The statement that is true about the quadratic functions is:
g(x) > h(x) for x = -1.
Which statements are true for functions g(x) and g(x)?Here we have the two quadratic functions:
g(x) = x^2
h(x) = -x^2
Notice that h(x) = -g(x).
Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.
g(0) = 0^2 = -0^2 = h(0)
Then the statement that is true is
g(x) > h(x) for x = -1.
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Convert (-z-2)^2 into a quadratic trinomial and (-n+4)^2 and (-m-10)^2
(please help)
The quadratic trinomial of the given expressions are z² + 4 + 4z, 16 + n² - 8n, m² + 100 + 20m respectively.
What do you understand by Quadratic Trinomial?A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms.
A polynomial is an algebraic expression that has one or more terms and is written as [tex]a_0x^n + a_1x^{ n - 1} + a_2x^{n-2} + ...+ a_n x^0[/tex] in the standard form. Where [tex]a_0, a_1, a_2, ....,a_n[/tex] are constants and n is a natural number.
A quadratic trinomial is a type of algebraic expression with variables and constants. It is expressed in the form ax² + bx + c, where x is the variable and a, b and c are non-zero real numbers. A quadratic trinomial also describes the discriminant D where it defines the quantity of an expression and it is written as D = b² - 4ac.
Given:
(-z - 2)²
⇒ [-(z + 2)]²
⇒ (z)² + (2)² + 2(z)(2)
⇒ z² + 4 + 4z
(4 - n)²
⇒ (4)² + (n)² - 2(4)(n)
⇒ 16 + n² - 8n
(-m - 10)²
[-(m + 10)]²
⇒ (m)² + (10)² + 2(m)(10)
⇒ m² + 100 + 20m
So, the expressions are converted into quadratic trinomial.
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Find the area of the semicircle.
Either enter an exact answer in terms of pi or use 3.14 for pi and enter ur answer as a decimal
The area of the semi circle is 14.13 units²
What is the area of a semi circle?a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.
The area of a semicircle is the half of the area of a full circle.
The area of a full circle is πr², therefore the area of a semicircle is ½πr²
r = d/2 = 6/2 = 3
A = ½πr²
= 1/2 × 3.14 × 3²
A = 28.26/2
A = 14.13 units²
therefore the area of the semi circle is 14.13 units²
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Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
To compare the two investment options, we must compute the future value (FV) of each account after 30 years of compounding at a 2.5% rate.As an outcome, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
How to find IRA?We have monthly payments of $416.66 for 30 years, or 360 months, on the IRA. Using the following formula to calculate the future value of an annuity:
[tex]FV = PMT * [(1 + r)^n - 1] / r[/tex]
We can calculate the future value of the IRA using the following formula: where PMT is the monthly payment, r is the monthly interest rate (2.5% / 12), and n is the number of payments (360):
[tex]FV IRA = 416.66 * [(1 + 0.025/12)^360 - 1] / (0.025/12) = $358,888.91[/tex]
We have annual payments of $5000 for 30 years on the Roth IRA. Using the following formula to calculate the future value of a lump sum:
[tex]PV * (1 + r)n = FV[/tex]
where PV is the present value (the lump sum), r is the annual interest rate (2.5%), and n is the number of years (30), we can calculate the Roth IRA's future value:
5000 * (1 + 0.025)30 = $251,772.58 FV Roth
As a result, the IRA will outperform the Roth IRA in terms of future value by:
$358,888.91 - $251,772.58 = $107,116.33 FV IRA - FV Roth
As a result, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
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suppose that 5 out of the 19 doctors in a small hospital are general practitioners, 9 out of the 19 are under the age of 50 , and 3 are both general practitioners and under the age of 50 . what is the probability that you are randomly assigned a general practitioner or a doctor under the age of 50 ? enter a fraction or round your answer to 4 decimal places, if necessary.
The probability of being assigned a general practitioner or a doctor under the age of 50 is 11/19 or approximately 0.5789 (rounded to four decimal places).
We are given that there are 5 general practitioners (GPs) out of 19 doctors in the hospital, which means that the probability of being assigned a GP is 5/19.
We are also given that there are 9 doctors under the age of 50 out of the 19 doctors in the hospital, which means that the probability of being assigned a doctor under the age of 50 is 9/19.
However, we need to subtract the probability of being assigned a doctor who is both a GP and under the age of 50 because this group is counted twice in the above probabilities.
We are given that there are 3 doctors who are both GPs and under the age of 50. Therefore, the probability of being assigned a doctor who is both a GP and under the age of 50 is 3/19.
To use the inclusion-exclusion principle, we add the probabilities of being assigned a GP and being assigned a doctor under the age of 50, and then subtract the probability of being assigned a doctor who is both a GP and under the age of 50.
P(GP or Under 50) = P(GP) + P(Under 50) - P(GP and Under 50)
= 5/19 + 9/19 - 3/19
= 11/19
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please help me i dont understand
Answer:
x=15°
∡Q= 75°
Step-by-step explanation:
supplementary angles means the sum of the angles =180°
so, 5x+105°=180°
5x=75°
x=15°
∡Q= 75°
Find the value of x and y
What is true about a system of two linear equations that has no solution?
Answer: The two lines never intersect
Step-by-step explanation:
An algebraic solution for a system of equations means that the graphs of the two equations intersect at some point. If no such point can be found, it means the graphs never intersect.
3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.
The equivalent expression to -4x² + 2x - 5(1 + x) is given as follows:
-4x² - 3x - 5.
How to obtain the equivalent expression?The expression for this problem is defined as follows:
-4x² + 2x - 5(1 + x)
To obtain the equivalent expression, we apply the distributive property to -5(1 + x) as follows:
-5(1 + x) = -5 - 5x.
Then the expression is given as follows:
-4x² + 2x - 5 - 5x.
Combining the like terms, we have that the expression is given as follows:
-4x² - 3x - 5.
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please answer asap i need helpp
Answer:
110°
Step-by-step explanation:
]%}}%¶¢{^[€{¢¶¢¶€¶
Answer: 110˚
Step-by-step explanation:
Complementary angles have a sum of 90˚
With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚
Supplementary angles have a sum of 180˚
With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚
∴ Measure of angle C = 110˚
Select a two-digit number whose 1st digit it 0,1,2,3, or 4, and whose 2nd digit is 5,6,7,8, or 9.
In 25 ways we can select 2-digit number from the given digits.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, a two-digit number whose 1st digit it 0,1,2,3, or 4, and whose 2nd digit is 5,6,7,8, or 9.
Number of ways selecting 1st digit is
P(5, 1) = 5!/(5-1)!
= 5
Number of ways selecting 2nd digit is
P(5, 1) = 5!/(5-1)!
= 5
Now, 5×5=25
Therefore, in 25 ways we can select 2-digit number.
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A pack of cinnamon-scented pencils sells for $6.00. What is the sales tax rate if the total cost of the pencils is $6.42?
Please show how you did it
Answer:
7% sales tax
Step-by-step explanation:
If the pencils cost $6, then the sales tax costs $6.42 - $6 = $0.42. To find the rate, we must divide $0.42 by $6. $0.42/$6 = 0.07. 0.07 is 7%.
A family purchased tickets to a museum and spent a total of $38.00. The family purchased 4 tickets. There was a $1.50 processing fee for each ticket. Write and solve an equation that can be used to find x, the cost of one ticket to the museum. Show your work or explain your answer.
Answer:
Equation: 4(x + 1.5) = 38
Ticket Cost: $8, or x = 8
Step-by-step explanation:
The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.
4(x + 1.5) = 38
4x + 6 = 38
4x = 32
x = 8
Check:
4 * 8 = 32 (cost of 4 tickets)
4 * 1.5 = 6 (cost of 4 processing fees)
32 + 6 = 38 (4 tickets + 4 processing fees = total)
Mr. Jackson had to attend a meeting in San Fransisco 300 miles from his home. He traveled the first 90 minutes at 64 miles per hour. The next hour he traveled 66 miles per hour. If he reached San Fransisco three hours later what was his average speed for the last three hours?
Let's call the average speed for the last three hours "S".
First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.
Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.
Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:
S = 170 miles / 2 hours = 85 miles per hour
So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.
Answer:
68 mph
Step-by-step explanation:
Let's call the average speed for the last three hours "S".
The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.
So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.
The time it took him to cover that distance is 3 hours.
We can use the formula distance = speed * time to find S:
204 = S * 3
Solving for S:
S = 68 mph
So the average speed for the last three hours was 68 mph.
Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y< 2x+3
Answer: 2
Step-by-step explanation:
Can someone explain this
There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:
Case A: y = (1 / 3) · (x + 4) · (x - 2)
Case B: y = (x + 4) · (x - 2)
Case C: y = 2 · (x + 4) · (x - 2)
Case D: y = - (1 / 3) · (x + 4) · (x - 2)
Case E: y = - 2 · (x + 4) · (x - 2)
How to determine a group of quadratic equations
In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:
y = a · (x + 4) · (x - 2)
Where a is the lead coefficient.
The following parameters are for each parabola:
Case A: (x, y) = (- 1, - 3)
Case B: (x, y) = (- 1, - 9)
Case C: (x, y) = (- 1, - 18)
Case D: (x, y) = (- 1, 3)
Case E: (x, y) = (- 1, 18)
Now we determine the lead coefficient for each case:
Case A
- 3 = a · (- 1 + 4) · (- 1 - 2)
- 3 = - 9 · a
a = 1 / 3
Case B
- 9 = a · (- 1 + 4) · (- 1 - 2)
- 9 = - 9 · a
a = 1
Case C
- 18 = a · (- 1 + 4) · (- 1 - 2)
- 18 = - 9 · a
a = 2
Case D
3 = a · (- 1 + 4) · (- 1 - 2)
3 = - 9 · a
a = - 1 / 3
Case E
18 = a · (- 1 + 4) · (- 1 - 2)
18 = - 9 · a
a = - 2
All differences between all quadratic equations are due to different lead coefficients.
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Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement.a) 14.8mb) $10.25c) 0.05 Ld) 1.000 g/mLe) 6200cmf) 403 kg
Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e) 6200cm = 6200x cm. f) 403 kg = 40x kg.
a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.
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Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times.
Robin ride her bike this week 35 miles.
Robin rides her bike 3 miles to school.
She rides home a different way that is 4 miles long.
This week, Robin rode to school and back 5 times.
For one time ride to school from house = Rode to School + Rode To home
For one time ride to school from house = 3 + 4
For one time ride to school from house = 7
Robin rides total of 5 times.
So, For five time ride to school from house = 5 × For one time ride to school from house
For five time ride to school from house = 5 × 7
For five time ride to school from house = 35 miles
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The complete question is:
Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times. How many miles did Robin ride her bike this week?
i have exactly ten coins whose total value is $. if three of the coins are quarters, what are the remaining coins?
it would be 5 pennies and two dimes
if 3 are quarters, that is 75 cents. if you add two dimes, it's now 95, and making the total number of coins 5. then you add 5 pennies, you get a total of 100 cents, one dollar, and now have 10 coins. hope its right
3x-1/2y=5x+4 what is the slope
Answer: The slope of a line in the form y = mx + b can be found by taking the coefficient of x, which is m. In this equation, the slope is not in that form, so we need to isolate y and put it in that form.
Starting with the equation:
3x - 1/2y = 5x + 4
We'll isolate y by subtracting 3x from both sides:
-1/2y = 2x + 4
And then multiply both sides by -2 to solve for y:
y = -4x - 8
So the slope of the line is -4.
Step-by-step explanation:
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.30 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
The total cost of the meal is $
Answer:
$82.21
Step-by-step explanation:
cost of meal: $78.30
15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75
tip: 20% of $78.30 = 0.20 × $78.30 = $15.66
total cost = $78.30 - $11.75 + 15.66 = $82.21
Answer: $82.21
please help meeeeeeeeeee
The number of pet-owners that are in the union of cat owners and other pet owners is given as follows:
20 pet-owners.
How to obtain the union of two sets?The set representing the union of two sets is composed by all the elements that belong to at least one of the sets.
Hence the union of pet-owners that are in the union of cat owners and other owners is composed as follows:
1 + 1 + 3 + 6 = 11 cat owners.7 + 2 = 9 other owners who are not cat owners.Hence the total number is given as follows:
11 + 9 = 20.
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let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) =
Answer: no exact answer
Step-by-step explanation:
please help! I'm struggling a lot with this domain and range.
=====================================================
Explanation:
The domain is the set of allowed x inputs.
In this case, we can plug in anything but x = 2 because of the vertical asymptote here.
This means the domain is the interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] that notation basically says "start with the entire real number line. Then poke a hole, or remove, 2 from the number line".
------------
The range is the set of possible y outputs. In this case, the domain and range lead to the same interval notation since we're kicking out "2" each time. This time we focus on the horizontal asymptote. The curve gets closer and closer to these dashed lines but never actually reaches them.
Since [tex](-\infty,2) \cup (2,\infty)[/tex] is one of the possible ways to represent the range, one of the answers is choice A.
The interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] is too vague because it's not clear if we're talking about the domain or range. The notation [tex]\left\{\text{y}|\text{y} \in \text{R}, \ \text{y} \ne 2\right\}[/tex] is more specific. It says "y is a real number such that it cannot equal 2". In other words "y can be anything but 2". This tells us that choice D is another answer.
So either y < 2 or y > 2 which represents us being below the horizontal asymptote or above it respectively.
The third and final answer is choice E.
Question 10 / 1 pointWhich one of the following best defines the notion of "the P-value of a hypothesistest?"Question options:The probability of a type I error.The probability of a type II error.The probability of rejectingH0{"version":"1.1","math":"H_0"}, whether it's true or not.The probability of obtaining a test statistic at least as extreme as the one you calculated, assuming the nullhypothesis is true.
Option A: The probability of rejecting H_o, whether it's true or not, best describes the notion of the P-value of a hypothesis test.
The level of marginal significance within the hypothesis test that represents the probability of occurrence of a given event is referred to as its P-value. In order to provide the least significance at which the null hypothesis would be rejected, it is utilized as a choice for the rejection point. This signifies that the option A is correct.
The P-value is known as the probability value. It can be defined as the probability of getting a result that is either the same or more advanced than the actual observations. There is more support for the alternative hypothesis when the P-value is low.
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Correct way to ask the question is:
Which one of the following best defines the notion of the P-value of a hypothesis test?
The probability of rejecting H_o, whether it's true or not
The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
The probability of the type I error
The probability of the type II error
three coplanar circles intersect as shown. what is the maximum number of points on the circles that a line passing through all three circles can touch?
The maximum number of points on the circles that a line passing through all three circles can touch is 36.
Two circles may cross in two points, one point, or no points on a aeroplane, digression circles are coplanar circles that cross at a single point.Concentric circles are coplanar circles that share a common centre.
You can select any two circles in (₂³) ways and each pair will intersect at 2 points. Therefore total 3*2=6 points.
Similarly, 4 lines will intersect at (₂⁴)=6
points.
Now each line will intersect at 2 points with a circle. And since we can select a circle in (³₁) ways and a line in (₁⁴) ways, therefore total (₁³)∗(₁⁴)∗2=24 points they will intersect.
Therefore, total number of intersection points = 6 + 6 + 24 = 36 points.
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can someone help pls
Answer:
55
Step-by-step explanation:
Since 1 rectangle is 10 and there are 5, that means the whole length is 50.
Which means with can set the equation equal to 50
[tex]x - 5 = 50[/tex]
Adding 5 gets us
[tex]x = 55[/tex]
60°
V
U
S
A
120°
T
?
Solve for X
The measure of x in the figure is 180 degrees
How to determine the measure of xFrom the question, we have the following parameters that can be used in our computation:
The circle and the intersecting chords
The value of x represented by ? is then calculated as
120 = 1/2(x + 60)
Cross multiply the equation
This gives
x + 60 = 240
Subtract 60 from both sides
x = 180
Hence, the measure of x is 180 degrees
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to identify the point in a distribution at which 50% of scores fall above and 50% fall below a given score, which measure of central tendency would you report? group of answer choices mode mean median average
The median is the point in a distribution where 50% of the scores fall above and 50% fall below a certain score.
In a distribution, the median is the number that separates the top 50% of scores from the bottom 50% of scores. When the data is organised from lowest to highest, it is the midway value.
The mode is the most common value in a distribution, and it is not always the same as the median. The mean is the total of all scores divided by the number of scores, and it is impacted by outliers or extreme values in the data. Depending on the context, the term "average" can refer to either the mean or the median. When individuals say "average" without any qualification, they typically mean the mean.
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please help me I'm frustrated at this problem i know nothing about percentaes and im in 10th grade cryin inside...
Step-by-step explanation:
To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.
So, to answer, let's find the total of children and adults.
34+27 = 61 is the total for children.
38+46 = 84 is the total for adults.
Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.
34/61 = 0.557 or 55.7%
27/61 = 0.442 or 44.2%
I'm leaving it in fractional form in case you need a specific decimal answer.
As for adults, it's the same procedure.
38/84 = 0.452 or 45.2%
46/84 = 0.548 or 54.8%
A jar contains 70 L of juice. It is poured into
glasses, each of 150 mL capacity. How many glasses
are completely filled with the juice and how much juice
is left in the jug?
First, we need to convert the volume of the juice in the jar from liters to milliliters, since the volume of the glasses is given in milliliters.
1 liter = 1000 milliliters
So, 70 liters = 70 * 1000 = 70,000 milliliters
Next, we'll divide the volume of the juice in the jar by the volume of each glass to find out how many glasses can be filled with the juice.
70,000 milliliters ÷ 150 milliliters/glass = 466.67 glasses (rounded to the nearest whole number)
Therefore, 466 glasses can be filled completely with the juice.
Finally, we can find out how much juice is left in the jar by subtracting the total volume of the juice used to fill the glasses from the volume of the juice in the jar.
70,000 milliliters - (466 glasses x 150 milliliters/glass) = 70,000 milliliters - 69900 milliliters = 800 milliliters
So, 800 milliliters of juice is left in the jar.
