Evaluate each expression. When the answer is not a whole number, write your answer as a simplified fraction.
1. -4 x (-6)
2. -24 x (-7/6)
3. 4 ÷ (-6)
4. 4/3 ÷ (-24)
The result of each arithmetic operation is
1) -4×(-6)=24
2) -24 × [tex]-(\frac{7}{6})[/tex] = 28
3) 4 ÷ (-6) = [tex]-\frac{2}{3}[/tex]
4) [tex]\frac{4}{3}[/tex]÷(-24)=[tex]-\frac{1}{18}[/tex]
Part 1
-4×(-6)=24
Part 2
-24 × [tex]-(\frac{7}{6})[/tex] =[tex]\frac{(24)(7)}{6}[/tex]
=[tex]\frac{168}{6}[/tex]
=28
Part 3
4 ÷ (-6) =[tex]-\frac{4}{6}[/tex]
=[tex]-\frac{2}{3}[/tex]
Part 4
[tex]\frac{4}{3}[/tex]÷(-24)= [tex](\frac{4}{3})(-\frac{1}{24} )[/tex]
=[tex]-\frac{4}{24}[/tex]
=[tex]-\frac{1}{18}[/tex]
Hence, the result of the following arithmetic operation is
1) -4×(-6)=24
2) -24 × [tex]-(\frac{7}{6})[/tex] = 28
3) 4 ÷ (-6) = [tex]-\frac{2}{3}[/tex]
4) [tex]\frac{4}{3}[/tex]÷(-24)=[tex]-\frac{1}{18}[/tex]
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10. The average age of 4 boys is 14 years, when one boy leaves the group, the average age of the remaining boys becomes 15 years. How old is the 4th boy?
Answer: the 4th boy is 11
Step-by-step explanation:
Let's denote the age of the boys as: x₁, x₂, x₃, x₄.
Then,
[tex]\displaystyle\\\frac{x_1+x_2+x_3}{3}=15[/tex]
Multiply both parts of the equation by denoting by 3:
x₁+x₂+x₃=15(3)
x₁+x₂+x₃=45
Hence,
[tex]\displaystyle\\\frac{x_1+x_2+x_3+x_4}{4} =14\\\\\frac{(x_1+x_2+x_3)+x_4}{4} =14\\\\\frac{45+x_4}{4}=14[/tex]
Multiply both parts of the equation by denoting by 4:
45+x₄=14(4)
45+x₄=56
45+x₄-45=56-45
x₄=11
a bag contains 1 gold marbles, 10 silver marbles, and 20 black marbles. someone offers to play this game: you randomly select one marble from the bag. if it is gold, you win $3. if it is silver, you win $2. if it is black, you lose $1.
The expected value is 3/31.
The number of gold marbles in the bag is 1.The number of silver marbles in the bag is 10.The number of black marbles in the bag is 20.The total number of marbles in the bag is 1 + 10 + 20.The total number of marbles in the bag is 31.The amount of money to be won if we select a gold marble is $3.The amount of money to be won if we select a silver marble is $2.The amount of money to be lost if we select a gold marble is $1.The probability of selecting a gold marble is 1/31.The probability of selecting a silver marble is 10/31.The probability of selecting a black marble is 20/31.The expectation value is the sum of the product of probabilities and the corresponding value of the marbles.Expectation = 3(1/31) + 2(10/31) - 1(20/31)Expectation = (3 + 20 - 20)/31Expectation =3/31To learn more about probability, visit :
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Please help - thanks
Insert parentheses in the appropriate places:
8+ 3-2 ×9 =17
28 ÷ 4+3 × 4+3 =28
5× 3+2 ×6 ÷3 =50
6× 9-4 +3-3 ×4=30
5 ×3+2× 6÷3 =19
5× 3+2×6 ÷3 =25
1. The correct arithmetic operation with parentheses is 8 + (3 - 2) × 9 = 17
2. The correct arithmetic operation with parentheses is 28 ÷ (4 + 3) × (4 + 3) = 28
3. The correct arithmetic operation with parentheses is 5 × (3 + 2) × 6 ÷ 3
4. The correct arithmetic operation with parentheses is 6 × (9 - 4) + (3 - 3) × 4
5. The correct arithmetic operation with parentheses is (5 × 3) + (2 × 6) ÷ 3 = 19
6. the correct arithmetic operation with parentheses is 5 × [3 + 2 × (6 ÷ 3)] = 35
What are arithmetic operations?Arithmetic operations are mathematical operations that involve multiplication, division , addition and subtraction.
Arithmetic operations follow the rule of BODMAS where
B represents brackets, O represents orders of powers or roots, D represents division, M represents multiplication,A represents addition and S represents subtractionHow to insert parentheses in the appropriate places:
1. How to insert parentheses in the appropriate places in 8 + 3 - 2 × 9 = 17Since the expression evaluates to 17, we put a parentheses between 3 and - 2. So,
8 + (3 - 2) × 9 = 8 + 1 × 9
= 8 + 9
= 17
So, the correct arithmetic operation with parentheses is 8 + (3 - 2) × 9 = 17
2. How to insert parentheses in the appropriate places in 28 ÷ 4 + 3 × 4 + 3 = 28Since the expression evaluates to 28, we a parentheses between 4 and + 3. So,
28 ÷ 4 + 3 × 4 + 3 = 28 ÷ (4 + 3) × (4 + 3)
= 28 ÷ 7 × (4 + 3)
= 4 × 7
= 28
So, the correct arithmetic operation with parentheses is 28 ÷ (4 + 3) × (4 + 3) = 28
3. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 50Since the expression evaluates to 50, we put a parentheses between 3 and + 2. So,
5 × 3 + 2 × 6 ÷ 3 = 5 × (3 + 2) × 6 ÷ 3
= 5 × 5 × 2
= 50
So, the correct arithmetic operation with parentheses is 5 × (3 + 2) × 6 ÷ 3
4. How to insert parentheses in the appropriate places in 6 × 9 - 4 + 3 - 3 × 4 = 30Since the expression evaluates to 30, we put a parentheses between 9 - 4 and 3 - 3. So,
6 × 9 - 4 + 3 - 3 × 4 = 6 × (9 - 4) + (3 - 3) × 4
= 6 × 5 + 0 × 4
= 30 + 0
= 30
So, the correct arithmetic operation with parentheses is 6 × (9 - 4) + (3 - 3) × 4
5. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 19Since the expression evaluates to 19, we put a parentheses between 2 and 6, and also 5 and 3. So,
5 × 3 + 2 × 6 ÷ 3 = (5 × 3) + (2 × 6) ÷ 3
= 15 + 12 ÷ 3
= 15 + 4
= 19
So, the correct arithmetic operation with parentheses is (5 × 3) + (2 × 6) ÷ 3 = 19
6. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 35Since the expression evaluates to 35, we put a parentheses between 6 and 3 and also both 3's. So,
5 × 3 + 2 × 6 ÷ 3 = 5 × [3 + 2 × (6 ÷ 3)]
= 5 × [3 + 2 × 2]
= 5 × [3 + 4]
= 5 × 7
= 35
So, the correct arithmetic operation with parentheses is 5 × [3 + 2 × (6 ÷ 3)] = 35
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on her desk.
Susan has a box for paperclips
The box is 6 centimeters long, 3 centimeters
wide, and 2 centimeters high. What is the
volume of the box?
Answer:
36 cm³
Step-by-step explanation:
6x3x2 = (36 cm³)
Length x Width x Height
Apply the distributive property to factor out the greatest common factor. 40 f + 30
Answer:
10(4f + 3)
Step-by-step explanation:
Both terms here are multiples of 10 hence we can factor out ten which is the greatest common factor resulting in 10(4f + 3)
pls solve this question step by step
Answer:
a) 50, b) -40, c) 3Step-by-step explanation:
Arithmetic mean is the average of the numbers.
a) (40 + 60)/2 = 100/2 = 50b) (- 60 - 20)/2 = - 80/2 = - 40c) (7/3 + 11/3)/2 = (18/3)/2 = 6/2 = 3Formula we use is,
→ Mean = (x + y)/2
a) 40 and 60 = ?
→ (40 + 60)/2
→ 100/2 = 50
Thus, the mean is 50.
b) -60 and -20 = ?
→ (-60 - 20)/2
→ -80/2 = -40
Thus, the mean is -40.
c) (7/3) and (11/3) = ?
→ ((7/3) + (11/3))/2
→ (18/3)/2
→ 6/2 = 3
Thus, the mean is 3.
Help me please, find area these shapes, easy, I will give brainliest and points
Answer:
red - 1/2 × b × h
=1/2 × 3 × 4
= 6
green - 1/2 × b × h
= 1/2 × 4 × 4
= 8
The price of Stock A at 9 A.M. was $12.74. Since then, the price has been increasing at the rate of $0.08 each hour. At noon the price of Stock B was $13.24. It begins to decrease at the rate of $0.09 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answer:
3 hours
Step-by-step explanation:
but it can be a cent off, so it might be wrong.
What is the frozen food example of the free market and exit concept?
Answer: Food is Food
Step-by-step explanation:
the cost of a can of coca-cola in 1960 was $ 0.10 . the function that models the cost of a coca-cola by year is c ( t )
The cost of the Coca-Cola can will be $1 in the year 2000.
Given that the cost of a can of Coca-Cola can in 1960 = $0.10
The function which models the cost of a Coca-Cola by year 't' is
c(t) = [tex]0.10e^{0.0576t}[/tex].
Here, 't' denotes the number of years since 1960.
c(t) is an exponential function.
We have to find the year in which the cost of a can will be $1.
So substitute c(t) = 1, we get,
1 = [tex]0.10e^{0.0576t}[/tex]
⇒ [tex]10 = e^{0.0576t}[/tex]
We have, [tex]ln(e^x) = x[/tex] .
Taking logarithm on both sides, we get,
log(10) = 0.0576t
⇒ [tex]t=\frac{ln(10)}{0.0576}[/tex] = 39.97 ≈ 40 years .
Thus the cost of a can of Coca-Cola will be $1 in the year, 1960 + 40 = 2000.
The question was incomplete. Find the complete question at:
The cost of a can of Coca-Cola in 1960 , was $0.10. The function that models the cost of a Coca-Cola by year is C(t)=0.10e^(0.0576t) , where t is the number of years since 1960 . In what year is it expected that a can of Coca-Cola will cost $1.00 ?
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PLEASE ANSWER QUICK
Evaluate the expression when n = 3:
−|−4n|
Answer:
12
Step-by-step explanation:
-4 X 3 =-12
=-(-12)
=12
Lily's limos charges $150 to rent a limo plus $40 an hour. ron's luxury rides charges $200 to rent a limo plus $30 an hour. at how many hours do the companies charge the same price? write and solve a single equation to prove and show at how many hours the companies charge the same price.
Upto 5 hours companies will charge at the same price.
what are comparing functions ?Functions can be represented in a variety of ways. A function, for instance, can be depicted using an input-output table, a graph, and an equation.It's occasionally necessary to compare two functions that are represented in different ways because of an issue. You might be asked, for instance, which function is greater for a given number or which function increases more quickly after being presented with a table and a graph.
Given that :For a limo rental, Lily's limos charges $150 plus $40 per hour. For a limo rental, Ron's Luxury Rides charges $200 plus $30 per hour.
Based on the given condition ,
equation is 150 + 40x = 200 + 30x
40x - 30x = 200 - 150
10x = 200 -150
10x = 50
x =[tex]\frac{50}{10}[/tex]
x = 5
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Hans needs to rent a moving truck. Suppose Company A charges a rate of $40 per day and Company B charges a $60 fee plus $20 per day. for what number of days is the cost the same. Please also explain how you got the answer
Answer: x=3
Step-by-step explanation:
1. Hans needs to rent a moving truck. Suppose Company A charges $40.00 per day and Company B charges a $60.00 fee plus $20.00 per day, for what number of days is the cost the same?
Let x = # of days, since Company A charges $40/day then cost after x days = 40x
Let x = # of days, since Company B charges $20/day plus $60 fee, then cost after x days = 20x + 60
a. For what # of days is the cost the same?
When the cost is the same => 40x = 20x + 60
40x - 20x = 60
20x = 60
x = 60/20
x = 3
The cost is the same after 3 days.
Checking:
$40(3) = $20(3) + $60
$120 = $60 + $60
$120 = $120
Can someone please help mee (20 points
brainliest!!!)
Answer:
16,300,000 viewers
Step-by-step explanation:
We have two ordered pairs and we can write an equation in the slope intercept form of the line from the information that we have.
y = mx + b y is the number of viewers and x in the number of minutes of ads.
m is the slope. That is the change in y over the change in x. We will use the two points given to find this.
(14, 10,000,000) (25, 17,000,000)
slope:
[tex]\frac{y{1}- y{2} }{x_{1}-x_{2} }[/tex] = [tex]\frac{17,000,000 - 10,000,000}{25-15}[/tex] =[tex]\frac{7,000,000}{10}[/tex] = 700,000
Now we need the b or the y-intercept. We will use the slope and one of the points to find this. We could use either point. I am going to use the point (15, 10,000,000)
y = mx + b
I will use 10,000,000 for y
I will use 15 for x
I will use 700,000 for the slope.
I will plug these numbers in and solve for b
10,000,000 = 700,000(15) + b
10,000,000 = 10,500,000 + b Subtract 10,500,000 from both sides
-500,000 = b
Now we can write the equation
y = mx + b
y = 700,000x -500,000 Plug is the 24 for x to solve for the number of views.
y = 700,000(24) -500,000
y = 16,800,000 - 500,000
y = 16,300,000
what are the probabilities that the three subsystems, as well as the entire system, are operational?
Three subsystems are reliability-wise in series and make up a system. Subsystem 1 has a reliability of 99.5%, subsystem 2 has a reliability of 98.7% and subsystem 3 has a reliability of 97.3% for a mission of 100 hours.
We suppose that the system consists of one operating series subsystem, an identical stand-by subsystem, and a switch. Each subsystem consists of N components.
When the operating subsystem fails, the spare is put in motion by the switch immediately. The failed subsystem is restoring or changing the failed component. Because of the memoryless property of the exponential distribution of components lifetime, the renewal of a failed element means the renewal of the whole subsystem. We assume that there is a single repair facility. A renewal time is a random variable having distribution depending on a failed component. We suppose that the lengths of restoring periods of components are represented by identical copies of nonnegative random variables.
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convert 1264 base 8 to base 10
1264₈ = 1•8³ + 2•8² + 6•8¹ + 4•8⁰
1264₈ = (2³)³ + 2•(2³)² + 3•2•2³ + 2²
1264₈ = 2⁹ + 2⁷ + 3•2⁴ + 2²
1264₈ = 512 + 128 + 3•16 + 4
1264₈ = 692
After converting the base, 1264 base 8 is equal to 692 base 10.
To convert a number from base 8 (octal) to base 10 (decimal), we need to evaluate the value of each digit in the base 8 number and then calculate the equivalent decimal value.
Given the number 1264 in base 8, we can break it down into its digits:
1 * 8³ + 2 * 8² + 6 * 8 + 4 * 1
Simplifying this expression:
1 * 512 + 2 * 64 + 6 * 8 + 4 * 1
Evaluating the multiplication:
512 + 128 + 48 + 4
Adding the products together:
692
In summary, to convert a number from base 8 to base 10, we evaluate the value of each digit by multiplying it with the corresponding power of 8, and then sum up the results. This gives us the equivalent decimal value of the number.
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Kylie is training for an upcoming marathon and has committed to running
more than 21 miles today. If she runs from her house, she can run along two
loops: a short path that is 3 miles in length, and a long path that is 6 miles in
length. Select the inequality in standard form that describes this situation. (x
= the number of loops on the short path, y = the number of loops on the long
path).
Answer: 3x+6y > 21
Step-by-step explanation:
total distance kylie runs is the combined amount of loops from both paths. 3x represents however many loops she runs times the length of the short path. 6y represents however many loops she runs times the long path. Both of them have to add up and be greater than 21.
English only please
Create an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six.
1.4 cubed over 1.2 squared
1.2 squared over 1.4 cubed
1.4 to the eighteenth power over 1.2 to the twenty-fourth power
1.2 to the twenty-fourth power over 1.4 to the eighteenth power
Answer:
2.8 squared
2.6 cubed
2.6 twenty-fourth power
2.6 eighteenth power
its korrect now
The required simplified solution of the given expression is 1.2 to the twenty-fourth power over 1.4 to the eighteenth power. Option D is correct.
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,
1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six is given as,
x = [1.4³/1.2⁴]⁻⁶
x = 1.4⁻¹⁸ / 1.2⁻²⁴
x = 1.2²⁴ / 1.4¹⁸
Thus, the required simplified solution of the given expression is 1.2 to the twenty-fourth power over 1.4 to the eighteenth power. Option D is correct.
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What is the equation of the given line?
y = 5
x = 3
x = 1
y = 3
Answer:
y=x+2
Step-by-step explanation:
use the formula y=mx+c
first u find m which is the gradient 3-1/5-3 = 2/2=1
sub in any point to find the c
5=1(3)+c
c=2
y=1x+2
x=7 y=4 HELP I WILL GIVE BRAINLIEST.
362x+836y+918334
Answer: 924212
Step-by-step explanation:
362x+836y+918334
362(7)+836(4)+918334
(362 x 7) + (836 x 4)+918334
question 12(multiple choice worth 1 points) (03.05 lc) what is the volume of a sphere with a radius of 6 inches? 112π cubic inches 288π cubic inches 290π cubic inches 300π cubic inches
volume of a sphere with a radius of 6 inches is 288π cubic inches.
What is volume of a sphere?A sphere is a collection of points in space that are separated from the center by an amount r. The volume of a solid in three dimensions is the area it occupies. The cubic is the unit of volume ( in3,ft3,cm3,m3 , etc ). Ensure that all measurements are made in the same unit before estimating the volume. A sphere's volume, V, is equal to four thirds of pi times the square of the radius.
V=43πr3
Half of the connected sphere's volume makes up a hemisphere. A sphere's volume is 2/3 that of a cylinder with the same radius and height that is equal to its diameter.
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maths lit scope term 3 grade 10
Answer:
add a pic
Step-by-step explanation:
Determine the quadrant in which each angle lies -7
It lies in the quadrant IV.
Since we know that a full circle is broken into four parts known as quadrants into regions of π/2.Since quadrant 1 ranges from 0 to π/2, quadrant 2 ranges from π/2 to π, then quadrant 3 ranges from π to 3π/2, and at last quadrant 4 ranges from 3π/2 to 2π.
And we know 2π is equal to approx 6.28 radians, so each quadrant will have 2π/ 4 = π2 ≈1.57 radians
So for angle -7 it will be = −7/(π/2) ≈−4.45.
So moving around the circle, it appears halfway through the quadrant IV.
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I need help with how to do the vertical line test on a graph, I forgot.
Answer: To graph a vertical line that goes through a given point, first plot that point. Then draw a straight line up and down that goes through the point, and you're done!
Step-by-step explanation: pls give brainliest
how do u solve subtraction of number bases
Answer: Say you want to perform the following subtraction in base 5. Borrow a 5 from 3 fives. 3 fives in now 2 fives. Then, add that 5 to the 1 to make it 6.
Step-by-step explanation: there
Ava read a total of 40 books over 5 months. If Ava has read 72 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
========================================================
Explanation:
She read 40 books over 5 months. This means her unit rate is 8 books per month (since 40/5 = 8)
x = number of months
(unit rate)*(number of months) = total books read
8x = 72
x = 72/8
x = 9
-------------
Another way to solve
(40 books)/(5 months) = (72 books)/(x months)
40/5 = 72/x
40x = 5*72 ... cross multiplying
40x = 360
x = 360/40
x = 9
I need help asap!!!!!
Answer:
last one
Step-by-step explanation:
6 3x2/8x2= 6 6/16
6 +5=11
6/16+11/16=17/16
11 17/16
127,056 rounded to the nearest to ten thousand
Answer: 10000
Step-by-step explanation: That is as close to ten thousand as you can get
What is the slope of the line that passes through the points (-7, -2) and
(-2, -22)? Write your answer in simplest form.
Answer:
m = -4
Step-by-step explanation:
We are given the points (-7, -2) and (-2, -22), and we want to write the slope of the line.
The slope (m) can be calculated from two points using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We already have everything we need to calculate the slope, however, let's label their values to help avoid any confusion and mistakes for later.
[tex]x_1=-7\\y_1=-2\\x_2=-2\\y_2=-22[/tex]
Now, substitute these values into the formula. Remember that the formula has subtraction, and we're dealing with negative numbers here.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-22--2}{-2--7}[/tex]
Simplify.
m=[tex]\frac{-22+2}{-2+7}[/tex]
Add.
m=[tex]\frac{-20}{5}[/tex]
Divide.
m = -4
The slope of the line is -4.
Topic: slope
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