Answer: c
Step-by-step explanation: because of the 2 in the first one there will be a 2 in the answer
The sum of the first eight terms in this series is 97,750.
We have,
We notice that each term in the series is obtained by multiplying the previous term by 5.
Therefore, this is a geometric series with a common ratio of 5.
We can use the formula for the sum of the first n terms of a geometric series:
[tex]S_n = a(1 - r^n)/(1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
In this case,
a = 2, r = 5, and n = 4 (since we have four terms).
Substituting these values into the formula gives:
[tex]S_4 = 2(1 - 5^4)/(1 - 5)[/tex]
= 2 (-624)/(-4)
= 156
The sum of the first four terms is 156.
To find the sum of the first eight terms, we need to find the sum of the first four terms and then multiply by the common ratio raised to the power of 4:
[tex]S_8 = S_4 \times 5^4[/tex]
= 156 x 625
= 97,500
Adding the last term (250) to this sum gives:
= [tex]S_8[/tex] + 250
= 97,500 + 250
= 97,750
Therefore,
The sum of the first eight terms in this series is 97,750.
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You take a bus from your neighborhood to your school. The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m. The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m. You arrive at the bus stop at 7:33 a.m. Find the probability that you missed both the express bus and the local bus. Express your answer as a fraction in simplest form.
Answer:
[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.
Step-by-step explanation:
Uniform distribution:
An uniform distribution has two bounds, a and b.
The probability of getting a value lower than x is:
[tex]P(X < x) = \frac{x - a}{x - b}[/tex]
The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m.
6 minutes, so [tex]a = 0, b = 6[/tex]
You arrive at 7:33, so if x < 3, you lose the express bus:
[tex]P_E = P(X < 3) = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2}[/tex]
The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m.
10 minutes, so [tex]a = 0, b = 10[/tex]
[tex]P_B = P(X < 3) = \frac{3 - 0}{10 - 0} = \frac{3}{10}[/tex]
Find the probability that you missed both the express bus and the local bus.
[tex]p = P_E*P_B = \frac{1}{2}*\frac{3}{10} = \frac{3}{20}[/tex]
[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.
The probability that you missed both the express bus and the local bus is 3/20
The individual probability of a uniform distribution is calculated as:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
For the express bus
At 7:30 am, a = 0
At 7:36 am, b = 6
You arrived at 7:33 am; this means that:
x = 3
For you to miss the express bus, it means that the express bus left before 7:33 am.
i.e. x < 3
So, the probability that you miss the express bus is:
[tex]P(X < 3) = \frac{3 - 0}{6 - 0}[/tex]
[tex]P(X < 3) = \frac{3}{6}[/tex]
[tex]P(X_E < 3) = \frac{1}{2}[/tex]
For the local bus
At 7:30 am, a = 0
At 7:40 am, b = 10
You arrived at 7:33 am; this means that:
x = 3
For you to miss the local bus, it means that the local bus left before 7:33 am.
i.e. x < 3
So, the probability that you miss the local bus is:
[tex]P(X < 3) = \frac{3 - 0}{10 - 0}[/tex]
[tex]P(X_L < 3) = \frac{3}{10}[/tex]
So, the probability that you miss both bus is:
[tex]P(Both) = P(X_E < 3) * P(X_L < 3)[/tex]
This gives
[tex]P(Both) = \frac 12 * \frac 3{10}[/tex]
[tex]P(Both) = \frac 3{20}[/tex]
Hence, the probability that you missed both the express bus and the local bus is 3/20
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Determine the value of X will give brainlyest
Answer:
x=you
Step-by-step explanation:
less than 9 but more than 1
Find the measure of the arc indicated. Assume that lines which appear tangent are tangent.
Answer:
Minor Arc AC = 360 - 235 = 125°
[tex]mABC = \frac{Major \ arc - Minor \ arc}{2} = \frac{235 - 125}{2} = \frac{110}{2} = 55[/tex]
Find v.
Write your answer in simplest radical form.
Answer:
v=3√3in
Step-by-step explanation:
Answer:
3√3in c:
Step-by-step explanation:
Consider the function graphed below. What is the average rate of change of the function over the interval [1, 3]?
A. 32
B. 36
C. 42
D. 48
The average rate of change of the function over the interval [1,3] will be around 45 which is nearest an option to 42 so option (C) will be correct.
What is a graph of a function?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph consists of various points and the separation between two of them. Neither the length of the lines nor the placement of the points matters. Each component of a graph has a name, known as a node.
For example to draw the equation y = 2x +9 this will draw a straight line in the coordinate geometry.
The rate of change is given by dy/dx
The average rate of change can be given as (difference in y coordinate)/(difference in x coordinate)
Average rate of change = ( 102 - 12 )/(3 - 1 ) = 45 which is nearest to option (C) hence it will be correct.
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Help me Please and thank you
Answer:
f(3) = -4
Step-by-step explanation:
f(3) = f(2)*-1/2; Solve for f(2) first;
f(2) = f(1)*-1/2
f(2) = -16*-1/2
f(2) = 8;
Now get back to f(3);
f(3) = f(2)*-1/2
f(3) = 8*-1/2
f(3) = -4
The diagram shows a campground in the shape of a right triangle. You walk along a path from the camp office
at point c to your campsite at point D on a path that bisects the right angle C. Determine how far you are from
the picnic area at Point A to the nearest tenth of a meter.
Find the area of a triangle with a height of 5 ft and a base of 4 ft.
Answer:
5 x 4 = 20, 20 divided by 2 ( x 1/2 ) = 10
Step-by-step explanation:
Formula area of a Triangle:
B(base) x H(height) x 1/2(basically just dividing by 2)
Suppose f(x) = x^3 +3. Find the graph of f(2/3x)
Answer:
First, when we have a function f(x), an horizontal dilation of scale factor k, is written as:
g(x) = f(x/k)
Then f((2/3)*x) is an horizontal dilation of scale factor 3/2 of the function f(x).
(The graph will be a little bit wider than the graph of f(x))
Also, knowing that f(x) = x^3 + 3
Then:
f((2/3)*x) = ( (2/3)*x)^3 + 3
= (8/27)*x^3 + 3
And the graph of this function is shown below:
The Box-and-Whisker Plot represents the ages of 40 people who responded to a telephone survey.
Which statement is true about this data set?
A. About 50% of the respondents were at or between 40 and 67.5 years old.
B. The range of the data is 84 years.
C. The outlier is 28 years.
D. The mean is 51 years.
Answer:
'A' is true; theoretically, 50% of the data items reside between the first and third quartiles (40 and 67.5)
Step-by-step explanation:
Range is 84-28 which is 56
Median is 51
1.5 x Interquartile Range (IQR) = 1.5(67.5-40) which equals 41.25
Q1 is 40
Q1 - IQR = -1.25
Low outliers are below -1.25 - 41.25; there are not data items below -42
Answer:
'A' is true; theoretically, 50% of the data items reside between the first and third quartiles (40 and 67.5)
Step-by-step explanation:
Range is 84-28 which is 56
Median is 51
1.5 x Interquartile Range (IQR) = 1.5(67.5-40) which equals 41.25
Q1 is 40
Q1 - IQR = -1.25
Low outliers are below -1.25 - 41.25; there are not data items below -42
Find the measure of the missing angle
128°
Help plz
Answer:
52 degrees
Step-by-step explanation:
a line is 180 degrees so just subtract 128 from 180 which is 52
What is the area, in square units, of trapezoid AEDC shown below?
Area of this trapezoid is 264 unit²
What is the area of a trapezoid?Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides.
Given perpendicular distance as 12 and parallel sides as 20,24 units respectively.
Thus Area is (20+24 /2) ×12=264 units²
Hence, the Area of trapezoid is 264 unit²
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Write the expression using exponents.
43 . 43 . 43 . 43 . 43
Answer:
43⁵
Step-by-step explanation:
43 · 43 · 43 · 43 · 43 = 43⁵
Rob's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 adult tickets and 1 student ticket
for a total of $15. The school took in $69 on the second day by selling 9 adult tickets and 7 student tickets. What is the price each
of one adult ticket and one student ticket?
