9514 1404 393
Answer:
(a) {(5, 2), (-4, 2), (3, 6), (0, 4), (-1, 2)}
Step-by-step explanation:
The only relation with no repeated x-values is the first one. The first relation is a function.
Let W be the solution set to the homogeneous system x + 2y + 3z = 0 2x + 4y + 6z = 0 Then W is a subspace of R3. Compute The Distance Between Y =[1 1 1] And W.
Answer:
Step-by-step explanation:
From the given information:
We can see that:
[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]
From equation (1), if we multiply it by 2, we will get what we have in equation (2).
It implies that,
x + 2y + 3z = 0 ⇔ 2x + 4y + 6z = 0
And, W satisfies the equation x + 2y + 3z = 0
i.e.
W = {(x,y,z) ∈ R³║x+2y+3z = 0}
Now, to determine the distance through the plane W and point is;
[tex]y = [1 \ 1 \ 1]^T[/tex]
Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0
Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:
[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]
[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]
[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]
[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]
[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]
H(0)=_______________
Answer:
5
Step-by-step explanation:
the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.
and that is automatically the result. there is not anything else to it.
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, T for turkey, I for Italian, and F for French. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: Italian, French
Answer: He can make 36 different salds
Step-by-step explanation:
Find the slope of the line which passes through the points A (-4, 2) and B (1,5).
Answer:
3/5 so A.
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)
m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 7 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is [larger, smaller] for New York because the sample size is [larger, smaller] than for California.
Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
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PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
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The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
if √3CosA = sin A , find the acute angle A
Answer:
Here is your answer.....
Hope it helps you....
Which statement is true about the slope of the graphed line?
Answer: positive
Step-by-step explanation: because it is going up from the left to the right
If in 1 month you can make 6 carpets, how many days will it take for making 10 carpets?
Si en 1 mes puedes hacer 6 alfombras, ¿cuántos días se necesitarán para hacer 10 alfombras?
Step-by-step explanation:
6 carpets=1month
10 carpets=?
1month=31 days
10 /6*31
51
Step-by-step explanatio
Solve the equation 10 + y√ = 14
9514 1404 393
Answer:
y = 16
Step-by-step explanation:
Perhaps you want to solve ...
10 +√y = 14
√y = 4 . . . . . . subtract 10
y = 4² = 16 . . . square both sides
What is the equation of the line that passes through the point (-4, 2) and has a
slope of -2?
Step-by-step explanation:
use the equation of the straight line
y-y1=m (x-x1)
y-2=-2(x+4)
y-2= -2x-8
y= -2x-8+2
y= -2x-6
I hope this helps
How long will it take for a home improvement loan for 22,800to earn interest of 608.00at 8 %ordinary interest
9514 1404 393
Answer:
120 days
Step-by-step explanation:
Using the formula for simple interest, we can solve for t:
I = Prt
t = I/(Pr) = 608/(22800×.08) = 608/1824 = 1/3 . . . . year
For "ordinary interest", a year is considered to be 360 days, so 1/3 year is ...
(1/3)(360 days) = 120 days
It will take 120 days for the loan to earn 608 in interest.
David can receive one of the following two payment streams:
i. 100 at time 0, 200 at time n, and 300 at time 2n
ii. 600 at time 1 0
At an annual effective interest rate of i, the present values of the two streams arc equal. Given v^n = 0.75941.
Determine i.
Answer:
3.51%
Step-by-step explanation:
From the given information:
For the first stream, the present value can be computed as:
[tex]= 100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}}[/tex]
Present value for the second stream is:
[tex]=\dfrac{600}{(1+i)^{10}}[/tex]
Relating the above two equations together;
[tex]100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}} =\dfrac{600}{(1+i)^{10}}[/tex]
consider [tex]v = \dfrac{1}{1+i}[/tex], Then:
[tex]\implies 100+200v^n + 300v^{2n} = 600 v^{10}[/tex]
where:
[tex]v^n = 0.75941[/tex]
Now;
[tex]\implies 100+200(0.75941) + 300(0.75941))^2 = 600 (v)^{10}[/tex]
[tex](v)^{10} = \dfrac{100+200(0.75941) + 300(0.75941))^2 }{600}[/tex]
[tex](v)^{10} = 0.7082[/tex]
[tex](v) = \sqrt[10]{0.7082}[/tex]
v = 0.9661
Recall that:
[tex]v = \dfrac{1}{1+i}[/tex]
We can say that:
[tex]\dfrac{1}{1+i} = 0.9661[/tex]
[tex]1 = 0.9661(1+i) \\ \\ 0.9661 + 0.9661 i = 1 \\ \\ 0.9661 i = 1 - 0.9661 \\ \\ 0.9661 i = 0.0339 \\ \\ i = \dfrac{0.0339}{0.9661} \\ \\ i = 0.0351 \\ \\ \mathbf{i = 3.51\%}[/tex]
I have 3 questionssss
∠A and ∠T are supplementary. Given m∠T = (7x+11)° and m∠A = (8x+19)°, what is m∠T?
The other two are in the pics attached! PLS!
Answer:
<T = 81
x = 10, angle = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
Step-by-step explanation:
Supplementary angles add to 180
(7x+11) + (8x+19) = 180
Combine like terms
15x + 30 = 180
Subtract 30 from each side
15x +30-30 = 180-30
15x= 150
Divide by 15
15x/15 = 150/15
x = 10
We want angle T
T = 7x+11 = 7(10)+11 = 70+11 = 81
The two angles add to 90
5x+10 + 30 = 90
Combine like terms
5x+40 = 90
5x+40-40 = 90-40
5x = 50
Divide by 5
5x/5 = 50/5
x=10
5x+10 = 5(10) +10 = 50+10 = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
Find m(angle) and give a trig equation
Step-by-step explanation:
Just using the Pythagoras theorem
How far can you travel in 19 hours at 63 mph
Answer:
1197 miles.
Step by step explanation:Speed(s) = 63 mph
Time(t) = 19 hours
Distance(d) = ?
We know,
D = S × T
= 63 × 19
= 1197 miles
In triangleABC, AC = 15 centimeters, m
Answer:
16.17 cm
Step-by-step explanation:
The solution triangle attached below :
To obtain BC ; we use the sine rule ;
a/ sin A = b / sin B
A = (180 - (68 + 24))
A = 180 - 92
A = 88°
a / Sin 88 = 15 / sin 68
Cross multiply :
(a * sin 68) = (15 * sin 88)
a = 14.990862 / sin 68
a = 16.168165
a = 16.168 cm
The following data show the number of candies in 15 different bags.
35, 48, 36, 48, 43, 37, 43, 39, 45, 46, 40, 35, 50, 38, 48
Answer:
How should we proceed with this question
Write the equation of the line for the graph shown below, please
Answer:
Given the proposed interrogate, as well as the graph provided, the correct answer is B. Y = 1/2 x + 4
Step-by-step explanation:
To evaluate such, a comprehension of linear Cartesian planes are obligated:
Slopes = rise/run
X- intercept: The peculiar point in which linear data is observed to intersect the x-axis.
Y- intercept: The peculiar point in which linear data is observed to intersect the y-axis.
Slope: 1/2 as for every individual space endeavored, a space of 2 to the right is required.
Y- intercept: (4,0)
Thus, the ameliorated answer to such interrogate is acknowledged as B. Y = 1/2 x + 4.
*I hope this helps.
For this question it’s asking for it in slope intercept form. So all you need to find is the slope and the y intercept.To find the y int look at where the line passes y. In this case it is y=4, then find slope by finding change in y/ change once which is 1/2, so you get y=1/2x+4
Tom and Carl start 200 miles apart, running towards each other. Tom runs 5 miles per hour faster than Carl. If they meet after 10 hours, how fast are they running?
Answer:
12.5 mph and 7.5 mphStep-by-step explanation:
Tom's speed = xCarl's speed = yWe have:
x = y + 5(x + y)*10 = 200Substitute x and solve for y:
(y + y + 5)*10 = 2002y + 5 = 202y = 15y = 7.5Find x:
x = 7.5 + 5 = 12.5Tom's speed is 12.5 mph
Carl's speed is 7.5 mph
Now
a=b+510(a+b)=200From eq(2)
a+b=20From eq(1)
a-b=5Adding these recent two
2a=25a=12.5mphPutting in eq(1)
b=a-5b=12.5-5b=7.5mphthe expectation students often have when doing the coin flip experiment is that thye will flip exactly 5 heads and 5 tails because there is 50% chance of flipping each. Is this a realistic expectation
Answer:
No
Explanation:
A coin which has a head and a tail has 1/2 probability of each which is a 50% chance of getting either a head or a tail. This means that given two sides of a coin, probability looks at the number of favorable outcomes and total number of outcomes, a formula that reflects a pattern seen in past experiences. Probability isn't absolute but relative. When we say there is a 50% chance of getting a head in a coin flip, it is relative to past experiences but doesn't assure of particular future occurrences regarding the coin flip.
Help please, don’t understand this
Answer:
b = -13/3
Step-by-step explanation:
Plug in the 13/3 into the t and then try to solve it. Like this:
(13/3 - 8/3)(13/3 + b) = 0 ----> 5/3(13/3+b) = 0 ----> from here you have to distribute ----> 65/9 + b = 0 (here you have to subtract from both sides)
b = -65/9 (you could simplified) ---> b = -13/3
