Answer:
The simplified result is: [tex]\frac{5a^3}{3}[/tex]
Step-by-step explanation:
[tex]a^2.\frac{a^{3}+a^2b }{5a}.\frac{25}{3b+3a}[/tex]
We need to solve the above equation.
We take a^2 common from a^3+a^2b
and we take 3 common from 3b+3a
Solving,
[tex]a^2\:\frac{a^2\left(a+b\right)\:}{5a}\frac{25}{3\left(b+a\right)}[/tex]
Since a+b = b+a we can cancel them with each other.
[tex]=a^2\:\frac{a^2}{5a}\frac{25}{3}\\=a^2\:\frac{a^2}{a}\frac{5}{3}\\=a^2\:a\:\frac{5}{3}\\=\frac{5a^3}{3}[/tex]
So, The simplified result is: [tex]\frac{5a^3}{3}[/tex]
The simplified expression is (5(a + b)) / (3a(b + 1)).
To simplify the given expression, we'll perform the indicated operation step by step:
a² * [(a³ + a²b) / 5a] * [25 / (3b + 3a)]
Step 1: Cancel common factors within each fraction:
a² * [(a³ + a²b) / (5a)] * [25 / (3(b + a))]
Step 2: Simplify further:
(a³ + a²b) * [25 / (5a * 3(b + a))]
Step 3: Factor out common terms:
(a²(a + b)) * [25 / (15a(b + a))]
Step 4: Cancel common factors between numerators and denominators:
(a + b) * (25 / (15a(b + a)))
Step 5: Simplify further:
(25(a + b)) / (15a(b + a))
Step 6: Factor out common terms again:
(25(a + b)) / (15a * a(b + 1))
Step 7: Cancel common factors:
(5(a + b)) / (3a(b + 1))
So, the simplified expression is (5(a + b)) / (3a(b + 1)).
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Solve the equation by graphing x2+5x+4=0 . If exact roots cannot be found, state the consecutive integers between which the roots are located.
Answer:
x = -4
x = -1
Step-by-step explanation:
We have been given the following quadratic equation;
x^2 + 5x + 4 = 0
We are required to determine the roots of the above quadratic equation via graphing.
To do this we formulate the following equations;
y = x^2 + 5x + 4
y = 0 (x -axis)
We then proceed to graph these functions on the same graph. The roots of the original quadratic equation will be the points where the graphs of the above functions will intersect.
The attachment below is the graphical solution obtained from desmos graphing tool;
The graph of the functions intersect at;
x = -4 and x = -1
These are the roots of the given quadratic equation
marcel said he can find 52 times 10 by adding a 0 to the end of 52 to get 520 is he correct?
Answer:
Yes he is Correct
Step-by-step explanation:
When multiply with numbers like 10,100,1000 ect or even like 20,200,2000 then you have to break it down. Since multiply by zero equals 0 anyways you will only have to focus on the number that is in front of it. And just and the zeros to the back of the number.
Answer:
Yes he is correct
Step-by-step explanation:
Whenever we are multiplying any number with 10 or multiples of ten we simply add the zeros to the end of that number.
For example:
134 x 10 = 1340
As you can see, to get the answer, you simply need to add 0 to the end of 134
Also 10 x 10 = 100
To get the answer we simply added zero to the end of ten which then give us 100
12 x 10= ? all you need to do is to add zero to the end of 12 which will give us 120
13 x 100 =? In this case, since the zeros are two, you will simply add two zeros to the end of 13 which will give you the answer 1300
So Marcel can find 52 times 10 by simply adding a 0 to the end of 52 to get 520 as the correct answer.
The weight of a basketball is normally distributed with a mean if 17 oz. And a standard version deviation of 2 oz. Suppose 50j0 different basketballs are in a warehouse. How many basketballs weigh more than 19 oz?
There would be 3 basketballs?
3 basketball because subtract
Heather received a 32% discount on a $34 shirt. After the 7% sales tax was added, how much did she pay for the shirt.
Answer:
24,74
Step-by-step explanation:
the price with tax= 34 : 100 x 107= 36.38
( start price : 100% x 100% with the 7% tax)
now you can calculate the discount = 36.38 ; 100 x 68= 24.74
( start price : 100% x 68 because the full price is 100% but there goes 32 from off so 100-32 = 68)
A percentage is a way to describe a part of a whole. The final cost of the shirt is $24.74.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The original cost of the shirt is $34, now since a 32% discount is given the cost will be,
$34 - (32% of $34)
= $34 - $10.88
= $23.12
Further, 7% tax is paid on the cost of the shirt after the discount, therefore, the final cost will be,
Final cost = $23.12 + (7% of $23.12) = $24.74
Hence, the final cost of the shirt is $24.74.
