Answer:
when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Step-by-step explanation:
Let the initial length of the sides of the cube = x unit
when the length of the cube = x ; volume of the cube = length × breadth × height = x × x × x = x³ (unit)³
when the length increased by 1 unit,
new length = (x + 1) unit
New volume = (x + 1) × (x + 1) × (x + 1)
multiplying the first two brackets
New volume = (x² + 2x + 1 ) (x + 1)
espanding the brackets
New volume = x³ + 2x² + x + x² + 2x + 1
New volume = x³ + 3x² + 3x + 1 (unit)³
Change in volume:
(New volume) - (old volume)
(x³ + 3x² + 3x + 1) - (x³)
x³ + 3x² + 3x + 1 - x³
collecting like terms:
(x³ - x³) + 3x² + 3x + 1
0 + 3x² + 3x + 1
change in volume = 3x² + 3x + 1
Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast
Graph -8x-y=8
Answer:
(-1,0) and (0,-8)
Step-by-step explanation:
Hey there!
Well first we’ll graph -8x - y = 8,
Look at the image below
By lookig at the image below we can tell the 2 points are at,
(-1,0) and (0,-8)
Hope this helps :)
what is sum of all palindromic numbers from 1 to 100
Answer:
540
Step-by-step explanation:
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99
Answer:
540
Step-by-step explanation:
Hey there!
Well we need to first find all the palindromic numbers,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99
Add
= 540
Hope this helps :)
Guess the rule and write down the missing number:
Answer:
17
Step-by-step explanation:
We are adding the previous two terms
1+5 = 6
5+6 = 11
6+11 = 17
11+17 = 28
The missing term is 17
Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.
Answer:
The minimum sample size is [tex]n =135[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]
The margin of error is [tex]E = 0.1[/tex]
Generally the sample proportion can be mathematically evaluated as
[tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]
[tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]
[tex]\r p = 0.475[/tex]
Given that the confidence level is 98% then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2\%[/tex]
[tex]\alpha =0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
Generally the minimum sample size is evaluated as
[tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]
[tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]
[tex]n =135[/tex]
Equivalent means having ___ ___
I need two answer omg pls helppp ;-;
Answer:
equal value and function
Step-by-step explanation:
The amount of money spent on textbooks per year for students is approximately normal.
a. To estimate the population mean, 19 students are randomly selected the sample mean was $390 and the standard deviation was $120. Find a 95% confidence for the population meam.
b. If the confidence level in part a changed from 95% 1to1999%, would the margin of error for the confidence interval (mark one answer): decrease stay the same increase not enough information to answer
c. If the sample size in part a changed from 19 10 22. would the margin of errot for the confidence interval (mark one answer): decrease in stay the same increase in not enough information to answer
d. To estimate the proportion of students who purchase their textbookslused, 500 students were sampled. 210 of these students purchased used textbooks. Find a 99% confidence interval for the proportion of students who purchase used text books.
Answer:a
a
[tex]336.04 < \mu < 443.96[/tex]
b
The margin of error will increase
c
The margin of error will decreases
d
The 99% confidence interval is [tex]0.4107 < p < 0.4293[/tex]
Step-by-step explanation:
From the question we are told that
The sample size [tex]n = 19[/tex]
The sample mean is [tex]\= x = \$\ 390[/tex]
The standard deviation is [tex]\sigma = \$ \ 120[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
So
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]
=> [tex]E = 53.96[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]
=> [tex]336.04 < \mu < 443.96[/tex]
When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider
Generally the sample size mathematically varies with margin of error as follows
[tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]
So if the sample size increases the margin of error decrease
The sample proportion is mathematically represented as
[tex]\r p = \frac{210}{500}[/tex]
[tex]\r p = 0.42[/tex]
Given that the confidence level is 0.99 the level of significance is [tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]
=> [tex]E = 0.0093[/tex]
The 99% confidence interval is
[tex]\r p - E < p < \r p + E[/tex]
[tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]
[tex]0.4107 < p < 0.4293[/tex]
If you have $100 in a savings account earning 3% interest per year, how much will you have in
two years?
Answer:
$106
Step-by-step explanation:
You have 100$ in savings account
Interest rate =3%
Time = 2 years
Total in 2 years:
100 + 2*3% = 100 *1.06= $106The interest formula is as follows:
Amount Invested · Rate = Interest Earned
If we invest $100 at 3% interest per year,
how much do we earn that year?
Well based on our formula, we can simply multiply 100 · 3%.
Think of the 3% as 3/100.
So we have 100 · 3/100 and the 100's cancel and we're left with 3.
So $3 is earned in 1 year.
So after two years, you will have double that or $6.
find the sum 7+7(2)+7(2^2)+...+7(2^9)
Answer:
7161
Step-by-step explanation:
7 + 7(2) + 7(2)² + ... + 7(2)⁹
= ∑₁¹⁰ 7(2)ⁿ⁻¹
= 7 (1 − 2¹⁰) / (1 − 2)
= 7161
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?
Step-by-step explanation:
Given that,
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.
It means that the total number of outcomes are 17
We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11
So, probability is given by :
[tex]P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}[/tex]
[tex]P(E)=\dfrac{11}{17}[/tex]
So, the probability that the toast lands buttered side down is 11/17.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases, how much would your cash back be?
Answer:
$16.43.
Step-by-step explanation:
At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.
At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.
9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.
Hope this helps!
The amount of cashback that you earned will be $16.42.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.
The total cashback is calculated as,
⇒ 0.02 x $485.72 + 0.01 x $671.28
⇒ $9.71 + $6.71
⇒ $16.42
More about the percentage link is given below.
https://brainly.com/question/8011401
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_Thirty-two holes are drilled in rows on a metal block. The number of rows is more than the number of holes in each
row. Find the number of row. (a)7 (b)25(c)67
(d)4 (e) 12
_
Answer:
D
Step-by-step explanation:
Let the number of rows be x
And the numbers of holes in each be y
xy = 32
x and y must be factors of 32
From options stated
4 is the only factor of 32
Hence option D is correct
There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble? StartFraction 4 over 10 EndFraction (StartFraction r over 10 EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction 4 over 10 r EndFraction) StartFraction 4 over 10 + r EndFraction (StartFraction r over 10 + r EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction r over 10 r EndFraction)
Answer:
4/ (10+r) * r/ (10+r)
Step-by-step explanation:
four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles
P( blue) = blue marbles / total marbles
= 4/ (10+r)
Then replace
P( r) = red marbles / total marbles
= r/ (10+r)
P( blue replace ,red) =P ( blue ) * P(red)
= 4/ (10+r) * r/ (10+r)
= 4r / ( 10+r) ^2
Answer:
C. 4/10+r (r/10+r)
Step-by-step explanation:
EDG20
Which statement about this function is true?
O A.
The value of a is positive, so the vertex is a minimum.
OB.
The value of a is negative, so the vertex is a minimum.
OC.
The value of a is negative, so the vertex is a maximum.
OD
The value of a is positive, so the vertex is a maximum.
Answer:
b
Step-by-step explanation:
The value of a is negative, so the vertex is a minimum.
Jullian measures the distance he drives to work each day using the odometer on his car, which measures distance in miles, accurate to the nearest tenth of a mile. Using that measurement, he claims that the exact distance he drives to work is 11.7 miles. Use complete sentences to explain why jullian is incorrect
Answer:
Kindly check explanation
Step-by-step explanation: Jullian's claim that the distance she drives to work is exactly 11.7miles is incorrect because, in other to record or get the exact result of a certain calculation such as Jullian's Distance, the value of the distance obtained will not be approximated or rounded. In this scenario, Distance was to the nearest tenth of a mile, thereby altering the true outcome of the calculation.
The word exact means that what is stated is very precise and does not fall below or above in any respect. However, a number whose accuracy is to the nearest tenth of a mile, violates this assertion.
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses. Examples to get 0: 0=4+4−(4+4); 0=44−44; 0=4×4−4×4
Answer:
0=4×4−4×4
Step-by-step explanation:
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
1 = 4 ÷ 4
2 = (4 + 4) ÷ 4
3 = (4 + 4 + 4) ÷ 4
4 = 4 + 4 - 4
5 = (4 × 4 + 4) ÷ 4
6 = (4 + 4) - (4 ÷ 4) - (4 ÷ 4)
7 = (4 + 4) - (4 ÷ 4)
8 = 4 + 4
9 = (4 + 4) + (4 ÷ 4)
10 = (4 + 4) + (4 ÷ 4) + (4 ÷ 4)
If your starting salary is $40000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn one the first 16 years that you work
Answer:
Total amount in dollars= $64614.00
Step-by-step explanation:
Initial starting salary is $40000.
Rate of increase is 3%
Number of years is 16 years
The salary is compounded yearly.
Amount A after 16 years is given as
A= p (1+r/n)^ (nt)
A=40000(1+0.03/16)^(16*16)
A= 40000(1.001875)^(256)
A=40000(1.61534824)
A= 64613.92959
Total amount in dollars= $64614.00
Answer: the answer is $806275
Step-by-step explanation:
A p e x
At a baby shower, 15 guests are in attendance and 4 of them are randomly selected to receive a door prize. If all 4 prizes are identical, in how many ways can the prizes be awarded?
Answer:
1365
Step-by-step explanation:
We figure out combinations using this formula: n!
r!(n-r)!
n=15
r=4
So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1
r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1
Put this together and you have 15x14x13x12/4x3x2x1=
There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.
Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).
So, the number of ways to award the prizes is:
C(15, 4) = 15! / (4! (15 - 4)!)
= 15! / (4! 11!)
= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)
= 1365.
Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
Learn more about permutation here:
brainly.com/question/1216161
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If f(x)=ax+b and f(2)=1 and f(-3)=11, what is the value of A?
Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
simplify the following expression by combining like terms 2x+7x^2-5x+8x^2
Answer:15x^2-3x
Step-by-step explanation:
16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
Reset
Next
Answer: A) g(x) = 3x - 14
Step-by-step explanation:
Solve the equation for y and replace y with g(x):
y - 3x = -14
y = 3x - 14
g(x) = 3x - 14
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
write 768,676 in words
Answer:
seven hundred sixty-eight thousand six hundred seventy-six
hope this answer correct :)
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
Sam have worked these hours during the week: 4.5, 8.75, 9.5, 10, and 4.25 hours. How many hours did Sam work?
Answer:
37 hours
Step-by-step explanation:
4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours
Answer:
37 hours
Step-by-step explanation:
4.5 hours = 4 hrs and 30 mins
8.75 hrs = 8 hrs and 45 mins
9.5 hrs = 9 hrs and 30 mins
10 hrs = 10 hrs and 0 min
4.25 hrs = 4 hrs and 15 mins
(30 + 45 + 30 + 15) mins = 2 hrs
Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours
If there are 80 students in a class and 20 are seniors, what proportion of students are not seniors?
Answer:
3/4
Step-by-step explanation:
First find the number that are not seniors
80 -20 = 60
60 are not seniors
The ratio of not seniors to total
60/80
Divide top and bottom by 20
3/4
Answer:
60 students
Step-by-step explanation:
80 -20 = 60
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
The probability distribution of number of televisions per household in a small town is given below.
x 0 1 2 3
P(x) 0.05 0.15 0.25 0.55
a. Find the probability of randomly selecting a household that has one or two televisions.
b. Find probability of randomly selecting a household that has one or two televisions
Answer: 0.20
Step-by-step explanation:
The given probability distribution of number of televisions per household in a small town:
x 0 1 2 3
P(x) 0.05 0.15 0.25 0.55
To find : The probability of randomly selecting a household that has one or two televisions ( in both parts a. and b.).
The computations for this would be :
P( 1 or 2) = P(1)+P(2)
= 0.05+0.15
= 0.20
Hence, the required probability= 0.20
Answer:
Step-by-step explanation:
The area formula, A = tr2, would be used to find the area of a
A. square.
B. rectangle.
O circle.
D. triangle
E parallelogram.
Assuming you meant to write [tex]A = \pi r^2[/tex], then the answer is C) circle
On your keyboard, you can say A = pi*r^2 to mean the same thing as above.
In a survey of 15000 students of different schools, 40% of them were found to have tuition before the see examination. Among them 50% studied only mathematics ,30% only science and 10% studied others subject. how many student studied mathematics as well as science.
Answer: 600 students.
Step-by-step explanation:
Ok, we start with 15,000 students.
40% of them had tuition, so the actual number of them that had tuition is:
15,000*0.40 = 6,000.
Now we want to find the number of students that studied math and science.
50% only studied math,
30% only studied science
10% studied other subjects.
So 50% + 30% + 10% did NOT studied both math and science
90% is the percentage that did not study math and mathematics as well as science, then the other 10% did.
Then, out of the 6,000 students that had tuition, 10% studied math and science, the total number is:
6,000*0.10 = 600
