Answer: X= 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
18=3(3x−6)
18=(3)(3x)+(3)(−6)(Distribute)
18=9x+−18
18=9x−18
Step 2: Flip the equation.
9x−18=18
Step 3: Add 18 to both sides.
9x−18+18=18+18
9x=36
Step 4: Divide both sides by 9.
9x
9
=
36
9
Answer:
X=4
Step-by-step explanation:
18=3(3X-6)
18=3><(3X-6)
18=9X-18
9X=-18-18
9X=36
X=36/9
X=4
Hope this helps
Brainliest please
Which graph shows a function whose domain and range exclude exactly one value?
Answer:
C (the third graph)
Step-by-step explanation:
This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.
Answer:
see below
Step-by-step explanation:
This graph has an asymptote at y = 0 and x=0
This excludes these values
The domain excludes x =0
The range excludes y=0
Is (1,2), (2,3) (3,4), (4,5) a function?
Answer:
yes
Step-by-step explanation:
The domain is the set of x-values: {1, 2, 3, 4}. None of these are repeated, so this relation is a function.
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.45 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.)
Required:
Find the probability that the subsystem operates longer than 1000 hours.
Answer:
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Eight components:
This means that [tex]n = 8[/tex]
Probability of 0.45 of failing in less than 1,000 hours.
So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]
Find the probability that the subsystem operates longer than 1000 hours.
We need at least four of the components operating. So
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]
[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]
[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]
[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]
[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then
[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
HURRY TIMEDD!!!!!
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has? The discriminant is −4, so the equation has 2 real solutions. The discriminant is −4, so the equation has no real solutions. The discriminant is 35, so the equation has 2 real solutions. The discriminant is 35, so the equation has no real solutions.
Answer:
Second option is the correct choice.
Step-by-step explanation:
"The discriminant is −4, so the equation has no real solutions."
[tex]x^2-4x+5=0\\\\a=1,\:b=-4,\:c=5:\\\\b^2-4ac=\left(-4\right)^2-4\cdot \:1\cdot \:5=-4[/tex]
Best Regards!
Answer: B
The discriminant is −4, so the equation has no real solutions.
Step-by-step explanation:
Just took quiz EDG2021
Mark Brainliest
If
f(x) = 13x + 1, then
f-1(x) =
Answer:
(x-1)/13
Step-by-step explanation:
y = 13x+1
To find the inverse, exchange x and y
x = 13y+1
Solve for y
Subtract 1 from each side
x-1 =13y+1-1
x-1 = 13y
Divide each side by 13
(x-1)/13 = y
The inverse is (x-1)/13
Answer:
f(x) = 13x + 1
To find the inverse let f(x) = y
y = 13x + 1
x = 13y + 1
13y = x - 1
y = (x-1)/13
The inverse is x-1/13.
A data set is shown in the table. The line of best fit modeling the data is y = 2.69x – 7.95.
Answer:
It’s 0.12
Step-by-step explanation:
Took test
What transformations to the linear parent function, f(x) = x, give the function
g(x) = 4x - 2? Select all that apply.
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
O c. Horizontally stretch by a factor of 4.
O D. Shift left 2 units.
Answer:
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
Step-by-step explanation:
Given the function
f(x)=x
If we stretch y vertically by a factor of m, we have: y=m·f (x)
Therefore:
Vertically stretching f(x) by a factor of 4, we have: 4x.
Next, if we take down f(x) by k units we have: y= f(x)-k
Therefore: Taking down 4x by 2 units, we obtain:
g(x)=4x-2
Therefore, Options A and B applies.
Find the volume of a right circular cone that has a height of 4.2m and a base with a radius of 3.4m
Answer:
about 50.8 cubic meters
Step-by-step explanation:
The formula for the volume of a cone is ...
V = (1/3)πr²h
Put the given values into the formula and do the arithmetic.
V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³
__
For π to calculator precision, this is ...
V ≈ 50.84 m³
For π = 3.14, this is ...
V ≈ 50.82 m³
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope intercept form.
Answer:
y = x-2
Step-by-step explanation:
Pick two points on the line
(0,-2) and (2,0)
We can find the slope
m = (y2-y1)/(x2-x1)
= (0--2)/(2-0)
= (0+2)/(2-0)
2/2
=
We know the y intercept is -2 ( where it crosses the y axis)
y = mx +b is the slope intercept form of the equation where m is the slope and b is the y intercept
y = 1x -2
y = x-2
Answer: [tex]y=x-2[/tex]
Step-by-step explanation:
I explained the other problem you asked, why couldnt you apply that info to this one? Either way, Ill explain it again.
We can see the slope intercept is -2, so b = -2
To get the slope, just from visualization. Look at the y value and x value direction for which you gotta take to get to the next coords. From the y-intercept, you go up 1 and then right 1. 1/1 = 1
According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year. Consider two babies being born independently of one another. 1. The probability that both babies have birth defects is;______ a. 0.0009. b. 0.0400.c. 0.0606. d. 0.2000. 2. The probability that neither baby catches the flu in a given year is:_____ a. 0.024. b. 0.040. c. 0.230 d. 0.640. 3. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then:______ a. P(A and B) = 0.06. b. P(A or B) = 0.70. c. P(A and B) = 0.70. d. P(A or B) = 0.06. 4. Event A occurs with probability 0.2. Event B occurs with probability 0.9. Event A and B:______ are disjoint cannot be independent. cannot be disjoint. are reciprocating. The center for Disease Control and Prevention reports that the rate of Chlamydia infections among American women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three American women in this age group. 5. The probability that all of them have a Chlamydia infection is:_____ a. nearly 0. b. 0.028. c. 0.084. d. 0.837 6. The probability that none of them have a Chlamydia infection is:_______ a. 0.084. b. 0.919. c. 0.972. d. nearly 1.
Answer:
(1) a. 0.0009
(2) d. 0.640
(3)
a. P(A and B) = 0.06. b. P(A or B) = 0.70.(4)Not disjoint
(5) a. nearly 0.
(6)b. 0.919
Step-by-Step Explanation:
(1)Probability of a baby being born with a birth defect =3%=0.03
The probability that both babies have birth defects=0.03 X 0.03= 0.0009.
(2)The probability of contracting the influenza virus each year = 20%=0.2
Therefore, the probability of not contracting the influenza virus =1-0.2=0.8
The probability that neither baby catches the flu in a given year:
=0.8 X 0.8
=0.64
(3)
P(A)=0.1
P(B)=0.6
P(A or B)=P(A)+P(B)=0.1 + 0.6 =0.7
P(A and B)=P(A)XP(B)=0.1 X 0.6 =0.06
(4)
P(A)=0.2
P(B)=0.9
Event A and B cannot be disjoint.
(5)
The probability of an American woman aged 20 to 24 having Chlamydia infection [tex]=\dfrac{2791.5}{100000}[/tex]
The probability that three randomly selected women in this age group have the infection
[tex]=\dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \\\\=0.00002175\\\approx 0[/tex]
(6)The probability of an American woman aged 20 to 24 not having Chlamydia infection [tex]=1-\dfrac{2791.5}{100000}[/tex]
The probability that three randomly selected women in this age group do not have the infection
[tex]=\left(1-\dfrac{2791.5}{100000}\right)^3\\\\=0.9186\\\approx 0.919[/tex]
2)
Which of these objects are two-dimensional? Check all that apply.
A.Point
B.Segment
C.Square
D. Line
E. Solid
F. Plane
Answer:
Option C and F
Step-by-step explanation:
=> Square and Plane a two-dimensional objects.
Rest of the objects are either 1 - dimensional or 3- dimensional.
If the radius of a circle is 31.2 cm, what is the approximate area if you use 3.14 for pi and the area is rounded to the nearest tenth?