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Charlotte puts a present in a box with a length of 114 ft, a width of 34 ft and a height of 1 foot.
What is the least amount of wrapping paper needed to cover the present box?
Answer:8048ft
Step-by-step explanation: A=2(wl+hl+hw) so 2(34*114)+(1*114)+(1*34)=8048
Help pleaseeeeeeeeeeee
Answer:
C
Step-by-step explanation:
Charlene has 8 more dollars so you would have to add it all together to get 86.
What type of relationship does this pair of angles have? 161 and 19 degrees
Answer:
There are supplementary
Step-by-step explanation:
The sum of the given angles is 180 degrees. So, the given angles are supplementary angles.
Important information:
The measures of two angles are 161 and 19 degrees.We need to find the type of relationship between the given angles.
Supplementary angles:Two angles are called supplementary angles if their sum is 180 degrees.
The sum of given angles is:
[tex]161^\circ+19^\circ=180^\circ[/tex]
The sum of the given angles is 180 degrees. So, the given angles are supplementary angles.
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What is the greatest common factor of the terms in the polynomial 4x^4-32x^3-60x^2?
Answer:
4x^2
Step-by-step explanation:
hope this helps :)
Answer:
ITS CCCCCCCCCCC (4x^2)
The dot plot below shows the number of wings contestants in a wing-eating contest ate.
What is the mean absolute deviation of the data set shown?
A. 18
B. 18.1
C. 3
D. 1.52
Answer:
the answer is D. 1.52
Step-by-step explanation:
you want to add all the numbers then divide by 10
15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21
10
then you find the difference between the mean and data point
Data point = 15 15 17 18 18 18 19 20 20 21
Mean Diff = 3.1 3.1 1.1 0.1 0.1 0.1 .9 1.9 1.9 2.9
then add the differences
3.1 + 3.1 + 1.1 + 0.1 + 0.1 + 0.1 + .9 + 1.9 + 1.9 + 2.9 and divide by 10
10
absolute deviation is 1.52 wings.
The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.
What is mean?The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.
here, we have,
we want to add all the numbers then divide by 10
15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21
__________________________________
10
then you find the difference between the mean and data point
Data point = 15 15 17 18 18 18 19 20 20 21
Mean Diff = 3.1 3.1 1.1 0.1 0.1 0.1 .9 1.9 1.9 2.9
then add the differences
3.1 + 3.1 + 1.1 + 0.1 + 0.1 + 0.1 + .9 + 1.9 + 1.9 + 2.9 [and divide by 10]
_______________________________________
10
=1.52
absolute deviation is 1.52 wings.
Hence, The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.
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What is the value of x?
Enter your answer in the box.
Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of squares on the other 2 sides, that is
x² + 12² = 13²
x² + 144 = 169 ( subtract 144 from both sides )
x² = 25 ( take the square root of both sides )
x = [tex]\sqrt{25}[/tex] = 5
Answer:
x = 25
Step-by-step explanation:
We are given a right angled triangle and we are to find the value of x.
For that, we will use the Pythagoras Theorem.
[tex] 1 3 ^ 2 = x ^ 2 + 1 2 ^ 2 [/tex]
[tex] 1 6 9 = x ^ 2 + 1 4 4 [/tex]
[tex] x ^ 2 = 1 6 9 - 1 4 4 [/tex]
[tex] x ^ 2 = 2 5 [/tex]
Taking square root on both sides to get:
x = 25
Suppose P(A) =0.9, P(B) = 0.6, and P(B|A) = 0.2. What is P(A|B)
A) 0.36
B)0.45
C)0.3
D)0.6
P(B|A): P(A and B) / P(A)
P(A and B): P(A)•P(B) so 0.9 • 0.6 = 0.54
P(A|B): 0.54 / 0.9 = 0.6
Answer: D) 0.6
The value of the conditional probability is given by Bayes theorem and the value of P ( A | B ) = 0.1333
What is Bayes Theorem?The likelihood that an event will occur based on the likelihood that a comparable outcome will occur in the future. The theorem offers a method for updating existing predictions or hypotheses in light of fresh or updated data. This is known as conditional probability.
Bayes Theorem states that based on past knowledge of circumstances that could be relevant to the occurrence, the Bayes Theorem estimates the likelihood of an event.
And , P ( A | B ) = [ P ( B | A ) P ( B ) ] / P ( A )
Given data ,
Let the conditional probability be represented as P
Now , the value of P ( A ) = 0.9
The value of P ( B ) = 0.6
The value of P ( B | A ) = 0.2
From the Bayes theorem , we get
P ( A | B ) = [ P ( B | A ) P ( B ) ] / P ( A )
On simplifying , we get
P ( A | B ) = [ 0.2 x 0.6 ] / 0.9
P ( A | B ) = 0.12 / 0.9
P ( A | B ) = 0.1333
Hence , the Bayes theorem is solved
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Which is the graph of the function f(x)=x^2+2x+3
Answer:
not one of those two...
Step-by-step explanation:
are there other options? when graphed on desmos it looks like this...
The graph of the given function f(x) = x² + 2x + 3 is attached with the answer. It is not from the given two options.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given equation is quadratic f(x) = x² + 2x + 3 so the curve on the graph will be parabolic.
When we put the different values of x in the input function f(x) the output function varies in the form of the parabolic curve the equation is quadratic so it will give two solutions which cut the axis at the points ( 0,3) you can see in the attached graph.
I have attached the correct graph showing the given quadratic equation with the answer below.
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What is the sum of the two vectors (-1,-4) and (3,5)
Answer:
Step-by-step explanation:
[tex]a(-1, -4)\\b(3, 5)\\a + b(2, 1)[/tex]
The sum of the vectors is (2,1)
How to find the sum of two vectors?A vector exists as an object that has both a magnitude and a direction. Geometrically, we can imagine a vector as a directed line segment, whose length exists the magnitude of the vector and with an arrow suggesting the direction. The direction of the vector exists from its tail to its head.
(-1,-4) + (3,5)
( -1+3 , -4+5 )
( 2,1)
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PLEASE HELP WILL MARK BRAINLIEST
-SEE ATTACHMENT-
ANSWER
[tex](x - 5) ^{5} = {x}^{5} - 25 {x}^{4} + 250 {x}^{3} - 1250 {x}^{2} + 3125x- 3125[/tex]
EXPLANATION
From the Pascal's triangle,
The coefficients are :
1, 5, 10,10, 5,1
Because of the negative sign, the expansion will alternate sign.
[tex](x - y) ^{5} = {x}^{5} - 5 {x}^{4} y + 10 {x}^{3} {y}^{2} - 10 {x}^{2} {y}^{3} + 5x {y}^{4} - {y}^{5} [/tex]
We now put y=5 into the expansion to get,
[tex](x - 5) ^{5} = {x}^{5} - 5 {x}^{4} (5) + 10 {x}^{3} ( {5}^{2}) - 10 {x}^{2} ({5})^{3} + 5x( {5})^{4} - {5}^{5} [/tex]
[tex](x - 5) ^{5} = {x}^{5} - 25 {x}^{4} + 250 {x}^{3} - 1250 {x}^{2} + 3125x- 3125[/tex]
Answer:
(x - 5)^5 = x^5 - 25x^4 + 250x³ - 1250x² + 3125x - 3125
Step-by-step explanation:
The explanation in the attached file
What number replaces the ◊?
15 = 15
15 + 4 + ◊ = 15 + 7
A. 3
B.4
C.19
D. 22
Answer:
The answer is A.
15 + 4 + 3 = 15 + 7
A. 3
First, simplify the equation. (x means the same thing as the symbol)
19 + x = 22
Subtract 19 from both sides of the equation.
x = 22 - 19
x = 3
There’s the answer!
The box and whisker plot displays a set of data obtained from a marketing survey. Drag each item to the appropriate position on the number line. Drag the extra item to the box not associated with the number line.
Choices...
mean
median
outlier
minimum number in summary of data
picture is where these are suppose to go
Answer:
the one for the arrow point to #26 is min # in summary of data
the one where the arrow points between#30 and 32: median
arrow pointing to #44 is: outlier
and the bottom choice is: mean
Step-by-step explanation:
What is the interquartile range of the following data set? 45,12,48,96,61,84,29,1,72,5,14
Answer:
60
Step-by-step explanation:
Population size : 11
To calculate inter-quartile range
Order the data from least to greatest.Find the median.Calculate the median of both the lower and upper half of the data.The IQR is the difference between the upper and lower medians.Step 1
1, 5 , 12 ,14 , 29 , 45 , 48, 61 , 72 , 84 , 96
Step 2
medium = 45
Step 3
Q1
1 , 5 , 12 ,14 , 29
median = 12
Q3
48 , 61 , 72 , 84 , 96
median = 72
Step 4
IQ = Q3 - Q1
= 72 - 12
= 60
Answer: 60
Step-by-step explanation: Apex said so
subtract (-9x^2+8x-14) from the sum of (-9x^2-10x) and (3x^2+3x+7)
Answer:
[tex]3x^2 - 15x + 21\\or\,\,3(x^2 -5x +7)[/tex]
Step-by-step explanation:
First we will find sum of [tex](-9x^2-10x)\,\, and\,\, (3x^2+3x+7)[/tex]
Adding the like terms:
[tex]= -9x^2-10x + 3x^2 +3x+7\\= -9x^2+ 3x^2 -10x+3x+7\\= -6x^2 - 7x +7[/tex]
Now subtract (-9x^2+8x-14) from (-6x^2 - 7x +7)
[tex]=(-6x^2 - 7x +7) - (-9x^2+8x-14)\\= -6x^2 - 7x +7 +9x^2-8x+14\\= -6x^2 +9x^2 - 7x -8x+7 +14\\= 3x^2 - 15x + 21\\=3(x^2 -5x +7)[/tex]
Write a subtraction problem involving pounds and ounces. Solve the problem and show your work.
