Answer: 12x3−21x2+67x−15
Step-by-step explanation:
(3x−5)(4−9x)+(2x+1)(6x2+5)
=12x+−27x2+−20+45x+12x3+10x+6x2+5
=12x+−27x2+−20+45x+12x3+10x+6x2+5
=(12x3)+(−27x2+6x2)+(12x+45x+10x)+(−20+5)
=12x3+−21x2+67x+−15
Answer:
12x^3 - 21x^2 + 67x - 15!
Step-by-step explanation:
A box contains 6 red balls, 7 yellow balls, and 2 green balls. All the balls are the same except for their color, Jaime picks a ball from the
box, records the color, then returns the ball to the box. He does this 3 times
What is the probability that all three balls that Jaime picked were red?
Answer:
The answer is 8/27
The probability that all three balls that Jaime picked were red is '0.064'
Now the box contains 6 red balls, 7 yellow balls, and 2 green balls
Thus the total number of balls in the box can be find by summing up all the balls in the box
Thus we get,
Total number of balls = 6 + 7 + 2 = 15 balls
Thus there are total of 15 balls in the box
Now Jamie picks a ball from the box, records the color, then returns the ball to the box.
Thus in the first try, the probability that the ball picked up is red:
Probability that the first ball picked is red = [tex]\frac{6}{15}[/tex]
where, '6' is the number of red balls
and '15' is the number of total balls in the box
Similarly as the ball picked up is again returned to the box the number of red balls and total number of balls won't change
Similarly probability that the second ball picked is red = [tex]\frac{6}{15}[/tex]
Similarly probability that the third ball picked is red = [tex]\frac{6}{15}[/tex]
Thus to find the combined probability we need to multiply all three probabilities
Thus probability that all three balls that Jaime picked were red is,
[tex]\frac{6}{15} *\frac{6}{15} *\frac{6}{15} = \frac{36}{225}* \frac{6}{15}\\ \frac{6}{15} *\frac{6}{15} *\frac{6}{15} =\frac{216}{3375}\\ \frac{6}{15} *\frac{6}{15} *\frac{6}{15} =0.064[/tex]
Thus '0.064' is our required answer
Using the properties of shapes, explain why all parallelograms are trapezoids.
Answer:
All parallelograms are trapezoids.
Step-by-step explanation:
A parallelogram has two pairs of parallel sides. A trapezoid has at least one pair of parallel sides. So if all parallelograms have two pairs, they are in the same category of the trapezoids.
Final answer:
A parallelogram is considered a trapezoid because it has at least one pair of parallel sides, which fits the basic definition of a trapezoid. Parallelograms have additional properties like equal opposite sides and angles, but these do not contradict the broader trapezoid classification.
Explanation:
Why All Parallelograms Are Trapezoids
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. A parallelogram, by definition, has two pairs of parallel sides. Therefore, since a parallelogram inherently possesses at least one pair of parallel sides, it meets the minimum criterion to be considered a trapezoid. This logical inclusion is based on the definition of shapes within geometry, and thus all parallelograms can be classified as trapezoids.
Properties of Parallelograms and Trapezoids
Parallelograms have some additional properties that trapezoids don't necessarily share, such as opposite sides being equal in length and opposite angles being equal. This does not, however, preclude them from the broader categorization of trapezoids because those extra properties do not contradict the definition of a trapezoid.
Applying similar triangles and their properties, although useful for understanding relationships between different shapes, is not directly necessary for explaining why parallelograms are trapezoids. Instead, it's the fundamental definitions of these shapes that establish the relationship between parallelograms and trapezoids. The Theorem 26 states that any triangle is always of equal area to a certain parallelogram having an equal base and half the altitude. While this theorem relates parallelograms to triangles, it does not affect the classification of parallelograms as trapezoids.
28 - 6(2x + 4) = 124
Answer: x = -12 is the correct answer
Step-by-step explanation: the moderator that deleted this if is so wrong then just tell me why is wrong if you are so smart.
If you're driving at 25 miles per hour through a school zone and a child runs out in front of you, how much distance will
your car cover before stopping?
Answer:
depending on the car type
probs about 5-10 feet
Step-by-step explanation:
Laura is looking for a way to save money this year on her medical expenses. Insurance is starting to get expensive, and her budget is tight. She figures that she has a 75% chance of needing to visit the doctor and get medication once in the winter, for a total of about $400. She also figures there should be some room in the budget for emergencies, so she estimates a 5% chance she will need to spend $300 at an emergency room.
