Answer:
The first term of the series is 81
Step-by-step explanation:
The sum of the nth term of a geometric sequence is expressed as shown;
Sn = a(1-rⁿ)/1-r for r<1
a is the first term
r is the common ratio
n is the number of terms
Given Sn = 171
r = 2/3
n = 3
a =?
Substituting the values in the equation
171 = a(1-(2/3)³)/1-2/3
171 = a(1-8/27)/(1/3)
171 = a(19/27)/(1/3)
171 = a × 19/27 × 3/1
171 = a × 19/9
Cross multiplying
171×9 = 19a
1539 = 19a
a = 1539/19
a = 81
The first term is 81
Answer:
81
Step-by-step explanation:
PLEASE HELP I NEED THE ANSWER ASAP
Jason wrote a computer program that randomly generate one of the letters of his name. He runs the program three times. What is the probability that it generates either a J or an N all 3 times?
Answer:
0.064
Step-by-step explanation:
(2/5) * (2/5) * (2/5)
= 0.064
Hope this is helpful!!! :)
The probability that it generates either a J or an N all 3 times would be 0.064.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Jason wrote a computer program that randomly generate one of the letters of his name. He runs the program three times.
The probability that it generates either a J or an N all 3 times
[tex](2/5) \times (2/5) \times (2/5)\\\\8/125\\\\0.064[/tex]
Thus, the answer is 0.064.
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What is the volume of this rectangular pyramid?
3 yd
5 yd
5 yd
cubic yards
How much concentrated 12 M sulfuric acid should be added to prepare a 250 mL of 1.5 m solution?
Use either the square of a binomial or the
difference of two squares to find the area of
each rectangle.
Answer:
9. 2916 sq. cm
10. 864 sq. in
Step-by-step explanation:
9.) 54 cm * 54 cm = area of square
(50 + 4)*(50 + 4) = 50*50 + 8*50 + 16
= 2500 + 400 + 16 = 2916 sq cm.
10. 24 in * 36 in. = area of rectangle
get: (30 - 6)*(30 + 6) = 30^2- 6^2
= 900 - 36 = 864 sq. in.
Choose the correct answer
Answer:
Option D
Step-by-step explanation:
Assuming you're referring to slope, the rule is rise/run or "rise over run" so as i look at this line i see it rises 1 unit and then runs back or negatively 4 units, therefor the answer is D 1/-4
Please mark as brainliest :)
In the figure, which angle has the same measure as Z2?
A. 21
B. 23
C. 24
D. 25
Answer:
I think it is D
Step-by-step explanation:
HURRY PLEASEEEEE!!!!
Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12 8 + 2r – 6
Complete the statements.
1.When r = 2, the first expression is ?.
2.When r = 2, the second expression is 6.
3.When r = 5, the first expression is 21.
4.When r = 5, the second expression is .?
5.The expressions are not equivalent.
The two expressions are not equivalent to each other at r =2 and r = 5.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12 8 + 2r – 6
First put r = 2 in both the expressions:-
E1 = 2 + 4 ( 2 + 2 ) -12
E1 =6
E2 = 8 + ( 2 x 2 ) - 6
E2 = 6
Secondly, put r = 5 in both the expressions.
E1 = 2 + 4 ( 2 + 5 ) - 12
E1 = 30
E2 = 8 + ( 2 x 5 ) -6
E2 = 12
The two expressions are not equivalent at r = 2 and r =5.
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Answer: 6, 12
Step-by-step explanation:
proof :)
Solve x :
[tex]{(3 {x}^{2} - 8x + 5)}^{x + 1} = 1[/tex]
We want this expression to fall in one of the two cases:
[tex]\alpha ^ 0 = 1 = 1^\beta[/tex]
So, if the exponent is zero, the base can assume any value, because everything (expect zero) to the power of zero is one.
Similarly, if the base is 1, the exponent can be any number, becuase 1 raised to any exponent is still one.
If we are looking for the "zero exponent" strategy, we simply have to impose
[tex]x+1=0\iff x=-1[/tex]
In this case, the expression becomes [tex]16^0=1[/tex], so we avoided the [tex]0^0[/tex] case and we're good.
If we are looking for the "base equals one" strategy, we must impose
[tex]3x^2-8x+5 = 1 \iff 3x^2-8x+4=0 \iff x=\dfrac{2}{3}\lor x=2[/tex]
Answer:
x = -1, ⅔, 2
Step-by-step explanation:
3x² - 8x + 5
3x² - 3x - 5x + 5
3x(x - 1) - 5(x - 1)
(3x - 5)(x - 1)
[3x² - 8x + 5]^(x+1) = 1
The ourput is 1 when:
1) The power is 0
x + 1 = 0
x = -1
2) base is 1
3x² - 8x + 5 = 1
3x² - 8x + 4 = 0
3x² - 6x - 2x + 4 = 0
3x(x - 2) - 2(x - 2) = 0
(3x - 2)(x - 2) = 0
x = 2 , ⅔
Therefore, 3 solutions
x = -1, ⅔ , 2
A circle has the equation x2−12x+27=−y2+8y.
What is the equation of the circle in standard form, the location of its center, and the length of its radius?
The equation of the circle is (x−6)2+(y−4)2=25; the center is at (6,4), and the radius is 5 units.
The equation of the circle is (x−6)2+(y−4)2=5; the center is at (6,4), and the radius is 5–√ units.
The equation of the circle is (x−6)2+(y−4)2=5; the center is at (−6,−4), and the radius is 5–√ units.
The equation of the circle is (x−6)2+(y−4)2=25; the center is at (−6,−4), and the radius is 5 units.
Answer:
It's the first option.
Step-by-step explanation:
x^2 - 12x + 27 = - y^2 + 8y
x^2 - 12x + y^2 - 8y = -27 Completing the squares:
(x - 6)^2 - 36 + (y - 4)^2 - 16 = -27
(x - 6)^2 + (y - 4)^2 = -27 + 36 + 16
(x- 6)^2 + (y - 4)^2 = 25 is the standard equation.
The center is at (6, 4) and the radius is 5 units.
Answer:
first option
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² - 12x + 27 = - y² + 8y ( subtract - y² + 8y from both sides )
x² - 12x + y² - 8y + 27 = 0 ( subtract 27 from both sides )
x² - 12x + y² - 8y = - 27
Using the method of completing the square on both the x and y terms
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 4)y + 16 = - 27 + 36 + 16
(x - 6)² + (y - 4)² = 25 ← in standard form
with centre = (6, 4 ) and r² = 25 ⇒ r = [tex]\sqrt{25}[/tex] = 5 → first option
The baker made 27 pies. Nine of the pies were cherry pies and the rest were pumpkin pies. The baker placed the pumpkin pies in rows of 3 pies each. How many rows of pumpkin pies did the baker make?
27-9=18. The baker made 18 pumpkin pies.
To prove our answer,,
18 divided by 3 is 6, so it is possible to place them in rows by three.
Your confirmed answer is 18.
I hope this helps!
Brainliest?
Use simple interest to find the ending balance.
$53,300 at 4.7% for
3 3/4 years URGENT I will give you brainliest
Answer:
The ending balance would be:
EB = Money x (1 + rate)^year
= 53300 x (1 + 4.7/100)^(3.75) = 63318.01
Hope this helps!
:)
Answer:
$62,694.125
Step-by-step explanation:
Interest = 53300 × (4.7/100) × 3.75
Interest = 9394.135
Balance = 53300 + 9394.135
= $62,694.125
3 - 2n = 7
Show work please
Answer:
-2
Step-by-step explanation:
3-2n=7
-3 -3
-2n=4
divide both sides by -2
n=-2
Which statement is true about this question -4(2p+5)+8p=-11
A. The equation has one solution, p=2
B. The equation has one solution, p=-2
C. The equation has no solution
D. The equation has infinetly many solutions
Option C. The equation has no solution is correct.
Which statement is true about this question -4(2p+5)+8p=-11
What is equation?
Equation is the relationship between variable and represented as is example of polynomial equation.
