The sample size if the probability that the mean life is less than 1120 hours is 0.92 is given as follows:
n = 24.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 1100, \sigma = 70, s = \frac{70}{\sqrt{n}}[/tex]
The p-value of Z when X = 1120 is of 0.92, hence Z = 1.405, and the sample size is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.405 = \frac{1120 - 1100}{\frac{70}{\sqrt{n}}}[/tex]
[tex]20\sqrt{n} = 70 \times 1.405[/tex]
[tex]n = \left(\frac{70 \times 1.405}{20}\right)^2[/tex]
n = 24.
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The triangles on the grid below represent a translation. On a coordinate plane, triangle A B C is shifted 5 units up to form triangle A prime B prime C prime. Which translation is shown on the grid? a horizontal translation only a vertical translation only a horizontal translation followed by a vertical translation a vertical translation followed by a horizontal translation Mark this and return
The triangle ABC is vertically translated only. Then the correct option is B.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
We know that;
Reflection does not change the size and shape of the geometry.
Rotation does not change the size and shape of the geometry.
Translation does not change the size and shape of the geometry.
Here, On a coordinate plane, triangle ABC is shifted 5 units up to form triangle A'B'C'.
The diagram is given below.
From the diagram, we can clearly observe that the triangle ABC is vertically translated only.
Then, The correct option is B.
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please answer this question who ever gets the best answer gets the brainliest
Answer:
5, second choice
Step-by-step explanation:
When x is 3, the purple line's y-value is between 4 and 6, which is 5.
Answer:
B
Step-by-step explanation:
You have two black lines with the arrows at the end. The one going left and right is your X-Axis. The one going up and down is the Y-Axis.
What they want to know is what is f(x) when x = 3
f(x) is another term for y
So they want to know, what is the value of the y-axis when x is 3 on the x-axis.
So on the line going left and right you find the line 3, between 2 and 4, then going up until you hit the purple line. Once you hit the purple line, go left until you hit the up and down line. That will give you an answer of 5
Hakim needs to simplify the expression below.
(1.85 minus 0.3) divided by 8 + 4 times 3
Which operation should he perform first?
A. addition
B. subtraction
C. multiplication
D. division
The Answer is B because we use pemdas (parentheses)(exponents)(multiplication)(division)(addition)(subtraction)
so first is what is inside of the parentheses which is a subtracting equation number b is subtraction so the answer is b
In ΔJKL, j = 1.7 inches, m m∠J=120° and m m∠K=47°. Find the length of k, to the nearest 10th of an inch.
Answer: We can use the Law of Cosines to find the length of side k in ΔJKL:
k^2 = j^2 + l^2 - 2 * j * l * cos(m∠K)
k = √(j^2 + l^2 - 2 * j * l * cos(m∠K))
Substituting the given values, we get:
k = √(1.7^2 + l^2 - 2 * 1.7 * l * cos(47°))
k = √(2.89 + l^2 - 2.94 * l * cos(47°))
To the nearest 10th of an inch, k = √(2.89 + l^2 - 2.94 * l * cos(47°)) = 3.3 inches.
Step-by-step explanation:
each person wants to make 36 wreaths to sell at the craft fair. Each wreath needs 2 1/4 yards of ribbon. How many yards of ribbon does the person need to make all the wreaths?
Answer:
81
Step-by-step explanation:
[tex]2\frac{1}{4}*36\\ \\\frac{9}{4}*\frac{36}{1} \\ \\\frac{324}{4} =81[/tex]
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on blue is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Answer: A; The probability of landing on blue is greater than the probability of landing on purple.
Step-by-step explanation: This statement is true because you need to analyze the problem. Since there is a 3/6 or 1/2 chance of getting a blue, it is higher than getting a purple spot, which is 2/6 or 1/3. So, we can model our answer as:
3/6 > 2/6
or
1/2 > 1/3
I hope this helped!
In which of these diagrams does the shaded region show
a) the locus of points that are less than 5 cm from P?
b) the locus of points that are closer to Q than to P?
c) the locus of points that are more than 5 cm from Q?
A
D
p
P"
5 cm
Q
5 cm
¹Q
B
E
P
P
5 cm
"Q
*Q
C
F
p²
P'
5 cm
*Q
Q
a) The locus of points that are less than 5 cm from P is (A)
b) The locus of points that are closer to Q than to P is (F)
c) The locus of points that are more than 5 cm from Q is (D),
What is Locus point in Circle?A locus is a curve or other shape created in mathematics from all the points that meet a specific equation describing the relationship between the coordinates, or from a point, line, or moving surface. The locus defines all shapes as a set of points, including circles, ellipses, parabolas, and hyperbolas.
Given:
a) The point A is less than 5cm away from point P is int he circle centered on P.
b) The option E is point closer to P than Q.
The option F is point closer to Q than P.
c) The option D point more than 5 cm away from Q on the outside of the circle centered on Q.
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How can you tell if someone has a growth mindset?
Answer:
Step-by-step explanation:
When someone has a growth mindset they believe that they can continue to learn and become more intelligent with effort.
PLEASE HELP!!!!!!!!!!!
The decimal number 0.4 is greater than 0.25.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
There are 25 out of 100 shaded cubic part.
That means, the number is 0.25.
From the given choices:
0.4 > 0.25.
Therefore, 0.4 is the required decimal number.
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Suppose that a single die with 19 sides (numbered 1, 2, 3, ... , 19) is rolled once. What is the probability of getting an even number.
Step-by-step explanation:
To find the probability of getting an even number, we need to count the number of even numbers and divide it by the total number of sides of the die:
Number of even numbers = 10 (2, 4, 6, 8, 10, 12, 14, 16, 18, 19)
Total number of sides = 19
P(even number) = Number of even numbers / Total number of sides = 10/19 = 0.526 (or 52.6%)
Central Angles
please type the solution and determine if it's minor or major arc or semi circle
need asap
Answer:
∠YPV = 50°
∠XPV = 130°
∠WPZ = 85°
1. Arc YZ is a minor arc.
2. Arc WX is a minor arc.
3. ∠VPZ = 95°
4. Arc VZ is a minor arc.
5. Arc VWX is a major arc.
6. Arc ZVW is a major arc.
7. Arc YWZ is a major arc.
8. Arc ZXW is a major arc.
9. ∠VPX = 130°
10. Arc XVY is a semicircle.
11. Arc XWY is a semicircle.
12. Arc WZX is a major arc.
Step-by-step explanation:
As WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.
As VW is a diameter of circle P, and angles on a straight line sum to 180°:
⇒ ∠WPX + ∠XPV = 180°
⇒ 50° + ∠XPV = 180°
⇒ ∠XPV = 130°
As XY is a diameter of circle P, and angles on a straight line sum to 180°:
⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°
⇒ ∠WPZ + 45° + 50° = 180°
⇒ ∠WPZ + 95° = 180°
⇒ ∠WPZ = 85°
Add the central angles to the given circle diagram (see attachment).
Definition of ArcsMinor arc: An arc whose measure is less than 180°.Note that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.
Note that three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.
As WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle.
1. Arc YZ is a minor arc.
2. Arc WX is a minor arc.
3. ∠VPZ = 50° + 45° = 95°
4. Arc VZ is a minor arc.
5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.
6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.
7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.
8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.
9. ∠VPX = 130°
10. Arc XVY is a semicircle.
11. Arc XWY is a semicircle.
12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.
The answers to the respective arcs are given as follows:
∠YPV = 50°∠XPV = 130°∠WPZ = 85°Arc YZ is a minor arc.Arc WX is a minor arc.∠VPZ = 95°Arc VZ is a minor arc.Arc VWX is a major arc.Arc ZVW is a major arc.Arc YWZ is a major arc.Arc ZXW is a major arc.∠VPX = 130°Arc XVY is a semicircle.Arc XWY is a semicircle.Arc WZX is a major arc. What is a Major or Minor Arc?The arcs are defined as follows:
Minor arc: An arc whose measure is less than 180°. Minor arcs are named using the two letters of the endpoints. The two letters can be in any order.Major arc: An arc whose measure is greater than 180°. Major arcs are named using three letters. The two letters at the end of the name are the endpoints of the arc. The middle letter is the name of the point contained in the arc.Semicircle: An arc whose measure is equal to 180°.It is to be noted that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.
Also, three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.
To solve for the arcs:
Given that WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.
As VW is a diameter of circle P, and angles on a straight line sum to 180°:
⇒ ∠WPX + ∠XPV = 180°
⇒ 50° + ∠XPV = 180°
⇒ ∠XPV = 130°
Since XY is a diameter of circle P, and angles on a straight line sum to 180°:
⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°
⇒ ∠WPZ + 45° + 50° = 180°
⇒ ∠WPZ + 95° = 180°
⇒ ∠WPZ = 85°
Given that WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle. Thus,
1. Arc YZ is a minor arc.
2. Arc WX is a minor arc.
3. ∠VPZ = 50° + 45° = 95°
4. Arc VZ is a minor arc.
5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.
6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.
7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.
8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.
9. ∠VPX = 130°
10. Arc XVY is a semicircle.
11. Arc XWY is a semicircle.
12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.
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There are 10 tricycles and bicycles in all.
If there are 23 wheels, how many are bicycles and how many are tricycles?
Answer:
see below
Step-by-step explanation:
tricycles = x
bicycles = y
x+y =10 so y=10-x
3x+2y=23
so 3x + 2(10-x) =x+20 =23
so x=3
y = 7
there are 12 balls to every 2 pits. If Fred has 40 balls in his room, how many pits are in his room?
Your answer may be exact or accurate to the nearest tenth.
if Fred has 40 balls in his room then there are 7 pits in his room.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that there are 12 balls to every 2 pits
Fred has 40 balls in his room
We have to find the number of pits for 40 balls
Let x be the number of pits for 40 balls.
Form an proportional equation
12/2=40/x
6=40/x
x=40/6=20/3
x=6.667=7
Hence, if Fred has 40 balls in his room then there are 7 pits in his room.
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Mrs. Larson May 12 pills from 16 yards of the same fabric how much fabric was used to make each pillow between what two whole numbers does your answer lie
The amount of the fabric is 4 / 3 yards.
How to determine the amount of the fabricLet's call the amount of fabric used to make each pillow "x".
Then, the total amount of fabric used was 12 * x = 16 yards.
Solving for x, we get x = 16 / 12 = 4 / 3 yards.
Since fabric is typically sold in whole yards, the answer lies between 1 and 2 yards.
The answer, 4 / 3 yards,
This can be rounded up to 1 yard or rounded down to 1 1/3 yards.
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if the economy is producing 12 units of guns and 4 units of butter, what is the opportunity cost of increasing the production of butter from 4 units to 11 units?
If the economy is producing 12 units of guns and 4 units of butter, the opportunity cost of increasing the production of butter from 4 units to 11 units is 4 units of guns.
What is an opportunity cost?In Economics, an opportunity cost is sometimes referred to as alternative forgone and it can be defined as the value, profit or benefits that are given up and forfeited by an individual or business organization, in order to choose or acquire something that is deemed most significant at a particular point in time.
This ultimately implies that, the opportunity cost of owning or earning a thing is the alternative that is foregone in the attainment or earning of another value, profit or benefits.
Cost increase = 11 units - 4 units = 7 units of butter.
In this context, we can reasonably infer and logically deduce that the opportunity cost of 7 more units of butter would be 4 units of guns.
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400 wrist watches in a box of 10,000 are defective. If 100 watches are selected at random, find the probability that 50 are defective
Step-by-step explanation:
The probability of selecting a defective watch is 400/10,000 = 2/50.
The probability of selecting 50 defective watches out of 100 selected is given by the binomial distribution:
(100 choose 50) * (2/50)^50 * (1/2)^(100-50) = 0.072.
So the probability that exactly 50 out of 100 selected watches are defective is approximately 0.072.
A survey of 219 SPC students was taken at registration. Of those surveyed:
68 students had signed up for a Math course
40 students had signed up for a Humanities course
20 students had signed up for both a Math and Language Arts course
5 students had signed up for both a Math and Humanities course
10 students had signed up for both a Language Arts and Humanities course
2 students had signed up for all three courses
5 students did not sign up for any of these classes
How many students signed up for only Language Arts (of these three)?
The number of students that signed up for only language art is 116
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
n( of Math and language only) = 20-2 = 18
n( of Math and humanities only) = 5-2 = 3
n( of humanities and language only) = 10-2 = 8
n( math only) = 68-(18+2+3)
= 68 - 23 = 45
n( humanities only) = 40-( 8+3+2)
= 40-13 = 27
represent number of student Who signed up for language by x
n( of language only) = x-( 18+2+8)
=x- 28
219 = 45+27+18+2+3+8+x-28
219 = 75 +x
x = 219-75
x= 144
therefore number of students that signed from language art only = 144-28
= 116
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A recipe calls for cup
of chopped walnuts. You chop 4 walnuts
and get of the amount you need.
-
4
How much more of a cup of chopped
walnuts do you need? All your walnuts
are the same size. How many more
walnuts should you chop? Explain.
If you already chopped 4 walnuts and you have only gotten 1/4 cup of the chopped walnuts, it means that each walnut yields 1/4 cup / 4 walnuts = 1/16 cup of chopped walnuts.
To find out how much more chopped walnuts you need, we can subtract the amount you have from the total amount the recipe calls for:
1 cup - 1/4 cup = 3/4 cup
So you need 3/4 cup of chopped walnuts more.
To find out how many more walnuts you should chop, divide the amount you need by the amount each walnut yields:
3/4 cup / (1/16 cup/walnut) = 12 walnuts
So you should chop 12 more walnuts to get the desired amount.
fill in the missing numbers: c) -----, 3.840, 3.836, 3.832------,3.824, 3.820
d) 30.565, 31.065, 31.565, -----32.565, 33.065,
Answer:
3.844, 3.840, 3.836, 3.832, 3.828 ,3.824, 3.820 - minus by 4
30.565, 31.065, 31.565, 32.065, 32.565, 33.065, - minus 0.5 , -0.5 , 0.5 .......
With only a part-time job and the need for a
professional wardrobe, Rachel quickly
maxed out her credit card the summer after
graduation.
With her first full-time paycheck in August,
she vowed to pay $320 each month toward
paying down her $8,975 outstanding
balance and not to use the card.
The card has an annual interest rate of 17%.
How long will it take Rachel to pay for her
wardrobe? Should she shop for a new card?
Why or why not?
It will take Rachel 5 months to pay off her debt at her current monthly payment rate.
What do you mean by Interest rate?Interest rate is a percentage that represents the amount of interest charged by a lender to a borrower for the use of money. It is used to calculate the interest that will accrue on a loan or deposit over a specific period of time, and is usually expressed as an annual rate. It is a key component in determining the cost of borrowing money, and affects the amount that must be paid back to the lender, including the principal amount and any additional interest charges.
Rachel's monthly payment of $320 will only cover the interest on her debt and will not significantly reduce the outstanding balance. She would need to pay more each month or find a way to reduce the interest rate in order to pay off her debt in a reasonable amount of time.
To calculate the time it will take for Rachel to pay off her debt, we can use the following formula:
n = ceil(log(P/A) / log(1 + r))
where n is the number of payments, P is the initial balance, A is the monthly payment, and r is the monthly interest rate (expressed as a decimal).
In this case, P = $8,975, A = $320, and r = 17% / 12 = 0.17 / 12 = 0.01417.
So, n = ceil(log($8975 / $320) / log(1 + 0.01417)) = ceil(log(28.09375) / log(1.01417)) = ceil(4.3626) = 5.
It will take Rachel 5 months to pay off her debt at her current monthly payment rate. This means that it will take her just over 4 years to pay off the debt, assuming no additional purchases are made on the card and the interest rate does not change.
As for shopping for a new card, Rachel should consider a card with a lower interest rate. This will allow her to pay off her debt more quickly and save money in interest charges. She may also consider a balance transfer card with an introductory 0% interest rate, which would give her time to pay off the debt without accruing interest. However, she should be aware of any balance transfer fees that may apply. It is best for Rachel to compare options and read the fine print before making a decision.
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Write a congruence statement for the above triangles
The congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.
What are congruent triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
For the given triangles ABC and triangle LMN we can see that:
Line segment AB = LM
Segment AC= LN
and, CB = MN
Hence, the congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.
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Using the rules of inference show that s is a conclusion
1. p → q
2. q → r
3. (q → r) → s
4. p
how to solve?
"s" can be concluded from the premises
How to show that s is the conclusionTo use the rules of inference to show that "s" is a conclusion, we can use modus ponens,
This is a rule that allows us to infer a conclusion from a premise and its conditional statement.
Using modus ponens, we can infer "q" from "p → q" and "p".Next, using modus ponens, we can infer "r" from "q → r" and "q".Finally, using modus ponens, we can infer "s" from "(q → r) → s" and "q → r".Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".
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How much should you invest each month in order to have $800,000 if your rate of return is 2.8% compounded monthly and you want to achieve your goal in 40 years? How much interest will you earn? How much should you invest each month in order to have $800,000 if you want to achieve your goal in 20 years? If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
Answer:
if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months. you will have 800,000 after 20 years.
Step-by-step explanation:
rate of return is 5.3% compounded monthly.
number of years = 40.
future value = 800,000
interest rate per month is 5.3% / 12 = .4416666....%
number of time periods if 40 * 12 = 480
payment required at the end of each month is equal to 484.5267545
your total payments are 480 * 484.5267545 = 232,572.8422
total interest earned would be 800,000 minus 232,572.8422 = 567,427.1578
if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months.
you will have 800,000 after 20 years.
if you deposit that money for an additional 10 years at the same rate of interest per year compounded annually, then you will have 1,357,560.674.
you can use an online calculator to get the results similar to this.
they might not be right on because of possible rounding errors, but they'll be close.
In rectangle PQRS, the diagonals intersect each other at point T. If PR = 9 and PQ = 7 what is the area of PQR? Round to the nearest tenth.
On solving the provided question, we can say that In rectangle, the two diagonals are in congruence , the diagonals bisect each other. PT=TR=ST=TQ=1/2PR=1/2QS =1/2×22.8=11.4
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Rectangle, two diagonals are in congruence
⇒PR=QS=22.8
The diagonals bisect each other.
⇒PT=TR=ST=TQ=1/2PR=1/2QS
=1/2×22.8=11.4
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Help 20 points (show your work)
The measure of angle ADC in the geometric system is equal to 55°.
How to determine the value of an angle related to a geometric system
In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:
m ∠ CDE + m ∠ EDF = 180°
(2 · x + 1) + (x - 7) = 180°
3 · x - 6 = 180°
3 · x = 186°
x = 62
m ∠ CDE = 2 · x + 1
m ∠ CDE = 2 · 62 + 1
m ∠ CDE = 125°
m ∠ ADC = 180° - 125°
m ∠ ADC = 55°
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Camilla bought a duffel bag costing $10.73. If Camilla received $0.95 in change, how much money did she give to the cashier?
The amount of money Camilla gave the cashier is
$11.68
What is Word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
For example, if there are 20mangoes and 20 oranges are in a basket, the total number of fruit is 20+20 = 40 fruits
Camilla bought a duffel bag for $10.73 and he collected $0.95 as change.
Therefore the total money he gave to the cashier is $10.73+$0.95 = $11.68
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20 POINTS PLEASE ANSWER QUICK
Solve the equation —1/6(12 + 18t) = 13 for t
Answer: t=-5
Step-by-step explanation:
Multiply by -6 on both sides to get rid of the -1/6
Subtract 12 on both sides
Divide 18 by -90 on the other side
[tex](-1/6(12+18t))(-6)=13(-6)\\12+18t=-78\\18t=-90\\\\t=-5[/tex]
Show that x-3 and x+5 are factors of x^4+2x^3-16x^2-2x+15. Explain your reasoning using long division, Synthetic Division and Remainder theorem.
Answer:
Step-by-step explanation:
To show that x-3 and x+5 are factors of x^4+2x^3-16x^2-2x+15, we can use polynomial division, synthetic division, and the Remainder theorem.
Using long division, we can divide x^4+2x^3-16x^2-2x+15 by x-3:
x^4 + 2x^3 - 16x^2 - 2x + 15
÷ x - 3
_________________________
x^3 + 5x^2 - 14x - 12
|__________
-3x^3 + 17x^2 + 26x + 36
|_________
-14x^2 - 23x - 36
|_________
-15x + 72
|___
57
So, the remainder is 57, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x - 3)(x^3 + 5x^2 - 14x - 12) + 57.
Using synthetic division, we can divide x^4 + 2x^3 - 16x^2 - 2x + 15 by x+5:
1 2 -16 -2 15
x + 5 |x^4 + 2x^3 - 16x^2 - 2x + 15|
____________________________
x^3 - 3x^2 + 21x + 75
So, the remainder is 0, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x + 5)(x^3 - 3x^2 + 21x + 75).
Using the Remainder theorem, we know that if a polynomial p(x) is divided by x-a, the remainder is p(a). So, when we plug in x=3, the remainder should be p(3) = 57. When we plug in x=-5, the remainder should be p(-5) = 0. This confirms that x-3 and x+5 are indeed factors of x^4 + 2x^3 - 16x^2 - 2x + 15.
Given EFG=XYZ, find m
Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.
What precisely does a triangle mean?Triangles are included in polygons because they have four aspects or more. It is simple and geometric in design. The triangle formed by the letters ABC has a square angle. A single rectangles or square is produced by euclidean geometry when the sides are not coinciding. Triangles are polygons because they have three parts and three corners. The intersection of a triangle's three sides forms its corners. A triangle has 180 degrees of angles in all.
Here,
Given :
=> ΔEFG ≅ ΔXYZ
In ΔEFG
=> 90° + 60° + x = 180°
=> 150° + x = 180°
=> x = 180° - 150°
=> x = 30°
Since . they are congruent .
So m∠x = 30°
Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.
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Select whether each of these factors was a reason for or against American neutrality. US trade with Europe was worth almost one billion dollars. for against Intro
________________________
Sunny ko behan mil gayi sonali ✨
The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.
Why did American neutrality benefit from commerce with Europe?Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.
The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.
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