The two rational expressions will be; (x + 2)/(x² - 36) and 1/(x² + 6x)
How to simplify Quadratic Expressions?We want to determine the two rational expressions whose difference completes the equation.
The two rational expressions will be;
(x + 2)/(x² - 36) and 1/(x² + 6x)
Now, this can be proved as follows;
Step 2 [(x + 2)/(x² - 36)] - [1/(x² + 6)]
= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]
Step 3; By subtracting, we have;
[x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]
Step 4; By further simplification of step 3, we have;
[x² + x + 6]/[x(x-6)(x + 6)]
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Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 560, 468, 685, 534, 658, 593. Find a 95% confidence interval for the mean sale price in San Luis Obispo County.
The interval for mean sale price is $582
According to statement
The given rates are 560, 468, 685, 534, 658, 593
Now,
Sample mean = X / n
Put the values in it and then
(560+ 468+ 685+ 534+ 658+ 593) / 6 = 582.1667
and use this formula S = sqrt [ X2 - n 2 / (n-1) ]
and put the values in these and
S = sqrt [ X2 - n 2 / (n-1) ] = 95.97179
So, The interval for mean sale price is $582
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Identify the type i error and the type ii error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to.
Option D: Type I error ("Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15").
Option B: Type II error ("Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15").
Type I error:
A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
B. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
C. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
A Type I error is when the null hypothesis is rejected when it is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".
The right option is D (reject the null hypothesis when it is true).
Type II error:
A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
B. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
C. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
A Type II error is when the null hypothesis is failed to be rejected when the alternative hypothesis is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".
The right option is B (failed to reject the null hypothesis when it is false).
The options A and C are correct decisions, as reject the null hypothesis when it is false (Option C) and not reject the null hypothesis when it is true (Option A).
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solve this mathematical equation 3x=5+7
Answer:
x=4
Step-by-step explanation:
3x=5+7
7+5=12
12/3=4
x=4
Hope this helps!!
Answer:
x=4
Step-by-step explanation:
add like terms
3x =5+7
3x=12
divide both sides by 3
3x=12
3 3
x=4
Samual has a collection of toy cars his favorites are the 27 red ones which makes up 60% of his collection how many toy cars dose he have??
Answer:
45
Step-by-step explanation:
Use khan acedaemy
Find the area of each figure. GEOMETRY PLS HELPPPP
Answer:
180
Step-by-step explanation:
For each of the two right triangles, by the Pythagorean theorem, she shared side is of length 15. So, the area of each of the top two rectangles is (½)(8)(15), so their combined area is 120.
Moving onto the trapezoid, we can use the formula for the area of a trapezoid to determine its area is (½)(14+16)(4)=60.
So, the answer is 120+60=180.
When f = 12, the value on the left side of the equation is
Answer:
12
Step-by-step explanation:
In an equation left side = right side.
Solve the following using the distributive property:
8x+12=2(x-3)
Answer:
x = - 3
Step-by-step explanation:
8x + 12 = 2(x - 3) ← distribute the parenthesis by 2
8x + 12 = 2x - 6 ( subtract 2x from both sides )
6x + 12 = - 6 ( subtract 12 from both sides )
6x = - 18 ( divide both sides by 6 )
x = - 3
Answer:
x = -3
Step-by-step explanation:
you first distribute 2(x-3) which gives you 2x-6 so 8x+12=2x-6.
next you move the terms to the correct side so you subtract 12 from the left side and subtract 2x from the right side then move them to the other side so you end up with 8x-2x=-6-12.
then you combine like terms so you will have 6x=-18.
then divide both sides by 6 which gives you x = -3.
8x+12=2(x-3)
8x+12 = 2x-6
8x-2x = 6-12
6x = -18
x = -3
Find the inverse of f(x)=5x^2-3
[tex]\large\boxed{y=\pm\sqrt{\frac{x+3}{5}}}[/tex]
To find the inverse, swap the [tex]y[/tex] (or [tex]f(x)[/tex] in this case) and the [tex]x[/tex], then solve for [tex]y[/tex].
[tex]\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\\frac{x+3}{5}&=\frac{5y^2}{5}\\\frac{x+3}{5}&=y^2\\\pm\sqrt{\frac{x+3}{5}}&=\sqrt{y^2}\\\pm\sqrt{\frac{x+3}{5}}&=y\end{aligned}[/tex]
HELP! BRainliest +20
A function f is defined such that 8f(x)=f([tex]\frac{1}{8}[/tex]x) for all values of x, and f(4) = 24. What is the value of f(32) ?
The value of f(32) is 3
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
8f(x) = f((1/8)x)
It is also given that
f(4) = 24
now to determine the value of f(32)
8 * f(32) = f((1/8) *32)
8 * f(32) = f(4 )
f(32) = 24 /8 = 3
Therefore the value of f(32) is 3
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Suppose a batch of steel rods produced at a steel plant have a mean length of 176 millimeters, and a variance of 100. If 446 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 millimeters
The probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
Mean length of the population (μ) = 176 mm.
Variance of the population (σ²) = 100.
Therefore, the standard deviation of the population (σ) = √100 = 10.
The sample size (n) = 446.
The mean of the sample = the mean of the population = μ = 176 mm.
The standard deviation of the sample (s) = σ/√n = 0.4735137.
We are asked to find the probability that the sample rods would differ the population mean by greater than 0.65 mm, that is,
either the length of the sample rods is less than (176 - 0.65) =175.35
or the length of the sample rods is more than (176 + 0.65) = 176.65.
This can be shown as P(X < 175.35 or X > 176.65) = 1 - P(175.35 < X < 176.65) = 1 - Normalcdf(175.35,176.65,176,0.4735137) = 1 - 0.8302 = 0.1698 or 16.98%.
Thus, the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
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What is the relationship between the angles?
Another answer is none of the above.
For the following exercises, graph the given functions by hand.
41. y = −| x |
Using translation concepts, the graph of the function y = -|x| is given at the end of this answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Graph y = -|x| is a reflection over the x-axis of the function y = |x|, and both functions(|x| in red, -|x| in blue) are given in the graph at the end of this answer.
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For what values of the variable are the following expressions defined?
7a/3+a
**The equation is given below**
**Please Help, include an explanation, and a equation/answer that can be entered on learning websites to answer the question**
Answer:
The Expression will be defined if the denominator is not equal to 0 since any number divided by 0 is undefined.Therfore our main priority here is to check the denominator only because it's the only part that can make the expression undefined the expression will be defined for all real numbers (a) BUT 3+a must not equal to 0 therfore (a) can be all real numbers but must never be equal to -3Step-by-step explanation:
[tex]a \: is \: an \: element \: of \: all \: real \: numbers \: but \: not \: not \: equal \: to \: -3[/tex]HOPE THIS HELPS!Fracciones heterogeneas
The information given illustrates that the equivalent fraction will be 2/6.
How to calculate the fraction?It should be noted that equivalent fraction simply means the fractions that are the same.
In this case, we are given 4/6 and 1/3. They have different numerators and denominators. The question is simply to change 1/3 to another fraction that has a denominator of 6.
This will be illustrated. The equivalent faction to 1/3 will be:
= 1/3 × 2/2
= 2/6
Therefore, the answer is 2/6.
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S
V
E
M
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Which of the following inequalities are correct?
Some of the numbers involved are shown on the number line below.
Choose all answers that apply:
12-18
-20
-18-12
-12 < 18
-12
←||||*|||||
-10
0
10
18
20
Answer:
I think -10 is the answer
In the triangle below, what is the cosine of 62 degrees?
Answer:
A. 8/17
Step-by-step explanation:
Cosine = adjacent over hypotenuse
Adjacent to angle 62 is 8 (The two angles are said to be adjacent angles when they share the common vertex and side).
The hypotenuse is 17 (opposite of right angle)
A rectangular shaped desk has a length of 30 inches and a width of 24 inches. A desk with a similar shape has a length of 48 inches. What is the width of this desk? ((solve fast!!))
The width of the desk will be 38.4inches
Similar shapesA rectangle is a quadrilateral that has 4 sides and angles.
If a rectangular shaped desk has a length of 30 inches and a width of 24 inches and a desk with a similar shape has a length of 48 inches, the width of the desk will be calculated using this expression;
l/w = L/W
30/24 =48/W
Cross multiply
30W = 24 * 48
W = 38.4inches
Hence the width of the desk will be 38.4inches
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The table below shows the number of pages Ilana read during summer vacation. Is the relationship between the number of pages and the number of days a proportional relationship? Why or why not?
Days: Pages:
1////////// 85
2 //////////170
3 //////////249
4 ////////////340
5 /////////////435
Answer Choices:
1.) The relationship is proportional because the ratio of pages to days is 85.
2.) The relationship is proportional because the ratio of pages to days is 87.
3.) The relationship is not proportional because the number of pages is not constant.
4.) The relationship is not proportional because the ratio of pages to days is not constant.
No links; only answer if you know
The correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.
What is a linear relationship?A linear relationship is a relationship in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.
A linear relationship with two variables, when graphed on the cartesian plane with axes of those variables, gives a straight line.
For the given relationship to be proportional, the number of pages read should be the same every day. Therefore, the ratio of the number of pages to the number of days should be equal.
85/1 = 85
170/2 = 85
249/3 = 83
340/4 = 85
435/5 = 87
Hence, the correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.
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For the following exercises, determine whether the functions are even, odd, or neither.
19. Solve |2x − 3 | = 17.
Answer:
The solutions of the equation |2 x-3|=17
are x=10
and x=-7
Step-by-step explanation:
Given equations is |2 x-3|=17.
It is required to find out the values of x satisfying the given equation.
To find it out, use the fact that the solution of this type of equation is 2x-3=17.
Or 2x-3=-17 and simplify the equations using simple mathematical operations.
Step 1 of 2
Solve the equation 2x-3=17,
Add 3 on both sides of the equation 2x-3=17,
2x-3+3=17+3
2x=20
Divide by 2 on both sides of the equation 2x=20,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{20}{2} \\&x=10\end{aligned}$$[/tex]
Step 2 of 2
Solve the equation 2x-3=-17,
Add 3 on both sides of the equation 2x-3=-17,
[tex]$2 x-3+3=-17+3$\\ $2 x=-14$[/tex]
Divide by 2 on both sides of the equation 2x=-14,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$[/tex]
Determine the inverse of g(x)
of g(x) = (x - 3)²
Answer:
The inverse of g(x) should be [tex]\sqrt{(x-3)}[/tex].
Step-by-step explanation:
The inverse means the opposite. The opposite of a term or expression squared will be the terms or expression square rooted.
The inverse of (x-3)² will be [tex]\sqrt{x-3}[/tex]
Hope this helps!
Please mark brainliest! Thanks!
Answer:
g(x)⁻¹ = √x + 3
Step-by-step explanation:
To find the inverse of an expression is to reverse the expression. This can be done by swapping the input and output variables. In other words, in g(x), you want to swap the places of the "x" variable the "y" variable.
Remember, g(x) = y.
y = (x - 3)² <----- Original function
x = (y - 3)² <----- Swap the variables
Now, you want to set the equation equal to "y" again. This can be done by rearranging/simplifying the expression.
x = (y - 3)² <----- Swapped variables
√x = √(y - 3)² <----- Take the square root of both sides
√x = y - 3 <----- Eliminate parentheses from previous step
√x + 3 = y <----- Add 3 to both sides
If g(x)⁻¹ represents the inverse of g(x), the new function is:
g(x)⁻¹ = √x + 3
what would be this answer for the algebra thing
Answer:
c. 4x + 20 = 140
Step-by-step explanation:
Perimeter = 140 feet
Width = L + 10
P = 2w + 2L
P = 2(L + 10) + 2L
P = 2L + 20 + 2L
P = 4L + 20
Find the indicated probability.
In one town, 39% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.
Using it's concept, it is found that there is a 0.152 = 15.2% probability that they are both Democrats.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Two voters are selected, each with 39% probability of being Democrats, hence the probability of both being Democrats is given by:
p = (0.39)² = 0.152.
0.152 = 15.2% probability that they are both Democrats.
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Answer: 0.152
Step-by-step explanation:
help asappppp
please
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The graphs can be described as shown below.
A.) The first graph has the y-intercept at 2. Therefore, the first graph can be described by the equation, y =5x + 2.
B.) For the second graph, the graph passes through the point (-1,0). Therefore, if we substitute the value of y as 0 in the equation y=3x+3, we will get x=-1.
Hence, the equation of the second graph is y=3x+3.
C.) For the third graph, the graph passes through the point (-1.5,0). Therefore, if we substitute the value of y as 0 in the equation y=2x+3, we will get x=-1.5.
Hence, the equation of the second graph is y=2x+3.
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The relation C= -31 t² - 80 t + 310 describes the cockroach population at
MCVI, where C is the number of cockroaches in thousands, and t is the time
in days. How many cockroaches are there at the start?
Answer:
310,000
Step-by-step explanation:
Since t represents time, the start would represent when no time has passed or in other words, when t=0, which is the y-intercept. You can plug in t as 0, but it's a bit redundant, since the y-intercept of a quadratic equation in the form: [tex]f(x)=ax^2+bx+c[/tex] will have a y-intercept at (0, c) where c is the constant, since whenever you plug in 0 as x, the ax^2 becomes 0 (since 0^2 = 0, and a * 0 = 0 since anything multiplied by 0... is 0) and the same thing goes for the bx, leaving the c alone. This means the y-intercept of the function is (0, 310) and since it's in the thousands there is 310,000 at the start
Answer:
310,000
Step-by-step explanation:
hope it helps!!!
10 points
please help me now!!!!
Answer:
Can't do much without a direct question or embedded image.
1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.
2. Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
3. A dog pen is 3 1/3 yards wide by 5 2/3 yards long. What is the area of the dog pen?
The area of the garden is 33 ft².
The number of tiles required to cover the floor is 17 tiles.
The area of a dog pen is 170/9 square yards.
We need to find the area and perimeter for the given questions.
What are the formulas to find the perimeter and the area of a rectangle?The formula to find the perimeter of a rectangle=2(Length+Breadth)
The formula to find the area of a rectangle=Length×Breadth.
Given that, a small garden has a perimeter of 24 1/4 ft and the length is 8 ft.
Now, perimeter = 2(8+Breadth)
⇒24 1/4=16+2×Breadth
⇒97/4-16=2×Breadth
⇒Breadth=97-64/4×2=33/8 ft
Now, Area=8×33/8=33 ft²
Therefore, the area of the garden is 33 ft².
Given that, the floor measures 4 1/2 ft by 3 3/4 ft.
The area of a floor=Length×Breadth=9/2×15/4=135/8 ft²
Number of tiles to cover the floor=135/8=16.875
Therefore, the number of tiles required to cover the floor is 17 tiles.
Given that, a dog pen is 3 1/3 yards wide by 5 2/3 yards long.
Now, the area of a dog pen=10/3×17/3=170/9 square yards.
Therefore, the area of a dog pen is 170/9 square yards.
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Draw an angle that measures 260° in standard position.
Answer:
attached
Step-by-step explanation:
Question 3 of 6
Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution set.
H
5 = 81
FOL
625
125
256
+243
= 32
Submit
64
Step-by-step explanation:
HOPE THIS HELPS!.....
ATTACHED IS THE SOLUTION!Answer: i hope this helps
Step-by-step explanation:
please help its timed i will give brainlyest
Answer:
20
Step-by-step explanation:
Long Division, cancel the zeroes, then 80/4 which is 20
Answer:
20
Step-by-step explanation:
8000/400= 20
John is throwing a dart at a dartboard. There are 4 rings that surround the bull's-eye ring,
which is located at the center of the dartboard.
The radius of the bulleyes region is 1 cm. The
radius of the first ring surrounding the bulleyes
is 2 cm more than that of the bulleyes and
the radius of every ring after that is 1 cm
more than that of the preceding ring. What is
the probability of John getting a dart on the
bulleyes if he cannot miss the darboard but is
randomly aiming at it?