Answer:
Step-by-step explanation:
Let's call the regular price of the stereo "x".
The stereo is sold at a 10% discount, which means the selling price is 90% of the regular price:
Selling price after discount = 0.9x
Then, a 10% tax is added to the selling price, so the final sale price is:
Final sale price = (1 + 0.1)(0.9x) = 1.1(0.9x) = 0.99x + 0.1(0.9x) = 0.99x + 0.09x = 1.08x
We are given that the final sale price is $589.05, so we can set up the equation:
1.08x = 589.05
Solving for x, we get:
x = 589.05 ÷ 1.08
x = 545.83 (rounded to the nearest cent)
Therefore, the regular price of the stereo was $545.83.
What is the value of x?
Enter your answer in the box.
Answer:
x = 54
Step-by-step explanation:
See picture below :)
a student estimated their mass to be 82.0 kg. upon stepping on the scale at the doctor's office, the actual (accepted) mass of 83.8 kg was recorded. use the formula on page 4 of lab 3v to calculate the % error of the student's estimated mass. remember to take the absolute value in the numerator and to round off to the proper degree of certainty. the unit that should be reported is % (use the symbol, do not type out the word).
The percentage error of the student's estimated mass is 2.15%.
What is the percentage error?The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.
The estimated mass of the student = 82.0 kg
The actual mass of the student = 83.8 kg
Absolute error = Actual Value - Estimated Value
= 1.8 kg (83.8 - 82.0)
Percentage error = Actual Value - Estimated Value /Actual Value x 100
= 2.15% (1.8/83.8 x 100)
Thus, we can conclude that the student's estimate contains a 2.15% error.
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Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.
On average, for every 25 patients calling in, how many do you expect to have the flu?
We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.
According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.
As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.
To figure this out, we can use the formula below:
Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.
Estimated number of influenza patients = 0.04 times 25
Expected number of influenza patients is one.
Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.
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Stretch y=|x|-3 in the y direction write the new equation and draw the new graph
The value of the transformed function after a vertical stretch in the y direction is h ( x ) = k ( | x | - 3 ) , where k is the scale factor
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = ( | x | - 3 ) be equation (1)
Now , when the function is stretched in the y direction , we get
Vertical stretch by a factor k: y = k × f(x)
On simplifying , we get
Let the transformed function be represented as h ( x )
where the value of h ( x ) is
Let the scale factor of stretching be k
h ( x ) = k ( | x | - 3 )
Hence , the transformed function is h ( x ) = k ( | x | - 3 )
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perform the calculation 50°21' - 38°48'
Answer:
11° 33'
Step-by-step explanation:
[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]
Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]
[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]
Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]
Subtract the whole numbers:
49 - 38 = 11
Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]
So
50°21' - 38°48' = 11° 33'
Mary invests $600 in a high-interest savings account. In the first year, the value of her savings increases by 8%. In the second year, there is a further increase of 8%. What is the total value of her investment after two years? Round your answer to the nearest dollar.
Answer:
Therefore, the total value of Mary's investment after two years is $700.
Step-by-step explanation:
To calculate the total value of Mary's investment after two years, we need to calculate the value of the investment after the first year, and then use that value to calculate the value after the second year.
In the first year, the value of the investment increases by 8%, so the value after the first year is:
Value after first year = $600 + 8% of $600
Value after first year = $600 + 0.08 * $600
Value after first year = $648
In the second year, the value of the investment increases by another 8%, so the value after the second year is:
Value after second year = Value after first year + 8% of Value after first year
Value after second year = $648 + 0.08 * $648
Value after second year = $699.84
Rounding to the nearest dollar, the total value of Mary's investment after two years is:
Total value after two years = $700
About 217,000 high school students took the AP Statistics exam in 2017. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers yielded a mean score of x =1.267 and a standard deviation of 1.230. a. Find and interpret the standard error of the mean. b. Construct and interpret a 90% confidence interval to estimate the true mean score on this question.
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
The confidence interval formula is [tex]\bar x\pm t\frac{s}{\sqrt{n}}[/tex].
Where, [tex]\bar x[/tex] is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.
Here,
[tex]\bar x[/tex] =1.267, s=1.23, n=30
The standard error is Se= 1.23/√30
= 0.2246
Item a:
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
Item b:
Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.
[tex]\bar x\pm tS_c[/tex]
[tex]\bar x+ tS_c[/tex] =1.267-2.7564(0.2246) =0.6479
[tex]\bar x- tS_c[/tex] =1.267+2.7564(0.2246) =1.8861
Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.
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Which of the following results in the difference of two squares?
Answer:
Step-by-step explanation:
(3x + 7y)(3x - 7y) FOIL
9x² -49y² yes, this is difference of two squares
(2x - 7y)(2x - 7y) FOIL
4x² -14x -14x +49y²
4x² -28x + 49y² not difference of two squares
9x²(5x - 7) Distribute the 9x²
45x³ - 63x² not difference of two squares because one term is cubed
(6x - 4y)² Distribute the square term
36x² - 16y² yes, difference of two squares
Difference Quotient Problem
The difference quotient expression for the given function is
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
Difference Quotient Formula:The expression in single-variable calculus is usually referred to as the difference quotient.
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.
The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.
Consider the difference quotient formula,
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Evaluate the function at x = x + h
replace the variable x with (x + h) in the given expression
[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]
simplify the result ,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
find the components of the definition,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]
plug in the components,
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
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D is partly constant and partly varies with V. When V = 40, D = 150, and when V = 54, D = 192. a Find the formula connecting D and V. b Hence find D when V = 73.
[tex]\textit{Partial Variation} \\\\ y = k_ox+k_1\hspace{5em}\textit{"y" varies partly with a constant and directly with "x"} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{"D" varies partly with a constant and directly with "V"}}{D=k_oV+k_1}\qquad \textit{we know that} \begin{cases} V=40\\ D=150\\[-0.5em] \hrulefill\\ V=54\\ D=192 \end{cases}[/tex]
[tex]\boxed{\begin{array}{llll} 150=40k_o+k_1\\\\ 192=54k_o+k_1 \end{array}}\qquad \stackrel{ \textit{using elimination method} }{\begin{array}{llll} -150=-40k_o-k_1\\\\ ~~ 192= ~~ 54k_o+k_1\\\cline{1-1} ~~ 42~= ~~ 14k_o+0 \end{array} }\qquad \implies 42=14k_o \\\\\\ \cfrac{42}{14}=k_o\implies \boxed{3=k_o}\hspace{5em}\stackrel{\textit{substituting on the 1st equation}}{150=40(3)+k_1}[/tex]
[tex]\cfrac{150}{40(3)}=k_1\implies \boxed{\cfrac{5}{4}=k_1}\hspace{5em} {\Large \begin{array}{llll} D=3V+\cfrac{5}{4} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when V=73, what is "D"?}\qquad D=3(73)+\cfrac{5}{4}\implies D=\cfrac{881}{4}\implies D=220\frac{1}{4}[/tex]
The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function 2(x+3) 0
The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.
What is the rationale for the above response?a.
Given: f(x) = 2(x+2)/5 , 0 <x< 1
Calculating P(0 <X< 1)
P(0 <X< 1) = ∫ f(x) dx {0.1}
Substitute 2(x+2)/5 for f(x)
P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}
P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}
Integrate with respect to x
P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}
P(0 <X< 1) = 2/5 (1²/2+2(1))
P(0 <X< 1) = 2/5 (½+2)
P(0 <X< 1) = 2/5 * 5/2
P(0 <X< 1) = 1 ----- Proved
b.
Here we're to solve for P(¼<X< ½)
P(¼<X< ½) = ∫ f(x) dx {¼,½}
Substitute 2(x+2)/5 for f(x)
P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}
P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}
P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}
P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]
P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]
P(¼<X< ½) = 0.2375
The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375
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Full Question:
The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.
(a) Show that P(0 <X< 1) = 1.
(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.
Calculate the mean, Variance and Standard deviation of the age of 12 student 16, 17, 18, 16/0.5, 17, 18, 19, 17, 17, 13, 17/½/2 and 16
The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:
Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16
= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16
= 204.25
Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years
To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:
Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)
= [ 0.16 + 1.96 + ... + 0.16 ] / 11
= 37.41
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = √(Variance) ≈ 6.117
Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.
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Given the Figure shown below is, ΔABC~ΔAXY if so, what is the scale factor between the two triangles?
Given the Figure shown below is, ΔABC~ΔAXY if so, 1.67 is the scale factor between the two triangles.
What is scale factor?The ratio between the scale of an original thing and a new object that is a representation of it but has a different size is known as a scale factor (bigger or smaller).
Consider two comparable squares as an illustration. One has a side length of 2 inches, while the other has a side length of 4 inches. This results in a scale factor of 1: 2 from the small square to the huge square. The scale factor between these two comparable squares is 1: 2, or tiny square to huge square.
Given that,
12 / 20 = 17 / x
or, 12 x = 340
or, x = 28.33
on the other hand,
25 / 15 = 1.66
20 / 12 = 1.66
28.33 / 17 = 1.66
now, scale factor = 1.67
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Question What is the value of the expression? 75÷5−[(9−7)×3]×2 Enter your answer in the box.
Answer:
3
Step-by-step explanation:
9-7=2
2*3=6
6*2=12
75/5=15
15-12=3
Answer:
Therefore, the value of the expression 75÷5−[(9−7)×3]×2 is 138.
Step-by-step explanation:
Using the order of operations (also known as PEMDAS), we simplify the expression as follows:
First, we solve the parentheses: (9-7) = 2.
Next, we multiply 2 by 3: 2 x 3 = 6.
Then, we subtract 6 from 75: 75 - 6 = 69.
Finally, we multiply 69 by 2: 69 x 2 = 138.
Therefore, the value of the expression 75÷5−[(9−7)×3]×2 is 138.
You pick a card at random. 4 5 6 7 8 What is P(not prime)?
the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
How we solved?
To determine the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8}, we first need to identify which numbers in the set are prime.
The prime numbers in the set are 5 and 7, so the non-prime numbers are 4, 6, and 8.
The total number of cards in the set is 5.
Therefore, the probability of selecting a non-prime card is:
P(not prime) = number of non-prime cards / total number of cards
P(not prime) = 3 / 5
P(not prime) = 0.6 or 60%
So the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
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a rectangle below has an area 84 cm saquered, what is half of the rectangle area?
Solve this system of equations by substitution or by linear combination
Answer:
No solution
Step-by-step explanation:
2x - 4y= -6 ----- eq(1)
-x + 2y = -2 ----- eq(2)
Simplifying eq(1) by taking 2 as common,
2(x-2y) = 2(-3)
x - 2y= -3 -----eq(1)
from eq(1)
x - 2y = -3
x = -3 + 2y ---eq(3)
substituting eq(3) into eq(2)
-(-3 + 2y) + 2y = -2
3 - 2y + 2y = -2
3 = -2
Therefore This pair of linear Equations Has No Solution
A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?Construct a two-sample z-interval for the difference between population proportions.Answer A: Construct a two-sample z -interval for the difference between population proportions.AConstruct a two-sample z-interval for the difference between sample proportions.Answer B: Construct a two-sample z -interval for the difference between sample proportions.BPerform a z-test for the difference in sample proportions.Answer C: Perform a z -test for the difference in sample proportions.CSubtract the proportions and construct a one-sample z-interval for a single population proportion.Answer D: Subtract the proportions and construct a one-sample z -interval for a single population proportion.DSubtract the proportions and construct a z-interval for a single sample proportion.
Answer A: Construct a two-sample z-interval for the difference between population proportions.
What is fraction?
A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as a/b, where a is called the numerator and b is called the denominator. The numerator represents the number of parts or units being considered, while the denominator represents the total number of parts or units in the whole.
According to given conditions:
The best method for the researcher to use to estimate the true difference between the population proportions would be to:
Answer A: Construct a two-sample z-interval for the difference between population proportions.
This is the most appropriate method for estimating the difference between population proportions, as it takes into account the variability of the sample proportions and provides a confidence interval for the true difference between the two populations. The formula for calculating the two-sample z-interval for the difference between population proportions is:
(p₁−p₂) ± z x √[(p₁(1−p₁))/₁ + (p₂(1−p₂))/₂]
Therefore, Answer A: Construct a two-sample z-interval for the difference between population proportions.
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In a Pew Research Poll, 287 out of 522 randomly selected US men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected US women were asked, 233 were able to do so. Construct a 98% confidence interval for the true proportion of US men and US women (m-w) who can identify Egypt on a map.
answer choices
(0.0384, 0.1650)
(0.0301, 0.1733)
(0.0413, 0.1621)
(0.0510, 0.1524)
Answer:
(0.0301, 0.1733)
Step-by-step explanation:
[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]
Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733
true/false. problem 3-1a (static) determine accrual-basis and cash-basis revenues and expenses (lo3-1, 3-2) required: for each transaction, determine the amount of revenue or expense, if any, that is recorded under accrual-basis accounting and under cash-basis accounting in the current period.
Answer:
true
Step-by-step explanation:
cause I’ve done this before
g bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.truefalse
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
What are error bars?A confidence intervals bar chart (shown as red lines)
In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.
According to the definition the statement is true.
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
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can somebody please help me
find the value of x
Answer:
x = 40
Step-by-step explanation:
Alternate exterior angles are congruent (equal).
2x + 16 = 96 Subtract 16 from both sides
2x + 16 -16 = 96 - 16
2x = 80 Divide both sides by 2
x = 40
Answer:
x=40
Step-by-step explanation:
Need helping solving this problem
The cost of the burger and the cost of an order of fries to Lynn would be :
Cost of burgher - $3.00Cost of fries - $ 1. 60How to find the cost ?From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:
4h + 5f = 20
10h + 7f = 41.20
Using substitution, we can express h in form of f to be :
4h + 5f = 20
4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20
6 f + 2 . 40 + 5 f = 20
11 f = 17. 60
f = $ 1. 60
We can then find the cost of hamburgers using the first equation :
4h + 5f = 20
4h + 5 ( 1. 60 ) = 20
4h + 8 = 20
4h = 12
h = $ 3
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Use a direct proof to show that the product of two rational numbers is rational.
We have shown that the product of two rational numbers is rational.
What is Number system?A number system is defined as a system of writing to express numbers.
Let a and b be two rational numbers, such that:
a = p/q
b = r/s
where p, q, r, and s are integers and q, s are non-zero.
We need to show that the product ab is also a rational number.
We have:
ab = (p/q) x (r/s)
= (p x r) / (q x s)
Since p, q, r, and s are all integers,
ab = m/n
where m = p x r and n = q x s.
Since both m and n are integers and n is non-zero ,we can conclude that ab is a rational number.
Therefore, we have shown that the product of two rational numbers is rational.
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Calculus please help
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
here, we have,
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = lim f((h - 1)) = (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = lim f(h + 1) = (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Can you help me find the point of intersection for the question in the picture attached?
Answer:
The ordered pair that is a solution is (2, 10)
Step-by-step explanation:
2x + 6 = 4x + 2 Subtract 2x from both sides
2x - 2x + 6 = 4x - 2x + 2
6 = 2x + 2 Subtract 2 from both sides
6 - 2 = 2x + 2 -2
4 = 2x Divide both sides by 2
2 = x
Substitute 2 for x in either of the two original equations.
y = 2x + 6
y = 2(2) + 6
y = 4 + 6
y = 10
The ordered pair that is a solution is (2, 10)
given a set of data that is skewed-right, there is at least % of the data within 3 standard deviations. use either chebyshev's theorem or the empirical rule to fill in the blank with the best answer:
The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.
What Is the Empirical Rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
Some points about standard deviation using Empirical Formula:
In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall within 3 standard deviations of the mean.According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.Learn more about Empirical Formula here:
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Hello I’m having a hard time with question
[-1.5, 3.5] and [-2, infty) are the range and domain of the equation.
Determining the domain and range of a quadratic functionQuadratic function are functions that have a leading degree of 2.
The domain of the function are values that lies along the x-axis of the graph. Hence the domain of the curve will be [-1.5, 3.5]
The range of the function are values that lies along the y-axis of the graph. Hence the domain of the curve will be [-2, infty)
Hence the range and domain of the graph are [-1.5, 3.5] and [-2, infty)
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Sketch the parabola, clearly labelling the points corresponding the vertex, x-intercepts and y-intercepts: (leave the vertex values in the form of a fraction). This may also help with 8a, remember that we want to use graphs to solve non-linear inequalities.
y=6x^2-17x+12
We kindly invite to see the image attached below to know the representation of the parabola according to its features.
How to graph a parabola
A parabola is the graphic representation of any quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. An alternative presentation is the vertex form:
y - k = C · (x - h)²
Where:
C - Vertex constanth, k - Coordinates of the vertex.The procedure to sketch the parabola according to its features is described below:
Determine the y-intercept.Determine the x-intercepts.Determine the coordinates of the vertex.Add the points on Cartesian plane.Match the points by a single curve.Step 1 - Determine the y-intercept:
y = 6 · 0² - 17 · 0 + 12
y = 12
Step 2 - Determine the x-intercepts.
6 · x² - 17 · x + 12 = 0
6 · [x² - (17 / 6) · x + 2] = 0
6 · (x - 3 / 2) · (x - 4 / 3) = 0
x = 3 / 2 or x = 4 / 3
Step 3 - Determine the coordinates of the vertex:
y = 6 · x² - 17 · x + 12
y = 6 · [x² - (17 / 6) · x + 2]
y + 6 · (1 / 144) = 6 · [x² - (17 / 6) · x + 2 + 1 / 144]
y + 1 / 24 = 6 · [x² - (17 / 6) · x + 289 / 144]
y + 1 / 24 = 6 · (x - 17 / 12)²
(h, k) = (17 / 12, - 1 / 24)
Steps 4 & 5 - Add the points on Cartesian plane and match the resulting curve.
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An engine supplies 110 hp to an electric generator, and the generator delivers 90 hp of electrical power. What is the
efficiency of the generator?
(Type a whole number or decimal rounded to two decimal places as needed)
Answer:
the efficiency of the generator is 81.82%.
Step-by-step explanation:
The efficiency of a generator is defined as the ratio of the electrical power output to the mechanical power input. In this problem, the electrical power output is given as 90 hp, and the mechanical power input is the power supplied by the engine, which is 110 hp. Therefore, the efficiency of the generator can be calculated as follows:
Efficiency = Electrical power output / Mechanical power input
Efficiency = 90 hp / 110 hp
Simplifying the fraction, we get:
Efficiency = 0.8182
To convert this decimal to a percentage, we multiply by 100:
Efficiency = 0.8182 * 100
Rounding to two decimal places, we get:
Efficiency = 81.82%
Therefore, the efficiency of the generator is 81.82%.
