Answer:
[tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
Step-by-step explanation:
Given
[tex]\frac{8-i}{6+i}[/tex]
Multiply numerator/ denominator by the conjugate of the denominator.
The conjugate of 6 + i is 6 - i, thus
= [tex]\frac{(8-i)(6-i)}{(6+i)(6-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{48-14i+i^2}{36-i^2}[/tex] → substitute i² = - 1
= [tex]\frac{48-14i-1}{36+1}[/tex]
= [tex]\frac{47-14i}{37}[/tex]
= [tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
I need help please for the answer and how to solve it
Answer:
32) a) x = 3/19 ounces
33) d) 0,2 meter per minute
Step-by-step explanation:
32)
7 1/2 = 15/2
47 1/2 = 95/2
95/2 dough 15/2 sugar
1 dough x = (15/2*1) / 95/2
x = (15/2)(95/2)
x = 15/95
x = 3/19 ounces
33)
Distance 16 | 18 | 20 | 22
Time 80 | 90 | 100 | 110
Time 90 - 80 = 10
Distance 18 - 16 = 2
Each 10 minutes go 10 meters
2 / 10 = 0,2 meter per minute
how to answer the (a) question?
help please
i believe its 4
Step-by-step explanation:
Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty and only has 0.98 gallon of gas left. He stops at a gas station that charges $2.05 per gallon of gas. How much does it cost for Gunnar to refill his tank? Round your answer to the nearest penny.
Answer:
399.17 miles
Step-by-step explanation:
Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.
Gunnar's car travels with one gallon of gas = 22.4 miles
He can travel with 17.82 gallon of gas = 17.82 × 22.4
= 399.168 ≈ 399.17 miles
Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.
Find the solution to the system of equations.
Answer: x=1, y=-4
Step-by-step explanation:
There are different ways to solve system of equation
graphingsubstitutioneliminationIn your case, since they are all put y on one side, then we should use substitution.
we should substitute y
-7x+3=-x-3
-7x+x=-3-3
-6x=-6
x=1
--------------------------
substitute x into any one of the equation to find y
y=-7x+3
y=-7×1+3
y=-7+3
y=-4
y=-x-3
y=-1-3
y=-4
#CarryOnLearning
Solve the equation for X 3(x+2)=2(2-x)
Answer:
x = - 2/5Step-by-step explanation:
[tex]3(x+2)=2(2-x)\\\\\mathrm{Expand\:}3\left(x+2\right):\quad 3x+6\\\\\mathrm{Expand\:}2\left(2-x\right):\quad 4-2x\\\\3x+6=4-2x\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\3x+6-6=4-2x-6\\\\3x=-2x-2\\\\\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\\\3x+2x=-2x-2+2x\\\\Simplify\\\\5x=-2\\\\Divide\:both\:sides\:by5\\\\\frac{5x}{5}=\frac{-2}{5}\\\\x=-\frac{2}{5}[/tex]
Which figure has one line of symmetry but no rotational symmetry?
Answer:
c because u can split it only once vertically but it’s not a rotationally symmetrical shape
Step-by-step explanation:
Choose the best answer from the four choices given. You may use scratch
paper.
(3x2y3 )3 =
3x5y6
O 9x6yº
O 27x5y6
O 27x6y
Answer:
27x^6y^9
Step-by-step explanation:
(3x^2y^3)^3 = 3^3 * (x^2)^3 * (y^3)^3 =
= 27x^6y^9
what is standered form of 6,600,000,000,000,000,000,000
Answer:
6.6×10²¹
Step-by-step explanation:
6,600,000,000,000,000,000,000 → there are 21 place values after the first non-zero number ''6''
to convert to standard form, we move the decimal point after the first non-zero number.
6,600,000,000,000,000,000,000.0 ← decimal in the end
the decimal will be moved, all the digits after the decimal are counted and they will resemble the index.
6.6×10²¹
Solve the following linear equation and explain how you did it 1.1z+5.5=2.2z
Answer:
z = 5
Step-by-step explanation:
1.1z+5.5=2.2z
Subtract 1.1z from each side
1.1z-1.1z+5.5=2.2z-1.1z
5.5 = 1.1z
Divide each side by 1.1
5.5/1.1 = 1.1z/1.1
5 = z
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. : : What type of test is being conducted in this problem?
Complete question is;
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
H0: μ = 4
H1: μ > 4
What type of test is being conducted in this problem? What parameter is being tested?
Answer:
Type of test = right tailed
Parameter being tested = population mean
Step-by-step explanation:
We are given the null and alternative hypothesis as;
H0: μ = 4
H1: μ > 4
Now, let's define terms;
The right tailed test and the left tailed test are both examples of one-tailed tests. This is because the area where we would reject the null hypothesis is only in one tail. Which means that in the case of left tail, the rejection region will occur only to the left of the graph while for the right tail, the rejection region will occur only to the right of the graph.
Whereas, for two tailed test, the area where we would reject the null hypothesis would not just be in one tail or one side of the graph but could be in either tail or either side of the graph. Hence, the name "two - tail".
Now, applying this to the question, the alternative hypothesis says the mean is greater than 4. On, a graph, an increase in number on the x-axis means going to the right. Thus, it is a right tailed test
Now, the sample being tested is population mean because in statistics, the symbol μ is generally used to denote population mean.
A man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answer:
0.48 rad/sec
Step-by-step explanation:
From the diagram:
We can find 'x' using trigonometry :
Tanθ = opposite / Adjacent
Opposite = x ; adjacent = 4
Tanθ = x / 4
x = 4tanθ
Let u = 4 and v = tanθ
If dx/dt = 3ft/s ;
dθ/dt when x = 3ft
Differentiate x with respect to t
dx/dt (4tanθ)
Let d/dθ tanθ = sec^2θ
Sec^2θ = 1 / cos^2θ
dθ/dt = 1/4cos^2θdx/dt
dθ/dt = 1/4cos^2θ(3)
dθ/dt = 3/4cos^2θ
When x = 3ft
Cosθ = Adjacent / Hypotenus
Hypotenus = √(4^2 + 3^2
Hypotenuse = √16 + 9 = √25 = 5
Cosθ = 4/5
dθ/dt = 3/4(4/5)^2
dθ/dt = 3/4(16/25)
dθ/dt = 48/100 = 12/25 = 0.48 rad/sec
Multiply.
(-7x - 2) (5x+3)
Simplify your answer.
Answer:
= -35x² - 31x - 6
Step-by-step explanation:
(-7x -2)(5x+3) = -7x*5x -7x*3 -2*5x -2*3 = -35x² - 21x - 10x - 6
= -35x² - 31x - 6
6.2×10 +6×10³ Brainiest if right
Answer: 6062
Add Parentheses
[tex](6.2*10)+(6*10^3)[/tex]
Note: Always Multiply the Parentheses first!
Multiply
[tex]6.2*10=62[/tex]
[tex]6*10^3=6000[/tex]
How is 6×10^3 6000?
Before you multiply the whole equation you first Multiply 10 3 times. This is called an Exponent. In my own words, an exponent is a number that tells you how many times to multiply that number. So if we had 6^2 I will multiply 6×6 2 times. So we multiply 10×10×10 and get 1000. Then we multiply 6×1000 and get 6000.
Add
Since the final step is to add we Add the answer we got for 6.2×10 and 6×10^3.
Therefore we are adding 62*6000 and we get 6062.
Hi I am a teacher or 52 years old and I am wondering how I can become an online tutor?
Answer:
Go online and do research, I'm pretty sure you have websites around your area that is looking for tutors
Step-by-step explanation:
examples of parallel lines and interesting lines
Answer:
when the lines are opposite and doesnot intersect at any point then the lines are parallel
for example the opposite lines of parallelogram are parallel
when the lines cut each other at one point then we can say that lines are intersecting
hope it helps u
Answer:
Parallel lines :When thè lines are parellel and opposte to each other then it is called parellel lines.
Intersecting lines :When thè lines intersect each other and meet at a point then it is called intersecting lines.
7/25 divided by 3/5 as a fraction
Answer:
[tex] \frac{7}{15} [/tex]
Step-by-step explanation:
[tex] \frac{7}{25} \div \frac{3}{5} = \frac{7}{25} \times \frac{5}{3} = \frac{35}{75} = \frac{7}{15} [/tex]
Hope this helps ;) ❤❤❤
The calculated division of the numbers 7/25 divided by 3/5 is 7/15
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
7/25 divided by 3/5
When represented as an equation, we have
7/25 divided by 3/5 = 7/25 ÷ 3/5
Represent as a product expression
So, we have
7/25 divided by 3/5 = 7/25 * 5/3
So, we have the following result
7/25 divided by 3/5 = 7/15
Using the above as a guide, we have the following:
the result is 7/15
Read more about quotient at
brainly.com/question/11418015
#SPJ6
Solve for x: three halves plus one half times x equals two x x equals two thirds x = 1 x = 2 x = 3
Answer:
x=1
Step-by-step explanation:
because 3 over 2 plus 1 over 2 is 4 over 2 and 2 fits in 4 2 times so its 2 x but since thats solving for 2 half of that is 1, thus its x=1
The required simplified value of x is x = 1. Option 1 is correct.
Given,
Three halves plus one-half times x equals two x.
To simplify the above expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3/2 + 1/2 x = 2x
3/2 = 2x - 1/2 x
3x / 2 = 3 / 2
x = 1
Thus, the required simplified value of x is x = 1. Option 1 is correct.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
helpppppp asappppp plsssss
Answer:
x = -2
Step-by-step explanation:
The segments described in the question are equidistant (meaning they are the same length). Therefore, using algebraic techniques, we can set these two equal to each other and solve for x.
4x - 8 = 6x - 4 Combine like terms by subtracting 6x from both sides.
-2x - 8 = -4 Combine like terms by adding 8 to both sides.
-2x = 4 Divide by -2 on both sides of the equation.
x = -2
Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
Answer:
1) When this does happen, how many posters will each Avenger have completed?
24 posters each.
2) If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
Step-by-step explanation:
1) When this does happen, how many posters will each Avenger have completed?
We are told in the question:
Number of days = x
Number of posters = y
Ms. Ironperson has completed 12 posters and will complete 6 more per day.
y = 12 + 6x.......... Equation 1
Mr. Thoro has not started yet but can make 12 per day.
y = 12x................Equation 2
Hence, the equations needed to solve this problem:
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
We substitute 12x for y in equation 1
y = 12 + 6x.......... Equation 1
12x = 12 + 6x
Collect like terms
12x - 6x = 12
6x = 12
x = 12/6
x = 2
Hence, since x = the number of days,
The number of days = 2 days
Substitute 2 for x in Equation 2
y = 12x .......... Equation 2
y = 12 × 2
y = 24 posters.
Since y = number of posters,
number of posters = 24 posters.
We were told in the question that, when Mr Thoro catches up with Ms Ironperson, that would both have completed the same number of posters.
Hence, both Avengers would have completed 12 posters each.
In an examination of purchasing patterns of shoppers, a sample of 36 shoppers revealed that they spent, on average, $50 per hour of shopping. Based on previous years, the population standard deviation is $4.80 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, calculate a 90% confidence interval.
Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for [tex]z_{\alpha/2} = z_{0.1/2}[/tex]
[tex]= z_{0.05}[/tex] = 1.645
The standard error S.E = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
=[tex]\dfrac{4.8}{\sqrt{36}}[/tex]
[tex]=\dfrac{4.8}{6}[/tex]
= 0.8
The Confidence interval level can be computed as:
[tex]\bar x \ \pm z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
For the lower limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ - 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ - 1.645 \times \ 0.8 }}[/tex]
=50 - 1.316
= 48.684
For the upper limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ + 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ + 1.645 \times \ 0.8 }}[/tex]
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
paper plus sells reams ofpaper of $5.25 each discount paper sells the same reams of paper for $3.99 each, how much would you save by purchasing 15 reams of paper at discount paper instead of at paper plus?
Answer: $18.90
Step-by-step explanation:
multiply both by 15
subtract from each other
add 5 to me then you divide by 7 if you add 12 then subtract 7 you get 10 what number am i
Answer:
x+5=x÷7+12=x-7=10 it is 30
Answer:
30
Step-by-step explanation:
Given number is x, then:
(x + 5) ÷ 7 + 12 - 7 = 10(x + 5) ÷ 7 + 5= 10(x + 5) ÷ 7 = 5x + 5 = 5*7x + 5 = 35x = 35 - 5x = 30The number is 30
plz solve it.anyone
Answer:
See below.
Step-by-step explanation:
1i
75 = 3 * 5^2
Multiply by 3
1ii
112 = 2^4 * 7
Multiply by 7
1iii
128 = 2^7
Multiply by 2
1iv
243 = 3^5
Multiply by 3
1v
392 = 2^3 * 7^2
Multiply by 2
Please help. Calculate the loading dose, in mg of heparin for a 5-year-old with a total body weight of 40 lbs., with 10% body fat (that is, 90% of that 40 lbs. is lean body mass). You may also be interested to know that 1 kg = 2.20 lbs. Think about the steps you need to go through to find the correct dose. Remember, first you need to find the dosing mass.
Answer:
≈ 3 mg
Step-by-step explanation:
Dose rate of heparin is 0.16 mg per kg of DMDosing mass calculation formula is:
DM = LBM + (TBM - LBM)/3, where LBM = lean body mass, TBM = total body massTBM = 40 lbsBody fat = 10%LBM = 90% of TBM = 0.9*TBMDosing mass
DM = 40 *0.9 + ( 40 - 40*0.9)/3 = 37.33 lbsConverting to kg
1 kg = 2.2 lbsDM = 37.33 lbs /2.2 = 16.97 kgLoading dose
dose = DM * dose rate per kgdose = 16.97 kg *0.16 mg/kg = 2.7152 mg ≈ 3 mgSimplify the expression:
(10x2 -1 + 4x) + (3 + 5x2 - 4x)
Answer:
15x^2+2
Step-by-step explanation:
(10x^2 -1 + 4x) + (3 + 5x^2 - 4x)
Combine like terms
10x^2+5x^2+4x-4x-1+3
15x^2+2
The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 100 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ________.
Answer:
The sample size is [tex]n =278[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 100[/tex]
The standard deviation is [tex]\sigma = 850[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100-95)\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = \frac{(Z_{\frac{\alpha }{2}})^2}{E^2} * \sigma^2[/tex]
=> [tex]n = \frac{(1.96)^2}{100^2} * 850^2[/tex]
=> [tex]n =278[/tex]
When grading English papers, the instructor checks every 4th paper for plagiarism. What form of sampling is used?
random
convenience
systematic
cluster
Answer: systematic
Step-by-step explanation:
In random sampling researcher choose elements randomly for sample .In convenience sampling individuals are selected as per his convenience and comfort.In systematic sampling individuals are selected in a systematic way by using a fix periodic interval k from the entire population .In cluster sampling clusters (of homogeneous elements) are selected to make a sample.Given, When grading English papers, the instructor checks every 4th paper for plagiarism which expresses a fixed periodic interval.
Hence, this is systematic sampling.
A past survey of 1, 068,000 students taking a standardized test revealed that 8.9% of the students were planning on studying engineering in college.
In a recent survey of 1, 476,000 students taking the SAT. 9.2% of the students were planning to study engineering.
Construct a 95% confidence interval for the difference between proportions ^p1−^p2 by using the following inequality. Assume the samples are random and independent.
(^p1−^p2)−zc√^p1^q1n1+^p2^q2n2
The confidence interval is _____
Complete Question
The complete question is shown on the first uploaded image
Answer:
The interval is [tex]-0.0037 < p_1-p_2<-0.0023[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n _1 = 1068000[/tex]
The first sample proportion is [tex]\r p_1 = 0.089[/tex]
The second sample size is [tex]n_2 = 1476000[/tex]
The second sample proportion is [tex]\r p_2 = 0.092[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95 )\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}[/tex]
Here [tex]\r q_1[/tex] is mathematically evaluated as [tex]\r q_1 = (1 - \r p_1)= 1-0.089 =0.911[/tex]
and [tex]\r q_2[/tex] is mathematically evaluated as [tex]\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908[/tex]
So
[tex](0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}[/tex]
[tex]-0.0037 < p_1-p_2<-0.0023[/tex]
Will Give Brainliest! (And 25 Points) Easy Algebra Question! Please show all steps! Solve for x [tex]b+3/x=f/2[/tex]
Answer:
Step-by-step explanation:
Hello, we assume that x is different from 0 and f different from 2b
[tex]b+\dfrac{3}{x}=\dfrac{f}{2}\\\\\text{Subtract b}\\\\+\dfrac{3}{x}=\dfrac{f}{2}-b\\\\\text{Mulitply by 2x}\\\\+\dfrac{3*2*x}{x}=6=\dfrac{2xf}{2}-2bx=(f-2b)x\\\\\text{Divide by f-2b}\\\\\Large \boxed{\sf \bf x=\dfrac{6}{f-2b}}[/tex]
Thanks
Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x2 y = 6x − x2
Answer:
81π for the x axis.
Step-by-step explanation:
STEP ONE: Determine the intersection.
we are given from the question that y = x^2 and y = 6x − x^2. Therefore if y = x^2, then we will have;
x^2 = 6x - x^2 ---------------------------------------------------------------------------------[1].
Solving and factorizing the equation [1] above give us x = 0 and x = 3 (that is x[6 -2x] = 0 ). Therefore, the point of intersection = (0,0) and (3,9).
STEP TWO: Determine the value for the cross sectional area.
The cross sectional area= [6x - x^2]π - [x2]^2 π. --------------[2].
The cross sectional area = -12 π[x -3]x^2.
STEP THREE: integrate the cross sectional area taking x =3 and x =0 as the upper and lower integration limits or boundaries with respect to dx to determine the vome in the x axis.
volume =∫-12 π[x -3]x^2 dx.volume = -12 π[ (3)^4/4 - (3)^3 ] = 81π.volume, v with respect to the x axis = 81π