The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Mathematics' field of probability deals with numerical assessments of how likely an event is to occur.
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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Pls help me with this question plssss
The average rate of the given function is 2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.
x={-6, -5, -4, -3, -2, -1, 0, 1, 2}
y=-x²-x+5
When x=-2
y=-(-2)²-(-2)+5
y=-4+4+5
y=5
When x=-1
y=-(-1)²-(-1)+5
y=5
When x=0
y=5
When x=1
y=-1-1+5
y=3
When x=2
y=-(2)²-(2)+5
y=-1
Now, rate using (1, 3) and (2, -1), we get
m =(-1-1)/(2-3)
m=2
Therefore, the average rate of the given function is 2.
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Mr. Wú needs to buy new carpet for his
office. The length of the office is 12 feet
and the width is 10 feet. If each square
foot of carpet costs $3, how much will it
cost Mr. Wú to buy carpet for his office? NEED HELP PLS!!!
Answer:
A - $360
Step-by-step explanation:
Length times width equals area.
12 × 10 = 120
His office has 120 sq ft of space. If each sq ft costs $3
120 × 3 = $360
A
Answer:
A ($360)
Step-by-step explanation:
imagine a rectangle with one side 12ft and one side 10ft
multiply the length and the width to find the square footage:
12*10=120ft^2
each square foot is $3 so multiply 3 by 120
$3*120ft^2= $360
oops didn't realize someone already answered sorry
How do you solve 3 to the power of 3?
As per the power rule of exponents, the solution of 3 to the power of 3 is 27.
The term exponent in math is defined as a number shows how many times the number is multiplied by itself.
Here we have to solve 3 to the power of 3.
Here according to the Power Rule of Exponents then we have the rule as
=> aⁿ = a × a × a... (n times)
Therefore, the given expression is written as
=> 3³
Now, based on the power of exponent rule it can be rewritten as,
=> 3 × 3 × 3
Then we have to multiply the values then we get
=> 27
Therefore, the value of 3 raised to 3rd power is 27.
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The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 15 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours
Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.
We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:
15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour
We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:
15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour
To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:
First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons
Second hour: 15 gallons/hour * 1 hour = 15 gallons
Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons
Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours
7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons
So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.
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[tex]{x}^{2} + x - 2[/tex]
solve this with first X last method
Answer:
[tex]x=-2,1[/tex]
Step-by-step explanation:
[tex]x^2+x-2=0\\(x+2)(x-1)=0\\x_1=-2,x_2=1[/tex]
please help: solve for x
Step-by-step explanation:
in an isoceles triangle (both legs have identical length) the height from the top corner to the baseline shots the baseline into 2 identical halves.
so,
6x + 6 = 9x - 15
6 = 3x - 15
21 = 3x
x = 21/3 = 7
many greetings to your teacher from me : he/ she made a formal mistake. the angles at Y have to be indicated as right angles. because if the line WY is not the height but could have any angle with the baseline, this cannot be solved.
When a problem is said to be decidable or undecidable give an example of an undecidable problem?
Example of an undecidable problem is given by the problems in the system created by computer viruses.
What is decidable and undecidable problems?According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.
A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.
When is a problem said to be decidable or undecidable?
whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.
If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.
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How do you check whether 7 3x is a factor of 3x3 7x?
7 + 3x is not a factor of expression 3x^3 + 7x
Consider given expression 3x^3 + 7x
Let f(x) = 3x^3 + 7x
Assume that 7 + 3x is a factor of 3x^3 + 7x
This means, 7 + 3x = 0 would be the root.
x = -7/3
If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0
We find the value of given polynomial for x = -7/3
f(x) = 3x^3 + 7x
f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)
f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)
f(-7/3) = [(-343) - 147] / 9
f(-7/3) = -490 / 9
f(-7/3) ≠ 0
Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial f(x) = 3x^3 + 7x
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The age at which small breed dogs are fully housebroken follows a Normal distribution with mean ms = 6 months and standard deviation ss = 2. 5 months. The age at which large breed dogs are fully housebroken follows a Normal distribution with mean mL = 4 months and standard deviation sL = 1. 5 months. Let xS – xL represent the sampling distribution. Be sure show all work and conditions. Let the sample size for both sets be 25 dogs. Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs? Explain your answer
The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.
HOUSEBROKEN AGE PROBABILITYThe sampling distribution for the difference in sample means, xS - xL, is also normally distributed with a mean of ms - mL = 6 - 4 = 2 months.The standard deviation of √((ss²/nS) + (sL²/nL)) = √((2.5²/25) + (1.5²/25)) = 0.5 months, where nS and nL are the sample sizes for the small and large breed dogs, respectively.Using a z-score, we can calculate the probability of observing a sample mean difference of at least 3 months between the small and large breed dogs, given that the true difference in population means is 2 months. This probability can be found using the standard normal table or calculator.The z-score formula is (x - mu) / sigma, where x is the observed sample mean difference, mu is the population mean difference, and sigma is the standard deviation of the sampling distribution.z = (3-2) / 0.5 = 2
The probability of observing a z-score of 2 or greater is approximately 0.0228, or 2.28%. This is a small probability, so we would be surprised if the sample mean housebroken age for small breed dogs was at least 3 months more than the sample mean housebroken age for the large breed dogs.So, the answer is no. Not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.Learn more about Probability here:
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Please Help!! Offering 8 points to each answerer and a Brainliest! Please answer the following parts of this question.
(02.05 HC)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answer:
Part A: Two types of transformations: translation and reflection.
Part B: g(x)=f(x)+k
-1= -1+ k
k= -1+1=0
g(x)=f(x)+k
-1= 5+k
k= -1-5=-6
g(x)=f(x)+k
14= 14+k
k= 0
k= -6,0,-6,0
Part C: For horizontal translation, g(x)=f(x+2)
In case of vertical translation, g(x)=f(x)+10
Therefore, the equation of transformation can be written as g(x)=f(x+2)+10.
Step-by-step explanation:
I thought. :') Ever since yesterday, and today. Hope this helps!
What is the solution to the equation 1 h 5 2 h 5?
h = 7 is the solution to the equation 1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The equation given that,
1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
The least common multiple of the denominators is:
h² - 25 = (h - 5) (h + 5)
We multiply through with the LCM to obtain:
= [(h - 5) × (h + 5)] × [1 / (h - 5)] + [(h - 5) × (h + 5)] × [2 / (h - 5)]
= 16 / (h² - 25) × [(h - 5) × (h + 5)]
We cancel out common factors to obtain:
= 1 (h + 5) + 2 (h - 5)
= 16
We expand the brackets to obtain
= h + 5 +2h - 10
We group like terms to get:
h + 2h = 16 - 5 + 10
This simplifies to:
3h = 21
We now divide through by 3 to obtain:
h = 7
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A seventh grade class and 7 adults go on a field trip. Two-thirds of the people ride on a bus.
Everyone else rides in vans. If 54 people ride on the bus, how many seventh graders go on the
field trip?
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
To find P P, divide P
P by the total number of participants (students and chaperones), which is 81.
Seventh graders totaling 81 - 7 =
74 participated in the field trip.
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
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par teme
d
Bookwork code, 021
Cessss chance Review your workings and see if you can comes your make
Ria buys 19 textbooks, which cost £6.82 each,
By first rounding both numbers to 1 significant figure, estimate the total
amount of money Ria spends,
Give your answer in pounds (L),
Answer?
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
Define unitary method.By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.
Here,
Given : Ria purchases 19 books for £6.82 apiece.
Thus,
Total cost of book = 19 * 6.82
=> 129.58
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
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If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420, find the principal
As per the given simple interest, the principal amount is $165.35.
The term simple interest in math is defined as the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.
Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.
Therefore, through the given question we have identified the value of
interest rate = 3.5%
time period = 44
sum amount = 420.
Then the principal amount is calculated by using the formula of simple interest as,
P = A / (1 + rt)
Here first we have to convert R percent to r a decimal, then we get
r = R/100 = 3.5%/100 = 0.035 per year.
Now, we have to apply the values on the equation and then we have to solve our equation, then we get
P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866
P = $165.35
Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.
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Find the solutions to x² = 24.
OA. x= 16-√4
B. x = +2√6
O C.
x = +6√ √2
OD. x +4√6
Answer:
x = 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{24}[/tex] = [tex]\sqrt{(2)(2)(2)(3)}[/tex] We can pull out a pair of 2's
2[tex]\sqrt{(2)(3)\\}[/tex] = 2[tex]\sqrt{6}[/tex]
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of
Weight of each type of box:
Weight of each big box = 18.75 kg
Weight of each small box = 13.75 kg
What is an equation?The relationship between two terms on either side of a letter is represented by a mathematical formula. Often there is a variable and an equals sign.
The definition of an equation in algebra is a formula that shows the equivalence of two mathematical terms. For example, in the expression 6x + 11 = 14 the two terms 6x + 11 and 14 are separated by the "equals" symbol.
To let
Weight of each big box = x
And the weight of each small box = y
Weight of 3 big boxes:
3 times
5 small box weights:
5 years
3x + 5y = 125 .......................(i)
resemble:
9x + 7y = 265 ......................(ii)
Equation (i) multiplied by -3:
-3 (3x + 5y) = 125 * (-3)
-9x - 15y = -375 ...................(iii)
Under (ii) and (iii):
9x + 7y = 265
-9x - 15y = -375
Adding this gives:
-8y = -110
or y = 110/8
or y = 55/4
y = 13.75
From equation (i), we have:
3x + 5y = 125
or 3x + 5(13.75) = 125
or 3x + 68.75 = 125
3x = 125 - 68.75
3x = 56.25
x = 56.25/3
x = 18.75
Each large box weighs:
18.75 kilograms
Weight of each small box:
13.75 kilograms
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help explanation required
Answer:
$68
Step-by-step explanation:
Let x = original price.
The sale price is 75% of the original price, so the sale price is 75% of x.
75% as a decimal is 75/100 = 0.75
75% of is the same as 0.75x
We are told the sale price is $51, so 0.75x must equal $51.
0.75x = 51
Divide both sides by 0.75 to find the value of x.
x = 51/0.75
x = 68
Answer: $68
Answer:
Step-by-step explanation:
$51 is 75% of 100%
75% = 3/4
51 / 3 = 17
17 = 1/4
51 + 17 = 68
$68 is the original price of the shoes
Joanne works two jobs to pay for college. She tutors for $25 per hour and also works as a receptionist for $12 per hour. Due to her class and study schedule, Joanne is only able to work up to 25 hours per week, but must earn at least $200 per week. If t represents the number of hours Joanne tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario?
A. t + r >= 25
25t + 12r = 200
B. t + r <= 25
25t + 12r <= 200
C. t + r <= 25
25t + 12r >= 200
D. None of the systems shown represent this scenario.
The required system of inequality will be
t + r ≤ 25
25t + 12r ≥ 200
What is system of equations?
A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.
If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.
Then the total hours she can work = t + r
Since she can work up to 25 hours.
Thus t + r ≤ 25
If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .
Then her total earning = $25t + 12r
Since she must earn $200.
Then 25t + 12r ≥ 200
Hence, the required system of inequality will be
t + r ≤ 25
25t + 12r ≥ 200
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What is the smallest multiple of 6 greater than 115?
Answer:
120
Step-by-step explanation:
First, divide 115 by 6:
115/6 =
(114 + 1)/6 = ==> 114 is a multiple of 6
114/6 + 1/6 = ==> distribution property
19 + 1/6 = ==> simplify
19 1/6 ==> the smallest integer greater than 19 1/6 is 20
Hence, multiply 20 by 6 to get 120.
what is the volume of cylinder when the radius is 3 and height is 13.33
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]
In this course, we'll begin to
explore "opposite" function types. For example, think about
a quadratic function and its key features. What key features do you think its opposite
function will have? Why?
Answer:
Some key features quadratic functions have are:
Axis of symmetryx and y-interceptsZeroesvertexPoint symmetric to y-interceptStep-by-step explanation:
Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''
Please help I have a learning disability and this is due today
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
0 + 32 and 0
yes, it uses the Commutative Property
No they are not equivalent. The first expression is equal to 32, not 0.
yes, it uses the Associative Property
yes, it uses the Identity Property
Answer:
yes, it uses the Commutative Property
Step-by-step explanation:
Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
2x-6y= -12 x intercept as a ordered pair and y intercept as ordered pair
I really also need help on this question lol
Answer:
13/15
For this question, you could type it into the calculator.
Hence, this question is too trivial, and your question might get deleted as a result. Since this is your first question, I will help you out but subsequently, do use a calculator to solve this kind of questions.
Step-by-step explanation:
4 1/3 can be converted to 13/3 as an improper fraction.
Next, evaluate 13/3 divided by 5
(13/3) / 5 = (13/3) x (1/5)
= 13/15
Answer:
Step-by-step explanation:
There are a number of ways to do this. I am going to take a little longer, but I am hoping that it will make sense to you.
4[tex]\frac{1}{3}[/tex] ÷ 5
Another name for 1 is [tex]\frac{3}{3}[/tex] I am going to rewrite 4[tex]\frac{1}{3}[/tex] knowing this.
[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]
Another way to write 5 is [tex]\frac{5}{1}[/tex].
I want both of my fraction to have the same denominator so I will multiple
[tex]\frac{5}{1}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{3}[/tex] I am now ready to divide by fractions
[tex]\frac{13}{3}[/tex] ÷ [tex]\frac{15}{3}[/tex] Divide across
[tex]\frac{\frac{13}{15} }{\frac{3}{3} }[/tex] = [tex]\frac{\frac{13}{15} }{1}[/tex] = [tex]\frac{13}{15}[/tex]
Graph the line that passes through the points (1, -2) and (-1,-6) and
determine the equation of the line.
Answer:
y = 2x - 4
Step-by-step explanation:
The equation is y = mx + b
m = The slope
b = y-intercept
To find the slope, we look for the rise/run or (y2 - y1) / (x2 - x1)
The slope here is 2, and the y-intercept is located at (0,-4), so the equation is
y = 2x - 4
which is the functions for increases 8.3%
Answer:
The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.
citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:
How do you solve this? 11t-t^2=30
Answer:
t = 5, 6
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{11t-t^2=30}[/tex]
First, arrange the expression in the standard quadratic form ax² + bx + c = 0
[tex]\displaystyle{t^2-11t+30=0}[/tex]
Then factor the expression, find two numbers that add up which result in -11 and multiply which result in 30 - that two numbers are -6 and -5
[tex]\displaystyle{(t-6)(t-5)=0}[/tex]
Solve like a linear equation
[tex]\displaystyle{t=5,6}[/tex]
Therefore, the solutions to the equation are t = 5, 6
Answer:
The solution set is {5, 6}.
Step-by-step explanation:
11t-t^2=30
t^2 - 11t + 30 = 0
(t - 5)(t - 6) = 0
t = 5, 6.
Why are the acute angles of an isosceles right triangle always 45?
An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.
The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.
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The price of a notebook has risen to $3.80 today. Yesterday's price was $3.30 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase in the price of the notebook is 15%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Finding the increase in the price of the notebook:
$3.80 - $3.30 = $0.50
Dividing the increase by the original amount:
0.50 / 3.30 = 0.1515
To change to a percent multiply by 100 and round off to significant numbers:
0.1515 *100 = 15.15% or, 15%.
Thus, the percentage increase in the price of the notebook is 15%.
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