The probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.
what is probability?
In general terms, probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty or randomness in various situations.
In formal terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in an event. It is usually represented as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an adult being willing to change their diet can be calculated using the given information as follows:
Probability of an adult being willing to change diet = Number of adults willing to change / Total number of adults
Total number of adults = 400 (as given in the question)
Number of adults willing to change = 116 (as given in the question)
Therefore, the probability of an adult being willing to change their diet can be calculated as:
Probability = 116/400
Probability = 0.29 or 29%
So, the probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.
To learn more about probability from the given link
https://brainly.com/question/30034780
#SPJ1
Which expressions are equivalent to the one below? Check all that apply.
log2 2 + log2 8
A. 4
B. log₂ (2^4)
C. log2^16
D. log 10
The expressions B and C are equivalent to the given expression:
B. log₂ (2^4) = log₂ 16C. log₂ 16What are logarithmic functions?A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.
How to find the equivalent expressions?Simplify the expression using logarithmic property,
log m + log n = log (m.n)
Expression can be written as,
log₂(2) + log₂(8) = log₂(2x8)
= log₂ 16
simplify further,
log₂16 = log₂(2)⁴
Learn about Logarithmic function here brainly.com/question/3181916
#SPJ1
Hey Sofa is being sold for 65% off the regular price the sale price is $247 what is the regular price
Answer: The regular price of the sofa is $705.71.
Step-by-step explanation:
Regular price = Sale price / (1 - Discount rate)
* 65% = 0.65
Regular price = $247 / (1 - 0.65) = $247 / 0.35 = $705.71
Use your quadratic cost function and the following demand curve.
P = 900 - 0.03Q MR = 900 - .06Q
Calculate marginal cost (MC) and average cost (AC), price (P) and marginal revenue (MR) Graph MC, AC, P, and MR as a function of output (you may use Excel or graph these relationships by hand). Show the price and output that maximizes profit in this graph. Then use algebra to calculate the price and output (view output as a measure of desired run production for the season) that will maximize the firm’s profit. Calculate your profits at this price and output level.
Calculate the level of output that minimizes average cost. Show this solution on your graph above. Calculate your profits at this output level.
Calculate the price and level of output that maximizes total revenue. Show this solution on your graph above. Calculate your profits at this output level.
Assume that the demand and cost data above is for the N. Y. Yankees and Major League Baseball owners impose a lump sum tax of $4 million dollars to help equalize talent across high revenue and low revenue teams. How will the tax affect your profit maximizing output and the price you charge? How will the tax affect your profits? Explain.
Extra Credit
Now suppose that the league owners impose a “luxury tax” of 50 percent on costs that are above $200,000. Calculate your profit maximizing output and pricing levels, and your profits. Now assume the players’ association has it’s way and the tax is only 25 percent on costs that are above $500,000. Calculate your profit maximizing output and pricing levels, and your profits. (Hint: you may find it useful to find the output level where the luxury tax kicks in and then examine how this tax affects your cost structure at higher output levels). Graph your solutions to the “luxury tax” in your graph above.
To find MR, we take the derivative of the demand curve with respect to Q:
MR = dP/dQ = 900 - 0.06Q
How to solveTo find MC, we need to take the derivative of the quadratic cost function with respect to Q:
C(Q) = 500 + 10Q + 0.005Q^2
MC = dC/dQ = 10 + 0.01Q
To find AC, we divide the total cost by the quantity:
AC = C(Q)/Q = (500 + 10Q + 0.005Q^2)/Q = 500/Q + 10 + 0.005Q
To find P, we use the demand curve and solve for Q:
P = 900 - 0.03Q
Q = (900 - P)/0.03
Explanation:
To find P, we use the demand curve and solve for Q:
P = 900 - 0.03Q
Q = (900 - P)/0.03
To find MR, we take the derivative of the demand curve with respect to Q:
MR = dP/dQ = 900 - 0.06Q
Now we can graph MC, AC, P, and MR:
|
P | /MR
| /
| /
| /
| /
| /
| / AC
| /
MC |/
|------------- Q
Note:
The graph is a rough sketch and not drawn to scale. The MC curve is upward-sloping, the AC curve is U-shaped, the P curve is downward-sloping, and the MR curve lies below the P curve and is also downward-sloping.
