Answer:
When we expand we get -9 - 33i + 30i². Since i² = -1 we can write this as -9 - 33i + 30 * (-1) = -9 - 33i - 30 = -33i - 39.
Answer:
-21-33i
Step-by-step explanation:
(-3+6i)(-3+5i)=9-15i-18i+30i²=9-33i+30(-1)=-21-33i
A man driving a car leaves a point A drives up to 32.5 km in a direction of 070. A cyclist leaves the same point in a direction 130 travelling. After some few hours both drivers are 80 km apart. Use this information to answer 3 questions. (1). What is the distance covered by the cyclist at this time in 2 d.p. (2). Find the bearing of Cyclist from the Car. correct to 1 d.p. (3). Find the shortest distance between the car and the line of path of the cyclist, in 2 d.p.
Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.
40 points!! What does this graph represent
Answer:
[tex]f(x)=0.2\,(x-2)^2+1[/tex]
Option "B" as per the list of possible answers
Step-by-step explanation:
Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you [tex]f(2) = 1[/tex]. You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.
Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square [tex](x-2)^2[/tex] which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:
[tex]f(x)=0.2\,(x-2)^2+1[/tex]
which you can check briefly by evaluating a couple of easy points (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.
A government agency has 6000 employees. As an alternative to the traditional five-day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The accompanying segmented bar chart is based on the data collected. Which of the following statements is true about work week preferences and age category? A. Preferences appear to be independent of age. B. The distribution of preferences is the same across different age groups. C. A greater percentage of employees who prefer flex hors are in the over 45 age category compared to those who prefer 4-day work week. D. A greater percentage of employees who prefer a 4-day work week are in the over 45 age category compared to those who prefer flax hours.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option D is the correct answer
Step-by-step explanation:
Now looking at the bar chart we see that a greater number of employee over the age of 45 preferred the 4-day work week compared to the number of employee between 30- 45 who preferred to have a flexible work hour and employee below 30 who' s preference are the same for both type of work hours
What is the final amount if 931 is decreased by 1% followed by a 1% increase?
Give your answer rounded to 2 DP.
Answer:
930.91
Step-by-step explanation:
931 x 99% = 921.69
921.69 x 101% = 930.9069
Answer:
930.91
Step-by-step explanation:
931*99%=921.69
921.69*101=930.91
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
What is the symbol for pi?
Answer:
π
Step-by-step explanation:
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 55 types of sandwiches, and 44 types of chips. How many different value meal packages are possible?
Answer:
159,720
Step-by-step explanation:
Calculation of how many different value meal packages are possible at Ron's Subs :
The meal package at Ron's Subs are:
Drink 66
Sandwich 55
Bag of chips 44
Since we are looking for the how many different value meal packages are possible that means we have to multiply all the three value meal package with each other.
Hence,
Drink 66 ×Sandwich 55 ×Bag of chips 44
=159,720
Therefore 159,720 is the number of different value meal packages that are possible at Ron's Subs
According to the Mortgage Bankers Association, 21% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of seven mortgages was selected. What is the standard deviation of this distribution
Answer:
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
Step-by-step explanation:
For each mortgage, there are only two possible outcomes. Either it is delinquent, or it is not. The probability of a mortgage being delinquent is independent of other mortgages. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
21% of U.S. mortgages were delinquent last year.
This means that [tex]p = 0.21[/tex]
A random sample of seven mortgages was selected.
This means that [tex]n = 7[/tex]
What is the standard deviation of this distribution
[tex]\sqrt{V(X)} = \sqrt{7*0.21*0.79} = 1.08[/tex]
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
Provide an appropriate response. A 28-year-old man pays $94 for a one-year life insurance policy with coverage of $120,000. If the probability that he will live through the year is 0.9991, what is the expected value for the insurance policy
Answer:
$ 14.08
Step-by-step explanation:
We have that the policy costs $ 94 and with life insurance with coverage of $ 120,000, to calculate the expected value, we must subtract the value of that life insurance multiplied with the probability of dying (complement of the probability of living) and the policy value multiplied by the probability of staying alive) like this:
120000 * (1 - 0.9991) - 94 * 0.9991 = 14.0846
Which means that the expected value of the policy is $ 14.08
Which of the following graphs represents the equation y=3x+2?
Answer:graph C is the answer because if you put the both values from the graph it satisfies the equation
Answer:
Graph C
Step-by-step explanation:
The given equation is in the form y=mx+b
This is slope-intercept form.
This is where m represents the slope, and b represents the y-intercept.
Therefore, the slope is 3 and the y-intercept is 2.
Let's first name all the equations with a y-intercept of 2.
That would be B and C.
Now, let's find the equation with a slope of 3.
Let's find the slope for B.
The formula for slope is: y1-y2/x1-x2
A point is: (x coordinate, y coordinate)
In the formula,
y1 is the y coordinate of the first point
y2 is the y coordinate of the second point
x1 is the x coordinate of the first point
x2 is the x coordinate of the second point
This said, we can plug our points in.
6-2/2-0
4/2
2
The slope for Graph B is 2, so it is incorrect.
Let's find the slope for Graph C.
2-(-1)/0-(-1)
2+1/0+1
3/1
3
The slope for Graph C is 3, and it has a y-intercept of 2, so Graph C is the correct choice.
El precio de un ordenador portátil ha aumentado un 25% y posteriormente fue rebajado un cierto porcentaje.Calcule que porcentaje de descuento habría que aplicar para que quede al precio original de antes del aumento. Porfa responder!!!
Answer:
Se requiere un 20 por ciento de descuento.
Step-by-step explanation:
(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)
Sea [tex]p_{o}[/tex] el precio original del computador portatil, el nuevo precio es:
[tex]p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}[/tex]
[tex]p_{1} = 1.25\cdot p_{o}[/tex]
Si [tex]p_{2} = p_{o}[/tex], entonces el porcentaje requerido para recuperar el precio original es:
[tex]r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%[/tex]
[tex]r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%[/tex]
[tex]r = \left(1-\frac{1}{1.25} \right)\times 100\,\%[/tex]
[tex]r = 20\,\%[/tex]
Se requiere un 20 por ciento de descuento.
Everyday, Jason has a 14-mile round-trip drive to work. He then has to drive his truck on a 296-mile delivery route 5 days a week. How many miles does he drive each day?
Answer:
73.2 miles i am not so sure
Step-by-step explanation:
If f(x) = 3x + 10 and g(x) = 2x – 4, find (f – g)(x).
Answer:
D
Step-by-step explanation:
Write the expressions "Four times the difference of a number and 1 is equal to six times the sum of the number and three. Find the number
Answer:
4(x - 1) = 6(x + 3)
x = -11
Step-by-step explanation:
x represents “the number” so we would substitute this with a variable.
(I hope this helps! Have a great day AND STAN BTS)
y= -x + 1/2+1
- 3x+y=6
What three-digit number with units digit 2 and hundreds digit 4 is divisible by 9?
Answer:
Dear user,
Answer to your query is provided below
A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.
Step-by-step explanation:
Here , It is given that the number is three digit in which units digit is 2 and hundreds digit is 4.
As per rule, the sum of its digits should've divisible by 9. So, Let the unknown digit be X .
Therefore, 2+X+4 =9
This implies, X = 9-2-4 = 3
So, the three digit number will be 432.
Verify - 432/9 = 48
Hence proved
The geometric sequence ; is defined by the formula: a i a 1 =10 a i =a i-1 * 9/10 Find the sum of the first 75 terms in the sequence .
Question:
The geometric sequence ; is defined by the formula: [tex]a_1 =10[/tex] ; [tex]a_i =a_{i-1} * \frac{9}{10}[/tex] Find the sum of the first 75 terms in the sequence .
Answer:
[tex]S_{75} = 99.963001151[/tex]
Step-by-step explanation:
Given
[tex]a_1 =10[/tex]
[tex]a_i =a_{i-1} * \frac{9}{10}[/tex]
Required
Find the sum of 75 terms
Given that the sequence is geometric;
First, the common ratio has to be calculated;
The common ratio is defined as follows;
[tex]r = \frac{a_{i}}{a_{i-1}}[/tex]
Let [tex]i = 2[/tex]
[tex]r = \frac{a_{2}}{a_{2-1}}[/tex]
[tex]r = \frac{a_{2}}{a_{1}}[/tex]
So,
[tex]a_i =a_{i-1} * \frac{9}{10}[/tex] becomes
[tex]a_2 =a_{2-1} * \frac{9}{10}[/tex]
[tex]a_2 =a_{1} * \frac{9}{10}[/tex]
Divide through by [tex]a_1[/tex]
[tex]\frac{a_2}{a_1} =\frac{a_{1} * \frac{9}{10}}{a_1}[/tex]
[tex]\frac{a_2}{a_1} = \frac{9}{10}[/tex]
Recall that [tex]r = \frac{a_{2}}{a_{1}}[/tex]
So, [tex]r = \frac{9}{10}[/tex]
Given that r < 1;
The sum of n terms is calculated as thus;
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
To calculate the sum of the first 75 terms, we have the following parameters
[tex]n = 75\\a = a_1 = 10\\r = \frac{9}{10} = 0.9[/tex]
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex] becomes
[tex]S_{75} = \frac{10(1-0.9^{75})}{1-0.9}[/tex]
[tex]S_{75} = \frac{10(1-0.9^{75})}{0.1}[/tex]
[tex]S_{75} = 100(1-0.9^{75})[/tex]
[tex]S_{75} = 100(1-0.00036998848)[/tex]
[tex]S_{75} = 100(0.99963001151)[/tex]
[tex]S_{75} = 99.963001151[/tex]
Barry has $30.00 to spend on soft drinks
for a party. A case of soft drinks costs
$4.65. Which inequality can be used to find how many cases (c) of soft drinks
Barry can purchase?
Answer:
30 ≥ 4.65x
Step-by-step explanation:
He cannot purchase more than $30, so the amount that he buys must always be less than 30.
I need help pls someone:(
Answer:
7/30
Step-by-step explanation:
What is the square root of -1 ?
Answer:
i
Step-by-step explanation:
17)Let f(x) = -2x + 5 and g(x) = 9x2 + 4. Find f(8) + g(8) . A)565 B)569 C)564 D)560
Answer:
answer B [tex]\boxed{ \ 569 \ }\\[/tex]
Step-by-step explanation:
f(8)=-2*8+5=-11
g(8)=9*8*8+4=580
f(8)+g(8)= -11+580=569
(80 POINTS) What rule describes a dilation with a scale factor of ½ and the center of dilation at the origin?
Answer:
C
Step-by-step explanation:
(x, y) -> (1/2x, 1/2y)
When you dilate a side, point, etc, you are multiplying the original dimension by the scale factor. That is represented in option C: the original x and y are multiplied by the scale factor, 1/2! Hope that helps! :)
Answer:
C. (x,y) → (1/2x,1/2y)
Step-by-step explanation:
Dialation means to multiply each coordinate by scale factor and in this case it's 1/2
An object travels along a horizontal path at a constant rate.the object travels 1/20 of the length of the path in 3/4 second.at that rate,how many seconds does it take the object to travel the entire length of the path?
Answer:
The onject 1/8 of the length of the path 3/4 in second.
Using the ratio and proportion to find the total time does it take the object to travel the entire length of the path as following
Length:time
X:(total time )
Total time x.(3/4)/(1/8x)=(3/4)/(1/8) = 6 seconds
PLZ help I will mark as brainliest
Decode the addition or subtraction problem (Change asterisks to digits, to make the operation correct.) 6*5* − *8*4=2856
Answer:
6750 - 3894 = 2856
Step-by-step explanation:
You have to make use of the arithmetic facts you know.
The least-significant asterisk must be 0, because the sum of 4 and 6 is 10.
The 10s asterisk must be 9,so that the sum 5 + 9 + 1 has a least-significant digit of 5.
The 100s asterisk must be 7, because that is the least-significant digit of the sum 8 + 8 + 1 = 17.
The 1000s asterisk must be 3, so that 2 + 3 + 1 = 6.
(The "1" in each of these sums is the carry from the sum of the digits with the next lower place value.)
So, the subtraction problem is ...
6750 - 3894 = 2856
_____
Comment on the solution method
For the most part, we worked this as an addition problem. The sum of the last two numbers must be equal to the first: 6570 = 3894 +2856. For some of us, addition facts are easier to work with than subtraction facts. The carry/borrow can be less confusing that way.
The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
Answer:
V(r) is the volume of basketball when the radius is r.
Answer:
B. the volume of the basketball when the radius is r
Step-by-step explanation:
Last years freshman class at big state university totaled $5330 students. Of those, $1258 received a merit scholarship to help offset tuition cost their freshman year. The amount a student received was N($3464, 489). If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?
Answer:
2.17% of students who received a merit scholarship did not receive enough to cover full tuition
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 3464, \sigma = 489[/tex]
If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?
This is 1 subtracted by the pvalue of Z when X = 4450. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4450 - 3464}{489}[/tex]
[tex]Z = 2.02[/tex]
[tex]Z = 2.02[/tex] has a pvalue of 0.9783.
1 - 0.9783 = 0.0217
2.17% of students who received a merit scholarship did not receive enough to cover full tuition
Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay
Answer:
$4.20
Step-by-step explanation:
Calculation for the standard deviation of the fare passengers pay of Blue Cab Company:
T = Total amount of the cab fare
Formula for Standard deviation of T will be:
T = σa+bX= bσX.
To convert the rate to dollars per mile from dollars per tenth of a mile, it will be:
b= 3
Hence,
Standard deviation of T is :
3.00(1.4) = $4.20.
Each have four possible answers left parenthesis a,b,c,d right parenthesis, one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find P(CWC), where C denotes a correct answer and W denotes a wrong answer.
b. Beginning with CWC, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list.P(CWC)minussee above P(WCC)equals? 0.046875 P(CCW)equals? 0.046875 (Type exact answers.)
c. Based on the preceding results, what is the probability of getting exactly two correct answers when three guesses aremade?
Answer:
a. P(CWC)=0.046875
b. P(WCC)=0.046875
P(CCW)=0.046875
c. P=0.140625
Step-by-step explanation:
By the rule of multiplication there are 64 forms to answer three questions. This is calculated as:
4 _ * 4 * 4 = 64
1st question 2nd question 3rd question
Because there are 4 options for every question. At the same way, from that 64 options, 3 are CWC and it is calculated as:
1 _ * 3 * 1 = 3
1st question 2nd question 3rd question
Because there is just one answer that is correct for the first question, there are 3 answers wrong for the second question and there are 1 answer correct for the third question.
So, the probability P(CWC) is equal to:
[tex]P(CWC)=\frac{3}{64}=0.046875[/tex]
Then, the complete list of the different possible arrangements of two correct answers and one wrong answer are: CWC, WCC and CCW
Therefore, the probabilities P(WCC) and P(CCW) are calculated as:
[tex]P(WCC)=\frac{3*1*1}{64}=\frac{3}{4}= 0.046875[/tex]
[tex]P(CCW)=\frac{1*1*3}{64}=\frac{3}{4}= 0.046875[/tex]
Finally, the probability of getting exactly two correct answers is the sum of the probabilities calculated before.
[tex]P=P(CWC)+P(WCC)+P(CCW)\\P=0.046875+0.046875+0.046875\\P=0.140625[/tex]
For the function, f(x) = -3x + 5.
If f(x) = -1, what is the value of x?
Answer:
x=2
Step-by-step explanation:
f(x) = -3x + 5.
f(x) =-1
-1 = -3x+5
Subtract 5 from each side
-1 -5 = -3x+5-5
-6 = -3x
Divide each side by -3
-6/-3 = -3x/-3
2 =x
Find the probability. Enter your answer as a simplified fraction.
Picking a purple marble from a jar with 14 green and 14 purple marbles.
Answer:
1/2
Step-by-step explanation:
14 green and 14 purple marbles = 28 marbles
P( purple) = purple/ total
= 14/28
=1/2