Answer:
The answer is
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Step-by-step explanation:
x² + 10x + 89 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 1 , b = 10 , c = 89
Substitute the values into the above formula and solve
We have
[tex]x = \frac{ - 10\pm \sqrt{ {10}^{2} - 4(1)(89)} }{2(1)} \\ = \frac{ - 10\pm \sqrt{100 - 356} }{2} \\ = \frac{ - 10\pm \sqrt{ - 256} }{2} \\ = \frac{10\pm 16 \: i}{2} [/tex]Separate the real and imaginary part
That's
[tex]x = - \frac{10}{2} \pm \frac{16}{2} \: i \\ x = - 5\pm8 \: i[/tex]We have the final answer as
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Hope this helps you
translate one half of a number is four into an equation
Answer:
(3/2)x=4
Step-by-step explanation:
Pretty self explanatory. X is the number.
If 6 more than the product of a number and - 2 is greater than 10, which of the following could be that number?
Answer:
-2x + 6 > 10
Step-by-step explanation:
Let the unknown number be x
the product of x and -2 is -2x
6 more than -2x is written as
-2x + 6
if the result of the above is greater than 10, then
-2x + 6 > 10
Can some fill this out for me please!!!
Answer:
Q2
a) 8 + - 8 = 0
b) -20 + 20 = 0
c) a+ - a = 0
Q3
3) Identity property
Answer:
1) 8 + - 8 = 0
2) -20 + 20 = 0
3) a+ - a = 0
Q3
3) Identity property
Step-by-step explanation:
The magnitude of an earthquake depending on the energy it produces can be modeled using the equation
M = 0.6666 log x - 3.2. Complete the sentences about the model.
The curve representing the relationship includes the point
The growth factor is
An earthquake with an energy level of has a magnitude of
Answer:
Step-by-step explanation:
Which of the following groups of users is the least affected by a company's accounting information? people who invest money in the company (investors), people who lend money to the company (creditors), people who run the company (the board of directors), people who buy the company’s products or services (customers)
Answer:
People who buy the company's products or services (customers)
Step-by-step explanation:
Can somebody please help me with this question
Answer:
(3^2) - n
Step-by-step explanation:
For this problem we will take it step by step to build the expression:
raise 3 to the 2nd power
= 3^2
then find the difference of the result and n
= (3^2) - n
Hence, your final expression should be (3^2) - n.
Cheers.
35,892 rounded nearest hundred
Answer:
35,900
Step-by-step explanation:
92 is higher than 50
The temperature in Passaic is 64 degrees at dawn. The temperature continued to go down another 8 degrees and then increased 6 degrees in the afternoon. Write a number sentence that represents the situation.
10x - 4.5 + 3x = 12x - 1.1
Answer:
x = 3.4
Step-by-step explanation:
[tex]10x-4.5+3x=12x-1.1\\\\10x+3x-4.5=12x-1.1\\\\13x-4.5=12x-1.1\\\\13x-4.5+4.5=12x-1.1+4.5\\\\13x=12x+3.4\\\\13x-12x=12x-12x+3.4\\\\\boxed{x=3.4}[/tex]
Hope this helps.
Use a scale of 2km to 1cm to find the length of a road
15km.
A. 6.0CM
B. 6.5CM
C. 7.0CM
D. 7.5CM
Question 14 of 60
Calculate the distance covered by running round a
circular field of radius 3.5cm
2 km = 1 cm
To Find:The length of the road of 15 km.
Solution:2 km = 1 cm
1 km = 1/2 = 0.5 cm
15 km = 0.5 × 15 = 7.5
Answer:The length of the road is 7.5 cm.
Therefore, Option D. 7.5 cm is correct.
A textbook has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly located on those pages. Find the probability that a random selection of 50 pages will contain no errors. Find the probability that 50 randomly selected pages will contain at least two errors.
