The expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The expression given in the problem is
f(x)=-4x³+x²-6x+8
The option given as,
(1) x² (-4x+1)-2(3x-4)(2) x(-4x²- x + 6) + 8(3) -4x³ + (x - 2)(x - 4)(4) -4(x³ - 2) + x(x - 6)From the given expression, if we take out x from the first three terms, it looks like option 2.
f(x)=-4x³+x²-6x+8
f(x)=x(-4x²+x-6)+8
From the given expression, if the last three terms factored, it looks like option 3.
f(x)=-4x³+x²-6x+8
f(x)=-4x³+x^2-4x-2x+8
f(x)=-4x³+x(x-4)-2(x-4)
f(x)=-4x³+(x-4)(x-2)
Rearrange the given expression, and make it looks like option 4.
f(x)=-4x³+x²-6x+8
f(x)=-4x²+8+x²-6x
f(x)=-4(x³-2)+x(x-6)
Thus, the expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
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Silver Springs Moving and Storage Inc. is studying the relationship between the number of rooms in a move and the number of labor
hours required for the move. Compute a correlation coefficient.
Rooms
Labor hours
Labor hours
Rooms
2.5
1
3
17
1
15
3
18
ed
1.5
35
1.5
28
2
19
33
9
40
ok
5
int
ences
8
16
17
2
15
2.5
16
2.5
24
3
3.5
4
4.5
5
The correlation coefficient of the dataset on the table is 0.8271
How to compute a correlation coefficient?See attachment for the proper table that represents the relationship
Next, we compute a correlation coefficient using a graphing calculator.
The graphing calculator has the following calculation summary:
X Values
∑ = 39.5Mean = 2.633∑(X - Mx)² = SSx = 20.733Y Values
∑ = 304Mean = 20.267∑(Y - My)² = SSy = 1410.933X and Y Combined
N = 15∑(X - Mx)(Y - My) = 141.467The correlation coefficient is calculated using:
[tex]r = \frac{\sum((X - \bar y)(Y - \bar x)) }{ \sqrt{(SSx)(SSy)}}[/tex]
So, we have:
[tex]r = \frac{141.467}{\sqrt{(20.733) * (1410.933)}}[/tex]
Evaluate
r = 0.8271
Hence, the correlation coefficient is 0.8271
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Match the trigonometric ratios with their values based on the triangle shown in the diagram.
The trigonometric ratios with their values are based on the triangle will be sin D = 4 / 5, sin C = 3 / 5, sin D x cos D = 12 / 25, tan C x tan D = 1, and cos C x tan D = 16 / 15.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The triangle is given below.
Then the trigonometric ratios with their values are based on the triangle shown in the diagram and will be
sin D = 4 / 5
sin C = 3 / 5
sin D x cos D = 4 / 5 x 3 / 5
sin D x cos D = 12 / 25
tan C x tan D = 3 / 4 x 4 / 3
tan C x tan D = 1
cos C x tan D = 4 / 5 x 4 / 3
cos C x tan D = 16 / 15
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John plots the point with the polar coordinates (3,5π6).
How does he plot this point?
Drag a value or phrase into each box to correctly complete the statements.
John first determines which line the angle of rotation places the point on. This line tells John that the point must lie in if r is positive or Response area if r is negative.
The radius of 3 tells John that the point lies on the third circle of the polar plane. The value of r is positive. Therefore, the point will lie Response area the angle of rotation.
This line tells John that the point must lie in Quadrant 1 if r is positive or Quadrant 2 if r is negative. Therefore, the point will lie Quadrant 3 or 4 the angle of rotation.
How to find Polar Coordinates?
Step 1; John will start plotting the point by first of all seeing the sign of the radius and the value of the given angle.
Step 2; John will make a circle of the given radius, and plot the point at an angle given as a coordinate on the circle.
If r is positive, then the point will lie in Quadrant 1 or 2. However, If r is negative, then the point will lie in Quadrant 3 or 4.
In case r is positive, the point will lie in the same quadrant as the angle of rotation.
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What do you call a line segment which passes throughthe center of the circle from on side to the other?
[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]
DiameterAnswer:
diameter of the circle
Step-by-step explanation:
A chord that passes through a circle's centre is a diameter of the circle.
find the area of the figure. use 3.14 for pi.
a 133.5
b 188.5
c 149.25
d 94.25
Answer:
d. 94.25 in²
Step-by-step explanation:
The area of this composite figure is the sum of the areas of a semicircle and a triangle. Each of those areas can be found using the appropriate formula:
semicircle: A = (π/2)r²
triangle: A = 1/2bh
__
semicircleThe semicircle has a radius equal to half its diameter. The radius is (10 in)/2 = 5 in. Its area is ...
A = (3.14/2)(5 in)² = 39.25 in²
triangleThe area of the triangle with base 11 in and height 10 in is ...
A = 1/2bh
A = 1/2(11 in)(10 in) = 55 in²
total areaThe area of the figure is the sum of the areas of the semicircle and triangle, so is ...
figure area = (39.25 in²) +(55 in²)
figure area = 94.25 in²
GIVING BRAINLIEST AND MAX POINTS! ANSWER ASAPPP! The initial velocity of a projectile is 217 ft/sec, and the firing angle is 12°. Calculate the horizontal distance.
a
599 feet
b
699 feet
c
499 feet
d
799 feet
Answer:
a) 599 feet
Step-by-step explanation:
** As the measure of distance is in feet, we must use the value of gravity in ft/s² **
Constant Acceleration Equations (in ft)
s = displacement in ftu = initial velocity in ft/sv = final velocity in ft/sa = acceleration in ft/s²t = time in s (seconds)Assuming that the projectile is fired at an angle of 12° above the horizontal.
Consider the vertical and horizontal motion separately.
Vertical motion
First, find time by resolving vertically, taking up as positive and
g = 32 ft/s²
[tex]\begin{aligned}\textsf{Using}\quad s & =ut+\dfrac{1}{2}at^2\\\implies 0 & = 217 \sin 12^{\circ}t+\dfrac{1}{2}(-32)t^2\\0 & = 217 \sin 12^{\circ}t-16t^2\\t(16t-217 \sin 12^{\circ}) & = 0\\16t & = 217 \sin 12^{\circ}\\t & = \dfrac{217 \sin 12^{\circ}}{16}\\t & = 2.819802307...\: \sf s\end{aligned}[/tex]
Horizontal motion
Resolving horizontally, taking right as positive:
(The horizontal component of velocity is constant, as there is no acceleration horizontally)
s = su = 217 cos 12°v = 217 cos 12°a = 0t = 2.819802307...[tex]\begin{aligned}\textsf{Using}\quad s & =ut+\dfrac{1}{2}at^2\\\implies s & = (217 \cos 12^{\circ})(2.819802307...)+\dfrac{1}{2}(0)t^2\\& =598.5256808...\end{aligned}[/tex]
Therefore, the horizontal distance is 599 ft (nearest foot)
Niki wants to buy all the fruits as shown on the menu. If she gets a discount of $50 off the cost of the Cherry and $25 each off the remaining fruits, how much will Niki pay after the discounts?
fruit menu
fruits. Quality. cost
1.cherry 11b. $150
2.bananas ¼ doz. $200
3.watermelon. 11b. $125
mangos. each. $ 75
Answer:
Niki will pay $425 after the discounts.
Step-by-step explanation:
Cherry originally costs 150$, and you can subtract the discount of 50$ from that to get 100$ total for cherries.
Banana originally costs 200$, and you can subtract the discount of 25$ from the original cost to get 175$ total for bananas.
Watermelon originally costs 125$, and after subtracting the discount of 25$, you can determine the total cost for watermelons, which is 100$.
Mangoes originally costs 75$, subtract the discount of 25$, and you get the total for mangoes at 50$.
Add the costs after discounts (100$ for cherry, 175$ for banana, 100$ for watermelon, 50$ for mangoes), and you get 425$, which is the total cost for the fruit after discounts.
Write the measure in degrees.
Hi Student!
Looking at the question, we are given a fraction that has a pi symbol. We learn in trigonometry that a whole circle is made up of 2 * pi and we know that a circle is 360 degrees. That means that just having pi means that we have 180 degrees.
Therefore, looking at the fraction that was given to us, we can basically interpret it as 180 degrees / 4. That will give us a solution of 45 degrees which is our final answer.
Answer:
[tex]45^{\circ}[/tex]
Step-by-step explanation:
[tex]\dfrac{\pi}4 = \left(\dfrac{\pi }{4} \times \dfrac{180}{\pi} \right)^{\circ} = \left( \dfrac{180}4 \right)^{\circ} = 45^{\circ}[/tex]
Which expression is another way to write 10,000?
10 × 10 × 10
10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10
==============================
[tex] \large \sf \underline{Question:}[/tex]
Which expression is another way to write 10,000?
==============================
[tex] \large \sf \underline{Answer:}[/tex]
[tex] \qquad\quad\large \bold{10 \times 10 \times 10 \times 10}[/tex]
==============================
[tex] \large \sf \underline{Solution:}[/tex]
By getting the answer you just multiply 10 directly by 10 until you get what you are looking for;
[tex] \rm{10 \times 10 = \pmb{100}}[/tex][tex] \rm{ 100 \times 10 = \pmb{1000}}[/tex][tex] \rm{1000 \times 10 = \pmb{10000}}[/tex][tex] \rm { \underline{ \pmb{10 \times 10 \times 10 \times 10 = 10000}}}[/tex]Hence, proven.
==============================
Answer:
Step-by-step explanation:
10000
Define an axiom in geometry
Answer:
In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful.
how to calculate annuity
Answer:
The formula for determining the present value of an annuity is PV = dollar amount of an individual annuity payment multiplied by P = PMT * [1 – [ (1 / 1+r)^n] / r] where: P = Present value of your annuity stream. PMT = Dollar amount of each payment. r = Discount or interest rate.
Step-by-step explanation:
Hope this helps :) :)
PLEASE HELP ASAP
What is an equation of the line that passes through the points (3, 2) and (6, -3)?
Answer:
(y+2)=2(x−3)
Or
(y−4)=2(x-6)
Or
y=2x−8
Step-by-step explanation:
Answer:
[tex]y= -\dfrac{5}{3} x+7[/tex]
In order to find equation:
Find slope:
[tex]\sf slope: \dfrac{y_2- y_1}{x_2 -x_1} = \dfrac{rise}{run}[/tex] where (x1, y1), (x2, y2)
[tex]\hookrightarrow \sf slope: \dfrac{-3-2}{6-3}[/tex]
[tex]\hookrightarrow \sf slope:- \dfrac{5}{3}[/tex]
Find Equation:
[tex]\boxed{\sf y - y_1 = m(x_1 -x)}[/tex] "m" is slope
[tex]\sf \rightarrow y-2 = -\dfrac{5}{3} (x-3)[/tex]
[tex]\sf \rightarrow y-2 = -\dfrac{5}{3} x+5[/tex]
[tex]\sf \rightarrow y= -\dfrac{5}{3} x+5+2[/tex]
[tex]\sf \rightarrow y= -\dfrac{5}{3} x+7[/tex]
URGENT which of the following linear equations represents the data chart
Answer:
y = -x + 7
Step-by-step explanation:
y = x + 5 works for the first row, but fails for the rest.
y = x + 3 fails for the first row
y = -x + 7 works for the first row ( -1 + 7 = 6)
It works for the second row ( -2 + 7 = 5)
It works for the third row ( -3 + 7 = 4)
And it works for the final row ( -4 + 7 = 3)
If a 714-mile trip takes 17 hours, the average speed is?
Answer:
42 mph
Step-by-step explanation:
brainliest/crown please :)
Point M(4, 3) is translated according to the rule (x,y) → (x+2, y-5). What are the coordinates of M'?
Answer: (6,-2)
Step-by-step explanation:
[tex]M'=(4+2, 3-5)=\boxed{(6,-2)}[/tex]
simplify (b-a)U(c-a)?
Answer:
Step-by-step explanation:
There are three different colored candies:
red, green, and white. The probability of
selecting a red candy is 2/5 and the probability
of selecting a green candy is 1/4 What is the
probability of selecting a white candy?
PLEASE HELP
Answer:
7/20
Step-by-step explanation:
add the probabilities together and minus it by the LCM which is 20
Wendy’s Big Bacon Classic contains how many calories after calculating the
nutrients below?
44 grams Carbohydrate= 44×4 =176_ Calories
36 Grams of Fat= 36×9 = 324 _ Calories
37 Grams of Protein= 37×4 =_148__ Calories
4. What is the percentage of total calories that come from fat in question 3?
Fat Calories:__________
% of Total Calories _________
help with number 4 please and explain it goes with the top answer
Answer:
Fat Calories: 342
50% of Total Calories
Step-by-step explanation:
Total calories:
Carbohydrates:
176
Fat:
324
Protein:
148
Total:
176+324+148=648
648/342 = 2
Meaning that half of the calories come from fat.
After sinéad lost 20% of her money, she had $1600 left. How much money did sinead lose?
Answer:
x - beginning money
x - .20x = 1,600
.80x = 1.600
Original money = 2,000
Therefore, Sinead lost $400.00
Step-by-step explanation:
Question 2 of 40
If a population is.
a sample of the population could be
A. 6th grade students whose last name begins with "T"; all students
in 6th grade
B. people in the front row; the entire audience
C. all the people at the park; the kids on the playground
о
D. trees over 20 feet tall; the entire forest
All of these can be samples but the best example is 6th grade students whose last name begins with "T"; all students in 6th grade
What is a sample?A sample refers to a small portion of a population. Most samples are selected randomly to make sure the sample represents all the population but they can also be selected based on a specific criterium.
What is one example of a sample?One example of this concept is 6th grade students whose last name begins with "T"; all students in 6th grade because the student whose last name begins with "T" are a fraction of all the population. Moreover, they are more likely to represent all the population.
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How many solutions does this system have?
x-3y=4
-2x+6y=3
O one
O two
O an infinite number
Ono solution
Answer:
two solutions B
Step-by-step explanation:
x-3y=4
-2x+6y=3
A rectangle has a width that measures 11 in. and a length that measures 5.5 in.
