Answer: 36 Students picked football
Step-by-step explanation: When calculating values by the use of given ratios, it is important to note that the ratio of one value as compared to the other is the same as the actual value compared to the other.
The ratio of students who picked rugby and tennis is given as ratio 9 : 19, which means for every 28 students (that was derived by 9 + 19), 9 would choose rugby and 19 would choose tennis. However, we have been given the total number of students who chose tennis as 57, hence the value 57 would now replace the ratio of 19. However the total number of those who chose rugby is not yet known, so we can write out an equation as shown below;
19/28 = t/x
Where t is the number of tennis players as represented by ratio 19 and x is the total number of both tennis and rugby players as represented by 28.
By cross multiplication we now have
19 * x = 28 * 57
x = (28 * 57)/19
x = 1596/19
x = 84
If a total of 84 students play both rugby and tennis, and 57 of them play only tennis, then the number of rugby players is derived as
r = x - t
r = 84 - 57
r = 27
Having determined that 27 students played rugby, and the ratio of football to rugby players is given as 4 : 3, the relationship can be mathematically represented as follows;
3/7 = r/y
Where r is the total number of rugby players and y is the total number of both football and rugby players
3/7 = 27/y
By cross multiplication you now have
3 * y = 7 * 27
y = (7 * 27)/3
y = 189/3
y = 63
If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;
f = y - r
f = 63 - 27
f = 36
Therefore the number of students who chose football is 36
True or false: the set of whole numbers is equal to the set of natural numbers
Answer:
False
Step-by-step explanation:
This statement is false.
The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}
We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}
Answer:
false
brainliest to me!
Step-by-step explanation:
0 is a whole number but not a natural number so its false!
Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit earning 5% annual simple interest to earn $390 of annual interest how much should she invest in each account?
Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.
Step-by-step explanation:
Let x represent the amount that he would deposit in the simple interest account.
Let y represent the amount that he would deposit in the certificate of deposit.
she will deposit twice as much in the certificate of deposit. It means that
y = 2x
Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x
Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.
The total interest from both accounts would be $390. It means that
0.07x + 0.05y = 390- - - - - - - - - - 1
Substituting y = 2x into equation 1, it becomes
0.07x + 0.05 × 2x = 390
0.07x + 0.1x = 390
0.17x = 390
x = 390/0.17 = $2294
y = 2x = 2 × 2294
y = 4588
Write the Equation for the line that goes through the points (30,75) and (60,50).
Answer:y=[tex]y=-\frac{5}{6} x+100[/tex]
Step-by-step explanation:
my answer was wrong and cannot be deleted :)
If BE is a diameter of the circle, find
MAB
A. 400
B 50°
C. 75
D 80
Answer:
B 50˚
Step-by-step explanation:
What you want to do is to find all other measures and subtract them from 360, or find all measures to the left of BE, and subtract from 180.
You can find mCE easily: since the measure of an arc is twice the measure of its corresponding angle (as long as that angle is not a central angle), mCE = 2(25), or 50˚.
mDE equals 100˚. This is because it and arc BD are the only arcs right of BE, the diameter, meaning they, together, must equal half the circle. Since half a circle = 180˚,
180˚=80˚+x
x=180-80
x=100
Now, you can solve:
Method 1:
360˚=80˚+80˚+50˚+100˚+x
360-80-80-50-100=x
x=50˚
Method 2:
180˚=80˚+50˚+x
x=180-80-50
x=50˚
This corresponds to answer choice B.
Answer:
B.
Step-by-step explanation:
Divide 140 in the ratio 1:2:7
Answer:14:28:98
Step-by-step explanation:
To divide a value by a ratio, we first find the total number of parts:
1+2+7 = 10
Then, we divide the value by the number of parts and multiply it by the number of parts in each section of the ratio:
140 divided by 10 = 14.
Part 1: 14 x 1 = 14
Part 2: 14 x 2 = 28
Part 3: 14 x 7 = 98
Write each statement as an algebraic expression. The quotient of the square of a number n and the cube of n increased by 5.
Will get brainiest answer
Answer:
n² / (n³ + 5)
An athletics squad trains on a long straight track with dots marked at 10m intervals. The coach sets out cones on some of the dots for the squad's sprint training drills. She wants the squad to be able to run any distance which is a multiple of 10m, up to some maximum distance which depends on the number of cones.
Explain why it is not possible to place four cones A, B, C, D, in a line so that each multiple of 10m up to 70m can be run between two of the cones.
Answer:
There are 6 ways to run 10 m between two cones of the four cones giving a maximum available distance to run as 60 meters
Step-by-step explanation:
The parameters given are
Distance between two cones = 10 m
Number of cones = 4
Therefore, number of ways to choose two 10 m distances (distance between two cones) from the four cones = [tex]\binom{4}{2}[/tex] = 6
Hence there are only six 10 m distances to run between two cones which gives a maximum distance available to run as 60 m.
Please answer. will mark brainliest.
Answer:
See explanation
Step-by-step explanation:
Line A
gradient = 4
x-intercept = -1
y-intercept = 4
Line B
gradient = -3
x-intercept = -1
y-intercept = -3
y + 8x = - 72
x-intercept = -9
y-intercept = -72
Solve the following quadratic equation.
(x - 16)^2 = 256
A. x = -32 and x = 0
B. x = 30 and x = -4
C. x = -30 and x = 4
D. x = 32 and x = 0
The answer is D. x = 32 and x = 0
============================================================
Explanation:
Think of x-16 as y. In other words, let y = x-16
We have (x-16)^2 = 256 become y^2 = 256.
Solve for y to get y = 16 or y = -16. You apply the square root to both sides. Don't forget about the plus/minus. This is because (-16)^2 = (-16)*(-16) = 256. We square the negative as well.
--------
If y = 16, then y = x-16 solves for x to get
y = x-16
16 = x-16
x-16 = 16
x = 16+16
x = 32 is one solution
---------
Plug in y = -16 and isolate x
y = x-16
x-16 = y
x-16 = -16
x = -16+16
x = 0 is the other solution
----------
We can check each answer by plugging them back into the original equation
Let's try x = 0
(x-16)^2 = 256
(0-16)^2 = 256
(-16)^2 = 256
256 = 256 ... works
Now try x = 32
(x-16)^2 = 256
(32-16)^2 = 256
(16)^2 = 256
256 = 256 ... also works; both answers have been confirmed
What’s the answer to this?
Answer:
256
Step-by-step explanation:
First..
8*2=16
Now
16 (squared)=256
Answer:
The answer is 32
Step-by-step explanation:
8 x 2 is 16
16 is 2 is 32
pls give me brainliest, I show work
The queen received a diamond brooch for her birthday. The largest gem weighed 5.1 carats. There were three other gems that weighed 0.7 carats, 1.4 carat, and 2.6 carats. What was the total weight of the gems?
Answer:
9.8 carats.
Step-by-step explanation:
5.1 + 0.7 + 1.4 + 2.6
= 9.8
(4+7+5+5+2)+( 12 5/8+ 12 3/4+ 12 7/8+ 13+ 13 1/8)=???
please help asp I will give ya 30 points
Answer:
87.375
Step-by-step explanation:
Answer:
699/8 or 87.375
Step-by-step explanation:
Assuming 12 5/8+ 12 3/4+ 12 7/8+ 13+ 13 1/8 are mixed numbers.
PLEASE HELP!
The following are the last 10 run scores Colin got in cricket: 31, 10, 26, 16, 28, 31, 9, 11, 8, 1 a) Work out Colin's mean score. b) Colin plays cricket again on Sunday. He gets 27 runs. What is his new mean score? Give your answers as decimals.
Answer:
Colin's mean score = 17.10
The new mean is 18.00
Step-by-step explanation:
Given scores: 31, 10, 26, 16, 28, 31, 9, 11, 8, 1
number of terms: 10
mean is calculated by given formula = sum of all the data set/ number of terms in the data set.
mean for the 10 scores = (31+ 10+ 26+ 16+ 28+ 31+ 9+ 11+ 8+ 1 )/10
= 171/10 = 17.1
Colin's mean score = 17.10
____________________________________________
runs scored by Colin in 11th match = 27
number of terms: 11
new mean = new sum /number of terms
new mean = (old sum score + 27)/11 = (171+27)/11
new mean = 198/11 = 18
The new mean is 18.00
What is the slope of the line shown?
