Answer:
Total area of the two rooms = (width1length1) + (width2length2)
Step-by-step explanation:
The area of the rectangular shape is given by = Length * breadth
Therefore the area of the two rooms can be calculated using the above formula when the variables lengths and widths are given.
Area 1= Area of the first room = length * breadth= (width1length1)
Area 2=Area of the second room = length * breadth= (width2length2)
Total area of the two rooms = Area1 + Area 2
= (width1length1) + (width2length2)
A shop that sells nuts has one mixture that is 30% pecans and 70% peanuts. A second mixture is 40% pecans and 60% peanuts. The manager wants to make a mixture that is 38% pecans. She wants to use 25 ounces more of the second mixture than of the first. How many ounces of each mixture should she use
Answer:
=> x = 8.33 oz weight of the first mixture therefore weight of the second mixture would be:
x+25= 8.33+25=33.33 oz
Step-by-step explanation:
We want to find the weight of each mixture which are unknown to us right now, therefore:
Let the weight of the first mixture be x. Then the weight of the second mixture would be (x+25) and the weight of final mixture would be (x + x + 25) = 2x+25.
The first mixture had 30% pecans, therefore the weight of pecans from the first mixture would be 0.3x.
The second mixture had 40% pecans, therefore the weight of pecans from the second mixture would be 0.4 * (x+25).
We will have 38% pecans in the final mixture hence the weight of pecans is 0.38 of the total weight of pecans in the final mixture.
0.38 * (2x + 25)
Therefore
0.38 * (2x + 25) = 0.3x + 0.4*(x + 25).
Now we have one equation one unknown and solve for x:
=> 0.76x + 9.5 = 0.7x + 10
=> 0.76x - 0.7x = 10 - 9.5
=> 0.06x = 0.5
=> x = 50/0.06
=> x = 50/6 = 25/3
=> x = 8.33 oz weight of the first mixture therefore weight of the second mixture would be:
x+25= 8.33+25=33.33 oz
Suppose that telephone calls arriving at a switchboard follow a Poisson process with an average of 5 calls per minute. What is the probability up to a minute will elapse by the time 2 calls have come into the switchboard
Answer:
The correct answer is "0.0842".
Step-by-step explanation:
Given:
X = 5
By using the Poisson's distribution formula, we get
The probability will be:
⇒ [tex]P(x=2)=\frac{\lambda^x.e^{-\lambda}}{x!}[/tex]
By substituting values, we get
[tex]=\frac{(5)^2\times e^{-5}}{2!}[/tex]
[tex]=\frac{25\times e^{-5}}{2!}[/tex]
[tex]=0.0842[/tex]
. There are 1,716 students participating in Field Day. They are put into teams of 16 for the
competition. How many teams are created?
Answer:
107 TEAMS
Step-by-step explanation:
1716/16=107
Boeing currently produces five models of airplanes for commercial sale. The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes. Her job is to analyze which three to buy. How many combinations will she have to analyze
Answer:
10 combinations
Step-by-step explanation:
Given
[tex]n = 5[/tex] --- total production
[tex]r = 3[/tex] --- aircraft to select
Required
The total number of combination
The number of combination is calculated using:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^5C_3 = \frac{5!}{(5 - 3)!*3!}[/tex]
[tex]^5C_3 = \frac{5!}{2!*3!}[/tex]
Expand
[tex]^5C_3 = \frac{5*4*3!}{2*1*3!}[/tex]
[tex]^5C_3 = \frac{5*4}{2*1}[/tex]
[tex]^5C_3 = \frac{20}{2}[/tex]
[tex]^5C_3 = 10[/tex]
Find the Circumference of the circle. Use 3.14 for π. Round your answer to the nearest tenth.
Answer:
28.3 cm
Step-by-step explanation:
The formula to find the circumference is 2•π•radius. The diameter is 9 cm, so the radius is 9/2 = 4.5 cm. So, the circumference is:
2•4.5•3.14 = 28.26 ≈ 28.3 cm
-55x / 2 - 10 > -185 / 2
Answer:
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 3
Interval Notation: ( −∞, 3)
You are saving to buy a speed boat. Starting today, you will put $1,000 into an investment account. Each month thereafter, your contribution will be .1% (.001) higher than the month before, so that your contribution next month will be .1% higher than today, and so forth and so on. The investment account has a periodic monthly interest rate of .4% (.004). Ignore taxes. You will make contributions until 5 years from today.
