The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.
Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.
Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].
So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is
|t - 48| <= 4
where t is the number of tablespoons of flour used. So, the correct option is D).
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Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
For the given data correct option is option a.) The range is the best measure of variability, and it equals 8.
How to find the measure of variability?The dots on the line plot reflect the quantity of roses purchased every day at a grocery shop based on the supplied data. The dots are scattered horizontally, with some dots above specific numbers.
1, 2, 6, 7, 8, and 9 have dots above them , thus,
for given problem,
[tex]\text{Number of Rose Bouquets: 1, 2, 6, 7, 8, 9}[/tex]
[tex]\text{The range is the difference between the highest and lowest values:}[/tex]
[tex]Range = \text{Highest value} - \text{ Lowest value}\\Range = 9 - 1\\Range = 8[/tex]
The Interquartile Range (IQR) is a measure of variability that considers the difference between the data set's 25th and 75th percentiles (Q3).
The median (Q2) would be towards these digits since there are dots above numbers 6, 7, and 8. As a result, using the information provided, the IQR cannot be computed precisely.
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Graph y=−4/7x+1.
Use the line tool and select two points on the line to graph the line.
To graph the line y=−4/7x+1, we can use the slope-intercept form of a linear equation, y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -4/7 and the y-intercept is 1.
To plot the line, we can select two points on the line and connect them with a straight line. One easy way to do this is to set x=0 and solve for y to find the y-intercept, which is (0,1). Then, we can set y=0 and solve for x to find another point on the line. This gives us (-7/4,0).
Once we have these two points, we can use a straight edge or ruler to draw a line through them to represent the graph of the equation. It should be a downward-sloping line that intercepts the y-axis at (0,1).
Alternatively, we can use a graphing calculator or an online graphing tool to plot the line more accurately. This will allow us to see more clearly the shape and direction of the line, as well as any other important features such as intercepts, slopes, and points of intersection with other lines.
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What is the slope/ rate of change? please?
The slope of the points in this table is equal to 1.2.
How to calculate the slope based on the table?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided in the table, we can logically deduce the following data points on the line:
Points on x-axis = (-3, 1).Points on y-axis = (-1.1, 3.7).Substituting the given points into the slope formula, we have the following;
Slope, m = (3.7 + 1.1)/(1 + 3)
Slope, m = 4.8/4
Slope, m = 1.2.
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4. {35, 38, 31, 40, 34, 37, 84, 32}
Mean
Median
Mode
The mean is 41.37
The Median is 36
The first step is to arrange the number orderly
31, 32,34,35,37,38,40,84
The mean is
= 31 + 32+34+35+38+37+40+84/8
= 331/8
= 41.37
The median
= 35+37/2
= 72/2
= 36
The mode
= N/A
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If the dimensions of a prism with surface area 42 m^2 and volume 18 m^3 are enlarged by a factor of 4, what is the surface area and volume of the prism?
SA = 2lw + 2lh + 2wh = 42 m^2 ... (1)
And the volume of the original prism is given by:
V = lwh = 18 m^3 ... (2)
If you enlarge the dimensions of the prism by a factor of 4, then the new dimensions will be 4l, 4w, and 4h. The new surface area of the prism will be:
New SA = 2(4l)(4w) + 2(4l)(4h) + 2(4w)(4h)
= 32lw + 32lh + 32wh
= 32(2lw + 2lh + 2wh)
= 32(42)
= 1344 m^2
So, the surface area of the enlarged prism is 1344 m^2.
Similarly, the new volume of the prism will be:
New V = (4l)(4w)(4h)
= 64lwh
= 64(18)
= 1152 m^3
So, the volume of the enlarged prism is 1152 m^3.
Therefore, the surface area of the prism is 1344 m^2 and the volume of the prism is 1152 m^3 after the dimensions are enlarged by a factor of 4.
*IG:whis.sama_ent
a band just recorded a new album with 13 tracks. the shortest song on the album is 1 minute and 14 seconds. The longest song is 5 minutes and 54 seconds. What is a reasonable estimate for the total time of the album?
To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.
What is a reasonable estimate for the total time of the album?The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.
The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.
Therefore, the average time per song is:
(74 + 354) / 2 = 214 seconds
And the total time of the album is approximately:
13 songs x 214 seconds/song = 2,782 seconds
Converting this to minutes and seconds, we get:
2,782 seconds = 46 minutes and 22 seconds
So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.
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if a statistically significant difference is found between the math scores of two groups, we can conclude the difference was due to a chance occurrence.TRUE/FALSE
The given statement after evaluating and considering the other options is false. Due to the criteria it falls under elaborates the case of statistically significant change is to be present while comparing the math scores between the two groups, In short there will always be difference between two group s while we compare them on a particular topic .
From here on we can come to the conclusion that the difference was not due to chance occurrence.
A statistically significant change refers to process which is unlikely to be elaborated solely by chance and random factors.
In short, a statistically significant has a very less chances of taking place if there is no true effect in a research study.
The famous examples of statistical significance of finding are
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In the hawk-dove game, at what value of c do doves and hawkshave equal payoffs when hawks are extremely rare?0.501There is no such value.
This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
The mathematical field of game theory helps shed light on how it emerges. Game theory is “the study of mathematical models of strategic interaction among rational decision-makers” (according to Wikipedia).
Game theory applies to “games” as varied as economics, politics, chess, and tic-tac-toe. In each case, there are some rules, some “players” or “agents”, and a set of strategies available to them.
Each player has a concept of “utility” – a “currency” they seek to individually maximize through the strategies they play.
The currency of evolution is the concept of fitness.
That is, the chance of being represented in the next generation. Genes and traits which increase the odds of survival to reproductive age are more likely to be passed on to future generations. Therefore, they confer a greater fitness to the individual which "hosts” them.
The evolutionary game theory takes the concepts from game theory and applies them in an evolutionary context.
In the hawk-dove game, at what value of c do doves and hawks have equal payoffs when hawks are extremely rare? The answer is that there is no such value. This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
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18 Two vans leave a campground at the
same time. One is traveling north at a
speed that is 10 miles per hour faster
than the other, which is traveling south.
After 2.5 hours, the vans are 255 miles
apart. What is the speed in miles per hour
of the van traveling south?
F 56
G 46
H 66
J 36
The speed of the van traveling south is 46 miles per hour. The correct option is (G) 46.
To solve this problemLet's call the speed of the van traveling south "x" in miles per hour. Then, the speed of the van traveling north is "x + 10" miles per hour.
We know that the vans have been traveling for 2.5 hours, and that they are 255 miles apart. This means that the total distance traveled by both vans is 255 miles:
Distance traveled by the van traveling south + Distance traveled by the van traveling north = 255 miles
Using the formula distance = speed × time, we can express the distances traveled by each van in terms of their speeds and the time they traveled:
Distance traveled by the van traveling south = x × 2.5 = 2.5x
Distance traveled by the van traveling north = (x + 10) × 2.5 = 2.5x + 25
Substituting these expressions into the equation above, we get:
2.5x + 2.5x + 25 = 255
Simplifying this equation, we get
5x + 25 = 255
Subtracting 25 from both sides, we get:
5x = 230
Dividing both sides by 5, we get:
x = 46
Therefore, the speed of the van traveling south is 46 miles per hour. Answer: (G) 46.
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The probability that Amber's bus arrives on time is 5/6.
If her bus is on time then the probability she arrives at work by 9 am is 4/5.
If her bus is late then the probability she arrives at work by 9 am is 3/10.
Work out the probability that Amber does not arrive at work by 9 am.
Give your answer as a fraction in it's simplest form.
The probability that Amber does not arrive at work by 9 am is calculated by summing the probabilities of two scenarios: the bus being on time and Amber not arriving by 9 am and the bus being late and Amber not arriving by 9 am. The calculated probability for her late arrival at work is 17/60.
Explanation:The subject of this problem is probability. There are two scenarios in which Amber may not arrive at work by 9 am: either the bus is on time but she does not arrive by 9 am or the bus is late and she does not arrive by 9 am.
First, let's consider the probability that Amber's bus arrives on time, which is said to be 5/6. If her bus is on time, the probability that she arrives at work by 9 am is 4/5, which means that the probability she does not arrive by 9 am is 1-4/5 = 1/5. Therefore, the probability that the bus is on time and she does not arrive by 9 am is 5/6 * 1/5 = 1/6.
Alternatively, consider the scenario where the bus is late. We can find the probability of this by subtracting the probability that the bus is on time (5/6) from 1, so the probability that the bus is late is 1/6. If her bus is late, the probability she arrives at work by 9 am is 3/10, implying that the probability she does not arrive by 9 am is 1-3/10 = 7/10. Hence, the probability that the bus is late and she does not arrive at work by 9 am equals 1/6 *7/10 = 7/60.
Thus, the total probability that Amber does not arrive at work by 9 am is 1/6 + 7/60 = 10/60 + 7/60 = 17/60.
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Convert 4.6 cm = ________mm
Maria has to buy apples at the grocery store. Apples cost $1.25 per pound. How much will she spend if she buys 3 pounds of apples?
Answer: $3.75
Step-by-step explanation:
Since apples cost $1.25 per pound and she needs to buy 3 pounds, the total cost would be $1.25*3 = $3.75.
A company claims that its tablet computers have an average recharge time of 3 hours with a standard deviation of 1.4 hours. Using a random sample of 50 company tablet computers, a consumer group determines a mean recharge time of 2.5 hours. H0: µ = 3 Ha: µ < 3 a = 5% σ = 1.4 z* = –1.65
A company claims that its tablet computers have an average recharge time of 3 hours with a standard deviation of 1.4 hours. Using a random sample of 50 company tablet computers, a consumer group determines a mean recharge time of 2.5 hours. H0: µ = 3 Ha: µ < 3 a = 5% σ = 1.4 z* = –1.65.
Based on the given information, we can perform a one-sample z-test to determine if the sample mean of 2.5 hours is significantly different from the claimed population mean of 3 hours, with a significance level of 0.05.
The null hypothesis H0 is that the population mean recharge time µ is equal to 3 hours, and the alternative hypothesis Ha is that µ is less than 3 hours.
We will find the test statistic z using the formula
z = (x - µ) / (σ / √n)
Where x is the sample mean of 2.5 hours, µ is the population mean of 3 hours, σ is the population standard deviation of 1.4 hours, and n is the sample size of 50.
z = (2.5 - 3) / (1.4 / √50) = -2.38
The calculated test statistic z of -2.38 is less than the critical value z* of -1.65 at a significance level of 0.05, indicating that we can reject the null hypothesis H0.
Hence, we can conclude that the mean recharge time of the company tablet computers is less than 3 hours, based on the sample of 50 tablets tested by the consumer group.
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help me with dis question please
The area of the given figure is 20cm².
What is a kite?
A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.
What is area of a kite?
A kite's diagonals are perpendicular. The area of a kite is calculated as half of the diagonal product, which is the same as the area of a rhombus. The formula: can be used to express the area of a kite.
Area of Kite =1/2×D1×D2
D1 is the kite's long diagonal.
D2 is the kite's short diagonal.
when we draw the figure in coordinate system we find that it is shape of a kite,
so area of kite = 1/2*4*4+1/2*4*6
= 20 cm²
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what is the best way to describe the center of the data represented in this line plot? select from the drop down menus to correctly complete the statement
Given that there are no outliers in the data, the mean of 3.2 inches should be used to characterise the centre of the data represented by this line plot.
What metric should be used to describe a data set's centre?It is dependent on whether or not the data set contains outliers.
If there are no outliers, the mean should be utilised.
If this is the case, the median should be utilised.
The dot plot shows how many times each measure appears. Because there are no outliers, all values are near, the mean should be utilised. It is provided by:
M = (2 x 1 + 3 x 2 + 2 x 3 + 1 x 5 + 1 x 6 + 1 x 7)/(2 + 3 + 2 + 1 + 1).
The mean of 3.2 inches should be used to define the data centre in this line graphic.
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Complete question:
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The Choose...is Mean or median Choose.... 2 inches 2.5 inches 3 inches or 3.2 inches
. While shopping, Sofia finds a dress she likes at a discounted price. The price on the tag before the discount is p dollars. She must pay sales tax on the discounted price of the dress. Sofia calculates that she must pay p-0.15p+ 0.07(0.85p) to buy the dress. What does 0.85p represent?
The 0.85p in the expression represents the price of the dress after removing the discount
What does 0.85p represent in the equation?From the question, we have the following parameters that can be used in our computation:
Sofia calculates that she must pay the following to buy the dress
p - 0.15p + 0.07(0.85p)
The 0.85p in the expression represents the price of the dress after removing the discount
Hence, 0.85 is the discounted price
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The Normal model is a goodâ first-choice to model data if the data are suspected to be
The Normal model is a good first-choice to model data if the data is normally distributed or approximately normally distributed
Normally distributed or approximately Normally distributed. The Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is widely used in statistical modeling due to its mathematical properties and practical applications in many fields.
When the data is Normally distributed, the Normal model provides a good approximation of the underlying distribution of the data. This means that the parameters of the Normal distribution can be estimated from the data using methods such as maximum likelihood estimation, and the resulting model can be used to make predictions and conduct statistical inference.
However, it is important to note that the Normal model may not be appropriate for all types of data, particularly if the data exhibits significant departures from Normality. In such cases, other distributional models or non-parametric methods may be more appropriate.
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Round your answer to the nearest tenth, and type it in the blank without units.
Answer:
Set your calculator to degree mode.
sin(72°) = x/25
x = 25sin(72°) = about 23.8 feet
1. discuss the internal validity of the regressions that you used to answer empirical exercise 8.2(l). include a discussion of possible omitted variable bias, misspecification of the functional form of the regression, errors in variables, sample selection, simultaneous causality, and inconsistency of the ols standard errors.
Answer: Empirical Exercise 8.2(l) involves running a regression to estimate the relationship between two variables of interest. In evaluating the internal validity of the regression used to answer this exercise, we need to consider several potential sources of bias and other issues that could affect the accuracy of the estimated relationship.
Omitted variable bias: This occurs when a relevant variable is left out of the regression model. If this happens, the estimated coefficients may be biased and inconsistent. For example, if we are estimating the effect of education on earnings but fail to include information about work experience, the coefficient on education may be biased upwards.
Misspecification of the functional form of the regression: If the relationship between the dependent variable and the independent variable(s) is nonlinear, we may need to use a different functional form of the regression equation to obtain accurate estimates. If we fail to do so, the estimated coefficients may be biased and inconsistent.
Errors in variables: When measurement errors occur in the independent variable(s), this can cause the estimated coefficients to be biased and inconsistent.
Sample selection: If the sample used to estimate the regression equation is not representative of the population of interest, then the estimated coefficients may be biased and inconsistent.
Simultaneous causality: When there is a two-way causal relationship between the dependent variable and the independent variable(s), it may not be possible to determine the direction of causality from the regression coefficients.
Inconsistency of the OLS standard errors: If there is heteroskedasticity or autocorrelation in the data, then the ordinary least squares (OLS) standard errors may be inconsistent. This can lead to incorrect conclusions about the statistical significance of the estimated coefficients.
To address these issues, researchers should take care to select an appropriate sample, use a suitable functional form of the regression equation, and account for any relevant variables that could be omitted or measured with errors. It may also be necessary to use alternative statistical techniques to account for simultaneous causality or heteroskedasticity in the data. Finally, researchers should always test the robustness of their results to different model specifications and sensitivity to potential sources of bias.
Step-by-step explanation:
You get a bag of 30 components. And you know that, with probability 0. 1, there is one faulty component in the bag, and with probability 0. 9, all the components are in good working. You are not sure you have a faulty component in the bag, so you propose to test k of the components. (a) How many ways are there of selecting k out of the 30 components? (b) Assume the bag has a faulty component. How many ways are there of selecting k out of the 30 components that include the faulty component? (c) Use your answers from parts (a) and (b) to determine a formula for the probability of including a faulty in the k selected ones, if there was a faulty component in the bag. (d) Evaluate your answer from part (c) for k = 5. (e) Assume now that you did select a batch of 5 components, measured each of them and found that none were faulty. What is the probability that there is a faulty component left in the bag? Remember that there were two original possibilities for the bag: all the components could be good, or one component could be faulty
The probability of having at least one faulty component in your selection is 0.41 or 41%.
The probability of having at least one faulty component in a selection of 5 can be found by calculating the probability of having no faulty components and then subtracting this from 1.
The probability of having no faulty components in a selection of 5 is:
P(no faulty) = (0.9)^5 = 0.59
Therefore, the probability of having at least one faulty component in a selection of 5 is:
P(at least one faulty) = 1 - P(no faulty) = 1 - 0.59 = 0.41
So the probability of having at least one faulty component in your selection is 0.41 or 41%.
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--The complete Question is, You randomly pick 5 components from the bag of 30. What is the probability that you have at least one faulty component in your selection? --
Solve for a. -3.7a 1.7 = -6.07
Answer:
a = 2.1
Step-by-step explanation:
-3.7a + 1.7 = -6.07
-3.7a = -7.77
a = 2.1
7 Find in degrees. 19 0 [?] degrees Round to the nearest hundredth.
Answer:
Θ ≈ 21.62°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{19}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{7}{19}[/tex] ) ≈ 21.62° ( to the nearest hundredth )
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15(Multiple Choice Worth 2 points)
Answer:Answer: A. tennis=17 , soccer= 12, baseball=27, basketball=44
BAR GRAPH make sure its not a histogram!!
Step-by-step explanation:
just took the test
a survey was given to 318 students at east river high school asking what their grade point average (gpa) was. which is the best graphical representation to display the data?
The best graphical representation to display the data on the GPA of 318 students at East River High School would be a histogram.
What is a histogram?A histogram is a graphical representation of data that groups data into bins or intervals and displays the frequency of occurrences of data within each bin. In this case, the bins would represent GPA ranges, and the frequency would represent the number of students falling within each GPA range.
A histogram is a good choice for displaying this data because it allows the viewer to see the distribution of GPA scores across the student population. It provides a visual representation of how many students fall within certain GPA ranges and can help identify trends in the data.
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Keep moving: find the perimeter of each figure
The perimeter of the figure is as follows
1. 93 cm
2. 42 cm
3. 45 cm
What is perimeterPerimeter is the total length of the boundary of a two-dimensional shape or figure. In other words, it is the sum of the lengths of all the sides or edges of the shape.
Perimeter is measured in units of length, such as centimeters, meters, or feet, depending on the system of measurement being used.
The perimeter of the figures is solved as follows
1.
= 12 + 15 + 20 + 11 + 7 + 10 + 6 + 12
= 93 cm
2.
= 8 + 12 + 5 + 5 + 12
= 42 cm
3.
= 15 + 15 + 15
= 45 cm
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function for domain -12,-7,0,4,12 range0,1,2
If the domain is{ -12,-7,0,4,12} and range is {0,1,2} then the function is {(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes
domain is{ -12,-7,0,4,12} range is {0,1,2}
The function that has the given domain and range is:
{(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}
Therefore, the function is {(4, 1), (-7, 0), (12, 2), (0, 0), (-12, 1)}
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Which function has the following domain and range?
Domain: {-12, - 7, 0, 4, 12}
Range: {0, 1, 2}
O {(-12, 12), (0, 2)}
O {(4, 1), (-7, 0), (12, 2), (0, 0), ( − 12, 1)}
O {(-12, 0), ( – 7, 1), (0, 2), ( – 4, 5), (3, -1)}
O {(0,4), (2, 12), (1, -7), (0, - 12), (1, 0)}
Corina makes 27$ for every 2 hours that she works.If she worked 36 hours this week,how much money did she make
Answer:
Corina makes $27 for every 2 hours that she works, so she makes $13.50 for every hour she works (since 2 times $13.50 equals $27).
If she worked 36 hours this week, then she made:
$13.50 x 36 = $486
Therefore, Corina made $486 this week.
Step-by-step explanation:
Answer: $486
Step-by-step explanation:
27/2= 13.5
$13.5 per hour
13.5 x 36 = $486
The positive GCF of -24y and -20 is 4. Complete each equation with an expression or integer factor.
The missing factor in the second equation is 1, and the completed equation is: -24y + (-5) = -4(6y + 5/4)
How to complete each equation with an expression or integer factor.We know that the GCF of -24y and -20 is 4. To find the missing factor in each equation, we can divide both terms by the GCF of 4.
For the first equation, we have:
-24y = 4 * (-6y)
Dividing both sides by 4, we get:
-6y = -24/4
Simplifying, we get:
-6y = -6
Therefore, the missing factor in the first equation is -1, and the completed equation is:
-24y + 20 = -4(6y - 5)
For the second equation, we have:
-20 = 4 * (-5)
Dividing both sides by 4, we get:
-5 = -20/4
Simplifying, we get:
-5 = -5/1
Therefore, the missing factor in the second equation is 1, and the completed equation is:
-24y + (-5) = -4(6y + 5/4)
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help me right now
Mixed numbers with unlike denominators ______ be subtracted from each other.
A. Mixed numbers with unlike denominators cannot be subtracted from each other.
B. Mixed numbers with unlike denominators can be subtracted from each other.
Answer:
B. Mixed numbers with unlike denominators can be subtracted from each other.
Step-by-step explanation:
Mixed numbers are numbers that have a whole part and a fractional part, such as 2 1/4 or 3 3/5. Unlike denominators are fractions that have different numbers in the bottom, such as 1/4 and 3/5. They are also called unlikeable denominators because they make math harder and more annoying. Who likes to deal with fractions anyway?
Mixed numbers with unlike denominators can be subtracted from each other, but only if you follow some tedious steps. First, you have to find a common denominator for the fractions, which is the smallest number that both denominators can divide into. This is like finding a common enemy for two rival gangs. For example, to subtract 2 1/4 from 3 3/5, we need to find a common denominator for 1/4 and 3/5. The least common denominator is 20, because both 4 and 5 can divide into it. Then, we have to multiply both fractions by the same factor to get equivalent fractions with the same denominator. This is like dressing up both gangs in the same uniform to make them look alike. For example, we multiply 1/4 by 5/5 and 3/5 by 4/4 to get:
2 1/4 = 2 5/20
3 3/5 = 3 12/20
Now we can subtract the fractions by subtracting the numerators and keeping the denominators the same. This is like taking away some members from each gang and seeing who has more left. For example, we subtract 5/20 from 12/20 and get 7/20. Then we subtract 2 from 3 and get 1. Finally, we add the whole part and the fractional part together to get the final answer. This is like adding up the remaining members of one gang and giving them a name. For example, we get:
3 12/20 - 2 5/20 = (3 - 2) + (12/20 - 5/20) = 1 + 7/20 = 1 7/20
Therefore, the correct answer is B. Mixed numbers with unlike denominators can be subtracted from each other. But why would you want to do that? It's much easier to use decimals or percentages instead. Fractions are so last century.
Solve for x in the equation 2x + 3 > 11
Hi !
[tex]2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4[/tex]
Have a nice day ;)
Answer:
x > 4
Isolate the variable by dividing each side by the factors that don't contain the variable