Start by putting the possible integers your friend can select
[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]
Then, call the 2 possible events as A and B, and what are the possible integers in each event:
A = Be more than 6
B = The number is odd
[tex]\text{A}=\{7,8,9,10\}[/tex]
[tex]\text{B}=\{1,3,5,7,9\}[/tex]
The probability of the union of two events can be calculated as:
[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]
Then,
[tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A)}=\dfrac{4}{10}[/tex]
[tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(B)}=\dfrac{5}{10}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]
Finally,
[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]
[tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]
Answer:
the probability that the number will be more than 6 or odd is: 7/10
Start by putting the possible integers your friend can select
[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]
Then, call the 2 possible events as A and B, and what are the possible integers in each event:
A = Be more than 6
B = The number is odd
[tex]\text{A}=\{7,8,9,10\}[/tex]
[tex]\text{B}=\{1,3,5,7,9\}[/tex]
The probability of the union of two events can be calculated as:
[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]
Then,
[tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A)}=\dfrac{4}{10}[/tex]
[tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(B)}=\dfrac{5}{10}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]
Finally,
[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]
[tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]
Answer:
the probability that the number will be more than 6 or odd is: 7/10
Question 9 of 10
A rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
For what values of x are the two expressions equal?
O A. All real numbers except -4 and 2
OB. All real numbers except 2
C. All real numbers
D. All real numbers except -4
The values of x are the two expressions equal to All real numbers except 2.
We are given that rational expression has been simplified below.
(x+4)(x-2)x+4
9(x-2)
WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.
The expression should be;
(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.
After simplification by (x - 2) , the remainder will be;
(x + 4)/9.
When x = -4, both sides equal to zero.
When x = 0 , both sides equal to 4/9
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Change 14,277 s to h, min, and s.
When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.
What is Conversion?Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.
How to determine this
When 60 seconds makes 1 minute
60 minutes makes 1 hour
14,277 seconds to minutes
When 60 seconds = 1 minute
14,277 seconds = x
x = 14,277/60 minutes
x = 237 minutes 7 seconds
By converting 237 minutes to hour
When 60 minutes = 1 hour
237 minutes = x
x = 237/60 hours
x = 3 hours 57 minutes.
Therefore, the conversion is 3 hours 57 minutes 7 seconds
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A recipe uses teaspoon of cinnamon for every 4 cups of granola mix.
How many teaspoons are needed for 12 cups of granola mix?
Okay, here are the steps to solve this:
* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.
* We are making 12 cups of granola.
* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.
* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.
Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.
Jan has set the sales target for 35,000 ice cream makers, which she thinks she can achieve by an additional fixed selling expense of $200,000 for advertising. All other costs remain as per the data in the above table. What will be the operating profit if the additional $200,000 is spent on advertising and sales rise to 35,000 units?
The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
What do sales mean?Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.
According to the given informationTo calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.
From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:
Contribution margin per unit = Selling price per unit - Variable cost per unit
= $900 - $600
= $300
Since the sales target is 35,000 units, the total contribution margin is:
Total contribution margin = Contribution margin per unit x Number of units sold
= $300 x 35,000
= $10,500,000
The total cost can be calculated as follows:
Total cost = Fixed cost + Variable cost
= $3,500,000 + ($600 x 35,000)
= $25,100,000
Adding the additional selling expense of $200,000, the new total cost becomes:
New total cost = $25,100,000 + $200,000
= $25,300,000
Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:
Operating profit = Total revenue - Total cost
= ($900 x 35,000) - $25,300,000
= $10,500,000 - $25,300,000
= -$14,800,000
This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
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based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Okay, let's evaluate each modeling equation candidate based on the r^2 value:
a. y=16.5839•1.0185^x
No r^2 value given, so cannot determine if this is the best fit.
b. y=0.985515x-2.81333
No r^2 value given for this linear model, so cannot determine if it is the best fit.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value, it would be the best fit.
Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.
Does this help explain the approach? Let me know if you have any other questions!
based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Okay, let's analyze the r^2 values for the 4 options:
a. y=16.5839•1.0185^x
r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.
b. y=0.985515x-2.81333
This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.
In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.
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question in screenshot
Answer:
hope this might help you!!
Which equation models the relationship between c cups of flour and m muffins baked?
Answer:
constant of proportionality: A 4equation: D m = 4cStep-by-step explanation:
Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).
SlopeThe slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).
The line goes through the origin (0, 0), so the slope is the ratio of y to x.
m = y/x = 4/1 = 4
This is the constant of proportionality.
The constant of proportionality is 4, choice A.
EquationThe equation of a proportional relationship is ...
y = kx . . . . . . where k is the constant of proportionality
Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...
m = 4c . . . . . choice D
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Running for public office is not a decision to be taken lightly, and requires considerable investments of both time and money. A local businesswoman is considering running for mayor, but will only do so if she has the support of more than 60% of voters in the city. She commissions a polling company, who take a random sample of eligible voters and find 64% would support this businesswoman.
(a) Which hypotheses should the businesswoman test, to determine if she has sufficient community support?
H0:
Ha:
(b) The polling company finds the p-value = 0.076. For = 0.05, what does this suggest the businesswoman should do?
____ for office. There is ___ evidence she ____ enough supporters.
The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.
What is a hypothesis?In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.
(a) The hypotheses that the businesswoman should test are:
H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.
Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.
(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.
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Football is 360ft.long 160ft.wide use 8lb. Fertilizer per 1000sqft it come in 50lb bag. How many bags will I need
We number of bags is 10 bags of fertilizer to complete the job.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.
In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.
The total area of the football field is:
360 feet × 160 feet = 57,600 square feet
To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:
57,600 square feet ÷ 1000 square feet/area = 57.6 areas
So there are 57.6 areas on the football field.
We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:
8 pounds/1000 square feet × 57.6 areas = 460.8 pounds
Therefore, we need 460.8 pounds of fertilizer to cover the football field.
Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:
460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags
We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.
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The complete question is:
You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?
Evaluate each expression (a) log7 1/7 =
(b) log 3 27 = 9
traveled 1/5 miles in 3/2 hour. how many in 1 hour. show model fraction representation
a)Traveled 0.3 miles in 1 hour.
b) The fraction representation is 3/10 miles per hour.
a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.
Distance traveled = 1/5 miles
Time taken = 3/2 hours
To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:
3/2 = 15/10
Now we can divide the distance by the time:
1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15
This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).
To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):
2/15 x 10/3 = 2/9
Therefore, the person traveled 2/9 miles per hour.
b) To write this as a model fraction representation, we can express it as a single fraction:
2/9 = 3/10 (rounded to the nearest tenth)
So the person traveled at a rate of 3/10 miles per hour.
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The circle below has center O, and its radius is 5 m. Given that m LAOB = 30°, find the area of the shaded region and the length of the arc ADB. Give exact answers in terms of it, and be sure to include the correct units in your answer.
Measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and arc length ADB is 10.67π m
Given that the circle has a center O.
The radius of the circle is 8 m.
The measure of ∠AOB is 120°
We need to determine the area of the shaded region and the length of the arc ADB.
The measure of ∠ADB is given by
∠ADB = 360 - ∠AOB
= 360 - 120
=240 degrees
The area of the shaded region can be determined using the formula,
A = (θ/360) πr²
A = (θ/360) ×3.14× 8²
A = 42.67 m²
Thus, the area of the shaded region is 42.67π m²
The length of arc ADB can be determined using the formula,
Arc length = (θ/360) 2πr
=10.67π m
Hence, measure of ∠ADB is 240 degrees, the area of the shaded region is 42.67π m² and length of arc ADB is 10.67π m
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If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is
fo =
c + vo
c − vs
fs
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 32 m/s and accelerating at 1.1 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.5 m/s2, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)
Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.
It can be calculated as:
[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]
where:
c is the speed of light (c = 332m/s)
all the subscripted s is related to the Source (frequency, velocity);
all the subscripted o is related to the Observer (frequency, velocity);
As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.
So, the frequency perceived by the observer:
[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]
[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]
[tex]f_o=460(1.247)[/tex]
[tex]f_o= 573.6 \ \text{Hz}[/tex]
At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz
Answer:
The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time
The perceived frequency you hear is
370.9 Hertz
The function is given as:
[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x [tex]f_{s}[/tex]
From the question
[tex]c=332[/tex] --- speed of the sound
[tex]V_{o} =32[/tex] ---current speed of the train
[tex]V_{s} = 40[/tex] --- speed of the opposite train
[tex]f_{s} =460[/tex] --- frequency of the sound wave
This gives:
[tex]f_{o}= \frac{332-32}{332+40}[/tex] ×[tex]460[/tex]
[tex]f_{o}= \frac{300}{372} x460[/tex]
Rewrite as:
[tex]f_{o}= \frac{300x460}{372}[/tex]
[tex]f_{o}= 370.9[/tex]
19 center: (8, 2), point on circle: (14, -1)
The radius of this circle with center (8, 2) is equal to 6.71 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;
Distance = √[(14 - 8)² + (-1 - 2)²]
Distance = √[(6)² + (-3)²]
Distance = √[36 + 9]
Distance = √45
Distance = 6.71 units.
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Complete Question:
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
Two forces of 637 newtons and 238 newtons act a point.The resultant force is 714 newtons. find the angle between the forces
I need help please I can’t figure this out
Answer: Area=3.125 square feet
Step-by-step explanation:
2.5x2.5=6.25
6.25/2= 3.125
Answer:
A = 50 ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
given that 1 inch equals 4 feet , then
b = 2.5 in = 2.5 × 4 feet = 10 feet
h = 2.5 in = 2.5 × 4 feet = 10 feet
then
A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²
1.- If f(x)= x^8, then f'(x) =
2.- If g(x)= -4x^4 then g'(x) =
3.- If h(x)= 1/x^5 then h'(x) =
1.
f'(x) = 8 · x^(8-1) = 8·x^7
2.
g'(x) = -4· 4·x^(4-1) = -16·x^3
3.
h(x) = 1/x^5 = x^(-5), so
h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6
During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched with an initial upward velocity of 78 feet per second. The hight of the t-shirt (h) in feet after t seconds is given by the function h=-16t^2+78t+5. How long will it take the T-shirt to reach its maximum height? What is its maximum height?
A T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.
The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.
To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.
The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.
t = -b/2a = -78/(2*(-16)) = 2.4375
Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.
To find the maximum height, we substitute this value of t into the equation for h:
h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet
Therefore, the maximum height of the T-shirt is approximately 97.19 feet.
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y = |x - 5| + |x + 5| if -5 < x < 5
Step-by-step explanation:
This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.
When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:
y = -(x - 5) - (x + 5) = -2x
When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:
y = (x - 5) + (x + 5) = 2x
So the function y = |x - 5| + |x + 5| can be written as:
y =
-2x if -5 < x < 0
2x if 0 ≤ x < 5
Notice that the function is not defined for x ≤ -5 or x ≥ 5.
Solve the system of equations.
y = 2 - 6x
1/2y - x = 1
Question 4 options:
(0,-2)
(2,0)
(-2,0)
(0,0)
(1,-4)
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=2 and x=0 making it (0,2)
Supplementary angles
Answer: ∠EGF and/or ∠CGB
Step-by-step explanation:
Starting Angle: ∠CGE
Possible Supplements: ∠EGF and ∠CGB
Find a polynomial with integer coefficients that satisfies the following conditions :
Degree of polynomial : 3
Zeros : 2, 4
-intercept : −96
What is the greatest commen factor of 72 and 96
the greatest common factor of 72 and 96 is 24
2(x-1)+3(x+1)=4(x+4)
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 15Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 154. Gabriel wants to learn how to play darts, so
he researches the costs of different dartboards
at stores in his area. What would be the most
appropriate way for him to display his data?
Answer will be marked!!
Answer:
a line graph
Step-by-step explanation:
Five friends-Allison, Beth, Carol, Diane, and Evelyn- have identical calculators and are studying for a statistics exam. They set their calculators down in a pile before taking a study break and then pick them up in random order when they return from the break. What is the probability that at least one of the five gets her own calculator? [Hint: Let A be the event that Alice gets her own calculator, and define events B, C, D, and E analogously for the other four stu- dents.] How can the event (at least one gets her own calcu- lator} be expressed in terms of the five events A, B, C, D, and E? Now use a general law of probability. [Note: This is called the matching problem. Its solution is easily extended to individuals. Can you recognize the result when n is large (the approximation to the resulting series)?]
When the student gets home, she gives 1/2 of her remaining fudge to her sister.
How many ounces of fudge does she give her sister?
The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces
What is a fraction?A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.
Part of the question obtained from a similar question posted online can be presented as follows;
The amount of fudge the student has = 3 pounds
The amount of fudge the student eats = 1 pound of the fudge
Required; The amount of fudge the student has left
The amount of fudge the student has left = 3 - 1 = 2 pounds
The fraction of the remaining fudge the student gives to her sister = (1/2)
Therefore;
The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound
1 pound = 16 ounces
The amount of fudge she gives her sister in ounces = 16 ouncesLearn more on fractions here: https://brainly.com/question/11249421
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Use spherical coordinates to evaluate the triple integral ∫∫∫Ex2+y2+z2dV
, where E is the ball: x2+y2+z2≤81
.
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Step-by-step explanation:
We have the triple integral:
∫∫∫E x^2 + y^2 + z^2 dV
where E is the ball x^2 + y^2 + z^2 ≤ 81.
In spherical coordinates, the volume element is given by:
dV = ρ^2 sin φ dρ dθ dφ
where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).
Substituting into the integral, we get:
∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ
= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ
= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π
= (2π/5)(9^5)(-(-1 - 1))
= (4π/5)(9^5)
≈ 114413.73
Therefore, the value of the triple integral is approximately 114413.73.
what is the product of -6
Answer:
The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.
Step-by-step explanation: