Answer:
1/2
Step-by-step explanation:
[tex]\dfrac{1}{3}\div \dfrac{2}{3}=\\\\\dfrac{1}{3}\times\dfrac{3}{2}=\\\\ \dfrac{3}{6}=\\\\\dfrac{1}{2}[/tex]
Hope this helps!
Part of a book fell out. The first page of this part has number 143. The last page has a number written with the same digits. How many pages are in the part of the book which has fallen out?
Answer:
142 pages
Step-by-step explanation:
The parameters given are
First page of part of the book available = 143
The last is numbered with the digits 143
Since the book is said to have been split into two parts with, we have that one part of the book starts from the beginning, while the other part continue from the first part stops
Number on the pages on the first part = from 1 to number on the first page on the second part - 1
Hence, the part of the book available is the second part and the number of pages in the first part = 1 to 142 or 142 pages.
Mark is making concrete. Concrete is made by mixing cement, sand and gravel in the ratio 1:2:3. Mark wants to make 600kg of concrete. How much sand does Mark need
Answer:
200 kg
Step-by-step explanation:
To satisfy the ratio 1:2:3, Mark must use 100 kg cement, 200 kg sand, and 300 kg gravel
Answer:
6 kg
Step-by-step explanation:
f(1)=3
f(n)=f(n−1)+5.5
f(3)=
Answer:
f(3) = 14
Step-by-step explanation:
Using the recursive formula and f(1) = 3 , then
f(2) = f(1) + 5.5 = 3 + 5.5 = 8.5
f(3) = f(2) + 5.5 = 8.5 + 5.5 = 14
Answer:
14
Step-by-step explanation:
7×10^-5
answer this
Hi! So we have to use the Order of Operations, aka PEMDAS so it's:
Parentheses
Exponents
Multiplication/Division
Addtion/Subtraction
Exponent comes first so we'll deal with that. 10^-5=0.00001
And then 7*0.00001=0.00007
choose the definition for the function
Answer:
The answer above is wrong it actually b
The function shown in the graph is option b.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
We have from the graph that graph touches the x axis at 2 and at a point between 0 and 1.
That is,
f(x) = 0 when x = 2
Substitute the value of x as 2 in the functions given in the option when x > 1 and find those functions which give y = f(x) = 0.
It is only possible for options 'a' and 'b'.
When x = 2, -2 + 2 = 0.
Also we have the point, when x = 1, y = 1.
x = 1, then -2x + 2 = 0 ≠ 1
x = 1, then -x + 2 = -1 + 2 = 1
So when x = 1, f(x) should be of the form f(x) = -x + 2.
Correct option is option b.
Hence the correct definition of the function is option b.
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How much is $100 U.S. dollars in Canadian dollars?
Answer:
133.98
Step-by-step explanation:
Can someone help me please?
Answer:
Inverse Variation
Step-by-step explanation:
y = k/x
Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won't the van catch up when the distances are equal?
Answer:
It takes 0.619 hours (approximately 37 minutes) for the van to catch up with the storm.
They have driven 33.43 miles
They will catch up when their distances are equal.
Step-by-step explanation:
The speed of the van is 54 mph, and the speed of the storm is 33 mph. They are going in the same direction, so the relative speed is the difference of their speeds:
relative speed = 54 - 33 = 21 mph
Now, to find the time when the van reaches the storm, we just need to use the equation:
distance = speed * time
13 = 21 * t
t = 13 / 21 = 0.619 hours
The distance traveled by the van is:
distance = 54 * 0.619 = 33.43 miles
The van will catch up when the distances are equal (the distance of the storm is 13 + 33*0.619 = 33.43 miles)
The sum of the digits of a two-digit number is 14. If the number formed by reversing the digits is less than the original number by 18. Find the original numbers.
Answer:
86
Step-by-step explanation:
1. a+b=14 ⇒ a= 14-b
2. 10a+b=18+10b+a ⇒ a= 2+b
comparing 1 and 2:
14-b= 2+b ⇒ 2b= 12 ⇒ b= 6
a= 14-b= 8
number = 86
reversed number = 68
A factory makes 750 cakes every day. The cakes are orange cakes or lemon cakes. Each day Aadil takes a sample of 25 cakes to check. The proportion of the cakes in his sample that are orange is the same as the proportion of the cakes made that day that are orange. On Monday Aadil calculated that he needed exactly 7 orange cakes in his sample. a) What is the total number of orange cakes that were made on Monday
A) 210
B) 0.18
Step-by-step explanation:A) On Monday, 7/25 of the 750 are orange cakes. 7/25 x 750 = 210
B) If the proportion of orange cakes is 5/25 where 5 is correct to the nearest whole number, then the 4.5 would be the lowest number that would still be rounded up to 5. 4.5/25 = 0.18
A certain virus is dying off at a rate of 18% per hour. Initially there were
40,000 grams of the strain. If this continues at this rate, how much of the
strain would still be alive after 48 hours? (Round your answer to the
nearest whole number.) *
Answer:
3 strain would still alive after 48 hours
Step-by-step explanation:
Initial population of virus = 40000 grams
A certain virus is dying off at a rate of 18% per hour.
We are supposed to find how much of the strain would still be alive after 48 hours
Formula : [tex]N(t)=N_0(1-r)^t[/tex]
[tex]N_0[/tex]=Initial population
N(t)= Population after t hours
r = rate of decrease = 18% = 0.18
t = time = 48 hours
So,the strain would still be alive after 48 hours=[tex]40000(1-0.18)^{48}=2.91 \sim 3[/tex]
Hence 3 strain would still alive after 48 hours
kinda stuck on this question. please help?
Answer:
The answer is b
Step-by-step explanation:
I know this because a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression and since 9 is being multiplied by x that would mean 9 is a coefficient in this expression.
HIIII HELP ME ME HE HE
Answer:
x = 28
y = 32
Step-by-step explanation:
3
4
(x−12)=12
(
3
4
)(x)+(
3
4
)(−12)=12(Distribute)
3
4
x+−9=12
3
4
x−9=12
Step 2: Add 9 to both sides.
3
4
x−9+9=12+9
3
4
x=21
Step 3: Multiply both sides by 4/3.
(
4
3
)*(
3
4
x)=(
4
3
)*(21)
x=28
Answer:
x=28
3
4
y−12+12=12+12
3
4
y=24
Step 2: Multiply both sides by 4/3.
(
4
3
)*(
3
4
y)=(
4
3
)*(24)
y=32
Answer:
x = 28
y = 32
Step-by-step explanation:
Equation 1:
First, we will distribute the 3/4 to everything in the parentheses like this:
[tex]\frac{3x}{4} - \frac{36}{4} = 12[/tex]
We can simplify the 36/4 down like this:
[tex]\frac{3x}{4} - 9 = 12[/tex]
We can add the 9 to the other side:
[tex]\frac{3x}{4} = 21[/tex]
Then multiply the 4 to the other side
[tex]3x = 84[/tex]
Finally, we can divide by 3
[tex]x = 28[/tex]
Equation 2:
We can add 12 to the other side:
[tex]\frac{3y}{4} = 24[/tex]
Then multiply 24 by the 4
[tex]3y = 96[/tex]
Then divide by 3
[tex]y = 32[/tex]
he factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot: 1 is labeled + x, 1 is labeled negative. 5 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 10 tiles are in the Product spot: 1 is labeled + x squared, 1 is labeled negative x, the 4 tiles below + x squared are labeled + x, and the 4 tiles below the negative x tiles are labeled negative. What are the factors of x2 + 3x – 4? (x + 4) and (x – 4) (x + 3) and (x – 4) (x + 4) and (x – 1) (x + 3) and (x – 1)
Answer:
x-1 and x+4. srry if i am wrong
Step-by-step explanation:
Simplify 7(A-6)
A-6
7A-42
7A-6
Answer:
7A - 42
Step-by-step explanation:
7(A-6)
Distribute
7*A - 7*6
7A - 42
∠A and ∠B are complementary. If m∠B = 64° , what is the measure of ∠A?
26°
36°
11°
64°
Answer: 26
Step-by-step explanation:
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then
∠A + ∠B = 90
∠A =90- ∠B
∠A = 26
Answer:
The measure of [tex]\angle A[/tex]:
[tex]\angle A = 26\textdegree[/tex]
Step-by-step explanation:
Since both [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary (Which they both add up to 90°), and you want to find the measure of
Measure of [tex]\angle A[/tex]: unknown
Measure of [tex]\angle B[/tex]: 64°
Finding the measure of [tex]\angle A[/tex]:
[tex]90 - 64 = 26[/tex]
[tex]\angle A = 26\textdegree[/tex]
So, the measure for [tex]\angle A[/tex] is [tex]26\textdegree[/tex].
If trapezoid JKLM is translated according to the rule (x,y)—> (x+2, y - 6), what are the coordinates of point L
Answer:
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Step-by-step explanation:
Explanation:-
Type of transformation change to co-ordinate point
vertical translation up 'd' units (x,y) changes to (x , y+d)
vertical translation down 'd' units (x,y) changes to (x , y-d)
Horizontal translation left 'c' units (x,y) changes to (x-c , y)
Horizontal translation right 'c' units (x,y) changes to (x+c , y)
Now by use above table
given data ( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Final answer:-
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
If someone could help me thank you it’s geometry :(
Answer:
<1 = 119
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
<1 = 57+62
<1 = 119
Answer:
119
Step-by-step explanation:
if i have 85 lessons and only 42 days to complete them how many lessons would i have to do a day to finish on time?
Answer:
At least 3 per day
Step-by-step explanation:
All you gotta do is divide 85 by 42. You get 2.024 but you can't do .024 parts of a class, i mean you probably can but its finna be hard to do it exact so just do 3 per day and you'll even finish before. By the way, if this is an actual scenario, you gotta remember that they be adding lessons everyday so good luck!
the middle number; put the values in order from lowest to highest, then find the number that is exactly in the middle
Communication Methods Among Teens
Frequency Two-Way Table
Which answer shows the relative frequency by the row
of girls?
O 52.5%, 23.0%, 24.6%, 100%
O 57.0%, 12.2%, 27.8%, 100%
O 60%, 12.2%, 27.8%, 100%
O 62.8%, 44.0%, 62.5%, 100%
Text
e-Mail
IM
Total
Boys
32
14
15
61
Girls
54
11
25
90
Total
86
25
40
151
Answer:
it’s c i think
Step-by-step explanation:
Answer C
Step-by-step explanation:
Which statement explains the relationship of sides BA and B'A' after rectangle BADC has been rotated 90° clockwise about the origin?
coordinate plane with rectangle ABCD at A (3,5), B (1,3), C (5,-1), and D (7,1)
Side B'A' has a slope of −1 and is perpendicular to side BA.
Side B'A' has a slope of 1 and is parallel to side BA.
Side B'A' has a slope of 1 and is perpendicular to side BA.
Side B'A' has a slope of −1 and is parallel to side BA.
Answer:
Numbering the options, we have;
1) Side B'A' has a slope of −1 and is perpendicular to side BA.
2) Side B'A' has a slope of 1 and is parallel to side BA.
3) Side B'A' has a slope of 1 and is perpendicular to side BA.
4) Side B'A' has a slope of −1 and is parallel to side BA.
The correct option is;
1) Side B'A' has a slope of -1 and is perpendicular to side BA
Step-by-step explanation:
The given coordinates are;
A(3, 5) B(1, 3), C(5, -1) and D(7, 1)
The slope of BA is found as follows;
[tex]Slope \, of BA= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} =\dfrac{3-5}{1-3}= \dfrac{-2}{-2} = 1[/tex]
Rotation of a line through 90 degrees gives
(x, y) will be (y, -x)
Therefore, the coordinates of A' = (5, -3)
The coordinates of B' = (3, -1)
Then the slope is given as follows;
[tex]Slope \, of \, B'A' =\dfrac{-1 -(-3)}{3-5}= \dfrac{2}{-2} = -1[/tex]
Therefore side B'A' has a slope of -1 and is perpendicular to side BA.
Option (4) will be the correct option.
Coordinates of the vertices of rectangle ABCD are,
A(3, 5), B(1, 3), C(5, -1) and D()Slope of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the expression,
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of segment BA (m₁) = [tex]\frac{3-5}{1-3}[/tex] = 1
If a point (h, k) is rotated 90° clockwise about the origin, rule to be followed,
(h, k) → (-k, h)
Following this rule,
B(1, 3) → B'(-3, 1)
A(3, 5)→ A'(-5, 3)
Slope of segment B'A' (m₂) = [tex]\frac{1-3}{-3+5}=-1[/tex]
Expression representing two segments with slopes [tex]m_1[/tex] and [tex]m_2[/tex] to be perpendicular,
[tex]m_1\times m_2=-1[/tex]
Since, slopes of two segments BA and B'A' are (1) and (-1).
(1) × (-1) = -1
Therefore, both the segments BA and B'A' will be perpendicular.
Option (4) will be the answer.
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Find F(5) for f(x)= 1/4 (2)
Answer:
a2+2a+2
Step-by-step explanation:
Find F(5) for f(x)= 1/4 (2) the answer is a2+2a+2
john has × marbles and max has twice as many.max give gives john 5 of his marbles does max now have
Answer: 2x -5
Step-by-step explanation:
Hi, to answer this question we have to write equations with the information given:
John has × marblesJohn=x
Max has twice (multiplied by 2) as many.max give gives john 5 of his marbles.We have to multiply by 2 the number of marbles that John has (x), and subtract 5.
Max = 2x -5
Feel free to ask for more if needed or if you did not understand something.
Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30. The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (3) minus 6 = negative 42. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (negative 2) minus 6 = 18. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answer:
The expressions are not equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(2)-6=-30
Step-by-step explanation:
Two expressions are said to be equal if after a number is substituted to the expression, they produce the same result (that is they have the same value).
To determine whether -3x(5-4)+3(x-6) is equivalent to -12x-6, we have to substitute the same number to the expression and see if it produces the same result.
Substituting 2 to the first expression gives:
-3×2(5-4) + 3(2 - 6) = -6 - 12 = -18
Substituting 2 to the second expression gives:
-12(2) - 6 = -24 - 6 = -30
Since -3×2(5-4) + 3(2 - 6) = -6 - 12 = -18 and -12(2) - 6 = -24 - 6 = -30, the expressions are not equivalent because they do not produce the same result.
The correct procedure that justifies their equality is the expressions are equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(1)-6=-18
Expressions and valuesEquations are written by equating two expressions
Given the following equation -3x(5-4)+3(x-6)
Expand
-15x + 12 + 3x - 18
Collect the like terms
-15x + 3x + 12 - 18
-12x - 6
Hence the correct procedure that justifies their equality is the expressions are equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(1)-6=-18
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which expression is equivalent to
Answer:
3
Step-by-step explanation:
"" = x^(0.5*(-2))*y^(-0.25*(-2))*z^(-2) = x^(-1)*y^(0.5)*z^(-2) =
(1/x^1)*y^(0.5)*(1/z^2) = 3
Answer:
Third one.
Step-by-step explanation:
The exponent negative 2 applies to all that's in the bracket. So, x^1/2 times exponent negative 2 equals x to the power negative one. And y to the power negative half and z to the power negative 2. Therefore, x^-1 = 1/x and y^1/2 remains same and z^-2 = 1/ z^2.
Which situation is best modeled with a division expression?
finding the number of equal-sized parts into which a number can be split
finding the combined value of several different numbers
finding the distance between two numbers on a number line
finding the total value when several of the same number are grouped together
Answer: Finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
Hi, a division expression is the division of 2 numbers that results in a quotient.
The quotient is the number of times that the second number in the division is contained in the first number.
For example 20 ÷ 2 = 10
Number 2 is contained 10 times in the number 10, or in other words, 20 can be split into ten equal-sized parts.
Feel free to ask for more if needed or if you did not understand something.
Answer:
A
Step-by-step explanation:
for edge
If 3 inch square is covered with 1inch squares how many of the 1 inch squares are needed? What is the area of the larger square
Answer:
9 1-inch squares will cover the bigger square. Its area is the same as the amount of squares needed, 9 inches.
the larger Area will be 9 square inch.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To cover a 3 inch square with 1 inch squares, we can arrange the 1 inch squares in a 3 by 3 grid.
So, we need 9 of the 1 inch squares to cover the 3 inch square.
The area of the larger square can be found by squaring the length of one of its sides.
Since the side length of the 3 inch square is 3 inches, the area of the larger square is:
Area = (side length)² = 3² = 9 square inches
Therefore, the larger Area will be 9 square inch.
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Jeremy analyses one of his parachute jumps. He draws a graph showing his velocity up to the opening of his parachute. a) Estimate Jeremy's acceleration at t = 10s to 1 decimal place. b) Estimate his average speed for this part of the jump. Give your answer to two significant figures.
Answer:
Jeremy's acceleration is about [tex]1\,\frac{m}{s^2}[/tex] at t =10 s
His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)
His average speed is about 46 m/s if using the tangent line (over estimate)
Step-by-step explanation:
Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.
These points are : (6, 42) and (14,50) which using the slope formula give:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}[/tex]
So his acceleration at that point is about [tex]1\,\frac{m}{s^2}[/tex]
Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:
[tex]v_{average}=\frac{area}{interval\,\,length}[/tex]
and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.
The area of this trapezoid is: approximately:
[tex]Trapezoid\,\, area=(49+40)\,8/2=356[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}[/tex]
If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):
[tex]Trapezoid\,\, area=(50+42)\,8/2=368[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}[/tex]
while his actual instantaneous velocity seems to be about 46 m/s from the graph
Answer:
a) 1.0
b) s=45
Step-by-step explanation:
The graph of g(x) = (x+2)^2 is a translation of the graph of f(x) ___by___units
Answer:
The graph of g(x)=(x+2)^2 is a translation of the graph of f(x) LEFT by TWO units.