Answer:
60500
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 4 and d = 7 - 4 = 3, thus
[tex]S_{200}[/tex] = [tex]\frac{200}{2}[/tex] [ (2 × 4) + (199 × 3) ]
= 100(8 + 597)
= 100 × 605
= 60500
If you are good at figuring out sequences in math please help! Rewarding more points!
Answer:
-62.5008
Step-by-step explanation:
Find the pattern first: -75/15 = -5
Find the first 7 terms: -3/-5, 3/25, -3/125, 3/625
Add: -62.5008
Answer:
-62.5008
Step-by-step explanation:
The terms form a geometric sequence with first term -75 and common ratio -1/5. The sum of n terms of such a sequence is...
Sn = a1(1 -r^n)/(1 -r)
For the values of a1, r, and n, this sum is ...
S7 = -75(1 -(-1/5)^7)/(1 -(-1/5)) = -75(1 +1/78125)/(1 +1/5)
= -75(13021/15625) = -62 313/625
= -62.5008
The sum of the first 7 terms of the sequence is -62.5008.
A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. A regular pentagon has an apothem with a length of 3 centimeters and a perimeter of 21.8 centimeters. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2
Answer:
C. [tex]32.7cm^{2}[/tex]
Step-by-step explanation:
Area = (Perimeter x apothem) / 2
Area = 21.8 x 3 / 2
Area = 65.4 / 2
Area = [tex]32.7cm^{2}[/tex]
C. The area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².
Area of the regular pentagonThe area of the regular pentagon is calculated as follows;
Area = aP/2
where;
a is apothem of the pentagonP is perimeter of the pentagonArea = (3 x 21.8)/2
Area = 32.7 cm²
Thus, the area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².
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A rocket is launched from atop a 104-foot cliff with an initial velocity of 110 ft/s. A. Substitute the values into the vertical motion formula . Let h = 0. B. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
Answer:
7.68 s
Step-by-step explanation:
The vertical motion formula is:
[tex] h_{t} = h_{0} + v_{0}t - \frac{gt^{2}}{2} [/tex]
Where:
h(t): is the final height = 0
h(0): is the height of the cliff = 104 foot
v(0): is the initial velocity = 110 ft/s
g: is the gravity = 9.8 m/s² = 32.15 ft/s²
Hence, from the vertical motion formula we can find the time that will take the rocket to hit the ground:
[tex] 0 = 104 + 110*t - \frac{32.15t^{2}}{2} [/tex]
[tex] 0 = 104 + t(110 - 16.08t) [/tex]
We have two solutions:
t₁= -0.84 s
t₂ = 7.68 s
We will take the positive value, thus the time that will take the rocket to hit the ground is 7.68 s.
I hope it helps you!
1. Which student correctly simplified the expression 5.2 + 3.6x – 8 + x?
To simplify the expression 5.2 + 3.6x - 8 + x, combine like terms to get -2.8 + 4.6x, which is the final simplified expression.
Explanation:The student's question involves simplifying the expression 5.2 + 3.6x – 8 + x. To simplify the given algebraic expression, combine like terms. Like terms in this expression are the constant terms (5.2 and -8) and the variable terms (3.6x and x).
First, add the constant terms together:
5.2 - 8 = -2.8
Then, combine the variable terms:
3.6x + x = (3.6 + 1)x = 4.6x
Now, put the constants and variable terms together to get the simplified expression:
-2.8 + 4.6x
To check if the simplified expression is reasonable, ensure that all like terms have been correctly combined. There is no further simplification possible, so this is the final answer.
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If 2 liters of sea water contain 70 grams of salt, how much salt is in 32 liters of sea water?
Answer:
1120 grams
Step-by-step explanation:
The amount of sea water is directly proportional to the amount of salt in the water.
Let the amount of sea water be W and the amount of salt be S.
This means that:
W α S
=> W = kS
where k = constant of proportionality
2 liters of sea water contain 70 grams of salt Therefore:
2 = k * 70
k = 2 / 70 = 1/35
Therefore, for 32 liters of sea water:
32 = 1/35 * S
S = 35 * 32
S = 1120 grams
There are 1120 grams of salt in 32 liters of water.
Keiko uses 8.8 pints of white paint and blue paint to paint her bedroom walls. 4/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
1.76pints of blue paintStep-by-step explanation:
The total number of paint used = 8.8pints
If 4/5 of this amount is white paint, then the amount of white pint is expressed as;
[tex]= \frac{4}{5}*8.8\\= \frac{35.2}{5}\\[/tex]
= 7.04
This means the amount of white paint used is 7.04pints.
amount of blue paint used = Total amount of paint - amount of white paint
amount of blue white paint used = 8.8 - 7.04
amount of blue paint used = 1.76pints of paint
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answer:
C.
D.
E.
Step-by-step explanation:
The two options that yield the same value for 'x' as the equation 'Three-fifths (30 x minus 15) = 72' are '3 (6 x minus 3) = 72' and 'x = 4.5'. The confusion can be eliminated by simply breaking down and solving the initial equation for 'x', and then substituting the calculated value for 'x' into the optional equations.
Explanation:To discover which options yield the same value as 'Three-fifths (30 x minus 15) = 72', we first need to solve the given equation for 'x'. This can be done as follows:
Multiply both sides by 5/3 to get rid of the 3/5 in front of the bracket: (30 x minus 15) = 120,Add 15 to both sides to isolate 30x on the left side: 30x = 135,Finally, divide by 30: x = 4.5.Substitute x = 4.5 into each option:
For '18 x minus 15 = 72', 18(4.5) - 15 isn’t equal to 72, so this is not correct.For '50 x minus 25 = 72', 50(4.5) - 25 isn’t equal to 72, so this isn’t correct as well.For '18 x minus 9 = 72', 18(4.5) - 9 isn’t equal to 72 either, hence, it is also incorrect.For '3 (6 x minus 3) = 72', 3(6*4.5 - 3) equals to 72, so this is correct.For 'x = 4.5', this is obviously correct as it matches our calculated value.Therefore, '3 (6 x minus 3) = 72' and 'x = 4.5' provide the same value for x as the initial equation 'Three-fifths (30 x minus 15) = 72'.
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What is the value of s3 when: (infinite geometric series)
The value of S₃ is 65/9.
what is a geometric series?A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. S= a + ar + ar² + ar³+ . . .
a=start term r =common ratio
Given here, the nth term is 5(1/3)ⁿ⁻¹
therefore the sum of the first 3 terms of the geometric series is
S₃ = 5(1/3⁰) +5(1/3)¹+5(1/3)²
= 1+ 5/3 + 5/9
= 65/9
Hence the final answer is 65/9
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Deanna has a balance of $324.55 in her checking account. She uses her debit card to pay$102.00 for a concert ticket. What is the balance in her checking account now? *
Answer:
$222.55
Step-by-step explanation:
Answer:
$222.55
Step-by-step explanation:
$324.55-$102.00
Rewrite the expression in the form 4^n4 n 4, start superscript, n, end superscript. (4^{6})(4^{-8})=(4 6 )(4 −8 )=(, 4, start superscript, 6, end superscript, ), (, 4, start superscript, minus, 8, end superscript, ), equals
To multiply powers with the same base, like (4^6)(4^-8), add the exponents to get 4^(6-8) = 4^-2. Converting the negative exponents gives us 1/4^2 or 1/16 as the simplified expression.
Explanation:To rewrite the expression in the form 4n4n, we use the rule that when multiplying two numbers with the same base, we add their exponents. So, (46)(4-8) = 4(6 + (-8)) = 4-2 = 1/42 = 1/16.
When multiplying powers with the same base, you simply add the exponents. In the expression (4^{6})(4^{-8}), we add the exponents 6 and -8. The rules of exponents tell us that 4^{6} \times 4^{-8} = 4^{6-8} = 4^{-2}. Negative exponents indicate the reciprocal of the base raised to the positive of that exponent. Therefore, 4^{-2} = \frac{1}{4^{2}} = \frac{1}{16}. This simplified expression demonstrates how to work with exponents and manage negative exponents effectively.
Use the table of values to calculate the linear correlation coefficient r.
X Y
4 -5
53 -1
86 13
162 16
The linear correlation coefficient r is **1.2237445080439002**.
To calculate the linear correlation coefficient r, we can use the following formula:
[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]
where:
* [tex]\sum[/tex] is the sum of the values
* [tex]\bar x[/tex] is the mean of x
* [tex]\bar y[/tex] is the mean of y
First, we need to calculate the mean of x and y:
[tex]\bar x[/tex] = (4 + 53 + 86 + 162) / 4 = 71.25
[tex]\bar y[/tex] = (-5 - 1 + 13 + 16) / 4 = 5.75
Next, we need to calculate the sum of the squared deviations from the mean for x and y:
[tex]\sum(x - \bar x)^2 = (47.25^2 + 17.25^2 + 14.25^2 + 90.75^2) = 10148.5[/tex]
[tex]\sum(y - \bar y)^2 = (11.25^2 + 6.75^2 + 7.25^2 + 10.25^2) = 317.5[/tex]
Now, we can calculate the linear correlation coefficient r:
[tex]r = (\sum(x - \bar x)(y - \bar y)) / \sqrt(\sum(x - \bar x)^2 \sum(y - \bar y)^2)[/tex]
r = (47.25 * 11.25 + 17.25 * 6.75 + 14.25 * 7.25 + 90.75 * 10.25) / √(10148.5 * 317.5)
r = 1.2237445080439002
Therefore, the linear correlation coefficient r is **1.2237445080439002**.
This value indicates a strong positive correlation between x and y.
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f(x) = 3^x Find f(x) when x = 8.
Answer:
f(8) = 3^8 = 6561
Step-by-step explanation:
f(x) = 3^x
Let x =8
f(8) = 3^8
= 6561
Answer:
f(8) = 6561
Step-by-step explanation:
f(x) = 3^x Substitute x = 8
f(8) = 3^8 Simplify the exponent
f(8) = 6561
is Circumference of a circle same as area?
Answer:
The circumference of a circle is not the same as the area of the circle because the circumference represents the distance around the circle while the area represents the amount of space within the circle. Hope this helps.
Answer:
No
Step-by-step explanation:
The circumference of a circle is the distance around the outside of the circle. It is similar to the perimeter of other shapes such as squares.
Hope this helps! :)
what is the equation of this line
A town has a population of 17000 and grows at 4% every year. What will be the population after 12 years, to the nearest whole number?
Answer:
27218
Step-by-step explanation:
y= 17000 (1.04) ^12
y=27217.54772
y= 27218
If a town has a population of 17000. The population after 12 years, to the nearest whole number is 27,218.
PopulationUsing this formula
A=P(1+r/100)^n
Let plug in the formula
A= 17000 (1+.04) ^12
A= 17000 (1.04) ^12
A=17000×1.601032
A=27217.54
A=27218 (Approximately)
Therefore the population after 12 years, to the nearest whole number is 27,218.
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i'll give 30 points and brainlist
Answer:
100 degrees
Step-by-step explanation:
Arc QM = Arc QN = 130°
Arc MN = 360 - Arc QM - Arc QN
= 360 - 2(130)
= 360 - 260
= 100°
A polynomial that has a degree of 0 is called ___.
Answer:
constant or constant polynomial
Some call is the zero polynomial
Step-by-step explanation:
Let x be raised to the 0 power
x^0 = 1
This is constant
3x^0 = 3*1 = 3
This is still constant
Answer:
Constant
Step-by-step explanation:
Degree 0 means the highest power of the variable is 0, which also means there's only one term
(Because the powers have to non-negative integers, and 0 is the smallest)
Ax⁰ is the form of a degree-0 polynomial
x⁰ = 1
Ax⁰ = A
Which is a constant
Which is the measure of
A)93
B.113
C.138
D.180
Answer:
Depends on the angel needed, I'll provide all answers
Step-by-step explanation:
Angel A is 93, because a straight line has an angel total of 180, so in order to find angel A you would just need to subtract
180-87 = 93
Angel B is 87, because angels opposite each other have the same value.
The Angel without a character would be 93 for the same reason :3
Exit
8-8: MathXL for School: Practice & Problem Solving
(x) 8.8.PS-14
E Question Help
A box has the shape of a rectangular prism with height 32 cm. If the
height is increased by 0.9 cm, by how much does the surface area of the
box increase?
32 cm
Use pencil and paper. Show your work. Then show a second way to
19 cm
7.2 cm
Answer:
47.16 Square centimeters
Step-by-step explanation:
Width=7.2cm
Length =19cm
Height =32cm
Surface Area=2(LW+LH+WH)
=2(19*7.2+19*32+7.2*32)
Surface Area [tex]=1950.4 cm^2[/tex]
When the height is increased by 0.9cm
Height =32.9cm
Surface Area=2(LW+LH+WH)
=2(19*7.2+19*32.9+7.2*32.9)
Surface Area [tex]=1997.56 cm^2[/tex]
Difference in Surface Area=1997.56-1950.4
=47.16 Square centimeters
An alternative way is to calculate the surface area dealing with the height only using the height difference,
Difference=2(LH+WH)
=2(19*0.9+7.2*0.9)
=47.16 Square centimeters
Solve 28 + 7y =91
Y=.....
Answer:
[tex]y = 9[/tex]
Step-by-step explanation:
[tex]28 + 7y = 91 \\ 7y = 91 - 28 \\ 7y = 63 \\ \frac{7y}{7} = \frac{63}{7} \\ y = 9[/tex]
Answer:
Y=9
Step-by-step explanation:
28 + 7y =91
first subtract 28 from both sides
28-28+7y=91-28
7y= 63
then divide both sides by 7
7y/7=63/7
y=9
ANSWER CHECK
to see if the answer is correct substitute the answer you got for the variable
y=9
28 + 7(9)
multiply 7 and 9
7(9)=63
63+28= 91
solve T = 7c-2d for d.
Answer:
[tex]d = \frac{t - 7c}{ - 2} [/tex]
Hope this helps at all. :)
To solve for d in T = 7c - 2d, isolate the variable d by moving the term with d to the other side of the equation and simplifying.
Explanation:To solve for d in the equation T = 7c - 2d, we need to isolate the variable d. First, we'll start by moving the term with d to the other side of the equation.
Step 1: Add 2d to both sides of the equation.
T + 2d = 7c
Step 2: Now, we'll isolate the variable d by subtracting T from both sides of the equation.
2d = 7c - T
Step 3: Finally, divide both sides of the equation by 2 to solve for d.
d = (7c - T)/2
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HELP ME PLZZ
The absolute value of a number is .|2| =
Answer:
The absolute value of a number is a distance /2/=2
Step-by-step explanation:
The absolute value of the absolute expression |2| will be 2.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute expression is given below.
⇒ |2|
The value will be always positive when the value inside the mode is taken out. Then we have
⇒ |2|
⇒ 2
The absolute value of the absolute expression |2| will be 2.
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Here are the first five terms of an arithmetic sequence. 4 9 14 19 24 Find, in terms of n, an expression for the nth term of this sequence
Answer:
The nth term can be represented by;
Tn = 5n- 1
Step-by-step explanation:
In this question, we are concerned with finding an expression in terms of n for then the term of the sequence.
Mathematically, the nth term of a sequence Tn can be represented by the formula;
Tn = a + (n-1)d
where a is the first term in the sequence which is 4 , and d is the common difference which is the difference between 2 consecutive terms which is 9-4= 5
our n is n, since we do not know the number of terms we are finding for
Plugging these values, we have;
Tn = 4 + (n-1)5
Tn = 4 + 5n -5
Tn = 5n- 1
find the equivalent expression: 12a+6b
1)6(6z+6b)
2)6(2a+b)
3)2(6a+4b)
4)2(10b+4b)
Answer:
2
Step-by-step explanation:
12a+6b
factor out 6
6(2a+b)
Find the value of x in the figure
Answer:
I am 99% sure it's [tex]x = 100[/tex]°, here's why (down)
Step-by-step explanation:
The total is 180°. When adding 57° + 23° = 80°. To get [tex]x[/tex], you have to subtract 80° from 180°. The difference is 100°, which is the answer of this problem.
In a city school of 1200 students 42% of the students are on the honorable 64% have a part time job and 28% are on the honor roll and have a part-time job what is the probability that a randomly selected student is on the honor roll given that the student has a part time job
Answer:
[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]
And replacing we got:
[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]
And the probability required for this case is 0.4375
Step-by-step explanation:
For this case we define the following events:
H = represent that the student is honorable
P= represent that the student have a part time job
And we have the following probabilities:
[tex] P(H) = 0.42 , P(P) = 0.64, P(H \cap P) =0.28[/tex]
And we want to find this probability:
[tex] P(H|P)[/tex]
And we can use the following probability:
[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]
And replacing we got:
[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]
And the probability required for this case is 0.4375
Which function represents exponential growth
Answer:
The answer is this.
[tex]y = 4x {}^{2} [/tex]
Hope this helps ya.
☆CHEERS!☆
4(sin3x-cos2x)=5(sinx-1)
The area of a rectangle is 36 sg in and the length of the rectangle is 9 in Which equation could be used to find the width of the
rectangle?
Answer:
Step-by-step explanation:
[tex]Width=\frac{Area}{length}\\\\=\frac{36}{9}\\\\[/tex]
= 4 inches
Answer:
9×W=36 or 36÷9=W
Step-by-step explanation:
to find the area of a figure you multiply L×W in this situation you only have length. soo find what times 9 = 36 or 36÷9 to find Width
Step 4: Factor the function to find the x-intercepts.
The x-intercepts are:
Answer:
(5,0) and (-1,0)
Step-by-step explanation: