we would expect m to be positive.
In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.
Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.
If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.
For more questions on variables
https://brainly.com/question/27894163
#SPJ8
The circumference would ……. For example, a circle with a radius of 3 feet would have a circumference that is about 18 feet. When the radius doubles to 6 feet, the circumference is about ………. feet.
Answer:
37.7 feet
Step-by-step explanation:
The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.
For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).
When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).
In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.
For the transformed equation y=-2sin(x)-3, find and explain in detail how to find:
The amplitude of a sine function is the absolute value of the coefficient multiplying the sin(x) term.
How to explain the informationIn this case, the coefficient is -2. Since the amplitude is always positive, we take the absolute value of -2, which gives us an amplitude of 2.
The period of a sine function is given by the formula 2π/b, where b is the coefficient multiplying the x variable. In our equation, the coefficient is 1 (since sin(x) has an implied coefficient of 1), so the period is 2π/1 = 2π.
The phase shift of a sine function is determined by the value inside the parentheses. In this case, there is no value inside the parentheses, so there is no phase shift. The function remains centered around the origin (x = 0).
The vertical shift of a function is the constant term added or subtracted from the trigonometric function. In this equation, the constant term is -3, which means the graph is shifted downward by 3 units.
Learn more about amplitude on
https://brainly.com/question/3613222
#SPJ1
A factory produces bicycles and motorcycles by using two machines A and B . Machine A has at most 120 hours available and machine B has a maximum of 144 hours available. Manufacturing a bicycle requires 5 hours in machine A and 4 hours in machine B while manufacturing of a motorcycle requires 4 hours in machine A and 8 hours in machine B . if he gets profit of Rs.40 per bicycle and Rs.50 per motorcycle , how many bicycles and motorcycles should be manufactured to get maximum profit
To maximize profit, the factory should manufacture 8 bicycles and 12 motorcycles.
What is the optimal number of bicycles and motorcycles to maximize profit?Let us assume the number of bicycles as 'x'
Let us assume the number of motorcycles as 'y'.
The time constraint on machine A can be expressed as: 5x + 4y ≤ 120
The time constraint on machine B can be expressed as: 4x + 8y ≤ 144
To maximize profit, we need to maximize the objective function:
P = 40x + 50y
By graphing the constraints and finding the feasible region, we can determine the optimal solution.
Graphing the constraints:
For 5x + 4y ≤ 120:
Let's solve for y in terms of x: y ≤ (120 - 5x) / 4
For 4x + 8y ≤ 144:
Let's solve for y in terms of x: y ≤ (144 - 4x) / 8
The feasible region will be the intersection of the shaded regions:
y ≤ (120 - 5x) / 4
y ≤ (144 - 4x) / 8
Now, we will find the corner points of the feasible region:
When x = 0, y = 0
When x = 24, y = 0
When x = 8, y = 12
Substituting values into objective function P = 40x + 50y:
When x = 0, y = 0:
P = 40(0) + 50(0)
P = 0
When x = 24, y = 0:
P = 40(24) + 50(0)
P= 960
When x = 8, y = 12:
P = 40(8) + 50(12)
P = 1360.
Read more about profit function
brainly.com/question/4618859
#SPJ1
Determine the missing side lengths and angles for the similar triangles in the picture below.
∠C =
∠F =
AB =
DF =
NO LINKS!
Answer:
∡C=53°
∡F=102°
AB=11
DF=27
Step-by-step explanation:
Similar triangles have the same shape but not necessarily the same size. If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.
Some of the properties of similar triangles:
The ratio of any two corresponding sides of similar triangles is the same.The ratio of the areas of two similar triangles is the square of the ratio of any two corresponding sides.°ZThe ratio of the perimeters of two similar triangles is the same as the ratio of any two corresponding sides.The heights and medians of similar triangles are proportional to the corresponding sides of the triangles.For the question:
In ΔABC and ΔEFD
Since the respective corresponding angles are equal.
so,
∡A=∡E=25°
∡B=∡F=102°
∡C=∡D=53°
so, ΔABC [tex]\sim[/tex] ΔEFD
Again
Since their corresponding sides are proportional.
First, we need to find the ratio of their respective side:
DE: CA=63:14=9:2 when compared to big triangle to small triangle.
CA: DE=14:63=2:9 when compared to big triangle to small triangle.
