Answer:
The mathematical property demonstrated by the statement 3 + (-6) = -6 + 3 is the commutative property of addition.
This states that: A + B = B + A
The commutative property of addition is the property that is demonstrated by the formula "3 + (-6) = -6 + 3".
This characteristic states that the sum is unaffected by the sequence in which two numbers are added. In other words, a + b = b + a for any two numbers a and b.
In this instance, the left side has 3 + (-6) which equals -3. We have -6 + 3 on the right side, which also equals -3. This indicates that the result is unaffected by the sequence in which the numbers are added.
We can thus write:
3 + (-6) = -6 + 3
-3 = -3
This demonstrates the truth of the assertion and serves as an illustration of the commutative property of addition.
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what are the best displays for bivariate categorical data
The best displays for bivariate categorical data depend on the nature of the data and the research question. Here are a few common types of displays for bivariate categorical data:
Clustered Bar Charts: This display shows the frequency of each category of two variables side-by-side.
Stacked Bar Charts: This display shows the frequency of each category of two variables stacked on top of each other.
Mosaic Plots: This display shows the relative proportion of each combination of two categorical variables by area.
Heat Maps: This display is a two-dimensional table that is color-coded to show the relationship between two categorical variables.
Tree Maps: This display shows the proportion of each category of two variables by area.
The choice of display should be guided by the nature of the data and the research question being addressed.
~~~Harsha~~~
in the newspaper article referred to in exercise 9.57, 32% of the 1600 adults polled said the u.s. space program should emphasize scientific exploration. how large a sample of adults is needed for the poll if one wishes to be 95% confident that the estimated per- centage will be within 2% of the true percentage?
develop an estimate regression equation with both television advertising and newspaper advertising as independent variables. what are the correct interpretations of the estimated regression parameters? are this interpretation reasonable?
In a regression equation, the estimated coefficients represent the change in the dependent variable for a one-unit increase in the corresponding independent variable, holding all other independent variables constant.
For example, if the estimated coefficient for television advertising is 0.5, then we can interpret it as a $0.5 increase in the dependent variable (such as sales) for every one-unit increase in television advertising expenditure, holding newspaper advertising constant.
Whether the interpretations of the estimated coefficients are reasonable depends on the data and the research question being investigated. It is important to examine the statistical significance, magnitude, and direction of the estimated coefficients, as well as their practical relevance and theoretical soundness, to evaluate the validity and usefulness of the regression model.
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50.12 in word form
PLEASE HELP ME I WILL DO WHATEVER
The population density in orange land is 18 oranges per acre exactly 792 oranges grow in orange land how many acres are there in orange light
Answer:
44 acres
Step-by-step explanation:
Population density is the number of individuals per unit area. It is a useful concept to measure how crowded or sparse a region is. For example, if we want to compare the population density of different countries, we can divide the total population by the total land area. This will give us the number of people per square kilometer or square mile.
In this case, the population density of oranges is 18 oranges per acre. This means that on average, there are 18 oranges in every acre of land that grows oranges. This can help us estimate how much land is needed to produce a certain amount of oranges. For example, if we want to know how many acres of land can produce 1000 oranges, we can divide 1000 by 18 and get 55.56 acres.
To find the area of orange land, we need to divide the total number of oranges by the population density. This will give us the number of acres that can fit 792 oranges. The formula is:
Area = Number of oranges / Population density
Plugging in the given values, we get:
Area = 792 / 18
Simplifying, we get:
Area = 44
Therefore, there are 44 acres in orange land. This means that if we have 792 oranges, we can distribute them evenly in 44 acres of land and have 18 oranges per acre.
how many mpg? ............
The fuel efficiency of the vehicle with the greatest weight which is around 2375kg on this scatter-plot showing vehicle weights & fuel efficiency is 16 mpg.
What is a scatter-plot?The relationships between two variables in a data set are represented by graphs or scatter plots. It displays data points on a Cartesian system or a two-dimensional plane. The dependent variable is represented or plotted on the Y-axis, while the independent variable or attribute is plotted or represented on the X-axis. The scatter plot's objective is to show what happens to one variable when another variable is modified. A theory that the two variables are connected is tested using the scatter plot.
The scatter plot shows the vehicle weights & fuel efficiency.
Data represented on X-axis(independent variable) : weights of vehicle
Data represented on Y-axis(dependent variable) : fuel efficiency.
Lowest weight of vehicle=1125 kg(approx)
Greatest weight of the vehicle=2375 kg(approx)
Lowest fuel efficiencies of surveyed vehicles=16 mpg.
Greatest fuel efficiency of surveyed vehicles=30 mpg.
∴The fuel efficiency of the heaviest vehicle=16 mpg.
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Could
7.7
cm
,
4.0
cm
,
7.7 cm,4.0 cm,7, point, 7, start text, space, c, m, end text, comma, 4, point, 0, start text, space, c, m, end text, comma and
1.7
cm
1.7 cm1, point, 7, start text, space, c, m, end text be the side lengths of a triangle?
Choose 1 answer:
yes
or
no?
By triangle inequality theorem 7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.
We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
For example, is a, b and c be sides of triangle then a + b ≥ c.
Here, the sides of triangle are: 7.7 cm, 4.0 cm, 1.7 cm
Let a = 7.7 cm,
b = 4.0 cm,
c = 1.7 cm
consider the sum of sides b and c.
b + c = 4. 0 + 1.7
b + c = 5.7 cm
which is not greater than 7.7 cm (length of side 'a')
This means that, by triangle inequality theorem 7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.
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The complete question is:
Could 7.7 cm,4.0 cm, 1.7 cm be the side lengths of a triangle?
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
The best prediction is that the college will have about 480 students who prefer cookies.
To solve this problem
According to the table, 27 out of 225 students prefer cookies. To find the prediction for the number of cookies the college will need, we can set up a proportion:
27/225 = x/4000
Where x is the predicted number of students who prefer cookies.
Solving for x, we get:
x = (27/225) * 4000
x ≈ 480
Therefore, the best prediction is that the college will have about 480 students who prefer cookies.
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Charlie jumped a distance of 81/feet. His younger 1 brother jumped a distance of 35/L feet and then jumped 21 feet Who jumped farther? How much farther? Explain how you found your answer.
Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.
To compare the distances that Charlie and his younger brother jumped, we need to find a common unit of measurement. We can convert the mixed numbers into improper fractions to make the calculation easier.
Charlie jumped 81/1 feet, which is the same as 81 feet.
His younger brother jumped 35/L feet and then 21 feet. We don't know the exact value of L, but we can still compare the distances by assuming L is a constant value. So, the total distance his younger brother jumped is:
35/L + 21 feet
We can simplify the expression by finding a common denominator:
(35 + 21L)/L feet
To compare the distances, we can subtract the distances jumped by Charlie and his younger brother:
81 - (35 + 21L)/L
To determine who jumped farther, we need to simplify this expression by finding a common denominator:
(81L - 35 - 21L)/L
Simplifying further:
(60L + 35)/L
We don't know the exact value of L, but we can say that if L is any positive value, then 60L + 35 is greater than 81. Therefore, Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.
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While Brian traveled, the pilot taught him
O how to steer a Cessna 406
O how to fill the gas tank on the Cessna 406
O how to read the instrument panel on the Cessna 406
While Brian traveled, the pilot taught him A. how to steer a Cessna 406.
What is a Cessna 406?The Cessna 406 is a twin-engine aircraft that is commonly used for various purposes, such as air ambulance services, freight transport, and surveillance operations. Steering the aircraft is an essential skill that any pilot must learn in order to control the aircraft's direction of flight.
Learning how to steer a Cessna 406 would be an important skill for Brian to acquire if he was planning to become a pilot or work in the aviation industry.
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Given a quadratic equation in vertex form, find the vertex, axis of symmetry, whether the graph
opens up or down, the maximum or minimum, and the y-intercept. Graph it!
16. y = -2(x + 2)² +4
Vertex:
Axis of symmetry:
Opens: up
Maximum
down
Minimum
X=h A must write
x=
Max/Min Value:
The key features of the given quadratic equation include the following:
Vertex = (-2, 4)
Axis of symmetry: x = -2.
Direction of opening: downward.
There is a maximum (max) at 4.
y-intercept = (0, 0).
roots: x = -4 and x = 0.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:
y = -2(x + 2)² +4
Vertex, (h, k) = (-2, 4)
Axis of symmetry, Xmax = -2.
