Answer:
-26
Step-by-step explanation:
a(6)=-2(6)-14
a(6)=-12-14
a(6)=-26
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The 6th value in the sequence = an=−2n−14 = -4.3
Take n = 6
⇒ a6 = -2·6 -14 = -12-14 = -26
∴ a= [tex]\frac{-26}{6}[/tex] = -4.3
Explicit formulaThe explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.
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A 1500 kg hippo is completely submerged, standing on the bottom of a lake. What is the approximate value of the upward normal force on the hippo?
Answer:
About 428 N
Step-by-step explanation:
Weight = 1,500 * 9.8 = 14,700 N
Density = Mass ÷ Volume
1,030 = 1,500 ÷ V
V = 1,500 ÷ 1,030 = 1.46 m^3.
Buoyant force = Density * g * V
Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)
Buoyant force = 9,800 * (1,500 ÷ 1,030) = 14,272 N.
Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]
The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.
Explanation:The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).
In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:
Normal Force = 1500 kg × 9.81 m/s² = 14715 N.
This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.
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Walk from home to the bus stop at the average speed of 5 km an hour he immediately got on the school bus and traveled at an average speed of 60 hour until he got the total distance from her is 35 km and the entire trip 1.5 hours how many kilometers did your Canon covered by walking and how many kilometers did you cover by traveling on the bus
Answer:
5 km walking, 30 km on the bus.
Step-by-step explanation:
Let
w
be the distance walking and
b
be the distance on the bus.
The total distance is 35 km.
w
+
b
=
35
The total time is 1.5 hours. Each leg has time equal to distance/speed.
w
5
+
b
60
=
1.5
Multiply by 60 to clear the fractions.
12
w
+
b
=
90
Subtract the first equation,
11
w
=
90
−
35
=
55
w
=
5
b
=
30
Check:
A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 98 % confident that the sample proportion will not differ from the true proportion by more than 6 %?
Answer:
n≅376
So sample size is 376.
Step-by-step explanation:
The formula we are going to use is:
[tex]n=pq(\frac{z_{\alpha/2}}{E})^{2}[/tex]
where:
n is the sample size
p is the probability of favor
q is the probability of not in favor
E is the Margin of error
z is the distribution
α=1-0.98=0.02
α/2=0.01
From cumulative standard Normal Distribution
[tex]z_{\alpha/2}=2.326[/tex]
p is taken 0.5 for least biased estimate, q=1-p=0.5
[tex]n=0.5*0.5(\frac{2.326}{0.06})^{2}\\n=375.71[/tex]
n≅376
So sample size is 376
Kerry's saving account has balance of $372 for grandmother is going to give her a birthday check was 1/4 of her savings parents are they going to give her a check or 33% of her new savings account balance would you have enough money to buy a plane ticket to alaska the cost $600
Answer:
Step-by-step explanation:
372 + 1/4*372 = $465
$465 is her new savings and 33% of it is $153.45
$465 + $153.45 = $618.45
So yes she would have enough money to buy a plane ticket to alaska the cost $600
Talia wants to play a basketball game at a carnival. the game cost the player $5 to play, and the player gets to take too long distance shots. if they missed both shots, they get nothing. if they make one shot, they get their $5 back. Thalia has a 40% chance of making this type of shot.
here is the probability distribution of x= the amount of money Talia gains from playing the game.
x= money gain -$5 $0 $5
P(x) 0.36 0.48 0.16
Given that μx = -$1, calculate Θ x.
round your answer to two decimal places
Θx = _______ dollars
Answer:3.46$
Step-by-step explanation:
Probability distribution:
[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]
[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]
[tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]
Therefore,
[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]
Therefore, the final answer is "3.464".
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which of the following terms is not a monomial a)6x b)1/3x^2 c)13 d) 3x^-3
Answer:
The answer is D.
Step-by-step explanation: A monomial is an algebraic expression that consists of one term. D consists of 2 terms and is considered a binomial.
