In the given function f(x) = 3ˣ, a function table is created from -2 to 2 which is represented on a graph.
Function TableA function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.
In the function given;
f(x) = 3ˣ
The values of y from x = -2 to 2 are
f(-2) = 1/9
f(-1) = 1/3
f(0) = 1
f(1) = 3
f(2) = 9
Kindly find the attached graph below;
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explain and answer please
Answer:
Ratio of men:women is 7:8
Step-by-step explanation:
Total number of people =150
number of women =80
hence number of men = total number of people - total number of women
number of mean =150 -80
= 70
therefore ratio of men: women =70:80
=70/80
=7/8
Answer:
7:8
Step-by-step explanation:
if there are 150 people and 80 are women we just subtract from 150 by 80 to find how many men
150-80
70 men
70: 80 is the ratio from men to women and we treat this like a fraction when simplifying
We divide both sides by 10th get simplest form
7:8
Hopes this helps please mark brainliest
A bag of potatoes and a bag of oranges weigh 30 pounds in all. The weight of the potatoes is 5 pounds less than 4 times the weight of the oranges. Let w represent the weight of the oranges. The equation that can be used to find the value of w is (4 w minus 5) + w = 30. Which shows the first step that should be taken to verify that w, the weight of the bag of oranges, equals 7? (4 (7) + 5) + 7 = 30 (4 (7) minus 7) + 5 = 30 (4 (7) + 5) minus 7 = 30 (4 (7) minus 5) + 7 = 30.
The equation to find the value of w is (4w - 5) + w = 30
and the value of w is 7.
Given, A bag of potatoes and a bag of oranges weigh 30 pounds in all.
The weight of the potatoes is 5 pounds less than 4 times the weight of the oranges.
Let w represent the weight of the oranges
we have to represent an equation to find the value of w.
as the weight of the oranges is w
then, the weight of the potatoes is 4w - 5.
so, the equation be
(4w - 5) + w = 30
5w - 5 = 30
5w = 35
w = 7
Hence, the equation to find the value of w is (4w - 5) + w = 30
and the value of w is 7.
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Answer:
D
Step-by-step explanation:
(4x3 + 6x)+(5x3 + x)=
The simplified form of the expression, (4x3 + 6x) + (5x3 + x), is 9x³ + 7
Simplifying an expressionFrom the question, we are to add and simplify the given expression.
The given expression is
(4x3 + 6x) + (5x3 + x)
First, we will write the given expression properly.
The given expression written properly is
(4x³ + 6x) + (5x³ + x)
Now, we will simplify the expression by adding the like terms
Simplifying the expression
(4x³ + 6x) + (5x³ + x)
Collect like term s
4x³ + 5x³ + 6x + x
Simplify the expression by adding up the like terms
9x³ + 7x
Hence, the simplified expression is 9x³ + 7x
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Please help guys what is the answer to this.
The sum of 6 consecutive integers is 387 what is the sixth number in this sequence?
Answer:
67
Step-by-step explanation:
Let x be the first integer.
Therefore, the six consecutive integers are:
xx + 1x + 2x + 3x + 4x + 5If the sum of the six consecutive integers is 387 then:
⇒ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 387
⇒ 6x + 15 = 387
⇒ 6x + 15 - 15 = 387 - 15
⇒ 6x = 372
⇒ 6x ÷ 6 = 372 ÷ 6
⇒ x = 62
To find the sixth number, substitute the found value of x into the expression for the sixth number:
⇒ x + 5 = 62 + 5 = 67
What is the answer to this problem?
Please help
The cost formula is C(x) = 20x + 18000
Give two instances and an explanation of what a linear equation is ?
A linear equation in two variables is one that has the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero. The linear equations 10x+4y = 3 and -x+5y = 2 are two-variable examples.
(a) Let a represent the number of canoes produced. The cost C(x) of producing a canoes is then
C(x) = 20x + 18000
(b) If x represents the number of canoes sold, then the revenue R(x) from selling a canoes will be
R(x) = 80x
(c) The break-even point is the x-value where C(x) = R(x) where the revenue generated from selling a canoes matches the cost of producing a canoes. This will happen when
20x + 18000 =80x → 18,000=60x → x=300
When 300 canoes are produced, this business will reach break-even threshold.
They will incur a $24,000 expense and generate a $24,000 profit. Anymore than 300 canoes will result in a profit that outweighs the cost. Anything less than 300 canoes will cause their expenses to outpace their income.
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the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm. which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth. use the z-table below:
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
What is a Normal distribution in statistics?
Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
Z = (X - μ)/σ
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
Z= (X - μ)/σ
X= (Z * σ) + μ
X = (-0.52 * 2) + 10
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
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What is the congruent of SAS?.
The triengle ABC and XZY are proved to be congruent by SAS.
Explain the concept of congruence.Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.
By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)
According to given figures:Here in he given triangle,
BC=YZ
AC=XZ
∠ACB=∠XZY
By SAS ΔABC≅ΔXYZ
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evelyn wants to show a comparison between the number of cable and satellite tv subscribers. what type of chart would work best?
The type of chart that would work best to show a comparison between the number of cable and satellite TV subscribers is bar chart.
What is bar chart?A bar chart or bar graph is a chart or graph that conveys categorical data with rectangular bars with heights or lengths proportional to the values which they represent. The bars may be plotted vertically or horizontally. A vertical bar chart is also called a column chart.
A bar chart is used when we want to show a distribution of data points or present a comparison of metric values between different subgroups of our data. From a bar chart, we can preview which groups are the highest or most common, and how the other groups compare to the others.
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Which linear function represents the line given by the point slope equation y 1 3 x 5 )? F x 3x 6 f/x 3x 4 F x 3x 16 F x 3x 14?.
The linear function which represents the line is y = - 3x + 14.
What is Point slope form?
Point slope form is used to represent a straight line using its slope and a point on the line. It means that the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point-slope form.
Main body:
y - y1 = m (x - x1)
where, (x, y) is a random point on the line and m is the slope of the line.
The given point-slope equation is
y + 1 = - 3 (x - 5)
By further calculation
y + 1 = -3x + 15
y = -3x + 15 - 1
y = -3x + 14
Therefore, the linear function which represents the line is y = - 3x + 14.
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A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct with 95% confidence?? Select one: O A. The machine is operating improperly because the target is below the lower limit. O B. The machine is operating improperly because the target is above the upper limit. O C. The machine is operating properly because the interval contains the target. D. There is not enough information to make a conclusion.
The machine is operating properly because the interval contains the target.
Option (C) is the correct one.
Given, A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds.
the mean is 1.22 pounds the confidence level is 95%.
standard deviation = 0.06 pounds.
The critical value we will use is (1.22 - 0.06 , 1.22 + 0.06) when, the mean is 1.22.
As, the interval contains the target.
Hence, the machine is operating properly because the interval contains the target with 95% confidence.
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The ratio of boy to girl in a chool play i 3:7 if there are 30 children in total how many boy are there
The total number of boys is 9.
What is a ratio?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls.
Here, we have
The ratio of boys to girls in a school play is 3:7
Based on the given conditions, formulate: 30× 3 ÷ (3 + 7)
Calculate the product or quotient: 90/(3+7)
Calculate the sum or difference: 90/10
Hence, the total number of boys is 9.
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Match each rule with the correct transformation.
The transformations are matched as follows:
Translation: B.Reflection across the x-axis: C.Reflection across the y-axis: G.Rotation 90 degrees clockwise: D.Rotation 180 degrees: A.Rotation 90 degrees counter-clockwise: E.Dilation with a scale factor of k: F.How to match the transformations?All of these transformations are applied to the vertices of the polygons, and each of them have standard definitions, given by formulas, which are matched in this problem.
Hence the rules are matched as follows:
Translation: B. -> x and y coordinate are moved.Reflection across the x-axis: C. -> y coordinate has the signal exchanged.Reflection across the y-axis: G. -> x coordinate has the signal exchanged.Rotation 90 degrees clockwise: D. -> coordinates are exchanged, with x having the inverted signal.Rotation 180 degrees: A. -> both coordinates have the signal exchanged.Rotation 90 degrees counter-clockwise: E -> coordinates are exchanged, with y having the inverted signal.Dilation with a scale factor of k: F. -> both coordinates are multiplied by the scale factor.More can be learned about transformations at https://brainly.com/question/28792248
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11. Tay wants to purchase a new cell phone and change her service provider to WestCell. She can
either buy the phone through WestCell or purchase the phone on her own at an electronics store
or website. If she buys the phone through WestCell, they are offering her a reduced price in
which they subsidize the difference between the discounted and regular price of the phone. She
will also need to purchase the service plan through them. If she buys the phone on her own, she
will then need to shop around for a service plan provider. Tay found the following information
on both types of plans for the latest version of a smart phone she wishes to purchase:
Subsidized by WestCell: $250 for the phone plus $80 per month for unlimited talk and text
and 3 GB of data.
Unsubsidized: $700 for the phone purchased at Great Buy plus a monthly $60 service plan
through the provider RingZ for unlimited talk and text and 3 GB of data.
Create an average cost rational function for each possibility. Graph the functions and interpret
the intersection point.
Answer: 250
Step-by-step explanation:
Is triangle ABC congruent to triangle AED?.
Triangles AED and ABC are congruent to one another according to SSS congruency.
Given,
The side BC is equal to side DE.
The side AC is equal to side AD.
∠BAC = ∠DAE
We have to find that whether triangle ABC congruent to triangle AED;
Here,
The side AB = 7 units.
The side AE = 7 units.
Therefore,
The side AB is equal to side AE.
The sum of all the angle of a triangle is 180°.
Consider the triangle ABC and triangle AED.
AB = AE
AC = AD
BC = DE
So, the triangle ABC is congruent to triangle AED by SSS congruency.
That is,
The triangle AED and triangle ABC are congruent by to each other by SSS congruency.
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The image for the question is attached below.
How do you solve the number of solutions to an equation?.
the number of solutions to an equation can be solved by either elimination method or substitution method or by factorization
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
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Chri work at an electronic tore. He earned $10 per hour plu 12. 5% commiion on hi computer ale. Today, Chri worked 5. 5 hour and old $1100 in computer. How much did Chri earn in total today
Chris earned a total of $192.5 today.
What is the commission rate?
The compensation for a commission is referred to as a commission rate. Some jobs pay a fixed percentage, while others pay a fixed dollar amount depending on the volume of sales.
Given, Chris earns $10 per hour and 12. 5% commission on computer sales.
And, he worked 5.5 hours and sold $1100 in computers
Total earning = 5.5*$10 + $1100*12. 5%
= $55 + 1100*(12.5/100)
= $55 + $137.5
= $192.5
Therefore, Chris earned a total of $192.5 today.
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PERSEVERE If three points a, b, and c lie on the same line, then b is between a and c if and only if
the distance from a to c is equal to the sum of the distances from a to b and from b to c. Write an
absolute value equation to represent the definition of betweenness.
An absolute value equation to represent the definition of betweenness will be;
⇒ B ∈ A,C ↔ AB +BC = AC
What is Absolute value equation?
An absolute value equation is a function that contains an algebraic expression within absolute value symbols.
Given,
There are three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.
Now,
We need to find the absolute value function for this statement as;
In order to find the absolute value equation,
First we have to identify the symbols for the terms mentioned in the statement as;
Between = ∈
If and only if = ↔
Now, We have to divide the statement as two parts as;
First one is,
"c lie on the same line, then b is between a and c"
It can be written as,
⇒ B ∈ A,C
Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."
Which can be written as
⇒ AB + BC = AC
When we combine it,
Then we get the absolute value equation as,
⇒ B ∈ A,C ↔ AB +BC = AC
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A bakery sold a total of 200 cupcakes in a day, and 42 of them were chocolate flavored. What percentage of cupcakes sold that day were chocolate flavored?.
Percentage of cupcakes which was chocolate flavored = 21%. The formula to calculate percentage is (x/100 * total number of items = given no of items).
Let x be the percentage of chocolate flavored cupcakes
Therefore,
x% of 200 = 42
Since the total no. of cupcakes is 20.
=> x/100 * 200 = 42
=> x * 2 = 42
=> x =21
Hence the required percentage is 21 %.
A % is a number without dimensions. It is a ratio or a number that is written as a fraction of one hundred. The percentage sign (%) is the symbol used to represent a percentage. Pct and pc are two examples of the acronyms used. Typically, the relative amount of the entire number is expressed using the percentage.
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the following are ages of 15 of the signers of the Declaration of Independence 47, 46, 54, 31, 50, 46, 27, 62, 40, 39, 50, 44, 35, 30, 41 Send data to Excel Find 25th and 60th percentiles for these ages. (If necessary, consult a list of formulas.) The 25th percentile: The 60th percentile:
The 25th percentile is 35 and the 60th percentile is 46.
Given,
The following are the ages of 15 of the signers of the declaration of Independence 47, 46, 54, 31, 50, 46, 27, 62, 40, 39, 50, 44, 35, 30, and 41 Send data to Excel Find 25th and 60th percentiles for these ages.
(a) 25th percentile = (n + 1) * Pth value
= (15 + 1) * 0.25th value
= 4th value
=35
(b) 60th percentile = (n + 1) * Pth value
= (15 + 1) * 0.6th value
= 9.6th value
=46
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Given the equation square root of quantity 3x minus 2 end quantity equals 4, solve for x and identify if it is an extraneous solution. 6; solution is extraneous 6; solution is not extraneous two thirds; solution is extraneous two thirds; solution is not extraneous.
After solving the equation, x=6 so the solution is extraneous.
In the given question, the equation square root of quantity 3x minus 2 end quantity equals 4.
We have to solve for x and identify if it is an extraneous solution.
A root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.
Now the equation is
√3x-2 = 4
Taking square on both side, we get
3x-2 = 16
Add 2 on both side, we get
3x = 18
Divide by 3 on both side, we get
x = 6
Hence, x=6 so the solution is extraneous.
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FILL IN THE BLANK. the rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as the market rate.
The rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as stated rate, therefore the given statement is false
The given statement is
The rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as market rate
The market price is defined as the price for goods or services is the usual price charged for them in a free market. Therefore the given statement is false and the correct answer is stated price
Hence, The given statement is false because the rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as stated rate
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how many solutions does 8+x/6=x/6-4+5x/12
The equation 8+x/6=x/6-4+5x/12 has one solution x = 144/5 or 28.8
what is equation?Equation is a mathematical statement that shows that two mathematical expressions are equal
[tex]8 +\frac{x}{6} = \frac{x}{6} -4 + \frac{5x}{12}[/tex]
collect the like terms
8 +4 = [tex]\frac{x}{6} -\frac{x}{6} + \frac{5x}{12}[/tex]
12 = [tex]\frac{5x}{12}[/tex]
cross multiply
144 = 5x
Divide both side by 5
[tex]\frac{144}{5} = \frac{5x}{5}[/tex]
x = 144/5 or 28.8
Therefore, the equation has one solution which is x = 144/5 or 28.8
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Can someone translate this photo it’s Russian
Giving 30 points
If not an appropriate answer
Report
Thankyou :D
The paragraph is translated from Russian language to English language as "Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
Translating Russian to EnglishIn translating the paragraph to English, if you're not a native Russian speaker or fully understand the language to read and write, it is advisable to apply an online free tool for this type of exercise. This tool can translate texts as well as words in an image.
Applying that here, the paragraph is roughly best translated as
"Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
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As a borrower, you have the option to choose between two 30-year, monthly-payment loans: 7% interest rate with 3 points, versus 7.5% interest with one-half point.
(a) Which loan option would you choose if you had a 10-year expected prepayment horizon?
(b) Which would you choose if you expect to pay off this loan in 5 years?
If we had a 10-year expected prepayment horizon then Option 1 is preferred less expense and if we had a 5-year expected prepayment horizon then Option 2 is preferred less expense.
In the given question, as a borrower, we have the option to choose between two to 30-year, monthly-payment loans: 7% interest rate with 3 points, versus 7.5% interest with one-half point.
If we assume the pricipal loan amount as $100,000 based on the two option need to monthly instalements for 30 years & the equivalent amount for the respective points.
Under mortgage loan, 3 points on $100,000 is equal to $3,000 and for 1.5 points would be $1500.
Formula for calculating the monthly instalments would be
[tex]\text{EMI} = P\times \frac{r}{12}\times\left [ \frac{(1+r/12)^n}{(1+r/12)^n- 1} \right ][/tex]
where P is Principal , r is rate of interest, n = time period in months.
Using the above said formula we can compute EMI for both the options with interest rates as 7% and 7.5% respectively.
(a) We have to find which loan option would you choose if we had a 10-year expected prepayment horizon.
If repayment is 10 years then EMI under both the options would be:
Option 1: Interest rates as 7%
[tex]\text{EMI} = 100,000\times \frac{7}{1200}\times\left [ \frac{(1+7/1200)^{120}}{(1+7/1200)^{120}- 1} \right ][/tex]
EMI = $1161.08
Option 2: With interest rate as 7.5%.
[tex]\text{EMI} = 100,000\times \frac{7.5}{1200}\times\left [ \frac{(1+7.5/1200)^{120}}{(1+7.5/1200)^{120}- 1} \right ][/tex]
EMI = $1187.02
We can respond to both questions in the following problem using the EMI calculated and the comparable amounts for the respective options.
The total price for each option is as follows.
Particulars Option 1 Option 2
EMI x 12 x 10 139330 142442
Points 3000 1500
Total cost 142,330 143,942
The less expensive Option 1 is preferred.
(b) In this question we have find which would you choose if you expect to pay off this loan in 5 years.
If repayment is 5 years then EMI under both the options would be:
Option 1: Interest rates as 7%
[tex]\text{EMI} = 100,000\times \frac{7}{1200}\times\left [ \frac{(1+7/1200)^{60}}{(1+7/1200)^{60}- 1} \right ][/tex]
EMI = $1980.12
Option 2: With interest rate as 7.5%.
[tex]\text{EMI} = 100,000\times \frac{7.5}{1200}\times\left [ \frac{(1+7.5/1200)^{60}}{(1+7.5/1200)^{60}- 1} \right ][/tex]
EMI = $2003.79
We can respond to both questions in the following problem using the EMI calculated and the comparable amounts for the respective options.
The total price for each option is as follows.
Particulars Option 1 Option 2
EMI x 60 118807.20 120,227
Points 3000 1500
Total cost 121,807.20 121,727
The less expensive Option 2 is preferred.
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in a completely randomized (one-way) anova, with other things being equal as the sample means get closer to each other, the probability of rejecting the null hypothesis decreases.trueor false
Its true that the probability of rejecting the null Hypothesis decreases.
What is sample mean?
In mathematics, particularly in statistics, there are various types of means. Each mean summarises a particular set of data, frequently to help determine the overall significance of a particular data set.
The sample mean is a fair estimation of the population mean, according to probability theory. We also observed in our simulations that the means of bigger samples are more likely to be closely grouped around the population mean than the means of smaller samples.
Since, when other things being equal as the sample means get closer to each other.
So, the given statement is true.
