Therefore , the solution of the given problem of cardinality comes out to be A×B×C is 3 .
What is an effective example of cardinality?
A's cardinality is equivalent to its element count if A has a finite amount of elements. Say |A|=5 if A=2, 4, 6, 8, 10. The outcome of a numbering process is referred to as "cardinality". A set's cardinality is determined by the number of components in it. For illustration, the group 1, 2, 3, 4, and 5 has a greater cardinality of five than the set 1, 2, 3, and 5, each of which has an attributes of three.
Here,
a)
I "Chinese New Year of 2023" has one cardinal element, making it one-dimensional.
ii) Since there are three elements in S and each element can either be included in a subset or not, the power set P(S) of S=1,,apple has 23 = 8 elements.
iii) xRx2=3 has two components because the squares of two real numbers, 3 and -3, are both 3.
iv) Since "0" is regarded as one element and there are five other distinct elements in the collection, {{0,1,2},3,4,5,∅,{{0}}} has six elements.
b)
=> A={0,1,2}, B={apple}, and C={apple}
The set difference between C and A is only the element 0, which is absent from C, so A=apple0,1,2=apple.
Consequently, A, B, and C include the following components:
=> {(0,apple,apple), (1,apple,apple), (2,apple,apple)}
=> A×B×C is 3 .
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1) How can we get Equation B from Equation A? Multiply/divide both sides by the same non-zero constant Multiply/divide only one side by a non-zero constant Rewrite one side (or both) by combining like terms Rewrite one side (or both) using the distributive property
The algebra Property used to get Equation B from Equation A is:
Rewrite one side (or both) using the distributive property
How to use algebra properties?The 2 equations given are:
A. 5 = -2(x - 1)
B. 5 = -2x + 2
Some of the popular properties of algebra are:
Commutative Property: This states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. For example: a + b = b + a , a b = b a
Associative Property: This is defined as when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For example: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Distributive Property: This is defined as multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. For example, a(b + c) = ab + bc
Equation A is given as 5 = -2(x - 1)
To get equation B, we rewrite one side (or both) using distributive property
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Complete question is:
A. 5=-2(x-1)
B. 5=-2x+2
How can we get equation B from equation A?
A. rewrite one side (or both) by combining like terms
B. rewrite one side (or both) using distributive property
C. multiply or divide both sides by the same non zero constant.
D. multiply or divide both sides by the same variable expression.
pairing arrangements are possible? derive the general formula for the number of different pairing arrangements when there are n cysteines (and n is even).
Yes, Pairing arrangements are possible.
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
If there are n cysteines, then there are n sulfur atoms that can form disulfide bonds. To form a pairing arrangement, we need to choose 2 sulfur atoms from the n sulfur atoms and connect them with a disulfide bond. We repeat this process until all sulfur atoms are paired up.
The number of ways to choose 2 sulfur atoms from n sulfur atoms is given by the binomial coefficient
[tex]$\binom{n}{2}$[/tex]
Once two sulfur atoms are paired up, we can remove them from the pool of sulfur atoms and continue pairing the remaining sulfur atoms in the same way.
Therefore, the total number of pairing arrangements is given by:
[tex]$\binom{n}{2} \cdot \binom{n-2}{2} \cdot \binom{n-4}{2} \cdots \binom{4}{2} \cdot \binom{2}{2}$[/tex]
which can be simplified as:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
Since we are choosing pairs, we divide by 2 for each pair and the order of the pairs doesn't matter. Also, we divide by (n/2)! to account for the fact that the pairs can be arranged in any order.
Note- that n must be even for this formula to hold.
Therefore, the general formula for the number of different pairing arrangements when there are n cysteines (and n is even) is:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
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Show your work for every single one plssssss
Therefore , the solution of the given problem of expressions comes out to be a) 10⁻4.10⁻⁶ = 10⁻¹⁰ , b) -5⁸/-5⁴ = -5⁴ and c) y⁶/y⁷ = 1/y.
What exactly is a expression?Calculations that involve joining, random subdivision variable changing multipliers, and removal are required. They could accomplish the following if they united: An algorithm, some information, and a mathematical challenge. Formulas, factors, and arithmetic operations like additions, deductions, errors, and groupings are all present in a declaration of truth. Words and phrases can be evaluated and analysed.
Here,
a) 10⁻4.10⁻⁶
b) -5⁸/-5⁴
c) y⁶/y⁷
and
To simplify this expression :
a) 10⁻4.10⁻⁶ = 10⁻¹⁰
b) -5⁸/-5⁴ = -5⁴
c) y⁶/y⁷ = 1/y
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Question three, please help
3/10
Answer:
The model train can travel 2 feet per second.
