}{100}=0.0175[/tex]Therefore, as a decimal is 0.0175.
Now, to find the simplified fraction, we divide the number by 10000, as follows
[tex]\frac{175}{10000}[/tex]The reason for dividing by 10000 is that we need to have a whole number in the numerator, so the extra two zeros allow us to get rid of the two of the number. Now, we simplify the fraction dividing each part by 5
[tex]\frac{175\colon5}{10000\colon5}=\frac{35}{2000}=\frac{7}{400}[/tex]Once we get the simplest fraction, we can finish.
Therefore, as a simplified fraction is 7/400.
x-6y>57x+2y>4Is (10,-2) a solution of the system?
Answers
To check if (10, -2) is a solution to the system, we have to replace x with "10" and y with "-2" and see if the inequalities hold true.
If both the inequalities hold true, then definitely (10, -2) is a solution!
Let's check the first inequality:
[tex]\begin{gathered} x-6y\stackrel{?}{>}5 \\ 10-6(-2)\stackrel{?}{>}5 \\ 10+12\stackrel{?}{>}5 \\ 22>5 \\ \text{True} \end{gathered}[/tex]Now, let's check the second inequality:
[tex]\begin{gathered} 7x+2y\stackrel{?}{>}4 \\ 7(10)+2(-2)\stackrel{?}{>}4 \\ 70-4\stackrel{?}{>}4 \\ 66>4 \\ \text{True} \end{gathered}[/tex]
Select all of the following that are statistical questions A. What is the price of the orangeB. What is the weight of an orange C. What is the average price of an orange D. What is the average weight of an orange grown in the U.S.A E. What percent of oranges grocery stores were grown in the USAThere is more than one answerPlease help no wrong answers please
Answers
Take into account that a statistical question refers to situation which data set are involved. Then, you can consider as statistical questions:
What is the average price of an orange
average takes into account the price of more than one orange.
What is the average weight of an orange grown in U.S.A
What percent of oranges grocery stores were grown in the USA
Sasha has $850 todeposit into twoaccounts.Sasha will deposit $450at First Oak Bank.She will deposit the restinto River Point Bank.Sasha will not make additionaldeposits or withdrawals.How much more money will bein her account at First Oak thanat River Point after 2 years?
Answers
Given
Sasha has $850 to deposit into two accounts.
Sasha will deposit $450 at First Oak Bank.
She will deposit the rest into River Point Bank.
Sasha will not make additional deposits or withdrawals.
To find how much more money will be in her account at First Oak than at River Point after 2 years.
Now,
It is given that,
In the first Oak bank the rate of interest is 6%.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P+\frac{Pnr}{100} \\ A=450+\frac{450\times2\times6}{100} \\ A=450+54 \\ A=454 \end{gathered}[/tex]Hence, the amount in the First Oak bank is $454.
In the River point bank the rate of interest is 2% compounded annually.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ A=P(1+\frac{2}{100})^2 \end{gathered}[/tex]Since Sasha will deposit $450 at First Oak Bank and she will deposit the rest into River Point Bank.
Then, the amount deosited in the River point bank is,
[tex]\begin{gathered} P=850-450 \\ =400 \end{gathered}[/tex]Therefore,
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D.) what is the probability of selling 25 cheesecakes ?E.) what is the probability of selling at most 10 cheesecakes ?F.) give the expected number of cheesecakes sold on any given day using the discrete probability distribution
Answers
D)
To find the probability of selling 25 cheesecakes:
It is impossible to find the probability of selling 25 cheesecakes.
So,
P(x=25)=0
The probability of selling 25 cheesecakes is 0.
E)
To find the probability of selling at most 10 cheesecakes:
That is,
[tex]\begin{gathered} P(x\leq10)=P(x=0)+P(x=5)+P(x=10) \\ =0.1+0.23+0.04 \\ =0.37 \end{gathered}[/tex]Therefore, the probability of selling at most 10 cheesecakes is 0.37.