AB=2/9*EF=2/9*49.5=11
DF=9/2*CB=9/2*6=27
Your lab regularly runs tests on mice, resulting in several bags of leftover mouse food sitting
in your storage closet. Your manager is setting a budget for next year and needs to know
if the lab can get by using just the leftovers or if you will need to purchase more mouse
food. Fortunately, you've been tracking the lab's food stores in your logs. Will the lab's
reserve of mouse food hold up for the entirety of next year? If not, when will the lab need
more food? Assume that next year is not a leap year.
Day
12/13
12/14
12/15
12/16
12/17
12/20
12/21
Food Reserves
112.6 kg
112.4 kg
111.2 kg
110.7 kg
110.4 kg
109.4kg
109.1kg
Your lab regularly runs tests on mice, resulting in several bags of leftover mouse food sitting in your storage closet, the lab will need more food around day 116 of the year.
To determine if the lab's reserve of mouse meals will hold up for the entirety of subsequent year, we need to research the fee at which the food reserves are reducing.
Let's calculate the common day by day decrease in meals reserves:
Average daily decrease = (Initial food reserves - Final food reserves) / (Number of days)
Initial food reserves = 112.6 kg
Final food reserves = 109.1 kg
Number of days = 8 (from December 13 to December 21)
Average daily decrease = (112.6 kg - 109.1 kg) / 8 ≈ 0.4375 kg/day
Number of days until food reserves reach zero = Final food reserves / Average daily decrease
Number of days until food reserves reach zero = 109.1 kg / 0.4375 kg/day ≈ 249.14 days
Thus, the lab will need more food approximately 365 - 249.14 = 115.86 days into the year. Round it up to the nearest whole number, and the lab will need more food around day 116 of the year.
For more details regarding reserve, visit:
https://brainly.com/question/31633083
#SPJ1
A broker gets 45% of the commission and an agent gets 55%. How much does an agent earn when a house is sold for $73,400.00 and the rate of commission is 5 1/2 %
When a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.
To calculate the agent's earnings, we need to determine the total commission earned from the sale of the house and then calculate 55% of that amount.
First, we need to calculate the total commission earned from the sale of the house. The commission rate is given as 5 1/2 %, which can be written as a decimal as 0.055.
The total commission can be found by multiplying the sale price of the house ($73,400.00) by the commission rate (0.055):
Total Commission = $73,400.00 * 0.055
= $4,037.00
Now, we need to determine the agent's earnings, which is 55% of the total commission. We can calculate this by multiplying the total commission by 55% or 0.55:
Agent's Earnings = $4,037.00 * 0.55
= $2,220.35
Therefore, when a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.
for such more question on commission rate
https://brainly.com/question/23377525
#SPJ8
Determine the value of x in the triangle below:
NO LINKS
Answer:
x = 12.85714286 (as a decimal)
x = [tex]\frac{90}{7}[/tex] (as a fraction)
Step-by-step explanation:
These 2 triangles are similar.
[tex]\frac{20}{x} = \frac{20 + 8}{x + 18}[/tex]
Cross-multiply both sides.20(x + 18) = x(20 + 8)
20x + 360 = 20x + 8x
20x + 360 = 28x
Take 20x away from both sides.360 = 28x
Divide both sides by 28.x = 12.85714286 or x = [tex]\frac{90}{7}[/tex]
I believe the correct anwser is 45
A sample obtained from a population with σ = 48 has a standard error of σM = 6. How many scores are in the sample?
The circle below is centered at the origin and has a radius of 4. What is its
equation?
OA. x^2 - y^2=16
OB.x²+ y^2=4
OC. x²+y^2=16
OD. x²- y²=4
Answer:
C) [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-0)^2+(y-0)^2=4^2\\x^2+y^2=16[/tex]
Therefore, C is correct
Answer:
option C:
x² + y² = 16
Step-by-step explanation:
general equation of a circle is,
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the center of the circle
r is the radius of the circle
according to the question the circle is centered at the origin so h and k will be 0
and r = 4
by substituting the values in the equation,
(x - 0)² + (y - 0)² = 4²
x² + y² = 16
.............................................................
Step-by-step explanation:
for the first one the sales on table is going downn while the days are increasing
for the second one the arrow going up signifies that the sales are going up according to days
(q3) Find the length of the curve described by the function
The length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately A. 7.982.