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The legs of a right triangle measure 39 and 80 units. What is the measure of the
hypotenuse? Answer as a number only.
Answer: probably 89
Step-by-step explanation: looked it up "you have the wrong picture up"
The hypotenuse of the given right-angled triangle is 89 units.
From the below figure, the base of the triangle AB = 39 units
The height of the triangle AC = 80 units
To know the hypotenuse of the given triangle we have to use the Pythagoras theorem as shown below,
From the given figure,
BC² = AB² + AC²
BC² = 39² + 80²
BC² = 1521 + 6400
BC² = 7921
BC = √7921
BC = 89.
From the above analysis, we can conclude that the hypotenuse of the given right-angled triangle is 89 units.
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Given question is having the wrong picture. I am attaching required correct picture as below,
A small can of beans is 3 in. high with a 1 in. radius and sells for $1.49. Which can of beans is a better deal?
a. 9 in. high; 3 in. radius; sells for $39.95
b. 3 in. high; 2. in. radius; sells for $5.96
c. 3 in. high; 3 in. radius; sells for $13.41
Therefore, can b and c are the same better deal since they have the same price per cubic inch using the volume of a cylinder.
Volume of a cylinder calculation.
To compare which can of beans is a better deal, we need to calculate the volume of each can and divide it by the price. The can with the highest volume per dollar is the better deal.
a) The volume of the can is V=πr²h=(3.14)(3²)(9)=254.34 cubic inches. The price per cubic inch is $39.95/254.34 = $0.157, rounded to three decimal places.
b) The volume of the can is V=πr²h=(3.14)(2²)(3)=37.68 cubic inches. The price per cubic inch is $5.96/37.68 = $0.158, rounded to three decimal places.
c) The volume of the can is V=πr²h=(3.14)(3²)(3)=84.78 cubic inches. The price per cubic inch is $13.41/84.78 = $0.158, rounded to three decimal places.
Therefore, can b and c are the same better deal since they have the same price per cubic inch.
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15 POINTS PLEASE I NEED HELP
Answer:
x = 7∠ECB = 65°Step-by-step explanation:
You want the measures of x and ∠ECB in rectangle ABCD with center point E and AE=3x+6, BD=5x+19, ∠EBA=25°.
DiagonalsThe diagonals of a rectangle are congruent and cross at their midponts. This means the triangles they form are all isosceles.
XThe value of x can be found by relating the length of a half-diagonal to the length of the whole diagonal.
2·AE = BD
2(3x +6) = 5x +19 . . . . . . . substitute given lengths
6x +12 = 5x +19 . . . . . eliminate parentheses
x = 7 . . . . . . . . . . . subtract 5x+12
The value of x is 7.
AngleAngle EBC is the complement of angle EBA, so its measure is ...
∠EBC = 90° -∠EBA
∠EBC = 90° -25° = 65°
Angle ECB is the other base angle of isosceles triangle BCE, so has the same measure as ∠EBC.
∠ECB = 65°
__
Additional comment
You know the corner angles of a rectangle are 90°, which is what makes angles EBA and EBC complementary.
With x = 7, AE = 27 and BD = 54. The full diagonal is double the length of the half-diagonal, as you expect.
<95141404393>
Clare bought her first home for $135,000 in 2001. In 2006, the value of real estate in her area had increased by 18%. Based on this, how much was Clare's home worth in 2006?
Answer:
To find the value of Clare's home in 2006 after an 18% increase, we can use the following formula:
Value in 2006 = Value in 2001 x (1 + Percent Increase)
Plugging in the values given in the problem, we get:
Value in 2006 = $135,000 x (1 + 0.18)
Simplifying this expression, we get:
Value in 2006 = $135,000 x 1.18
Value in 2006 = $159,300
Therefore, Clare's home was worth $159,300 in 2006 after an 18% increase in value from its original price of $135,000 in 2001.
Central Limit Theorem forms the foundation for the ___ branch of statistics
Central Limit Theorem forms the foundation for the inferential statistics branch of statistics
The Central Limit Theorem is a statistical concept that describes the behavior of the mean of a sufficiently large sample size drawn from any population with a finite mean and variance.
The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. This theorem provides a basis for inferential statistics, which involves making inferences about a population based on a sample.