Since,
The equation terminated while simplifying
-8p-20+8p=-11
-20≠-11
Thus the given equation has no solution at any point.
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what is the median 3 2 -9 9 -3 -4 -1
Answer:
the median is -1
-9 -4 -3 (-1) 2 3 9
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Answer:
-1
Step-by-step explanation:
First put the numbers in order from smallest to largest
-9 -4 -3 -1 2 3 9
The median is the middle number
The middle number is -1
3.Can we multiply a 2x3 matrix by a 3x2 matrix? If yes, what dimensions will the product matrix AB have ?
Answer:
Yes, the dimensions will be 2x2
Step-by-step explanation:
When multiplying matrices you have AxB by CxD. You can only multiply matrices if the inner number is the same.
Ex. 2x3 by 3x2 or QxD by DxW
The dimensions of the result will depend on the outer numbers.
Ex. 2x3 by 3x2 has a 2x2 result or QxD by DxW has a QxW result
Yes, you can multiply a 2x3 matrix by a 3x2 matrix. The result will be a 2x2 matrix because the number of rows in the first matrix and the number of columns in the second matrix define the dimensions of the product matrix.
Explanation:Yes, it is possible to multiply a 2x3 matrix by a 3x2 matrix. When multiplying matrices, the number of columns in the first matrix must be the same as the number of rows in the second matrix. Therefore, in this case, where we have a 2x3 matrix and a 3x2 matrix, the 3 columns in the first matrix and the 3 rows in the second matrix make multiplication possible.
The resulting product from the multiplication of these two matrices will be a new matrix whose dimensions are determined by the number of rows in the first matrix and the number of columns in the second matrix. In this case, as the first matrix has 2 rows and the second matrix has 2 columns, the resulting matrix will have dimensions of 2x2.
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Find the value of r in the following diagram.
The value of r is 3.75 from the diagram.
We have to find the value of r which is a radius.
ABC is a right angle triangle in the circle.
We find the value of r by using pythagoras theorem.
r²+9²=(6+r)²
r²+9²=36+12r+r²
9²=36+12r
81=36+12r
Subtract 36 from both sides:
81-36=12r
45=12r
Divide both sides by 12:
r=45/12
r=3.75
Hence, the value of r is 3.75.
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What is the area of the following parallelogram in square centimeters?
396 cm2
360 cm2
3.6 cm2
3.96 cm2
Answer:
3.6 cm²
Step-by-step explanation:
18 mm = 1.8 cm
A = 2cm×1.8cm = 3.6 cm²
Your answer would be the third option, 3.6 cm².
The equation for the area of a parallelogram is the same for the area of a rectangle, which is base multiplied by perpendicular height. Because all of the answers are given in cm², we should convert all lengths in mm to cm.
This means that 18mm because 1.8cm (by dividing by 10).
Now we just do 1.8 × 2 = 3.6cm²
I hope this helps!
Determine the area of a triangle with m
Answer:
I'm guessing they're asking about trig functions, topic test. Answer: B) 10 units^2
Step-by-step explanation:
just took the topic test on edge2021
Find the parallelogram below. Use the formula: A = b x h.
Answer:A = b x h
Step-by-step explanation:
I can't see the problem but i can give help u have to follow the formuls
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. Find the length (l) of aluminum surrounding the pool as shown if the radius is 15 feet. (use π=3.14 )
Answer:
The length of aluminium surrounding the pool is 94.20 ft.
Step-by-step explanation:
The picture represents the circular swimming pool that has walls of aluminium surround it.
The circumference of a circle is the distance around a circle. It is the curved line that goes round the circle. The question wants us to find the circumference of the aluminium surrounding the circular pool.
circumference of a circle = 2πr
circumference of a circle = 2 × 3.14 × 15
circumference of a circle = 30 × 3.14
circumference of a circle = 94.2 ft
The length of aluminium surrounding the pool is 94.20 ft.
Describe what pie is and explain how it Is used in finding the circumference of a circle
Answer:
Step-by-step explanation:
Pi is the ratio of a circle's circumference to its diameter.
The circumference = π * the diameter of the circle (Pi multiplied by the diameter of the circle)
Hope this helps!
What quadrants is csc less than 0.
Answer:
Quadrant 2
Step-by-step explanation:
An Ice Hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. What equation describes this problem? (Remember that the perimeter is twice the length plus twice the width)
Answer:
Let width be x metres
so, length is "9 metres more than twice the width" --> 9+2x
So, perimeter is x + x + (9+2x) + (9+2x) = 174
6x + 18 = 174
6x = 156
x = 156/6
x = 26m
width = 26m
length is therefore 9+2(26) --> 9+52 --> 61m
Step-by-step explanation:
Is this right? if it isn't, what IS right?
Answer:
You are wrong and the correct answer is vaunted.
Step-by-step explanation:
Why? Because it would be the only applicable word for this sentence.
Omnipotent: Having unlimited power; able to do anything.
Overt: One or shown openly; plainly or readily apparent, not secret or hidden.
Annihilated: Destroy utterly; obliterate.
Vaunted: Praised or boasted about, especially in an excessive way.
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 3 dots above the third mark, and 5 dots above the fourth mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
A. Group B, because five children have a forearm length longer than 12 inches.
B. Group B, because a child in the group has the least forearm length of 10 inches.
C. Group A, because no child in the group has a forearm length longer than 12 inches.
D. Group A, because four children in the group have the least forearm length of 10 inches.
Answer:
The corect answer is : Group A because 4 children have a forarm length longer than 12 inches.
Step-by-step explanation:
I did the test and got it right! :D
Answer:
D. Group A, because four children in the group have the least forearm length of 10 inches.
Step-by-step explanation:
It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A. So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.In order to verify the claim let us find the meanMean of Group A
[tex]\dfrac{10\times 4+11\times 4+12\times 2}{10}=10.8\ \text{inches}[/tex]
Mean of Group B
[tex]\dfrac{11\times 2+12\times 3+13\times 5}{10}=12.3\ \text{inches}[/tex]
So, group A has shorter average forearm length.
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Anyone know what part B is?
The Exterior Angle Theorem states that basically ∠ACB and ∠ACD are supplementary, meaning they should equal 180 when added together. Since you know one side of the whole angle is 35, simply do 180-35, which equals 145°.
a drum have a diameter of 22 in and a 16 in deep find the volume of this drum
≈ 6079 in³
Step-by-step explanation:drum = cylinder
d = 2r => r = d/2 = 22in/2 = 11 in
h = 16 in
V = π·r²·h
= 3.14·(11in)²·16in
= 3.14·121in²·16in
= 6079, 04 in³
≈ 6079 in³
5 in
Q
2 in
R
PQ =
Using Pythagorean theorem
By applying Pythagorean's theorem to right-angled triangle PQR, the length of segment PQ is equal to [tex]\sqrt{29}[/tex] units.
In Mathematics and Geometry, Pythagorean theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:
[tex]c^2=a^2+b^2[/tex]
Where:
a is the opposite side of a right-angled triangle.b is the adjacent side of a right-angled triangle.c is the hypotenuse of a right-angled triangle.By applying Pythagorean's theorem to right-angled triangle PQR, the length of segment PQ can be calculated as follows;
[tex]PQ^2=QR^2+PR^2\\\\PQ^2=2^2+5^2\\\\PQ^2=4 + 25\\\\PQ=\sqrt{29}[/tex]units.
A certain shampoo is available in two sizes. A 23.7-ounce bottle costs $4.97 . A 33.8 -ounce bottle costs $7.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Unit price for the 23.7 Price per ounce
33.8 Price per ounce
Answer:
23.7 ounce = 20 cents per ounce
33.8 ounce = 22 cents per ounce
The 23.7 ounce bottle is a better deal because it is only 20 cents per ounce, rather than 22 cents per ounce.
The data to represent average test scores for a class of 16 students includes an outlier value of 91. If the outlier is included, then the mean is 80. Which statement is always true about the new data when the outlier is removed?
The median would decrease.
The median would increase.
The mean would decrease.
The mean would increase.
Answer:
c the mean would decrease
Step-by-step explanation:
Answer:
C) The mean would decrease!!