Domain (infinity,infinity)
Range (infinity,[tex]\sqrt{7}[/tex])
Find z1z2 if z1 = 3(cos37° + isin37°) and z2 = 2/3(cos53° + isin53°).
Answer:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Step-by-step explanation:
Both variable can be rewritten into polar form:
[tex]z_{1} = 3\cdot e^{i\cdot 0.205\pi}[/tex] and [tex]z_{2} = \frac{2}{3}\cdot e^{i\cdot 0.294\pi}[/tex]
The complex product is equal to:
[tex]z_{1}\cdot z_{2} = (3)\cdot \left(\frac{2}{3}) \cdot e^{i\cdot (0.205\pi+0.294\pi)}[/tex]
[tex]z_{1}\cdot z_{2} = 2 \cdot e^{i\cdot 0.499\pi}}[/tex]
The resultant expression in rectangular form is:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Answer:
The correct question is:
Find [tex]z_{1}.z_{2}[/tex] if [tex]z_{1}= 3(cos37 + isin37)[/tex] and [tex]z_{2}= \frac{2}{3} (cos53 + isin53)[/tex].
(Note: the angles mentioned in the equations above are in degrees)
The answer is [tex]z_{1}.z_{2}= 2i[/tex]
Step-by-step explanation:
[tex]z_{1}.z_{2}= 3(cos37 + isin37)* \frac{2}{3} (cos53 + isin53)[/tex]
[tex]z_{1}.z_{2}= (3cos37 + 3isin37)* (\frac{2}{3} cos53 + \frac{2}{3}isin53)[/tex]
[tex]z_{1}.z_{2}= 3cos37*\frac{2}{3} cos53 + 3cos37*\frac{2}{3}isin53+3isin37*\frac{2}{3} cos53+3isin37*\frac{2}{3}isin53[/tex]
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex] (Because [tex]i*i=i^{2}=-1[/tex] & [tex]i=\sqrt{-1}[/tex])
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex]
[tex]z_{1}.z_{2}= 2i[/tex]
A friendly contest involves randomly drawing a marble from a bag that contains 16 blue marbles, 12 red
marbles, and 8 yellow marbles. If a blue marble is drawn, Nathan wins. If a red marble is drawn, Taylor wins.
If a yellow marble is drawn, Cady wins.
Who is most likely to win the contest?
1 Nathan
2 Cady
3 They are equally likely to win.
4 Taylor
Answer: I have a huge feeling it would be Nathan because he has the most blue marble. Yk?
Consider that point A is reflected across the x-axis. What is the distance between point A and the point of its reflection?
Answer:
It would be 2 x the absolute value of the y coordinate.
Step-by-step explanation:
Example:
(5,-3)
Absolute value of y-coordinate is 3 and distance would equal 2 x 3 = 6 units apart.
A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The p-value is
Answer:
The p-value of the test is 0.023.
Step-by-step explanation:
In this case we need to determine whether the addition of several advertising campaigns increased the sales or not.
The hypothesis can be defined as follows:
H₀: The stores average sales is $8000 per day, i.e. μ = 8000.
Hₐ: The stores average sales is more than $8000 per day, i.e. μ > 8000.
The information provided is:
[tex]n=64\\\bar x=\$8300\\\sigma=\$1200[/tex]
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{8300-8000}{1200/\sqrt{64}}=2[/tex]
The test statistic value is 2.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=P(Z>2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.023[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.023.
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03? Use a 95% confidence level. (Round your answer up to the nearest whole number.)
Answer:
A sample size of 657 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent.
This means that [tex]\pi = 0.19[/tex]
(a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03?
A sample size of n is needed.
n is found when [tex]M = 0.03[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.19*0.81}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.19*0.81}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.19*0.81}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.19*0.81}}{0.03})^{2}[/tex]
[tex]n = 656.91[/tex]
Rounding up to the nearest whole number.
A sample size of 657 is needed.
In the figure below, which term best describes point T?
Answer:
A
Step-by-step explanation:
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
Answer:
88 25/27
Step-by-step explanation:
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
PEMDAS
Parentheses first
(7)^2 (7)^2÷(3)^3
Then exponents
49*49 ÷27
Then multiply and divide from left to right
2401÷27
2401/27
88 25/27
88.92592593
Answer:
Step-by-step explanation:
(7)^2(7)^2 / (3)^3
49*49 / 27
2401/27
88 25/27
Which expression represents a factorization of 32m + 56mp ?
Answer:
8m(4 + 7p)
Step-by-step explanation:
Take out the greatest common factor:
8m(4 + 7p)
j+ 12 =25 find the solution to equation algebtaically
Answer:
j= 13
just subtract 12 from 25
Start by isolating the j.
Subtract 12 from both sides.
On the left, the 12 and -12 cancel.
On the right, 25 - 12 is 13.
So we have j = 13.
I will make you the brainliest if you can help me with my geometry homework.
Answer:
SAS
Step-by-step explanation:
Sides WV and XV on either side of angle WVX have been shown to be congruent to their corresponding parts. When you're concerned with a Side, Angle, and Side in that geometrical sequence, the SAS theorem is applicable.
Two math students were asked to write an exeponential growth equations that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?
Answer:
Pierre is right.
Step-by-step explanation:
A growth rate of 2% means that the values is increasing by 0.02 each year so the multiplying factor is 1.02.
Pierre is correct y = 300(1.02)^x.
Scotts answer 1.2 = a growth rate of 20%.
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
Answer:
93.25% probability that they have taken this steroid
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test
Event B: Taking the steroid.
Suppose the probability of an athlete taking a certain illegal steroid is 10%.
This means that [tex]P(B) = 0.1[/tex]
Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.
This means that [tex]P(A|B) = 0.995[/tex]
Positive test:
99.5% of 10%(If the athlete has taken).
100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)
Then
[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]
Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]
93.25% probability that they have taken this steroid
What is the slope for the linear function y=3x-4
Answer:
3
Step-by-step explanation:
This is written in the form
y= mx+b
where m is the slope and b is the y intercept
3 is the slope and -4 is the y intercept
g(t) = 6t - 1
g ( ) = -7
Answer:
g(-1) = -7
Step-by-step explanation:
Put the given value for g(t) into the first equation and solve for t.
-7 = 6t -1
-6 = 6t . . . . . . add 1
-1 = t . . . . . . . . divide by 6
g(-1) = -7
Answer: -1
Step-by-step explanation:
Brainliest for anyone if they get this CORRECT.
answer is D7/2
hope it helps!!!!!!!!!!!!!!!!!!!!!!
Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29
Question:
1. How many full boxes of lemon bars can Shira fill?
2. How many delicious lemon bars will she be taking home?
Answer:
1. Number of filled box = 21
2. Number of take home = 2
Step-by-step explanation:
Given
Number of lemon bars = 170
Each bar contains 8 lemon bars
Required
(1) & (2)
To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .
i.e.
Number of filled box = 170/8
Number of filled box = 21.25
But here, we only need the quotient of the division because it represents the filled boxed.
So,
Number of filled box = 21
Calculating the number of take home.
We'll follow the same steps as (1) above but here, we only need the remainder of the division.
When 170 is divided by 8, the remainder is 2.
So, number of boxes she'll take home is 2.
See calculation below
Number of take home = 170 % 8
Number of take home = 2
a rectangular rug measures 8 feet long and 12 feet wide . what is the area of the rug
Answer:
96 square feet
Step-by-step explanation:
Area= length x width
So for the rug it would be 12x8
12x8=96
What is the quotient?
(6 * 108) = (1.5 x 10-4)
4 x 1012
4 x 104
4 x 10-32
4 * 10-2
Answer:
The first choice.
Step-by-step explanation:
6 * 10^8 / 1.5 * 10^-4
= (6/1.5) * (10^(8 - (-4))
= 4 * 10^12.
Answer:
4 x 1012
Step-by-step explanation:
We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude
Answer:
we can conclude that more than 50% of community college students plan to vote in the next presidential election
Step-by-step explanation:
Decision Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Null hypothesis H0: 50% of community college students plan to vote in the next presidential election
H0: p = 0.50
Ha: More than 50% of community college students plan to vote in the next presidential election
Ha: p > 0.50
P-value = 0.02
From the decision rule;
Since the p-value for this study is less than the significance level.
0.02 < 0.05
So, we reject the null hypothesis, there is enough evidence to reject the null hypothesis. We thereby accept the alternative hypothesis.
Therefore, we can conclude that more than 50% of community college students plan to vote in the next presidential election
How do I type in exponents
Answer:
on what
Step-by-step explanation: normaly you have a button that you can have certain characters
Barnes and Nobles buys a book for $14.25. They markup the price of the book by 35%.
Answer:
$19.24
Step-by-step explanation:
Take 14.25 times 1.35.
The markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.
What is the markup rate?The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.
Barnes and Noble buy a book for $14.25. They mark up the price of the book by 35%.
As per the question, we have
cost = $14.25
markup rate = 35% = 0.35
Let's x represent markup for the book,
markup rate = markup/sale price × 100%
35% = x / $14.25
0.35 = x / $14.25
x = $14.25 × 0.35
Apply the multiplication operation, and we get
x = 4.9875
So sale price = markup + cost
So sale price = $4.9875 + $14.25
So sale price = $19.237
Thus, the markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.
To learn about the markup rate click here:
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When Jonas becomes the Receiver of Memory, he gets a rule that he may not tell his dreams. He wants to know how many of his 505050 classmates have the same rule. He asks 555 friends from his class whether they may tell their dreams. Of those, 444 say that they may.
Answer:
101010 classmates can't tell their dreams.
Step-by-step explanation:
I'm not sure what the question is, but if it is an average thing than 444 of 555 is 80 percent, so if that is what it wants 404040 of the students can share their dreams, and 101010 can't.
Hope this helps!
A sphere is inscribed in a cube. Explain the relationship between the surface areas of the two solid figures
Answer:
No one knows. Jk just go look at the other brainly links. the question has already been asked and answered so you can go see them there.
Step-by-step explanation:
:)
The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.
Answer:
The equation for the height of the penny in function of time is:
[tex]h(t)=1451-16t^2[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Step-by-step explanation:
The penny will have a free fall.
The initial velocity is zero, and the initial height is h(0)=1,451.
The acceleration will be the gravity, that has a value g=32 ft/s^2.
Then, we can model this starting by the speed:
[tex]dv/dt=-g\\\\v(t)=v_0-gt=-gt[/tex]
Then, the height becomes:
[tex]dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2[/tex]
The approximate height of the penny after 7 seconds can be calculated as:
[tex]h(7)=1451-16(7^2)=1451-16*49=1451-784=667[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
how many thousands make 5crore
Answer:
50,000 thousands make a crore.
Step-by-step explanation:
One crore (1,00,00,000) is equal to one hundred lakh (10,000 × 1,000). Thus, 10,000 thousands make a crore.
what is this phrase in numerical expression
triple the sum of seventeen and ten
pls help
Answer: so you would do 17 plus ten which is 27 so triple 3 so your answer is 27^3
Step-by-step explanation:
sum so your adding plus you need the exponent which is times 3
Which fraction equals a repeating decimal?
30/50
13/25
5/30
13/10
Answer:
5/30
Step-by-step explanation:
5/30 = 1/6 =0.166666666...
The fraction equals a repeating decimal is 5/30.
What are decimals?A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.
Now the given fractions are,
30/50
13/25
5/30
13/10
Converting them into decimals we get,
30/50 = 0.6
13/25 = 0.52
5/30 = 0.1666..
13/10 = 1.3
Thus the repeating decimal is 0.1666..
So, the fraction with repeating decimal is 5/30 = 0.1666..
Thus, the fraction equals a repeating decimal is 5/30.
To learn more about fraction :
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3/4 x 1/4
next problme: 3/5 x 1/5
100 pts
Answer:
0.1875 and 0.12
Step-by-step explanation:
3/4x1/4 is 0.1875. 3/5 x 1/5 is 0.12
Answer:
1)0.1875
2)0.12
Step-by-step explanation:
What is the area of a rectangle with sides length of 5/12 feet and 2/3 feet
Answer:
The answer is 10/36 or if you want to simplify, 5/18
Step-by-step explanation:
To solve the area of a rectangle, you need to multiply the sides with each other, so 5/12 x 2/3 is 10/36 (unsimplified) . You multiply the numerators and then the denominators and simplify.
