Answer: B. Population X will require a larger sample size
Step-by-step explanation:
If a random variable say p has skewed distribution (whether right or left ) in a population then a bigger sample size is needed to make sure that the sampling distribution follows normal distribution.Given : Two population distributions labeled X and Y.
Distribution X → highly skewed
Distribution Y → slightly skewed.
Since Distribution X more skewed so , we will need a larger sample size of population X as compared to Y.
Hence, the correct answer is B. Population X will require a larger sample size
The correct option is B. Population X will require a larger sample size.
According to the Central Limit Theorem, the sampling distribution of the sample mean will tend to be normally distributed as the sample size becomes larger, regardless of the shape of the population distribution. However, the rate at which the sampling distribution approaches normality depends on the degree of skewness in the population distribution.
For a population distribution that is highly skewed (like Distribution X), a larger sample size is needed for the sampling distribution to approximate a normal distribution compared to a population distribution that is only slightly skewed (like Distribution Y). This is because the effects of skewness are more pronounced and take longer to "average out" in larger samples.
Therefore, to achieve the same degree of normality in their respective sampling distributions, Population X, with its high skewness, will require a larger sample size than Population Y, which is only slightly skewed.
Having trouble with this and 3 others
Answer:
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Step-by-step explanation:
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Chris is purchasing a house and needs to finance a $150,000 mortgage from the bank with an annual percentage rate (APR) of 3.8%
He is financing it over 30 years and making monthly payments. What is the total amount Chris will pay back to the bank?
Group of answer choices
$501,796
$299,998
$251,618
$150,001
Answer:
$251,618 is the answer
Step-by-step explanation:
From the previous question, we know he pays $698.94 monthly.
He has to make 360 payments. $698.94 * 360 = $251,618
In the year 2011, Ryan's boat had a value of $23,000. When he bought the boat in 2004 he paid $26,500. If the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
The constant amount of depreciation in the value of boat per year is $ 500
Solution:
When he bought the boat in 2004 he paid $26,500
Therefore,
Initial value in 2004 = $ 26500
In the year 2011, Ryan's boat had a value of $23,000
Value in 2011 = $ 23000
The value of the boat depreciated linearly
If the boat depreciation is linear, then the amount by which the value of boat depreciates must be constant.
Let x be the constant depreciation in the value of boat per year
Then we can say,
Value in 2011 = Initial value in 2004 - nx
Here, "n" is the number of years
2011 - 2004 = 7 years
Therefore,
23000 = 26500 - 7x
7x = 26500 - 23000
7x = 3500
Divide both sides by 7
x = 500
Thus the rate of depreciation per year is $ 500
The annual rate of change of the boat's value is approximately -71.43 dollars.
Explanation:The annual rate of change of the boat's value can be calculated using the formula for slope of a line. We subtract the initial value from the final value and divide it by the number of years the boat has depreciated. In this case, the initial value is $26,500 and the final value is $23,000. The number of years is 7 (2011 - 2004). So the annual rate of change is ($23,000 - $26,500)/7 = -$500/7 = -71.43. Therefore, the annual rate of change of the boat's value is approximately -71.43 dollars.
The student is asking about the annual rate of change in the value of a boat, which is a problem related to linear depreciation. To solve this, we need to calculate the total amount the boat depreciated over a certain period and then divide by the number of years to get the annual rate.
Ryan's boat was worth $23,000 in 2011 and was purchased for $26,500 in 2004. The total depreciation over these 7 years is $26,500 - $23,000 = $3,500. To find the annual depreciation rate, we divide the total depreciation by the number of years: $3,500 ÷ 7 years = $500 per year.
Therefore, the annual rate of change of the boat's value is $500 per year, which means the boat's value decreased by $500 every year on average.
Biologists tagged 103 fish in a lake january 1. On feburary 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged. How many fish does the lake have
Answer:
206
Step-by-step explanation:
We have been given that Biologists tagged 103 fish in a lake January 1. On February 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged.
To find the number of fish in the lake, we will use proportions because ratio of tagged fish and collected fish on February 1 will be equal to ratio of tagged fish and total fish on January 1.
[tex]\frac{\text{Tagged fish}}{\text{Collected fish}}=\frac{12}{24}[/tex]
Upon substituting the number of tagged fish in our proportion, we will get:
[tex]\frac{103}{\text{Total fish}}=\frac{12}{24}\\\\\frac{103}{\text{Total fish}}=\frac{1}{2}[/tex]
Cross multiply:
[tex]1\cdot \text{Total fish}=103\cdot 2\\\\\text{Total fish}=206[/tex]
Therefore, there are approximately 206 fishes in the lake.
100 points , please help. I am not sure if I did this correct if anyone can double-check me thanks!
my answer:
2. In order to find the definite integral of the riemann sum given to us. We need to label everything out. We know that our delta x = 3/n , a=1 and that b=4. We found B by subtracting
b-a=delta x
b-1=3
b=4.
Then now we plug everything in giving us our final answer, ⎰^4 and 1 on the bottom (sqrt 1 + 3/n) dx.
Step-by-step explanation:
[tex]\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
Jamaica is considering buying either a car which goes 25 miles on 1 gallon of gas, or a truck that goes 10 miles on a gallon of gas. If gasoline costs $2.50 per gallon and Jamaica drives 1000 miles per month, how much less would it cost to drive the car each month than it would to drive the truck?
Answer: if he drives the car each month, he would spend $150 lesser than when he drives the truck.
Step-by-step explanation:
The car goes 25 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/25 = 40 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a car, the cost of gas per month would be
2.5 × 40 = $100
The truck goes 10 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/10 = 100 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a truck, the cost of gas per month would be
2.5 × 100 = $250
The difference between both costs is
250 - 100 = $150
Riley needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. If Riley only has $50 to spend on the car rental, what is the maximum number of miles she can drive
Answer:
Step-by-step explanation:
Let x represent the maximum number of miles that she can drive.
Riley needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. Converting 16 cents to dollars, it becomes 16/100 = $0.16
Assuming Riley drives the car for x miles, the total charge would be
0.16x + 18.95
If Riley only has $50 to spend on the car rental, it means that
0.16x + 18.95 = 50
0.16x = 50 - 18.95
0.16x = 31.05
x = 31.05/0.16 = 194.0625
The maximum number of miles that
she can drive is 194 miles.
The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees , will the outside temperature be represented by a positive integer or negative integer?Explain your reasoning
Answer:
The temperature would be -5 degrees Fahrenheit
Step-by-step explanation: It's represented by a negative integer because 15 - 20 = -5. This means the temperature outside would be -5 degrees Fahrenheit.
Hope this helps! (:
The temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees,
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.
It is given that:
The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees
=15 - 20
= -5.
A negative sign means the temperature outside would be -5 degrees Fahrenheit.
Thus, the temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit. If the temperature drops 20 degrees,
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Let x1, x2, and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?a.x1+ x2+ x3>2b.x1+ x2+ x3<2c.x1+ x2+ x3= 2d.x1- x2= 0
Answer:
Correct statement: a. x₁ + x₂ + x₃ > 2
Step-by-step explanation:
The variables x₁, x₂ and x₃ takes value 0 if the projects are not done and 1 if the projects are done.
Consider that at least two projects are done, i.e. 2 or more projects are done.
This can happen in:
x₁ = 0, x₂ = 1 and x₃ = 1
x₁ = 1, x₂ = 0 and x₃ = 1
x₁ = 1, x₂ = 1 and x₃ = 0
x₁ = 1, x₂ = 1 and x₃ = 1
The statement (x₁ + x₂ + x₃ > 2) will be true only when all the variables takes the value 1.
This statement implies that 2 projects are definitely done.
Thus, the correct statement is (a).
Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister's house partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen's average speed was 10 miles per hour faster than Anne's. Find Helen's average speed and Anne's average speed.
Answer:
Helen: 60mph and Anne: 50mph
Step-by-step explanation:
3.2r+2.8(r-10)=332 is the equation that we use, given the information we have.
We distribute and combine like terms and add 28 to both sides and divide by 6.
3.2r+2.8(r-10)=332
3.2r+2.8r-28=332
6r=360
6r/6=360/6
r=60 So, Helen's speed is 60mph.
Next, we'll solve Anne's speed.
r-10=50
60-10=50 So, Anne's speed is 50mph.
Anne's average speed was approximately 45 mph, and Helen's average speed was approximately 55 mph.
Let's denote Helen's average speed as "H" and Anne's average speed as "A." We are given that Helen drove for 3.2 hours, and Anne drove for 2.8 hours. We also know that Helen's average speed was 10 miles per hour faster than Anne's, so we can write this relationship as:
H = A + 10
Now, using the formula Speed = Distance / Time, we can express the distances traveled by Helen and Anne:
Distance covered by Helen = H * 3.2
Distance covered by Anne = A * 2.8
Given that the sum of their distances equals the distance between their homes (332 miles):
H * 3.2 + A * 2.8 = 332
Substituting the relationship H = A + 10, we get:
(A + 10) * 3.2 + A * 2.8 = 332
Solving this equation will provide us with Anne's average speed (A), and subsequently, we can find Helen's average speed (H) using the relationship H = A + 10.
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Solve for x. −6≥10−8x Enter your answer as an inequality in the box.
The solution of the expression of the inequality - 6 ≥ 10 - 8x for x
would be;
⇒ x ≥ 2
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression of the inequality is;
⇒ - 6 ≥ 10 - 8x
Now,
Solve the inequality for x as;
The inequality is;
⇒ - 6 ≥ 10 - 8x
Add 8x both side, we get;
⇒ - 6 + 8x ≥ 10 - 8x + 8x
⇒ - 6 + 8x ≥ 10
Add 6 both side, we get;
⇒ - 6 + 8x + 6 ≥ 10 + 6
⇒ 8x ≥ 16
Divide by 8 both side, we get;
⇒ x ≥ 16/8
⇒ x ≥ 2
Hence, - 6 ≥ 10 - 8x ⇒ x ≥ 2
Thus, The solution of the expression of the inequality - 6 ≥ 10 - 8x, for x will be;
⇒ x ≥ 2
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Which relation is a function?
Which statement best describes how to determine whether f(x) = 9 – 4x2 is an odd function?
A. Determine whether 9 – 4(–x)2 is equivalent to 9 – 4x2.
B. Determine whether 9 – 4(–x2) is equivalent to 9 + 4x2.
C. Determine whether 9 – 4(–x)2 is equivalent to –(9 – 4x2).
D. Determine whether 9 – 4(–x2) is equivalent to –(9 + 4x2).
Answer:
Option C - determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.
Step-by-step explanation:
To find : Which statement best describes how to determine whether [tex]f(x) = 9-4x^2[/tex] is an odd function?
Solution :
We have a property for odd functions,
Let f(x) be an odd function then it must satisfy
[tex]f(-x)= -f(x)[/tex]
Now, we have been given the function [tex]f(x) = 9-4x^2[/tex]
For this function to be odd, it must satisfy the above property.
Replace x with -x,
[tex]f(-x)=9-4(-x)^2[/tex]
and
[tex]-f(x)=-(9-4x^2)[/tex]
Hence, in order to the given function to be an odd function, we must determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.
Therefore, C is the correct option.
A swimming pool has to be drained for maintenance. The pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.7 m. Suppose water is pumped out of the pool at a rate of 12 m3 per hour. If the pool starts completely full, how many hours will it take to empty the pool?
Answer:
2.78hrs
Step-by-step explanation:
Volume of water in the pool =πr2h
V = 3.142 * 2.5² *1.7
V = 33.38m³
Emptying the pool out at 12m³ per hour
= 33.38/12
= 2.78hrs
Need help doing this
Answer:
A. -2
B. -10
Step-by-step explanation:
The slope of a perpendicular line will be the negative reciprocal of the slope of the given line:
-1/(1/2) = -2 . . . . slope of the perpendicular line
__
The y-intercept will let the given point satisfy the equation ...
y = -2x +b
2 = -2(-6) +b
-10 = b . . . . . . . subtract 12. This is the y-intercept.
_____
The graph shows the two lines and the points they go through.
Isaac is painting a wall that is 9 feet by 18 feet.So far he has painted a part of the wall that is a 4feet by 7feet rectangle.How much of the wall does Isaac have left to paint?
Final answer:
Isaac has 134 square feet of the wall left to paint after subtracting the area he has already painted (28 square feet) from the total area of the wall (162 square feet).
Explanation:
The student's question is regarding an area calculation problem. Isaac is painting a wall with dimensions of 9 feet by 18 feet and has painted a 4 feet by 7 feet section so far. To find the area left to paint, we need to calculate the total area of the wall and subtract the area that's already been painted.
Step 1: Calculate the total area of the wall
The total area of the wall is:
(Length of the wall) × (Width of the wall) = 9 ft × 18 ft = 162 square feet.
Step 2: Calculate the area that has been painted
The area that Isaac has painted is:
(Length of painted section) × (Width of painted section) = 4 ft × 7 ft = 28 square feet.
Step 3: Calculate the area left to paint
To find the remaining area to paint:
(Total area of the wall) - (Area painted) = 162 sq ft - 28 sq ft = 134 square feet.
So, Isaac has 134 square feet of the wall left to paint.
In one U.S. city, the quadratic function f (x )equals 0.0039 x squared minus 0.42 x plus 36.79 models the median, or average, age, y, at which men were first married x years after 1900. In which year was this average age at a minimum (round to the nearest year)? What was the average age at first marriage for that year (round to the nearest tenth)?
Answer:
The average age was minimum at 1954 and the average age is 25.5.
Step-by-step explanation:
The given quadratic function is
[tex]f(x)=0.0039x^2-0.42x+36.79[/tex]
It models the median, or average, age, y, at which men were first married x years after 1900.
In the above equation leading coefficient is positive, so it is an upward parabola and vertex of an upward parabola, is point of minima.
We need to find the year in which the average age was at a minimum.
If a quadratic polynomial is [tex]f(x)=ax^2+bx+c[/tex], then vertex is
[tex]Vertex=(-\dfrac{b}{2a},f(-\dfrac{b}{2a}))[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{(-0.42)}{2(0.0039)}=53.846153\approx 54[/tex]
54 years after 1900 is
[tex]1900+54=1954[/tex]
Substitute x=54 in the given function.
[tex]f(54)=0.0039(54)^2-0.42(54)+36.79=25.4824\approx 25.5[/tex]
Therefore, the average age was minimum at 1954 and the average age is 25.5.
The year when the average age at first marriage was at a minimum in a specific U.S. city was approximately 1954. The average age at first marriage for that year was approximately 28.4 years.
Explanation:To find the year when the average age at first marriage was at a minimum, we need to determine the x-value at the vertex of the quadratic function. The x-value at the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. For the given function f(x) = 0.0039x2 - 0.42x + 36.79, the x-value at the vertex is x = -(-0.42)/(2*0.0039) = 53.85. Since the x-value represents years after 1900, we add 1900 to get the year: 1900 + 53.85 ≈ 1954.
To find the average age at first marriage for that year, we substitute x = 53.85 into the quadratic function. f(53.85) = 0.0039(53.85)2 - 0.42(53.85) + 36.79 ≈ 28.4. Therefore, the average age at first marriage for the year 1954 was approximately 28.4 years.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
[tex]m\angle R=69.4^o[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(R)=\frac{8}{3}[/tex]
using a calculator
[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies he spent a total of $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation
Answer:
d = $5.50 - p
Step-by-step explanation:
Answer: d = $5.50 - p
Step-by-step explanation:
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Peter takes16 minutes longer to mow the lawn by himself than Charles . Together they can mow the lawn in 18 minutes. How long will it take Charles to do it alone?
Answer:
about 29.7 minutes
Step-by-step explanation:
If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:
1/c + 1/(c+16) = 1/18
Multiplying by 18c(c+16), we get ...
18(c +16) + 18(c) = c(c+16)/18
36c +288 = c^2 +16c
c^2 -20c = 288 . . . . . subtract 36c
c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square
(c -10)^2 = 388
c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root
It takes Charles about 29.7 minutes to mow the lawn by himself.
One night a theater sold 548 movie tickets. An adult's costs $6.50 an child's cost $3.50. In all, $2,881 was takin in. How many of each kind of tickets were sold?
Answer:
321 adult227 childStep-by-step explanation:
The fraction of tickets that are adult tickets is ...
((average price per ticket) - (child's ticket cost)) / (difference in ticket costs)
so the fraction of adult tickets is ...
((2881/548) -3.50)/(6.50 -3.50) = 321/548
Then the number of adult tickets is ...
(321/548)·548 = 321
and the number of child tickets is ...
548 -321 = 227
321 adult and 227 child tickets were sold that night.
_____
If you want to write an equation, you can let "a" represent the number of adult tickets sold. Total revenue is ...
6.50a +3.50(548 -a) = 2881
3.00a +1918 = 2881 . . . . . . eliminate parentheses
3a = 963 . . . . . . . . . . . . . . . subtract 1918
a = 321 . . . . . . . . . . . . . . . . . divide by 3
The number of child tickets is ...
548 -a = 548 -321 = 227
What is the surface area of the figure?
144π cm²
12π cm²
36π cm²
24π cm²
Answer:
36π cm^2.
Step-by-step explanation:
This is a sphere . Surface area = 4πr^2.
This sphere has surface area = 4π3^2
= 36π.
The surface area of the sphere would be = 36πcm². That is option C.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
to calculate the surface area of a sphere:
The surface area of a sphere can be calculated through the use of the formula = 4πr²
Where,
radius (r) = 3 cm
surface area
=4πr²
= 4π × 3²
= 36π cm² ( in the terms of π)
Hence, The surface area of the sphere would be = 36πcm². That is option C.
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what does 124.06=2.35h+72.36
a.16
b.22
c.2.2
d.none of these
Answer:
B. 22
Step-by-step explanation:
124.06 = 2.35h + 72.36
124.06 - 72.36 = 2.35h
51.7 = 2.35h
51.7/2.35 = h
22 = h
In each diagram below, determine whether the triangles are congruent, similar, but not congruent, or not similar. If you claim that the triangles are similar or congruent, make a flowchart justifying your answer.
Part a
Angle ABC = angle CDA (given by the angle markers)
Angle BAC = angle DCA (alternate interior angles)
Segment AC = segment AC (reflexive property)
Through AAS (angle angle side) we can prove the two triangles are congruent. We have a pair of congruent angles, and we have a pair of congruent sides that are not between the previously mentioned angles.
If two triangles are congruent, they are always similar as well (scale factor = 1).
The same cannot be said the other way around. Not all similar triangles are congruent.
Answer: Congruent======================================================
Part b
Angle FGH = angle JIH (both shown to be 50 degrees)
Angle FHG = angle JHI (vertical angles)
We have enough information to prove the triangles to be similar triangles. This is through the AA (angle angle) similarity rule. Since FG and JI are different lengths, this means the triangles are not congruent.
Answer: Similar but not congruent======================================================
Part c
For each right triangle shown, divide the longer leg over the shorter leg
larger triangle: (long leg)/(short leg) = 6/3 = 2
smaller triangle: (long leg)/(short leg) = 3/2 = 1.5
The two results are different, so the sides are not in proportion to one another, therefore the triangles are not similar.
Any triangles that are not similar will also never be congruent.
Answer: Not similar======================================================
Part d
Use the pythagorean theorem to find that PQ = 5 and KL = 12
We have two triangles with corresponding sides that are the same length
So we use the SSS (side side side) triangle congruence theorem to prove the triangles congruent. The triangles are also similar triangles (scale factor = 1)
Answer: Congruent======================================================
Summary of the answers:a. Congruentb. Similar but not congruentc. Not similard. CongruentIn Mathematics, triangles can be congruent, similar, or neither. Congruency means the triangles have the same three sides and angles. Similarity means the triangles have the same shape but not necessarily the same size.
Explanation:In Mathematics, particularly in Geometry, determining whether two triangles are congruent, similar, or neither is a pivotal concept. Triangles are congruent when they have exactly the same three sides and exactly the same three angles. On the other hand, triangles are similar when they have the same shape but not necessarily the same size.
To determine if triangles are congruent, you can use several postulates, including the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) postulates. For triangle similarity, the Angle-Angle (AA) postulate is often used. In the absence of sufficient information, the triangles cannot be declared similar or congruent.
A flowchart to justify the congruence or similarity would begin by assessing if all corresponding angles and sides match. If so, the triangles are congruent. If only the angles match and the sides are proportional, then the triangles are similar. In the absence of either, the triangles are neither similar nor congruent.
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Function A and Function B are linear functions. Compare the two functions and choose all that are correct.
1. The slope of Function A is greater than the slope of Function B.
2 .The slope of Function A is less than the slope of Function B.
3. The y-intercept of Function A is greater than the y-intercept of Function B.
4 .The y-intercept of Function A is less than the y-intercept of Function B.
Answer:
2 .The slope of Function A is less than the slope of Function B
Step-by-step explanation:
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
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The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
A bacteria culture initially contains cells and grows at a rate proportional to its size. After an hour the population has increased to . (a) Find an expression for the number of bacteria after
hours.(b) Find the number of bacteria after 3 hours.(c) Find the rate of growth after 3 hours.(d) When will the population reach 10,000?
Answer:
Step-by-step explanation:
given that a bacteria culture initially contains cells and grows at a rate proportional to its size.
If P be the size then growth rate
[tex]P'=kP[/tex] where k is constant of proportionality
separate the variables as
[tex]\frac{dP}{P} =kdt\\ln P =kt+C\\P = Ae^{kt}[/tex]
If after 1 hour population is B (say)
[tex]B=Ae^{k} \\\\k = ln B - ln A[/tex]
then k = ln B - ln A
Using this
P(t) = [tex]Ae^{(lnB-lnA)t}[/tex]
b) P(e) = [tex]Ae^{(lnB-lnA)3}[/tex]
c) Rate of growth = [tex](ln B- ln A)Ae^{(lnB-lnA)3}[/tex]
Unless you give B value, d cannot be solved
Which expression is equivalent to 30 (one-half x minus 2) + 40 (three-fourths y minus 4)? 45 x y minus 220 15 x minus 30 y minus 220 15 x + 30 y minus 220 15 x + 30 y minus 64
Answer:
The third option is correct i.e. 15 x + 30 y minus 220.
Step-by-step explanation:
We have to choose expression from the option that is equivalent to
[tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]
Now, [tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]
= 15x - 60 + 30y - 160
= 15x + 30y - 220
Therefore, the third option is correct i.e. 15 x + 30 y minus 220. (Answer)
Step-by-step explanation: C.
To rental car companies are running specials this month at Joseph rentals customers will pay $47 to rent a midsize car for the first day plus Two dollars for each additional day affair Fox rental the price for a midsize car is $36 for the first day and $13 for every additional day beyond that at some point renting from either one of these companies would cost to customer the same amount how many additional days would it take? How much with the customer pay?
Answer: it will take 2 days and the customer will pay $49
Step-by-step explanation:
Let x represent the number of days for which the cost would be the same.
At Joseph rentals, customers will pay $47 to rent a midsize car for the first day plus two dollars for each additional day. This means that the total cost of using Joseph rental for x days would be
47 + 2(x - 1) = 47 + 2x - 2
= 45 + 2x
At Fox rental, the price for a midsize car is $36 for the first day and $13 for every additional day beyond that. This means that the total cost of using Fox rental for x days would be
36 + 13(x - 1) = 36 + 13x - 13
= 23 + 13x
At the point where renting at either companies will cost the customer the same amount, then
45 + 2x = 23 + 13x
13x - 2x = 45 - 23
11x = 22
x = 22/11 = 2
The amount that the customer will psy is
23 + 13 × 2 = 49
A college has a 30% completion rate, meaning that 30% of all students who start at the college complete the goal they set. The president of the college sets a goal of increasing this number by 50%. What will the completion rate goal be as a percentage.
Answer:
45%
Step-by-step explanation:
For simplicity, let use assume there are 100 students in the school.
No. of students to complete college = (30/100) x 100 = 30 Students
President wants to increase by 50% = (50/100) x 30 = 15 Students
New set goal = 30 + 15 = 45 students.
Total number of students = 100 students
Therefore;
Rate goal % = (45/100) x 100% = 45%
The population of grand island, nebraska, grew by 600,000 people between 1995 and 2005, one fifth more than the town council originally predicted the city's population would grow by ?
Answer:
500000 people
Step-by-step explanation:
The population grew by 600,000 which is 120% the earlier prediction by the town council.
Using direct proportion
600,000 -------- 120%
X --------- 100%
X = (600000 × 100) ÷ 120 = 500000
Therefore the earlier prediction by the town council is 500000 people
The student's question is a mathematical problem calculating population growth predictions. The town council of Grand Island originally predicted a growth of 500,000 people, which is 20% less than the actual growth of 600,000 people.
To determine the prediction made by the town council, we can use the fact that the actual growth exceeded the prediction by one fifth (or 20%). If the actual growth was 600,000 people, the predicted growth can be calculated by dividing 600,000 by 1.2, as the actual growth represents 120% of the predicted value (100% original prediction + 20% excess).
Calculating the Predicted Population Growth
To find the town council's predicted growth, we can set up the equation:
Actual Growth = Predicted Growth + (Predicted Growth × 0.20)600,000 = Predicted Growth × 1.20Predicted Growth = 600,000 / 1.20Predicted Growth = 500,000Therefore, the town council had originally predicted that the population of Grand Island, Nebraska, would increase by 500,000 people between 1995 and 2005.