(1) it is (C) the commutative property of multiplication: a*b = b*a, so 2*(-6/7) = (-6/7)*2
(2) it is (D) the commutative property of addition: a+b=b+a, so 5*4+3=3+5*4
commutate = "swap around"
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Andy and Samantha are performing an experiment in a science lab. The number of bacteria cells recorded by Andy in his experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. The number of bacteria cells recorded by Samantha in her experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. Using graphing technology, complete the statements. After hours, the total number of bacteria cells for both experiments will be the same. The total number of bacteria cells at that hour will be .
Answer:
after 5
time will be 35
Step-by-step explanation:
juan is saving money for a trip. he has already saved 100 he saves 50 each week what would be the rate of change of the situation?
Answer:
The rate of change would be 50
Step-by-step explanation:
The rate of change in any equation is simply the amount in changes for every value of x. Since it goes up by 50 for every increase of the week, it means that the rate of change is 50.
What is 659.003 as a mixed number??
*Thanks*
Six hundred fifty-nine and three thousandths is ...
... 659 3/1000
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answer:
x = 28°
Step-by-step explanation:
∠AOD and ∠BOC are vertical angles, hence congruent. That means the sum of ∠COE, ∠EOF, and ∠FOB is ∠BOC.
... 3x +x +(x+12°) = 152°
... 5x = 140° . . . . collect terms, subtract 12°
... x = 28° . . . . . . divide by 5
If line AB and CD are parallel to each other, hence the value of x from the given diagram is 39.2
To find the value of x from the given diagram, we will have to use the formula for finding the angle at a point.
The sum of all the angles at a point is 360 degreesTaking the sum of the angles and equating to 360 degrees is;152 + 3x + x + x + 12 = 360
152 + 12 + 5x = 360
164 + 5x = 360
5x = 360 -164
5x = 196
x = 196/5
x = 39.2
Hence the value of x from the given diagram is 39.2
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The school bookstore has 108 book covers. They will be equally distibuted among the students in the 2 sixth grade classes. Each class has 18 students. How many books covers does each student receive?
Each student will receive 3 book covers when 108 book covers are equally distributed among 36 students from two sixth-grade classes.
The question asks us to figure out how many book covers each student will receive if 108 book covers are distributed equally among students in two sixth-grade classes, with each class having 18 students.
First, calculate the total number of students by multiplying the number of classes by the number of students in each class: 2 classes * 18 students/class = 36 students.Then, divide the total number of book covers by the total number of students: 108 book covers / 36 students = 3 book covers per student.As a result, each student will receive 3 book covers.
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 6.8% daily failure rate.
a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
nothing (Round to three decimal places as needed.)
b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
nothing (Round to five decimal places as needed.)
c. What is the probability of not being awakened if the student uses three independent alarm clocks?
nothing (Round to five decimal places as needed.)
d. Do the second and third alarm clocks result in greatly improved reliability?
A.
No, because total malfunction would still not be unlikely.
B.
No, because the malfunction of both is equally or more likely than the malfunction of one.
C.
Yes, because total malfunction would not be impossible, but it would be unlikely.
D.
Yes, because you can always be certain that at least one alarm clock will work.
Answer:
Step-by-step explanation:
let X be the random variable for number of times the clock fails .
X is Poisson with average = 6.8% = 0.0068
PDF of x = e^(-0.0068) 0.0068^x/x!
a) The probability that the student's alarm clock will not work on the morning of an important final exam = P(X=0) = 0.00675
b) If the student has two such alarm clocks, the probability that they both fail on the morning of an important final exam:
Since both clocks are independent prob for both failing is
P(x1 fails) *P(x2 fails) = 0.00675(0.00675) = 0.000455625
c) the probability of not being awakened if the student uses three independent alarm clocks = Prob for all 3 fails = 0.00675^3
= 0.00000307546
d) Yes. Because all three fail probability is almost zero.
D. Yes, because you can always be certain that at least one alarm clock will work.
write an equation for a function , g(x), that is obtained by shifting the graph of f(x)= | x | three units to the left, reflecting that result over the x-axis, and then translating the graph up four unita.
g(x) =- | x + 3 | + 4
adding 3 units to x shifts the graph 3 units to the left
the negative reflects the function in the x- axis
adding + 4 translates the graph vertically up by 4 units
What is the value of the expression? (5/2)2+3^3/4 Enter your answer in the box.
To evaluate the expression (5/2)^2 + 3^3/4, we simplify each part separately, then add the results. The final value of the expression is 13.
Explanation:To evaluate the expression (5/2)^2 + 3^3/4, we'll start by simplifying each part separately.
The first part, (5/2)^2, means we raise 5/2 to the power of 2. To do that, we multiply the numerator and denominator of 5/2 by itself:
(5/2)^2 = (5/2) x (5/2) = 25/4.
The second part, 3^3/4, means we raise 3 to the power of 3, and divide the result by 4:
3^3/4 = 27/4.
Now we can add the two simplified parts together:
(5/2)^2 + 3^3/4 = 25/4 + 27/4 = 52/4 = 13.
The difference between 72 and 16
72 - 16 = 56
-Nicole :) <3
72 - 16 = 56
If a question says "find the difference" it usually means that you can use subtraction :)
what is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
the equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, 4)
m = [tex]\frac{4+1}{-3-4}[/tex] = [tex]\frac{5}{-7}[/tex] = - [tex]\frac{5}{7}[/tex]
use either of the 2 points as a point on the line
using (a, b) = (- 3, 4 ), then
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
Write an equation of the line passing through each of the following pairs of points. (−3, 1), (0, 3)
The 2-point form of the equation for a line is applicable. For points (x₁, y₁) and (x₂, y₂) that equation is ...
... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁
Filling in your point values gives ...
... y = (3 -1)/(0 -(-3))·(x -(-3)) +1
This can be simplified to ...
... y = (2/3)(x +3) +1
... y = (2/3)x +3
In a table do you have to list the x and y coordinates in order (largest to smallest)?
Answer:
No. (maybe)
Step-by-step explanation:
For expressing the corresponding values of x and y, any ordering will do. It is usually convenient for the user of the table if there is some recognizable order (so that a value can be found without searching the entire table). The usual expected order is by x-value, smallest to largest.
Some problem statements may specify that the table entries be listed in order. In those cases, yes, the table values must be listed as specified. (This accounts for the (maybe) answer, above.)
Tavon has a gift card for $ 50 that loses $ 2 for each 30-day period it is not used. He has another gift card for $ 40 that loses $ 1.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value?
To find the number of 30-day periods until the value of the gift cards will be equal, we set up and solve an equation. The value of each card will be $10 when they have equal value.
Explanation:To solve this problem, we can set up an equation to represent the value of each gift card over time and find when they will be equal.
Let x be the number of 30-day periods that have passed. After x periods, the value of the first gift card will be $50 - $2x, and the value of the second gift card will be $40 - $1.50x.
Setting the two expressions equal, we get:
$50 - $2x = $40 - $1.50x
Simplifying the equation, we have:
$10 = $0.5x
Dividing both sides by $0.5, we get:
x = 20
So, after 20 periods (or 20 months), the value of each gift card will be equal.
To find the value of each card at that point, we can substitute x = 20 into one of the expressions. Let's use the first gift card:
Value = $50 - $2(20) = $50 - $40 = $10
Therefore, when they have equal value, each gift card will be worth $10.
What is the value of the expression? (5/2)2+33/4 Enter your answer in the box.
Answer:
Step-by-step explanation:
its 43
Choose the equation that could be used to solve this problem. The product of a number and 3 is 87. What is the number?
A) 3x = 87
B) x + 3 = 87
C) x 3 = 87
D) x − 3 = 87
A
in mathematics the product of numbers means multiply the numbers
let x be the number, then the product of x and 3 = 3x
the result of this multiplication is 87
so 3x = 87 is the equation to solve the problem
the solution is x = 29
The equation used to solve this problem is 3x = 87. The solution, found by isolating x, is 29.
Explanation:The equation that could be used to solve the problem 'The product of a number and 3 is 87. What is the number?' is 3x = 87. This equation represents 'the product of a number (x) and 3 equals 87'. You would solve this by dividing both sides by 3 to isolate x, resulting in the solution x = 29. Thus, the number that when multiplied by 3 equals 87 is 29.
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What is the answer to this? −4 1/2÷(−2 2/3) (it has to be a mixed number)
Here is you're answer:
In order to solve this equation you must first change the mixed numbers into improper fractions then use KCF. (Keep, Change, Flip)
[tex]-4\frac{1}{2} \div -2\frac{2}{3}[/tex]Change into improper fractions:[tex]-4\frac{1}{2} =\frac{-9}{2}[/tex][tex]-2\frac{2}{3} = \frac{-8}{3}[/tex][tex]\frac{-9}{2} \div \frac{-8}{3}[/tex]Apply KCF:[tex]\frac{-9}{2} \times \frac{-3}{8}[/tex]Now multiply: [tex]\frac{-9}{2} \times \frac{-3}{8} = \frac{27}{16}[/tex]Remember that a negative times a negative is a positive:[tex]= \frac{27}{16}[/tex]Change into a mixed number:[tex]\frac{27}{16} = 1\frac{11}{16}[/tex][tex]= 1\frac{11}{16}[/tex]Therefore you're answer is "1 11/16."
Hope this helps!
PLEASE HELP
Find the rectangular coordinates of the point with the polar coordinates (3, 3 divided by 2 pi).
Answer:
(0, -3)
Step-by-step explanation:
The terminal ray of the angle with measure 3π/2 radians is the negative y-axis. The point that is 3 units from the origin on that ray has x-coordinate 0 and y-coordinate -3. The point is (0, -3).
At a school concert the orchestra plays 8 songs that are 4.25 min long and 3 songs that are twice as long as each of the others. How long is the concert ?
Answer:
Total time of the concert = 59.5 min = 59 minute 30 seconds
Explanation:
At a school concert the orchestra plays 8 songs that are 4.25 min and 3 songs that are twice as long as each of the others.
Total length of 8 songs = 4.25*8 = 34 min
Length of 3 songs = 2*4.25 = 8.5 min
Total length of 3 songs = 3* 8.5 = 25.5 min
Total time of the concert = 34 + 25.5 = 59.5 min = 59 minute 30 seconds
The concert is 59.5 minutes long: 8 shorter songs at 4.25 min each and 3 longer songs at 8.5 min each.
To find the total duration of the concert, we first calculate the duration of the 8 shorter songs and then the longer ones.
1. Shorter songs:
Duration of each shorter song = 4.25 minutes
Total duration of 8 shorter songs = 8 × 4.25 = 34 minutes
2. Longer songs:
Each longer song is twice as long as the shorter ones, so its duration is 2 × 4.25 = 8.5 minutes
Total duration of 3 longer songs = 3 × 8.5 = 25.5 minutes
Now, add the durations of both types of songs to find the total duration of the concert:
Total duration = Duration of shorter songs + Duration of longer songs
Total duration = 34 minutes + 25.5 minutes = 59.5 minutes
So, the concert is 59.5 minutes long.
JK and JL in the xy-coordinate plane both have a common endpointJ(-4,11) and midpoints at M, (2,16) and M2(-3,5), respectively. What is the distance between M, and M2? Round to the nearest tenth.
okay so the coordinates are (2,16) & (-3,5) & what you have to do is use the distance formula. if you use it & solve your way through it, your answer should be 5 rounded to the nearest tenth
One US dollar is currently worth 0.79 euro (€). If you exchange $522 for euros, how many euros will you have?
I'm pretty sure you would have 412.38 (€) because the equation would be $522 × 0.79.
Answer:412.38
Step-by-step explanation:
What is the solution of the system of inequalities
Answer:
There are four (4) whole-number solutions to these inequalities:
... {(4, 1), (5, 0), (6, 0), (7, 0)}
Step-by-step explanation:
These are nicely solved by graphing. Whole numbers are non-negative integers, so x and y can be any values 0, 1, 2, .... The area of overlap on the graph clearly shows that y=0 and y=1 are the only viable choices for y, and that the values for x are limited in each of these cases.
Find the equation of the line in slope-intercept form.Slope is 3/5 and (0, −2)
Answer:
[tex]y = \frac{3}{5}x - 2[/tex]
Step-by-step explanation:
Using the point slope form of a line equation, substitute m = 3/5 and the point (0,-2).
[tex]y - y_1 = m(x-x_1)\\y --2 = \frac{3}{5}(x - 0)\\y + 2 = \frac{3}{5}x \\ y = \frac{3}{5}x - 2 [/tex]
What are the steps for using a compass and straightedge to construct a line through point P that is parallel to line m? A horizontal line m and a point P are drawn. The point P is above the horizontal line m. Drag the steps and drop them in order from start to finish.
Answer:
Here's the list of the following sequence in the right order for you (I took the test myself and got this whole sequence right)
1. Use the straightedge to draw a line n that passes through P and intersects line m. Label the point of intersection as point X.
2. Place the point of the compass on point X and draw an arc that intersects lines m and n. Label the intersections as points A and B.
3. Without changing the width of the compass opening, place the point of the compass on point P and draw an arc that intersects line n. Label the intersection as point C.
4. Place the point of the compass on point A and open it to width AB.
5. With the compass opening set to width AB, place the point of the compass on point C and draw an arc that intersects the arc that was drawn from point P. Label the intersection of the arcs as point Y.
6. Use the straightedge to draw line PY.
Answer:
Here, m is a line and we have to find the draw parallel line of line of m through a point P with the help of straightedge and compass,
The correct order of steps for constructing a line through point P that is parallel to line m are as follows,
Step 1 : Use the straightedge to draw a line n that passes through P and intersect line m, lebel the point of intersection as X,
Step 2 : Place the point of the compass on point X and draw an arc that intersect line m and n, label the intersection point A and B,
Step 3 : Without changing the width of the compass opening, place the point of compass on point P and draw an arc that intersect line n label the intersection point as C,
Step 4 : Place the point of compass on point A and open it to the width of AB,
Step 5 : With the compass opening set the width of AB, place the point of the compass On point C and draw an arc that intersects the arc that was drawn from point P lebel the intersection of arc as point Y,
Step 6 : Use the straightedge to draw PY
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The product of (3 + 2i) and a complex number is (17 + 7i).
The complex number is ?
The product of (3 + 2i) and a complex number is (17 + 7i)
The product of (3 + 2i) and a complex number is (17 + 7i).
Let the complex number be a + ib
Product means we multiply
So (3+2i) * (a + ib) = (17+7i)
WE need to find a+ ib
Divie by 3 + 2i on both sides
a + ib = (17+7i) / (3+2i)
To divide multiply by the conjugate (3-2i)
[tex]a + ib = (\frac{ 17+7i)*(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]a + ib = (\frac{(17*3+7*2)+(7*3-17*2)i}{3^2-2^2}[/tex]
[tex]a + ib = (\frac{(65)+(-13)i}{13}[/tex]
[tex]a+ib = \frac{65}{13} - \frac{13}{13}[/tex]
a+ib = 5 - i
The required complex number is 5 - i
Answer:
37+55i
Step-by-step explanation:
The product of (3 + 2i) and a complex number is (17 + 7i) is expressed as shown below:
(3+2i)(17+7i)
Expanding the bracket,
= 51+21i+34i+14i²
= 51+55i+14i²
Note that in complex numbers i² = -1
Substituting this into the result, we have:
= 51+55i+14(-1)
= 51+55i-14
= 37+55i
The product of both complex number is 37+55i
Find the point, M, that divides segment AB into a ratio of 5:5 if A is at (0, 15) and B is at (20, 0).
A) (35, 10)
B) (20, 10)
C) (10, 7.5)
D) (17.5, 5)
C
a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment
using the midpoint formula
M = [[tex]\frac{1}{2}[/tex] (0 + 20 ), [tex]\frac{1}{2}[/tex] (15 + 0)] = (10, 7.5 )
Answer:
Option C). (10, 7.5)
Step-by-step explanation:
We have to find the coordinates of point M that divides the segment AB into a ratio of 5:5.
Vertices A and B are (0, 15) and (20, 0)
Ratio 5:5 is simply the ratio 1:1 means point M is the midpoint of segment AB.
So x-coordinate of M will be [tex]\frac{(20+0)}{2}=10[/tex]
and y - coordinate will be = [tex]\frac{(15+0)}{2}=7.5[/tex]
Therefore Option C. (10, 7.5) are the coordinates of point M.
The president of a certain university receives a salary that is three times the salary of one of the department heads. The total of the two salaries is $190,000.
What is the salary of the department head?
3(X)+X=190000 is how you'd find the answer the answer is 47,500
please help! cube root
(-5,-7),(0,-5),(5,-3) Determine the intercepts of the line that passes through the following points.
x-intercept ( , )
y intercept ( , )
Answer:
x-intercept (12.5, 0)y-intercept (0, -5)Step-by-step explanation:
The slope of the line is ...
... (change in y)/(change in x) = (-3 -(-5))/(5 - 0) = 2/5
The y-intercept is given: (0, -5).
The slope-intercept form of the equation can be written from this information as ...
... y = (2/5)x - 5
Solving this for y=0 (to find the x-intercept), we have
... 0 = (2/5)x - 5
... 5 = (2/5)x
... 5·(5/2) = x = 12.5
So, the x-intercept is 12.5, and the y-intercept (given) is -5.
Does anyone know this answer??
For this case we have the following equation:
[tex](2x + 3) ^ 2 + 8 (2x + 3) + 11 = 0[/tex]
Let [tex]u = 2x + 3[/tex]
We have:
[tex]u ^ 2 + 8u + 11 = 0[/tex]
By definition, given an equation of the form [tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula, to find the solution can be written as:
[tex]x = \frac{-b+/-\sqrt{b ^ 2-4 (a) (c)} }{2(a)}[/tex]
In this case we have:
[tex]a = 1\\b = 8\\c = 11[/tex]
Substituting in the quadratic formula we have:
See attached image
Answer:
Option B
x = (- 7 ± √5) / 2
use the substitution u = 2x + 3
equation can now be written as
u² + 8u + 11 = 0
solve for u using the quadratic formula with a = 1, b = 8 and c = 11
u = ( - 8 ± √( 64 - 44 ) )/2
= ( - 8 ± √20 )/2 = ( - 8 ± 2√5 ) / 2 = - 4 ± √5
change the variable back into terms of x
2x + 3 = - 4 ± √5 ( subtract 3 from both sides )
2x = - 7 ± √5 ( divide both sides by 2 )
x = ( - 7 ± √5 ) / 2
a store is having a dealer close-out sale. A computer desk, originally priced at $83, is now on sale for $78.85. what is the close-out discount rate? This is a percent of decrease.
A computer desk, originally priced at $83, is now on sale for $78.85
originally priced at $83. After discount the price becomes $78.85
Discount amount = $83 - $78.85 = $4.15
Decrease rate = discount amount divide by original price
Decrease rate = [tex]\frac{4.15}{83}= 0.05[/tex]
Decrease rate = 0.05
To find percent of decrease we multiply by 100
0.05 * 100 = 5%
Decrease percentage = 5%