Answer:
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that the selection of the random pages will contain at least two errors is 0.2644
Step-by-step explanation:
From the information given:
Let q represent the no of typographical errors.
Suppose that there are exactly 10 such errors randomly located on a textbook of 500 pages. Let [tex]\mu[/tex] be the random variable that follows a Poisson distribution, then mean [tex]\mu = \dfrac{10}{500}= 0.02[/tex]
and the mean that the random selection of 50 pages will contain no error is [tex]\lambda = 50 \times 0.02 =1[/tex]
∴
[tex]Pr(q= 0) = \dfrac{e^{-1} (1)^0}{0!}[/tex]
Pr(q =0) = 0.368
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that 50 randomly page contains at least 2 errors is computed as follows:
P(X ≥ 2) = 1 - P( X < 2)
P(X ≥ 2) = 1 - [ P(X = 0) + P (X =1 )] since it is less than 2
[tex]P(X \geq 2) = 1 - [ \dfrac{e^{-1} 1^0}{0!} +\dfrac{e^{-1} 1^1}{1!} ][/tex]
[tex]P(X \geq 2) = 1 - [0.3678 +0.3678][/tex]
[tex]P(X \geq 2) = 1 -0.7356[/tex]
P(X ≥ 2) = 0.2644
The probability that the selection of the random pages will contain at least two errors is 0.2644
The possibility of a random selection of 50 pages will contain at least two errors is [tex]0.264242[/tex].
To understand the calculations, check below
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]X[/tex] denotes the number of errors on [tex]50[/tex] randomly selected pages.
[tex]X\sim Poisson(\frac{50}{500}\ast 10)[/tex] or [tex]X\sim Poisson(1)[/tex]
The probability mass function of [tex]X[/tex] is,
[tex]P\left ( X=x \right )=\frac{e^{-1}\ast 1^{x}}{x!}=0,1,2...[/tex]
Now,
The probability that a random selection of [tex]50[/tex] pages will contain no errors,
[tex]=P\left ( X=0 \right ) \\ =\frac{e^{1}\ast 1^{0}}{0!} \\ =0.367879[/tex]
Learn more about the topic of Probability: https://brainly.com/question/19032615
What is the solution to the following inequality?
3x-1 < 2x + 4
Answer:
[tex]x<5[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]3x-1<2x+4[/tex]
First, let's subtract 2x from both sides. The right cancels:
[tex]x-1<4[/tex]
Add 1 to both sides:
[tex]x<5[/tex]
And we're done!
Our solution is all number less than 5.
Evaluate P(6, 6).
720
01
6
Answer:
720
Step-by-step explanation:
6!/(6-6)! = 6!/0! or 6!/1
6! =720
A wild animal generally stays at least x mi from the edge of a forest. For a rectangular forest preserve that is 2 mi
long and 5 mi wide, write a polynomial that represents the area of the available habitat for the wild animal.
(Note: diagram not drawn to scale)
Answer:
[tex]Area = 4x^2 - 14x + 10[/tex]
Step-by-step explanation:
See Attachment for Complete Question
Given
[tex]Width = 5mi[/tex] --- For the forest
[tex]Length = 2mi[/tex] -- --- For the forest
Required
Determine the area of the habitat
Since the distance between the animal's habitat is x mi on both sides;
The length and width of the habitat is:
[tex]Width = 5 - (x + x)[/tex]
[tex]Width = 5 - 2x[/tex]
[tex]Height = 2 - (x +x)[/tex]
[tex]Height = 2 - 2x[/tex]
The area is then calculated as follows;
[tex]Area = Width * Height[/tex]
[tex]Area = (5 - 2x) * (2 - 2x)[/tex]
Expand
[tex]Area = 5(2 - 2x) -2x(2 - 2x)[/tex]
Open Brackets
[tex]Area = 10 - 10x - 4x + 4x^2[/tex]
[tex]Area = 10 - 14x + 4x^2[/tex]
Reorder
[tex]Area = 4x^2 - 14x + 10[/tex]
Hence; the required polynomial for the habitat area is:
[tex]Area = 4x^2 - 14x + 10[/tex]
I NEED THIS DONE SOON Find the solution set if the replacement set is b = {3, 3.5, 4, 4.5, 5} 28/b+9 = 16
A restaurant owner is interested in the proportion of his customers who order dessert. He looks at 65 randomly selected receipts. Match the vocabulary word with its corresponding example.
