Answer: True.
Step-by-step explanation:
Let [tex]\mu[/tex] be the population mean.
Given : Null hypothesis = [tex]H_0:\mu=160[/tex]
Alternative hypothesis =[tex]H_1:\mu<160[/tex]
Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.
The sample mean ([tex]\overlien{x}[/tex]) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.
We know that p-value gives that probability that if the null hypothesis is true, than the sample mean ([tex]\overlien{x}[/tex]) will be at least as small as the actual mean ([tex]\mu[/tex]).
It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.
Hence, the answer is "True".
Final answer:
The statement is true; a p-value of 0.03 indicates a 3% chance of observing a sample mean weight of 142 lbs or less if the true mean weight of all college students is 160 lbs, suggesting strong evidence against the null hypothesis.
Explanation:
The statement provided is true: if the null hypothesis is true (that college students' average weight is 160 lbs), there would only be a 3% chance that a random sample of 80 students would have a mean weight of 142 lbs or less. This small p-value (0.03) typically indicates strong evidence against the null hypothesis, suggesting that the average weight of college students is indeed less than the average American.
In other words, a p-value is the probability that we observe a sample statistic as extreme as the one measured (or more extreme) given that the null hypothesis is true. Taking another example to illustrate the concept: if the null hypothesis assumes no difference in the average height between male and female students, and we observe a sample where the difference is 4 inches with a p-value of 0.04, this means there's a 4% chance we would see at least this large a difference if in reality there was no difference at all.
At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x ?
A. x/2B. x/3C. x/4D. x/5E. x/6
Answer:
[tex]\dfrac{x}{4}[/tex]
C is correct.
Step-by-step explanation:
At a picnic,
Number of adults is 3 times as number of children.
Number of women is twice as number of men.
Total number of men, women and children at the picnic be x
Let number of children be c
Let number of men be m
Let number of women be w
# Number of women is twice as number of men, w = 2m
# Number of adults is 3 times as number of children, w + m = 3c
2m + m = 3c (∴ w=2m )
c = m
Total number of men, women and children at the picnic be x
∵ c + m + w = x
m + m + 2m = x
4m = x
Number of men, [tex]m=\dfrac{x}{4}[/tex]
Hence, The total number of men will be [tex]\dfrac{x}{4}[/tex]
Jimmy is planning his birthday party! He spent $35 on balloons and chocolate cake. He bought balloons that cost $0.25 each and a chocolate cake for $10. He wrote the equation 0.25x+10=35 to represent the situation. Explain what each piece of the equation represents and why the equation is in that order
In the equation, x represents the number of balloons. We say that 25 cents per balloon becomes 0.25x.
Jimmy also purchased a chocolate cake. This is the PLUS sign in the equation.
The total for everything purchased is $35.
Balloons x at 25 cents each = 0.25x plus a chocolate cake for $10 together equals $35.
A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5, 6. Suppose C1 = {1, 2, 3, 4} and C2 = {3, 4, 5, 6}. If the probability set function P assigns a probability of 1 6 to each of the elements of C, compute P(C1), P(C2), P(C1 ∩ C2), and P(C1 ∪ C2).
Answer with Step-by-step explanation:
We are given that six integers 1,2,3,4,5 and 6.
We are given that sample space
C={1,2,3,4,5,6}
Probability of each element=[tex]\frac{1}{6}[/tex]
We have to find that [tex]P(C_1),P(C_2),P(C_1\cap C_2) \;and\; P(C_1\cup C_2)[/tex]
Total number of elements=6
[tex]C_1[/tex]={1,2,3,4}
Number of elements in [tex]C_1[/tex]=4
[tex]P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}[/tex]
Using the formula
[tex]P(C_1)=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]C_2[/tex]={3,4,5,6}
Number of elements in [tex]C_2[/tex]=4
[tex]P(C_2)=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]C_1\cap C_2[/tex]={3,4}
Number of elements in [tex](C_1\cap C_2)=2[/tex]
[tex]P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}[/tex]
[tex]C_1\cup C_2=[/tex]{1,2,3,4,5,6}
[tex]P(C_1\cup C_2)=\frac{6}{6}=1[/tex]
The volume of a rectangular prism is 655.2 Ft cubed. If the base of the prism is 9 ft by 5.2 ft, find the height of the prism.
Answer:
Step-by-step explanWe can easily calculate for the height of the prism since all needed measurements are given. Volume of a rectangular prism is expressed by the equation:
V = lwh
where l is the length, w is the width and h is the height of the prism.
655 = 9 (5.2) hation:
h=14ft
I need help with 25.
so the area A is no more than 10, namely A ⩽ 10 , it could be 10 or less, but no more than that.
let's recall the area of a triangle is A = (1/2)bh
[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=4\\ h=2x-3 \end{cases}\implies A=\cfrac{1}{2}(4)(2x-3) \\\\[-0.35em] ~\dotfill\\\\ A\leqslant 10\implies \cfrac{1}{2}(4)(2x-3)\leqslant 10\implies 2(2x-3)\leqslant 10\implies 4x-6\leqslant 10 \\\\\\ 4x\leqslant 16\implies x\leqslant \cfrac{16}{4}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{maximum height of the triangle}}{2(4)-3}\implies 8-3\implies 5[/tex]
when x = 4 is the maximum height, since x ⩽ 4, so it could be 4 at most, could be less than 4 or equals but never higher.
Judy Clark went to Reel Bank. She borrowed $7,800 at a rate of 6 1/2%. The date of the loan was September 2. Judy hoped to repay the loan on January 20. Assuming the loan is based on ordinary interest, Judy will pay back on January 20: ____________
Judy Clark will pay back $7,993.03 on January 20 for her loan of $7,800 at a 6.5% interest rate, with the interest being calculated for 140 days.
Explanation:To calculate the amount Judy Clark will repay for a loan of $7,800 borrowed from Reel Bank at an ordinary interest rate of 6.5%, we need to determine the amount of interest accumulated by the loan from September 2 to January 20. This involves calculating the time period for the loan, applying the ordinary interest formula, and then adding the interest to the principal amount to find the total repayment amount.
We first calculate the number of days between September 2 and January 20. Without knowing the year of the loan, we can use an approximate count and consider a non-leap year for this example, which would be 140 days (30 days for September after the 2nd, 31 for October, 30 for November, 31 for December, and 18 for January).
Using the formula I = PRT, where P is the principal ($7,800), R is the annual interest rate (0.065), and T is the time in years (140/365), we can calculate the interest:
I = 7,800 × 0.065 × (140/365) = $193.03 (rounded to two decimal places).
To find the total repayment amount, we add the interest to the principal: $7,800 + $193.03 = $7,993.03.
Therefore, Judy Clark will pay back $7,993.03 on January 20.
A population of bacteria is growing exponentially. At 7:00 a.m. the mass of the population is 12 mg. Five hours later it is 14 mg. (a) What will be the mass of the bacteria after another 5 hours? (b) At 7:00 p.m. what do we expect the mass to be? (c) What was the mass of the population at 8:00 a.m.? Given your answer, by what percent is the mass of the population increasing each hour? By what percent is it increasing each day?
Answer with Step-by-step explanation:
The exponential growth function is given by
[tex]N(t)=N_oe^{mt}[/tex]
where
[tex]N(t)[/tex] is the population of the bacteria at any time 't'
[tex]N_o[/tex] is the population of the bacteria at any time 't = 0'
'm' is a constant and 't' is time after 7.00 a.m in hours
Assuming we start our measurement at 7.00 a.m as reference time t = 0
Thus we get[tex]N(0)=N_oe^{m\times 0}\\\\12=N_o[/tex]
Now since it is given after 5 hours the population becomes 14 mg thus from the above relation we get
[tex]12\times e^{m\times 5}=14\\\\e^{5m}=\frac{14}{12}\\\\m=\frac{1}{5}\cdot ln(\frac{14}{12})\\\\m=0.031[/tex]
Thus the population of bacteria at any time 't' is given by
[tex]N(t)=12e^{0.031t}[/tex]
Part a)
Population of bacteria after another 5 hours equals the population after 10 hours from start
[tex]N(10)=12e^{0.031\times 10}=16.361mg[/tex]
Part b)
Population of bacteria at 7:00 p.m is mass after 12 hours
[tex]N(1)=12e^{0.031\times 12}=17.41mg[/tex]
Part c)
Population of bacteria at 8:00 p.m is mass after 1 hour
[tex]N(1)=12e^{0.031\times 1}=12.3378mg[/tex]
Part d)
Differentiating the relation of population with respect to time we get
[tex]N'(t)=\frac{d(12\cdot e^{0.031t})}{dt}\\\\N'(t)=12\times 0.031=0.372e^{0.031t}[/tex]
Thus we can see that the percentage increase varies with time initially the percentage increase is 37.2% but this percentage increase increases with increase in time
Part 4)
Since there are 24 hours in 1 day thus the percentage increase in the population is
[tex]\frac{N(24)-N_o}{N_o}\times 100\\\\=\frac{25.25-12}{12}\times 100=110.42[/tex]
Thus there is an increase of 110.42% in the population each day.
First, rewrite 16//21 and 7/9 so that they have a common denominator.
(I'm so confused on how to do this, someone please help me out a bit)
Answer:
Step-by-step explanation:
The lengths (in inches) of two sides of a regular triangle are given by the expressions 5x+40 and 8x-13. Find the length of a side of a triangle.
Answer:
Length = 128.3
Step-by-step explanation:
The 3 sides of a regular triangle are the same, the 2 sides that are in terms of x are equal:
5x + 40 = 8x - 13
40 + 13 = 8x - 5x
53 = 3x
17.7 = x
The length of a side = 5(17.7) + 40 = 128.3
1.7/14 reduced=
2.6/9 reduced=
3.3/8 reduced=
4.16/20 reduced=
Help plsssssss
1. 14 can be divided by 7 ( 14/7 = 2) so 7/14 reduces to 1/2
2. Both 6 and 9 can be divided by 3: 6/9 reduces to 2/3
3. 3/8 cannot be reduced, they do not have a common multiple, so this stays 3/8
4. Both 16 and 20 can be divided by 4, so this reduces to 4/5
To win the jackpot, 4 different numbers are randomly selected from 1 to 46 and one number from 1 to 22. The order of the first 4 numbers does not matter. What is the probability of winning the jackpot on one try?
Answer:
Probability of winning on one try : 1.16060875e-8
Step-by-step explanation:
For the first first 4 numbers.
Probability is 1/46 for the first number. Since the numbers are different, and it doesnt matter the order, the second number has a probability now of 1/45, the third has a probability of 1/44 and the last one a probability of 1/43.
Since the probability is dependan of the results of hitting the other number the probability of the first for numbers is the multiple of the 4 probabilities.
So it is 1/46 * 1/45 * 1/44 * 1/43 = 1 / 3916440
And that number is then multiplied by the probabilty of hitting the last number. 1/22
So the final probability is :
1/86161680 = 1.16060875e-8
Answer:
The probability of winning the jackpot on one try is 2.78 * 10^-7
Step-by-step explanation:
There are 46 balls in total (46-1)+1 = 46 . (b-a)+1 is the formula for number of elements between a and b included.
We need to find the number of combinations possible of 4 balls ( as order doesn't matter - 1234 is the sames as 2341) . So the number of possible combinations of 4 balls taken from 1 - 46 is given by
C= n!/(r!(n-r)!) where n is the number of possible balls = 46 and r the size of combination = 4 and ! is factorial ( ex 3! = 3*2*1) This gives for this case
C= n!/(r!(n-r)!) = 46!/(4!(46-4)!)= 163,185 combinations.
But as there is a fifth ball with (22-1)+1 = 22 posible options each combination must be multiplied by 22( for example 1234 22 is one but also 1234 10 is other)
163,185*22= 3,590,070 possibilities.
The probability of winning is 1 in 3,590,070 possibilities. or
p = 1/ 3,590,070= 2.78 * 10^-7
Ken drew a pair of intersecting rays and marked a angle between them.
Which of these statements best compares the pair of intersecting rays with the angle?
1) The rays and the angle have two endpoints each.
2) The rays have the number lying on them, and the angle has only one point lying on it.
3) The rays extend infinity, and the angle is made by the rays,which have a common endpoint.
4) The rays and the angles have their lines extending in opposite directions.
Answer:
Option 3 is the best option that compares the pair of intersecting rays with the angle
Step-by-step explanation:
The definition of angle says that an angle is a shape that is produced by the intersection of two rays that have a common end point.
A ray is a line segment that has only one end point and is extended infinitely in a unique direction
So Yeah. :) Hope I've helped
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11+4-3/4
Answer:
57/4
Step-by-step explanation:
Answer:
11 + 4 = 15
Rewrite the problem:
15-3/4= ?
15-3= 12
the divide it by 4:
12 / 4 = 3
ANSWER: 3
Step-by-step explanation:
The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer, and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?
Answer:
The probability that a particular death is due to an automobile accident is 2.72%
Step-by-step explanation:
The probability can be calculated as the percentage of each particular death.
The formula for this case is:
P(car accident) = (Number of death due a car accident / Total of deaths) * 100
P(car accident) = (24/883)100 = 2.72%
Probabilities of each particular death:
Automobile accident = (24/883)100 = 2.72%
Cancer = (182/883)*100 = 20.61%
Heart disease = (333/883) * 100 = 37.71%
Draw the preimage and image of the triangle under a translation along (8, -3)
Triangle with coordinates: X(−2, 5), Y(−3, 2), Z(−6, 6).
Answer:
see the attachment
Step-by-step explanation:
(8, -3) is added to each of the preimage coordinates to get the coordinates of the image. For example, ...
X' = X + (8, -3) = (-2, 5) + (8, -3) = (-2+8, 5-3)
X' = (6, 2)
Final answer:
Explanation of how to find the preimage and image of a triangle under a translation along specified vector.
Explanation:
Translation is a transformation that moves all points of a figure the same distance in the same direction. Given a translation along (8, -3), we can find the preimage and image of the triangle with the given vertices by shifting each point 8 units to the right and 3 units down.
Preimage: X'(-2+8, 5-3) = X(6, 2), Y'(-3+8, 2-3) = Y(5, -1), Z'(-6+8, 6-3) = Z(2, 3).
Image: Triangle XYZ under the translation along (8, -3) has vertices X'(6, 2), Y'(5, -1), Z'(2, 3).
How can factors help you find a common denominator
Explanation:
A "common denominator" is the least common multiple (LCM) of the denominators of the rational expressions involved. As such it can be found as the product of the unique factors of those denominators, each to its highest power.
For example, the common denominator for fractions with denominators of 20 and 25 will be 100. It can be found by considering the factors ...
20 = 2² × 5
25 = 5²
The unique factors here are 2 and 5, each with a highest power of 2. The product of these unique factors to their highest powers is ...
2²·5² = 4·25 = 100.
___
Using this method of finding the LCM, it is essential that we know the factors of the numbers.
The LCM can also be found as the product of the numbers, divided by their greatest common factor (GCF). For this method, too, you need to know factors of the numbers involved--or, at least, the greatest common factor.
For the above example numbers, the GCF is 5, so their LCM is ...
20·25/5 = 500/5 = 100
Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. Simplify the resulting fraction by canceling out any common factors.
Explanation:Finding a common denominator involves identifying a common multiple of the denominators of the fractions you are working with. Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. It's important to simplify the resulting fraction by canceling out any common factors.
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Please please help me out with this problem
Answer:
y = 3x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m = [tex]\frac{2+4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4
y = 3x - 4 ← equation of line
The distance from Earth to the sun is about 9.3 × 107 miles. The distance from Earth to the Moon is about 2.4 × 105 miles. About how many times greater is the distance from Earth to the Sun than Earth to the Moon?
Answer:
The answer to your question is: 387.5 times distance from earth to the sun than distance from the earth to the moon
Step-by-step explanation:
Data
distance from earth to the sun = 9.3 x 10⁷ miles
distance from the earth to the moon = 2.4 x 10⁵ miles
distance ES to EM
Then we need to divide
distance from earth to the sun / distance from the earth to the moon
9.3 x 10⁷ miles / 2.4 x 10⁵ miles
= 387.5 times is greater.
The distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon. This is calculated by dividing the distance from Earth to the Sun by the distance from Earth to the Moon.
Explanation:To determine how many times greater the distance from Earth to the Sun is than the distance from Earth to the Moon, we need to divide the distance from Earth to the Sun by the distance from Earth to the Moon. So, we have 9.3 × 107 miles (distance to the Sun) divided by 2.4 × 105 miles (distance to the Moon).
When you perform this calculation, you get a value of approximately 387.5. Therefore, the distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon.
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Correct answers only please! If you don't know the answer, then please don't guess or say what you think it is.
Mike recently increased the size of his truck tires from the original P215/60R16 to the larger P235/7016. If Mike didn't recalibrate his speedometer, how fast is really going on the new tires when his speedometer shows he is traveling 60 mph?
A. 54.2 mph
B. 63.8 mph
C. 66.4 mph
D. 69.7 mph
Final answer:
When Mike increased the size of his truck tires from the original P215/60R16 to the larger P235/70R16 without recalibrating his speedometer, the actual speed he was going on the new tires when his speedometer showed 60 mph was approximately 54.2 mph.
Explanation:
When Mike increased the size of his truck tires without recalibrating his speedometer, his speedometer reading would be inaccurate. To determine how fast he is going on the new tires when his speedometer shows 60 mph, we can use the concept of tire revolutions per mile.
The original tire size, P215/60R16, has a diameter of approximately 25.7 inches, while the larger tire size, P235/70R16, has a diameter of approximately 29.0 inches. The new tires cover a greater distance in one revolution compared to the original tires.
To calculate the actual speed, we can use the equation:
Actual Speed = Speedometer Reading * (Original Tire Diameter / New Tire Diameter)
Substituting the given values:
60 mph * (25.7 inches / 29.0 inches)
By simplifying this calculation, the actual speed is approximately 54.2 mph. Therefore, the correct answer is A. 54.2 mph.
Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.
Calculate the difference in tire circumference:
Original circumference: 2 * π * radius = 2 * π * (215 mm / 25.4 mm/inch) * (60 + 30%) = 79.3 inches (assuming 30% aspect ratio)
New circumference: 2 * π * (235 mm / 25.4 mm/inch) * (70 + 30%) = 85.1 inches
Difference: 85.1 inches - 79.3 inches = 5.8 inches
Calculate the percentage increase in circumference:
(5.8 inches / 79.3 inches) * 100% = 7.3%
Apply the percentage increase to the speedometer reading:
Actual speed = Speedometer reading * (1 + % increase)
Actual speed = 60 mph * (1 + 7.3%) = 60 mph * 1.073
Actual speed ≈ 64.4 mph
Therefore, when the speedometer shows 60 mph, Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.
please solve
-(6x+7)+8=19
On solving the equation -(6x+7)+8=19, we get value of x = -3.
To solve the equation -(6x+7)+8=19, we will first simplify each side of the equation and then solve for x. Here's how to do it step-by-step:
Distribute the negative sign across the parenthesis: -6x - 7 + 8 = 19.
Combine like terms on the left side: -6x + 1 = 19.
Subtract 1 from both sides: -6x = 18.
Divide both sides by -6 to find the value of x: x = -3.
Please help!!!step by step
Step-by-step explanation:
3y-x-5=0
3y=x+5
y=(x+5)/3
y= (1/3)*x + (5/3)
The general equation of y is:
y=mx+b
where:
slope=m
b= y intercept
so, slope is (1/3) and y intercept is (5/3)
and x intercept=0, when you star to graphic you can see that the only option for have y=(5/3) is necessary that the value of x=0. Or:
y intercept= (1/3)*x +(5/3) =(5/3)
(5/3)-(5/3)=(1/3)x
0=(1/3)*x
0/(1/3)=x
x=0.
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.
A company's international marketing group asked the following question to residents of 50 countries: "What has been your experience with American products?"
1) Below Average 2) Average 3) Above Average 4) Good to Excellent
A supervisor must give a summary evaluation rating from among the choices given below:
1) Poor 2) Fair 3) Good 4) Very good 5) Excellent
Are these data qualitativeor quantitative?
Are these data discrete or continuous?
What is the highest level of measurement the data possesses?
1) Nominal
2) Ordinal
3) Interval
4) Ratio
The data obtained from both questions is qualitative and discrete. The highest level of measurement for the data is ordinal.
Explanation:The data obtained from the first question, "What has been your experience with American products?", is qualitative as it involves responses categorized into below average, average, above average, and good to excellent. The data from the second question, where a supervisor gives a summary evaluation rating, is also qualitative, with choices ranging from poor to excellent.
Both sets of data are discrete since they are categorized into distinct choices. The highest level of measurement for these data is ordinal since the choices have a specific order but do not have equal intervals between them.
In triangle ΔABC, ∠C is a right angle and CD is the height to AB Find the angles in ΔCBD and ΔCAD if m∠A = 65° m∠DBC = ? m∠DCB = ? m∠CDB = ? m∠ACD = ? m∠ADC = ?
Answer:
Part 1) m∠DBC=25°
Part 2) m∠DCB=65°
Part 3) m∠CDB=90°
Part 4) m∠ACD=25°
Part 5) m∠ADC=90°
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle DBC
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
In the right triangle ABC
m∠A+m∠B+m∠C=180° ----> equation A
we have
m∠A=65° ----> given problem
m∠C=90° ----> given problem
Substitute the given values in the equation A and solve for m∠B
65°+m∠B+90°=180°
m∠B+155°=180°
m∠B=180°-155°
m∠B=25°
Remember that the measure of Angle B is equal to say the measure of angle DBC
so
m∠B=m∠DBC
therefore
m∠DBC=25°
step 2
Find the measure of angle DCB and angle CDB
In the right triangle DBC
The sum of the interior angles of a triangle must be equal to 180 degrees
m∠DBC+m∠DCB+m∠CDB=180°
we have
m∠DBC=25°
m∠CDB=90° ----> is a right angle (CD is the height to AB)
substitute the values and solve for m∠DCB
25°+m∠DCB+90°=180°
m∠DCB+115°=180°
m∠DCB=180°-115°=65°
step 3
Find the measure of angle ACD
we know that
m∠ACD+m∠DCB=90° -----> by complementary angles
we have
m∠DCB=65°
substitute the value
m∠ACD+65°=90°
m∠ACD=90°-65°=25°
step 4
Find the measure of angle ADC
m∠ADC=90° ----> is a right angle (CD is the height to AB)
Recall that the symbol z represents the complex conjugate of z. If z = a + bi, show that the statement is true. Z − z is a pure imaginary number. Use the definition of complex conjugates to simplify the expression.
Answer:
Step-by-step explanation:
z = a + bi
the complex conjugate is : Z = a-bi
so : Z-z = (a-bi) - ( a + bi ) = a-bi -a -bi
Z-z = -2bi ...is a pure imaginary number (the statement is true)
The statement is true, Z-z is a pure imaginary number = -2bi.
What is conjugate complex?
A conjugate of a complex number is another complex number which has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.
Here, given that, z = a+ib,
Let, Z be the complex conjugate of z, then, Z=a-ib
Now, Z-z = (a-ib)-(a+ib)
=a-ib-a-ib
=-i2b (which is purely imaginary)
Hence, proved. The given statement is true.
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What is the value of (16 1/2) 1/2
Answer:
4
Step-by-step explanation:
(16*1/2)*1/2
((16*1)/2)*1/2
(16/2)*1/2
8*1/2
8/2
4
or
16*1/2*1/2
16*(1/4)
16/4
4
Stuart's best golf score is 4 under par or -4. He wants to beat this score by an additional 3 strokes under par. With one hole remaining, stuart is 5 under par, or -5. What must his score be on the last hole to beat his best score
Answer:
-2
Step-by-step explanation:
he wants to get -7 because -4 + -3 = -7
he has -5 currently, so to get to -7 I added -2 which is the amount he needs.
I hope this helps you :)
Stuart requires a score of atleast - 2 on his last hole in other to beat his best score.
Best score = - 4
Required score < Best score + (-2)
Required score < - 4 + (-2)
Current score = - 5
Therefore, the least score required to beat his best score is - 7
Therefore, the required score on last hole will be :
-7 - (-5) = - 7 + 5 = - 2Therefore, a score of - 2 is required on last hole in other to beat his best score.
Learn more :https://brainly.com/question/18112348
please help me out........!!!!!!!
Answer:
h(- 8) = - 8
Step-by-step explanation:
To evaluate h(- 8) substitute x = - 8 into h(x), that is
h(- 8) = [tex]\frac{(-8)^2+3(-8)}{4(-8)+27}[/tex]
= [tex]\frac{64-24}{-32+27}[/tex]
= [tex]\frac{40}{-5}[/tex] = - 8
(30 Points)
Solve the compound inequality 6b < 36 or 2b + 12 > 6.
A) b < 6 or b > 6
B) b < 6 or b > 3
C) b > 6 or b < −3
D) b < 6 or b > −3
Answer:
C is your answer
Step-by-step explanation:
Perimeter, Circumference,
Guided Practice
Type your answer and then click or tap Done.
Find the perimeter of a rectangle with a base of 24 m and a height of 36 m.
m
Answer:
Perimeter = 120 m
Step-by-step explanation:
Perimeter = (24+36)*2 = 120 m
Which is the best method for solving the system? and explain why it is the best
9x+ 8y=7
18x-15y=14
a:table
b:elimination
c:graphing
d:substiution
Answer:
b: elimination
Step-by-step explanation:
My vote is for elimination, though any of these methods (and some not listed) will get an answer quickly.
Subtracting the second equation from twice the first gives ...
2(9x +8y) -(18x -15y) = 2(7) -(14)
31y = 0 . . . simplify
y = 0 . . . . . divide by 31 (or invoke the zero-product rule)
Then the value of x can be found from the first equation:
9x = 7
x = 7/9
__
I like this method because it tells you that y=0 in one step. (Graphing does the same.) For the numbers here, you can do it mentally. Once you recognize that the x-coefficients and the constants are related by the same factor, and that factor is different for the y-coefficients, it becomes apparent that elimination will immediately tell you that y=0.