You have 1/5 of a box of erasers
Number of box of erasers = 1/5.
you need to share them with 3 total people, including yourself
Total number of people = 3 + 1( yourself)
Total number of people = 4
Since, we have to distribute the box of erasers to 4 people
So, divide 1/5 by 4:
[tex]\begin{gathered} \frac{1}{5}\text{ }\div4=\frac{\frac{1}{5}}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5}\times\frac{1}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5\times4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{20} \end{gathered}[/tex]The fraction of the box that each person will get is 1/20
Answer: 1/20
Consider the graph below.(3,1) (4,2) (6,3) (4,4) (8,5) Which correlation coefficient and interpretation best represent the given points?1.) 0.625, no correlation 2.) 0.791. no correlation 3.) 0.625, positive correlation4.) 0.791. positive correlation
Given the information on the problem,we have that the correlation coefficient of the data given is:
[tex]r=\frac{\sum^{}_{}(x-\bar{y})(y-\bar{x})}{\sqrt[]{SS_x\cdot SSy}}=\frac{10}{\sqrt[]{16\cdot10}}=0.79[/tex]therefore, the value of the correlation coeficient is 0.79, which shows a strong positive correlation
Imagine you asked students to draw an area model for the expression 5+4x2.
Walking around the room, you see the following three area models.
First, briefly explain the student thinking process you think might be behind each answer.
Answer Describe the thinking process
Which order would you call students A, B and C to present their work to the class and how would you guide the discussion?
Answer:
area 1
Step-by-step explanation:
quadrilateral WXYZ is reflected across the line y=x to create quadrilateral W’X’Y’Z'. What are the coordinates of quadrilateral W’X’Y’Z'.
Explanation
We are required to determine the coordinates of W’X’Y’Z' when WXYZ is reflected across the line y = x.
This is achieved thus:
From the image, we can deduce the following:
[tex]\begin{gathered} W(-7,3) \\ X(-5,6) \\ Y(-3,7) \\ Z(-2,3) \end{gathered}[/tex]We know that the following reflection rules exist:
Therefore, we have:
[tex]\begin{gathered} (x,y)\to(y,x) \\ W(-7,3)\to W^{\prime}(3,-7) \\ X(-5,6)\to X^{\prime}(6,-5) \\ Y(-3,7)\to Y^{\prime}(7,-3) \\ Z(-2,3)\to Z^{\prime}(3,-2) \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} \begin{equation*} W^{\prime}(3,-7) \end{equation*} \\ \begin{equation*} X^{\prime}(6,-5) \end{equation*} \\ \begin{equation*} Y^{\prime}(7,-3) \end{equation*} \\ \begin{equation*} Z^{\prime}(3,-2) \end{equation*} \end{gathered}[/tex]This is shown in the graph bwlow for further undertanding:
"Solve for x. Enter as a decimal not as a fraction. Round to the nearest hundredth if necessary."
Answer:
x =
5
Explanation
From the given diagram, it can be infered that WY = 2QR
From the diagram
WY = x+9
QR = 2x-3
substitute into the expression
x+9 = 2(2x-3)
x+9 = 4x - 6
Collect the like terms
x-4x = -6-9
-3x = -15
x = -15/-3
x = 5
Hence the value of x is 5
DataNot ReceivingReceivingFinancial AidFinancial AidUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%UniversityTotal
There are 10730 students total as shown in the bottom right hand corner. So, the probability that the student receives aid and is a graduate is given by:
[tex]P=\frac{1879}{10730}\times100=17.51[/tex]Round to the nearest percent is 17.5%
Answer: 17.5%
Answer:
There are a total of 10730 students and 1879 students who are graduates as well as receiving financial aid. So the probability would be
(1879/10730)*100 = 17.51%
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. Theamounts she spent in each category are pictured here.Food$333Rent$417Other$500Fun$250What percent of her total spending did she spend on Fun? Answer to the nearest whole percent.