Hence, its true that the probability of rejecting the null Hypothesis decreases.
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In a certain company, the measured thickness m of a helicopter blade must not differ from the standard s by more than 0.14 millimeters. The manufacturing engineer expresses
Kthis as Im-s/s0.14. Find the limits of m if the standards is 18.92 millimeters.
What is the solution? Select the correct choice below and fill in any answer boxes within your choice.
If In a certain company, the measured thickness m of a helicopter blade must not differ from the standard s by more than 0.14 millimeters. The solution is 18.78 ≤m≤ 19.06.
How to find the limits?In order to find the limits we would have to add Standard 18.92 to the expression and as well less the standard from the expression 0.14.
Given data:
Manufacturing engineer expression /m-s/ ≤ 0.14
Standard = 18.92 millimeters
Hence,
Limit of m:
18.92 ± 0.14
m - 18.92 ≤ 0.14
= 19.06
And
-(m- 18.92) ≤ 0.14
m ≥ 18.78
So,
Solution =18.78 ≤m≤ 19.06
Therefore the solution is 18.78 ≤m≤ 19.06.
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which of the following equations represents a linear function?
x = 1
y equals one third times x squared
y equals one fourth times x minus 1
4x − 2 = 6
The equation which represents a linear as required in the task content is; y equals one fourth times x minus 1.
What is a linear function?A linear function has one independent variable and one dependent variable in which case the degree of the equation is 1; meaning- the highest power of the variables is 1.
Conventionally, The independent variable in this regard is x and the dependent variable in this regard is y.
The required equation which represents a linear function is; y equals one fourth times x minus 1; y = (1/4)x - 1
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Answer: C
Step-by-step explanation: Took the test
a toy maker claims his best product has an average lifespan of exactly 18 years. a skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim. the product evaluator was provided data collected from a random sample of 35 people who used the product. using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated. select the 99%, confidence interval for the true mean lifespan of this product. a) [-0.8722, 0.8722] b) [12.128, 13.872] c) [17.128, 18.872] d) [11.986, 14.014] e) [12.853, 13.147] f) none of the above
The 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].
What is standard deviation?
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
Given: A toy maker claims his best product has an average lifespan of exactly 18 years.
A skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim.
The product evaluator was provided data collected from a random sample of 35 people who used the product.
Using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated.
As sample size is large we will use z value to calculate confidence Interval 99% confidence Interval is
{x bar} Z_({1 - alpha/2}) (s/√{n})
13\ 2.576* 2/ √13
(12.128, 13.872).
Hence, the 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].
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What are the elements of a treaty?.
The elements of a treaty includes, satisfaction of both sides, a proper set of rules and obligation towards the actions.
By the definition are Treaty is a diplomatic agreement between two countries on global issues.
According to the constitution of The United States of America the president of the state can make the treaty with other countries with the support of the two third of the sinters present in the house as per the section 2 of Article II.
An agreement can only be called a Treaty if the agreement is agreed upon by both the sides and the Treaty has a proper set of rules define for both the countries and both the countries give their consent towards their actions which comes under the treaty.
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How much grape juice would you need to mix with 15 over 4 quarts of sparkling water?.
The amount of grape juice that you need to mix with 15 over 4 quarts of sparkling water is 15/8 quarts
Given that,
The amount of Sparkling water is 15/4 quarters
To find : The amount of grape juice that you need to mix with 15 over 4 quarts of sparkling water
Sparkling water measuring 1 1/2 quarters is required for the recipe. This can be expressed as the improper fraction 3/2 (since 1 whole equals 2/2 and 2/2 plus 1/2 equals 3/2).
We used 5/2 times as much sparkling water as the recipe called for, or 15/4 quarts (15/4 gallons). This implies that we would also use 5/2 times as much grape juice, or 5/2(3/4) = 15/8.
As a result, you need to combine 15 over 4 quarters of sparkling water with 15/8 quarts of grape juice.
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