Answer and Step-by-step explanation:
a) Statistic -the proportion of the 65 randomly selected customer
Statistic refers to the practice of gathering and examination data of numerical in a higher number of quantities, mainly for the motive of proportions inferring in a full form for that in a representative sample.
b) variable: the answer yes or no to weather.
The Variable is never being constant or a pattern of fixed; liable to change.
c) sample: The 65 customers of the hotel whose receipts the owner noticed.
Sample refers to the small part that is applied to present the whole thing
d) Data: the list of the 65 yes or no answers.
The data is the facts and the figures that are collected simultaneously
e) Population: all customer who comes to the restaurant
Population refer to a whole group of people and events
f) Parameter: the proportion of all customer who orders desert
The parameter refers to an average of a population that represents the whole population
What is 6.25 divided by 132
Answer:
0.04734848484
Step-by-step explanation:
The 6.25 divided by 132 equals 0.235 (rounded to three decimal places).
To calculate 6.25 divided by 132, perform the following steps:
Step 1: Divide the whole number part.
Divide 6 by 132, which equals 0 with a remainder of 6.
Step 2: Convert the remainder to a fraction.
The remainder 6 becomes 6/132.
Step 3: Divide the fractional part.
Divide 25 by 132, which gives the fraction 25/132.
Step 4: Add the results from Step 2 and Step 3.
Combine the fractions obtained in Step 2 and Step 3: 6/132 + 25/132 = 31/132.
The final result is 0 31/132, which can be simplified to 0 7/44 or written as a decimal as approximately 0.235. Therefore, 6.25 divided by 132 equals 0.235 (rounded to three decimal places).
To know more about divided:
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Martin decided to buy 3 bags of grapes weighing 4 1/5 pounds each. How much did all 3 bags of grapes weigh?
Answer:
12 3/5
Step-by-step explanation:
Answer:
12 3/5
Step-by-step explanation:
Got it right on my test.
when rolling a die (1) what's the probability of getting an even number in two successive throws??
Answer: I think it would be a 50/50 chance of getting 2 even numbers.
The department of transportation in a particular city knows from past records that 27% of workers in the downtown district use the subway system each day to commute to and from work. The department suspects that this proportion has increased owing to decreased parking spaces in the downtown district. A random sample of 130 workers in the downtown district showed that 49 used the subway daily. Test the claim at the 5% level of significance. What is the value of sample statistics
Answer:
We conclude that the proportion has increased owing to decreased parking spaces in the downtown district.
Step-by-step explanation:
We are given that the department of transportation in a particular city knows from past records that 27% of workers in the downtown district use the subway system each day to commute to and from work.
A random sample of 130 workers in the downtown district showed that 49 used the subway daily.
Let p = population proportion of workers in the downtown district use the subway system each day to commute to and from work.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 27% {means that the proportion has decreased or remain equal owing to decreased parking spaces in the downtown district}
Alternate Hypothesis, [tex]H_A[/tex] : p > 27% {means that the proportion has increased owing to decreased parking spaces in the downtown district}
The test statistics that will be used here is One-sample z-test statistics for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1- p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample proportion of workers who used the subway daily = [tex]\frac{49}{130}[/tex] = 0.38
n = sample of workers = 130
So, the test statistics = [tex]\frac{0.38-0.27}{\sqrt{\frac{0.27(1-0.27)}{130} } }[/tex]
= 2.825
The value of z-test statistics is 2.825.
Now, at a 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 2.825 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the proportion has increased owing to decreased parking spaces in the downtown district.