Answer:
Adult Tickets =$3
Student Tickets =$6
Step-by-step explanation:
3×3=9 9+6=15
9×3=27
7×6=42
27+42=67
Expand and combine like terms.
(4m^5) – 5m^6) (4m^5 + 5m^6) =
Answer:
[tex]16m^{10} -25m^{12}[/tex]
Step-by-step explanation:
hope this helps :)
The expand and combination like terms (4m^5) – 5m^6) (4m^5 + 5m^6) is -9m^12 + (16)m^10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The equation=(4m^5) – 5m^6) (4m^5 + 5m^6)
Now,
To expand the expression, we need to multiply each term inside the first parentheses by each term inside the second parentheses. This gives us:
(4m^5 - 5m^6) (4m^5 + 5m^6) = 4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6
To simplify the expression, we need to use the exponent rule that a^b * a^c = a^(b + c) and combine the terms that have the same base and exponent. This gives us:
4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6 = 16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6)
To further simplify the expression, we need to add the exponents and simplify the coefficients. This gives us:
16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6) = 16m^10 + 20m^11 - 20m^11 - 25m^12
To combine like terms, we need to add or subtract the coefficients of the terms that have the same base and exponent. This gives us:
16m^10 + 20m^11 - 20m^11 - 25m^12 = (16 - 25)m^12 + (20 - 20)m^11 + (16)m^10
= -9m^12 + (0)m^11 + (16)m^10
= -9m^12 + (16)m^10
Therefore, the equation will be equal to -9m^12 + (16)m^10.
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4. Tyquan had his car towed by Lakeview's Towing Service. It cost him $3.00 per mile to have it towed
plus a flat fee of $70.00. The function for his cost is represented by the function C(m) = 3m + 70. What
does C(22) represent in this situation?
a. Tyquan had hisbear towed for 136 mile and it cost $22.00
b. Tyquan had his car towed for 22 miles and it cost him $136.00
c. Tyquan had his car towed for 3 miles at $70.00
d. Tyquan had his car towed 22 miles for $70.00
The answer is b. because the other ones don't charge money according to the number of miles.
Answer:
The structure that you used in your research paper can also be used for your presentation. For example, just like how your
Step-by-step explanation:
write an equation with a slope of -1/2 in each form.
point-slope form
slope-intercept form.
For the case of a line through
(
2
,
7
)
and
(
1
,
−
4
)
we have
slope
m
=
Δ
y
Δ
x
=
−
4
−
7
1
−
2
=
−
11
−
1
=
11
Using the point
(
2
,
7
)
we can write the equation of the line in point slope form as:
y
−
7
=
m
(
x
−
2
)
where the slope
m
=
11
.
That is:
y
−
7
=
11
(
x
−
2
)
To get point intercept form, first expand the right hand side so...
y
−
7
=
11
x
−
(
11
⋅
2
)
=
11
x
−
22
Then add
7
to both sides to get:
y
=
11
x
−
15
=
11
x
+
(
−
15
)
This is point intercept (
y
=
m
x
+
c
) form with slope
m
=
11
and intercept
c
=
−
15
.
Which of the following numbers is between 0.40 and 0.47 ?
7/50
19/50
21/50
43/50
The Answer is 21/50 which is = 0.42
Please help. Image up top.
Answer:
6/5t + 4/15s - 3
Step-by-step explanation:
(-4/5t + 5/3s) + (-3 -7/5s + 2t)
You can only add like terms together so convert like terms to have the same denominator:
(-4/5t + 25/15s) + (-3 - 21/15s + 10/5t)
Get rid of the parentheses:
-4/5t + 25/15s - 3 - 21/15s + 10/5t
Combine like terms:
6/5t + 4/15s - 3
Which of the following inequalities are true
Answer: The answer is E: |-4|<|-7| and C: |-7|>|4|
Solve using the Quadratic Formula
5x2-3x-7=0
A)
B)
C)
D)
Answer:
C) [tex]\displaystyle x=\frac{3 \pm \sqrt{149}}{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]Step-by-step explanation:
Step 1: Define
Identify
5x² - 3x - 7 = 0
↓
a = 5, b = -3, c = -7
Step 2: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{3 \pm \sqrt{(-3)^2-4(5)(-7)}}{2(5)}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{3 \pm \sqrt{9-4(5)(-7)}}{2(5)}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{3 \pm \sqrt{9+140}}{2(5)}[/tex][√Radical] Add: [tex]\displaystyle x=\frac{3 \pm \sqrt{149}}{2(5)}[/tex][Fraction] Multiply: [tex]\displaystyle x=\frac{3 \pm \sqrt{149}}{10}[/tex]3(2^2x+3)-5(2^x+2)-156=0
Answer: [tex]x=3.0206[/tex]
Step-by-step explanation:
Given
[tex]3(2^{2x}+3)-5(2^x+2)-156=0[/tex]
Replace [tex]2^x[/tex] by [tex]y[/tex]
We can write
[tex]\Rightarrow 3(y^2+3)-5(y+2)-156=0\\\Rightarrow 3y^2+9-5y-10-156=0\\\Rightarrow 3y^2-5y-157=0\\\\\Rightarrow y=\dfrac{5\pm \sqrt{25-4(3)(-157)}}{2\times 3}\\\\\Rightarrow y=\dfrac{5+43.69}{6}\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206[/tex]
i will give brainliest if you solve #11 please and thank you!!!
Answer:
[tex]A)~ 39.6[/tex] %----------------
[tex]Total~ number~ of~ students:-[/tex]
[tex]42+58+20+84+41+5[/tex]
[tex]=250[/tex]
[tex]soccer=58+41[/tex]
[tex]=99[/tex]
[tex]99/250*100[/tex]
[tex]=0.39*100[/tex]
[tex]=39[/tex]
------------------------
hope it helps...
have a great day!!
Stanley attempted to simplify the expression below.
−4●(2.5x−1.25)−3x
His work, step by step, is shown below.
Step 1: −4●{(2.5x+(−1.25)}−3x
Step 2:−10x+(−5)−3x
Step 3:−10x−3x+(−5)
Step 4: −13x−5
In which step did he make his first error simplifying the expression?
Find the measure of angle C
Answer:
ajnasnnanananandbabbabbansbansbz svabsvsb
What is the quotient of 1.728 x 109 and 4.8 x 106 expressed in scientific
notation?
Answer:
3.7018867924 × [tex]10^{-1}[/tex]
Step-by-step explanation:
First you want to find what these two numbers are, then you divide, then you put that answer in scientific notation.
1.728(109) = 188.352
4.8(106) = 508.80
Now we divide :
188.352 ÷ 508.80 = 0.37018867924
That's a crazy decimal, but luckily because of scientific notation we can make it look a lot simpler.
0.37018867924 = 3.7018867924 × [tex]10^{-1}[/tex]
This should be right. Please comment if you are confused and want more detail.
What is the quotient of [tex]1.728*10^9 and, 4.8*10^6[/tex] expressed in scientific notation?
[tex]\frac{1.728*10^9}{4.8*10^6}[/tex] Divide
[tex]\frac{1.728}{4.8} * \frac{10^9}{10^6}[/tex] Divide numbers and 10's separately.
[tex]0.36*10^3[/tex] Subtract exponents.
[tex](3.6*10^-^1 )*10^3[/tex] Rewrite as a number bigger than 1
[tex]3.6*(10^-^1*10^3)[/tex] Associate
The answer is
[tex]3.6*10^2[/tex] Add exponents
11/3 as a decimal pls help
Answer:
3.7 rounded
Step-by-step explanation:
Just divide 11/3
What is the average rate of change of h over the interval −6 ≤ x ≤ 3? Give an exact number.
Answer:
-1/9
Step-by-step explanation:
PLEASE HELP IF POSSIBLE :)
Answer:
Step-by-step explanation:
Name the side that’s opposite to angle A. (Geometry)
1.) AB
2.) AC
3.) BC
Answer:
The answer gonna be A and C because their both is the same length
Answer:
BC
Step-by-step explanation:
The side opposite the right angle is called the hypotenuse. It is the largest side right angled triangle.If you stand at A in the triangle ABC, the side BC is opposite to you and the side BC is next to you. We therefore say that BC is the opposite side to angle A and AB is the adjacent side ti angle A.