Given:
Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score.
Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna.
To find:
The individual score of each person.
Solution:
Let x be the score of Jamie.
Marshall scores 12 less than Jamie.
Marshall score = x-12
Shawna scored twice as much as Marshall.
Shawna score = 2(x-12)
Wyatt scored 4 less than Shawna.
Wyatt score = 2(x-12)-4
Now,
Score of Jamie and Marshall's team [tex]=x+(x-12)[/tex]
Score of Shawna and Wyatt's team [tex]=2(x-12)+2(x-12)-4[/tex]
Jamie and Marshall's team tied Shawna and Wyatt's team
[tex]x+(x-12)=2(x-12)+2(x-12)-4[/tex]
[tex]x+x-12=2x-24+2x-24-4[/tex]
[tex]2x-12=4x-52[/tex]
Isolate x.
[tex]2x-4x=-52+12[/tex]
[tex]-2x=-40[/tex]
Divide both sides by -2.
[tex]x=\dfrac{-40}{-2}[/tex]
[tex]x=20[/tex]
So, Jamie score = 20
Marshall score = 20-12
= 8
Shawna score = 2(20-12)
= 2(8)
= 16
Wyatt score = 2(20-12)-4
= 2(8)-4
= 16-4
= 12
Therefore, the scores of Jamie, Marshall, Shawna and Wyatt are 20, 8, 16 and 12 respectively.
An isosceles triangle has a perimeter of 45 cm. If the two equal sides are each twice as long as the smallest side, what is the length of the smallest side?
A: 3
B: 7
C: 9
D: 15
E: 18
The linear function y=2x+28 models the average cost of a haircut in a certain city, where y, is the average price of a haircut x years after 2000. Find the slope for the model. Then describe what this means in terms of the unit rate of change in the average cost of a haircut over time.
Answer:
The slope of the model is [tex]m = 2\,\frac{USD}{yr}[/tex].
The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.
Step-by-step explanation:
We have to notice that given function is a linear function, that is, a first order polynomial, whose standard form is described below:
[tex]y =m\cdot x + b[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
In this case, we use the linear function [tex]y = 2\cdot x + 28[/tex], where [tex]x[/tex] is the time after 2000, measured in years, and [tex]y[/tex] is the average cost of a hair cut. The slope of the model is [tex]m = 2\,\frac{USD}{yr}[/tex].
The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.
Sue solved an equation below. Check her work.
Answer:
You cant see the equation
Step-by-step explanation:
(5) P-4-7 set up & solve, rate
A gold dredge is a machine that was used in the early 1900s to extract gold from a river or pond. The amount of
dirt a gold dredge can dig in 1 minute is equal to the amount it would take 3 people, each digging at the same
rate, to dig in 1 day. At this rate, how many days would it take 2 persons to dig as much dirt as a gold dredge
can dig in 60 minutes ?
A) 30 B) 45 C) 60 D) 90
Show work please.
Answer:
D) 90 Days
Step-by-step explanation:
dredge 1 min = 3 people days
when I say people days, I mean 3 people working one day
multiply each side by 60 to get the desired 60 min of dredge:
dredge 60 min = 180 people days
As we currently have this set up, it will take 180 people, 1 day to do the same amount of work as 60 min of dredge, but we only want 2 people. This means we need to divide the people days by 2 to get how many days are needed for 2 people, thus:
dredge 60 min = 2 people for 90 days
Solve the system of equations by multiplying. Check the answer by graphing the system of equations.
{
- 4x + 3y = 15
2x +y = -5
The solution is _______?
- 4x + 3y = 15
2x + y = -5
I multiply x 3 the second equality
we will get
- 4x + 3y = 15
6x + 3y = - 15
difference of the 2 equalities
- 4x - 6x + 3y - 3y = 15 - (-15)
- 10x = 30
x = -3
so - 4*(-3) + 3y = 15
3y = 3
y = 1
check
- 4 * (-3) + 3 * 1 = 12 + 3 = 15
Skylar has a bag that contains pineapple chews, apple chews, and peach chews. She performs an experiment. Skylar randomly removes a chew from the bag, records the result, and returns the chew to the bag. Skylar performs the experiment 23 times. The results are shown below:
A pineapple chew was selected 8 times.
A apple chew was selected 9 times.
A peach chew was selected 6 times.
If the experiment is repeated 2000 more times, about how many times would you expect Skylar to remove a peach chew from the bag? Round your answer to the nearest whole number.
Answer:
522 times
Step-by-step explanation:
a peach chew was chosen 6 out of 23 times so we can create a proportion out of 2000 based on that ratio:
'p' = times peach is chosen out of 2000
6/23 =p/2000
cross-multiply to get:
23p = 12000
p = 12000/23
p = 522 times
Answer:
522 times
Step-by-step explanation:
From this experiment, Skylar selects a peach chew 6/23 of the time. 6/23*2000=522. This works because 6/23 is the amount of chance Skylar has of selecting a peach chew if she selects one chew. If she selects 2000 chews, therefore, her odds of getting a peach chew would mean that she would get about 522 peach chews.
3) Louise has 500 cents in her piggy bank. Uncle Jim gave her a few cents on his visit.
If Louise has 765 cents, how many cents did Uncle Jim give her?
Answer:
265
Step-by-step explanation:
because she had 500 and now she has 765 so he gave her 265
Answer:
265
Step-by-step explanation:
Because before her Uncle visited she had 500 cents and he gave her a total of ? cents she now has 765.
Meaning what = 765 when you add it to 500.
500 + ?=765. we know 500 + 200=700 but she has 65 more than 700 so s you add that to our answer we get 765.
5 0 0
2 6 5
+______
7 6 5=765
Hope it helps have a great day:)
I need help asap please
Answer:2.25
Step-by-step explanation:
you would move the variables to one side
-9= -6p+5p-3p
Then combine
-9= -4p
Then divide both sides by -4 which equals
2.25=p
Answer:
HKSHKSBSKSBZKSJSJSJKSSKJSSJJZJSKSBSKSKS B)
Triangles RST and XYZ are shown at right. Emma knows
ZTELZ. She claims that triangles RST and XYZ are congruent. As part of her
reasoning, which theorem could she use? Select two that apply.
Answer:
Step-by-step explanation:
Given :-
TR = ZXSR = YXTo Prove :-
ΔRST ≅ ΔXYZSolving :-
TR = ZX (Given)SR = YX (Given)∠R = ∠X (Angle that lies between equal sides of respective parts of the triangle)ΔRST ≅ ΔXYZ (1,2,3, SAS congruence)3(y-6)=42 what is the answer
Answer:
y=20
Step-by-step explanation:
expand bracket
3y-18=42 add 18
3y=60 divide by 3
y=20
need answer plz answer I NEEED ANSWER
Answer:
I believe Han's tastes stronger.
Step-by-step explanation:
His is less of a water fraction and more orange juice fraction.
Answer:
Han
Step-by-step explanation:
The answer is Han because she adds less water and water makes things less strong.
Demi solves 30 questions in 10 minutes. Which statement correctly describes the unit rate of questions
per minute
Answer:
She answers 3 questions per minute!!
Step-by-step explanation:
I know this because 3x10 = 30 and if she solves 30 questions in 10 minutes, that means in 1 minute she solves 3 questions.
Determine what the constant, coefficient, and variable are in the expression 9x + 4
Answer:
constant-4
variable-x
coefficient-9
Step-by-step explanation:
Coefficient- the number being multiplied by a variable
Variable- the unknown, usually 'x'
Constant- the number that is all by itself.
Please help with my algebra
Determine whether the situation involves a permutation or combination. Then, find the number of
possibilities.
In how many ways could you choose 3 side dishes from a menu that offers 5 vegetable side dishes
and 3 starches if you want at least one vegetable and one starch?
The situation involves combination
There are 45 possibilities of choosing the 3 side dishes from the menu
How to determine the number of ways?The given parameters are
Dishes to choose = 3Vegetable = 5Starch = 3The keyword choose means that the situation involves combination.