F)
To find the expected number of cheesecakes sold on any given day using the discrete probability distribution:
[tex]\begin{gathered} \sum ^5_{i\mathop=1}x_ip_i=x_1p_1+x_2p_2+x_3p_3+x_4p_4+x_5p_5 \\ =0(0.1)+5(0.23)+10(0.04)+15(0.46)+20(0.17)_{}_{}_{} \\ =0+1.15+0.4+6.9+3.4 \\ =11.85 \end{gathered}[/tex]Hence, the expected number of cheesecakes sold on any given day using the discrete probability distribution is 11.85.
how do I solve for x and y when I have no information for these triangles?
Answers
y is equal to 140 because they are congruent
the complement of y is 40 because 180 - 140 = 40
x = 180 - 40 - 40 = 180 - 80 = 100
1. y and 140 are congruent angles, so y = 140
2. a = 180 - 140 = 40 because it is complementary with y
3. b = a = 40 because the sides of the triangle are equal, so the angles are equal
4. c = 180 - a - b = 180 - 40 - 40 = 100 because the sum of the inner angles of a triangle measure 180
5. x = c = 100 because they are opposed by the vertex
Answer:
y = 140
x = 100
What are the terms in the expression 5b + 6m + 8?O 5,6,8O 11 b + mO 5b, 6m, 8
Answers
By definition a term is a single mathematical expression; it may be a number, a variable, or a multiplication of them.
Then, the terms in the expression given are 5b, 6m and 8.
Therefore the answer is the last choice.
Write an algebraic expression for each phrase.1.the product of r and seven7x3. two more than the product of y and four2. the sum of 8 and p4. the quotient of k and ten
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2) The symbol used to repesent sum is '+'. Thus, the algebraic expression for the the sum of 8 and p is
8 + p
Solve the inequality and graph your answerx + 19 < 16
Answers
Solution
For this case we have this inequality:
x+19 <16
We can subtract 16 in both sides and we got:
x +19-19 < 16-19
x < -3
For the second part we have:
[tex]\frac{x}{5}\ge-2[/tex]We can multiply both sides by 5 and we got.
[tex]x\ge-10[/tex]What system of inequalities would you use to solve the problem below?Suppose you have a job teaching swimming lessons and get paid $6 an hour. You also have a job as a cashier and get paid $8 an hour. If you cannot work more than 15 hours a week, what are the number of hours you can work at each job and still make at least $100?A.s + c 1006s + 8c 15B.s + c 156s + 8c 100C.s + c < 156s + 8c > 100D.s + c 156s + 8c 100
Answers
Answer:
s + c <= 15
6s + 8c >= 100
Explanation:
Express the function graphed on the axes below as a piecewise function.108642-10-8-6-4-22416810-4-6-8-10
Answers
Answer:
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]Explanation:
The equation of the line to the left is 2x + 3 and we see that it only exists for x <= -4.
The equation of the line to the right is 2x - 12 and we see that it only exists for x > 2.
Therefore, we can write
f(x) = 2x + 3 for x < = -4
f(x) = 2x -12 for x > 2
Or in the notation of piecewise function, the above can be written consicely as
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]
which is our answer!
Timothy mows his neighbor lawn for $6.50 per week. He continues to do this for 37 weeks until winter. In winter he shovels snow off their lawn for $10.25 per week for 25 weeks. How much money did Timothy earn in total?
Answers
ANSWER
$496.75
EXPLANATION
Timothy mows his neighbor's lawn for $6.50 per week for 37 weeks until winter.
This means that the amount of money he made mowing is the product of the amount per weeks and the number of weeks.
That is:
[tex]\begin{gathered} 6.50\cdot37 \\ =\text{ \$}240.50 \end{gathered}[/tex]He shovels the snow for $10.25 per week for 25 weeks.
