Answer:
a = 2 , b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]
=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]
=> [tex]\frac{24+13i-2i^2}{13}[/tex]
=> [tex]\frac{26+13i}{13}[/tex]
Comparing it with a+bi
a = 26/13 , b = 13/13
a = 2, b = 1
Answer:
a = 2
b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}[/tex]
Write the fraction in this form:
[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]
[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]
Evaluate.
[tex]\frac{26+13i}{13}[/tex]
Factor the numerator.
[tex]\frac{13\left(2+i\right)}{13}[/tex]
[tex]2+1i[/tex]
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
Please answer this correctly
Answer:
50%
Step-by-step explanation:
Even numbers on a 6-sided die are 2, 4, and 6.
3 numbers out of 6 are even.
3/6 = 1/2
0.5 = 50%
PLEASE HELP! Max has as many sisters as brothers. However, his sister Emily has half as many sisters as brothers. How many girls and boys are in their family?
Answer:
Four brothers and three sisters.
Step-by-step explanation:
There is no overlap between the graphs of y< x+ 2 and y> x-2.
True or False
Someone help please
Answer:I think it's TRUE not sure
Step-by-step explanation:
3. A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles. (20 points)
a. What is the plane's speed in miles per hour?
b. At this rate, how many miles can it travel in 10 hours?
Answer:
a. The plane's speed in mph is 560
b. At this rate, the plane can travel 5,600 miles in 10 hours.
Step-by-step explanation:
In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6. Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.
Answer:
A. 560B. 5,600Step-by-step explanation:
A. = 3,360 / 6 = 560B. = 560 x 10 = 5,600a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answer:
0.42
Process:
1 - 0.58
0.42
Find the values of a and b in the rhombus. Solve for the value of c, if c=a+b.
Answer:
a = 5
b = 1.3
c = 6.3
Step-by-step explanation:
To find the values of a, b and C respectively, let's find a first by recalling that the diagonals of a rhombus are perpendicular to each other.
Therefore, the angle given as (14a + 20) = 90°
Solve for a
14a + 20 = 90
14a = 90 - 20
14a = 70
a = 70/14
a = 5
==>To find b, also recall that all sides of a rhombus are equal.
Therefore 3b + 4 = 13b - 9
Solve for b
4 + 9 = 13b - 3b
13 = 10b
13/10 = b
b = 1.3
==>Find value of c
c = a + b
c = 5 + 1.3
c = 6.3
1) Which statement contains an exact number? A) A gross of paper contains 144 sheets. B) One sheet of paper is 0.0042 inches thick. C) One sheet of paper measures 8.5 x 11 inches. D) A ream of medium weight paper weighs 20 pounds. Answer: A
Answer:
B) One sheet of paper is 0.0042 inches thick
Step-by-step explanation:
All the other values are not give from just a sheet of paper, and/or they are either a cumulative value, or values that will be used to calculate another value
Only option B defines a value for a unit of paper, and the value is definite.
Option A indicates the number in a group (gross)
Option C shows two values that can be used to calculate one value; the area.
Option D indicates an accumulated value of weight.
A sample of 1600 computer chips revealed that 43% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 41% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer: The value of the test statistic is z= 1.63 .
Step-by-step explanation:
Test statistic for proportion :
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p =population proportion.
[tex]\hat{p}[/tex] = sample proportion
n= sample size.
Let p be the proportion of chips do not fail in the first 1000 hours of their use.
As per given, we have
[tex]p=0.41\\ n= 1600\\\hat{p}=0.43[/tex]
Then, required test statistic would be
[tex]z=\dfrac{0.43-0.41}{\sqrt{\dfrac{0.41(1-0.41)}{1600}}}\\\\=\dfrac{0.02}{\sqrt{0.0001511875}}\\\\\approx\dfrac{0.02}{0.0123}\approx1.63[/tex]
Hence, the value of the test statistic is z= 1.63 .
what does r equal? 1/13r=-8/15
Answer:
[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]
Step-by-step explanation:
hello,
first of all let's assume that r is different from 0 as this is not allowed to divide by 0
[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]
multiply by 13r it comes
[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]
now multiply by 15
[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]
hope this helps
Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....
Step-by-step explanation:
[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]
[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex] =-104/15
simplify
[tex]r=-\frac{104}{15}[/tex]
MARK BRAINLIEST PLEASE
You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4, -7), B(8, -7),A(4,−7),B(8,−7),A, left parenthesis, 4, comma, minus, 7, right parenthesis, comma, B, left parenthesis, 8, comma, minus, 7, right parenthesis, comma and C(8, -3)C(8,−3)C, left parenthesis, 8, comma, minus, 3, right parenthesis. What are the coordinates of point DDD? \large((left parenthesis , \large))right parenthesis
Answer:
D(4,-3)
Step-by-step explanation:
Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)
Let the coordinate of the fourth vertex be D(x,y).
We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.
The diagonals are BD and AC
Midpoint of BD = Midpoint of AC
[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]
The coordinates of the fourth vertex is D(4,-3)
Answer:
(4,-3)
Step-by-step explanation:
What is the answer? ABCD ~ EFGH
Answer:
x = 3.6
Step-by-step explanation:
In similar polygons, corresponding sides are in same ratio
[tex]\frac{AB}{EF}=\frac{AD}{EH}\\\\\frac{3}{2}=\frac{x}{2.4}\\\\\frac{3}{2}*2.4=x\\[/tex]
3 * 1.2 = x
x = 3.6
The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?
OA. Rx) = (x - 1)2
OB. Rx) = (x + 1)2
OC. Rx) = -1(x - 1)
OD. Rx) = -1(x + 1)2
Reset
Next
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 0) , thus
y = a(x - 1)² + 0
To find a substitute the coordinates of the y- intercept (0, 1) into the equation
1 = a(- 1)² = a , thus
a = 1
y = (x - 1)² → A
Considering it's y-intercept and vertex, the equation of the parabola is given by:
[tex]y = (x - 1)^2[/tex]
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
In this problem, the vertex is (1,0), hence h = 1, k = 0 and:
[tex]y = a(x - 1)^2[/tex]
The y-intercept is of 1, hence, when x = 0, y = 1, so:
[tex]y = a(x - 1)^2[/tex]
[tex]1 = a(0 - 1)^2[/tex]
[tex]a = 1[/tex]
Hence, the equation is:
[tex]y = (x - 1)^2[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
5(2x - 3) = 5
What does x equal?
Answer:
x=2
Step-by-step explanation:
5(2x - 3) = 5
Divide by 5
5/5(2x - 3) = 5/5
2x-3 = 1
Add 3 to each side
2x-3 +3 = 1+3
2x = 4
Divide by 2
2x/2 = 4/2
x =2
Answer:
x = 2
Step-by-step explain:
5(2x-3) = 5
Divide both sides by 5
2x-3 = 1
Add 3 to both sides
2x = 4
Divide both sides by 2
x = 2
A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
Pls help me I’ll mark brainLiest
Answer:y times 20 p
Step-by-step explanation:
Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at MicrosoftMicrosoft selects every 1414th software CDsoftware CD that comes off the assembly line starting with the eightheighth until she obtains a sample of 140140 software CDssoftware CDs. Which type of sampling is used?
Answer:
Systematic sampling is used.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Every 14th CD.
So systematic sampling is used.
What tool is used to draw circles
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
Find the value of x that makes A||B
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
How do you solve 36 times [tex]\sqrt{3}[/tex]
Answer:
62.3538
Step-by-step explanation:
There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps
Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?
Hey there! :)
Answer:
x = 18 minutes.
Step-by-step explanation:
To solve this equation, set up a ratio.
# of towels over time taken:
[tex]\frac{6}{3} = \frac{36}{x}[/tex]
Cross multiply:
6x = 108
Divide both sides by 6:
6x/6 = 108/6
x = 18 minutes.
Answer:
In eighteen minutes she will have folded all 36
Do class limits and class marks make sense for qualitative data classes? Explain
your answer.
NEED QUICKLY
Answer: NO, class limits and class marks are not meaningful to qualitative data.
Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.
Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.
Help me plzzzzz!!!!
Answer:124
Step-by-step explanation:
2x + 8 + x - 2 = 180
Add like terms
3x + 6 = 180
Subtract the 6 from both sides
3x + 6 - 6 = 180 - 6
3x = 174
Divide by 3
x = 58
Now we have to find the measure of angle ACD
2(58) + 8 = 124