The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.
Quadratic equation:
In math, quadratic equation is the algebraic equation of the second degree in x.
The general form of quadratic equation is
ax² + bx + c = 0,
where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).
Given,
Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,
Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,
=> y = (x-4)² – 1,
=> y = -(x-4)² + 1,
=> y = -3(x-4)² + 3.
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Select the correct answer from each drop-down menu
-Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack A before and some have not. The results
of the test are shown in a table. Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person
Prefers Snack A
Prefers Snack B
Total
Has Eaten Snack
A before
144
92
Has Not Eaten
108
228
Snack A before
Total
252
320
Complete the conclusions based on the data in the table.
236
336
572
Given a person who has eaten snack A before, the customer will
Given a person who has not eaten snack A before, the customer will want to eat snack
The probability of the customer wants to take snack B is 144/320 as they have already taken snack A
and the probability of the customer who has not taken snack A before
wants to take snack A =108/252
What is probability?
It is the ratio of favorable outcome to total possible outcome of an event.
How can we determine the probability in this question?based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.
hence, probability to take snack B = 144/320
probability to take A =108/252
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a) The probability a person who has eaten snack A before is 59/143.
b) The probability a person who has eaten snack A before is 84/143
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given that the total number of people that are taken for the event is 572.
The number of people who have eaten snack A before is 236.
The number of people who have not eaten snack A before is 336.
Probability = The number of outcomes of favorable event/ Total number of outcomes
The probability getting a person who has eaten snack A before is
= 236/ 572
= 59/143 [Divide denominator and numerator by 4]
The probability getting a person who has not eaten snack A before is
= 336/ 572
= 84/143 [Divide denominator and numerator by 4]
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Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
Answer:im assuming you need to know the difference and its nine
Step-by-step explanation: 34-25=9
How much must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily
There are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given:
A = Final amount = $25000
P = Initial principle balance
r = interest rate = 5% = 0.05
t = Number of time of years
n = number of times interest applied per time period = 365
Since, the formula for compound interest,
[tex]A = P(1+\frac{r}{n})^n^t[/tex]
Plug the values of A, r, n and t in the above formula
[tex]25000 = P(1 + \frac{0.05}{365})^3^6^5^*^4 \\25000 = P(1.0001369863)^1^4^6^0\\25000 = P(1.2213860258)\\P = 20,468.549231702[/tex]
P ≈ 20,468.55
Hence, there are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.
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p+ 1.4 ≤ 0.5; p = 0.1
The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1
How to determine if the expression is trueFrom the question, we have the following parameters that can be used in our computation:
p + 1.4 ≤ 0.5;
p = 0.1
Substitute p = 0.1 in p+ 1.4 ≤ 0.5;
So, we have the following representation
0.1 + 1.4 ≤ 0.5;
Evaluate the like terms
This gives
1.5 ≤ 0.5;
The above inequality is false
This is because 1.5 is greater than 0.5
Hence, p + 1.4 ≤ 0.5; p = 0.1 is false
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What is the slope of the line shown below?
Answer: -3/2
yeah use rise over run
Answer:
-2/3
Step-by-step explanation:
slope = rise/run
First find the y-intercept (point of crossing on the y-axis (the vertical one)), then find the next point that intercepts a box PERFECTLY, this next point is (4, -2)
Looking at the y-intercept's coordinates (0,1), count how many blocks down it takes to get to to 4 (2 blocks which is the RISE) and now count how many blocks to the right it takes to get to -2 (3 blocks)
Therefore it is 2/3 but it is also negative because it is going DOWN from left to right which is a negative decine
What is the slope-intercept equation for the linear function represented by the
table?
X
y
O Ay=-¹2-2
OB. y = 2x --2
OC. y =
-2
OD. y = 2x+4
0
-2
2
-1
4
0
6 8
1
2
The linear equation represented in the table is:
y = (1/2)*x - 2
What is the equation of the line in the table?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line goes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table (0, -2) and (2, -1), so we will get:
a = (-1 + 2)/(2 - 0) = 1/2
And because of the point (0, -2) we know that the y-intercept is -2, so we can write:
y = (1/2)*x - 2
The correct option is C.
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Stock in a certain company sold for $2.50 per share in June. The price of the stock increased $4.75 after one month. It then decreased $1.25 and $2.45 over the next two months. What was the price of the stock after these changes?
Responses
Answer: $3.55
Step-by-step explanation:
Started at 2.50 increased 4.75 which means the stock is 7.25 then decreased 1.25 making it 6 then another decrease of 2.45 making it $3.55
The mean amount of time it takes a kidney stone to pass is 14 days and the standard
deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass
the kidney stone. Round all answers to two decimal places.
The probability that an individual will take far longer than 21 days to complete it is 0.12.
What is standard deviation?In the descriptive analysis, the standard deviation is the amount of scatter or dispersal of the pieces of data in relation to their mean. It provides information on the distribution of values within the sample data and serves as a gauge for how widely apart the measured values are from the mean.
As per the information available in the question,
Meantime, μ = 14 days
Standard deviation, ρ = 6 days
Assume the time to pass the kidney stone be x.
The probability that it will take someone more time than 21 days to complete it.
Let's find out the Z-score first,
Z-score = (x - μ)/ρ
Substitute values in above equation,
= (21 - 14)/6
Z-score = 1.166.
The probability that it will take someone more time than 21 days to complete it :
P(x > Z) = P(x > 1.16) = 0.12
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The radius of a circle is 8 meters. What is the circle's area?
r=8 m
Use 3.14 for .
Answer:
200.96
Step-by-step explanation:
3.14*r²
so 3.14*8²=200.96
Pls help with this and explain why it is wrong
The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)
What is logarithm?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.
In(9) can be written as ln3^2
which according law of logarithm is 2ln(3)
Expression becomes
ln(3) + 2ln(3) which is 3ln(3)
In conclusion, the simplified form of the expression in base 3 is 3ln(3)
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A tree is currently 8 feet tall and grows 3 feet per year
a. Model this scenario with an arithmetic sequence in explicit form
b. Rewrite the explicit form of the sequence using function notation
c. How tall will the tree be in 12 years?
Answer:
You have to multiple to get you answer
Step-by-step explanation:
Ann is 11 more than two times older than Stacy. If Ann is 59 years old,
solve an equation to determine Stacy's age
The age of Stacy is 24 years old provided the age of Ann is 59 years old.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Ann is 11 more than two times older than Stacy.
Let the age of Stacy and Ann be s and a respectively, then:
a = 11 + 2s
Substitute a = 59 into the above equation:
59 = 11 + 2s
2s = 59 -11
s = 24
Hence, the age of Stacy is 24 years old provided the age of Ann is 59 years old.
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Determine the degree measure of one angle of a 45-sided regular polygon.
8,100°
7,740°
172°
180°
The measure of one interior angle of the 45-sided polygon is (c) 172 degrees
How to determine the measure of one interior angle?From the question, we have the following parameters that can be used in our computation:
Shape = 45-sided polygon
Parameter to calculate = the measure of one interior angle
The sum of the interior angles is calculated using the following angle formula
The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides
In this case
n = 45
Substitute the known values in the above equation, so, we have the following representation
The sum of the interior angles = (45 − 2) × 180∘
Evaluate
The sum of the interior angles = 7740∘
So, the internal angle is
Angle = 7740/45
Evaluate
Angle = 172
Hence, the angle is (c) 172 degrees
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Kevin and Randy Muise have a jar containing 83 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $12.95. How many of each type of coin do they have?
The amounts of each type of coin that they have is given as follows:
Quarters: 44.Nickels: 39.How to obtain the amounts?The amounts of each type of coin are obtained using a system of equations, in which the variables are given as follows:
Variable x: amount of quarters.Variable y: amount of nickels.Kevin and Randy Muise have a jar containing 83 coins, hence:
x + y = 83.
The value of a nickel is of $0.05, while the value of a quarter is of $0.25. The total value of the coins in the jar is $12.95, hence:
0.25x + 0.05y = 12.95.
From the first equation, we have that:
y = 83 - x.
Replacing on the second equation, the amount of quarters is given as follows:
0.25x + 0.05(83 - x) = 12.95
0.2x = 8.8
x = 8.8/0.2
x = 44.
Then the amount of nickels is given as follows:
y = 83 - x = 83 - 44 = 39.
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A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear? Any combination
Answer: A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. This means that she has a total of 8 * 5 * 5 = <<855=200>>200 different skirt-blouse-shoe outfits that she can wear.
Step-by-step explanation: To find the number of different skirt-blouse-shoe outfits that a woman can wear, we need to find the total number of combinations of skirts, blouses, and shoes that she has. To do this, we simply multiply the number of skirts that she has by the number of blouses that she has by the number of pairs of shoes that she has. In this case, the woman has 8 skirts, 5 blouses, and 5 pairs of shoes, so the total number of combinations is 8 * 5 * 5 = 200. This means that she can wear 200 different skirt-blouse-shoe outfits.
Please help asap!!!!!!
By SAS congruence triangle MLN and triangle OLN are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, LM≅LO, ∠MLN≅∠OLN.
LM≅LO (Given)
∠MLN≅∠OLN (Given)
LN≅LN (Reflexive property of congruence)
ΔMLN≅ΔOLN (SAS congruence)
∠M≅∠O (CPTC)
MN≅ON (CPTC)
Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.
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Parking Spaces múltipl
"x/3" is division
x/3 - 4 = -6
what does x equal?
Answer:
x = -6
Step-by-step explanation:
-6/3-4= -6
Multiply. Write the answer in simplest form.
4 2/3 x 9/10
Answer:
[tex] 4\frac{1}{5} [/tex]
Step-by-step explanation:
[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]
[tex] \frac{14}{3} \times \frac{9}{10} [/tex]
[tex] \frac{126}{30} [/tex]
[tex] \frac{21}{5} [/tex]
Help Which number line shows the solution set to this inequality?
-20 + 9
Answer:
A
Step-by-step explanation:
-2x + 9 < x - 9
-2x - x < -9 - 9
-3x < -18
x > -18/-3
x > 6
bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental. how many games must be played for the cost to be the same at both places? Define variables and solve the system of equations
The number of games that must be played for the cost to be the same at both places is 4.
How to solve system of equations?Bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental.
The number of games that must be played for the cost to be the same at both places is as follows:
Using system of equation,
let
x = number of games
Hence,
2.50x + 2 = 2x + 4
2.50x - 2x = 4 - 2
0.5x = 2
divide both sides by 0.5
x = 2 / 0.5
x = 4
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Use four of the eight image tiles below to graph the solution to this inequality on the number line. Be sure to cover the entire number line.
To represent an inequality on a number line, such as x>3, first draw a circle around the number. Fill in the circle if the sign also says equal to (or ).
How do you graph an inequality's solution on a number line?To represent an inequality on a number line, such as x>3, first draw a circle around the number.Fill in the circle if the sign also says equal to (or ).Leave the circle blank if the sign doesn't include equal to (> or ).Equation notation, set notation, interval notation, and solution graph are the four ways to display an inequality.Always begin by separating the variable y from the inequality's left side.Step 2: Replace the inequality symbol with the equality symbol.Step 3: In the X, Y, XY, XY plane, graph the boundary line from step 2.The final step is to shade a portion or one side of the boundary line.To learn more about Graphing Linear Inequalities refer to:
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(8x + 6) - (x + 4).
The probability of rain on Monday is .1. The probability of rain on Tuesday is .8. What is the probability of rain on both Monday and Tuesday?
Answer:
The probability of rain on both Monday and Tuesday is .08, or approximately 8%.
Step-by-step explanation:
The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:
Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08
Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.
It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.
Question #8
Cameron read that his favorite NBA team won their game last night by a score of 142 to 124.
Which is true about the digit 2 in each number?
The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
How to identify the place value of a digit in a number?The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.
The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.
We are given that encore or points for an NBA Team are usually as whole numbers.
For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.
The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.
Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
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Bruno recorded 2/12 of his new album in
August, 1/3 of his new album in July, and the
rest in June.
What fraction of the album did he record in June?
The fraction of the album he recorded in June is 1/2
How to determine this?When all the fractions of the album will be = 1
Bruno recorded 2/12 was recorded in August
2/12 to the lowest term = 1/6
And 1/3 was recorded in July
So,
The fraction of the rest of the album in June is unknown
Let fraction recorded in June will be = x
x = 1 - 1/6 - 1/3
x = 1/1 - 1/6 - 1/3
x = [tex]\frac{18 - 3 - 6}{18}[/tex]
x = [tex]\frac{9}{18}[/tex]
x = [tex]\frac{1}{2}[/tex] to lowest term
Therefore, he recorded 1/2 of his Album in June
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3. Un barco de exploración de aguas profundas está sacando a un buzo a
razón de 25 pies por
minuto. El buzo está a 200 pies bajo el nivel del mar. ¿Qué tan profundo
estaba el buzo
hace 10 minutos?
The diver was 450 feet deep in the water 10 minutes ago.
How deep was the diver 10 minutes ago?Let our D be the depth of the diver 10 minutes ago.
Since diver is pulled out at 25 ft/minute, the depth formula can be written as:
[tex]D - 25t = 200[/tex] where t is the time in minutes.
Substituting t = 10, we have:
[tex]D - 25(10) = 200\\D - 250 = 200\\D = 200 + 250\\D = 450 feet.[/tex]
Translated question "A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?"
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Note that given the speed at which he is being pulled out, the diver was 50 feet about 10 minutes ago.
How is this so?The diver is being pulled out at the rate of 25 feet per minute.
This means that after 10 minutes, he would have been pulled by a total of
25 x 10 = 250 feet.
Since the diver was 200 feet below sea level,
200-250 = -50ft.
hence 10 minutes ago, he was 50 feet below sea level.
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Translation:
A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. how deep there was the diver 10 minutes ago?
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x^4 = -x^2 + 5.
How do you write a quadratic form?
A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.
What is quadratic standard form?
Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.
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John entered a cross-country ski race. The first part of the race was 14 km long, and he completed it in 1 hour. The second part was 18 km long, and he completed this part in an hour and a half. What was John's average speed for the whole race?
A.
12.8 kilometers per hour
B.
26 kilometers per hour
C.
27.3 kilometers per hour
John's average speed for the whole race would be; 12.8 kilometers per hour
How to calculate the average speed?The first part of the race was 14 km long, and he completed it in 1 hour.
Now, formula for speed is;
Speed = distance/time
Thus, John's speed in the first part of the race would be;
14/1 = 14km/hr
The second part was 18 km long, and he completed this part in an hour and a half. This means that his speed in the second part of the race is;
18/1.5 = 12km/hr
Average speed = Total distance/total time
Total distance for both parts of the race is;
14 + 18 = 32km
Total time for the race is;
1 + 1.5 = 2.5 hours
John's average speed for the whole race would be;
32/2.5 = 12.8 kilometers per hour
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$2, 900 is invested in an account earning 6.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer: The value of the account after t years can be found using the formula:
Value = 2900 * (1 + 0.0061/4)^(4t)
The annual growth rate, or APR, is 6.1%. When this rate is compounded quarterly, the effective annual growth rate, or APY, is 6.17%, which is the nearest hundredth of a percent.
Therefore, the function showing the value of the account after t years is:
Value = 2900 * (1 + 0.0061/4)^(4t)
And the annual growth rate, or APY, is 6.17%.