Answer: 4 units
Step-by-step explanation:
The given position function: [tex]x(t)=-t^3+6t^2-9t+42.[/tex], where t≥0.
To determine: Total distance traveled by the particle from 0≤ t ≤ 4.0.
At t=0,
[tex]x(0)=-(0)^3+6(0)^2-9(0)+42=42\\[/tex]
At, t=4,
[tex]x(4)=-(4)^3+6(4)^2-9(4)+42\\\\=-64+6(16)-36+42=38[/tex]
Total distance traveled by the particle from 0≤ t ≤ 4.0 = |42-38| units
= 4 units
Hence, the distance traveled by the particle from 0≤t≤4.0 is 4 units.
1.
Plot the figure on a graph. Label the vertices: P(-2, 4), Q(3, 4), R(3,1), S(-2,
1).
What is the shape of the figure?
Express in simplest radical form
Answer:
gg
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
2 x 2 =4
Which questions are True or False?
1.) Supplementary angles always add up to 90°.
2.) Complementary angles always add up to 180°.
3.) Vertical angles always have the same measure.
4.) ∠x is complementary to the 34°angle.
5.) ∠z is vertical to the 112°angle.
6.) ∠y is a linear pair with the 146°angle.
Answer:
1) false
2) false
3) true
4)false
5) true
6) true
Find the percent of a number 20% of 155
Hey there!
[tex]\text{The word \underline{of} means \underline{multiply} in \underline{mathematical terms}}[/tex]
[tex]\bold{Equation: 20\% \times 155}\\\bold{20\% = \dfrac{20}{100}=\dfrac{20\div20}{100\div20}=\dfrac{1}{5}}\\\bold{\dfrac{1}{5}\times 155=?}\\\bold{155\times1=155}\\\\\bold{\dfrac{155}{5}=31}\\\boxed{\boxed{\bold{Answer: 31}}}\huge\checkmark[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\frak{Amphitrite1040:)}[/tex]
A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the length of the rectangle.
Answer:
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
Step-by-step explanation:
Step(i):-
Let 'x' be the length of the rectangle
Given that the width is 3 feet shorter than the length
The width of the rectangle = x -3
Area of the rectangle = length × width
Step(ii):-
Area of the rectangle = length × width
= x ( x-3)
Given that the area of the rectangle = 70 square feet
x ( x-3) = 70
⇒ x² - 3x - 70 =0
⇒ x² - 10 x + 7 x - 70 =0
⇒ x (x -10) +7( x-10) =0
⇒ ( x+7) ( x-10) = 0
⇒ x =-7 and x=10
Final answer:-
we choose x=10
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
You owe $748.11 in taxes, and you have paid $692.40. Which statement best describes your refund/taxes due?
A): You owe an additional $55.71.
B): You will receive a refund of $55.71.
C): You owe an additional $155.71.
D): You will receive a refund of $155.71.
Answer:
A.
Step-by-step explanation:
748.11 - 692.40 = 55.71
so you will still owe 55.71
Answer: A). You owe an additional $55.71.
Hope this helps :)
Nora baked 40 cupcakes. She ate 4 cupcakes and gave 25% of the remaining
cupcakes to her neighbours. How many cupcakes did Nora have left?I want this answer it percentage
Answer:
27 cupcakes left
In percentage of the number of cupcakes left after she ate 4 = 75%
In percentage of the total number of cupcakes she baked = 67.5%
Step-by-step explanation:
Given that Nora baked 40 cupcakes and ate 4 cupcakes then, the remainder
= 40 - 4
= 36 cupcakes
If she gave 25% of the remaining, the number of cupcakes given
= 25% * 36
= 25/100 * 36
= 9 cupcakes
the number of cupcakes left
= 36 - 9
= 27 cupcakes
In percentage of the number of cupcakes left after she ate 4, this will be
= 100% - 25%
= 75%
In percentage of the total number of cupcakes she baked
= 27/40 * 100%
= 67.5%
You place a 1-dollar bet on the number 17 at Las Vegas, and your friend places a 1-dollar bet on black (see Exercises 1.1.6 and 1.1.7). Let X be your winnings and Y be her winnings. Compare E(X), E(Y ), and V(X), V(Y). What do these computations tell you about the nature of your winnings if you and your friend make a sequence of bets, with you betting each time on a number and your friend betting on a color
Answer:
E(x) = -$0.05263
E(y) = -$0.05263
V(x) = 0.9972
V(y) = 32.23
the expectations are the same, both will lose the same amount of money if they play for 38 times.
Though Variance is different. The girl betting on colors has little chance to gain and lose but the boy betting on number has huge deviation
Step-by-step explanation:
Given that; you place a 1-dollar bet on the number 17 at Las Vegas and your friend places a 1-dollar bet on black.
Let x represent your winnings and y represent your friends winnings
we know that, There are 18 black slots, 18 red slots and two green slots (0 and 00) on a US roulette wheel.
so, the chances of getting black(red) = 18/38
now, E(y) = (18/38)$1 + (20/38)(-$1)
E(y) = -$0.05263
Now, bets made on the chart of the various numbers 1 to 36 and zero, Just put a chip down in the middle of the square with the number you select. If it comes up, it pays 35-to-1. It is called a straight up bet.
hence, the chance of getting selected number will be 1/38
so E(x) will be;
E(x) = (1/38)$35 + (37/38)(-$1)
E(x) = -$0.05263
So, V(x) will be;
V(x) = [ 1 - (1/19)² ]
= 1 - 0.00277
V(x) = 0.9972
V(y) = { [ (35)² × (1/38) ] - (1/19)² }
= 32.2368 - 0.00277
V(y) = 32.23
Therefore, the expectations are the same, both will lose the same amount of money if they play for 38 times.
Though Variance is different. The girl betting on colors has little chance to gain and lose but the boy betting on number has huge deviation.
Sarah interviewed for a job that promised her a starting salary of $37,000
with a $1550 raise at the end of each year. What will her salary be during
her sixth year if she accepts the job
The price of a new car was $22,800vin April. However, the price of the car was reduced 5% in May. Find the price in May.
Answer: 1140
Step-by-step explanation: Sorry if its wrong
Answer:21660
Step-by-step explanation:
95*22800/100
8. There were 512 people at the Talent Show,
Admission was $1.25 for adults and 50
for children. The receipts were $406.75.
How many of each attended?
Answer:
7.9 of each
Step-by-step explanation:
can someone explain to me what it means to be marked as branliest? & what it does ?
Honestly, for me, it just provides bragging rights. Also, I guess it makes you feel better about getting your rank higher. (～￣▽￣)～
____________________________________________________________
正直なところ、私にとって、それは自慢する権利を提供するだけです。また、ランクを上げることで気分が良くなると思います。(～￣▽￣)～
What happens to the mode of the data set shown below if
the number 16 is added to the data set?
18
19
26
24
18
25
19
20
19
OA) The mode is increased by 1.
OB) The mode does not change.
Oc) The mode is increased by 2.
OD) The mode is increased by 7.
Answer:
OB) The mode does not change
The probability of eating a sugar cookie is 0/35
the chance of eating a sugar cookie is ____
Answer:
0
Step-by-step explanation:
Well if the probability is 0 then the chance is 0
A series of maths books consists of four volumes. The first has x pages and the second has 54 more. The third and fourth volumes have 32 more pages than the second volume. The number of pages of all volumes is 866. Calculate the number of pages in each volume.
Answer:
1st volume = 160
2nd volume = 160 + 54 = 214
3rd volume = 160 + 54 + 32 = 246
4th volume = x + 54 + 32 = 246
Step-by-step explanation:
Given that:
Number of volumes = 4
1st volume = x pages
2nd volume = 54 more = x + 54
3rd volume = 32 more = x + 54 + 32
4th volume = 32 more = x + 54 + 32
Total number of pages = 866
Hence,
1st + 2nd + 3rd + 4th = 866
x + x + 54 + x + 54 + 32 + x + 54 + 32 = 866
4x + 226 = 866
4x = 640
x = 160
1st volume = 160
2nd volume = 160 + 54 = 214
3rd volume = 160 + 54 + 32 = 246
4th volume = x + 54 + 32 = 246
Account A has a simple annual interest rate of 2% and Account B has a simple annual interest rate of 3.5%. How much more interest do you eam per year when
you deposit x dollars in Account B instead of A?
9514 1404 393
Answer:
0.015x
Step-by-step explanation:
The amounts earned at the different rates are ...
at 2%: 0.02x
at 3.5%: 0.035x
The difference in earnings is ...
0.035x -0.02x = 0.015x
Q2) A meat pie contains chicken and turkey in the ratio 4 : 1. ( 3 marks)
The pie contains 300 g of chicken.
How much turkey is in the pie?
How much meat is there altogether in the pie?
Plz i begggg
please
a recipe for 30 cookies calls for 4 tablespoons of sugar. If you make 40 cookies and use 5 tablespoons of sugar, will the cookies taste the same? HELP ASAP WILL MARK BRAINLISET IF CORRECT
I need to find what's in those four boxes
Answer:
-500 + 200, -300
|0 - 200|, +200
Step-by-step explanation:
what is x10=22130 bc i have no idea
Answer:
x = 2213
Step-by-step explanation:
We need to find the value of x, which is multiplied by 10. We know that 10x = 22130, so all we need to do is divide both sides by ten.
