Answer:
The mean of the remaining 3 boys is 51.
Step-by-step explanation:
The mean mark of the entire group ([tex]p_{10}[/tex]), dimensionless, is:
[tex]p_{10} = \frac{1}{10}\cdot \Sigma_{i = 1}^{10} x_{i}[/tex] (Eq. 1)
([tex]p_{10} = 58[/tex])
[tex]\frac{1}{10}\cdot \Sigma_{i=1}^{10} x_{i} = 58[/tex] (Eq. 1b)
Where [tex]x_{i}[/tex] is the mark of the i-th boy, dimensionless.
In addition, we know the following mean marks from statement:
[tex]p_{7} = \frac{1}{7} \cdot \Sigma_{i = 1}^{7} x_{i}[/tex] (Eq. 2)
([tex]p_{7} = 61[/tex])
[tex]\frac{1}{7}\cdot \Sigma_{i=1}^{7} x_{i} = 61[/tex] (Eq. 2b)
[tex]p_{3} = \frac{1}{3}\cdot \Sigma_{i=8}^{10}x_{i}[/tex] (Eq. 3)
Where:
[tex]p_{7}[/tex] - Mean mark of the first 7 boys, dimensionless.
[tex]p_{3}[/tex] - Mean mark of the remaining 3 boys, dimensionless.
By applying sum properties in (Eq. 1b) and using (Eq. 2b) and (Eq. 3), we obtain the mean of the remaining 3 boys:
[tex]\frac{1}{10}\cdot [\Sigma_{i = 1}^{7}x_{i}+\Sigma_{i=8}^{10}x_{i}] = 58[/tex]
[tex]\frac{1}{10}\cdot [7\cdot (61)+3\cdot p_{3}] = 58[/tex]
[tex]7\cdot (61) + 3\cdot p_{3} = 580[/tex]
[tex]3\cdot p_{3} = 153[/tex]
[tex]p_{3} = \frac{153}{3}[/tex]
[tex]p_{3} = 51[/tex]
The mean of the remaining 3 boys is 51.
Convert to decimal form: 1.118×10−6.
Find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.43% per week
Answer choices:
A) f(t) = 70 x 0.9957^t
B) f(t) = 70 x 1.43^t
C) f(t) = 0.43 x 0.3^t
D) f(t) = 70 x 1.0043^t
Answer:
a- just took the test
Step-by-step explanation:
i will KISS U ON THE MOUTH IF U HURRY PLS HELP find the derivative dy/dx for y=(x^2+4x) / (x^3-5)
Use the quotient rule:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^3-5)\frac{\mathrm d(x^2+4x)}{\mathrm dx}-(x^2+4x)\frac{\mathrm d(x^3-5)}{\mathrm dx}}{(x^3-5)^2}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(2x+4)(x^3-5)-3x^2(x^2-4x)}{(x^3-5)^2}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{x^4 - 16 x^3 + 10 x + 20}{(x^3-5)^2}[/tex]
PLZ HELP BASIC c ALGEBRA BRAINLIEST TO QUICKEST ANSWER
Biologists have found that the number of chips some crickets make per minute are related to temperature. When crickets chirp 124 times a minute it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.
Write an equation in Slope Intercept, Standard, or Point Slope form that represents the situation.
Salty's Surf Shop loses $35,000 during cold, rainy summers and profits $175,000 during summers that
are hot and dry. The probability that it will be hot and dry during summers is 30%. What is the expected
profit Salty would realize over 10 years?
Answer:
$280,000
Step-by-step explanation:
Given that:
Loss during cold = $35000
P(hot and dry) = 30% = 0.3
Hence ; P(cold) = 1 - 0.3 = 0.7
Profit during hot and dry= $175,000
Expected profit over 10 years =?
________Hot & Dry __________ Cold __
X : _______ 175,000 ________ -35,000
P(X) : _______ 0.3 ____________ 0.7
Expected probability (E(X)) = Σx*p(x)
= 0.3(175,000) + 0.7(-35,000)
= 52,500 + (-24,500)
= $28,000
Hence, expected profit over 10 years :
$28,000 * 10 = $280,000
Please help!
Simplify the expression using order of operations:25 - 5 + 36/9 - 6(7)
Answer:
-18
Step-by-step explanation:
Follow these steps to get your answer!
Divide 36/9 and multiply -6(7)
25 - 5 + 4 - 42
Subtract 25-5
20 + 4 -42
Add 4 to 20.
24-42
Subtract 42 from 24.
-18
Answer:
-18
Step-by-step explanation:
start with the figure in brackets. 6(7)=42
then do division. 36/9=4
our expression now is 25-5+4-42
addition first 25+4=29
finish with subtraction. 29-5-42=-18
answer=-18
what is the branch of mathematics that uses variables and operations?
