Answer:
(4, -3)
Step-by-step explanation:
the equation f(x-5) is a translation of the equation f(x) by 5 units to the right.
So, if all points of the equation f(x) are shifted 5 units to the right, the minimum point of the graph is also shifted 5 units to the right, so to find the minimum point of y = f(x - 5), we just need to sum 5 units to the x-coordinate:
Minimum point = (-1 + 5, -3) = (4, -3)
So the minimum point of y = f(x - 5) is (4, -3).
The minimum point on the graph of y = f(x - 5) is (-6,3)
On the graph of the equation y = f(x);
The minimum point is given as (-1,-3)
The graph of y = f(x - 5) means that, f(x) is shifted to the right by 5 units
So, the corresponding point of (x,y) of f(x) on the graph of f(x - 5) is:
[tex](x,y) \to (x - 5,y)[/tex]
This gives
[tex](-1,-3) \to (-1 - 5,3)[/tex]
Subtract 5 from -1
[tex](-1,-3) \to (-6,3)[/tex]
Hence, the minimum point on the graph of y = f(x - 5) is (-6,3)
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9. Express 400cm3 as a fraction of 2 litres
in the lowest form. *
options
1/10
1/5
2/5
Answer:
[tex]\boxed{\red{\frac{1}{5} }}[/tex]
Step-by-step explanation:
[tex]400 {cm}^{3} = 400ml \\ 2l = 2000ml[/tex]
So, now we have to write 400cm^3 as a fraction of 2l
[tex] \frac{400}{2000} = \frac{4}{20} = \frac{1}{5} [/tex]
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
3) The chance that a salmon jumps up the waterfall to upstream successfully 35%. We have a group of 9 salmon. What is the chance that none of them jump up successfully? What is the chance that all of them reach up-stream? What is the chance that at least 2 of them reach up-stream? What is the chance that at most 1 of them reaches up-stream? Is “at least 1” complement of the event “at most 1”?
Answer:
(a) P(0,9) = 0.0207
(b) P(2-9,9) = 0.1004
(c) P(0-1,9) = 0.1211
(d) "at least 1" and "at most 1" are not complements of each other because there is an overlap of "1" in both cases.
Step-by-step explanation:
With appropriate assumptions, this can be solved using the binomial distribution.
Probability of success for each trial, p = 35%
Number of trials, n = 9
using formula for x successes out of n trials, each with probability p
P(x,n) = C(n,x) p^x (1-p)^(n-x)
where C(n,x) = n!/(x!(n-x)!)
(a) zero success
n=9
p=0.35
x = 0
P(0,9) = 9!/(0!9!) 0.35^0 * 0.65^9
= 1*1* 0.0207
= 0.0207
(b) 2 or more successes
We need the sum of probabilities of 2,3,4,5,6,7,8,9 successes, which is easier calculated by (1-P(0,9)-P(1,9))
P(1,9) = C(9,1) * p^1 * p^8
= 9 * 0.35 * 0.65^8
= 9 * 0.35 * 0.3186
= 0.1004
Therefore
P(2 to 8, 9)
= 1 - P(0,9) - P(1,9)
= 1 - 0.0207 - 0.1004
= 0.8789
(c) at most 1 success
P(0,9) + P(1,9)
= 0.0207 + 0.1004
= 0.1211
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
Find the surface area of the solid shown or described. If necessary, round to the nearest tenth
7cm
10cm
14 cm
Answer:
616cm²or³
Step-by-step explanation:
SA = 2(lw)+2(lh)+2(hw)
SA=2(10×14) + 2(10×7) + 2(7×14)
SA= 2(140) + 2(70) + 2(98)
SA=280+140+196
SA=616cm²or³
Which inequality is represented by the graph?
Answer:
Step-by-step explanation:
the inequality represented by the graph is B
Plot the points
2x - 4/5y ≥ 3
y ≤ 2/5x - 3/2
x y
0 -3/2
15/4 0
Every year the United States Department of Transportation publishes reports on the number of alcohol related and non-alcohol related highway vehicle fatalities. Below is a summary of the number of alcohol related highway vehicle fatalities from 2001 to 2010.
Line graph about Alcohol related fatalities
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
Complete question:
The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.
Answer:
17,209
Step-by-step explanation:
The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :
From the graph:
Year - - - - - - - - - - Number of fatalities
2001 - - - - - - - - - - 17401
2002 - - - - - - - - - 17525
2003 - - - - - - - - - 17013
2004 - - - - - - - - - 16694
2005 - - - - - - - - - 16885
2006 - - - - - - - - - 17738
To get the average :
Sum of fatalities / number of years
(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6
= 103256 / 6
= 17209.333
Average number of alcohol related fatalities is 17,209 (to the nearest whole number)
A rhombus has interior angle measures of 104∘, 104∘, 76∘ and X degrees. Find the measure of angle X in the rhombus. Enter only the number of degrees in the answer box. Angle X measures degrees.
Answer:
76°
Interior angle of a rhombus =360
104° +104° +76° +X =360
X= 360 - 284
X= 76°
We know that the value of ∠x in the given rhombus is 76°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal. A rhombus' internal angles add up to 360 degrees, just like in other quadrilaterals, and, like in a parallelogram, the angles of opposite pairs of vertices are identical. The total of the angles of two neighboring vertices is 180 degrees.So, get the ∠x as follows:
We now know that sum of all angles in a rhombus is 360°.Then,
104 + 104 + 76 + x = 360284 + x = 360x = 360 - 284x = 76°Therefore, we know that the value of ∠x in the given rhombus is 76°.
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50 Points. Select all correct graphs. Choose the graph that indicate equation with no solutions.
Concepts:
Graph equationsAnswer:
First option and fifth option
-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.
Therefore, the graphs have no solution.
please Help will mark brainliest !!1!Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x -3y = 13 x+2=- 4
Answer:
work is shown and pictured
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
n
f0 and
102
130
are
The area of the shaded region is (Round to four decimal places as needed.)
sions
Kented in
V3 and
andomly
d by in-
on affect
otes
ents
le
Enter your answer in the answer box and then click Check Answer.
section
different
version
Clear All
Check Answer
All parts showing
Answer: 0.4255
Step-by-step explanation:
Given: IQ scores of adults, and those scores are normally distributed
Mean: [tex]\mu=100[/tex]
Standard deviation: [tex]\sigma= 15[/tex]
Let X denotes the IQ of a random adults.
The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]
[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]
Hence, area between 102 and 130 = 0.4255
A stained-glass window is shaped like a right triangle. The hypotenuse is 15feet. The length of one leg is three more than the other. Find the lengths of the legs.
let us build equation for unknown legs
If we keep the length pf one leg as x
the other leg would be x +3
so we can build a relationship using pythagoras theorem
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x+ 9-225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0 dividing whole equation by 2
x^2 + 12x - 9x - 108 = 0
x ( x + 12 ) - 9 (x + 12) = 0
(x -9) ( x +12) = 0
solutions for x are
x = 9 or x = -12
as lengths cannot be negative
one side length is 9cm
and other which is( x + 3)
9 + 3
12cm
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = First Leg² + Second leg²
Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:
15² = x² + (x + 3)²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
x² + 3x - 108 = 0
x = - 12 or x = 9
Since the length cant the negative hence x= 9, x + 3 = 12
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
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An after-school care facility tries to maintain a 2-to-1 ratio of children to adults. If the facility hired five adults, what is the maximum number of children that can enroll?
Answer:
10 children
Step-by-step explanation:
If we have a ratio of 2:1 children:adults, then we can find out how many children max can enroll if there are 5 adults.
Our original ratio was 2:1 and now it's x:5, assuming x is the number of children enrolled. We multiply 1 by 5 to get to 5, so we need to multiply 2 by 5 to get the total number of chlidren.
2 × 5 = 10
Hope this helped!
A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ after a 180° rotation about the origin and a translation 5 units to the right and 1 unit down? I need Help
Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
Please answer this correctly without making mistakes
Answer:
16 km
Step-by-step explanation:
From Washington, as the question asks, will now be considered 0 aka the starting point.
So as of now, we know Washington from Oakdale is 6.2 km.
And from Stanford to Salem is 11.9 km, also Salem to Washington is 10.3 km. Hence the addition of 11.9 km and 10.3 km to figure out the whole distance between Stanford and Washington.
11.9 km + 10.3 km = 22.2 km
Now we subtract 22.2 km to 6.2 km for the product of 16 km.
(03.03)
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Answer:
Your answer is -3.5 which lies between -4 and -3.
The point R is halfway between the integers on the number line below and represents the number -3.5 .
which is true about the solution to the system of inequalities shown?
A) y ≥ 1/3x + 3 AND 3x - y > 2
B) y ≥ 1/2x + 3 AND 3x - y > 2
C) y ≥ 1/3x + 3 AND 3x + y > 2
D) y ≥ 1/3x + 3 AND 2x - y > 2
Answer:
the solution to the system of inequality is C
Find the probability of each event. A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Eight horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?
Answer: [tex]\dfrac{1}{56}[/tex]
Step-by-step explanation:
Total horses = 6
Number of ways to choose top 3 finishers in order = 3! = 6
Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex] [By permutations]
[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]
Now, the probability that the gambler will win his bet =
[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]
[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]
Hence, the required probability = [tex]\dfrac{1}{56}[/tex]
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high
Answer:
(11π/9 )ft/s
Step by step Explanation
Let us denote the height as h ft
But we were told that The diameter of the base of the cone is approximately three times the altitude, then
Let us denote the diameter = 3h ft, and the radius is 3h/2
The volume of the cone is
V = (1/3)π r^2 h
Then if we substitute the values we have
= (1/3)π (9h^2/4)(h) = (3/4)π h^3
dV/dt = (9/4)π h^2 dh/dt
We were given as 22feet and rate of 8 cubic feet per minute
h = 22
dV/dt = 8
8= (9/4)π (22) dh/dt
= 11π/9ft/s
Therefore, the rate is the height of the pile changing when the pile is 22 feet is
11π/9ft/s
Question
Given that cot(0)= -1/2
and O is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.
Provide your answer below:
Answer:
sin(O) = 2/sqrt(5) or 2sqrt(1/5)
Step-by-step explanation:
using 1+cot^2(x) = csc^2(x)
we have, taking reciprocal on both sides,
sin(x) = 1/sqrt(1+cot^2(x)
= 1/sqrt(1+(-1/2)^2)
= 1/sqrt(5/4)
= 2/sqrt(5) or 2sqrt(1/5)
Since angle x is in the second quadrant, sin(x) is positive.
Find the value of the chi-square test statistic for the goodness-of-fit test. You wish to test the claim that a die is fair. You roll it 48 times with the following results. Number 1 2 3 4 5 6Frequency 5 10 12 9 4 8Observed frequency (O) 5,10,12,9,4,8Expected frequency (E) 8,8,8,8,8,8What is the value of the 2 test statistic?a. X2 = 3.538b. X2 = 4.182c. X2 = 5.75d. X2 = 7.667
Answer:
The value of Chi-square test statistic is χ² = 5.75.
Step-by-step explanation:
The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.
The hypothesis can be defined as follows:
H₀: The die is fair.
Hₐ: The die is not fair.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table attached below.
The value of Chi-square test statistic is χ² = 5.75.
G(x) = 5x + 3
Find G(2b)
Answer:
G(2b) = 10b + 3
Step-by-step explanation:
To find G(2b), simply plug in 2b wherever there is an x in G(x).
G(x) = 5x + 3
G(2b) = 5(2b) + 3
G(2b) = 10b + 3
Answer:
3 + 10b maybe?
Step-by-step explanation:
Solve of the following equations for x: 3 − x = 2
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
3 − x = 2 =
X = 1
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you. Brainliest would be nice!
Answer: x = 1 / 1 = x.
Step-by-step explanation:
3 - x = 2
First, since you can't subtract x from 3, we find ways to subtract 2 from 3.
So, we write the 3 and attach (-) minus/negative sign to the 3 with 2. Because when a number crosses the equal sign and it is negative, it becomes positive and when it is positive, it becomes negative.
And 2 will cross the equal sign so,it will be (-) just like: -2. And -x will cross the equal sign so it will be x. Let's solve it with the steps above:
3 - x = 2
3 - 2 = x
1. = x
OR
3 - x = 2
-x = 2 - 3
-x/- = -1/-
So, negative will cancel negative.
x =1.
Please mark me as the brainliest!!
Thanks!!
Which of these is the opposite reciprocal of 3/4
Answer: -4/3
Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.
So the negative reciprocal of 3/4 is -4/3.
Change 3Y - 2X = -6 to the slope-intercept form of the equation of a line.
Answer:
y = 2/3x -2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
3y -2x = -6
Solve for y
Add 2x to each side
3y = 2x-6
Divide by 3
3y/3 = 2x/3 -6/3
y = 2/3x -2
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes. Y
Answer:
yyy = xxx + 151515
Step-by-step explanation:
Since you want to swim 151515 minutes longer one day at practice (note this time is actually 105 days), you simply need to swim the same amount of time as your friend, plus the extra time. Hence, your time will be equal to your friends time plus the extra time you plan to swim.
What is the length of JM in the given figure?
Answer: B. 30
Step-by-step explanation:
When given a secant and a tangent, the formula is:
exterior of secant × secant = tangent²
KM × JK = LK²
10 × (JM + 10) = 20²
10JM + 100 = 400
10JM = 300
JM = 30
One positive number is 4 more than twice another. Their product is 198
Answer:
[tex]\large \boxed{\sf \ \ 9 \text{ and } 22 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write that, x being the second number
(4 + 2*x) *x = 198
Let's solve this equation.
[tex](4+2x)x=198\\\\4x+2x^2=198 \\\\\text{*** subtract 198 from both sides ***}\\\\2x^2+4x-198 = 0\\\\\text{*** The product of the zeroes is -198/2=-99=-11*9 and their sum is -4/2=-2 ***}\\\\2x^2+4x-198=2(x-9)(x+11)=0\\\\x=9 \ \ or \ \ x=-11[/tex]
We are looking for positive number so the solution is 9.
And the first number is 4 + 2 * 9 = 4 + 18 = 22
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
22 and 9
Step-by-step explanation:
Let the positive number be x.
Let the other number be y.
x = 2y + 4
xy = 198
Substitute x as 2y + 4 in the second equation.
(2y+4)y = 198
2y² + 4y = 198
2y² + 4y - 198 = 0
2(y-9)(y+11) = 0
y-9=0 or y+11=0
y=9
y=-11
The product is 198, so y is positive.
x(9)=198
x=22
I need help I just don't understand
Answer: 9/7 or -5/2
Step-by-step explanation:
We can only factorise quadratics if they're in the format ax^2 + bx + c
Re-arranging the equation gives 14x^2 + 17x - 45 = 0
Factorising this quadratic gives:
(7x - 9)(2x + 5) = 0
There are numerous ways to factorise quadratics, using a calculator or via alternate methods you may have learnt in class. (E.g. 2 numbers multiply to make (14 * -45) and add up to make (17).
This gives us our solutions.
x = 9/7 or x = -5/2
Answer:
See below.
Step-by-step explanation:
First, move all the terms to one side so we have only a zero on the right:
[tex]6x^2-17x+13=20x^2-32\\-14x^2-17x+45=0\\14x^2+17x-45=0[/tex]
(I divided everything by negative 1 in the third step. This is optional, but I like having the first term positive.)
Now, we just need to factor it. To factor, what you want to do is find two numbers a and b such that:
When a and b is multiplied together, they equal the first coefficient and constant multiplied together.
And when a and b is added together, they equal the second term.
In other words, we want to find two numbers that when multiplied equals 14(-45)=-630 and when added equals 17. Then, we can substitute this into the 17. You do this by guessing and checking. It's useful to have a calculator.
After a bit, you can find that 35 and -18 works. Thus:
[tex]14x^2+17x-45=0\\14x^2+35x-18x-45=0\\7x(2x+5)-9(2x+5)=0\\(7x-9)(2x+5)=0[/tex]
Now, the finish the problem, we just need to use the Zero Product Property and solve for x:
[tex]2x+5=0\\x=-5/2\\\\7x-9=0\\x=9/7[/tex]
Note: This only works for quadratics.
