Answers
Answer:
- 85
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
1[tex](-2)^{n-1}[/tex] ← is the n th term of a geometric series
with a = 1 and r = - 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
= [tex]\frac{1((-2)^{8}-1 }{-2-1}[/tex]
= [tex]\frac{256-1}{-3}[/tex]
= [tex]\frac{255}{-3}[/tex]
= - 85
Related Questions
The seventh-grade spring class trip will either be to a zoo or an art museum. Which survey
method is most likely to provide a biased sample?
A. survey all of the seventh-grade students
B. survey every fifth seventh-grade student that arrives at school
C. survey 50 seventh-grade students whose names are chosen from an alphabetical list
D. survey those seventh-grade students who participated in this year’s art fair
Answers
Answer:
D. survey those seventh-grade students who participated in this year’s art fair
Step-by-step explanation:
The people who participated in the art fair will most likely want to go to the art museum, which is a biased result.
Answer:
it's d
Step-by-step explanation:
hope it helps :)
The surface area of a triangular prism is 78 square inches. What is the surface area of a similar prism that is three times as large?
Answers
Answer:
234 inches
Step-by-step explanation:
The prism is 3× larger so you would multiply 78 by 3
Final answer:
To find the surface area of a similar prism three times as large, you need to square the scaling factor and multiply it by the original surface area.
Explanation:
The surface area of a triangular prism is 78 square inches. Given that the area scales in proportion to the square of the linear dimensions, if a similar prism is three times as large, the surface area of the larger prism would be 3² = 9 times the original surface area. Therefore, the surface area of the similar prism that is three times as large would be 78 square inches x 9 = 702 square inches.
What is the measure of QS?
84°
Answers
The measurement of arc QS is 168 degree.
Now, Let the center of the given circle is O .
And central angle is double of the angle subtended by the arc.
So central angle is twice of 84 degree.
Hence, the measure of QS is,
= 2 x 84
= 168 degree
So, the central angle is of measurement 168 degree.
Therefore, The measurement of arc QS is 168 degree.
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a triangle has vertices at (-1,5), (4,2), and (0,0). What is the perimeter of the triangle
Answers
The perimeter of the triangle is 15.4 units.
Step-by-step explanation:
The triangle has vertices at (-1,5), (4,2), and (0,0).
To find the perimeter of the triangle, you need to find the distance of the three points which is the length of the three sides of the triangle.
Let us consider the points as A (-1,5) and B (4,2) and C (0,0).
The distance formula is given by :
⇒ [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
Distance of AB :
A (-1,5) ⇒ (x1,y1)
B (4,2) ⇒ (x2,y2)
⇒ [tex]\sqrt{(4+1)^{2}+(2-5)^{2} }[/tex]
⇒ [tex]\sqrt{5^{2}+-3^{2} }[/tex]
⇒ [tex]\sqrt{25+9}[/tex]
⇒ [tex]\sqrt{34}[/tex]
⇒ 5.8
∴ The length of the side AB of the triangle is 5.8 units.
Distance of BC :
B (4,2) ⇒ (x1,y1)
C (0,0) ⇒ (x2,y2)
⇒ [tex]\sqrt{(0-4)^{2}+(0-2)^{2} }[/tex]
⇒ [tex]\sqrt{16+4 }[/tex]
⇒ [tex]\sqrt{20}[/tex]
⇒ 4.5
∴ The length of the side BC of the triangle is 4.5 units.
Distance of CA :
C (0,0) ⇒ (x1,y1)
A (-1,5) ⇒ (x2,y2)
⇒ [tex]\sqrt{(-1-0)^{2}+(5-0)^{2} }[/tex]
⇒ [tex]\sqrt{1+25}[/tex]
⇒ [tex]\sqrt{26}[/tex]
⇒ 5.1
∴ The length of the side CA of the triangle is 5.1 units.
Now, the perimeter of the triangle is given by :
Perimeter = Sum of the lengths of all three sides of the triangle.
⇒ 5.8 + 4.5 + 5.1
⇒ 15.4 units.
∴ The perimeter of the triangle is 15.4 units.
What is the slope of the line on the graph below?
On a coordinate plane, a line goes through points (0, negative 5), (3, negative 4), and (6, negative 3).
Answers
Answer:
i think the answer is 1/3 but i'm not positive
Step-by-step explanation:
The slope of a linear line which is passing through the lines (0,-5), (3, -4) , (6,3) is 1/3. The slope of a straight line is the ratio of y values of two points to the difference in x values of the two points.
What is slope ?In mathematics, slope of a line describes the steepness or inclination and the direction of the line. Slope of a line is calculated based on the characteristic of the line.
For straight line passing through some points, the x and y coordinates are related by the following expression:
y = mx +c
Where c is the intercept m be the slope.
For a line passing through two points, the slope m is :
m = y2 - y1 / (x2- x1)
Consider the line passing through the points (0, -5) and (3, -4). The slope m = -4 - (-5) / (3 - 0) = 1/3
Similarly if we consider the points (3, -4) and (6, -3) we get the same slope 1/3.
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The quadrilateral shown is a parallelogram. What is the measure of DC?
A) 8 B) 12 C) 18 D) 23
Help me I’ll give you best brainliest!!
Answers
Answer:
B) 12
Step-by-step explanation:
Opposite sides are congruent
An employee put $5,000 in a retirement account that offers 9% interest compounded annually. The employee makes no additional deposits or withdrawals. How much interest will the employee have earned at the end of 5 years. Make sure to round your answer to the hundredths.
Answers
Answer:
$2,693.12 will the employee have eared at the end of 5 years.
Step-by-step explanation:
The formula of compound interest:
[tex]A=P(1+r)^n[/tex]
[tex]I[/tex] = A-P
A= The amount in the account after n years
P= Principal
r= rate of interest annually
n= time in years.
An employee put $5,000 in retirement account that offer 9% interest compounded annually.
Here P=$5,000, r=9%=0.09, n= 5 years
[tex]A=5,000(1+0.09)^5[/tex]
=$7,693.12
The interest = A-P
=$(7,693.12-5,000)
=$2,693.12
$2,693.12 will the employee have eared at the end of 5 years.
Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2
Answers
Answer:
[tex]U_n=5(-2)^{n-1}[/tex]
Step-by-step explanation:
Given a geometric sequence, the nth term of the geometric sequence is obtained by using the formula:
[tex]U_n=ar^{n-1}[/tex]
If the eleventh term, [tex]a_{11}=5120[/tex]
and the common ratio, r=-2.
Then:
[tex]5120=a(-2)^{11-1}\\a=\frac{5120}{2^{10}} =5[/tex]
The explicit formula for the sequence is:
[tex]U_n=5(-2)^{n-1}[/tex]
What is the probability that in two rolls of a single die, a man will roll a 2 on the first roll and a number greater than five on the second?
(A) 1/3
(B) 1/6
(C) 1/12
(D) 1/18
(E) None of the above
I got; (E) None of the above. Because I got 1/36.
Is this correct?
Answers
Answer:
Step-by-step explanation:
I got A because the probability of rolling a 2 is 1/6 chance. Then the probability of getting a number greater than 5 is a 1/6 chance because there’s only one number bigger than five on a die. So I added them together got 2/6 and simplified down is 1/3
Answer:
That's right.
A 2 on the first roll means 1 possibility out of 6.
The only number greater than 5 in a dice is 6, therefore it's the same case from above.
1/6 on first roll
1/6 on second roll
[tex]\frac{1}{6} * \frac{1}{6} = \frac{1}{36}[/tex]
4) The hospital and the fire department are 46 meters apart. From a window in the hospital,
the angle of elevation to the top of the fire department is 730. From the same window, the
angle of depression to the ground at the base of the fire department is 640. Find the height
of the fire department to the nearest tenth.
Answers
The height of the fire department is 244.72 m
Step-by-step explanation:
A)
Angle of elevation = 73°
The distance between the two buildings = 46 m
tan 73° = b/46
tan 73° = 3.27
tan 73° = b/46
3.27 = b/46
b = 3.27 x 46
b = 150.42 m
B)
Angel of depression= 64°
The distance between the two buildings = 46 m
tan 64° = a/46
tan 64° = 2.05
tan 64° a/46
2.05 = a/46
a = 2.05 x 46
a = 94.3 m
The total height of the fire department building = a + b
= 94.3 + 150.42
= 244.72 m
The height of the fire department is 244.72 m
select the number like that matches the expression |-6-(-3)|
Answers
Answer:
3
Step-by-step explanation:
Firstly, do the numbers inside the absolute value bars.
-6-(-3)
The two negatives that are together turn to a addition sign.
-6+3
You can just subtract 6 and 3 which is 3 and add the - to it.
|-3|
The -3 turns to a 3 since the absolute value bars make all numbers positive within the bars.
Hope this helped.
The Pythagorean theorem states that if two side lengths of a(n) _____ triangle are known, the length of the third side can be found.
Answers
Answer:
right triangle
Step-by-step explanation:
35% off $85.98. I'm having trouble with this.
Answers
Answer:
$55.89
Step-by-step explanation:
To figure out the discounted price, you multiply the original price (85.98) by the percentage, (35% = .35) Then subtract that number, (30.093) from the original price to find the discounted price.
Answer:
$24.56
Step-by-step explanation:
85.98 / 35 = 2.456
2.456 x 10 = 24.56
Please help :/ whoever answers I will put as brainpower answer ;)
Answers
Answer:
(x-9)^3
Step-by-step explanation:
so first you see "the cube" which means ^3 to whatever you are going to have
the difference means the answer of a subtraction equation
the the difference between "a number" (x) and 9 is (x-9)
then you see that when "adding" those together you get (x-9)^3
hope this helps
Here is an inequality: -2x>10
Select all the values in the list for x that would make this inequality true
-10
-4
2
-6
-5
-8
0
-43
Answers
Answer:
The answer is -6, -8, -10 and -43.
Step-by-step explanation:
You can solve it :
-2x > 10
x < 10 ÷ -2
x < -5
(take note: you have to change symbol when it is divided by a negative no.)
Then choose the numbers from the options that satisfies the inequality, x < -5
Answer:
-10
-6
-8
-43
Step-by-step explanation:
(-2)*(-10)=20, 20>10
(-2)*(-4)=8, 8<10
(-2)*2=-2, -2<10
(-2)*(-6)=12, 12>10
(-2)*(-5)=10, 10=10, so it is not true
(-2)*(-8)=16, 16>10
(-2)*0=0, 0<10
(-2)*(-43)=86, 86>10
hope this helps :D
Which value of x makes the following equation true?
3(x - 4) - 12 = 2(x - 6) + 5
Answers
Answer:
x = 17
Step-by-step explanation:
3(x - 4) - 12 = 2(x - 6) + 5
3x - 12 - 12 = 2x - 12 + 5
3x - 24 = 2x - 7
3x - 2x = -7 + 24
x = 17
Answer:
x=17
Step-by-step explanation:
3(x - 4) - 12 = 2(x - 6) + 5
Distribute
3x -12 -12 =2x-12 +5
Combine like terms
3x-24 = 2x -7
Subtract 2x from each side
3x-2x -24 =2x-2x-7
x-24 = -7
Add 24 from each side
x-24+24 = -7+24
x = 17
A new park was designed to contain two circular gardens. Garden A has a diameter of 50m and garden B has diameter of 70m if the gardener wants to outline the gardens edging, how many meters will be needed to outline the smaller garden?
Answers
Answer:
157
Step-by-step explanation:
The circumference of a circle with diameter d is given by ...
C = πd
The circumference of a 50 meter circle will be ...
C = π(50 m) ≈ 157.08 m
It will take about 157 meters of edging to outline the smaller garden.
if i multiply a number by 3 and then subtract 4, the result is the same as adding 6 to twice the number. Find this number
Answers
Final answer:
By setting up and solving the equation 3x - 4 = 2x + 6, we find that the number in question is 10. This process involves aligning the equation to solve for the variable x, representing the number we seek.
Explanation:
If we multiply a number by 3 and then subtract 4, the result is the same as adding 6 to twice the number. To find this number, we can set up an equation based on the given conditions.
Let's let the number be x. According to the first condition, multiplying x by 3 and then subtracting 4 can be represented as 3x - 4. According to the second condition, adding 6 to twice the number can be represented as 2x + 6.
The two expressions are equal, so our equation is 3x - 4 = 2x + 6.
Subtract 2x from both sides: x - 4 = 6.
Add 4 to both sides: x = 10.
Therefore, the number we are looking for is 10.
All of the following statements are true, except . . .
The product of b and c is positive.
The product of a and c is negative.
The product of b and 0 is 0.
The product of a and b is positive.
Answers
The only definite conclusion from the given information is that the product of b and c is positive, while the signs of a and b individually cannot be determined conclusively. Here option B is correct.
The product of a and c is negative: We cannot determine the signs of a and c individually, but from the given information, we can say that their product is negative. This is because the sum of a and c is 0 (a + b + c = 0), and b is positive.
If both a and c were positive or negative, their sum would be positive or negative, respectively. Therefore, one must be positive and the other negative for their sum to be zero.
The product of b and c is positive: As mentioned above, we know that b is positive and the product of a and c is negative. Since the sum of a, b, and c is zero, if b is positive and the product of a and c is negative, then the product of b and c must be positive to balance the equation.
The product of b and O is 0: This statement is always true because any number multiplied by zero is zero.
The product of a and b is positive: We cannot determine the signs of a and b individually based on the given information. As explained earlier, we only know that their sum is positive and the product of a and c is negative.
Therefore, the only statement that is guaranteed to be true based on the given information is that the product of b and c is positive. Here option B is correct.
Find the slope of the line that passes through (97,-54) and (-1, -15)
Answers
Answer:
The slope is -39/98
also known as m=-39/98
The volume of a cone with a radius of 7 cm is 147 pi cubic centimeters. Which expression can be used to find h, the height of the cone?
147 pi = one-third (7) (h) squared
147 pi = one-third pi (7 squared) (h)
147 pi = one-third pi h
147 pi = one-third pi (7) (h)
Answers
Answer:
147 pi = one-third pi (7 squared) (h) 147 pi = one-third pi h
explanation:
Answer:
b. 147 pi = one-third pi (7 squared) (h)
Step-by-step explanation:
did test on e2021
what two numbers give you the difference of 4 and the sum of 58?
Answers
Answer:
46.4 & 11.6
Step-by-step explanation:
I just did some guess and check, but 46.4/11.6 = 4 and 46.4+11.6 = 58
PLEASE HELP ASAP IT IMPORTANT THAT I GET THIS RIGHT PLEASE
Answers
Answer:
x=12, both angles are 144°
Step-by-step explanation:
Since the angles are Z-angles (lookup 'alternate exterior angles') they are the same.
This means that 10x+24 = 6x+72, which can be simplified to
10-6x = 72-24
4x = 48
x = 12
Substitute x=12 in either expression and you get 144.
What is the probability of an event that is impossible?
Answers
Answer:
0
Step-by-step explanation:
If the event is not possible it's not going to happen
If 2x – 3 + 3x = – 27, what is the value of x?
Answers
Answer:
x = -24/5
Step-by-step explanation:
2x – 3 + 3x = – 27
Combine like terms
5x -3 = -27
Add 3 to each side
5x-3+3 = -27+3
5x = -24
Divide each side by 5
5x/5 = -24/5
x = -24/5
Answer:
x= -24/5
Step-by-step explanation:
To solve, we need to get x by itself.
2x – 3 + 3x = – 27
Combine like terms
(2x+3x)-3= -27
5x-3=-27
Add 3 to both sides
5x-3+3=-27+3
5x= -24
Divide both sides by 5
5x/5= -24/5
x= -24/5
In ΔEFG, the measure of ∠G=90°, FG = 2.3 feet, and EF = 6.4 feet. Find the measure of ∠F to the nearest degree.
Answers
this is super complicated
Answer:
69
Step-by-step explanation:
the inverse cosine of 2.3/6.4 is 69 degrees
Help please I’m on a time limit
Answers
Answer:
I think that it is 295 degrees
Step-by-step explanation:
Pren recorded this data set, which contains an outlier. 204, 216, 111, 224, 230, 211, 210, 198, 200, 218 What numbers represent the range, lower quartile, and upper quartiles? range: 210.5 lower quartile: 200 upper quartile: 218 range: 14 lower quartile: 111 upper quartile: 198 range: 119 lower quartile: 218 upper quartile: 200 range: 119 lower quartile: 200 upper quartile: 218
Answers
The numbers that bes represent the range, lower quartile and upper quartiles is:
d. 200 range: 119 lower quartile: 200 upper quartile: 218.What are the range, lower quartile, and upper quartiles?Range:
Range = Maximum Value - Minimum Value
Range = 230 - 111
Range = 119
Lower Quartile (Q1):
Lower Half: 111, 198, 200, 204, 210
Median of Lower Half = (200 + 204) / 2 = 202
Upper Quartile (Q3):
Upper Half: 211, 216, 218, 224, 230
Median of Upper Half = (216 + 218) / 2 = 217.
Read more about Medians
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Which number is an integer?
-3/4
0
2.3
Square root
Answers
Answer:
0
Step-by-step explanation:
An integer is a whole number with no decimals. 0 is the only one.
Answer:the last answer is pi not square root
Step-by-step explanation:
Find the inner product for (8,4)(2,4)and state whether the vectors are perpendicular.
a.
8; no
c.
32; no
b.
8; yes
d.
32; yes
Please select the best answer from the choices provided
A
B
C
D
Answers
The inner product of vectors (8,4) and (2,4) is 32, and since the dot product is not zero, the vectors are not perpendicular.
The inner product (also known as the dot product) of two vectors can be calculated by multiplying the corresponding components of the vectors and then summing those products. For the vectors (8,4) and (2,4), the inner product is calculated as (8 × 2) + (4 × 4), which equals 16 + 16, and thus the inner product is 32.
To determine if the vectors are perpendicular, we need to check if their dot product is zero. In this case, since the dot product is 32, not zero, the vectors are not perpendicular to each other.
Therefore, the correct answer is C: 32; no.