Answer:
Algebra
Step-by-step explanation:
Answer:
algebra, you can check on google as well
Teresa babysits for her neighbors. She charges $13 for the first hour and $10 for each additional hour. Write a rule for the total amount of money she charges, T, based on the number of hours she babysits, H. Angela also babysits for her neighbors. She charges $11 per hour. Which babysitter, Teresa or Angela, will charge less to babysit for 2 hours? 3 hours? 4 hours? Show evidence for your answers.
Answer:
13 + 10 + 10= 23, 33
11 + 11 + 11 = 22, 33
Angela is cheaper for two
Same price for 3
Teresa is cheaper for 4
Step-by-step explanation:
You should choose who you want by the hours you will be gone knowing who is more and less
The time it takes to completely clean an office building follows an exponential distribution with a mean of 135 minutes. What is the probability of cleaning an office building in 135 minutes or less?
Answer:
0.63212
Step-by-step explanation:
Given that :
Mean cleaning time (μ) = 135
Probability of cleaning the office is 135 minutes or less
Using an exponential distribution probability calculator :
P(X ≤ 135) = 0.63212
How many 2/3 cup servings are in 28/3 cups of yogurt
The answer fam is..... 14
In how many different ways can a ski club consisting of 15 people selected a team for national championship? There are 4 spots available on the team going to national championship.
Answer:
Step-by-step explanation:
Combination has to selection. When selecting 4 people out of a pool of 15 people, this can be done as thus according to combination formuka:
15C4 = 15!/(15-4)!4!
15C4 = 15!/11!4!
15C4 = 15*14*13*12*11!/11!*4*3*2
15C4 = 15*14*13*12/24
15C4 = 32760/24
15C4 = 1365 different ways.
Hence this can be done in 1365 different ways
F(t) = 1,500(1.045)^t
The future value, F(t), of an investment after t years is given by the function defined above.
What is the initial value of the investment?
Answer: F(t)=1500
Step-by-step explanation:
hope this helps
The initial value of the investment in the given function is 1500.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
Given that the future value, [tex]F(t) = 1,500(1.045)^t,[/tex] of an investment after t years is given by the function defined above. Therefore, the initial value of the investment in the given function is 1500.
Learn more about Compound Interest:
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find the value of x. PLEASE HELP!!!!
The answer is 8 - but I need to show my work.
Thanks so much
Answer:
Step-by-step explanation:
Because of the right angle (90 deg) in red, and the horizontal line on the bottom axis,
we know that :
49 + (1+5x) = 90
solving for x delivers x=8
1,032 divided by 10 to the 4th power
Answer:
0.1032
Step-by-step explanation:
Answer:
25000
Step-by-step explanation:
10x10=100
100x10=1000
1000x10=10000
10000x10=100000
100000 divied by 4= 25000
The coordinates of point T are (0,6). The midpoint of ST is (4.-6). Find the coordinates
point S.
Answer:
The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].
Step-by-step explanation:
Let [tex]T(x, y) = (0, 6)[/tex] and [tex]M(x,y) = (4,-6)[/tex], which is the midpoint of line segment ST. From Linear Algebra we get that midpoint is the following vector sum of endpoints S and T. That is:
[tex]M(x,y) = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot T(x,y)[/tex] (Eq. 1)
Now clear S in the previous expression:
[tex]S(x,y) = 2\cdot M(x,y) - T(x,y)[/tex] (Eq. 1b)
Then, the coordinates of point S are:
[tex]S(x,y) = 2\cdot (4,-6) - (0,6)[/tex]
[tex]S(x,y) = (8, -18)[/tex]
The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].
Cindy is three years older than her brother and 8 years older than her sister. If the sum of
their ages is 25 years, how old is Cindy now?
Answer:
She is 12 years old
12-3=9
12-8=4
12+9+4=25
Coca-Cola bottling company makes both glass and aluminum containers for their soda. The bottle machine is able to produce 2100 bottles every 6 hours. How many more bottles could they make in 8 hours that they can in 6 hour?
Group of answer choices
Jacob is a construction worker who earns a yearly income given by the expression 2000x + 3000, where x is the number of hours he works each week. Carlos works with Jacob and earns a yearly income given by the expression 3800x – 40000. A manager predicts that if Carlos and Jacob each work 35 hours, they will earn the same amount of money.
PART A:The number of hours that makes the equation true is
Options: 24, 27, 29,31,34
PART B:Round your answer to the nearest whole number. The manager's prediction is
Options: equal to, less than, greater than
the actual number of hours that Carlos and Jacob need to work to earn the same amount of money.
Answer:
[tex]x = 24[/tex]
24 is less than 35
Step-by-step explanation:
Given
Jacob: 2000x + 3000
Carlos: 3800x - 40000
Solving (a):
To solve (a), we need to equate both expressions;
[tex]3800x - 40000 = 2000x + 3000[/tex]
Collect Like Terms
[tex]3800x - 2000x = 40000 + 3000[/tex]
[tex]1800x = 43000[/tex]
Solve for x
[tex]x = 43000/1800[/tex]
[tex]x = 24[/tex] --- Approximated
Solving (b);
The manager's prediction is 35 hours.
And the actual hours is 24.
By comparison;
24 is less than 35
HELP ASAP
What is the value of x?
O x = 55°
O x = 60°
O x = 70°
O x = 110°
Answer:
the answer is the answer the answer is x=55 degrees because the angle sum for a triangle is 180 degrees and because we are told angle A and angle C are congruent that means you can simply take 180 - 70 to get 110 and i simply divided that by 2 and got 55 degrees
Step-by-step explanation:
Please help me everyone!
In Kennington, 25 legislators represent 500,000 people.
Kennington has 2,500,000 people. How much legislators do they need?
Please help, I repeat.
[tex]\huge\boxed{125.}[/tex]
[tex]\boxed{-------------------------------------}[/tex]
Explanation...
So, 25 legislators represents 500,000 people.
We are trying to find how much legislators you need to represent 2,500,000.
500,000*5=2,500,000.
25*5=125.
Therefore, your answer is 125.
[tex]\boxed{-------------------------------------}[/tex]
Hope i helped!
[tex]\huge\boxed{Thanks,Plip.}[/tex]
Answer: 125
In Kennington, 25 legislators represent 500,000 people.
Find how many times 500,000 go into 2,500,000 people.
2,500,000 ÷ 500,000 = 5
Now, multiply 5 by 25, because each 500,000 people are represented by 25 legislators.
25 x 5 = 125.
Answer = 125.
Hope this helps you!
si compro una camisa de 100 pesos con el 10% de descuento cuanto tengo que pagar en total
Answer:
$90
Step-by-step explanation:
10% de 100 es 10; 100-10=90
Answer:
90 pesos
Step-by-step explanation:
10% de 100 es 10. Resta esos 10 pesos de los 100, y te da tu resultado de 90 pesos.
Si necesitas que te lo explique mas, dime y te ayudare :)
Menu
BBQ Chicken Platter: $11.99
Sirloin Steak Fajitas: $14.99
Vegetarian Fajitas: $7.99
Shrimp Tacos: $8.59
Your family is going to their favorite restaurant this evening. Both your parents order the sirloin steak fajitas. Your little brother and sister are going to split the BBQ chicken platter. You order the shrimp tacos. What is the total bill for the family?
Answer:
$50.56
Step-by-step explanation:
First- Calculate the number of dishes ordered and their prices-
Parents order-
Sirloin Steak Fajitas: $14.99 x 2
Little Sister and little brother-
BBQ Chicken Platter: $11.99
Your order-
Shrimp Tacos: $8.59
Add the amount-
14.99 + 14.99 + 11.99 + 8.59 = 50.56
Total bill 50.56
find the rate of change ffor Y=4/5x-7/5
Answer:
4/5
Step-by-step explanation:
thats the slope so im assuming
What is the domain for...
y=0.25x-12
Answer:
Domain: (-infinity,infinity)
Step-by-step explanation:
You're welcome. :)
(I couldn't write the infinity symbol so I wrote infinity.)
What is the simplified form of this expression (6^-4)-9 over 6^6
Answer:hope this helps
Step-by-step explanation:
Hector has 11 model trains. On each model train there are 8 wheels. In total, how many wheels are on Hector’s model trains?
Answer:
I think the answer is 88 wheels.
Step-by-step explanation:
You multiple 11 and 8 to get your answer or you can take 8+8+8+8+8+8+8+8+8+8+8 to get your answer.
raphael takes 15 pages of notes during math class. Then he takes 35 pages of notes during 14 hours of math class. How many pages of notes would raphael expect to take during 3 hours of math class?
Answer:
Raphael will take 7.5 pages of notes during 3 hours of math class.
Step-by-step explanation:
Given;
35 pages were taken during 14 hours maths class
how many pages of math would Raphael take during 3 hours maths class ?
14 hours --------------35 pages
3 hours --------------- ?
= (3 x 35) / 14
= 7.5 pages
Therefore, Raphael will take 7.5 pages of notes during 3 hours of math class.
I need help nowwwwww !!!!!????
you should just have to times the yards by three like the second one is 12
estimate for 6 x 9 1/3
Answer:
Exact Form:
54/13
Decimal Form:
4.153846
Mixed Number Form:
4 2/13
Step-by-step explanation:
25x 10 ^ 6 in standard form
25x10⁶ = 2.5x10⁷=25000000
#Learn more
-34/51 in standard form
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