A cable 84 meters long is cut into two pieces so
that one piece is 20 meters longer than the other.
Find the length of each piece of cable.
Answer: 33
Step-by-step explanation: Let x equal the shorter piece.
x + (x + 18) = 84
2x + 18 = 84
2x = 66
x = 33
Whats the difference between a closed eye and an open eye in algebra
Answer:
If the inequality is "strict" ( < or > ), we use an open dot to indicate that the endpoint of the ray is not part of the solution. For the other types of inequalities ( ≤ and ≥ ), we use a closed dot to indicate that the endpoint is part of the solution.
Step-by-step explanation:
Suppose that $3000 is placed in a savings account at an annual rate of 3.6%, compounded monthly. Assuming that no withdrawals are made, how long will it take for the account to grow to $4500? Do not round any intermediate computations, and round your answer to the nearest hundredth.
Using compound interest, it is found that it will take 11.28 years for the the account to grow to $4500.
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
A(t) is the amount of money after t years.
P is the principal(the initial sum of money).
r is the interest rate(as a decimal value).
n is the number of times that interest is compounded per year.
t is the time in years for which the money is invested or borrowed.
In this problem:
$3000 is placed in the account, thus [tex]P = 3000[/tex].Interest rate of 3.6%, thus [tex]r = 0.036[/tex].Monthly compounding, thus [tex]n = 12[/tex].We have to solve for t when [tex]A(t) = 4500[/tex], thus:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]4500 = 3000(1 + \frac{0.036}{12})^{12t}[/tex]
[tex](1.003)^{12t} = 1.5[/tex]
[tex]\log{(1.003)^{12t}} = \log{1.5}[/tex]
[tex]12t\log{1.003} = \log{1.5}[/tex]
[tex]t = \frac{\log{1.5}}{12\log{1.003}}[/tex]
[tex]t = 11.28[/tex]
It will take 11.28 years for the the account to grow to $4500.
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the number of girls in the class was 1 less than 3 times the number of boys there were 15 students in all. How many were boys, and how many were girls
There was 4 boys and 11 girls in the class.
Let x represent the number of boys and y represent the number of girls.
Since the number of girls in the class was 1 less than 3 times the number of boys, hence:
y = 3x - 1
3x - y = 1 (1)
Also, there were 15 students in all, hence:
x + y = 15 (2)
Solving equations 1 and 2 simultaneously gives:
x = 4, y = 11
Hence, there was 4 boys and 11 girls in the class.
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What's the answer to this world problem please:
Mr. See got $1675 from selling 50 thumb drives and computer keyboards. Each thumb drives cost $24 and each computer keyboard cost $49. How many computer keyboards did he sell?
Answer:
19 keyboards
Step-by-step explanation:
Let d = thumb drives; and k = computer keyboards
Total number of sales of thumb drives and keyboards is 50
50 = d + k
Rearranged:
d = 50 - k
Total revenue from the sale of $24 thumb drives and $49 keyboards is $1675
1675 = 24d + 49k
Sub in d = 50 - k
1675 = 24(50 - k) + 49k
1675 = 1200 - 24k + 49k
475 = 25k
k = 475/25
k = 19
(To check, d = 50 - 19 = 31)
Please help! What values of x make the matrix M have an inverse?
Answer:
I'm not sure I'm only in middle school, but I'll put what I know.
Step-by-step explanation:
Step 1: Calculate the minor for the given matrix.
Step 2: Turn the obtained matrix into the matrix of cofactors.
Step 3: Then, the adjugate, and.
Step 4: Multiply that by reciprocal of determinant.
A fish store can place 5 fish in each fish bowl. If there are 263 fish to place, how many fish bowls are needed for all 263 fish?
Answer:
Step-by-step explanation:
1 bowl holds 5 fish
x bowls hold 263 fish
1/x = 5/263 Cross multiply
5x = 263 Divide by 5
5x/5 = 263/5
x = 52.6
So you actually need 53 fishbowls. One of them holds only 3 fish
Marie is reading a 271-page book. She has already read 119 pages. She uses the equation 119+8h=271 to find out how long it will take her to finish the book if she reads at about 8 pages per hour.
