Answer:
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PLEASE HELP ME WITH THIS ALGEBRA QUESTION!! THANK YOU!!
Answer:
The first four terms of the sequence are: {-10,-23,-62,-179}
Step-by-step explanation:
Given recursive formula is:
[tex]a_n = 3a_{n-1}+7[/tex]
First term = a1 = -10
The first term is already known. In order to find the next terms, we will put n=2,3,4 in the recursive formula.
Putting n=2
[tex]a_2 = 3a_{2-1}+7\\a_2 = 3a_1+7\\a_2 = 3(-10)+7\\a_2 = -30+7\\a_2 = -23[/tex]
Putting n=3
[tex]a_3 = 3a_{3-1}+7\\a_3 = 3a_2+7\\a_3 = 3(-23)+7\\a_3 = -69+7\\a_3 = -62[/tex]
Putting n=4
[tex]a_4 = 3a_{4-1}+7\\a_4 = 3a_3+7\\a_4 = 3(-62)+7\\a_4 = -186+7\\a_4 = -179[/tex]
Hence,
The first four terms of the sequence are: {-10,-23,-62,-179}
What is the probability that a randomly selected camper likes swimming or having a cookout, but not both?
A.
B.
C.
D
The probability that a randomly selected camper likes to have a cookout or swimming, but not both, is 0.10.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
The Venn diagram displays the campers’ preferences.
One circle is labeled S, 0.06,
the other circle is labeled C, 0.04,
the shared area is labeled 0.89,
and the outside area is labeled 0.01.
The probability that a randomly selected camper likes to have a cookout or swimming, but not both,
= 0.06 + 0.04
= 0.10
Therefore, 0.10 is the required probability.
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how many hectares of land are there in a field that is 450 m long and 1200 dm wide.
Answer:
Step-by-step explanation:
Given
[tex]Length = 450\ m[/tex]
[tex]Width = 1200\ m[/tex]
Required
Determine the number of hectares in this dimension
First, we need to calculate the area of the land
[tex]Area = Length * Width[/tex]
[tex]Area = 450m * 1200dm[/tex]
Convert dm to m
[tex]Area = 450m * 120m[/tex]
[tex]Area = 54 000 m^2[/tex]
[tex]1 hectare = 0.0001m^2[/tex]
So, we have:
[tex]1\ hectare = 0.0001m^2[/tex]
Multiply by 54000
[tex]Hectare = 0.0001 * 54000[/tex]
[tex]Hectare = 5.4[/tex]
Hence, there are 5.4 hectares
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y=−16x 2 +193x+128
Let x be -b/2a
x = -193/2•(-16)
x = -193/-32
x = 6.03125
Now, plug this value of x into every x in the function and simplify. The max is the y value.
Can you finish?
The time at which the rocket will hit the ground to the nearest hundredth of seconds is 13 seconds.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given height of tower y in terms of time is seconds x
y = -16x² + 193x + 128
The height of the tower when the rocket hit the ground will be zero.
Thus, y = 0
0 = -16x² + 193x + 128
16x² - 193x - 128=0
By quadratic equation formula,
x = [-(-193) ± √((-193)²-4×16×(-128))]/ 2×16
x = [193 ± 213.168]/32
x = 12.69 and x = -0.63 since time can be never negative thus 12.69 seconds will be correct.
12.69 to the nearest hundred is 13.
Hence "The time at which the rocket will hit the ground to the nearest hundredth of seconds is 15 seconds".
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If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section?
Answer:
Yes, that's right: the cross section will be a rectangle (but also a parallelogram).
Step-by-step explanation:
The minimum diameter for a hyperbolic cooling tower is 57 feet...
Answer:
Can give you the example then you have to figure out.
Step-by-step explanation:
We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1
a
2
x
2
−
b
2
y
2
=1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a
2
and \displaystyle {b}^{2}b
2
to complete the model.
First, we find \displaystyle {a}^{2}a
2
. Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3 meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a
2
=900.
To solve for \displaystyle {b}^{2}b
2
, we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,
x
2
a
2
−
y
2
b
2
=
1
Standard form of horizontal hyperbola
.
b
2
=
y
2
x
2
a
2
−
1
Isolate
b
2
=
(
79.6
)
2
(
36
)
2
900
−
1
Substitute for
a
2
,
x
,
and
y
≈
14400.3636
Round to four decimal places
The sides of the tower can be modeled by the hyperbolic equation
\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1
900
x
2
−
14400.3636
y
2
=1,or
30
2
x
2
−
120.0015
2
y
2
=1
The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.
a = 28.5, b ≈ 52.65
[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
Reasons:
The parameters of the hyperbolic cooling tower are;
Minimum diameter = 57 feet
The height at which the diameter occurs = 155 ft.
The diameter of the tower = 175 feet
Total height of the tower = 200 feet
Height at which the center of the hyperbola occurs = 155 feet
Solution:
The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]
The center of the hyperbola = (0, 155)
[tex]a = \dfrac{57}{2} = 28.5[/tex]
At y = 155,
Therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]
At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]
Therefore;
[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]
b² = 2769.0340909
b ≈ 52.62
The equation of the hyperbola is therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
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What is the value of 5x when x=3.2
Answer: 16
Step-by-step explanation:
All you have to do is plug 3.2 into the expression. So 5 * 3.2 is 16.
what apple group is the correct one
Answer:
i don`t understand you
Step-by-step explanation:
but i think i phone...?
