Answer:
f⁻¹(x) = (1/2)x +5
Step-by-step explanation:
In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).
... y = 2x -10
... x = 2y -10 . . . . . . swapped variables
... x +10 = 2y . . . . . add 10
... (1/2)x + 5 = y . . . . divide by 2
... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation
When simplified, what is the value of square root of negative 45 end square root,if i2 = −1?
The following table gives the scores of 30 students in a mathematics examination. Scores 90–99 80–89 70–79 60–69 50–59 Students 3 7 12 4 4 Find the mean and the standard deviation of the given data. Hint: Assume that all scores lying within a group interval take the middle value of that group. (Round your answers to two decimal places.)
Let f(x)=2x^2+7x-5 and g(x)=-8^2-3x+5. What is g(x)+f(x)?
Using addition of two polynomials, f(x) + g(x) = 2x² +4x - 64
What is polynomials?Polynomials are "algebraic expressions that may comprise of exponents which are added, subtracted and multiplied".
According to the question,
f(x) = 2x² + 7x - 5
g(x) = -8² - 3x + 5
f(x) + g(x) = 2x² +4x - 64.
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Solve the equation what is 2y-3y=5
What does h(40) = 1400 mean in terms of the problem
Answer:
The correct option is B.
Step-by-step explanation:
From the given table it is clear that left column represents the hours of training and the right column represents the Monthly pay.
Here, left column is input (x) and right column is output (y). It means a worker with x hours of training is paid $y per month.
[tex]h(40)=1400[/tex]
In this equation the value of y is 1400 at x=40.
A worker with 40 hours of training is paid $1400 per month.
Therefore, correct option is B.
60 minutes is 20% of blank kilometers
Patrick is reading a book about forest animals. He has read 3/4 of the 100 pages in his book. Nicholas has read 2/3 of the 120 pages about alpine flowers. who has more pages to read in his book?
Final answer:
Upon calculating, Nicholas, who is reading about alpine flowers, has more pages left to read (40 pages) in his book compared to Patrick, who is reading about forest animals and has 25 pages left.
Explanation:
The question asks who has more pages to read in his book between Patrick, who is reading about forest animals, and Nicholas, who is reading about alpine flowers. To determine this, let's calculate the pages each has already read and then subtract that from the total number of pages in their respective books.
For Patrick: He has read 3/4 of the 100 pages. This means he has read 75 pages (since 3/4 of 100 is 75), leaving him with 25 pages to read.
For Nicholas: He has read 2/3 of the 120 pages. This means he has read 80 pages (since 2/3 of 120 is 80), leaving him with 40 pages to read.
Comparing the pages left to read, Nicholas has more pages to read in his book about alpine flowers than Patrick does in his book about forest animals.
About 22/40 of a lawn is planted with Kentucky bluegrass. What percent of the lawn is planted with Kentucky bluegrass
Using only the values given in the table for the function, f(x) = x3 – 3x – 2, what is the interval of x-values over which the function is decreasing? (–4, 1) (–4, –1) (–1,1) (–1, 2)
Using only the values given in the table for the function , f(x) = x3-3x-2 , what is the interval of x-values over which the function is decreased. Advertisement ... 3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).
The interval of x-values over which the given function is decreasing is (-1,1) and this can be determined by differentiating the given function.
Given :
[tex]\rm f(x) = x^3-3x-2[/tex]
The following steps can be used in order to determine the interval in which the given function is decreasing:
Step 1 - Write the given function.
[tex]\rm f(x) = x^3-3x-2[/tex]
Step 2 - Now, differentiate the above function with respect to 'x'.
[tex]\rm f'(x) = 3x^2-3[/tex]
Step 3 - Now, equate the above expression to zero.
[tex]\rm x^2 = 1[/tex]
x = 1 or -1
Therefore, the correct option is C).
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(9-13)-(56-65) =5
Replace the question mark to create a TRUE STATEMENT.
What is the scale factor of Triangle ABC to Triangle DEF?
Answer:
1
Step-by-step explanation:
Checking account A charges a monthly service fee of $25 and a wire transfer fee of $6.50 each, while checking account B charges a monthly service fee of $16 and a wire transfer fee of $8.50 each. Which checking account is the better deal if 4 wire transfers are made per month?
write an equivalent expression for 3 (1-7)
What is the length y of the remaining, vertical side of the 30-60 right triangle?
The length of side y in the right triangle, with a hypotenuse of 14 cm and legs measuring 7 cm and y cm is determined to be 16.16 cm.
The triangle has a hypotenuse of 14 cm, and the other two sides are 7 cm and y cm.
Setting up the Equation for sin 60°:
In the given figure, sin 60° is defined as the ratio of the side opposite the angle to the hypotenuse.
The equation is set up as sin 60° = y / 14.
Substituting the Value of sin 60°:
The sine of 60 degrees is known to be √3/2.
Substitute sin 60° with √3/2 in the equation: √3/2 = y / 14.
Isolating y in the Equation:
Multiply both sides of the equation by 14 to isolate y: √3y = 28.
Solving for y:
Divide both sides of the equation by √3 to solve for y: y = 28/√3.
Rationalizing the Denominator:
Multiply the numerator and denominator of y by √3 to rationalize the denominator: y = (28√3)/3.
Simplifying the Expression for y:
The final step simplifies the expression by dividing both numerator and denominator by 3: y = 16.16 cm.
Therefore, the length of side y in the given right triangle is 16.16 cm.
A hypotenuse of 14 cm and legs of 7 cm and y cm, the length of side y in a right triangle is calculated to be 16.16 cm.
The triangle's two other sides are 7 cm and y cm, and its hypotenuse measures 14 cm.
Configuring the Equation for 60° Sin:
As seen in the illustration, sin 60° is the side opposite the angle divided by the hypotenuse.
The formula is written as follows: sin 60° = y / 14.
Replacing the Value of Sin 60° with:
It is known that the sine of sixty degrees is √3/2.
Replace √3/2 with sin 60° in the equation: y / 14 = √3/2.
Calculating y in the Equation: To isolate y, multiply both sides by 14: √3y = 28.
Finding y':
To find y, divide both sides of the equation by √3. y = 28/√3.
Making Sense of the Denominator
To rationalize the denominator, multiply both the numerator and denominator of y by √3. y = (28−3)/3.
The Expression for y Simplified:
In the last stage, the formula is made simpler by dividing the denominator and numerator by three: y is equal to 16.16 cm.
As a result, side y in the supplied right triangle has a length of 16.16 cm.
The table shows the number of miles driven over time time 4,6,8,10 distance 232, 348, 464, 580
Express the relationship between distance and time and simplified form as a unit rate. Determine which statement correctly interprets this relationship
Final answer:
The relationship between distance and time is that the vehicle travels at a constant speed of 58 miles per hour, meaning for every hour of driving, the distance covered is 58 miles.
Explanation:
To express the relationship between distance and time in simplified form as a unit rate, we divide the distance by the time for every given value. Based on the provided data, for each time interval, the distance driven is 58 times the number of hours.
Therefore, the unit rate or speed is 58 miles per hour. This can be explained by the fact that at each time interval, the distance increases by 116 miles every 2 hours, which simplifies down to 58 miles per hour (58 miles/1 hour).
To interpret this, one could say that for every hour of driving, the vehicle covers a distance of 58 miles. Thus, speed or velocity is the constant rate at which distance is covered over time in this scenario.
Which is a valid proportion?
A. 3/4=21/28
B. 5/6=29/30
C.4/7=16/49
D.2/5=12/15
A survey of 100 people found that 35 people exercise in the morning, 45 people exercise in the afternoon, and 20 people exercise at night. Tara claims that 35:55, 45:80, and 20:65 are possible ratios from this data. Jim claims that 35:100, 45:100, and 20:100 are possible ratios from this data. Who is correct? Explain.
Jim is correct as he has shown the ratio of people exercising at various times to total people in survey , correctly.
It is given that total 100 people participated in a survey and data of people doing exercises in morning , evening and at night is given.
We have to find out who is correct , if Tara and Jim has shown the possible ratios.
What do you mean by ratio ?
A ratio is defined as the relative sizes of two or more values i.e., 12 : 24 or 13 : 26 , etc.
As per the question ;
Total no. of people in survey = 100
People exercising in morning = 35
People exercising in afternoon = 45
People exercising at night = 20
and
Possible ratio claimed ;
According to Tara is ;
35:55, 45:80, and 20:65
and
According to Jim is ;
35:100, 45:100, and 20:100
Let's check who has got it correct ;
So ;
Ratio of people exercising in morning to total people in survey will be ;
= 35 : 100
and
Ratio of people exercising in afternoon to total people in survey will be ;
= 45 : 100
Ratio of people exercising at night to total people in survey will be ;
= 20 : 100
So ;
We found that Jim has shown the correct possible ratio.
Thus , Jim is correct as he has shown the ratio of people exercising at various times to total people in survey , correctly.
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13+8 POINTS!!!! PLEASE HELP ME PLEASE!!!!! DUE TODAY PLEASE HELP!!!
Complete the coordinate proof of the theorem.
Enter your answers in the boxes.
The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C(??), and D(c, b) .
The coordinates of the midpoint of AC¯¯¯¯¯ are (, b2 ).
The coordinates of the midpoint of BD¯¯¯¯¯ are ( a+c2 , ).
The midpoints of the diagonals have the same coordinates.
Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
Answer:
Step-by-step explanation:
1). Coordinates of point C will be
x - coordinates = [Distance of B from the origin + Distance of D from y axis]
= (a + c)
y - coordinates = (Distance of D from x - axis)
= b
Therefore, coordinates of C will be [(a + c), b]
2). Coordinates of the midpoint of AC = [tex][\frac{(a+c)+0}{2}, \frac{b+0}{2}][/tex]
= [tex][\frac{(a+c)}{2}, \frac{b}{2}][/tex]
[Since coordinates of the midpoint of (x, y) and (x', y') are denoted by ([tex]\frac{x+x'}{2},\frac{y+y'}{2}[/tex])]
3). Coordinates of the midpoint of BD = [tex][\frac{(a+c)}{2}, \frac{b+0}{2}][/tex]
= [tex][\frac{(a+c)}{2}, \frac{b}{2}][/tex]
Solve the system of linear equations. separate the x- and y- values with a coma.
7x-7y=7
14x-4y=74
Martha placed $2,500 in a college savings account with a simple interest rate of 5% when when Ryan was born. How much will be in the account in 18 years when her son is ready to go to college?
A hospital discards 1000 patient gowns every 3 months how many gallons will they need to replace the discarded ones over the next year
skylar paid $18 to park at the airport. she bought 4 plane tickets for her family.each plane ticket cost the same. altogether she paid $610 for the plane tickets and parking
The price of an item has dropped to $46 today yesterday was $115 find the percent decrease
Answer:
percent decrease = 40%
Step-by-step explanation:
The price of an item yesterday = $115
Today the price of the item has dropped to = $46
The percent decrease = [tex]\frac{46}{115}\times 100[/tex]
= 0.40 × 100
= 40%
The percent decrease would be 40%.
Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour?
………………………………………………………………
When solving -1/3 (x − 15) = −4, what is the correct sequence of operations? Please help!! 15 points
-1/3(x-15) = -4
1st step distribute(multiply) the -1/3 with what is inside parenthesis
-1/3x + 5 = -4
2nd step subtract 5 from both sides of the equation
-1/3x = -9
3rd step divide both sides of the equation by -1/3 to get x
x = -9 / -1/3
x = 27
Factor −1/3
out of −1/3x−8
Answer:
The factor form is [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
Step-by-step explanation:
To find : Factor [tex]-\frac{1}{3}[/tex] out of [tex]-\frac{1}{3}x-8[/tex]
Solution :
Taking the term common means we the number multiply inside give you the same result.
Taking [tex]-\frac{1}{3}[/tex] out of [tex]-\frac{1}{3}x[/tex] is left with
[tex]\frac{-\frac{1}{3}x}{-\frac{1}{3}}=x[/tex]
Taking [tex]-\frac{1}{3}[/tex] out of [tex]8[/tex] is left with
[tex]\frac{8}{-\frac{1}{3}}=-8\times 3=-24[/tex]
So, [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x-(-24))[/tex]
[tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
The factor form is [tex]-\frac{1}{3}x-8=-\frac{1}{3}(x+24)[/tex]
Write an expression for the calculation 4 times the difference of 10 and 8 minus 3
An expression for the calculation '4 times the difference of 10 and 8 minus 3' is written as[tex]4 imes (10 - 8) - 3.[/tex]When evaluated, this expression results in the value of 5.
To write an expression for the calculation 4 times the difference of 10 and 8 minus 3, you need to apply the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
The difference of 10 and 8 is calculated first, which is 10 - 8. This equals 2. Then, you need to multiply this difference by 4, resulting in [tex]4 imes 2.[/tex] Finally, subtract 3 from that product to find the value of the entire expression. So, the expression is
To evaluate this expression, first calculate the difference inside the parentheses (10 - 8 = 2), then multiply by 4 ([tex]4 imes[/tex]2 = 8), and finally subtract 3 (8 - 3 = 5). So, the expression evaluates to 5.
Jenny read 3 books in 7.5 hours. At this rate, how many books can Jenny read in one hour?
A. crystal lund has been your trusted employee for 25 years. she performs all cash-handling and accounting duties. crystal just purchased a new lexus and a new home in an expensive suburb. as owner of the company, you wonder how she can afford these luxuries because you pay her only $42,000 a year and she has no sources of outside income
The level of calcium in the blood of healthy young adults follows a normal distribution with mean $\mu=10$ milligrams per deciliter and standard deviation $\sigma=0.4$. a clinic measures the blood calcium of 25 healthy pregnant young women at their first visit for prenatal care. the mean of these 25 measurements is $\bar{x}=9.6$ we want to test the hypotheses $h_0$: $\mu=10$ vs. $h_a$: $\mu<10$ what does it mean if the p-value is 0.0002.
The p-value of 0.0002 indicates strong evidence against the null hypothesis and suggests that the mean blood calcium level in pregnant young women is less than 10 milligrams per deciliter.
The p-value of 0.0002 indicates the probability of obtaining a sample mean as extreme as 9.6, assuming the null hypothesis (μ = 10) is true.
A p-value of 0.0002 is less than the commonly used significance level of 0.05, which suggests strong evidence against the null hypothesis.
Therefore, we reject the null hypothesis in favor of the alternative hypothesis (μ < 10).
This means that there is sufficient evidence to suggest that the mean blood calcium level in pregnant young women is less than 10 milligrams per deciliter.
The probable question may be:
The level of calcium in the blood of healthy young adults follows a normal distribution with a mean (\(\mu\)) of 10 milligrams per deciliter and a standard deviation (\(\sigma\)) of 0.4. A clinic measures the blood calcium of 25 healthy pregnant young women at their first prenatal care visit, resulting in a sample mean (\(\bar{x}\)) of 9.6.
Now, we want to test the hypotheses \(H_0: \mu = 10\) versus \(H_a: \mu < 10\). If the computed p-value is 0.0002, what does this indicate in the context of hypothesis testing?