Answer: Edgur eats 12 ounces of popcorn. Before he ate any, he had 2 pounds of popcorn. How much popcorn, in ounces, of popcorn does Edgur have now? Edgur has 20 ounces of popcorn.
Step-by-step explanation:
Pounds to ounces: 1 pound = 16 ounces.
2 * 16 = 32.
He ate 12 of those ounces. 32 - 12 = 20.
Final answer:
To solve a problem involving subtraction of pounds and ounces, convert everything to ounces, subtract, and convert back if necessary. In this example, after removing 3 pounds 5 ounces from 9 pounds 8 ounces, the remaining weight is 6 pounds 3 ounces.
Explanation:
Let's create a subtraction problem involving pounds and ounces. Imagine you have a sack of potatoes weighing 9 pounds 8 ounces, and you remove a bag of potatoes weighing 3 pounds 5 ounces. How much does the sack of potatoes now weigh?
First, we need to ensure that both weights are in the same units. We have:
Initial weight: 9 pounds 8 ounces
Weight removed: 3 pounds 5 ounces
To subtract these weights, we will convert pounds to ounces for each weight, then subtract, and finally convert back to pounds and ounces if necessary.
Convert 9 pounds to ounces: 9 × 16 = 144 ounces
Therefore, the initial weight in ounces is 144 ounces + 8 ounces = 152 ounces.
Convert 3 pounds to ounces: 3 × 16 = 48 ounces
The weight removed in ounces is 48 ounces + 5 ounces = 53 ounces.
Subtract the smaller weight from the initial weight: 152 ounces - 53 ounces = 99 ounces
Now we convert 99 ounces back to pounds and ounces. Since 1 pound is 16 ounces:
99 ÷ 16 = 6 pounds with a remainder of 3 ounces.
So, the sack of potatoes now weighs 6 pounds 3 ounces.
Which situation could the expression 1/4÷3 represent A 1/4 of a package of pencils shared equally among three friends. B the number of 1/4 cup servings in three cups of popcorn C 1/3 of a stadium split into four equal sections or D a four-foot-long rope cut into 1/3 -foot pieces
"1/4 of a package of pencils shared equally among three friends" this expression represents expression [tex]\frac{1}{4} /3[/tex].
What is Division?
The action of separating something into parts or the process of being separated is known as Division. Ex: "The division of the land into small fields"
The meaning of the given expression is to divide one fourth part into three persons.
This is clearly represents in option A....1/4 of a package of pencils shared equally among three friends.
Thus, option A express perfectly for the given expression [tex]\frac{1}{4} /3[/tex] as "1/4 of a package of pencils shared equally among three friends".
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Final answer:
The expression 1/4÷3 matches Scenario A, which represents 1/4 of a package of pencils being shared equally among three friends.
Explanation:
The expression 1/4÷3 represents taking one fourth of something and then dividing it into 3 equal parts. Out of the scenarios provided:
Scenario A is about sharing 1/4 of a package of pencils among three friends, which can be represented by this expression.Scenario B involves calculating the number of 1/4 cup servings in three cups, which would imply multiplying, not dividing, so it doesn't fit.Scenario C speaks of splitting 1/3 of a stadium into four sections, which also does not align with the expression.Scenario D is about cutting a four-foot-long rope into pieces that are each 1/3-foot in length. This implies a different division than the one in the expression.Therefore, the expression 1/4÷3 best matches with Scenario A, where 1/4 of a package of pencils is shared equally among three friends.
Ryan is buying a triangular tract of land. The triangle has a base of 100 yards and a height of 30 yards. What is the area of the tact to land? HELPPPP PLZZZ
Answer:may be crazy but its 300.
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
Area is multiplying the numbers together basically. 100*30=300.
need help asap!!!
A baseball team averages one win to every one loss.The coach tosses three coins to simulate three games.Heads represents a win and tails represents a loss.The results of 10 coin tosses are shown.Find the experimental probability of 3 losses.
(A)1/5
(B)1/4
(C)1/2
A is the correct answer
Answer:
(A) 1/5Step-by-step explanation:
The experimental probability is defined as the ratio between the number of time certain events occurs and the total number of trials.
In this case, there are 10 coin tosses. Notice that there are only two events where the lose three times, that means the probability is
[tex]P=\frac{2}{10}=\frac{1}{5}[/tex]
Which means that in two cases out of ten the lose three games.
Therefore, the right answer is A.
8 Look at the following nutrition label.
Nutrition Facts
Serving Size 1/2 cup (1159)
Servings Per Container About 4
Amount per serving
Calories 250
Calories from Fat 130
% Daily Value
22%
45%
Total Fat 14g
Saturated Fat 9g
how many calories are in 1 cup?
Final answer:
To find the number of calories in one cup, we double the amount of calories in a 1/2 cup serving. In this case, 250 calories are in 1/2 cup, so 500 calories are in one full cup.
Explanation:
To calculate the number of calories in one cup based on the given nutrition label, we can use a simple multiplication. Given that 1/2 cup contains 250 calories, we just need to double this amount, because 1 cup is equivalent to two servings of 1/2 cup each.
The equation to find the calories in one cup is:
Calories per 1/2 cup × 2 = Calories per cup
Therefore, the calculation would be:
250 calories × 2 = 500 calories
So, one cup of the food item contains 500 calories.
Write an equation with the point (3,7) and has a slope of 7
Answer:
slope = 7 and point = (3, 7)
b = y - slope*x
b = 7 -7 * 3
b = -14
Then we enter "b" and the slope into this equation:
y = 7x -14
Step-by-step explanation:
Which Value Is The Eighth Term In The Sequence?
A. -3125
B. -125
C. -625
Answer:
C
Step-by-step explanation:
Substitute n = 8 into the explicit rule
[tex]a_{8}[/tex] = - [tex]\frac{1}{125}[/tex] × [tex]5^{7}[/tex]
= - [tex]\frac{1}{5^{3} }[/tex] × [tex]5^{7}[/tex]
= - [tex]5^{4}[/tex] = - 625 → C
Geometry pls help
will give 30 points
The 1st and 4th ones
Answer: the correct answers are
1. <EGO ≈ <EOG
4. TW = 1/4GO
Step-by-step explanation:
1. all the angles are corresponding therefore it’s correct
4. TW is 1/2 of PQ therefore it would be 1/4 of GO
An artist made purple paint by mixing 1/2 quart of red paint and 3/4 quart of blue paint. What is the ration of red paint to blue paint in simplest form
Answer:
(1/2)/(3/4) = (1/2)(4/3) = 2/3
Step-by-step explanation:
what is 18 mm in cm's
Answer: 1.8 centimeters hope this helps i really need brainlist :)
Answer: answer is 1.8cm
Step-by-step explanation: take 18 and add a decimal in front then move it back 1
What is the length of XY
Answer:
F. 2cmStep-by-step explanation:
If RSTU ≅ XWZY, then RS = XW, RU = XY, ST = WZ and TU = ZY.
RU = 2cm. Therefore XY = 2cm.
A bag contains 10 counters. 6 of them are white. a counter is taken at random and not replaced. A second counter is taken out of the bag at random. Calculate the probability that only one of the two counters are white
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
The ways we can get "1 counter to be white out of 2 draws" is:
1. If 1st one taken out is white and next one different color, and
2. If 2nd one taken out is white and 1st one different color
In probability, AND means MULTIPLY and OR means ADD
Here, we are actually looking for ways of 1st one white, next one different OR first one different and next one white. Let's find them separately.
1. If 1st one taken out is white and next one different color
there are 6 white and 10 total, so 1st one white is 6/10
not replaced, so now there are 9 total and 4 of them are different,so different probabililty is 4/9
We multiply these two to get: 6/10 * 4/9 = 4/15
2. If 2nd one taken out is white and 1st one different color
probabilty 1st one different color is 4/10 since 4 are different and we have total of 10
since not replaced, now we have 9 total and still 6 white.
probability of white in 2nd draw is 6/9
We multiply these two to get: 4/10 * 6/9 = 4/15
Now we add these 2 as stated earlier, so 4/15 + 4/ 15 = 8/15
Answer:
Step-by-step explanation: