Answer:
0.73 and 0.92
Step-by-step explanation:
The answers are 0.73 and 0.92 because:
1) Subtract 0.54 with 0.35, you will get 0.19
2) Therefore, we know the patter is adding 0.19 for each number
3) 0.54 + 0.19 = 0.73
4) 0.73 + 0.19 = 0.92
Hope this helps!
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The next two terms in the pattern will be 0.73 and 0.92.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
aₙ = a₁ + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
The given series is an arithmetic series. Therefore, the common difference between any of the two terms in the series is,
Common difference = 0.35 - 0.16 = 0.19
Now, the next term of the series will be,
Next term = Previous term + common difference
= 0.54 + 0.19
= 0.73
Next term = 0.73 + 0.19
= 0.92
Hence, the next two terms in the pattern will be 0.73 and 0.92.
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A rocket leaves the surface of Earth at time t=0 and travels straight up from the surface. The height, in feet, of the rocket above the surface of Earth is given by y(t), where t is measured in seconds for 0≤t≤600. Values of y(t) for selected values of t are given in the table above. Of the following values of t, at which value would the speed of the rocket most likely be greatest based on the data in the table?
(1) t=100
(2) t=200
(3)t=300
(4) t=400
Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Speed is simply the rate of change of distance over time.
The greatest speed is at [tex]t = 400[/tex]
To calculate the time of the greatest speed, we simply calculate the slope between each interval.
The slope (m) of a line is:
[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]
When [tex]t = 100[/tex]
[tex](t_1,y_1) = (0,0)[/tex]
[tex](t_2,y_2) = (200,400)[/tex]
So, we have:
[tex]m = \frac{400-0}{200 -0}[/tex]
[tex]m= \frac{400}{200}[/tex]
[tex]m = 2[/tex]
When [tex]t = 200[/tex]
[tex](t_1,y_1) = (100,50)[/tex]
[tex](t_2,y_2) = (300,1360)[/tex]
So, we have:
[tex]m = \frac{1360-50}{300 -100}[/tex]
[tex]m = \frac{1310}{200}[/tex]
[tex]m = 6.55[/tex]
When [tex]t = 300[/tex]
[tex](t_1,y_1) = (200,400)[/tex]
[tex](t_2,y_2) = (400,3200)[/tex]
So, we have:
[tex]m = \frac{3200-400}{400 -200}[/tex]
[tex]m = \frac{2800}{200}[/tex]
[tex]m = 14[/tex]
When [tex]t = 400[/tex]
[tex](t_1,y_1) = (300,1360)[/tex]
[tex](t_2,y_2) = (500,6250)[/tex]
So, we have:
[tex]m = \frac{6250-1360}{500-300}[/tex]
[tex]m = \frac{4890}{200}[/tex]
[tex]m = 24.45[/tex]
From the above computation, the greatest speed (i.e. slope) is
[tex]m = 24.45[/tex]
The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]
Hence, the greatest speed is at [tex]t = 400[/tex]
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Find the midpoint of the line segment with the given endpoints (-1,-6) (-6,5)
The correct answer is (-7/2,-1/2) or (-3.5,-0.5) To find the midpoint of a segment, add both "x" coordinates, divide by 2. Then add both "y" coordinates, and divide by 2
A club is choosing 2 members to serve on a committee. The club has
nominated 3 women and 3 men. Based on chance alone, what is the
probability no women are chosen to be on the committee?
Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.
Step-by-step explanation:
We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.
If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.
If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:
p1 = 3/6 = 1/2.
Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:
p2 = 2/5
And the joint probability will be the product of the individual probabilities, then we have:
P = p1*p2 = (1/2)*(2/5) = 2/5.
The probability that no women are chosen to be in the committee is 2/5 or 0.40.
The probability that no woman is chosen to be on the committee is 0.40.
GivenA club is choosing 2 members to serve on a committee.
The club has nominated 3 women and 3 men.
The number of ways to select two persons from 6 will be:
[tex]\rm = ^6C_2[/tex]
Therefore,
The probability that no woman is chosen to be on the committee is;
[tex]= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40[/tex]
Hence, the probability that no woman is chosen to be on the committee is 0.40.
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A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a period of three months.) The increase in production can be modeled by the equation y = x6 − 25x4 + 199x2, where x is the number of quarters. What is the minimum duration required for the company to reach a production capacity of 4,975 units?