Answer:
ummm there is no other context did you mean to post a picture? All I could find was this
The Apple User Group Connection (AUGC) was established in 1985 by Apple and led by Apple employee Ellen Petry Leanse.
Help Please!! I WILL give brainliest and thanks!!
Which of these inequalities are equivalent to r > -11?
Check all that apply.
-r -33
-3r 33
Random answers get reported
Answer:
ez pts tysm
Step-by-step explanation:
The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Find
a) the first term and common ratio
b) the sum of the first five terms
Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
Calculating Percent Change
Determine the Percent Change for each of the following.
Express each answer as a percent, rounded to the nearest tenth.
A quantity decreases from 20 to 15-% decreased
A quantity increases from 15 to 20-% increase
The price of a Latte dropped from $3.12 to $2.9-% decrease
The cost of Gasoline rose from $2.9 to $3.12-% increase
Answer:
the last one is an increase of $.22
Step-by-step explanation:
the last one is an increase of $.22
Combine 2x^2+5x-6+8x
5+1000000000000000000
Answer:
1000000000000000005
Answer:
1000000000000005
Step-by-step explanation:
Please help.
Will rate Brainliest!
Thanks in advance!
Answer:
y = 8x + 13
Step-by-step explanation:
slope-intercept form: y = mx + b
Given equation: [tex]y = -\frac{1}{8}x -2[/tex]
Second equation: unknown
Slope: unknown
Given point: (-2, -3)
When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.
Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:
y = mx + b
-3 = 8(-2) + b
-3 = -16 + b
13 = b
The y-intercept is 13.
Now that we know the slope and the y-intercept, we can write the equation:
y = 8x + 13
Hope this helps :)
how many 2/3 size pieces are in 4 wholes
Divide 4 wholes by 2/3 pieces to fnd number of pieces.
4 / 2/3
When you divide by a fraction, flip the fraction over then multiply:
4 x 3/2 = (4 x 3)/2 = 12/2 = 6
There are 6 pieces.
Answer:
6
Step-by-step explanation:
lets put this in terms of 3, because of 2/3. the number above the three will be divided by three to get to four. So if we multiply three by four to get twelve, we can put that over 3, and then find our answer. 12/3=4, so we know that is correct. and since we need to find how many 2/3 pieces we need, we divide 12/3 by 2/3 to get 6. so you need 6 2/3 pieces to get four wholes.
PLEAS HURRY I HAVE NO TIME LEFT
PLEASE HELP ME WITH THIS QUESTION
Question: Name each polygon by its number of sides and then classify it as CONVEX or CONCAVE and REGULAR or IRREGULAR
Answer:
no you scam me if I see what is promises I will help you
10 kg of potatoes cost $4.50. How much will 50 kg of potatoes cost at this rate?
Answer:
$22.5
Step-by-step explanation:
10 kg=$4.50
50kg = x
(do cross multiplication)
10x =225
x=$22.5
This is my study island math and I need all the questions to be done so I’m doing them in order.
Answer:
A
Step-by-step explanation:
Hope I helped
Answer:
The answer is A, $11.60
Step-by-step explanation:
0.66=spent 9 minutes
0.66x9=5.94
5.94+5.66=$11.60
Btw, luv ur profile pic uwu!
1/4 divided 3 please help me
Answer: 1/12
Step-by-step explanation:
Please help I’m stuck on this question
Answer:
C. Supplementary angles
Step-by-step explanation:
Supplementary angles always equal 180 degrees.
The answer is (C) because, the sum of both the angle is equals to 180° i.e they are pair of supplementary angles.
A ceramics teacher orders 5 blocks of gray clay for every 3 blocks of red clay.
How many blocks of gray clay will the teacher order if she orders 15 blocks of red
clay? *
17
20
25
28 ( plz help if you can)
Answer:
25
Step-by-step explanation:
trust me it's right it might be easier if you use paoer
x^2-x-12 factor completely
Write an equation in point-slope form of the line that passes through (-4,1) and (4.3).
Answer:
a
Step-by-step explanation:
:P
A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
Which of the following shows the correct sums that would be found when clustering is used to find the answer to the problem 34 x 12?
340 + 68 = 408
340 + 34 = 374
340 + 68 = 398
300 + 8 = 308
The first option is correct.
The calculation is as follows:if we multiply the 34 and 12 so it comes 408
And according to first option, it we add 340 and 68 so it comes 408.
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00
3-2 Checking Accounts
12. Justin Nucci listed these items on his deposit slip: (bills) 8 one-hundreds,
27 fifties, 83 fives, 141 ones; (coins) 13 quarters, 117 nickels; (checks) $317.94,
$57.89, $527.24 and $77.49. He received cash back of 30 twenties and 11 tens.
What total deposit did he make?
603
120] Chapter 3 Banking
Answer: 4,405.66
Step-by-step explanation:
Add all the amounts together.
Use trigonometric identities to transform the left side of the equation into the right side (0 < < /2).
37/6 divided by 1/2.
Answer: 12 1/3
hope this helps.. stay safe and have a great day
Step-by-step explanation:
i give up on math. help.
Answer:
try b
Step-by-step explanation:
Answer:
The answer is A. g(x) = f(x) + 4
If y= 6x + 8 what is y when x= -3
Answer:
y=2
Step-by-step explanation:
y = 26
If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:
y = 6(-3) + 8 now you can simplify it and solve for y
6 x -3 = -18
18 + 8 = 26
y = 26