Determine the area of the rectangle.
Answer: 60.5 in
Step-by-step explanation:
Area of rectangle = length times width
Length = 5.5 in
Width = 11 in
11 x 5.5 = 60.5
The area of the rectangle is 60.5 in
Two similar polygons have a scale factor of three. The smaller polygon has an area of 42 cm² and perimeter of 50 cm. what is the area of the larger polygon? and what is the perimeter of the larger polygon?
Step-by-step explanation:
a scale factor applies to every line, that means also to every side of the polygon.
the area of a polygon is always created out of the product (multiplication) of 2 dimensions (or sides).
while a perimeter is a pure sum of sides.
so the perimeter grows by the same factor as the sides : scale factor 3.
the perimeter of the larger polygon is therefore :
50 × 3 = 150 cm
and the area of the larger polygon ?
remember, that the area is always the product of 2 sides (or the sum of products of 2 sides).
and so, the scale factor enters these multiplications twice, and it gets therefore squared : 3×3 = 9.
so, the area of the larger polygon is then
42 × 9 = 378 cm²
Can anyone help me with this please?
Step-by-step explanation:
since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.
if we cannot find it for the first point, then we would need to try the same thing for the serving points.
let's put (0, 6) into the first equation :
-2×0² + 6 = 6
6 = 6 true
let's put it into the second equation ;
4×0² + 3×6 = 28
18 = 28 false
that eliminates the first 2 answers.
let's put (-1, 4) into the first equation :
-2×(-1)² + 4 = 6
-2×1 + 4 = 6
-2 + 4 = 6
2 = 6 false
that eliminates the third answer.
let's put (-1, 8) into the first equation :
-2×(-1)² + 8 = 6
-2 + 8 = 6
6 = 6 true
let's put it into the second equation :
4×(-1)² + 3×8 = 28
4 + 24 = 28
28 = 28 true
and because the square function delivers the same result for -1 and +1, it is also true for the second point.
and the 4th answer is therefore correct.
which expression is equivalent to 2^5*2^x?
What does 2 3/4 x 2 add all together?
Step-by-step explanation:
its confusing the way the numbers are placed. But..
if the question is 2 whole number times 3 ÷4x2
=2×3/4×2
=6/8
=3/4
if it's 2 whole number, 3/4 fraction, multiplied by 2
2³/⁴ × 2
=4×2+3=11/4
=11/4 ×2
=11/2 or 5 1/2
A bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books. If a book is selected at random. What is the probability of selecting a biography or a mystery?
The probability of selecting a biography or a mystery is 0.8
How to get the probability?
We assume that all the books have the same probability of being randomly selected.
The probability of getting a particular type of book is given by the quotient between the number of these books and the total number of books.
Here we want to find the probability of selecting a biography or a mystery, there are 9 mysteries and 7 biographies, and a total of 20 books in the shelf, so the probability is:
P = (7 + 9)/20 = 16/20 = 4/5 =0.8
The probability is 0.8
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fractions were never my strong suit can anyone help?
Answer:
See below ~
Step-by-step explanation:
Find the decimal values of the fractions on each side :
Left side Right side
⇒ 4/10 = 0.4 ⇒ 2/5 = 0.4
⇒ 1/2 = 0.5 ⇒ 9/12 = 0.75
⇒ 1/4 = 0.25 ⇒ 2/8 = 0.25
⇒ 3/4 = 0.75 ⇒ 5/10 = 0.5
Hence, the matched fractions are :
4/10 ↔ 2/5
1/2 ↔ 5/10
1/4 ↔ 2/8
3/4 ↔ 9/12
Answer:
Step-by-step explanation:
3x-4y=0 2x+y=110 no solution
Answer:
(x, y) = (40, 30)
Step-by-step explanation:
A graphing calculator can show you the solution to this system of equations is (x, y) = (40, 30). That is the point of intersection where the two lines cross.
__
An algebraic solution can be found by using the substitution method. An expression for y can be found using the second equation:
y = 110 -2x . . . . . . subtract 2x from both sides
Using this in the first equation gives ...
3x -4(110 -2x) = 0 . . . . substitute for y
11x = 440 . . . . . . . . . simplify, add 440
x = 40 . . . . . . . . . . divide by 11
y = 110 -2(40) = 30
The solution is (x, y) = (40, 30).
Is the following statement true? Justify your answer to get credit: “If X1, · · · , Xn are independently distributed, then for large enough n, the central limit theorem says that the sample mean Xn has a normal distribution.”
Using the Central Limit Theorem, it is found that the statement is true, as for sample sizes of 30 or more, the sampling distribution of sample means is normal.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
Hence, the statement is true, as for sample sizes of 30 or more, the sampling distribution of sample means is normal, no matter the underlying distribution of the variable.
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