Answer:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Step-by-step explanation:
We assume that the function of interest is:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
What is the simplified expression for 3 y squared minus 6 y z minus 7 + 4 y squared minus 4 y z + 2 minus y squared z?
WILL MARK BRAINLEST
Answer:
7y⁴- 10yz - y²z - 5
Step-by-step explanation:
First collect like terms
3y²+ 4y²- 6yz - 4yz - y²z - 7+2
7y⁴-10yz - y²z - 5
Answer:
Its C
Step-by-step explanation:
¿Cuál es la fórmula para calcular el área de cualquier triangulo?
¡Hola! ¡Ojalá esto ayude!
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La fórmula para calcular el área de cualquier triángulo es:
base multiplicada por la altura y dividida por dos.
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Bh / 2.
The marked price of a mobile set is Rs3500 and the shopkeeper allows of 10%discount? (I) find the amount of discount. (ii)How much should a customer pay for it after discount.
Step-by-step explanation:
3500 × 10/100
rs. 350 is the discount
and to find the amnt the customer should pay subtract 350 from 3500
which is,
3150 Rupees
2| x-3| - 5 = 7 Helpp
Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}6th grade math, help pleasee:)
Answer:
1/5 cup
Step-by-step explanation:
Sugar: water
1 5
We want 1 cup water, so divide each side by 5
1/5 : 5/5
1/5 : 1
There is 1/5 cup sugar to 1 cup water
Total length of a pole is 21.3 m. If 0.2m of the length of the pole is inside the ground. Find how much of its length is outside the ground
Answer:
21.1 mStep by step explanation
Total length of pole = 21.3 m
Length of pole inside the ground = 0.2 m
Let length of pole outside the ground be X,
So, according to the Question,
[tex]x + 0.2 = 21.3[/tex]
Move constant to R.H.S and change its sign
[tex]x = 21.3 - 0.2[/tex]
Calculate the difference
[tex]x = 21.1 \: m[/tex]
Hope this helps...
Good luck on your assignment...
What is the value of x?
Answer:
54
Step-by-step explanation:
x is half the difference of the two arcs:
x = (136 -28)/2 = 54
The value of x is 54.
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. Let I(t) denote the number of infected individuals. Suppose that the total population is 2000, the proportionality constant is 0.0001, and that 1% of the population is infected at time t-0, write down the intial value problem and the solution I(t).
dI/dt =
1(0) =
I(t) =
symbolic formatting help
Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]
Given total population is 2000. So the non infected population = 2000 - I.
[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]
[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
The required expressions are presented below:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
Analysis of an ordinary differential equation for the spread of a disease in an isolated population
After reading the statement, we obtain the following differential equation:
[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)
Where:
[tex]k[/tex] - Proportionality constant[tex]I[/tex] - Number of infected individuals[tex]n[/tex] - Total population[tex]\frac{dI}{dt}[/tex] - Rate of change of the infected population.Then, we solve the expression by variable separation and partial fraction integration:
[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]
[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]
[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)
Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.
If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/1164377
Solving exponential functions
Answer:
Option B
an increasing exponential graph
what is the answer to 100×338
Answer:
33800
Step-by-step explanation:
100 x 338 = 33800
Answer:
33800
Step-by-step explanation:
338x10=3380 then 3380x10=33800
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Good luck with your assignment...
In 2005, there were 14,100 students at college A, with a projected enrollment increase of 750 students per year. In the same year, there were 42,100 students at college B, with a projected enrollment decline of 1250 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
Set up two equations and set equal to each other. Let number of years = x:
College A = 14100+750x
College B = 42100-1250x
Set equal:
14100 + 750x = 42100 - 1250x
Subtract 750x from both sides:
14100 = 42100 - 2000x
Subtract 42100 from both sides:
-28000 = -2000x
Divide both sides by -2000:
x = -28000 / -2000
x = 14
It will take 14 years for the schools to have the same enrollment.
Enrollment will be:
14100 + 750(14) = 14100 + 10500 = 24,600
Answer:
(a)2019 (14 years after)
(b)24,600
Step-by-step explanation:
Let the number of years =n
College A
Initial Population in 2005 = 14,100
Increase per year = 750
Therefore, the population after n years = 14,100+750n
College B
Initial Population in 2005 = 42,100
Decline per year = 1250
Therefore, the population after n years = 42,100-1250n
When the enrollments are the same
14,100+750n=42,100-1250n
1250n+750n=42100-14100
2000n=28000
n=14
Therefore, in 2019 (14 years after), the colleges will have the same enrollment.
Enrollment in 2019 =42,100-1250(14)
=24,600
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?
Answer:
0.0668 or 6.68%
Step-by-step explanation:
Variance (V) = 10,000
Standard deviation (σ) = √V= 100
Mean score (μ) = 500
The z-score for any test score X is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 650:
[tex]z=\frac{650-500}{100}\\z=1.5[/tex]
A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
The probability that he or she will make a score of 650 or more is 0.0668.
Let X = Scores made on a certain aptitude test by nursing students
X follows normal distribution with mean = 500 and variance of 10,000.
So, standard deviation = [tex]\sqrt{10000}=100[/tex].
z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].
The probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]
Learn more: https://brainly.com/question/14109853
Circle the numbers divisible by 2.
320;5,763; 9,308; 5,857;3,219; 5,656; 83,001;53,634
g The average salary in this city is $45,600. Is the average different for single people? 53 randomly selected single people who were surveyed had an average salary of $46,356 and a standard deviation of $15,930. What can be concluded at the α α = 0.05 level of significance?
Answer:
Step-by-step explanation:
The average salary in this city is $45,600.
Using the formula
z score = x - u /(sd/√n)
Where x is 46,356, u is 45,600 sd is 15,930 and n is 53.
z = 46,356 - 45600 / (15930/√53)
z = 756/(15930/7.2801)
z = 756/(2188.1568)
z = 0.3455
To draw a conclusion, we have to determine the p value, at 0.05 level of significance for a two tailed test, the p value is 0.7297. The p value is higher than the significance level, thus we will fail to reject the null and can conclude that there is not enough statistical evidence to prove that the average is any different for single people.
Write the following numbers in increasing order: −1.4; 2; −3 1 2 ; −1; − 1 2 ; 0.25; −10; 5.2
Answer:
-12,-10,-3,-1.4,-1,0.25,2,5.2,12
Step-by-step explanation:
The following number −1.4; 2; −3 1 2 ; −1; − 1 2 ; 0.25; −10; 5.2 in increasing order
-12,-10,-3,-1.4,-1,0.25,2,5.2,12
It's arranged this way starting from the negative sign because positive it's greater than negative and if the negative gets to approach zero it's get smaller
Answer:
-10 ; -3 1/2 ; -1.4 ; -1 ; -1/2 ; 0.25 ; 2 ; 5.2
What does it mean to say "correlation does not imply causation"? Choose the correct answer below. A. Two variables can only be strongly correlated if there existed a cause-and-effect relationship between the variables. B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables. C. The fact that two variables are strongly correlated implies a cause-and-effect relationship between the variables. D. Two variables that have a cause-and-effect relationship are never correlated.
Answer:
B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables.
Step-by-step explanation:
The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.
While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.
Answer: B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables.
Step-by-step explanation:
A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18-29 year-olds is obtained today. What is the probability that no more than 70% would prefer to start their own business?
Answer:
The probability that no more than 70% would prefer to start their own business is 0.1423.
Step-by-step explanation:
We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.
Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion who would prefer to start their own business = 72%
n = sample of 18-29 year-olds = 600
Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)
P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)
= 1 - 0.8577 = 0.1423
The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.
a(b + c) = a × b + a × c where a, b, and c are real numbers
use the distributive property to simplify the expression
8(3 + 4) = 24 + ?
Answer:
32
Step-by-step explanation:
8(3 + 4) = 24 + ?
8(3)+8(4)= 24 + ?
24+32= 24 + ?
24-24+32=?
32=?
Answer:
? = 32
Step-by-step explanation:
Let's assume a = 8 , b = 3 , c = 4
[tex] \sf \: So :- \: \: a(b + c) = 8(3 + 4)[/tex]
[tex]8 \times 3 + 8 \times 4[/tex]
[tex]24 + 32[/tex]
Hence, The required value of ? = 32 .
PLEASE HELP I DO NOT UNDERSTAND AT ALL ITS PRECALC PLEASE SERIOUS ANSWERS
You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].
We also need to have
[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]
Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means
[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]
Then
[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]
So we end up with
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
Answer:
y(t) = √29·sin(4πt +1.1903)amplitude: √29angular frequency: 4πphase shift: 1.1903 radiansStep-by-step explanation:
In the form ...
y(t) = Asin(ωt +φ)
you have ...
Amplitude = Aangular frequency = ωphase shift = φThe translation from ...
y(t) = 2sin(4πt) +5cos(4πt)
is ...
A = √(2² +5²) = √29 . . . . the amplitude
ω = 4π . . . . the angular frequency in radians per second
φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift
Then, ...
y(t) = √29·sin(4πt +1.1903)
_____
Comment on the conversion
You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)
If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.
If w'(t) is the rate of growth of a child in pounds per year, what does 7 w'(t)dt 4 represent? The change in the child's weight (in pounds) between the ages of 4 and 7. The change in the child's age (in years) between the ages of 4 and 7. The child's weight at age 7. The child's weight at age 4. The child's initial weight at birth.
Complete Question
If w'(t) is the rate of growth of a child in pounds per year, what does
[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] represent?
a) The change in the child's weight (in pounds) between the ages of 4 and 7.
b) The change in the child's age (in years) between the ages of 4 and 7.
c) The child's weight at age 7.
d) The child's weight at age 4. The child's initial weight at birth.
Answer:
The correct option is option a
Step-by-step explanation:
From the question we are told that
[tex]w'(t)[/tex] represents the rate of growth of a child in [tex]\frac{pounds}{year}[/tex]
So [tex]{w'(t)} \, dt[/tex] will be in [tex]pounds[/tex]
Which then mean that this [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] the change in the weight of the child between the ages of [tex]4 \to 7[/tex] years
A coin is thrown at random into the rectangle below.
A rectangle is about 90 percent white and 10 percent green.
What is the likelihood that the coin will land in the green region?
It is certain.
It is impossible.
It is likely.
It is unlikely.
Answer:
It is unlikely.
Step-by-step explanation:
Certain = 100%
Impossible = 0%
Likely = more than 50%
Unlikely = less than 50%
It is less than 50%, so it is unlikely.
Answer:
(A) it is likely
Step-by-step explanation:
i took the test on edge
Which of the following algebraic expressions represents the statement given below?
A number is increased by five and squared.
A. x+5²
В.
x²+5
c. ° +5
D. (x+5)
Answer:
Let the number be x
The statement
A number is increased by five is written as
x + 5
Then it's squared
So we the final answer as
(x + 5)²Hope this helps
Which of the following statements is correct about quadratic number patterns? A. The third difference is greater than zero. B. The first difference is constant. C. The difference between terms is always positive. D. The second difference is constant.
Answer: D.) The second difference is constant.
Step-by-step explanation:
The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.
Answer:
D.
Step-by-step explanation:
1000 randomly selected Americans were asked if they believed the minimum wage should be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised.
a. Write down the formula you intend to use with variable notation).
b. Write down the above formula with numeric values replacing the symbols.
c. Write down the confidence interval in interval notation.
Answer:
a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]
b.0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. { -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
Step-by-step explanation:
Here the total number of trials is n= 1000
The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4
The degree of confidence is 95 % therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)
a. The formula used will be
p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ( z with the base alpha by 2 (α/2 = 0.025))
b. Putting the values
0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. Confidence Interval in Interval Notation.
{ -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
{ -z( base alpha by 2) ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ z( base alpha by 2) } = 1- α
please help!!!!!!!!!!!!
Answer:
csc B = 13/12
Step-by-step explanation:
csc B = 1 / sin B
The sin B is
sin B = opp/ hyp so
csc B = hyp /opp
csc B = 26 / 24
csc B = 13/12
Answer:
13/12
Step-by-step explanation:
sin θ = opposite/ hypotenuse
csc θ = 1/sinθ
csc θ = hypotenuse/opposite
csc (B) = 26/24
csc (B) = 13/12
What is the cube of the square of the second smallest prime number?
Answer:8
Step-by-step explanation:
The smallest prime is 2
cube of 2 is equal to 8
2*2*2=8
Answer:
729
Step-by-step explanation:
The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.
Hope this helped! :)
Suppose the weather forecast calls for a 60% chance of rain each day for the next 3 days. What is the probability that it will NOT rain during the next 3 days
Answer:
Probability that it'll not rain during the next three days = 0.064
Step-by-step explanation:
Given
Let:
P(R) represent the probability that it'll rain each day
P(R') represent the probability that it'll not
[tex]P(R) = 60\%[/tex]
Required
Probability that it'll not rain during the next three days
From concept of probability;
[tex]P(R) + P(R') = 1[/tex]
Substitute 60% for P(R)
[tex]60\% + P(R') = 1[/tex]
Subtract 60% from both sides
[tex]60\% - 60\% + P(R') = 1 - 60\%[/tex]
[tex]P(R') = 1 - 60\%[/tex]
Convert % to decimal
[tex]P(R') = 1 - 0.6[/tex]
[tex]P(R') = 0.4[/tex]
The probability that it'll not rain during the next 3 days is:
[tex]P(R') * P(R') * P(R')[/tex]
[tex]P(R') * P(R') * P(R') =0.4 * 0.4 * 0.4[/tex]
[tex]P(R') * P(R') * P(R') = 0.064[/tex]
WILL GIVE BRAINLIEST IF CORRECT!! Please help ! -50 POINTS -
Answer:
i think (d) one i think it will help you
The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
G(x)=
Answer:
[tex]g(x)=4x^{2} +10[/tex]
Step-by-step explanation:
If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.
Let:
[tex]a>0,\hspace{10}a\in R[/tex]
For:
y = f (x) + a: The graph shifts a units up.y = f (x) - a, The graph shifts a units down.If:
[tex]f(x)=4x^{2} +6[/tex]
and is translated vertically upward by 4 units, this means:
[tex]a=4[/tex]
and:
[tex]g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10[/tex]
Therefore:
[tex]g(x)=4x^{2} +10[/tex]
I attached you the graphs, so you can verify the result easily.
At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only $3 . The sandwiches are made with either turkey or ham. The fruit is either an apple or an orange. The drink is either bottled water or juice. The number of boxes they make for every possible combination is the same. If you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get an orange and not get juice in your box?
Answer:
Step-by-step explanation:
Given that sandwiches are made with either turkey or ham.
Prob for turkey or ham = 1/2
The fruit can be either apple or orange. Hence p(apple) = p(orange) =12
Drinks can be either bottled water or juice
P(water) = P(juice) = 1/2
We find that sandwiches, fruits, and drinks are mutually independent of each other.
Hence the probability you will get an orange and not get juice in your box
Prob (you get an orange and bottled water)
= Prob (orange) *Prob (bottled water) (since the two are independent
= 1/2 (1/2)= 1/4
Hence answer is 0.25