Given that:
- You have $200 to spend.
- The store sells all jeans for $25 and all dresses for $50.
- You want to take home 6 items of clothing.
Let be "j" the number of jeans and "d" the number of dresses you can buy so you use the whole $200 (not including the tax).
Set up this System of Equations using the data provided in the exercise:
[tex]\begin{cases}j+d=6{} \\ 25j+50d={200}\end{cases}[/tex]You can follow these steps in order to solve the System of Equations using the Elimination Method:
1. You can multiply the first equation by -25:
[tex]\begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases} \\ ------------ \\ 0j+25d=50 \\ 25d=50 \end{gathered}[/tex]3. Solve for "d":
[tex]\begin{gathered} d=\frac{50}{25} \\ \\ d=2 \end{gathered}[/tex]4. Substitute the value of "d" into the first original equation and solve for "j":
[tex]\begin{gathered} j+(2)=6 \\ j=6-2 \\ j=4 \end{gathered}[/tex]Hence, the answer is: You can buy 2 dresses and 4 jeans.
How does the multiplicity of a zero determine the behavior of the graph at that zero? the drop down options are: is tangent to, crosses straight through, and crosses though while hugging
Given: A seventh-degree polynomial function has zeros of -6, 0 (multiplicity of 2), 1, and 4 (multiplicity of 3).
Required: To determine the behavior of the graph at the zeros.
Explanation: The given seventh-degree polynomial can be represented as
[tex]\left(x+6\right)\left(x-0\right)^2\left(x-1\right)(x-4)^3[/tex]Now, the graph will cross straight through at x=-6 and x=1.
We have an odd multiplicity at x=4; hence the graph will cross through while hugging.
We have an even multiplicity at x=0; therefore, the graph will be tangent.
Here is the graph of the given function-
Final Answer: The graph will cross straight through at x=-6 and x=1,
the graph will cross through while hugging at x=4,
the graph will be tangent at x=0.
What can you say about the 3s in 43,862 and 75,398?4 grade student Lesson Place value relationship
Remember that a place value can be defined as the value represented by a digit in a number based on its position in the number. With decimal numbers, we can have a guide from the decimal point, and with natural numbers, we have a guide from the comma.
So, if we look at the numbers on the exercise we note that
- 3s in 43,862 is placed first before the comma indicating that their place is in the thousands.
- 3s in 75,398 is placed first after the comma indicating that its place is in the hundred.
Explain why this is true.6x1/9=3x2/9
prove that
[tex]6\cdot(\frac{1}{9})=3\cdot(\frac{2}{9})[/tex]start on the left side
[tex]\frac{6}{1}\cdot\frac{1}{9}=\frac{6}{9}=\frac{2}{3}[/tex]continue with the right side
[tex]\frac{3}{1}\cdot\frac{2}{9}=\frac{6}{9}=\frac{2}{3}[/tex]we can conclude that both expressions are equal to 2/3.
Divide and round to the nearest hundredths place25.7 ÷ 0.3
85.67
Explanation:[tex]\frac{25.7}{0.3}[/tex]Using a calculator, the result is 85.6667
To the nearest hundredth: The hundredth position is at second 6. The next number after it is more than 5. So it would be rounded to 1 and added to the second 6
To the nearest hundredth, the answer is 85.67
Dirk is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. Knee pain Ankle pain 3 3 0-12 years old 13-19 years old 2 3 What is the probability that a randomly selected patient is 13-19 years old or suffers from ankle pain? Simplify any fractions.
The probability of a patient being 13-19 years old is
[tex]P=\frac{5}{11}[/tex]The probability of a patient who suffers from ankle pain is
[tex]P=\frac{6}{11}[/tex]Then, we use the following formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Where,
[tex]P(A\cap B)=\frac{5}{11}\cdot\frac{6}{11}=\frac{30}{121}[/tex]Then,
[tex]P(A\cup B)=\frac{5}{11}+\frac{6}{11}-\frac{30}{121}=\frac{91}{121}\approx0.75[/tex]Hence, the probability is 91/121, or 75%.the heart of an elephant, at rest, will beat an average of 1560 beats in 60 minutes. what's the rate in beats per minute?
Hello hope all is well. Can you help me with this i don't understand what I need to write
mean
Explanation:The measures of centaral tendency: mean, median and the mode
The most used one is the mean.
The mean obtained here = 86%
median = 85%
mose = 81%
Since the measures are not in a scale, the mode cannnot be used.
Also there are no missing information in the data set and there are no extreeme outliers.
Most of the data are within the range of the mean gotten.
Hence, Mario should use the mean to convince his parents that he is a maths superstar.
how do I find which of the following statements are true?
Verify each statement
Option A is true because M is between A and B
Option B
Is not true
because AM=AB/2
Option C
Is true
because M is the midpoint
Option D
Is not true
because M is between A and B
Option E
we have
Is true because AB=AM+MB ------> AB-AM=MB
Option F
Is true because AB=AM+MB
Option G
Is not true
because AB=2AM
Option H
Is true
because AB=2AM
Mark used 0.08 of the gas in the tank. What % of the gas in the tank did Mark use?
We know that he used 0.08 of the gas in the tank where 1 represents 100%.
Let's multiply 0.08 by 100 to express it in percentage.
[tex]0.08\cdot100=8[/tex]Hence, Mark used 8% of the gas in the tank.Determine whether the equation x + y2 = 5 is linear. If so, graph the function. If not, explain why.
What is the average mean high temperature and low temperature for the five day period? please explain
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
temperature table
average high temperature = ?
average low temperature = ?
Step 02:
We must calculate the average for the temperatures.
Average high temperature:
Average HT = (22 + 12 + 9 + 23 + 32) °F / 5
= 98 °F / 5
= 19.6 °F ===> rational number
Average low temperature:
Average LT = (0 + (-6) + (-10) + (-14) + 4) °F / 5
= (0 - 6 - 10 - 14 + 4) °F / 5
= - 26 °F / 5
= - 5.2 °F ===> rational number
The answer is:
The average high temperature is 19.6 °F
The average low temperature is - 5.2 °F
Both are rational numbers
Megan scored 5 points less than twice the number scored by Darin. Together they scored a total of 42 points. How many points were scored by Megan?
If Darin scored x points, and Megan scored 5 points less than twice that score, that means Darin scored x while Megan scored 2x - 5. Together they scored a total of 42 points. Adding both scores together, we now have the equation shown;
[tex]\begin{gathered} x+(2x-5)=42 \\ x+2x-5=42 \\ 3x-5=42 \\ \text{Add 5 to both sides } \\ 3x=47 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{47}{3} \\ x=15\frac{2}{3} \\ \text{Therefore Megan scored } \\ 2x-5 \\ =2(\frac{47}{3})-5 \\ =\frac{94}{3}-5 \\ =\frac{32}{3} \\ =10\frac{2}{3} \end{gathered}[/tex]Therefore, Megan scored 10 2/3 points
if point c, shown on the coordinate plane below is reflected over both axes to create c what will be the coordinate of c
Explanation:
The coordinate of c in the plane looks like x= 3 while y = 2
This we assumed because there is no grid line to determine the numbers. The location shows it is within that coordinate
c (3, 2):
Reflecting acrossboth axes means reflecting across the y and reflection across the x axis
Reflection across y axis: (x, y) to (-x, y)
The coordinate of becomes: (-3, 2)
If a quadratic equation can be factored as (ax +b)(ex+d) = 0, what information do these factors provide about the graph of the equation?
Answer:
The 4th choice: The graph of the equation has roots at x = -b/a and x = -d/c
Explanation:
If we have an equation of the form
[tex](ax+b)(bx+c)=0[/tex]then it must be that either
[tex](ax+b)=0[/tex]or
[tex](bx+c)=0[/tex]The first equation gives
[tex]\begin{gathered} ax+b=0 \\ x=-\frac{b}{a} \end{gathered}[/tex]and the second equation gives
[tex]\begin{gathered} cx+d=0 \\ x=-\frac{d}{c} \end{gathered}[/tex]Hence, the roots of the equation turn out to be
[tex]x=-\frac{b}{a},x=-\frac{d}{c}[/tex]Therefore, we conclude that the equation of the form (ax + b) (cx + d) tells us about the roots of the function, and hence, choice 4 is correct.
A hospital has been vaccinating people in two different locations. At the start of the month, Location Ahas reported it has vaccinated 10 thousand people already. Since new shipments have arrived, theyclaim they can now start vaccinating 12 thousand people per week. Location B has vaccinated 40thousand people at the start of the month. They can now vaccinate 6 thousand people per week
For Location A:
People already vaccinated = 10,000
Number of people vaccinated per week after new shipments arrived = 12,000
Number of people vaccinated in location A can be modelled by the Equation
N = 10,000 + 12000x
where x is the number of weeks
When x = 0, N = 10000
When x = 1, N = 10,000 + 12,000(1) = 22,000
When x = 2, N = 10,000 + 12,000(2) = 34,000
When x = 3, N = 10,000 + 12,000(3) = 46,000
When x = 4, N = 10,000 + 12,000(4) = 58,000
When x = 5, N = 10,000 + 12,000(5) = 70,000
When x = 6, N = 10,000 + 12,000(6) = 82,000
For Location B:
People already vaccinated = 40,000
Number of people vaccinated per week after new shipments arrived = 6,000
Number of people vaccinated in location B can be modelled by the Equation
N = 40,000 + 6000x
where x is the number of weeks
When x = 0, N = 40,000
When x = 1, N = 40,000+ 6000(1) = 46000
When x = 2, N = 40,000+ 6000(2) = 52,000
When x = 3, N = 40,000+ 6000(3) = 58,000
When x = 4, N = 40,000+ 6000(4) = 64,000
When x = 5, N = 40,000+ 6000(5) = 70,000
When x = 6, N = 40,000+ 6000(6) = 76,000
The table is shown below
Find the distance between the points (2,4) and (8,2) round to the nearest tenth if necessary
6.3 units
Explanations
The formula for calculating the distance between two points is given as:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given the following coordinate points
A(2,4) and B(8,2)
Substitute the given parameters into the formula to have:
[tex]\begin{gathered} D=\sqrt[]{(8-2)^2+(2-4)^2} \\ D=\sqrt[]{6^2+(-2_{})^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \\ D\approx6.3\text{units} \end{gathered}[/tex]Hence the distance between the points (2,4) and (8,2) round to the nearest tenth is 6.3 units
What is the value of the expression when y = 2?2-y+4 + y3(y + 2)yO 3212
We have the following:
[tex]\frac{2-y}{4+y}+\frac{3(y+2)}{y}[/tex]replacing, y =2:
[tex]\begin{gathered} \frac{2-2}{4+2}+\frac{3(2+2)}{2} \\ \frac{0}{6}+\frac{3\cdot4}{2} \\ 0+\frac{12}{2}=6 \end{gathered}[/tex]the answer is 6, the second option
Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?[?] edges
Using Euler's Formula:
F + V - E = 2
Given:
F = 20, V = 12 and E = a
According to the formula:
20 + 12 - a = 2
32 - a = 2
a = 32 - 2
a = 30
ANSWER
30 edges
the table below gives the price for different numbers of books. is the price proportional to the number of books? number of books 1- price 3 3 books price-9 4 books price-12 7 books price 18
Two quantities are proportional if the ratio between those quantities is always the same.
Find the ratio of price/number of books for each row in the table:
[tex]\begin{gathered} \frac{3}{1}=3 \\ \frac{9}{3}=3 \\ \frac{12}{4}=3 \\ \frac{18}{7}=2.57\ldots \end{gathered}[/tex]We can see that the ratio price:books is 3 if the number of books is 1, 3 or 4 but it is a different ratio when the number of books is 7.
Therefore, the price is not proportional to the number of books.
Sidenote:
If the number of books on the last row was 6 instead of 7, then the ratio would still be 3 and the price would be in fact proportional. Make sure that it is not a printing error of the problem sheet.
the coordinates of the point shown in fig 23.16 are (3,5)
Answer:
False
Explanation:
In the coordinate notation (x, y), the left entry represents the x-coordinate and the right entry the y-coordinate. Therefore, if we want to represent the point x = 5, y = 3, we would write
[tex](5,3)[/tex]Hence, the representation (3, 5) does not represent the point x =5, y = 3, rather, it represents x = 3, y = 5, and therefore, the statement given is false.
I need help on a problem
1.
[tex]PQ\cong RQ\to Given[/tex]2.
[tex]\begin{gathered} \angle PQS\cong\angle RQS\to Given \\ \end{gathered}[/tex]3.
[tex]QS\cong QS\to Reflexive_{\text{ }}property[/tex]4.
[tex]\Delta PQS\cong\Delta RQS\to SAS_{\text{ }}congruence[/tex]5.
[tex]\begin{gathered} \angle P\cong\angle R\to CPCTC_{} \\ \end{gathered}[/tex]4. Pietro buys 24 candy bars for $6. He plans to sellall 24 candy bars in 1 day. He needs to make aprofit of $12 per day to meet his fundraising goal.How much must he charge for each candy bar?(Hint: He spent $6 on the candy bars so his startingprofit is $-6. How much does he need to make inorder to have a profit of $12?)He needs to charge $per candy bar.
The cost of the 24 candy bars is $6.
If he is to make a profit of $12, that means that he must sell all the candy bars for:
[tex]\Rightarrow12+6=18\text{ dollars}[/tex]Since there are 24 candy bars, the cost of 1 candy bar can be calculated to be:
[tex]\Rightarrow\frac{18}{24}=0.75\text{ dollars}[/tex]He needs to charge $0.75 per candy bar.
Identify the volume of a rectangular pyramid with length 7 cm, width 15 cm, and height 16 m.
To answer this question, we will use the following formula for the volume of a rectangular pyramid:
[tex]V=\frac{lwh}{3},[/tex]where l is the length, w is the width, and h is the height.
Substituting w= 15 m, l = 7 m, and h = 16 m in the above formula, we get:
[tex]V=\frac{15m\cdot16m\cdot7m}{3}\text{.}[/tex]Simplifying the above result we get:
[tex]V=560m^3.[/tex]Answer:
[tex]560m^3.[/tex]What is the value of x in the equation 7x+2y=48, when y=3?
We have the following equation:
[tex]7x+2y=48[/tex]Which represents a line, and we need to determine the value of x when y = 3.
To achieve that, we can proceed as follows:
1. Substitute the value of y = 3 into the equation:
[tex][/tex]In 30 words of your identify which form slope intercept or point slope would be better to use why
As indicated in the question, parallel lines have the same slope.
This means the slope of the fourth parallel line is also 2. A point on that line has been identified as;
[tex](3,15)[/tex]Using the point-lope form which is;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where,} \\ x_1=3,y_1=15 \\ \text{The equation becomes;} \\ y-15=2(x-3) \end{gathered}[/tex]Further simplified, this now becomes;
[tex]\begin{gathered} y-15=2(x-3) \\ y-15=2x-6 \\ \text{Add 15 to both sides;} \\ y=2x+9 \end{gathered}[/tex]ANSWER:
It would be better to use the point-slope form to derive the equation of the 4th line because we already have the slope and one point on the equation.
Which points are on the graph of a linear function? Select all that apply
We will determine the points that belong to a linear function as follows:
*First set: We calculate the slope of the three points:
[tex]m_1=\frac{5-7}{0-(-1)}\Rightarrow m_1=-2[/tex][tex]m_2=\frac{3-7}{1-(-1)}\Rightarrow m_2=-2[/tex]So, the first set belongs to a linear function.
*second set:
[tex]m_1=\frac{0-1}{0-(-1)}\Rightarrow m_1=-1[/tex][tex]m_2=\frac{1-1}{1-(-1)}\Rightarrow m_2=0[/tex]So, the second set does not belong to a linear function.
*Third set:
[tex]m_1=\frac{5-5}{2-0}\Rightarrow m_1=0[/tex][tex]m_2=\frac{14-5}{3-0}\Rightarrow m_2=3[/tex]So, the third set does not belong to a linear function.
*Fourth set:
[tex]m_1=\frac{5-(-3)}{2-0}\Rightarrow m_1=4[/tex][tex]m_2=\frac{13-(-3)}{4-0}\Rightarrow m_2=4[/tex]So, the fourth set belongs to a linear function.
which of the following is not a line of symmetry in the figure below
From the graph the line of symmetry is the line that divides the shape into two equal halves
These lines are at
1) x = -4
2) y = 4
3) y = -x
An equation of a line that does not divides the shape into equal halves is not a line of symmetry
Ray and Jon play a game of chance with two dice. If the sum of the dice is seven, Ray pays Jon $15. But if the sum is anything else, Jon pays Ray $10. What is the expected value of the game for Jon?Answer:
Step 1
[tex]\text{Probability of any event = }\frac{\text{number of required outcomes}}{n\text{umber of possible outcomes}}[/tex]Step 2:
Draw the table of the possible outcomes.
Step 3:
Draw the table for the expected value
Number of the sum of seven = 6
Number of anything else = 30
Total possible outcomes = 36
[tex]\begin{gathered} \text{Expected value formula = Value }\times\text{ Probability of event} \\ \text{Expected value formula = xp(x)} \end{gathered}[/tex]Final answer
The expected value of the game for Jon
[tex]\begin{gathered} =\text{ }\frac{15}{6}\text{ + }\frac{50}{6} \\ =\text{ }\frac{65}{6}\text{ } \\ =\text{ 10.83} \end{gathered}[/tex]What are some numbers that equal -3Here’s my equation:-5XAnd then what number could I put for the Y so it could equal -3
Equation y = -5x
-3 = -5x
Solve for x
x = -3/-5
x = 3/5 y = -3
This is my answer, could you check it please?
Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase er decrease.y = 2500(1.04)
The equation of a exponential function is of the form
[tex]y=a(b)^x[/tex]where
b is the base of the exponential function
If the value of b>1 -----> is a growth function
If the value of b<1 ----> is a decay function
In this problem
b=1.04
1.04 > 1
therefore
Is a growth functionPart b
Determine the percentage rate of increase
we have that
b=1+r
r=b-1
r=1.04-1
r=0.04
convert to percentage
r=0.04*100
r=4%