[tex]1\pm\sqrt{2}i[/tex]
Step-by-step explanation:
We already know that one of the roots is x = -4 so we can factor this out to get
[tex]x^3+2x^2-5x+12=(x+4)(x^2-2x+3)[/tex]
Using the quadratic equation on the 2nd factor, we find the roots are
[tex]x= \dfrac{2\pm\sqrt{(2)^2 - 4(1)(3)}}{2}=1\pm\sqrt{2}i[/tex]
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
A ship sailed 30 kilometers in 1 1/2 hours. What is was its rate in kilometers per hour?
1) 20
2)30
3)45
4)90
5)Not enough information is given.
Answer:
20km/hr
Step-by-step explanation:
Given that a ship sailed 30km in one and a half hours. We need to find out the rate of ship in kilometres/hour . The rate is also called Speed.
Speed:- Distance travelled per unit time is called Speed .
Here , according to Question,
Distance = 30 km
Time = 1½ hrs .
We know that ,
[tex]\rm\implies Distance = Speed \times Time [/tex]
Subsequently ,
[tex]\rm\implies Time = \dfrac{Distance}{Time} [/tex]
Substitute the respective values ,
[tex]\rm\implies Rate =\dfrac{ 30km}{ 1.5 hrs } [/tex]
We can write 1.5 as 3/2 , therefore ,
[tex]\rm\implies Rate = \dfrac{ 2\times 30}{3} km/hr[/tex]
Simplify the RHS ,
[tex]\rm\implies\boxed{\blue{\rm Rate = 20\ km/hr}} [/tex]
Hence the Rate/Speed of the ship is 20km/hr .
in the given figure poq is a line. if x=30 then find qor and ros
Answer:
[tex]2y + 3y + x = 180 \\ 5y + 30 = 180 \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30[/tex]
QOR =3Y
=3×30
=90°
ROS = 2Y
=2×30
=60°
help I was never taught how to do this im confused
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
¿COMO PUTAS SE HACE i¹⁰⁰²?
Answer:
nose
Step-by-step explanation:
The ________ and variance are derived from a subset of the population data and are used to make inferences about the population.
a. population standard deviation.
b. population variance.
c. population mean.
d. sample mean.
Answer:
the answer is option A population standard deviation
The temperature on a cold winter day starts out at 10 degrees, but it drops rapidly 24 degrees due to a strong cold front moving in. What is the current temperature?
Plz help me find zero x on the triangle and show work thanks
Answer:
x= 30 degrees
Step-by-step explanation:
This is an isosceles triangle as indicates by the lines on the sides.
Since the sides lengths are equal, the base angles are equal
x= 30 degrees
Which set of angles listed are supplementary
Answer:
A. <BED and <DEA, <AEC and <BEC
Step-by-step explanation:
Supplementary angles add up to give 180°.
m<BED = 90°
m<DEA = 90°
m<BED + m<DEA = 180°
Therefore, <BED and <DEA are supplementary.
m<AEC = 90°
m<BEC = 90°
m<AEC + m<BEC = 180°
Therefore, <AEC and <BEC are supplementary.
An integer is 18 more than 4 times another. If the product of the two integers is -18, then find the integers.
Answer:
Step-by-step explanation:
x = 4y+18
xy = -18
x = -18/y
-18/y = 4y+18
4y² + 18y + 18 = 0
2y² + 9y + 9 = 0
y = [-9 ±√(9²-4(2)(9))]/[2(2)] = [-9 ± 3]/4 = -1.5, -3
-1.5 is an extraneous solution, so y = -3
x = 6
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? 60
60/100
60/40
40/100
Answer:
60/100
Step-by-step explanation:
Hope it helps you in your learning process
A woodworker makes wooden checkerboards. her profit is a function of the price she charges. this graph shows her total profits, y, based on the sales price, x, of each checkerboard.
identify any zeros of the function, and interpret what the zeros mean in terms of the situation.
Answer:
Option B.
Step-by-step explanation:
Remember that the profit is defined as the difference between the revenue and the cost.
So, having a profit y = 0 means that the woodworker did not win nor lose anything.
Then the zeros of the function, the values of x such that the graph intersects the x-axis, are the prices such that she does not win nor loss anything.
In the graph we can see that the zeros are at:
x = 15 (the first one)
x = 70 (the second one)
so the zeros are at x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
The correct option is B.
Answer:
x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
Step-by-step explanation:
PLEASE HELP ME WITH THIS QUESTION!! HELP ME!!!
During one 8-hour work-day, Bill began work one hour late, took 2 breaks of a half hour each, and went to lunch for an hour. Out of 24 hours, how many hours did Bill spend not working that day?
Answer: 17 hours
Step-by-step explanation: Because he worked an hour over I added an hour. Then I subtracted his lunch break and and 2 breaks. I then took that number and subtracted it by 24.
what’s 9-3 2/5? because i can’t find it
Answer:
Step-by-step explanation:
(9-3)(2/5) = 6(2/5) = 12/5 = 2 2/5
9-32/5 = 2.6
Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?
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Answer:
they are not collinear
Step-by-step explanation:
A graph shows that a line through points A and C misses point B, so the points are not collinear.
__
If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.
m = (y2 -y1)/(x2 -x1)
m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB
__
m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB
The points are not collinear.
_____
Additional comment
With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
A high school baseball player has a 0.305 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 7 hits in the game
The probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
To solve this problem, we need to use the binomial distribution formula. The binomial distribution is used when we have a fixed number of independent trials (in this case, 9 at bats), where each trial has only two possible outcomes (hit or no hit), and the probability of success (getting a hit) is constant across all trials (0.305 in this case).
Let X be the number of hits the player gets in the game. Then X follows a binomial distribution with parameters n=9 (number of trials) and p=0.305 (probability of success).
The probability of getting at least 7 hits is equal to the sum of the probabilities of getting exactly 7, 8, or 9 hits:
P(X ≥ 7) = P(X=7) + P(X=8) + P(X=9)
Using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
For k=7:
P(X=7) = C(9,7) * 0.305^7 * (1-0.305)^(9-7) = 0.154
For k=8:
P(X=8) = C(9,8) * 0.305^8 * (1-0.305)^(9-8) = 0.036
For k=9:
P(X=9) = C(9,9) * 0.305^9 * (1-0.305)^(9-9) = 0.002
Therefore:
P(X ≥ 7) = 0.154 + 0.036 + 0.002 = 0.192
Therefore, the probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
To learn more about Probability from given link.
https://brainly.com/question/30034780
#SPJ1
How can the distributive property be use to solve this expression?
53x24
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Answer:
= 53(20 +4) or =24(50 +3) or =(20 +4)(50 +3)
Step-by-step explanation:
Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.
The usual method of multiplication taught in grade school makes use of this sort of rewriting.
53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272
__
Additional comment
We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.
In grade school, we did this digit by digit, so ...
53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20
= 12 +60 +200 +1000 = 1272
Which is equivalent to 104
༡/16**?
o (10)4x
4(10)3
o (10)**
O (10)
Answer:
I think it is the last one.
Apply radical rule
= (10^1/2)3/4x
Apply exponent rule: (a^b)^c = a^bc
= 10^1/2 . 3/4x
Simplify: 1/2 . 3/4x: 3x/8
= 10^3x/8
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?
Answer:
23
Step-by-step explanation:
We are given that
f(2)=13
[tex]f'(x)\geq 2[/tex]
[tex]2\leq x\leq 7[/tex]
We have to find the possible small value of f(7).
We know that
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
[tex]f'(x)=\frac{f(7)-f(2)}{7-2}[/tex]
[tex]f'(x)=\frac{f(7)-13}{5}[/tex]
We have
[tex]f'(x)\geq 2[/tex]
[tex]\frac{f(7)-13}{5}\geq 2[/tex]
[tex]f(7)-13\geq 2\times 5[/tex]
[tex]f(7)-13\geq 10[/tex]
[tex]f(7)\geq 10+13[/tex]
[tex]f(7)\geq 23[/tex]
The small value of f(7) can be 23.
g Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. In poker, a flush (5 in same suit) in any suit
Answer:
The answer is "[tex]1.54 \times 10^{-6}[/tex]".
Step-by-step explanation:
Calculating the probability of the cards that hand from a 52-card deck.
The aces are high or low in poker.
There are 13 cards in the bridge hand.
A royal flush (5 suit top cards) in poker.
There are 5 various poker hands with [tex]\binom{52}{5}[/tex].
There are four royal flushes, one in each suit.
