Factor
1 out of -x +6
The factored expression is
Answers
Answer:
6+f=21
Step-by-step explanation:
Related Questions
consider the sequence of numbers: $4$, $7$, $1$, $8$, $9$, $7$, $6$, $\ldots$. for $n>2$, the $n$th term of the sequence is the units digit of the sum of the two previous terms. let $s n$ denote the sum of the first $n$ terms of this sequence. what is $s {100}?$
Answers
The sum of the first 100 terms of the sequence is $620$.
\($s_3 = 4 + 7 = 11$\)
\($s_4 = 11 + 1 = 12$\)
\($s_5 = 12 + 8 = 20$\)
\($s_6 = 20 + 9 = 29$\)
\($s_7 = 29 + 7 = 36$\)
\($s_8 = 36 + 6 = 42$\)
\($s_9 = 42 + 4 = 46$\)
\($s_{10} = 46 + 7 = 53$\)
\($s_{100} = 620$\)
The given sequence is 4, 7, 1, 8, 9, 7, 6 and so on. The nth term of the sequence is the units digit of the sum of the two previous terms. To find the sum of the first 100 terms, we need to calculate the sum of the first two terms, 4 and 7. This is 11. The next term is the units digit of 11, 1. The sum of the first three terms is 12. The next term is the units digit of 12, which is 2. This process is repeated until we reach the 100th term. The sum of the first 100 terms is 620.
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what is the value of x in the figure shown?
Answers
X = 3
Answer:
12
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answers
Answer:
7.3
Step-by-step explanation:
Using the half-life formula,
\(30(1/2)^{200/98} \approx 7.3\)
Divide the sum of 8 and e by 9
Answers
Answer:
1.19
Step-by-step explanation:
write as a product:
a^3-m^3 n^9
Answers
Answer:
=−m3n9+a3
Step-by-step explanation:
Let's simplify step-by-step.
a3−m3n9
=a3+−m3n9
finding the missing digits on this photo PLS
Answers
im learning about isosceles trapezoids right now, and i forgot to take notes of the formulas. can someone please list them for me? thanks
Answers
Nora was offered a job that paid a salary of $40,000 in its first year. The salary was set to increase by 3% per year every year. If Nora worked at the job for 21 years, what was the total amount of money earned over the 21 years, to the nearest whole number?
Answers
The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.
In the first year, Nora's salary is $40,000.
In the second year, her salary will be increased by 3%, so it will be:
$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.
In the third year, her salary will again increase by 3%, so it will be:
$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.
We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.
To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:
Total = $40,000 + $41,200 + $42,436 + ... (21 terms)
To simplify the calculation, we can use the formula for the sum of an arithmetic series:
Total = (n/2) * (2a + (n - 1)d)
where:
n = number of terms (21 in this case)
a = first term ($40,000)
d = common difference (3% of the previous year's salary)
Plugging in the values:
Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]
Simplifying further:
Total = (21/2) * [80,000 + 20(0.03)(40,000)]
= (21/2) * [80,000 + 2,400(40,000)]
= (21/2) * [80,000 + 96,000]
= (21/2) * 176,000
= 21 * 88,000
= 1,848,000
Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
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M is the midpoint of segment GR. G has coordinates (11,-5) and M is (4,-4) Find the coordinates of R
Answers
Answer:
(3, -3)Step-by-step explanation:
Given:
G = (11,-5) M = (4,-4) R = ?Solution
R(x, y)As per midpoint formula;
4 = (11 + x)/2 ⇒ x + 11 = 8 ⇒ x = 3-4 = (-5 + y)/2 ⇒ y - 5 = -8 ⇒ y = -3R = (3, -3)the radius of the earth - the distance from surface to core - is 6,370 kilometers. the planet neptune is 24,620 kilometers. if a scale model of the earth is drawn with a radius of 2.5 centimeters, how large would a scale model of neptune have to be drawn? group of answer choices 9848 cm 9.7 cm 2548 cm 0.02548 cm 3.86 cm
Answers
We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.
We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:
Neptune's radius is equal to the product of Earth's radius and its scale model.
With the provided values, we may simplify and obtain:
24620 km / 6370 km equals 2.5 cm / r
We obtain the following when solving for "r":
r = (24620 km * 2.5 cm) / (6370 km)
r ≈ 9.7 cm
Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.
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is 0.324 a rational number
Answers
Answer:
324/1000
Step-by-step explanation:
Find the volume
A. 150 cm3
B. 180 cm3
C. 90 cm3
D. 90 cm2
Answers
Answer:
268 in²
Step-by-step explanation:
The surface area is basically the entire area of the figure. You can do it multiple ways, but this is how I did it. I found the area of each side and added them all together. There are three sets of identical sides. First, we'll calculate the area of the side with lengths 10" and 8".
10 · 8 = 80
There are two of these sides, so currently we have 80 + 80.
Next, the area of the sides with lengths 8" and 3". These are the sides at the top and bottom.
8 · 3 = 24
So to our equation we now have 80 + 80 + 24 +24.
For the final two sides, we have the dimensions 10" and 3".
10 · 3 = 30
To our equation, we add this to get 80 + 80 + 24 + 24 + 30 +30.
Add all these numbers together for 268.
In the correct form, we add the square symbol to show that we are talking about area. The answer is 268 in². Good luck :D
suppose veronica sells teapots in the perfectly competitive teapot market. her output per day and her costs are as follows: output per day total cost 0 $20 1 32 2 37 3 48 4 61 5 75 6 92 7 113 8 136
Answers
Where the perfect competitive teapot market is above is given,
Veronica will produce 5 teapots.Veronica will charge a price of $15 per teapot. Veronica will make neither a profit nor a loss; she will break even. Her profit will be $0.How is this so?1) To maximize profit, Veronica should produce the quantity of teapots where her marginal cost equals the market price.
First, we can calculate the marginal cost (MC) by finding the change in total cost (TC) for each additional unit of output -
Output per Day Total Cost (TC) Marginal Cost (MC)
0 $20 N/A
1 $32 $32 - $20 = $12
2 $37 $37 - $32 = $5
3 $48 $48 - $37 = $11
4 $61 $61 - $48 = $13
5 $75 $75 - $61 = $14
6 $92 $92 - $75 = $17
7 $113 $113 - $92 = $21
8 $136 $136 - $113 = $23
Next, we compare the marginal cost to the market price of $15 -
Output per Day Marginal Cost (MC) Market Price
0 N/A $15
1 $12 $15
2 $5 $15
3 $11 $15
4 $13 $15
5 $14 $15
6 $17 $15
7 $21 $15
8 $23 $15
Veronica will produce up to the quantity where MC = market price, which is 5 teapots.
2) Beyond this quantity, the marginal cost exceeds the market price, resulting in losses.
To determine the price Veronica will charge, we look at the market equilibrium price, which is $15.
Therefore,Veronica will produce and sell 5 teapots at a price of $15 each.
3) To calculate the profit (or loss),we need to subtract the total cost (TC) from the total revenue (TR). The total revenue is calculated by multiplying the price by the quantity sold -
Total Revenue (TR) = Price * Quantity
= $15 * 5
= $75
Total Cost (TC) for producing 5 teapots is $75.
Profit (or Loss) = Total Revenue - Total Cost
= $75 - $75
= $0
Veronica will make neither a profit nor a loss; she will break even by producing and selling 5 teapots at a price of $15 each.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Suppose Veronica sells teapots in the perfectly competitive teapot market. Her output per day and her costs are as follows: Output per Day Total Cost 0 $20 1 32 2 37 3 48 4 61 5 75 6 92 7 113 8 136 Suppose the current equilibrium price in the teapot market is $15. To maximize profit, how many teapots will Veronica produce, what price will she charge, and how much profit (or loss) will she make?
given : AD is perpendicular to DC, <1 and <2 are complementary Proven: <1 is congruent to <3
Answers
When two straight lines or rays intersect at a single endpoint, an angle exists formed. If 2 and 3 exists complements, and m2= 55°, then m3 = 90 - 55 = 35 degrees.
What is meant by angle?When two straight lines or rays intersect at a single endpoint, an angle exists formed. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Complements sum to 90 degrees.
If 1 and 2 are complements and m1 = 35°, then
m2 = 90 - 35 = 55 degrees.
Now if 2 and 3 are complements, and m2= 55°,
then m3 = 90 - 55 = 35 degrees.
The complete question is:
Given: 1 and 2 are complements, 2 and 3 are complements, and m1 = 35°. Prove: m3 = 35° Complete the missing parts of the paragraph proof. By then, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of angles. Then, using the property, the measure of angle 3 is the degree.
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Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared. (x +___)2 = ___
Answers
Answer:
(x + 4)2 = 19
4 and 19 is the answer.
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answers
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55
Enter an expression equivalent to (3x2 + 2y2 – 3x) - (2x2 + y2 - 2x) using the fewest number of possible terms
Answers
Answer:
x2+y2-x
Step-by-step explanation:
subtract like terms.
The required equivalent expression is \(x^2+y^2-x\).
Important information:
The given expression is \((3x^2+2y^2-3x)-(2x^2+y^2-2x)\).Equivalent expression:The given expression can be written as:
\(3x^2+2y^2-3x-2x^2-y^2+2x\)
Combining like terms, we get
\((3x^2-2x^2)+(2y^2-y^2)+(-3x+2x)\)
On simplification, we get
\(x^2+y^2-x\)
Therefore, the required equivalent expression is \(x^2+y^2-x\).
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Problem 2 How many nonzero entries does the matrix representing the relation R on A = {1,2,3,...,100} consisting of the first positive 100 integers have if R is (a) {(a, b)|a > b} (b) {(a, b) | b - a = 51} (c){(a,b) | ab is multiple of 3}
Answers
(a) Matrix for relation R {(a, b) | a > b} has 4950 nonzero entries.
(b) Matrix for relation R {(a, b) | b - a = 51} has 49 nonzero entries.
(c) Matrix for relation R {(a, b) | ab is a multiple of 3} has 5644 nonzero entries.
Let's analyze each relation separately to determine the number of nonzero entries in the corresponding matrix.
(a) Relation R: {(a, b) | a > b}
In this case, for every pair (a, b) in the relation, a must be greater than b. We need to count the number of such pairs.
Since the set A consists of the first positive 100 integers, we have 100 choices for a. For each a, there are (a - 1) choices for b (all the integers less than a). Thus, the number of pairs (a, b) satisfying a > b is:
Number of pairs = 99 + 98 + ... + 1 = (99 × 100) / 2 = 4950
Therefore, the matrix representing relation R has 4950 nonzero entries
(b) Relation R: {(a, b) | b - a = 51}
In this case, for every pair (a, b) in the relation, the difference between b and a is 51. We need to count the number of such pairs.
Since the set A consists of the first positive 100 integers, we can choose a from 1 to 49 (inclusive), as for any greater than 49, b would exceed 100.
Thus, the number of pairs (a, b) satisfying b - a = 51 is:
Number of pairs = 49
Therefore, the matrix representing relation R has 49 nonzero entries.
(c) Relation R: {(a, b) | ab is a multiple of 3}
In this case, for every pair (a, b) in the relation, the product of a and b must be a multiple of 3. We need to count the number of such pairs.
Since the set A consists of the first positive 100 integers, we have 100 choices for both a and b.
To calculate the number of pairs (a, b) satisfying ab is a multiple of 3, we need to exclude the pairs where both a and b are not multiples of 3.
Number of pairs = (100 × 100) - (66 × 66) = 10000 - 4356 = 5644
Therefore, the matrix representing relation R has 5644 nonzero entries.
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a construction crew need to lay a total of 240 feet of underground pipes . on day one the team was able to lay 145 feet and 3 inches . how much pipe still needs to be laied? .
Answers
Answer:
240ft-143ft-3in= 96 feet & 9 inches
Michael buy a baket of mangoe on ale for \$ 4$4 before tax.
The ale tax i 12%.
What i the total price Michael pay for the baket of mangoe?
Answers
Total price paid by Michael for the basket of mangoes is $4.48.
For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -
Total price = 4 + 12%×4
Calculating the percentage of sales tax on Right Hand Side of the equation
Total price = 4 + 12×4/100
Solving the percentage part on Right Hand Side of the equation
Total price = 4 + 0.48
Performing addition on Right Hand Side of the equation
Total price = $4.48
Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.
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Stan bought a car that was valued at $24000 at the time of purchase. Stan calculates that the car will depreciate, lose value, at a rate of $1100 per year before it has no value. Write a function that will represent the value of the car, V, with respect to the number of years, t.
Answers
Answer:
in which year does a car lose the most of its value
Step-by-step explanation:
1
Spoints
Which is the image of vertex O after the triangle has been rotated 90 degrees counterclockwise about the origin?
6+
5
3
2
L
2
3
-653 -2.1
s! S6
o
w
s
.67
0 -1.2)
Answers
Answer:
(2, - 1 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , thus
O(- 1, - 2 ) → (2, - 1 )
The joint and marginal pdf's of x = amount of almonds and Y = amount of cashews are
F(x,y) = fx(x) =
with fy(y) obtained by replacing x by y in fx(x). It is easily verified that Mu x = Mu y = A, and E(XY) = 2/ 5 Compute the correlation coefficient p for X and Y. P=
Answers
The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.
What is correlation coefficient?The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.
Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.
Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).
The correlation coefficient is computed as,
\($ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}\)
\($=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}\)
= -0.6675
Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.
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Find the measure of each angle indicated.
Answers
The measure of the unknown angle in the triangle is 58 degrees.
What is a triangle ?A triangle has three sides and the sum of the angles of a triangle is 180 degrees.
Triangles can be classified base on there angles and length of the sides.
Therefore,
let the length of the unknown angle = x
x + 65° + 57° = 180°
x + 122 = 180
subtract 122 from both sides
x + 122 - 122 = 180 - 122
x = 58 degrees
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Subject: Add Maths
Pleasee helpp
x-2 is a factor of x^3-x^2-x-2
Show that x^3-x^2-x-2=0 has only one real root and state the value of this root
Answers
Ce clasă ești sa văd daca te pot ajuta
Little Scotty's favorite toy is a grizzly beat that is 6 inches tall. A full grown grizzly bear in the wild is 84 inches tall. What is the scale factor of Scotty's toy compared to a grizzly in real life?
(Don't forget to simplify)
Scale Factor = ????
Answers
9514 1404 393
Answer:
1 : 14
Step-by-step explanation:
The scale factor model/real = (6 in)/(84 in) simplifies to 1/14.
Suppose that 53% of families living in a certain country own a minivan and 24% own a SUV. The addition rule mightsuggest, then, that 77% of families own either a minivan or a SUV. What's wrong with that reasoning?
Choose the correct answer below.
A. If one family owns a minivan or a SUV, it can influence another family to also own a minivan or a SUV. The events are not independent, so the addition rule does not apply.
B.The sum of the probabilities of the two given events does not equal 1, so this is not a legitimate probability assignment.
C. A family may own both a minivan and a SUV. The events are not disjoint, so the addition rule does not apply.
D. The reasoning is correct. Thus, 77% a minivan or a SUV.
Answers
The correct answer is C. A family may own both a minivan and an SUV. The events are not disjoint, so the addition rule does not apply.
The addition rule of probability states that if two events are disjoint (or mutually exclusive), meaning they cannot occur simultaneously, then the probability of either event occurring is equal to the sum of their individual probabilities. However, in this case, owning a minivan and owning an SUV are not mutually exclusive events. It is possible for a family to own both a minivan and an SUV at the same time.
When using the addition rule, we assume that the events being considered are mutually exclusive, meaning they cannot happen together. Since owning a minivan and owning an SUV can occur together, adding their individual probabilities will result in double-counting the families who own both types of vehicles. This means that simply adding the percentages of families who own a minivan (53%) and those who own an SUV (24%) will overestimate the total percentage of families who own either a minivan or an SUV.
To calculate the correct percentage of families who own either a minivan or an SUV, we need to take into account the overlap between the two groups. This can be done by subtracting the percentage of families who own both from the sum of the individual percentages. Without information about the percentage of families who own both a minivan and an SUV, we cannot determine the exact percentage of families who own either vehicle.
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please answer asap! Please dont get it wrong T0T
Answers
Answer:
Step-by-step explanation:
x + 165° = 180° ( being linear pair )
x = 180° - 165°
x = 15°
hope it helps :)
In the following questions, the bold letters X, Y, Z are variables. They can stand for any sentence of TFL. (3 points each) 4.1 Suppose that X is contingent and Y is a tautology. What kind of sentence must ¬XV y be? Explain your answer. 4.2 Suppose that X and Y are logically equivalent, and suppose that X and Z are inconsistent. Does it follow that Y must entail ¬Z? Explain your answer. 4.3 Suppose that X and X → > Z are both tautologies. Does it follow that Z is also a tautology? Explain your answer.
Answers
4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), ¬X V Y is a tautology.
4.2 No, it does not necessarily follow that Y must entail ¬Z. Y does not necessarily entail ¬Z.
4.3 The tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.
4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), the sentence ¬X V Y must be a tautology. This is because the disjunction (∨) operator evaluates to true if at least one of its operands is true. In this case, since Y is a tautology and always true, the entire sentence ¬X V Y will also be true regardless of the truth value of X. Therefore, ¬X V Y is a tautology.
4.2 No, it does not necessarily follow that Y must entail ¬Z. Logical equivalence between X and Y means that they have the same truth values for all possible interpretations. Inconsistency between X and Z means that they cannot both be true at the same time. However, logical equivalence and inconsistency do not imply entailment.
Y being logically equivalent to X means that they have the same truth values, but it does not determine the truth value of ¬Z. There could be cases where Y is true, but Z is also true, making the negation of Z (¬Z) false. Therefore, Y does not necessarily entail ¬Z.
4.3 No, it does not necessarily follow that Z is also a tautology. The fact that X and X → Z are both tautologies means that they are always true regardless of the interpretation. However, this does not guarantee that Z itself is always true.
Consider a case where X is true and X → Z is true, which means Z is also true. In this case, Z is a tautology. However, it is also possible for X to be true and X → Z to be true while Z is false for some other interpretations. In such cases, Z would not be a tautology.
Therefore, the tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.
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if right ill give brainiest answer fast pls
Answers
Answer:The answer is the second choice $45,250.
Step-by-step explanation: