Answer:
10 (positive 10)
Step-by-step explanation:
5 times -2 is equal to -10.
-10 times -1 is equal to 10.
Answer:
postive 10
Step-by-step explanation:
part 2 of math help me please
Answer:
<1 = <5 is True
<2 = <4 is True
<2 = <7 is False
<3 and <6 are not a linear pair
<4 and <5 are not supplementary angles
m<5 is 75°
m<11 is 75°
m<16 is 65°
How many 2-letter words can be made from the letters MATH if
Answer:
ham
tam
mat
hat
at
ha
am
ma
Step-by-step explanation:
In the following shape, two semicircles have been placed at the end of a rectangle whose length is twice its height. Which of the following gives the length around this figure in terms of the semicircle's radius, r?
Answer:
Perimeter of the figure is 2r([tex]\pi[/tex] + 6)
Step-by-step explanation:
Perimeter of a shape is total length of the boundaries of the shape. In the given question, we have two semicircles and a rectangle.
The circumference of a circle = 2[tex]\pi[/tex]r, thus the length of the arc of a semicircle = [tex]\pi[/tex]r.
The height of the rectangle is h, radius 'r' of the semicircle = [tex]\frac{h}{2}[/tex]
⇒ h = 2r
The perimeter of a rectangle = 2(l +b).
Given that: the length is twice its height, so that:
length = 2h
Perimeter of the rectangle = 2 (2h + h)
= 6h
But, h = 2r
Perimeter of the rectangle = 6 × 2r
= 12r
Perimeter of the figure in terms of the semicircle's radius = [tex]\pi[/tex]r + 12r + [tex]\pi[/tex]r
= 2[tex]\pi[/tex]r + 12r
= 2r([tex]\pi[/tex] + 6)
Assume {v1, . . . , vn} is a basis of a vector space V , and T : V ------> W is an isomorphism where W is another vector space. Show that the vectors w1 = T(v1), . . . ,wn = T(vn) are a basis of W.
This statement becomes false if we drop the assumption that T is invertible. Demonstrate this by finding a counterexample.
Answer:
Step-by-step explanation:
To prove that [tex]w_1,\dots w_n[/tex] form a basis for W, we must check that this set is a set of linearly independent vector and it generates the whole space W. We are given that T is an isomorphism. That is, T is injective and surjective. A linear transformation is injective if and only if it maps the zero of the domain vector space to the codomain's zero and that is the only vector that is mapped to 0. Also, a linear transformation is surjective if for every vector w in W there exists v in V such that T(v) =w
Recall that the set [tex]w_1,\dots w_n[/tex] is linearly independent if and only if the equation
[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex] implies that
[tex]\lambda_1 = \cdots = \lambda_n[/tex].
Recall that [tex]w_i = T(v_i)[/tex] for i=1,...,n. Consider [tex]T^{-1}[/tex] to be the inverse transformation of T. Consider the equation
[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex]
If we apply [tex]T^{-1}[/tex] to this equation, then, we get
[tex] T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) =T^{-1}(0) = 0[/tex]
Since T is linear, its inverse is also linear, hence
[tex]T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) = \lambda_1T^{-1}(w_1)+\dots + \lambda_nT^{-1}(w_n)=0[/tex]
which is equivalent to the equation
[tex]\lambda_1v_1+\dots + \lambda_nv_n =0[/tex]
Since [tex]v_1,\dots,v_n[/tex] are linearly independt, this implies that [tex]\lambda_1=\dots \lambda_n =0[/tex], so the set [tex]\{w_1, \dots, w_n\}[/tex] is linearly independent.
Now, we will prove that this set generates W. To do so, let w be a vector in W. We must prove that there exist [tex]a_1, \dots a_n[/tex] such that
[tex] w = a_1w_1+\dots+a_nw_n[/tex]
Since T is surjective, there exists a vector v in V such that T(v) = w. Since [tex]v_1,\dots, v_n[/tex] is a basis of v, there exist [tex]a_1,\dots a_n[/tex], such that
[tex]a_1v_1+\dots a_nv_n=v[/tex]
Then, applying T on both sides, we have that
[tex]T(a_1v_1+\dots a_nv_n)=a_1T(v_1)+\dots a_n T(v_n) = a_1w_1+\dots a_n w_n= T(v) =w[/tex]
which proves that [tex]w_1,\dots w_n[/tex] generate the whole space W. Hence, the set [tex]\{w_1, \dots, w_n\}[/tex] is a basis of W.
