Answer:
3020 runs
Step-by-step explanation:
Because he wants 10000 but only has 6980 so you have to minus 6980 from 10000. 10000-6980=3020
so 3020 is the answer
Answer:
3020 runs
Step-by-step explanation:
10,000-6980=3020
Find the third term of a geometric progression if the sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
HELP AGAIN
235 ≤-8(1+5x)+3
i need the steps as well
Answer:
x ≤ -6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
235 ≤ -8(1 + 5x) + 3
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 3 on both sides: 232 ≤ -8(1 + 5x)[Division Property of Equality] Divide -8 on both sides: -29 ≥ 1 + 5x[Subtraction Property of Equality] Subtract 1 on both sides: -30 ≥ 5x[Division Property of Equality] Divide 5 on both sides: -6 ≥ xRewrite: x ≤ -6Step-by-step explanation:
To solve for x, make sure you move everything else to the other side of the ≤ sign.
So,
[tex]235\leq -8(1+5x)+3\\232\leq -8-40x\\240\leq -40x\\-6\geq x[/tex]
* Remember that the sign changes anytime you divide by a negative number!
So your answer is:
[tex]x\leq -6[/tex], x is less than or equal to -6.
Suppose the figure KLMN is dilated using a scale factor of 1/3 with the center of dilation at the origin. Which are the ordered pairs for the image?
1. K’(-1,3), L’(-3,0), M’(⅔, -8/3), N’(2, 4/3)
2. K’(-9,27), L’(-27,0), M’(6, -24), N’(18, 12)
3. K’(0,6), L’(-6,-3), M’(-1, -5), N’(3, 1)
4. K’(3,-1), L’(0,-3), M’(-8/3, ⅔), N’(4/3,2)
Answer:
K’(-1,3), L’(-3,0), M’(⅔, -8/3), N’(2, 4/3)
Step-by-step explanation:
simplify 3x⁵y³ ÷2y² step by step
Answer:
3/2 x^5 y
Step-by-step explanation:
3x^5y^3
----------------
2y^2
Simplify the y terms
y^3 / y^2 = y^(3-2) = y
3/2 x^5 y
Answer:
[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]
Step-by-step explanation:
it's all in the image
We roll a pair dice 10,000 times. Estimate the probability that the number of times we get snake eyes (two ones) is between 280 and 300.
Answer:
0.3573 = 35.7%
Step-by-step explanation:
We roll a pair of dice 10,000 times so the mean and standard deviation is,
μ = 10000/36 =277.7 σ = [tex]\sqrt{10000*\frac{35}{36^{2} } } =16.4[/tex]
[tex]z_{1}[/tex] = (280 - 277.7)/16.4 = .14
[tex]z_{2}[/tex] = (300 - 277.7)/16.4 = 1.35
Probablity (range)
0.3573
Z(low)=0.14 0.555766357
Z(upper)=1.36 0.91304644
please simplify this one. I need answers fast as possible.
This is the answer.
Hope it helps!!
Answer:
[tex]120.\sqrt{2}.\sqrt[3]{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{32} = \sqrt{16.2} =\sqrt{4^{2}.2} = 4\sqrt{2}[/tex]
[tex]\sqrt[3]{81} =\sqrt[3]{27.3} =\sqrt[3]{3^{3}.3 }=3\sqrt[3]{3}[/tex]
∴[tex]5\sqrt{32}.2\sqrt[3]{81} =5. [4\sqrt{2}].2.[3\sqrt[3]{3} ][/tex]
[tex]=120.\sqrt{2}.\sqrt[3]{3}[/tex]
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
A board is 87 cm in length and must be cut so that one piece is 21 cm longer than the other piece. Find the length of each piece. Round your answers to the nearest centimeter, if necessary. * + 21?
Thank you for answer Yey can I answer in my subject
Factorize : 4(x+y)^2 -9(x-y)^2
Answer:
Step-by-step explanation:
[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]
= -5x² + 25xy + xy - 5y²
= 5x(-x + 5y) - y(-x +5y)
= (-x + 5y)(5x - y)
Tamir wants to buy a snowboard. The original price is $760. How much will Tamir pay if he buys it during the sale?
find the are of a polygon.
Answer: 54 SQUARE UNITS ITHINK!!
Step-by-step explanation:
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
Can someone help please
Answer:
-10.5
Step-by-step explanation:
3(7)÷(7+7-2)
21÷(0-2)
21÷ (-2)
-10.5
The vertical test line
Step-by-step explanation:
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.hope it helpsstay safe healthy and happy....Answer:
It is a graphical method
Will give brainliest if correct
Which congruence theorem can be used to prove △BDA ≅ △BDC?
Triangles B D A and B D C share side B D. Sides B C and B A are congruent. Sides A D and D C are congruent.
HL
SSA
AAS
SSS
Answer:
SSS or D on edge
Step-by-step explanation:
.
The three sides of triangle ΔBDA are equal to the three sides of triangle ΔBDC.
The congruency theorem that can be used to prove ΔBDA ≅ ΔBDC is; SSSReasons:
The given parameters are;
The common side to ΔBDA and ΔBD = BD
BC ≅ BA
AD ≅ DC
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
BC ≅ BA [tex]{}[/tex] Given
AD ≅ DC [tex]{}[/tex] Given
BD ≅ BD [tex]{}[/tex] By reflexive property
Therefore, we have;
ΔBDA ≅ ΔBDC [tex]{}[/tex] By Side-Side-Side SSS, congruency ruleThe congruency theorem that can be used to prove ΔBDA ≅ ΔBDC is therefore;
SSSThe Side-Side-Side congruency rule states that if three sides of on triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Learn more about Side-Side-Side, SSS congruency rule here:
https://brainly.com/question/10684250
If Mr. David does a job in x hours and Mr. Ludwig in y hours. What part of the job they could do together if they worked for k hrs?
Answer:
(1/x + 1/y)k is the answer :)
calculate the value of X in the diagram
Answer:
that is the answer
Step-by-step explanation:
use triangle RSQ
from pythogrus theorem
a² + b² = c²
4² + 5² = RQ²
16 + 25 = RQ²
41 = R
Complete the following statement.
Answer:
Hello dude
[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]
so it's positive
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
solve 5x^2-2=-12 by taking the square root
Answer:
[tex]x = \sqrt{-2} = 2i[/tex]
Step-by-step explanation:
[tex]5x^2-2=-12[/tex]
[tex]5x^2 =-10[/tex]
[tex]x^2 =-2[/tex]
[tex]x = \sqrt{-2} = 2i[/tex]
26.3 times 1.2 please do with explanation worth 15 points
Answer - It’s 31.56
Step-by-step explanation: You just do regular multiplication and then add the decimal point
convert 23/4 into mixed number
How would I solve the question below? In what order would I solve it?
4 ⋅ 3 + 2 ⋅ 9 − 40
Step-by-step explanation:
You would multiply 4 and 3, and 2 and 9 separately, then add them, then subtract 40. Remember PEMDAS.
(4*3) + (2*9) - 40
12 + 18 - 40
-10
Hope that helps
If BcA, AnB=(1,4,5)and AuB= (1,2,3,4,5,6) find B?
Hello,
if B ⊂ A then A∩B=B
So B={1,4,5}
As per the given value of sets, B is (1,4,5).
What is a set?A set is a collection of one or multiple data.
Given,
B ⊂ A
[tex]A[/tex] ∩ [tex]B = (1,4,5)[/tex]
[tex]A[/tex] ∪ [tex]B = (1,2,3,4,5,6)[/tex]
As B ⊂ A, therefor, B is a subset of A.
Therefore, [tex]A[/tex] ∩ [tex]B = B[/tex] and [tex]A[/tex] ∪ [tex]B = A[/tex]
Hence, [tex]B = A[/tex] ∩ [tex]B = (1,4,5)[/tex].
Learn more about a set here:
https://brainly.com/question/20516078
#SPJ2
I have sons but no daughter ,each of my sons has twice as many brothers as he has children . each of my sons has same no of children each of my grand children has many cousins as uncle. how many grand children do I have ?
Answer:
Step-by-step explanation:
keeping track of family relations can be difficult. If Edna marries your mother’s uncle Charlie, what should you call her? If your father’s cousin’s daughter just had a baby boy, how should you two be introduced? Who is your “great great aunt”, and how can you find your “first cousin twice removed”? Fortunately, a bit of mathematical logic can clarify who should be called what, and why – and even measure the degree of genetic similarity between different relatives.
NEEED HELP FROM BRAINLIEST??????
If the point (1,4) is on the graph of an equation, which statement must be
true?
A. The values x= 1 and y= 4 make the equation true.
B. The values x= 4 and y= 1 make the equation true.
C. The values x= 1 and y= 4 are the only values that make the
equation true.
D. There are solutions to the equation for the values x= 1 and x= 4.
Answer:
A
Step-by-step explanation:
Help asap!!!!!!
A.
B.
C.
D.
Answer:
Function has a minimum value
So, f(x)=0 and f(4)=-3
f(x)= - 1/2x^2+4x-11f(4)=-3 and f(x)=-x+4
f(4)=0
OAmalOHopeO
7/3a - 8/5 +4/15a
Simplified
Answer:
13/5a - 8/5
Step-by-step explanation:
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,7/3a - 8/5 +4/15a.
We have to simplify the expression.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=7/3a - 8/5 +4/15a
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
Learn more about the expression here:
brainly.com/question/14083225
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What is the value of x?
Answer:
22
Step-by-step explanation:
3x-14= 4(x-9)
3×-14= 4x-36
4x-36-3x+14=0
×-22÷0
x=22
write the following sets in the set builder form C={1,4,9,16,25}
C={ check example in book}
I need a fast help please
Answer:
(5) c
(6) c
(7) b
(8) a
Step-by-step explanation:
(5) The multiplicative inverse of a number n, is the number which when multiplied by n will give a result of 1 which is a multiplicative identity. The multiplicative inverse of a number is actually the reciprocal of that number. For example, the multiplicative inverse of n is 1/n. The multiplicative inverse of 5 is 1/5. The multiplicative inverse of 5/6 is 6/5.
Therefore, the multiplicative inverse of [tex]\frac{-11}{15}[/tex] is [tex]\frac{-15}{11}[/tex]
(6) To solve 7m + 12 = -4m + 78, follow these steps;
i. Collect like terms by putting terms with m on the left hand side and the terms without m on the right hand side as follows;
7m + 4m = 78 - 12
ii. Now solve both sides;
11m = 66
iii. Divide both sides by 11;
[tex]\frac{11m}{11} = \frac{66}{11}[/tex]
m = 6
(7) Let the number be x;
10 more than twice number is 22 implies that
10 + 2x = 22
Now solve the equation;
2x = 22 - 10
2x = 12
x = 6
(8) The interior angles of a given polygon are the angles of its vertices that are within or inside of the polygon.
The sum of the interior angles of a polygon is given by;
(n-2) x 180°
where;
n = number of sides of the polygon.
For example;
For a triangle, which has n = 3 sides, the sum of these interior angles is (3 - 2) x 180° = 180°
For a rectangle/square, which has n = 4 sides, the sum of these interior angles is (4 - 2) x 180° = 360°.
For a pentagon, which has n = 5 sides, the sum of these interior angles is (5 - 2) x 180° = 540°
Therefore, depending on the number of sides n, the sum of the interior angles of a given polygon is given by;
(n-2) x 180°