Answer:
3056.6 cm^2
Step-by-step explanation:
A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2
Answer: 3056.60 sq. cm.
Step-by-step explanation:
Area of a circle = π x r^2
= 3.14 x 31.2^2
= 3056.60
What is AB? Geometry help please
Answer:
AB = 37 units.
Step-by-step explanation:
Solve for AB using the Pythagorean theorem:
c² = a² + b² (c being AB in this instance)
Plug in the values of the legs of the triangle:
c² = 12² + 35²
c² = 144 + 1225
c² = 1369
c = √1369
c = 37
Therefore, AB = 37.
Help solve attached question.
Answer:
[tex]\mathrm{12\sqrt{5} \: \: inches}[/tex]
Step-by-step explanation:
Use Pythagorean theorem, where:
[tex]a^2+b^2=c^2[/tex]
Substitute in the values.
[tex]24^2+12^2=c^2[/tex]
[tex]c^2=576+144[/tex]
[tex]c^2=720[/tex]
[tex]c=\sqrt{720}[/tex]
[tex]c=12\sqrt{5}[/tex]
[tex]c=26.83281[/tex]
The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power. The probabilities that these two sources will be successfully developed and commercially viable in the next 10 years are 0.70 and 0.85, respectively. The successful development of these two energy sources are statistically independent. Determine the following: a. The probability that there will be energy supplied by these two alternative sources in the next 10 years. b. The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years.
Answer:
Step-by-step explanation:
a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S
Write the probability of energy supplied by these energy sources in the next 10 years
P(energy supplied) = P(S ∪ F) -----(1)
Rewrite eqn (1)
P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)
substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources
P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)
= 0.85 + 0.7 - (0.595)
= 1.55 - 0.595
= 0.955
Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955
B) write the probability of only one source of energy available
P(only one source of energy available) = [tex]P(\bar F S)[/tex] ∪ [tex]P( \bar S F)[/tex] ---(3)
Rewrite the equation (3)
P(only one source of energy available) =
[tex]=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)[/tex]
[tex]=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36[/tex]
Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36
What is the relative change from 6546 to 4392
Answer:
The relative change from 6546 and 4392 is 49.04
Step-by-step explanation:
In a sample of 22 people, the average cost of a cup of coffee is $2.70. Assume the population standard deviation is $0.93. What is the 90% confidence interval for the cost of a cup of coffee
Answer:
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $2.70
Standard deviation r = $0.93
Number of samples n = 22
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
$2.70+/-1.645($0.93/√22)
$2.70+/-1.645($0.198276666210)
$2.70+/-$0.326165115916
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
A polynomial is factorable, but it is not a perfect square trinomial or a
difference of two squares. Can you factor the polynomial without finding the GCF?
Answer:
So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the
Step-by-step explanation:
Glad i could help!
The area of a triangle is 80cm² and its base is 8cm. If its height is (6+k) cm, find the value if k.
(3marks)
Answer:
K=14
Step-by-step explanation:
A=1/2*b*h
80=1/2*8*(6+k) multiply by 2 on both sides
160=8*(6+k) distribute by 8
160=48+8k subtract 48 from both sides
112=8k divide by 8
14=K
Question 2: The average price for a BMW 3 Series Coupe 335i is $39,368. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe? Round your answer to 3 decimal places.
Answer:
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 39368, \sigma = 2367[/tex]
What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe?
This is 1 subtracted by the pvalue of Z when X = 44520. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44520 - 39368}{2367}[/tex]
[tex]Z = 2.18[/tex]
[tex]Z = 2.18[/tex] has a pvalue of 0.985
1 - 0.985 = 0.015
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
What is the volume of this container?
Step-by-step explanation:
Concepto 20 pies, 20´ × 8´ × 8´6" 40 pies High Cube, 40´ × 8´ × 9´ 6"
Ancho 2352 mm / 7´9" 2352 mm / 7´9"
Altura 2393 mm / 7´10" 2698 mm / 8´10"
Capacidad 33,2 m³ / 1172 ft³ 76, m³ / 2700 ft³
ESPERO QUE TE AYUDE :D
How many units of insulin are in 0.75 ML a regular U – 100 insulin
Answer:
0.75 ML of insulin contains 75 units of insulin
Step-by-step explanation:
U - 100 insulin hold 100 units of insulin per ml
This means that:
1 ML = 100 units
∴ 0.75 ML = 100 × 0.75 = 75 units
Therefore 0.75 ML of insulin contains 75 units of insulin
What is the algebraic expression for "the sum of three times a number and seven"? A. 3 x + 7 B. 3 x + 11 x C. 3 + 7 x
Answer:
3x+7
Step-by-step explanation:
Three times a number, let x be the number and 7 so plus 7
The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.
The given phrase is "the sum of three times a number and seven".
Variables and constants are combined to generate algebraic expressions using a variety of techniques. Terms comprise expressions. A term is the sum of several elements. Both numerical and algebraic (literal) factors are acceptable.
Let the unknown number be x.
Three times of a number = 3x
The number 7 is added to the obtained sum.
That is, 3x+7
So, the expression is 3x+7
The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.
To learn more about an expression visit:
https://brainly.com/question/28170201.
#SPJ4
paulina plays both volleyball and soccer .the probability of her getting injured playing soccer is 0.10 and the probability of her getting injured playing soccer is 0.20 .which of the event is more likely
Step-by-step explanation:
While playing volleyball, probability of getting hurt is
P(A) = 0.1 = 1/10
and in the case of soccer, it is
P(B) = 0.2 = 2/10 = 1/5
Here we see, P(A) < P(B)
Answer: We can conclude that the probability of getting injured while playing soccer is more likely.
a) find the value of 2x+y wehn x =4 and y =3 b) find the value of a^2 + b when a = -2 and b = 5
Answer:
a. 11b. 9Solution,
a. Given,
X=4
y=3
Now,
[tex]2x + y \\ = 2 \times 4 + 3 \\ = 8 + 3 \\ = 11[/tex]
b. Given,
a=-2
b=5
Now,
[tex] {a}^{2} + b \\ = {( - 2)}^{2} + 5 \\ = 4 + 5 \\ = 9[/tex]
hope this helps...
Good luck on your assignment..
An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2000 individuals, what is the approximate distribution of the number who carry this gene
Answer:
Brianliest!
Step-by-step explanation:
4
1 in 500
500 x 4 = 2000
4 in 2000
A jar contains 5 red marbles and 8 white marbles . Event A = drawing a white marble on the first draw Event B = drav drawing a red marble on the second draw If two marbles are drawn from the jar , one after the other without replacement , what is P(AandB) expressed in simplest form?
a: 3/13
b: 10/39
c: 5/12
d: 8/13
Answer:
(B) [tex]\dfrac{10}{39}[/tex]
Step-by-step explanation:
Number of red marbles = 5
Number of white marbles = 8
Total =8+5=13
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
P(A)=8/13
P(B)=5/12
Therefore:
P(A and B)
[tex]=\dfrac{8}{13} \times \dfrac{5}{12}\\\\=\dfrac{10}{39}[/tex]
Answer:
Your answer is B
Step-by-step explanation:
When 1760 is divided into 14 equal parts, the remainder is 10. What is a correct way to write the quotient?
Answer:
125 r. 10
Step-by-step explanation:
for a sample size of 115 and a population parameter of 0.1,what is the standard deviation of the normal curve that can be used to approximate the binomial probability histogram. Round your answer to three decimal places
A.0.028
B.0.054
C.0.043
D.0.035
Answer:
A) 0.028
Step-by-step explanation:
Given:
Sample size, n = 115
Population parameter, p = 0.1
The X-Bin(n=155, p=0.1)
Required:
Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.
To find the standard deviation, use the formula below:
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
Substitute figures in the equation:
[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]
[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]
[tex] \sigma = 0.028 [/tex]
The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028