The probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
Probability = Number of Favorable Outcomes/Number of outcomes
For a) P( getting 5) = 1/10
b) P( getting less than 5) = 4/10 , (Favorable outcomes = 1,2,3,4)
= 2/5
c) P (divisible by 3 ) = 3/10 , (Favorable outcomes = 3,6,9)
d) P( divisible by 4) = 2/10 , (Favorable outcomes = 4, 8)
= 1/5
So, the probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
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the gas/oil ratio for a certain chainsaw is 20 to 1 a.how much oil (in gallons) shouls be mixed with 8 gallons of gasoline b.if 1 gallon equals 128 fluid ounces write the answer to part a in fluid ounces
As per the given ratio
a. Quantity of oil mixed with 8 gallons of gasoline is (8/20) gallons.
b. If 1 gallons=128fluid ounces then (8/20)gallons=51.2 fluid ounces.
As given in the question,
(Gas /oil) ratio=20: 1
Let x gallons of oil mixed with 8 gallons of gasoline
a.
21:1=8 : x
⇒x=(8/20) gallons
b.
1 gallon=128 fluid ounces
⇒(8/20)gallons=(8/20)×128
=51.2fluid ounces
Therefore, as per the given ratio
a. Quantity of oil should be mixed with 8 gallons of gasoline is (8/20) gallons.
b. If 1 gallons = 128fluid ounces then (8/20)gallons=51.2 fluid ounces.
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A total of $35,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested
in bonds is to exceed that in CDs by $1,000, how much will be invested in each type of investment?
The amount invested in CDs is S
The amount invested in bonds is
The amount invested in each type of investment should be $17,000 and $18,000, respectively, as this problem is based on simple interest.
What is a simple mathematical interest?Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
based on the facts provided;
Calculating the investment amount:
Since the certificate of deposit is assumed to be x in this instance, the bond should be $35,000 - x.
The formula now should be
($35,000 - x) - x = $1,000
$35,000 - 2x = $1,000
$34,000 = 2x
x = $17,000
So, the bond should be
= $35,000 - $17,000
= $18,000
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Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
Write a polynomial that will be the area of the framed picture.
What will be the area of the picture with the frame if x=3?
If the width of the painting is w, then its length is 2w. Then, since the frame is 2 inches thick on each side of the painting, its width is w+4 and its length is 2w+4. So the area of the rectangle bounded by the frame (which includes both the area of the frame and the area of the painting) is (w+4)(2w+4).
The area of the painting is w×2w=2w2, and the area of the frame is 196 square inches, so the area of the two combined is 2w2+196. However, that is the same area as the other one I described, so we can then equate the two, i.e. (w+4)(2w+4)=2w2+196. You can then solve that equation for w, and hence find all of the relevant dimensions.
what values of a and b make this equaltion true? /sqrt648 = /sqrt2^a x 3^b
The values of a and b make this equation true/sqrt648 = /sqrt2^a x 3^b will be a = 3 and b = 4.
How to illustrate the information?It should be noted that from the information given, the equation is given as:
✓648 = ✓(2^a × 3^b)
when a = 3
b = 4
This will be illustrated as:
✓648 = ✓(2^a × 3^b)
✓648 = ✓(2³ × 3⁴)
✓648 = ✓(8 × 729)
Therefore, the values of a and b make this equation true? /sqrt648 = /sqrt2^a x 3^b will be a = 3 and b = 4.
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There are 48 people at a party. There are seven times as many adults as children. There are twice
s many females as males. If there are 5 girls (female children) at the party, how many men (male
adults) are there?
48 persons are present at the gathering. There are seven times more adults than children in the world. The number of women is two times that of men. If there are five females (young women) in attendance. The total number of male adults are15
The total number of people are in the party is equal to 48
Let the number of children be x
So, the number of adults in the party is equal to 7 x
x + 7 x =48 ( This is a linear equation)
So, the number of children in the comes to be 6
Number of adults in the party = 6 * 7 = 42
Now let the number of males be y
So total number of females = 2 y
Y+2y = 48 ( This is a linear equation)
Y=16
Therefore, the number of males is 16 and the number of females is 32
The number of children in the party is 6 and the female child is equal to 5
Then, the number of male children =6-5 = 1
So total number of males in the party is equal to 16
Adult males =total number of males - number of male children
=16 - 1 = 15
Hence the total number of male adults =15
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What’s next in this pattern and what would be the conjecture of this pattern? Please I really need help fast
The next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
How to determine the next in the pattern?The pattern is given as:
↑, →, ↓
In the above pattern, we can see that each arrow is rotated 90 degrees in the clockwise direction
When the arrow ↓ is rotated in this direction, we have:
←
Hence, the next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
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What’s 8^2x4^2 please help lol
Answer:
1024
Step-by-step explanation:
8^2=8x8=64
4^2=4x4=16
64x16=1024 :)
Answer: 1024
Step-by-step explanation: 8^2 times 4^2=80. When you square a number, you multiply it by itself. So, 8^2 = 8 times 8 which equals 64. 4^2 = 4 times 4 which equals 16. 64 times 16 = 1024.
The sum of three lengths of a fence rages from 31 to 40 inches. Two side lengths are 9 and 12 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side
Answer:
10 ≤ x ≤ 19
Step-by-step explanation
The sum of the three lengths is 9 + 12 +x = 21 + x
We know the sum ranges from 31 to 40
So we get the inequality
31 ≤ 21 + x ≤ 40
Subtracting 21 from each part of this inequality give
31-21 ≤ x ≤40-21
10 ≤ x ≤ 19
The compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given as,
Range of sum of three lengths of a fence = 31 to 40 inches
Length of two sides = 9 and 12 inches
Length of third sides = x inches
So, length of sum of three lengths of a fence = 9 + 12 + x
⇒ length of sum of three lengths of a fence = 21 + x
∵ Range of sum of three lengths of a fence = 31 to 40 inches
31 ≤ length of sum of three lengths of a fence ≤ 40
⇒ 31 ≤ 21 + x ≤ 40
Subtracting 21 we get.
10 ≤ x ≤ 19
Thus, the compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
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What is the solution to the inequality? |x−2|≥9
Due to modulus there can be two answers, one with greater than equal to and one with less than equal to. So the answer is 11 and -7.
Solve the inequality |x−2|≥9
Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.
a) |x−2|≥9 = x-2≥ 9
=> x≥ 9+2
=> x≥ 11
b) |x−2|≥9 = x-2≥ -9 (when sign the negative the greater than equal to sign changes to less than equal to sign)
= x ≤ -9+2 ≤-7
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F(x) = 2x-1. Translation 3 units right followed by a vertical stretch by a factor of 2.
According to the parameters given, the rule again for graph of g after so transformations of a function F(x) = 2x - 1 is g(x) = -4x + 4.
What is defined by the term translation?A translation is a form of transformation in which every point in a figure moves the same distance within the same direction. are frequently alluded to as slides A translation can be described using words such as "moved up 3 more than 5 to the left" or even with notation.The graph for the given function defined by the equation;
F(x) = 2x - 1
Initially, the graph of g is a three-unit translation, so we have;
g(x) = f(x) + 3g(x) = 2x - 1 + 3 = 2x + 2Then comes a vertical stretch by such a factor of two and a reflection in the x axis.
The above means that graph must all be multiplied by 2 and that x values containing x are now considered to be -x.
g(x) = 4x + 4And an x-axis reflection yields;
g(x) = 4(-x) + 4g(x) = -4x + 4Thus, the rule for making the graph of function g(x) is by; g(x) = -4x + 4.
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If a function is differentiable, then it is continuous. True or false?
f(1)=30,f(n)=2•f(n-1)-50
The explicit formula of the sequence is Tn = 30 - 20(n - 1)
How to determine the explicit formula of the sequence?The recursive formula of the sequence is given as
f(1) = 30, f(n) = 2 • f(n - 1) - 50
The above means that
f(n) = 2 • f(n - 1) - 50
f(1) = 30
Substitute 2 for n
So, we have
f(2) = 2 • f(2 - 1) - 50
Evaluate the difference
So, we have
f(2) = 2 • f(1) - 50
Substitute f(1) = 30 in f(2) = 2 • f(1) - 50
f(2) = 2 • 30 - 50
Evaluate
f(2) = 10
Substitute 3 for n
So, we have
f(3) = 2 • f(3 - 1) - 50
Evaluate the difference
So, we have
f(3) = 2 • f(2) - 50
Substitute f(2) = 10 in f(3) = 2 • f(2) - 50
f(3) = 2 • 10 - 50
Evaluate
f(3) = -30
So, we have the first three terms to be
30, 10, -10
The above represents an arithmetic sequence, where
First term, a = 30
Common difference = -20
The nth term of the sequence is
Tn = a + (n - 1)d
So, we have
Tn = 30 - 20(n - 1)
Hence, the explicit formula of the sequence is Tn = 30 - 20(n - 1)
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Can someone help me please
Using translation concepts, the graph of square CDEF after a rotation 270º counterclockwise around the origin is given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a rotation 270º counterclockwise around the origin is:
(x,y) -> (y,-x).
Hence the vertices of the rotated graph will be given as follows:
E': (-4,-3) -> (-3, 4).F': (-9,-3) -> (-3, 9).D': (-4,-8) -> (-8, 4).C': (-9,-8) -> (-8, 9).The graph with these vertices is given at the end of the answer.
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SOMEONE HELP PLS ILL MARK BRAINLIEST
Answer:
Statements:
1) -2(x-4)=2x+12
2) -2x+8=2x+12
3) -4x+8=12
4) -4x=4
5) x=-1
Reasons:
1) Given
2) Distributive Property
3) Combine like terms/Subtraction Property of Equality (subtract 2x from both sides).
4) Subtraction Property of Equality
5) Division Property of Equality
find the volume of a cylinder with radius 6 and height 16,pi= 3.142
The volume of the cylinder is 1809.5 cubic units.
What is the volume of a cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it
V = πr²h
where 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given that a cylinder with a radius of 6 and height of 16.
Here r = 6 and h = 16,
the volume of a cylinder = πr²h
the volume of a cylinder = π(6)²×16
the volume of a cylinder = 1809.5 cubic units
Thus, the volume of the cylinder is 1809.5 cubic units.
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30. Place the following values in order from
greatest to least:
3п, 4√5, 5√4
9. Steven wants to buy a $595 bicycle. Steven has no money saved, but will be able to deposit $30 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he
must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his
savings account before he can pay back his sister and buy the bike?
22 weeks
b.
21 weeks
d.
23 weeks
26 weeks
C.
a.
5
Answer:
22 weeks
Step-by-step explanation:
595+65=660
22x30=660
so he could buy a bicycle and owes his sister the money after 22 weeks
A p e x Algebra II
f(x) = |2x +1| + 3
g(x) = -2
Find (f + g) (x).
A. (f + g) (x) = |2x + 2|
B. (f + g) (x) = |2x + 1| + 1
C.（f + g) (x) = |2x + 4| - 2
D. (f + g) (2) = |2x| + 2
The solution to (f + g) (x) is Option B: |2x +1| + 1
How to add functions?
We are given the functions;
f(x) = |2x +1| + 3
g(x) = -2
Now, we want to solve for (f + g) (x). From operations of functions, we know that there are different operations which could include addition, division, multiplication and subtraction. However, in this case;
(f + g) (x) simply means;
(f + g) (x) = f(x) + g(x)
Thus, we have;
(f + g) (x) = |2x +1| + 3 + (-2)
= |2x +1| + 3 - 2
= |2x +1| + 1
Thus, the solution to (f + g) (x) is Option B: |2x +1| + 1
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5 Four friends volunteered to help Mr. Kirby build a new fence around
his property. If the property had a perimeter of 880 ft., how many feet
of fence would each man, including Mr. Kirby, have to build?
Hello,
Does this exercise look correct?
10. Rebecca goes to a bank with $2000 she has saved over the summer. The bank advertises a 3% interest rate when opening a savings account. The bank compounds the money daily with an exponential formula of A(t) = Pe^rt, where P represents the initial amount deposited, e is Euler's constant (approximately 2.71828), r is the rate in decimal form, and t is the total time. Rebecca wants to know how much money will be in her savings account after 10 years.
P = 2000
e = Euler's constant (2.71828)
r = 0.03
t = 10
A(t) = Pe^rt
A(10) = 2000 * 2.71828^ 0.03*10
A(10) = 2000 * 2.71828^ 0.3
A(10) = 2699.71707036 ≈ $2700
Answer: Yes it looks correct i also did it myself and got the same answer
Step-by-step explanation:
I need to prove x*0=0 with field axioms?
Hence proved, x*0 = 0.
A statement that is assumed to be true is referred to as a postulate, axiom, or assumption. It is used as the foundation for further deductive reasoning and arguments.
Given many of the typical formulations of the Peano axioms, for example, this is the base case for the definition of multiplication, so it’s an axiom, not a theorem.
x*o = 0
By using an example as rings:
Therefore, By definition of negotiation
= x + (-x)
0 = x · 1 + ( - x) where 1 is the multiplicative identity,
Now,
= x · ( 0 + 1) + ( - x)
Therefore by distributive law,
= x · 0 + x · 1 + (-x)
Where 1 is the multiplicative identity.
By definition of negotiation,
= x · 0 + x + (-x)
= x · 0 + 0
Where 0 is the additive identity.
= x · 0
Therefore, x*0 = 0
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A survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many people like neither animal?
Step-by-step explanation:
two people like neither animal
Answer:
13
Step-by-step explanation:
15+75-32-45
90-32-45
58-45
13
What's the length of segment LM?
Answer:
6
Step-by-step explanation:
17 is the total length
11 is part of the length
17-11 =6
If nC3=120 the value of n is
The value of n in [tex]^nC_3=120[/tex] is 10 .
Combining is defined as "arrangement of objects in any order in which objects are selected", meaning "selection of objects" in any order. The number of combinations of n different things for each r is " n " and it is given by [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex] ....(1) where 0 ≤ r ≤ n. This forms a general combination formula. Prime factorization means that writing a number into its product of prime numbers .
It is given that [tex]^nC_3=120[/tex]
Using equation (1) , we get
[tex]\frac{n!}{3!(n-3)!} =120\\\ \\\frac{n(n-1)(n-2)(n-3)!}{3\times2(n-3)!} =120\\\\\n(n-1)(n-2)=720\\[/tex] ....(2)
Prime factorization of 720 is given by
[tex]720=2^4\times3^2\times5\\720=10\times9\times8[/tex]
720 can be written as [tex]10(10-1)(10-2)[/tex]
Putting above value in equation (2) , we get
[tex]n(n-1)(n-2)=10(10-1)(10-2)[/tex]
On comparing LHS = RHS we get
n = 10
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The closest star to Earth is approximately 3.99 x 10¹3 kilometers away.
When written in standard notation, how many zeros does this number contain
before the decimal point?
A. 11
B. 12
C. 13
D. 15
When written in standard notation, there are 11 zeroes before the decimal point.
We have the distance of earth from a closest star.
We have to write it in the standard notation and determine how many zeros does this number contain before the decimal point.
What is Standard notation ?Standard notation of a number is when a number is written with only number digits.
According to the question -
Distance from the star to earth = d = 3.99 x 10¹³ Km
In Standard notation, it will be written as -
399 , 000 , 000 , 000 , 00.00
Before the decimal point the standard notation consists of 11 zeroes.
Hence, when written in standard notation, there are 11 zeroes before the decimal point.
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What Is the correct answer?
The correct answer is x/ 7 = 9. Option D
What are algebraic expressions?Algebraic expressions are simply defined as expressions comprising of terms, variables, coefficients, constants and factors.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
It is important to note that quotient represents division.
Example;
The quotient of 1 and 2 is 1/ 2
The quotient of 3 and 4 is 3/ 4
From the information given, we have that;
The quotient of a number and 7 is 9
Let the number be x
We have;
x/ 7 = 9
Thus, the correct answer is x/ 7 = 9. Option D
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Calculate the average GPA for Andy after each of his four years of high school if he gets a good start his Freshman year?
Answer:
Freshman Sophomore Junior Senior
3.5 3.25 3.0 3.2
Step-by-step explanation:
Average GPA = Total GPA / number of years
Freshman Year (1 year): 3.5 = 3.5
Sophomore Year (2 years) = (3.5 + 3.0) = 6.5/2 = 3.25
Junior Year(3 years) = (3.5 + 3.0 + 2.5)/3 = 9.0/3 = 3.0
Senior Year(4 years) = (3.5 + 3.0 + 2.5 + 3.8) = 12.8/4 = 3.2
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 56 feet less than the height of the pole. If the wire is to be 8 feet longer than the height of the pole, what is the height of the pole?
The distance first from bottom of both the pole to the anchor point is approximately 56 feet smaller than the height of the pole, hence 44 feet cannot be the height of the pole. the height of both pole is 496 feet.
What exactly is a quadratic equation?In mathematics, a quadratic equation is a second-degree equation of both the form ax2 + bx + c = 0. The coefficients are a and b, the constant term is c, and the variable is x. Because the variable x has a second degree, this quadratic equation has two roots or answers.
According to the given data:A telephone pole is said to have a cable attached to its top that is secured to the ground. The distance from the pole's bottom to the anchor point is 56 feet less than the pole's height. So the distance from the bottom of the pole to the anchor point is:
x - 56
The wire must be 8 feet longer than just the height of the pole, thus the wire length would be:
x + 8
We know that the length of the wire is the hypotenuse of a right triangle, thus we can apply Pythagoras' theorem as follows:
(x + 8)² = x² + (x - 56)²
x² + 16x +64 = x² + x² - 112x + 3136
x² + 16x +64 = 2x² - 112x + 3136
2x² + 32x + 128 = x² - 56x + 1568
2x² + 32x + 128 - x² + 56x - 1568 = 0
x² - 88x + 1440 = 0
The value pf x will be:
x = 44
x = 496
The distance first from bottom of both the pole to the anchor point is approximately 56 feet smaller than the height of the pole, hence 44 feet cannot be the height of the pole. the height of both pole is 496 feet.
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What is the solution for Elena's equation
Answer:
Step-by-step explanation:
The equation which has exactly one solution is .
The equation which has exactly infinitely many solutions is .
Find the horizontal limit(s) of the following function:
f(x)=2x3−8x2−9x/11−10x−5x3
The horizontal limit of the given function is given as follows:
y = -2/5.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. For a standard function, we just calculate the numeric value of a function.
However, in this problem, an horizontal limit means that x goes to infinity, hence it we replace and calculate the numeric values we would have a fraction of infinity divided by infinity as a result, which is an undetermined limit.
Then, we use the algorithm to solve an infinity limit, in which we consider just the term with the highest exponent of both the numerator and of the denominator.
Hence:
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{2x^3}{-5x^3} = \lim_{x \rightarrow \infty} -\frac{2}{5} = -\frac{2}[5}[/tex]
Because the limit of a constant is the constant, hence the horizontal limit of the given function is given as follows:
y = -2/5.
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