In this problem we have to calculate the total spences so we add all the costs so:
[tex]\begin{gathered} T=333+417+500+250 \\ T=1500 \end{gathered}[/tex]So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:
[tex]\begin{gathered} 1500\to100 \\ 250\to x \end{gathered}[/tex]so the equation is:
[tex]\begin{gathered} x=\frac{250\cdot100}{1500} \\ x=16.66 \end{gathered}[/tex]So she spend 16.66% in fun
0.75 greater than 1/2
True
0.75 is greater than 0.5
Explanation
Step 1
remember
[tex]\frac{a}{b}=\text{ a divided by b}[/tex]then
[tex]\frac{1}{2}=\text{ 1 divided by 2 = 0.5}[/tex]Step 2
compare
0.75 and 0.5
[tex]0.75\text{ is greater than 0.5}[/tex]I hope this helps you
FOR GREATER THAN WE ADD THE TERMS.
MATHEMATICALLY THIS MEANS
[tex] = 0.75 + \frac{1}{2} \\ = 0.75 + 0.5 \\ = 1.25[/tex]
1.25 is the answer.
At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $12. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks costs $15. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, write a system that represents these statements. p: slices of pizza b: bread sticks d: juice drinks Choose the correct verbal expressions for problems into a system of equations or inequalities.
p = slices of pizza
b = bread sticks
d = juice drinks
Equation 1
3p + 4b + 2d = 12
Equation 2
5p + 2b + 3d = 15
Equation 3
4b + 1d = 1p + 0.3
That's all
The sum of three numbers is140 . The first number is 8 more than the third. The second number is 4 times the third. What are the numbers? First number: Second number: Third number:
Answer:
x= 30
y= 88
z= 22
Step-by-step explanation:
x= z+8
y= 4z
x + y + z = 140
we substitute to the third equation (z+8) + (4z) + z= 140 so we obtain 6z+8= 140. Z is then equal to 140-8/6= 22.
Then x= 22+8= 30, y=22(4)= 88
30+88+22= 140
HELP ASAP!!!
Find the square of 1-4i.
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
What is the slope of the line with points (3,7) and (3,-2)
Answer:
slope = 0
Given:
(3, 7)
(3, -2)
The formula for the slope is solved by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the given, we know that:
x₁ = 3
x₂ = 3
y₁ = 7
y₂ = -2
Substituting these values to the formula, we will get:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-2-7}{3-3} \\ m=\frac{-9}{0} \\ m=0 \end{gathered}[/tex]Therefore, the slope would be 0.
find a slope of the line that passes through (8,8) and (1,9)
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we can use this formula by introducing the values of the given points. In our case
[tex]\begin{gathered} (x_1,y_1)=(8,8) \\ (x_2,y_2)=(1,9) \end{gathered}[/tex]Hence, we have
[tex]m=\frac{9-8}{1-8}[/tex]It yields,
[tex]m=\frac{1}{-7}[/tex]hence, the answer is
[tex]m=-\frac{1}{7}[/tex]Round 7488 to the nearest thousand
The thousand place value is the 4th digit to the left of the decimal point. This means that the digit is 7.
If the first digit after 7 is greater than or equal to 5, 7 would increase by 1. If it is less than 5, 7 remains the same. Since 4 is less than 5, 7 remains. The rest digits turns to 0. Thus, the answer is
7000
The next algebra test is worth 100 points and contains 35 problems. Multiple-Choice questions are worth 2 points each and word problems are 7 points each. How many of each type equation are there?
Let
x ----->number of multiple-choice questions
y ----> number of word problems
so
we have
x+y=35 --------> equation 1
2x+7y=100 -----> equation 2
solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
therefore
x=29
y=6
number of multiple-choice questions is 29
number of word problems is 6
Write a cosine function that has a midline of 4, an amplitude of 3 and a period of 8/5
A cosine function has the form
[tex]y=A\cdot\cos (Bx+C)+D[/tex]Where A is the amplitude, B is 2pi/T, and C is null in this case because the phase is not being specified, and D is the vertical shift (midline).
