Doing factorization, we know that the factors of the given equation are ±√5 and ±10i.
In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.
For example, 3 × 5 is a factorization of an integer 15 and is a factorization of an equation x² – 4.
So, we have the equation:
x⁴ + 95x² – 500 = 0
Factorizing the above equation:
x⁴ + 100x² - 5x² - 500 = 0
x²(x² + 100) - 5(x² + 100) = 0
(x² - 5)(x² + 100) = 0
Solving further:
x² = 5
x² = -100
x = ±√5
x = √-100
Factors: ±√5 and ±10i
Therefore, doing factorization, we know that the factors of the given equation are ±√5 and ±10i.
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Complete question:
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10
PLS HELP ASAP
QUESTION ON SCREENSHOT
Answer: D
Step-by-step explanation:
Drawing a straight line between the two x's would give the line bisecting MN.
point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
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a manufacturer of mp3 players conducts a set of comprehensive tests on the electrical functions of its product. all mp3 players must pass all tests prior to being sold. of a random sample of 500 mp3 players, 15 failed one or more tests. find a 90% confidence interval for the proportion of mp3 players from the population that pass all tests.
0.957 < p < 0983 is a 90% confidence interval for the proportion of mp3 players from the population that pass all tests
How do I calculate 90% confidence interval?Add and subtract the margin of error from the sample mean to get this confidence interval. The confidence interval's top and lower limits are represented by this result.We can be 90% certain that the interval contains the population mean,, if the degree of confidence is 90%. The associated z-scores are 1.645. In order to calculate a confidence interval, the sample mean (X) and, if applicable, the population standard deviation () must be known. When the sample size is more than 30, the sample standard deviation, s, can be used in place of the population standard deviation..Given :
a random sample of 500 mp3 players, 15 failed one or more tests.
no of passed mp3 players = 500-15 =485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
90% confidence interval.
1- [tex]\alpha[/tex] = 90%
[tex]\alpha = 0.1[/tex]
[tex]Z_{\alpha/2}[/tex] = [tex]z_{.05} =1.645[/tex]
[tex]\hat{p} -[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]< p< [tex]\hat{p} +[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]
0.957 < p < 0983
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A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
How can I determine the confidence interval at 90%?To obtain this confidence interval, add and subtract the margin of error from the sample mean. This result represents the upper and lower bounds of the confidence interval.
If the level of confidence is 90%, we can be 90% confident that the interval contains the population mean. The corresponding z-score is 1.645.
The sample mean (X) and, if relevant, the population standard deviation must be known in order to compute a confidence interval. The sample standard deviation, s, can be used in place of the population standard deviation when the sample size is greater than 30.
According to the given information
15 out of 500 mp3 players in a random sample failed one or more tests.
MP3 players that have been passed: 500-15 = 485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
Confidence interval of 90%.
[tex]1-\alpha[/tex] = 90%
[tex]\alpha[/tex] = 0.1
[tex]Z_{\frac{\alpha }{2} } = Z_{.05} = 1.645[/tex]
[tex]p-Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]<p<[tex]p+Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]
0.957 < p < 0983
A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
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What is the value of m?
The value of m in the diagram is 18°
What is a right-angle?
A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.
A right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life.
From the diagram, the two angles sum up to 90°
∠WZX + ∠XZY = ∠WZY
3m + 3 + 33 = 90
3m + 36 = 90
3m = 90 - 36
3m = 54
m = 54/3
m = 18°
In conclusion the value of m is 18°
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Which of the following is the discriminant of the quadratic equation: ax- bx +c= 0, where a,b,c are real number and a 0? A. b2
B. Vb2 - 4ac
C. b2 - 4ac
D. -b + Vb2 - 4ac
The required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
What is discriminant?In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows some root properties to be inferred without having to compute them.
It is essentially a polynomial function of the coefficients of the initial polynomial.
So, we have the quadratic equation:
ax- bx +c= 0
We know that the discriminant formula is as follows:
Discriminate = b² - 4c
Now, get the discriminant:
D = b² - 4c
Therefore, the required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
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what are the numbers for h?
Answer:
0,1
2,2
4,3
6,4
Step-by-step explanation:
Some Examples
4 = 1/2 (6) + 1
4 = 3 + 1
4=4
----------
2 = 1/2 (2) + 1
2 = 1 + 1
2 = 2
h
0
2
4
6
...................
Solve for X. Please help me
Answer:
x = 9
Step-by-step explanation:
Mawsynram, a village in India, is the wettest place on earth. It gets about 11,850 millimeters of rain per year.
About how many centimeters of rain fall in the village?
About how many inches if rain fall in the village?
Answer: 467 inches and 1185 centimeters
Step-by-step explanation:
1. Divide by 10 to find centimeters
2. Divide by 25.4 and round to find inches
Name Yala. Al Write down each of the following expressions in the form of a power of one number a) 5³x5⁴ b) (-7)² ×(-7)³ c) 3⁶x3³ d) 27⁰x27² e) (-2)² ×(-2)³ × (-2)⁴ f) 3⁴x9²x(-3)⁶ g) (-4)⁶ × (-4)⁵ (-4)³ h) (-8)x(-8)x2² i) (0.25)×(0.25)⁴ × (0.25)⁰ J) 7³x7²x7
Answer:
A. [tex] {5}^{7} [/tex]
B. [tex] ( { - 7})^{5} [/tex]
C. [tex] {3}^{9} [/tex]
D. [tex] {27}^{2} [/tex]
E. [tex] ({ - 2})^{9} [/tex]
F. [tex] {3}^{14} [/tex]
G. [tex] {( - 4)}^{14} [/tex]
H. [tex] {2}^{8} [/tex]
I. [tex] {(0.25)}^{5} [/tex]
J. [tex] {7}^{6} [/tex]
Step-by-step explanation:
A.
[tex] {5}^{3} \times {5}^{4} \\ = {5}^{3 + 4} \\ = {5}^{7} [/tex]
B.
[tex]( { - 7})^{2} \times ( { - 7})^{3} \\ = ( { - 7})^{2 + 3} \\ = ( { - 7})^{5} [/tex]
C.
[tex] {3}^{6} \times {3}^{3} \\ = {3}^{6 + 3} \\ = {3}^{9} [/tex]
D.
[tex] {27}^{0} \times {27}^{2} \\ = {27}^{0 + 2} \\ = {27}^{2} [/tex]
E.
[tex]( { - 2})^{2} \times ( { - 2})^{3} \times ( { - 2})^{4} \\ = ( { - 2})^{2 + 3 + 4} \\ = ({ - 2})^{9} [/tex]
F.
[tex] {3}^{4} \times {9}^{2} \times ( { - 3})^{6} \\ = {3}^{4} \times {3}^{2 \times 2} \times {3}^{6} \\ = {3}^{4} \times {3}^{4} \times {3}^{6} \\ = {3}^{4 + 4 + 6} \\ = {3}^{14} [/tex]
G.
[tex] {( - 4)}^{6} \times {( - 4)}^{5} \times {( - 4)}^{3} \\ = {( - 4)}^{6 + 5 + 3} \\ = {( - 4)}^{14} [/tex]
H.
[tex] ( - 8) \times ( - 8) \times {2}^{2} \\ = 8 \times 8 \times {2}^{2} \\ = {2}^{3} \times {2}^{3} \times {2}^{2} \\ = {2}^{3 + 3 + 2} \\ = {2}^{8} [/tex]
I.
[tex] 0.25 \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = {(0.25)}^{1} \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = \times {(0.25)}^{1+4+0} \\ = \times {(0.25)}^{5} [/tex]
J.
[tex] {7}^{3} \times {7}^{2} \times 7 \\ = {7}^{3} \times {7}^{2} \times {7}^{1} \\ = {7}^{3+2+1} \\ = {7}^{6} [/tex]
How many packages does Ellis need to buy to build the extension?
Answer:
To find out how many tiles Ellis will need, we first need to find the total area of the extension that she plans to build. To do this, we can find the area of each of the three sides of the extension separately and then add them together.The extension will have a length of 6.25 m and a width of 1.5 m, so its area will be 6.25 m * 1.5 m = 9.375 m^2.There will be three sides of the extension, so the total area of the extension will be 3 * 9.375 m^2 = 28.125 m^2.Each tile has an area of 0.25 m * 0.25 m = 0.0625 m^2.Therefore, Ellis will need a total of 28.125 m^2 / 0.0625 m^2 = 448 tiles. Since each package contains 25 tiles, she will need to buy 448 tiles / 25 tiles/package = 18 packages of tiles.
Step-by-step explanation:
how many cups is it?
The number of cups that will be in 3 gallons is 48 cups.
How to calculate the number of cups?It is important to note that ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Based on the information, the number of cups won a gallons will be:
= 64 / 4
= 16 cups.
Therefore, the cups that will be in 3 gallons will be:
= 3 × 16. cups
= 48 cups.
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a company surveyed college students to determine their need and want for a new portable computer accessory. once the data was gathered, the company began designing the accessory to specifications determined by the data. this is an example of .
On solving the provided question, from the information we can say that this is a example of Research and development (R&D).
What means research and development?Research and development (R&D) refers to the knowledge a business accumulates to create new items or discover innovative ways to enhance current goods and services. Before using their products or processes for commercial purposes, large corporations may have their own R&D teams that test and improve them.
What is the role of research and development?Research and development (R&D) refers to the processes businesses use to innovate and launch new goods and services. It is frequently the initial stage of the development process. Typically, the objective is to expand the company's revenue while introducing a new good or service to the market.
This is an example of Research and development (R&D)
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At the first school , there were 5 Sixth graders for every 2 seventh graders. At the second school dance, there were 7 sixth graders for 8 seventh graders . Are the ratios of sixth to Seventh on graders at both school dance equivalents. Explain
Answer:
No
Step-by-step explanation:
The ratio of the first school is 5/2. The ratio of the second school is 7/8.
Solve the equation.
4/7 = 10/X
x=
Answer:
x = 17.5
Step-by-step explanation:
4/7 = 10/X
We can use cross products to solve for x
4*x = 7 * 10
4x = 70
Divide by 4
4x/4 = 70/4
x = 17.5
Answer:
17.5
Step-by-step explanation:
[tex] \frac{4}{7} = \frac{10}{x} \\ [/tex]
Use cross multiplication.
4x = 7 × 10
4x = 70
Divide both sides by 4.
x = 70/4
x = 17.5
Damon and Nicholas are racing to see who can get his community service hours for scouting completed first. Damon, who has already completed 2 hours, plans to volunteer for 2 hours per week going forward. Nicholas hasn't started yet, but plans to dedicate 3 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take? How many hours will each boy have volunteered by then?
The number of hours when Damon and Nicholas will be tied is 2 hours.
The number of hours for the volunteer is 6 hours.
How long will it take for them to be at same project?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, Damon, who has already completed 2 hours, plans to volunteer for 2 hours per week going forward. Nicholas hasn't started yet, but plans to dedicate 3 hours per week to his volunteer project from now on.
Let the number of hours be h.
Damon's equation will be 2 + 2h
Nicholas equation will be 3h
The number of hours to be tied will be:
2 + 2h = 3h
3h - 2h = 2
h = 2
The number of hours is 2.
The number of hours for the volunteer will be:
= 3h
= 3(2)
= 6 hours.
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Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Prior to performing the clustering analysis, we choose the value for k. In a cluster analysis, the distance between the clusters should be minimized.
K-means clustering is an unsupervised machine learning technique used to identify clusters of data points. Before performing the clustering analysis, we must first choose the value of k (the number of clusters we wish to identify). The cluster analysis will then attempt to find the k clusters by minimizing the distances between the data points in each cluster. Once the clusters have been identified, the distance between them should be minimized to ensure that the clusters are as distinct as possible.
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Max is already 224 miles into his road trip. if he is averaging 52 miles per hour and the trip is 640 miles total, how many more hours does he have left to drive.
What is the length of the sides of this equilateral triangle?
3x + 6
6x - 3
9x - 12
Answer:
15
Step-by-step explanation:
In an equilateral triangle all the sides length are the same. Set two sides equal to each other and solve for x
3x + 6 = 6x - 3 Subtract 3x from both sides
6 = 3x -3 Add 3 to both sides
9 = 3x Divide each side by 3
3 = x
Now that we know x is 3, plug this into the expression for any side and find the side length
3x + 6
3(3) + 6
9 + 6 = 15
5x4x5x3+56
help ma pls why they got such long multipictacion in -8th garde
[tex]\fbox{356}[/tex]
[tex](5\times4\times5\times3)+56[/tex]
[tex]5\times4=20\\5\times3=15\\20\times15=300[/tex]
[tex]300+56=356[/tex]
Answer: 356
Step-by-step explanation:
-start by grouping numbers into smaller portions (ex. the 5x5)
-5x5=25
-4x3=12
-Now we have 25x12.
-10x25=250, now add two more 25's
-250+50=300 or 25x12=300
-Add 56 to get 356
2 flower shops sell tulip for different,prices as shown below. What is the cheaper peice for 12 tulips?Give your answer in (£) £9.80 for 4 tulips were £4.20 each now 1/3 off
The cost of 12 tulips in the first shop (£29.40) is cheaper than the second shop (£33.60).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
2 bloom shops sell tulips at various costs as displayed underneath.
£9.80 for 4 tulips and £4.20 every now 1/3 off.
The cost of the 12 tulips in the first shop, then we have
⇒ (£9.80 / 4) x 12
⇒ £2.45 x 12
⇒ £29.40
The cost of the 12 tulips in the second shop, then we have
⇒ £4.20 x 12 x (1 - 1/3)
⇒ £50.40 x 2/3
⇒ £33.60
The cost of 12 tulips in the first shop (£29.40) is cheaper than the second shop (£33.60).
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Suppose we select every fifth invoice in a file. What type of sampling is this? Multiple Choice Cluster Simple random Stratified random Systematic
This is an example of Systematic sampling.
Here we are drawing out every fifth invoice from the file available. Hence here we create an order where every fifth item is selected.
Hence this is called systematic sampling.
This is a type of probability sampling. In this method, samples are selected by the researcher at regular intervals.
This type of sampling is most suitable when we want to conduct a sampling method similar to simple random sampling but the list of population is unknown to us. However, this can also be used when the list of the same is available to us.
Another important condition is the order os the population, i.e ow it is spread must be random and not in some particular order or sample. Else the reult obtained will lose its credibility.
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If the perimeter of triangle is 15 centimeters what is value of n
Answer:
5 cms
Step-by-step explanation:
This is assuming that it is equilateral and that n is the length of one side
Gabriella owned so many CDs that she gave 64 of them away. After donating the CDs she had 147 left. Write an equation to find the number of CDs c gabriella had originaly
Answer:
147+64=c
Step-by-step explanation:
you would add the two numbers together to get the original.
HELPPPP!!!
Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?
x=1/12(y+4)^2-2
y=1/12(x+4)^2+2
x=-1/12(y+4)^2+2
y=-1/12(x+4)^2-2
Following equation represents the parabola in the graph:
x=1/12(y+4)^2-2
How to find the focus and directrix of a parabola?From the graph, we see that;
Focus = (-4, -2)
We use the equation x=h−p to find the directrix.
General form of equation of a parabola is;
(y - k)² = 4p(x - h)
where;
focus is (h + p, k)
directrix is x = h - p
Can a parabola not cross the y-axis?If we are talking about the function y = ax² + bx + c, then since it is a continuous function on the whole real line, it must cross the y–axis at (0 , c).
However x = y² + 1 is a parabola(not a function) that does not cross the y–axis.
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adam is racing around a circular running track. the time he takes to run each lap is 5 seconds less than he took for the previous one. he completes the first lap in 1 minute and 58 seconds. how long (in seconds) does he take to run his seventh lap?
Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.
As given in the question,
Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec
First term t₁ = 1 minute 58seconds
Time taken by each successive lap is 5seconds less then the previous lap
Common difference 'd' = -5seconds
let time taken to complete the seventh lap be t₇
t₇ = t₁ + ( 7 - 1 ) d
⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)
= 1 minute 58 seconds - 30seconds
= 1 minute 28 seconds
Therefore, the time taken by Adam to complete his seventh lap is equal to
1 minute 28 seconds.
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Which equation best describes the line whose graph is shown?
A y=x+3
By = 3x
Cy=3
D x=3
Answer:
i have done this mano time ago, but problaply the answer is x=3
Express 2log 4 + 3log 2 as a single logarithm.
A 6log 8
B log 48
C 5log 6
D log 128
To express 2log 4 + 3log 2 as a single logarithm, you can use the property of logarithms that states that loga(mn) = logam + logan. This property can be used to rewrite the given expression as follows:
2log 4 + 3log 2 = log 4^2 + log 2^3
= log 16 + log 8
= log 16 * 8
= log 128
here 2log 4 + 3log 2 equals to log 128
Therefore, 2log 4 + 3log 2 = log 128, which is answer choice (D) log 128.
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A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from each restaurant, and he records the time it takes for each pizza to be delivered.
a) When performing an ANOVA with this data, what is the alternative hypothesis?
- All of the restaurants have different mean delivery times
- At least two of the restaurants have different mean delivery times
- Two of the restaurants have different mean delivery times
- One of the restaurants has a different mean delivery time than the others
b) A partial ANOVA table for his data is shown below. What is the value of B?
Source DF SS MS F P-value
Treatment B 19.31 D F G
Error C 15.667 E
Total 18 34.977
What is the value of C in the ANOVA table?
d) What is the value of D in the ANOVA table? Give your answer to three decimal places.
e) What is the value of E in the ANOVA table? Give your answer to three decimal places.
f) What is the value of F in the ANOVA table? Give your answer to two decimal places.
g) What is the value of G in the ANOVA table? Give your answer to four decimal places.
h) Using a 0.1 level of significance, what should his conclusion be in this case?
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.1.
- He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.1.
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.1.
- He should conclude that at all of the restaurants have the same mean delivery times because the P- value is less than 0.1.
(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.
(b)75.8
Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.
The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.
It is given that a pizza lover wants to compare the average delivery times.
Therefore the null hypothesis and alternate hypothesis implies that,
H₀ = all restaurants have equal mean delivery time
Hₐ = at least two restaurants have different two deliveries
Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.
The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.
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Consider the line y = 2x - 3. Write the equation of the line that is perpendicular to this line and that contains the point (-5, 3) Please help!!!
Considering the definition of perpendicular line, the equation of the perpendicular line is y= -1/2x + 1/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 2x -3
where:
The slope m is 2.The ordinate to the origin b is -3.If you multiply the slopes of two perpendicular lines, you get –1, you get:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 2
slope perpendicular line= -1/2
The line passes through the point (-5, 3). Replacing the point and the slope in the expression for a line:
3= (-1/2)× (-5) + b
3= 5/2 + b
3 -5/2 = b
1/2= b
Finally, the perpendicular line is y= -1/2x + 1/2.
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Find the derivative of this with respect to x