Given that you want at least one vegetable and one starch, the selections are:
(Vegetable, Starch) = (1,2) and (2,1)
So, the number (n) of ways the dishes can be selected is:
n = 5C1 * 3C2 + 5C2 * 3C1
Apply the combination formula on each expression
n = 5 * 3 + 10 * 3
Evaluate the sum
n = 45
Hence, there are 45 possibilities of choosing the 3 side dishes from the menu
Read more about combination at:
https://brainly.com/question/11732255
A dartboard consists of a circle inscribed in a square. The area of the circle is square inches. The area of the square is 64 square inches. A dartboard consists of a circle inscribed in a square. Izzy randomly throws a dart at the square, and it lands inside the square. To the nearest percent, what is the probability that the dart lands inside the square but not on the circular dartboard? Use 3. 14 for π. 22% 25% 75% 79%.
The probability that the dart lands inside the square but not on the circular dartboard is 0.215
What is the probability?The chances of the happening of any event are called the probability.
The dartboard is in the form of a square and the circle is inscribed in it
The area of the dartboard is [tex]a_d=54\ inch^2[/tex]
Since the circle is inscribed on the dashboard so the diameter of the circle will be the length of the square
[tex]a_d=s^2=64[/tex]
[tex]s=\sqrt{64}=8\ inch[/tex]
Thus the diameter of the circle
[tex]d=8\ \ \ r= \dfrac{8}{2} =4 \ inches[/tex]
Now we will calculate the area of the circle
[tex]a_c=\pi r^2[/tex]
[tex]a_c=\ 3.14\times 4^2=50.24\ inch^2[/tex]
The area of the square outside the circle will be the difference of the area of the square and the area of the circle
[tex]64-50.24=13.76\ inch^2[/tex]
Now to find out the probability of the dart hitting outside the circle will be calculated as.
[tex]\rm Probability = \dfrac{Area \ outside \ circle }{Area \ of \ square}[/tex]
[tex]P= \dfrac{13.76}{64} =0.215[/tex]
Thus the probability that the dart lands inside the square but not on the circular dartboard is 0.215
To know more about probability follow
https://brainly.com/question/24756209
Answer:
22%
Step-by-step explanation:
Solve the following system of equations using substitution, show all steps. 2x-4y=20 / x= 4
Answer:
(4, -3)
Step-by-step explanation:
Since we know that X = 4, when can set X = 4 in the other equation in order to solve for Y
2x - 4y = 20
2(4) - 4y = 20
8 - 4y = 20
-8 -8
-4y = 12
-4y/-4 = 12/-4
y = -3
Since we already know X = 4, the intersection point or solution to the System is (4, -3)
Hope this helps!
For his science fair project, Ernesto is investigating the water quality in his school's water fountains. He finds that the water is safe to drink; a 50-milliliter water sample has just 13 milligrams of dissolved solids. If Ernesto fills a 2-liter bottle from one of the water fountains at his school, how many grams of dissolved solids would his bottle have?
Answer:
0.52grams of dissolved solids.
Step-by-step explanation:
; a 50-milliliter water sample has just 13 milligrams of dissolved solids. If Ernesto fills a 2-liter bottle from one of the water fountains at his school, how many grams of dissolved solids would his bottle have
50ml = 13mg of dissolved solids
1 litre = 1000 millilitres
2 liter = 2 × 1000 = 2000millilitres
50ml = 13mg
2000ml =
Cross Multiply
2000ml × 13m/50ml
= 520mg of dissolved solids.
We are to convert our final answer to grams
= 1 milligram = 0.001 gram
520 milligram =
520 mg × 0.001g/1 mg
= 0.52 grams of dissolved solids
One card is randomly selected from a deck of cards. Find the odds in favor of drawing a red card.
Answer:
The probability of selecting a red card is 3/26.
Given the following information find the height.Volume=2,178πft³
Answer:
[tex]h = 5.73[/tex]
Step-by-step explanation:
Formula: [tex]V = \pi r^{2} h[/tex]
[tex]2178 = \pi (11)^{2} h[/tex]
[tex]2178 = 121\pi h[/tex]
[tex]2178 = 121 (3.14) h[/tex]
[tex]2178 = 379.94h[/tex]
[tex]h = 5.73[/tex]
Perform the operation
(3x^2-10x+4)+(10x^2-5x+8)
Answer: 13x^2 - 15x + 12
Step-by-step explanation:
[tex]\left(3x^2-10x+4\right)+\left(10x^2-5x+8\right)[/tex]
[tex]=3x^2-10x+4+10x^2-5x+8[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=3x^2+10x^2-10x-5x+4+8[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:4+8=12[/tex]
[tex]=3x^2+10x^2-10x-5x+12[/tex]
[tex]\mathrm{Add\:similar\:terms:}\:3x^2+10x^2=13x^2[/tex]
[tex]=13x^2-10x-5x+12[/tex]
[tex]\mathrm{Add\:similar\:terms:}\:-10x-5x=-15x[/tex]
[tex]=13x^2-15x+12[/tex]
Which expression is equivalent to (-4y-x)-(3y-9x)?
Answer: Is there any answers to choose from
Answer:
-7y - 8x
the person who answered the question before me is buggin
the distance across the united states from Florida to Washington is 2,802 Miles. this is the longest straight line distance across the united states. how far is it in yards? one mile = 1760 yards
Answer:4931520 yd
Step-by-step explanation:2,
802x1760=4931520yds
The water level in a well decreased by 6 inches every month due to evaporation. What is the change in the water level after a six month period of time?
Step-by-step explanation:
we don't know what level it was originally at so well use a variable for the unknown number. If you take 6 inches and do that 6 times for each month you will have 36 inches lost so w= water i = inches
w-(6i x 6) = 36
This isn't the best explanation but I hope this helps you
AnEgg is bought at 550 and sold at a percentage of loss of 22%. Calculate the Selling Price
Hey there!
=> [tex]550 \times \frac{22}{100} [/tex]
=> [tex] \frac{550}{1} \times \frac{22}{100} [/tex]
cancel the zeros of 100 and 550
=> [tex] \frac{55}{1} \times \frac{22}{10} [/tex]
=> [tex] \frac{1,210}{10} [/tex]
=> 121 ( Substract 121 from 550)
=> 429
Therefore, Selling price is 429
what is the sum of the degrees of the exterior angles of a convex pentagon
Answer:
The sum of the measures of the exterior angles of a convex polygon is 360 degrees.
Step-by-step explanation:
James has a piece of construction paper with an area of 65 1/4. It is 9 2/3 inches long. What is the width of the piece of construction paper in inches
Answer:
James has a piece of construction paper with an area of 6514inches. It is 293inches long. What is the width of the piece of construction paper in inches?
Step-by-step explanation:
fist cdsddghjjhgfghjkl;'
Are the pair of lines parallel, perpendicular or neither? 8x-4y=12 and 4x-y=-15
Answer:
neither, would technically be intersecting lines tho
Step-by-step explanation:
What is 70.5 rounded to the nearest whole number?
Answer:
71
Step-by-step explanation:
If a decimal needs to be rounded to a whole number, you need to refer to the tenths place in the decimal. In this case, that is "5" and in math, when rounding, if it is 5 or more, you round up to the next whole number. If it is 4 or less, you round down. So 70.5 rounded to the nearest whole number is 71. :)
here, what do we do if it says y=-x or y=x
You plot the points on the graph first with a pencil. Draw the given line, in this case, it's y=-x.
From a point, you do rise and run to the line and reverse it on the other side of the line to get the points.
Refer the attached diagram, for easy method.
Hope it helps :)
hello people ~
factorise: 21x²+43-14
Answer:
[tex]\displaystyle [7x - 2][3x + 7][/tex]
Step-by-step explanation:
Find two quantities that when differed to 43, they also multiply to 294. Those will be 6 and 49. The TINIER quantity gets the minus symbol because the B-value is 43, therefore 49 gets the plus symbol, leaving 6 with the minus symbol. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:
[tex]\displaystyle 21x^2 + 43x - 14 \\ \\ [21x^2 - 6x] + [49x - 14] \\ 3x[7x - 2] + 7[7x - 2] \\ \\ \boxed{[7x - 2][3x + 7]}[/tex]
I am joyous to assist you at any time.
[tex]\\ \rm\rightarrowtail 21x^2+43x-14[/tex]
[tex]\\ \rm\rightarrowtail 21x^2+49x-6x-14[/tex]
[tex]\\ \rm\rightarrowtail 7x(3x+7)-2(3x+7)[/tex]
[tex]\\ \rm\rightarrowtail (7x-2)(3x+7)[/tex]
Done!