The amount of money he made shoveling is therefore:
[tex]\begin{gathered} 10.25\cdot25 \\ =\text{ \$256.25} \end{gathered}[/tex]The total amount of money that he made in total is the sum of money he made mowing and shoveling:gg
[tex]\begin{gathered} 240.50+256.25 \\ =\text{ \$496.75} \end{gathered}[/tex]That is the answer.
what is the equation of the line? O y=3/2x O y=2/3x O y=3x O y=2x
Answers
Explanation:
We would apply the slope formula:
slope = change in y/change in x
change in y = 4 - 0 = 4
change in x = 6 - 0 = 6
Also note on the graph, the change in y is represented by y. And the change in x is represented by x
[tex]\begin{gathered} slope=\frac{4}{6} \\ \text{slope =}\frac{y}{x} \end{gathered}[/tex]Equating both:
[tex]\begin{gathered} \frac{y}{x}=\frac{4}{6} \\ \frac{y}{x}=\frac{2}{3} \end{gathered}[/tex]Multiply both sides by x:
[tex]\begin{gathered} \frac{y}{x}\times x=\frac{2}{3}\text{ }\times\text{ x} \\ y\text{ = }\frac{2x}{3}\text{ (option B)} \end{gathered}[/tex]good morning I really need help with numbers 3 and 4
Answers
a) 6 x 18 = 108
b) 8 x 74 = 592
Explanations:According to the distributive property:
a (b + c) = ab + ac
Let us do each of the exercises 3 and 4 using the distributive property:
3) 6 x 18
Step 1: Write 18 as 10 + 8
18 = 10 + 8
6 x 18 = 6 ( 10 + 8)
Step 2: Apply the distributive property
6 ( 10 + 8) = (6 x 10) + (6x8)
Step 3: Multiply each of the terms
60 + 48
Step 4: Add the two together
108
Therefore, 6 x 18 = 108
4) 8 x 74
Step 1: Write 74 as 70 + 4
74 = 70 + 4
8 x 74 = 8 ( 70 + 4)
Step 2: Apply the distributive property
8 ( 70 + 4) = (8 x 70) + (8x4)
Step 3: Multiply each of the terms
560 + 32
Step 4: Add the two together
592
Therefore, 8 x 74 = 592
When the clock first starts counting down time, there are more than 300 seconds before the start of the game. Write an inequality statement that best describes t, the time in seconds, when the clock first starts counting down time.
Answers
"When the clock first starts counting down time, there are more than 300 seconds before the start of the game", that means the variable t we will use to represent when the clock first starts counting down time is greater than 300, so we can represent this sentence with the following inequality:
[tex]t>300[/tex]So the inequality statement that best describes t is t > 300.
what is 3 1/6 + 5 2/3
Answers
The given expression is
[tex]3\frac{1}{6}+5\frac{2}{3}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} 3\frac{1}{6}=\frac{3\cdot6+1}{6}=\frac{18+1}{6}=\frac{19}{6} \\ 5\frac{2}{3}=\frac{5\cdot3+2}{3}=\frac{15+2}{3}=\frac{17}{3} \end{gathered}[/tex]We use these fractions to make the sum
[tex]\frac{19}{6}+\frac{17}{3}[/tex]Now, we use the following property
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex][tex]\frac{19\cdot3+17\cdot6}{6\cdot3}=\frac{57+102}{16}=\frac{159}{16}[/tex]Hence, the result is 159/16.The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is 7 feet. Find tje length of the three sides of the triangle. Answer exactly or round to 2 decimal places. The legs of the triangle are 7_ feet and the hypotenuse is _ feet
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Taking l as the length of one of the legs and using the pythagorean theorem we have that:
[tex](2l)^2=l^2+7^2[/tex]Solve the equation for l:
[tex]\begin{gathered} 4l^2=l^2+49 \\ 4l^2-l^2=49 \\ 3l^2=49 \\ l^2=\frac{49}{3} \\ l=\sqrt[]{\frac{49}{3}} \\ l=\frac{7}{\sqrt[]{3}}=\frac{7\sqrt[]{3}}{3} \end{gathered}[/tex]It means that the hypotenuse is:
[tex]\frac{14\sqrt[]{3}}{3}[/tex]And the leg is:
[tex]\frac{7\sqrt[]{3}}{3}[/tex]what is 13 divide by 113.1 in long division
Answers
The value of 13 divided by 113.1 is 0.1149425.
How to calculate the division?It should be noted that the steps to calculate the division will be:
Step 1: Take the first digit of the dividend from the left. ...
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend
Therefore, 13 divided by 113.1 will be:
= 13 ÷ 113.1
= 0.1149425
In conclusion, the value is 0.1149425.
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