Answer:1/2 slope
Step-by-step explanation:
Answer: -2
Step-by-step explanation: Using rise/run, take two points of the line. I took the points (3,1) (2,3). I then went down 2 (run) and then I went 1 to the right(run). Since the graph goes by 2, the equation is -4/2 resulting in the answer -2.
Please help! Correct answer only!
Out of 250 tickets in a raffle, one ticket will win a $190 prize, one ticket will win a $120 prize, one ticket will win a $90 prize, and one ticket will win a $50 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
$____
Answer:
$1.80
Step-by-step explanation:
(190+120+90+50)/250= a total expected payoff of 1.8 dollars. Hope this helps!
Find the surface area of the composite solid.
PLZ HELP
Answer:
613.5 m^2
Step-by-step explanation:
The area of the base is
A = 1/2 bh
= 1/2 (10) (8.7) =43.5 m^2
We have three sides with all the same area
The area of one side is 10 * 16 = 160
3 * 160 = 480 m^2
Now to the top
We have 3 sides with the same area
The area of one side
A = 1/2 bh
A = 1/2 (10) (6)
= 30 m^2
3* 30 = 90
Add all the areas together to get the total surface area
43.5 m^2+ 480 m^2 + 90 m^2
613.5 m^2
Answer:
[tex]\Huge \boxed{\mathrm{613.5 \ m^2 }}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.
Surface area of the triangular prism:
10 × 8.7 × 1/2 + 16 × 10 × 3
⇒ 523.5
Surface area of the triangular pyramid:
6 × 10 × 1/2 × 3
⇒ 90
Adding the surface areas:
523.5 + 90
⇒ 613.5
[tex]\rule[225]{225}{2}[/tex]
How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 40% solution of acid? Answer: quarts
Answer:
Step-by-step explanation:
How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 40% solution of acid? Answer: quarts
let x = amount of the 50% solution
A typical mixture equation using the decimal equivalent to
0.50x +0 .20(20) =0 .40(x+20)
0.50x + 4 = 0.40x + 8
0.50x - 0.40x = 8 - 4
0.10x = 4
x = 4/0.1
x = 40 qts of 50% solution
Hence 40 quarts of 50% solution must be added.Answer:
40 quarts I checked in RSM portal
The slope of the rafter is 15 m.Half the run of the rafter measure 12m.find the height of the ridge from the base
Answer:
[tex]9\; \rm m[/tex].
Step-by-step explanation:
Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with [tex]\rm 12\; m[/tex]. The three labelled lines in this diagram will form a right triangle.
The line marked as [tex]15\; \rm m[/tex] will be the hypotenuse of this right triangle.The line marked as [tex]12\; \rm m[/tex] will be one of the triangle's legs.The line representing the height of the ridge (the one with the question mark) will be the other leg of this right triangle.Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:
[tex](\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2[/tex].
In this particular right triangle:
[tex](\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2[/tex].
[tex](\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2[/tex].
Therefore, the height of this ridge would be [tex]\sqrt{81}\; \rm m = 9\; \rm m[/tex]. (Note the unit.)
8. The difference between two numbers is 14. If 1/3of the larger number is subtracted from the smaller number, the
result equals 1/10 of their sum. Find both numbers.
Answer:
The values of the 2 numbers whose sum is 13 and difference is 3, are: {8 ; 5}.
Step-by-step explanation:
i think of a number, multiply it by 2, subtract 3, and multiply the result by 4
Answer:
4(2x-3)
Step-by-step explanation:
Let the number be x
⇒ Multiplying by 2 makes it 2x
⇒ Subtracting 3 makes it 2x-3
⇒ Multiplying the whole by 4 gives 4(2x-3)
13. Jane buys a set of 17 spiral notebooks. Each notebook has 95 pages. What is total number of pages?
Multiply number of notebooks by number of pages in each one.
17 x 95 = 1615
The answer is 1,615 total pages
Answer:
A. 1615
Step-by-step explanation:
Solve as shown:
17 books that each have 95 pages equals the total pages.
17(95)=?
17(95)=1615
My question is 3x + (2− 4x)
Answer:
3x+(2-4x)
= 2 (3x+4x)
=2 (7x)
=2/7x
=7x/2
=3.5
Step-by-step explanation:=3.5
You roll a twelve-sided die (having values one through twelve on its faces). What is the probability that the value of the roll will be a composite number?
show work pls!
help pls!
Step-by-step explanation:
Probability
Probability is a measure of the likelihood that an event will happen.
When dealing with probability, the outcomes of a process are the possible results. For example, when a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the "event" happening. For instance, "rolling an even number" is an event that corresponds to the set of outcomes {2, 4, 6}. The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its "favorable outcomes".
Probability =
A rectangular prism with length and, width w, and height hhh has a volume of, w, h. What is the volume of a prism which has a base of 5\text{ m}5 m5, start text, space, m, end text by 3\text{ m}3 m3, start text, space, m, end text, and a height of 4\text{ m}4 m4, start text, space, m, end text
Answer:
60 m³
Step-by-step explanation:
A rectangular prism also called a cuboid is a shape that have six faces that are rectangles. The volume of a rectangular prism is the product of its length, width and height, i.e volume = length (l) × breadth (b) × height (h).
Given a prism with a base of length (l) = 5 m by width (w) = 3 m and a height (h) = 4 m.
Volume= l × b × h
Volume = 5 m × 4 m × 3 m = 60 m³
Answer:
60m3
Step-by-step explanation:
what is the answer to 18−(2x+1) = ???
Answer & Step-by-step explanation:
18 - (2x + 1)
Distribute the negative sign (-) to 2x + 1.
18 - 2x - 1
Put -2x in the beginning of the expression and combine like terms.
-2x + 17
So, the answer to 18 - (2x + 1) is -2x + 17.
£880 is divided between Jim, Krutika & Natasha so that Jim gets twice as much as Krutika, and Krutika gets three times as much as Natasha. How much does Krutika get?
Answer:
264 pounds
Step-by-step explanation:
Write the question in the form of a ratio:
Natasha: Krutika: Jim
1:3:6
Now, we divide the amount of 880 in the ratio.
there are 10 parts in total.
1 part = 880 divided by 10 = 88.
since Krutika gets 3 parts, she gets 88 x 3 = 264
If f(x) = 1 + x2 and g(x) = 1-, which is the rule of function (f-)(x)?
Answer:
= -x^2 +x
Step-by-step explanation:
(x) = 1 - x^2
g(x) = 1-x,
(f-g)(x) = 1-x^2 - ( 1-x)
Distribute the minus sign
= 1-x^2 -1 +x
Combine like terms
= -x^2 +x
(6x?+ 5) - (4x - 3)
A. 6x2 - 4x + 2
B. 2x2 + 2
C. 2x2 + 8
O D. 6x2 - 4x + 8
Answer:
6x^2 -4x +8
Step-by-step explanation:
(6x^2+ 5) - (4x - 3)
Distribute the minus sign
(6x^2+ 5) - 4x + 3
Combine like terms
6x^2 -4x +8
Answer:
Step-by-step explanation:
C
What is the measure of angle BCD? WILL GIVE BRAINLIEST!
Answer:
m∠BCD = 120°
Step-by-step explanation:
Since the interior angles of a quadrilateral add up to 360°, then we get:
2x+x+2x+x=360°
6x=360°
Divide both sides by 6
x=60°
Since ∠BCD's value is 2x and x is equal to 60°, then ∠BCD is 120°.
The slope-intercept form of the equation of a line that passes through point (–3, 8) is y=-2/3 x+6.What is the point-slope form of the equation for this line?
Answer:
Step-by-step explanation:
y - 8 = -2/3(x + 3)
y - 8 = -2/3x - 2
y = -2/3x + 6
