The difference of the given fraction is Negative three-fourths.
Sum and difference of fractionsGiven the following fraction difference as shown:
[tex]\sf -2 \dfrac{1}{2} - \huge \text(-1 \dfrac{3}{4} \huge \text)[/tex]
Convert to improper fraction
[tex]\sf -\dfrac{5}{2} + \dfrac{7}{4}[/tex]
Find the LCM
[tex]\sf 2(-5)+\dfrac{7}{4}[/tex]
[tex]\sf -10+\dfrac{7}{4}[/tex]
[tex]\sf -\dfrac{3}{4}[/tex]
Hence, the difference of the given fraction is Negative three-fourths.
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HELP WILL MARK BRAINIEST
What is the median for the set of data?
71
70
72
74
Answer:
Step-by-step explanation:
To find the median, we need to arrange the data in ascending order:
70, 71, 72, 74
Since the data set has an even number of values, the median is the average of the two middle values. In this case, the two middle values are 71 and 72. Therefore, the median is:
(71 + 72) / 2 = 143 / 2 = 71.5
So, the median for the given set of data is 71.5.
15 points to whoever gets this right <3
Answer:
77.5
Step-by-step explanation:
Given:
Scores: 65, 70, 75, 80, 85, 90, 95
Number of Students: 8, 5, 3, 6, 6, 4, 2
Step 1: Calculate the sum
Sum = (65 * 8) + (70 * 5) + (75 * 3) + (80 * 6) + (85 * 6) + (90 * 4) + (95 * 2)
= 520 + 350 + 225 + 480 + 510 + 360 + 190
= 2635
Step 2: Calculate the mean
Mean = Sum / Total Number of Students
= 2635 / (8 + 5 + 3 + 6 + 6 + 4 + 2)
= 2635 / 34
≈ 77.5
Answer:77.5
Step-by-step explanation:
A data set is displayed using a dot plot. The range of the data is between 50 and 90, and the distribution is skewed left. Which measure of center, the mean or median, is probably a better representation of the data? Explain your reasoning.
A submarine hovers at 66 and two-thirds yards below sea level. If it ascends 24 and StartFraction 1 over 8 EndFraction yards and then descends 78 and three-fourths yards, what is the submarine’s new position, in yards, with respect to sea level?
15 points to whoever gets this right:)
A chemist wants to dilute a 30% phosphoric acid solution to a 15% solution. He needs 10 liters of the 15% solution. How many liters of the 30% solution and water must the chemist use?
The chemist needs to use 5 liters of the 30% solution and 5 liters of water.
Answer:
30% solution x liters
30%(water) 10-x liters
15% 10 liters
Step-by-step explanation:
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multiply and simplify is possible (2x+4)(x-2)
SHOW YOUR WORK PLEASE!!!
Answer:
2x^2-8
Step-by-step explanation:
(2x+4)(x-2)
2x(x-2)+4(x-2
2x^2-4x+4(x-2)
2x^2-4x+4x-8
2x^2-8
2x^2-8
Answer:
2x^2 - 8
Step-by-step explanation:
You have to take one of the equations and distribute it to the other equation. I'll distribute the 1st equation.
(2x+4)(x-2)
2x times x = 2x^2
2x times -2 = -4x
4 times x = 4x
4 times -2 = -8
So you get 2x^2 - 4x + 4x - 8.
- 4x + 4x cancel out each other
So your final answer is 2x^2 - 8
Select all shapes below that are nets of a pentagonal-based pyramid.
Answer:
A and B
Step-by-step explanation:
I took some paper and cut it to the shapes and folded them to see which ones are the answer and got those 2. :3
HELP ASAP!! A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−4, 2), (−4, −11), (4, 2), and (4, −11). What is the area, in square inches, of the painted face of the brick?
A. 42 in2
B. 52 in2
C. 104 in2
D. 128 in2
Answer:
104in2
Step-by-step explanation:
The area, in square inches, of the painted face of the brick is Option C 104 [tex]in^{2}[/tex].
Using the Quadrant system of the Number line
B (-4,2) lies in the 2nd quadrant.
C (-4,-11) lies in the 3rd quadrant
A (4,2) lies in the 1st quadrant
D (4,-11) lies in the 4th quadrant
Length of Side AB= Length of Side CD= Distance between x coordinate of A & B OR Between C & D i.e. 8 in
Length of Side BC= Length of side AD= Distance between y coordinate of A & D OR Between B & C i.e. 13 in
Area of the Square ABCD= (length of Side AB or CD) X (Length of Side BC or AD)
= (8 x 13) [tex]in^{2}[/tex]
= 104 [tex]in^{2}[/tex]
Thus, Area of square is 104 [tex]in^{2}[/tex].
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Does the series converge or diverge? if it converges, what is the sum? SHOW YOUR WORK!!!!!!
equation is in picture.
=============================================
Reason:
This is a geometric series with
a = -4 = first termr = -1/3 = common ratioThe template is [tex]a(r)^{n-1}[/tex]
If -1 < r < 1, then the infinite geometric series converges to a finite number. This is because we add on smaller and smaller pieces, which prevents the sum going off to infinity.
In the case of r = -1/3, it fits the interval -1 < r < 1. In other words -1 < -1/3 < 1 is true.
We'll plug those values into the formula below to wrap things up.
[tex]S = \frac{a}{1-r}\\\\S = \frac{-4}{1-(-1/3)}\\\\S = \frac{-4}{1+1/3}\\\\S = \frac{-4}{3/3+1/3}\\\\[/tex]
[tex]S = \frac{-4}{4/3}\\\\S = -4 \div \frac{4}{3}\\\\S = \frac{-4}{1} \times \frac{3}{4}\\\\S = \frac{-4*3}{1*4}\\\\S = -3\\\\[/tex]
Therefore,
[tex]\displaystyle \sum_{n=1}^{\infty} -4\left(-\frac{1}{3}\right)^{n-1} = -3[/tex]
The final answer is -3.
You can verify the answer by generating partial sums with a spreadsheet. The partial sums should steadily get closer to -3.
Here's a few partial sums.
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{n} & \text{a}_{\text{n}} & \text{S}_{\text{n}}\\\cline{1-3}1 & -4 & -4\\\cline{1-3}2 & 1.333333 & -2.666667\\\cline{1-3}3 & -0.444444 & -3.111111\\\cline{1-3}4 & 0.148148 & -2.962963\\\cline{1-3}5 & -0.049383 & -3.012346\\\cline{1-3}6 & 0.016461 & -2.995885\\\cline{1-3}7 & -0.005487 & -3.001372\\\cline{1-3}8 & 0.001829 & -2.999543\\\cline{1-3}9 & -0.00061 & -3.000153\\\cline{1-3}10 & 0.000203 & -2.99995\\\cline{1-3}\end{array}[/tex]
The interesting thing is that the partial sums [tex]S_n[/tex] bounce around -3 while also getting closer to it.