Using all the given information, we have
[tex]y=3\cdot\cos (\frac{2\pi}{T}x)+4[/tex]Then,
[tex]y=3\cdot\cos (\frac{2\pi}{\frac{8}{5}}x)+4=3\cdot\cos (\frac{10\pi}{8}x)+4=3\cdot\cos (\frac{5\pi}{4}x)+4[/tex]Hence, the function is
[tex]y=3\cos (\frac{5\pi}{4}x)+4[/tex]Solve each system of the equation by elimination method. x+3y=-204x+5y=-38
Given the equation system:
[tex]\begin{gathered} x+3y=-20 \\ 4x+5y=-38 \end{gathered}[/tex]To solve this system using the elimination method, the first step is to multiply the first equation by 4 so that the leading coefficient is the same, i.e., both equations start with "4x"
[tex]\begin{gathered} 4(x+3y=-20) \\ 4\cdot x+4\cdot3y=4\cdot(-20) \\ 4x+12y=-80 \end{gathered}[/tex]Then subtract the second equation from the first one
From the resulting expression, you can calculate the value of y
[tex]\begin{gathered} 7y=-42 \\ \frac{7y}{7}=-\frac{42}{7} \\ y=-6 \end{gathered}[/tex]Next, you have to substitute the value of y in either the first or second equation to find the value of x:
[tex]\begin{gathered} x+3y=-20 \\ x+3\cdot(-6)=-20 \\ x-18=-20 \\ x=-20+18 \\ x=-2 \end{gathered}[/tex]The solution of the system is (-2,-6)
The length of the hypotenuse in a 30°-60°-90° triangle is 6√10yd. What is thelength of the long leg?
In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}[/tex]So the length of the long leg is 3√30 yd.
explain why 4 x 3/5=12x 1/5
Answer:
They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]Explanation:
We want to explain why;
[tex]4\times\frac{3}{5}=12\times\frac{1}{5}[/tex]They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]So, they give the same answer when simplified.
Also you can derive one from the other;
[tex]\begin{gathered} 4\times\frac{3}{5}=12\times\frac{1}{5} \\ 4\times3\times\frac{1}{5}=12\times\frac{1}{5} \\ 12\times\frac{1}{5}=12\times\frac{1}{5} \\ \frac{12}{5}=\frac{12}{5} \end{gathered}[/tex]Therefore, both sides are equal.
If R is between G and Z, GZ = 12in., and RG =3in., then RZ =
Given R is between G and Z.
GZ=12 inches
RG=3 inches.
Since, R is between G and Z,
[tex]GZ=GR+RZ[/tex]It follows
[tex]\begin{gathered} RZ=GZ-GR \\ =12-3 \\ =9 \end{gathered}[/tex]So, RZ is 9 inches.
using the converse of the same-side interior angles postulate what equation shows that g∥h
Answer: [tex]\angle 2+\angle 4=180^{\circ}[/tex] or [tex]\angle 1+\angle 3=180^{\circ}[/tex]
How much of the wall does the mirror cover? Use the π button in your calculations and round your answer to the nearest hundredths. Include units.
Since the diameter of the mirror is given, calculate the area of the mirror using the formula
[tex]A=\frac{1}{4}\pi\cdot(D)^2[/tex]replace with the information given
[tex]\begin{gathered} A=\frac{1}{4}\pi\cdot24^2 \\ A=144\pi\approx452.39in^2 \end{gathered}[/tex]The mirror covers 452.39 square inches.
Which of the following could be the points that Jamur plots?
To solve this problem, we need to calculate the midpoint for the two points in each option and check if it corresponds to the given midpoint (-3,4).
Calculating the midpoint for the two points of option A.
We have the points:
[tex](-1,7)and(2,3)[/tex]We label the coordinates as follows:
[tex]\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=2 \\ y_2=3 \end{gathered}[/tex]And use the midpoint formula:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Substituting our values:
[tex](\frac{-1_{}+2_{}}{2},\frac{7_{}+3_{}}{2})[/tex]Solving the operations:
[tex](\frac{1_{}}{2},\frac{10_{}}{2})=(\frac{1_{}}{2},5)[/tex]Since the midpoint is not the one given by the problem, this option is not correct.
Calculating the midpoint for the two points of option B.
We have the points:
[tex](-2,6)and(-4,2)[/tex]We follow the same procedure, label the coordinates:
[tex]\begin{gathered} x_1=-2 \\ y_1=6 \\ x_2=-4 \\ y_2=2 \end{gathered}[/tex]And use the midpoint formula:
[tex]\begin{gathered} (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{Substituting our values} \\ (\frac{-2-4_{}}{2},\frac{6+2_{}}{2}) \\ \text{Solving the operations:} \\ (\frac{-6}{2},\frac{8}{2}) \\ (-3,4) \end{gathered}[/tex]The midpoint for the two points in option B is (-3,4) which is the midpoint given by the problem.
Answer: B (-2,6) and (-4,2)
A rectangular parking lot has length that is 3 yards less than twice its width. If the area of the land is 299 square yards, what are the dimensions of the land?The parking lot has a width of square yards.
Answer:
• Width = 13 yards
,• Length = 23 yards
Explanation:
Let the width of the parking lot = w yards.
The length is 3 yards less than twice its width.
[tex]\implies\text{Length}=(2w-3)\text{ yards}[/tex]The area of the land = 299 square yards.
[tex]w(2w-3)=299[/tex]We then solve the equation above for w.
[tex]\begin{gathered} 2w^2-3w=299 \\ \implies2w^2-3w-299=0 \end{gathered}[/tex]Factor the resulting quadratic expression.
[tex]\begin{gathered} 2w^2-26w+23w-299=0 \\ 2w(w-13)+23(w-13)=0 \\ (2w+23)(w-13)=0 \end{gathered}[/tex]Solve for w.
[tex]\begin{gathered} 2w+23=0\text{ or }w-13=0 \\ 2w=-23\text{ or }w=13 \\ w\neq-\frac{23}{2},w=13 \end{gathered}[/tex]Since w cannot be negative, the parking lot has a width of 13 yards.
Finally, find the length of the parking lot.
[tex]\begin{gathered} 13l=299 \\ l=\frac{299}{13}=23\text{ yards} \end{gathered}[/tex]The length of the parking lot is 23 yards.
Translate to an equation and solve W divided by 6 is equal to 36 w=
Answer:
[tex]w\text{ = 216}[/tex]Explanation:
Here, we want to translate it into an equation and solve
W divided by 6 equal to 36:
[tex]\begin{gathered} \frac{w}{6}\text{ = 36} \\ \\ w\text{ = 6}\times36 \\ w\text{ = 216} \end{gathered}[/tex]4 5 3 7 89 65Each time, you pick one card randomly and then put it back.What is the probability that the number on the card you pickfirst time is odd and the number on the second card you take isa multiple of 2? Keep your answers in simplified improperfraction form.Enter the answer
We have a total of 8 cards, where 3 of them are a multiple of 2, and 5 is an odd number. Consider that event A represents the probability of picking an odd number and event B is picking a multiple of 2. We know that the events are independent (because we put the cards back), therefore the probability of A and B can be expressed as
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]Where
[tex]\begin{gathered} P(A)=\frac{5}{8} \\ \\ P(B)=\frac{3}{8} \end{gathered}[/tex]Therefore
[tex]P(A\text{ and }B)=\frac{5}{8}\cdot\frac{3}{8}=\frac{15}{64}[/tex]The final answer is
[tex]P(A\text{ and }B)=\frac{15}{64}[/tex]A coin is tossed an eight sided die numbered 1 through 8 is rolled find the probability of tossing a head and then rolling a number greater than 6. Round to three decimal places if needed
We are given that a coin is tossed and a die numbered from 1 through 8 is rolled. To determine the probability of tossing head and then rolling a number greater than 6 is given by the following formula:
[tex]P(\text{head and n>6)=p(head)}\cdot p(n>6)[/tex]This is because we are trying to determine the probability of two independent events. The probability of getting heads is given by:
[tex]P(\text{heads})=\frac{1}{2}[/tex]This is because there are two possible outcomes, heads or tails and we are interested in one of the outcomes.