It allows us to use sample statistics to estimate population parameters with a certain level of confidence. This theorem has practical applications in many areas of research, such as in quality control, social sciences, and healthcare.
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The price of bike one year ago was Rs.268000.The current price is Rs.290900.what is the increment percentage?
note answer to the nearest whole number.
The percentage increment of the bike is 86%
What is Percentage Increment?Percentage Increment is the percentage measurement of how much a certain figure changes or increases over time. It is the difference between the final value and the initial value, expressed in the form of a percentage.
How to determine this
When the price of a bike one year ago was Rs.268,000
i.e Initial value = Rs.268,000
The current price is Rs.290,900
i.e final value = Rs.290,900
To calculate the percentage increment
Percentage Increase = Final value - Initial value/Initial value * 100%
Percentage increase = Rs.290,900 - Rs.268,000/Rs.268,000 *100%
Percentage Increase = Rs.22,900/Rs.268,000 *100%
Percentage Increase = 2,290,000/268,000
Percentage Increase = 86%
Therefore, the percentage increment is 86%
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fP=\ (x, y) : y = 3x-1, x ≤ 4, xe N}, find P * 1 State the elements of the following relations: (b) y = 4x (d) x + y >= 20 y = x (a) (c) x + y
Answer:
Step-by-step explanation:
To find P * 1, we need to find all pairs of elements in P that have a difference of 1. Let's start by listing the elements of P:
P = {(1, 2), (2, 5), (3, 8), (4, 11)}
Now, we can find all pairs of elements in P that have a difference of 1:
(1, 2), (2, 5) -> (1, 5)
(2, 5), (3, 8) -> (1, 3)
(3, 8), (4, 11) -> (1, 3)
Therefore, P * 1 = {(1, 5), (1, 3), (1, 3)} = {(1, 5), (1, 3)} (since the last pair is a duplicate).
(b) The given relation is: y = 4x
The elements of this relation are all pairs (x, y) such that y = 4x. For example, (1, 4), (2, 8), (3, 12), etc.
(c) The given relation is: x + y ≥ 20
The elements of this relation are all pairs (x, y) such that x + y is greater than or equal to 20. For example, (1, 19), (2, 18), (3, 17), etc.
(d) The given relation is: y = x
The elements of this relation are all pairs (x, y) such that y = x. For example, (1, 1), (2, 2), (3, 3), etc.
6. age of his son by A two-digit number is such that the sum of the digits is 13 and the product of the digits is 40. Find the number.
7 A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.
Answer:
6.
solution:
8+5=13
8×5=40
Kiera had 1 1/3 cups of coffee in the morning and 1 1/4 cups of coffee in the afternoon. She wants to add the fractions 1 1/3+ 1 1/4 to find how much coffee she drank in all.
She can add the whole numbers, but before she can add the fractions she must find the common denominator. Drag and drop the numbers into the boxes to make the statement true.
Picture attached to
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To add and Kiera found the common denominator is Response area. Before adding the fractions together she wrote the numerator of the first fraction as Response area and the numerator of the second fraction as Response area.
For given problem, The common denominator is 12 and Before adding the fractions the numerator of first fraction was 16 and numerator of second fraction was 15.
What are fractions?The representation of sections or portions of a whole using fractions is common. It consists of Numerator and the denominator reflects the total number of equally sized pieces that make up the whole, whereas the numerator represents the number of components we have.
For example, in the fraction 5/4, 4 is the denominator and 5 is the numerator.
Now for given problem,
Kiera had [tex]1\frac{1}{3}[/tex] cups of coffee in the morning, equivalent to [tex](4/3)[/tex] cups of coffee.
Kiera also had[tex]1 \frac{1}{4}[/tex] cups of coffee in the afternoon, equivalent to [tex](5/4)[/tex] cups of coffee.
Now we can add the two fractions together:
[tex](4/3) + (5/4)[/tex]
To find common Denominator;
(LCM) of 3 and 4 is 12
Making denominator of both fraction 12;
[tex](4/3) * (4/4) + (5/4) * (3/3)[/tex]
[tex](16/12) + (15/12)[/tex]
[tex]16/12 + 15/12 = (16 + 15)/12 = 31/12[/tex]
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Let's take a collection of any three 'high mountains of Nepal' and answer following questions. a) Is it a well-defined collection? Give reason. b) Is it a set? Give reason. c) Let's express it as a well-defined collection.
The collection of "high mountains of Nepal" is subjective and not well-defined, it may or may not be a set depending on the criteria specified, and to express it as a well-defined collection.
a) It is not a well-defined collection because the term "high mountains of Nepal" is subjective and does not have a clear definition. What one person considers high might be different from what another person considers high.
b) It is not necessarily a set, depending on how the collection is specified. If the collection is specified using clear criteria (such as mountains over a certain height), then it could be a set.
However, if the collection is just described using vague language like "high mountains of Nepal," then it is not necessarily a set.
c) In order to articulate it as a precise collection, we may define a precise standard for what constitutes a "high mountain of Nepal." As an illustration, we could say that any peak in Nepal that rises higher than 7,000 meters qualifies as a high mountain there.
With this precise definition, we could then pinpoint a trio of Nepalese mountains.
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given that a test statistic for testing if the true proportion exceeds 0.75 is 1.91. what is the p-value for this test? round to 3 d.p.
p-value of 0.028 is considered statistically significant at a significance level of 0.05. This suggests that we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis that the true proportion exceeds 0.75.
To calculate the p-value for this test, we need to use the standard normal distribution table or a statistical software.
First, we need to find the area under the standard normal distribution curve to the right of the test statistic of 1.91.
Using a standard normal distribution table, we can find that the area to the right of 1.91 is 0.0287 (rounded to four decimal places).
Since this is a one-tailed test (the alternative hypothesis is that the true proportion is greater than 0.75), the p-value is equal to the area to the right of the test statistic, which is 0.0287.
Therefore, the p-value for this test is 0.028 (rounded to three decimal places). This means that if the null hypothesis (that the true proportion is less than or equal to 0.75) were true, we would expect to see a test statistic as extreme as 1.91 or more extreme in only 0.028 of all possible samples.
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The p-value for the test when the test statistic is 1.91 and we are testing if the true proportion exceeds 0.75 is
approximately 0.028, rounded to 3 decimal places.
Given that the test statistic for testing, if the true proportion exceeds 0.75, is 1.91, we need to find the p-value for this
test and round it to 3 decimal places.
Identify the test statistic
The test statistic provided is 1.91.
Determine the tail of the test
Since we are testing if the true proportion exceeds 0.75, it is a right-tailed test.
Find the p-value
Using a Z-table or statistical software, find the area to the right of the test statistic (1.91) under the standard normal
distribution. This area corresponds to the p-value.
The area to the right of 1.91 in the Z-table is approximately 0.028. Therefore, the p-value for this test is approximately
0.028.
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What is the term for the digits that exceed the certainty of the instrument?
The term you're looking for is "uncertain digits."
Uncertain digits refer to the digits in a measurement that exceed the level of certainty provided by the measuring instrument.
Measurements, it is crucial to recognize the limitations of the instruments being used, as this can impact the precision and accuracy of the results.
Precision is the degree to which an instrument can consistently produce the same measurement, while accuracy is the closeness of a measurement to its true value.
Uncertain digits can affect both of these aspects.
To better understand uncertain digits, consider the following step-by-step explanation:
Identify the measuring instrument:
This could be a ruler, thermometer, or any other device used to take measurements.
Determine the instrument's least count:
The least count is the smallest unit the instrument can measure.
A ruler with millimeter markings has a least count of 1 millimeter.
Record the measurement:
When taking a measurement, include all the certain digits (those within the instrument's least count) and one uncertain digit.
The uncertain digit is an estimate, and it represents the best guess within the least count of the instrument.
Keep in mind the limitations:
Recognize that uncertain digits are an inherent part of the measuring process and that they affect the precision and accuracy of the results.
Uncertain digits are the digits that exceed the certainty of a measuring instrument.
It is important to consider these digits and the limitations of the instruments used when conducting experiments or making measurements.
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Find all angle measures in the diagram.
The measure of ZKJL =
The measure of ZNJM =
The measure of ZMJL=
Answer: 1. 45%
2. 32%
3. 67%
which ones multi answer
191 cm
191 cm
162 cm
162 cm
170 cm
170 cm
152 cm
152 cm
192 cm
192 cm
168 cm
168 cm
201 cm
201 cm
205 cm
205 cm
190 cm
190 cm
161 cm
161 cm
193 cm
193 cm
195 cm
195 cm
177 cm
The heights that people had a foot size smaller than 24 centimetres would be = 162cm, 152cm, 162cm, 161cm,162cm.
How to determine the number of foot size lees than 24cm?The total number of people whose foot sizes and heights where obtained for the study = 15
The heights that had foot sizes less than 24cm= 162cm, 152cm,162cm,161cm,162cm.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
are(-1, , -8) and (5, 4).
An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 + 8)/(5 + 1)
Slope (m) = 12/6
Slope (m) = 2.
At data point (-1, -8) and a slope of 2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2x + 2
y = 2x - 6.
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If you get paid $520 for 2 weeks at $13 per hour, how many hours did you
work each week?
O 40
O 30
O 20
O 10
Answer:
20 hours
Step-by-step explanation:
for 1 week 560/2
=260
calculation for working hours
Total wage=Rate per hour × actual time spend on working.
Let actual working hours be (x)
260=13×X
260/13=X
20=X
20 hours
Jerel runs 6 days each week. He runs 4.2 km each day for the first 6 days. If Jerel runs a total of 25km, write and solve an equation to find how many kilometers he runs on the sixth day.
Jerel runs 4 km on the sixth day.
How to determine how many kilometers he runs on the sixth day.Let's call the distance Jerel runs on the sixth day "x". We know that he runs 4.2 km each day for the first 6 days, so the total distance he runs in those 6 days is:
Total distance = 4.2 km/day x 6 days = 25.2 km
We also know that the total distance Jerel runs is 25 km, so we can set up an equation to solve for "x":
4.2 km/day x 5 days + x = 25 km
Simplifying the equation, we get:
21 km + x = 25 km
Subtracting 21 km from both sides, we get:
x = 25 km - 21 km
x = 4 km
Therefore, Jerel runs 4 km on the sixth day.
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A chemist wishes to make a 10% acid solution. she has a 4% acid solution and a solution that is 28% acid. how many liters of each should she use if she needs 5 liters of the 10% solution?
The chemist should use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
Let's denote the volume of the 4% acid solution as x and the volume of the 28% acid solution as y, both in liters.
To make a 10% acid solution, we need to mix the two solutions in such a way that the resulting mixture has a total volume of 5 liters, and the concentration of acid in the mixture is 10%.
Since we want 5 liters of the final mixture, we can write the following equation based on the conservation of volume:
x + y = 5
The total amount of acid in the final mixture should be 10% of the total volume of the mixture, so we can write the following equation:
0.04x + 0.28y = 0.1(5)
On simplifying:
0.04x + 0.28y = 0.5
From the first equation:
y = 5 - x
Substituting into second equation:
0.04x + 0.28(5 - x) = 0.5
Simplifying and solving for x:
0.04x + 1.4 - 0.28x = 0.5
-0.24x = -0.9
x = 3.75
Using first equation,
x + y = 5
3.75 + y = 5
y = 1.25
Therefore, she needs to use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
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The chef at Pickin' Chicken Café bought 4 bunches of celery that each weighed 2 pounds. She cut up 3 pounds to serve with chicken wings. Then, she diced 8 ounces to put on garden salads. How many pounds of celery does she have left?
As per the unitary method, the chef has 9.14 pounds of celery left after cutting up 3 pounds to serve with chicken wings and dicing 8 ounces to put on garden salads.
To start, let's convert all of the weights to the same units. The chef bought 4 bunches of celery, each weighing 2 pounds, so in total she bought:
4 bunches * 2 pounds per bunch = 8 pounds
Next, we know that she used 3 pounds of celery for the chicken wings and 8 ounces (which is half a pound) for the garden salads. So in total she used:
3 pounds + 0.5 pounds = 3.5 pounds
To find the value of one pound of celery, we can subtract the amount of celery the chef used from the total amount of celery she bought, and then divide by the number of pounds she bought:
(8 pounds - 3.5 pounds) / 8 = 0.4375 pounds per pound
So one pound of celery is worth 0.4375 pounds. Now we can use this value to find out how many pounds of celery the chef has left. We know she started with 8 pounds of celery, and she used 3.5 pounds, so she must have:
(8 pounds - 3.5 pounds) / 0.4375 pounds per pound = 9.14 pounds left
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