Answer:
5 , 4.5, 13.5 and 40.5
Step-by-step explanation:
Since the numbers are in geometric progression, their form is essentially:
a, ar, ar^2 and ar^3
Where a and r are first term and common ratio respectively.
From the information given in the catalog:
Third term is greater than the first by 12 while fourth is greater than second by 36.
Let’s now translate this to mathematics.
ar^2 - a = 12
ar^3 - ar = 36
From 1, a(r^2 - 1) = 12 and 2:
ar(r^2 - 1) = 36
From 2 again r[a(r^2 -1] = 36
The expression inside square bracket looks exactly like equation 1 and equals 12.
Hence, 12r = 36 and r = 3
Substituting this in equation 1,
a( 9 - 1) = 12
8a = 12
a = 12/8 = 1.5
Thus, the numbers are 1.5, (1.5 * 3) , (1.5 * 9), (1.5 * 27) = 1.5 , 4.5, 13.5 and 40.5
Final Answer:
The four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.
Explanation:
Let's start by defining what a geometric progression (GP) is. A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Let's denote the four numbers in the GP as a, ar, ar², and ar³, where:
- a is the first term,
- r is the common ratio.
We've been given two conditions:
1. The third term is greater than the first by 12, which gives us the equation:
ar² = a + 12
2. The fourth term is greater than the second by 36, which leads us to:
ar³ = ar + 36
We need to solve this system of equations to find the values of a and r.
Starting with the first equation:
ar² = a + 12
We can subtract 'a' from each side to get:
ar - a = 12
Factor out 'a' from the left side:
a(r² - 1) = 12
Now notice that r² - 1 is a difference of squares and can be factored to (r + 1)(r - 1):
a(r + 1)(r - 1) = 12
This equation tells us that the product of 'a' and (r + 1)(r - 1) is 12. For now, let's keep this equation aside and look at the second condition.
Proceeding with the second equation:
ar = ar + 36
Subtract 'ar' from each side:
ar³ - ar = 36
Factor out 'ar':
ar(r² - 1) = 36
Again, we recognize a difference of squares in the parentheses, so we factor it:
ar(r + 1)(r - 1) = 36
This equation relates 'ar', and (r + 1)(r - 1), and tells us the product is 36.
Now, because we have a similar term in both equations, (r + 1)(r - 1), we can set the products equal to each other to find a relationship between 'a' and 'ar':
From the first equation, we have a(r + 1)(r - 1) = 12,
From the second equation, we have ar(r + 1)(r - 1) = 36.
Dividing the second equation by the first one gives us:
ar(r + 1)(r - 1) / a(r + 1)(r - 1) = 36 / 12
ar / a = 36 / 12
r = 3
Now that we have the value of 'r', let's substitute it back into either of the original equations to find 'a'. Let's use the first equation:
a(r² - 1) = 12
a(3² - 1) = 12
a(9 - 1) = 12
a(8) = 12
a = 12 / 8
a = 3 / 2
a = 1.5
Now we have both 'a' and 'r', which allows us to determine the four numbers in the GP:
The first number, a, is 1.5.
The second number, ar, is 1.5 * 3 = 4.5.
The third number, ar², is 4.5 * 3 = 13.5.
The fourth number, ar², is 13.5 * 3 = 40.5.
So, the four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.
Running at an average rate of 4 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and the jog back was 2 minutes 6 seconds. Find the length of the track.
Step-by-step explanation:
Let l be the length of track.
Running speed = 4 m/s
Jogging speed = 2 m/s
Total time taken = 2 minutes 6 seconds. = 126 seconds
That is
[tex]\frac{l}{4}+\frac{l}{2}=126\\\\0.75l=126\\\\l=168m[/tex]
Length of track is 168 meter
To find the length of the track, we need to calculate the time it took for the sprint and the jog back, and set up an equation using the formula for distance. Simplifying the equation will give us the length of the track. The length of the track is 168 meters.
Explanation:To find the length of the track, we need to use the formula for distance: distance = rate × time. Let's call the length of the track 'd' meters. The sprinter ran to the end of the track at 4 meters per second, so the time it took for the sprint is d/4 seconds. The jog back to the starting point at 2 meters per second takes a time of d/2 seconds. And the total time given is 2 minutes 6 seconds, which can be converted to seconds as 126 seconds. So we can set up the equation: d/4 + d/2 = 126.
