Use the number line to find 1/4+-21/8
Answers
Answer:
[tex]-\frac{19}{8}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}-\frac{21}{8}=\frac{2}{8}-\frac{21}{8}=\frac{2-21}{8}=-\frac{19}{8}[/tex]
The required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
To add fractions with different denominators, we need to find a common denominator. In this case, we can use 8 as the common denominator:
1/4 + -21/8
1/4 - 21/8
2/8 - 21/8
-19/8
-2 3/8
To represent 19/8 on a number line, we need to divide the interval between 0 and 3 into 8 equal parts, and then count 23 of these parts from 0.
The number line would look something like below as shown.
Thus, the required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.
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Related Questions
cleveland has 64 fl Oz of orange juice how many pints of orange juice does cleveland have??
Answers
Answer:
4 pints
Step-by-step explanation:
16 oz in a pint
Which number is less than 8.3507
O A 8,503
OB. 8.305
O c. 8,530
D. 8.355
Answers
If for two non-zero vectors a,b : ∣a+b∣=∣a−b∣ then angle between them is:______a. 0b. 45c. 60d. 90
Answers
Answer:
[tex]90^\circ[/tex]
Step-by-step explanation:
Given two non zero vectors, [tex]\vec a, \vec b[/tex].
Let the angle between the two vectors = [tex]\theta[/tex]
Given that:
[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]
Let us have a look at the formula for magnitude of addition of two vectors:
[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]
Where [tex]\theta[/tex] is the angle between the two vectors.
formula for magnitude of subtraction of two vectors:
[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]
As per the given condition:
[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]
Squaring both sides:
[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]
So, the angle between the two vectors is: [tex]90^\circ[/tex]
Jack is running back on his football team. The first play he gained 12 yards, second play loss 15 yards, third play gained 25 yards, and fourth play loss 2 yards. What was his total gains or losses?
Answers
Answer:
20
Step-by-step explanation:
The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.
What is Subtraction?The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.
Assume the gains can be denoted by positive and loss by negative,
Gains = 12 yards, 25 yards.
Total gain = 12 + 25 = 37 yards
Loss = -15 yards, -2 yards
Total loss = -15 + (-2) = -17 yards
Calculate the total gain as shown below,
Total gain = total gain + total loss
Total gain = 37 + (-17)
Total gain = 20 yards.
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Given segment AB with points (-4, 8) and (6, 3) respectively. Find the coordinates of point P that partitions Segment AB in the ratio 3:2. The answer should be entered in the form (x,y) with out any spaces between characters.
Answers
Answer:
The coordinates of point P are (2,5)
Step-by-step explanation:
We know that point P divides AB internally in the ratio 3:2, that is AP/PB = 3/2,
we thus use the formula for internal division.
Let A = (x₁, y₁) = (-4, 8), B = (x₂, y₂) = (6, 3) and P = (x, y)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
where m = 3 and n = 2
Substituting the values of the x coordinates of A and B into x, we have
x = (mx₂ + nx₁)/(m + n)
x = (3 × 6 + 2 × (-4))/(3 + 2)
x = (18 - 8)/5
x = 10/5
x = 2
Substituting the values of the y coordinates of A and B into y, we have
y = (my₂ + ny₁)/(m + n)
y = (3 × 3 + 2 × 8)/(3 + 2)
y = (9 + 16)/5
y = 25/5
y = 5
Therefore, the coordinates of point P are (2,5)
Which is the graph of y<2x-1
Answers
Answer:
the last one is the only one with a y intercept of -1
Step-by-step explanation:
in 1971 the us dollar became part of the total fiat system meaning what?
Answers
Answer:
Step-by-step explanation:
Unit rate for 150 students in 3 classes.
Answers
Answer:
Step-by-step explanation:
150 students/3 classes= 50 students per class
Calculus 2 master needed; stuck on evaluating the integral please show steps [tex]\int {sec(x/2)tan^5(x/2)} \, dx[/tex] I am thinking that we want to split up the tan^5, making [tex]\int {sec(x/2)tan^2 tan^3(x/2)} \, dx[/tex] and then [tex]\int {sec(x/2)*sec^2x-1* tan^3(x/2)} \, dx[/tex] but I am not sure this is correct. Can anyone help? The thing I am unsure of is that tan^3 is still odd, so would we do the same thing again and factor so we will be left with just tanx?
Answers
Answer:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Step-by-step explanation:
We want to find the integral:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]
First, perform the substitution y = x / 2. This yields:
[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]
Hence, the integral becomes;
[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]
Next, as you had done, let's expand the tangent term but to the fourth:
[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]
Recall that:
[tex]\tan^2(y)=\sec^2(y)-1[/tex]
Hence:
[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]
We can use substitution once more. This time, let u = sec(y). Hence:
[tex]\displaystyle du = \sec y \tan y \, dy[/tex]
Rewrite:
[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]
Therefore:
[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]
Expand:
[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]
Reverse Power Rule:
[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]
Simplify:
[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]
Back-substitute:
[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]
Back-substitute:
[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]
Therefore:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Answer:
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
Step-by-step explanation:
∫sec(x/2) tan⁵(x/2) dx
apply u substitute u = x/2
= ∫sec(u) tan⁵(u) * 2du
= 2 * ∫sec(u) tan⁴(u) tan(u) du
= 2 * ∫sec(u) (tan²(u))² tan(u) du
= 2 * ∫sec(u) (-1 + sec²(u))² tan(u) du
apply u substitute v = sec(u)
= 2 * ∫(-1 + v²)² dv
expand
= 2 * ∫1 - 2v² + v⁴ dv
sum
= 2 (v - 2v³ + v⁵ )
3 5
substitute it back
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) )
3 5
add constant to the solution.
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
Which of the following fractions is greater than 2/5 and less than 3/5 ?
Answers
Answer:the answer would be 2.5/5
In need of some major help!!
Answers
The answer to your question is 4.8 kilometers. Brainliest?
Answer:
1.86
Step-by-step explanation:
John invests $200 at 4.5% compounded annually. About how long will it take for John’s investment to double in value?
Answers
Answer:
The number of years needed is 15.75 years.
Step-by-step explanation:
The investment amount (present value) = $200
Interest rate =4.5%
Double of investment = $400
Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.
Future value = present value ×(1+interest rate)^n
400 = 200×(1+4.5%)^n
N = 15.75 years
The number of years required to double the amount is 15.75 years.
If 1,000 gallons of oil cost $4,861, what is the cost of 35 gallons
Answers
Answer:
$170.14
Step-by-step explanation:
4,861 / 1,000 = $4.861 per gallon
35 x $4.681 = $170.135, so you need to round up to the nearest penny
Step-by-step explanation:
For 1000 gallons=$4861
For 1 gallon =$4861/1000
For 35 gallons=$4861/1000 x 35=170.135
Consider the strength data for beams given below :5.7 7.2 7.3 6.2 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.08.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.5 11.8 10.6Required:a. Construct a stem-and-leaf display of the data. What appears to be a representative strength value? Do the observations appear to be highly concentrated about the representative value or rather spread out?b. Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way?c. Do there appear to be any outlying strength values?d. What proportion of strength observations in this sample exceed 10 MPa?
Answers
Answer:
(a) Shown below
(b) Positively Skewed
(c) No Outlier
(d) 15%
Step-by-step explanation:
Arrange the data set in ascending order as follows:
S = {5.7 , 6.2 , 6.3 , 6.5 , 6.8 , 6.8 , 7 .0, 7 .0, 7.2 , 7.3 , 7.4 , 7.6 , 7.7 , 7.7 , 7.8 , 7.8 , 7.9 , 8.1 , 8.2 , 8.7 , 9 .0, 9.7 , 9.7 , 10.6 , 11.5 , 11.6 , 11.8}
(a)
Construct a stem-and-leaf display of the data as follows:
5 | 7
6 | 2 3 5 8 8
7 | 0 0 2 3 4 6 7 7 8 8 9
8 | 1 2 7
9 | 0 7 7
10 | 6
11 | 5 6 8
The representative strength value is the mid-value.
The mid-value is: 7.7
Thus, the representative strength value is 7.7.
(b)
No, the data does not appear to be highly concentrated about the representative value or rather spread out.
As we take the stem-and-leaf plot into consideration we observe that most of the observations are concentrated towards the right of the graph.
So, the data is right or positively skewed.
(c)
No, there doesn't appear to be any outlying strength values.
This is because all the values are closer to each other and none of the observations are too extreme.
(d)
The number of observations more than 10 MPa is, 4.
Total number of observations, 27.
Compute the proportion of strength observations that exceed 10 MPa as follows:
[tex]P(>10\ \text{MPa})=\frac{4}{27}=0.14815\approx 0.15[/tex]
Thus, the proportion of strength observations that exceed 10 MPa is 15%.
You are going shopping for some new sweaters, t-shirts, and pants. Sweaters (s) cost $29, t-shirts (t) cost $16, and pants (p)
cost $25. What algebraic expression models the total cost of clothes that you buy?
Suppose you bought 28 sweaters, 7 t-shirts, and 17 pairs of pants. How much did you spend?
Answers
Answer:
You spent $1349
Step-by-step explanation:
sweaters s = $29
t-shirts t = $16
pants p = $25
Cost = C
28s + 7t + 17p = C
28 ($29) + 7 ($16) + 17 ($25) = C
$812 + $112 + $425 = C
$1349 = C
can you find two fractions that multiply together to make 12/20 can you find two fractions that multiply together to make 12/35
Answers
Answer:
4/5*3/4&6/7*2/5
Step-by-step explanation:
4/5*3/4=12/20
6/7*2/5=12/35
(4³)² simplified can anyone help
Answers
Answer:
4096
Step-by-step explanation:
Answer:
4096
Step-by-step explanation:
4 to the third power is 64 and 64 to the 2nd power is 4096 so that should be your answer
Can some body check my math on this one(question #6) I think it’s n=26 am I right?
Answers
Answer:
[tex]n=26[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-413.4=-15.9n[/tex]
To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:
[tex]n=(-413.4)/(-15.9)[/tex]
Use a calculator:
[tex]n=26[/tex]
So, the answer is 26.
So, yes, you are very correct!
Answer:
n=26
Step-by-step explanation:
We are given the equation:
[tex]-413.4=-15.9n[/tex]
We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.
n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9
[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]
[tex]\frac{-413.4}{-15.9}=n[/tex]
[tex]26=n[/tex]
Let's check our solution. Plug 26 in for n and solve.
[tex]-413.4=-15.9n[/tex]
[tex]-413.4=-15.9(26)[/tex]
Multiply -15.9 and 26.
[tex]-413.4=-413.4[/tex]
This checks out, so we know our solution is correct.
The solution to this equation is n=26 and you are correct!
1.
Adrienne and Michelle are two hairstylists at a new age salon. They pay two different monthly
fees to rent a station at the salon.
The graph below represents Adrienne's profit she makes each month based on the number of
haircuts she performs.
Answers
Answer:
$50 is profit because every $50 it intersects.
X would be the $50 so 10x50=500-150=which would be $350.
I think this is right hope this helps!
Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation
represents all numbers of points, p, a player may have after his or her first turn of the game?
O p = 4
O p = -4
O pl = 4
Op = -4
Answers
Answer:
Equation to represent all number of points = |4|
Step-by-step explanation:
We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.
Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.
Thus, it's |4|
x2+9-8x in standard form
Answers
Answer:
x^2 - 8x + 9
Step-by-step explanation:
Please write x2+9-8x as x^2 + 9 - 8x. The " ^ " indicates exponentiation.
Next, please write x^2 + 9 - 8x in descending powers of x:
x^2 - 8x + 9
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.) (a) 1 + 2 + 3 + 4 + . . . + 397 + 398 + 399 + 400 (b) 1 + 2 + 3 + 4 + . . . + 542 + 543 + 544 + 545 (c) 2 + 4 + 6 + 8 + . . . + 72 + 74 + 76 + 78
Answers
What is the value of the 5 in the number 975,178
Answers
Answer:
thousands place
Step-by-step explanation:
A tire shop had to fill 3 1/2 tires with air. It took a small air
compressor 3 3/5 seconds to fill them up. How long would it take to fill 3 tires?
Answers
Answer: 3 seconds
Step-by-step explanation: the pump fills 1 tire per second
3 3/5 = 18/5
(7/2)/3 = (18/5)/t
3(18/5) = (7/2)t
54/5 = (7/2)t
108/35 = t
t = 3 3/35
By switching service providers, a family’s telephone bill decrease from about $50 a month to about $46. What was the percent of decrease?
Answers
Answer:
92%
Step-by-step explanation:
the product of 9 and the sum of a number x and 12
Answers
Answer:
X * 12 = 9
Step-by-step explanation:
The required model of the given situation is given as y = 9 (x + 12).
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
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,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)
Thus, the required model of the given situation is given as y = 9 (x + 12).
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TRUE OR FALSE: When two lines intersect then they create 4 linear pairs
Answers
the sum of 5x and 8x is less than the sum of 4x and -7
Answers
Answer:
false or not true
Step-by-step explanation:
5x + 8x < 4x + -7
combine like terms
13x<4x+-7
4x divided by 4 -7 divided by 4
x= -7/4
13x<-7/4
Jamie is sewing her own dress for the school dance. She bought 2 1/4 yards of fabric. The total cost was $10. What was the cost per yard?
Answers
Answer:
$4.44
Step-by-step explanation:
Cost per yard = $10/2.25
= $4.44 (nearest cent)
the answer $ 4.44
explanation :
so first of all you need to divide 10 by 2 1/4
when you divide both number you'll get 4 4/9
4 4/9 can also be written as 4.44444444444
which is also 4.4 recurring
now we can round this off
when you round it off, you should round it off to two decimal points cause the answer should be in dollars
you should get 4.44 as an answer
so the answer will be $ 4.44
really hope that helped :)
2+3+4+3+3+3x3x3x3x3x3x3x3x3x3x3x3x3x3
Answers
Answer:4782984
Step-by-step explanation:
Answer:4782984
Step-by-step explanation: