Answer:
x = -4, 4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Rewrite 16:
[tex]x^2-4^2=0[/tex]
The difference of squares rule states that [tex]a^2-b^2=(a+b)(a-b)[/tex]. With this, apply the difference of squares to the equation:
[tex](x+4)(x-4)=0[/tex]
The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:
[tex]x+4=0\\x=-4[/tex]
[tex]x-4=0\\x=4[/tex]
Therefore, the solutions are -4 and 4.
I hope this helps!
In a small metropolitan area, annual losses due to storm, fire, andtheft are assumed to be independent, exponentially distributed random variableswith respective means 1.0, 1.5, 2.4. Determine the probability that the maximumof these losses exceeds 3.
Answer:
[tex]0.4138[/tex]
Step-by-step explanation:
Given
[tex]x \to storm[/tex]
[tex]\mu_x = 1.0[/tex]
[tex]y \to fire[/tex]
[tex]\mu_y = 1.5[/tex]
[tex]z \to theft[/tex]
[tex]\mu_z = 2.4[/tex]
Let the event that the above three factors is greater than 3 be represented as:
[tex]P(A > 3)[/tex]
Using complement rule, we have:
[tex]P(A > 3) = 1 - P(A \le 3)[/tex]
This gives:
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
-----------------------------------------------------------------------------------------------------------
The exponential distribution formula of each is:
[tex]P(x \le k) = 1 - e^{-\frac{k}{\mu}}[/tex]
So, we have:
[tex]k = 3; \mu_x = 1[/tex]
[tex]P(x \le 3) = 1 - e^{-\frac{3}{1}} = 1 - e^{-3} = 0.9502[/tex]
[tex]k=3; \mu_y = 1.5[/tex]
[tex]P(y \le 3) = 1 - e^{-\frac{3}{1.5}} = 1 - e^{-2} = 0.8647[/tex]
[tex]k = 3; \mu_z = 2.4[/tex]
[tex]P(z \le 3) = 1 - e^{-\frac{3}{2.4}} = 1 - e^{-1.25} = 0.7135[/tex]
-----------------------------------------------------------------------------------------------------------
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
[tex]P(A > 3) = 1 - (0.9502 * 0.8647 *0.7135)[/tex]
[tex]P(A > 3) = 1 - 0.5862[/tex]
[tex]P(A > 3) = 0.4138[/tex]
Sum of 4x^3+6x^2+2x^2-3 and 3x^3+3x^2-5x-5 is
9514 1404 393
Answer:
7x^3 +11x^2 -5x -8
Step-by-step explanation:
Combine like terms.
(4x^3+6x^2+2x^2-3) + (3x^3+3x^2-5x-5)
= (4 +3)x^3 +(6 +2 +3)x^2 +(-5)x + (-3 -5)
= 7x^3 +11x^2 -5x -8
_____
Noting that the first expression contains two x^2 terms, we wonder if you actually want the sum ...
(4x^3+6x^2+2x-3) + (3x^3+3x^2-5x-5)
= (4 +3)x^3 +(6 +3)x^2 +(2 -5)x +(-3 -5)
= 7x^3 +9x^2 -3x -8
A teacher is comparing the quarter grades between two of her classes. She takes a random sample of 8 students from each class and lists the grades as shown. Find the mean for Class A.
Class A: 80, 83, 74, 91, 76, 87, 93, 72
Class B: 90, 75, 82, 86, 73, 85, 79, 94
A distance of 400 km is represented in the map by 3 cm. What is the distance between two towns if they are 7.5 cm apart in the map?
Answer:
The distance between the two towns is of 1000 km.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
We have that:
3 cm represents a distance of 400 km.
What is the distance represented by 7.5 cm?
3 cm - 400 km
7.5 cm - x km
Applying cross multiplication:
[tex]3x = 400*7.5[/tex]
[tex]x = \frac{400*7.5}{3}[/tex]
[tex]x = 1000[/tex]
The distance between the two towns is of 1000 km.
Order the following units of a capacity families to greatest gallon paint cup quart
Answer:
7 yards
Step-by-step explanation:
Need the answer ASAP!! 20 points
Answer:
I think C. is it
Step-by-step explanation:
I neeeddddd help on this I’m failing
Answer:
AB = 9
Step-by-step explanation:
Here is a simple case of a proportion.
We see that:
3:4
x:12
what can we do to make 4 into 12?
we multiply it by 3
so we do the same to 3
3*3=9
ellus
Find the surface area of the composite figure.
2 cm
7 cm
2 cm
12 cm
12 cm
7 cm
7 cm
SA = [?] cm2
Answer:
SA = 484 cm²
Step-by-step explanation:
Surface area of the composite figure = surface area of the larger rectangular prism + (surface area of the smaller rectangular prism - base area of the smaller rectangular prism)
✔️Surface are of the larger rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 7 cm
H = 12 cm
S.A = 2(7*7 + 7*12 + 7*12) = 434 cm²
✔️Surface are of the smaller rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 2 cm
H = 2 cm
S.A = 2(7*2 + 7*2 + 2*2) = 64 cm²
✔️Base area of the smaller rectangular prism = L*W
L = 7 cm
W = 2 cm
Area = 7*2 = 14 cm²
✅Surface area of the composite figure = 434 + (64 - 14)
= 434 + 50
= 484 cm²
How do you solve the equation 3 1/5 +n=9?
Answer:
n = [tex]5\frac{4}{5}[/tex]
Step-by-step explanation:
You obviously have to solve for n
Leia needs to make at least 40 necklaces to sell at a craft show. So far, she has made 7. Which inequality shows the
number of necklaces, n, that she still needs to make?
A). n - 7 less than or equal to 40
B) n - 7 greater than or equal to 40
C). n + 7 less than or equal to 40
D). n + 7 greater than or equal to 40
Answer:
The answer is D
Hope this helps!
Brainliest??
Answer:
D
Step-by-step explanation:
the answer is D because if she already made 7 she need to add n to 7 to get 40 or greater
Five classmates want to know how many of the 2688 students in their school prefer pop music. They each randomly survey 64 students. The table shows the results.
Use the results from each classmate to make an inference about the number of students in the school who prefer pop music.
Based on Shannon's results, the number is __
students.
Based on Trey's results, the number is __
students.
Based on Robert's results, the number is __
students.
Based on Callie's results, the number is __
students.
Based on Lani's results, the number is __
students.
Question 2
Describe the variation of the five inferences. Which one would you use to describe the number of students at the school who prefer pop music? Explain.
The greatest is __
students. The least is __
students. The median of the data is __
. The mode of the data is __
. So, use the inference of __
students to describe the number of students at the school who prefer pop music.
Answer:
Question 1
Shannon: 882/2688
Trey: 1008/2688
Robert: 798/2688
Callie: 882/2688
Lani: 840/2688
Question 2
The greatest is 1008/2688 students.
The least is 798/2688 students.
The median of the data is 882/2688 students.
The mode of the data is 882/2688 students.
So, use the inference of 882/2688 students to describe the number of students at the school who prefer pop music.
Step-by-step explanation
Question 1
Shannon: Because 21/64 in Shannon's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 21 gets us 882/2688 who might prefer pop music in the entire school without surveying all of the students.
Trey: Because 24/64 in Trey's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 24 gets us 1008/2688 who might prefer pop music in the entire school without surveying all of the students.
Robert: Because 19/64 in Robert's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 19 gets us 798/2688 who might prefer pop music in the entire school without surveying all of the students.
Callie: Because 21/64 in Callie's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 21 gets us 882/2688 who might prefer pop music in the entire school without surveying all of the students.
Lani: Because 20/64 in Lani's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 20 gets us 840/2688 who might prefer pop music in the entire school without surveying all of the students.
Question 2
Using Shannon's or Callie's survey would best describe the number of students in the entire school because their individual results (21/64) is the average of all of the individual results of the 5 students. If you decide to use any of the other individual survey results, you will not get the closest answer to the actual amount of students who prefer pop music in the entire school.
Using the individual survey results to estimate the number of students who prefer pop music in the entire school:
The greatest was Trey's results, which estimated about 1008 out of 2688 students in the entire school who would prefer pop music.
The least was Robert's results, which estimated about 798 out of 2688 students in the entire school who would prefer pop music.
The median of the data was 882 out of 2688 students in the entire school who would prefer pop music, as shown in Shannon's and Callie's individual survey results.
To find the median, list the results least to greatest, then look at the number that is in the exact middle. If there is no middle, but instead two middle numbers, find the average of the two.
The mode of the data was Shannon's or Callie's results, which estimated about 882 out of 2688 students in the entire school who would prefer pop music.
To find the mode, look for the number or result that it repeated the most (Ex: the result of 21/64 students who preferred pop music was found twice compared to the other individual survey results which did not repeat more than once).
So, in the end using Shannon's or Callie's individual survey results to estimate the amount of students in the entire school who prefer pop music is the best way to do so.
Please comment if you think I made a mistake, misunderstood, or missed something.
Given the set of data below, which measure(s) will change if the outlier is removed? (Check all that apply.) 1,6,8,8,8
mean
range
median
mode
The mean, range, and median will vary if the outlier is eliminated. Options A, B, and C are correct.
What is mean?The arithmetic mean is a term used to describe the average. It's the ratio of the total number of observations to the sum of the observations.
The data set is;
1,6,8,8,8
Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.
There is an aberration in the graph below, on the far left. The value in January is much lower than the value in the other months.
If the outlier is removed mean, range, and median will changes.
Hence options A, B and C are correct.
To learn more about mean refer:
https://brainly.com/question/13451489
#SPJ2
Answer nyo po to...Ang hirap(;-;)....pls. Lang po
The answer goes here,
a) We have to tell the time and day which simone has to tell her sister, for picking her up from airport.
b) We have given the day (monday), time(7:00 pm) and total time to reach the destination(18 hours).
c) No such formula will be used here, we will just use our mental ability to solve this question.
d) She will leave at 7:00 pm, day has 24 hours. So, she will be in the flight on monday:
= 24 - (12 + 7) ----------- [12 here means the time of rest of the day,(morning to noon)]
= 24 - 19
= 5 hours
So, she will complete 5 hours of her destination on monday,now the time left is:
= 18 - 5
= 13
= (12 + 1 )hours
So, on tuesday, she will be in the flight for 12 hours (noon) and then on 1:00 pm she will reach the airport, as she needs and extra hour to plane so, the final time is 1:30 pm. And finally, the time she should tell her sister is 1.30 pm.
What do the value of
(5 1/3)^3
Answer:
[tex] \frac{4096}{27} [/tex] or [tex]151 \frac{19}{27} [/tex]Step-by-step explanation:
[tex](5 \frac{1}{3} {)}^{3} [/tex][tex](5 + \frac{1}{3} {)}^{3} [/tex][tex]( \frac{16}{3} {)}^{3} [/tex][tex] \frac{ {16}^{3} }{ {3}^{3} } [/tex][tex] \frac{4096}{27} [/tex][tex]151 \frac{19}{27} [/tex]Hope it is helpful....The time spent waiting in the line is approximately normally distributed. The mean waiting time is 55 minutes and the variance of the waiting time is 11. Find the probability that a person will wait for more than 33 minutes. Round your answer to four decimal places.
Answer:
1 = 100% probability that a person will wait for more than 33 minutes.
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.
The mean waiting time is 55 minutes and the variance of the waiting time is 11.
This means that [tex]\mu = 55, \sigma = \sqrt{11}[/tex]
Find the probability that a person will wait for more than 33 minutes.
This is 1 subtracted by the p-value of Z when X = 33. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 55}{\sqrt{11}}[/tex]
[tex]Z = -6.63[/tex]
[tex]Z = -6.63[/tex] has a p-value of 0.
1 - 0 = 1
1 = 100% probability that a person will wait for more than 33 minutes.
brainliest for answer
Answer:
what is the question?
Step-by-step explanation:
Answer:
i answered
Step-by-step explanation:
320% of 69 is what number?
Answer:
220.8
Step-by-step explanation:
I believe 220.8
sorry if I am wrong.
Answer:
320×69÷100
answer * number is 220
Which of the following CANNOT be true for a triangle?
A. A triangle can be equilateral and obtuse at the same time.
B. A triangle can be equilateral and equiangular at the same time.
C. A triangle can be isosceles and right at the same time.
D. A triangle can be scalene and obtuse at the same time.
Answer:
A. A triangle can be equilateral and obtuse at the same time
Step-by-step explanation:
All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°
Divide the following complex numbers:
(4-i)/(3+4i)
A.-8/7 + 19/7i
B. 16/25 - 19/25i
C. 8/25 - 19/25i
D. -16/7 + 19/7i
Answer:
C. 8/25 - 19/25i
Step-by-step explanation:
Given that:
[tex]\dfrac{4-i}{3+4i}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}[/tex]
[tex]=\dfrac{8}{25}- \dfrac{19i}{25}[/tex]
Quadrilateral ABCD is inscribed. The measure of ∠A=67°. What is the measure of ∠C?
Answer:
angle C =113 degree
Step-by-step explanation:
angle A + angle C =180 degree
angle C = 180 degree - angle A
angle C = 180 degree - 67 degree
=113 degree
Solve for x. Round to the nearest tenth, if necessary.
P.
х
50°
Q
R
4.2
Answer:
5.0 =x
Step-by-step explanation:
Since this is a right triangle
tan theta = opp side/ adjacent side
tan 50 = x / 4.2
4.2 tan 50 = x
5.005365089 =x
Rounding to the nearest tent
5.0 =x
An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield from a certain chemical reaction. She considers 6 different temperatures, 5 different pressures, and 4 different catalysts are under consideration.
a. If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?
b. How many experimental runs are there that involve use of the lowest temperature and two lowest pressures?
c. Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?
Answer:
a) 120 possible experimental runs
b) 8 possible experimental runs
c) 0
Step-by-step explanation:
a. For the experiment, there are 6 different temperatures (T), 5 different pressures (P), and 4 different catalysts (C). We can find the total number of combinations using the product rule.
N = T × P × C
N = 6 × 5 × 4 = 120
b) If we use only the lowest temperature, we have T = 1, and if we use the two lowest pressures, we have P = 2. We can find the total number of combinations using the product rule.
N = T × P × C
N = 1 × 2 × 4 = 8
c) If we perform 5 experimental runs with 4 possible catalysts, it is not possible to use a different catalyst each time. At least, 1 catalyst must be repeated twice. Then, the event "a different catalyst is used on each run" has a probability of 0.
10 points! If correct you get brainliest.
Which one's apply?
Answer:
The answer is C and E
Step-by-step explanation:
1. How much salt and baking powder together is needed to make 36 cup cakes?
Answer:
too much salt will not bring taste to the cup cakes
Step-by-step explanation:
What is perimeter of 300 315 55
1800=3×N
help asap plzzz
Ive been stuck on this problem for an hour, help pleaseee.
The graph of the function is given below. Give all y-intercepts and x-intercepts shown.
Answer:
y intercept: [tex]y = 1[/tex]
x intercept: [tex]x = -1[/tex] and [tex]x = -3[/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): The y intercepts
This is the point where [tex]x = 0[/tex]
From the attached graph, [tex]x = 0[/tex] when
[tex]y = 1[/tex]
Hence, the y intercept is 1
Solving (b): The x intercepts
This is the point where [tex]y = 0[/tex]
From the attached graph, [tex]y = 0[/tex] when
[tex]x = -1[/tex] and [tex]x = -3[/tex]
Hence, the x intercept are -1 and -3
2. Suppose over several years of offering AP Statistics, a high school finds that final exam scores are normally distributed with a mean of 78 and a standard deviation of 6. A. What are the mean, standard deviation, and shape of the distribution of x-bar for n
Answer:
By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 78 and a standard deviation of 6
This means that [tex]\mu = 78, \sigma = 6[/tex]
Samples of n:
This means that the standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{n}}[/tex]
What are the mean, standard deviation, and shape of the distribution of x-bar for n?
By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.
Complete all the problems.
1.
X - 6 = -24
Solve for x.
Answer:
x= -18
Step-by-step explanation:
x= -24 + 6
Add -24 and 6.
x= -18
Answer:
X = -18
Step-by-step explanation:
You want to isolate X by itself. To isolate X on one side of the = sign, use the addition property of equality (to undo the subtraction of 6 from x) by adding 6 to both sides of the equation. We use the addition property of equality because this is the inverse operation. It is important to add 6 to both sides of to maintain an equivalent equation.
1. Set up your equation
X - 6 = -24
+6 +6
2. Solve out
X - 6 = -24
+6 +6
X = -18
Answer: -18
In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of West Campus and failed
Answer:
57.5
Step-by-step explanation:
The expected frequency of West Campus and Failed :
Let :
Failed = F
East Campus = C
West Campus = W
Passed = P
Frequency of FnW :
[(FnE) + (FnW) * (PnW) + (FnW)] / total samples
[(52 + 63) * (63 + 37)] / 200
[(115 * 100)] / 200
11500 / 200
= 57.5
n(Failed n East campus)
Answer:
57.5
Step-by-step explanation:
Got it right on the test.