Answer:
[tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex]
Step-by-step explanation:
Let be [tex]f(x) = \frac{3}{5}-\frac{8}{x}[/tex] and [tex]F[/tex] is the antiderivative of [tex]f(x)[/tex] such that:
1) [tex]F = \int {\left(\frac{3}{5}-\frac{8}{x} \right)} \, dx[/tex] Given.
2) [tex]F = \frac{3}{5} \int \, dx -8\int {\frac{dx}{x} }[/tex] ([tex]\int {[f(x)+g(x)]} \, dx = \int {f(x)} \, dx + \int {g(x)} \, dx[/tex])
3) [tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex], where [tex]C[/tex] is the integration constant. ([tex]\int {k} \, dx = k\cdot x[/tex]; [tex]\int {\frac{dx}{x} } = \ln|x|[/tex], [tex]\int {k\cdot f(x)} \, dx = k\int {f(x)} \, dx[/tex]) Result.
Solve : 1 − | 0.2(m−3)+ 1/4| =0
Answer:
1-{0.2(m-3)+¼}=0
1{0.2m-0.6+¼}=0
1-{(0.8m-2.4+1)/4}=0
1-(0.8m-1.4)/4=0
lcm
(4-0.8m-1.4)/4=0
(2.6-0.8m)/4=0
cross multiply
2.6-0.8m=0
m=2.6/0.8
m=3.25
The solution of the expression are,
⇒ m = 3.25
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Expression is,
⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0
Now, We can simplify as;
⇒ 1 - | 0.2m - 0.6 + 1/4| = 0
⇒ 1 - |0.2m - 0.6 + 0.25| = 0
⇒ 1 - |0.2m - 0.35| = 0
⇒ 1 = 0.2m + 0.35
⇒ 1 - 0.35 = 0.2m
⇒ 0.2m = 0.65
⇒ m = 3.25
Thus, The solution of the expression are,
⇒ m = 3.25
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the price of apples at three different stores is shown below. Store R sells apples for $1.20 per pound. Store S sells 4 pounds of apples for $5.00. Store T sells 3 pounds of apples for $3.48.
which of these is a true statemnt
Store R sells apples at the lowest rate
Store T sells apples at the lowest rate
Store s charges a lower rate than Store T
Store t charges the same rate as Store R
Store T sells apples at the lowest rate
Step-by-step explanation:
1st We need to make every statement in order of 1 pound. Then We will easily find the lowest rate of apple.
i) R sell 1.20 $ per pound.
ii) S sell 4 pounds for 5$
i.e S sell 1 pound for 5/4 = 1.25$
iii) T sell 3 pound for 3.48$
i.e T sell 1 pound for 3.48/3 = 1.16$
Analysing the above data I get,
Store T sells apples at the lowest rate
Find the unknown side length, x. Write your answer in simplest radical form.
A. 3
B. 34
C. 6.
D. 41
Answer:
√41
Step-by-step explanation:
Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t
52² = 48² + t²
t² = 52² - 48²
= 2704 - 2304
= 400
t = √400
= 20
Considering the next triangle with sides t (20 units) and 12 units, again using the theorem
20² = 12² + y²
where y is the third side
400 = 144 + y²
y² = 400 - 144
= 256
y = √256
= 16 units
Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)
13² = 5² + u²
where u is the 3rd side
169 = 25 + u²
u² = 169 - 25
u² = 144
u = √144
u = 12
The other part of the side of that triangle
= 16 - 12
= 4
Considering the smallest triangle whose sides are x, 5 and 4,
x² = 5² + 4²
= 25 + 16
= 41
x = √41
What is the rate of change of the function
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
Hey there!
If a line is horizontal, the entire line is at the same elevation. On a line, the elevation is the y-value. So, all of the points with the same y-value are on the same horizontal line.
We see that all of these points have different y-values so none of them would be on the same horizontal line.
I hope that this helps! Have a wonderful day!
Find the common ratio of the following geometric sequence:
11,55, 275, 1375, ....
Answer:
Hey there!
The common ratio is 5, because you multiply by 5 to get from one term to the next.
Hope this helps :)
Answer:
5
Step-by-step explanation:
To find the common ratio take the second term and divide by the first term
55/11 = 5
The common ratio would be 5
Please help asap.
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures $90$ degrees If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.) What is the degree measure of the fifth slice Larry eats?
Answer:
The answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Step-by-step explanation:
Given that pizza is divided into six unequal slices.
Largest slice has an angle of [tex]90^\circ[/tex].
He eats the pizza from largest to smallest.
Let the difference in angles in each slice = [tex]d^\circ[/tex]
1st angle = [tex]90^\circ[/tex]
2nd angle = 90-d
3rd angle = 90-d-d = 90 - 2d
4th angle = 90-2d-d = 90 - 3d
5th angle = 90-3d-d = 90 - 4d
6th angle = 90-4d -d = 90 - 5d
We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).
i.e.
[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]
So, the angles will be:
1st angle = [tex]90^\circ[/tex]
2nd angle = 90- 12 = 78
3rd angle = 78-12 = 66
4th angle = 66-12 = 54
5th angle = 54-12 = 42
6th angle = 42 -12 = 30
So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]
which is greater 7.955 or 7.95
Answer:
[tex]\boxed{7.955>7.95}[/tex]
Step-by-step explanation:
7.95 can also be written as 7.950 .
So, we'll compare 7.955 and 7.950.
All the digits in ones, tenths, hundredths place are equal so we'll look at the thousandths place.
5 is in the thousandths place of 7.955 and 0 is in the thousandths place of 7.950. Since 5 is greater than 0 so 7.955 is greater than 7.95. It can also be written as:
7.955 > 7.950
Simplify 12/ |-4| x3 + |5|
Answer: 14
Step-by-step explanation:
12/4 times 3 +5
= 3 times 3 + 5
= 9 + 5
= 14
What is the area of this triangle on a Coordinate Grid?
Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2), is drawn inside a rectangle
Answer: 8.5 sq. units.
Step-by-step explanation:
Formula:
Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)
Then, Area of triangle IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]
[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]
Hence, the area of this triangle IJK on a Coordinate Grid = 8.5 sq. units.
let x = the amoun of raw sugar in tons a procesing plant is a sugar refinery process in one day . suppose x can be model as exponetial distribution with mean of 4 ton per day . The amount of raw sugar (x) has
Answer:
The answer is below
Step-by-step explanation:
A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?
Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:
[tex]f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\[/tex]
a) P(x > 5) = [tex]\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865[/tex]
b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.
That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757
c) Let b be the amount of raw sugar should be stocked for the plant each day.
P(x > a) = [tex]\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}[/tex]
But P(x > a) = 0.05
Therefore:
[tex]e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98[/tex]
a ≅ 12
Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = y cos(xy), (0, 1), θ = π/3
Answer:
√3/2
Explanation:
The directional derivative at the given point is gotten using the formula;
∇f(x,y)•u where u is the unit vector in that direction.
∇f(x,y) = f/x i + f/y j
Given the function f(x, y) = y cos(xy),
f/x = -y²sin(xy) and
f/y = -xysin(xy)+cos(xy)
∇f(x,y) = -y²sin(xy) i + (cos(xy)-xysin(xy)) j
∇f(x,y) at (0,1) will give;
∇f(0,1) = -0sin0 i + cos0j
∇f(0,1) = 0i+j
The unit vector in the direction of angle θ is given as u = cosθ i + sinθ j
u = cos(π/3)i+ sin(π/3)j
u = 1/2 i + √3/2 j
Taking the dot product of both vectors;
∇f(x,y)•u = (0i+j)•(1/2 i + √3/2 j)
Note that i.i = j.j = 1 and i.j = 0
∇f(x,y)•u = 0 + √3/2
∇f(x,y)•u = √3/2
The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex].
How to calculate the directional derivative of a multivariate functionThe directional derivative is represented by the following formula:
[tex]\nabla_{\vec v} f = \nabla f(x_{o},y_{o}) \cdot \vec v[/tex] (1)
Where:
[tex]\nabla f(x_{o}, y_{o})[/tex] - Gradient evaluated at point [tex](x_{o},y_{o})[/tex].[tex]\vec v[/tex] - Directional vectorThe gradient of [tex]f[/tex] is calculated below:
[tex]\nabla f (x_{o},y_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial x} (x_{o}, y_{o}) \\\frac{\partial f}{\partial y} (x_{o}, y_{o})\end{array}\right][/tex] (2)
Where [tex]\frac{\partial f}{\partial x}[/tex] and [tex]\frac{\partial f}{\partial y}[/tex] are the partial derivatives with respect to [tex]x[/tex] and [tex]y[/tex], respectively.