Simplifying the equation, we can multiply each term by 4 to get d + 2d = 504. Combining like terms gives us 3d = 504. Dividing both sides by 3, we find that the length of the track is d = 168 meters.
Therefore, the length of the track is 168 meters.
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Select the perfect square trinomial for each polynomial. (There are 2 correct answers)
Question 1 options:
x^2−10x−25
x^2−18x+81
x^2+2x+1
x^2+7x+49
Answer:
x^2−18x+81
x^2+2x+1
Step-by-step explanation:
we know that
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself
so
[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]
Verify each case
case a) x^2−10x−25
we know that
[tex](x-5)^2=x^2-10x+25[/tex]
therefore
Is not a perfect square trinomial
case b) x^2−18x+81
we know that
[tex](x-9)^2=x^2-18x+81[/tex]
therefore
Is a perfect square trinomial
case c) x^2+2x+1
we know that
[tex](x+1)^2=x^2+2x+1[/tex]
therefore
Is a perfect square trinomial
case d) x^2+7x+49
we know that
[tex](x+3.5)^2=x^2+7x+12.25[/tex]
therefore
Is not a perfect square trinomial
Plan A is a flat rate of $50 per month unlimited data. Plan B is zero dollars per month but you pay five dollars per gigabyte of data used. If you average about 6 GB of data used per month, which option will be least expensive?
Answer:
B
Step-by-step explanation:
For Plan A ---> you pay $50 per month flat
For Plan B,
average usage = 6 GB
cost per GB = $5 per GB
average cost per month = $5 per GB x 6 GB = $30
comparing the cost per month between the 2, we can clearly see that for plan B, $30 a month is the least expensive option
Plan B would be the least expensive option for someone who uses about 6 GB of data per month, costing $30, compared to Plan A's flat rate of $50 per month. It is important to also consider other costs and usage patterns when selecting a phone data plan.
When finding the least expensive phone data plan between a flat rate plan and a pay-per-gigabyte plan, you need to calculate the total costs based on the average data usage. In this case, Plan A offers unlimited data for a flat rate of $50 per month, while Plan B charges $5 per gigabyte of data used, with no monthly base cost.
For an average use of 6 GB of data per month:
Plan A would cost $50 every month, regardless of how much data you use.
Plan B would be 6 GB x $5/GB = $30 per month.
Comparing the two plans, Plan B is the least expensive option for someone who uses about 6 GB of data each month, as it would cost $30 as opposed to the $50 charged by Plan A.
However, it's important to consider your personal usage patterns and other potential costs, such as monthly charges for other services, occasional charges for peripherals or repairs, and any relevant annual costs or major costs when choosing a plan that fits your budget effectively.
Thirty-eight is [tex]\frac{2}{5}[/tex] of what number?
Answer:
The number is 95.
Step-by-step explanation:
Solution,
Let the number be 'x'.
So, [tex]\frac{2}{5}[/tex] of 'x' = [tex]\frac{2}{5}x[/tex]
Now according to question, [tex]\frac{2}{5}x[/tex] is equal to 38.
So we can frame it as;
[tex]\frac{2}{5}x=38[/tex]
Now we solve it;
For solving it we will multiply both side by '5' using multiplication property and get;
[tex]\frac{2}{5}x\times5=38\times5\\\\2x=38\times5[/tex]
Now using division property, we will divide both side by '2' and get;
[tex]\frac{2x}{2}=\frac{38\times5}{2}\\\\x=19\times5=95[/tex]
Hence The number is 95.
How do you solve for 2-9|-8b+8|=-70?
Answer:
The solution for the given equation is 0 and 2.
Step-by-step explanation:
Given equation:
[tex]2-9|-8b+8|=-70[/tex]
To solve for [tex]b[/tex].
Solution:
In order to solve the given equation, we will first isolate the absolute value expression:
Step 1: Isolating the absolute value expression
[tex]2-9|-8b+8|=-70[/tex]
Subtracting both sides by 2.
[tex]2-2-9|-8b+8|=-70-2[/tex]
[tex]-9|-8b+8|=-72[/tex]
Dividing both sides by -9.
[tex]\frac{-9|-8b+8|}{-9}=\frac{-72}{-9}[/tex]
[tex]|-8b+8|=8[/tex]
Step 2: Set the value of the absolute value expression to positive and negative.
[tex]-8b+8=8[/tex] and [tex]-8b+8=-8[/tex]
Step 3: Solve for the unknown.
Solving for [tex]b[/tex].
Subtracting both sides by 8.
[tex]-8b+8-8=8-8[/tex] and [tex]-8b+8-8=-8-8[/tex]
[tex]-8b=0[/tex] and [tex]-8b=-16[/tex]
Dividing both sides by -8.
[tex]\frac{-8b}{-8}=\frac{0}{-8}[/tex] and [tex]\frac{-8b}{-8}=\frac{-16}{-8}[/tex]
[tex]b=0[/tex] and [tex]b=2[/tex] (Answer)
Thus, the solution for the given equation is 0 and 2.
Simplifying an Expression with the Numerator and the Denominator Raised to a Power
Answer:
The answer to your question is the second option [tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]
Step-by-step explanation:
Expression
[tex][\frac{(x^{2}y^{3})^{-2}}{(x^{6}y^{3}z)^{2}}]^{3}[/tex]
Process
1.- Divide the fraction in numerator and denominator
a) Numerator
[(x²y³)⁻²]³ = (x⁻⁴y⁻⁶)³ = x⁻¹²y⁻¹⁸
b) Denominator
[(x⁶y³z)²]²= (x¹²y⁶z²)³ = x³⁶y¹⁸z⁶
2.- Simplify like terms
a) x⁻¹²x⁻³⁶ = x⁻⁴⁸
b) y⁻¹⁸y⁻¹⁸= y⁻³⁶
c) z⁻⁶
3.- Write the fraction
[tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]
Answer:
First, Second, and fourth answers :)
Step-by-step explanation:
Two hunters started to walk towards each other simultaneously from two different locations in the forest. The distance between them was 21 miles. The first hunter walked at a rate of 4 mph, while the second one walked at a rate of 3 mph. The first hunter took a dog with him, who ran at an average rate of 5 mph. The dog started to run towards the second hunter, met him and ran back to the first hunter. The dog repeated this until the two hunters met each other. How many miles did the dog run?
Answer:
The dog ran 15 miles
Step-by-step explanation:
The combined speed of the 2 hunters is 7mph, therefore, they will met in 21/7 = 3 hours, becuse they are walking in opposite directions. In this 3 hours the dog kept running and thus it ran 3*5 = 15 miles. Note that the position of the dog is always between the position of both hunters, therefore when both hunters met each other, the dog will be alredy there.
Daniel and Elizabech had to choose between making a 600-mile round trip by car or plane. Round-trip
airfare was $260 for each of them and would take 2 hours. Round-trip cab fare to the airport would add
$15. Driving their car would take 2 days each way and would add the cost of gas, food, and lodging.
Elizabeth estimated that gas would cost $60, that food would be $25 per day (4 days) for each of them,
and that lodging would be $48 for each night of the 2 nights they would stay in a motel. Find the total
cost for each mode of transportation.
Select one:
a. Car: $256.00Plane: $435.00
b. Car: $456.00Plane: $535.00
C. Car: $356.00Plane: $535.00
Answer:
C
Step-by-step explanation:
Final answer:
Traveling by car would cost a total of $356, while traveling by plane would total $535. These costs include expenses for gas, food, and lodging when traveling by car, and the airfare and cab fare when traveling by plane. Therefore, Option c is the correct answer.
Explanation:
To find the total cost for each mode of transportation for Daniel and Elizabeth, one must calculate the expenses for both the car trip and the plane trip.
Cost by Car:
Gas: $60
Food: $25 per day for 4 days for 2 people = $200 ($25 x 4 days x 2 people)
Lodging: $48 per night for 2 nights = $96 ($48 x 2 nights)
Total Car Cost: $60 (gas) + $200 (food) + $96 (lodging) = $356
Cost by Plane:
Round-trip airfare for two: $260 per person x 2 = $520
Round-trip cab fare: $15
Total Plane Cost: $520 (airfare) + $15 (cab) = $535
Comparing both options, traveling by car would cost $356, and by plane, it would cost $535. Therefore, Option C is the correct answer.
Test scores were recorded for students in a statistics class. The scores for the first test had a standard deviation of 3.8 points. The scores from the second test had a standard deviation of 4.8 points. Choose the correct statement below.
1. The average test grade rose by 1 point
2. The scores of the second test were closer together than the first
3. The higher standard deviation of the second test indicates higher average scores on the second test than on the first
4. None of the above are true
Answer:
Step-by-step explanation:
The higher standard deviation of any data represents diversified data or data having more scattered value . Average value may be same for two samples of data having different standard deviation . So option one is incorrect. 3 rd option is also incorrect.
The scores of the second test were more widespread than the first , because its standard deviation is more for second test. option 2 is in- correct .
none is correct.
None of the supplied statements are true. The standard deviation is a measure of dispersion from an average, showing the spread of test scores, not average scores or proximity of scores. Therefore, a higher standard deviation means scores were more dispersed, not closer together.
Explanation:The correct statement is None of the above are true. The standard deviation is a measure of dispersion from an average. It reflects the variability or spread in a set of data. It does not provide information about the actual scores, their averages, or whether one test's scores were generally higher or lower than another's.
In this case, a standard deviation of 3.8 for the first test and 4.8 for the second test indicates that the test scores were more spread out around the mean on the second test compared to the first. It does not point to an increase in the average test grade. Furthermore, a higher standard deviation does not mean that the test scores were closer together; actually, it's the opposite – a higher standard deviation indicates that scores were more widely dispersed.
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w is less than or equal to – 2 and greater than or equal to - 8
Use w only once in your inequality.
Answer:
-8 ≤w ≤-2
Step-by-step explanation:
The inequality -8 ≤ w ≤ -2 combines the given conditions into a single expression stating that the variable 'w' can take any value between -8 and -2 inclusive.
Explanation:In mathematics, when a single variable needs to satisfy multiple inequalities, we can write it in a combined form. Your conditions state that 'w' is less than or equal to -2, and 'w' is also greater than or equal to -8. This can be combined into a single inequality as follows: -8 ≤ w ≤ -2. This inequality indicates that the variable 'w' can take any value from -8 to -2, inclusive.
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A basketball hoop in your backyard casts a shadow 109 inches long. You are 5‘8" tall in cast a shadow 62 inches long. Find the height of the basketball hoop in inches round your answer to the nearest whole number
Step-by-step explanation:
Height of shadow of basketball hoop = 109 inches
Height of person = 5 foot 8 inches = 68 inches
Height of shadow of person = 62 inches
[tex]\frac{\texttt{Height of person}}{\texttt{Height shadow of person}}=\frac{68}{62}=\frac{34}{31}[/tex]
[tex]\frac{\texttt{Height of basketball hoop}}{\texttt{Height of shadow of basketball hoop}}=\frac{34}{31}\\\\\frac{\texttt{Height of basketball hoop}}{109}=\frac{34}{31}\\\\\texttt{Height of basketball hoop}=119.55inches=120inches[/tex]
Height of the basketball hoop = 120 inches
A solid right pyramid has a square base with an edge length of s units and a height of h units. A solid right pyramid with a square base has an edge length of s units and a height of h units. Which expression represents the volume of the pyramid?
Answer:
The required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.
Step-by-step explanation:
Consider the provided information.
The Volume square base pyramid is: [tex]V=\dfrac{a^2h}{3}[/tex]
Where a is the edge length and h is the height of the pyramid.
It is given that length of the side is s units and height of the pyramid is h unit.
Substitute the respective values in the formula above
The Volume square base pyramid is:
[tex]V=\dfrac{s^2h}{3}[/tex]
Hence the required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.
The combined height of one oak tree and one pine tree is 21 meters. The height of 4 oak trees stacked on top of each other is 24 meters taller than one pine tree. How tall is the oak tree and the pine tree
Answer:
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Step-by-step explanation:
Given:
The combined height of 1 oak tree and 1 pine tree = 21 meters
Height of 4 oak trees = 24 meters more than 1 pine tree
To find the height of 1 pine tree and height of one oak tree.
Solution:
Let the height of one oak tree be = [tex]x[/tex] meters.
Let height of one pine tree = [tex]y[/tex] meters.
Combined height can be given as :
[tex]x+y=21[/tex]-------------[1]
Height of 4 oak trees = 24 meters more than 1 pine tree
The above statement can be given as :
[tex]4x=24+y[/tex]------------[2]
Rearranging equation [2] by subtracting both sides by [tex]y[/tex].
[tex]4x-y=24+y-y[/tex]
[tex]4x-y=24[/tex]-------------[2]
Adding rearranged equation [2] to [1].
[tex]x+y=21[/tex]
[tex]4x-y=24[/tex]
+--------------------
[tex]5x\ = 45[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
∴ [tex]x=9[/tex]
Plugging in [tex]x=9[/tex] in equation [1]
[tex]9+y=21[/tex]
Subtracting both sides by 9.
[tex]9-9+y=21-9\\\therefore y=12[/tex]
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Match the following. 1 . congruent circles the set of all points in a plane that are at a given distance from a given point in the plane 2 . circle two or more circles that lie in the same plane and have the same center 3 . concentric circles circles that have equal radii 4 . diameter a chord of a circle that contains the center of the circle 5 . radius a segment joining the center of a circle to a point of the circle
Answer:
1 is concentric circles
2 is concentric circles, they have same center
3 is congruent circles, they have equal radii
4 is correct
5 is correct
Step-by-step explanation:
Congruent circles are circles of the same size while concentric circles are circles that have same center but different radii. Diameter is the line passing through the center of a circle joining two points on the circumference while radius is the joining the center of the circle to any point on the circumference.
Benjamin threw a rock straight up from a cliff that was 48 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h = -16 t² + 52 t + 48, how long will it take for the rock to hit the water?
It will take 4 seconds for the rock to hit the water.
To find out when the rock hits the water, we need to determine the time at which the height h becomes 0, because hitting the water means the height is 0.
Given the equation for the height h of the rock as a function of time t:
[tex]\[ h = -16t^2 + 52t + 48 \][/tex]
We set h to 0 and solve for t:
[tex]\[ 0 = -16t^2 + 52t + 48 \][/tex]
This is a quadratic equation. We can solve it using the quadratic formula:
[tex]\[ t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where a = -16, b = 52, and c = 48 .
Plugging in these values:
[tex]\[ t = \frac{{-52 \pm \sqrt{{52^2 - 4(-16)(48)}}}}{{2(-16)}} \][/tex]
[tex]\[ t = \frac{{-52 \pm \sqrt{{2704 + 3072}}}}{{-32}} \][/tex]
[tex]\[ t = \frac{{-52 \pm \sqrt{{5776}}}}{{-32}} \][/tex]
[tex]\[ t = \frac{{-52 \pm 76}}{{-32}} \][/tex]
Now we have two possible values for t:
[tex]\[ t_1 = \frac{{-52 + 76}}{{-32}} \][/tex]
[tex]\[ t_2 = \frac{{-52 - 76}}{{-32}} \][/tex]
[tex]\[ t_1 = \frac{{24}}{{-32}} = -\frac{3}{4} \][/tex]
[tex]\[ t_2 = \frac{{-128}}{{-32}} = 4 \][/tex]
Since time cannot be negative, we discuss, and the only valid solution is t = 4.
Therefore, it will take 4 seconds for the rock to hit the water.
You are asked to draw a triangle with side lengths of 8 inches and 10 inches. What is the longest whole number length that your third side can be? Group of answer choices 18 20 16 21
Answer:
Correct number : c = 16
Step-by-step explanation:
The triangle theorem states that each side of the triangle is smaller than the sum of the other two and larger than their difference. We denote the three sides of a triangle as a, b, and c.
Suppose that a = 8 and b = 10 and as we see b is greater than a , b > a
b - a < c < b + a => 10 - 8 < c < 10 + 8 => 2 < c < 18
from the offered answers we choose number 16
c = 16
God is with you!!!
Answer:
Step-by-step explanation:
if a,b,c are three sides of a triangle,then a<b+c,b<c+a,c<a+b
or in general we can say any side < sum of other two sides.
third side<8+10
or third side <18
Here third side=16
if you are asked smallest side then any side >difference of other two sides.
third side >10-8 or>2
WILL GIVE BRAINLEST NEED HELP ASAP THANK YOU <3
In a race Derek is 10 yards ahead of mike, Mike is 5 yards ahead of Tom, and Ed is 20 yards ahead of Derek. List the runners in order from 1st to 4th.
A. Ed,Derek,Mike,Tom
B. Derek, Tom, Mike, Ed
C. Tom, Ed, Derek, Mike
D. Mike, Tom, Ed, Derek
Answer:
The answer is letter A, Ed, Derek, Mike, Tom
Explanation:
The question is asking for the order from the 1st to the 4th (first to last). All you have to do is to follow the instruction or draw an illustration (if you can).
If Derek is 10 yards ahead of Mike, this means that Derek's position is ahead of Mike.
If Mike is 5 yards ahead of Tom, then this means that Mike's position is ahead of Tom.
If Ed is 20 yards ahead of Derek, then this means that Ed's position is ahead of Derek.
If Derek is ahead of Mike, Mike being ahead of Tom and Ed being ahead of Derek, then you'll be able to tell the positions now.
This means that the 1st runner is Ed, while the second runner is Derek. The third runner is Mike, while the fourth runner is Tom.
Thus, this explains the answer.
The correct order of runners from 1st to 4th based on their positions relative to each other is Ed, Derek, Mike, Tom. This placement was determined by analyzing the distances between each runner as provided.
Explanation:To solve this problem, let's visually represent the position of each runner in relation to each other based on the information provided. We start by listing the distances given in the question: Ed is 20 yards ahead of Derek, Derek is 10 yards ahead of Mike, and Mike is 5 yards ahead of Tom. This information allows us to order the runners from first to last.
At the front, we have Ed; since Ed is 20 yards ahead of Derek, Ed is in the lead.Following Ed, we have Derek; Derek is placed here because we are told he is 20 yards behind Ed.After Derek comes Mike, who is 10 yards behind Derek but ahead of Tom by 5 yards.Last, we have Tom, who is 5 yards behind Mike, making him the last in this sequence.Therefore, the correct order from 1st to 4th is Ed, Derek, Mike, Tom, which corresponds to option A. Ed,Derek,Mike,Tom.
Tiva earns $48 of 6 hours of babysitting. Complete each statement if Tiva keeps earning her babysitting money at this rate. For 8.5 hours of babysitting Tiva will earn? If Tiva babysits for Hours, she will earn $35.
Answer:
67
Step-by-step explanation:
48=6
35=8.5
67
Answer:
A.)$68
B.)$32
Step-by-step explanation:
For 8.5 hours of babysitting, Tiva will earn $ 68
If Tiva babysits for 4 hours, she will earn $32.
Solve |2x - 2| < 8
A) { x| x < -3 or x > 5}
B) { x|-5 < x < 3}
C) { x|-3 < x < 5}
Josie took a long multiple choice test. The ratio of the questions she got incorrect to the number of problems she got correct was 4:9. If there were 65 questions on the test, how many did Josie get incorrect
Answer:20 incorrect questions
Step-by-step explanation: using the ratio formula
Add up the correct n incorrect
4+9= 13 is the total ratio
Incorrect answer ratio is 4
So to know the number of incorrect answer is
4/13* number of questions on the test
4/13* 65= 20 incorrect answer
Four out of 12 pieces of fruit in the basket are apples.Select all the fractions below that are equivalent to the fraction of fruit that is apples. 3/6 1/3 2/6 1/4 1/6
Four out of twelve converts to the fraction
4/12
if both sides are divided by four, you can simplify this fraction to
1/3
therefore, a is correct
1/3 times two makes
2/6
therefore, c is correct
1/3 has no more multiples in this selection
The equivalent fraction are 1/3 and 2/6.
What is Fraction?The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.
How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned in the fraction's upper portion.
Given:
Four out of twelve converts to the fraction
= 4/12
Now, simplifying the fraction we get
= 4/12
= 1/3
Now, 3/6 = 1/2
2/6 = 1/3
Hence, the equivalent fraction are 1/3 and 2/6.
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Perform the indicated operation. 5/8-[1/2-(-1/4)]
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Solution:
Given that, we have to perform the indicated operation
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})][/tex]
We can use BODMAS rule to perform the operation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
So, in the given expression, we have to solve for brackets first
Solve the innermost bracket
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}][/tex]
Now solve the bracket again
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}] = \frac{5}{8}-[\frac{4+2}{8}] = \frac{5}{8}-[\frac{6}{8}][/tex]
Now remove the parenthesis
[tex]\rightarrow \frac{5}{8} - \frac{6}{8}[/tex]
Now perform subtraction operation
[tex]\rightarrow \frac{5}{8} - \frac{6}{8} = \frac{5-6}{8} = \frac{-1}{8}[/tex]
Thus we got,
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Thus the indicated operation is performed
Zacarías and paz together have $756.80 if Zacarías has $489.50, how much does Paz have? Write and solve an addition equation to find how much money belongs to Paz.
ANSWER: Paz have $267.30
STEP BY STEP EXPLANATION
Let be Z for Zacarías and P for Pax
Z+P= 756.80
Z= 489.50
P=756.8 - Z
P=756.80 - 489.50
P= 267.30
In a computer catalogue, a computer monitor is listed as being 19 inches. This distance is the diagonal across the screen. If the height is 10 inches, what is the width to the nearest inch?
Answer:
[tex]3\sqrt{29}[/tex] or approximately 16.16
Step-by-step explanation:
The diagonal (hypotenuse) mesures 19 inches.
The height of the computer monitor is 10 inches.
Use the Pythagorean theorem:
a and b are the triangle's legs
h is the hypotenuse
[tex]a^{2} + b^{2} = c^{2}\\ \\a^{2} + 10^{2} = 19^{2}\\ \\361 - 100 = a^{2}\\ \\a = \sqrt{261} \\\\a = 3\sqrt{29}[/tex]
What is [tex]x^{4} (x^{4} )[/tex]?
I will thank, comment and mark as Brainliest!
Answer:
The answer is x^8
Step-by-step explanation:
x^4(x^4)
=x^4*x^4
=(x*x*x*x)*(x*x*x*x)
=x*x*x*x*x*x*x*x
=x8
Question 3 1 10 (1 point)
Question Attempt 1 of Unlimited
Incorrect
Your answer is incorrect
The diameter, D. of a sphere is 12.2 mm Calculate the sphere's volume, V.
Use the value 3.14 for 11, and round your answer to the nearest tenth (Do not round any intermediate computations.)
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Recheck
Answer:
V≈950.3
Step-by-step explanation:
d = 12.2mm
r = 1/2 d = 6.1
V = 4/3 Pi r^3
V = 1.33 (3.14) (6.1)^3
V = 950.3
what is 32% of 240 PLEASE I WILL GIVE BRAINLIEST
Answer:
76.8
Step-by-step explanation:
How many different ways can a teacher select 3 students from a class of 15 students to each perform a different classroom task?
Answer: 455ways
Step-by-step explanation:
This can be done according to rule of combination because it talks about selection.
In order to select r object from a pool of n objects, it is represented as nCr = n!/(n-r)!r!
Therefore to select 3 students from a class of 15students, this will give us 15C3.
15C3 = 15!/(15-3)!3!
= 15!/12!3!
= 15×14×13×12!/12!×6
= 15×14×13/6
= 455ways
This selection can be done in 455ways
The question is an illustration of combination
There are 455 ways of selecting the students
The number of students is 15, and the students to select are 3.
So, the number of selections is:
[tex]*nC_r = \frac{n!}{(n -r)!r!}[/tex]
This gives
[tex]^nC_r = \frac{15!}{(15 -3)!3!}[/tex]
Evaluate
[tex]^nC_r = 455[/tex]
Hence, there are 455 ways of selecting the students
Read more about combination at:
https://brainly.com/question/1216161
Choose which statement is true.
Question 3 options:
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2+13x+5 because the following are like term pairs: 6x^2+5x^2 and −2x+15x
The product of (2x−5)(x^2+3x−1)is 2x^3−11x^2−17x+5 because the following are like term pairs: −6x^2−5x^2 and −2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2−13x+5 because the following are like term pairs: 6x^2+5x^2 and 2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+x^2−17x+5 because the following are like term pairs: 6x^2−5x^2 and −2x−15x
The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the correct statement about the expression.
Now, We have;
The expression is,
⇒ (2x - 5) (x² + 3x - 1)
Hence, We can simplify as;
⇒ (2x - 5) (x² + 3x - 1)
⇒ (2x³ + 6x² - 2x - 5x² - 15x + 5
⇒ 2x³ + x² - 17x + 5
Thus., The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
Learn more about the multiplication visit:
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There are a total of 32 staff members working in the aquarium 5/8 of the staff are security guards. How many security guards are there in the aquarium
Answer:
Step-by-step explanation:
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20 security guards
There were total 20 security guards.
What is fraction?Fractions are used to represent smaller pieces of a whole.
Given that, There are a total of 32 staff members working in the aquarium, 5/8 of the staff are security guards.
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20
Hence, there were 20 security guards.
For more references on fractions, click;
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