Answer:
8 pounds
Step-by-step explanation:
Let a, b, c represent the number of pounds of nuts in the first, second, and third boxes, respectively. We can write the equations ...
a = b +c -6 . . . . . first box has 6# fewer than the total of the others
b = a +c -10 . . . . second box has 10# fewer than the total of the others
Substituting the second equation into the first, we find ...
a = (a +c -10) +c -6
0 = 2c -16 . . . . subtract a
0 = c -8 . . . . . . divide by 2
8 = c . . . . . . . . . add 8
There are 8 pounds of nuts in the third box.
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]
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
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
Issa knows that ΔRED ≅ ΔTAN by the SSS theorem. She then concluded that ∠R ≅ ∠T. What reason can she use as a justification? a CPCTC b vertical angle theorem c alternate interior angles d None of these choices are correct.
Answer:
(A)CPCTC
Step-by-step explanation:
Issa knows that ΔRED ≅ ΔTAN by the SSS theorem.
If two triangles are congruent, their corresponding parts will always be congruent. In fact, their corresponding angles will be equal.
Therefore, Issa concluded that ∠R ≅ ∠T by the fact that Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
The correct option is A.
Similarly, we can also conclude that:
∠E ≅ ∠A; and∠D ≅ ∠NEvaluate: m - 12 when m = 23.
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
Please answer this question in two minutes
Answer:
work is shown and pictured
factorise this expression as fully as possible 2x^2+6x
Answer:
(Factor out 2x from the expression)
2x (x +3)
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.
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
mr rai bys a radio for rs 1880ans sell it to mr Sherpa at 20 percent .how much money does he pay for it
Answer:
Rs 1504
Step-by-step explanation:
Mr. Rai buys for Rs 1880.
He sells it to Mr. Sherpa at 20% discount.
1880 × 20%
= 376
1880 - 376
= 1504
Mr. Sherpa buys it for Rs 1504.
Answer:
Mr. Rai will be receiving $1504 if he sells the radio for 20%.
Step-by-step explanation:
To find a discount, move the decimal over twice on the percentage. After doing this, multiply that number by the original number. You will get a new number. Subtract the price by the new number and there is your answer.
For Example:
20% = .20
1880*.20= 376
1880-376= 1504
There is a simpler way of doing this as well. Multiplying by .8 (which is the remainder of 100% after taking away 20% if this makes sense) will give you the answer immediately. Hopefully this helps.
Good luck!
PLEASE HELP ME ASAP!
Answer:
x =- 3 and y = -7
Step-by-step explanation:
2X-2Y=-8
X=2y + 11
We need to isolate both X and Y in both equations
so
2x-2y=-8
(add 2y to both sides)
2x=-8+ 2y
(divide both sides by 2)
x=-4+y and x=2y+11
because both of these equations are the same we can put them together
4+y=2y+11
(subtract y)
4=y+11
(subtract 11)
-7=y
so y = -7
then to find x you just need to plug in y to one of the equations
x=2(-7) + 11
x= -14 +11
x = -3
Answer:
x = - 19, y = - 15
Step-by-step explanation:
Given the 2 equations
2x - 2y = - 8 → (1)
x = 2y + 11 → (2)
Substitute x = 2y + 11 into (1)
2(2y + 11) - 2y = - 8 ← distribute and simplify left side
4y + 22 - 2y = - 8
2y + 22 = - 8 ( subtract 22 from both sides )
2y = - 30 ( divide both sides by 2 )
y = - 15
Substitute y = - 15 into (2) for corresponding value of x
x = 2(- 15) + 11 = - 30 + 11 = - 19
Solution is x = - 19, y = - 15
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
Please answer this question fast in two minutes
Answer:
132 degree
Step-by-step explanation: angle kjh is 132 degree and since lk is a straight line it is 180 degree. angle kjh is 132 degree so, angle LJM is 132 degree. This is because adjacent angles are equal as you can see, Angle LJM is adjacent to Angle KJH.
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
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
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 small community organization consists of 20 families, of which 4 have one child,8 have two children, 5 have three children, 2 have four children, and 1 has fivechildren. If one of these families is chosen at random, what is the probability it has`children,`= 1,2,3,4,5?
Answer and Step-by-step explanation:
According to the situation, The probabilities for each one is given below:
As there are 20 families
So the probabilities for each one is
For four families have one child is
[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]
For eight families have two children is
[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]
For five families have three children is
[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]
For two families have four children is
[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]
For one family have five children is
[tex]= \frac{1}{20}[/tex]
Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8 PLZ HELP
Answer:
Answer:
3x + 3y = 0
7x - y = 8
Step-by-step explanation:
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:
If you are given the graph of h(x) = log6x, how could you graph M(x) = log6(x+3)?
Answer:
Translate 3 units to the left
Step-by-step explanation:
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:
Anyone know please help!!
Answer:
only the inverse is a function
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!
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.
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.
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
Find the value of x. Round the length to the nearest tenth.
Answer:
[tex] x = 5.1 yd [/tex]
Step-by-step Explanation:
Angle of depression is congruent to angle of elevation.
Therefore, angle of elevation of the given figure, which is opposite to x is 25°.
Adjacent length = 11 yd
Opposite length = x
Trigonometric ratio formula for finding x is shown below:
[tex] tan(25) = \frac{opposite}{adjacent} [/tex]
[tex] tan(25) = \frac{x}{11} [/tex]
Multiply both sides by 11 to solve for x
[tex] 11*tan(25) = x [/tex]
[tex] 5.129 = x [/tex]
[tex] x = 5.1 yd [/tex] (to the nearest tenth)
Find the values of the variables and the measures of the angles
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
The tape diagram represents an equation. Write an equation to represent the image.
Answer:
5n = 1.75
Step-by-step explanation:
The 2 bars are equal thus lower equals upper, that is
5n = 1.75
How is it that it is (-11/4,-1/2) ?
Answer:
Choice 3
Step-by-step explanation:
A(-5,-1) and B(4, 1)
Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2
Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:
-5 + 9/4= (-20+9)/4= -11/4-1 +2/4= (-4+2)/4= -2/4= -1/2So P= (-11/4, -1/2) and choice 3