Answer:
5 months
Step-by-step explanation:
We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...
x^6 -25x^4 +199x^2 -4975 = 0
This can be factored in groups as ...
x^4(x^2 -25) + 199(x^2 -25) = 0
(x^4 +199)(x^2 -25) = 0
This has 4 complex solutions and 2 real solutions.
x^2 = 25
x = ±5
The duration required for capacity to reach 4975 units is 5 months.
Find the midpoint of the line segment with the given endpoints (-3,1 -2,8) (-4.92,-3.3)
coeffecient of x in -7xyz2
☽------------❀-------------☾
Hi there!
~
The coefficient of x in -7xyz2 is -7.
❀Hope this helped you!❀
☽------------❀-------------☾
Is 7.0001 is terminating or repeating decimals
Answer:
it is terminating
Step-by-step explanation:
solve integers -32+ 10
Answer:
-22
Step-by-step explanation:
You have to add -32+10
and you will get the answer -22
Answer:
-22
Step-by-step explanation:
On a number line, negative numbers go left and posative numbers go right. So on a numberline, if you find -32 and jump ten spaces to the right, you land on -22
make doubles. add 5+6
Answer:11
Step-by-step explanation:
The expression that represents the area of this rectangle is . When b = 10, the area of the rectangle is square units.
Answer: 8b and 80
Step-by-step explanation: H3h3
The Area of Rectangle is 80 unit².
What is Area of rectangle?The Area of rectangle is the product of its length to its width.
Area of rectangle = length x width
Given:
Expression that represents the area of this rectangle is 8b.
Now, b = 10
As, area of rectangle = l x w
area of rectangle = 8b
area of rectangle = 8 x 10
area of rectangle = 80 unit².
Hence, the area is 80 unit².
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what point on a number line repersent sae level
0 because anything below sea level will be in the negatives and anything above will be and positive number higher than 0 :D
Hope this helped
Classify the equation as a conditional equation, an identity, or a contradiction. 6x−10−8=9+4x−4x
Step-by-step explanation:
this is your answer.........
Answer:
conditional equation
Step-by-step explanation:
Collecting terms on both sides, we get
6x−10−86x−18=9+4x−4x=9
Adding 18 to both sides of the equation, we get
6x=27
This can be solved by dividing by 6 on both sides of the equation, which gives a unique solution of 92. So, this is a conditional equation.
Approximtely how many 27cubic volume cabinets will a container98,000cbic volume hold?
Answer: 3630
Step-by-step explanation:
Given that:
Volume of container = 98,000 cubic volume
Volume of cabinet = 27 cubic volume
The number of cabinets which the container will. Hold equals:
Volume of container / volume of cabinet
= 98000 cubic volume / 27 cubic volume
= 3629.6296
The container will hold approximately 3630 27 cubic volume of cabinet.
Hi okay no question hello
Answer:
Hello
Step-by-step explanation:
yUh GeT iNtO iT
P(n)=4n+1 ; find p(3)
Answer:
13
Step-by-step explanation:
you plug in 3 for n
4n+1
4(3)+1
12+1
13
How many terms of the series of - 3+0+3+6+9+...are needed to give a sum of 105?
Answer:
10
Step-by-step explanation:
Remember that the formula for the sum of an arithmetic series is:
[tex]S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term of the series.
We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the first term, d is the common difference, and n is the nth term.
From our sequence, we can see that the first term is -3.
Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.
Therefore, our explicit formula is:
[tex]x_n=-3+3(n-1)[/tex]
Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:
[tex]x_k=-3+3(k-1)[/tex]
Now that we know what x_k is, we can substitute that into our original equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:
[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]
And now, all we have to do is to solve for k.
First, distribute the 3:
[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]
Add within the parentheses:
[tex]105=\frac{k}{2}(3k-9)[/tex]
Multiply both sides by 2. This removes the fraction on the right:
[tex]210=k(3k-9)[/tex]
Distribute. We will get a quadratic:
[tex]210=3k^2-9k[/tex]
So, let's solve for k. Let's divide everything by 3:
[tex]70=k^2-3k[/tex]
Subtract 70 from both sides:
[tex]0=k^2-3k-70[/tex]
Factor. We can use -10 and 7. So:
[tex]0=(k-10)(k+7)[/tex]
Zero Product Property:
[tex]k-10=0\text{ or } k+7=0[/tex]
Solve for k for each equation:
[tex]k=10\text{ or } k=-7[/tex]
-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:
[tex]k=10[/tex]
Therefore, the number of terms we have in our series for our sum to be 105 is 10.
And we're done!
A tourist information center is between a bus station and a train station. When mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) The train station is located at point
Answer: The train station is located at point (5,1).
Step-by-step explanation:
Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).
A tourist information center is between bus station and train station.
i.e. tourist information center is a mid point of line joining bus station and train station.
Midpoint between (a,b) and (c,d) is given by :-
[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]
Let (a,b) be the coordinates of train station , then
[tex](1,4)=(\dfrac{-3+a}{2},\dfrac{7+b}{2})\\\\\Rightarrow\ 1=\dfrac{-3+a}{2}\ \ \ , 4=\dfrac{7+b}{2}\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1[/tex]
Hence, the train station is located at point (5,1).
Pls help with the explanation and answer ty!
find the value of x so that f (x)=7
Answer:
i think its 24
Step-by-step explanation:
Lila works 40 hours a week and earns $9 an hour . Her baby stays with a sitter during the hours Lila works . Lila pays the sitter $5 an hour . After paying the sitter , how much of her paycheck does Lila have left
Answer: $160
Step-by-step explanation: If she works 40 hours a week, than that is $360 a week, if she pays the sitter $5 a week, then that means she pays the sitter $200 a week. Subtract and you get $160.
Question 8
Solve the equation.
1/3x + 205
Your answer:
A.-9
B.13
C.9
Answer: none of thoses
Step-by-step explanation:
What type of number is 3π+1?
Answer:
irrational
Step-by-step explanation:
I hope it helped you!!
Answer:
10.42478
Step-by-step explanation:
Find the surface area of a square pyramid if the area of the base is 324 cm squared and the height is 40 cm.
Answer:
height h = 324 cm
slant height s = 324.61669704438 cm
side length a = 40 cm
lateral edge length e = 325.23222472566 cm
1/2 side length r = 20 cm
volume V = 172800 cm^3
lateral surface area L = 25969.33576355 cm^2
base surface area B = 1600 cm^2
total surface area A = 27569.33576355 cm^2
Step-by-step explanation:
Total Surface Area of a square pyramid:
A = L + B = a^2 + a√(a^2 + 4h^2))
A = a(a + √(a^2 + 4h^2))
Agenda:
h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
L = lateral surface area
B = base surface area
A = total surface area
3x + 2(4x - 4) = 3
What’s the answer?
Solve and graph -4<-1-4x<-1
Answer:
x<3/4 and x>0
for graphs, refer to the images attached.
Step-by-step explanation:
-1-4x > -4 AND -1-4x <-1
-1-4x >-4-4x > -3x < 3/4-1-4x<-1-4x<0x>01-89. On graph paper, draw the quadrilateral with vertices A(–1, 3), B(4, 3), C(–1, –2), and D(4, –2). a. What kind of quadrilateral is this?
Answer:
it is a square
because
as we can see in the graph the
distance from A to B is 5 cm
distance from B to C is 5 cm
distance from C to D is 5 cm
distance from D to A is 5 cm
please mark me as the brainliest I really need it
Graph the line with slope -1/2
passing through the point (-2, 4).
This image should help with that.
Can someone help pls the question in the pic (geometry)
Answer:
Reflection over y axis, and translate right 1
Step-by-step explanation:
What is 15 x minus 3 y = 0 written in slope-intercept form? y = 5x y = negative 5 x x = one-fifth y x = 5 y
Answer:
y=5x
Step-by-step explanation:
Answer:
y=5x
Step-by-step explanation:
In 1970, a farmer using a two-row combine with a corn head could easily harvest 0.75 ha (1.85 acres) per hour and a typical corn yield was 5000 kg/ha (80 bu/acre). Before 1940, most corn was harvested by hand and a skilled person could harvest 250 kg/h (10 bu/h). Calculate the productivity ratio.
Answer:
The value is [tex]w = 6.7 \%[/tex]
Step-by-step explanation:
Generally the productivity rate is mathematically represented as
[tex]P_r = K * Z[/tex]
Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha
Now considering 1970
The productivity rate is
[tex]P_r = 0.75 *5000[/tex]
=> [tex]P_r = 3750 \ kg/h [/tex]
Now considering 1940
The productivity rate is given as [tex]P_R = 250 \ kg/h [/tex]
Generally the productivity ratio is mathematically ration is mathematically represented as
[tex]w = \frac{P_R}{P_r} * 100[/tex]
=> [tex]w = \frac{250}{3750} * 100[/tex]
=> [tex]w = 6.7 \%[/tex]