If we know that [tex](x_{o}, y_{o}) = (0, 1)[/tex], then the gradient is:
[tex]\nabla f(x_{o}, y_{o}) = \left[\begin{array}{cc}-y^{2}\cdot \sin xy\\\cos xy -x\cdot y\cdot \sin xy\end{array}\right][/tex]
[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}-1^{2}\cdot \sin 0\\\cos 0-0\cdot 1\cdot \sin 0\end{array}\right][/tex]
[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}0\\1\end{array}\right][/tex]
If we know that [tex]\vec v = \cos \frac{\pi}{3}\,\hat{i} + \sin \frac{\pi}{3} \,\hat{j}[/tex], then the directional derivative is:
[tex]\Delta_{\vec v} f = \left[\begin{array}{cc}0\\1\end{array}\right]\cdot \left[\begin{array}{cc}\cos \frac{\pi}{3} \\\sin \frac{\pi}{3} \end{array}\right][/tex]
[tex]\nabla_{\vec v} f = (0)\cdot \cos \frac{\pi}{3} + (1)\cdot \sin \frac{\pi}{3}[/tex]
[tex]\nabla_{\vec v} f = \frac{\sqrt{3}}{2}[/tex]
The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex]. [tex]\blacksquare[/tex]
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prove that 1/3 root2 is irrational
Step-by-step explanation:
Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .
which formulas can be used to find the surface area of a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area click all that apply options: A. SA= 1/2BA + 1/2ps B. SA= BA-LA C. SA= BA+LA D. SA= BA • LA E. SA= BA + 1/2ps
Answer:
C and E
Step-by-step explanation:
He got it on ap.ex
The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a pyramid with a square base:
The perimeter of the base is p
The slant height is s.
The base area is BA
The lateral area is LA.
We can find the area of the pyramid as follows:
SA = BA + LA
SA= BA + 1/2ps
Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
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may someone assist me?
Answer:
28
Step-by-step explanation:
Let x be the missing segment
We will use the proportionality property to find x
24/16 = 42/x
Simplify 24/16
24/16= (4×6)/(4×4)= 4/6 = 3/2
So 3/2 = 42/x
3x = 42×2
3x = 84
x = 84/3
x= 28
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 155 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 155 and standard deviation 30 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answer:
the probability that one parachute of the five parachute is damaged is 0.156
Step-by-step explanation:
From the given information;
Let consider X to be the altitude above the ground that a parachute opens
Then; we can posit that the probability that the parachute is damaged is:
P(X ≤ 100 )
Given that the population mean μ = 155
the standard deviation σ = 30
Then;
[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]
[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]
[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]
From standard normal tables
[tex]P(X \leq 100 ) = 0.0334[/tex]
Hence; the probability of the given parachute damaged is 0.0334
Let consider Q to be the dropped parachute
Given that the number of parachute be n= 5
The probability that the parachute opens in each trail be p = 0.0334
Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334
The probability mass function is:
Q [tex]\sim[/tex] B(5, 0.0334)
Similarly; the event that one parachute is damaged is :
Q ≥ 1
P( Q ≥ 1 ) = 1 - P( Q < 1 )
P( Q ≥ 1 ) = 1 - P( Y = 0 )
P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )
P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = 1 - 0.8437891838
P( Q ≥ 1 ) = 0.1562108162
P( Q ≥ 1 ) [tex]\approx[/tex] 0.156
Therefore; the probability that one parachute of the five parachute is damaged is 0.156
The following data values represent a sample. What is the variance of the
sample? X = 8. Use the information in the table to help you.
х
12
9
11
5
3
(x; - x)²
16
1
9
9
25
Answer:
The variance of the data is 15.
σ² = 15
Step-by-step explanation:
The mean is given as
X = 8
х | (x - X) | (x - X) ²
12 | 4 | 16
9 | 1 | 1
11 | 3 | 9
5 | -3 | 9
3 | -5 | 25
The variance is given by
[tex]\sigma^2 = \frac{1}{n-1} \sum (x - X)^2[/tex]
[tex]\sigma^2 = \frac{1}{5 - 1} (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} (60) \\\\\sigma^2 = 15[/tex]
Therefore, the variance of the data is 15.
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xey + yez + zex, (0, 0, 0), v = 4, 3, −1
Answer: 6 / √26
Step-by-step explanation:
Given that f(x, y, z) = xe^y + ye^z + ze^x
so first we compute the gradient vector at (0, 0, 0)
Δf ( x, y, z ) = [ e^y + ze^x, xe^y + e^z, ye^z + e^x ]
Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]
Now we were also given that V = < 4, 3, -1 >
so ║v║ = √ ( 4² + 3² + (-1)² )
║v║ = √ ( 16 + 9 + 1 )
║v║ = √ 26
It must be noted that "v" is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)
so
⊆ = ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]
therefore by equation D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆
D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]
= ( 1×4 + 1×3 -1×1 ) / √26
= (4 + 3 - 1) / √26
= 6 / √26
Which statement about the following equation is true?
2x2-9x+2-1
Complete Question:
Which statement about the following equation is true?
[tex]2x^2-9x+2 = -1[/tex]
A) The discriminant is less than 0, so there are two real roots
B) The discriminant is less than 0, so there are two complex roots
C) The discriminant is greater than 0, so there are two real roots
D) The discriminant is greater than 0, so there are two complex roots
Answer:
C) The discriminant is greater than 0, so there are two real roots
Step-by-step explanation:
The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes
[tex]2x^2 - 9x + 3 = 0[/tex]
For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]
If the discriminant D is greater than 0, the roots are real and different
If the discriminant D is equal to 0, the roots are real and equal
If the discriminant D is less than 0, the roots are imaginary
For the quadratic equation under consideration, a = 2, b = -9, c = 3
Let us calculate the discriminant D
D = (-9)² - 4(2)(3)
D = 81 - 24
D = 57
Since the Discriminant D is greater than 0, the roots are real and different.
Answer:
Step-by-step explanation:
C) The discriminant is greater than 0, so there are two real roots
Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
The lines of the inequalities are parallel, and the system of inequalities do not have any solution.
How to determine the solution of the inequalitiesThe system of inequalities are given as:
y ≥ 2x + 1 y ≤ 2x – 2The inequality y ≥ 2x + 1 has the following characteristics:
A slope of 2A y-intercept of 1A closed line, where the upper region is shadedThe inequality y ≤ 2x – 2 has the following characteristics:
A slope of 2A y-intercept of -2A closed line, where the lower region is shadedSee attachment for the graphs of the system of inequalities
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what is the surface area of a cylinder height is 4 cm and diameter is 5 cm
Answer:
20cm it's is the answers
Step-by-step explanation:
5*4=20
A tech company is curious about marketing their new drones for home security. Let the proportion of houses that have home security be p. If the tech company would like to know if the proportion of houses that have home security is different than 45%, what are the null and alternative hypotheses
Answer:
Step-by-step explanation:
The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.
In this case study, Let the proportion of houses that have home security be p
Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%
The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%
An angle measures 125.6° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
The measure of each angle:
152.8° and 27.2°
Step-by-step explanation:
Supplementary angles sum 180°
then:
a + b = 180°
a - b = 125.6°
then:
a = 180 - b
a = 125.6 + b
180 - b = 125.6 + b
180 - 125.6 = b + b
54.4 = 2b
b = 54.4/2
b = 27.2°
a = 180 - b
a = 180 - 27.2
a = 152.8°
Check:
152.8 + 27.2 = 180°
Answers:
152.8° & 27.2°Step-by-step explanation:
Let x and y be the measures of each angle.
x + y = 180°
x - y = 125.6°
180 - 125.6 = 54.4
Now we divide 54.4 evenly to get y.
y = 27.2°
To get x, we substitute y into the equation.
x = 27.2 + 125.6
x = 152.8°
To check, we plug these in to see if they equal 180°.
27.2 + 152.8 = 180° ✅
I'm always happy to help :)Find the perimeter and total area of the polygon shape shown below. All measurements are given in inches. Helps please !!!!
Answer:
perimeter = 56 in
area = 192 sq. in.
Step-by-step explanation:
area of a triangle = 0.5 * b * h
b = 12
h = 8
At = (0.5 * 12 * 8) = 48
Area of a square
As = 12 * 12 = 144
total area = At + As
total area = 48 + 144
total area = 192 sq. in.
perimeter = add all sides
12 + 12 + 12 + 10 + 10 = 56 in
hope it helps
What is the range of the function F(x) graphed below?F(x)= -(x+2)^2+3
Answer:
range of the function F(x) is (-infinity, 3)
Step-by-step explanation:
I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).
As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.
So the range of the function F(x) is (-infinity, 3)
In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults eat in a day be μ. If the CDC wanted to know if adults were eating, on average, more than the recommended 2 cups of vegetables a day, what are the null and alternative hypothesis? Select the correct answer below: H0: μ=2; Ha: μ>2 H0: μ>2; Ha: μ=2 H0: μ=2; Ha: μ<2 H0: μ=2; Ha: μ≠2
Answer:
H0: μ=2; Ha: μ>2
Step-by-step explanation:
The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.
In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.
Can someone answer this for me. My teacher gave me this As a Hint so once I get this I’m good plz help
To find the decay factor, b,
find the ratio of the
consecutive y-
values between the
points (0,16) and (1.12)?
Answer:
b = 4/3
Step-by-step explanation:
In an exponential equation:
f(x) = a (b)ˣ
Evaluated at x+1:
f(x+1) = a (b)ˣ⁺¹
The ratio between them is:
f(x+1) / f(x)
= (a (b)ˣ⁺¹) / (a (b)ˣ)
= b
So the decay factor b can be found by dividing the consecutive y values.
b = 16 / 12
b = 4/3
find the equation of a straight line joining the points (6,9) and (4,7). Please help im bad at mathematic :( and please do a calculation too.
Answer:
y = x+3
Step-by-step explanation:
First step is to find the slope
m = ( y2-y1)/(x2-x1)
= ( 7-9)/(4 - 6)
= -2 / -2
= 1
The we can put is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 1x+b
Putting in one of the points
9 = 1*6+b
Subtracting 6
9-6 = b
3=b
y = 1x+3
y = x+3
Answer:
[tex]\boxed{y=x+3}[/tex]
Step-by-step explanation:
Solve for slope first.
The slope can be found through 2 points.
[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]
[tex]slope=\frac{7-9}{4-6}[/tex]
[tex]slope=\frac{-2}{-2}[/tex]
[tex]slope=1[/tex]
Using slope-intercept form.
[tex]y=mx+b\\m=slope\\b=y \: intercept[/tex]
[tex]y=1x+b[/tex]
Let x = 6 and y = 9.
[tex]9=1(6)+b[/tex]
[tex]9-6=b[/tex]
[tex]3=b[/tex]
[tex]y=1x+3[/tex]
17. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. How large a sample is need it if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean
Answer:
A sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.
Step-by-step explanation:
We are given that an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours.
We have to find a sample such that we are 98% confident that our sample mean will be within 4 hours of the true mean.
As we know that the Margin of error formula is given by;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\sigma[/tex] = standard deviation = 40 hours
n = sample size
[tex]\alpha[/tex] = level of significance = 1 - 0.98 = 0.02 or 2%
Now, the critical value of z at ([tex]\frac{0.02}{2}[/tex] = 1%) level of significance n the z table is given as 2.3263.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
[tex]4=2.3263 \times \frac{40}{\sqrt{n} }[/tex]
[tex]\sqrt{n}= \frac{40 \times 2.3263}{ 4}[/tex]
[tex]\sqrt{n}=23.26[/tex]
n = [tex]23.26^{2}[/tex] = 541.03 ≈ 541
Hence, a sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.
The rule r_y-axis ° R_0,90 (x,y) is applied to ABC. Which triangle shows the final image?
a. 1
b. 2
c. 3
d. 4
Answer: 4
Step-by-step explanation:
Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.
The attachment shows the graph rotated 1-turn to the left (90°).
Notice it is in the exact same position as #4.