In pea plants, smooth pea shape is dominant towrinkled and yellow pea color is dominant togreen. A plant that is heterozygous for pea shape and has green peas is crossed with a plant that is has wrinkled peas and is heterozygous forpeacolor. What is the probability of having offspringwith wrinkledgreen peas?
The probability of having wrinkled green peas is 25% or 0.25
Explanation:
Given:
Pea shape - smooth and wrinkled
Pea color - Yellow and green
Smooth is dominant to wrinkled
Yellow color is dominant to green
So, the genotype of smooth pea is SS or Ss
wrinkled pea is ss
The genotype of yellow pea is YY or Yy
green pea is yy
According to the question,
Ssyy X ssYy
Possible gametes of Ssyy - Sy , Sy, sy, sy
Possible gametes of ssYy - sY, sy, sY, sy
Cross between these gametes are shown in the punnett square drawn in the word file attached.
According to the cross,
The probability of having wrinkled green peas is 25% or 0.25
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠E.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠E = °
Answer:
[tex]m\angle E=58^o[/tex]
Step-by-step explanation:
we know that
In the right triangle DEF
[tex]tan(E)=\frac{DF}{EF}[/tex] ----> by TOA (opposite side divided by adjacent side)
[tex]tan(E)=\frac{8}{5}[/tex]
[tex]m\angle E=tan^{-1}(\frac{8}{5})=58^o[/tex]
ik to use the pythagoream theorem, but idk how to set it up and therefore solve the problem? could someone pls help :))
Answer:
52.2
Step-by-step explanation:
Light reflects off a mirror at the same angle it hits it at (as shown in the image). Since both triangles are right triangles, we can say they are similar by AA similarity.
Since they're similar, we can write a proportion.
HT / TV = JS / SV
Plugging in values:
5.8 / 4 = JS / 36
JS = 52.2
The wall is 52.2 feet tall.
Some of helen's plants need water every day,some need water every other day,and others need water every third day.If she waters them all today,how many days will it be before she waters them all again?
Answer: Waters on 7th day
Step-by-step explanation:
If she waters everyday then days= 1,2,3,4,5,6,7,8,9
If she waters every other day= 1,3,5,7,9
If she waters every third day= 1,4,7,10,13
So the common day to all is either 1st day or 7th day.
To prepare for a marathon, Henry gets a new pair of running shoes. If Henry runs 20 miles each day in week 1 and adds 12mi to his daily routine each week, what is the total mileage on Henry's shoes after 5 weeks?
Henry will have run a total of 1540 miles on his new running shoes after 5 weeks.
Explanation:To find the total mileage on Henry's shoes after 5 weeks, we need to calculate the distance he runs each week and add them up.
In week 1, Henry runs 20 miles per day, so the total distance he runs in week 1 is 20 miles * 7 days = 140 miles.
In week 2, he adds 12 miles to his daily routine, so he runs 20 miles + 12 miles = 32 miles per day. The total distance he runs in week 2 is 32 miles * 7 days = 224 miles.
We can continue this pattern for the remaining weeks:
Week 3: 44 miles per day, total distance = 44 miles * 7 days = 308 miles
Week 4: 56 miles per day, total distance = 56 miles * 7 days = 392 miles
Week 5: 68 miles per day, total distance = 68 miles * 7 days = 476 miles
The total mileage on Henry's shoes after 5 weeks is the sum of the total distances in each week: 140 + 224 + 308 + 392 + 476 = 1540 miles.
The altitude of a model rocket launched into the air from a rooftop is given by the quadratic equation A(t) = −16t2 + 32t + 48, where t is the time in seconds since launch, and A is measured in feet. At what time does the rocket land on the ground?
Answer:
Rocket will land on the ground in 3 seconds.
Step-by-step explanation:
Given:
[tex]A(t) = -16t^2 + 32t + 48[/tex]
where [tex]t[/tex] ⇒ time in seconds since launch.
[tex]A(t)[/tex] ⇒ altitude of the rocket after reaching the ground.
we need to find the time at which rocket will land on the ground.
Solution:
Now we can say that;
altitude of the rocket after reaching the ground will be equal to 0.
So;
[tex]A(t)=0[/tex]
Now Substituting [tex]A(t)=0[/tex] in given expression we get;
[tex]0=-16t^2+32+48[/tex]
Now we take -16 common we get;
[tex]0=-16(t^2-2t-3)[/tex]
Now Dividing both side by -16 we get;
[tex]\frac0{-16}=\frac{-16(t^2-2t-3)}{-16}\\\\0=t^2-2t-3[/tex]
Now factorizing the above equation we get;
[tex]0=t^2-3t+t-3\\\\0=t(t-3)+1(t-3)\\\\0=(t+1)(t-3)[/tex]
Now we will find 2 values of t by substituting each separately.
[tex]t+1=0 \ \ \ Or \ \ \ \ t-3 =0\\\\t =-1 \ \ \ \ \ \ Or \ \ \ \ \ \ t=3[/tex]
Now we get 2 values of t one positive and one negative.
Now we know that time cannot e negative hence we will discard it and consider positive value of t.
Hence Rocket will land on the ground in 3 seconds.
Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. Last year she earned $1995 in interest. How much money did she invest at each rate?
Answer: she invested $17000 in the account earning 6% annual interest.
she invested $13000 in the account earning 7.5% annual interest.
Step-by-step explanation:
Let x represent the amount that she invested in the account earning 6% annual interest.
Let y represent the amount that she invested in the account earning 7.5% annual interest.
Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that
x + y = 30000
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account earning 6% annual interest.
P = x
R = 6%
T = 1 year
I = (x × 6 × 1)/100 = 0.06x
Considering the account earning 7.5% annual interest,
P = y
R = 7.5
T = 1
I = (y × 7.5 × 1)/100 = 0.075y
Last year she earned $1995 in interest. This means that
0.06x + 0.075y = 1995 - - - - - - - -
Substituting x = 30000 - y into equation 1, it becomes
0.06(30000 - y) + 0.075y = 1995
1800 - 0.06y + 0.075y = 1995
- 0.06y + 0.075y = 1995 - 1800
0.015y = 195
y = 195/0.015 = 13000
x = 30000 - y = 30000 - 13000
x = 17000
Leah gets to paint her room since she bought a new bedspread set. Two gallons of paint covers 800 square feet. How many gallons of paint will Leah need to paint her entire room, which is 1,200 square feet?
Answer:
3 gallons
Step-by-step explanation:
If two gallons of paint covers 800 square feet, 'x' gallons of paints will cover 1200square feet room where x is the number of gallons needed to paint the 1200 square feet room.
Mathematically,
2 gallons = 800sq.ft
x gallons = 1,200sq.ft
x × 800 = 2 × 1200
x = 2 × 1200/800
x = 3 gallons
Therefore Leah will need 3gallons of paint for 1200sq.ft room
Let V be a vector space and assume that T, U, W are sub spaces of V. Show that if T cup U W is a sub space of V, then two of these subspaces must be contained in the other one?
Answer: T⊂U⊂W are subspaces of V
Step-by-step explanation:
Proof: This is the easier direction.
If T⊂U⊂W or W⊂U⊂T then we have U⊂T⊂W = T or T⊂U⊂W = U
orT⊂U⊂W=W respectively.
SoT⊂U⊂W is a subspace as T, U and W are subspaces.
1st case :T⊂U⊂W is true Then the disjunction W⊂U⊂T or U⊂T⊂W is trivially true.
Let x∈W1 and y∈W2−W1.
By the definition of the union, we have x∈W∪T∪C and y∈T⊂U⊂W
As T∪U∪W is a subspace, x+y∈T∪C∪W which, again by the definition of the union, means that x+y∈W∪T∪C
V∈W∪T∪C
As V was arbitrary, as desired.
Final answer:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one.
Explanation:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one. We can prove this by contradiction. Assume that none of the subspaces is contained in the other. This means that there is an element in T that is not in U ∪ W, an element in U that is not in T ∪ W, and an element in W that is not in T ∪ U. If we take any two of these elements, one from each subspace, and add them together, the result will not be in T ∪ U ∪ W, which contradicts the assumption.
Therefore, two of the subspaces must be contained in the other one.
Alfred Juarez owns a small publishing house specializing in Latin American poetry. His fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2675. His books sell for $4.95 each.
(A) Find the linear cost function for Alfred's book production.
(B) How many poetry books must he produce and sell in order to break even?
(C) How many books must he produce and sell to make a profit of $1000?
Answer:
(A) [tex]C(x)=2.15x+525[/tex]
(B) 188 books
(C) 545 books
Step-by-step explanation:
We have been given that Alfred Juarez's fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2675.
(A) The cost function will be in form [tex]C(x)=ax+b[/tex], where, a is cost of each copy, x is number of books and b is fixed cost.
Upon substituting our given information, we will get:
[tex]2675=1000a+525[/tex]
Let us solve for a.
[tex]2675-525=1000a[/tex]
[tex]2150=1000a[/tex]
[tex]a=\frac{2150}{1000}=2.15[/tex]
Therefore, the cost function would be [tex]C(x)=2.15x+525[/tex].
(B) Since each book sells for $4.95, so amount earned by selling x books would be [tex]4.95x[/tex]
Revenue function would be [tex]R(x)=4.95x[/tex]
We know that break-even is a point, where cost is equal to revenue or when there is a 0 profit.
[tex]R(x)=C(x)\\\\4.95x=2.15x+525[/tex]
[tex]4.95x-2.15x=525[/tex]
[tex]2.8x=525[/tex]
[tex]x=\frac{525}{2.8}[/tex]
[tex]x=187.5\approx 188[/tex]
Therefore, Alfred must produce 188 poetry books to break even.
(C) We know that profit is equal to difference of revenue and cost.
[tex]\text{Profit}=\text{Revenue}-\text{Cost}[/tex]
[tex]P(x)=4.95x-(2.15x+525)[/tex]
[tex]1000=4.95x-(2.15x+525)[/tex]
[tex]1000=4.95x-2.15x-525[/tex]
[tex]1000=2.8x-525[/tex]
[tex]1000+525=2.8x[/tex]
[tex]1525=2.8x[/tex]
[tex]x=\frac{1525}{2.8}[/tex]
[tex]x=544.642857\approx 545[/tex]
Therefore, Alfred must produce and sell 545 books to make a profit of $1000.
What is the value of t=1 ∑³ (4 x 1/2^t-1)
Answer:
7
Step-by-step explanation:
[tex]\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})[/tex]
This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.
We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.
4 · (½)¹⁻¹ = 4
4 · (½)²⁻¹ = 2
4 · (½)³⁻¹ = 1
4 + 2 + 1 = 7
For which problem do you need to regroup 1 ten as 10 ones? Fill in the bubble next to the correct answer. Subtract 16 from 38, subtract 27 from 85, subtract 51 from 72
Answer:
subtract 27 from 85
Step-by-step explanation:
85
-27
———
58
7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracted from 15 and then the 8 tens becomes 7 tens so 7-2=5
58+27=85 to check your work
We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85
What is a numerical expression?A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Given that regroup 1 ten as 10 one
85 -27 = 58
Since 7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracbecomem 15 and then the 8 tens becomes 7 tens thus, 7-2=5
Therefore,
58 + 27 = 85
We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85
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Find the value of x. Show all your work for full credit.
Can anyone help me!!!
Answer:
Therefore the value of x is
[tex]x=5[/tex]
Step-by-step explanation:
Given:
Consider the figure such that
PQ || BC
AP = 20 , AB = 36
AQ = 5x , AC = 45
To Find:
x = ?
