Answer:
(3rd listed choice) Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse."
Step-by-step explanation:
If f(y) = x can be solved for a relation for y that is a function, then f(x) has an inverse. It will be the function defined by y.
Zamba has found a little black dress on sale for 50% off the original price of $239.99. She also has a coupon offering free shipping and an additional 10% off of her entire online purchase. If she buys the dress and a pair of shoes costing $34.70, how much will she pay for her ensemble?
108.00
$139.23
$94.23
$104.70
Answer: $139.23
Step-by-step explanation: Take 50% of original dress price and add price of shoes. Subtract 10% of that.
In your gym class, your teacher can create teams of 4 for a
relay race and have no students left over. The next day, your
teacher creates teams of 5 for dodge ball and has no
students left over. What are some possible numbers of
students in your class?
Answer: 20, 40, 60, 80, 100,....
Step-by-step explanation:
Given that :
It is possible to create teams of 4 for a relay race with no student leftover
Also,
It is possible to create teams of 5 for dodgeball with no student left over from the same class
To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5
Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....
Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....
OMG HELP PLEASE!!!!!!!!!!
Answer:
Step-by-step explanation:
Hello, please consider the following.
We will multiply the numerator and denominator by
[tex]3-\sqrt{3}[/tex] to get rid of the root in the denominator.
Let's do it!
[tex]\begin{aligned}\dfrac{\sqrt{12}}{\sqrt{3}+3}&=\dfrac{\sqrt{2^2*3}*(3-\sqrt{3})}{(3+\sqrt{3})*(3-\sqrt{3})}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{3^2-\sqrt{3}^2}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{9-3}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{6}\\\\&=\dfrac{6\sqrt{3}}{6}-\dfrac{2*3}{6}\\\\&=\sqrt{3}-1\\\\\large &\boxed{=-1+\sqrt{3}}\\\end{aligned}[/tex]
Thank you
Step-by-step explanation:
Here,
[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} [/tex]
is given.
Now, rationalizing it,
[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} \times \frac{ \sqrt{3} - 3 }{ \sqrt{3} - 3} [/tex]
now, simplifying it,
[tex] = \frac{ \sqrt{12 } \times \sqrt{3 } - 3 }{( { \sqrt{3} )}^{2} - 9} [/tex]
or, simplifying it we get,
[tex] = \frac{3}{ - 6} [/tex]
= 1/ -2
Hope it helps...
Part of a regression output is provided below. Some of the information has been omitted.
Source of variation SS df MS F
Regression 3177.17 2 1588.6
Residual 17 17.717
Total 3478.36 19
The SS(Residual) is?
Answer:
301.189
Step-by-step explanation:
Given the table :
Source of Variation - - SS - - - df - - - MS - - - - F
Regression - - - - - -3177.17 - - -2 - - 1588.6
Residual - - - - - - - - ______ --17 - - -17.717
Total - - - - - - - - - - 3478.36 - - 19
Calculate the SSR, Sum of Square residual
The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR) and Degree of Freedom RESIDUAL (DFR) are related by the formular :
MSR = SSR / DFR
Hence,
SSR = MSR × DFR
Fr the table ;
MSR = 17.717 ; DFR = 17
SSR = (17.717 × 17)
SSR = 301.189
find the midpoint of (-1, -5) and (-5, 9)
Answer:
(-3,-2) is the midpoint
Step-by-step explanation:
To find the midpoint
Add the x coordinates and divide by 2 to find the x coordinate of the midpoint
(-1+-5) /2 = -6/2 = -3
Add the y coordinates and divide by 2 to find the y coordinate of the midpoint
(-5+-9) /2 = -4/2 = -2
(-3,-2) is the midpoint
Step-by-step explanation:
To solve, we have to use the midpoint formula:
[tex]M=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2})[/tex]
Our points:
(-1, -5) (-5, 9)
Our x1 is -1, and our x2 is -5. Our y1 is -5, and our y2 is 9.
[tex]M=(\frac{-1+(-5) }{2} ,\frac{-5+9 }{2})[/tex]
[tex]M=(\frac{-6 }{2} ,\frac{4}{2})[/tex]
[tex]M=(-3 ,2)[/tex]
Answer: our midpoint: (-3, 2)
Net to seller equals the ______ multiplied by the percent to seller.
I assumed you are referring to the Net (take away by the seller after removing their commissions).
Answer:
Selling price
Step-by-step explanation:
To determine what amount goes to the seller, we multiply the selling price of a commodity in question by the percentage (commissions) to the seller.
Note that the resulting amount is the value of the commission paid to the seller, the actual net is gotten by substracting the selling price from the commission paid.
Given point (-6, -2) and a slope of 5, write an equation in slope-intercept form.
a. y = 5x + 28
c. y + 2 = 5(x + 6)
b. y = -5x + 28
d. y - 2 = 5(x - 6)
Answer:
y=ax+b
y=5(-6)+28=-2
a
The area of a rectangular parking lot is represented by A = 6x^2 − 19x − 7 If x represents 15 m, what are the length and width of the parking lot?
=====================================
Work Shown:
Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19
Turns out that those two numbers are -21 and 2, which you find by trial and error.
-21 * 2 = -42
-21 + 2 = -19
Break up -19x as -21x+2x and use the factor by grouping method
6x^2 - 19x - 7
6x^2 - 21x + 2x - 7
(6x^2 - 21x) + (2x - 7)
3x(2x - 7) + 1(2x - 7)
(3x+1)(2x-7)
The factorization represents the length*width, since this product is equal to the rectangle's area.
----------------------
Plug x = 15 into each factor
3x+1 = 3*15+1 = 46
2x-7 = 2*15-7 = 23
The length and width are 46 and 23
Find the area of the region between the curve y= 2ln(x) and the horizontal axis for 1<= x <= 4
Answer:
5.09 units
Step-by-step explanation:
Given equation
[tex]y=2\ln x=f(x)[/tex] in the interval [tex]1\le x\le 4[/tex]
So we integrate [tex]y[/tex] in the given interaval
[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx[/tex]
Let us integrate [tex]\ln x[/tex] first.
let
[tex]u=\ln x, dv=dx[/tex]
[tex]du=\dfrac{1}{x}, v=x[/tex]
[tex]\int\ln x dx=udv[/tex]
Using integration by parts we get
[tex]uv-\int vdu[/tex]
[tex]=x\ln x-\int x\dfrac{1}{x}dx[/tex]
[tex]=x\ln x-dx[/tex]
[tex]=x\ln x-x+C[/tex]
So here
[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx\\ =2(x\ln x-x)_1^4\\ =2[(4\ln 4-4)-(1\ln 1-1)]\\ =2[4\ln 4-4+1]\\ =5.09\ units[/tex]
The area of the the region between the curve and horizontal axis is 5.09 units.
Find the equation of the line passing through (0,5) with a slope of 2/3
Answer:
y= 2/3x +5
Step-by-step explanation:
(0,5) is the y intercept and the slope is 2/3 so we can use the y intercept form
y = mx+b where m is the slope and b is the y intercept
y= 2/3x +5
Answer:
y= 2/3x+5
Step-by-step explanation:
Okay, to write the equation of a line you need two values. The y intercept and the slope. The y intercept has an x coordinate of zero, and lucky us, the point you were given has an x coordinate of zero so that's done. You were also given the slope, so you don't have to calculate it. Anyways, the formula of a line is written in slope intercept form usually, so y=mx+b. Just fill in the gaps, m= the slope and b=the y intercept. The slope is 2/3, and the y intercept is 5. So, inserting in the variables you get y=2/3x+5.
Hope that helps!
need halp solving this step by step to further understand. please and thank you!
Answer:
w=6
Step-by-step explanation:
Since the triangles are similar, we can use ratios to solve
4 3
----- = --------
8 w
4w = 3*8
4w = 24
Divide by 4
4w/4 = 24/4
w = 6
Answer:
As hard as this may seem, it's actually quite simple. Because these two figures are similar, their sides can be compared.
See how on the left side of both of the triangles the numbers are 4 and 8? This shows that the left triangle is twice as small as the right one, which means that if you multiply any of the sides of the triangle on the left by 2, you'll get the triangle on the right.
We can apply this to w. Look at the left triangle on the bottom and see how there is a 3. Well, we've already noticed how the triangle on the left just needs to be multiplied by 2 in order to get to the one on the right, so that's what we should do! When you multiply 3 by 2, you get 6 which is w.
So, long answer short, w is 6.
ILL GIVE YOU BRAINLIST !
b/2 - 1 as a verbal phrase
Answer:
b/2-1 has a verbal phrase can be one minus the quotient of b and 2.
The volume of a cube is 3,375 cubic inches. What is the measure of each side of the cube?
Answer:
l=w=h=15
Step-by-step explanation:
Volume of a cube= l*w*h
where l=w=h
[tex]l = {}^{3} \sqrt{ v} \: \: \: l = {}^{3} \sqrt{3375} = 15 [/tex]
15*15*15=3375
Hope this helps ;) ❤❤❤
The measure of each side of the cube will be 15 inches.
What is volume?The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. Volume is defined as the space occupied by an object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid
The cube has all the sides equal means that the length, width, and height of the cube will be the same. Let's suppose the length, width, and height of the cube is a.
The volume of a cube will be given by the formula:-
Volume = side³ = a³
a³ = 3375
a = ∛3375
a = ∛( 15 x 15 x 15 )
a = 15 cubic inches.
Therefore, the measure of each side of the cube will be 15 inches.
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sheila___ her case, look .( had picked,have picked , picked.)
Answer:
picked
Step-by-step explanation:
It is the only one that sounds correct.
Answer:
hi,
i think the answer can be picked
Step-by-step explanation:
picked is the answer
The manufacturer wants to estimate the proportion of their cars that get over 100 mpg. Their sample of 30 indicates that 28% can obtain over 100 mpg. Construct a 95% confidence interval for the population proportion.
Answer:
The 95% confidence interval is [tex]0.1193 < p <0.4407[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]m = 30[/tex]
The sample proportion is [tex]\r p = 0.28[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of the [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \sqrt{\frac{ ( \r p (1 - \r p ))}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ (0.28 (1 - 0.28 ))}{ 30} }[/tex]
=> [tex]E = 0.1607[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.28 - 0.1607 < p < 0.28 + 0.1607[/tex]
=> [tex]0.1193 < p <0.4407[/tex]
The salaries of 235 nurses were recorded and analyzed. The analyst later found that the highest salary was incorrectly recorded as 10 times the actual amount. After the error was corrected, the report showed that the corrected value was still higher than any other salary. Which sample statistic must have changed after the correction was made? mean median (know it is not this) mode minimum
The correct answer is A. Mean
Explanation:
In the analysis of numerical data, means refers to the average value. This is found by adding all the values, in this case, all the salaries and then dividing the total by the total of values, in this case, 235. This sample statistic is affected by each of the values that are added, due to this, if a value changes or was corrected, the mean needs to be revised. Also, this does not occur in the case of the minimum (lowest value), the median (value in the middle), or in the mode (most frequent value.)
Find the indicated angle measures. pls help i’m dyin lol
Answer:
utv = 24° wtx=113°
Step-by-step explanation:
I solved in the picture
hope this helps ^-^
The vertices of triangle PQR are listed below.
P(-5, 3), Q(-13, -3), R(-5, -9)
What is the perimeter of triangle PQR?
A.
32 units
B.
51 units
C.
22 units
D.
48 units
Answer:
A. 32 units
Step-by-step explanation:
First, we need to find all of the side lengths of triangle using distance formula:
[tex]Distance = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]Now, we can calculate length of PQ, QR and PR sides by using their vertices and above formula:
[tex]PQ=\sqrt{(-13-(-5))^2+(-3-3)^2} =\sqrt{8^2+6^2}=10[/tex] [tex]QR=\sqrt{(-5-(-13))^2+(-9-(-3))^2} =\sqrt{8^2+6^2}=10[/tex] [tex]PR=\sqrt{(-5-(-5))^2+(-9-3)^2} =\sqrt{0^2+12^2}=12[/tex]For perimeter we add up the length of all of its sides:
[tex]Perimeter = PQ +QR + PR=10+10+12=32[/tex]
Dave tried to evaluate 55 – 15 + 20 step-by-step.
55 - 15 + 20
Step 1: =40 + 20
Step 2: = 20
Find Dave’s mistake
Choose 1 answer:
A: step 1
B: step 2
C: Dave did not make a mistake
Answer:
Step 2
Step-by-step explanation:
In step 2 the expression was 40+20 which would have been 60 but he might have thought addition sign was subtraction so he did 40-20 which is 20 so he is wrong made mistake in step 2
Simplify the following expression and put in standard form:
(4x – 5x2) + (3x4 – 4x + 2) – (62° + 1)
Convert the decimal expansion of each of these integers to a binary expansion.
a) 321
b) 1023
c) 100632
Answer:
[tex]321_{10} = 101000001_{2}[/tex]
[tex]1023_{10} = 1111111111_2[/tex]
[tex]100632_{10} = 11000100100011000_{2}[/tex]
Step-by-step explanation:
Given
a) 321
b) 1023
c) 100632
Required
Convert to decimal
To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;
Solving (a)
321 / 2 = 160 R 1
160 / 2 = 80 R 0
80 / 2 = 40 R 0
40 / 2 = 20 R 0
20 / 2 = 10 R 0
10 / 2 = 5 R 0
5 / 2 = 2 R 1
2 / 2 = 1 R 0
1 / 2 = 0 R 1
Hence;
[tex]321_{10} = 101000001_{2}[/tex]
Solving (b)
1023 / 2 = 511 R 1
511 / 2 = 255 R 1
255 / 2 = 127 R 1
127 / 2 = 63 R 1
63 / 2 = 31 R 1
31 / 2 = 15 R 1
15 / 2 = 7 R 1
7 / 2 = 3 R 1
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]1023_{10} = 1111111111_2[/tex]
Solving (c)
100632 / 2 = 50316 R 0
50316 / 2 = 25158 R 0
25158 / 2 = 12579 R 0
12579 / 2 = 6289 R 1
6289 / 2 = 3144 R 1
3144 / 2 = 1572 R 0
1572 / 2 = 786 R 0
786 / 2 = 393 R 0
393 / 2 = 196 R 1
196 / 2 = 98 R 0
98 / 2 = 49 R 0
49 / 2 = 24 R 1
24 / 2 = 12 R 0
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]100632_{10} = 11000100100011000_{2}[/tex]
To attend a field trip, a person must be at least 10 years old. which graph best represents this situation?
Answer:
(b
Step-by-step explanation:
the line graph is showing this: x<10
Answer:
Option H (the third option)
Step-by-step explanation:
A person must be at least 10 years old.
Let the person's age be x years
therefore, he has to be x≥ 10 (the person's age has to be equal or more than 10 )
alicia rides her bike 4 miles due north and 3 miles due west to a playground. What is the shortest distance to alicias home from the playground
Answer:
5 miles.
Step-by-step explanation:
We would be using the Pythagoras Theorem to solve for this.
I have attached a diagram to better help you to better understand my explanation this.
The shortest distance from her playground to her house = Hypotenuse
Pythagoras Theorem for a triangle =
c² = a² + b²
Where c = Hypotenuse
a = 3 miles due west
b = 4 miles north
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25
c = 5 miles
Therefore, the shortest distance to Alicia's home from the playground is 5 miles.
write an expression for each sentence
1. The sum of the square of a number and a second number.
2. Three times the difference of a number and seven.
3. 9.85 less then the product of 37 and a number.
Answer:
x^2+y3(n-7)37x-9.85Step-by-step explanation:
1. If x represents a number, then x^2 represents its square. If y represents a second number, then the sum of that square and the second number is ...
x^2 + y
__
2. The difference of a number (n) and 7 is (n-7). Three times that difference is ...
3(n - 7)
__
3. If x represents a number, then the product of 37 and a number is 37x. 9.85 less than that is ...
37x - 9.85
Factorise:
( a²- 1) ( b²- 1) + 4ab
pls give a detailed explanation
pls answer it......
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{ a^2 b^2 + -a^2 + -b^2 + 1 + 4ab}[/tex]
Let's simplify step-by-step.
[tex]( a^2 - 1 ) ( b^2 -1) + 4ab[/tex]
Distribute:
[tex]=( a^2) (b^2) + (a^2) (-1) + ( -1) (b^2) + (-1) (-1) + 4ab[/tex]
[tex]= a^2 b^2 + -a^2 + -b^2 + 1 + 4ab[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
a²b² - a² - b² + 4ab + 1
Step-by-step explanation:
( a²- 1) ( b²- 1) + 4ab
(a²b² - a² - b² + 1) + 4ab
a²b² - a² - b² + 4ab + 1
Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 214 square feet. To the nearest tenth of a foot, how long can a side of his garden be?
Answer:
14.6 feet
Step-by-step explanation:
Let A be the area of a square and S be the length of one of its sides.
The area of a square is A = S². We know A = 214 in this problem, so:
214 = S²
√214 = S
S ≈ 14.629 ≈ 14.6 feet (to the nearest tenth of a foot)
Express the formula P=2L+2W in terms of the width,W. Use the formula to find the width when the perimeter is 70 and the length is 22.
Answer:
The width is 13Step-by-step explanation:
From the question
P=2L+2W
where
L is the length
W is the width
To make W the subject move 2L to the left side of the equation
That's
2W = P - 2L
Divide both sides of 2 to make W stand alone
We have
[tex]W = \frac{P - 2L}{2} [/tex]
when
P = 70
L = 22
W is
[tex]W = \frac{70 - 2(22)}{2} \\ W = \frac{70 - 44}{2} \\ W = \frac{26}{2} [/tex]
We have the final answer as
W = 13Hope this helps you
Answer:
Width W = 13
Step-by-step explanation:
P = 2L + 2W
if the perimeter P = 70
and Length L = 22
find the Width W
P = 2L + 2W
70 = 2(22) + 2W
70 - 44 = 2W
26 = 2W
W = 26 / 2
W = 13
therefore,
the Width W = 13
check:
P = 2L + 2W
70 = 2(22) + 2(13)
70 = 44 + 26
70 = 70 --- OK
Simplify the expression to a polynomial in standard form:
(x + 3)(2x^2+ 3x + 7) PLEASEEE HELP ME WITH THISS
Answer:
[tex]2x^3+9x^2+16x+21[/tex]
Step-by-step explanation:
So we have the expression:
[tex](x+3)(2x^2+3x+7)[/tex]
Use the distribute property. Multiply each term on the right by (x+3):
[tex](2x^2)(x+3)+(3x)(x+3)+(7)(x+3)[/tex]
Distribute further:
[tex]=(2x^3+6x^2)+(3x^2+9x)+(7x+21)[/tex]
Combine like terms:
[tex]=(2x^3)+(6x^2+3x^2)+(9x+7x)+21\\=2x^3+9x^2+16x+21[/tex]
A polynomial in standard form has terms in descending order based on degree.
And we have that. Thus, we are done :)
Triangle ABC is a right triangle. The sides measure AB = 6 and BC = 8. Use the
Pythagorean theorem to find CA.
Answer:
AC = 10 units
Step-by-step explanation:
From the picture attached,
Triangle ABC is a right triangle.
Opposite side of the right angle B = Hypotenuse (AC)
and the other two legs are AB and BC
Pythagoras Theorem states
(hypotenuse)² = (leg 1)² + (leg 2)²
AC² = AB² + BC²
AC² = (6)² + (8)²
AC² = 36 + 64
AC² = 100
AC = √100
AC = 10
Therefore, length of the hypotenuse (AC) = 10 units will be the answer.
Find an equation for the plane y=4x in cylindrical coordinates. (Type theta for θ in your answer.)
Answer:
sinθ - 4cosθ = 0Step-by-step explanation:
Given the equation of a plane in rectangular coordinates to be y = 4x.
The cylindrical coordinates of the axis is as given below;
x = rcosθ
y = rsinθ
z = z
Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;
y = 4x
rsinθ = 4( rcosθ)
rsinθ = 4rcosθ
sinθ = 4cosθ
sinθ - 4cosθ = 0
Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0
The equation of the plane y=4x in cylindrical coordinates is, [tex]sin\theta-4cos\theta=0[/tex]
Equation of plane:To find the equation of plane in cylindrical coordinates,
We have to substitute ,
[tex]x=rcos\theta\\\\y=rsin\theta\\\\z=z[/tex]
Given equation of plane is, [tex]y=4x[/tex]
Substitute values in equation of plane.
[tex]rsin\theta=4(rcos\theta)\\\\sin\theta=4cos\theta\\\\sin\theta-4cos\theta=0[/tex]
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