It is not a function because: C) the element 1 is in both the domain and the range.
What makes a Relation a Function?A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.
In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.
Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.
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A5.1 m long ladder is leaning against a
wall. The wall stands perpendicular to the
ground. The base of the ladder is 1.8 m
away from the wall.
Work out the size of the acute angle that
the ladder makes with the ground.
Give your answer in degrees to 1 d.p.
The acute angle the ladder makes with the ground is 69.3 degrees.
How to find the acute angles formed from the right triangle ?The ladder is 5.1 m and it is leaning against a wall.
The wall is perpendicular to the ground.
This means the ground forms 90 degrees with the wall.
This situation forms a right angle triangle.
Therefore, the acute angle the ladder forms with the ground can be found as follows:
Using trigonometric ratios,
cos ∅ = adjacent / hypotenuse
where
∅ = acute angle
Therefore,
adjacent side = 1.8 m
hypotenuse side = 5.1 m
Hence,
cos ∅ = 1.8 / 5.1
∅ = cos⁻¹ 0.35294117647
∅ = 69.3326835065
∅ = 69.3°
Therefore, the acute angle the ladder makes with the ground is 69.3 degrees.
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At the arcade, Ryan, Sara, and Tim played video racing games, pinball, and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Sara spent $12 for 3 racing games, 4 pinball games, and 5 games of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games, and 4 games of air hockey. How much did each of the games cost?
Answer: Racing $.50
Pinball $.75
Air Hockey $1.50
HELP MEEEEE OUTTTT PLEASEEE
Answer:
other answer is right
Step-by-step explanation:
just answering so they can get brainliest:)
The sum of a daughter and mother's age is 55. The age of the daughter is the
mother's age reversed. Find the age of the daughter if the age of the mother is
greater than 40 years.
Evaluate-nx + x when x = 2.
Answer:
-2n + 2
Step-by-step explanation:
They give you the X value which is 2
All you do is substitute
-2n + 2
Hope this helped
Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one
paying 5%, and one paying 6% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding, least-risky
account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of
$2120?
Answer:
$25,333.33 at 3%$12000 at 5%$12,666.67 at 6%Step-by-step explanation:
Cyndee invests $50,000 in accounts earning 3%, 5%, and 6% annually, for a total annual return of $2120. She puts twice as much in the first account as in the third. You want to know the amount invested in each account.
SetupLet x represent the amount invested in the third account. Then 2x is the amount invested in the first account, and (50000 -3x) is the amount invested in the second account. The total return is ...
0.03(2x) +0.05(50000 -3x) +0.06(x) = 2120
SolutionSimplifying the equation gives ...
-0.03x +2500 = 2120
380 = 0.03x . . . . . . . . . . add 0.03x-2120
12,666 2/3 = x . . . . . . . divide by 0.03
2x = 25,333 1/3
50000 -3x = 12,000
Cyndee should invest 25,333.33 at 3%, $12,000 at 5%, and $12,666.67 at 6%.
I need help I dot understand someone explain it step by step
Leah is training to run half marathon Her goal For training is to run 20 miles a week. she ran 3 1/2 Miles on Monday 4. 3/4 miles on Tuesday 5 miles on Wednesday And 4 miles On Thursday. how Many Miles will She Need to run On Friday In Order to meet her goal?
The number of miles she should run on Friday is 2 3/4 miles.
Given that, Leah is training to run a half marathon her goal training is to run 20 miles a week. she ran 3 1/2 miles on Monday 4 3/4 miles on Tuesday 5 miles on Wednesday and 4 miles on Thursday.
We need to find how many miles will she need to run on Friday in order to meet her goal.
How to add mixed fractions?Follow these steps to add mixed fractions:
Add the whole numbers together. Find the lowest common denominator (LCD) of both fractions. The LCD is the lowest number that is evenly divisible by both numbers.Convert the fractions to have the LCD as their denominator.Once you have a common denominator, the fractions can be added by simply adding the numerators.Now, the number of miles she ran together from Monday to Thursday
=3 1/2 + 4 3/4 + 5 + 4 =(3+4+5+4)(1/2 + 3/4)
=16 (2/4 + 3/4)
=16 5/4
=17 1/4
Remaining miles = 20-17 1/4
=20-69/4
=(80-69)/4
=11/4
=2 3/4
Therefore, the number of miles she should run on Friday is 2 3/4 miles.
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6. Reggie went to the grocery
store and purchased several
items. The cereal he bought cost
$2.10, which was twice as much as
the eggs. What was the price of the
eggs?
If Cindy shoots a ball at a basket 40 times
and scores 15 times, what is the
experimental probability of Cindy scoring?
Experimental probability of Cindy scoring=0.375
Probability:
Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain.
The probabilities in a probability model must sum to 1.
When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.
To find the probability of the union of two events, we add the probabilities of the two events and subtract the probability that both events occur simultaneously.
To find the probability of the union of two mutually exclusive events, we add the probabilities of each of the events.
The probability of the complement of an event is the difference between 1 and the probability that the event occurs.
In some probability problems, we need to use permutations and combinations to find the number of elements in events and sample spaces.
Formula :
probability of an event with equally likely outcomes : [tex]\frac{n( experimental-event )}{n(total no. of event )}[/tex]
Given :
Total no. of event =Cindy shoots a ball at a basket 40 times
experimental event = 15 times
[tex]P(E)= \frac{15}{40} \\P(E)=\frac{3}{8} \\P(E)= 0.375\\[/tex]
experimental probability of Cindy scoring=0.375
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Please Help Me! Will be brainlest
E=-7g^4+3g^2h^2-11h^4
F=6g^4-13g^2h^2+8h^4
E+F=
The addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
ExponentE = - 7g⁴ + 3g²h² - 11g⁴
F = 6g⁴ - 13g²h² + 8h⁴
E + F = (- 7g⁴ + 3g²h² - 11g⁴) + (6g⁴ - 13g²h² + 8h⁴)
= - 7g⁴ + 3g²h² - 11g⁴ + 6g⁴ - 13g²h² + 8h⁴
collect like terms= -7g⁴ + 6g⁴ + 3g²h² - 13g²h² - 11g⁴ + 8h⁴
evaluate= - g⁴ - 10g²h² - 3g⁴
Therefore, the addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
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Polygon B is a scaled copy of Polygon A using a scale factor of 5. Polygon A's area is what fraction of Polygon B's area?
Polygon A's area is 1/25 times of Polygon B's area.
What do you understand by polygon?In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges.
A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.Polygons are named after the number of sides they have. Polygons are commonly represented by the symbol n-gon, where n indicates the number of sides.A 5-sided polygon is called a 5-gon, a ten-sided polygon is called a 10-gon, and so on.Now, as per the given question;
The formula of the scale factor is given as;
Area of Polygon B = (scale factor)²×(Area of Polygon A).
The scale factor is given as 5.
(Area of Polygon B) = (5)²×(Area of Polygon A)
Further simplifying;
(Area of Polygon B) = (25)×(Area of Polygon A)
or,
Area of Polygon A = (1/25)×Area of Polygon B
Therefore, the area of polygon A is found to be 1/25 times times the area of the polygon B.
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For each function, find the vertex, the axis of symmetry, the y-intercept, the x- intercepts (if any), whether the parabola opens upward or downward, the intervals on which the function is increasing or decreasing, the maximum or minimum value, and the range. Then sketch the graph. y = -2(x + 3)² + 8
Given parabola [tex]y=-2(x+3)^{2} +8[/tex] have vertex (-3,8)
axis of symmetry :x=-3
x intercepts (-1,0),(5,0)
y intercepts (0,-10)
Maximum value (-3,8)
Range is y[tex]\leq 8[/tex] or (-∞,8]
Parabola is increasing in (-∞,-3) and decreasing in (-3,∞)
How to identify parabola type from vertex form and its attributes?
The parabola equation y=ax²+bx+c
The parabola equation in its vertex form is
y = a(x - h)² + k, where
a is same as the a coefficient in the standard form;
(h, k) is coordinates of the vertex of parabola
h and k can be calculated as
h = - b/(2a)
k = c - b²/(4a)
If a is negative the parabola opens downward and if a is positive the the parabola opens upward
Axis of symmetry : x= h
For a parabola y=ax²+bx+c if a<0 then the range is y [tex]\leq k[/tex] and if a>0 then range is y[tex]\geq k[/tex]
For Maximum and minimum value , if a<0 then vertex is the maximum value and if a>0 then vertex is the minimum value.
For given equation [tex]y=-2(x+3)^{2} +8[/tex]
As this equation is in vertex form
h=-3, a=-2, k=8
Therefore, vertex = (-3,8)
For x intercept put y=0
Then [tex]y=-2(x+3)^{2} +8\\y\\=-2x^{2} -12x-10\\y=0\\\\x=-1,-5\\put x=0 \\y= -10[/tex]x intercepts (-1,0),(5,0)
y intercepts (0,-10)
Axis of symmetry : x= -3
[tex]y=-2(x+3)^{2} +8\\y=-2x^{2} -12x-10[/tex]
As a is negative therefore range is y[tex]\leq 8[/tex] or (-∞,8]
As a is negative therefore vertex (-3,8) is the maximum value
f'(x)= -4x-12
f'(x)=0 gives x= -3
f'(x)>0 in (-∞,-3), parabola is increasing in (-∞,-3)
f'(x)<0 in (-3,∞), parabola is decreasing in (-3,∞)
Please find the graph attached.
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Someone can help me please
4-3i^2
Step-by-step explanation:
the weight of an organ in adult male has a bell shaped distribution with a mean of 300 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following:
a.) About 95% of organs will be between what weights?
b.) What percentage of organs weighs between 225 grams and 375 grams?
c.) What percentage of organs weighs less than 225 grams or more than 275 grams?
d.) what percentage of organs weighs between 275 grams and 275 grams?
Using the Empirical Rule, it is found that:
a) About 95% of the organs will be between 250 and 350 grams.
b) 99.7% of organs weighs between 225 grams and 375 grams.
c) 84.15% of organs weighs less than 225 grams or more than 275 grams.
d) 0% of organs weight exactly 275 grams.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the weights are within 2 standard deviations of the mean, hence:
300 - 2 x 25 = 250 grams.300 + 2 x 25 = 350 grams.About 95% of the organs will be between 250 and 350 grams.
For item b, the amounts are within 3 standard deviations of the mean, hence:
99.7% of organs weighs between 225 grams and 375 grams.
For item c, considering the symmetry of the normal distribution, we have that:
0.5 x 0.003 = 0.15% weigh less than 225 grams.0.5 x 68% + 50% = 84% weight more than 275 grams.Hence:
84.15% of organs weighs less than 225 grams or more than 275 grams.
For item d, considering that the normal distribution is continuous, the percentage of an exact value is 0, hence:
0% of organs weight exactly 275 grams.
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write an equation using f(x) notation to show how the numbers in the domain and the range are related {(1,2), (-2,-4), (3,6), (0,0)
Answer:
f(x) = 2x
Step-by-step explanation:
It is obvious that the relationship between x and y is y = 2x from the numbers given
So equation is f(x) = 2x
please help with this one! ASAP
Answer: 699 m^2
Step-by-step explanation:
Aisha drove 17 miles in 3 hours. On average, how fast did she drive, in miles per
hour? Enter your answer as a whole number, proper fraction, or mixed number in
simplest form.
Answer: 5.6 repeating
Step-by-step explanation: No explanation added.
4x = y + 3
8x - 3= 2y
Graph the system
What is a sticker price of higher education
Sticker price refers to the published tuition and fees, whereas net price refers to the amount the student actually pays after financial help which is much lower than the sticker price.
Sticker priceThe sticker price of a college education is the entire annual cost. This cost covers the whole cost of tuition every year, books, lodging, and board, as well as any other charges the campus may levy, such as a parking permit or library card fee.
In this report, there are two prices listed: a sticker price and a net price. The sticker price of a college education is the entire annual cost. Every year's full tuition, books, housing, and board are included in this amount.
Hence sticker price refers to the published tuition and fees
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Answer this question please
'less than' corresponds to the < symbol, so the inequality is x<1.2. However, the weight cannot be negative or zero, so the inequality is 0<x<1.2.
In interval notation, this is (0, 1.2).
At the movie theatre, child admission is 5.50 and adult admission is 9.20. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of 662.00 . How many child tickets were sold that day?
A manufacturer estimates his marginal cost and revenue at various levels of output to be the following. If fixed cost is 500, estimate, using the Simpsons rule, the total profit or loss of producing 100 units is Blank 1. Fill in the blank, read surrounding text.
GHC
q (units)
0
20
40
60
80
100
120
MC
260
250
240
200
240
250
270
MR
410
350
300
250
270
250
300
If the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
What is the profit when MC = MR?When the marginal cost (MC) equals the marginal revenue (MR), the company breaks even, and from that point, profit maximization starts.
When MR is more than MC, the tendency is for the firm to produce more and earn more profit, and when MR is less than MC, the firm produces fewer as it incurs losses.
The profit maximization level occurs where the MR and the MC are equal.
Data and Calculations:Total revenue = fixed cost + variable cost (MR x Units)
Total revenue = 500 + (100 x 250)
Total revenue = 500 + 25,000
Total revenue = GHC 25,500
Total profit or loss at 100 units = GHC0 (GHC25,500 - GHC25,500)
GHC
q (units) 0 20 40 60 80 100 120
MC 260 250 240 200 240 250 270
MR 410 350 300 250 270 250 300
Thus, if the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
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Which is the mean? a density curve that models the distribution of a quantitative variable shown here. identify the location of the mean and median by letter. justify your answer.
The location of the mean and median by letter are C and B, respectively
How to identify the location of the mean and median by letter?The given parameter is the density curve that models the distribution of a quantitative variable
From the density curve, we can see that:
The density curve is a right-skewed distribution
In a right-skewed distribution, the median is the middle line and the mean is to the right of the median
This means that
Median = B
Mean = C
Hence, the location of the mean and median by letter are C and B, respectively
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gina visits her local farm to buy apples oranges to make a fruit salad. she has 10.00 to spend.
Based on the fact that Gina has $10.00 to spend, if she only buys oranges, the number of oranges she can buy is 29.41176 oranges.
How to find the number of oranges?The number of oranges that Gina can buy when she visits her local farm to buy apples and oranges for a fruit salad can be found as:
= Amount that Gina has to spend / Price of oranges
Solving for the total amount of oranges gives:
= 10 / $0.34
= 29.41176 oranges.
The full question is:
Gina visits her local farm stand to buy apples and oranges to make a fruit salad. She has $10.00 to spend. If she buys only oranges and oranges are $0.34 how much oranges can she buy
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A cube-shaped box has a side length of 6n³ centimeters. Amelia has several cube-shaped blocks with a side length of 2n centimeters that she needs to store in the box. what is the volume of one block? what is the volume of the box
The volume of blocks is 8n³ cm³ and volume of box is 216 n⁹ cm³.
According to the question we have been given that the
side length of the cube shaped box = 6n³ cm
side length of the cube shaped blocks = 2n cm
We need to find the volume of the box and the blocks.
The formula for the volume of cube is
V = (s)³ cubic units.
where, s = side length of the cube
Now putting the required values in the above formula we get
volume of box = (6n³)³ cm³
= 216 n⁹ cm³
volume of the blocks = (2n)³ cm³
= 8n³ cm³
Hence the volume of blocks is 8n³ cm³ and volume of box is
216 n⁹ cm³.
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Simplify the expressions:
−8y³ x 5y8
Hi! Your answer is 11. When multiplying terms with exponents, the exponents add up.
Step-by-step explanation:
You want to multiply the terms with the exponents. You should get 3 and 8, add those up and you will get 11.
Hope this helps! Have a good day :)
Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level, What will be the answer?
It should be noted that Ruby will be able to reach the fish
What is sea level?It should be noted that sea level simply means the sea base level that is used for measuring the elevation and the depth on the Earth.
It should be noted that Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water and Ruby holds a 1-meter long net at 0.5 meter above sea level.
It should be noted that he will be able to each the fish. This will be illustrated as:
=1m - (0.4 + 0.5)
= 1 - 0.9
= 0.1m
Therefore, the long net is enough to reach the fish.
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Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level. Can she reach the fish?
Which of the following expressions is equivalent to 9x-27
Answer:
3
Step-by-step explanation:
9x-27=0
+27. +27
9x=27
x=3
Chloe reads 7 pages of a mystery book in 9 minutes. What is her average reading rate in pages per
minute?
Answer:
1.25
Step-by-step explanation:
you have to take the 9 pages and divide by 7 and then divide that by 60 and u get 1.25