homework! This is a stats problem I’ve been struggling with and need help thanks!!!
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f(x)=3√x + 7. Find the inverse of f(x).
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step 1- switch x and y
step 2- isolate y, and get to (x-7)/3=sqrty
step 3- square each side to get rid of the square root and isolate y
step 4- f(x)=(x^2-14x+49)/9
Answer:
[tex]f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3\sqrt{x}+7[/tex]
To find the inverse of the function
Swap f(x) for y:
[tex]\implies y=3 \sqrt{x}+7[/tex]
Subtract 7 from both sides:
[tex]\implies y-7=3 \sqrt{x}+7-7[/tex]
[tex]\implies y-7=3\sqrt{x}[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3\sqrt{x}}{3}=\dfrac{y-7}{3}[/tex]
[tex]\implies \sqrt{x}=\dfrac{y-7}{3}[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{y-7}{3}\right)^2[/tex]
[tex]\implies x=\left(\dfrac{y-7}{3}\right)^2[/tex]
Swap the x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
Which statement best describes the relationship between lines m& n
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The relationship between lines m & n is (a) the lines M and N have positive slope
How to describe the relationship?The points are given as:
Line M: (1, 4) and (2, 7)Line N: (1, 3) and (, 5)From the above points, we can see that:
As x increases, the y values of both lines increase
This is an illustration of positive slope
Hence, the lines M and N have positive slope
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Graph the line that passes through the two points. Then find the slope of the line. (2,9), (4, 18)
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The slope of the line is 4.5
How to determine the slope?The points are given as:
(2,9) and (4, 18)
The slope (m) is calculated using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (18 - 9)/(4 -2)
Evaluate
m = 4.5
Hence, the slope of the line is 4.5
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At Hinsdale College, students are employed by the college library to re-shelve books.
The students claim that a 15-minute coffee break every hour would relive boredom and
increase the average number of books re-shelved per hour. To test the student's claim,
the following data were gathered on a random sample of seven student employees.
Over a period of one week, each student worked a normal schedule without coffee
breaks. Then, during the next week, the students were allowed coffee breaks.
Unknown to the students, a member of the library staff secretly recorded the average
number of books shelved per hour and computed the averages with and without the
coffee break system. The results are below. Test the claim that the students shelve
more books when they have a coffee break, use a 0.05 level of significance.
Student 1 2 3 4 5 6 7
Without
Coffee
breaks
75 63 82 53 79 96 73
With
Coffee
Breaks
90 72 95 50 85 110 89
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The p value is less, therefore one should reject the null hypothesis.
How to illustrate the information?From the information given, the test statistic will be:
t = (10 - 0)/(6.733/✓7)
t = 3.930.
The degree of freedom will be:
= 7 - 1 = 6
Using the table, the p value will be 0.0039.
Since the p value is less than 0.05 one should reject the null hypothesis.
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Which function is the inverse of if the domain of f(x) is x ≥ 0?
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The question was incomplete. Please find full content below.
Which function is the inverse of
[tex]f(x)=x^2-16[/tex]
if the domain of f(x) is x ≥ 0?
The inverse funtion of the given function is given by
[tex]\mathbf{f(x)=\sqrt{x+16}}[/tex]
where the domain is x ≥ -16.
Given the function is,
[tex]f(x) =x^2-16[/tex]
Let, y = f(x)
[tex]y = x^2-16[/tex]
Adding 16 to both sides we get,
[tex]y + 16 = {x}^{2} - 16 + 16[/tex]
[tex] {x}^{2} = y + 16[/tex]
Now, square rooting to both sides we get, since x ≥ 0
[tex]\sqrt{x^2}=\sqrt{y+16}[/tex]
[tex]x=\sqrt{y+16}[/tex]
[tex]f^{-1}(y)=\sqrt{y+16}[/tex]
Hence substituting x in place of y,
[tex]f^{-1}(x)=\sqrt{x+16}[/tex]
Above function is the required inverse function where the domain of that is given by, x ≥ -16.
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6/9 is a rational number. Select all the rational numbers that are equivalent to .
0.6(line over 6)
2/3
0.66(line over 66)7
0. 66(line over 66)
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Option b) and c) is correct, i.e. 2/3 and 0.66(line over 66)7
6/9 is a rational number.
similar ration number can be given as -
Rational numbers are the numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
From the option, by above definition 2/3, 0.66(line over 66)7 seems to be an equivalent rational numbers because
6/9=2/3= 0.66(line over 66)7.
Thus, Rational numbers 2/3, 0.66(line over 66)7 are equivalent to 6/9.
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M=−8r
2
+11r−6
T=−7r
2
−9r+14
M
+
T
=
M+T=M, plus, T, equals
Your answer should be a polynomial in standard form.
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M + T in standard form polynomial is -15r² + 2r + 8
How to represent polynomial in standard form?Polynomial in standard is when all its terms are arranged by decreasing order of degree.
Therefore,
M = - 8r²+ 11r - 6
T = -7r² - 9r + 14
M + T = - 8r²+ 11r - 6 + (-7r² - 9r + 14)
M + T = - 8r²+ 11r - 6 - 7r² - 9r + 14
combine like terms
M + T = - 8r² - 7r² + 11r - 9r - 6 + 14
In standard form, the polynomial is represented as follows;
M + T = -15r² + 2r + 8
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What is the following quotient?
2
√13+√11
O√13-2√11
√13+√11
6
O
113 + √11
12
O
● √13 - √11
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[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]
The solution is: our final quotient is: (√13 - √11).
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Explanation
Since we have radicals in the denominator, we need to rationalize our expression.
To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.
Remember that the conjugate of a binomial is the same binomial with the sing in between changed.
given that,
2/ (√13 + √11)
Now, we can simplify the denominator:
multiplying by (√13 - √11)
we get,
2 * (√13 - √11) / (√13 + √11)* (√13 - √11)
The only radical that we can simplify in the numerator is , which simplifies to:
2 (√13 - √11) / 13 - 11
= 2(√13 - √11) /2
= (√13 - √11)
So, our final quotient is: (√13 - √11)
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Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
C A. Similarity cannot be determined.
• B. SSS theorem
• C. AA postulate
D. SAS theorem
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The AA postulate can be used to verify that the two triangles shown below are a similar option (C) is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We can utilize the AA postulate since we know two of each triangle's three angles.
In every triangle, they are the same. We may also determine each triangle's third angle.
They are comparable because both triangles have the same angles.
Thus, the AA postulate can be used to verify that the two triangles shown below are similar.
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The Robinsons family drove for 4000 miles. This was the
distance the Jones family drove. How many miles did the Jones
family drive?
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Answer:1333.3 Contiuous
Step-by-step explanation:
.
4000/3,=1333.3x1,=1333.3
I'm not sure
A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. During a week in which the company has budgeted $1,600 for materials and $2,700 for labor, how many mountain bikes does the company plan to manufacture?
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An equation is formed when two equal expressions. The company is planning to produce 25 mountain bikes and 15 trail bikes.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of mountain bikes produced by the company be x, while the number of trail bikes produced by the company is y.
The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. Also, the budget of the company is $1,600. Therefore,
1600 = 40x + 40y
x + y = 40
y = 40-x
The cost of labour to manufacture a mountain bike is $90, and the cost of labour to manufacture a trail bike is $30. Also, the budget for labour is $2,700.
2700 = 90x + 30y
2700 = 90x + 30(40-x)
2700 = 90x + 1200 - 30x
1500 = 60x
x = 25
Substitute the value of x,
y = 40 - x
y = 15
Hence, the company is planning to produce 25 mountain bikes and 15 trail bikes.
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Nadia says the hypotenuse of this right triangle has a length of 73 because the pythagorean theorem states that (28 45) squared = 73 squared. 3 squares are positioned to form a right triangle. the small square is labeled 28, medium square is 45, and large square is not labeled. which best describes nadia’s solution?
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Both the options that Nadia gives are wrong about the length of hypotenuse.
Given length of hypotenuse is 73 and options which are :
1) Because the pythagoras theorem states that [tex]28^{2} +45^{2}[/tex] squared = 73 squared.
2) 3 squares are positioned to form a right triangle.
We have to choose the correct option which shows the calculation of length of hypotenuse.
Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to sum of the square of base and square of perpendicular.
[tex]H^{2} =P^{2} +B^{2}[/tex]
First option says that [tex]28^{2} +45^{2} =73^{2}[/tex]
784+2025=5329
2809≠5329
so it is wrong.
Second option says that the length of hypotenuse is the sum of three squares but we have seen that the square of the length of hypotenuse is equal to sum of two square one is the square of base and the square of perpendicular.
Hence both the options are incorrect about the length of hypotenuse.
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Answer:
C
Step-by-step explanation:
I’m so confused please help
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Answer:
976cm squared
Step-by-step explanation:
that's all I could do .hope it helps. in case of any questions please ask.
approximate the value of 3^3x when x+1 using the first six terms of the Maclaurin expansion
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Answer:
x could be anything but might be 3<4 or 5?8 u really never kno
NEED HELP ASAP
there should be a picture giving you info
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Answer:
to find this radius you need to square the area and divide it by pi or 3.14 if your using Alex
The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)?
X =
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The coordinates of X in the pre-image of the figure is (3.2, 0.6) if the transformation rule is T_(-5.2, 1.4)(x, y)
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we can see in the figure.
The transformation rule is T_(-5.2, 1.4)(x, y)
X'(-2, 2)
Before the transformation:
X = (-2+5.2, 2-1.4)
X = (3.2, 0.6)
Thus, the coordinates of X in the pre-image of the figure is (3.2, 0.6) if the transformation rule is T_(-5.2, 1.4)(x, y)
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Which transformation is a isometry?
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Answer:
second transformation
Perform the operation and simplify
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Answer:
[tex]\frac{(x-2)(x+4)}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{(x+4)^2}{x+2} :\frac{(x+2)(x+4)}{(x+2)(x-2)} =\frac{(x+4)^2(x+2)(x-2)}{(x+2)(x+2)(x+4)}=\frac{(x-2)(x+4)}{x+2} .[/tex]
order 0.76 grams of med each pill contains 0.02 grams of med how many pill will the patient need
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Answer:
38 pills
Step-by-step explanation:
To find the number of pills, you need to divide the weight of each pill by the total weight needed.
0.76 grams / 0.02 grams = 38 pills
Darla places a wooden stick along the diagonal of a cubical box as shown below . If the length of the stick is 3√3 feet , what is the length of the edge of the cube ? A.9√ / 2 feet B. 3 feet C.3√2 feet D.9 feet
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Answer:
3
Step-by-step explanation:
1) Which part of a circle is a portion of the boundary of a circle?
A. arc
B. center
C. circumference
D. radius
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Answer:
A. arc
Step-by-step explanation:
The circumference is the entire boundary of a circle.
A portion of the circumference is called an arc.
Find the range of the function f(n) = n² - 2n for the domain (1, 3, 5).
Range:
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Answer: {-1, 3, 15}
Step-by-step explanation:
[tex]f(1)=-1\\\\f(3)=3\\\\f(5)=15[/tex]
So, the range is {-1, 3, 15}.
A local hospital currently has 184 male patients. If the ratio of male to female patients is 4:3, how many female patients are there in the hospital?
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There are 138 female patients in the hospital.
Solving word problems involving ratios.The solution to the word problem involving ratios in the given problem can be determined as follows.
From the given information:
The total number of people in the hospital = male + female
= 184 + x(unknown)
If the ratio of male to female is 4: 3. The total ratio is 4+3 = 7The ratio of males in the hospital is:
[tex]\mathbf{184= \dfrac{4}{7} \times x }[/tex]
[tex]\mathbf{184\times 7= 4 x }[/tex]
x = 322
The number of female patients in the hospital can now be computed as:
[tex]\mathbf{=\dfrac{3}{7}\times 322}[/tex]
= 138 female patients
Check:
The total number of people in the hospital is:
= 184 + 138
= 322 patients
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HELP ASAP GIVING BRAILIEST!!!!!!!
15 POINTS
photo of problem below>>
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Answer:
B) y = 4/5x - 2
Answer:
B
Step-by-step explanation:
First, we can find the slope of the graph.
The distance of x between the two points is 5, and the distance of y between the two points is 4.
The slope formula is (Increase in y)/(increase in x)
So the slope will be 4/5.
The y-intercept is (0,-2), so the number at the very end of the equation will be -2.
With all this in mind, we can be sure that our answer is B: y=4/5x-2
MD writes an order for Lortab Elixir 5mg by mouth as needed for pain every 4 hours. Pharmacy dispenses you with 7.5mg/15ml. How many tablespoons will you administer per dose?
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Following the prescription, You will need to administer a 0.7 tablespoon per dose.
Determining the number of tablespoons by using equivalent expressions?We can determine the number of tablespoons that are administered by using equivalent expressions.
From the standard conversion rate, we know that:
1 ml = 0.067628 tbsp15 ml = 1.01442 tbspUsing equivalent expressions:
7.5 mg/1.01442 tbsp = 5 mg/x tbsp
x = (1.01442 × 5)/7.5 tbsp
x = 0.67 tbsp
x = 0.7 tbsp per dose.
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-3x + 2y = 9
x - 3y = 4
Answers
Answer:
(-5, -3)
Step-by-step explanation:
Isolate x:
x - 3y = 4
x = 3y + 4
Substitute to get y:
-3x + 2y = 9
-3(3y + 4) + 2y = 9
-9y - 12 + 2y = 9
-7y = 21
y = -3
Substitute to get x:
x = 3y + 4
= 3(-3) + 4
-9 + 4
= -5
14 ) Mark Achin sells 3,600 electric motors each year . The cost of these is $ 200 each , and demand is constant throughout the year . The cost of placing an order is $ 40 , while the holding cost is $ 20 per unit per year . There are 360 working days per year and the lead - time is 5 days . What is his economic order quantity in units ? A ) 100 B ) 200 C ) 60 D 120
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Mark Achin's economic order quantity in units is D. 120 units.
What is economic order quantity?The economic order quantity (EOQ) is the optimal order quantity that minimizes the total costs (ordering, receiving, and holding inventory).
The formula for the economic order quantity is the square root of [2(setup costs)(demand rate)] / holding costs.
Data and Calculations:Annual demand = 3,600
Cost price per unit = $200
Ordering cost = $40
Holding cost per unit = $20
Working days per year = 360
Lead time = 5 days
Economic order quantity (EOQ) = square root of: [2(setup costs)(demand rate)] / holding costs.
= square root of (2 x $40 x 3,600)/$20
= 120
Thus, Mark Achin's economic order quantity in units is D. 120 units.
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Linda needs to buy pencils brands has a pack of 28 pencils for 5.29 brand b has a pack of 48 pencils for 8.47 find the unit price for each brand.
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Answer:
Brand A is the best buy.
Step-by-step explanation:
Brand A has a pack of 28 pencils for 5.29 dollars. This means that the unit cost of one pencil in Brand A would be 5.29/28 = 0.2$ per pencil rounded up to the nearest tenth.Brand B has a pack of 48 pencils for 8.47 dollars. This means that the unit cost of one pencil in Brand B would be 8.47/48 = $0.8 per pencil rounded up to the nearest tenth.Since $0.2 is lesser than $0.8, it means that Brand A is the best buy.
7.
At the metal-casting company where you work, you must
set up a conveyor system to move castings from the furnace
to the heat treatment area 55 yards away. The castings cool
at the rate of 0.3°F (degrees Fahrenheit) per second and
must not be allowed to cool more than 7°F before being
heat treated. What is the minimum speed, in feet per
second, that the conveyor must move?
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Answer:
xxfdjdjwkoq9w Woow Kike sosl
which statement is true about finding the midpoint between two points located on a horizontal or vertical line ?
A . When finding the midpoint between two points on a vertical line, keep the y-coordinate and find the average of the x-coordinate
B . When finding the midpoint between two points on vertical line, keep x-coordinate and find the average of the y-coordinates
C . When finding the midpoint between two points on a horizontal line, the x-coordinate is always 0 and the y-coordinates are averaged
D. When finding the midpoint between two points on a horizontal line , the y-coordinate is always zero and the x-coordinates are averaged
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Answer: B. When finding the midpoint between two points on a vertical line, keep the x-coordinate and find the average of the y-coordinates