Answer:
There are 14 pencils and 8 are blue
The probability of picking blue in the first pick = 8/14 =4/7.
The probability of picking blue in the second pick = 7/13 (as no replacement was there).
There are 14pencils and 6 are red.
The probability of picking red in the first pick = 6/14 =3/7
The probability of picking red in the second pick = 5/13. (as no replacement was there).
which fraction is equivalent to 2/6
Answer:
1/3, 2/6, 3/9, 4/12..are equivalent fractions. Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get.
Step-by-step explanation:
The equivalent fractions of the given fraction [tex]\dfrac{2}{6}[/tex] are [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex] .
The fractions which have the same value but can have different numerators or denominators when either multiplying , dividing or converting it into the lowest form is called equivalent fractions
The upper part of a fraction or part of a whole is called numerator and the lower part of a fraction or the whole is called denominator.
Equivalent fraction can be obtained by multiplying numerator and denominator with the same number .
Example : equivalent fraction of [tex]\dfrac{5}{8}[/tex] is
[tex]\dfrac{5}{8} = \dfrac{5 \times 1 }{8 \times 1} =\dfrac{5\times2}{8\times2} ........=\dfrac{5}{8}[/tex]
According to the data provided in the problem
[tex]\dfrac{2}{6} = \dfrac{2 \times 1 }{6 \times 1} =\dfrac{2\times2}{6\times2} ........=\dfrac{2}{6}[/tex]
Thus the equivalent fractions of [tex]\dfrac{2}{6}[/tex] are [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex]
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(4x+3 )+ (-2x+4 )expressions
Urgent please help..
Evaluation the expression
Answer:3b+10
Explanation:Distribution:5(b+2)-2b
5b+10b-2b
Combine like terms:5b+10b-2b
=3b+10
Answer:
3b+10
Step-by-step explanation:
What is the answer to this?
Answer:
7= -3c - 2
7+2= -3
9= -3c
c=9/-3
c= -3
ax + 7 = 2x + b
Find x
Answer:
x = [tex]\frac{b-7}{a-2}[/tex]
Step-by-step explanation:
Given
ax + 7 = 2x + b ( subtract 2x from both sides )
ax - 2x + 7 = b ( subtract 7 from both sides )
ax - 2x = b - 7 ← factor out x from each term on the left side
x(a - 2) = b - 7 ← divide both sides by (a - 2)
x = [tex]\frac{b-7}{a-2}[/tex]
Find the 7th term in the
sequence
-1, 2, -4, 8,...
Answer:
every other term is negative, so it would be -64
Step-by-step explanation:
hope it helps!
Use a calculator to find an angle that has a tangent of 5/4 Round your answer to the nearest degree. Verify your
answer by using a right triangle.
a. 510
b. 45°
C. 60°
d. 57°
Answer:
The answer is 51 degrees
Step-by-step explanation:
i like to convert the fraction first and then round up
Use trigonometric identities to simplify each expression.
1/cot^2 (x) - 1/cos^2(x)
Answer:
- 1
Step-by-step explanation:
[tex]\frac{1}{\cot ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cos \left(x\right)}=\sec \left(x\right),\\\frac{1}{\cot ^2\left(x\right)}-\sec ^2\left(x\right)\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cot \left(x\right)}=\tan \left(x\right),\\\tan ^2\left(x\right)-\sec ^2\left(x\right)\\\\=> \frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\[/tex]
[tex]=> \frac{\sin ^2\left(x\right)-1}{\cos ^2\left(x\right)}\\\\=> -\frac{\cos ^2\left(x\right)}{\cos ^2\left(x\right)}\\=> - 1[/tex]
Hope that helps!
By using trigonometric identities, [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1
What are trigonometric identities?"Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain."
Given expression
[tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex]
We know the trigonometric identity
[tex]{cot^{2}(x) } =( \frac{sinx}{cosx})^{2}[/tex]
= [tex]\frac{1}{(\frac{cosx}{sinx} )^{2} } -\frac{1}{cos^{2}(x) }[/tex]
= [tex]\frac{sin^{2} (x)}{cos^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex]
= [tex]\frac{sin^{2}(x)-1}{cos^{2}x }[/tex]
= [tex]\frac{-(1- sin^{2}(x))}{cos^{2}x }[/tex]
We know the trigonometric identity
[tex]sin^{2}(x) +cos^{2}(x) = 1[/tex]
= [tex]\frac{-(cos^{2}x)}{cos^{2}x }[/tex]
= -1
Hence, [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1
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A local council is concerned that there are too many students for staff to look after in schools. There are 18 staff and 225 students in school A. a Write the staff : student ratio in the form 1 : n.
you have to find a number they are both divisible by to get it to simplest form. 18:225.
divide both by 3. 6:75.
you can divide it by 3 again.
answer: 2:25
The ratio of two quantities can be obtained by writing them as a fraction. The ratio in the form of 1 : n is given as 225 / 18.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
Given that,
The number of staff in the school = 18
And, the number of students in the school = 225
Since, the ratio of two numbers a and b is given as a : b = a / b.
In the form of 1 : n it can be written as, a : b = 1 / (b / a).
Similarly, the ratio of staff and students n the form of 1 : n can be written as,
Staff : Students = 18 : 225
=> Staff : Students = 1 / (18 / 225)
=> Staff : Students = 225 / 18.
Hence, the ratio Staff : Students can be written in the form 1 : n as 225 / 18.
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A number cube is rolled and a letter is selected from the word PENGUIN.
P(an even number and N)
A. 1/7
B. 2/9
C. 4/15
D. 1/14
Find the unit rate.
1/2 pound : 5 days
Answer:
= 0.2 pound per day
Step-by-step explanation:
This is a fraction equal to
1 pound ÷ 5 days
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 5
1 pound ÷ 5
5 days ÷ 5
=
0.2 pound
1 day
=
0.2 pound
day
= 0.2 pound per day
[tex] - \frac{2}{3} + 4 \times \frac{1}{3} [/tex]
Answer:
2/3
Step-by-step explanation:
You first multiply 4x1/3 which equals 4/3. Now you do -2/3+4/3=2/3. Hope this helps!
Answer:
2/3
Step-by-step explanation:
[tex]\frac{-2}{3}+4*\frac{1}{3}=\frac{-2}{3}+\frac{4}{3}\\\\=\frac{(-2) + 4}{3}\\\\\\= \frac{2}{3}[/tex]
Pls help ASAP An operation * is defined on the set of real numbers R by a*b=a³+b³ -3ab for all a,b is an element of R. Is the Operation * commutative
Answer:
The operation is commutative
Step-by-step explanation:
Operations
The * operation is defined on the set of real numbers R by
[tex]a * b=a^3+b^3-3ab[/tex]
For the operation to be commutative a*b should be equal to b*a.
Computing b*a:
[tex]b * a=b^3+a^3-3ba[/tex]
Rearranging:
[tex]b * a=a^3+b^3-3ab[/tex]
It's apparent that a*b=b*a, thus the operation is commutative
What is the starting point of the quadratic function defined by y=-2x2-25x+10?
Step-by-step explanation:
y=-2x²-25x+10
=x²+25/2x-5
Eleman sayısı 2 arttırıldığında alt küme sayısı 24 artan bir kümenin eleman sayısı kaçtır
Answer:
What?
Step-by-step explanation:
The sign of the leading coefficient for the polynomial equation of the graph is . This graph has turning point(s). Possible degrees for this graph include: 4 5 6 7
Answer:
negative
1
4,6
Step-by-step explanation:
Answer:
A&C
Step-by-step explanation:
help me with this mathematic problem
Answer:
I dont know
Step-by-step explanation:
The diagram shows a prism.
The cross section of the prism is a right-angled triangle.
The lengths of the sides of the triangle are 8 cm, 15 cm and 17 cm.
The length of the prism is 20 cm.
Work out the total surface area of the prism.
Diagram NOT
accurately drawn
8 cm
17 cm
20 cm
15 cm
Answer:
Total surface area of the prism = 920 cm²
Step-by-step explanation:
Given prism has 2 similar triangular surfaces and 3 rectangular surfaces of different dimensions.
Area of one triangular side = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
Area of 2 similar sides = Base × Height
= 8 × 15
= 120 cm²
Area of rectangular side with dimensions 17cm × 20cm
Area of the side = 17 × 20 = 340 cm²
Area of the second rectangular side with dimensions 8cm × 20cm
Area of the side = 8 × 20 = 160 cm²
Area of third rectangular side with dimensions 20cm × 15cm
Area of the side = 20 × 15 = 300 cm²
Total surface area of the given triangular prism = 120 + 340 + 160 + 300
= 920 cm²
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
Given:
The two points on a coordinate plane are C(-5,-1) and D(0,3).
To find:
The distance between C and D.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the distance formula, the distance between C(-5,-1) and D(0,3) is
[tex]CD=\sqrt{(0-(-5))^2+(3-(-1))^2}[/tex]
[tex]CD=\sqrt{(0+5)^2+(3+1)^2}[/tex]
[tex]CD=\sqrt{(5)^2+(4)^2}[/tex]
[tex]CD=\sqrt{25+16}[/tex]
On further simplification, we get
[tex]CD=\sqrt{41}[/tex]
[tex]CD=6.40312424[/tex]
[tex]CD\approx 6.40[/tex]
Therefore, the distance between C and D is 6.40 units.
Which decimal is equal to 6/20?
1. 0.6
2. 0.15
3. 0.2
4. 0.3
5. 04
Answer:
6/20 as a decimal is 0.3 i hope i helped you
What is the median of this data set?
Answer:
The median is 2
Step-by-step explanation:
The middle number of the data set(highlighted dots) is 2.
Hope this helps!
:)
What is the sum of the digits in the expansion of (10^36+26/18)
Answer:
=177
Step-by-step explanation:
The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (10³⁶ + 26/18)
The sum of the digits in the expansion is given as,
⇒ 1 + 0 + 2 + 6 + 1 + 8
⇒ 18
The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.
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Jeremy wants to build a cage for his rabbits. The pet store suggests he build a cage in the shape of a rectangular prism with a floor space of at least 1,080 in.2 and a surface area of no more than 4,272 in.2. Which measurements could Jeremy use for his cage?
Answer:
Step-by-step explanation:
I am unsure on how to solve x
Answer:
180-165= 15
(They tried to throw you off with the second line)
Answer is 15 degrees
How much money does Bob the Brick-layer need for his material costs?
He can lay 100 bricks in an hour. He charges $150 per hour for brick laying,
What is the total cost for Bob to do the job?
I need help with my math homework
Answer:
y = 3x - 14
Step-by-step explanation:
y - y₁ = m(x - x₁)
⇒ y - 1 = 3(x - 5)
⇒ y - 1 = 3x - 15
⇒ y = 3x - 14
Triangles multiple choice!!
Answer:
B
Step-by-step explanation:
Using Pythagoras' identity in right triangle ABC
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AB² + AC² = BC² , substitute values
5² + AC² = 13²
25 + AC² = 169 ( subtract 25 from both sides )
AC² = 144 ( take the square root of both sides )
AC = [tex]\sqrt{144}[/tex] = 12
Since the triangles are congruent then corresponding sides are congruent, then
DE = AC = 12 inches → B
There are 60 seventh-grade students in William's school. The students need to choose someone to wear the mascot costume on field day. Huey and Sal are texting about it. Huey: We can give everyone a number from 1 to 60. The we can roll 10 number cubes and add it to the results. The person whose number is equal to the sum wears the costume. Sal: That doesnt seem fair how about this? Everyone gets a number from 0 to 59. Put blocks numbered 0 to 5 in a bag. In another bag, put blocks numbered 0 to 9. Pick a block from the first bag for the tens digit and a block from the second bag for the ones digit. A. Is Huey's plan unfair as Sal claims? If so, why is it unfair? B. Is Sal's plan fair or unfair? Explain your answer. HURRY ANSWERING THIS PLS THIS THING DUE BEFORE 11:59PM
Answer:
Step-by-step explanation:
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the value of a dirtbike increases by 30% each year if you purchased this dirtbike today for $500 to the nearest dollar how much will the bike be worth five years later
Answer:
$1856.47
Step-by-step explanation:
500 x 1.3^5=1856.465