Answer:
a. 3⁄10 + 6⁄10 = 9/10
b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4
c. 5⁄6 – 3⁄6 = 1/3
d. 2⁄3 – 6⁄10 = 1/15
e. 4⁄10 × 3⁄7 = 6/35
f. 1⁄6 × 6⁄15 = 1/15
g. 1⁄8 ÷ 4⁄9 = 9/32
h. 1⁄5 ÷ 3⁄4 = 4/15
Step-by-step explanation:
a. 3⁄10 + 6⁄10
= 3*1 + 6*1 / 10
= 3+6/10
= 9/10
b. 1⁄3 + 1⁄4 + 1⁄6
since denominators are different we take LCM of 3,4,6 which is 12
= 1*4 + 1*3 + 1*2 / 12
= 4+3+2/12
= 9 ÷ 3 / 12 ÷ 3
= 3 / 4
c. 5⁄6 – 3⁄6
= 5 - 3 / 6
= 2 ÷ 2 / 6 ÷ 2 = 1/3
d. 2⁄3 – 6⁄10
LCM of 3 and 10 is 30
= 2 * 10 - 6 * 3 / 30
= 20 - 18 / 30
= 2 ÷ 2 / 30 ÷ 2 = 1/15
e. 4⁄10 × 3⁄7
= 12 ÷ 2 / 70 ÷ 2 = 6/35
f. 1⁄6 × 6⁄15
= 6 ÷ 6/90 ÷ 6 = 1/15
g. 1⁄8 ÷ 4⁄9
= 1/ 8 * 9/4
=9/32
h. 1⁄5 ÷ 3⁄4
=1/5 * 4/3
= 4/15
a)
[tex]\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{4}{15}[/tex]
Step-by-step explanation:a)
[tex]\dfrac{3}{10}+\dfrac{6}{10}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{6+3}{10}\\\\=\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}[/tex]
On taking the least common multiple of the denominator we have:
[tex]L.C.M\{3,4,6\}=12[/tex]
Hence, we have:
[tex]=\dfrac{1\times 4+1\times 3+1\times 2}{12}\\\\=\dfrac{4+3+2}{12}\\\\=\dfrac{9}{12}\\\\=\dfrac{3\times 3}{3\times 4}\\\\=\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{5}{6}-\dfrac{3}{6}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{5-3}{6}\\\\=\dfrac{2}{6}[/tex]
which on reducing to the lowest terms is given by:
[tex]=\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{2}{3}-\dfrac{6}{10}[/tex]
on reducing the second term we have:
[tex]=\dfrac{2}{3}-\dfrac{3}{5}[/tex]
Now on simplifying the expression we have:
[tex]=\dfrac{2\times 5-3\times 3}{15}\\\\=\dfrac{10-9}{15}\\\\=\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{4}{10}\times \dfrac{3}{7}[/tex]
We know that:
[tex]\dfrac{4}{10}=\dfrac{2}{5}[/tex]
Hence, we have:
[tex]=\dfrac{2}{5}\times \dfrac{3}{7}\\\\=\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{6}\times \dfrac{6}{15}[/tex]
which on simplifying gives:
[tex]=\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{\dfrac{1}{8}}{\dfrac{4}{9}}[/tex]
which is further written as:
[tex]=\dfrac{1\times 9}{4\times 8}\\\\=\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}[/tex]
which is given by:
[tex]=\dfrac{1\times 4}{3\times 5}\\\\=\dfrac{4}{15}[/tex]
Which ordered pair is a solution of the equation? 7x-2y=-5
answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest
Answer:
2y=-x7
Love mORgan
what is the difference between the mean high and mean low temperature for this 5-day period?
Answer:
the mean high temperature is 71 degrees and the mean low is 31 degrees
Step-by-step explanation:
what are the steps to solve 2+8-z=-24?
Move z and 24, switch signs then add numbers
Answer:
z=34
Step-by-step explanation:
Here is:
2+8-z=-24
2+8+24=z
z=34
Best regards
What is the value of x
Answer:
x = 149
Step-by-step explanation:
Lines m and n are parallel lines as shown by the double arrows on each line.
The angles marked x and 149 deg are corresponding angles of parallel lines cut by a transversal.
Postulate:
If parallel lines are cut by a transversal, then corresponding angles are congruent.
According to the postulate above, since the angles marked 149 and x are corresponding angles, they are congruent.
x = 149
Answer:
X=149
Step-by-step explanation:
Lines m and n are parallel. You know this because the 2 marks on both lines mean that they are the same and parallel.
What is the range of the graph
Answer:
Range: all real numbers greater than or equal to 2
Step-by-step explanation:
The range is the possible numbers that the output can take
Y can be any number greater than or equal to 2
Range: all real numbers greater than or equal to 2
Steps to convert fractions into decimals 4/25
Divide 4 by 25 either by hand or by calculator. Hope this helped.
Answer: [tex]\frac{4}{25}[/tex]=0.16
Step-by-step explanation:
How convert 4/25 into a decimal is :
4÷25 Then using Long Division for 4 divided by 25 and rounding to a Max of 3 Decimal Places gives us.Which will give you your answer as 0.16 in decimal form.:)* Hopefully this helps:)!! Mark me the brainliest:)!!!
ANSWERRRR<3 5. It took 12 reams of paper to produce 500 pamphlets. How many reams can produce 48
pamplets?
(A)0.096 (B)2000 (C)125 (D) 1 19/125
Answer:6
Step-by-step explanation:
500/12 is 41 so therefore you do 48/12 is 6.
Answer:
1 19/125
Step-by-step explanation:
1.) 12/500 = 0.024
2.) 0.024 * 48 = 1.152
3.) 1.152 converted to a fraction is 144/125, or 1 19/125
The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h = -15 cos(2pi/5 t). At which times will the spring be at a height of 8 in. above equilibrium? Select two of the following, make two selections.
Answer:
1.7 seconds, and
3.3 seconds
Step-by-step explanation:
We simply need to plug in 8 into h and solve for t:
[tex]h=-15Cos(\frac{2\pi}{5}t)\\8=-15Cos(\frac{2\pi}{5}t)\\-\frac{8}{15}=Cos(\frac{2\pi}{5}t)\\\frac{2\pi}{5}t=Cos^{-1}(-\frac{8}{15})\\\frac{2\pi}{5}t=2.13\\t=\frac{2.13}{\frac{2\pi}{5}}\\t=1.70[/tex]
Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.
First, π - 2.13 radians = 1.01 radians.
Then, we add 1.01 to π radians, so we get 4.15 radians
Solving from the last part, we have:
[tex]t=\frac{4.15}{\frac{2\pi}{5}}\\t=3.3[/tex]
also, t = 3.30 seconds
*Note: we put the calculator mode in radians when solving
So, t = 1.7 seconds & 3.30 seconds
Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. x + y > 3 x + y < -4
Answer:
The graph for the following system of inequalities is attached below.
Step-by-step explanation:
The given system of inequalities is
[tex]x+y>3[/tex] .... (1)
[tex]x+y<-4[/tex] .... (2)
From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.
The related equation of first inequality is
[tex]x+y=3[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=3\Rightarrow y=3[/tex]
The y-intercept is 3.
Put y=0 to find the x-intercept.
[tex]x+0=3\Rightarrow x=3[/tex]
The x-intercept is 3.
The related equation of second inequality is
[tex]x+y=-4[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=-4\Rightarrow y=-4[/tex]
The y-intercept is -4.
Put y=0 to find the x-intercept.
[tex]x+0=-4\Rightarrow x=-4[/tex]
The x-intercept is -4.
The related lines are dotted line because the sign of inequalities are > and <.
Check each inequality be (0,0).
[tex]0+0>3[/tex]
[tex]0>3[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
[tex]0+0<-4[/tex]
[tex]0<-4[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
The graph for the following system of inequalities is attached below.
Answer:
This is the correct graph on Odyssey :)
x^2 − 8 = 8 pls help
if you're solving for x,
start by isolating x squared to get
x^2 = 16 (we added 8 to both sides)
then square root each side:
sqrt of x^2 = x; sqrt of 16 = 4.
we end up with x = 4 (positive and neg)
if you're factoring
minus 8 from both sides to get
x^2 - 16
from there we can factor to get
(x + 4)(x - 4)
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,5)?
Answer:
C
Step-by-step explanation:
The point slope form of a line is [tex]y - y_1 = m(x-x_1)[/tex]. If the point is (2,5) then the equation will be [tex]y - 5=m(x-2)[/tex]. Only option C matches this equation.
As part of your training schedule you plan to jog once a week around the reservoir shown below on the map.
One lap along the perimeter of the reservoir is 25 cm. What is the actual length of a lap?
The actual length of a lap cannot be determined without the scale of the map. The 25 cm measurement seems to be from the map, so without knowing the real-world equivalent of the map's measurements, we can't find the actual distance.
Explanation:The length of a lap around the reservoir cannot be directly determined from the information given. The measurement provided (25 cm) appears to be a distance measured on a map or plan of the area, and not in real life. In order to convert that measurement into a real-world distance, we need the scale of the map. A map's scale is typically represented as a ratio that indicates the relationship between a certain distance on the map and the real-world distance it represents.
For example, if the map's scale was 1 cm : 1 km, then a measurement of 25 cm on the map would represent a real-world distance of 25 km. However, without the scale, we cannot accurately determine the actual length of a lap around the reservoir. This concept is extremely important in geography and cartography as well as in mathematical problems dealing with maps and scales.
Learn more about Map Scale here:https://brainly.com/question/24486949
#SPJ11
Dnhdhdbdvdeh hellllllpppppppp
Find the area of the triangle that has a base of 5in -‘d a height of 3 3/4
Answer:
its either c or b
Step-by-step explanation:
formula: 1/2*b*h or 1/2*5*3+3/4
the answer i got was 33/4
how long can the run be made?
Answer:
[tex]L=15\ m[/tex]
Step-by-step explanation:
we know that
The perimeter of rectangle is equal to
[tex]P=2L+2W[/tex]
In this problem we have
[tex]P=42\ m[/tex]
[tex]W=6\ m[/tex]
substitute in the formula and solve for L
[tex]42=2L+2(6)[/tex]
simplify
[tex]21=L+(6)[/tex]
[tex]L=21-6=15\ m[/tex]
What is the value of x in the equation −6 + x = −1
Answer:
x=5
Step-by-step explanation:
-6+5=-1
start at -6 then go right units until u get -1 you got right 5 units
The value of x in the given equation is:
x=5
Step-by-step explanation:We are given a algebraic expression in terms of the variable x by:
[tex]-6+x=-1[/tex]
Now, we are asked to find the value of x from the equation.
i.e. we have to solve for x.
i.e. by some appropriate algebraic operation we need to solve for x.
so we will add 6 on both the sides of the equation to get:
[tex]-6+x+6=-1+6\\\\i.e.\\\\-6+6+x=5\\\\i.e.\\\\0+x=5\\\\i.e.\\\\x=5[/tex]
Hence, the value of x is: 5
Choose the correct answer. Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = _____ hours.
Please do not round
Final answer:
Using the given information, the total travel time by airplane and bus is calculated as 4.47616 hours, which includes flying time and additional travel time by bus.
Explanation:
To calculate the total travel time by airplane including the additional travel time by bus, we must first find out the time taken by the airplane to cover the distance between the two airports. This can be done by dividing the distance by the airplane's average speed. Afterward, we add the bus travel time to get the total travel time.
The time taken by the airplane to cover 1,450 miles at an average speed of 350 mph is calculated by dividing distance by speed: 1,450 miles ÷ 350 mph = 4.142857 hours. Note that we do not round this number to maintain accuracy.
Next, we convert the bus travel time of 20 minutes into hours: 20 minutes ÷ 60 minutes per hour = 0.3333 hours.
Now, we add both the airplane and bus travel times together: 4.142857 hours + 0.3333 hours = 4.47616 hours total travel time.
A jar contains balls numbered 1 to 10. Two balls are drawn with replacement. What is the probability that both balls are numbered 2 or less?
Answer:
Step-by-step explanation:
The number of ways that you can draw 2 balls without restriction is 10 * 10 = 100
Two balls will give you 2 or less (meaning 1) or 2*2 = 4
Four ways are possible
2 and 2
2 and 1
1 and 2
1 and 1
4/100 = 1/25 is the probability of making this happen.
how much empty space is inside the can of tennis balls? the radius of each tennis ball is 1.5 inches. The radius of the can is 1.75 inches and the height is 9 inches. Use 3.14 for pi, and round your answers to the nearest hundredth.
Final answer:
To find the empty space in the can of tennis balls, calculate the volume of one tennis ball and multiply by three (since there are typically three balls per can), then subtract from the volume of the can. There are 43.54 inches³ of empty space in the can, after rounding to the nearest hundredth.
Explanation:
To calculate the empty space inside the can of tennis balls, we first need to determine the volume of one tennis ball and then the volume of the can. Given the radius of each tennis ball is 1.5 inches, we use the formula for the volume of a sphere:
V_ball = 4/3 π r³
Substitute with r = 1.5 inches and π = 3.14:
V_ball = 4/3 × 3.14 × (1.5 inches)³
V_ball = 4/3 × 3.14 × 3.375 inches³
V_ball = 14.13 inches³ (rounded to the nearest hundredth)
Next, we calculate the volume of the can, using the formula for the volume of a cylinder:
V_can = π r² h
Substitute with r = 1.75 inches and h = 9 inches:
V_can = 3.14 × (1.75 inches)² × 9 inches
V_can = 3.14 × 3.0625 inches² × 9 inches
V_can = 85.93 inches³ (rounded to the nearest hundredth)
The empty space within the can is therefore the volume of the can minus the volume of three tennis balls (assuming the can holds three balls):
Empty space = V_can - 3 × V_ball
Empty space = 85.93 inches³ - 3 × 14.13 inches³
Empty space = 85.93 inches³ - 42.39 inches³
Empty space = 43.54 inches³ (rounded to the nearest hundredth)
Therefore, there are approximately 43.54 inches³ of empty space inside the can.
Please help me I’m begging you please please please help me I need your help I’m begging you for your help please do me this favor it’s an emergency and I need your help please please help me please I’m begging you on my knees please please
Hey there!
The first thing we can do is find the number of third in 4.
We can do this by multiplying 4 by 3 since there are 3 thirds in a whole.
4 x 3 = 12
So, 4 = 12/3
If she studies for 2/3 an hour each night, then we can divide 12 by 2 to figure out how many 2/3 go into 12/3.
12 ÷ 2 = 6
So, she studied for 6 days.
Hope this helps!
Please help with my homework
Answer:
It is 2 1/2
Step-by-step explanation:
. Find the area of a trapezoid with b1 = 13.8 cm, b2 = 16.8 cm, and h = 4 cm.
61.2 cm2
33.6 cm2
122.4 cm2
27.6 cm2
Answer:
61.2 cm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h ([tex]b_{1}[/tex] + [tex]b_{2}[/tex] )
Substitute in given values
A = [tex]\frac{1}{2}[/tex] × 4 × (13.8 + 16.8 ) = 2 × 30.6 = 61.2 cm²
The answer is 61.2cm² .
[tex]((13.8 + 16.8) \times 4) \div 2[/tex]
This equation helps you get the answer.
What is the difference between an approximate and an exact number?
Answer:
An approximate number is a close number that is only off by x number of places (Like a rounded number). An exact number is exactly correct. For example:
3 - 1.5 is approximately 2, but is exactly 1.5.
Mark Brainliest if this helps!
Final answer:
An exact number is one that is known with complete precision, such as the number of books on a shelf. An approximate number, or inexact number, includes uncertainty and comes with an error range, often due to measuring limitations such as estimating a length with a ruler. The level of rounding applies to approximate values determines their reliability, and significant figures are influenced by inexact numbers.
Explanation:
The difference between an exact number and an approximate number lies in their level of precision and the source of the number. Exact numbers are count numbers that are known with complete precision. An example of an exact number is the number of students in a classroom, which might be exactly 25. On the other hand, inexact numbers, also known as measured numbers, come with an error range due to the limitations of measuring instruments or methods. For instance, when using a ruler, you might measure a length as approximately 12.7 cm, but the true length might be slightly less or more.
It's important to note that the more rounding that is applied to a number, the less reliable it becomes. Approximations are common in various fields, including physics, where scientists and engineers make educated guesses, or 'guesstimates', based on available data and formulae with limited accuracy. These approximations are essential for problem-solving and can help in making quantitative decisions and realistic predictions.
Conversion factors in measurements are considered to be exact numbers because they are defined as such by the measurement systems. In calculations involving both exact and inexact numbers, the precision of the inexact numbers dictates the number of significant figures in the result.
1.simplifyyyyyyyyyyyy
Answer:
Choice A
Step-by-step explanation:
We apply the law of exponents;
[tex](a^{b})^{c}=a^{bc}[/tex]
[tex]\sqrt{0.08^{12}}=(0.08^{12})^{\frac{1}{2}}[/tex]
applying the law of exponents we simply multiply 12 and 1/2 to get;
[tex]0.08^{6}[/tex]
Simplify 6 to the fifth power over 7 cubed all raised to the second power
Step-by-step explanation:
Do you mean:
(6^5/7^3)^2?
If so, you will get
6^10/7^6 or about 513.954016
It is to be note that (6⁵ / 7³)² simplifies to become approximately 514.64
How to compute the above simplificationTo simplify the expression (6⁵ / 7³)², we start by evaluating the exponents first.
6⁵ means 6 raised to the power of 5, which is 6 * 6 * 6 * 6 * 6 = 7776.
7³ means 7 raised to the power of 3, which is 7 * 7 * 7 = 343.
Now, we substitute these values back into the expression -
(7776 / 343)² = (22.6666666667)² = 514.64197531
Therefore, it is right to state that (6⁵ / 7³)² simplifies to 514.64197531 which is approximately, 514.64.
Learn more about simplification at:
https://brainly.com/question/28595186
#SPJ6
Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)
Which of them factored 14y3 correctly ?
Answer:
Hiro factored them correctly.
Step-by-step explanation:
The factors of 14 are 1, 2, 7, and 14.
7 * 2 = 14
10 and 4 make the product of 14.
10 + 4 = 14
Bilial factored 14y3 correctly.
Explanation:Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)
To determine which one factored 14y3 correctly, we need to compare their factorizations to the original expression: 14y3. Hiro's factorization (7y2)(2y) does not match the original expression, as it is missing a y term. On the other hand, Bilial's factorization (10y)(4y2) matches the original expression.
Therefore, "Bilial factored 14y3 correctly."
Learn more about factoring here:https://brainly.com/question/34290719
#SPJ3
Simplify 4/16 to lowest terms and find and equivalent fraction that has a denominator of 32
8/32 is the answer to your problem
The equivalent fraction of given fraction is [tex]\frac{8}{32}[/tex].
Given fraction is, [tex]\frac{4}{16}[/tex]
It is observed that both numerator and denominator of given fraction is divisible by 4.
Simplest form of [tex]\frac{4}{16}[/tex] is,
[tex]\frac{4}{16}=\frac{4*1}{4*4} =\frac{1}{4}[/tex]
Equivalent fraction that has a denominator of 32 is,
[tex]\frac{1}{4}=\frac{1*8}{4*8}=\frac{8}{32}[/tex]
Learn more:
https://brainly.com/question/12526529
The numbers of hours that 12 students say they typically spend on homework in a week are 2, 0, 10, 8,10, 8, 8, 8, 10, 10, 8, and 8. What is the mean number of hours? What are the outliers in the data set?
Answer:
The mean is 7.5 and the outliers are 0 and 2
Step-by-step explanation:
To find the mean, add all of the numbers together and divide by the amount of numbers.
2 + 0 + 10 + 8 + 10 + 8 + 8 + 8 + 10 + 10 + 8 + 8 = 90
90/12 = 7.5
To see the outliers, look for the numbers far away from the mean.
what is 3(x-4)-7=(2x-3)
Solve for x by simplifying both sides of the equation, then isolating the variable.
So the answer to your question is :
x = 16.
Hope this helps,
Davinia.
Answer:
x = 16
Step-by-step explanation:
distribute parenthesis on both sides and simplify
3x - 12 - 7 = 2x - 3
3x - 19 = 2x - 3 ( subtract 2x from both sides )
x - 19 = - 3 ( add 19 to both sides )
x = 16
What is the area of this triangle? please help me.
Answer:
6
Step-by-step explanation:
Area of a triangle: bh/2
4*3/2=6
Answer:
6 units²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = DE = 3 units and
h is the distance from the vertex F to DE = 4 units, hence
A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²