a. What are the keywords and information needed to solve this problem?
The keywords are the words that allow us to solve the problem, So they are:
The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. Write the inequality that describes this situation.
Now, we can formulate an equation for the number of hamburgers H that each guest is going to receive if Radash buys p packages:
H = 8p/62
Because 8p is the number of total hamburgers and there are 62 guests.
Then, we know that H needs to be at least 1, so:
H ≥ 1
8p/62 ≥ 1
c. How many packages of hamburgers will Rashad need to purchase to feed his guests?
Then, we need to solve for p as:
Multiplying by 62 on both sides:
(8p/62)*62 ≥ 1 * 62
8p ≥ 62
Dividing by 8:
8p/8 ≥ 62/8
p ≥ 7.75
Therefore, Radash needs to buy at least 8 packages of hamburgers.
Answers:
a. The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. 8p/62 ≥ 1
c. At least 8 packages
Please help with this math problem so my son can understand better I have attached the image. For some reason he keeps getting it incorrect cause he's not sure were the point should be placed on the graph please help.
Step 1
Choose input values for x for both equations based on his graph. The x-values on his graph sheet range from -10 to 10. we will choose; -10, -8,0,4 and 10.
Step 2
Input these x-values in the first equation and get values for the output y.
[tex]\begin{gathered} 3x+y=6 \\ \text{Transforming the above equation we will have; y=6-3x} \\ y=6-3x \\ x=-10 \\ y=6-3(-10) \\ y=6+30 \\ y=36 \\ \text{First point(-10,36)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=-8} \\ y=6-3(-8) \\ y=6+24 \\ y=30 \\ \text{second point}(-8,30) \end{gathered}[/tex][tex]\begin{gathered} \text{If x=0} \\ y=6-3(0_{}) \\ y=6 \\ \text{Third point(0,6)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=4} \\ y=6-3(4) \\ y=6-12 \\ y=-6 \\ \text{Fourth point(4,-6)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=10} \\ y=6-3(10) \\ y=6-30=-24 \\ \text{fifth point(10,-24)} \\ \end{gathered}[/tex]Step 3
Find similar points using the same x values for line 2, the second equation
[tex]\begin{gathered} -3x-4y=12 \\ -4y=12+3x \\ -\frac{4y}{-4}=\frac{12}{-4}+(\frac{3x}{-4}) \\ y=-3-\frac{3x}{4} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=-10, points are }(-10,4.5) \\ \text{If x=-8 points are (-8,}3) \\ \text{if x =0 points are (}0,-3) \\ \text{if x=4 points are (4,}-6) \\ \text{if x=10 points are (10},-10.5) \end{gathered}[/tex]Evaluate the expression for r = 4, s = -4, and t = 6. 8+s^2(t +4-4r)
Given the below expression;
[tex]8+s^2(t+4-4r)[/tex]We're asked to evaluate for r = 4, s = -4 and t = 6, all we need to do is substitute the given values of r, s and t into the expression above;
[tex]\begin{gathered} 8+(-4)^2\lbrack(6)+4-4(4)\rbrack \\ \end{gathered}[/tex]Let's go ahead and clear the brackets and solve;
[tex]\begin{gathered} 8+16(-6) \\ =8-96 \\ =-88 \end{gathered}[/tex]Therefore, our answer is -88.
Help find the unit prices while rounding to the nearest cent.
It is clear that brand A has the lower unit price hence it is the better buy.
Which is the better buy?We know that the better buy has to do with the commodity that would give us the least unit price for the item. Hence we must have to look at the unit price of each of the items before we decide the better buy. The unit price is the price of only one spoon.
In the first case;
Unit price = $2.17/42 = $0.05
In the second case;
Unit price = $3.97/48
= $0.08
The brand that has a higher unit price here is Brand B.
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What is the scale factor of a pair of figures whose preimage has coordinates(2, 3), (3, 1), and (4,5), and whose image has coordinates (4, 6), (6, 2), and (8, 10)?
The scale factor is a factor that affects coordinate x and y of all the points in an image, using one of the points of th preimage and the image we can find the realtion between both
[tex](2,3)\rightarrow(4,6)[/tex]if we analyse this the scale factor is 2, since both x and y coordinate are doubling the pre image.
Also if we analyse the other 2 points the same happens.
Answer:
The scale factor is a factor that affects coordinates x and y of all the points in an image; using one of the points of the preimage and the image, we can find the relation between both
If we analyze this, the scale factor is two since both the x and y coordinates are doubling the pre-image.
Also, if we analyze the other 2 points, the same happens.
Step-by-step explanation:
Exam Instructions.Question 11 of 20 :Select the best answer for the question11. Which of the following statements about trapezoids is true?O A. Both pairs of opposite sides are parallel.O B. One pair of opposite sides is parallel.O C. Opposite angles are congruent.OD. Opposite sides are congruent.+ 5Mark for review (Will be highlighted on the review page)
Consider that trapezoid is a type of quadrilateral, which has one pair of opposite sides unequal but parallel, and the other pair of opposite sides are non-parallel.
Now, read the options carefully. We have to mark the option that is always true for a trapezoid.
Option A:
It is not necessary for a trapezoid to have both pairs of opposite sides as parallel. Only one pair being parallel is required for a quadrilateral to be a trapezoid.
Option B:
As discussed above, the statement is correct for every trapezoid.
Option C:
This is not a necessary condition for a trapezoid. There exist some trapezoids that don't have the opposite angles congruent.
Option D:
Again, this is not a necessary condition for a trapezoid. Since one pair of sides is non-parallel, the other pair must be unequal.
Therefore, it can be concluded that option B is the correct choice.
Use the figure below to complete the following problem.Given:ZH= 2x + 60Z T= x+ 30HALT is aT=
Answer: 60 degrees
The figure there is a parallelogram
< H = 2x + 60
< T = x + 30
Therefore, supplementary angles is 180 degrees
< H + < T = 180
2x + 60 + x + 30 = 180
Collect the like terms
2x + x + 60 + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
Divide both sides by 3
3x/3 = 90/3
x = 30
Since < T = x + 30
Hence,
< T = 30 + 30
< T = 60 degrees
Graph the equation Y =7x
step 1
we have the equation
y=7x
This is the equation of a line that passes through the origin (0,0)
To graph a line we need at least two points
so
assume any value of x and then calculate the value of y
For x=2
y=7(2)=14
the second point is (2,14)
step 2
Graph the line
Plot the points (0,0) and (2,14)
join them to graph the line
using a graphing tool
see the figure below
6 of the people in Bob's family like dolphins and 6 like polar bears. 3 people like both dolphinsand polar bears. How many people like dolphins but not polar bears?
ANSWER
3
EXPLANATION
To answer this question we can make a Venn diagram. Each circle will represent the people who like dolphins and the people who like polar bears. We know that 3 people like both, so there are 3 people in the area shared by both circles. If 6 people like dolphins and 6 like polar bears, knowing that already 3 people are in the area shared by both circles, in the individual area of each circle there will be 3 people:
So, we can see that there are 3 people out of the 6 that like dolphins that also like polar bears.
Hence, there are 3 people that like dolphins but not polar bears.
The circumcenter of a triangle is also the center ofA. a circle inscribed inside the triangleB. mass and balanceC. a circle circumscribing the triangleD. all of these
We have that the circumcenter is located at the intersection of the perpendicular bisectors of the sides if we have a circle circumscribing the triangle the enter of this circle will be the circumcenter of the triangle
therefore the correct answer is C.
Write the inequality shown by the shaded region in the graph with the boundary line y = 1/3x+1
From the graph, the suitable inequality is
[tex]y\leq\frac{1}{3}x+1[/tex]On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made adeposit, and those deposits were equal to each other.(a) Explain how you can determine, just by looking at the graph, whether the amounts she depositedafter Day 16 were each less than $100, $100, or more than $100.(b) Use the graph to estimate B(21) in hundreds. Explain how you determined this estimate. Then showhow you can estimate the amount of money Ebony deposited into her account each day after Day 16.
Given that on day 15 the balance was $0 and on day 16 the balance is $100, then we have:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{100-0}{16-15}=100 \\ \text{for point (15,0) and slope m=100:} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-0=100(x-15) \\ \Rightarrow y=100x-1500 \end{gathered}[/tex]we have that the relation function for this period is B(x)=100x-1500. Then for x=21 we have the following:
[tex]\begin{gathered} B(x)=100x-1500 \\ B(21)=100\cdot21-1500=2100-1500=600 \\ \end{gathered}[/tex]therefore, using the relation function, we have that B(21) = 600.
To find the amount of money deposited into the account after day 16, we have to find B(17), B(18), B(19) and B(20):
[tex]\begin{gathered} B(17)=100\cdot17-1500=1700-1200=200 \\ B(18)=100\cdot18-1500=1800-1500=300 \\ B(19)=100\cdot19-1500=1900-1500=400 \\ B(20)=100\cdot20-1500=2000-1500=500 \end{gathered}[/tex]solve the following system of equations using substitution.y=2x-2-4x-y=26solve for x and y m
system equation is
y = 2x - 2
-4x - y = 26
we will be solving this equation simultaneously by using substitution method
y = 2x - 2 --------- equation 1
-4x - y = 26 ------- equation 2
substiute y = 2x - 2 into equation 2
equation 2 becomes
-4x - (2x - 2) = 26
-4x - 2x + 2 = 26
collect the like terms
-4x -2x = 26 - 2
x(-4 - 2) = 24
x(-6) = 24
-6x = 24
to find x, divide both sides by -6
-6x/-6 = 24/-6
x = 24/-6
x = -4
to find y put x = -4 into equation 2
-4x - y = 26
-4(-4) - y = 26
16 - y = 26
collect the like terms
-y = 26 - 16
-y = 10
divide both sides by -1
-y/-1 = 10/-1
y = -10
the answer is x= -4 and y = -10
Using elimination method for the following equation
5x + y = 24
-5x - 4y = -56
in elimination method, you need to eliminate one of the variables before you can get the other variable
so let us eliminate x first
5x + y = 24
-5x -4y = - 56
since the second equation have a negative value of 5x then, we need to sum up the two equations to eliminate x
5x + (-5x) + y +(-4y) = 24 + (-56)
0x + y - 4y = 24 -56
-3y = -32
divide both sides by -3
-3y / -3 = -32/-3
y = 32/3
The answer is 32/3
3. Calculate the:RadiusBase Area of the coneVolume of the Cone (solve b only)
Answer:
• (a)The radius of the cone is 8cm.
,• (b)The base area of the cone is 200.96 cm².
,• (c)The volume of the cone is 1004.8 cm³.
Explanation:
(a)Radius
Using the right triangle above, we find the radius of the cone using the Pythagorean theorem.
[tex]\begin{gathered} 17^2=15^2+r^2 \\ r^2=17^2-15^2 \\ r^2=64 \\ r^2=8^2 \\ r=8\text{ cm} \end{gathered}[/tex]The radius of the cone is 8cm.
(b)Base Area of the cone
The base of the cone is a circle.
In part(a), the radius of the circle was found to be 8 cm.
[tex]\begin{gathered} \text{ The area of a circle}=\pi r^2 \\ =3.14\times8^2 \\ =200.96\;cm^2 \end{gathered}[/tex]The base area of the cone is 200.96 cm².
(c)Volume of the cone
The volume of a cone is calculated using the formula:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Substitute the values: π=3.14, h=15cm, r=8cm
[tex]\begin{gathered} V=\frac{1}{3}\times200.96\times15 \\ =1004.8\;cm^3 \end{gathered}[/tex]The volume of the cone is 1004.8 cm³.
Select all intervals where h is increasing A:-5
Given the graph of the function y = h(x) as shown below
From the plot, it's observed that h increases at the interval as shown below
Thus, h is increasing at the intervals
[tex]-2 The correct option is BA battery is charged. The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed 0 IT) HE + What was the battery's charging level when the charging began?
look closely to the graph
when the time (which is on the x-axis) was zero (0),
the capacity of the battery (which is on y-axis) was already at 40% left
Now, the battery's charging level when the charging began was 40%
Solve the equation graphically and check the solution. 2x+5y=0. X+6y=14
Given:
The system of equations is,
[tex]\begin{gathered} 2x+5y=0 \\ x+6y=14 \end{gathered}[/tex]First, find the points on both lines to draw the graph of the line.
Then find the point of intersection of the line.
[tex]\begin{gathered} 2x+5y=0 \\ x=0\Rightarrow y=0 \\ x=5\Rightarrow y=-2 \\ x=-10\Rightarrow y=4 \end{gathered}[/tex]And,
[tex]\begin{gathered} x+6y=14 \\ x=0\Rightarrow y=\frac{7}{3} \\ x=14\Rightarrow y=0 \\ x=-10\Rightarrow y=4 \end{gathered}[/tex]The graph is,
As the point of intersection is (-10,4).
The solution of the given system of equation is x = -10 and y =4
does 1/2y+ 3.2y=20 have a solution?
3.7 is multiplying on the left, then it will divide on the right
[tex]\begin{gathered} y=\frac{20}{3.7} \\ y\approx5.4 \end{gathered}[/tex]The graph shows f(x) (1/2) and it transitions, g(x). Witch discribes the translation of (x) to g (x)
The translation from f(x) to g(x) is a translation of 4 units up (option A)
Explanation:Given:
Graph of f(x) =(1/2)^x ang g(x)
To find:
the transformation from f(x) to g(x)
To determine this, we will pick points on the x-axis and compare the result on the y axis for both graphs
when x = 0
f(x) = 1
g(x) = 5
The difference in value = 5 - 1 = 4
when x = 5
f(x) = 0
g(x) = 4
The difference in value = 4 - 0 = 4
We see the difference in value for the y is constant. This means to get g(x), we will add 4 units to the y coordinates of f(x)
The translation from f(x) to g(x) is a translation of 4 units up (this is because the value of y is positive and on the graph g(x) moves above f(x) on the vertical)
What is the Identity Property of multiplication?Select one:a. The product of 2 and any number is that number. b. The product of 1 and any number is that number.c. The product of 10 and any number is that number.
The Identity Property of multiplication is a property that states that there exist a number such that when you multiply it to second number, the product is still the second number.
The product of 1 and any number is that number.
Find the half-life (in hours) of a radioactive substance that is reduced by 5 percent in 75 hours.half life = ___ include units
Let's list down the given information.
Time = 75 hours
Final Value = reduced by 5% = 95%
To get the half life, the formula is:
[tex]t=\frac{\ln 0.5}{k}[/tex]Before we can get the half-life, we need to get the value of k or the decay rate first. The formula is:
[tex]k=\frac{\ln A}{t}[/tex]where A is the final value in percentage and t = time. Since we have this information above, let's plug it in the formula and solve for k.
[tex]k=\frac{\ln0.95}{75}=-0.0006839105918[/tex]Now that we have the value of "k", let's solve for "t" using the formula stated above as well.
[tex]t=\frac{\ln 0.5}{k}=\frac{\ln 0.5}{-0.0006839105918}=1013.51[/tex]Hence, the half life of the radioactive substance is approximately 1,013.51 hours or 1,013 hours and 30 minutes.
I have no clue on how to do this, someone help me please!
(a) Let the total cost of renting a company truck = C
Let the drive unit per miles = d
Hence the formular = C(d) = $36.95 + 0.7d
(b) If the truck was driven for 45 miles, then the Cost of renting a company truck
[tex]\begin{gathered} C(d)\text{ = \$36.95 + 0.7(45)} \\ C(d)\text{ = \$36.95 + 31.5} \\ C(d)\text{ = \$68.45} \\ C(d)\text{ = \$68.5} \end{gathered}[/tex]
(c) Suppose you have a $100 budget the move, the
If the truck was driven with that budget then the further distance covered by the truck is
[tex]\begin{gathered} C(d)\text{ = \$36.95 + 0.7d} \\ \text{ \$100= \$36.95 + 0}.7d \\ \text{\$}100\text{ - \$36.95 = 0.7d} \\ \text{ \$63}.05\text{ = 0.7d} \\ \text{ d = }\frac{\text{ 63.05}}{7} \\ \text{ d = 90.007 miles} \\ \text{ d = 90miles (nearest miles)} \end{gathered}[/tex]
The miles per gallon(mpg) measurement for the fuel economy for a brand of compact car is approximately normally distributed with the mean u= 26.7 mpg and standard deviation o=7.2 mpg Let x= fuel economy( in miles per gallon) A) what percent of compact cars( for this brand) have a fuel economy grater than 26.7 mpg?Answer: ( include the percent (%) symbol in your answer) B) What is the z-score( or standard score) for fuel economy of 25 mpg ( rounded to 2 decimal places)?Answer: z= C) find the probability that a random selected new compact ( from this brand) has a fuel economy less than 25 mpg. Write your answer as a complete probability statement. Do not round your answer. Answer:
Given
mean = 26.7 mpg
standard deviation =7.2 mpg
Find
a) what percent of compact cars( for this brand) have a fuel economy greater than 26.7 mpg
b) What is the z-score( or standard score) for fuel economy of 25 mpg
c) find the probability that a random selected new compact ( from this brand) has a fuel economy less than 25 mpg.
Explanation
a)
mean = 26.7 mpg
standard deviation =7.2 mpg
P(X > 26.7) =
[tex]\begin{gathered} P\left(X>26.7\right)=P(\frac{X-\mu}{\sigma}>\frac{26.7-26.7}{7.2}) \\ \\ =P(Z>0) \\ =0.5 \end{gathered}[/tex]b)
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ =\frac{25-26.7}{7.5} \\ =-0.22667 \\ =-0.23 \end{gathered}[/tex]c)
[tex]\begin{gathered} P(Z<-0.23)=P(Z>0.23) \\ =1-P(Z\leq0.23) \\ =1-0.590954 \\ =0.409046 \\ =0.40905 \end{gathered}[/tex]Final Answer
a)
b)
c)0.40905
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.7 % loan. Frederick doesn't want to pay more than $423 in interest. How many years does Frederick have to pay back the loan? years
Given:
The initial money = $3000
Rate = 4.7% = 0.047
Frederick doesn't want to pay more than $423 in interest.
So, we need to find the number of years
Assume simple interest rate:
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=423 \\ P=3000 \\ r=0.047 \\ \\ 423=3000\cdot0.047\cdot t \\ 423=141\cdot t \\ \\ t=\frac{423}{141}=3 \end{gathered}[/tex]so, the number of years = 3 years
Hi could you help me with my homework Number 1
Slope-intercept form:
[tex]y=mx+b[/tex]This form reveal the slope (m) that describes the steepness of a line, and the y-coordinate of the y-intercept (b) (The y-intercept has coordinates (0,b))
The graph shows the cost,c, in dollars of using a food-delivery service for w weeks which equation represents the cost of food-delivery service?
A c=1/60w
B w=60c
C c=60w
D c=60
show ur work plsssssssssssssss
Picture:
The equation for a straight line can be found if its slope and coordinate of the point it passes through is given. The equation for the given graph is c = 60w. The correct answer is option C.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The cost of food delivery is taken as c.
The number of weeks is w.
Since the graph given in the problem is a straight line, in order to find its equation its slope has to be found as follows,
From the graph, it is clear that at w = 2, c = 120.
Now, there are two points for the given straight line as (0, 0) and (2, 120).
Thus, the slope is given by (120 - 0) / (2 - 0) = 60
Then the equation for the straight line is,
(c - 0) / (w - 0) = 60
=> c = 60w
Hence, the equation of the given graph is c = 60w.
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Solve for tH=1/2gt^2+v0t(note that the 0 is like an exponent but lower than the v)
Let's solve for t, the following equation:
H = 1/2gt^2 + v0t
Using the quadratic formula, we have:
t = - (v +/- √v² + gh)/g
How to evaluate:16% of 575102% of 75080 is 25% of what number?
you can evaluate a percentage like follow.
the 16% of 575 is 0.16(575)=345
the 102% of 250 will be 750
Can you explain/show the steps to me how to solve
Step 1: Identify the overall set
Which in this case is the Dangerous
Step2: poisonous things are dangerous
These are contained in the dangerous things, hence contained in the big circle
Step3: Some Chemicals are poisonous
Then the chemicals are contained in the poisonous things
Hence since some chemicals are poisonous then they are dangerous as in the diagram above
Therefore the argument is valid
hurry and anwser please im dying
Answer:
the answers to your question would be 65 aka D
The students in Mr. Collin's class used a surveyor's measuring device to find the angle from their location the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. Building 100 2400 ft b. 72 ft 308 ft 33 ft D
The height of the building is 308 ft
here, we want to get the height of the building
From what we have, the angle given faces the building which makes the building the opposite
The length given does not face the angle nor the right-angle and that makes it the adjacent
The relationship between the opposite and the adjacent is the tan
In fact, tan is the ratio of the opposite to the adjacent
Let us call the height of the buliding h
Thus, we have it that;
[tex]\begin{gathered} \tan \text{ 72 = }\frac{h}{100} \\ h\text{ = 100}\times\tan \text{ 72} \\ h\text{ = 307.76} \\ h\text{ = 308 ft} \end{gathered}[/tex]