Answer:
Can not be solved
Step-by-step explanation:
5x+10y = 3............. Equation 1
10x+20y = 8 ............ Equation 2
From the equation above,
both equations can not be solved by elimination method, because both variables will be eliminated
In 2019, 15.9% of Broadway actors were acting in their first role on Broadway. Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers. What are the mean and standard deviation for the sampling distribution of pÌ p^? 1. Mean: 0.159, Standard Deviation: 0.0592. Mean: 0.159, Standard Deviation: 0.36573. Mean: 0.184, Standard Deviation: 0.0634. Mean: 0.184, Standard Deviation: 0.0595. Mean: 0.159, Standard Deviation: 0.063In 2019 the CDC reported that 14.0% of US adults are smokers. Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.What is the mean and the standard deviation of the sampling distribution of pÌ p^ ?1. mean = 0.140, standard deviation = 0.0682. mean = 0.167, standard deviation = 0.0633. mean = 0.140, standard deviation = 0.0634. mean = 0.167, standard deviation = 0.068
Answer:
For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.
For the proportion of smokers, mean = 0.167, standard deviation = 0.068
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.
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]
Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.
This means that [tex]p = 0.184, n = 38[/tex]
What are the mean and standard deviation for the sampling distribution of p^?
Mean:
[tex]\mu = p = 0.184[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]
Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.
This means that [tex]n = 30, p = 0.167[/tex]
What is the mean and the standard deviation of the sampling distribution of p^ ?
Mean:
[tex]\mu = p = 0.167[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]
In a group of 450 students, 250 like oranges 280 like apples and 40 dislike both
the fruits
Answer:
Could you please question correctly??
Step-by-step explanation:
Total Students:450
Oranges:250
Apples:280
Dislike:40
like:280-250+40
Answer
i dont see the question sorry
1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4
X -1 0 1
f(x) 3c 3c 6c
Answer:
[tex]c = \frac{1}{12}[/tex]
The mean of the distribution is 0.25.
The variance of the distribution is of 0.6875.
Step-by-step explanation:
Probability density function:
For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:
[tex]3c + 3c + 6c = 1[/tex]
[tex]12c = 1[/tex]
[tex]c = \frac{1}{12}[/tex]
So the probability distribution is:
[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]
Mean:
Sum of each outcome multiplied by its probability. So
[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]
The mean of the distribution is 0.25.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probability. So
[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]
The variance of the distribution is of 0.6875.
The average THC content of marijuana sold on the street is 9.6%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,
a. What is the distribution of X? X ~ N(
9.6
Correct,
1
Correct)
b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.8.
c. Find the 67th percentile for this distribution.
%
Answer:
Im sorry but why is this a question? Like what school gives this out
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
Find the measure of the arc
The answer is kindly 21 (100% correct)
The cone and the cylinder below have equal surface area. O A. True O B. False
Answer:
the answer is false
Step-by-step explanation:
comment if you want explanation
Answer:
True
Step-by-step explanation:
When using the formulas to find the surface area, both have equal surface area
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
9514 1404 393
Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
2 - (-8) + (-3) =
O A) 12
OB) 7
O C
C) 14
OD 1
Answer:
B)7
Step-by-step explanation:
2-(-8)=10
10+(-3)=7
What number increased by 11.8% equals 185
Answer:165.47
Step-by-step explanation:
Complete the steps to solve the equation. 3x - 6(5x + 3) = 9x + 6 1. The distributive property 3x - 30x 18 = gr + 6 2 Combine like terms. -27x - 18 = 9x + 6 3. Addition property of equality: -18 = 36x + 6 4. Subtraction property of equality: -24 = 36x 5. Division property of equality I
Answer:
see below
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute
3x -30x-18 = 9x+6
Combine like terms
-27x - 18 = 9x+6
Add 27x to each side
-27x+27x-18 = 9x+27x+6
-18 = 36x+6
Subtract 6 from each side
-18-6 = 36x+6-6
-24 = 36x
Divide by 36
-24/36 = 36x/36
Simplify
-2/3 = x
Answer:
[tex]\small \sf x = \frac{2}{-3} \\ [/tex]
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6.
Use the distributive property to multiply -6 by 5x + 3.
3x - 30x - 18 = 9x + 6
Combine 3x and -30x to get -27x.
-27x - 18 = 9x + 6
Subtract 9x from both sides.
-27x - 9x - 18 = 9x - 9x + 6
-36x - 18 = 6
Add 18 to both sides.
-36x - 18 + 18 = 6 + 18
-36x = 24
Divide both sides by -36.
[tex]\small \sf \frac{ -36x}{ -36} = \frac{24}{-36} \\ [/tex]
Reduce the fraction [tex]\frac{24}{-36} [/tex] to lowest terms by extracting and canceling out 12.
[tex]\small \sf x = \frac{2}{-3} \\ [/tex]
Let v=-9i+j and w=-i-6j find 8v-6w
Answer:
78i+52j
Step-by-step explanation:
8(9i+2j)-6(-i-6j)
72i+16j+6i+36j
=78i+52j
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
urdxvjok NCAA earth bno
Sebastian is going to choose the color pattern
Answer:
use blue red blue red
Step-by-step explanation:
BRE
What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?
2 units
ОО
4 units
8 units
16 units
Answer:
2
Step-by-step explanation:
The equation of a circle is given as:
(x-h)^2 + (y-k)^2 = r^2
so r^2 = 4
r = sqrt(4)
r = 2
Answer:
A
Step-by-step explanation:
Evaluate x2 + 4x + 1 when x = -3
Answer:
[tex]-2[/tex]
Step-by-step explanation:
Just substitute -3 for all instances of x.
[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]
[tex]9 - 12 + 1[/tex]
[tex]-2[/tex]
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
Find the equation of the line passing through the points (2, 4) and (3, 2).
Which statement is true about the equations
-3x + 4y = 12 and 1/4x-1/3y = 1
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.
An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 11 students who took the course last semester follow:
# of observation(s) n = 30
# of independent variable(s) = 1
SSR = 1,297 SSE= 920
Required:
Find the F test statistic.
Answer:
[tex]F = 39.47[/tex]
Step-by-step explanation:
Given
[tex]n = 30[/tex] --- observations
[tex]p = 1[/tex] -- variables
[tex]SSR = 1,297[/tex]
[tex]SSE= 920[/tex]
Required
The F statistic
This is calculated using:
[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]
[tex]F = 1297 \div \frac{920}{28}[/tex]
Rewrite as:
[tex]F = 1297 * \frac{28}{920}[/tex]
[tex]F = \frac{1297 *28}{920}[/tex]
[tex]F = \frac{36316}{920}[/tex]
[tex]F = 39.47[/tex]
The heights (in inches) of a sample of eight mother/daughter pairs of subjects were measured. Using a spreadsheet with the paired mother/daughter heights, the linear correlation coefficient is found to be 0.693. Find the critical value, assuming a 0.05 significance level. Is there sufficient evidence to support the claim that there is a linear correlation between the heights of mothers and the heights of their daughters?
A. Critical value = ± 0.666; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
B. Critical value = ± 0.707; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
C. Critical value =± 0.666; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Answer:
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Step-by-step explanation:
Given that :
Correlation Coefficient, r = 0.693
The sample size, n = 8
The degree of freedom used for linear correlation :
df = n - 2
df = 8 - 2 = 6
Using a critical value calculator for correlation Coefficient at α = 0.05
The critical value obtained is : 0.707
The test statistic :
T = r / √(1 - r²) / (n - 2)
T = 0.693 / √(1 - 0.693²) / (8 - 2)
T = 0.693 / 0.2943215
T = 2.354
Since ;
Test statistic < Critical value ; we fail to reject the null and conclude that there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
if x+y=12 and xy =27,then find the value of x^2+y^2
PLEASE HELP !
Answer:
90
Step-by-step explanation:
=> x + y = 12
=> x² + y² + 2xy = 144
=> x² + y² + 2 * 27 = 144
=> x² + y² = 144 - 54
=> x² + y² = 90
helppp
True or false: f(x) represents a function.
What angles can you construct using just a pair of compasses and a ruler?
Answer:
By using a pair of compasses and a ruler you can draw all angles
The slope of diagonal AB is ___ , and it’s equation is ___.
Answer:
The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].
Step-by-step explanation:
Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.
Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].
what is the slope of the line plotted below?
Answer:
A, or 0.5
Step-by-step explanation:
1. BasicsSlope formula: Rise/run
([tex]y[/tex]₂[tex]-y[/tex]₁)/([tex]x[/tex]₂[tex]-x[/tex]₁)
2. SolvingPoints: (-4,-4), and (2,-1)
Let's say that (-4,-4) is the first point, and (2,-1) is the second. It doesn't really matter which ones we choose.
[tex]\frac{-1-(-4)}{2-(-4)}[/tex][tex]=\frac{3}{6}=\frac{1}{2} = 0.5[/tex]
A
Hope this helped! Please mark brainliest :)
Which of the following consists of discrete data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.
Answer:
A
Step-by-step explanation:
Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.
Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answer:
.
Step-by-step explanation:
.
Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.
Answer:
[tex]P = (7, -\frac{3}{5})[/tex]
Step-by-step explanation:
Given
[tex]A = (-9,5)[/tex]
[tex]B = (11,-2)[/tex]
[tex]m : n = 4 : 1[/tex]
Required
Point P
This is calculated as:
[tex]P = (\frac{m * x_2 + n * x_1}{m + n}, \frac{m * y_2 + n * y_1}{m + n})[/tex]
So, we have:
[tex]P = (\frac{4 * 11 + 1 * -9}{4 + 1}, \frac{4 * -2 + 1 * 5}{4+1})[/tex]
[tex]P = (\frac{35}{5}, \frac{-3}{5})[/tex]
[tex]P = (7, -\frac{3}{5})[/tex]
27
78%
Work out the area of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
21
0
Type here to search
I
Answer: See explanation
Step-by-step explanation:
Your question isn't complete and well written but I'll give examples on the calculation of the area of a circle.
1. Let's assume that a circle has a radius of 14cm and we want to know the area.
Area of a circle = πr²
where π = 3.142
r = radius = 14cm
Area = πr² = 3.142 × 14²
= 3.142 × 196
= 615.382cm²
2. Let's assume that we are given a diameter of 10cm and told to calculate the area of the circle.
Note that Diameter is twice the radius.
Area of a circle = πr²
where π = 3.142
r = radius = Diameter/2 = 10cm/2 = 5cm
Area = πr² = 3.142 × 5²
= 3.142 × 25
= 78.55cm²
