If x = -1, you have
2(-1) + 3 cos(-1) + e ⁻¹ ≈ -0.0112136 < 0
and if x = 0, you have
2(0) + 3 cos(0) + e ⁰ = 4 > 0
The function f(x) = 2x + 3 cos(x) + eˣ is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < c < 0 such that f(c) = 0.
find the probability that in a random arrangements of the letters of the word 'science' that all vowels may never be together.
Answer:
i dont know
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 10 more than the second. Let , y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
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Answer:
(36°, 67°, 77°)
Step-by-step explanation:
The problem statement lets us write the equations ...
x + y + z = 180 . . . . sum of angles in a triangle
y + z = 4x . . . . . 2nd and 3rd total 4 times the first
z = y +10 . . . . . . 3rd is 10 more than 2nd
__
Substituting for z in the second equation, we have ...
y +(y +10) = 4x
y +5 = 2x . . . . . . divide by 2
y = 2x -5 . . . . . . rearranged
z = 2x +5 . . . . . . substitute for y in the last equation
Now, we can write the first equation entirely in terms of x:
x +(2x -5) +(2x +5) = 180
5x = 180
x = 36
y = 2(36) -5 = 67
z = 67 +10 = 77
The three angles are (x, y, z) = (36°, 67°, 77°).
Wires manufactured for use in a computer system are specified to have resistances between 0.14 and 0.16 ohms. The actual measured resistances of the wires produced by company A have a normal probability distribution with mean 0.15 ohm and standard deviation 0.005 ohm. (Round your answers to four decimal places.) (a) What is the probability that a randomly selected wire from company A's production will meet the specifications
Answer:
Hence the probability that a randomly selected wire from company A's production will meet the specifications is 0.95455.
Step-by-step explanation:
a)[tex]P(0.14 < x < 0.16 ) = P[(0.14 - 0.15)/ 0.005) < (x - \mu) /\sigma < (0.16 - 0.15) / 0.005) ][/tex]
[tex]=P(0.14 < x < 0.16 ) = P[(0.14 - 0.15)/ 0.005)< ((x - 0.15) /0.005) < (0.16 - 0.15) / 0.005) ][/tex]
[tex]=P(z<\frac{0.01}{0.005} )- P(z<-\frac{0.01}{0.005})[/tex]
Using z table,
= 0.9773 - 0.02275
= 0.95455.
State the counting number in the periodic table of elements of the element considered to be the heaviest gas. (the answer should consist of numbers only)
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Answer:
118
Step-by-step explanation:
Oganesson is the heaviest element ever created. It is a "super-heavy" noble gas with a half-life less than 1 millisecond. Its atomic number is 118.
Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 99% confidence; n=23, s=0.28 mg.
df = (Type a whole number.)
χ2L = (Round to three decimal places as needed.)
χ2R = (Round to three decimal places as needed.)
The confidence interval estimate of σ is __ mg < σ < __ mg. (Round to two decimal places as needed.)
Answer:
χ²R = 8.643
χ²L = 42.796
0.20 < σ < 0.45
Step-by-step explanation:
Given :
Sample size, n = 23
The degree of freedom, df = n - 1 = 23 - 1 = 22
At α - level = 99%
For χ²R ; 1 - (1 - 0.99)/2= 0.995 ; df = 22 ; χ²R = 8.643
For χ²L ; (1 - 0.99)/2 = 0.005 ; df = 22 ; χ²L = 42.796
The confidence interval of σ ;
s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]
0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)
0.2008 < σ < 0.4467
0.20 < σ < 0.45
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
solve similar triangles (advanced)
solve for x
Answer:
x = 27/8
Step-by-step explanation:
We can write a ratio to solve
x 3
------- = ----------
x+9 11
Using cross products
x*11 = 3(x+9)
11x = 3x+27
Subtract 3x from each side
8x = 27
8x/8 = 27/8
x = 27/8
The maximum and minimum values of a quadratic function are called as________of the function.
Vertex is the point where the function is at its maximum/ minimum.
There is a swimming pool which has a length of 15 m and a width of 12 m. There is a 2 m wide path around the pool. If the cost of the path is $5 per , what is the cost of the path? Use words, numbers, and/or symbols to justify your answer.
Answer:
15m+12m+15m+13m=54m
2m×12m=24m
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
-6
Step-by-step explanation:
f(x) = -2x - 7 and g(x) = -4x + 6
Find f(-5)
f(-5) = -2(-5) -7 = 10-7 = 3
The find g(3)
g(3) = -4(3) +6
= -12 +6 =-6
g(f(-5)) = -6
Một công ty sản xuất ván trượt có thể bán một cái ván trượt với giá $60.
Tổng chi phí cho sản xuất bao gồm chi phí cố định là $1200 và chi phí để sản xuất một cái ván trượt là $35.
Nếu công ty đó bán được 80 cái ván trượt thì công ty đó
A 90% confidence interval is (35 45). What is the margin of error?
A.5
B.4.5
C.9
D.10
Answer:
option a 5......
...
I hope it's correct
How many edges are there?
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Answer:
24
Step-by-step explanation:
The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.
The total number of edges is 8 + 8 + 8 = 24.
When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
A patient consumes 2,000 calories of which 1200 calories were from carbohydrates. What percent of calories were from carbohydrates? Round the answer to the nearest integer.
Answer:
60%
Step-by-step explanation:
1200/2000=.6 or 60%
60%of calories were from carbohydrates.
What is percentage?a relative value that represents one tenth of any amount. One percent (symbolized as 1%) is equal to 100 parts; hence, 100 percent denotes the complete amount, and 200 percent designates double the amount specified. percentage. Percentile in mathematics is a related topic.
Given
1200/2000=.6 or 60%
Hence, 60%of calories were from carbohydrates.
To learn more about percentage refer to:
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If (-2, y) lies on the graph of y = 3Y, then y =
Answer:
[tex]\displaystyle \frac{1}{9}[/tex]
Step-by-step explanation:
Hi there!
This question is asking us what the value of y is when x is -2, hence the point (-2,y).
[tex]y=3^x[/tex]
To find y, replace x in the equation with -2 and evaluate:
[tex]y=3^-^2[/tex]
When [tex]a^-^n[/tex] where n>0, [tex]a^-^n=\displaystyle \frac{1}{a^n}[/tex]:
[tex]y=\displaystyle \frac{1}{3^2} \\\\y=\displaystyle \frac{1}{9}[/tex]
I hope this helps!
If Damien does a job in 21 hours less time than Caitlyn, and they can do the job together in 14 hours, how
long will it take each to do the job alone?
Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours
Step-by-step explanation:
Damien = X -21
Caitlyn = X
2X - 21 = 14
2X = 14 + 21
X = (14+21)/2
X = 7.5
A son is 8 years old. his father is 5 times as old. How old will the father be when he is twice as old as his son?
if you run 250 ft of cable and lose rate 3.6 dB how much rate you lose at 100 ft
Answer:
99
Step-by-step explanation:
99
What is the probability that z equals 1.5
Answer:
0.1
Step-by-step explanation:
The probability value corresponding to z = 1.5 is 0.9332.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The standard normal curve is a special case of a normal curve with a mean of 0 and a standard deviation of 1. Since it is symmetric around the mean, 50% of the observations lie under the mean while the other 50% of the observations lie above the mean.
Thus the probability value corresponding to z = 1.5 is 0.9332.
Since the total probability value under the curve is 1, we subtract 0.9332 from 1 to calculate the area to the right.
P(Z>1.5)
=P(Z≤1.5)
=1−0.9332
=0.0668
Learn more about probability here:
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solve 3x-4=√(2x^2-2x+2)
Answer:
Step-by-step explanation:
Begin the solution by squaring both sides of the given equation. We get:
(3x - 4)^2 = 2x^2 - 2x + 2, or:
9x^2 - 24x + 16 = 2x ^2 - 2x + 2
Combining like terms results in:
7x^2 - 22x + 14 = 0
and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92
According to the quadratic formula, the solutions are
-b ± √discriminant -(-22) ± √92 22 ± √92
x = ------------------------------- = ----------------------- = ------------------------
2a 14 14
You measure 49 turtles' weights, and find they have a mean weight of 80 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Round your answers to 2 decimal places.
Answer:
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.
The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
The function g(x)=8(4*) is reflected across the x-axis to
create f(x).
What is the equation of f(x)?
O f(x)=8(4)
O f(x)=-8(4)*
14
9(x)
12
10
o f(x)=8(4)
o f(x)=-8()
do
OR
4
2
A
-3
-2
2
3
х
-10
-12
f(x)
14
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Answer:
(b) f(x) = -8(4^x)
Step-by-step explanation:
Reflection across the x-axis multiplies the function by -1.
f(x) = -g(x) = -8(4^x)
A =
1
9
4 1 −8
7 4 4
4 −8 1
I don't know sorry I am weak in math
f(x) = 3x3
3.3 – 2.02 + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).
Answer:
C) (f+g)(x)= 3x^3-2x^2+10x-12
what value of x is in the solution set of 8x-6>12+2x
Answer:
x>3
Step-by-step explanation:
8x - 2x > 12+ 6
-> 6x > 18
-> x > 3
[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]
➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]
25(0.3x-4)-5(1.5x-6)+100(13/4) simplify the following expression and evaluate for x=0.345
Answer:
255
Step-by-step explanation:
Given :
Simplify the expression :
25(0.3x-4)-5(1.5x-6)+100(13/4)
Open each Bracket:
7.5x - 100 - 7.5x + 30 + 325
7.5x - 7.5x - 100 + 30 + 325
= 255
The simplified equation = 255
1. The curve y = (x - 1)(x – 5) cuts the x-axis at A and B and the y-axis at C.
(a) Find the coordinates of A and B.
(b) Hence, find the coordinates of the turning point, M.
Is M a maximum or a minimum point?
(c) Find the coordinates of C.
(d) Sketch the graph of y = (x - 1)(x - 5).
In a plane, line e is parallel to line f, line f is parallel to line g, and line h is perpendicular to line e. Which of the following cannot be true? e ⊥ h g ∥ h e ∥ g h ⊥ f
Answer:
g ∥ h
Step-by-step explanation:
since lines e,f,g are parallel to each other,
h is perpendicular to lines e,f,g
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?
Answer:
The standard error of the estimated difference is of 0.0313.
Step-by-step explanation:
To solve this question, 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.
Brand A:
33 out of 197, so:
[tex]p_A = \frac{33}{197} = 0.1675[/tex]
[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]
Brand B:
25 out of 290, so:
[tex]p_B = \frac{25}{290} = 0.0862[/tex]
[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]
What would be the standard error of the estimated difference?
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]
The standard error of the estimated difference is of 0.0313.
