Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.
Calculating how to fill a container rightSince Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses
From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.
What is a Pitcher
Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.
Learn more about container here:
https://brainly.com/question/30361079
#SPJ1
A plane is flying at a speed of 360 miles per hour on a bearing of N * 65 deg * E Its ground speed is 390 miles per hour and its true course, given by the direction angle of the ground speed vector, is 30 deg Find the speed, in miles per hour, and the direction angle, in degrees, of the wind.
Answer:w = 74.66 mph
d = 19.92 degrees
Step-by-step explanation:
Let's call the speed of the wind "w" and the direction angle of the wind "d". We can use vector addition to solve for these unknowns.
First, let's find the direction of the plane. The bearing of N * 65 deg * E can be represented as a vector with an initial point at the North pole and a terminal point 65 degrees east of due north. Since the plane is flying on this bearing, its direction vector is the same as the bearing vector. We can find the components of this vector as follows:
cos(65) = x / 1
x = cos(65)
y = sin(65)
So the direction vector of the plane is <cos(65), sin(65)>.
Next, let's find the ground speed vector. We can represent this vector as the sum of the plane's airspeed vector and the wind vector:
ground speed = airspeed + wind speed
We know that the magnitude of the ground speed vector is 390 mph, and we know the direction angle of the ground speed vector is 30 degrees. We can use this information to set up two equations:
|airspeed + wind speed| = 390
tan(d) = (wind speed)_y / (wind speed)_x
Since we know the direction vector of the plane, we can express the airspeed vector in terms of this vector as follows:
airspeed = 360 <cos(65), sin(65)>
Now we can substitute the airspeed vector and the wind speed vector into the equation for the ground speed vector, and use the fact that the magnitude of the ground speed vector is 390 to solve for the components of the wind speed vector:
|360 <cos(65), sin(65)> + <(wind speed)_x, (wind speed)_y>| = 390
Squaring both sides and using the fact that cos^2(x) + sin^2(x) = 1, we get:
129600 cos^2(65) + 129600 sin^2(65) + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Simplifying, we get:
51840 + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Substituting the equation for the direction angle of the wind and simplifying, we get:
51840 + 720w cos(65 - d) + w^2 = 152100 tan^2(d)
We now have two equations and two unknowns: w and d. We can solve for them using algebra or a numerical solver. Using a numerical solver, we find:
w = 74.66 mph
d = 19.92 degrees
Therefore, the speed of the wind is 74.66 mph, and its direction angle is 19.92 degrees.
You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2
HELP ME PLEASE AND SHOW WORK THANK YOU WILL MARK BRAINLIEST.
Based on the image, we can infer that the router cannot cover the kitchen area.
How to calculate if the router covers the living room and kitchen area?To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.
From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.
Learn more about routers in: https://brainly.com/question/29869351
#SPJ1
Please can someone assist me on this question I have no idea
Answer:
x2+10x+25
Step-by-step explanation:
It goes like this:
X2+2*1x*5+5*5
Ilana is training for a half marathon. For the first three days of her training plan, she will need to run 4.125 miles each day. For the next two days she will increase her mileage to 5.675 miles per day. How many miles total did Ilana run during her first training week?
Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.
What does distance mean?Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.
According to the given informationIlana will run 4.125 miles each day for the first three days, which gives a total distance of:
4.125 miles/day × 3 days = 12.375 miles
For the next two days, she will run 5.675 miles per day, which gives a total distance of:
5.675 miles/day × 2 days = 11.35 miles
To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:
12.375 miles + 11.35 miles = 23.725 miles
Therefore, Ilana ran a total of 23.725 miles during her first week of training.
To know more about distance visit:
brainly.com/question/29172881
#SPJ1
parallel and perpendicular line math homework
a. The slopes of the lines are:
Slope of line 1 = -5/2
Slope of line 2 = 7/5
Slope of line 3 = -5/2
b.
Line 1 and Line 2 : Neither
Line 1 and Line 3 : Parallel
Line 2 and Line 3 : Neither
Calculating the slope of linesFrom the question, we are to determine the slope of each of the given lines:
Using the formula,
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope
(-4, 7) and (-2, 2)m = (2 - 7) / (-2 - (-4))
m = (-5) / (2)
m = -5/2
(0, -1) and (-5, -8)m = (-8 - (-1)) / (-5 - 0)
m = (-7) / (-5)
m = 7/5
(-2, 8) and (2, -2)m = (-2 - 8) / (2 - (-2))
m = (-10) / (4)
m = -5/2
b.
NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.
Thus,
Line 1 and Line 2 : Neither
Line 1 and Line 3 : Parallel
Line 2 and Line 3 : Neither
Learn more on Calculating the slope of lines here: https://brainly.com/question/3493733
#SPJ1
Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously?
Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18
What is continous compounding interest formula?The continuous compounding interest formula is given by P = Peⁿˣ where
P = final amount after time, t, P' = initial amount n = interest rate and x = timeSince Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.
Given that
P' = $7000n = 50% per year = 0.5 per year andx = 5 yearsSubstituting the values of the variables into the equation, we have that
P = Peⁿˣ
P = $7000e⁰°⁵ ˣ ⁵
P = $7000e⁰°²⁵
P = $7000(1.28)
P = $ 8988.18
So, the amount of debt owed is $ 8988.18
Learn more about continuously compounded interest here:
https://brainly.com/question/30446525
#SPJ1
HELP PLEASE
at big 5, the percent of sales tax is 6 percent. you want to buy a skateboard that costs 98 dollars. you have 100 dollars to spend. do you have enough money? if you don't, how much more money would you need in order to buy the skateboard.
You would need an additional $3.88 to buy the skateboard.
To find out if you have enough money to buy the skateboardWe need to calculate the total cost, including sales tax.
The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:
tax = 0.06 x $98 = $5.88
Consequently, the skateboard would have a total cost of:
total cost = $98 + $5.88 = $103.88
Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:
additional money = $103.88 - $100 = $3.88
Therefore, you would need an additional $3.88 to buy the skateboard.
Learn more about cost here : brainly.com/question/28147009
#SPJ1
PLS HELP ASAP
I AM SO CONFUSED WID THIS!
The numbers 1-20 are written on pieces of paper and put in a box. Two pieces of paper are randomly selected and not replaced.
a) Are the events dependent or independent? _________
b) What is the probability of selecting a number less than 6 both times? ________
the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.
how to find probability ?a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.
b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.
The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.
Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.
To find the probability of both events occurring, we multiply the probabilities:
P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)
P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19
Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.
To know more about probability visit :-
https://brainly.com/question/30034780
#SPJ1
The estimated population of a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
49,372
58,207
66,998
75,798
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.
How to determine that it is a linear functionTo determine which type of function best fits the data, we can analyze the difference in the y values (Estimated Population) as x increases.
Differences between consecutive y values:
58,207 - 49,372 = 8,835
66,998 - 58,207 = 8,791
75,798 - 66,998 = 8,800
The differences between consecutive y values are relatively constant as x increases. This suggests that a linear function would be more appropriate than an exponential function
Read more on linear function here:https://brainly.com/question/15602982
#SPJ1
100 Points!!! Algebra question. Find the third term of (11x+3y)^6. Photo attached. Please show as much work as possible. Thank you!
Answer: If you are trying to find the third derivative
It would be f'''(x)=159720(11x+3y)^3
Step-by-step explanation:
The third term of the given expression [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].
The binomial theorem states that [tex](a+b)^n[/tex] can be expanded as follows:
[tex](a+b)^n[/tex] = nC0*[tex]a^n[/tex] + nC1*[tex]a^{n-1[/tex]*b + nC2*[tex]a^{n-2[/tex]*[tex]b^2[/tex] + ... + nCn*[tex]b^n[/tex]
where nCk is the binomial coefficient, which is defined as n! / k!(n-k)!.
In this case, we have [tex](11x+3y)^6[/tex], so n = 6.
The third term of the expansion is given by nC2[tex]a^{n-2[/tex][tex]b^2[/tex], which is equal to 6C211[tex]x^4[/tex]3[tex]y^2[/tex].
6C2 is equal to 6! / 2!4! = 15, so the third term is equal to 1511[tex]x^4[/tex]3[tex]y^2[/tex] = 135[tex]x^4y^2[/tex].
Therefore, the third term of [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].
Here is a breakdown of the steps:
Find the binomial coefficient nC2.
Multiply nC2 by 11[tex]x^4[/tex] and 3[tex]y^2[/tex].
Simplify the expression.
The answer is 135[tex]x^4y^2[/tex].
To learn more about expression here:
https://brainly.com/question/34132400
#SPJ2
What is the surface area of a triangular prism
Answer:
surface area=bh+2ls+lb
Step-by-step explanation:
If you think it is too long to remember, just find the area of each of the shapes on it and add them together.
Hope this helps :)
HELP!!!!!!!! Which system of linear equations can be solved using the information below?
The system of linear equations that can be solved from the matrices is given as follows:
-5x + 4y = 3.-8x + y = -6.How to obtain the system of equations?Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:
A = [-5 4; -8 1]
Hence the multiplication of matrices representing the system is given as follows:
[-5 4; -8 1][x; y] = [3; -6]
Applying the multiplication of matrices, the system of equations is given as follows:
-5x + 4y = 3.-8x + y = -6.More can be learned about a system of equations at https://brainly.com/question/13729904
#SPJ1
What is the probability that
both events will occur?
