Part A: Calculation of the limit at x = 3In order to find the limit of the function, we can factorize the numerator by factoring out (x-3). Limit [tex][tex](x 3)\frac{(x^3 - 27)}{ (x-3)} )[/tex]Now, factorize x³ - 27 to get the difference of cubes. The
limit equation becomes, Limit [tex](x 3) \frac{ (x-3)(x² + 3x + 9)]}{(x-3)}[/tex] Now, we can cancel out the term (x-3) from the numerator and denominator to get the limit equation as
Part B: Limit [tex](x 3) (x^2 + 3x + 9)[/tex]The limit of the function at x = 3 is the value of the function as x approaches 3. By plugging in x = 3 in the equation above, we get, Limit ([tex](x 3) (x^2 + 3x + 9) = (3)^2 + 3(3) + 9[/tex] = 27Part B: Equation of line through f(3) with slope = 27
The slope of the line is 27, and it passes through the point (3, f(3)). The equation of the line can be found using the point-slope form. [tex]y - f(3) = 27(x - 3)[/tex]
Part C: Simplifying the equation, we get,[tex]y = 27x - 78[/tex] Part C: Graphical representation of the line and the function
The graph of the function f(x) is a parabola opening upward with a vertex at (3, 0). The slope of the line is positive, which means the line will have a positive y-intercept.
The line will intersect the y-axis at (0, -78).Both the graph of the function and the line pass through the point (3, 0). The line is tangent to the graph of the function at that point.
The slope of the line represents the instantaneous rate of change of the function at the point (3, 0). It is the same as the limit we calculated in Part A.
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if a sum of two real numbers is less than 50, then at least one of the numbers is less than 25.
We may demonstrate via a contrapositive assertion that if the total of two real numbers is less than 50, then at least one of the numbers must be less than 25.
The purpose is to demonstrate the following using contraposition:
Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.
Contrapositive assertions, in other words, result from adding "not" to both component claims and reversing the order of the given conditional statements.
Two real numbers will have a sum that is larger than or equal to 50 if neither of them is smaller than 25.
Assume for all real numbers r and s r≥25, s≥25
By using inequality algebra,
r+s≥25+25
≥50
This demonstrates that two numbers will add up to a value more than or equal to 50 if neither of them is less than 25.
Hence, r + s<50, then r<25, s<25 by contrapositive statement.
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How can you use coordinates, ordered pairs, or equations to graph points or lines on a coordinate plane? Give an example and explain how you use coordinates, ordered pairs, or equations to graph them.
A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes.
This is a typical coordinate system:
coordinate plane1
The horizontal axis is called the x-axis and the vertical axis is called the y-axis.
The center of the coordinate system is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).
An ordered pair contains the coordinates of one point in the coordinate system. That is named by its ordered pair of the form of (x, y).
The first number corresponds to the x-coordinate and the second to the y-coordinate.
To graph a point, we have to draw a dot at the coordinates that correspond to the ordered pair. It is one of the best ways to start at the origin.
The x-coordinate shows how many steps have to take from positive to negative on the x-axis, the same as the y-coordinate tells how to have many steps from positive to negative on the y-axis.
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PLEASE HELP!!! I really need help on this question!
a) The probability that an apple from the tree has a weight greater than 90 grams is of: 0.2514 = 25.14%.
b) i) The p-value of the test is of: 0.0045.
b) ii) The conclusion of the test is given as follows: There is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B, as the p-value of the test is less than the significance level.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the weight of the apples are given as follows:
[tex]\mu = 85, \sigma = 7.5[/tex]
The probability that an apple from the tree has a weight greater than 90 grams is one subtracted by the p-value of Z when X = 90, hence:
Z = (90 - 85)/7.5
Z = 0.67
Z = 0.67 has a p-value of 0.7486.
1 - 0.7486 = 0.2514 = 25.14%.
Test hypothesisFor each sample, the mean and the standard error are given as follows:
Tree A: [tex]\mu_A = 86.5, s_A = 1.26[/tex]Tree B: [tex]\mu_B = 82.3, s_B = 1[/tex]Hence, for the distribution of differences, the mean and the standard error are given as follows:
[tex]\mu = \mu_A - \mu_B = 86.5 - 82.3 = 4.2[/tex][tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.26^2 + 1^2} = 1.61[/tex]The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:
z = 4.2/1.61 = 2.61.
