Picture shown!
If f(x) = x^2, and
g(x) = x - 1, then
g(f(x)) = x^[?]+[?]
Answer:
g(f(x)) = x^2 + 1
? = 2
grey box = 1
Step-by-step explanation:
Answer:
g(f(x)) = \(x^{2}\) + 1
in a bag, there are 4 red shapes, 5 blue shapes, and 3 yellow shapes. there is one triangle, one square, and one circle in each group. there is 1 red and blue rectangle, and 1 blue hexagon. what is the probability of selecting a shape that is blue or a triangle?
im pulling my hair out with this problem my calculator simplified it to \(\frac{1+/-\sqrt{14}}{10}\)
What am i doing wrong?? :')
\(~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(-5)}}{2(3)} \implies x = \cfrac{ -2 \pm \sqrt { 4 +60}}{ 6 } \\\\\\ x= \cfrac{ -2 \pm \sqrt { 64 }}{ 6 }\implies x=\cfrac{ -2 \pm 8}{ 6 }\implies x= \begin{cases} ~~ 1\\ -\frac{5}{3} \end{cases}\)
Answer:
-5/3 and -1
Step-by-step explanation:
I am not sure what you mistake is, but here is my solution. I hope that it helps. I am sorry that you are frustrated. We have all been there.
What is the slope of line m?
The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
Slope of a lineThe formula for calculating the slope of a line is expressed as
slope = y2-y1/x2-x1
Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:
Slope = 1-0/-2-0
Slope = 1/-2
Slope = -1/2
Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
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The slope of the line m is - 1 / 2.
How to find the slope of a line?The slope a line can be found as follows:
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, -1)
hence,
slope = - 1 - 0 / 2 - 0
slope = - 1 / 2
hence,
slope = - 1 / 2
Therefore, the slope of the line m is - 1 / 2.
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P=√5+vt make v the subject
Answer:
p = √5 + vt
p - √5 = vt
p - 2.24 = vt
p - 2.24/t = t
If m<0=111 degrees find the value of x
Step-by-step explanation:
The sum of the measures insiqe the quadriateral = 360
one is angle o = 111 and two of them aare 90 degrees each
so 360 - 111 - 90 - 90 = x = 69 degrees
I need help solving questions 28 and 34 by expanding and simplifying please
#28
The given expression is
\(\lbrack x+(y-2)\rbrack\lbrack x-(y-2)\rbrack\)At first, we will simplify each square bracket
Note that, the + sign does not change the terms in the bracket but the - sign change the signs of the terms inside the bracket
\(\begin{gathered} \lbrack x+(y-2)\rbrack=\lbrack x+y-2\rbrack \\ \lbrack x-(y-2)\rbrack=\lbrack x-y+2\rbrack \end{gathered}\)Now, we will multiply the 2 brackets
\(\begin{gathered} \lbrack x+y-2\rbrack\lbrack x-y+2\rbrack= \\ (x)(x)+(x)(-y)+(x)(2)+(y)(x)+(y)(-y)+(y)(2)+(-2)(x)+(-2)(-y)+(-2)(2)= \\ x^2-xy+2x+xy-y^2+2y-2x+2y-4 \end{gathered}\)Now we will add the like terms
\(\begin{gathered} x^2+(-xy+xy)+(2x-2x)-y^2+(2y+2y)-4= \\ x^2-y^2+4y-4 \end{gathered}\)the graph shows the function f(x) = 2^x.what is the value of x when f(x) = 4
Answer: answer is 2
Step-by-step explanation:
if 2 equal chords of a circle intersect within a circle prove that the segment of one chord are equal to corresponding segments of the other chord !!
The segments of AB in the circle are equal to the corresponding segments of CD.
chord of circleIn geometry, a chord of a circle is a straight line segment whose endpoints lie on the circle. The chord does not necessarily pass through the center of the circle.
To prove this, we can draw two perpendiculars from point P to the chords AB and CD,
Let's label the points where the perpendiculars meet the chords as E and F, respectively. By the intersecting chords theorem, we have:
AE × BE = CE × DE
And
PE × EF = FE × PD
Since AB and CD are equal chords, we have:
AE = CE
BE = DE
CF = DF
Also, since the perpendiculars from point P are equal in length, we have:
PE = PF
Substituting these values into the equations above, we get:
AE × BE = CE × DE
AE × (AE + EF) = CE × (CE + EF)
AE²+ AE × EF = CE² + CE × EF
AE² - CE² = CE × EF - AE × EF
(AE + CE) × (AE - CE) = EF × (CE - AE)
AB × EF = CD × EF
Since EF is common to both sides, we can divide both sides by EF, and we get:
AB = CD
Therefore, the segments of AB are equal to the corresponding segments of CD, as required.
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The complete question is:
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angles with the chords.
If the function m(x) = [x] is multiplied by -3 (p(x) = -3|x) how will it change?
Answer:
Step-by-step explanation:
Distribute: -3(x+2)
-3x + 2
-3x + 6
-3x - 6
X-1
Answer:
it would be -3x-6
Step-by-step explanation:
if you distribute right you will change the two and the positive change into a negative and the last one x is not by itself plus it only change to one
4. The two trapezoids below are similar. What
is the length of segment EF?
24 am
A
D
30 cm
B
C
G.
7.5 cm
X
E
H
Help please
The length of the segment EF for the given trapezoids is 6 cm.
How do trapezoids work?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided shape.
An opposing set of sides are parallel. The four angles of a trapezium add up to 360 degrees, and their diagonals cut each other in half. It has four odd-numbered sides. Thus, the opposing sides of an isosceles trapezium are congruent, as well as the diagonals.
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal:
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, the length of the segment EF is 6 cm.
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Fuel costs have risen quickly during recent years as consumption, refining and production costs have risen sharply. Supply and demand conditions in the perfectly competitive domestic crude oil market are: QS = -250 + 7P (Supply) QD = 260 - 7P (Demand) where Q is quantity in millions of barrels per day, and P is price per barrel. Find the market equilibrium price. Note: To be at equilibrium, QS must equal QD
Answer:
The market equilibrium price is approximately $36.43 per barrel.
Step-by-step explanation:
To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).
Given:
QS = -250 + 7P
QD = 260 - 7P
Setting QS equal to QD:
-250 + 7P = 260 - 7P
Now, let's solve for P:
Add 7P to both sides:
-250 + 7P + 7P = 260 - 7P + 7P
Combine like terms:
14P - 250 = 260
Add 250 to both sides:
14P - 250 + 250 = 260 + 250
Simplify:
14P = 510
Divide both sides by 14:
14P/14 = 510/14
Simplify:
P = 36.43
The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.
In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:
-250 + 7P = 260 - 7P
Simplifying the equation, we get:
14P = 510
Dividing both sides by 14, we find:
P = 36.43
Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.
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question the random variable x is exponentially distributed, where x represents the time it takes for a whale watcher to spot a whale. if x has an average value of 45 minutes, what is the probability that x is less than 45 minutes? round the final answer to three decimal places.
0.368 .
The probability that a random variable x is exponentially distributed and less than 45 minutes,
given that the average value is 45 minutes, is 0.368.
This can be calculated by taking the negative of the natural logarithm of 1/2 (i.e. -ln(0.5)) and dividing it by the average value of 45 minutes.
The result, -ln(0.5)/45, equals 0.368, rounded to three decimal places.
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Phone calls arrive at the rate of 48 per hour at the reservation desk for regional airways.
A) Compute the probability of receiving three calls in a 10-minute interval of time?(to 4 decimals)
B) Compute the probability of receiving exactly 13 calls in 15 minutes. (To 4 decimals)
C) Suppose no calls are currently on hold. If an agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?
D) What is the probability that none will be waiting?
E) If no calls are being processed, what is the probability that the agent can take 5 minutes for a personal time without being interrupted by a call?
The different probabilities and number of callers expected to be waiting are;
A) P(x = 3) = 0.0286
B) P(x = 13) = 0.1056
C) 8 will be waiting
D) P(x = 0) = 0.0003
E) P(x = 0) = 0.0067
How to find probability using Poisson distribution?
We are given the rate of 48 phone calls per hour.
Thus, we will use poisson's distribution formula;
P(x) = (λˣ × e^(-λ))/x!
A) Probability of receiving three calls in a 10-minute interval of time which is P(x = 3). Thus;
λ = 48 * (10/60)
λ = 8
P(x = 3) = (8³ × e⁻⁸)/3!
P(x = 3) = 0.0286
B) Probability of receiving exactly 13 calls in 15 minutes is P(x = 13). Thus;
λ = 48 * (15/60)
λ = 12
P(x = 13) = (12¹³ × e⁻¹²)/13!
P(x = 13) = 0.1056
C) No calls are currently on hold and it takes 10 minutes to complete one call. Thus;
λ = 48 * (10/60)
λ = 8
Thus, 8 will be waiting after 10 minutes.
D) Probability that no one will be waiting is;
P(x = 0) = (8⁰ × e⁻⁸)/0!
P(x = 0) = 0.0003
E) No calls being processed and it takes 5 minutes for a personal time without being interrupted by a call. Thus;
λ = 48 * (5/60)
λ = 4
P(x = 0) = (4⁰ × e⁻⁵)/0!
P(x = 0) = 0.0067
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Find the solution of the differential equation that satisfies the given initial condition. 5. (ex + y)dx + (2 + x + yey)dy = 0, y(0) = 1 6. (x + y)2dx + (2xy + x2 – 1)dy = 0, y(1) = 1
5. The solution to the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with y(0) = 1 is y = 2e^(-x) – x – 1. 6. The solution to the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with y(1) = 1 is y = x – 1.
5. To solve the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with the initial condition y(0) = 1, we can use the method of exact differential equations. By identifying the integrating factor as e^(∫dy/(2+yey)), we can rewrite the equation as an exact differential. Solving the resulting equation yields the solution y = 2e^(-x) – x – 1.
To solve the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with the initial condition y(1) = 1, we can use the method of separable variables. Rearranging the equation and integrating both sides with respect to x and y, we obtain the solution y = x – 1.
These solutions satisfy their respective initial conditions and represent the family of curves that satisfy the given differential equations.
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In sampling distributions, all the samples contain sets of raw scores from
In sampling distributions, all the samples contain sets of raw scores from the population of interest.
In sampling distributions, the goal is to understand the characteristics of a population by examining samples drawn from that population. Each sample represents a subset of raw scores obtained from individuals within the population. These raw scores can be measurements, observations, or responses to certain variables of interest.
By collecting multiple samples from the population, the sampling distribution provides a theoretical distribution that represents the distribution of sample statistics (such as means, proportions, or variances). Each sample's raw scores contribute to calculating these sample statistics, which help estimate and infer population parameters.
The underlying assumption is that the samples are representative of the population, meaning that they reflect the variability and characteristics of the larger population. By analyzing the sampling distribution, we can gain insights into the variability and properties of the population based on the collected raw scores from the samples.
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Gabriella's morning exercise routine includes both jogging and power yoga. On average, she
burns about 450 calories per hour while doing power yoga and about 660 calories per hour
while jogging. Gabriella wants to burn a total of 675 calories during her 75 minute workout this
morning. Which of the following systems could be used to find the number of minutes that she
should spend jogging, j. and the number of minutes that she should spend doing power yoga, p.
in order to meet this goal?
The question is an illustration of systems of equations, where 2 or more equations model a particular subject.
The system of equations is:
\(\mathbf{j + p = 75}\)
\(\mathbf{660j + 450p = 675}\)
Let:
j represents jogging
p represents power yoga
She wants to spend 75 minutes.
This is represented as:
\(\mathbf{j + p = 75}\)
The total calories to burn out is 675.
This is represented as:
\(\mathbf{660j + 450p = 675}\)
Hence, the system of equations is:
\(\mathbf{j + p = 75}\)
\(\mathbf{660j + 450p = 675}\)
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i need help pls help
Answer: 1x²+6x-1 is the answer
what is 2.085x10^5 in scientific notation
The number in scientific notation is 2.1×10⁵.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 2.085×10⁵.
Round the number 2.085 to the nearest tenth:
2.085 ≈ 2.1
Therefore, the number in scientific notation is 2.1×10⁵.
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Solve for x. (Round to the nearest thousandth.)
3x - 8 = 15
Answer:x = 7.667
Step-by-step explanation:
3x - 8 = 15
+ 8 = 23
3x = 23
divide 3 by 3 and 23 so you get x by itself
answer = 7.667
Answer:
x = 7.667
Step-by-step explanation:
3x - 8 = 15 (Rearrange expression)
-8 - 15 = -3x (Combine like terms)
-23 = -3x (Divide)
x = 7.667
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of 18$. Option B is a commission rate of 8% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Answer:
$9000
Step-by-step explanation:
First find how much is made in a week by option A
40*18=720
In order to match this the salesperson must make $720 from 8% commissions. Divide 720 by 0.08 to get the necessary sales for $720 from commissions.
720/0.08=9000
Final answer is 9000 in sales.
A trucking company needs to move a pile of pebbles. The pebbles are stored in a pile shaped like a cone. The pile is 10 yards high,
and its base has a diameter of 6 yards. How many truckloads will the company need, if each truck holds 7.85 yd³ of pebbles?
Use 3.14 for it, and do not round your answer.
truckloads
The trucking company will need 12 truckloads to move the pile of pebbles.
How to find the volume of the cone?
The volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where V is the volume, r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14.
We are given that the pile of pebbles has a height of 10 yards and a base diameter of 6 yards, which means that the radius is 3 yards.
We can use these values to calculate the volume of the pile:
V = (1/3) × 3.14 × 3² × 10
V = 94.2 yd³
Therefore, the pile has a volume of 94.2 cubic yards.
If each truck holds 7.85 yd³ of pebbles, the number of truckloads required can be calculated by dividing the total volume of the pile by the volume of each truck:
Number of truckloads = Volume of pile / Volume of each truck
Number of truckloads = 94.2 / 7.85
Number of truckloads = 12
Therefore, the trucking company will need 12 truckloads to move the pile of pebbles.
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How to answer this, I don't understand.
The length of the tangent segment PQ of the circle is approximately 4.9 units
What is the length of the tangent segment PQ?The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment".
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the diagram:
Secant segment SQ = 12
External part of the secant segment QR = SQ - SR = 12 - 10 = 2
Secant segment.
Tangent segment PQ = ?
Plug the given values into the above formula and solve for tangent segment PQ:
( tangent segment )² = External part of the secant segment × Secant segment
( PQ )² = 2 × 12
( PQ )² = 24
PQ = √24
PQ = 4.9
Therefore, the measure of line PQ is 4.9.
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What is the simplest form of
(2p + 1)(2p - 5)?
Answer:
4p^2-8p-5
Step-by-step explanation:
Answer:
4p^2-8p-5
Step-by-step explanation:
Hope this helps :)
Math question 10 points
Answer:
D.
Step-by-step explanation:
242-44
198/2 = inequality
r/20-5=(-4) Help please :)
Answer:
r=20
Step-by-step explanation:
r/20−5=−4
r/20=−4+5
r/20=1
r=1×20
r=20
Answer:
20
step by step
Question 1
What would be the best next step in solving the following equation for x?
8x - 4 = 10
A
Divide both sides of the equation by 8.
B
Add 4 to both sides of the equation.
С
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by 8.
Answer:
B) Add 4 to both sides of the equation.
Step-by-step explanation:
i need answer please
Answer: Parallel
Step-by-step explanation:
Parallel lines have the same slope, both line and and k have a slope of 3/4 (y=mx+b, m is the slope). Therefore the lines are paralell
Find the value of k and yz if y is between x and z. x y = 3 k − 2 , y z = 7 k 4 , x z = 4 k 38
Considering that y is between x and z, we have that:
The value of k is of k = 6.The length of yz is 46 units.How to find the value of k and of yz?We consider that y is between x and z, hence the length of the segment is given by:
xz = xy + yz
The separate lengths are given as follows:
xz = 4k + 38.xy = 3k - 2.yz = 7k + 4.Hence:
4k + 38 = 3k - 2 + 7k + 4.
4k + 38 = 10k + 2
6k = 36
k = 6.
Hence the length of yz is given by:
yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.
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