Answer:
With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]
Step-by-step explanation:
Given zeros are x=-2,1,4
Now to find the polynomial function:
With the given zeros we can write it as below:
x=-2 implies that x+2=0
x=-1 implies that x-1=0
x=4 implies that x-4=0
Then we can the zeros or factors by (x+2)(x-1)(x-4)
Now expanding the zeros or factors:
[tex](x+2)(x-1)(x-4)[/tex]
[tex](x+2)(x-1)(x-4)=(x^2-x+2x-2)(x-4)[/tex] ( multiply each term with each term of another factor)
[tex]=(x^2+x-2)(x-4)[/tex] ( adding the like terms)
[tex]=x^3-4x^2+x^2-4x-2x+8[/tex] ( multiply each term with each term of another factor)
[tex]=x^3-3x^2-6x+8[/tex] ( adding the like terms)
[tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]
Therefore the polynomial function is [tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]
With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]
If each light fixture on a job requires 4 lamps and each room requires 16 fixtures, how many lamps will be required for 6 rooms?
Answer:
384 lamps
Step-by-step explanation:
This is simply a multiplication problem. From the question, we know that each fixture needs 4 lamps with a single room needing 16 fixtures.
The number of lamps required by each room is thus 16 * 4 = 64 lamps
Now, the total number of lamps required by 6 rooms is thus 64 * 6 = 384 lamps
To find the total number of lamps required for 6 rooms, multiply the number of fixtures per room by the number of rooms, then multiply the result by the number of lamps per fixture.
Explanation:To find the total number of lamps required for 6 rooms, we need to first determine the number of fixtures in 6 rooms. Since each room requires 16 fixtures, the total number of fixtures in 6 rooms would be 16 x 6 = 96 fixtures.
Each fixture requires 4 lamps, so to find the total number of lamps required for 96 fixtures, we multiply 96 x 4 = 384 lamps.
Therefore, 384 lamps will be required for 6 rooms.
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The average life of Canadian women is 73.75 years, and the standard deviation of the life expectancy of Canadian women is 6.5 years. Based on Chebyshev's theorem, determine the upper and lower bounds on the average life expectancy of Canadian women such that at least 90 percent of the population is included. a. 53.20; 94.30b. 66.38, 81.13 c. 67.25, 80.25 d. 12.09, 135.41
Answer:
a. 53.20; 94.30
Step-by-step explanation:
Data given
[tex]\mu =73.75[/tex] reprsent the population mean
[tex]\sigma=6.5[/tex] represent the population standard deviation
The Chebyshev's Theorem states that for any dataset
• We have at least 75% of all the data within two deviations from the mean.
• We have at least 88.9% of all the data within three deviations from the mean.
• We have at least 93.8% of all the data within four deviations from the mean.
Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: [tex] 1-\frac{1}{k^2}"[/tex]
We want the limits that have at least 90% of the population is include. And using the theorem we have this:
[tex]0.9 =1-\frac{1}{k^2}[/tex]
And solving for k we have this:
[tex]\frac{1}{k^2}=0.1[/tex]
[tex]k^2 =\frac{1}{0.1}=10[/tex]
[tex]k=\pm 3.162[/tex]
So then we need the limits between two deviations from the mean in order to have at least 90% of the data will reside.
Lower bound:
[tex]\mu -3.162\sigma=73.75-3.162(6.5)=53.195 \apporx 53.20[/tex]
Upper bound:
[tex]\mu +3.192\sigma=73.75+3.162(6.5)=94.304 \approx 94.30[/tex]
So the final answer would be between (53.20;94.30)
Using Chebyshev's theorem to find the range of life expectancy for Canadian women that includes at least 90% of the population, the lower and upper bounds are approximately 53.21 years and 94.29 years, respectively.
Explanation:The question pertains to calculating bounds on life expectancy using Chebyshev's theorem, which is a statistical rule that applies to different types of distributions, regardless of their shape. To calculate the bounds that include at least 90% of the data for the life expectancy of Canadian women, where the mean is 73.75 years, and the standard deviation is 6.5 years, we need to use the formula k = 1/√(1-(1/p)), where p is the proportion of the population. In this case, since we want to include at least 90% of the population, p=0.9.
First, we solve for k:
k = 1/√(1-(1/0.9))
k ≈ 3.16
Then, we multiply k by the standard deviation and subtract it from and add it to the mean to find the bounds:
Lower Bound = Mean - k * Standard Deviation
Lower Bound = 73.75 - (3.16 * 6.5) ≈ 53.21
Upper Bound = Mean + k * Standard Deviation
Upper Bound = 73.75 + (3.16 * 6.5) ≈ 94.29
Therefore, the bounds are approximately 53.21 years and 94.29 years, which corresponds to option a. 53.20; 94.30.
Select all the correct systems of equations.
Which systems of equations have infinite solutions?
Answer: Comment: From the explanations below,
2x + y = 10
-6x = 3y + 7 had an infinite solution, while y = 14 -2x
6x + 3y = 42 has a fictitious solution, so also equation
2x + y = 17
-6x = 3y - 51.
Step-by-step explanation:
Answer:
(C) y = 14 - 2x
6x + 3y+ 42
(F) 2x + y = 17
-6x = 3y - 51
Step-by-step explanation:
Plato Correct answer. Got them right. Select the two boxes that have the equation written above.
the russian ice breaker Yamal can move forward through 2.3 meter 2.3 meter thick ice at a speed 5.5 kilometers 5.5 kilometers per hour . hour . Write and solve a multiplication equation to find the number of hours hours it takes to travel 82 kilometers 82 kilometers through ice Evaluate
Answer:
Yamal can move the ice to 82 km in approximately 15 hrs.
Step-by-step explanation:
Given:
Speed = 5.5 km/hr
Distance = 82 km
Let time be represented as 'x'.
We need to find the number of hours required to travel 82 km.
We know that Distance can be calculated by the product of Speed and time.
Framing above sentence in equation form we get;
Distance = Speed × Time
Substituting the given value we get;
[tex]82 = 5.5x[/tex]
Hence The expression for number of hours is [tex]82 = 5.5x[/tex]
Solving the equation to find the value of x we get;
[tex]82 = 5.5x\\\\x=\frac{82}{5.5} = 14.90 \approx 15\ hrs[/tex]
Hence Yamal can move the ice to 82 km in approximately 15 hrs.
If you write all the whole numbers from 1 to 500 in a row, what will be the 500th digit?
a. 0 or 1b. 2 or 3c. 4 or 5d. 6 or 7e. 8 or 9
The 500th digit from 1 to 500 in a row will be;
A: 0 or 1
We want to write all the whole numbers from 1 to 500 in a row. The single digit numbers are; 1 to 9 = 9 numbers = 9 digitsThe double digit numbers are; 10 to 99 = 90 numbers × 2 = 180 digits
This is a total of 180 + 9 = 189 digits
We want to find the 500th digit.Thus, after 99, we are looking for the;
500 - 189 digit = 311th digit
311 is not divisible by 3 and so the nearest term that is divisible by 3 is 312. Thus;(100 + x)3 = 312
100 + x = 312/3
100 + x = 104
x = 104 - 100
x = 4
Thus, the 104th term after 99 would contain the 500th digit.The 104th term after 99 is;
104 + 99 = 203
Since we used the 312th instead of 311th, it means that 0 is the 311th term.Read more on sequence at; https://brainly.com/question/7882626
As per the question, the 500th digit would be:
a). 0 or 1
To write,
Numbers from [tex]1 to 500[/tex]
The numbers containing 1 digit [tex]= 9[/tex] digits (1 to 9)
The numbers containing 2 digits [tex]= 90[/tex] × [tex]2 = 180[/tex] (from 10 to 99)
To find,
[tex]500th[/tex] digit
Remaining [tex]= 500 - (180 + 9)[/tex]
[tex]= 311th[/tex]
As we know, 311 can not be divided by 3, and therefore, we will look for the nearest number that is divisible by 3 i.e. 312
So, assuming the x as 100 + nth digit
[tex](100 + x)3 = 312[/tex]
[tex]100 + x = 312/3[/tex]
[tex]100 + x = 104[/tex]
[tex]x = 104 - 100[/tex]
∵[tex]x = 4[/tex]
Now,
[tex]100 + 4 = 104th digit[/tex]
∵ [tex]104 + 99 = 203[/tex]
Since the [tex]312th[/tex] term is employed rather than the [tex]311th[/tex], it implies that[tex]203 - 3 = 200[/tex]. Thus, 0 would be the [tex]500th[/tex] digit.
Thus, option a is the correct answer.
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Really need help with this.
Answer:
B = 47°
Step-by-step explanation:
THe theorem to solve this is very simple. The angle created Angle B intercepts to arcs, one major, another minor.
The major arc is DE, 142 degrees.
The minor arc is AC, 48 degrees.
The two secants intersect outside the circle and creates a vertex angle, Angle B. The theorem tells us that the measure of that vertex angle would be ONE HALF of the difference of the two intercepted arcs. So, we have:
[tex]B=\frac{1}{2}(142-48)=47[/tex]
So, B = 47°
Stephen recently purchased a camper. The value of the camper after t years is given by the following expression.
22,475(0.81)^t
Which of the following best describes the expression?
A.
the product of the initial value of the camper and its decay factor raised to the number of months since it was purchased
B.
the product of the initial value of the camper and its growth factor raised to the number of years since it was purchased
C.
the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased
D.
the product of the initial value of the camper and its growth factor raised to the number of months since it was purchased
Answer:
C
Step-by-step explanation:
since the camper gets old we will choose decay factor over the years and since t is in years in the explanation so t in the expression means years as well
The expression describes the initial value of the camper multiplied by its annual decay factor raised to the power of the number of years since purchase, corresponding to option C.
The expression 22,475(0.81)^t best describes the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased. The correct choice that describes the expression is C. The initial value of the camper is given as $22,475. The factor 0.81 represents the annual depreciation rate, meaning that the camper loses 19% of its value each year (100% - 81% = 19% decay). The variable t stands for the number of years since the purchase. Therefore, each year, the value is multiplied by 0.81, repeatedly, to reflect the continuous decrease in value.
A trough is 8 feet long and has perpendicular cross section in the shape of an isosceles triangle (point down) with base 1 foot and height 2 feet. The trough is being filled with water at a rate of 1 cubic foot every 5 minutes. How fast is the water level rising whenthe water is 1/2 foot deep?
Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
WILL GIVE BRAINLIEST
Mia has 50 feet of fencing to make a rectangular kennel for her dog. She decides to use a part of her house as one side of the kennel. She needs a minimum enclosed area of 300 square feet. Of the inequalities listed, which forms of the inequality represent this situation?
-2l2 + 50l − 300 ≥ 0
(l − 15)(l − 10) ≥ 0
l(50 − 2l) ≥ 300
(l − 15)(l − 10) ≤ 0
l(2l − 50) ≥ 300
-2l2 + 50l − 300 ≤ 0
Answer:
-2L² + 50L − 300 ≥ 0
Step-by-step explanation:
View Image
Perimeter is the sum of all the sides. She got 50 feet of fence work with. So our equation right now is:
y + y + x + x = 50
However, she used her house for one of the side, so we can remove one of the side. Our new equation is now:
y + y + x = 50
Solve for one of the side. I solved for x because it's easier to work with and substitute later. I got x = 50 - 2y.
Now I solve for area. Area of a rectangle is Length * Width.
A = LW
I used x and y for my sides so my area is this instead:
A = yx
Substitute in x.
A = y(50 - 2y)
A = 50y - 2y²
Area must be a minimum of 300ft², so
50y - 2y² ≥ 300
50y - 2y² - 300 ≥ 0
replace y with L because that's what they used in the answer choice
-2L² + 50L − 300 ≥ 0
Answer:
-2l^2+50l-300 ≥ 0
l(50 − 2l) ≥ 300
(l − 15)(l − 10) ≤ 0
Step-by-step explanation:
What is the unit rate for each size to the nearest cent? If the cost is less than a dollar, put a zero to the left of the decimal point.
Answer:
Size C can is the best buy.
Step-by-step explanation:
The given question is incomplete; here is the complete question.
One brand of canned salmon is sold in four different sizes.
Size A The 7 1/5 -ounce can costs $3.49.
Size B The 16 1/2 -ounce can costs $6.49.
Size C The 24 3/4 -ounce can costs $8.49.
Size D The 30 2/3 -ounce can costs $10.99. What is the unit rate for each size to the nearest cent? If the cost is less than a dollar, put a zero to the left of the decimal point.
Size Unit rate
A (Blank)
B (Blank)
C (Blank)
D (Blank)
What size is best to buy? explain how you know.
For Size A - [tex]7\frac{1}{5}[/tex] ounce or [tex]\frac{36}{5}[/tex] ounce can costs $3.49
Therefore, per ounce cost = [tex]\frac{\text{Total cost}}{\text{Size of can}}[/tex]
= [tex]\frac{3.49}{\frac{36}{5}}[/tex]
= [tex]\frac{3.49\times 5}{36}[/tex]
= $0.48
For Size B - [tex]16\frac{1}{2}[/tex] or [tex]\frac{33}{2}[/tex] ounce can costs $6.49
Per ounce cost = [tex]\frac{6.49}{\frac{33}{2}}[/tex]
= [tex]\frac{6.49\times 2}{33}[/tex]
= 0.39
For size C - [tex]24\frac{3}{4}[/tex] ounce or [tex]\frac{99}{4}[/tex] ounce can costs $8.49
Per ounce cost = [tex]\frac{8.49}{\frac{99}{4}}[/tex]
= [tex]\frac{8.49\times 4}{99}[/tex]
= $0.34
For size D - [tex]30\frac{2}{3}[/tex] or [tex]\frac{92}{3}[/tex] ounce can for $10.99
Per ounce cost = [tex]\frac{10.99}{\frac{92}{3} }[/tex]
= [tex]\frac{10.99\times 3}{92}[/tex]
= $0.36
For size C, per ounce cost of the can is the least. Therefore, size C can is the best buy.
Help please!! Stuck on this question!! ∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the measure of angle ABC?
Answer:
63 degrees
Step-by-step explanation:
add 4x + 23 and 6x + 7, then equal that to 130. When you find x, plug it into 4x+23 and get 63.
Tim ate four more cookies than Alice.Bob ate twice as many cookies as Tim. If x represents the number of cookies alive ate,which expression represents the number of cookies bob ate
Answer:
(x + 4) x 2
Step-by-step explanation:
x represents number of cookies Alice ate.
x + 4 represents the number of cookies Tim ate.
As Bob had eaten twice the number of cookies that Alice ate the expression should be
(x + 4) x 2
A farmer needs to ship 71 pumpkins to a grocery store if each crates can hold 19 pumpkins how many crates Will the farmer need ? Write an expression you could use to determine how many crates you would need
Answer:
The farmer will need 7 crates.
Step-by-step explanation:
It is given that there are 71 pumpkins in total.
And each crate holds 19 pumpkins.
Let the number of crates required be "n".
The total number of pumpkins can be calculated by multiplying number of pumpkins in each crate with total number of crates.
Thus, the equation is
[tex]19(n) = 71[/tex]
[tex]n = \frac{71}{19} = 7[/tex]
Thus, the farmer needs 7 crates to hold total of 71 pumpkins.
For a certain experiment, the available experimental units are eight rats, of which four are female (F1, F2, F3, F4) and four are male (M1, M2, M3, M4). There are to be four treatment groups, A, B, C, and D. If a randomized block design is used, with the experimental units blocked by gender, which of the following assignments of treatments is impossible?
a. A (F1, M1), B (F2, M2), C (F3, M3), D (F4, M4)
b. A (F1, M2), B (F2, M3), C (F3, M4), D (F4, M1)
c. A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)
d. A (F4, M1), B (F2, M3), C (F3, M2), D (F1, M4)
e. A (F4, M1), B (F1, M4), C (F3, M2), D (F2, M3)
Answer:
c
Step-by-step explanation:
In the experimental design we are choosing a random rats from both sets either male and female.
each set contains 2 elements (A,B), where A is a Female i.e F1, F2,F3,F4
and B is a male i.e M1,M2,M3,M4.
none of the sets can have 2 male or 2 female.
Only option 'C' has sets which contains B (F3, F2) and D (M3, M4) which is impossible.
Hence c is the answer.
The assignment of treatments that is impossible is given as
c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)
Which of the following assignments of treatments is impossible?Treatment, the way by which someone acts towards someone else.
Generally, from the parameters, we see that
A is a Female i.e F1, F2,F3,F4
B is a male i.e M1,M2,M3,M4.
In conclusion, the sets can't have 2 male or 2 female.
Therefore, we have
c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)
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A number has three digits the tens digit is five When the hundreds digit and the ones digit Are switched the number increases by 495 what is the number
There are 4 numbers possible 156, 257, 358 and 459.
What is place value?The value a digit in a number represents based on where it is in the number is known as place value.
Let 25 is a number, then the place value of 2 is 20.
Let the three-digit number is x5y,
Then the number whose digits are switched is y5x,
The number x5y can be written according to its place value = 100x + 50 + y
Similarly, y5x can be written according to its place value = 100 y + 50 + x
The number y5x is 495 more than the number x5y
Implies that,
100 y + 50 + x - (100x + 50 + y) = 495
99y-99x - 495
99(y-x) = 495
y-x = 5
The numbers can be 156, 257, 358 and 459.
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Final answer:
To find the three-digit number with the tens digit being 5 and the number increasing by 495 when the hundreds and ones digits are switched, set up an equation using placeholders for the hundreds and ones digits, solve the equation to find these digits, and deduce the original number, which is 459.
Explanation:
The question involves finding a three-digit number based on given conditions about digits and their positions. We know that the tens digit is 5. If we switch the hundreds and the ones digits, the number increases by 495. This implies that the ones digit must be less than the hundreds digit, as switching them results in a larger number. Let's denote the hundreds digit by 'a' and the ones digit by 'c'.
The original number can be represented as 100a + 50 + c, and after switching, the number becomes 100c + 50 + a. The problem states that the latter is 495 units larger than the original number. So, we can set up the following equation:
100c + 50 + a = (100a + 50 + c) + 495
Simplifying the equation gives us:
99c - 99a = 495
This simplifies to:
c - a = 5
Since 'a' and 'c' are digits, the only possibility is that a = 4 and c = 9. Therefore, the original number is 459.
A contractor is considering a project that promises a profit of $46,000 with a probability of 0.7, or a loss (due to bad weather, strikes, and such) of $12,000 with a probability of 0.3.
If many projects have these same probabilities and costs, how much should the contractor expect to earn on average per contract?
Answer:
$28,600
Step-by-step explanation:
Probably of 0.7 = 46000
Probability of 0.3 = 12000
The average profit = Sum of (x*Pr(x)
=0.7(46000) + 0.3(-12000)
= 32200 - 3600
= $28,600
The contractor should expect to earn $28,600 on the average
Describe where the function has a vertical asymptote and EXPLAIN how you found your answer.
[tex]f(x) \frac{x^2 +7x+10}{x^2+9x+20}[/tex]
Answer:
x = -4
Step-by-step explanation:
Vertical asymptotes are found where the denominator has a zero that is not cancelled by a numerator zero. Here, the expression simplifies to ...
[tex]f(x)=\dfrac{x^2+7x+10}{x^2+9x+20}=\dfrac{(x+5)(x+2)}{(x+5)(x+4)}=\dfrac{x+2}{x+4} \qquad x\ne -5[/tex]
The function is undefined at x=-5, but has a vertical asymptote at x=-4.
A car rental costs $70 per day plus an additional $0.50 for each mile driven. The daily cost y is given by the equation y = 0.50x + 70
Answer:
Cannot give answer until Mile (x) is given
Step-by-step explanation:
Ayanna jumps rope 32 times every minute. What is the algebraic equation to express the function of the total number of times Ayanna jumped rope? A. 32 = j - m B. j = 32m C. m = 32j D. m + j =32
Answer:
B) [tex]j=32m[/tex]
Step-by-step explanation:
Given:
Ayanna jumps at the rate of = 32 times/minute
To find the algebraic equation to express the function of the total number of time Ayanna jumped the rope.
Solution:
Let [tex]j[/tex] represent the total jumps made by Ayanna.
Let Ayanna jump for [tex]m[/tex] minutes.
Using unitary method to calculate total number of jumps made by Ayanna in [tex]m[/tex] minutes.
In 1 minute, Ayanna jumps = 32 times
Thus, in [tex]m[/tex] minutes Ayanna will jump = [tex]32\times m=32m[/tex] times
Thus, the function can be represented as;
[tex]j=32m[/tex] (Answer)
Answer: b
Step-by-step explanation:
In 2000, the population of Israel was approximately 6.27 million and by 2040 it is projected to grow to 9 million. Use the exponential growth model:A=A_o.e^(kt)in which t is the number of years after 2000, to find an exponential growth function that models the data.
The exponential growth function that models the data is: A(t) = 6.27 million * e^(0.0173t)
We can use the given information to solve for the parameters in the exponential growth model:
1. Set up the equation:
We know the initial population (A_0) is 6.27 million and the projected population after 40 years (t = 40) is 9 million. Therefore:
A(t) = 6.27 million * e^(kt)
2. Solve for k:
Substitute the final population value and time into the equation and solve for k:
9 million = 6.27 million * e^(40k)
e^(40k) = 9 million / 6.27 million
e^(40k) ≈ 1.433
Take the natural logarithm of both sides to isolate k:
40k ≈ ln(1.433)
k ≈ ln(1.433) / 40
k ≈ 0.0173
3. Write the complete function:
Now that we know k, we can substitute it back into the original equation to find the complete function:
A(t) = 6.27 million * e^(0.0173t)
Therefore, the exponential growth function that models the data is: A(t) = 6.27 million * e^(0.0173t)
Need this please help
Answer:
Step-by-step explanation:
a) Steps to prove that two triangles are similar are
1) AA(angle angle)if two angles of each triangle is congruent to two angles of another triangle, then the third angles of both triangles must be congruent since the sum of angles in the triangle is 180 degrees
2) SSS(side side side) if the three sides of both triangles are proportional to each other, then the triangles are similar.
3) SAS(side angle side) if two sides of a triangle are proportional to two sides of another triangle and and the angle formed by both lines in the two triangles are equal, then the third sides of both triangles are proportional. Therefore, the triangles are similar.
b) triangle ABC would be similar to triangle QRS if
1) angle A is congruent to angle Q and angle B is congruent to angle R
2)if the ratio of AB to QR is proportional to the ratio of AC to QS, and to BC to RS
3) if AC is proportional to QS, AB is proportional to QR and angle A = angle Q
c) AC/AB = QS/QR
60/50 = 6/QR
6/5 = 6/QR
6QR = 6×5 = 30
QR = 30/6 = 5 cm
In a random sample of 400 items where 84 were found to be defective, the null hypothesis that 20% of the items in the population are defective produced Upper Z Subscript STATequalsplus 0.50. Suppose someone is testing the null hypothesis Upper H 0: piequals0.20 against the two-tail alternative hypothesis Upper H 1: pinot equals0.20 and they choose the level of significance alphaequals0.10. What is their statistical decision?
Answer:
[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]
[tex]p_v =2*P(Z>0.5)=0.617[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.
Step-by-step explanation:
1) Data given and notation
n=400 represent the random sample taken
X=84 represent the number of items defective
[tex]\hat p=\frac{84}{400}=0.21[/tex] estimated proportion of defectives
[tex]p_o=0.2[/tex] is the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
Confidence=90% or 0.90
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.2 or 20%:
Null hypothesis:[tex]p=0.2[/tex]
Alternative hypothesis:[tex]p \neq 0.2[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.1[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(Z>0.5)=0.617[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.
Rowan has $50 in a savings jar and is putting in $5 every week. Jonah has $10 in his own jar and is putting in $15 every week. Each of them plots his progress on a graph with time on the horizontal axis and amount in the jar on the vertical axis. Which statement about their graphs is true?
(1) Rowan's graph has a steeper slope than Jonah's.(2) Rowan's graph always lies above Jonah's.(3) Jonah's graph has a steeper slope than Rowan's.(4) Jonah's graph always lies above Rowan's.
Answer:
(3) Jonah's graph has a steeper slope than Rowan's
Step-by-step explanation:
First we are going to write the equations for the amount of money that each one save
y = a+bx
Where y: Amount of money in the jar
a: Initial saving
b: Money saved every week ( graph's slope )
x: Number of week
Then, for Rowan
y = 50 + 5x
and for Jonah
y = 10 + 15x
Initially Rowan's graph lies above Jonah's graph but this situation change with time.
It is always true that Jonah's graph has a steeper slope than Rowan's, because for Rowan's graph the slope is 5 and for Jonah's graph the slope is 15
Then the answer is:
(3) Jonah's graph has a steeper slope than Rowan's
3) Jonah's curve has a steeper slope than Rowan's is True, All others are false
Rowan savings already (Intercept of Curve) = $ 50 ; Rowan Additional savings per week Slope with time) = $ 5Rowan Savings Equation = 50 + 5t , where t is weekly time
Jonah savings already (Intercept of Curve) = $ 10 ; Jonah Additional savings per week (Slope with time) = $ 15Rowan Savings = 10 + 15t , where t is weekly time
Jonah's curve has higher (steeper) slope, denoting more change in dependent variable 'savings' with change in independent variable weekly time. t weeks Rowan savings Jonah savings1 50 + 5 (1) = 55 10 + 15 (1) = 25
2 50 + 5 (2) = 60 10 + 15 (2) = 40
3 50 + 5 (3) = 65 10 + 15 (3) = 55
4 50 + 5 (4) = 70 10 + 15 (4) = 70
5 50 + 5 (5) = 75 10 + 15 (5) = 85
At t weeks < 3 , Rowan savings > Jonah savings. At t weeks > 4, Jonah savings > Rowan savings. At t = 4 units, their savings are equal. So, none savings curve is above the other 'always'.
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PLEASE HELP ASAP THANK UU
[I'm still thinking sorry]
I'm assuming 2x-12 is the angle measure of DAC in degrees.
Let p=AB=AD, q=AC
By the Law of Cosines,
22² = p² + q² - 2pq cos 48°
q² - 2pq cos 48° + p² - 22² = 0
We also require by the triangle inequality
CD+AD < AC
16 + p < q
Let's set them equal and see where we are.
q=p+16
(p+16)² - 2p(p+16) cos 48° + p² - 22² = 0
p≈12.2125,
q≈28.2125
16² = p² + q² - 2 pq cos DAC
16² = 12.2125² + 28.2125² - 2 (12.2125)(28.2125) cos DAC
cos DAC = (12.2125² + 28.2125² - 16²)/(2 (12.2125)(28.2125) ) = 1
That's a surprise, DAC maxes out at a right angle
90 = 2x - 12
102 = 2x
x = 51
Answer: 6 < x < 51
HELP!!!!
What’s the length of a segment that begins at the point (4,7) and ends at the point (13,19)?
A. 24
B. 15
C. 20
D. 18
Answer:
Step-by-step explanation:
You just need the distance formula here. It's very simple to follow:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
which, for us, looks like this:
[tex]d=\sqrt{(13-4)^2+(19-7)^2}[/tex] and
[tex]d=\sqrt{9^2+12^2}[/tex] and
[tex]d=\sqrt{81+144}[/tex] and
[tex]d=\sqrt{225}[/tex] so
d = 15
Jakes truck can tow a max weight of 5,000 pounds. What is the max number of horses he can take in his trailer at one time without going over the max weight his truck can tow
Answer:
He can take 5 Horses at max in his trailer at one time without going over the max weight his truck can tow. (Assuming the average weight of one horse to be equal to 1000 pounds)
Step-by-step explanation:
The no. of horses that can be carried by the truck can be found by simply dividing the maximum weight, that the truck can tow by the weight of a horse.
Max. No of Horses = (Max weight truck can tow)/(Average weight of one horse)
The weight of a horse is not given in the question .Thus, we assume the average weight of one horse, to be equal to 1000 pounds, we get:
Max. No of Horses = 5000 pounds/ 1000 pounds
Max. No of Horses = 5
Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear
Answer:
Step-by-step explanation:
Let B divides AB in the ratio K:1
[tex]x=\frac{nx1+mx2}{m+n} \\y=\frac{ny1+my2}{m+n} \\\frac{-4}{5} =\frac{1*\frac{2}{3}+k*4}{k+1} \\-4k-4=\frac{10}{3} +20k\\-12 k-12=10+60k\\72k=-22\\36k=-11\\k=-\frac{11}{36} \\[/tex]
so B divides AB in the ratio 11:-36
[tex]x=\frac{-36*1+11 *\frac{-1}{2} }{11-36} \\x=\frac{83}{50}[/tex]
Answer:
[tex]\large \boxed{1.66}[/tex]
Step-by-step explanation:
1. Calculate the equation of the straight line joining A and C.
The equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (-½, 4) and (1, ⅔)
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{\frac{2}{3} - 4}{1 - (-\frac{1}{2})}\\\\& = & \dfrac{-\frac{10}{3}}{\frac{3}{2}}\\\\& = & \dfrac{-10}{3}\times{\dfrac{2}{3}}\\\\& = & \dfrac{-20}{9}\\\\\end{array}[/tex]
(b) Find the y-intercept
Insert the coordinates of one of the points into the equation
[tex]\begin{array}{rcl}y & = & mx + b\\4 & = & \dfrac{-20}{9}\left(-\dfrac{1}{2}\right) + b \\\\4 & = & \dfrac{10}{9} + b\\\\b & = & \dfrac{36}{9} - \dfrac{10}{9}\\\\b & = & \dfrac{26}{9}\\\\\end{array}[/tex]
(c) Write the equation for the line
[tex]y = -\dfrac{20}{9}x + \dfrac{26}{9}[/tex]
2. Calculate the value of x when y = -⅘
[tex]\begin{array}{rcl}y & = & -\dfrac{20}{9}x + \dfrac{26}{9}\\\\-\dfrac{4}{5} & = & -\dfrac{20}{9}x+ \dfrac{26}{9}\\\\36 & = & 100x -130\\100x & = & 166\\x & = & 1.66\\\end{array}\\\text{The value of x is $\large \boxed{\mathbf{1.66}}$}[/tex]
The graph below shows your three collinear points.
ind the probability of answering the two multiple choice questions correctly if random guesses are made. Assume the questions each have five choices for the answer. Only one of the choices is correct.a. 0.04 b. 0.4 c. 0.02 d. 0.004
Answer: a. 0.04
Step-by-step explanation:
Given : Number of multiple choice questions = 2
Choices given in each question = 5
Since only one choice is correct out of 5.
So, the probability of selecting the correct answer = [tex]\dfrac{1}{5}[/tex]
Also, both questions are independent of each other.
It means , The probability of answering the two multiple choice questions correctly if random guesses are made
=( Probability of selecting the correct answer in question 1 ) x ( Probability of selecting the correct answer in question 2 )
= [tex]\dfrac{1}{5}\times\dfrac{1}{5}= 0.04[/tex]
Hence, the required probability =0.04
The first four stripes on a wall with 100 stripes are red , blue, white, and purple, These four colors repeat in the same order. What color is the 55th stripe ?
Answer: the 55th stripe is white
Step-by-step explanation:
The first four stripes on a wall with 100 stripes are red , blue, white, and purple. The four colors repeat in the same order. This means that Red always follow blue which is followed by white and then purple. This means that red would always start each new and consecutive set of four stripes and purple will always end it
We want to determine the 55th stripe. The last four stripes that include 55 ends with the 56th stripe. This means that the 56th stripe is purple. Therefore, the 55th stripe would be white because it follows purple.
The color of the 55th stripe on the wall is white. The colors repeat every four stripes implying that the 55th, as per our calculation, falls on the third color in the pattern, white.
Explanation:This is a repetition pattern problem in Mathematics. The pattern of colors (red, blue, white, purple) on the wall repeats every four stripes. To determine the 55th stripe color, we divide 55 by 4, getting a quotient of 13 and a remainder of 3. The remainder indicates that the 55th stripe is the third color in our repeating pattern which is white.
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When interest rates being paid on new bonds are higher but the interest payments on an existing bond remain fixed, the only way for the existing bond to compete is for its price to go _______________..
Answer: The bond has to go down.
Step-by-step explanation: A bond is a loan usually given by an issuer to an investor that pays back a fixed rate of return.
Although bonds have a fixed rate of return, bonds itself are not fixed which means when bond price can rise or fall. When bond rises, interest falls and when bond price falls, interest rises. A vice versa relationship.
What this means is that the investor has to pay more, take for example.
-If a bond of $100 has a return rate of 10%, this means investor will pay back $10.
-If bond price increases $120, investor will have to pay $12. Investor pays more
-However, if bond price decreases to $80, investor will pay $8. Investor pays less
Therefore, for an existing bond to compete with a new bond which has a higher interest rate, the existing bond price has to go down so that interest can go up.