At the end of five years, when you put in your last contribution, how much will you have saved?
Answer:
You will have saved $69,612 after five years.
Step-by-step explanation:
This can be calculated using the for formula for calculating the future value of a growing annuity as follows:
FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)
Where;
FW = future value or amount you will have saved after five years = ?
C = first deposit = $1,000
r = periodic monthly interest rate of = 0.4%, or 0.004
g = growth rate of contribution = 0.1%, or 0.001
n = number of months = 5 years * 12 = 60
Substituting all the values into equation (1), we have:
FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))
FV = $1,000 * 69.612001854052
FV = $69,612.00
Therefore, you will have saved $69,612 after five years.
A coffee pot holds 5 1/2 quarts of coffee. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
22 cups
Step-by-step explanation:
1 quart is 4 cups. So therfore 5 1/2 * 4 =22
Hope this helped :)
solve all for brainiest
Answer:
a =55
b =16
c = 25
d = 9
Step-by-step explanation:
of means multiply is means equals
20% of a is 11
.20 a = 11
Divide by .20
a = 11/.20
a=55
75% of b is 12
.75 b =12
Divide by .75
b = 12/.75
b = 16
80% of c is 20
.80 c =20
Divide by .80
c = 20/.80
c =25
200% of d is 18
2.00 d = 18
Divide by 2.0
d = 18/2
d =9
the profit when selling 'x' pairs of shoes is P(x)=-4x^2+32x-39. How many pairs of shoes should be sold in order to maximize the profit
4 pairs
5 pairs
6 pairs
7 pairs
Answer:
A
Step-by-step explanation:
The profit for selling x pairs of shoes is given by:
[tex]P(x)=-4x^2+32x-39[/tex]
And we want to determine the number of pairs that needs to be sold in order to maximize profit.
Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex point. The x-coordinate of the vertex of a quadratic is given by:
[tex]\displaystyle x=-\frac{b}{2a}[/tex]
In this case, a = -4, b = 32, and c = -39. Substitute and evaluate:
[tex]\displaystyle x=-\frac{(32)}{2(-4)}=\frac{32}{8}=4[/tex]
So, in order to maximize profit, only four pairs of sohoes should be sold.
Our answer is A.
Answer:
A
Step-by-step explanation:
f(x) = x3 + 6x2 – x
f(x) = 30?
Answer and Step-by-step explanation:
The answer is 2 (which is equal to x).
If you were to plug 2 in to the function, the result if 30.
[tex]x^{3}+ 6x^{2} -x\\\\\\\\(2)^3+6(2)^2 - 2 = 30 = f(2)[/tex]
#teamtrees #PAW (Plant And Water)
In 9b3 + 2b4 − 17b + b2, which term has the largest exponent?
You put $425 Into a savings account that earned 8% annual interest compounded quarterly a) Write a function that represents the balance of the account after t years. b) How much money will you have in the account after 6 years? (Be sure to round appropriately, this is money!)
9514 1404 393
Answer:
a) f(t) = 425(1.02)^(4t)
b) $683.59
Step-by-step explanation:
a) The compound interest formula is ...
A = P(1 +r/n)^(nt)
giving the balance A of an investment of principal P for t years at annual rate r compounded n times per year.
We have P = 425, r=0.08, and n=4, so we can write the function f(t) as ...
f(t) = 425(1+0.08/4)^(4t)
f(t) = 425(1.02)^(4t)
__
b) The balance after 6 years is ...
f(6) = 425(1.02^(4·6)) = 425(1.02^24) = 683.59
The account balance after 6 year will be $683.59.
(4+2)+8=14 choose an equivalent addition sentence that shows the associative of addition
Answer:
14 = 14
Step-by-step explanation:
(4 + 2) + 8 = 14
6 + 8 = 14
14 = 14
help if you can! no links please :)
Answer:5/12
Step-by-step explanation:
Using the following image-solve the problems below given that M the midpoint of LN.
Hello,
[tex]11x-21=8x+15\\\\3x=36\\\\x=12\\\\LM=11*12-21=111\\\\MN=8*12+15=111\\\\LN=2*111=222\\\\[/tex]
The table shows the first three terms of a
geometric sequence. Which of the following is a
formula for f(n) ?
Answer: E
Step-by-step explanation:
By using substitution we can find the answer is correct or not.
[tex]3(-2)^n\\3(-2)^1\\3(-2)\\-6\\3(-2)^2\\3(4)\\12\\3(-2)^3\\3(-8)\\-24[/tex]
as you can see the equation in answer E worked every time
The table shows the relationship between Megan’s earnings and the hours that she worked.
What is the missing value in the table?
Earnings ($) 19 38 57 ? 95
Hours 2 4 6 8 10
A. 65
B. 66.5
C. 76
D. 85.5
Answer:
C.76
Step-by-step explanation:
2x= 19
x= 9.5
8x =?
8(9.5)= ?
76= ?
please please pleaseee help asapppp
Answer:
Step-by-step explanation:
volume of a cylinder=πr^2h
=π*5^2*15
=π*25*15
=375π cm^3
Volume of a cylinder = πr^2h
→ π × 5^2 × 15
→ π × 25 × 15
→ 375π cm^3
Is this True or false ?
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Radical expression.
Find the slope of the line
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 421 grams with a standard deviation of 20. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled
Answer:
The p-value of the test is of 0.0086 < 0.01, which means that there is sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags.
At the null hypothesis, we test if they are at the correct weight, that is:
[tex]H_0: \mu = 431[/tex]
At the alternative hypothesis, we test if they are underfilled, that is:
[tex]H_1: \mu < 431[/tex]
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
431 is tested at the null hypothesis:
This means that [tex]\mu = 431[/tex]
A 26 bag sample had a mean of 421 grams with a standard deviation of 20.
This means that [tex]n = 26, X = 421, s = 20[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{421 - 431}{\frac{20}{\sqrt{26}}}[/tex]
[tex]t = -2.55[/tex]
P-value of the test and decision:
Using a t-distirbution calculator, the p-value is found using a left-tailed test(test if the mean is less than a value), with 26 - 1 = 25 df and t = -2.55. This p-value is of 0.0086.
The p-value of the test is of 0.0086 < 0.01, which means that there is sufficient evidence to support the claim that the bags are underfilled
Solve for ? Round to near whole number
Answer:
? =50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos ? = adj/hyp
Taking the inverse cos of each side
cos^-1 (cos ?) = cos^-1( 14/22)
? =50.47880364
To the nearest degree
? =50
Can y’all help me please
Answer:
w = 5
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
28 = 2(2w-1 + w)
Combine like terms
28 =2(3w-1)
Divide each side by 2
28/2 = 2/2(3w-1)
14 = 3w-1
Add 1 to each side
14+1 = 3w-1+1
15 = 3w
Divide each side by 3
15/3 =3w/3
5 =w
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y= -2/5x-6
Step-by-step explanation:
y int is at -6
rise/run= -2/5
Find the greatest common factor of 56, 42, and 98.
Question 13 options:
A)
7
B)
36
C)
14
D)
24
Answer:
C, 14
Step-by-step explanation:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
The factors of 98 are: 1, 2, 7, 14, 49, 98
Then the greatest common factor is 14. (The greatest factor that they all have in common.)
Please vote brainliest, thanks!
Select the correct measures for x and y.
*Will mark brainliest if correct*
Amy's art class is 6 hours long. How long is her class in minutes?
Answer:
360 minutes.
Step-by-step explanation:
Answer:
360 minutes
Step-by-step explanation:
The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately how far from the base of the building should the bottom of the ladder
be placed?
Answer:
Assuming that ladders should be placed at an 75° angle, let's translate it into a slope of 3.732 of a line (looked the value up, was too lazy to calculate it)
the distance from the orign in the picture is your answer, and one side of a triangle formed by the wall, the ground and the ladder
What is the area of this trapezoid
