Answer:
651.
Step-by-step explanation:
Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.
Consider the given series is
[tex]91+85+79+...+(-29)[/tex]
It is the sum of an AP. Here,
First term = 91
Common difference = 85 - 91 = -6
Last term = -29
nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
[tex]-29=91+(n-1)(-6)[/tex]
[tex]-29-91=(n-1)(-6)[/tex]
[tex]\dfrac{-120}{-6}=(n-1)[/tex]
[tex]20=(n-1)[/tex]
[tex]n=20+1=21[/tex]
Sum of AP is
[tex]Sum=\dfrac{n}{2}[\text{First term + Last term}][/tex]
[tex]Sum=\dfrac{21}{2}[91+(-29)][/tex]
[tex]Sum=\dfrac{21}{2}[62][/tex]
[tex]Sum=651[/tex]
Therefore, the sum of given series is 651.
A company rounds its losses to the nearest dollar. The error on each loss is independently and uniformly distributed on [–0.5, 0.5]. If the company rounds 2000 such claims, find the 95th percentile for the sum of the rounding errors.
Answer:
the 95th percentile for the sum of the rounding errors is 21.236
Step-by-step explanation:
Let consider X to be the rounding errors
Then; [tex]X \sim U (a,b)[/tex]
where;
a = -0.5 and b = 0.5
Also;
Since The error on each loss is independently and uniformly distributed
Then;
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
where;
n = 2000
Mean [tex]\mu = \dfrac{a+b}{2}[/tex]
[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]
[tex]\mu =0[/tex]
[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{1}{12}[/tex]
Recall:
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
[tex]n\mu = 2000 \times 0 = 0[/tex]
[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]
For 95th percentile or below
[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]
[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]
[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]
From Normal table; Z > 1.645 = 0.05
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]
[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]
[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]
[tex]\mathbf{P_{95} = 21.236}[/tex]
the 95th percentile for the sum of the rounding errors is 21.236
What are the solutions to the quadratic equation below? x^2+34x-72=0
Answer:
( x + 36 ) ( x - 2 ) = 0
Step-by-step explanation:
x^2 + 36x - 2x -72 = 0
x ( x + 36 ) - 2 ( x + 36 ) = 0
( x + 36 ) ( x - 2 ) = 0
i'm desperate at this point :( Please help.
Answer:
C. 0.377
Step-by-step explanation:
20 people drive to work in suburban areas out of 53.
20/53 = 0.377358
factorise this expression as fully as possible 2x^2+6x
Answer:
(Factor out 2x from the expression)
2x (x +3)
. Find the measure of angle A.
A
160°
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
Simple and easy question
please help
Answer:
Volume of a sphere = 4/3πr³
π = 3.14
r = radius which is 3in
Volume = 4/3 × 3.14 × 3²
= 37.68
= 38 cubic inches to the nearest hundredth
Hope this helps
Answer:
38 cubic inches
Step-by-step explanation:
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
SNOG HELP OR SOMEONE THANK YOUUUU
Which unit rate is equivalent to 14 miles per gallon?
two gallons over thirty two miles
thirty two miles over two gallons
three gallons over forty two miles
forty two miles over three gallons
Answer:
forty two miles over three gallons
Step-by-step explanation:
2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.
32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.
3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.
By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!
A country has a total biocapacity of 6.21 ha/person, a biocapacity of grazing land of 0.85 ha/person, and a biocapacity of forest land of 2.53 ha/person. Calculate the percentage of biocapacity from grazing and forest land.
Answer:
3.38/6.21=54.428% (0.54428)
Step-by-step explanation:
biocapacity of grazing land of 0.85 ha/person+biocapacity of forest land of 2.53 ha/person
2.53+0.85=3.38
the percentage of biocapacity from grazing and forest land
3.38/6.21=54.428% (0.54428)
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
A company borrows 60,000 for 10 years at a simple interest rate of 8.5%. Find the interest paid on the loan and the total amount paid.
Answer: 51,000 ; 111,000
Step-by-step explanation:
The formula to calculate the simple interest is: PRT/100
where,
P = principal = 60,000
R = rate = 8.5%
T = time = 10 years
Simple interest =(60000 × 8.5 × 10)/100
= 5100000/100
= 51,000
Total Amount Paid= Principal + Interest
= 60,000 + 51,000
= 111,000
Evaluate: m - 12 when m = 23.
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
If x-14=y+196 and y is 14 times of x then x=WHAT??
Answer:
x is 226.154…
Step-by-step explanation:
1) x-14=y+196
x=y+196+14
x=y+210
2)x=14y
3) 14y=y+210 collect like terms together
14y-y=210
13y=210 divide both sides by 13
y=16.154
4)x=y+210 meaning:
x=16.154+210
=226.154
Which of the polygons listed below have at least four sides? Triangles Quadrilaterals Pentagons Hexagons Heptagons
Answer:
"Correct"
Triangles: Have three (3) sides
Quadriliaterals: QUAD being the key word means four (4)
"Incorrect"
Pentagons: Have five (5) sides
Hexagons: Have six (6) sides; key word being HEX
Heptagons: 7 sides (7)
Step-by-step explanation:
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answer:
b=3.1 cm
Step-by-step explanation:
Both of the longer sides will be equal so you can set up the equation (6.3+6.3)+b=15.7. Simplified you get 12.6+b=15.7, subtracting 12.6 from both sides you get that b=3.1 cm. This can be checked because it is also shorter than 6.3 and works correctly in the perimeter.
HELP please!!
“Find the volume of the sphere rounded to the nearest hundredth
Answer:
904.32 cm^3
Step-by-step explanation:
The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.
17. The length of a swing is 2.1 m. If the length
of the arc that is made by the swing
4.4 m, calculate the angle swept by the
swing
Answer:
dose it tell you want angle the arc is at?
Step-by-step explanation:
2. Solve 4(3c + 10) < 12c + 40.
use photo for Choices
Answer:
no solution
Step-by-step explanation:
4 (3c + 10) < 12c + 4012c +40 < 12c +4012c- 12c < 40 -40 0 < 0Left and right sides are equal so no solution
Answer:No solution
Step-by-step explanation: I got it right on the test :)
Find the nth term -1 8 19 32 47
[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]
Step-by-step explanation:
-1 → 8 = +9
8 → 19 = +11
19 → 32 = +13
32 → 47 = + 15
a₁ = -1
d = 2n + 5
Recursive formula is: the previous term plus the difference (d)
[tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]
Explicit formula is the first term plus the product of d and n-1:
[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]
In a collection of 1050 flowers, 3/10 of them are red , 2/5 of them are
white and the rest are yellow. Find the no. of red, white and yellow flowers
Answer:
315 red flowers420 white flowers315 yellow flowersStep-by-step explanation:
1050 flowers
3/10 of them are red=> 3/10 *1050=3*105=315 red flowers
2/5, (or 4/10), are white =>4/10 * 1050=4*105=420 white flowers
=> 1050-(315+420)=1050-735=315 yellow flowers
Please help ASAP I’m very unsure on how to do these 2 questions please give answers for both :)
Answer:
1) Option 2
2) Option 1
Step-by-step explanation:
1) 3a-2b
Where a = 3, b = 2
=> 3(3)-2(2)
=> 9-4
=> 5
2) 5c+3d
Where c = 4, d = -5
=> 5(4) + 3(-5)
=> 20 - 15
=> 5
Answers:
5, 5
Step-by-step explanation:
Put a as 3 and b as 2 and evaluate:
3(3) - 2(2)
9 - 4
= 5
Put c as 4 and d as -5 and evaluate:
5(4) + 3(-5)
20 - 15
= 5
Which statement illustrates the distributive property?
3 (4 + 5) = 3 (4) + 5
3 (4 + 5) = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Answer:
B. 3(4 + 5) = 3(4) + 3(5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Step-by-step explanation:
Distributive property of multiplication over addition:
a(b + c) = ab + ac
You have
3(4 + 5), so following the pattern above, you should get:
3(4 + 5) = 3(4) + 3(5)
Answer:
b
Step-by-step explanation:
I took the test
For the diagram shown, which pairs of angles are vertical angles? Select all that apply. Angle1 and Angle3 Angle2 and Angle4 Angle2 and Angle3 Angle5 and Angle7 Angle5 and Angle8 Angle8 and Angle6
Answer:
2 & 4
1 & 3
5 & 7
8 & 6
Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.
Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Recall:
Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.
From the image given,<1 and <3 are directly opposite each other and share same vertex.
<1 and <3 are therefore are a pair of angles that are vertical angles.
In the same vein, the following pairs:<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.
Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Learn more here:
https://brainly.com/question/2889556
Find the value of x.
helpppp pleaseee!!
Answer:
x = 50
Step-by-step explanation:
Since this is a quadrilateral, the sum is 360 degrees
2x+x+10 + 3x+x = 360
Combine like terms
7x+10 =360
Subtract 10 from each side
7x+10-10 = 360-10
7x = 350
Divide by 7
7x/7 = 350/7
x = 50
Answer:
[tex]x = 50[/tex]
Step-by-step explanation:
Sum of the interior angles in a quadrilateral
= 360°
Let's solve now
[tex]x + 10 + 3x + x + 2x = 360 \\ 7x + 10 = 360 \\ 7x = 360 - 10 \\ 7x = 350 \\ \frac{7x}{7} = \frac{350}{7} \\ x = 50[/tex]
hope this helps you.
Matt has c baseball cards, and Jen has 9 fewer than 5 times as many cards as Matt. Jen gives Matt 14 cards. How many cards does Jen have now?
Answer:
Jen has 5c -23 cards now
Step-by-step explanation:
Matt has c baseballs.
Jen has 9 fewer than 5 times as Matt.
Mathematically, what Jen has will be 5c -9 baseballs
Now, Jen gives Matt 14 cards. This means that she lost 14 of her cards and we are going to subtract.
The number of cards she has now is thus 5c-9-14 = 5c -23 cards
The points (-2,4), (0,8), (1,10), and (3,14) are on a line. Which of the following statements are true?
Answer: y = 2x+8
Check out this graph I supplied you with!
which of the following shows the correct steps to find the value of 8^1/3? (1 point)
Answer:
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
Step-by-step explanation:
Options are below
8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16
16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8
Given:
8^1/3
if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent
if 8 can be rewritten as a number to the 3rd power.
We have
8 = 2*2*2 = 2³
Therefore,
8^1/3=(2^3)^1/3
=2^3×1/3
=2^3/3
=2^1
=2
Please answer this question in two minutes
Answer:
work is shown and pictured