Find the sum of the first four terms of the geometric series 2 + 1 +....
Answer:
15/4
Step-by-step explanation:
This is a geometric sequence with a common ratio of 1/2. Therefore, the sum of the first four terms of the geometric sequence is 2 + 1 + 1/2 + 1/4 = 15/4.
PLEASE HELP!!! CALCULUS ASSIGNMENT
Answer:
(d) [tex]\displaystyle 12x^3 - 15x^2 + 2[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 3x^4 - 5x^3 + 2x - 1[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = 4(3x^{4 - 1}) - 3(5x^{3 - 1}) + 2x^{1 - 1} - 0[/tex]Simplify: [tex]\displaystyle y' = 4(3x^3) - 3(5x^2) + 2[/tex]Multiply: [tex]\displaystyle y' = 12x^3 - 15x^2 + 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
( d ) 12x³ - 15x² + 2
Step-by-step explanation:
y = 3x⁴ - 5x³ + 2x - 1
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of axⁿ is nax^{n-1}.[tex] \small \sf \: y = 4\times 3x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
multiply 4 × 3.[tex] \small \sf \: y = 12x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
Multiply 3 × -5[tex] \small \sf \: y = 12x^{3}-15x^{3-1}+2x^{1-1} [/tex]
subtract the exponentsy = 12x³ - 15x² + 2⁰
For any term t except 0, t⁰ = 1.y = 12x³ - 15x² + 2 × 1
y = 12x³ - 15x² + 2
Hence, option ( d ) is the correct answer.
The accompanying table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the value of the car, to the nearest cent, after 15 years.
Answer:
equation: 14506.226(0.870)^x
answer: 1796.15
Step-by-step explanation:
Plugging in the tables into your calcuator
a= 14506.226
b= .870
y=ab^x
y= 14506.226(0.870)^x
= 1796.15
The equation of the exponential regression is [tex]\rm y = 14100 \ e^{-0.087x}[/tex]. And the value of a car after 15 years is $ 3,823.53.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The accompanying table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars.
The exponential regression equation will be given as
[tex]\rm y = A_o e^{kx}[/tex]
Where A₀ is the coefficient of exponential regression and k is the constant.
For x = 0, the value of y will be $ 14100. Then we have
[tex]\rm 14100= A_o e^{k*0}\\\\ A_o \ \ \ \ = 14100[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{kx}[/tex]
For x = 1, the value of y will be $12,929. Then we have
[tex]\rm 12929= 14100 e^{k*1}\\\\ e^k \ \ \ \ = 0.91695[/tex]
Taking ln both sides, then we have
[tex]\begin{aligned} \rm ln\ e^k &= ln \ 0.91695\\\\\rm k*ln \ e &= -0.087\\\\\rm k &= -0.087 \end{aligned}[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{-0.087x}[/tex]
Then after 15, the value of a car will be
[tex]\rm y = 14100 \ e^{-0.087*15}\\\\\rm y = 14100 * 0.2712\\\\\rm y = 3823.53[/tex]
More about the exponent link is given below.
https://brainly.com/question/5497425
In parallelogram ABCD shown, point E and F are located on diagonal BD and point G is located on side AB such that GE and CF are perpendicular to BD. Prove: trainge BEG is similar to traingle DFC
Answer:
Match the Statement number with the Reason number.
Step-by-step explanation:
Statements:
1.GE is perpendicular to BD
CF is perpendicular to BD
2. Angle GED equal 90
Angle DFC equal 90
3. Angle GED is congruent to Angle DFC
4. Angle GBE is congruent to Angle FDC
5. Triangle BEG is similar to DFC
Reasons:
1.Given
2. Definition of perpendicular lines
3. Transitive property
4. Alternate Interior Angles
5. AA Similarity
By satisfying essential conditions for two triangles to be similar, we can say that triangle BEG is similar to triangle DFC.
What is a parallelogram?A quadrilateral in which opposites sides are equal and parallel. Also, opposite angles are equal to each other.
As we know that AB║ DC
so,∠GBE = ∠CDF (alternate angles)
∠GEB= ∠DFC = 90°
so triangle BEG≈DFC
Therefore, we can say that triangle BEG is similar to triangle DFC
to get more about parallelograms visit:
https://brainly.com/question/12167853
0.199999 a fraccion porfavor
Answer:
199999/1000000
Step-by-step explanation:
tessa burned 357 calories in 42 minutes on the elliptical. ashley only spent 0 minutes on the elliptical and burned 267 calories. who burned calories at a faster rate
Answer:
ashley
Step-by-step explanation:
because she didnt spend any time
Answer this please Help
Answer:
x=10.75 in
Step-by-step explanation:
A = 390 = x(3x+4)
3x²+4x-390 =0
ax²+bx+c=0
x= (-b±√b²-4ac)/2a
x= (-4±√(16+4680))/6 = (-4±2√1174)/6 = (-2±√1174)/3
We will consider only the x that gives us a positive answer because the dimensions cannot be negative.
x= (-2+√1174)/3 = 10.75456113≈ 10.75
10 POINTS
Which statement best describes the expression 2 + 3 ÷ y?
a. The sum of 2 and the quotient of 3 and y
b. The sum of 2 and the quotient of y and 3
c. The quotient of y and the sum of 2 and 3
d. The quotient of the sum of 2 and 3, and y
Answer:
a. The sum of 2 and the quotient of 3 and y
Step-by-step explanation:
# form the greatest and smallest 4 digit number repetition of digits is allowed
1) the number is an even number and 2)the number is an odd number
Answer:
1) The smallest is 1000, and the greatest is 9998.