Is it reasonable for Laura to set her medical budget at $300 for the year?
Answer: A
Step-by-step explanation: The expected value is over $300, so Laura will likely need more money to cover her expenses.
its not that hard
It's not reasonable for Laura to set her medical budget at $300 for the year. Considering her predicted medical expenses, her expected annual cost is $315, making her budget slightly understated.
Explanation:The answer to whether Laura's medical budget of $300 for the year is reasonable or not involves a concept in probability known as expected costs. Let's consider both events: there is a 75% chance of spending $400 and a 5% chance of spending $300.
We calculate the expected cost for both scenarios:
The expected cost for the doctor visit and medication is 0.75 * $400 = $300The expected cost for emergency spending is 0.05 * $300 = $15
Adding these costs, we find that her expected annual medical costs are $315, not $300. Therefore, Laura might need to reconsider her budget, possibly increasing it slightly.
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There are 13 chickens and 9 roosters. What is the
ratio of chickens to roosters in lowest terms?
Answer:
13/9 or 1 4/9
Step-by-step explanation:
Evaluate the expression
2,322÷27
this will equal 86 is the anwer to question u have asked
Answer:86
Step-by-step explanation:
Step 1:Put 2,332 the (dividend) in the brackets,(in the box)
The divisor is 27 ,so it's outside of the brackets or outside of the box
Step 2:What is 232 into 27 , the reason I skipped 2 and 3 because there smaller than 27. 232 into 27 is 8 because it's closest to 232 which is 216 because 27*8 equals 216. 8 is now on top of the bracket and now you subtract 232-216 which is 16.
Step 3:Bring down 2 ,because 2 is the last number left.
Now we have to figure out what goes into 162
6 goes into 162 because 27*6=162
Step 4:Subtract 162-162=0
We stop because there's no more to go into unless it was a different number than 162 then we would of brung down the 0 because there's no more numbers after 2 and the number would of been a decimal but there's no more to go into.
6 down goes above the bracket next to 8 now we have an answer of 86.
So the quotient/answer=86
Explain how you can use multiplication to find the quotient 3/5 ÷ 3/15 then evaluate
To divide two fractions, multiply them by their reciprocals.
3/5 / 3/15
3/5 * 15/3
45/15
3
The perimeter of a rectangle is 38 in. The width
is 6 in. shorter than the length. Find the width
of the rectangle.
Good evening ,
______
Answer:
w=6.5in
___________________
Step-by-step explanation:
L : length
w : width
p : perimeter
38=2L+2w
38 =2(w+6)+2w
38 = 4w+12
38-12=4w
26=4w
26/4=w
w=6.5 in.
:)
Henry is 4 years younger than Linda. Linda is 20 years old.
After correctly carrying out the Solve step of the five-step problem-solving plan, which solution should you arrive at to find Henry’s age?
28
24
16
12
Answer:
16
Step-by-step explanation:
20-4=16
pls give brainliest
Find the slope of the line joining each pair of points. Then draw the line in a coordinate plane:
I(5, 2), J(5, −4)
I know this should be infinity or no solutions, but my homework site is marking both answers as wrong. I don't know what else it can be.
Answer:
Step-by-step explanation:
Here slope = (y2-y1)/(x2-x1)
Which comes out to be: (-4-2)/5-5 = -6/0 !!!
But we cannot divide by 0. So the slope is undefined. This is basically a vertical line. The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate.
If your hw website is not accepting undefined as answer then what are the options that it provides?
The capacity of the milk pitcher on the counter is 9/10 liter each one pitcher has3/8 of milk in it and the other pitcher has 5/12 of a liter milk in it much is there altogether?
Answer:
57/80L
Step-by-step explanation:
Given that the capacity (i.e maximum possible volume) of a pitcher is 9/10L
1st Pitcher is 3/8 full of milk
Hence Vol of milk in 1st pitcher = 9/10 x 3/8 = 27/80L
2nd Pitcher is 5/12 full of milk
Hence Vol of milk in 2nd pitcher = 9/10 x 5/12 = 3/8 = 30/80L
Total volume = 27/80 + 30/80 = 57/80L
Final answer:
Adding the milk from the two separate pitchers gives a total of 19/24 liters of milk together.
Explanation:
You are asking about a volume measurement related to liters, which indeed is a unit of capacity. One pitcher contains 3/8 of a liter of milk, and the other pitcher contains 5/12 of a liter. To find out how much milk is there altogether, we will simply add the volumes:
[tex]\(\frac{3}{8} + \frac{5}{12} = \frac{9}{24} + \frac{10}{24} = \frac{19}{24}\) liters[/tex]
To calculate this, we first find a common denominator, which is 24 (the least common multiple of 8 and 12). Then we convert each fraction to an equivalent fraction with a denominator of 24, before adding them together. So, the total amount of milk in both pitchers together is 19/24 liters.
2. Nine more than the opposite of a number is three less than twice the number. What is
the number?
Answer:
The number is 4
Step-by-step explanation:
* Lets revise some words in mathematics and how change them to
mathematical symbols
- More than ⇒ add (+)
- Less than ⇒ subtract (-)
- Twice ⇒ Multiplied by 2 (× 2)
- Opposite of a number ⇒ change its sign (additive inverse of it)
* Now lets solve the problem
- Nine more than the opposite of a number is three less than twice
the number
- Assume that the number is x
∴ 9 more than the opposite of x
- That means find the opposite of x and add it by 9
∵ The opposite of x is -x
∴ Nine more than the opposite of a number = -x + 9
- Three less than twice the number means 3 less than twice x
∵ The number is x
∴ Twice the number = 2 × x = 2x
∵ Three less than twice x = 2x - 3
∴ Three less than twice the number = 2x - 3
- The meaning of "is" between the two the statements is "="
∴ Nine more than the opposite of a number is three less than twice
the number is ⇒ -x + 9 = 2x - 3
* Lets solve the equation to find x
∵ -x + 9 = 2x - 3
- add x in both sides
∴ 9 = 3x - 3
- Add 3 to both sides
∴ 12 = 3x
- Divide both sides by 3
∴ x = 4
∵ x represents the number
∴ The number is 4
* Lets check the answer
9 more than opposite 4 is 3 less than twice 4
9 + (-4) = 2 × 4 - 3
9 - 4 = 8 - 3
5 = 5
The answer is right
The function f(x) = 5One-fifth is reflected over the y-axis. Which equations represent the reflected function? Select two options.
f(x) = One-fifth
f(x) = One-fifthOne-fifthOne-fifth
f(x) = 5One-fifth
f(x) = 5(5)x
f(x) = 5(5)–x
Answer:
The equations that represent the reflected function are
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
[tex]f(x)=5(5)^{x}[/tex]
Step-by-step explanation:
The correct question in the attached figure
we have the function
[tex]f(x)=5(\frac{1}{5})^{x}[/tex]
we know that
A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.
therefore
[tex]f(−x) = f(x).[/tex]
The reflection of the given function across the y-axis will be equal to
(Remember interchanges positive x-values with negative x-values)
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
An equivalent form will be
[tex]f(x)=5(\frac{1}{5})^{(-1)(x)}=5[(\frac{1}{5})^{-1})]^{x}=5(5)^{x}[/tex]
therefore
The equations that represent the reflected function are
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
[tex]f(x)=5(5)^{x}[/tex]
Answer:
c,d
Step-by-step explanation:
PLEASE HELP ME(picture is shown) Set up the equation and find the length of BC
Step-by-step explanation:
From the diagram,
AC = AB + BC
BC = AC - AB
BC = 54 - 25 = 29
whats the answer too -8(x + 4) -6x
Answer:
Step-by-step explanation:
-8(x + 4) -6x = -8 * x + (-8) * 4 - 6x
= -8x - 32 -6x
= -14x -32
Miss Wheeler has 15 3/4 cups of flour in a container she uses one 1/4 cups of flour to make a loaf of bread how much flour does she have left
Answer: 15.5 or 15 1/2
Step-by-step explanation: becuz 15 3/4 - 1/4 = 15.5
The cost of renting a car is $25 per day plus a one-time fee
of $75.50 for insurance. How many days can the car be
rented if the total cost is to be no more than $525? Write
and solve an inequality to find the solution, and graph the
solution on a number line.
For $525 we can rent the car for 17 complete days.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, The cost of renting a car is $25 per day plus a one-time fee
of $75.50 for insurance.
