The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
What is summation?In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.
Now we have a given term
[tex]\sum_{n=1}^{4} 3(4)^{n-1}[/tex]
By solving the above term;
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}[/tex]
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3[/tex]
[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192[/tex]
Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
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Answer:
1. 3 + 12 +48 + 192
2. 255 edge
Step-by-step explanation:
Please help me with this math problem!! Will give brainliest!! :)
Answer:
5 for both.
Step-by-step explanation:
Multiplying exponents rule with like bases;
Add powers with like bases.
So, if we look at x to the power of the blank multiplied by x to the power of 5, we know that 5 added to that unknown/blank power would equal in 10(using the multiplication of exponents rule), because in the results it says x^10.
Thus,
x to the power of __ · x to the power of 5 = x to the power of 10
And, 5 would make a solution for the blank, because;
x to the power of 5 · x to the power of 5 = x to the power of 10, which is true because their exponents added together would be 10 → (5 + 5).
Now, if we look at y to the power of 3 multiplied by y to the power of the blank, we know that 3 added to the unknown/blank power would equal in 8(using the multiplication of exponents rule) because in the results says y^8.
Thus,
y to the power of 3 · y to the power of __ = y to the power of 8
And, 5 would make a solution for the blank, because;
y to the power of 3 · y to the power of 5 = y to the power of 8, which is true because their exponents added together would be 8 → (3 + 5).
Therefore, 5 would be the answer.Overall you're basically just multiplying all those exponents together.
Jupiter has a diameter
86.881 mi. What is the
circumference of the
planet?
Answer:
about 272944 miles
Step-by-step explanation:
d=86,881mi
c=d(pi)
c=86881pi
c≈272944mi
A card is selected at random from a deck of cards.
Determine the probability that the card selected is A 5
Answer:
8/52 = 4/26 =2/13
Step-by-step explanation:
A there are 4 aces
5 there are 4 5s
4+4=8
Solve the equation 6
2 =
1
= 2-1.
4
Answer:
26
Step-by-step explanation:
welll i have no clue just guess i cant even read the question
Consider the diagram below, where h represents height and 2 represents length.
Which of the following represents the approximate area of both figures?
Answer:
Both figures have an area of (6hl) by Cavalieri's Principle for two-dimensional figures.
Step-by-step explanation:
Math Nation
help please help me
Answer:
19.6
Step-by-step explanation:
A = πr²
A = (3.14159)(2.5 in.)²
A = 19.6 in.²
A coin is tossed two times what is the probability of getting tails twice
Answer:
1/4
Step-by-step explanation1/4
90 over 7 EndFraction divided by 1 and three-fourths
Answer:
120/7
Step-by-step explanation:
means90/7÷3/4
= 90/7 ×4/3
= 120/7
The length of a rectangle is five time it’s width. If the perimeter of a rectangle is 84ft, find its area
Answer:
Area = 245 ft
(Width
Step-by-step explanation:
l = 5w
Where l is length and w is width.
We also know that the perimeter is 84 ft, so:
2l + 2w = 84
Now we can plug in 5w for l since we found the equality earlier:
2(5w) + 2w = 84
and then solve for w:
10w + 2w = 84
12w = 84
w = 7
so
l = 5 × 7
l = 35
The length is 35 and width is 7 so
the area of the rectangle is
[tex]7 \times 35 = 245ft [/tex]
Simplify: -15 + 23r + 9r^2 - 16r + 10
Answer:
9r^2 + 7r - 5
Step-by-step explanation:
Edgy question please help
What is the true solution to the equation below?
2 in en 2x - In en 10x - In 30
x - 30
O x - 75
OX-150
X-300
Answer:
B
Step-by-step explanation:
Answer:
x=75
Step-by-step explanation:
2 * ln (e ^ ln (2x)) - ln (e ^ ln (10x)) = ln (30)
Apply exponent rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) +logc (b)
Apply exponent rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (2x) = ln (2) + ln (2)
2(ln (2) + ln (x)) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
ln (2x) = ln (2) + ln (2)
2(ln (2) + ln (x)) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
2(ln(2)+ln(x))-(ln(10)+ln(x))=]
Expand 2(ln(2) +ln(x)
ln (x) + 2 * ln (2) - ln (10) = ln (30)
Subtract 2 * ln (2) - ln (10) from both sides
In(x) + 2ln(2) - In(10) - (2ln(2) - In
Simplify
ln (x) = ln (30) - 2 * ln (2) + ln (10)
Simplifify ln (30) - 2 * ln (2) + ln 10
ln (x) = ln (75)
Apply log rule: If logb(f(x)) = logb (g(x)) then f(x) = g(x)
x = 75
Verify Solutions: X = 75
Check the solutions by plugging them
into 2 * ln (2x) - ln (10x) = ln (30) Remove the ones that don't agree with the equation.
Plug in x =75
2 * ln (2 * 75) - ln (10 * 75) = ln (30)
2 * ln (2 * 75) - ln (10 * 75) = ln (30)
ln (30) = ln (30)
True
Over the past 10 years, what is the warmest temperature recorded, in degrees Fahrenheit, for the month of December in Miami, Florida?
What is the volume of the figure below if a = 8 units and b = 6 units?
A.
536 cubic units
B.
704 cubic units
C.
256 cubic units
Answer:
704 cubic units
Step-by-step explanation:
First let's calculate the volume of the cube. The formula to calculate the volume of a cube is V = a^3, a being the edge length of the cube. So we need to cube the value of a, which is 8. 8 cubed is 512 cubic units.
Now we need to calculate the volume of the triangular prism. The formula to calculate the volume of a cube is V = 1/2b * a * h, a being the side edge length of the prism, b being the height of the triangular side, and h being the base edge length of the triangular side, if that makes any sense (easier to explain visually). h and a are equal to the given a, which is 8 in this case. And b in the formula is equal to b in the given problem. So we substitute the values into the formula: V = (1/2*6) * 8 * 8 = 3 * 64 = 192 cubic units.
Now we take the sum of both of the figures:
512 + 192 = 704 cubic units.
What is the arc measure of minor arc AB on circle P in degrees?
Answer:
74
Step-by-step explanation:
This is called a central angle, meaning that what ever te angle measure is, is the same to its ark measure.
So to find that inside angle measure you have to subtract 360 by 286
whitch is 74
74 is your inside angle and the angle for ark AB
What is the equation of the line that passes through the point (-5,-2) and has a slope of 3/5?
Answer:
y = 3/5x + 1
Step-by-step explanation:
Formula:
y - y1 = m(x - x1)
Plug in:
y - (-2) = 3/5(x - (-5))
Two negatives make a positive:
y + 2 = 3/5(x +5)
Distribute 3/5 to (x + 5):
y + 2 = 3/5x + 3
Get y by itself by - 2:
y = 3/5x + 1
Hope this helps you :)
How is the scale factor, surface area ratio and volume ratio related?
If two solids are similar with a scale factor of a/b, then the surface areas are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^2[/tex].
If two solids are similar with a scale factor of a/b, then the volumes are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^3[/tex].
What are the area and volume of similar solids?Two shapes are similar if all their corresponding angles are congruent and their corresponding sides are proportional.
Two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.
When two shapes are similar in two dimensions, the ratio of their areas is the square of the scale factor.
A comparable relationship holds in three dimensions as well.
Surface Area Ratio: If two solids are similar with a scale factor of a/b, then the surface areas are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^2[/tex].
Volumes of Similar Solids; Just like surface area, volumes of similar solids have a relationship that is related to the scale factor.
Volume Ratio: If two solids are similar with a scale factor of a/b, then the volumes are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^3[/tex].
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Is rectangle efgh the result of a dilation of rectangle abcd with a center of dilation at the origin? why or why not? yes, because corresponding sides are parallel and have lengths in the ratio four-thirds yes, because both figures are rectangles and all rectangles are similar. no, because the center of dilation is not at (0, 0). no, because corresponding sides have different slopes.
The rectangle is symmetrical about the y-axis. Then both the figures are rectangles and all the rectangles are similar. Then the correct option is B.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
The rectangle EFGH is dilated of the rectangle ABCD with a center of the dilation at the origin.
From the figure, it is clear that the rectangle is symmetrical about the y-axis. Then both the figures are rectangles and all the rectangles are similar.
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A b c d or e what one
Answer: A its B
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
if y = 0
0 = -2x + 4 _ eq 1
0 - 4 = -2x
-4 = -2x
divide through by 2
x = -4 ÷ -2
x = 2
if x = 0
y = -2(0) + 4_ eq 2
y = 0 + 4
y = 4
:.(x,y) = (2,4)
In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?
A: (h + x)2 + (k + y)2 = r2
B: (x – h)2 + (y – k)2 = r2
C: (k + x)2 + (h + y)2 = r2
D: (x – k)2 + (y – h)2 = r2
Answer:
B
Step-by-step explanation:
[tex]\textsf{Let}\:(x_1,y_1)=(h,k)[/tex] → new center of the circle
[tex]\textsf{Let}\:(x_2,y_2)=(x,y)[/tex] → point on the circle
Therefore, the radius (r) is the distance between (x, y) and (h, k)
Use the distance formula:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=d[/tex]
[tex]\implies \sqrt{(x-h)^2+(y-k)^2}=r[/tex]
Square both sides:
[tex]\implies (x-h)^2+(y-k)=r^2[/tex]
Answer:
Option B
Step-by-step explanation:
Then we have to use distance formula to derive it
√(x-h)²+(y-k)²=r(x-h)²+(y-k)²=r²Option B is correct
Helpppppppppppppppppp
Answer:
They need $60.32 in order to purchase the swing set.
Step-by-step explanation:
682.56-200.000 = 482.56
482.56/8 = $60.32
Find the value of x
I need the answer ASAP
Answer:
15
Step-by-step explanation:
i kinda remember i think
2(x+8)=46
Helppp meeeeee please
Answer:
The answer is F
Step-by-step explanation:
Because I said so
Rewrite the log expression in exponential form:
logbA=x
Answer:
[tex]b^x =A[/tex]
Step-by-step explanation:
I NEED THAT ANSWER ASAP
Answer:
12.7
Solving steps:-
d = a√2
d = 9 (1.41)
d = 12.69
d = 12.7
laws of exponents:
Squares and Square roots:
√9a¹⁶b³⁶
Step-by-step explanation:
Square root is equivalent to 1/2 power:
[tex] {(9 {a}^{16} {b}^{36} )}^{ \frac{1}{2} } [/tex]
Square root of 9 is 3. Multiply the exponents by 1/2 to get:
[tex] 3{a}^{8} {b}^{18} [/tex]
PLEASE HELP ME!!!
I WILL MARK BRAINLIEST
Answer:
Equation:
(5x)° + (x - 6)° = 90
OR
5x + x - 6 = 90
x = 16
m
Angle1 = 80°
mAngle2 = 10°
Step-by-step explanation:
Angle 1 + Angle 2 adds up to 90°. The tiny square in the corner of the image shows you that the whole thing is 90°.
So write the equation base on that.
5x + x - 6 = 90
Combine like terms(add the x's)
6x - 6 = 90
Add 6.
6x = 96
Divide by 6.
x = 16
Fill in 16 for x to find the measures of the angles.
Angle 1 = 5x
= 5(16)
= 80°
Angle 2
= x - 6
= 16 -6
= 10°
And 80°+ 10° is 90° so that's a good check. Hope this helps!
Hi, I need help, am struggling with this. Question is in image below.
Answer:
I believe that would be -24/16, -√2, 21/51, and then 0.42
Step-by-step explanation:
This is according to math app
1. What is the type of association between variables x and y?
options:
strong positive
strong negative
perfect positive
no association
2. What is the type of association between variables x and y?
options:
no association
moderate positive
weak negative
strong negative
The statements that describe the variables x and y are:
The association between variables x and y is (d) no associationThe type of association between variables x and y is (a) no associationHow to determine the associationIn the graph that relates variables x and y (see attachment), we can see that the points are scattered on the coordinate plane and they do not follow a specific pattern.
If the points are scattered, then the graph shows no association.
Hence, the graph shows no association
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Can someone help me?
Answer:
CE
Step-by-step explanation:
CE IS THE REQUIRED ANSWER FOR THE GIVEN QUESTION
Fatoumata owns a small business selling ice-cream. She knows that in the last week 13 customers paid cash, 39 customers used a debit card, and 5 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a percent to the nearest whole number.
Answer:
40
Step-by-step explanation:
40 because 39 will round up to 40 by 1
The probability in percentage that the next customer will pay with a debit card will be 68.42%.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,
P = (Favorable event) / (Total event)
She knows that in the last week, 13 customers paid cash, 39 customers used a debit card, and 5 customers used a credit card.
The probability that the next customer that will pay with a debit card will be given as,
P = 39 / (13 + 39 + 5)
P = 39 / 57
P = 0.6842 or 68.42%
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