Consider the linear transformation [tex]T:\mathbb{R}^2\to \mathbb{R}^2[/tex], given by T(x,y) = T(x,0). This transformations fails to be injective, since T(1,2) = T(1,3) = (1,0). Consider the base of [tex]\mathbb{R}^2[/tex] given by (1,0), (0,1). We have that T(1,0) = (1,0), T(0,1) = (0,0). This set is not linearly independent, and hence cannot be a base of [tex]\mathbb{R}^2[/tex]
How is adding mixed numbers with unlike denominators the same as adding fractions with unlike denominators? How is it different?
Mrs. Williams has 1/4 gallon of juice left in a bottle. She pours an equal amount of
juice into 5 glasses to empty the bottle. Which model represents the fractional
amount of the gallon of juice in each glass?
Answer:
1/20 of a gallon
Step-by-step explanation:
If she divides 1/4 into 5 glasses, the answer would be 0.05, or 1/20 gallons, if its right please give 5 stars
A row of tiny red beads is placed at the beginning and at the end of a 20‐centimeter bookmark.
A row of the same beads is also placed every 4 millimeters along the bookmark.
How many rows of the beads are used on the bookmark?
Answer:
51 rows
Step-by-step explanation:
Given
Length of bookmark = 20cm
Distance between beads = 4mm
Required
Number of rows of beads
First, the distance between the rows of beads must be converted to cm
if 1mm = 0.1cm
then
4mm = 4*0.1cm
4mm = 0.4 cm
This means that each row of beads is placed at 0.4 cm mark.
The distance between each row follows an arithmetic progression and it can be solved as follows;
[tex]T_n = a + (n-1)d[/tex]
Where [tex]Tn = 20cm[/tex] (The last term)
[tex]a = 0 cm[/tex] (The first term)
[tex]d = 0.4cm[/tex] (The distance between each row of beads)
n = ?? (number of rows)
Solving for n; we have the following;
[tex]T_n = a + (n-1)d[/tex] becomes
[tex]20 = 0 + (n-1)0.4[/tex]
[tex]20 = (n-1)0.4[/tex]
DIvide both sides by 0.4
[tex]\frac{20}{0.4} = \frac{(n-1)0.4}{0.4}[/tex]
[tex]50 = (n-1)[/tex]
[tex]50 = n-1[/tex]
Add 1 to both sides
[tex]50 + 1= n-1 + 1[/tex]
[tex]n = 51[/tex]
Hence, the number of rows of beads is 51
Which deduction is optional?
A. Federal income tax
B. Life insurance
C. Medicare
D. Social Security
Answer:
B. Life insurance
Step-by-step explanation:
A. Federal income tax required by law
B. Life insurance usually employer paid for a small amount and then optional
C. Medicare required by law
D. Social Security required by law
Consider a vat that at time t contains a volume V (t) of salt solution containing an amount Q(t) of salt, evenly distributed throughout the vat with a concentration c(t), where c(t) = Q(t) / V(t). Assume that water containing a concentration k of salt enters the vat at a rate rin, and that water is drained from the vat at a rate rout > rin.
(a) If V (0) = V0, find an expression for the amount of solution in the vat at time t. At what time T will the vat become empty? Find an initial value problem that describes the amount of salt in the vat at time t <= T. You may assume that Q(0) = Q0.
(b) Solve the initial value problem in part (a). What is the amount of salt in the vat at time t? What is the concentration of the last drop that leaves the vat at time t = T
Answer:
a.i [tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii. time at which vat will be empty
[tex]T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex] when dQ/dt = 0
b. i Amount of salt at time t
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
ii. Concentration at t = T
c(T) = [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Step-by-step explanation:
a.
i. We determine the differential equation for the solution in the vat at time,t.
Let Q be the quantity of salt in the vat at any time,t.
So, dQ/dt = rate of change of quantity of salt in the vat. = rate of change of quantity of salt into the vat - rate of change of quantity of salt out of the vat.
Now, since a concentration of salt, k enter the vat at a rate of rin, rate of change of quantity of salt into the vat = krin.
Let V(0) = V₀ be the volume of water int the vat at time t = 0. Now, the volume of water in the vat increases at a rate of (rin - rout). The increase in volume after a time t is (rin - rout)t. So the volume after a time, t is V(t) = V₀ + (rin - rout)t. The concentration of this liquid is thus Q(t)/V(t) = Q(t)/V₀ + (rin - rout)t. Now, the rate of change of quantity of salt out of the vat is thus [Q(t)/V₀ + (rin - rout)t]rin = Q(t)rout/[V₀ + (rin - rout)t].
So, dQ(t)/dt = krin - Q(t)rout/[V₀ + (rin - rout)t].
[tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii Time T at which vat will be empty
At time T, when the vat is empty, dQ(T)/dt = 0.
So
[tex]\\\frac{dQ(T)}{dt} + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\0 + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex]
b. i
i. We solve the differential equation to find the amount of salt at time,t
The integrating factor is ex
[tex]exp(\int\limits {\frac{r_{out} }{V_{0} + (r_{in} - r_{out})t} } \, dt ) = exp(\frac{r_{out}}{(r_{in} - r_{out})} \int\limits {\frac{ (r_{in} - r_{out})}{V_{0} + (r_{in} - r_{out})t} } \, dt )\\= exp(\frac{r_{out}}{(r_{in} - r_{out})} ln [V_{0} + (r_{in} - r_{out})t} ]) \\\= [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]
Multiplying both side of the equation by the integrating factor, we have
[tex][V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{dQ(t)}{dt} + [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt = krin[V(0) + (rin - rout)texp(rout/(rin - rout))]
Integrating both sides we have
∫(dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt)dt = ∫(krin[V(0) + (rin - rout)texp(rout/(rin - rout))])dt
Let exp(rout/(rin - rout) = A
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + C
At t = 0, Q(t) = Q(0),
So,
Q(0)[V(0) + A(rin - rout)×0] = AkrinV(0)t + A(rin - rout)×0²/2 + C
C = Q(0)V(0)
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + Q(0)V(0)
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
The above is the amount of salt at time ,t.
ii. The concentration of the last drop of salt at time, t = T
To find the concentration of the last drop of salt at time t = T, we insert T into Q(t) to find its quantity and insert t = T into V(t) = V₀ + (rin - rout)t.
So
Q(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]
Q(T) = [[exp(rout/(rin - rout)]krin[V(0)T + [exp(rout/(rin - rout)](rin - rout)T²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)T]
the volume at t = T is
V(T) = V₀ + (rin - rout)T.
The concentration at t = T is c(T) = Q(T)/V(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]/V₀ + (rin - rout)T.
= [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/([V(0) + A(rin - rout)T][V₀ + (rin - rout)T])
= [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Mean is 22 and standard deviation is 0.2, what is the spread
Answer:
:v What??
jwkwlwmwbwjqkq
.........
.
........
..
Answer:
0.04
Step-by-step explanation:
Standard deviations== square root of variance define as spread.
Standard deviations square = variance
[0.2]^2= 0.04
according to the picture, which of the following is true?
A. I-
B. Hahahaha OMG It's mega mind!!
C. What is wrong with the world
D. I love this, plz make more
E. All of the above
Answer:
B is the answer for but I don't now about others thank you
Kim's business earns $10,000 per month. Kim's non-employee expenses are $3,000 per month. If Kim wants $2,000 in profit per month, how many employees can Kim have if each employee costs $1,000 per month?
Answer:
Kim's business earns $10,000 per month.
Kim's non-employee expenses are $3,000 per month.
If Kim wants $2,000 in profit per month, then the maximum amount Kim can spend for employee:
10000 - 3000 - 2000 =5000
If each employee costs $1,000 per month, Kim can recruit 5000/1000 = 5 as the maximum number of employees.
Hope this helps
:)
Answer:
5
Step-by-step explanation:
Revenue - profit = expense
10000 - 2000 = 8000
8000 = 3000 + 1000n
1000n = 5000
n = 5
Find the area 9cm 8cm 13cm 9cm 11cm
Answer:
460
Step-by-step explanation: multiply all numbers to get your answer
graph y=-2/3x-3 i need help quick
Answer: just get gud at math lol
Step-by-step explanation: no
The outlier of a data set causes the _____(mean/median) to be greater than the ______(mean/median) when the outlier is in the upper part of the data set.
Answer:
Mean, Median
Step-by-step explanation:
Outliers affect the mean because it is not resistant to outliers. They will affect the sum and therefore the mean.
The solution is, Mean, Median.
i.e. The outlier of a data set causes the Mean (mean/median) to be greater than the Median (mean/median) when the outlier is in the upper part of the data set.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
here, we have,
we know that,
Outliers affect the mean because it is not resistant to outliers.
They will affect the sum and therefore the mean.
so, we get,
The outlier of a data set causes the Mean (mean/median) to be greater than the Median (mean/median) when the outlier is in the upper part of the data set.
hence, The solution is, Mean, and, Median.
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Juan spins two different fair spinners. One spinner has numbers 1 through 8. The other has letters A through F. What is the probaility that one spinner will land on 3 and the other will land on C?
Answer:
...
Step-by-step explanation:
You entered a room, there are 34 people. You killed 30. How many people are left in the room?
Answer:
5
Step-by-step explanation:
4 people you didnt kill and that were already there and you
can i have brainliest if i got it right pls
Answer:
31
Step-by-step explanation:
there were 34 people and you killed 30. the other people would have gotten scared and ran away leaving you with 30 other bodies in the room
A cylinder has a volume of 315 pi cubic meters and a height of 21 meters. What is the area of the base?
Answer:
The area of base is 47.1 m² or 15π m².
Step-by-step explanation:
Given that the formula of volume of cylinder is V = πr²h where πr² is the base area of cylinder so you have to substitute the following values into the formula :
[tex]v = \pi \times {r}^{2} \times h[/tex]
Let v = 315π,
Let h = 21,
[tex]315\pi = \pi {r}^{2} \times 21[/tex]
[tex]\pi {r}^{2} = 315\pi \div 21[/tex]
[tex]\pi {r}^{2} = 15\pi[/tex]
[tex]base \: area = 15\pi \: {m}^{2} [/tex]
[tex]base \: area = 47.1 \: {m}^{2} (3s.f)[/tex]
Answer:
a
Step-by-step explanation:
On a math test ,there are 60 questions, Elena answered 50 correctly.
a)what percent did she answer correctly?
b)What is her radio to incorrect answers?
c)what is the radio of correct answers to the total number of questions fielded on her test?
Answer:
YOU MAY NEED TO CHAN
Step-by-step explanation:
WHEN CALCULATING THE AREA OF A TRAPEZOID, HOW DO YOU DETERMINE WHICH SIDES ARE THE BASES
Answer:
a bc they are parallel
Step-by-step explanation:
How tall is the monument?
Answer:
43.125
Step-by-step explanation:
From trigonometry;
Tan87.4 =height of monument / 25
Height of monument = 25 * Tan 87.4
= 25 * 1.525
=38.125 ft
There is an extra substention of 5ft we add that
38.125 + 5 = 43.125 ft
What is the measure JKL?
O A. 186°
O B. 267°
0 C. 174°
o D. 87°
Answer:
c
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
C
Step-by-step explanation:
Since the output is just the input multiplied by 3, the output will be 15.4*3=46.2, or answer choice C. Hope this helps!
Answer:
C. 46. 2
Step-by-step explanation:
All you need to do is multiply 15.4 by 3, like so:
15.4 · 3 = 46.2
Please answer this correctly
Answer:
30
Step-by-step explanation:
If these two shapes are similar, then ratios of corresponding sides will stay constant. Therefore:
[tex]\dfrac{g}{45}=\dfrac{50}{75}[/tex]
Multiply both sides by 45:
[tex]g=\dfrac{50\cdot 45}{75}=30[/tex]
Hope this helps!
PLEASE HELP ME with an explanation. Thanks in advance
Answer:
3) 0.30
The probability a randomly selected student plays a sport given they work part time = 0.30
Step-by-step explanation:
Step(i):-
Given 'A' plays a sport
B work part time
Given P(A) = 0.48
P(B) = 0.40
P(A∩B) =0.12
P(A∪B)¹ =0.24
Step(ii):-
By using conditional probability
[tex]P(B/A) = \frac{P(BnA}{P(A)}[/tex]
and similarly [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
The probability a randomly selected student plays a sport given they work part time
Now [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
[tex]P(A/B) = \frac{0.12}{0.40}= 0.30[/tex]
Final answer:-
The probability a randomly selected student plays a sport given they work part time = 0.30
think your a pro at riddles?
Mr. and Mrs. Mustard have six daughters and each daughter has one brother. How many people are in the Mustard family?
Answer:
nine
Step-by-step explanation:
A football team scored fewer than 16 points in Saturday’s game. Than wants to write an inequality for the number of points. He uses the variable s in his inequality. What does s represent? A - the number of fans of the team
B - the number of games played by the team
C - the number of points scored by the team
D - the number of players on the team
what is the median? 10, 50, 30, 90, 90, 0, 50, 80, 90, 90
Answer:
65
Step-by-step explanation:
Order the numbers in order
Find the middle number
Since there were 2, find the average
Answer:65
Step-by-step explanation:
median is the middle
there is 2 and they are 50 and 80
add it up and divide by 2
If 6 pens cost $2.40 What is the cost of 9 pens?
Answer:
3.60$
Step-by-step explanation:
if we bought 3 pens that would equal 1.20$ so we add 1.20$ to 2.40$ we get 3.60$
Please answer quick
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor need to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning m. What is the probability that Taylor will win the game?
A. P(winning)= 4/6=66%
B.P(winning)= 3/6=50%
C. P(winning)= 5/6=83%
D. P(winning)= 2/6=33%
Answer:
It would be 2/6.
Step-by-step explanation:
2/6 simplified is 1/3 and she is going against two of her friends in which makes three.
The probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three.
To win, Taylor needs to roll a 4, a 5, or a 6.
Total number in a standard roll = 6
Favorable outcomes = 3
Probability = 3/6 or
= (3/6)×100
= 50 %
Thus, the probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
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