ANSWER
[tex]P=\frac{81}{625}[/tex]EXPLANATION
There are 4 defects out of 10 total computers. This means that there are 6 computers without defects.
The probability that 1 computer selected will not be defective is the total number of non-defective computers divided by the total number of computers:
[tex]P(one-without-defect)=\frac{6}{10}[/tex]Therefore, if a sample of 4 computers is selected, the probability that the sample will not contain a defective computer is:
[tex]\begin{gathered} P=\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}=(\frac{6}{10})^4 \\ P=\frac{81}{625} \end{gathered}[/tex]Oh no! You have just discovered Superhero C is actually a villain! He plans toactivate an underwater volcano that is 50 miles away. Superhero A is goingto try to stop him.Suppose getting to the underwater volcano requires a combination ofrunning, flying, and swimming.Using the rates from Table 1, make a plan for how far each Superheroshould run, fly, and swim to make sure that Superhero A gets to the volcanobefore Superhero C and can save the world.Note: You must use all three modes of travel.
SOLUTION:
First, let's calculate for superhero C the villian.
Using the three modes of travelling,
He needs to cover a distance of 50 miles
If he:
i. Runs
1 mile in 2 minutes, Hence
50 miles will be in 100 minutes
ii) Flys
2 miles in 2 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
4 miles in 3 minutes, Hence
50 miles will be in 37.5 minutes
Next, let's calculate for superhero A.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
4 miles in 1 minute, Hence
50 miles will be in 12.5 minutes
ii) Flys
4 miles in 4 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
3 miles in 1 minute, Hence
50 miles will be in 16.67 minutes.
Finally, let's calculate for superhero B.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
5 miles in 1 minute, Hence
50 miles will be in 10 minutes
ii) Flys
7 miles in 2 minutes, Hence
50 miles will be in 14.29 minutes
iii) Swims
10 miles in 3 minutes, Hence
50 miles will be in 15 minutes.
Evaluate the expression (-4-4i) +(-8-11) and write the result in the form a + bi.The real number a equalsThe real number b equals
The answer is supposed to be in the form
[tex]a+bi[/tex]Therefore,
[tex](-4-4i)+(-8-1i)[/tex][tex]\begin{gathered} -4-4i-8-1i \\ \end{gathered}[/tex]combine like terms
[tex]-4-8-4i-1i[/tex]Finally,
[tex]-12-5i[/tex]a = -12
b = -5
What is the approximate area of the shaded region? 6 5 3 a 2 1 X 0 1 2 3 4 5 6 O A. 3 units? B. 6 units c. 10 units D. 13 units
Area aof shaded region is
Difference of areas between square, and circle
Area of square is = (5-1)^2 = 16
Area of circle is = π•[(5-1)/2]^2 = π•2^2 = π•4
Shaded Area = 16 - (π•4) = 16 - 12.564 = 3.436
THEN option A , is the value most aproximate to 3.436
e inverse operations to solve the equations below. x^2+3=19
We have the expression:
[tex]x^2+3=19\Rightarrow x^2=16[/tex][tex]\Rightarrow x=\pm4[/tex]Are the triangle below congruent? If so, write a congruence statement and say why
what is the name of the geometric figure that begins at a point and is a set of all points that make a never-ending straight path extending in only one direction?
hi.
to start this exercise, let's remember some definitions about the alternatives:
a. ray
distance between the center of the circle and a point on its circumference (one straight line)
b. vertex
is a point where two edges meet
c. angle
is formed by two semi-straights that come from the same origin
d. opposite rays
is the same definition of radius, only now it considers two rays: one and its opposite. joining a radius to its opposite, we get a straight line.
Given triangle ABC below, if angle B=(x-60)^ and angle C=(x- 45)^ find the measure of angle x
Given:
m∠B = (x - 60)°
m∠C = (x - 45)°
Opposite angle = x°
Let's find the measure of angle x.
To find the measure of angle x, apply the Exterior Angle Theorem which states that the exterior angle of a triangle is equal to the sum of the two opposite angles.
Thus, we have:
∠B + ∠C = x
(x - 60) + (x - 45) = x
Solve for x.
• Remove the parentheses and combine like terms:
x - 60 + x - 45 = x
x + x - 60 - 45 = x
2x - 105 = x
• Move all terms containing x to the left, then move 105 to the right
2x - x = 105
x = 105°
Therefore, the measure of angle x is 105°
ANSWER:
x = 105°
Please help!! I keep getting crazy fractions for the one for equation of a line and for the other one I have no idea how to solve. I'll be eternally grateful!
We will find the equation of the line passes through the points:
[tex](\frac{5}{8},\frac{31}{16})and(-\frac{-5}{7},\frac{13}{14})[/tex]The general neral
Find the scale factor of the two prisms, the ratio of their surface areas, and the ratio of theirvolumes. List the larger values first.6 cm8 cm9 cm10 cm12 cm15 cmScale FactorSurface AreasVolumesBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:Blank 6:
We will operate as follows:
*Scale factor:
We determine the scale factor using two respective sides, that is:
[tex]9x=6\Rightarrow x=\frac{6}{9}\Rightarrow x=\frac{2}{3}[/tex]So, the scale factor is 2 : 3.
*Surface area:
We determine the surface are of each prism:
[tex]S_{A1}=(9\cdot12)+2(\frac{15\cdot9}{2})+(12\cdot\sqrt[]{15^2+9^2})+(15\cdot12)\Rightarrow S_{A1}=(108)+(135)+(36\sqrt[]{34})+(180)[/tex][tex]\Rightarrow S_{A1}=423+36\sqrt[]{34}\Rightarrow S_{A1}=632.9142682\ldots[/tex][tex]S_{A2}=(6\cdot8)+2(\frac{6\cdot10}{2})+(10\cdot8)+(8\cdot\sqrt[]{6^2+10^2})\Rightarrow S_{A2}=(48)+(60)+(80)+(16\sqrt[]{34})[/tex][tex]\Rightarrow S_{A2}=188+16\sqrt[]{34}\Rightarrow S_{A2}=281.2952303\ldots[/tex]Now:
[tex](423+36\sqrt[]{34})x=188+16\sqrt[]{34}\Rightarrow x=\frac{188+16\sqrt[]{34}}{423+36\sqrt[]{34}}\Rightarrow x=\frac{4}{9}[/tex]So, the ratio of the surface areas is 4 : 9.
*Volume:
We determine the volume of each prism and proceed as before:
[tex]V_1=\frac{9\cdot15\cdot12}{2}\Rightarrow V_1=810[/tex][tex]V_2=\frac{6\cdot10\cdot8}{2}\Rightarrow V_2=240[/tex]Now:
[tex]810x=240\Rightarrow x=\frac{240}{810}\Rightarrow x=\frac{8}{27}[/tex]So, the ratio for the volumes is 8 : 27.
What is the domain of the cubic function f(x)= 9x³ + 2x-12 ?
GIVEN:
We are given the function below;
[tex]f(x)=9x^3+2x-12[/tex]Required;
To find the domain of the cubic function.
Step-by-step solution/explanation;
The domain of a function is the set of all input values (that is, x values) for which the function is defined.
For the function given, there is no constraint, which means the function is always true for any value of x.
Therefore,
ANSWER:
[tex]Domain=(-\infty,+\infty)[/tex]The domain is the set of all real numbers.
Option B
14) What is the slope of the line below *
Nancy bought a pack of 10 cookies for her 3 children to share equally. How many cookies should each child get if the cookies are shared equally between the 3 children?
Given:
Total pack is 10.
Share divied in 3 children.
So each children share is:
[tex]\begin{gathered} 3\text{ total share is 10} \\ for\text{ each share}=\frac{10}{3} \\ =3.33 \end{gathered}[/tex]each children share is 3.33 cookies.
6)Find the solution set of the quadratic equation over the set of complex numbers.5x2 + 12x + 8 = 0A)x = −34 − i4 or −34 + i4B)x = −65 − 2i5 or −65 + 2i5C)x = −25i(11 − 2i) or −25i(11 + 2i)D)x = −16i(11 − 2i) or −16i(11 + 2i)
The given quadratic equation is expressed as
5x^2 + 12x + 8 = 0
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing both equations, we have
a = 5, b = 12, c = 8
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ 12}\pm\sqrt[]{12^2-4(5\times8)}}{2\times5}\text{ } \\ x\text{ = }\frac{-\text{ 12 }\pm\sqrt[]{144\text{ - 160}}}{10}\text{ = }\frac{-\text{ 12}\pm\sqrt[]{-\text{ 16}}}{10} \\ x\text{ = }\frac{-\text{ 12}\pm4i}{10} \\ x\text{ = }\frac{-\text{ 12 + 4i}}{10}\text{ or x = }\frac{-\text{ 12 - 4i}}{10} \\ x\text{ = }\frac{-\text{ 12}}{10}\text{ + }\frac{4i}{10}\text{ or x = }\frac{-\text{ 12}}{10}\text{ - }\frac{4i}{10} \\ x\text{ = }\frac{-\text{ 6}}{5}+\text{ }\frac{2i}{5}\text{ or x = }\frac{-6}{5}-\text{ }\frac{2i}{5} \end{gathered}[/tex]Find the value of each variable in the parallelogram.5u – 10162u + 2V3U =0V=
The diagonals of a parallelogram bisect each other. It means the segments, after bisection, are equal to each other.
From the figure, we can write:
[tex]\begin{gathered} 2u+2=5u-10 \\ \text{and} \\ 6=\frac{v}{3} \end{gathered}[/tex]We can solve the first equation and get the value of u:
[tex]\begin{gathered} 2u+2=5u-10 \\ 2+10=5u-2u \\ 12=3u \\ u=\frac{12}{3} \\ u=4 \end{gathered}[/tex]Solving the second equation, we find the value of v:
[tex]\begin{gathered} 6=\frac{v}{3} \\ 6\times3=v \\ v=18 \end{gathered}[/tex]Answer:
u = 4v = 18homework practice what is the 5th term of this sequence?
based on the graph which equation can be used to describe the relationship between x and y?
hello
to solve this problem, we can easily find the slope of the line
this will give us the an insight to the answer
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]now let's identify our points
[tex]\begin{gathered} y_2=2 \\ y_1=-4.5 \\ x_2=-13.5 \\ x_1=6 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2--4.5}{-13.5-6} \\ m=\frac{6.5}{-19.5} \\ m=-\frac{1}{3} \end{gathered}[/tex]the slope of the line is -1/3 and this corresponds to option B
the equation of the line is given as
[tex]y=-\frac{1}{3}x-2.5[/tex]Solve the system of linear equations using the graphing method. Use “no solution” and “infinitely many” when appropriate.
Given the system of equations:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Let's solve the system using graphing method.
Let's plot both equations on a graph. The point where both lines meet.
• Equation 1:
Let's plot using 3 points.
Substitute random values of x and solve for y.
We have:
[tex]\begin{gathered} x=-4;\text{ y = }\frac{1}{2}(-4)+2=-2+2=0 \\ \\ x=0;y=\frac{1}{2}(0)+2=0+2=2 \\ \\ x=4;y=\frac{1}{2}(4)+2=2+2=4 \end{gathered}[/tex]For equation 1, we have the points:
(x, y) ==> (-4, 0), (0, 2), (4, 4)
Plot the points and connect the points with a straight line.
• Equation 2:
Let's create 3 points:
[tex]\begin{gathered} x=-2;y=\frac{1}{2}(-2)+1=-1+1=0 \\ \\ x=0;y=\frac{1}{2}(0)+1=0+1=1 \\ \\ x=2;y=\frac{1}{2}(2)+1=1+1=2 \end{gathered}[/tex]FOr equation 2, we have the points:
(x, y) ==> (-2, 0), (0, 1), (2, 2)
Now, plot the points and connect using a straight line.
We have the graph of both equations below:
From the graph, we can see that both lines do not meet at any point.
They are parallel lines,
Since they will not meet at any point, there is NO SOLUTION.
ANSWER:
No solution.
Piper works at a camera store. He is paid an hourly rate plus 16% commission on everything he sells. One week, he was paid $515 for working 20 hours and selling $1,500 worth of camera equipment. What is his hourly rate?
His hourly rate is $13.75
Here, we want to get Piper's hourly pay at work
Let the hourly rate be h
Thus, for working 20 hours, the amount for this will be; 20 * h = 20h
Now, out of the $1500 sales, he is entitled to 16%
That means;
[tex]\frac{16}{100}\times\text{ 1500 = 240}[/tex]Thus, we have it that;
[tex]\begin{gathered} 20h\text{ + 240 = 515} \\ 20h\text{ = 515-240} \\ 20h\text{ = 275} \\ h\text{ = }\frac{275}{20} \\ h\text{ = \$13.75} \end{gathered}[/tex]What type of angle is shown on the protractor below?
Given data:
The given angle .
The given angle AOB is an obtuse angle.
Thus, third option is correct.
Distributive Property equation8x4=(_x_)+(_x_)
Answer:
8 x 4 = (8 x 2) + (8 x 2)
Explanation:
The distributive property says that:
a x (b + c) = (a x b) + (a x c)
Then, we can write 4 as (2 + 2), so:
8 x 4 = 8 x ( 2 + 2)
Now, we can apply the distributive property:
8 x 4 = (8 x 2) + (8 x 2)
Therefore, the answer is:
8 x 4 = (8 x 2) + (8 x 2)
on a graph if it has (-5,5) and (5,5) is it proportional or non- proportional
A proportional graph is when y increases/decreases, if x increases. The graph shows that as x increases, the value of y stays the same, therefore it is not proportional.
Can you help me please? If there is a solution what’s the solution as well
Solution:
Given;
[tex]-7y^2+7y+1=0[/tex]Where;
[tex]a=-7,b=7,c=1[/tex]Thus;
[tex]\begin{gathered} b^2-4ac=7^2-4(-7)(1) \\ \\ b^2-4ac>0 \end{gathered}[/tex]Hence, the quadratic equation has two different real solutions.
Then;
[tex]\begin{gathered} y=\frac{-7\pm\sqrt{7^2-4(-7)(1)}}{2(-7)} \\ \\ y=1.13,y=-0.13 \end{gathered}[/tex]I need help on this equationTo simplify each and state the excluded value.
To answer this question, we need to factor each of the polynomials as follows:
First Polynomial
[tex]x^2+4x+3[/tex]To factor it, we need to find two numbers:
a*b = 3
a + b = 4
These numbers are:
a = 3
b = 1
Therefore, we have:
[tex]x^2+4x+3=(x+1)(x+3)[/tex]The sequence below shows the number of trees that a nursery plants each year.2, 8, 32, 128 ...Let an represent the current term in the sequence and an-1 represent the previous term in thesequence. Which formula could be used to determine the number of trees the nursery will plantin year n?
According to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is [tex]a_{n}= 4a_{n-1}[/tex]. Thus, option (A) is correct.
The given sequence of the number of trees that a nursery plants each year is -
2, 8, 32, 128, .....
[tex]a_{n}[/tex] = The current term in the sequence
[tex]a_{n-1}[/tex] = The previous term in the sequence
We have to find out the formula that could be used to determine the number of trees that the nursery will plant in the year n.
From the sequence we can see that -
8 = 2*4
32 = 8*4
128 = 32*4
So, this can be said that the current term in the sequence ([tex]a_{n}[/tex]) is 4 times the previous term in the sequence ([tex]a_{n-1}[/tex]).
=> [tex]a_{n}= 4a_{n-1}[/tex]
Thus, according to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is
[tex]a_{n}= 4a_{n-1}[/tex]
Thus, option (A) is correct.
To learn more about sequence visit https://brainly.com/question/21961097
#SPJ9
Choose the graph that illustrates both g (x) andg (x+4)
Explanation:
If we have a function f(x) = g(x + c), we can say that f(x) is g(x) shifted c units to the left.
So, the graph of g(x + 4) will be the same graph of g(x) shifted 4 units to the left
Answer:
The only graph that has two functions and one if equal to the other shifted 4 units to the left is the following:
What is the measure of the 5x+25
As you can see:
RM+MT = RT
Where:
RM = 5x + 9
MT = 8x - 6
RT = 198
Replacing the data:
5x + 9 + 8x - 6 = 198
Add like terms:
(5x + 8x) + (9 - 6) = 198
13x + 3 = 198
Solve for x:
Subtract 3 from both sides:
13x + 3 - 3 = 198 - 3
13x = 195
Divide both sides by 13:
13x/13 = 195/13
x = 15
Delta Airlines' flights from Chicago to Atlanta are on time 80 % of the time. Suppose 14 flights are randomly selected, and the number on-time flights is recorded.1.The probability that at least 9 flights are on time is =2.The probability that at most 2 flights are on time is =3.The probability that exactly 10 flights are on time is =
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Given that 14 flights are randomly selected from the record list and that the flights from Chicago to Atlanta are on time 80% of the time, we have to determine:
a) The probability that at least 9 flights are on time
If we choose a flight randomly out of the 14 and 80% of the time it is on time (success), then we can use the binomial theorem for probability:
[tex]\binom{n}{x}p^x(1-p)^{n-x}[/tex]Where p is the probability of success and x is the number of times we want to check.
In this case, let p = 80% or 0.8, n = 14, such that
[tex]\binom{14}{x}0.8^x\cdot0.2^{14-x}[/tex]To find the probability that at least 9 flights are on time, we calculate the probability that at least 5 are not on time. That is, we make
[tex]\begin{gathered} 14-x=5 \\ x=9 \end{gathered}[/tex]Thus
[tex]\binom{14}{9}0.8^9\cdot0.2^5=\frac{14!}{9!\cdot(14-9)!}\cdot0.8^9\cdot0.2^5\approx0.086[/tex]In fact, we have to sum all of the contributions as follows:
[tex]\sum ^{14}_{x=9}\binom{14}{x}0.8^x\cdot0.2^{14-x}[/tex]And we get:
[tex]\approx0.956[/tex]In other words, the probability that at least 9 flights are on time is 95.6%
b) The probability that at most 2 flights are on time
For this, we need to find the probability that at least 13 flights are not on time, such that
[tex]undefined[/tex]the paper didnt explain how to do this clearly could you take me step by step how to do this
Given data:
The given point is (2,-2).
The equation of the line is y= -2x+3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the given equation with the above equation.
[tex]m=-2[/tex]Two parallel lines have equal slope, the equation of the line parallel to the given line and passing through (2, -2) is,
[tex]\begin{gathered} y-(-2)=m(x-2) \\ y+2=-2(x-2) \\ y+2=-2x+4 \\ y=-2x+2 \end{gathered}[/tex]Thus, the equation of the line is y= -2x+2.
A painter charges $20 for every hour that he paints. Let h equal the number of hours he paints and e represent his earnings.Select TWO equations that represent the situation.A. e= 20hB. h=20+eC. 20=h+eD. 20=hxeE. e/h=20
The form of the linear equation is
[tex]y=mx+b[/tex]m is the rate of change
b is the initial amount
Since The painter charges $20 every hour, then
The rate is 20
m = 20
Since there is no initial amount of payment, then
b = 0
Since the number of hours is h, then
x = h
Since the earning is e, then
y = e
The equation is
[tex]e=20h[/tex]Then the first equation is A
Divide both sides by h
[tex]\begin{gathered} \frac{e}{h}=\frac{20h}{h} \\ \frac{e}{h}=20 \end{gathered}[/tex]The 2nd equation is E
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.(2x - 20)INNISmaller angle:Larger angle:O0UNSFANA(4x - 10)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define complementary angles
When the sum of two angles is 90°, then the angles are known as complementary angles.
STEP 2: Write the pairs of the angles formed
[tex]\begin{gathered} (2x-20)\degree \\ (4x-10)\degree \end{gathered}[/tex]STEP 3: find the value of x
Following the definition in step 1, this goes that;
[tex]\begin{gathered} (2x-20)+(4x-10)=90\degree \\ 2x-20+4x-10=90\degree \\ 6x-30=90 \\ 6x=90+30 \\ 6x=120 \\ x=\frac{120}{6}=20 \end{gathered}[/tex]STEP 4: Find the two pair of angles
[tex]\begin{gathered} (2x-20)=2(20)-20=40-20=20\degree \\ 4x-10=4(20)-10=80-10=70\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} smaller\text{ }angle=20\degree \\ Larger\text{ }angle=70\degree \end{gathered}[/tex]