Solve for h.
Answer: the answer is 19
Step-by-step explanation:okay so she already have read 119 pages and the total pages is 271 so we substract 271-119=152 so she has 152 pages left so we divide 152 pages divided by 8 because she read 8 pages per hour so 152/8=19
3. The cost of a taxi ride is the sum of a fixed cost of $2,50 for the first kilometer, plus
$175 for each additional kilometer,
a. White an equation that relates the cost of the taxi ride, Fdollars, to the distance
travelled,
Determine the cost of a 28km taxi ride. Show all the math!
Answer:
y=2.50+175*(x-1)
$4727.50
Step-by-step explanation:
y=2.50+175*(x-1)
The first km costs 2.50 which is why you add it. You do x-1 because the 175 is charged for each additional km. So, if you traveled one km it would cost 2.50.
y=2.5+175*(28-1)
y=2.5+175*27
y=2.5+4725
y=$4727.50
Helene, who drives a cab, is paid $250 per week. She averages $75 per day in tips. About how much does she earn per 5 day work week?
COORDINATE GEOMETRY Find the perimeter and area of each figure with the given vertices. 20. D(-2,-2), E(-2, 3), and F(2, -1)
Step-by-step explanation:
Find the sides and perimeter:
DE = 3 - (-2) = 5EF = [tex]\sqrt{(2+2)^2+(-1+2)^2} =\sqrt{17}[/tex] ≈ 4.1DF = [tex]\sqrt{(2+2)^2+(3+2)^2} =\sqrt{41}[/tex] ≈ 6.4Perimeter:
P = 5 + 4.1 + 6.4 = 15.5 unitsFind the area using shoelace formula:
A = 1/2|(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)|=1/2|(-2*3 + -2* -1 + 2* -2) - (-2* -2 + 3*2 - 1* -2)|=1/2|(-6 + 2 - 4) - (4 + 6 + 2)| =1/2|-8 - 12| =1/2(20) = 10 units²The sum of the speeds two trains is 717.6 miles per hour. If the speed of the first train is 6.4 mph faster than that of the second train, find the speeds
of each.
What is the speed of the first train?
Train 1 = x + 6.4
Train 2 = x
(x) + (x + 6.4) = 717.6
2x + 6.4 = 717.6
2x = 711.2
x = 355.6
Train 1 = 355.6 + 6.4 = 362 mph
Train 2 = 355.6 mph
Hope this helps!! :)
NO LINKS OR ASSESSMENT!!!
Part 2: Graph a function when give the following Domain and Range:
Answer:
Step-by-step explanation:
The domain is the x value between - 5 and 7
The range is the y value between -2 and 6
You can find all sorts of definitions for the domain and range, but in this example it is really straight forward. If you put - 5 into the function, you get -2. If you put 7 into the function, you get 6. Now just draw a line between the two end points.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The point at the left end of the domain is not included in the function, but the function includes the limits of its range. One such function is shown in the attachment.
Y+2=-(x+4) in slope intercept form
Answer:
y=-x-6
Step-by-step explanation:
First, you have to distribute the - that is outside the parentheses. That leaves you with -x-4. So now your equation is y+2=-x-4. You want the y by itself so you subtract two from both sides leaving you with y=-x-4-2, which adds up to y=-x-6.
if ab=2√3 then find the value of a^4+b^4
Answer:
umm wait
Step-by-step explanation:
Answer:
Step-by-step explanation:
I NEED HELP ON THIS 10 POINTS
Answer:
-x-x-0.7
is equivalent to 1-2x-1.7
At a hockey game, a vender sold a combined total of 127 sodas and hot dogs. The number of sodas sold was 43 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold. Number of sodas sold:
Answer:
85 sodas
Step-by-step explanation:
Total sold was 127
The number of sodas was 43 + the number of hotdogs
Let x represent hotdogs:
x + (43 + x) = 127 (The 43 + x is the number of sodas sold.)
2x + 43 = 127
2x = 84
x = 42
42 hotdogs were sold., Since sodas are 42 + 43, 85 sodas were sold
-Chetan K
Which situation represents the greatest percent of increase?
a. Original: 60
New: 75
b. Original: 140
New: 200
c. Original: 900
New: 1000
d. Original: 30
New: 60
Answer:
d because it incresed by 50binstead of 13 12 and 23 percent
Help me with this please ;(
Answer:
5 cubes , so 5 cubic units
Step-by-step explanation:
There are 5 cubes in this figure.
Since each cube is a cubic unit, the answer is 5 cubic units.
-Chetan K
13, 69, 89, 25, 55, 20, 99, 75, 42, 18, 66, 88, 89, 79, 75, 65, 25, 99, 66, 78. Order from least to greatest
HELP ME ON THIS QUESTION 10 POINTS PLZ
Answer:
0.5 or 1/2
Step-by-step explanation:
-1+3[(10-12)^3÷(-16)]
(10-12)^3÷(-16)
(-2)^3=-8
-8÷(-16)=0.5
jamarius 5th grade class was working on a reading project during the school year he wants to read 22 pages for 125 days if jamarius wants to meet his goal how man books will he have to read
Answer:
2750 pages
Step-by-step explanation:
but i am not sure how many books exactly .
Problem Set
100 yd. =
Answer:
1 yard = 3 feet
We can re-write this by dividing both sides by yards or feet to get
1 = 3 feet / 1 yard
or
1 yard / 3 feet = 1
Since we're solving for feet we want yards to cancel, so use the top proportion
(3 feet / 1 yard)(100 yards) = 300 feet / 1 = 300 feet
Commutative property of multipcation 3x4=12
Answer:
3x4=12 is the same as
4x3=12 and
12/3=4 and
12/4=3
The commutative property of multiplication is true for the expression 4 x 3 = 3 x 4 = 12.
What is multiplication?Multiplication is one of four mathematical arithmetic operations.
It is also a process of adding the same types of expression for some number of times.
The repeated addition is multiplication.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
The commutative property of multiplication:
Let a and b are the two numbers.
And the product of a x b is n.
So, a x b = b x a = n
Changing the numbers position does not affect the result.
Here,
3 x 4 = 4 x 3
12 = 12
This expression holds the commutative property of multiplication.
Therefore, 3 x 4 = 12 holds the commutative property.
To learn more about the multiplication;
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Please help maths question which box is it and why!
Answer:
the third one because it will make more sense
Step-by-step explanation:
Which number is closest to the square root of 84 ?
Translate the sentence into an inequality.
The sum of a number times 9 and 16 is at least 22.
Use the variable c for the unknown number.
medical tests. Task Compute the requested probabilities using the contingency table. A group of 7500 individuals take part in a survey about a rare disease and medical test. The data for the group is given in the table below. A person listed as "Sick" has the disease, while someone listed as "Not Sick does not "Tested Positive means the test indicated the person was sick, and "Tested Negative" means the test indicated they were not sick. The test is believed to be around 99% accurate. Sick Not Sick Tested Positive 59 75 Tested Negative 1 7365 h One person at random is chosen from the group (3 pts) Find the probability the person is sick. b. (3 pts) Find the probability the test is positive given that the person is sick (3 pts) Find the probability the test is negative given that the person is not sick. d. (pts) Find the probability the person is sick given that the test is positive (3 pts) Find the probability the person is not sick given that the test is negative. f. (5 pts) When we say a test is 99% accurate, to what is that referring? Given vour calculations, should information other than a single test be considered when diagnosing a rare condition? If so, what other information might be considered? Criteria for Success
Probabilities are used to determine the chances of an event
The probability that a person is sick is: 0.008The probability that a test is positive, given that the person is sick is 0.9833The probability that a test is negative, given that the person is not sick is: 0.9899The probability that a person is sick, given that the test is positive is: 0.4403The probability that a person is not sick, given that the test is negative is: 0.9998A 99% accurate test is a correct test(a) Probability that a person is sick
From the table, we have:
[tex]\mathbf{Sick = 59+1 = 60}[/tex]
So, the probability that a person is sick is:
[tex]\mathbf{Pr = \frac{Sick}{Total}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{60}{7500}}[/tex]
[tex]\mathbf{Pr = 0.008}[/tex]
The probability that a person is sick is: 0.008
(b) Probability that a test is positive, given that the person is sick
From the table, we have:
[tex]\mathbf{Positive\ and\ Sick=59}[/tex]
So, the probability that a test is positive, given that the person is sick is:
[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{59}{60}}[/tex]
[tex]\mathbf{Pr = 0.9833}[/tex]
The probability that a test is positive, given that the person is sick is 0.9833
(c) Probability that a test is negative, given that the person is not sick
From the table, we have:
[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]
[tex]\mathbf{Not\ Sick = 75 + 7365 = 7440}[/tex]
So, the probability that a test is negative, given that the person is not sick is:
[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7365}{7440}}[/tex]
[tex]\mathbf{Pr = 0.9899}[/tex]
The probability that a test is negative, given that the person is not sick is: 0.9899
(d) Probability that a person is sick, given that the test is positive
From the table, we have:
[tex]\mathbf{Positive\ and\ Sick=59}[/tex]
[tex]\mathbf{Positive=59 + 75 = 134}[/tex]
So, the probability that a person is sick, given that the test is positive is:
[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{59}{134}}[/tex]
[tex]\mathbf{Pr = 0.4403}[/tex]
The probability that a person is sick, given that the test is positive is: 0.4403
(e) Probability that a person is not sick, given that the test is negative
From the table, we have:
[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]
[tex]\mathbf{Negative = 1+ 7365 = 7366}[/tex]
So, the probability that a person is not sick, given that the test is negative is:
[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7365}{7366}}[/tex]
[tex]\mathbf{Pr = 0.9998}[/tex]
The probability that a person is not sick, given that the test is negative is: 0.9998
(f) When a test is 99% accurate
The accuracy of test is the measure of its sensitivity, prevalence and specificity.
So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.
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What is the image of the point (-9, -1) after a rotation of 270° counterclockwise
about the origin?
Answer:
(1,-9)
Step-by-step explanation:
During rotation anytime you rotate the figures the arrangement will change and also since you are rotating to 270 counter-clockwise(anti-clockwise)your answer will be (1,-9)
Answer: The correct answer is -1,9
Step-by-step explanation:
270 rule - (x, y) ⇒ (y, -x)
(-9, -1) ⇒ (-1, 9)
Help me please is is odd or even or neither?
Answer:
it's odd
Step-by-step explanation:
sysysysy character limit
9514 1404 393
Answer:
odd
Step-by-step explanation:
An odd function has the characteristics ...
symmetrical about the originf(-x) = -f(x)An even function has the characteristics ...
symmetrical about the y-axisf(-x) = f(x)__
The graph of the function shows symmetry about the origin. If we substitute -x for x, we get ...
[tex]h(-x)=\dfrac{3(-x)^3}{8(-x)^2-9}=\dfrac{-3x^3}{8x^2-9}\\\\h(-x)=-\dfrac{3x^3}{8x^2-9}=-h(x)\qquad\text{the function is odd}[/tex]
_____
Additional comment
Both the numerator and denominator are polynomial functions. A polynomial function is odd if it contains only odd-degree terms, like the function in the numerator. A polynomial function is even if it contains only even-degree terms, like the function in the denominator. (A constant is 0 degree--even.)
A rational function consisting of the ratio of odd or even functions (not "neither"), will be odd or even according to the parity of the ratio:
odd/odd = even/even = even function
odd/even = even/odd = odd function . . . . . the situation in this problem