How to calculate the valueSubstituting the values back into the arc length formula, we have:
L = ∫√(dx/dt)² + (dy/dt)² dt
L = ∫√(2(t - 5))² + 1² dt
L = ∫√(4(t - 5)² + 1) dt
Now, let's integrate this expression over the given range 0 ≤ y ≤ 1:
L = ∫[0,1]√(4(t - 5)² + 1) dt
Approximating the integral with the midpoint rule:
L ≈ ∑[i=0 to n-1] √(4(t_i+1 - 5)² + 1) Δt
Let's choose n = 1000 for a reasonably accurate result. Thus, Δt = (1 - 0) / 1000 = 0.001.
Calculating the sum:
L ≈ ∑[i=0 to 999] √(4(t_i+1 - 5)² + 1) * 0.001
Performing this calculation, we find that L ≈ 7.982.
Therefore, the length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately 7.982.
Learn more about functions on
https://brainly.com/question/11624077
#SPJ1
In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
To learn more about : angle
https://brainly.com/question/25770607
#SPJ8
The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)*.
What is the multiplicative rate of change of the function?
O 0.5
02
2.5
5
Mark this and return
Save and Exit
Next
Submit
The multiplicative rate of change of the function is,
⇒ 0.5
We have to given that,
The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function,
⇒ f(x) = 10(0.5)ˣ
Now, For the multiplicative rate of change of the function,
Let two values, of points are x = 1 and x = 0
Put x = 1 in function,
⇒ f(1) = 10(0.5)¹
⇒ f(1) = 10(0.5)
⇒ f(1) = 5
Put x = 0;
⇒ f(0) = 10(0.5)⁰
⇒ f(0) = 10
Hence, The ratio is,
⇒ f (1)) / f (0)
⇒ 5 / 10
⇒ 0.5
Thus, the multiplicative rate of change of the function is,
⇒ 0.5
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
MARK AS BRAINLIEST!!!
H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.7. A random sample of 7 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5.0. The population standard deviations are unknown but assumed to be equal. At the 0.10 significance level, is there a difference between the population means? Required: a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) d. State your decision about the null hypothesis. multiple choice 1 Reject H0. Do not reject H0. e. The p-value is multiple choice 2 between 0.1 and 0.05. less than 0.001. between 0.02 and 0.05. between 0.001 and 0.01. between 0.1 and 0.2.
Answer:
(a) Decision rule: reject null hypothesis if [tex]t < -1.753[/tex] or [tex]t > 1.753[/tex], and fail to reject null hypothesis if [tex]-1.753\leq t\leq 1.753[/tex]
(b) [tex]s_{p}^{2}=18.214[/tex]
(c) [tex]t=-1.902[/tex]
(d) Reject [tex]H_{0}[/tex]
(e) The p-value is between 0.1 and 0.05
Step-by-step explanation:
The explanation is attached below.
Show your work please please
Answer:
[tex]9\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{4}+\biggr(3\frac{2}{3}+5\frac{3}{4}\biggr)\\\\1\frac{3}{12}+3\frac{8}{12}+5\frac{9}{12}\\\\(1+3+5)+\biggr(\frac{3}{12}+\frac{8}{12}+\frac{9}{12}\biggr)\\\\9+\frac{20}{12}\\\\9+1\frac{8}{12}\\\\9+\frac{2}{3}\\\\9\frac{2}{3}[/tex]
Again, least common denominator is 3*4=12
Step-by-step explanation:
1 1/4 + ( 3 2/3 + 5 3/4)
First change them from mixed fractions to normal fractions.
= 5/4 + ( 11/3 + 23/4)
Then Find the LCM(lowest common factor) of 4 and 3 which is 12 so we'll multiply both 4 and 3 to the number so the answer would be 12. and also if we multiply the denominator we do the same to the numerator.
= 5/4 + (44/12 + 69/12)
add them.
= 5/4 + (44 + 69/12)
now find their LCM and do the same to them since 4 is a factor of 12 we'll multiply it by 3 to get 12 as a denominator to add.
= 5/4 + 113/12
= 15/4 + 113/12
= 15 + 113/12
add them.
= 128/12
Divide both numerator and the denominator by the LCM.
= 64/6
= 32/3
Answer: 32/3 or in mixed fraction: 10 2/3
3. Determine the total cost of the automobile after down payment and finance cost. Round your answer to the nearest penny, do not use commas in your answer.
price of car: $46,890.00, percent down: 26%, finance cost: $792.00 per month for 60 months
answer: $___
The cost of the car is $59,711.4.
Since, A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.
Given here:
Price of the car = $46,890.00,
percent down: 26%,
finance cost: $792.00 per month for 60 months
Thus Total cost= $46,890.00×0.26+60×792
= $12191.4 + $47520
= $59,711.4
Hence, The cost of the car is $59,711.4
Learn more about percentages here:
brainly.com/question/29306119
#SPJ1
the set of integers that are multiple of 5
use set notation
Answer:
Step-by-step explanation:
\[y={5x,x \n I\]
={...,-10,-5,0,5,10,...}
[tex]{\Large \begin{array}{llll} y=\{5x; ~~ x\in \mathbb{Z}\} \end{array}} \qquad \textit{integers multiples of 5}[/tex]
Oliver wants to invest $15,000 in an account that pays 4.5% per year. After 3 years, if he pulls out his money, will he have enough to pay for his son’s college tuition of $20,000?
Answer:
No
Step-by-step explanation:
[tex]A=Pe^{rt}\\20000\stackrel{?}{\leq}15000e^{0.045(3)}\\20000\nleq17168.05[/tex]
Therefore, Oliver will not be able to pay for his son's college tuition of $20,000 after 3 years. He'll be short by about $3000.
...................................................................................................
Answer:
60 in.²
Step-by-step explanation:
A = (B + b)h/2
A = (14 in. + 6 in.)(6 in.)(1/2)
A = 60 in.²
Answer:
60 in^2
Step-by-step explanation:
solution Given:
Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE
we have
Area of Rectangle ABCD= length* breadth =BC*AB=14*6=84 in^2
Area of Triangle CDE= 1/2* base*height=1/2*DE*CD=1/2*8*6=24 in ^2
Now
Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE
=84 in^2-24in^2
=60 in^2
Similarly, we have another way to calculate the area of the trapezoid;
Area = 1/2*h*(side1*side2)
=1/2*AB*(AE+BC)
=1/2*6*(6+14)
=60 in^2
This sample of jelly beans has been selected from a bag containing 500 jelly beans. Based on this sample, how many blue jelly beans would you expect to find in the bag?
Blue: 3
Yellow: 1
Purple: 2
Pink: 1
Green: 2
Red: 1
Answer:
Step-by-step explanation:
[tex]P(blue)=\frac{3}{10} \\[/tex]
For sample of 500 jellybeans:
[tex]E(blue)=\frac{3}{10}\times500=150[/tex]
Solution: 150 blue jellybeans.
Triangle D has been dilated to create triangle D’. Use the image to answer the question.
Determine the scale factor used.
A. Scale factor of 1/3
B. Scale factor of 3
C. Scale factor of 1/2
D. Scale factor of 2
The scale factor that was used to create triangle D' include the following: C. Scale factor of 1/2
We have,
In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Compare the corresponding sides of triangle D and triangle D':
Side DE in triangle D corresponds to side D'E in triangle D'.
Side EF in triangle D corresponds to side E'F in triangle D'.
Side FD in triangle D corresponds to side F'D in triangle D'.
Determine the ratios of the corresponding sides:
The ratio of side D'E to DE is 2:1.
The ratio of side E'F to EF is 2:1.
The ratio of side F'D to FD is 2:1.
Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)
By substituting the given dimensions into the formula for scale factor, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
Scale factor = 8/16 = 6/12 = 10/20
Scale factor = 1/2.
Read more on scale factor here:
brainly.com/question/29967135
#SPJ1
Concept Check
Complete the problem. (From Example 1)
1. Liz Reynolds deposited $2,000 into a savings account that pays 8% compounded quarterly, Complete the
table to compute the amount in the account after 1 year.
Original Principal
Interest for First Quarter
Amount at End of First Quarter
Interest for Second Quarter
Amount at End of Second Quarter
Interest for Third Quarter
Amount at End of Third Quarter
Interest for Fourth Quarter
Amount at End of Fourth Quarter
$2,000.00 x 8%*%=
$2,000.00+ $40,00-
$2,040.00 x 8% x = b.
e.
$40.00
h.
F
4
m
a.
+C.
d.
+1.
W
98 +1.
$2,000,00
$40.00
Liz table that shows her compounded interest should be completed the following way;
Original Principal $2,000
Interest for First Quarter $2,000.00 x 8% ×1/4 = $40 = + $ 40
Amount/End of First Quarter $2,000.00+ $40.00 = $2040 = + $ 2040
Interest for Second Quarter $ 2040 × 8% ×1/4 = $ 40.8 = + $ $ 40.8
Amount/End of Second Quarter 2040 + 40.8 = $ 2080.8 = + $ 2080.8
Interest for Third Quarter 2080.8 × 8% ×1/4 = $ 41.616 = + $ 41.616
Amount/End Third Quarter 2080.8+41.616 = $2122.416 = + $ 2122.416
Interest/Fourth Quarter 2122.416 × 8% ×1/4 = $ 42.4483 = + 42.4483
Amount/ End of Fourth Quarter $2122.416 + $42.4483 = 2164.8643
What is meant by quarterly compound interest?Quarterly compound interest is a type of interest that is calculated and paid out four times in a year. This means that the interest earned in one quarter is added to the principal amount, and then interest is calculated on the new, larger principal amount in the next quarter.
Quarterly compound interest is more profitable than annual compound interest in many cases, however, it depends on the percentage increase.
Find more exercises on compounded interest;
https://brainly.com/question/14295570
#SPJ1
Find the Value of X.
What amount must be remitted if the following invoices, all with terms 5/10, 2/30, n/60, are paid together on December 8?
Invoice No. 312 dated November 2 for $923.00
Invoice No. 429 dated November 14 for $784.00
Invoice No. 563 dated November 30 for $873.00
Question content area bottom
Part 1
The amount remitted is $
The amount to be remitted when paying the invoices together on December 8 is $2,477.19.
To calculate the amount that must be remitted when paying the invoices together on December 8, we need to consider the available discount periods and the due date.
Let's break down the information provided:
Invoice No. 312 dated November 2 for $923.00
Invoice No. 429 dated November 14 for $784.00
Invoice No. 563 dated November 30 for $873.00
Given the terms 5/10, 2/30, n/60, this means that a 5% discount is offered if payment is made within 10 days, a 2% discount is offered if payment is made within 30 days, and the net amount is due within 60 days.
To calculate the amount to be remitted, we need to consider the applicable discount periods. For payments made on or before December 8, the following discounts apply:
Invoice No. 312: 5% discount if paid within 10 days
Invoice No. 429: 5% discount if paid within 10 days
Invoice No. 563: 2% discount if paid within 30 days
To calculate the remitted amount, we subtract the applicable discount from each invoice amount and sum them up:
Invoice No. 312: $923.00 - (5% of $923.00) = $923.00 - ($46.15) = $876.85
Invoice No. 429: $784.00 - (5% of $784.00) = $784.00 - ($39.20) = $744.80
Invoice No. 563: $873.00 - (2% of $873.00) = $873.00 - ($17.46) = $855.54
Total amount to be remitted = $876.85 + $744.80 + $855.54 = $2,477.19
Therefore, the amount to be remitted when paying the invoices together on December 8 is $2,477.19.
For more questions on amount
https://brainly.com/question/28275721
#SPJ8
Caleb has twice as many cousins as amanda. Ruby has 5 cousins, which is 11 less than caleb has. How many cousins does amanda have?
Answer:
Amanda has 8 cousins
Step-by-step explanation:
Let C be the number of cousins Caleb has, A be the number of cousins Amanda has, and R be the number of cousins Ruby has:
[tex]C=2A\\R=5\\R=C-11\\\\R=C-11\\5=C-11\\16=C\\\\C=2A\\16=2A\\8=A[/tex]
Therefore, Amanda has 8 cousins.
Answer:
Amanda has 8 cousins.
Step-by-step explanation:
Let's use algebraic variables to solve the problem.
Let's assume the number of cousins Amanda has is represented by 'A'.
Since Caleb has twice as many cousins as Amanda, the number of cousins Caleb has is '2A'.
And Ruby has 5 cousins, which is 11 less than what Caleb has, so the number of cousins Caleb has is '5 + 11 = 16'.
Equating the two expressions for the number of cousins Caleb has:
2A = 16
Now we can solve for 'A', the number of cousins Amanda has:
Divide both sides of the equation by 2:
A = 16 / 2
A = 8
Therefore, Amanda has 8 cousins.
A life insurance company has determined that each week an average of seven claims is filed .what is the probability that during the next week exactly sevent claims will be filled?
The probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.
To determine the probability of exactly seven claims being filed during the next week, we need to use the Poisson distribution. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events occur with a known average rate and independently of the time since the last event.
In this case, we are given that the average number of claims filed per week is seven. This average rate is also the parameter λ (lambda) of the Poisson distribution.
The probability mass function (PMF) of the Poisson distribution is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where X is the random variable representing the number of claims filed, k is the specific number of claims we are interested in (in this case, k = 7), e is the base of the natural logarithm (approximately 2.71828), and k! represents the factorial of k.
Substituting the given average rate of seven claims per week into the equation, we have:
P(X = 7) = (e^(-7) * 7^7) / 7!
Calculating this expression will give us the probability of exactly seven claims being filed during the next week.
P(X = 7) ≈ 0.1038
Therefore, the probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.
This means that, on average, we can expect approximately 10.38% of weeks to have exactly seven claims filed based on the given average rate of seven claims per week.
For more such questions on probability visit:
https://brainly.com/question/251701
#SPJ8
(q12) Apply Poiseuille’s Law to calculate the volume of blood that passes a cross–section per unit time
Viscosity = 0.0010
Radius = 0.030 cm
Length = 3 cm
P = 1000 dynes/square cm
The volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.
Poiseuille's Law describes the flow of fluid through a cylindrical tube. It can be used to calculate the volume of blood that passes through a cross-section per unit time. The formula for Poiseuille's Law is as follows:
Q = (π * ΔP * r^4) / (8 * η * L)
Where:
Q is the volume flow rate,
ΔP is the pressure difference across the tube,
r is the radius of the tube,
η is the viscosity of the fluid, and
L is the length of the tube.
Given information:
Viscosity (η) = 0.0010
Radius (r) = 0.030 cm
Length (L) = 3 cm
Pressure difference (ΔP) = 1000 dynes/square cm
First, we need to convert the radius and length to meters, as the SI unit system is typically used in scientific calculations:
Radius (r) = 0.030 cm = 0.030 * 0.01 m = 0.0003 m
Length (L) = 3 cm = 3 * 0.01 m = 0.03 m
Now, we can calculate the volume flow rate (Q) using Poiseuille's Law:
Q = (π * ΔP * r^4) / (8 * η * L)
= (π * 1000 * (0.0003)^4) / (8 * 0.0010 * 0.03)
= (3.1416 * 1000 * 0.000000000027) / (0.024)
= 0.0036756 / 0.024
≈ 0.1532 cm^3/s
Therefore, the volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.
for such more question on volume
https://brainly.com/question/6204273
#SPJ8
(q15) A supply of soaps available at different prices is given by the supply curve s(x)= 180+0.3x^3/2 , where x is the product quantity. If the selling price is $250, find the producer surplus.
The producer surplus is approximately $663.772.
To find the producer surplus, we need to calculate the area between the supply curve and the selling price line.
The supply curve is given by the equation:
[tex]s(x) = 180 + 0.3x^{(3/2)[/tex]
where x is the product quantity.
Let's set the selling price to $250.
We want to find the quantity (x) at which the selling price intersects the supply curve. So, we can set:
[tex]250 = 180 + 0.3x^{(3/2)[/tex]
Now, let's solve this equation to find the value of x:
[tex]250 - 180 = 0.3x^{(3/2)[/tex]
[tex]70 = 0.3x^{(3/2)[/tex]
Divide both sides by 0.3:
[tex]x^{(3/2)} = 70 / 0.3[/tex]
[tex]x^{(3/2)} = 233.33[/tex]
Now, we can solve for x by raising both sides to the power of 2/3:
[tex]x = (233.33)^{(2/3)[/tex]
x ≈ 24.88
So, the quantity (x) at which the selling price intersects the supply curve is approximately 24.88.
To calculate the producer surplus, we need to find the area between the supply curve and the selling price line from 0 to x.
The formula for the producer surplus is:
Producer Surplus = ∫[0 to x] (s(x) - Selling Price) dx
Using the given supply curve [tex]s(x) = 180 + 0.3x^{(3/2)[/tex] and the selling price of $250, we can evaluate the integral:
Producer Surplus = ∫[0 to 24.88] ([tex]180 + 0.3x^{(3/2)[/tex]) dx
Calculating the integral we get,
= 663.772
Therefore, the producer surplus is approximately $663.772.
Learn more about producer surplus click;
https://brainly.com/question/32106601
#SPJ1
Please help!!! 83 points
Answer:
a is -13
b is 31
c is 24
Step-by-step explanation: