There are 24 students in the class. Take 2/3 of this to get (2/3)*24 = 16
A more detailed step by step would be
(2/3)*24 = (2/3)*(24/1) = (2*24)/(3*1) = 48/3 = 16
The result 16 is smaller than the original number 24. This is expected because 2/3 is smaller than 1. The key thing here is that the result 16 is a whole number.
You can think of 2/3 as the approximate percentage 66.7%, so you're applying roughly 66.7% to the entire class to get 16 people who like hip hop.
It appears you're thinking in reverse when you went from 24 to 36, because 2/3 of 36 is 24, but not the other way around. Keep in mind there are 24 students total in the class, and we can't go higher than this. We can't say there are 36 people who like hip hop.
So to answer the question, yes it is possible Gertrude's survey is correct because 2/3 of 24 is a whole number.
What is the mean of this data set? {10, 15, 12, 6, 2}
The diagram below shows two circles which have the same centre O and radii 16 cm and
10 cm respectively. The two arcs AB and CD have the same sector angle 8 =1.5 radians.
В
Find the area of the shaded region.
Answer:PPlEASeee
Step-by-step explanation:
Point A(4, 5) is translated two units left and three units up. What are the new coordinates of point A
Answer:
A': (2, 8)
Step-by-step explanation:
I have attached the work to your problem below.
I hope this helps.
Solve by factorisation
2x2 + 3x - 20 = 0
Step-by-step explanation:
4 + 3x -20 = 0
3x - 16 = 0
3x = 16
x = 16/3
A square has a diagonal that measures 6 inches. Which of the following is the length of its perimeter?
(1) 8/3
(2) 1272
(3) 673
6 inches
(4) 1872
PLEASE HELP
Answer:
Perimeter of square = [tex]12\sqrt{2}\,\,inches[/tex].
None of the given options is correct
Step-by-step explanation:
Given: Length of diagonal of the square = 6 inches
To find: perimeter of square
Solution:
Let x denotes side of square
Diagonal of square = [tex]\sqrt{2}x[/tex]
Also, length of diagonal of the square = 6 inches
So,
[tex]x=\frac{6}{\sqrt{2}}\\=\frac{6}{\sqrt{2}}\left ( \frac{\sqrt{2}}{\sqrt{2}} \right )\\=3\sqrt{2}[/tex]
Perimeter refers to the distance around a two-dimensional shape.
Perimeter of square = 4×side
=[tex]4(3\sqrt{2})=12\sqrt{2}\,\,inches[/tex]
So, none of the given options is correct.
A group of 2 adults and 4 children spent $38 on
tickets to a museum. A group of 3 adults and 3
children spent $40.50 on tickets to the museum.
Based on this information, how much is an adult
ticket, and how much is a child ticket?
2a + 4c = 38.00
3a + 3c = 40.50
What values of a and c represent the solution to
the system?
a=
C=
DONE
Answer:
A) 2a + 4c = 38.00
B) 3a + 3c = 40.50
We multiply A) by -1.5
A) -3a -6c = -57 then we add B)
B) 3a + 3c = 40.50
-3c = -16.50
c = 5.50
a = 8.00
Step-by-step explanation:
After travelling 2/5 of a Journey
a driver found that he had
60km
more to go
find the length
of the whole Journey?
Answer:
= 100 km
Step-by-step explanation:
Total length = 5/5
Covered length = 2/5
Remaining length = 5/5 - 2/5 = 3/5
If 3/5 = 60 km
What about 5/5 = ?
= 5/5 x 60 x 5/3 (reciprical)
= 60 x 5/3
= 300/3
= 100 km
Covered distance = 100 - 60 = 40 km
3. Garrison deposited $500 in an account that
earns 3% interest compounded annually. How
much interest will the account earn after 6
years?
Answer:
$90
Step-by-step explanation:
3% $500= $15
$15 times 6yrs = $90
Answer:
97.03
Step-by-step explanation:
the other guy is wrong.
Select the protractor measuring an angle that is 55°.
A. Figure A
B. Figure B
C. Figure C
D. Figure D
Answer:
A. Figure A
Step-by-step explanation:
The protractor on the top left has an arrow halfway inbetween 50° and 60, making the angle 55°.
Therefore, the answer is Figure A.
Jack bought 5 pounds5 \text{ pounds} 5 pounds 5, start text, space, p, o, u, n, d, s, end text of Halloween candy. He gave out 3 pounds3\text{ pounds} 3 pounds 3, start text, space, p, o, u, n, d, s, end text of the candy to trick or treaters and ate 10 ounces10\text{ ounces} 10 ounces 10, start text, space, o, u, n, c, e, s, end text of the candy. How many ounces of Halloween candy does Jack have left?
Answer:
Amount of ounces of candy left = 22ouncesStep-by-step explanation:
Amount of halloween candy bought by Jack = 5pounds
Amount he gave trick = 3pounds
Amount jack ate = 10ounces
Before we can determine the amount of halloween candy that Jack has left, we need to convert the pounds to ounces in order to make the units consistent.
given 1pound = 16ounces
5pounds = 16* 5 ounces
5pounds = 80ounces
Also;
3pounds = 16*3 ounces
3pounds = 48ounces
Total amount of halloween used up by Jack = 48ounces + 10ounces
= 58ounces
Amount of ounces of candy left = Total amount of candy bought -amount used up
Amount of ounces of candy left = 80ounces - 58ounces
Amount of ounces of candy left = 22ounces
please help quickly !
Answer:
i think its 2nd , 3rd and last one but im not sure
Step-by-step explanation:
Please what is the answer to this question
2^2x–4^x+16
Answer:
x = 6
Step-by-step explanation:
At a glass vase factory, 2 out of the last 12 vases produced were chipped. Considering this
data, how many of the next 18 vases would you expect to be chipped?
Vases
Answer:
3 vases chipped.
Step-by-step explanation:
Let's use a ratio:
chipped : all
2 : 12
1 : 6
3 : 18
We can expect 3 out of 18 vases to be chipped.
Answer:
1
Step-by-step explanation:
First, write the experimental probability as a fraction in simplest form.
P(chipped)
=
chipped
total
=
2
20
=
1
10
The experimental probability is
1
10
.
We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.
1
10
=
n
10
1
10
(1010)
=
n
10
(1010) Multiply both sides by (1010)
110
= 10n Simplify
10
= 10n Simplify
1
= n Divide both sides by 10
You would expect 1 of the next 10 vases to be chipped.
4 rational numbers between 3/8 and 2/5
Step-by-step explanation:
3/8 = 15/40= 75/200
2/5 = 16/40 = 80/200
-> 4 rational numbers between 75/200 and 80/200 are 76/200, 77/200, 78/200, 79/200
THE HIGHEST POINT ON EARTH IS
MT. EVEREST AT 29,028 FEET. THE
LOWEST POINT ON EARTH IS ON ANTARCTICA
AT 8,327 FEET BELOW SEA LEVEL. DETERMINE THE
DIFFERENCE BETWEEN THE HIGHEST AND LOWEST
POINTS ON EARTH
Answer:
20,701 feet
Step-by-step explanation:
29,028-8,327= 20,701
answer these question
SOLVE these
1.(5x + 3 = x + 11)
2.(7x - 2 = 5x +14)
3.(18x - 15 - 12x + 16)
4.(9x - 19 = 2x - 5)
Answer:
x =2x = 8 x= 5.1667x =2Step-by-step explanation:
I hope it helps
solve f(x)=−3(x+1)(x−5)
Answer:
x=-1 x=5
Step-by-step explanation:
f(x) =−3(x+1)(x−5)
0 = −3(x+1)(x−5)
Using the zero product property
x+1 = 0 x-5=0
x=-1 x=5
Help me PLEASEEE I need help
Answer:
area of shaded portion=56 - 1/2 ×3×4=56-6= 50 yd^2
Edith is balancing her lawn care business’ check registry. Her initial balance was $5,850.25. She deposited a check for $45.00 and a check for $55.50. Edith then purchased a new rake for $32.65 and spent $17.50 on gas for the lawn mower. What is the balance after the deposits and purchases? $5,900.60 $5,699.60 $150.65 $6,000.90
3/6+3/6+1/6 what is the answeR
Answer: 1.16
Step-by-step explanation:
So we know [tex]\frac{3}{6} + \frac{3}{6}[/tex] will equal 1.
Now, let's take apart [tex]\frac{1}{6}[/tex] and divide it...
1 ÷ 6 = 0.16
1 + 0.16 = 1.16
[tex]\frac{3}{6} + \frac{3}{6} + \frac{1}{6} = 1.16[/tex]
I hope this helps!
What is the explicit formula for the arithmetic sequence?
an = 1.2 + (n - 1)1.5 an = 1.5 + (n − 1)1.2
an = 1.5+ (n - 1)3.9
an = 3.9+(n-1)1.5
Answer:
an = 1.2 + (n - 1) 1.5
Step-by-step explanation: opt A on edg
3) Smurfette is glad you're getting on with your adventure, but she wants to warn you that this last
system is "Smurfity smurf smurf!". She has a wire that is 100 inches long and cut into two pieces.
She wants you to find out if it's possible to bend one piece of wire into the shape of a square and the
other into the shape of a circle, so that the total area enclosed by the two pieces is 650 inches
squared. If this is possible, find the length of the side of the square, x, and the radius of the circle,
y. (Smurfette's Hint: Just smurf the smurf and the smurf...then smurf smurf the
smurf...and...smurf!!)
Answer:
take x=2.515834 and r=14.31386
Step-by-step explanation:
Let us call the the lenght of the side of the square as x. The total lenght of the wire is 100. Note that if we have a square of side x, it has a perimeter of 4x. That means, that we need a wire of length 4x to build a square of side x. Note that if we take a wire of length 4x, we have that the remainder is 100-4x. We will use this to form a circle. As for the square, since we are using the wire of length 100-4x to build a circle, it must happen that the perimeter of the circle is 100-4x.
Recall that the perimeter of a circle of radius r is [tex]2\pi r[/tex], so in this case , we have that [tex] 2\pi r = 100-4x[/tex] which implies that [tex]r =\frac{100-4x}{2\pi}[/tex].
Now, recall that the area of a square of side x is [tex]x^2[/tex]. Also, recall that the area of a circle of radius r is [tex]\pi r^2[/tex]. In our case, the area of the circle is given by
[tex] \pi r^2 = \pi (\frac{100-4x}{2\pi})^2[/tex]
Also, we are given that the sum of the areas of both figures is 650. That is
[tex] x^2 + \pi (\frac{100-4x}{2\pi})^2 = x^2+\frac{(100-4x)^2}{4\pi}=650[/tex]
By substracting 650 on both sides and multiplying by [tex]4\pi[/tex] this equation is equivalent to
[tex]4\pi x^2 + (100-4x)^2-650\cdot 4\pi =0[/tex]
if we expand [tex](100-4x)^2[/tex] and then group each term of x, x^2 we get :
[tex](4\pi+16)x^2-800x+100^2-650\cdot 4\pi =0[/tex]
Recall that given a cuadractic equation of the form [tex]ax^2+bx+c=0[/tex] the solution is given by
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In this case, the existence of a real solution is given by the expression [tex]b^2-4ac[/tex]. For it to have a real solution, it must happen that [tex]b^2-4ac\geq 0[/tex]
In this case, b=-800, c = 100^2-650\cdot 4\pi, a = 4\pi+16[/tex]
For this values, we get that [tex]b^2-4ac = 430681\geq 0[/tex], so the is a solution for our problem.
In this case,
[tex] x = \frac{-b - \sqrt[]{b^2-4ac}}{2a}= 2.515834[/tex]
and [tex] x = \frac{-b + \sqrt[]{b^2-4ac}}{2a}= 25.4891[/tex] are the two possible solutions for this problem. We can check that this values of x fulfill our restrictions. Note that if x=25.4891, by replacing in the value of r, we get that r=-0.3113853. Since r is the radius of the circle, it must be positive. Hence, x=25.4891 is discarted.For x=2.515834 we get a value of r=14.31386, so this is the answer
How do I find mGD and mDEF?
Answer:
118 degrees; 30 degrees
Step-by-step explanation:
2x+14=1/2((6+14x)-58)
2x+14=1/2(-52+14x)
2x+14=-26+7x
40=5x
x=8
6+14(8)=6+112=118
2(8)+14=16+14=30
Approximate the real zeros of f(x)= 3x^4 + x^2 - 1 to the nearest tenth. a. -0.7 , 0.7 c. -7, 7 b. -0.5, 0.5 d. -0.6, 0.6 Please select the best answer from the choices provided
A
B
C
D
Answer:
x ≈ - 0.7 ≈ 0.7; Option A
Step-by-step explanation:
Let us substitute f ( x ) with 0, as to find the " real zero value( s ) " of the function;
0 = 3x^4 + x^2 - 1 ⇒ Swap sides, as such,
3x^4 + x^2 - 1 = 0 ⇒ Rewrite equation with u being = x^2, u^2 = x^2,
3u^2 + u - 1 = 0 ⇒ And solve for u by completing the square,
3u^2 + u = 1 ⇒ Divide either side by 3,
u^2 + u / 3 = 1 / 3 ⇒ Write equation in the form x^2 + 2ax + a^2 = ( x + a )^2, solving for a,
2au = 1 / 3u,
a = ( 1 / 3u ) / 2u,
a = 1 / 6 ⇒ Add value of a^2 to either side of equation,
u^2 + u / 3 + ( 1 / 6 )^2 = 13 / 36,
( u + 1/ 6 )^2 = 13 / 36 ⇒ Solve for u,
u = ( √13 - 1 ) / 6, and u = ( - √13 - 1 ) / 6 ⇒ Substitute value of u back into first equation to solve for x,
x = √( - 1 + √13 ) / 6 ), x = - √( - 1 + √13 ) / 6 ), x = √( - 1 - √13 ) / 6 ), x = - √( - 1 - √13 ) / 6 ) ⇒ Convert to approximate decimal form,
x = 0.6589.... = - 0.6589....
Answer; x ≈ - 0.7 ≈ 0.7; Option A
Help ASAP! need to hand in by today
Q 5) No. of boys = 20
Answer:
Q 6) Total time taken to answer both the quizzes = 90 minutes
Step-by-step explanation:
Q 5.
Let the number of boys = x
Therefore, number of girls = x - 5
Since,
No. of boys + No. of girls = 35
hence,
x + x- 5 = 35
2x-5 = 35
2x = 35 + 5
2x = 40
x = 40/2
x = 20
Hence 20 boys participated in the activity.
Let the time taken to answer history quiz= x min
Therefore, time taken to answer geography quiz = (x + 30) min
According to the given information:
x = 1/2(x + 30)
2x = x + 30
2x - x = 30
x = 30 min
Hence, x + 30 = 30 + 30 = 60 min
Total time taken to answer both the quizzes = 30 + 60 = 90 minutes
3/11÷3/11 what is the answer
Answer:
1
Step-by-step explanation:
3/11 / 3/11
=3/11 * 11/3
=1
Need DESPERATE help! I'm taking a unit test for math (k12, 10th grade) I got 3 done already so here's the ones I missed: Question 5: Use the inverse sine to find the measure of J J<->L: 16 L<->K: 5 OPTIONS: 20.0, 19.4, 18.2, and 18.0 Question 6: ΔXYZ is a right triangle with right angle X, sin Y = m, and cos Y = k.What is cos Z − sin Z ? OPTIONS: m-k, 2m, k+m, k-m Question 7: Given, sin x (1161) and cos x (6061). What is tan x? OPTIONS: 61/60, 61/11, 11/60, 1 Question 8: ΔABC is a 30-60-90 triangle where m∠B = 90°. The length of the shorter leg is 11 units. What is the length of the hypotenuse? ______ units
Answer:
Step-by-step explanation:
Question 6)
sin Y= m
sin Y = m/1
So, hypotenuse is 1
Since sine is opposite over hypotenuse
So XZ= m and YZ = 1
Similarly, cos Y = k
cos Y = k/1
So adjacent side of angle Y is k
So XY = k
cos z - sin z = [tex]\frac{XZ }{YZ } - \frac{XY}{YZ}[/tex]
cos z - sin z = [tex]\frac{m }{1 } - \frac{k}{1}[/tex]
cos z - sin z = m - k
Question 7)
the relationship between sine, cosine, and tangent.
tan(x) = sin(x)/cos(x) = (11/61)/(60/61)
tan(x) = 11/60
Question 8)
Start with where the shorter leg is. It must be opposite the smallest angle.
In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it.
That being said, if the shortest side is x, the hypotenuse will be 2x.
Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22
The answer is 22
Given the sequence 7, 14, 28, 56, ..., which expression shown would give the tenth term? 7^10 7·2^10 7·2^9
Answer:
F(1) = 7
F(2) = 14 = 7 x 2^1
F(3) = 28 = 7 x 2^2
F(4) =56 = 7 x 2^3
...
F(10) = 7 x 2^9
Hope this helps!
:)
What is the algebraic expression for the area of this house block?
Answer:
x² + 27x + 180
Step-by-step explanation:
(12 + x)(15 +x) = 12*15 + 12x + 15x + x² = x² + 27x + 180
Pablo is simplifying the expression below.
Negative one-fourth (8 x + 12) minus (negative 2 x + 5)
He used the steps below to simplify the expression.
Negative one-fourth (8 x + 12) minus (negative 2 x + 5) = negative 2 x minus 3 + 2 x minus 5 = negative 8
Which statement is true about the steps that Pablo used to simplify the expression?
He combined like terms inside the parentheses, distributed Negative one-fourth over (8 x + 12), and then combined the remaining like terms.
He combined like terms inside the parentheses, distributed Negative one-fourth over (Negative 2 x + 5), and then combined the remaining like terms.
He distributed Negative one-fourth over (8 x + 12), distributed 1 over (Negative 2 x + 5), and then combined like terms.
He distributed Negative one-fourth over (8 x + 12), distributed –1 over (Negative 2 x + 5), and then combined like terms.
Answer:
D. He distributed Negative one-fourth over (8 x + 12), distributed –1 over (Negative 2 x + 5), and then combined like terms.
Step-by-step explanation:
We know that when using the distributive property, you have to multiply the outside value with the inside value and then either subtract or add.
You can combine like terms first, but that is only if there are like terms inside the parentheses. In this case, there are not, so you would distribute first.
So, to do that, you have to first distribute -1/4 to the 8x+12 and then distribute the -1 to the -2x+5. (note that they did not include the 1, but it is still there)
So, it is D