First, find the probability of event A.
Two dice are rolled.
Event A: The first die is a 4 or less.
Event B: The second die is even.
The probability that both events A and B will occur is 1/3 or approximately 0.3333.
To find the probability of both events A and B occurring, we need to calculate the individual probabilities of each event and then multiply them together.
Event A: The first die is a 4 or less.
In a standard six-sided die, there are four outcomes (1, 2, 3, 4) that satisfy this condition. Out of the six possible outcomes, four are favorable, so the probability of event A is 4/6 or 2/3.
Event B: The second die is even.
In a standard six-sided die, there are three even outcomes (2, 4, 6) out of the six possible outcomes.
Therefore, the probability of event B is 3/6 or 1/2.
To find the probability of both events occurring, we multiply the probabilities of each event:
[tex]P(A and B) = P(A) \times P(B) = (2/3) \times (1/2) = 1/3[/tex]
For similar question on probability.
https://brainly.com/question/30768613
#SPJ11
I need help figuring out this answer
The proof that angles D and E are congruent is added below
Proving that angles D and E are congruentFrom the question, we have the following parameters that can be used in our computation:
∠CDB and ∠CEB are inscribed in a circle A.
The general rule is that angles that are inscribed in the same arc are congruent.
So, we have the following two column proof
Statements Reasons
∠CDB = ∠CEB Given
Segments BD = CE CPCTC
Segments BE = CD CPCTC
Arcs BE = CD Corresponding arcs
∠D = ∠E Corresponding angles
Read more about two column proof at
https://brainly.com/question/18286984
#SPJ1
PLEASE SOLVE THIS QUICKLY!!!!!
The ratio of the two arc lengths is equal to a / b. (Correct choice: B)
How to find the ratio of two arc lengths
In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:
s = θ · r
Where:
s - Arc length
θ - Angle, in radians.
r - Radius
And the ratio of the length JK to the length MN is:
JK / MN = (θ · a) / (θ · b)
JK / MN = a / b
To learn more on arc lengths: https://brainly.com/question/16403495
#SPJ1
What type of pay is modeled below?
(See chart)
A. Piece rate
B. Hourly pay with no bonus
c. Commission pay
D. Hourly pay with a bonus
The type of pay modeled in the given image is c. Commission pay.
What is commission pay?Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.
The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.
Therefore the correct option is C.
Learn more about commission pay here:https://brainly.com/question/1024047
#SPJ1
Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)
cross out
B)
(−2,2)
cross out
C)
(1,6)
cross out
D)
(0,1)
cross out
E)
(1,4)
cross out
F)
(−2,7)
From the graph attached below, the solution to the system of linear inequalities are (1, 4)
What is the solution to the system of linear inequalities?A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.
In the problem given;
y < - x + 5 ...eq(i)
y ≥ 3x + 1 ...eq(ii)
To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.
From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E
Kindly find attached graph below
Learn more on system of linear inequalities here;
https://brainly.com/question/23093488
#SPJ1
If there are 300 jellybeans in a container. You made a guess of 315 jellybeans. What is the percent error
Answer:
5%
Step-by-step explanation:
Percent error equation is:
(Absolute value of experimental value - actual value / actual value) * 100
Experimental Value: 315
Actual Value: 300
315 - 300 / 300 = 0.05
0.05*100 = 5
Percent error is 5%
Answer: the percent error is 5%
Step-by-step explanation:
what principal will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021?
A principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
To calculate the interest earned by a principal at a given interest rate over a certain period of time, we use the following formula:
Interest = Principal x Rate x Time
In this case, we need to find the principal, so we can rearrange the formula as follows:
Principal = Interest / (Rate x Time)
First, we need to calculate the time period in years between February 4, 2021, and July 6, 2021.
February 4, 2021 to July 6, 2021 is 152 days or approximately 0.416 years (calculated as (July 6, 2021 - February 4, 2021) / 365).
Principal = 55.99 / (0.0975 x 0.416) = $1,380.89 (rounded to the nearest cent)
Therefore, a principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
Learn more about Interest here
https://brainly.com/question/25845758
#SPJ1
A local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52. Which is the better value?
If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.
To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.
For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:
Price per soda = $3.48 / 12 = $0.29
For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:
Price per soda = $11.52 / 36 = $0.32
From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.
To learn more about costs click on,
https://brainly.com/question/14695236
#SPJ1
3 The circles in the model represent positive and negative units.
O O O
оо
Which equation is true based on the model?
A (-3) + 5 = -2
B (-3) + 5 = 2
C -3+ (-5) = -2
D 3+ (-5) = 2
KEY
= 1
=-1
The equation is true based on the model is B) (-3) + 5 = 2.
If we consider the circles on the left as negative units and the circles on the right as positive units.
Then we can see that there are 5 positive units and 3 negative units, so the sum is
= 5 - 3
= 2.
Therefore, the correct equation is: B) (-3) + 5 = 2.
Learn more about Integers here:
https://brainly.com/question/15276410
#SPJ1
Which expression represents the volume of a shipping box? s(2^3) (8 + 2)3 (8x2)3 8+23
As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.
what is volume ?A tri object's volume is a measurement of how much space it takes up. The usual measurement tool is a cubic unit, such as a cubic metre (m3) or cubic foot (ft3). The formula used to determine a solid item's volume depends on the shape of the object. For instance, the volume of a cube is determined by multiplying the length of a single of its sides by six, whereas the capacity of a cylinder is determined by dividing the area of its base by the diameter. Engineering, mathematics, and architecture are just a few of the disciplines where the idea of volume is crucial.
given
The formula used to calculate a shipping box's volume is based on the box's dimensions.
The box's volume can be expressed as follows if its side length is s:
[tex]V = s^3[/tex]
As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.
To know more about volume visit :-
https://brainly.com/question/1578538
#SPJ1
Is this a parallelogram and why?
Answer:
Yes, it's a parallelogram bcz the opposite sides are parallel and equal.
If the number 48700 is written in scientific notation, it will be in the form 4.87×10n. What is the value of n?
If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.
What is scientific notation?Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.
Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.
48700 = 4.87×10ⁿ = 4.87×10⁴
Thus, the n represents the exponent of power 10 to which the number is reduced.
Learn more about scientific notations at https://brainly.com/question/27862246.
#SPJ1
Place the indicated product in the proper location on the grid.
a²b(3a² +4ab²)
The simplified expression based on tej values given is 3a⁴b + 4a³b³.
How to solve the expressionAn expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.
It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:
a²b(3a² +4ab²) = 3a⁴b + 4a³b³
Therefore, the simplified expression is 3a⁴b + 4a³b³.
Learn more about expressions on;
https://brainly.com/question/2164351
#SPJ1
Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q
Answer:
A. P
Step-by-step explanation:
You want to identify the point that represents a striking deviation in the given box plot.
IQRThe interquartile range for this box plot is the difference between the upper and lower quartiles:
29 -26 = 3
OutlierThe "fence" that is 1.5 times the IQR below the lower quartile is ...
26 -3·1.5 = 21.5
Point P lies beyond this fence, so is considered an outlier in the data set.
Point P represents a striking deviation, choice A.
<95141404393>
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
9ft
Step-by-step explanation:
From the left side, you know one length is 4ft abd the one below is 5ft, when you add them together its the answer of 9ft, which is the missing side.
it's 9ft
its 9ft because when you add 4 +5 you get 9. two rectangles a present in the diagram. the 4ft and 5ft are apart of the rectangle where the missing side is, adding those two together would give you 9 and in a rectangle sides facing each other are epual therefore the missing side is 9
can some one help me
Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.
What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection?
The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.
There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.
Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.
Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:
P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)
= (1/3) x (1/3)
= 1/9
Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.
To know more about Probability:
https://brainly.com/question/11234923
#SPJ1
The solution set of the following equations 2x-y=8 , 3x+2y=5 is ..............
*
Answer:
x = 3,
y = -2
Step-by-step explanation:
Let's write the given equations into a system:
{2x - y = 8,
{3x + 2y = 5;
Let's make y the subject from the 1st equation:
-y = 8 - 2x / × (-1)
y = 2x - 8
Replace y in the 2nd equation with its value from the 1st one:
3x + 2(2x - 8) = 5
Expand the brackets:
3x + 4x - 16 = 5
Collect like-terms:
7x = 5 + 16
7x = 21 / : 7
x = 3
y = 2 × 3 - 8 = -2
help struggling pealse if do brainliest!
Based on the data in the table, if Colin draws a marble 336 times, he predicts a yellow marble will be drawn roughly 63 times, but probably not exactly 63 times.
Based on the data in the table, if Colin draws a marble 216 times, he predicts a white marble will be drawn roughly 2 times that a purple marble will be drawn.
What is the number of times the yellow marble can be drawn?If Colin draws a marble x times, he predicts a yellow marble will be drawn roughly 63 times.
The number of times = 63 / 3/16)
The number of times = 336 times.
If Colin draws a marble 216 times,
Number of times he can draw a white marble = 216 * 1/4
Number of times he can draw a white marble = 54 times
Number of times he can draw a purple marble = 216 * 1/6
Number of times he can draw a purple marble = 36 times
The number of times a white marble can be drawn more than a purple marble = 54/36 or 1.5 times more
The number of times a white marble can be drawn more than a purple marble is approximately two times.
Learn more about probability at: https://brainly.com/question/25870256
#SPJ1