Assuming the no. of days we can rent the car for $525 is x.
∴ 25x + 75.50 ≤ 525.
25x ≤ 449.5
x ≤ 449.5/25.
x ≤ 17.98 Or 17 complete days.
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Evaluate −5(12)^3x for x = 1.
Answer:
x=3
Step-by-step explanation:
Answer: The answer is -8640.
Step-by-step explanation:You would first off by multiplying what's in the parenthesis by its exponent: (12)^3(1)= 1720. Then multiply 1728 by 5 so get your overall correct answer of -8640. Hope I helped you a lot and my answer is correct.!!
(1 point) The histogram below gives the length of service of members of the Department of English at a particular university. The classes, in
years of service, are 0-4.9.5-9.9, etc., and the vertical axis represents the number of faculty
What percent of the department faculty have 5 or more years of service?
Answer
English Faculty
10
15
20
25
Years of Service
To find the percentage of faculty with 5 or more years of service, count the faculty with 5 or more years on the histogram, divide by the total faculty and multiply by 100.
Explanation:The task requires calculating the percentage of English department faculty with 5 or more years of service based on the data presented in the histogram.
Percentages
are calculated by dividing the part by the whole and multiplying by 100. We need to find the number of faculty members (y-axis) corresponding to service years of 5 and above (x-axis) and then calculate it as a percentage of the total faculty. Assume the total number of faculty is T and the number of faculty with 5 or more years of service is F, the percentage can be calculated as (F/T)*100. Please remember to count all the faculty in the histogram values starting from 5 years of service to the end. Ensure to consider these steps of data interpretation when dealing with histograms
.
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The 40% of the department faculty have 5 or more years of service.
To calculate the percentage of department faculty with 5 or more years of service, we can divide the number of faculty with 5 or more years of service by the total number of faculty and multiply by 100%.
% with 5 or more years of service = (number with 5 or more years of service) / (total number of faculty) * 100%
From the histogram, we can see that there are 10 faculty with 5 or more years of service and a total of 25 faculty in the department. Therefore, the percentage of department faculty with 5 or more years of service is:
% with 5 or more years of service = (10 faculty) / (25 faculty) * 100%
% with 5 or more years of service = 40%
Therefore, 40% of the department faculty have 5 or more years of service.
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6 hundreds divided by 10=
2 thousands divided by 10=
Answer:
1. 60 2. 200
Step-by-step explanation:
600÷10= 60
2000÷10=200
Answer:
60 and 200
Step-by-step explanation:
When divideing by 10 you can cancel the zeros from both the numertor and denominator
HURRY PLZZZZ!!!!!!!!!!
The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74, what is the width? Perimeter of rectangle: P = 2l + 2w
i'll give brainliest
Answer:Width = 15 units .
Step-by-step explanation:
Given : The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74,
To find : what is the width.
Solution : We have given perimeter of the rectangle is 74,
Let the Length = x .
According to question :
The width of a rectangle is 4 more than half the length.
Width = 4 + [tex]\frac{x}{2}[/tex].
Perimeter = 2 length + 2 width .
Plugging the values,
74 = 2 ( x ) + 2 (4+[tex]\frac{x}{2}[/tex]).
74 = 2x + 8 + x .
Combine like terms
74 = 2x +x + 8.
74 = 3x +8.
On subtracting both sides by 8.
74 -8= 3x .
66 = 3x
On dividing both sides by 3
x = 22.
Width = Width = 4 + [tex]\frac{22}{2}[/tex].
Width = 4 +11.
Width = 15 units .
Therefore, Width = 15 units .
Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coherent sequence of equations that correspond to your reasoning
Answer:
The required way is shown above.
Step-by-step explanation:
Consider the provided calculation.
304 – 81 is very close to 304 – 100,
Now subtract 100 from 304 mentally, it will gives us 204
Now add 19 as we round 81 to 100.
204 + 19 = 223
So, the answer is 223.
Now write a coherent sequence of equations that correspond to your reasoning.
304 – 81 = 304 – (100 – 19)
= (304 – 100) + 19
= 204 + 19 = 223
Hence, the required way is shown above.
To subtract 81 from 304 mentally, round 81 to 80, subtract from 304 to get 224, and then add 1 to compensate for the rounding, giving a final answer of 225.
Explanation:To calculate 304-81 mentally, we can use the strategy of rounding and compensating. First, we can round 81 up to a number that is easier to subtract from 304, such as 80 or 100, and then we adjust the final result to account for the rounding. Here's how to think through it:
The coherent sequence of equations that correspond to this reasoning would be:
This mental math strategy involves rounding and compensation, which allows us to handle subtraction problems quickly without having to use the standard subtraction algorithm. Checking that the answer makes sense in the context of the original problem is a good practice to ensure accuracy.
Find the nth term of this number sequence
1, 10, 19, 28, ...
Pls help
Answer:
9n - 8
Step-by-step explanation:
The sequence is arithmetic since the difference between consecutive terms is common
d = 10 - 1 = 19 - 10 = 28 - 19 = 9
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 9, thus
[tex]a_{n}[/tex] = 1 + 9(n - 1) = 1 + 9n - 9 = 9n - 8, hence
[tex]a_{n}[/tex] = 9n - 8
We are required to find the nth term of the sequence 1, 10, 19, 28,....
The nth term of the sequence 1, 10, 19, 28, is 9n - 8
Given:
1, 10, 19, 28,
First term, a = 1
Common difference, d = difference between consecutive terms
10 - 1 = 9
19 - 10 = 9
28 - 19 = 9
nth term = a + (n - 1)d
nth term = 1 + (n - 1)9
= 1 + 9n - 9
= 9n - 8
Therefore, nth term of the sequence 1, 10, 19, 28, is 9n - 8
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3m-(7m+12)=2(m-3)solve this and show work
Answer:
[tex]m = - 1[/tex]
Step-by-step explanation:
[tex]3m - (7m + 12) = 2(m - 3)[/tex]
simplifying bracket first
[tex]3m - 7m - 12 = 2m - 6[/tex]
[tex] - 4m - 12 = 2m - 6[/tex]
grouping like terms
[tex] - 4m - 2m = - 6 + 12[/tex]
[tex] - 6m = 6[/tex]
dividing through by -6
[tex] \frac{ - 6m}{ - 6} = \frac{6}{ - 6} [/tex]
[tex]m = - 1[/tex]
Which two numbers are 4 units away from -1
The two numbers are 3 and -5. Let's start with 3. To get three, add 4 to -1. That means, going 4 to the right on a number line. When you do so, you will end up with 3. Since adding always go up.
Let's move onto -5 now. For this, go 4 to the left. Subtracting from negative numbers will be negative numbers. Since subtracting is going down, you go down on the number line.
Therefore, 3 and -5 is the answer!
Explaining channel:
Type HWsolver-Brainly. It should pop up at the bottom with a person thumbs up.
The two numbers that are 4 units away from -1 are -5 and 3.
What is a number line?In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
Now the given integer is, -1.
To find the numbers that are 4 units away we need to subtract and add 4 to get the required number.
So, 4 units forward from -1 is,
-1 + 4 = 3
And 4 units backward from -1 is,
-1 - 4 = -5
So the two numbers we get are 3 and -5.
Thus, the two numbers that are 4 units away from -1 are -5 and 3.
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What’s the value of the 3 in 783.97
10 POINTS BOIII
What is the slope of the line on the graph? P.S it's supposed to be a number.
Answer:
1/2
Step-by-step explanation:
the sum of two numbers is 84. The first is 9 more than 4 times the second. Find the numbers.
Answer:
69 and 15
Step-by-step explanation:
Second number=x
First number 4x+9
4x+9 +x = 84
5x+9=84
5x=75
x=15
15*4=60
60+9=69
69+15=84
Yara multiplies and divides a certain number by the same
power of 10. The product she gets is 40,000 and the
quotient she gets is 0.000004. Find Yara's number and
the power of 10 she used. Explain your reasoning.
For this case we have to:
x: Represents the unknown number
y: Represents the exponent of base 10
So, considering a system of equations we have:
[tex]x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004[/tex]
From the first equation we have:
[tex]10 ^ y = \frac {40,000} {x}[/tex]
Substituting in the second equation:
[tex]\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}[/tex]
We choose the positive value:
[tex]x = 0.4[/tex]
So, the number is 0.4.
So:
[tex]10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5[/tex]
Thus, the exponent is 5.
Answer:
Yara use 0.4 and[tex]10 ^ 5[/tex]
Answer:
0.4 and 10.5
Step-by-step explanation: