Answers
The answer is 23/40
To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.
Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:
2/40 - 25/40 = -23/40.
The absolute value of any number is always positive so it becomes 23/40.
The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.
Related Questions
Kenya is conducting a probability experiment with one number cube with numbers 1 through 6 on each face. She rolls the number cube, records the number on the side that is face up, and repeats the process.
If Kenya rolls the number cube 90 times, what is a reasonable prediction for the number of times that a 1 or a 6 will land face up?
Answers
Answer:
The number cube has 6 equally likely outcomes, so the probability of rolling a 1 or a 6 on any given roll is 2/6 = 1/3.
If Kenya rolls the number cube 90 times, we can use the expected value formula to find the expected number of times that a 1 or a 6 will land face up:
Expected number of 1's or 6's = (number of rolls) x (probability of rolling a 1 or a 6)
Expected number of 1's or 6's = 90 x (1/3)
Expected number of 1's or 6's = 30
Therefore, a reasonable prediction for the number of times that a 1 or a 6 will land face up is 30.
help please i dont get this
Answers
● < P=R " angles opp =sides"
●PQ =QR " Angles opposite = sides"
therefore PQR is an isosceles " 2 opp angles and sides are equal "
Exact value of sec 5pi/6
Answers
By trigonometric formula, the trigonometric function sec (5π / 6) has the exact value - 2√3 / 3.
How to determine the exact value of a trigonometric function
In this problem we find the case of a trigonometric function, whose exact value can be found by means of trigonometric formula and tables of values:
sec θ = 1 / cos θ
sec (5π / 6) = 1 / cos (5π / 6)
sec (5π / 6) = - 1 / cos (π / 6)
sec (5π / 6) = 1 / (- √3 / 2)
sec (5π / 6) = - 2 / √3
sec (5π / 6) = - 2√3 / 3
The exact value of the trigonometric function sec (5π / 6) is equal to - 2√3 / 3.
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the gallup poll surveyed a representative sample of american adults and offered a list of seven personal economic problems that many people face. what are the top financial concerns that people have?
Answers
According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.
Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.
How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.
The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).
This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
John has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict John to sell if the day’s high temperature were 30 F
Answers
Based on this linear equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F.
What is linear equation ?
A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
The slope, m, represents the rate of change of y with respect to x.
According to the question:
Assuming that the relationship between the high temperature and the number of hot cocoas sold is roughly linear, we can use the equation of the line of best fit to estimate the number of hot cocoas sold at a high temperature of 30 F.
If we know the equation of the line of best fit in the form y = mx + b, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 and solve for y.
For example, if the equation of the line of best fit is y = 2x - 10, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 to get:
y = 2(30) - 10 = 50
Therefore, based on this equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F. However, it's important to note that this is just an estimate and the actual number of hot cocoas sold could be different.
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What is -10 + +10 please help
Answers
Answer:
0
-10++10=0
+10 can be rewritten as 10
-10+10=0
:)
ten families have an average of 2 children per family. if exactly two of these families are childless, what is the average number of children in the families with children? express your answer as a decimal to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
If there are ten families and exactly two of them are childless, then there are 10 - 2 = 8 families with children.
The total number of children in these families is 8 x 2 = 16.
Therefore, the average number of children in the families with children is:
16 / 8 = 2
So the average number of children in the families with children is 2.0 (to the nearest tenth).
The average number of children in the families with children is 2.2.
To calculate this, first we need to determine the total number of children in the ten families. Since each family has an average of 2 children, this means that the total number of children in the ten families is 10 x 2 = 20.
Since two of these families are childless, this means that the total number of children in the remaining 8 families is 20 – 0 = 20.
Now, we need to determine the average number of children in the 8 families with children. To do this, we divide the total number of children (20) by the number of families with children (8):
20/8 = 2.5
Finally, we express the answer to the nearest tenth, which is 2.2.
In conclusion, the average number of children in the families with children is 2.2.
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nineteen students are eligible to play doubles tennis. what is the maximum number of different 2-person teams possible?
Answers
By permutation and combination, Maximum 171 number of different 2 - person teams are possible.
Provide an example of permutation and combination?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.
As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.
Total number of ways to choose different 2 person out of 19 person.
= ¹⁹C₂
= 19!/2! (19 - 2)!
= 19!/2! 17!
= 19 * 18 * 17!/2 * 1 * 17!
= 19 * 7
= 171
Hence, maximum 171 number of different 2 - person teams are possible.
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if the jewler buys 49.8 lb of silver to make the hearts, how many sterling silver hearts can the jewlers make?
Answers
Which of the following explains why it is easier to reject the null hypothesis with a one-tailed test than with a two-tailed test with all the same parameters?
a. Because the standard deviation in a one-tailed test is larger than that for a two-tailed test
b. Because z-scores are calculated differently in a one-tailed test
c. Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test
d. Because a two-tailed test uses a bimodal distributio
Answers
Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test.
What is the difference between a one-tailed test and a two-tailed test in hypothesis testing?In a one-tailed test, the alternative hypothesis is directional and the critical region is all on one side of the distribution. In a two-tailed test, the alternative hypothesis is non-directional and the critical region is split between the two tails of the distribution.
Why is it easier to reject the null hypothesis with a one-tailed test than with a two-tailed test?It is easier to reject the null hypothesis with a one-tailed test because the critical region is all on one side of the distribution, making it more likely to observe a significant difference and reject the null hypothesis. In contrast, the critical region is split between the two tails in a two-tailed test, making it less likely to observe a significant difference and reject the null hypothesis.
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Compute the interest on 250000 at a 7. 5% interest rates for half a year
Answers
the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
To calculate the interest on 250000 at a 7.5% interest rate for half a year, we first need to determine the annual interest rate, as most interest rates are quoted on an annual basis. To do this, we can divide the annual interest rate of 7.5% by 2 to get the half-yearly interest rate, which is 3.75%.
Next, we can use the formula for simple interest to calculate the interest earned over half a year. Simple interest is calculated by multiplying the principal amount (in this case, 250000) by the interest rate (3.75%) and the time period (0.5 years).
So, the interest earned would be:
Interest = Principal x Rate x Time
= 250000 x 0.0375 x 0.5
= 4687.50
Therefore, the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
It's worth noting that this calculation assumes that the interest is simple interest, which means that the interest earned is not reinvested. If the interest is compounded (i.e., the interest earned is reinvested), then the interest earned would be higher.
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prove that cn, an n-cycle, has exactly n labeled spanning trees. you may use any method you wish to do this problem. write a good, detailed, and thoughtful proof!
Answers
To prove that a cycle graph Cn has exactly n labeled spanning trees, we can use the principle of inclusion-exclusion. First, consider a tree T that is composed of the n edges of Cn. This tree has n edges and is therefore an n-edge tree. In order for it to be a labeled spanning tree, every vertex must be labeled with a distinct label. Since Cn has n vertices, there are n! ways to label the vertices, giving us n! labeled spanning trees.
Now, we can use inclusion-exclusion to determine the number of labeled spanning trees that are a subset of T. For each vertex vi in T, we can choose any label from the set of n labels. For each of these labels, we can choose any edge from the n edges in T. The total number of labeled spanning trees that are a subset of T is therefore: n2 × n!
Now, we can subtract the number of labeled spanning trees that are a subset of T from the total number of labeled spanning trees to get the number of labeled spanning trees that are not a subset of T. The number of labeled spanning trees that are not a subset of T is: n! - n2 × n! = n! - n2! Therefore, the total number of labeled spanning trees of Cn is n!.
This proves that a cycle graph Cn has exactly n labeled spanning trees.
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Which function results after applying the sequence of transformations to
f(x) = x5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
Answers
Answer:
[tex]3(x + 2)^5 + 1[/tex]
Step-by-step explanation:
we have,
[tex]y = x^5[/tex]
1. stretch vertically up by 3
[tex]y = 3x^5[/tex]
2. translate up 1 unit (Y = y + 1)
[tex]y = 3x^5 + 1[/tex]
3. translate left 2 units (X = x + 2)
[tex]y = 3(x + 2)^5 + 1[/tex]
Hopefully this answer helped you!!!
5. the number of people arriving for treatment at an emergency room can be modeled by a poisson process with a mean of 5 people per hour. how many people do you expect to arrive during a 45-min period?
Answers
If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.
The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.
To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.
Next, we can use the Poisson distribution formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).
Expected number of arrivals = λ * t = 5 * 0.75 = 3.75
Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.
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I need help asap please sb
Answers
LN/RT = NM/TS is the correct option in congruent triangle .
What in mathematics is congruent?
If two shapes are similar in size and shape, they are said to be congruent. The mirror image of one shape is the same as the other if two shapes are congruent.
Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
In ΔLMN ≅ ΔRST
In triangle are congruent .
LN/RT = NM/TS
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now standardize this distance by dividing it by the population standard-deviation (or standard error). in other words, how many population-standard-deviations (or standard-error) away is your sample mean from the population mean?
Answers
Population-standard-deviations (or standard-error) away is your sample mean from the population mean is therefore (x - μ) / σ.
In order to standardize the distance, we must divide it by the standard deviation of the population (or standard error).How far the sample mean is from the population mean in terms of population-standard-deviations (or standard-error) can be determined by dividing it by the population standard deviation (or standard error). The equation for the same is as follows:
z = (x - μ) / σ
where,
z = standard score,
x = sample mean,
μ = population mean,
σ = population standard deviation.
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9. There are 8 black socks, 6 blue socks, and 14 white socks in a drawer. If one sock is randomly chosen from the
drawer, then what is the probability that the sock will not be blue?
Answers
The probability that the socks will not be blue would be =11/14.
How to calculate the probability of socks that are not blue in colour?Probability can be defined as the expression that shows the possibility of the occurrence of an event.
The formula that is used to calculate probability = the chosen events/total number of outcomes.
The total number of black socks = 8
The total number of blue socks = 6
The total number of white socks = 14
The total number of socks (outcomes) = 8+6+14 = 28
The socks that are not blue = 8+14 = 2
Therefore the probability that they socks won't be blue = 22/28 = 11/14.
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please help!! I need this by the end of tonight..!
Answers
Answer:
y=2.05x
Step-by-step explanation:
Figure out what the total cost is for 1 of them then you put that in as your M value, then X stands for number of sheets so 2.05 multiplied by the number of sheets sold you get your Y which is the total cost in dollars for x sheets.
A rectangular prism has dimensions of 4 inches by 3 inches by 7 inches.
Calculate the surface area. Show your work
Answers
Answer: the answer would be 122
Step-by-step explanation:
To find the surface area you need to find the area of each face and add them together
2 (W L+H L+H W) = surface area
2·(4·7+3·7+3·4)=122
Answer:
Step-by-step explanation:
Given dimensions of the rectangular prism ,
4"×3"×7"
We know, Total surface area of a cuboid= 2(lb+bh+hl)
where, l=length of the cuboid
b= breadth " " "
h= height " " "
Since, a rectangular prism holds the shape of a cuboid, therefore it's surface area should also be 2(lb+bh+hl)
Now, surface area of the rectangular prism = 2(4×3+3×7+7×4)
=2(12+21+28)
=2×61
=122 square inches.
Last night, the two dinner specials at Adam's favorite restaurant were salmon filet and steak. The restaurant served 35 specials in all, 35 of which were the salmon filet. What percentage of the specials were salmon filets?
Write your answer using a percent sign (%).
Answers
Answer:
100%
Step-by-step explanation:
If 35 specials were served and 35 of them were salmon, then salmon was 100% of the special served.
pleaseeee help!!!!!!!!!
Answers
The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is: [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.
What number of records will increase by a factor?o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".
To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:
New number of records = N x F
For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:
New number of records [tex]= 100 x 3 = 300[/tex]
So, the new number of records would be 300.
The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:
[tex]12,000 x (1.02)^48[/tex]
Simplifying this expression, we get:
[tex]12,00x0 1.02^48[/tex]
Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48
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I need help on this asap!
Answers
Step-by-step explanation:
Let's start by defining some variables:
y: the maximum amount Geno can spend
x: the number of months he will have the gym membership
T: the total cost of the membership at Total Fitness
G: the total cost of the membership at Gymania
Using these variables, we can set up the following system of inequalities:
T = 30x + 100 (Total Fitness charges $30 per month plus an initial fee of $100)
G = 50x + 25 (Gymania charges $50 per month plus an initial fee of $25)
Geno can spend no more than y dollars, so we can add the following constraint:
T ≤ y
G ≤ y
Now we can solve this system of inequalities to find out which company offers the better deal. We can start by substituting the expressions for T and G:
30x + 100 ≤ y
50x + 25 ≤ y
Next, we can simplify these inequalities:
30x ≤ y - 100
50x ≤ y - 25
Finally, we can solve for x:
x ≤ (y - 100) / 30
x ≤ (y - 25) / 50
The better deal is the gym membership that has the smaller total cost, so we want to find the values of x that satisfy both inequalities. Therefore, we need to take the smaller of the two right-hand sides:
x ≤ min((y - 100) / 30, (y - 25) / 50)
So, the system of inequalities we can use to determine which company offers the better deal is:
x ≤ min((y - 100) / 30, (y - 25) / 50)
A club sponsor collects and analyzes data to estimate the number of students, y
, in attendance at a club meeting x
weeks after the start of the school year. The linear model y=11x+41
can be used to represent the data when x≥0
.
Which two best describe the value 41
?
Responses
change in number of students in attendance per week
change in number of students in attendance per week
initial number of students in attendance when x=0
initial number of students in attendance when x = 0
slope
slope
x
-intercept
x -intercept
y
-intercept
y -intercept
Answers
Since the linear model y = 11x + 41 can be used to represent the data when x≥0, the two statement which best describe the value 41 include the following:
B. initial number of students in attendance when x = 0.
E. y-intercept.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = 11x + 41
By comparison, we have the following:
mx = 11x
Slope, m = 11.
Initial number or y-intercept, c = 41.
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when conducting a logistic regression analysis, what is the problem of class imbalance in a dataset?
Answers
Class imbalance is a common problem in logistic regression analysis, where one class of data significantly outnumbers the other.
Class imbalance can be problematic because it leads to an over-representation of one class and an under-representation of the other, which can bias the model’s prediction towards the more frequently occurring class.
Class imbalance can cause the model to focus on optimizing accuracy by predicting the majority class more often than the minority class, leading to an underestimation of the minority class. It can also reduce the model’s ability to capture the nuances of the data that can be associated with the minority class. To address this, techniques such as oversampling, undersampling, and cost-sensitive learning can be employed to balance the data and improve model performance.
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2sin(2x-π÷2)≥√3
[tex]2 \sin(2x - \frac{\pi }{2 } ) \geqslant \sqrt{3} [/tex]
solve it with steps
Answers
The inequality trigonometry expression 2sin(2x - π/2) ≥ √3 when solved has a solution of x ≥ 5π/12
How to solve the inequality trigonometry expressionIn the question, we have the following expression
2sin(2x - π/2) ≥ √3
The above expresson is an inequality and a trigonometry expression
So, we have
2sin(2x - π/2) ≥ √3
Divide by 2
sin(2x - π/2) ≥ 1/2√3
Take the arc sin of both sides
2x - π/2 ≥ π/3
Add π/2 to both sides of the expression
2x ≥ π/2 + π/3
Evaluate the like terms
2x ≥ 5π/6
Divide both sides by 2
x ≥ 5π/12
Hence, the solution to the variable x is x ≥ 5π/12
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let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6. what is the the cov(1.07x, 2y)? select one:a. 11. 984b. 0.3821c. 2.616d. 7.982
Answers
let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6.
The covariance of 1.07x and 2y is 11.984
What is covariance?
Covariance refers to the way two variables shift together. It is a measurement that evaluates how close two variables are to one another. It examines whether they change in the same direction (positive covariance) or in the opposite direction (negative covariance)
.Calculating Covariance:
Given that Cov(X,Y) = 5.6
we need to find Cov(1.07X,2Y)Hence,
Cov(1.07X,2Y) = 2 * 1.07 * Cov(X,Y) = 2.2996 * 5.6 = 11.984
Therefore, the covariance of 1.07x and 2y is 11.984.
Hence option (a) is the correct answer.
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a rectangle has an area that is decreasing at a rate of 541 square inches per hour with the width being held constant. determine the rate of change of the length if the width is 3 square inches.
Answers
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
what is rectangle ?A rectangle is a flat, four-sided shape with parallel, equal-length opposite sides on each side. There are four right angles (90-degree angles). The distance between the two longer sides, also known as the longer sides or the longer edges, is the rectangle's length. The distance between the two shorter sides, also known as the shorter sides or the shorter edges, determines the rectangle's width. The perimeter of a rectangle is equal to the total of the lengths of all of its sides, and the area of a rectangle is equal to the product of its length and width.
given
Let A represent the rectangle's area, l its length, and w its width. So, we are aware of:
A = lw
By applying the derivative to time t, we obtain:
(d/dt) = dA/dt (lw)
l(dw/dt) + w(dl/dt) = dA/dt
dw/dt = 0 since the width is kept constant, which results in:
w(dl/dt) = dA/dt
We are informed that w = 3 in and that dA/dt = –541 in2/hour. By replacing these values, we obtain:
-541 = 3(dl/dt)
By calculating dl/dt, we obtain:
dl/dt = -541/3
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
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four times the sum of a number and four is 136. translate into an equation and then solve for the number?
Answers
Answer: y-98
Step-by-step explanation:
An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 6 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Does doubling all three dimensions mean the den will have double the volume of the bedroom? Why or why not? Does doubling all three dimensions mean the den will have double the volume of the bedroom? No If he doubles all three dimensions, the den's volume will be more than double the volume of the bedroom.
Answers
Answer:
(2 x 10) x (2 x 6) x (2 x 7) = 3360ft³ <-- the den would be that
The volume:
10 x 6 x 7 = 420ft³ Volume = 8
Help, please!
The answer is presented on the image, thank you!
Answers
Answer:
PQ = 3QR = 5EF = 10Step-by-step explanation:
You want to know the side lengths of the triangles shown if DE = 8.
Value of xSide DE is marked as x+6. If its length is 8, then we have ...
x +6 = 8
x = 2 . . . . . subtract 6
Side lengthsThe unknown side lengths are then ...
PQ = x+1 = 3
QR = x+3 = 5
EF = x+8 = 10
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Additional comment
These are both 3:4:5 right triangles. The larger is twice the size of the smaller. You can guess this because a 3:4:5 right triangle is the only one with a side length of 4 and integer lengths for the other sides.