Find the area of the figure. 6 ft 3 ft 4f The area is square feet
Answers
Answer:
18 ft square
Step-by-step explanation:
area = lenth × wedth
area= 6ft × 3ft
a = 18ft square
Related Questions
sketch the parabola y = f(x) which has the following properties:
1. f(-3) = 0
2. f(0) = 6
3. f(-1) = 0
4. f(x) > 0 when x < -1
5. f(x) < 0 when x > -1
Answers
Based on the given properties, we can sketch the parabola y = f(x) as follows:
1. The first property, f(-3) = 0, tells us that the parabola has an x-intercept at x = -3.
2. The second property, f(0) = 6, tells us that the parabola has a y-intercept at y = 6.
3. The third property, f(-1) = 0, tells us that the parabola has another x-intercept at x = -1.
4. The fourth and fifth properties tell us that the parabola is positive (above the x-axis) when x < -1 and negative (below the x-axis) when x > -1.
Based on these properties, we can sketch a parabola that opens downward with x-intercepts at x = -3 and x = -1 and a y-intercept at y = 6. The vertex of the parabola would be located at the midpoint of the two x-intercepts, which is (-3 + (-1)) / 2 = -2. Since the parabola opens downward and has a y-intercept of 6, the vertex must be located above the y-intercept.
Here is one possible sketch of the parabola y = f(x) based on the given properties:
Answer:
See attachment.
Step-by-step explanation:
The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.
Given f(-3) = 0 and f(-1) = 0, this indicates that the two x-intercepts of the parabola y = f(x) are x = -3 and x = -1.
For a parabola that opens upwards:
f(x) > 0 for the x-values either side of the the x-intercepts.f(x) < 0 for the x-values between the the x-intercepts.
For a parabola that opens downwards:
f(x) < 0 for the x-values either side of the the x-intercepts.f(x) > 0 for the x-values between the the x-intercepts.
The x-intercepts are x = -1 and x = -3.
Given that f(x) > 0 when x < -1, and f(x) < 0 when x > -1, this indicated that the parabola opens upwards.
The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. Given f(0) = 6, this indicates that the y-intercept is y = 6.
The x-value of the vertex is the midpoint of the two x-intercepts.
Given the x-intercepts are x = -3 and x = -1, then the x-value of the vertex of the parabola is x = -2.
To find the y-value of the vertex, we need to create the equation of the function and substitute x = -2 into it.
Substitute the x-values into the intercept formula:
\(\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is the leading coefficient.\\\end{minipage}}\)
\(y=a(x-(-3))(x-(-1))\)
\(y=a(x+3)(x+1)\)
To find the value of a, we can substitute the given point (0, 6) into the equation:
\(6=a(0+3)(0+1)\)
\(6=a(3)(1)\)
\(6=3a\)
\(a=2\)
Substitute the found value of a into the equation and expand to standard form:
\(y=2(x+3)(x+1)\)
\(y=2(x^2+4x+3)\)
\(y=2x^2+8x+6\)
To find the y-value of the vertex, substitute x = -2 into the equation of the parabola:
\(y=2(-2)^2+8(-2)+6=-2\)
Therefore, the vertex of the parabola is (-2, -2).
Sketch an upwards opening parabola with:
x-intercepts at x = -3 and x = -1.Vertex at (-2, -2).y-intercept at y = 6.The x-value of the vertex is the axis of symmetry. Therefore, ensure your parabola has symmetry about the vertical line x = -2.
\(\hrulefill\)
Please note that there is likely an error in the properties you have been given. If the y-intercept is positive, and both x-intercepts are negative, the parabola opens upwards. Therefore, f(x) > 0 when x > -1, and f(x) < 0 when x < -1.
Match each multiplication expression on the left with the best estimate of its product on the right. (80)(30) = 2,400 29.3 x 5.9 81.4 x 32.1 32.9 x 4.81 46.7 x 31.7 59.3 x 3.57 (30)(6) = 180 (30)(5) = 150 (60)(4) = 240 (50)(30) = 1,500 Done
Answers
Here is the final matching of multiplication expressions with their estimated products:
(80)(30) = 2,400
(30)(6) = 180
(30)(5) = 150
(60)(4) = 240
(50)(30) = 1,500
29.3 x 5.9 ≈ 173
81.4 x 32.1 ≈ 2,618
32.9 x 4.81 ≈ 158
46.7 x 31.7 ≈ 1,479
59.3 x 3.57 ≈ 212
Match each multiplication expression on the left with the best estimate of its product on the right:
(80)(30) = 2,400
(30)(6) = 180
(30)(5) = 150
(60)(4) = 240
(50)(30) = 1,500
29.3 x 5.9
81.4 x 32.1
32.9 x 4.81
46.7 x 31.7
59.3 x 3.57
Matching the expressions with their estimated products:
(80)(30) = 2,400
(30)(6) = 180
(30)(5) = 150
(60)(4) = 240
(50)(30) = 1,500
Estimates for the remaining expressions:
29.3 x 5.9 ≈ 173.27
81.4 x 32.1 ≈ 2,612.94
32.9 x 4.81 ≈ 158.05
46.7 x 31.7 ≈ 1,480.39
59.3 x 3.57 ≈ 211.46
Matching the expressions with their estimated products:
(80)(30) = 2,400
(30)(6) = 180
(30)(5) = 150
(60)(4) = 240
(50)(30) = 1,500
29.3 x 5.9 ≈ 173.27
81.4 x 32.1 ≈ 2,612.94
32.9 x 4.81 ≈ 158.05
46.7 x 31.7 ≈ 1,480.39
59.3 x 3.57 ≈ 211.46
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I need help on this one to sorry
Answers
Answer:
250 and 250.1
Answer:
250.1
Step-by-step explanation:
5002 divided by 20 equals 250.1
16% are green, Bag contains 200 candies and find 20% are green. what's the probabilty of geting a sample proporttion
Answers
Answer:
200 × 16 /100= 32
32 ×20/100 = 6.4 Candies or 6 Candies
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
2c + c
3c + 3
2c + 3
2c + c – 3
2c – c + 3
2c + c + 3
Answers
It cost Brody $9.80 to send 196 text messages. How many text messages did he send if he spent $4.20? *
Answers
Answer:
84 text messages
Step-by-step explanation:
Set up a proportion and solve:
dollars / texts = dollars / texts
9.8 / 196 + 4.2 / x
9.8 * x = 4.2 * 196
9.8x = 823.2
9.8x / 9.8 = 823.2 / 9.8
x = 84
Brody would have sent 84 messages if he spent $4.20.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, the cost of sending 196 text messages is $9.80.
Therefore,
$9.80 = 196 messages
$1 = 196/9.80 messages
$4.20 = (196/9.80)×4.20 messages
$4.20 = 84 messages
Hence, Brody would have sent 84 messages, if he spent $4.20.
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Jayda has 12 library books checked out Anaheim has 1/3 less than that how many books does hon have checked out
Answers
Answer:
We know that Jada has 12 books checked out, and Hon has one third less than that.
one-third of a number is equal to the number divided by 3, in this case, we have the number 12, so a third of 12 is: 12/3 = 4
then if Hon has a third less than 12, Hon has 12 - 4 = 8 books checked out.
Also can u pls mark me brainliest im new
Need help answering these questions I would appreciate it
Answers
Answer:
1. 160 candidates
2. 2,3,5 (not sure tho)
3. i don think there's any.
For the soccer team fundraiser, you carn 5 points
for every $3 you raise. If Tyson carned 85 points,
how much money did he raise?
Answers
Answer:
He raised 51 dollars
Step-by-step explanation:
If for every 5 points he raised 3 dollars he would have raised 51 dollars because he had 85 points.
Solve solve solve solve solve
Answers
Step-by-step explanation:
Simplifying X + 8y = 4
Solving X + 8y = 4
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-8y' to each side of the equation.
X + 8y + -8y = 4 + -8y
Combine like terms: 8y + -8y = 0 X + 0 = 4 + -8y X = 4 + -8y Simplifying X = 4 + -8y
STEP 1:
8y
Simplify : 4
Equation at the end of step
1: x + 2y
2: Final result : x + 2y
I know I'm prob wrong, lol!
Which of the following is an arithmetic sequence?
O A. -2,3, 8, 13, 18,...
O B. 1,1, 2, 3, 5, 8, ...
O C. 4,-4, 4, -4, 4, ...
O D. 1, 1/2,1/4,1/16
Answers
pls help me solve this
Answers
The results of operations between vectors are, respectively:
Case A: u + w = <- 3, - 1>
Case B: - 6 · v = <6, 6>
Case C: 3 · v - 6 · w = <- 21, - 15>
Case D: 4 · w + 3 · v - 5 · u = <39, 4>
Case E: |w - v| = √(4² + 3²) = 5
How to determine the operations between vectors
In this problem we must determine the operations between vectors, this can be done by following definitions:
Vector addition
v + u = (x, y) + (x', y') = (x + x', y + y')
Scalar multiplication
α · v = α · (x, y) = (α · x, α · y)
Norm of a vector
|u| = √(x² + y²)
Now we proceed to determine the result of each operation:
Case A:
u + w = <- 6, - 3> + <3, 2>
u + w = <- 3, - 1>
Case B:
- 6 · v = - 6 · <- 1, - 1>
- 6 · v = <6, 6>
Case C:
3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>
3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>
3 · v - 6 · w = <- 21, - 15>
Case D:
4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>
4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>
4 · w + 3 · v - 5 · u = <39, 4>
Case E:
|w - v| = |<3, 2> - <- 1, - 1>|
|w - v| = |<4, 3>|
|w - v| = √(4² + 3²) = 5
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Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function. Compare your response to the sample response above. What did you include in your explanation? a reference to the horizontal-line test a statement that the function is one-to-one the conclusion that the inverse is a function
Answers
Based on the sample response given, the statements included in the explanation on the horizontal line test are:
a reference to the horizontal-line test.a statement that the function is one-to-one. inverse is a function.What is the horizontal-line test?The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.
To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.
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When chords intersect in a circle, the vertical angles formed intercept congruent arcs.
Answers
Answer:
sometimes
Step-by-step explanation:
if those are the options you have then that's the correct answer
If the number of observations for each sample is 150 units, what is the 3-sigma upper control limit of the process
Answers
Complete Question
Complete Question is attached below
Answer:
\(UCL= 0.25\)
Step-by-step explanation:
From the question we are told that:
Sample size\(n=150\)
Sample Variants \(s=7\)
Sigma control limits \(Z = 3\)
Therefore
Total number of observations is Given as
\(T_o=n*s\)
\(T_o=150 *7\)
\(T_0=1050\)
Generally
Summation of defectivee
\(\sum np=23+34+15+30+25+22+18\)
\(\sum np= 167\)
Generally the equation for P-bar is mathematically given by
\(P-bar=\frac{\sum np}{T_o}\)
\(P-bar=\frac{167}{1050}\)
\(P-bar=0.16\)
Therefore
\(Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}\)
\(Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}\)
\(Sp=0.03\)
Generally the equation for 3-sigma upper control limit of the process is mathematically given by
\(UCL = P-bar + Z*Sp\)
\(UCL= 0.16 + 3*0.03\)
\(UCL= 0.25\)
Hailey is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Hailey will earn $30 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Hailey's songs were played on 4 times as many commercials as movies and her total earnings on the royalties from all commercials and movies was $440. Determine the number of commercials and the number of movies on which Hailey's songs were played.
Answers
Hailey's song was played in 8 commercials and 2 movies .
In the question ,
it is given that ,
commission earned by Hailey if song played in commercial = $30
commission earned by Hailey if song played in movie = $100
let the number of commercials = x
and let the number of movies be = y
given that Hailey's songs were played on 4 times as many commercials as movies , that means
x = 4y
and the royalties from all commercials and movies was $440 ,
the equation is 30x + 100y = 440
Substituting x=4y , we get
30(4y) + 100y = 440
120y + 100y = 440
220y = 440
y = 440/220
y = 2
and x = 4(2) = 8
Therefore , Hailey's song was played in 8 commercials and 2 movies .
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i am confused on finding the answer i have tried a few times and i do not understand
Answers
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
100 point math question pls help, no fake answers
Answers
The sequence of the terms is -7,-1+5, and +11. A series is a collection of sequences.
What is the difference between a sequence and a series?A sequence is a collection of items that have been arranged in a logical order, with members appearing either before or after each other.
Given equation ;
\(\rm a_n = a_{n-1}+6\)
If,
\(\rm a_1 = -13\)
The next term in the sequence is;
\(\rm a_2 = a_{2-1}+6 \\\\ \rm a_2 = a_{1}+6 \\\\ a_2 = -13 +6 \\\\ a_2 =-7\)
\(\rm a_3 = a_{3-1}+6 \\\\ \rm a_3 = a_{3}+6 \\\\ a_3 = -7 +6 \\\\ a_3 =-1\)
\(\rm a_4 = a_{4-1}+6 \\\\ \rm a_4 = a_{3}+6 \\\\ a_4 = -1 +6 \\\\ a_4 =+5\)
\(\rm a_5 = a_{5-1}+6 \\\\ \rm a_5 = a_{4}+6 \\\\ a_5 = 5 +6 \\\\ a_5 =11\)
Hence, the sequence of the terms is -7,-1+5, and +11.
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Write a quadratic equation with solutions -3 and 4/7.
Answers
X^2 +7x-4x-28=0
X^2 +3x-28=0
If a city’s maximum temperature was 42 degrees and the minimum was 9 degrees, what is the difference between the two temperatures?
Answers
The difference between the two temperatures is 33 degrees.
How to find the difference between the two temperatures?The city's maximum temperature was 42 degrees and the minimum was 9 degrees.
The difference between the two temperatures can be calculated as follows;
The difference in temperature is the subtraction of the minimum temperature from the maximum temperature.
Therefore,
difference between the temperature = maximum temperature - minimum temperature
maximum temperature = 42 degrees
minimum temperature = 9 degrees
Hence,
difference between the temperature = 42 - 9
difference between the temperature = 33 degrees.
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help i need the value of y
Answers
Answer:
y = 87º
Step-by-step explanation:
Vertical angles are congruent
y = 87º
Answer:
87°
Step-by-step explanation:
y is vertical to 87° meaning that the two are congruent which makes them the same
One of the Starbucks managers strongly believes that the primary functions are to make valued or desired rewards available in the
workplace and clarify for the subordinate the kinds of behavior that will lead to goal accomplishment and valued
rewards Accordingli he is referring to - motivational theory, which is part of the --- motivational perspective/theories
A Substitute, Content
(B) Substitute, Process
Expectancy. Content
D) Expectancy, Process
Answers
Answer:
eyeyywhwywhwhehehhehehehehhehe the answer is a
Which describes the combined variation shown in
the equation F= kxy/z?
varies directly with x, and inversely with y
and z.
F varies directly with z, and inversely with x
and y.
F varies directly with y, and inversely with x
and z.
F varies directly with x and y, and inversely
with z.
Answers
Step-by-step explanation:
F varies directly with x and y, and inversely with z.
k is the constant of variation.
Which function has a period of 4π?
Answers
Answer:
Step-by-step explanation:
y = one-half sine (one-half x)
based on the equation, period=2pi/b, you can just plug in the values for the equation on each option, b being the constant in front of x.
plz mark as brainliest
Determine if the triangles in each pair are similar. If so, write a similarity statement and state whether AAA, SAS, Or SSS
Answers
the triangle are congruent by AAA
What is congruent by AAA?
It can also be stated as the AAA (angle-angle-angle) similarity theorem, which states that two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.given, ABC and XYZ, are congruent according to the AAA rule by looking at the image provided below. According to the AAA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.
In the given two triangles,
The ratio of the sides are similar
And hence the angles are similar.
Hence the triangle are congruent by AAA
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A recent study reported the mean body mass index (BMI) for adults in the United States was 26. 8. A researcher believes the mean BMI of marathon runners is less than 26. 8. A random sample of 35 marathon runners had a mean BMI of 22. 7 with a standard deviation of 3. 1. The researcher will conduct a one-sample t-test for a population mean. Have the conditions for inference been met
Answers
Since the samples of the study are independent, the condition for inference have been met
The body mass index for adults in the United States = 26.8
BMI stands for Body Mass Index
Body mass index of marathon runners = less than 26.8
The random samples = 35
The body mass index of the random samples = 22.7
Standard deviation = 3.1
Then the researchers will conduct a one sample t test for a population mean.
The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value
Here the samples are independent
Therefore, the condition for inference have been met
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The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment.
(b) Assuming his suspicion that 7.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 14 customers buy a magazine? Give your answer as a decimal number rounded to two digits.
(c) What is the expected number of customers from this sample that will buy a magazine?
Answers
The experiment is binomial , probability that 3 out of 14 customers buy a magazine is 0.06 and the expected value is 1.036.
Part AThe experiment described is binomial because it satisfies the following conditions:
There are a fixed number of trials, which is 14 in this case.Each trial has two possible outcomes: The outcome of each trial is whether or not a customer buys a magazine. The probability of success is constant. 7.4%The trials are independent: Each customer's behavior is independent of others.Part BThe probability that exactly 3 out of the first 14 customers buy a magazine. Using the binomial probability formula:
\(P(X = k) = (nCk) \times (p^k) \times {q}^{n - k} \)
Where:
n = number of trials (14 in this case)
k = number of successful trials (3 in this case)
p = probability of success (7.4% or 0.074)
q = 1-p
Plugging in the values:
P(X = 3) = (14C3) × (0.074³) × 0.926¹¹
P(X= 3) = 0.0633
Part CThe expected number of customers from this sample that will buy a magazine can be calculated using the formula:
E(X) = n × p
Where:
- n is the number of trials
- p is the probability of success
Plugging in the values:
E(X) = 14 × 0.074 = 1.036
Therefore, the experiment is binomial and the expected value is 1.036.
Learn more on Binomial probability: https://brainly.com/question/15246027
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Eleven times one number is 9 more than 8 times another number. The first number minus four is half the second number. Enter the smaller of the two numbers.
Answers
Let the numbers are: x and y
Eleven times one number is 9 more than 8 times another number
so,
\(11x=8y+9\rightarrow(1)\)And, The first number minus four is half the second number
so,
\(x-4=0.5y\rightarrow(2)\)from equation (2):
\(x=0.5y+4\)substitute with (x) into equation (1) then solve for (y):
\(\begin{gathered} 11(0.5y+4)=8y+9 \\ 5.5y+44=8y+9 \\ 5.5y-8y=9-44 \\ -2.5y=-35 \\ \\ y=\frac{-35}{-2.5}=14 \end{gathered}\)substitute with (y) into equation (2) to find (x):
\(\begin{gathered} x-4=0.5\cdot14 \\ x-4=7 \\ x=7+4 \\ x=11 \end{gathered}\)so, the answer will be:
The smaller of the two numbers = 11