2) The smallest is 1001 and the greatest is 9999.
Step-by-step explanation:
Four digit numbers:
The set of four digit numbers is: {1000, 1001, ...., 9998, 9999}
Even numbers:
End in 0, 2, 4, 6, 8
Odd numbers:
End in 1, 3, 5, 7, 9
1) the number is an even number
The smallest is 1000, and the greatest is 9998.
2)the number is an odd number
The smallest is 1001 and the greatest is 9999.
6. Two linear equations are shown in the graph.
*(0.6)
(6,5),
COD).
(6.0)
dat
35344
tett
What are the coordinates of the point where the two lines intersect?
A. (-2, 3)
B. (3, 0)
C.(-3.3)
D. (3, 3)
Mark for review (Will be highlighted on the review page)
Alaviation
Answer:
(3,3)
Step-by-step explanation:
Linear equations of lines are given in the form:
y = mx + b;
where m is the slope of the line, b is the y intercept and x, y are variables.
From the graph, we can see that line 1 passes through (0,6) and (6,0) while line 2 passes through (0, 1) and (6, 5).
The equation of line 1 is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-6=\frac{0-6}{6-0} (x-0)\\\\y=-x + 6\ \ \ (1)[/tex]
The equation of line 2 is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\frac{5-1}{6-0} (x-0)\\\\y=\frac{2}{3}x + 1\ \ \ (2)[/tex]
Solving equation 1 and 2 simultaneously by subtracting equation 1 from 2 gives:
(5/3)x - 5 = 0
(5/3)x = 5
x = 3
Put x = 3 in equation 1:
y = -3 + 6 = 3
Therefore the two lines meet at (3, 3).
In January I saved £10 then double the amount each month. How much would I save in April?
Answer:
$80Step-by-step explanation:
Jan >> Feb >> Mar >> Apr
x2 x2 x2
$10 >> $20 >> $40 >> $80
50 PTS AND BRAINLIEST FOR CORRECT ANSWER
Answer: I asked my teacher, she said it is c
Step-by-step explanation:
Answer:
yes it's c
have a great day
At a concession stand, seven hot dog(s) and four hamburger(s) cost $15.00; four hot dog(s) and seven hamburger(s) cost $18.00. Find the cost of one hot dog and the cost of one hamburger.
Answer:
hotdog $1, and hamburger $2
Step-by-step explanation:
D-is hot dogs, H-hamburgers
7D +4H = 15
4D +7H = 18
we got 2 equations with 2 unknown so we can solve
7D +4H = 15 multiply by 7
4D +7H = 18 multiply by -4
49D +28H = 105
-16D -28H = -72 add the two equations
33D= 33 so D=$1
go back to the first equation:
7*1 +4H =15 gives us 4H = 15-7; 4H = 8 so H= $2
What is the value of X equal?
Answer:
113º
Step-by-step explanation:
(x + 14) + (180 - 83) + x + 90 + x = 540
3x + 201 = 540
3x = 339
x = 113
please helpppppppppppppp
Answer=A
Area=Length ×Breath
Length=2cm
Breath=5cm +4cm=9cm
area = 2cm ×9cm=18cm square
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n
Answer:
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours
This means that [tex]\mu = 945, \sigma = 21[/tex].
What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
What does 7 x 1/3 equal to
[tex]7 \times \frac{1}{3} \\ \\ = \frac{7 }{3} [/tex]
please help, thanks!
Answer:
[tex]x=99^{\circ},\\y=81^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of a polygon with [tex]n[/tex] sides is [tex]180(n-2)[/tex]. Since the shape in the figure has 5 sides, the sum of its interior angles is [tex]180(5-2)=180\cdot 2=540^{\circ}[/tex].
Therefore, we can set up the following equation:
[tex]95+125+105+116+x=540,\\441+x=540,\\x=\boxed{99^{\circ}}[/tex]
Since [tex]\angle x[/tex] and [tex]\angle y[/tex] make up one side of a line, they are supplementary, as each side of a line is [tex]180^{\circ}[/tex].
Thus, we have:
[tex]x+y=180,\\99+y=180,\\y=\boxed{81^{\circ}}[/tex]
Which point is located at (2, -5)?
Answer:
J
Step-by-step explanation:
Go to the right 2 units from the origin (0,0) and then down 5 units
The point at that location is J
The area of a parallelogram is 120 cm ^ 2 and the height is 30 cm . Find the corresponding base
Answer:
4 cm
Step-by-step explanation:
The Area of a parallelogram is given by :
Area = base * height
Area = 120 cm² ; height = 30
Area = base * height
120 = base * 30
Base = 120 / 30
Base of parallelogram = 4 cm
Which expression represents the following calculation?
Add 3 to the quotient of 8 divided by 6.
(8 + 6) + 3
(8 + 6) = 3
(8 + 3) = 6
6+ (3 * 8)
Answer:
[tex](8 \div 6) + 3[/tex]
Step-by-step explanation:
Required
The equivalent expression
To do this, we take it one step at a time.
First, the quotient of 8 divided by 6;
This means 8 divided by 6: [tex](8 \div 6)[/tex]
3 added to it;
The expression becomes: [tex](8 \div 6) + 3[/tex]
Last week, Becky went to dance class 4 times. Each class was 3/2 hours. This week, Becky went to dance class 5 times. Each class was 1 hour which week did Becky spend more total time in dance class
Answer:
Last week
Step-by-step explanation:
last week because, the class that week was only 1 hour and last weeks was 3/2 an hour
There are 6 shipping boxes that each contain 36 kg of merchandise from a toy store. Before the boxes are loaded onto a delivery truck, the same amount of additional merchandise is added to each box. The total weight of all of the boxes is 258 kg. How much additional weight was added to each box?
Answer: 7 kg
Step-by-step explanation:
If the equation y = |x| is graphed and then
moved up 3 units on the y-axis, what will be
the equation of the new graph?
Answer:
Step-by-step explanation:
The new equation will be
y = abs(x) + 3
I have made a graph to show you this.
The red graph is y = abs(x)
The blue graph is y = abs(x) + 3
You need only look at the point 0,0 to see what happened. On the red graph (0,0) is the lowest point. When you add 3 to get the lowest point, you should notice that the lowest point is now (0,3)
27
Sara is considering purchasing a certain stock. After doing her research, she determins that there is a 68%
chance of making $3,500 and a 32% of losing $1,800. Find the expected value of this purchase.
1
$2,158
$2,956
$1,804
$3,071
Which statement is false?
A. Negative numbers are always less than positive numbers.
B. The sum of two negative numbers is always negative.
O C. The difference between two negative numbers is sometimes positive.
D. The product of two negative numbers is always negative.
E. The quotient of two negative numbers is always positive.
Answer:
So, the option (D) is the answer.
Step-by-step explanation:
A. The negative numbers are always less than positive numbers.
It is true.
For example, - 2 < + 2
B. The sum of two negative numbers is always negative.
It is true.
For example, - 3 + (- 3) = - 6
C. The difference between two negative numbers is sometimes positive.
It is true.
For example, (- 3) - (-4) = 1
D. The product of two negative numbers is always negative.
It is false.
For example, (-3)(-3) = 9
E. The quotient of two negative numbers is always positive.
It is true.
For example, (-3)/(-1) = 3
Determine the area of the figure. Note that each unit is one unit in length.
Answer:
nao sei ispoosksjjdkdddks
Answer:
54
Step-by-step explanation:
Split into 2 rectangles and 2 triangles and calculate area
10 points
Which equation should you solve to find x?
Answer:
B.
Step-by-step explanation:
Using SOHCAHTOA,
sin 24 = 4/10
cos 24 = x/10
tan 24 = 4/x
Answer: B.
Option B. is correct. Using cosine formula the equation cos 24° = [tex]\frac{x}{10}[/tex] is used to find value of 'x'.
What is cosine?The ratio of the "adjacent side of a right angle triangle to the hypotenuse" is called cosine and given by the symbol 'cos'.
According to the question,
Angle of Right angle triangle is 24°
Adjacent = x
Opposite = 4
Hypotenuse = 10
In order to value of 'x' only if using cosine formula.
Formula for cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
= [tex]\frac{x}{10}[/tex]
Hence, the equation cos 24° = [tex]\frac{x}{10}[/tex] is used to find value of 'x'.
Learn more about cosine here
https://brainly.com/question/20839703
#SPJ2
The dot plot shows the number of goals Erin's soccer team scored this season Goals Scored Per Game 2 Which is a true statement about the dot plot? The team never scored exactly 2 goals in a single game. OThe team scored exactly 1 goal in 3 games this season. OThe most goals the team scored in a single game were 8. O The team scored exactly 3 goalsin 4 games this season. thank you so much
Answer:
The answer is A. The team never scored exactly 2 goals in a single game.
Step-by-step explanation:
Edg 2021
The correct answer is Option A , The team never scored exactly 2 goals in a single game.
What is a dot plot ?A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.
These types of charts are used to graphically depict certain data trends or groupings.
The team never scored exactly 2 goals in a single game.
It is Option A , because it says the team never scored exactly 2 goals in a single game
and the dot plot shows 0 dots in number 2 which means A. is the correct answer.
To know more about dot plot
https://brainly.com/question/22746300
#SPJ2
The sales tax rate is 10%. If Kamal buys a gold ring priced at $391, how much tax will he
pay?
Round your answer to the nearest dollar: $
Answer: $39
Step-by-step explanation: Actual answer is $39.1 but I rounded down