Solution:
In Δ APQ and Δ ABC
∠APQ ≅ ∠ACB {Corresponding angles are equal since PQ is parallel to BC}
∠A≅ ∠A ……….....{Reflexive Property}
Δ APQ~ Δ ABC….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}=\dfrac{PQ}{BC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}\\\\\dfrac{20}{36} =\dfrac{5x}{45}\\\\x=\dfrac{20\times 45}{36\times 5}=5\\\\x=5[/tex]
Therefore the value of x is
[tex]x=5[/tex]
Select TWO equivalent expression to the function 3x^2−12x−36.
Question 1 options:
3(x+6)(x−2)
3(x−6)(x+2)
(3x+6)(x−6)
(3x−6)(x+6)
Answer:
3(x-6)(x+2) and (3x+6)(x-6)
Step-by-step explanation:
The other two answers are wrong because the value for their x will be positive.
In 2019, Paul, a single taxpayer, has taxable income of $30,000 exclusive of capital gains and losses. Paul incurred a $1,000 short-term capital loss and a $4,000 long-term capital loss. What is the amount of his long-term capital loss carryover to 2019?
Answer:
Our answer is $2000
Step-by-step explanation:
Short term capital loss = $1000
Long term capital loss = $4000
Taxable Income = $30000
Long term capital loss carryover to 2019 = ($1000 + $4000) - $3000 = $2000
A tire for a car is 24 inches in diameter. If the car is traveling at a speed of 60 mi/hr, find the number of revolutions the tire makes per minute. (Round your answer to the nearest hundredth.)
Answer: The number of revolutions the tire makes per minute= 840.76
Step-by-step explanation:
Given : Diameter of tire = 24 inches
Speed of car = 60 mi/ hr
We know that 1 mile =63360 inches and 1 hour = 60 minutes
Then, Speed of car = ( 60 mi/ hr) x( 63360 inches) ÷ (60 minutes)
[tex]=\dfrac{60\times63360 }{60}[/tex] inches/minute
=63360 inches / minute
Circumference of tire = [tex]\pi (diameter)[/tex]
[tex](3.14)(24)=75.36\ inches[/tex]
Now , the number of revolutions the tire makes per minute = [tex]\dfrac{\text{speed of car}}{\text{Circumference of tire}}[/tex]
[tex]=\dfrac{63360}{75.36}=840.76433121\approx840.76[/tex]
Hence, the number of revolutions the tire makes per minute= 840.76
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. 1. Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees. 2. Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. 3. The lengths of sides A C and C B are congruent. 4. Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees. 5. Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answer:
The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.
Step-by-step explanation:
It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.
Let the acute angle be m∠A.
For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.
The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,
[tex]Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }[/tex]
So for acute angle 45° the ratio of Sin 45° and Cos 45° is:
[tex]\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1[/tex]
Hence one of the angles of a triangle is, m∠A = 45°.
Comparing with the options provided the triangle is,
Triangle ABC that has angle measures 45°, 45° and 90°.
Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.
Answer:
IT'S the second option
Step-by-step explanation:
Need help doing this question, thanks
Answer:
The first one.
Step-by-step explanation:
We can say lines L and K are parallel, because they have the same slope and different y intercepts.
This would mean they will always be moving in the same direction, hence causing them to never touch.
Why is the answer C?
Step-by-step explanation:
∫₋₂² (f(x) + 6) dx
Split the integral:
∫₋₂² f(x) dx + ∫₋₂² 6 dx
Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0. But we can also show this algebraically.
Split the first integral:
∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Using substitution, write the first integral in terms of -x.
∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Flip the limits and multiply by -1.
∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Rewrite f(-x) as -f(x).
∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
The integrals cancel out:
∫₋₂² 6 dx
Evaluating:
6x |₋₂²
6 (2 − (-2))
24
What is the radius of a sphere with a surface area of 144πcm2?
A. 36 cm
B. 12 cm
C. 6 cm
D. 4 cm
Answer:
Step-by-step explanation:
4π r²=144 π
r²=36
r=6 cm
A cube of mass m 1 = 7.0 kg is sitting on top of a second cube of the same size and mass m 2 = 0.7 kg while both are in free fall. Ignoring any air resistance, what is the magnitude of the normal force with which the bottom cube is acting on the top cube?
Answer:
0 N
Step-by-step explanation:
We are given that
[tex]m_1=7 kg[/tex]
[tex]m_2=0.7 kg[/tex]
Total mass =[tex]m_1+m_2=7+0.7=7.7 Kg[/tex]
We have to find the magnitude of the normal force with which the bottom cube is acting on the top cube.
When both cube are fall freely then
g=[tex]0m/s^2[/tex]
Then, the weight=[tex]mg=7.7\times 0=0 N[/tex]
The direction of weight is downward.
We know that
Normal force is equal to weight and act in opposite direction of weight.
When the weight is zero N then
The magnitude of the normal force with which the bottom cube is acting on the top cube=0 N
Use the graph that shows the solution to
f(x)=g(x) .
f(x)=−3/4x^2+3x+1
g(x)=2x
Graph A is the correct representation, as it aligns with the functions f(x) and g(x), resulting in the accurate intersection point (2, 4). Graph B does not accurately represent the functions based on the reported intersection point (4, 1).
The correct graph can be determined by analyzing the given functions and the specified intersection points. The functions are f(x) = -3/4 * x^2 + 3x + 1 and g(x) = 2x, and the reported intersection points are (2, 4) for graph A and (4, 1) for graph B.
To verify the accuracy, substitute the x-values into both functions:
Graph A (Intersection at (2, 4)):
f(2) = -3/4 * (2)^2 + 3 * 2 + 1 = 4
g(2) = 2 * 2 = 4
Both functions align, confirming the correctness of the reported intersection point.
Graph B (Intersection at (4, 1)):
f(4) = -3/4 * (4)^2 + 3 * 4 + 1 = 1
g(4) = 2 * 4 = 8
There is a discrepancy here, as the y-values do not match. Therefore, graph B does not accurately represent the functions f(x) and g(x).
In conclusion, graph A is correct since it accurately reflects the given functions and results in the reported intersection point (2, 4).
Diane received 300 votes in the election for student council president. That was 60% of the students who voted election. How many students voted in the election?
Answer:
500
Step-by-step explanation:
The problem statement tells you ...
300 = 0.60×voters
Dividing by the coefficient of the variable gives ...
300/0.60 = voters = 500
500 students voted in the election.
Answer:
500
Step-by-step explanation:
Two pools are being drained. To start, the first pool had 3700 liters of water and the second pool had 4228 liters of water. Water is being drained from the first pool at a rate of 31 liters per minute. Water is being drained from the second pool at a rate of 42 liters per minute.
This is a comparison problem involving rates. We multiply the rate of draining by the time and subtract the result from the initial amount, which gives us the amount of water after that time.
Explanation:This problem is considerate a comparison problem that involves rates of draining water from two pools. In these cases, it's crucial to keep the rates and the initial amounts separate to correctly solve the problem.
The first pool is initialy with 3700 liters of water and the draining rate is 31 liters per minute. The second pool from the start has 4228 liters and is being drained at a rate of 42 liters per minute.
To know the amount of water in each pool after any given time in minutes, we would multiply the rate by that time, and subtract the result from the initial amount of water.
For example, if we wanted to find out how much water was left after 10 minutes, we would do the following calculations:
For the first pool: 3700 - (31 * 10) = 3400 liters remained.For the second pool: 4228 - (42 * 10) = 3828 liters remained.Therefore, after 10 minutes, the first pool had 3700 liters and the second one had 3828 liters of water.
Learn more about Comparison problem here:
https://brainly.com/question/33509333
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