10x ÷ 10 = x
22130 ÷ 10 = 2213
Therefore, x = 2213
NOTE:
I'm not sure if you meant to type x10, because if so, that's an entirely new equation. If you just meant 10x, you can ignore this.
To solve this, you have to take the root of both sides and solve.
Exact Form:
x = 10 √ 22130 , − 10 √ 22130
Decimal Form: x = 2.71955684 … , − 2.71955684 …
Answer:
x = 2213
Step-by-step explanation:
22130/10 = 2213
Rewrite the inequality:
a ≥ 9
I need help on this problem
Please
The tutor button has not been working
Answer: 14 and 3.5
Step-by-step explanation:
If the triangles are congruent,
then y = [?].
4x+1
13
2x+y
8x-2y
Answer:
4x+1
Step-by-step explanation:
The way i got this was because sometimes on shapes there are 4 side and so you would multiply the number of sides then add some more to it.
What is the mean income of the following three people surveyed? Person A: S22,000, Person B: $31,000, Person :
$21,000. Round to the nearest $100
Answer:
$24,700
to get this answer you add all the numbers together so in this case 22,000 31,000 and 21,000 and you get 74,000 then you divide by how many numbers you originally had so in this case 3. so you get 24,666.666666667 and since the tens place is 5 or higher you round the hundreds up one so you get 24,700.
Here's the work
22,000+31,000+21,000=74,000
74,000÷3=24,666.666666667
which rounds to 24,700
Which Fraction is equivalent to 3/12?
3/4
1/4
3/36
Answer:
1/4
Step-by-step explanation:
3/12 ÷3= 3÷3=1 and 12÷3=4
Subtract the complex numbers.
(5 + 4i) - (7 + 8i)
Answer:
Step-by-step explanation:
5 + 4i - 7 - 8i
-2 - 4i
100 point please help me
Answer:
it says 5 points
Step-by-step explanation:
Answer:
2m+4
(twice the students in maths(2m) plus four more (+4))
The random variable R has the binomial distribution B (12,0.35) .find P(R>4)
Answer: [tex]0.416655[/tex]
Step-by-step explanation:
If random variable X has the binomial distribution B(n, p), then
[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex]
, where n= Total number of trials, x = number of successes , p= probability of success in each trial.
Given: The random variable R has the binomial distribution B (12,0.35).
n= 12, = 0.35
[tex]P(R>4)=1-P(R\leq4)\\\\=1-[P(R=0)+P(R=1)+P(R=3)+P(R=4)]\\\\\\=1-[^{12}C_0(0.35)^{0}(1-0.35)^{12}+^{12}C_1(0.35)^{1}(1-0.35)^{11}+^{12}C_2(0.35)^{2}(1-0.35)^{10}+^{12}C_3(0.35)^{3}(1-0.35)^{9}+^{12}C_4(0.35)^{4}(1-0.35)^{8}]\\\\= 1-[(1)(0.65)^{12}+(12)(0.35)(0.65)^{11}+\dfrac{12!}{2!10!}(0.35)^2(0.65)^{10}+\dfrac{12!}{9!3!}(0.35)^3(0.65)^{9}+\dfrac{12!}{8!4!}(0.35)^4(0.65)^{8}]\\\\=1-0.583345\\\\\approx0.416655[/tex]
Hence, P(R>4)=0.416655
Simplify: x^2-16/x-4 What does the given expression simplify to? What is the excluded value of x for the given expression?
Step-by-step explanation:
Difference of Squares: a² - b² = (a + b)(a - b)
(x² - 16) / (x - 4)
= [(x + 4)(x - 4)] / (x - 4)
= x + 4, where x =/= 4.
Answer:
1. (x+4)
2. 4
Step-by-step explanation:
got right on edge
What are the roots of the equation 16x2 + 40x + 27 = 0 in simplest a + bi form?
9514 1404 393
Answer:
-5/4 +i(√2)/4 and -5/4 -i(√2)/4
Step-by-step explanation:
I find simplest form to be easier to get to if the leading coefficient is 1. Dividing by 16, we have ...
x^2 +5/2x +27/16 = 0
Completing the square by adding and subtracting the square of half the x-coefficient, we get ...
(x^2 +5/2x +25/16) +27/16 -25/16 = 0
(x +5/4)^2 = 2/16
Subtracting 2/16, taking the square root, and subtracting 5/4 gives ...
x +5/4 = ±√(-2/16)
x = -5/4 ±i(√2)/4
The roots are -5/4 +i(√2)/4 and -5/4 -i(√2)/4.