Solve Each system of equations.
-r + t = 5
-2r+t=4
Answers
Solve equations
-(1) + 6 = 5
5= 5
-2(1) + 6 = 4
4=4
_________
Step by step
We have two equations
-r + t = 5 to t = r + 5 when put in y intercept form for easy math
t = r + 5
-2r + t = 4
To solve, substitute the t value from the first equation for t in the second
-2r + (r + 5) = 4
Combine like terms
-1r + 5 = 4
Subtract 5 from both sides to solve for r
-1r + 5 - 5 = 4 - 5
Combine
-1r = -1
Divide both sides by -1 to solve for r
-1/-1 r = -1/-1
r = 1
Now substitute the r value into one of the equations to solve for t
(-1)(1) + t = 5
-1 + t = 5
Subtract (-1) from both sides to solve for
t = 6
Graph in the attachment
Related Questions
In a recent study, 50 males used a new weight-loss supplement, and all but 15 of them lost weight. In the same study, 100 females used the supplement, and
all but 45 of them lost weight.
Fill in the blanks below to make the statement the most reasonable possible.
The new weight-loss supplement was less effective on [(choose one) in the study because % of them failed to lose weight, whereas only
% of the [(choose one) failed to lose weight.
Answers
Answer: The new weight-loss supplement was less effective on females because 45% of the females failed to lose weight.
Step-by-step explanation:
30% of the males didn't lose weight and 45% of the females didn't lose weight out of 100.
on the males 30% out of 100% did not lose weight
on the females 45% out of 100% did not lose weight
Hope this is helpful or correct.
Paint the Walls
The height of the bedroom is 9 feet. There are 4 rectangular windows in the room that are
each 30 inches wide and 36 inches high. You will not paint the windows, the floor, or the
ceiling. You will paint the rest of the room, including the door. Your client likes two colors,
Light-at-Dawn and Cloudy Sunrise. Both colors are only available in 1-gallon cans. Light-at-
Dawn: The regular price of a 1-gallon can is $24, but it is on sale for 25% off the regular price.
This type of paint requires 2 coats. Cloudy Sunrise: The price of a 1-gallon can is $28. This type
of paint only requires 1 coat. Each gallon of paint will cover an area of about 350 square feet.
Your client has stated that if the cost for using Cloudy Sunrise is no more than 5% greater
than the cost for using Light-at-Dawn, then you should use Cloudy Sunrise. Which paint color
should you use? Explain or show your reasoning. You may use diagrams, drawings, or
equations as well as words.
Answers
The paint should be used is Cloudy Sunrise.
What is Percent?As a fraction of 100, a percentage is a number or ratio. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no associated unit of measurement.
Light-at-Dawn: A 1-gallon can normally costs $24, however it is now on sale for 25% less than that amount. This kind of paint needs two coats.
Cloudy Sunrise: A gallon-sized can costs $28. Only one coat of this kind of paint is necessary.
350 square feet will be covered by each gallon at a time.
The price of 1 gallon of light at dawn is 24 - 25/100 * 24 = 18.
1 gallon of clouded sunrise color costs 28 dollars.
It appears overcast. Prior to accounting for the number of square feet that each hue may cover, sunrise color is more expensive.
350 square feet are claimed to be covered by both cans.
if everything else remains the same,.
Dawn color lighting would cost:
18 / 350, or.0514285714, per square foot.
However, the light at dawn color needs two coats.
The total cost per square foot for the light at dawn color would be
2 * 0.0514285714 = 0.1028571429.
The price of a cloudy sunrise is 28/350 = 0.08 per square foot.
This represents the total cost per square foot for cloudy sunrise color since it only needs one coat.
It looks that the total cost of cloudy sunrise color is less expensive than the total cost of light at dawn color, assuming that the second coat of paint uses the same amount of paint as the first coat.
Hence, The paint should be used is Cloudy Sunrise
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Fatima us on the track team. One day at practice, it took her 19 minutes to run2 miles ,select the expression that gives this as a unit rate
Answers
The unit rate expression is 19/2 or 7.5 units.
What is unitary Method?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
This approach allows us to calculate both the value of many units from the value of one unit and the value of one unit from the value of many unit.
Given:
Total time taken= 19 minutes
Total distance = 2 miles
Now, find the unit rate we have to divide the
unit rate = 19/2
= 7.5
Hence, the unit rate is 7.5 units.
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If u = 5 inches, v = 7 inches, w = 4 inches, x = 7 inches, y = 12 inches, and z = 4 inches, then what is the perimeter of the object?
Answers
The perimeter of a figure is the sum of all its sides.
In the given figure, we have two unknown sides, let's call them a and b:
Also, we can say that:
[tex]\begin{gathered} w+a+u=y\text{ Equation 1} \\ b+x=v+z\text{ Equation 2} \end{gathered}[/tex]By replacing the known values, we can find a and b:
[tex]\begin{gathered} a=y-w-u \\ a=12-4-5=12-9=3inches \\ \\ b=v+z-x \\ b=7+4-7=4inches \end{gathered}[/tex]So, the perimeter is given by:
[tex]\begin{gathered} P=a+b+u+v+w+x+y+z \\ P=3+4+5+7+4+7+12+4 \\ P=46\text{ inches} \end{gathered}[/tex]The answer is B. 46 inches
A tennis ball has a diameter of 2.5”. Find the total surface area of the smallest cylindrical can that can hold three tennis balls vertically (including the top and the bottom) around answer to the nearest hundredth. No pi in your answer.
Answers
For the cylinder to be able to contain the balls it has to have a radius equals to the radius of the ball, then the radius of the cylinder must be at least 1.25 inches. The height of the cylinder is 3 times the 'height' of each sphere, which is equal to the diameter of the sphere, the diamenter of a sphere is 2 times its radius then the height of the cylinder is h=6r = 7.5 inches.
Finally we apply the formula for the surface area of a cylinder:
[tex]\begin{gathered} A=\text{ 2}\pi rh\text{ + 2}\pi r^2=\text{ 2}\pi\text{ (1.25 in }\cdot7.5in+(1.25in)^2)=68.72in^2 \\ \end{gathered}[/tex]Indicate whether the terms are like or unlike. The two terms 3,3 and – x3 arelike terms unlike tems
Answers
The given terms are
[tex]\begin{gathered} 3,3 \\ x^3 \end{gathered}[/tex]Notice that these terms are not like terms because one has variable and the other one doesn't.
Remember that like terms are those terms that have the same variable with the same exponent.
Therefore, the given terms are unlike terms.If QR = 13 and PT = 8, find QT.
Answers
Since the diagram is symmetric ,
so,
[tex]\begin{gathered} QR=QP \\ QP=13 \end{gathered}[/tex]Considering the triangle PQT is,
Using the pythagoras theorem on triangle PQT,
[tex]\begin{gathered} QP^2=PT^2+QT^2 \\ 13^2=8^2+QT^2 \\ QT^2=13^2-8^2 \\ ^{}QT^2=169-64 \\ QT^2=105 \\ QT=\sqrt[]{105} \\ QT=\text{ 10.24 } \end{gathered}[/tex]Hence, the value of QT is 10.24
Find the value of EF in the triangle below.H8FE4O 472O 43O8V2
Answers
From the triangle shown, we have three important informations:
- It is a right triangle, because it has a right angle, mHEF.
- Its hypotenuse has length 8, HF = 8.
- Its two legs has the same length, HE = EF.
Because it is a right triangle, we can use the Pythagora's Theorem:
[tex]HE^2+EF^2=HF^2[/tex]And we know that:
[tex]\begin{gathered} HE=EF \\ HF=8 \end{gathered}[/tex]Thus:
[tex]\begin{gathered} EF^2+EF^2=8^2 \\ 2EF^2=64 \\ EF^2=32 \\ EF=\sqrt[]{32} \\ EF=\sqrt[]{2^5} \\ EF=4\sqrt[]{2} \end{gathered}[/tex]Find all zeroes of h(x)=2x⁴-x³-18x²+9x
Answers
When you have a polynomial with no independent term you can start by factorizing the polynomial, as follows:
[tex]h(x)=2x^4-x^3-18x^2+9x[/tex]The common factor is x, then:
[tex]h(x)=x(2x^3-x^2-18x+9)[/tex]Now you have a third-degree polynomial inside the ( ), let's called it j(x):
[tex]j(x)=2x^3-x^2-18x+9[/tex]You need to factorize this polynomial, then find all the numbers that divide the independent term 9.
These numbers are:
[tex]1,-1,3,-3[/tex]Let's probe if any of these numbers makes j(x)=0:
[tex]\begin{gathered} j(1)=2(1)^3-(1)^2-18(1)+9 \\ j(1)=2-1-18+9_{} \\ j(1)=-8 \end{gathered}[/tex]Then 1 is not a root, let's try -1:
[tex]\begin{gathered} j(-1)=2(-1)^3-(-1)^2-18(-1)+9 \\ j(-1)=-2-1+18+9 \\ j(-1)=24 \end{gathered}[/tex]Then -1 is not a root, let's try 3:
[tex]\begin{gathered} j(3)=2(3)^3-(3)^2-18(3)+9 \\ j(3)=2\cdot27-9-18\cdot3+9 \\ j(3)=54-9-54+9 \\ j(3)=0 \end{gathered}[/tex]Then 3 is a root and you can apply synthetic division to find the others:
The new polynomial is:
[tex]2x^2+5x-3[/tex]Now you can factorize it as follows:
[tex]2x^2+5x-3=(2x-1)(x+3)[/tex]And finally, your 4th-grade polynomial can be written as:
[tex]h(x)=x(x-3)(2x-1)(x+3)[/tex]Thus, the zeros are at:
[tex]\begin{gathered} x=0 \\ (x-3)=0\text{ then x=3} \\ (2x-1)=0\text{ then x=1/2} \\ (x+3)=0\text{ then x=-3} \end{gathered}[/tex]The answer is 0, 3, 1/2 and -3
- 2 + {-3 - [7 + 4 (-2+5)]}-4
Answers
Answer:
-28
Step-by-step explanation:
- 2 + {-3 - [7 + 4 (-2+5)]}-4
-2 + {-3 - [7 + 4 * 3]}-4
-2 + {-3 - 19}-4
-2 + -22 -4
-28
Paint the Walls
The height of the bedroom is 9 feet. There are 4 rectangular windows in the room that are each 30 inches wide and 36 inches high. You will not paint the windows, the floor, or the ceiling. You will paint the rest of the room, including the door. Your client likes two colors, Light-at-Dawn and Cloudy Sunrise. Both colors are only available in 1-gallon cans. Light-at-Dawn: The regular price of a 1-gallon can is $24, but it is on sale for 25% off the regular price.
This type of paint requires 2 coats. Cloudy Sunrise: The price of a 1-gallon can is $28. This type of paint only requires 1 coat. Each gallon of paint will cover an area of about 350 square feet.
Your client has stated that if the cost for using Cloudy Sunrise is no more than 5% greater than the cost for using Light-at-Dawn, then you should use Cloudy Sunrise. Which paint color should you use? Explain or show your reasoning. You may use diagrams, drawings, or equations as well as words.
Answers
You should use cloudy Sunrise because the overall cost of the cloudy sunrise color seems to be less expensive than the total cost of light at dawn color.
Light-at-Dawn: A 1-gallon bottle ordinarily costs $24, but it is presently 25% off that price. This paint requires two coats.
A gallon of Cloudy Sunrise costs $28. This type of paint just requires one coat.
Each gallon will cover 350 square feet at a time.
The price of 1 gallon of light at dawn = 24 - 25/100(24) = 18
One gallon of cloudy sunrise color costs $28.
It seems cloudy. Sunrise color is more costly before accounting for the number of square feet that each color may cover.
Both cans are supposed to cover 350 square feet.
If everything else remains constant,
Dawn color lighting would cost:
⇒ 18 / 350 = 0.0514285714, per square foot.
However, the light at dawn color needs two coats.
The total cost per square foot for the light at-dawn color would be
⇒ 2×0.0514285714 = 0.1028571429.
A cloudy sunrise costs 28/350 = 0.08 per square foot.
Because overcast dawn only requires one coat, this is the total cost per square foot.
If the second coat of paint uses the same amount of paint as the first, the overall cost of the cloudy sunrise color seems to be less expensive than the total cost of light at dawn color.
As a result, cloudy Sunrise should be used.
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Mario's has $893.11 In his savings account. The bank stated that he will be charged a $17 fee if his balance is less than $400 at any point. Yesterday.
he cashed a check of $500 from his account. What was his balance after the withdrawal?
His balance was
Answers
Answer: $376.11 I believe is the answer
Step-by-step explanation:
Since the $500 made the balance go below $400 he got charged a $17 fee which made his balance go to $376.11
in the equation c²-4=0 c is equal to
Answers
Given the following equation:
[tex]c^2-4=0[/tex]notice that we can factor the expression using the conjugate binomials:
[tex]\begin{gathered} c^2-4=0 \\ \Rightarrow(c-2)(c+2)=0 \end{gathered}[/tex]thus, the only values for c that make the equation true are c = 2 and c = -2
help me pleaseeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer:
Domain: [tex][2, \infty)[/tex], Range: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount c
gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams
The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold.
Determine the number of bracelets made and the number of necklaces made.
The jeweler made
Submit Answer
bracelets and
necklaces.
attempt 1 out of
Answers
The jeweler made 7 bracelets and 9 necklaces .
In the question ,
it is given that
amount of gold in each bracelet is [tex]=[/tex] 6 grams
amount of gold in each necklace is [tex]=[/tex] 24 grams .
let the number of bracelets [tex]=[/tex] "b" .
let the number of necklaces [tex]=[/tex] "n" .
since the total number of necklace and bracelet is 16 .
the equation is b + n = 16
so , b = 16 - n
also given that total gold used is 258 grams .
so the equation is 6b + 24n = 258
Substituting b= 16 - n in the equation ,
we get , 6*(16 - n) + 24n = 258
96 - 6n + 24n = 258
96 + 18n = 258
18n = 258 - 96
18n = 162
n = 162/18
n = 9
and b = 16 - 9 = 7
Therefore , The jeweler made 7 bracelets and 9 necklaces .
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The scatter plot shows the number of years of experience
Answers
(a)
Let's use the given equation to calculate the value of y when x = 7:
[tex]\begin{gathered} y=0.92x+7.88\\ \\ y=0.92\cdot7+7.88\\ \\ y=6.44+7.88\\ \\ y=14.32 \end{gathered}[/tex]Therefore the hourly pay rate is $14.32.
(b)
Now, let's use x = 0 and calculate the value of y:
[tex]\begin{gathered} y=0.92\cdot0+7.88\\ \\ y=7.88 \end{gathered}[/tex]Therefore the hourly pay rate is $7.88.
(c)
The relation of increase in hourly pay rate by increase of years of experience is given by the slope of the line.
The slope is the constant value multiplying the variable x in the equation.
That means if the value of x increases by 1, the value of y increases by the slope value, that is, 0.92.
Therefore the predicted increase is $0.92.
A grocer has a bag of fruit containing 3 apples, 2 oranges, and 4 pears. The grocer randomly chooses two pieces of fruit from the bag without looking. What is the probability that the grocer chooses two apples?
Answers
Answer:
The probability that the grocer chooses two apples is;
[tex]P=\frac{1}{12}[/tex]Explanation:
Given that;
A grocer has a bag of fruit containing 3 apples, 2 oranges, and 4 pears.
The total number of fruits is;
[tex]\begin{gathered} \text{Apples = 3} \\ \text{Orange = 2} \\ \text{Pears = 4} \\ \text{Total = 3+2+4= 9} \end{gathered}[/tex]Assuming that the grocer did not replace the fruit after picking, the probability of Picking two apples is;
[tex]P=P_1\times P_2[/tex]For the first pick;
[tex]\begin{gathered} P_1=\frac{\text{ number of apple}}{\text{ total number of fruits}}=\frac{3}{9} \\ P_1=\frac{1}{3} \end{gathered}[/tex]For the second pick, the number of apple and the total number of fruits would have reduced by 1;
[tex]\begin{gathered} P_2=\frac{2}{8} \\ P_2=\frac{1}{4} \end{gathered}[/tex]The overall probability is;
[tex]\begin{gathered} P=\frac{1}{3}\times\frac{1}{4} \\ P=\frac{1}{12} \end{gathered}[/tex]Therefore, the probability that the grocer chooses two apples is;
[tex]P=\frac{1}{12}[/tex]
a. What is the center of dilation?
b. What is the shape that was dilated?
c. Is the scale factor one-third, two, or three?
Answers
Answer:
well I can answer b the shape here is a 3D Hexagonal pyramid
a gannet flies 24 1/2 ft above sea level. it increases its elevation by 5ft. then it dives and changes its elevation by - 47 2/3. after it dives, what is the gannets elevation relative to sea level? show your work.
Answers
A gannet initial elevation is 24 1/2 ft
it increases its elevation by 5ft then the elevation is 5 + 24 1/2 = 29 1/2 ft
now it dives 47 2/3 ft
so the final elevation is,
[tex]29\frac{1}{2}-47\frac{2}{3}[/tex][tex]=\frac{59}{2}-\frac{143}{3}[/tex][tex]=\frac{177-286}{6}=\frac{-109}{6}[/tex]so its elevation below to the sea level is -109/6 or -18 1/6 ft
PLEASE HELP ME I WAS SICK AND I DONT UNDERSTAND.DUE IN 1 HOUR!!!!!
Answers
Answer:
x=11 again
Step-by-step explanation:
Like the previous problem, the interior angles of a triangle add up to 180 (well, it's always true but whatever), so you want to find angle GFH (the acute angle at F) to complete your information. 180-137=43, so angle F equals 43
The sum of angles F, G, and H equal 180, so add them all up
This gives 10x+70, set this equal to 180
10x+70=180
Solving gives 10x=110
x=11
(Once again wow)
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2 . The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.) Part b: Find two values of x that will create a profit of $300 Part c: Is it possible for the company to make a profit of $15,000 ?
Answers
Given that
The cost for producing items is 40x + 300 and the revenue collected is 80x - 0.5x^2
And we have to write an equation for the profit and also we have to find the profit.
Explanation -
The profit is basically the difference between revenue and cost.
So the profit will be
[tex]Profit=Revenue-cost[/tex]Substituting the values
[tex]\begin{gathered} Profit=80x-0.5x^2-(40x+300) \\ Profit=80x-0.5x^2-40x-300 \\ P=40x-0.5x^2-300 \end{gathered}[/tex](a). The profit equation will be, P = 40x - 0.5x^2 - 300
(b). Here the profit given is $300 (P=300) and we have to find the values of x.
Then,
[tex]\begin{gathered} 300=40x-0.5x^2-300 \\ 600=40x-0.5x^2 \\ 0.5x^2-40x+600=0 \\ Dividing\text{ by 0.5 we have} \\ x^2-80x+1200=0 \\ x^2-60x-20x+1200=0 \\ x(x-60)-20(x-60)=0 \\ (x-20)(x-60)=0 \\ x=20\text{ and x = 60} \end{gathered}[/tex]So the two values of x are 20 and 60.
(c). Now we have to check whether the profit can be $15000 or not.
For this, we have to put P = 15000 in the quadratic equation and if we get a solution for x then it is possible otherwise it is not.
So, substituting P = 15000
[tex]\begin{gathered} 15000=40x-0.5x^2-300 \\ 0.5x^2-40x+15300=0 \\ Dividing\text{ by 0.5 in the above equation} \\ x^2-80x+30600=0 \\ \end{gathered}[/tex]The solution to this equation is not possible. So Company cannot make a profit of $15000.
Hence the final answers are(a). P = 40x - 0.5x^2 - 300(b). 20 and 60(c). NoWhich pair of numbers has a GCF of 5? A.15 and 30 C.45 and 9 B.5 and 21 D.20 and 55
Answers
Answer:
D
Step-by-step explanation:
The GCF in answer choice A is 15.
The GCF in answer choice B is none.
The GCF in answer choice C is 9 since 45 is divisible by 9 and 9 is divisible by itself
D is correct as 55/5 = 11 and cannot be divided anymore. And 20 is divisible by 5
A plane is beginning its descent to the ground. After 3
minutes, the plane is at an altitude of 31,275', and after 7
minutes it is at an altitude of 22,975'. At what rate, in feet
per minute, is the plane descending?
Answers
Answer:
2075 ft/minute
Step-by-step explanation:
31,275 - 22,975 = 8300, this is the decrease in altitude over 4 minutes.
By dividing the change in position by time you can find the rate of change.
8300/4
= 2075 ft/minute
Given AB || DC and AC is the segment bisector of BD, complete the flowchartproof below. Note that the last statement and reason have both been filled in foryou. Triangle ABE is congruent to Triangle CDE, the reason is SAS.**there are also two 3 boxes that got cut off, they are the same as the first two.**
Answers
Solution
First, we have CD and AB
Which expression should you simplify to find the 90% confidence interval,given a sample of 50 people with a sample proportion of 0.65?
Answers
Answer
Explanation
The confidence interval
Can you explain the vertical line test for graphs simply. (I am doing 8th grade algebra)
Answers
The vertical line test is a visual, graphing methid that helps us to determine if the relation given is a function or not by doing vertical lines that cut the graph.
The vertical line test follow the definition of a function every value of x must be paried to a single value of y.
Therefore if we do a vertical line ans we cut tewo times the graph of the relation this relation is not a function
EASY PLEASE ANSWER
A flight from Toronto to Miami usually takes 3 hours and 5 minutes. Unfortunately, your plane takes off 45 minutes late. As your plane approaches Miami, it needs to circle the airport for another 12 minutes. How much longer than expected has your flight taken as a percentage?
Answers
The flight has taken 30.8 % longer as compared to the usual time.
Given that:-
Usual time taken by the flight from Toronto to Miami = 3 hours 5 minutes = 185 minutes
Time by which the plane is late for take off = 45 minutes
Time taken by plane to circle the airport = 12 minutes
We have to find by how much percentage the plane has taken more time as compared to the usual time.
Extra time taken by the flight = 45 minutes + 12 minutes = 57 minutes
Percentage by which the plane has taken more time as compared to the usual time = (57/185)*100 = 30.8 %
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On the following table, which best reflects the values of a function g for which lim g (x) =5?
Answers
We have the following limit:
[tex]\lim_{n\to9}g(x)=5.[/tex]To determine which table best reflects function g(x) values, we analyse the limit.
0. x → 9 means that we must analyze the function g(x) in the range of values of x very near the value x = 9.
,1. lim = 5 means that for the values of x very near to x = 9, the value of the function must be a number near to 5.
1) From point 1, we can discard the second option because the table shows values of x near x = 5, not x = 9.
2) From point 2, we can discard the first and fourth options:
• the first option shows a jump up from the value y = 4.997 to y = 10.030,
,• the fourth option shows a jump down from the value y = 100.00 to y = 4.570.
3) The third option is the correct one. It has values of y near to y = 5 for values of x near to x = 9.
AnswerThird option
Answer:
Third one
Step-by-step explanation:
The third one down has g(x) values across the board that are just about '5' for any value of x, thus g(x) = 5
the others have widely varying values not close to 5
Candice and Porter each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Candice has 21 signatures, and Porter has 18. Candice is collecting signatures at an average rate of 2 per day, whereas Porter is averaging 5 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?
In ______ days, Candice and Porter will each have collected ________ signatures.
Answers
In 1 day, Candice and Porter will have collected 23 signatures each, using a system of equations.
What are equations?Equations are mathematical statements that claim that two expressions are equal or equivalent.
Equality is depicted using the equation sign (=).
Candice Porter
The number of signatures collected for nomination 21 18
Average collection of signatures per day 2 5
Let the total signatures collected by Candice on day x = 21 + 2x
Let the total signatures collected by Porter on day x = 18 + 5x
The day the two candidates will have collected the same signatures is set as equality:
21 + 2x = 18 + 5x
21 - 18 = 5x - 2x
3 = 3x
x = 1
Check:
Total signatures collected by on day 1:
Candice = 21 + 2x = 21 + 2(1) = 23
Porter = 18 + 5x = 18 + 5(1) = 23
Thus, for Candice and Porter to have collected the same number of signatures, it will take them 1 day and each will have 23 signatures, using a system of equations.
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The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.66 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.54 inches.
Answers
The probability of women is more from its z score.
What is a Z score?
A score's connection to the mean within a group of scores is statistically measured by a Z-Score.A Z-score can show a trader whether a value is normal for a given data collection or not.For instance, a Z-score below 1.8 indicates that a business may be on the verge of bankruptcy, while a number closer to 3 indicates that a business is in good financial standing.95% of the time, a score from -1.96 & +1.96 standard deviation and variance out from the mean will be chosen at random.This is considered a statistically meaningful result if the probability of a raw score being chosen at random is less than 5%.For men:
m=69.2, s=2.66
when x=6 feet 3 inches = 75 inches
z score, z=x-m/s=75-69.2/2.66=2.18
P(z<2.18)=0.98537
For women:
m=64.7, s=2.54
when x= 5 feet 11 inches =71 inches
z score, z=x-m/s=71-64.7/2.54=2.48
P(z>2.48)=0.99343
The probability of women is more from its z score.
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