Answer:
2 15/28
Step-by-step explanation:
First we will convert both mixed fractions into improper fractions.
5 1/4 becomes 21/4
2 5/7 becomes 19/7
21/4 - 19/7 does not work, so we must make the denominator the same
147/28 - 76/28 = 71/28
Now we convert back to a mixed number:
2 15/28
Answer: [tex]-11\frac{15}{28}[/tex]
Step-by-step explanation:
Convert to Improper fractions
[tex]5\frac{1}{4} = \frac{21}{4} \\2\frac{5}{7} = \frac{19}{7} \\[/tex]
Find a lowest common multiple
lcm(4,7) = 28 (7 * 4)
since they are just multiplying each other, we can cross multiply
[tex]\frac{(21*7) - (19*4)}{4*7} = \frac{147-76}{28} \\= \frac{71}{28} \\=2\frac{15}{28}[/tex]
a piece of string measures 2 16/20 meters which of the following is equivalent to the length of the string in meters
The equivalent to the length of the string in meters is 14 / 5 meters
How to find the equivalent length of a string?The length of the string is expressed in a mixed fraction form.
length of the string = 2 16 / 20
let's express it in a simplified form. This is usually in an improper fraction form.
Therefore,
2 16 / 20 = 56 / 20
Hence,
56 / 20 = 14 / 5 meters
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if f(x)= x²+x(2a+2b)+4ab-x. f'(x)=....
DON'T COPY PASTE!!! please use the methods and steps
[tex]f(x) = x^2 +x (2a+2b) +4ab-x\\\\f'(x) = 2x+x \cdot 0 + 2a+2b + 0 -1\\\\~~~~~~~~=2x+0+2a+2b-1\\\\~~~~~~~~=2x+2a+2b-1[/tex]
From the definition of the derivative,
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]
We have
[tex]f(x) = x^2 + x(2a+2b) + 4ab - x = x^2 + (2a+2b-1)x + 4ab[/tex]
and so
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{\left((x+h)^2 + (2a+2b-1)(x+h) + 4ab\right) - \left(x^2 + (2a+2b-1)x + 4ab\right)}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{x^2 + 2xh + h^2 + (2a+2b-1)x + (2a+2b-1)h + 4ab - x^2 - (2a+2b-1)x - 4ab}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{2xh + h^2 + (2a+2b-1)h}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} (2x + h + 2a+2b-1)[/tex]
[tex]\displaystyle f'(x) = \boxed{2x + 2a + 2b - 1}[/tex]
A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
We will see that there are 156,000 different combinations, so the correct option is C.
How many possibilities are there?
First, we need to find the selections, here we have:
First letter.Second letter.Third letter.Number.Now we need to find the number of options for each of these selections.
First letter. (26 options)Second letter. (25 options, because we can't repeat letters)Third letter. (24 options)Number. (10 options).We assumed that the number can be any integer from 0 to 9.
The total number of possibilities is equal to the product between the numbers of options, we will have:
P = 26*25*24*10 = 156,000
So, the correct option is C.
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3 + 15 + 75 + 375 + 1,875
What’s the sigma notation
Answer:
292,968
Step-by-step explanation:
1/2 + 1/4 = how many quarters
Answer:
3
Step-by-step explanation:
1/2 = 0.5
1/4 = 0.25
1/2 + 1/4
= 0.5 + 0.25
= 0.75
= 75/100
= 3/4
Quarter is 1/4.
3/4 can be written as 3 x 1/4
Hence,
1/2 + 1/4 is 3 times 1/4
1/2 + 1/4 = 3 quarters.
Answer:
3/4
Step-by-step explanation:
1*(1/2)= (2/2)*(1/2)= (2*1)/(2*2)=2/4
1/2+1/4=2/4+1/4=3/4
The difference of twice a number and 3 is at most-26.
Answer:
x < & = -23/2
Step-by-step explanation:
Let a number be x.
Twice a number = 2x
2x - 3 = -26 and 2x - 3 < -26
2x = -23 and 2x < -23
x = -23/2 and x < -23/2
On a test that has a normal distribution, a score of 49 falls two standard deviations
below the mean, and a score of 61 falls one standard deviation above the mean.
Determine the mean of this test.
Answer:
57 mean
Step-by-step explanation:
x = mean
(x - 49 ) = 2 ( 61 -x)
x = 57
Need help please answer ASAP!
Let's see
3x²-9x3x(x-3)3x is one factor
Other one is x-3#2
Mass of 1000 protons
1000×Mass of one proton1.67×10^{-24}×10³1.67×10^{-21}gAnswer:
22. (3) x - 3
23. (4) [tex]1.67 \times 10^{-21}\: \sf g[/tex]
Step-by-step explanation:
Question 22Given expression:
[tex]3x^2-9x[/tex]
Factor out common term [tex]3x[/tex]:
[tex]\implies 3x \cdot x - 3 \cdot 3x[/tex]
[tex]\implies 3x(x-3)[/tex]
Therefore, the two factors are [tex]3x[/tex] and [tex]x-3[/tex]
Question 23[tex]\textsf{Mass of 1 proton}=1.67 \times 10^{-24}\: \sf g[/tex]
[tex]1000=10 \times 10 \times 10=10^3[/tex]
[tex]\begin{aligned}\implies \textsf{Mass of 1000 protons} & = \textsf{mass of 1 proton} \times 1000\\& =(1.67 \times 10^{-24}) \times 1000\\& =1.67 \times 10^{-24}\times 10^3\\ & =1.67 \times 10^{-24+3}\\ & = 1.67 \times 10^{-21}\: \sf g\end{aligned}[/tex]
if a+b = -6 , a^2 + b^2 = 20 then ab =
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
By squaring the sum of two variables identity ~
[tex]\qquad \sf \dashrightarrow \:(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab[/tex]
Now, plug in the given values ~
[tex]\qquad \sf \dashrightarrow \:( - 6) {}^{2} = 20 + 2ab[/tex]
[tex]\qquad \sf \dashrightarrow \:36 = 2(10 + ab)[/tex]
[tex]\qquad \sf \dashrightarrow \:10 + ab = 36 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:10 + ab = 18[/tex]
[tex]\qquad \sf \dashrightarrow \:ab = 18 - 10[/tex]
[tex]\qquad \sf \dashrightarrow \:ab = 8[/tex]
I hope it was clear through my steps ~
Answer:
8
Step-by-step explanation:
(a+b)^2 = (-6)^2
a^2 + 2ab + b^2 = 36
a^2 + b^2 = 36 - 2ab
Equating 36 - 2ab with 20
36 - 2ab = 20
2ab = 16
ab = 8
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factor 6x(x + 12) – 15(x + 12)
The zeroes of the function are___
Answer:
The zeros are x = -2, x = 0, x = 4.
Step-by-step explanation:
The zeros describe where the function crosses the x-axis, or where the y-value is zero. In this case, the zeros are x = -2, x = 0, x = 4.
Clay and his friend Lacey are making cookies for the school dance. Clay started early and has already made 3 dozen cookies. He can make an additional 2 dozen cookies an hour. Lacey has not started making cookies yet, but she has a bigger oven and can make 4 dozen cookies an hour. If Lacey starts baking her cookies right away, how long will it take for her to have made as many cookies as Clay? How many cookies will they each have made?
HELP PLEASE
If Lacey starts baking her cookies right away, then the time is taken for her to have made as many cookies as Clay will be 1.5 hours.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Clay and his friend Lacey are making cookies for the school dance.
Clay started early and has already made 3 dozen cookies.
He can make an additional 2 dozen cookies an hour.
Lacey has not started making cookies yet, but she has a bigger oven and can make 4 dozen cookies an hour.
Let y be the number of the cookies (in dozen) and x be the number of the hours.
Then the equations will be
y = 2x + 3 ...1
y = 4x ...2
If Lacey starts baking her cookies right away, then the time taken for her to have made as many cookies as Clay will be
From equations 1 and 2, we have
2x + 3 = 4x
2x = 3
x = 1.5
Then the number of hours will be 1.5 hours.
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You are told that in a sample of size 225 the mean is 48.5 and the standard deviation is 1.8. the study is reported with 90% confidence level. explain how to determine if 48.8 is within the confidence interval.
Using the t-distribution, it is found that the 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 225 - 1 = 224 df, is t = 1.6517.
The other parameters are given as follows:
[tex]\overline{x} = 48.5, s = 1.8, n = 225[/tex].
Hence the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 48.5 - 1.6517\frac{1.8}{\sqrt{225}} = 48.3[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 48.5 + 1.6517\frac{1.8}{\sqrt{225}} = 48.7[/tex]
The 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.
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Please help me with question 12. I don’t know the answer.
Answer: B. ((5-x))/(x^(2)+3x-4)-:((x^(2)-2x-15))/(x^(2)+5x+4)
exclusions: x≠1, x≠-1, x≠-3, x≠-4, x≠5
Step-by-step explanation:
help me please
[tex]if \: \sin(x) = \cos(50degree) \: find \: x [/tex]
Answer:
x = 40°
Step-by-step explanation:
using the cofunction identity
cos(90 - x) = sin x , so
90 - x = 50 , then
x = 40
that is sin40° = cos50°
1. 2x - 12 = 6
2. 2x + 6= 8
3. 12 = 12s - 12
4. 14s + 6 = 35
5. 3s - 12 = 6
6. 18t + 9 = 34
7. 21x + 7 = 28
8. 105 = 50y + 5
9. 1/4x - 6 = 24
10. 13x + 2 = 18
11. 6 - 3x = 18
12. 14 + s = 21
13. 28 = 16x - 4
14. 19x + 2 = 40
15. 10t = 194
16. 400x + 100 = 1100
17. - 3x + 43 = 113
1. x=9
2. x=1
3. s=2
4. s= 2.5
5. s=6
6. T=5/6
7. x=1
8. y=2
9. x=120
10. x=16/13
11. x=-4
12. s=7
13. x=2
14. x=2
15. t=97/5
16. x=5/2
17. x=-70/3
I need help I don’t know the answer
Answer: The date tree is 3 times as tall as the lemon tree
Step-by-step explanation:
There are two trees.
Date tree = unknown height
Lemon tree = 8 feet
Equation
? = 3 x 8
We can assume that the 8 in the equation is the height of the lemon tree since it was already given. The equation's purpose is to find the height of the date tree resulting in 3 times 8 which is 24.
If we compare their heights, we can say that the date tree is 3 times taller than the lemon tree since 24 is 3 times greater than 8.
Which of the following is in standard form of quadratic?
What is the diameter of the circle (x + 25/4)² + y² = 25?
Answer:
10 units
Step-by-step explanation:
Compare the given equation to the standard-form equation for a circle to identify the relevant dimension.
The equation of a circle is written in standard form as ...
(x -h)² +(y -k)² = r² . . . . . . . centered at (h, k) with radius r
__
Comparing this to what you are given, you see that ...
h = -25/4
k = 0
r² = 25
The radius is ...
r = √25 = 5
The diameter is twice the radius, so is ...
d = 2r = 2(5)
d = 10
The diameter of the circle is 10 units.
what is the value of...
4x - x + 5, when x = 3
???
Answer:
The value of 4x-x + 5 when x + 3 is 14
Step-by-step explanation:
4(3)= 12 - 3= 9 + 5= 14
The value of 4x - x + 5 when x = 3 is 14.
To find the value of 4x - x + 5 when x = 3, we substitute the value of x into the expression and simplify.
Plugging in x = 3, we have:
4(3) - 3 + 5
Now let's simplify each term:
4(3) = 12
-3 = -3
Now we can substitute the simplified terms back into the expression:
12 - 3 + 5
Next, we perform the addition and subtraction in order from left to right:
12 - 3 = 9
9 + 5 = 14
Therefore, the value of 4x - x + 5 when x = 3 is 14.
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How many more pairs of parallel sides does a regular octogon have then a regular hexagon
Answer:
1 more.
Step-by-step explanation:
A regular octagon has 4 pairs.
A regular hexagon has 3 pairs.
Hope this helped. :)
What is the Parent Function?
What Are The Transformations?
Answer:
Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15
If you help me you have a special place in my heart forever I swear .
Answer:
x = 9
y = 116
Step-by-step explanation:
116 and y are vertically opposite angles.
Vertically opposite angles are equal.
So,
y = 116
116 and ( 13x - 53 ) are linear pair angles.
Sum of linear pair angles is 180,
13x - 53 + 116 = 180
13x + 63 = 180
Subtract 63 on both sides,
13x = 180 - 63
13x = 117
Divide 13 on both the sides,
x = 117 / 13
x = 9
Question 3 :
Find the value of 3x3 - 4x2 + x - 5 when x = -3
(A) -54 (B) -71 (C) -32
A classroom floor is 20 metres wide.
If the total area of the floor is 300 square metres, how long is it?
Answer:
It is 15 m long.
Step-by-step explanation:
Given
width (b) = 20 m
Area of the floor (A) = 300 m^2
Length (L) = ?
we know
A = L * b
300 = L * 20
L = 15 m
Hope it will help :)
2 similar rectangular pyramids have a similarity ratio of 4:5. What is the ratio of their volumes? Put your answer in the form a:b
Answer:
64:125
Step-by-step explanation:
When you go from a length ratio to an area ratio you need to square the numbers involved: [tex]4^{2} :5^{2}[/tex] = 16 : 25
By the same logic, if you want to go from length to volume you need to cube the numbers involved: [tex]4^{3} :5^{3}[/tex] = 64 : 125
12
y
8
41.81
48.199
33.69
56.31
ninate Education, Inc.
Answer:
hope this help you
Step-by-step explanation:
[tex] \cos(y) = \frac{b}{h} \\ \cos(y) = \frac{8}{12} \\ y = \cos {}^{ - 1} ( { 0.6666}^{ } ) \\ y = 48.19[/tex]
4 meters to 100 centimeters
Answer:
This is incorrect because 1 meter is 100 centimeters. But then when you keep going and when you get to 4 meters, you would get 400.
For example:
1 meter - 100 centimeters
2 meters - 200 centimeters
3 meters - 300 centimeters
4 meters - 400 centimeters
Hope this helps!
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
The correlation coefficient is 0.92
What is Correlation Coefficient ?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
In other words, it reflects how similar the measurements of two or more variables are across a dataset.
When one variable changes, the other variables change in the same direction or opposite direction.
Perfect positive correlation :When one variable changes, the other variables change in the same direction.
Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.
[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]
After calculation we get
r = 0.92
Therefore it is a Perfect positive correlation
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Todd bought g boxes of granola bars. There are 12 granola bars in each box. Write an expression that shows how many granola bars Todd bought.
The expression that shows the granola bars Todd bought is 12g.
What is an algebraic expression?The algebraic expression stands for the mixture of variables, coefficient, constant, or all three in a mathematical form where both sides are set equivalent to each other.
Given: Todd bought g boxes of granola bars.
There are 12 granola bars in each box.
Let g be the boxes of granola bars.
Therefore, the expression that shows the granola bars Todd bought is 12g.
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