Step-by-step explanation:
let's write this properly :
f(x) = x³
g(x) = (x - 7)³ + 9
this translation means that every point of f(x) is shifted up by 9 units (by the "+ 9" term), and shifted right by 7 units (the " x - 7" term means that for every x the original result of x-7 happens, so, 7 units "later" or more to the right than originally).
so, the original (0, 0) point corresponds to (7, 9).
Suppose the equilibrium wage for unskilled workers in New Jersey is $16 per hour. How will the wages and employment of unskilled
workers in New Jersey change if the state legislature raises the minimum wage from $8.85 per hour to $15 per hour?
Wages of unskilled workers will increase/decrease/or not change?
Employment of unskilled workers will increase/decrease/or not change?
Answer:
it will increase the production
Step-by-step explanation:
Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N(P).
(a) Determine N(P) if N(1000) = 10000 and N(1700) = 6500. (Use symbolic notation and fractions where needed.)
N(P) =?
(b) Select the statement that gives the slope of the graph of N(P), including units and describes what the slope represents.
●5 computers per dollar
● -1/5computers per dollar
● -5 computers per dollar
● -5 dollars per computer
(c) What is the change N in the number of computers sold if the price is increased by AP = 110 dollars? (Give your answer as a whole number.)
AN = ?
Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6
Step-by-step explanation:
What is the slope of this line? the equation for a line that passes through the points (5,-3) and (-10,15)?
Part 1: Finding slope
The slope is [tex]\frac{-3-15}{5-(-10)}=\frac{-18}{15}=\boxed{-\frac{6}{5}}[/tex]
Part 2: Finding the equation
Using the point (-10, 15) to substitute into point-slope form,
[tex]y-15=-\frac{6}{5}(x+10)\\\\y-15=-\frac{6}{5}x-12\\\\\boxed{y=-\frac{6}{5}x+3}[/tex]
Answer:
Using the given points we find that the slope is -1.2 and using the slope-point form we find that the equation of line is y+1.2x = 3.
Step-by-step explanation:
In the question, two points are given, (5,-3) and (-10,15). Using them we can find the slope using the formula, (y2 - y1) / (x2 - x1). So, the slope is
(-3-15) / (5+10) = -18 / 15 = -1.2
Now, we have to find the equation of line. We have two points and a slope. Using any one point and the slope, we can find the equation of line using slope-point form of line. Let us take (5,-3).
(y+3) / (x-5) = -1.2
y+3 = -1.2(x-5)
y+3 = -1.2x + 6
y+1.2x = 3
So, the slope of line is -1.2 and the equation of line is y+1.2x = 3.
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Write the number five and a quarter million in figures.
Answer:
5 and a 250,000
Step-by-step explanation:
A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000
Answer:
It is: 5,250,000
Question
Find the distance between the points (-5, 8) and (-3,0).
To calculate the distance between two points we use this formula:
[tex] \boxed{ \boxed{{d \: = \: \sqrt{(x_2 \: - \: x_1)^{2} \: + \: (y_2 \: - \: y_1)^{2} } }}}[/tex]
______________________We organize the values:x₁ = -5 x₂ = -3 y₁ = 8 y₂ = 0______________________
We apply the values already obtained to the formula to get the distance:
[tex]d \: = \: \sqrt{( - 3 \: - \:( - 5))^{2} \: + \: (0 \: - \: 8)^{2} }[/tex]
[tex]d \: = \: \sqrt{( - 3 \: - \: ( - 5))^{2} \: + \: ( - 8)^{2} }[/tex]
[tex]d \: = \: \sqrt{( - 3 \: + \: 5) ^{2} \: + \: 64 } [/tex]
[tex]d \: = \: \sqrt{ {2}^{2} \: + \: 64 } [/tex]
[tex]d \: = \: \sqrt{4 \: + \: 64} [/tex]
[tex]d \: = \: \sqrt{68} [/tex]
[tex]d \: = \boxed{ \bold{ \: 2 \sqrt{17} \: units}}[/tex]
Answer:[tex] \huge{\boxed{ \bold{2 \sqrt{17} \: units }}}[/tex]
MissSpanishI need help question 4
Answer:
-51
Step-by-step explanation:
If the limits are reversed, then place a negative sign in front of the integral.
[tex]\int\limits^a_bf ({x}) \, dx =-\int\limits^b_a f({x}) \, dx[/tex]
[tex]\int\limits^a_3 f({x}) \, dx = 51\\[/tex] where [tex]\alpha =10\\[/tex]
[tex]\int\limits^3_\alpha f( {x}) \, dx =-51[/tex] where[tex]\alpha =10[/tex]
This year Rafael has 60 regular customers which is 150 percent of the 40 regular customers he had last year.
The base is 60, the part is 40 and the rate is 150%.
How to depict the information?The base is the whole quantity or amount that the problem is about.
The part is referred to as the percentage is the portion of the base. The rate is the number with the percentage.
In this case, the base is 60, the part is 40 and the rate is 150%.
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Which of the following could represent the
interval (5, 100]? Select two that apply.
Answer:
5 < x ≤ 100
(this is inequality form)
{x| 5 < x ≤ 100}
(this is set notation form)
(options B and C)
Step-by-step explanation:
In interval notation,
( or ) : does not include value
[ or ] : does include value
{and remember:
< or > : does not include value
≤ or ≥ : does include value}
when we write something in interval notation, the range of values is from (lowest value, highest value)
for this equation, we know that we are looking for : (5, 100]
which means that the range of numbers goes from
5 (does not include 5) to 100 [does include 100]
so, x > 5 (not equal to); x ≤ 100
we can combine these two concepts: 5 < x ≤ 100
(inequality form)
{when {x | ...} is present, it means the same thing as without it, so
{x| 5 < x ≤ 100} is also correct
(set notation)
hope this helps!!
Answer:
B and C
Step-by-step explanation:
from interval notation we are including 100 but not 5,
x > 5 and x ≤ 100
so B and C are correct
The mean diastolic blood pressure for a random sample of 80 people was 100 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit.
The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41
How to determine the confidence interval?We have:
Mean = 100
Sample size = 80
Standard deviation = 11
At 95% confidence interval, the critical z value is:
z = 1.96
The confidence interval is then calculated as:
[tex]CI = \bar x \pm z \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}[/tex]
Evaluate the product
[tex]CI = 100 \pm \frac{21.56}{\sqrt {80}}[/tex]
Divide
[tex]CI = 100 \pm 2.41[/tex]
Split
CI = (100 - 2.41,100 + 2.41)
Evaluate
CI = (97.59,102.41)
Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41
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I need helpppppp asap
Answer:
graph A
Step-by-step explanation:
When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"
The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"
For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.
Values to the right side of the origin are positive--greater than 0.
For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.
Ordered pairs (points) are written as (x,y)
(x-value, y-value)
We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.
When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).
So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)
hope this helps!!
Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f(x) = 8x² +2
h(x) = -8x²-2
a. fopens upward with a y-intercept at (2, 0); h opens downward with a y-intercept at (-2, 0)
b. f opens downward with a y-intercept at (0, -2); h opens upward with a y-intercept at (0, 2)
c. fopens downward with a y-intercept a(0, 2); h opens upward with a y-intercept at (0, -2)
d. fopens upward with a y-intercept at (0, 2); h opens downward with a y-intercept at (0, -2).
The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.
What is a Function ?A function is a law that defines relation between two variables.
The function given in the question is
f(x) = 8x² +2
h(x) = -8x²-2
The graph is plotted and the similarities or differences are studied ,
It can be seen from the graph that
f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).
Therefore Option D is the right answer.
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Which sequences are arithmetic sequences? Select all that apply.
a) 100, 95, 90, 85, ...
b) 10, 20, 40, 80, ...
c) 5, 17, 29, 41, 53, ...
d) -1, 1, -1, 1, -1, 1, ...
e) 42, 52, 62, 72, 82, ...
Answer:
state Avogadro's hypothesis and prove that molecular weight
Evaluate sin ( Cos^-1( -15/17)) enter your answer as a fraction using the slash bar (/)
Answer:
sin(cos^-1(-15/17))=8/17
Step-by-step explanation:
I apologize for the bad writing, I hope you can read it
please i need help so bad
Dilbert invests $2,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answer:
$2,120
Step-by-step explanation:
Simple interest formula
A = P(1 + rt)
where:
A = final amountP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $2000r = 6% = 0.06t = 1 yearSubstitute the given values into the formula and solve for A:
⇒ A = 2000(1 + 0.06(1))
⇒ A = 2000(1.06)
⇒ A = 2120
Therefore, there will be $2,120 in the account at the end of the 1 year period.
A rake is priced at $28.49. Tax is $1.85. What is
the total cost of the rake?
Somebody please assist me here
The base case of [tex]n=1[/tex] is trivially true, since
[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]
but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle
[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]
with equality if [tex]E_1\cap E_2=\emptyset[/tex].
Now assume the case of [tex]n=k[/tex] is true, that
[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]
We want to use this to prove the claim for [tex]n=k+1[/tex], that
[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]
The I/EP tells us
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]
and by the same argument as in the [tex]n=2[/tex] case, this leads to
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]
By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.
[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]
V
On March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
(a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar.
dollars
(b) On that date, how many rupees was 125.29 dollars worth?
Round your answer to the nearest hundredth of a rupee.
I need help with this problem.
Answer:
a=1.66
b=8368.12
Step-by-step explanation:
hope it helps
factor completely
0.09y² - 0.81
Answer:
[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]
Step-by-step explanation:
The difference of squares formula gives us
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
(you can multiply this out to confirm)
[tex]0.09y^2 = (0.3y)^2[/tex]
and
[tex]0.81 = 0.9^2[/tex]
Thus, by the difference of squares formula
[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]
How to do this please?️
Step-by-step explanation:
Using dimensional analysis, let convert km to cm.
[tex] \frac{4cm}{1km} \times \frac{km}{100000 \: cm} [/tex]
Cancel out the km
[tex] \frac{4cm}{100000 \: cm} [/tex]
[tex] \frac{1}{25000 } [/tex]
So n= 25000
iii.
Dimensional Analysis
[tex] \frac{3 \: cm}{1 } \times \frac{km}{100000 \: cm} [/tex]
[tex] \frac{3 \: km}{100000} [/tex]
Or
[tex]0.00003 \: km[/tex]
Samantha invests $11,000 at 6% simple interest for 25 years.
Round your answers to the nearest cent.
Answer:
$27,500.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.
Solving our equation:
A = 11000(1 + (0.06 × 25)) = 27500
A = $27,500.00
The total amount accrued, principal plus interest, from simple interest on a principal of $11,000.00 at a rate of 6% per year for 25 years is $27,500.00.
Find the domain and range
Answer:
Domain: (-∞, ∞)
Range: [-2, ∞)
Step-by-step explanation:
The domain of any parabola is (-∞, ∞)
The range of this parabola is [-2, ∞) because the vertex is at (-2, -2).
Javier is going to a water park with his little brother, Caden. Since Caden is only 4 feet tall, they check to see if he is tall enough to ride the Super Slide. Sadly, the park's website says that he needs to be at least 52 inches tall. How many more inches does Caden need to grow before he is tall enough to ride the Super Slide?
Caden needs to grow 4 inches tall enough to ride the Super Slide.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that:-
Javier is going to a water park with his little brother, Caden. Since Caden is only 4 feet tall, they check to see if he is tall enough to ride the Super Slide. Sadly, the park's website says that he needs to be at least 52 inches tall.Caden's height = 4 feet
Min height to ride the Super slide is = 52 inches
Caden's height in inches will be:-
1 feet = 12 inches
4 feet = 12 x 4 = 48 inches.
The difference between the height will be given as:-
D = 50 - 48 = 4 inches
So Caden should grow his height by 4 inches to ride the super slide.
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Question 1 Fill in the missing (yellow) interior angle with (4x)° to solve for x. Diagram may not be to scale.
Please help!
Answer:
x=100/7
Step-by-step explanation:
The interior angles will sum to 360 so 72+89+99+7x=360
260+7x=360
7x=100
x=100/7
Out of 2,000 high school seniors, 191 were enrolled into Honor Society.What percentage of the entire group of 2,000 seniors were in Honor Society?PLEASE EXPLAIN
A.0.955%
B.1.91%
C.9.55%
D.19.1%
Divide number in honor society by total students:
191/2000 = 0.0955
Multiply by 100 to get percent:
0.0955 x 100 = 9.55%
Answer is C. 9.55%
Hi can someone please help me with this geometry problem? Thanks!
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The triangles ΔEST and ΔEFD are similar triangles, therefore, we can write,
[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}[/tex]
Since S and T are midpoints of EF and ED, the lines will be divided into two equal parts. Therefore,
[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}= \dfrac12[/tex]
Therefore, we can write it as,
[tex]FD = 2 (ST)[/tex]
In ΔEST and ΔTDR
∠T ≅ ∠T {Vertical angles}
ET ≅ TD {T is the midpoint of ED}
∠SET ≅ ∠TDR {Alternate interior angles}
Therefore, ΔEST ≅ ΔTDR.
Since the two triangles are equal we can write,
ST ≅ TR
Further, it can be written as,
FD = 2(ST)
FD = ST + ST
FD = ST + TR
FD = SR
Hence, FD≅SR.
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GIVING 100 POINTS: The graph shown here displays the distance, in miles. traveled by a jet in a certain number of hours. Based on the graph, which of the following equations indicates the correct variables, and in how many hours does the jet travel 12,000 miles if it travels at the same speed?
Graph titled Motion of a Jet shows Time in hours on x axis and Distance in miles on y axis. A straight line joins the ordered pairs 0, 0 and 2, 1200 and 4, 2400 and 6, 3600.
y = 600x, the jet travels 12,000 miles in 20 hours
x = 600y, the jet travels 12,000 miles in 20 hours
y = 600x, the jet travels 12,000 miles in 22 hours
x = 600y, the jet travels 12,000 miles in 22 hours
Answer:
A. y = 600x, the jet travels 12,000 miles in 20 hours
Explanation:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Take two points: (2, 1200), (4, 2400)
[tex]\sf slope : \dfrac{2400-1200}{4-2 } = 600[/tex]
Equation:
y - 1200 = 600(x - 2)
y - 1200 = 600x - 1200
y = 600x
Miles the Jet travels at 20 hours:
y = 600(20) = 12000 milesMiles the Jet travels at 22 hours:
y = 600(22) = 13200 milesAnswer:
y = 600x, the jet travels 12,000 miles in 20 hours
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y = mx + b[/tex]
where:
m = slopeb = y-interceptTo find the slope, define two points on the line and use the slope formula to find the slope:
[tex]\textsf{let}\:(x_1,y_1)=(0,0)[/tex][tex]\textsf{let}\:(x_2,y_2)=(2, 1200)[/tex][tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1200-0}{2-0}=600[/tex]
From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0). Therefore, the equation of the line is:
y = 600x
y is defined as the distance (in miles). Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:
[tex]\sf \implies 600x=12000[/tex]
[tex]\sf \implies x=\dfrac{12000}{600}[/tex]
[tex]\sf \implies x=\dfrac{120}{6}[/tex]
[tex]\implies \sf x=20[/tex]
Therefore, it takes the jet 20 hours to travel 12,000 miles.
The Research Triangle in North Carolina is formed by Raleigh, Durham, and Chapel Hill. Is this triangle a right triangle? Explain.
The triangle is not a right triangle. This is because the sum of the square of the two shorter lengths is not equal to the square of the longest length.
Is the triangle a right triangle?
In order to determine if the triangle is a right triangle, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
12 ² + 24²
= 144 + 576 = 720
29² = 841
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A. 6x 10y=9
B. 6x=9
C. -10y = 15
D. 2x= 15
Answer:
6x = 9
Step-by-step explanation:
4x-5y = 12
2x+5y = -3
Add the equations together
4x-5y = 12
2x+5y = -3
-------------------
6x + 0y = 9
6x = 9
Answer:
B. 6x = 9
Step-by-step explanation:
4x - 5y = 12
+ 2x + 5y = -3
____________
6x + 0 = 9
Hence, option B. 6x = 9 is the correct answer.
Point T is at (–16.8, 31.7) and point M is at (1.2, 12.5). Point M is the midpoint of the line segment whose endpoints are S and T. What are the coordinates of endpoint S? (–34.8, 50.9) (–7.8, 22.1) (19.2, –6.7) (20.4, –5.5)
Answer:
option c (19.2, -6.7) is correct
Step-by-step explanation:
Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.
if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is
given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]
according to question :
given : end point T(-16.8, 31.7) and mid point M(1.2, 12.5)
let coordinates of another end point S (a, b)
therefore, using mid point formula
1.2 = (-16.8 + a)/2
2.4= (-16.8 + a)
19.2 = a
and,
12.5 = (31.7 + b)/2
25 = 31.7 + b
-6.7 = b
so the option c (19.2, -6.7) is the correct answer
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which of the following is most likely the next step in the series?
Answer:
errrrrr a not too sure but try
Step-by-step explanation:
i did the test got a 90
