Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
Real Zeros of a Polynomial Function
The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.
To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).
Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:
f(x) = a(x + 5)(x - 0)(x - 6)
where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.
Multiplying out the factors, we get:
f(x) = (x + 5)(x)(x - 6)
= x³ - x² - 30x
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Please help me this is so hard. Please if you help i give you 60 points. This is really hard for me and i dont get this.
Answer:
The discriminant is:
(-3)^2 - 4(1)(18) = 9 - 72 = -63
Since this discriminant is negative, f(x) does not have any real number solutions.
You roll a die 2 times. What is the probability or rolling a 6 and then a 2?
Answer:
1 out of 6
Step-by-step explanation:
Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.
Use Chebyshev’s inequality and the value of W to decide whether there is statistical evidence, at the significance level of α=0.05 , that D, the average proportion of all lightbulbs that are defective, is greater than 0.10.
Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.
Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.
Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,
P(|X - μ| ≥ kσ) ≤ 1/k²,
where μ and σ are the mean and standard deviation of X, respectively.
Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.
Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,
P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,
where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,
P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².
To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.
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know how I can find the measurements in Bloxburg?
Answer:
I'm sorry, but there is no feature for this in this game. But, there is a grid and a sizing tool. You'll just have to make an educated guess based on the size of your character and your character's stage of life (baby, toddler, kid, teen, adult). Hope I helped! I once had the same question, but just did this. I think each big grid square maybe is 3-5 ft?
Prepare the journal entry to record Jevonte Company's issuance of 29,000 shares of its common stock assuming the shares have a
a. $3 par value and sell for $16 cash per share.
b. $3 stated value and sell for $16 cash per share.
View transaction list
Journal entry worksheet
<
2
Record the issuance of 29,000 shares of common stock assuming the shares
have a $3 par value and sell for $16 cash per share.
Note: Enter debits before credits.
Transaction
General Journal
Cash
Common stock, $3 par value
Paid-in capital in excess
Debit
Credit
The journal entry to record the transaction is given:
Account Debit Credit
Cash $464,000
Common Stock, $3 par value $87,000
Paid-in capital in excess of par $377,000
What is a journal entry?A journal entry is used to record a business transaction in the accounting records of a business.
A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger
Assuming the shares have a $3 par value and sell for $16 cash per share:
Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000
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PLEASE HELP ME QUICK!!
According to the information, Sandra charges $2.25 for each necklace. So the correct option would be A.
How to find the answer to this problem?To find the answer to this problem we must identify the information that the function raises. In this case we must replace the n by a number (in this case it will be 5) to find the value of P as shown below:
P = 7.5*5 - (2.25 * 5 + 15)P = 37.5 - (11.25 + 15)P = 11.25Once we identify how much 5 necklaces are worth, we divide that value by 5 to find the unit value.
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A coach left woodlands and travelled towards Muar at an average speed of 50 Km/h.
Half an hour later, a car left Woodlands, travelled along the same route, and reached
Muar at 12.30 p.m. The distance between the two places was 150 km. The coach reached
Muar at 1.00 p.m
a) At what time did the car leave Woodlands?
b) What was the average speed of the car?
Answer:
a) 10:30 a.m.
b) 75 km/h
Step-by-step explanation:
You want to know the leaving time and speed of a car from Woodlands to Muar if it left half an hour later and arrived half an hour earlier than a coach that traveled the 150 km distance at a speed of 50 km/h and arrived at 1 p.m..
Travel timeThe travel time of the coach is found from the relation ...
time = distance/speed
time = (150 km)/(50 km/h) = (150/50) h = 3 h
Then the coach left Woodlands at ...
1 pm -3 h = 10 am
a) Leaving timeThe car left half an hour later than the coach, so left at 10:30 a.m..
b) SpeedThe car arrived at Muar at 12:30 p.m. so had a travel time of ...
12:30 -10:30 = 2 h
The speed over the 150 km distance is given by ...
speed = distance/time
speed = (150 km)/(2 h) = (150/2) km/h = 75 km/h
The average speed of the car was 75 km/h.
