Answer:
[tex]\boxed{-3(x+3)(x^2-6x+10)}[/tex]
Step-by-step explanation:
Hello,
As the polynomial has only real coefficients, it means that 3-i is a zero too, because we apply the Conjugate Zeros Theorem.
It means that we can write the expression as below, k being a real number that we will have to identify.
[tex]k(x+3)(x-3-i)(x-3+i)=k(x+3)((x-3)^2-i^2)\\\\=k(x+3)(x^2-6x+9+1)\\\\=k(x+3)(x^2-6x+10)[/tex]
And for x = 0, y = -90 so we can write
-90=k*3*10, meaning that k=-3
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
in need of assistance answers are greatly appreciated thank you for your time and effort
Answer:
x = (h+g)/-f
Step-by-step explanation:
-fx-g = h
Add g to each side
-fx-g+g = h+g
-fx = h+g
Divide each side by -f
-fx/-f = (h+g)/-f
x = (h+g)/-f
cSuppose you are standing such that a 45-foot tree is directly between you and the sun. If you are standing 200 feet away from the tree and the tree casts a 225-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 225 ft 200 ft 45 ft Your height is ft (If needed, round to 1 decimal place.)
Answer:
you could stand at 5.0 ft and still be completely in the shadow of the tree
Step-by-step explanation:
From the diagram attached below;
We consider;
[tex]\overline {BC}[/tex] to be the height of the tree and [tex]\overline {DE}[/tex] to be the height of how tall you could be and still be completely in the shadow of the tree.
∠D = ∠B = 90°
Also;
ΔEAD = ΔBAC (similar triangles)
Therefore, their sides will also be proportional
i.e
[tex]\dfrac{\overline {DE}}{ \overline {BC}}= \dfrac{\overline{AD}}{ \overline{AC}}[/tex]
[tex]\dfrac{x}{ 45}= \dfrac{225-220}{225}[/tex]
[tex]\dfrac{x}{ 45}= \dfrac{25}{225}[/tex]
By cross multiply
225x = 45 × 25
[tex]x = \dfrac{45 \times 25}{225}[/tex]
[tex]x = \dfrac{1125}{225}[/tex]
x = 5.0 ft
Therefore, you could stand at 5.0 ft and still be completely in the shadow of the tree
A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27 It is known that the population standard deviation is 7. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours. Test to determine whether there is evidence at the 0.07 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.A. The value of the standardized test statistic:Note: For the next part, your answer should use interval notation. An answer of the form (−[infinity],a) is expressed (-infty, a), an answer of the form (b,[infinity]) is expressed (b, infty), and an answer of the form (−[infinity],a)∪(b,[infinity]) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic:C. The p-value isD. Your decision for the hypothesis test: A. Reject H0. B. Do Not Reject H1. C. Do Not Reject H0. D. Reject H1.
Answer:
Reject H₀.
Step-by-step explanation:
In this case, we need to test whether the average student spent less than the recommended amount of time doing homework in statistics.
The provided data is:
S = {20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27}
Compute the sample mean:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{12}\cdot [20+29+...+27]=23.167[/tex]
The population standard deviation is σ = 7.
The hypothesis for the test is:
H₀: The average student does not spent less than the recommended amount of time doing homework, i.e. μ ≥ 24.
Hₐ: The average student spent less than the recommended amount of time doing homework, i.e. μ < 24.
(A)
Compute the standardized test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{23.167-24}{7/\sqrt{12}}\\\\=-0.412[/tex]
Thus, the standardized test statistic value is -0.412.
(B)
The significance level of the test is:
α = 0.07
The critical value of z is:
z₀.₀₇ = -1.476
The rejection region is:
(-∞, -0.1476)
(C)
Compute the p-value as follows:
[tex]p-value=P(Z<-0.412)=0.34[/tex]
*Use a z-table.
Thus, the p-value is 0.34.
(D)
Since, p-value = 0.34 > α = 0.07, the null hypothesis was failed to be rejected at 7% level of significance.
Thus, the correct option is (A).
Does anyone know how to find the area of this problem?
Answer:
Step-by-step explanation:
2x2=4 4x1=4
Answer:
7units²
Step-by-step explanation:
I cut the shape into smaller shapes, found the area of each smaller shape, then added those areas together to find the total area for the whole shape :)
Please find the answer
Answer:
0.3 is the right answer.
Step-by-step explanation:
hope this helps
look at the image below
Answer:
1520.5 yd²
Step-by-step explanation:
Surface area of a sphere = 4πr², where r is the radius
so,
4πr²
= 4×π×11²
= 484π
= 1520.5 yd²
A line passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3
Answer:
y= -(1/6)x -2
Step-by-step explanation:
We know:
y= mx +b is the general equation of the line
Was given:
y= 6x +3, has the slope m=6
Find the equation of the line
y= -(1/6)x + b, perpendicular lines have their slope negative reciprocal m=-1/6
Find the y-intercept that is b
for point (x=12, y= -4) the equation of our line becomes
-4 = -(1/6)(12) + b, multiply a fraction and a number (a/b)*c = ab/c
-4 = -12/6 +b, simplify the fraction
-4 = -2 + b , add 2 to both sides
-4+2 = -2+2 +b , solve for b
-2 = b
The equation of the line that passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3 is :
y= -(1/6)x -2
A manager wants to determine an appropriate learning percentage for processing insurance claims for storm damage. Toward that end, times have been recorded for completion of each of the first six repetitions:
Repetition 1 2 3 4 5 6
Time (minutes) 46 39 35 33 32 30
a. Determine the approximate learning percentage. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.)
P %
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
Answer:
Step-by-step explanation:
The approximate learning percentage can be estimated by using a doubling method.
If we breakdown the repetitions into three consecutive parts, we have:
1 - 2
2 - 4
3 - 6
then
1 - 2 → 46P = 39
P =39/46
P = 0.8478
P = 84.8%
2 - 4 → 39P = 33
P = 33/39
P = 0.84615
P = 84.6%
3 - 6 → 35P = 30
P = 30/35
P = 0.8571
P = 85.7%
The average value of P = (84.8 + 84.6 + 85.7)/3 = 85.03%
[tex]\simeq[/tex] 85%
From the tables of Learning Curves coefficient
The values are likened against times derived from 85% table factors at T[tex]_1[/tex] = 46
Unit 1 2 3 4 5 6
Date 46 39 35 33 32 30
Computed - 39.1 35.56 33.26 31.56 30.22
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
The average completion time = [tex]\mathtt{\dfrac{T_1 \times \ Total \ time\ factor}{n}}[/tex]
At the total time factor 30, from the learning curves table , n(30) = 17.091
Thus:
The average completion time = [tex]\mathtt{\dfrac{46 \times \ 17.091}{30}}[/tex]
The average completion time = [tex]\mathtt{\dfrac{786.186}{30}}[/tex]
The average completion time = [tex]\mathtt{26.2062}[/tex]
The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 14 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 4 hr after dosage.
a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours after a 1000-mg dosage.
b) Estimate the concentration of the drug 3 hr after a 1000-mg dosage.
c) To relieve a fever, the concentration of the drug should go no lower than 4 mcg/mL. After how many hours will a 1000-mg dosage drop to that level?
k = ________(Round to three decimal places as needed.)
Answer:
Step-by-step explanation:
14 = 1000 [tex]e^{ k*1}[/tex]
.014 = [tex]e^{k*1}[/tex]
ln(.014) = k ln(e)
k = -4.268
~~~~~~~~~~~~~~~~~~
after 3 hrs
1000 [tex]e^{ -4.268*3}[/tex]
0.00274
~~~~~~~~~~~~~~~
4 = 1000 [tex]e^{ -4.268*t}[/tex]
.004 = [tex]e^{ -4.268*t}[/tex]
ln(.004)/-4.268 = t
t = 1.29368 hrs
Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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2 1/2 cases of soda to split between 5 families
The fraction that each person gets is 1/2.
How to compute the fraction?It should be noted that 2 1/2 cases of soda to split between 5 families.
In their case, the fraction that each person will get will be:
= Total / Number of people
= 2 1/2 ÷ 5
= 2.5/5
= 0.5 or 1/2.
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2 1/2 cases of soda to split between 5 families. What fraction will each person get?
Find the value of x
9
7
X
9
Answer:
13.41
Step-by-step explanation:
You are so welcomed
The measure of each of the remaining angles in the right angle triangle is 45 degrees.
To find the measure of the remaining angles in the triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees. Since we know one angle is 90 degrees, we can find the measure of the other two angles by subtracting 90 from 180.
Let's call the remaining two angles A and B. Thus, we have:
Angle A + Angle B + 90 degrees = 180 degrees.
Rearranging the equation, we get:
Angle A + Angle B = 90 degrees.
Since the two sides of the triangle adjacent to the right angle are equal (given as 9 and 9), we can conclude that the remaining two angles are congruent (equal). Let's call the measure of each of these angles x.
Therefore, we have:
x + x = 90 degrees.
Simplifying, we get:
2x = 90 degrees.
Dividing both sides by 2, we find:
x = 45 degrees.
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Cuánto es 324 por 171
Answer:
la respuesta es 55,404
I hope this helped
3a-27=0
How to solve
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
How to convert 2cm to feet?
Answer:
Divide by 30.48: It would be 0.0656168 feet.
Step-by-step explanation:
Answer:
0.0656
Step-by-step explanation:
2.54 cm = 1 in
12 in = 1 ft
2.54 * 12 = 30.48
2/30.48 = 0.0656167979
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero
Answer:
-11/13
Step-by-step explanation:
The equation of the line through these points can be written using the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-3))/(-9-4)/(x -4) -3
y = (-7/13)x +28/13 -3
For x=0, the value of y is ...
y = 28/13 -39/13 = -11/13
The output for an input of 0 is -11/13.
If f(x) = 2x – 1 and g(x) = x^2 – 2, find [g ◦ f](x).
Show work please
Answer:
2x^3-x^2-4x+2
Step-by-step explanation:
(g*f)(x) = g(x)*f(x) = (x^2-2)*(2x-1) = 2x^3-x^2-4x+2
Give an example of when and why one would use a continuity correction factor?
Answer:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
and continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution
Step-by-step explanation:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution, continuity correction factor creates an adjustment on a discrete distribution while using a continuous distribution
A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.
Answer:
1/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event /total outcome
Since the population consists of 100 elements, the total outcome of event = 100.
If random sample of 20 element is drawn from the population, the expected outcome = 20
On the first selection, the probability of any particular element being selected = 20/100 = 1/5
Ms. Suzie invested $35,000 in two accounts, one yielding 6% interest and the other yielding 11%. If she received a total of $2900 in interest at the end of the year, how much did she invest in each account?
Answer:
Step-by-step explanation:
6% = 0.06
11% = 0.11
x + y = 35,000 ....................... (1)
0.06x + 0.11y = 2,900 .......... (2)
(1) × 0.06 - (2)
0.06y - 0.11y = 0.06 × 35,000 - 2,900
- 0.05y = - 800
y = 16,000
x = 19,000
Ms. Suzie invested $19,000 in 6% interest account and $16,000 in 11% interest account.
What is the value of (–7 + 3i) + (2 – 6i)?
a. –9 – 3i
b. –9 + 9i
c. –5 + 9i
d. –5 – 3i
Answer:
d
Step-by-step explanation:
(-7 + 3i) + (2-6i)
=-7 + 3i + 2 -6i
=(-7+2) + (3i -6i)
=-5 -3i
Answer:
(-7+3I)+(2-6I)
= -7+3i+2-6i
= -5-3I
so answer is d ie -5-3i
given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9
Answer:
f(g(9)) = 945/16
Step-by-step explanation:
To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).
g(x) = x + 3/4
f(x) = x² - 4x - 3
f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3
f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3
f(g(x)) = x² - 5/2x + 9/16 + 3 - 3
f(g(x)) = x² - 5/2x + 9/16
Now, put a 9 wherever there is an x in f(g(x)).
f(g(9)) = (9)² - 5/2(9) + 9/16
f(g(9)) = 81 - 5/2(9) + 9/16
f(g(9)) = 81 - 45/2 + 9/16
f(g(9)) = 117/2 + 9/16
f(g(9)) = 945/16
In December 2004, a report based on the National Survey on Drug Use and Health estimated that 20% of all Americans aged 16 to 20 drove under the influence of drugs or alcohol in the previous year. We would like to update this information by calculating a 98% confidence interval. How large a sample is necessary in order for the bound on the error of estimation to be 0.04?
Answer:
542
Step-by-step explanation:
We are required to find the sample size at 98% confidence interval in this question
E = 0.04
P* = 20% = 0.20
n = p* x (1-p)(Zα/2÷E)²
α = 1 - 0.98
= 0.02
To get Critical value
= 0.02/2 = 0.01
The critical value at 0.01 is 2.33
Inserting values into formula:
O.2 x 0.8(2.33/0.04)²
= 0.8 x 0.2 x 58.25²
= 542.89
The value of n must be an integer therefore the answer is 542.
A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
13.) Jessica earns 5 points for every assignment she completes, plus 15 points just for being in class on a given day. How many assignments does she need to complete to earn 65 points? First, write the equation that fits this model. Let z be the amount of assignments completed. *
Answer:
10
5z+15=65
Step-by-step explanation:
5z+15=65
5(10)+15=65
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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Suppose that 22 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
cents
Х
?
Answer:
51 cents for 17 inches of wire
Step-by-step explanation:
22 = 66
17 = x
22x = 66 * 17
22x = 1122
x = 51 cents
or
22 inches costs 66 cents
1 inch costs 3 cents (66 / 22 = 3 cents)
17 inches costs 51 cents (17 * 3 = 51 cents)
Which methods could you use to calculate the y-coordinate of the midpoint of vertical line segment with endpoints at (0,0) and (0,15)? Check all that apply
Answer:
Midpoint formula.
The midpoint formula is (x_1+x_2)/2 , (y_1+y_2)/2
Step-by-step explanation:
This is one method. A list wasn't provided.
Which of the following is a solution to 6x - 5y=4?
(2,7)
(-1, -2)
(-2, -1)
(2, -7)
Answer:
2,7
Step-by-step explanation:
Answer:
(-1,-2)
Step-by-step explanation:
(6 x -1) -(-2 x 5) = 4
-6 + 10 = 4