1) 16 is 45% of what Number
2) 5 is what percent of 18 ?
my teacher gave us the answer but can you show how you did it the Cross multiply method thank you
Answer:
i solved it .I hope you got it too
plz mark brainliest.
The function f (x )equals 2.9 square root of x plus 20.1, models the median height, f(x), in inches, of boys who are x months of age and for girls the function is f (x )equals 3.1 square root of x plus 19. Use a calculator to find the median height for both a boy and a girl who is 24 months old. Repeat the process for a child 48 months old. The actual median height for boys 48 months old is 40.8 inches and 40.2 inches for girls 48 months old. Does the model overestimate or underestimate the actual median heights and by how much
Answer:
Kindly check explanation
Step-by-step explanation:
Given the models for the median height of biys and giels:
BOY:
f(x) = 2.9√x + 20.1
GIRL:
f(x) = 3.1√x + 19
If x = 24 months
BOY:
HEIGHT = 2.9√24 + 20.1
= 2.9× 4.8989794 + 20.1
= 14.207040 + 20.1
= 34.307 inches
GIRL:
HEIGHT = 3.1√24 + 19
= 3.1 × 4.8989794 + 19
= 15.186836 + 19
= 34.1868 inches
If x = 48
Boy:
HEIGHT = 2.9√48 + 20.1
= 2.9× 6.9282032 + 20.1
= 20.091789 + 20.1
= 40.19 inches
Actual median height = 40.8
Hence, model underestimates by (40.80 - 40.19) = 0.61 inches
Girl:
HEIGHT = 3.1√48 + 19
= 3.1 × 6.9282032 + 19
= 21.477430 + 19
= 40.48 inches
Actual median height = 40.20
Hence, model overestimates by (40.48 - 40.20) = 0.28 inches
solve the equation by using Properties of Equality 5x-10=20
Answer:
5x-10=20
5x=20-10
x=10:5
x=2
Answer:
x = 6.
Step-by-step explanation:
5x - 10 = 20
5x - 10 + 10 = 20 + 10
5x = 30
5x/5 = 30/5
x = 6.
John bought 15 cookies and ate 3 of them what %of the cookies
Answer:
1200% I think hats what the calculator says
Step-by-step explanation:
What is the best base unit that is used to measure distance
Answer:
The correct answer is centimeter.
which statement is true in this equation?
Answer:
B) Stan made a mistake in step one.
Step-by-step explanation:
B) Stan made a mistake in step one.
When he multiplied 8(n+20), he should have gotten 8n+160, not 8n+20.
Answer:
B
Step-by-step explanation:
He made a mistake in Step: 1
it's supposed to be
n+8n+8(20)=110
distributive property
Hope this helps :)
five to the fifth power minus two to the third power
Answer:
3117Step-by-step explanation:
[tex]5^5 - 2^3\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:5^5\::\quad 3125\\\\=3125-2^3\\\\\mathrm{Calculate\:exponents}\:2^3\::\quad 8\\\\=3125-8\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:3125-8\:\\\\:\quad 3117[/tex]
The expression (8x + 4) inches represents the perimeter of a rectangle whose width is (3x − 4) inches. Find the length of the rectangle if x = 2.
Answer:
Length of the rectangle is 8 inches.
Step-by-step explanation:
Perimeter of rectangle = 2L + 2W
(8x+4) = 2L + 2(3x-4) where x = 2
(8(2)+4) = 2L + 2(3(2)-4)
20 = 2L + 4
16 = 2L
8 = L
Answer:
The length of the perimeter is 8
Step-by-step explanation:
write 21 and 4/5 as a decimal
Answer:
21 as a decimal: 21.00; 4/5 as a decimal: .8, 0.80
Step-by-step explanation:
Hope i helped, SJ
-3 is less than or equal to W and W is less than or equal to 4
Answer:
-3 ≤ W ≤ 4
I hope this helps!