__
Additional comment
The car passed the coach at 11:30 a.m., when both had covered half the distance.
Can someone please help me with this problem? I'm struggling and the assignment is already late :(
Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5
The area of the similar triangle B is derived to be equal to 1.8 which makes option B correct.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
We shall represent the hight of triangle B with the letter h so that;
h/2 = 3/5
h = (2 × 3)/5 {cross multiplication}
h = 1.2
area of triangle B = 1/2 × 3 × 1.2
area of triangle B = 1.8
Therefore, the area of the similar triangle B is derived to be equal to 1.8
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If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and then shifted down 2 units, what is the resulting function? Write your answer in the form y=ceax+b
The resulting function is given as follows:
[tex]y = \frac{e^{2x}}{3} - 2[/tex]
How to obtain the resulting function?The parent function in the context of this problem is given as follows:
[tex]y = e^{-2x}[/tex]
When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:
[tex]y = \frac{e^{-2x}}{3}[/tex]
When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:
[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.
When it is shifted down two units, we subtract by two on the range, hence:
[tex]y = \frac{e^{2x}}{3} - 2[/tex]
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The coordinates of the midpoints of the four sides of a square are S(-4, 11), Q(2, 5), U(-4, -1), and A(-10, 5).
Determine the perimeter and area of the square.
5
O perimeter is 144 units; area is 48 square units
O perimeter is 48 units; area is 144 square units
O perimeter is 24√/2 units; area is 72 square units
O perimeter is 72 units; area is 24√/2 square units
The perimeter and area of the square are 24√2 units and 12 units² respectively
What is the perimeter and area of the square?
To determine the perimeter and area of the square, we have to find the lengths of the sides.
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find for QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find for UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance from AS = 6√2
The perimeter of the square = 4 * (6√2)
Perimeter = 24√2 units
The area of the square is l²
Area of the square = (6√2)²
Area of square = 12 units²
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Which one of the following examples represents a proper
fraction?
A. 15/22
B. 12/9
C. 3/2
O D. 8/8
A.15/22 is the correct answer.
The correct answer is:
A. 15/22, represents a proper fraction.
Here, we have,
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
Out of the given options, only option A,
15/22, represents a proper fraction because 15 is smaller than 22.
Therefore, the correct answer is:
A. 15/22, represents a proper fraction.
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An accountant drives 50 miles a day to work. Write an expression that represents the total number of miles he drives after x days
Answer:
It is 50x or 50*x or 50(x).
On Monday Harriet ate 1/4 of a 8 slice of pizza on Tuesday she ate 1/2 of the same pizza what fraction of The Whole Pizza did she eat
Harriet ate a total of 3/4 of the total pizza
Given data ,
On Monday Harriet ate 1/4 of a 8 slice of pizza
And , on Tuesday she ate 1/2 of the same pizza
Now , If the pizza has 8 slices, then Harriet ate 1/4 of 8 slices on Monday, which is 2 slices.
On Tuesday, Harriet ate 1/2 of the same pizza, which is 4 slices.
So, in total, Harriet ate 2 + 4 = 6 slices of pizza
On simplifying the equation , we get
The whole pizza has 8 slices, so Harriet ate 6/8 of the pizza, which simplifies to 3/4.
Hence , Harriet ate 3/4 of the whole pizza
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What is the area of this figure? 9 cm 2 cm 9 cm 7 cm Submit 4 cm 2 cm 3 cm Write your answer using decimals, if necessary. square centimeters 6 cm Work it out
Therefore , the solution of the given problem of area comes out to be the trapezium has a surface area of 39 square centimetres.
What does an area actually mean?Calculating how much space would be needed for fully covering its exterior will reveal its overall dimensions. The surrounding environment is considered while selecting a comparable product with a rectangular shape. The surface area of anything determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal shapes determines how much water it can contain.
Here,
We can use the formula for a trapezoid's area if we assume that the shape is a trapezoid with parallel sides that are 9 cm and 4 cm and a height of 6 cm.
=> A = (a + b)h/2
where h is the height, and a and b are the lengths of the parallel sides.
When we enter the values we have, we obtain:
=> A = (9 + 4)(6)/2
=> A = 13(3)
=> A = 39
Consequently, the trapezium has a surface area of 39 square centimetres.
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whats the answer to this
The calculated length of XY in the right triangle XYZ is 6
Calculating the length of XY in the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of XY in the right triangle can be calculated using the following sine ratio
sin(30) = XY/XZ
So, we have
sin(30) = XY/12
Cross multiply the equation
So, we have
XY = 12 * sin(30)
Evaluate the products
XY = 6
Hence, the length of XY in the right triangle is 6
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The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 30 to 10 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is negative one third, which means that the swimmer completes a lap in one third of a minute.
The slope of the line is −3, which means that the swimmer will complete 3 laps every minute.
The slope of the line is 10, which means that the swimmer will finish the race after 10 minutes.
The slope of the line is 30, which means that the swimmer must complete 30 laps in the race.
The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.
In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.
On the y-axis, the graph represents the number of laps the swimmer is completing.
When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:
Number of laps remaining----------Time (in minutes)
30 --- 0
27 --- 1
24 --- 2
21 --- 3
18 --- 4
15 --- 5
12 --- 6
9 --- 7
6 --- 8
3 --- 9
0 --- 10
From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.
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How many yards are in 150 in.
The answer
4.16666667 yards
six increased by the product of a number and 8 is at most -15
Answer:Answer and Explanation: An algebraic expression for the phrase '6 more than the product of 8 and n' is '8n + 6.
Step-by-step explanation:
Jenny is going to design and sell digital greeting cards through CelebrationStock. The online
platform informs Jenny that, based on market research, she will sell -15x + 120 cards in her
first month if she charges x dollars per card.
CelebrationStock will charge Jenny 30% of the amount she charges per card. So, Jenny will
earn 70% of the amount she charges per card, or 0.7x dollars, in profit.
To the nearest dollar, what is the highest price Jenny can charge per card to earn $125 in
profit in her first month?
Answer:
6
Step-by-step explanation:
To find the highest price Jenny can charge to earn $125 in profit, first write an equation.
total profit = profit per card * number of cards
You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.
125=0.7x(–15x+120)
Now, solve for x. Start by writing the equation in standard form
125=0.7x(–15x+120)
125= –10.5x2+84x
0= –10.5x2+84x–125
Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and
So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.
Which of the following is an exponential equation?
A.
3x + 2 = 23
B.
5 ‒ x2 = 4
C.
3x + 2 = 23
D.
7 ‒ 0.5x = 2x
Answer:
a. 3x = 23-2
3x = 21
x = 21÷3
x = 7
b. 5x - 2 = 4
5x = 4+2
5x = 6
x = 6÷5
x = 1.2
c. 3x = 23-2
3x = 21
x = 21÷3
x = 7
d. 7 = 2x+0.5x
7 = 2.5
x = 2.5÷7
x = 2.8
(a) In the figure below, two secants are drawn to a circle from exterior point H.
Suppose that HZ=16.8, HX-14, and HY=42. Find HW.
H
w
M
HW = 0
(b) In the figure below, two chords intersect inside the circle at point V.
Suppose that VJ-18, VM-36, and VK=27. Find MN.
MN = 0
Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units; MN = 49.5 units.
How to Apply the Intersecting Secants and Chords Theorem?To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.
a. HZ * HW = HX * HY [based on the intersecting secants theorem]
Plug in the values:
16.8 * HW = 14 * 42
HW = 588/16.8
HW = 35 units
b. VK * VJ = VM * VN [based on the intersecting chords theorem]
Plug in the values:
27 * 18 = 36 * VN
VN = 486/36
VN = 13.5 units
MN = VM + VN = 36 + 13.5
MN = 49.5 units
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What is the perimeter and area of the Rhombus?
Z
6.2,
W
Y
7.4
9.7 cm
X
Answer:
Perimeter of rhombus = 4(9.7) = 38.8 cm
Area of rhombus = 4(1/2)(6.2)(7.4)
= 91.76 cm^2
A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, then compiles the results into a probability distribution as shown in the table:
a.) There is a 25% chance that a party will contain 5 or more people. b.) There is a 50% chance that a party will contain 4 or more people. c.) There is a 50% chance that a party will contain 2 or fewer people.
d.) There is a 75% chance that a party will contain 3 or more people.
There are 25% chance of 5 more people in the party.
Hence option (a) is correct.
Relative frequency = (number of times of occurrence of an event )/ (number of trials)
For the given table
relative frequency for 1 people = 0.05 = 5%
relative frequency for 2 people = 0.46 = 46%
relative frequency for 3 people = 0.18 = 18%
relative frequency for 4 people = 0.22 = 22%
relative frequency for 5 people = 0.06 = 6%
relative frequency for 6 people = 0.03 = 3%
Since relative frequency for 1 people is 5%
Therefore,
Relative frequency for 5 people is = 5x5%
= 25 %
Hence,
Relative frequency of 5 more people 25%.
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Find the distance between the zeros of the (2x-8)^2-4=12
The distance between the zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12 is 4 units.
First, we can simplify the equation [tex](2x-8)^{2}[/tex] - 4 = 12 by adding 4 to both sides:
[tex](2x-8)^{2}[/tex] = 16
Next, we can take the square root of both sides:
2x-8 = ±4
Solving for x in each case, we get:
2x-8 = 4: 2x = 12 → x = 6
2x-8 = -4: 2x = 4 → x = 2
So the zeros of the equation are x=6 and x=2. The distance between them is:
distance = |6 - 2| = 4
As a result, there are 4 units between zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12.
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Select all true statements about the graph that represents y=2x(x−11) .
The correct answers for the quadratic equation are:
Roots of a quadratic equation are the points where y = 0.
Abscissa of a quadratic equation are the points where x = 0.
If the equation of a quadratic equation is in the vertex form,
y = a(x - h)² + k
Vertex of the U-shaped curve will be (h, k)
Given in the question, where the equation of the u-shaped curve is
y = 2x(x - 11)
Convert the equation in the vertex form,
y = 2x² - 22x
y = 2(x² - 11x)
y = 2 * (x² - 2 ( 5.5x) + (5.5)² - (5.5)²)
y = 2[(x - 5.5)² - 30.25]
y = 2(x - 5.5)² - 60.5
Hence, the vertex of the U-shaped curve will be (5.5, -60.5).
For x-intercepts,
Substitute y = 0,
0 = 2x(x - 11)
⇒ x = 0, 11
Therefore, roots of the parabola will be (0, 0) and (11, 0).
and the ordinate of the vertex is x = 5.5
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Question 15 (1 point)
You have purchased a new farm. Your lawn will be watered by central pivot irrigation,
where sprinklers rotate around a central point. If the line of sprinklers turning around
the central pivot is 300 ft long, write an equation to model the circular boundary of
your sprinkler. Assume the center is (0,0).
x² + y² = 360000
x²+²=90000
x² + y² = 900
x² + y² = 3600
The equation of the circle in this problem is given as follows:
x² + y² = 90000
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The center for this problem is given as follows:
(0,0).
The radius is given as follows:
300 ft.
Hence the equation is of:
x² + y² = 90000
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A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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Mia is designing a cake for a birthday party. She plans for a total of 20 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?
The square cake can be distributed in such a way that each person out of 15 guest may get 8 , with the least amount left over .
The Correct option is (1).
What is Volume of any shape?
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.
First find the volume of square cake,
Volume = l x b x h
= 8 x 8 x 2
=128
Now there are total 15 guests, Each of get
=
= 8.533
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume=
=
=
=28.26
Now there are total 15 guests, Each of get
=
= 1.884
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume=
=
=
=50.24
Now there are total 15 guests, Each of get
=
= 3.349
4. Volume = l x b x h
= 6 x 9 x 2
=108
Now there are total 15 guests, Each of get
=
= 7.2
According to question each person may get 8 .
Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .