Answer:(x + 1)(x - 1)(x + 5)(x - 3) is the fully factored form of the polynomial.
The zeros are (-1, 0), (1, 0), (-5, 0), and (3, 0).
x^4 + 2x^3 - 16x^2 - 2x + 15
We can use the rational roots theorem to find some of the possible roots, and after finding just one root, we can simplify this polynomial.
List factors of 15:
1, 3, 5, 15.
List factors of 1:
1.
Our possible rational factors are:
+/- 1, +/- 3, +/- 5, +/- 15.
To find factors, we can use the remainder theorem.
Replace all x values with 1.
1^4 + 2(1)^3 - 16(1)^2 - 2(1) + 15 = 0
Because the answer is zero, it means that 1 is a root.
We can divide this polynomial by x - 1 to find a simplified form.
After dividing, our quotient is: x^3 + 3x^2 - 13x - 15
We can continue finding factors by using the rational roots theorem. Once we have only three terms, we can try to factor using the AC method.
Our next possible root is -1.
(-1)^3 + 3(-1)^2 - 13(-1) - 15 = 0
We know that -1 is also a root, and so we can divide the polynomial by x + 1.
After diving we're left with x^2 + 2x - 15.
Now, we can try to factor using the AC method.
List factors of -15.
1 * -15
-1 * 15
3 * -5
-3 * 5 (these digits satisfy the criteria.)
Split the middle term.
x^2 - 3x + 5x - 15
Factor binomials.
x(x - 3) + 5(x - 3)
Rearrange binomials.
(x + 5)(x - 3)
Add in the two factors we already factored out.
(x - 1)(x + 1)(x + 5)(x - 3)
Step-by-step explanation:
2. A paving company is paving the rectangular student parking lot at Hamilton High School. The
length of the parking lot can be represented as (5p - 7) and the width as (3p + 4). Which
expression represents the area of the parking lot?
Answer:
15p2 - p - 28
Step-by-step explanation:
where is the hundredth in the number 5870.23
Answer:
5870.23
The digit 3
Step-by-step explanation:
Which expression is equivalent to 6x-9•3
Shannon states that
7
5
8
−
5
1
3
=
2
4
5
because
7
−
5
=
2
,
5
−
1
=
4
, and
8
−
3
=
5
.
First, state whether you agree or disagree. Then, explain briefly how to subtract mixed numbers with unlike denominators. Be sure to show your solution as a subtraction equation.
I disagree with Shannon's statement that 758−513=245 based on the reasoning provided.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.
Here,
While it is true that 7−5=2, 5−1=4, and 8−3=5, this reasoning only applies to the individual digits in each place value, not the numbers as a whole. To subtract the two mixed numbers 7 5/8 and 5 1/3, we need to find a common denominator first.
To subtract mixed numbers with unlike denominators, we follow these steps:
Convert each mixed number to an improper fraction.
Find a common denominator for the two fractions.
Subtract the numerators and write the result over the common denominator.
Simplify the result, if possible, by reducing the fraction to lowest terms or converting it back to a mixed number.
Let's apply these steps to the problem:
7 5/8 - 5 1/3
Step 1: Convert each mixed number to an improper fraction.
7 5/8 = (87 + 5)/8 = 59/8
5 1/3 = (35 + 1)/3 = 16/3
Step 2: Find a common denominator for the two fractions.
The least common multiple of 3 and 8 is 24, so we'll use 24 as the common denominator.
59/8 = (593)/(83) = 177/24
16/3 = (168)/(38) = 128/24
Step 3: Subtract the numerators and write the result over the common denominator.
177/24 - 128/24 = 49/24
Step 4: Simplify the result, if possible, by reducing the fraction to lowest terms or converting it back to a mixed number.
49/24 is already in its simplest form, so the final answer is 49/24.
Therefore, the correct result of 7 5/8 - 5 1/3 is 49/24, not 245.
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Someone please want to do my algebra assignments all due at 11 tn I need help at least ;(
Answer:
-48
Step-by-step explanation:
I think!! :)
17 m
17 m
16 m
Find the area of the isoceles triangle.
The area is
square meters.
9514 1404 393
Answer:
120 m²
Step-by-step explanation:
If you divide the isosceles triangle into two right triangles, each has a leg and hypotenuse of 8 and 17, respectively. You may recognize these numbers as part of the Pythagorean triple (8, 15, 17). That recognition tells you the triangle's height is 15 m, so its area is ...
A = 1/2bh
A = 1/2(16 m)(15 m) = 120 m² . . . . triangle area
__
Alternate solutions
Given the three sides, you can find the smallest angle from the Law of Cosines. It will be ...
α = arccos((17² +17² -16²)/(2·17·17)) ≈ 56.144°
Then the area is ...
A = 1/2·ab·sin(C) . . . for triangle with sides a, b, c and opposite angles A, B, C
A = 1/2sin(α)·17·17 = 120 . . . m²
__
Using Heron's formula:
s = (17 +17 +16)/2 = 25
A = √(25(25 -17)(25 -17)(25 -16)) = 5×8×3 = 120 . . . m²
__
If you need to, you can compute the triangle's height from the Pythagorean theorem.
a² +b² = c² . . . . generic Pythagorean theorem equation
8² + h² = 17² . . . with relevant values filled in
h² = 289 -64 = 225
h = √225 = 15
A bank wants to estimate the difference in the proportion of its "big" customers who have a second account with a different bank and the proportion of its "small" customers who also have an account with another bank. Of the 200 "big" customers randomly selected, 160 claimed to also bank elsewhere. Of the 300 "small" customers randomly selected, 120 claimed to also bank with other banks. Check the conditions for constructing a confidence interval for the difference in proportions.
Answer:
Kindly check explanation
Step-by-step explanation:
To construct confidence interval for difference in proportion ; the following conditions must be met :
1.) The selected samples must have been randomly chosen or selected from a larger population. This is essential in other to eliminate bias.
Each group of samples must be independently chosen. That is, the samples of bug customers chosen must be independent of the sample of small customers selected.
The population from which the samples are drawn must be considerably larger than the sample size. Sample size, n should be ≤ 10% of the population size.
p1 = 160 / 200 = 0.8 ; (1 - p1) = 0.2
p2 = 120 / 300 = 0.4 ; (1 - p2) = 0.6
(p1 - p2) ± Zcritical * sqrt[(p1(1 - p1) /n1) + (p2(1 - p2) / n2)]
Answer: A
Step-by-step explanation:
Before starting to play the roulette in a casino you want to look for biases that you can exploit. Youtherefore watch 100 rounds that result in a number between 1 and 36 and you count the number ofrounds for which the result is odd. If the count exceeds 55, you decide that the roulette is not fair.Assuming that the roulette is fair, find an approximation for the probability that you will makethe wrong decision.
Answer:
[tex]P(n>55)=0.1357[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size n=100
Sample space n'=36
Generally the equation for the mean number of times odds appears is mathematically given by
[tex]\=x_o=hp[/tex]
[tex]\=x_o=100*0.5[/tex]
[tex]\=x_o=50[/tex]
Generally the equation for standard deviation is mathematically given by
[tex]\sigma=(hp(1-p))^{1/2}\\\sigma=(50(0.5))^{1/2}[/tex]
[tex]\sigma=5[/tex]
Therefore probability to make wrong decision P(n>55)
[tex]P(n>55)=1-P(z<50.5/5)\\P(n>55)=1-P(z<1.1)\\P(n>55)=1-0.86[/tex]
[tex]P(n>55)=0.1357[/tex]
An approximation for the probability that you will make the wrong decision is 0.1587.
ProbabilityS=Number of time that the result was odd
n=100
p=0.5
Hence:
E[S]=100×0.5
E[S]=50
Standard deviation=√100×0.5×0.5
Standard deviation√25
Standard deviation=5
Using normal approximation to the binomial
P(S≥55)=P(S-50/5 ≥ 55-50/5)
P(S≥55)=1-P(z ≤ 1)
P(S≥55)=1-0.8413
P(S≥55)= 0.1587
Inconclusion an approximation for the probability that you will make the wrong decision is 0.1587.
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Someone please help me asnwer this!!
Answer:
89 cm
Step-by-step explanation:
By Pythagoras Theorem,
c² = 80² + 39²
c² = 6400 + 1521
c² = 7921
c = 89 cm
Hope it helps :)
Would anyone please help me with these if they can?
Answer:
12) F.0
13) 3/2
Step-by-step explanation:
12)
(5, 0) and (10, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-0)/(10-5)
m = 0
13)
(3, 2) and (-1, -4)
Slope:
m=(y2-y1)/(x2-x1)
m=(-4-2)/(-1-3)
m=(-6)/(-4)
m= 3/2
please help me with this as soon as you can
9514 1404 393
Answer:
14.14
Step-by-step explanation:
The diagonal of a square is √2 times the side length.
AC = AB×√2
AC = 10√2 ≈ 14.14
_____
The diagonal of a square is the hypotenuse of an isosceles right triangle. If the sides of that are s and the diagonal is d, the Pythagorean theorem tells us ...
d² = s² + s²
d² = 2s²
d = (√2)(√s²) = s√2
This relation holds for any isosceles right triangle, not just for the diagonal of this square. It is useful to remember.
Easy Work! Please look at the picture and yes it’s easy for other people but not for me for people asking please and thank you.
3 + (2 + 8)2 ÷ 4 × 1/ 2 to the power of 4
Answer:
The answer to this is 4 and 9 over 16.
Step-by-step explanation:
The expression is 3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 . it can be represented mathematically as
3 + (2 + 8)^2 ÷ 4 × (1/2)^4
using PEMDAS
parenthesis come first
3 + 10^2 ÷ 4 × (1/2)^4
exponential comes next
3 + 100 ÷ 4 × 1/16
3 + 25 × 1/16
3 + 25/16
(48 + 25)/16
73/16
4 9/16
what is robert hoover’s name? only for robbie
Answer:
Hoover flew Spitfires in the United States Army Air Forces during World War II and was shot down in 1944 off the coast of France. He was held for over a year in a German POW camp before eventually escaping and flying to safety in a stolen enemy aircraft. He then worked as a United States Air Force and civilian test pilot after the war, flying chase for the Bell X-1 supersonic flight, and as a flight instructor for North American Aviation during the Korean War.
He is best known as an air show display pilot, who flew for nearly 50 years until his retirement in 1999.[1] Known as the "pilot's pilot", Hoover revolutionized modern aerobatic flying and has been described in many aviation circles as one of the greatest pilots of all time.
Step-by-step explanation:
pls give me brainless
15 cm
15 cm
16 cm
20 cm
57 cm
What is the perimeter of the polygon?
Answer:
C.
Step-by-step explanation:
15 x 16=240 x 2= 480
57 x 20= 1140
1140 + 480 = 1620
What Are the missing numbers?
Answer:
[tex] y = -\frac{3}{2}x + 12 [/tex]
Step-by-step explanation:
The missing numbers represent the slope/rate of change (m) and y-intercept (b) of the table of values given.
✔️Let's find slope (m) using any two given pairs of values, say (2, 9) and (4, 6):
Slope (m) = change in y/change in x
= (6 - 9)/(4 - 2)
= -3/2
m = -³/2
✔️Find b by substituting (x, y) = (2, 9), and m = -³/2 into y = mx + b
Thus,
9 = -³/2(2) + b
9 = -3 + b
9 + 3 = b
b = 12
The missing numbers are -³/2 and 12.
Which will give us:
[tex] y = -\frac{3}{2}x + 12 [/tex]
Solve for x.
7(x + 2) = 6(x + 5)
X=-44
x = -16
x = 16
X= 44
Look in picture
Help please
Answer:
x= 16
Step-by-step explanation:
First, you want to distribute each side! (you're gonna wanna learn this because you will be having to do it for the next 3 years no joke it sucks)
7(x+2) can be distributed as 7x+14 after multiplying 7 times x and 7 times 2, and 6(x+5) can be distributed as 6x+30.
Now, you have to get the x on one side to solve for x (so like x=__).
To do this, look at the equation as of now. 7x+14=6x+30.
We can minus 14 and bring that to the right, and minus 6x and bring that to the left to separate the x's and the regular numbers.
Now we have 16=x (or x=16).
Find mZDOC.
A)
22°
B)
44°
C)
107
D)
126
Answer: [tex]107^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle DOC=\frac{170+44}{2}=\boxed{107^{\circ}}[/tex]
Evaluate 7 + 5^ 2 . 4.
7+5^2.4
=7+47.591348
=54.591348
Answer: 7 + 5^ 2 . 4= 107 if you evaluate sorry if i am wrong
Step-by-step explanation:
2.6 cm = .........................mm
Answer:
26 mm
Step-by-step explanation:
1 cm is equal to 10 mm
2.6 cm
> 2.6 x 10
> 26 mm
helpppp meeee! pleaseeee!
Answer:
9
11
17
25
Step-by-step explanation:
Input the x into the equation
Answer:
2×2+5=9
2×3+5=11
2×6+5=17
2×10+5=25
Canine Crunchies Inc. (CCI) sells bags of dog food to warehouse clubs. CCI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 45 kilograms and a standard deviation of 1.2 kilograms.
Requried:
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?
Answer:
a) 0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b) 0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c) 46.24 kilograms
d) The standard deviation would have to be of 3.41 kilograms.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 45 kilograms and a standard deviation of 1.2 kilograms.
This means that [tex]\mu = 45, \sigma = 1.2[/tex]
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
This is the pvalue of Z when X = 49.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49.5 - 45}{1.2}[/tex]
[tex]Z = 3.75[/tex]
[tex]Z = 3.75[/tex] has a pvalue of 0.9999
0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
This is the pvalue of Z when X = 51 subtracted by the pvalue of Z when X = 48.5.
X = 51
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51 - 45}{1.2}[/tex]
[tex]Z = 5[/tex]
[tex]Z = 5[/tex] has a pvalue of 1
X = 48.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48.5 - 45}{1.2}[/tex]
[tex]Z = 2.92[/tex]
[tex]Z = 2.92[/tex] has a pvalue of 0.9982
1 - 0.9982 = 0.0018
0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
This is the 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 45}{1.2}[/tex]
[tex]X - 45 = 1.037*1.2[/tex]
[tex]X = 46.24[/tex]
46.24 kilograms.
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?
X = 52 would have to be the 100 - 2 = 98th percentile, which is X when Z has a pvalue of 0.98, so X when Z = 2.054. We would need to find the value of [tex]\sigma[/tex] for this.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{52 - 45}{\sigma}[/tex]
[tex]2.054\sigma = 7[/tex]
[tex]\sigma = \frac{7}{2.054}[/tex]
[tex]\sigma = 3.41[/tex]
The standard deviation would have to be of 3.41 kilograms.
What's the surface area?
Answer:
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area
Step-by-step explanation:
Answer:
of what
Step-by-step explanation:
Describe the shape that results from a cross section that is parallel to the base of a right cylinder.
Answer:
Circles
Step-by-step explanation:
Think of a soup can sitting on its base on a kitchen counter. The counter is an example of a plane (through) parallel to the base. The points where the can and counter intersect form a circle. Put a book on top of the can. Again, the plane of the book is parallel to the base and the book and can intersect in a circle.
The same thing would happen if you cut the can open with a plane anywhere in between the two mentioned above, but it would make a mess!
The answer is circles. If you cut this shape in half you will get two circles.
In a lab experiment, 290 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 26 hours. How long would it be, to
the nearest tenth of an hour, until there are 330 bacteria present?
GUYS NEED HELP I HAVE A MATH TEST
Answer:
4.8
Step-by-step explanation:
PLEASE PLEASE HELP
find the value of y
Answer:
Step-by-step explanation:
y=108/2=54°
Answer:
Y = 54
Step-by-step explanation:
PLEASE HELPP!!!!!! FOR 10 POINTS. Am I right? Show work if I’m wrong
Answer:
you are correct, they are supplementary
Step-by-step explanation:
Answer:
Yes! You are correct! The angles added together produce 180degrees, therefore, is supplementary. Just like the fellow above me said :)
Step-by-step explanation:
A rectangular field has side lengths that measure 9/10 mile and 1/2 mile. What is the area of the field?
What is the factored form of x^3 - x^2 - 30x?
Answer:
x(x − 6) (x + 5)
Step-by-step explanation:
this is the factored form of x^3 - x^2 - 30x
hope this helps and is right :)
Given f x please help me
Try math-way, it gives you the answers to stuff in mathematics, in this case algebra. Also there's no - between the two words, I had to do this because of brainly.