[tex]P (royal\ flush) =\frac{4}{\binom{52}{5}}\\\\[/tex]
[tex]=\frac{4}{2598960}\approx 1.54 \times 10^{-6}[/tex]
I need to know what goes in the amount box is someone will be kind enough to help me that would be very appreciated
Answer:
123
Step-by-step explanation:
Yw
Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean and median number of apples in a bag. (Round your answers to 2 decimal places.)
Answer:
The mean and median number of apples in a bag are 21.71 and 22 respectively.
Step-by-step explanation:
The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.
The mean is calculated by adding all the values and dividing the sum by the total number of values. In this case:
[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]
[tex]Mean=\frac{152}{7}[/tex]
Mean= 21.71
The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.
The median can be calculated by putting the numbers in ascending order and then:
if the quantity is numbers it is odd: the median is the number in the center of that distribution. if the number of numbers is even: the median is the mean of the two middle numbers.In this case:
Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26
Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22
The mean and median number of apples in a bag are 21.71 and 22 respectively.
At a store, 2 gallons of milk cost $6.
Which is the value of the ratio of dollars to gallons of milk?
0.33
per gallon
$3 per gallon
Answer:
B
Step-by-step explanation:
$3 per gallon
that is the procedure above
Which of the following best describes a type of growth that is exponential at
first but slows as the amount reaches a certain maximum value?
A. Exponential decay
B. Exponential growth
C. Linear growth
D. Logistic growth
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Answer:
D. Logistic growth
Step-by-step explanation:
The logistic growth function models a situation where the rate of growth is jointly proportional to the population and to the difference between the population and the carrying capacity.
Attached is an example of such a function.
identify the function as a power function, a polynomial function, or neither.
f(x)=4(x^3)^3
Answer:7
Step-by-step explanation:7
Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = m x + c
Answer:
I think the answer would be
y = 0.5x -8
tough this might be wrong?
Step-by-step explanation:
(2, 7) ( 4,6)
to find the gradient- mx
y2-y1/ x2 - x1
chose which would be 1/ 2
if I chose (2,7) as 1 then (4, 6) as 2
mx = 6- 7/ 4-2
= -0.5x
y = -0.5x + c
substitute
6 = -0.5(4) + c
6= -2+ c
c = -8
The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three others were sprayed with Action. When the grapes ripened, 390 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 420 vines sprayed with Action were checked. The results are:
Insecticide Number of Vines Checked (sample size) Number of Infested Vines
Pernod 5 390 23
Action 420 46
At the 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answer:
The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Pernod 5:
23 out of 390, so:
[tex]p_P = \frac{23}{390} = 0.059[/tex]
[tex]s_P = \sqrt{\frac{0.059*0.941}{390}} = 0.0119[/tex]
Action:
46 out of 420, so:
[tex]p_A = \frac{46}{420} = 0.1095[/tex]
[tex]s_A = \sqrt{\frac{0.1095*0.8905}{420}} = 0.0152[/tex]
Test if there is a difference in proportions:
At the null hypothesis, we test if there is not a difference, that is, the subtraction of the proportions is 0. So
[tex]H_0: p_A - p_P = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So
[tex]H_1: p_A - p_P \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_A - p_P = 0.1095 - 0.059 = 0.0505[/tex]
[tex]s = \sqrt{s_A^2+s_P^2} = \sqrt{0.0119^2+0.0152^2} = 0.0193[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.0505 - 0}{0.0193}[/tex]
[tex]z = 2.62[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a difference in proportions of at least 0.0505 to either side, which is P(|z| > 2.62), that is, 2 multiplied by the p-value of z = -2.62.
Looking at the z-table, z = -2.62 has a p-value of 0.0044.
2*0.0044 = 0.0088
The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.
How to do questions 19 and 20
Answer & Step-by-step explanation:
Using the information given in the question we can form the following 3 equations (in the order of the first 3 sentences)
w = 2h (twice the price)
t = h - 4 ($4 less)
3w + 2h + 5t = 136 (total purchasing and cost)
We can solve all 3 equations for h first, by substituting the first two equations, into the third equations w and t
3(2h) + 2h + 5(h-4) = 136
Simplify
6h + 2h + 5h - 20 = 136
13h = 136 + 20
13h = 156
h = 156/13
h = $12
Using this information, we can solve for w and t
w = 2h
w = 2(12)
w = $24
And finally
t = h - 4
t = 12 - 4
t = $8