Read more about graphs here:
https://brainly.com/question/26233943e
#SPJ1
Please help me solve these! Fast thanks!
The expansion will be:
a) (x-6) (x+7) = x² + x - 42
b) (2x-3)(5x-4) = 10x² - 23x + 12
c (x+3)(x+5) = x² + 8x + 15
The factorization will be:
a) 2(x+3)
b) 3x(3x-4)
c) 2(12x² + 8x-1)
What is an equation?An equation simply has to do with the statement that illustrates the variables given.
In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Therefore, the expansion will be:
a) (x-6) (x+7) = x² + x - 42
b) (2x-3)(5x-4) = 10x² - 23x + 12
c (x+3)(x+5) = x² + 8x + 15
Learn more about equations on
https://brainly.com/question/2972832
#SPJ1
What is 2 3/4+5/4 in an number line
In a study of the effects of college student employment on academic performance, two random samples (one from students who worked and the other from students who did not work) were selected from college students at a large university. The following summary statistics for GPA were reported.
Employed students
sample size 114
Mean GPA 3.15
Std deviation 0.485
Non-employed students
Sample size 114
Mean GPA 3.23
std deviation 0.524
Compute a 90% confidence interval for the mean GPAs of non-employed students. Assume that the normal condition is met.
a. Identify the variables needed to solve the problem.
b. Find the standard deviation.
c. Calculate the point estimate and margin of error.
d. Calculate the confidence interval
Therefore the 95% confidence interval is,
(219.25, 534.75)
How to solveHere sample standard deviation is given but the sample size is large. Therefore we use z table to find the critical value.
Therefore the 90% confidence interval for the mean GPA for students at the University who are employed and who are not employed is,
(0.112, 0.308)
For the next problem,
We follow the same procedure as we have done in the first problem.
And here the data is different and we construct 95% confidence interval.
Therefore the 95% confidence interval is,
(219.25, 534.75)
And we interpret this confidence interval as,
We are 95% confident that the true difference in the mean daily caorie intake for teens who do eat fast food on a typical day and those who do not falls within this interval.
Read more about confidence interval here:
https://brainly.com/question/15712887
#SPJ1
How many ways can steve select a song
Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:
��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!
For the rock songs, we have three from a set of eleven, hence:
�11,3=11!3!8!=165C11,3=3!8!11!=165
For the alternative songs, we have four from a set of five, hence:
�5,4=5!4!1!=5C5,4=4!1!5!=5
For the rap songs, we have three from a set of four, hence:
�4,3=4!3!1!=4C4,3=3!1!4!=4
Since the songs are independent, the total number of ways is given by:
�=165×5×4=3300T=165×5×4=3300
hope this helps you
Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:
��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!
For the rock songs, we have three from a set of eleven, hence:
�11,3=11!3!8!=165C11,3=3!8!11!=165
For the alternative songs, we have four from a set of five, hence:
�5,4=5!4!1!=5C5,4=4!1!5!=5
For the rap songs, we have three from a set of four, hence:
�4,3=4!3!1!=4C4,3=3!1!4!=4
Since the songs are independent, the total number of ways is given by:
�=165×5×4=3300T=165×5×4=3300
hope this helps you
Dolls were sold for ₱42,356 gross, with returns amounting to ₱3,479. The cost of the dolls sold is ₱27,212. What is the gross profit?
Answer:
To find the gross profit, we need to subtract the cost of the dolls sold from the gross sales revenue (after returns have been deducted).
First, we need to calculate the net sales revenue, which is the gross sales revenue minus the returns:
Net sales revenue = Gross sales revenue - Returns
Net sales revenue = ₱42,356 - ₱3,479
Net sales revenue = ₱38,877
Next, we can calculate the gross profit:
Gross profit = Net sales revenue - Cost of goods sold
Gross profit = ₱38,877 - ₱27,212
Gross profit = ₱11,665
Therefore, the gross profit from the sale of the dolls is ₱11,665.