Julie Spiros, age 21 and unmarried, drives her vehicle to and from work. Her driver-rating factor is
1.85. Her vehicle is classified A-11. She has $25,000 property damage, 50/100 bodily injury, 50-
deductible comprehensive, and $50-deductible collision coverage. What is her annual base
premium? What is her annual premium?
Julie Spiros's basic premium is [tex]740[/tex] per year, and her premium is [tex]1,067.20[/tex] per year.
How are base premiums determined?The basic price factor is multiplied by the regular premium to determine the basic premium. The converted loss is computed by dividing the losses suffered by the loss conversion factor. Due to the basic premium component, the basic premium is lower than the standard premium.
How is the basic premium in insurance determined?By dividing the amount insured by sum assured, the insurance rate is determined. This indicates that your monthly price would be 10% if you had an insurance coverage of Rs. 10,000 and an adequate amounts of Rs. One of the most important steps in the insurance buying process is figuring out the insurance premium rate.
annual base premium = (vehicle factor) x (driver-rating factor) x (base rate)
[tex]= 1 * 1.85 * 400[/tex]
[tex]= 740[/tex]
Property damage coverage [tex]\frac{25000}{1000}*0.8=20[/tex]
Bodily injury coverage [tex]\frac{50}{100}*2*300=300[/tex]
Comprehensive coverage [tex]\frac{50}{1000}*0.6*12=3.60[/tex]
Collision coverage [tex]\frac{50}{1000}*0.6*12=3.60[/tex]
Adding these costs to the annual base premium, we get:
annual premium = annual base premium + property damage + bodily injury + comprehensive + collision
[tex]= 740 + 20 + 300 + 3.60 + 3.60[/tex]
[tex]= 1,067.20[/tex]
Therefore, Julie's annual premium is [tex]1067.20[/tex]
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Max bought m 8-ounce jars of olives and n 12-ounce jars of olives. The total amount of olives was at least 80 ounces. Which inequality models this situation?
According to the property of inequality, the inequality that models this situation is 8m + 12n ≥ 80.
What is inequality?
An inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not, or which one is greater or smaller.
Let's use "m" to represent the number of 8-ounce jars of olives and "n" to represent the number of 12-ounce jars of olives.
The total amount of olives can be found by multiplying the number of 8-ounce jars by 8 and the number of 12-ounce jars by 12, and then adding them together:
total amount of olives = 8m + 12n
The problem tells us that the total amount of olives is at least 80 ounces. We can represent this information as an inequality:
8m + 12n ≥ 80
Therefore, the inequality that models this situation is 8m + 12n ≥ 80.
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Nate had 300 cookies for class. He dropped 145 on his way to school. His mom brought him 123 more cookies. How many cookies does Nate have now?
423
278
350
155
Answer: Nate have 278 cookies now.
Step-by-step explanation:
the original amount of cookies for Nate is 300, and he dropped 145, which means we need to subtract 145 from 300. And his mom brought him 123 more, which means we need to add 123.
300 - 145 + 123 = 278
A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges?
The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.
What is linear equatiοn?An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.
let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs
And, f(x) = 6x + 14 (Given)
Sο The flat fee that the stοre charge $14.
Reasοnable dοmain is 1 ≤ x ≤ 12
The cοst fοr 7 hοurs is,
f(7) = 6(7) + 14 = 56.
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Picture not drawn to scale. Make sure you show all your work for full points.
What is w, m, and n?
Answer:
w = 102
m = 78
n = 58
Step-by-step explanation:
Three angles of a triangle add up to 180°
∴ w = 180 - (36 + 42)
= 180 - 78
= 102
w and m are supplementary angles:
m + w = 180
m + 102 = 180
m = 180 - 102 = 78
Three angles of a triangle add up to 180°
m + 44 + n = 180
78 + 44+ n = 180
122 + n = 180
n = 180 - 122
n = 58
Which expression could be used to determine the area of the triangle?
A triangle has a base of 2 and three-fourths and height of StartFraction 7 Over 8 EndFraction.
One-half + 2 and three-fourths + StartFraction 7 Over 8 EndFraction
(2 and three-fourths) (StartFraction 7 Over 8 EndFraction)
One-half (2 and three-fourths) (StartFraction 7 Over 8 EndFraction)
One-half (2) (three-fourths) (StartFraction 7 Over 8 EndFraction)
HELP IT TIMED AND IM GIVING 100 POINTS AND HEARTS AND 5.0 !!!IF!!! CORRECT!
The expression which could be used to determine the area of the triangle is: One-half (2) (three-fourths) (StartFraction 7 Over 8 EndFraction).
What is expression in math?Expression in math is a combination of numbers, operations, variables, and/or other mathematical symbols that represent a quantity or an action. It is a statement that can be evaluated to a single value, or a set of values. Expressions in math can be used to solve equations, calculate values, and form models of real-world scenarios.
This expression multiplies together the base, two and three-fourths, and the height, StartFraction 7 Over 8 EndFraction, and then divides the result by two to give the area of the triangle.
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Mr. Stenfanski's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both girls? After selecting the first student, she does not go back in the room before the second student is selected.
A. 10/17
B. 59/143
C. 10/7
D. 45/136
Answer:
[tex] \frac{45}{136} [/tex]
Step-by-step explanation:
The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.
After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.
To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:
[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]
So the probability of selecting two girls in a row is
[tex] \frac{90}{272} [/tex]
which can be simplified to
[tex] \frac{45}{136} [/tex]
A coin is flipped and a card is randomly selected from a deck of 52. What is the probability the coin will land on heads and the card will be a Queen? There are 4 queens in a deck of cards.
A. 1/104
B. 6/13
C. 1/26
D. 4/52
Answer:
The probability is 4/52
What is Probability?
the extent to which something is probable; the likelihood of something happening or being the case.
"the rain will make the probability of their arrival even greater"
Similar:
likelihood
likeliness
prospect
expectation
chance
chances
odds
possibility
a probable or the most probable event.
plural noun: probabilities
"for a time revolution was a strong probability"
Similar:
probable event
prospect
possibility
good/fair/reasonable bet
the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
"the area under the curve represents probability"
Brandon deposited $3600 into a savings account that has an annual simple interest rate of 0.5%. How much is in the account after 5 years?
Answer: 3690
Step-by-step explanation: i think
The total amount in the account after 5 years is $3690.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The Formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.
In this case, the principal is $3600, the rate is 0.5% (or 0.005 as a decimal), and the time is 5 years.
Plugging these values into the formula, we get:
Interest = $3600 x 0.005 x 5 = $90
So after 5 years, the interest earned on the account is $90. To find the total amount in the account, we need to add the interest to the principal:
Total amount = Principal + Interest = $3600 + $90 = $3690
Therefore, the total amount in the account after 5 years is $3690.
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what is the f(5) in the function below? f(x)={3x-5;x<5
{-x^2 +4;x>= 5
The value of the range of function is found as f(5) = -21.
Explain about the domain and range of the function?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Graphs can be used as another tool for determining the domain as well as range of functions. The domain of a graph is made up of each of the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.The given function:
f(x) = {3x-5;x<5
{-x^2 +4;x>= 5
f(5) = -x^2 +4
Put x = 5
f(5) = -(5)^2 +4
f(5) = -25 +4
f(5) = -21
Thus, the value of the range of the function is found as f(5) = -21.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at -3
Step-by-step explanation:
-3 is 6 points away from t and 4 away from s. thus 3/5
Which expression gives the volume of a sphere with radius 15? A. 4π(15^3) B. 4/3π(15^3) C. 4/3π(15^2) D. 4π(15^2)
The proper formula states that a sphere with a radius of [tex]15[/tex] has a volume of 4/3π([tex]15^{3}[/tex]).
How can we calculate a sphere's volume?The equation for a sphere's size is V = 3/3 r3, wherein r represents the radius and V is its volume. 1⁄2 of an object's circumference makes up its radius. Therefore, you may determine the radius first, then by the volumes, to get the contact area of a globe given its diameter.
Why is a sphere's volume 4 3?Both a circle as well as a sphere are round, if you compare them. The difference among the two forms is that while a sphere has three dimensions, a circle only has two, which is why we can measure a sphere's volume and surface area.
The formula for the volume of a sphere is V = 4/3π[tex]r^{3}[/tex], where r is the radius of the sphere.
Substituting [tex]r=15[/tex], we get
V = 4/3π([tex]15^{3}[/tex])
Therefore, the expression 4/3π([tex]15^{3}[/tex]) gives the volume of a sphere with radius [tex]15[/tex].
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Suppose the standard deviation of the weights of all Florida manatees is 33 pounds. Let be the mean
weight for a sample of a certain number of Florida manatees. What sample size will give the standard
deviation of equal to 10 pounds?
A sample size of 11 would give a standard deviation of 10 pounds for the Florida Manatees
What is an equation?An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.
The standard deviation of a sample is:
[tex]\sigma_n=\frac{\sigma}{\sqrt{n} } \\\\Where\ n\ is\ sample\ size,\sigma\ is\ standard\ deviation\ and\ \sigma_n\ is\ standard\ deviation\ of\ sample[/tex]
Given that:
[tex]\sigma_n=10,\sigma=33,hence:\\\\10=\frac{33}{\sqrt{n} } \\\\n=10.89[/tex]
A sample size of 11 would give a standard deviation of 10 pounds
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The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%. What will the probability be? Or is the proportion satisfied?
satisfied=88%
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.
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y=lx-5|+ lx+5| if x>5 what is y
Answer:
If x > 5, then y = 2x.
Step-by-step explanation:
If x > 5, then both expressions inside the absolute values are positive, so we can simplify the expression:
y = |x - 5| + |x + 5|
Since x > 5, we know that x - 5 > 0 and x + 5 > 0. Therefore, we can write:
y = (x - 5) + (x + 5)
Simplifying this expression, we get:
y = 2x
So, if x > 5, then y = 2x.
Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]
Sally wants to buy a new iPhone that costs $200. She has already saved $75. Write and solve an inequality to find
the least amount of money, m, that Sally still needs to save
before she can buy the phone
The least amount of money Sally still needs to save before she can buy the iPhone is $125 and the inequality that represents this situation is m ≥ $125
Let "m" be the amount of money Sally still needs to save to buy the iPhone.
The total cost of the iPhone is $200, and Sally has already saved $75. Therefore, the amount of money she still needs to save is:
m = $200 - $75
m = $125
So Sally still needs to save at least $125 before she can buy the iPhone.
Therefore, the inequality that represents this situation is
m ≥ $125
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I shall give brainliest
Classify the angle according to its measure. Straight acute obtuse right
100 degrees I think
Answer:
Obtuse
Step-by-step explanation:
In general speaking of your options
Straight angles equal exactly 180
Acute angles equal anything less than 90
Obtuse equals anything above 91
Right angles equal exactly 90
Shelton mixed 1 1/4 cups of purple cabbage and 2 3/8 cups of lettuce to make a big salad. Each day he eats 3/4 of a cup of salad. Which expression shows how many servings of salad Shelton has?
Answer
Choice C: (1 1/4 + 2 3/8) / 3/4
Step-by-step explanation:
His salad consists of 1 1/4 cups of purple cabbage and 2 3/8 cups of lettuce. First, you would add those two together to get how much the salad is. THEN divide by how much he eats each day which is 3/4.
What is the surface area of the rectangular prism?
Start out by finding the area of each rectangle.
Rectangle 1 __________
Rectangle 2 ____________
Rectangle 3 ___________
Answer__________________________
The surface area of the mentioned rectangular prism is calculated to be 168 yd².
Define surface area.The surface area of a three-dimensional object is the total area of all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.
Area of rectangle 1
= 6 × 2
= 12 yd²
Area of rectangle 2
= 9 × 2
= 18 yd²
Area of rectangle 3
= 9 × 6
= 54 yd²
Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:
Area of prism = (12 × 2) + (18 × 2) + (54 × 2)
Area of prism = 24 + 36 + 108
Area of prism = 168 yd²
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Y=2-(x-7)2
What’s the side length of the square
The side length of the square is 1/2 - 1/4(x - 7)^2
How to determine the side length of the squareTo find the side length of the square, we need to first express the perimeter in terms of the side length.
Let s be the side length of the square.
Since a square has four equal sides, the perimeter of the square is given by:
y = 4s
Now, we can express s in terms of y:
s = y/4
Substituting this into the given expression for y:
y = 2 - (x - 7)^2
We get:
s = [2 - (x - 7)^2]/4
Simplifying this equation:
s = 1/2 - 1/4(x - 7)^2
Hence, the side length expression is 1/2 - 1/4(x - 7)^2
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Complete question
The perimeter (y) of a square is y =2 - (x - 7)^2. What’s the side length of the square?
How many ways can you
represent the number of
dots shown?
There are 5 ways we can represent the number of dots shown.
What is the combination?
A combination is a choice of items from a group of different items where the order of the choices is irrelevant. either the process of combining or the condition of combining. a combination of several things a synthesis of concepts. something created through fusion: A chord is made up of several notes.
Here, we have
Given: Dots shown and we have to find the ways can you represent the number of dots shown.
We apply here combination and we get
⁵C₁ = 5!/4!
= 5
Hence, there are 5 ways we can represent the number of
dots shown.
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The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \] where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground. How long does it take for the pedal to reach a height of \( 34.48 \) inches for the second time?
Choose one of the answers below:
A. 3 seconds
B. 4 seconds
C. 6 seconds
D. 5 seconds
The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30
The option (B) is the correct answer.
Given equation is \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \]where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground.Now, we are asked to find the time when the pedal reaches a height of 34.48 inches for the second time.In order to find that, we can solve the equation as follows:\[34.48-30=14.5\cos\left[\frac{2\pi}{5}t\right]\]\[\cos\left[\frac{2\pi}{5}t\right]=\frac{4.48}{14.5}\]\[\cos^{-1}\left(\frac{4.48}{14.5}\right)=\frac{2\pi}{5}t\]\[t=\frac{5\cos^{-1}\left(\frac{4.48}{14.5}\right)}{2\pi}\]This gives us,\[t \approx 1.6 \text{ or } 3.7\]The pedal reaches the given height for the second time when \( t = 3.7\) seconds. Therefore, option (B) is the correct answer.
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Mike can do the job one hour quicker than mike. They worked together for 4 hours until homer went home. Mike finished the job working by himself for an additional 4 hours. How long would homer have taken to do it by himself?
Homer would have taken approximately 8.11 hours to do the job by himself.
Let h be the time it would take Homer to do the job by himself, and let m be the time it would take Mike to do the job by himself. We know from the problem that:
m = h - 1 (Mike can do the job one hour quicker than Homer)
We also know that they worked together for 4 hours, so they completed 4/h + 4/m of the job. We can set up an equation based on this:
4/h + 4/m = 1 (they completed the entire job)
Substituting m = h - 1, we get:
4/h + 4/(h-1) = 1
Multiplying both sides by h(h-1), we get:
4(h-1) + 4h = h(h-1)
Simplifying:
8h - 4 =
[tex]h^2 - h[/tex]
Rearranging:
[tex]h^2 - 9h + 4 = 0[/tex]
Using the quadratic formula, we get:
[tex]h = (9 ± \sqrt{(9^2 - 414)) / 2} [/tex]
Since we are looking for a positive value of h, we take the positive square root:
h ≈ 8.11
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Please help my homework is due tomorrow 10 3/4 + 12 1/4
The sum of 10 3/4 and 12 1/4 is 23.
To add the mixed numbers 10 3/4 and 12 1/4, follow these steps:
Step 1: Add the whole number of parts.
Add the whole numbers 10 and 12 to get:
10 + 12 = 22
Step 2: Add the fractional parts separately.
Add the fractions 3/4 and 1/4 separately. To do this, find a common denominator, which in this case is 4. Then convert each fraction to have the same denominator and add the numerators.
For 10 3/4, the fraction 3/4 has the same denominator, so we keep it as is.
For 12 1/4, the fraction 1/4 also has the same denominator, so we keep it as is.
Then we add the numerators of the fractions:
3/4 + 1/4 = 4/4 = 1
Step 3: Add the results from Step 1 and Step 2.
Add the result from Step 1 (the sum of the whole numbers) to the result from Step 2 (the sum of the fractions):
22 + 1 = 23
Therefore, the sum of 10 3/4 and 12 1/4 is 23.
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The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $350.00. What was it worth a year ago?
The autograph of the professional basketball player's was worth $250.00 a year ago.
What was the worth of the professional basketball player's autographa year ago?Given that, in the last year, the value of a professional basketball player's autograph rose 40% and it is now worth $350.00.
To determine it worth a year ago, let's call the original value of the autograph "x".
We know that the value increased by 40%, which means it became:
100% + 40% = 140% of its original value.
We can set up the following equation:
140% × x = 350
(140/100)x = 350
1.4x = 350
To solve for x, we can divide both sides by 1.4:
x = 350 ÷ 1.4
x = 250
Therefore, the autograph was worth $250.00 a year ago.
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Solve the system of equations.
−9y+4x−11=0
−3y+10x+31=0
Answer:
Multiplying the first equation by 3 and the second equation by 9, we get:
-27y + 12x - 33 = 0
-27y + 90x + 279 = 0
Now, we can subtract the first equation from the second to eliminate y:
-27y + 90x + 279 - (-27y + 12x - 33) = 0
78x + 312 = 0
78x = -312
x = -4
Substituting x = -4 into the first equation, we get:
-9y + 4(-4) - 11 = 0
-9y - 27 = 0
y = -3
Therefore, the solution to the system of equations is (x, y) = (-4, -3).