Now we determine the probability of getting a number greater than 6 when rolling the dice. For this, there are 8 possible outcomes and we are interested in two of them, these are the numbers greater than 6 on the die (7, 8). Therefore, the probability is:
[tex]P(n>6)=\frac{2}{8}=\frac{1}{4}[/tex]Now we determine the product of both probabilities:
[tex]P(\text{head and n>6)=}\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}[/tex]Now we rewrite the answer as a decimal:
[tex]P(\text{head and n>6)=}0.125[/tex]Therefore, the probability is 0.125.
Caitlyn is 160 centimeters tall. How tall is she in feet and inches, rounded to the nearest inch?
Answer:
5 ft 3 in.
Explanation:
First, recall the standard conversion rates below.
• 1 foot = 30.48 cm
,• 1 foot = 12 inches
First, convert 160 cm to feet.
[tex]\begin{gathered} \frac{1ft}{30.48\operatorname{cm}}=\frac{x\text{ ft}}{160\text{ cm}} \\ 30.48x=160 \\ x=\frac{160}{30.48} \\ x=5.2493\text{ ft} \\ x=(5+0.2493)\text{ ft} \end{gathered}[/tex]Next, we convert the decimal part (0.2493 ft) of the result above to inches.
[tex]\begin{gathered} 1ft=12\text{ inches} \\ \frac{1\text{ ft}}{12\text{ inches}}=\frac{0.2493\text{ ft}}{y\text{ inches}} \\ y=0.2493\times12 \\ y=2.9916 \\ y\approx3\text{ inches (to the nearest inch)} \end{gathered}[/tex]Therefore, 160 centimeters in feet and inches is:
[tex]5\text{ feet 3 inches}[/tex]can you help me figure out the equation in the drop down menus
To find:
The piecewise function for the graph.
Solution:
From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).
It is known that the equation of a line passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]So, the equation of line passing through (-1, -3) and (-2, -5) is:
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{-2-(-1)}(x-(-1)) \\ y+3=\frac{-2}{-1}(x+1) \\ y+3=2x+2 \\ y=2x-1 \end{gathered}[/tex]So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".
Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:
[tex]\begin{gathered} y-5=\frac{6-5}{2-1}(x-1) \\ y-5=x-1 \\ y=x+4 \end{gathered}[/tex]So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".
14. Given: JM bisects JL JM perpendicular to KLProve: TRIANGLE JMK congruent to TRIANGLE JML
1) is already written, so we start with the second line.
2)
JM is parallel to KL ----> Given
3) ∠KML = ∠JML ----> They are angles on two perpendicular lines, and Since JM bisects LK, they are equal.
4) ∠KJL=∠MKL ---> Since JM bisects ∠J, the angles KJL and MKL are equal
5) ∠JKM=∠JLM ----> Since 3) and 4), the angles JKM and JLM must also be equal so that the sum of internal angles of each triangle will be 180°
Thus: Triangle JMK is congruent to triangle JML
I need help creating a tree diagram for this probability scenario
We need to draw a tree diagram for the information given
The total is 400
120 in finance course
220 in a speech course
55 in both courses
Then we start for a tree for the given number
Then to make the tree for probability we will divide each number by a total 400
Then the probability of finance only is 65/400
The probability of speech only is 165/400
The probability of both is 55/400
The probability of neither is 5/400
The probability of finance or speech is 285/400