[ rate 5 stars po and thanks if this helps u po! welcome! ]
HELPPPP IT IXL PLEASEE
Answer:
32
Step-by-step explanation:
m∠S = tan⁻¹(5/8) = 32⁰
Find the weighted mean. Round your answer to one decimal place.
Deliveries Per Week Frequency
4 7
8 2
12 5
16 6
Weighted mean =
deliveries per week
You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately o = 78.5 dollars. You would like to be 95% confident that your estimate is within 2 dollar(s) of average spending on the birthday parties. How many parents do you have to sample? Hint: Video [+] n = Submit Question
The number of parents you have to sample is calculated as: 5918
How to calculate the confidence Interval?The formula for the margin of error here is:
E = z(σ/√n)
where:
E is margin of error
σ is standard deviation
n is sample size
We are given:
E = 2
σ = $78.5
At 95% Confidence Level, z = 1.96
Thus:
2 = 1.96(78.5/√n)
Square both sides to get:
4 = 23672.9/n
n = 23672.9/4
n = 5918
Read more about Confidence Interval at: https://brainly.com/question/17097944
#SPJ1
A stock can go up, go down, or stay unchanged . How many possibilities are there if you own 9 stocks?
Find the volume for each figure. Use 3.14 for Pi
1.
r=21 ft-
35 ft
Answer:
V = 16155.3 cubic feet
Step-by-step explanation:
The formula for volume (V) of a cone is
[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.
In the diagram, we're shown that the radius is 21 feet and the height is 35 feet. Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:
[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]
What is the radius of a sector when 0+3pi/8 radians and the area is 75pi/16 square units
Answer:Let's use the formula for the area of a sector to find the radius of the sector:
Area of sector = (1/2) * radius^2 * angle in radians
We know the area of the sector is 75pi/16 and the angle in radians is 3pi/8, so we can plug those values in and solve for the radius:
75pi/16 = (1/2) * radius^2 * 3pi/8
Simplifying:
75pi/16 = (3/16) * radius^2 * pi
Multiplying both sides by 16/3pi:
25 = radius^2
Taking the square root of both sides:
radius = ±5
Since a radius can't be negative, we have:
radius = 5
Therefore, the radius of the sector is 5 units.
Calculator What is the area of this figure? Enter your answer in the box. units²
The area of the irregular pentagon is determined using it's coordinates. Its area is: 30.5
First indicate the coordinates:
A (1,4)
B(4, 3)
C(4, -3)
D(-1-2)
E(-1.5, 2)
Using the shoe lace formula:
Area = (1/2) | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |
where n is the number of vertices, and
(x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices in clockwise or counterclockwise order.
Plugging in the values,
Area = Area = (1/2) | (1*3 + 4*(-3) + 4*2 + (-1.5)*(-2) + (-1)*4) - (4*3 + 4*(-1.5) + (-1)*(-3) + 3*2 + (-2)*1) |
Area = 30.5
Learn more about irregular pentagons:
https://brainly.com/question/929013
#SPJ1
What do you know about this data before finding the range or the interquartile range?
187, 191, 202, 209, 218, 1984
The values are not in order.
The outlier will have no affect on the range.
The data has an outlier, therefore the interquartile range is much greater than it would be without the outlier.
The data has an outlier, therefore the range will be much greater than it would be without the outlier.
Answer:
D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.
Step-by-step explanation:
The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.
Answer:
d got it right in edge.
i need help with this trig question part A and B
Answer:
Part A: ∠A ≈ 27.7 °
Part B: c ≈ 8.75
Step-by-step explanation:
Part A:
Use the Law of Cosines.
Cosθ =
[ a² + b² - c² ] / [ 2ab ]
Sub in all the information where θ is A.
A = cos⁻¹ { [10² + 7² - 5²] / [2×10×7]
A ≈ 27.7 ° (1 decimal place)
Part B:
Use the Law of Cosines, but instead the unknown is the side c.
Rearrange to isolate c:
c² = a² + b² - 2ab×cosθ
c = √(5² + 6² - 2×5×6×cos(105°))
c ≈ 8.75 (2 decimal places)
State the restriction and then simplify
Restrictions
X=
And
X=
Simplify =
The restrictions on the expression are x = -9/5 and x = -4 and the simplified expression is (2x - 1)/(x + 4)
Stating the restriction and then simplifying the expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36}[/tex]
When the above expressions are factorized, we have
[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]
To calculate the restrictions, we set the denominator to 0
So, we have
(5x + 9)(x + 4) = 0
Evaluate
x = -9/5 and x = -4
So, the restrictions are x = -9/5 and x = -4
Next, we simplify the expression
[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]
Cancel out the common factors
[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{2x - 1}{x + 4}[/tex]
Hence, the simplified expression is (2x - 1)/(x + 4)
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
Can someone help me solve this?
The values of x and y in the given figure are 10.5 and 15 respectively in the quadrilateral
We have to find the values of x and y in quadrilateral
4y+14+7y+1=180
Combine like terms
11y+15=180
Subtract 15 from both sides
11y=180-15
11y=165
Divide both sides by 11
y=15
The value of y is 15
Now 7x+1+105=180
7x+106=180
Subtract 106 from both sides
7x=180-106
7x=74
Divide both sides by 7
x=10.5
Hence, the values of x and y in the given figure are 10.5 and 15 respectively
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ1
What meaning of the statement this?
Every subgroup of Z is cyclic and is generated by a unique nonnegative integer. This property makes Z a particularly simple and well-behaved group for studying group theory.
What exactly is a "group theory"?Group theory is a branch of abstract algebra that studies mathematical structures called groups. Group theory provides a powerful framework for studying symmetry, structures, and transformations in various areas of mathematics, physics, chemistry, and other fields of science. It has applications in cryptography, coding theory, crystallography, quantum mechanics, and many other areas of science and engineering.
The set of integers subject to addition, or Z, is an example of an abelian group in group theory. A subset that also forms a group by addition is referred to as a subgroup of Z. It turns out that every Z subgroup is cyclic, i.e., created by a single element.
Let H be a subgroup of Z to be more precise. H is closed under addition since Z is an additive group, and it includes the identity element (0). We can demonstrate that H is produced by a, which means that every element in H can be written as a multiple of a, by looking at the lowest positive integer in H (if any), indicated as a. Thus, H becomes a cyclic subgroup with an as its generator.
Moreover, this generator a is exclusive to H. Assume that H contains a second positive integer b that likewise yields H. We can demonstrate that the set of multiples of a and b is indeed the same set, which suggests that a and b produce the same subgroup H. As a result, a = b, and H has a unique generator.
Learn more about group theory here:
https://brainly.com/question/10405946
#SPJ1
If x = 3 units, y = 5 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
The area of the rhombus by decomposition is
32 square unitsHow to find the area o the rhombsThe rhombus is decomposed into simpler elements which are
2 triangles and a parallelogramArea of 2 triangles
= 2 * 1/2 * base * height
= 2 * 1/2 * x * h
= 2 * 1/2 * 3 * 4
= 12 square units
Area of a parallelogram
= base x height
= y * h
= 5 * 4
= 20 square units
Area of the rhombus
= 20 square units + 12 square units
= 32 square units
Learn more about rhombus at
https://brainly.com/question/20627264
#SPJ1
what is the value of 12.5- 31/2 + 1 1/4
Answer:
-1.75
Step-by-step explanation:
12.5 - (31 / 2) + 1 1/4 = -1.75
What is 4x+1 subtract 2x+1
Answer: 2x
Step-by-step explanation: Separate variables from numbers, 4x-2x=2x, and 1-1=0. Therefore, the answer is 2x.
Answer:
2(x+1)
Step-by-step explanation:
Add you 1s together, than take a 2x out and that vies you 2 on the outside 2x/2= x and 2/2= 1 which gives you your answer.
Someone please help me with this question
Answer:
y = - [tex]\frac{1}{5}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x + 1 ← is in slope- intercept form
with slope m = 5
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex]
the y- intercept c = 6 , then
y = - [tex]\frac{1}{5}[/tex] x + 6 ← equation of line A
Pizza sizes are based on the diameters of the pizza. Matthew, Raul, and Jerome ordered a 16-inch pizza that was cut into 12 equal slices. Each boy ate 4 slices of the pizza.
How many square inches of pizza did each boy eat? (Round your answer to the nearest whole square inch.)
A. 268 square inches
B. 50 square inches
C. 38 square inches
D. 67 square inches
Answer:
D. 67 square inches
Step-by-step explanation:
The area of a 16-inch pizza is:
A = πr^2 = π(8)^2 = 64π
Since the pizza was cut into 12 equal slices, each slice has an area of:
64π / 12 = 16π/3
Each boy ate 4 slices, so the total area of pizza each boy ate is:
4(16π/3) = 64π/3
Rounding to the nearest whole square inch, we have:
64π/3 ≈ 67 square inches
Therefore, the answer is D. Each boy ate approximately 67 square inches of pizza.
Hope this helps!
10. Katherine has diabetes. At each meal, she must estimate the mass in grams of carbohydrates she plans to eat, then inject the appropriate amount of insulin. Katherine needs 1 unit of insulin for 15 g of carbohydrates. Katherine's lunch has 60 g of carbohydrates. How many units of insulin should Katherine inject?
Answer:
Katherine needs 1 unit of insulin for 15 g of carbohydrates.
Step-by-step explanation:
To find out how many units of insulin Katherine should inject for her lunch which has 60 g of carbohydrates, we can use the following proportion:
1 unit : 15 g = x units : 60 g
where x is the number of units of insulin Katherine should inject.
To solve for x, we can cross-multiply:
1 unit * 60 g = 15 g * x units
60 = 15x
x = 4
Therefore, Katherine should inject 4 units of insulin for her lunch.
7
MTR
12345 6 7 8 9 10 x
Tickets
mowing lawns in you
How
much do you earn when you mow 17 lawns?
(See Example 4.)
48. MODELING REAL LIFE It costs $35 a month for membership at a wholesale store. Write and
graph an equation that represents the monthly cost (in dollars) of a membership. What is the
cost of a membership for an entire year?
What is the quotient of 4 1/2÷2/3
The value of the quotient of 4 1/2 ÷ 2/3 is,
⇒ 27/4
We have to given that;
The expression is,
⇒ 4 1/2 ÷ 2/3
Now, We can simplify as;
⇒ 4 1/2 ÷ 2/3
⇒ 9/2 × 3/2
⇒ 27/4
Thus, The value of the quotient of 4 1/2 ÷ 2/3 is,
⇒ 27/4
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ1
can an answer be incorrect even if it looks reasonable? Explain.
Yes, an answer can be incorrect even if it looks reasonable
Explaining the statementYes, an answer can be incorrect even if it looks reasonable. This is because an answer might seem reasonable on the surface but may not be correct due to various reasons such as calculation errors, incorrect assumptions, or misinterpretation of the problem.
For instance, in a math problem that involves converting units of measurement, a student may have calculated the answer and arrived at a number that seems reasonable.
However, if the student used the wrong conversion factor or made an error in calculations, the answer would be incorrect despite appearing reasonable.
Similarly, in a word problem, an answer may seem reasonable but might not take into account all the given information, resulting in an incorrect solution.
Therefore, it is important to double-check answers and verify that they make sense in the context of the problem and that all the given information has been taken into account to ensure accuracy.
Read more about mathematical statements at
https://brainly.com/question/9048478
#SPJ1
A bag contains two Pennie’s,two nickels, two dimes and two quarters. If a coin selected at random from the bag, what is the probability that the coin selected will be worth less than 10 cents