Using the z-table, with z = 2.61, the p-value is of:
0.0045.
As the p-value is less than the significance level, there is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B.
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5. A pound cake recipe calls for 3/4 cups of milk
and makes 4 1/2 servings. How many cups of milk
are needed for 16 servings?
8/3 or 2 2/3 cups of milk are needed for 16 servings.
What is the unitary method?
The unitary method is a technique for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.
Given that 3/4 cups of milk needs to make 4 1/2 servings
Converting mixed fraction into improper fraction:
or, 3/4 cups of milk needs to make 9/2 servings.
To make 9/2 servings, needs 3/4 cups of milk
Applying unitary method:
To make 1 servings, needs (3/4)/(9/2) cups of milk.
To make 16 servings, needs [(3/4) × 16]/(9/2) cups of milk.
Simplify the numerical expression:
[(3/4) × 16]/(9/2)
= [3 × 4]/(9/2)
= [3 × 4 × 2] /9
= 8/3
Convert improper fraction into mixed fraction:
=(6 + 2)/3
= 6/3 + 2/3
= 2 2/3
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Solve the equation.
-5x³+x+2x³=7-3x³
Answer:3.3
Step-by-step explanation:
leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes startfraction 2 over 3 endfraction. of her daily calories at dinner. if x represents the calories consumed at dinner, which statements describe the situation? check all that apply.leena consumed 1,500 calories at dinner.the equation startfraction 2 over 3 endfraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x 400 350)
The correct statements are:
1) Leena consumed 1,500 calories at dinner.
2) The equation 2/3(x + 400 + 350) = x
In this question we have been given Leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes 2/3 of her daily calories at dinner.
We need to select a statement that describes the situation if x represents the calories consumed at dinner.
Let x be the calories consumed at dinner.
Leena consumes 400 calories at breakfast and 350 calories at lunch.
So, the daily calories consumed by her:
400 + 350 + x
Given that she consumes 2/3 of her daily calories at dinner.
From given conditions we get an equation,
x = 2/3(x + 400 + 350)
3x = 2(x + 750) ............(multiply both sides by 3)
3x = 2x + 1500
3x - 2x = 2x + 1500 - 2x ...............(subtract 2x from both sides)
x = 1500 calories
Therefore, Leena consumed 1500 calories at dinner.
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A clothesline rope is 8 feet long. Which of these is another way to express 8 feet?answer choicesa. A/Fb. B/Gc. C/Hd. D/J
As per the concept of unitary method, the another way to express 8 feet is 2 [tex]\frac{2}{3}[/tex] yards.
In math, unitary method is known as a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
Here we have given that a clothesline rope is 8 feet long.
Now we need to find another way to express 8 feet
We know that the formula to convert the measurement it to divide the length by the conversion ratio.
As we know that one yard is equal to 3 feet, then we can use this simple formula to convert is written as
yards = [tex]\frac{feet}{3}[/tex]
Then we have to convert the improper fraction into mixed fraction from, then we get,
2[tex]\frac{2}{3}[/tex] yards
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Enter the value of x below.
x+4=12
X=?
what formula is used to gain information about an individual data value when the variable is normally distributed?
The formula used to gain information about an individual data value when the variable is normally distributed is called the z-score formula.
It is used to calculate how many standard deviations a value lies above or below the mean of the data set. The formula is:
z-score = (x - μ) / σ
where x is the data value, μ is the mean of the data set, and σ is the standard deviation of the data set.
To find the z-score of an individual data value when the variable is normally distributed, use the z-score formula. This formula subtracts the mean (μ) from the data value (x) and divides by the standard deviation (σ). This calculation will give you the number of standard deviations the data value lies above or below the mean.
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Find the values for each box using the image shown
Answer:
answer on the picture..........
Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 9cm,12cm
Answer:
15 cm
Step-by-step explanation:
a² + b² = c²
(9 cm)² + (12 cm)² = c²
81 cm² + 144 cm² = c²
225 cm² = c²
c = √(225 cm²)
c = 15 cm
Answer: 15 cm
Which integer has a greater value? -2 or -5?
The integer has a greater value is -2
What is the integer with a greater value?An integer is a whole number (rather than a fraction) that can be positive, negative, or zero. Positive numbers, negative numbers, and zero are all examples of integers. 'Integers include both whole and negative numbers. This means that if we add negative numbers to whole numbers, we get a set of integers.
An integer is a number that has no decimal or fractional part and can be negative or positive, including zero. In this case, the numbers are -5 and -2. It should be noted that -2 is more than -5.
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a certain bridge is 4,024 feet long. approximately how many minutes does it take to cross this bridge at a constant speed of 20 miles per hour? (1 mile
At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge.
What is a unitary approach?The unitary method is used to calculate the value of a single unit and then multiply that value by itself in order obtain the desired value. Unitary refers to a single, unique, or solitary unit. As a result,
this method's objective is to establish values in terms of a single unit. If a car can drive 44 kilometer two litres of gas, for instance, the unitary approach can be used to calculate how many kilometers it can travel on one litre of gas. The value of a single unit is determined by the unitary technique, and also the value of the required quantity of units can then be calculated using this value.
given,
0.76 miles = (4024/5280) miles
Speed =20 miles per hour
Time: =(Distance / Speed) = (0.76/20)
= 0.038 ( in hours )
into minutes = 2 min
At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge
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the ages for a random sample of 30 employees at house mart resulted in the following descriptive statistics. the lower and upper limits for a 99% confidence interval would be approximately and ?
The lower and the upper limit for a 99% confidence interval would be approximately 37.51 and 50.03
Here,
Mean = 43.77
Standard deviation (s)= 12.43655
n= 30
So,
CI= mean ± t (s/√n)
= 43.77±2.756(12.43655/√30)
= 43.77±6.26
= 37.51,50.03
So, the lower and upper limit would be 37.51 and 50.03
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question 1: is the null hypothesis rejected or not rejected for an observed p-value of at 0.07 at a significance level of 0.05?
the null hypothesis is rejected for an observed p-value of at 0.07 at a significance level of 0.05.
At a significance level of 0.05, the p-value of 0.07 indicates that the observed value is not statistically significant. As a result, the null hypothesis cannot be disproven.In other words, the observed value is not strong enough to prove that the null hypothesis is false. Therefore, the null hypothesis is not rejected for an observed p-value of 0.07 at the significance level of 0.05.
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Respond these question please
The percentile rank of the score 71 on the test is 26.7.
What is a percentile?The value that a specific percentage falls under is known as the percentile. Ben, for instance, is the fourth-tallest child in a group of 20, and eighty percent of the kids are shorter than you.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
[tex]Percentile = n / N \times 100[/tex]
Here, n is the number of scores below 71 and N is the total number of scores,
Percentile = 4 / 15 × 100
Percentile = 0.267 × 100
Percentile = 26.7 percentile
Therefore, the percentile rank of the score 71 on the test is 26.7
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Suppoe that 19% of people have a dog,24% of people have a cat , and 14% of people have both
19% of people have a dog,24% of people have a cat , and 14% percentage of people have both 62% of people have either a dog or a cat.
To find the percentage of people that have either a dog or a cat, we need to add the percentage of people that have a dog to the percentage of people that have a cat.
19% + 24% = 43%
Therefore, 62% of people have either a dog or a cat.
43% of people have either a dog or a cat, but do not have both. We can find this by subtracting the percentage of people that have both a dog and a cat from the total percentage.
43% - 14% = 29%
Therefore, 29% of people have a dog or a cat, but not both.
The complete question is:
Suppoe that 19% of people have a dog,24% of people have a cat , and 14% of people have both dog and cat.
What percentage of people have either a dog nor a cat?
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from a point 1.5 mi from a launcch pad at cape canaveral, an observer sights a space shuttle at an angle of elevation of 10 degrees moments after it is launched. after 10 seconds, the angle of elevation is 50 degrees. how far does the space shuttle travel vertically during the 10 second interval? what is the average speed of the space shuttle during that interval?
Answer:
1.523 mi548 mi/hStep-by-step explanation:
Given angles of elevation of 10° and 50° measured 10 seconds apart from an observation point 1.5 miles away, you want to know the vertical change in distance, and the average speed of the shuttle between the two observations.
HeightThe tangent relation tells you ...
Tan = Opposite/Adjacent
Then the height of the shuttle at the observed angles was ...
Opposite = Tan · Adjacent
h1 = tan(10°)·(1.5 mi) ≈ 0.264490 mi
h2 = tan(50°)·(1.5 mi) ≈ 1.787630 mi
Vertical travelThe amount of vertical travel in the 10-second interval was ...
1.787630 mi -0.264490 mi = 1.523240 mi
The space shuttle traveled about 1.523 miles vertically in the 10-second interval.
SpeedIn miles per second, the average speed during that time was about ...
(1.523 mi)/(10 s) = 0.1523 mi/s
In miles per hour, that's about ...
(0.1523 mi/s)(3600 s/h) ≈ 548 mi/h
show your work
please
Answer:
C
Step-by-step explanation:
[tex]\frac{6y }{x^{8} } . \frac{4y}{x^{14} }\\\\\frac{24y^{2} }{x^{8+14} } \\\\\frac{24y^{2} }{x^{22} }[/tex]
2.
What are the coordinates of the midpoint of the line
segment with endpoints (2,-5) and (8,3)?
1) (3,-4) 2) (3,-1) 3) (5,-4) 4) (5,-1)
Answer:
4) (5, -1)
Step-by-step explanation:
To find the midpoint, we must average the x coordinates to find the x-coordinate of the midpoint and average the y-coordinates to find the y-coordinate of the midpoint.
Thus, we do:
x-coordinate: [tex]\frac{2 + 8}{2}[/tex] = [tex]\frac{10}{2}[/tex] = [tex]5[/tex]
y-coordinate: [tex]\frac{-5 + 3}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = [tex]-1[/tex]
This means the midpoint has an x-coordinate of 5 and a y-coordinate of -1. This can be expressed as the point (5, -1), which is option 4
Which is a solution for the equation y= 6x + 6 (both x and y needed as answer)
The solutions for the given equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=6x+6.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Substitute, x=1, 2, 3, 4, 5,.....
When x=1
y=6x+6
y=12
When x=2
y=6x+6
y=6(2)+6
y=18
When x=3
y=6x+6
y=6(3)+6
y=24
When x=4
y=6x+6
y=6(4)+6
y=30
When x=5
y=6x+6
y=6(5)+6
y=36
Therefore, the solutions for the equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).
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If f(2x + 5) = 6x + 19, find fof(2).)
Answer:
x = 4.083
Step-by-step explanation:
6(2x+5)+19=0
12x+30+19=0
12x+49=0
12x=-49
x=4.083
Answer:
f(2x + 5) = 6x + 19
= 6(2x + 5) + 19
= 12x + 30 + 19
= 12x + 49
f(2) = 12x + 49
= 12(2) + 49
= 73
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Hong runs 4 miles in 30 minutes. At the same rate, how many miles would he run in 48 minutes?
Answer: 6.4 miles
Step-by-step explanation:
Take 30 divided by 4 = 1 mile every 7.5 minutes
Then take 48 divided by 7.5 = 6.4 miles in 48 minutes
how do you ensure accurate predictions using data correlation? which are the most effective methods?
The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.
Explanation:
Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.
The most effective methods for ensuring accurate predictions using data correlation are:
1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.
2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.
3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.
4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.
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on her way home from the school board meeting, kelly fills up her car. she likes the idea of using gasoline with ethanol, but thinks her car can only handle 50% ethanol. at the gas station, she can use regular gas with 15% ethanol or e78 fuel with 78% ethanol. how many gallons of each type of fuel should kelly use if she wants to fill up her car with 9 gallons of fuel containing 50% ethanol? 5 gallons of regular gas with 15% ethanol; 4 gallons of e78 fuel with 78% ethanol 6 gallons of regular gas with 15% ethanol; 3 gallons of e78 fuel with 78% ethanol 4 gallons of regular gas with 15% ethanol; 5 gallons of e78 fuel with 78% ethanol 3 gallons of regular gas with 15% ethanol;
She'll need 4 gallons of 15% ethanol gasoline and 5 gallons of 78% ethanol gasoline.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
Here,
The number of gallons required of both kind would be as follows:
4 gallons having 15% ethanol
5 gallons having 78% ethanol
Given that,
The 2 kinds of gases are:
One with 15% ethanol
Other with 78% ethanol
Given that,
The gases(ethanol and gasoline) are diluted in a such a manner that it involves a total of only 50% ethanol.
Number of gallons she wants to use = 9
This shows that only 50% of 9 gallons i.e. 4.5 gallons of ethanol can be used.
Assuming x being the gasoline's measure that is diluted with 15% ethanol.
Now,
The gasoline's measure that is diluted with 78% ethanol would be = 9 - x gallons
Therefore,
x × 15% + (9-x) × 78% = 4.5
On solving, we get
x = 4 gallons
Thus,
The measure of gallons having 15% ethanol = 4
The measure of gallons having 78% ethanol = (9 - x)
= (9 - 4)
= 5 gallons
She will use 4 gallon of 15% ethanol gas and 5 gallon of 78% ethanol gas.
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Help on this ez math table question
Answer:x=-3
Step-by-step explanation:
if you were to plug in -3 for f(x) you would get, f(-3)=1/3(-3) +2, which then equals f(-3)=-1+2, so f(-3)=1
Now you do the same thing for g(x), so you would get g(-3)=2^(-3+3), meaning you first add -3 and 3 leaving you with g(-3)=2^0, which is equal to 1.
f(-3)=1=g(-3)
A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 80 patients. The sample mean was 1. 5 hours, with a sample standard deviation of 0. 7 hours. The upper- bound 95% confidence interval is.
In an effort to reduce wait times in the emergency room. Eighty patients were polled at random by the investigating committee. And, the upper-bound 95% confidence interval is found to be 1.64.
For small sample numbers or unidentified changes, the t-distribution is used in statistics to calculate the significance of population parameters.
Given sample mean [tex]\overline{X}[/tex] is 1.5 hours, sample size n is 80, and sample standard deviation s is 0.7 hours. Then, the standard error for the mean is,
[tex]\begin{aligned}SE_x&=\frac{s}{\sqrt{n}}\\&=\frac{0.7}{\sqrt{80}}\\&=0.07826\end{aligned}[/tex]
The degree of freedom is given by, df = n-1 = 80-1 = 79.
From the t-distribution table, [tex]t_{\alpha/2, 79}=1.7735[/tex]
Then, the upper-bound 95% confidence interval is calculated as,
[tex]\begin{aligned}\overline{X}+t_{\alpha,(n-1)}\frac{s}{\sqrt{n}}&\geq \mu\\&=\overline{X}+t_{0.08, 79}\frac{s}{\sqrt{n}}\\&=1.5+1.7735\left(\frac{0.7}{\sqrt{80}}\right)\\&=1.5+1.7735(0.07826)\\&=1.5+0.13879\\&=1.63879\\&\approx1.64\end{aligned}[/tex]
The required answer is 1.64.
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If a woman making $35,000 a year receives a cost-ofliving increase of 2.9%, what will her new salary be?
Answer:
36,015.
Step-by-step explanation:
To calculate the cost-of-living increase, you would first multiply the current salary by the percentage increase: $35,000 * 0.029 = $1,015.
Then, to find the new salary, you would add the cost-of-living increase to the current salary: $35,000 + $1,015 = $36,015.
So, the woman's new salary would be $36,015 per year.
what to put for 1 and 2
Answer:
Wdym what to put for 1 and 2??
Step-by-step explanation:
there’s no picture on my screen ;-;
What value of x is in the solution set of the inequality –2(3x 2) > –8x 6? –6 –5 5 6
The value of x in the solution set of the inequality -2(3x + 2) > -8x + 6 is 6.
Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-2(3x + 2) > -8x + 6
-6x - 4 > -8x + 6
8x - 6x > 6 + 4
2x > 10
x > 5
x = (5, +∞)
Hence, the solution set of the given inequality is the set of numbers greater than 5. Among the given choices, only 6 is greater than 5. Therefore, the value of x is 6.
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Answer:
6
Step-by-step explanation:
edge on
What value of x is in the solution set of the inequality –2(3x + 2) > –8x + 6?
6