The average rate of change for this function for the interval from x = 2
to x = 4 is 20
How to determine the average rate of change?The function is given as:
x y
0 18
2 32
3 50
4 72
The average rate of change at the interval from x = 2 to x = 4 is calculated using:
m = (f(4) - f(2))/(4 - 2)
Using the table values, we have:
m = (72 - 32)/(4 - 2)
Evaluate
m = 20
Hence, the average rate of change is 20
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To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?
The height of the pole is 6.50 meters
How to calculate the height?To calculate the height of the pole, we will use of the following equivalent ratios.
By Pythagoras theorem, we have:
[tex]x ^2 = 2^2 + 3^2\\\\x ^2 = 4 + 9\\\\x = \sqrt{13}[/tex]
So, we have:
[tex]h = \dfrac{\sqrt{13}^2 }{2} \\\\h = \dfrac{13}{2}\\\\h = 6.5[/tex]
Hence, the height of the pole is 6.50 meters
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Find the solution to the system
of equations.
432G
K
3
-4-3-2-1 1 2 3 4
-1
==x+2
21
4234
([?], [ ])
Enter
Answer:
(-2, 0)
Step-by-step explanation:
The solution to the system is the point where the graphs intersect.
A=CD-B how to solve for B
Answer:
Step-by-step explanation:
B=CD-A
if m=p/2+3r. find the value of p if r=1 and m=5
Answer:
p = 4
Step-by-step explanation:
[tex]m =\frac{p}{2} +3r[/tex]
[tex]\Longrightarrow m-3r=\frac{p}{2}[/tex]
[tex]\Longrightarrow 2m-6r=p[/tex]
[tex]\Longrightarrow p = 2m-6r[/tex]
If m = 5 and r = 1
Then
p = 2(5) - 6(1)
= 10 - 6
= 4
Write a slope-intercept equation for a line that passes through (-2,1) and (3,-14).
Skyler, Robert, and Kaitlyn all solve the same exponential problem but have different approaches. Skyler Robert Kaitlyn 729=9 729=9 729=9 (36)=9 (93)=91 (36)=32 6x = 9 3x = 1 6x = 2 x = 96 x = 13 x = 26 x = 32 x = 13 Explain Sklyer's processes. Is Skyler correct? If not, where did she go wrong? Explain Robert's processes. Is Robert correct? If not, where did he go wrong? Explain Kaitlyn's processes. Is Kaitlyn correct? If not, where did she go wrong?
The justification for whether Skyler, Robert, or Kaitlyn was right or wrong stems from how they went about their processes:
Skyler erred by failing to equalize the bases of both sides before equating the exponents.Robert is right since he equalized the exponents before comparing the bases of the two sides.Since Kaitlyn made the bases of both sides equal before equating the exponents, she is accurate.1) SKYLER'S PROCESS:
Skyler wants to resolve the following issue;
Reduce 729 to the lowest base possible as a first step; [3^(6)]^x = 9
729^(x) = 9
The next thing she did was convert 6x to 9.
Since both sides must have the same base when dealing with exponent equality, she may have transformed 9 to have the same base of 3 as the left hand side before equating the exponents.
So Skyler is wrong.
2) ROBERT'S PROCESS:
Skyler failed to capture both bases equally, as we witnessed, but Robert has now made the right decision by;
9^(3x) = 9¹
After which he equated the exponents to get;
3x = 1
x = 1/3
Thus; Robert is correct
3) KAITLYN'S PROCESS:
Kaitlyn is also accurate since she adhered to the same method, which calls for comparing bases before comparing exponents.
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urgent help algebra 2 quick please
Answer: y = -3/2x + 6, y intercept is (0, 6)
Step-by-step explanation: You are dividing 2 from both -3x and 12. -3/2x cannot be simplified any further unless it's a decimal, so we leave it as -3/2x. But, since the equation was y = -3x+12 originally, we divide 12 from 2 as well and not just from 3x, and we get 6.
Hope this helped.
Which graph represents the function f(x)=−3x−2?
Answer:
Step-by-step explanation:
Which values of x and y would make the following expression represent a real number?
(4 +51)(x + yı)
O x = 4, y =
O x=-4, y = 0
Ox = 4, y = -5
O x = 0, y = 5
The values of x and y would make the following expression represent a real number is 4 and -5 respectively
Complex and real numberThe standard form of writing a complex number is given asl
z= x + iy
where
x is the real part
y is the imaginary part
Given the expression below;
(4 +5i)(x + yi)
Expand
4x + 4yi + 5ix + 5y(-1)
4x + 4yi + 5ix - 5y
Hence the values of x and y would make the following expression represent a real number is 4 and -5 respectively
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List five rational numbers between:
−4
7
and
1
2
5 rational number between -47 and 12 are {-46, -45, -44, -43, -42}
How to find the rational numbers?
Remember that any integer is also a rational number.
So, if we want to find 5 rational numbers between -47 and 12, we can just find 5 integers between these two numbers.
To do that, we can just add 1 to the lowest bound, we will et:
-47 + 1 = -46
-45 + 1 = -45
-44 + 1 = -44
-43 + 1= -43
-43 + 1 = -42
So 5 rational number between -47 and 12 are {-46, -45, -44, -43, -42}
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Write and simplify the equation you would use to solve the problem below.
A farmer builds a rectangular pen with a perimeter of 116 feet. If the length is 5 feet more than the width, what is the width?
A.w + 5 = 116
B.4w + 10 = 116
C.2w + 5 = 116
D.2w + 10 = 116
need a hand i cant figure this one out
Answer:
4w + 10 = 116
Step-by-step explanation:
Call the width w.
The length is 5 more than that, so the length is w + 5
Perimeter is 2w + 2l
2w + 2(w+5) = 116
Distribute the 2 to the values in the parentheses.
2w + 2w + 10 = 116
Combine like terms
4w + 10 = 116
20 percent of 180 hours
Answer:
36 hours
Step-by-step explanation:
To find the percentage of a number, change the percent to decimal form
20 percent = .20
Multiply this by the number
.20 * 180
36
20 percent of 180 = 36
if f(x)=x+10 find f(7)
Answer:
17
Step-by-step explanation:
→ Substitute 7 f(x) into the function
7 + 10
→ Solve
17
Answer:
f(7) = 17
Step-by-step explanation:
To find f(7), substitute x = 7 in the function. Thus, you will receive:
[tex]\displaystyle{f(7)=7+10}\\\\\displaystyle{f(7)=17}[/tex]
Henceforth, the value of f(7) is 17.
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https://brainly.com/question/27923727Find each percent of change. 30 is decreased to 6
Answer:
80
Step-by-step explanation:
we know that 1 percent of 30 is just 30 / 10 which is 3. Is 6 a multiple of 3? yes it is. 6 / 3 = 2. that means 6 is 20 percent of 30 but it hasn't been decreased by 6, it is 6. meaning that the answer is 100 - 20 which is 80
A binomial experiment has the given number of trials N and the given success probability P.
N=8 and P=0.1
P(1)
The probability of the success will be 0.3826.
What is binomial distribution?Bernoulli's trials are those trials which end up randomly either on success (with probability p) or on failures (with probability 1- p = q (say))
The probability that out of n trials, there'd be x successes is given by
[tex]\rm P(x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
We have
n = 8
p = 0.1
q = 1 – 0.1 = 0.9
x = 1
Then we have
P(1) = ⁸C₁ x (0.1)¹ x (0.9)⁷
P(1) = 0.3826
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a die is tossed twice and the number of dots facing up in each toss is counted and noted in the order of occurrence. (a) find the sample space. (b) find the set a corresponding to the event “number of dots in first toss is not less than number of dots in second toss.” (c) find the set b corresponding to the event “number of dots in first toss is 6.” (d) does a imply b or does b imply a? (e) find and describe this event in words. (f) let c correspond to the event “number of dots in dice differs by 2.”
A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.
a) The sample space is given as:
Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
What is the sample space?A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.
b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.
{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}
c) find the set b corresponding to the event number of dots in the first toss is 6.
{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
e) a does not imply b or does b imply a.
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A rectangular basketball court measures with a length of 82yds and
Width of 38 yards What is the perimeter and area?
Answer:
area:3116 perimeter:240
Step-by-step explanation:
the formula of area is always length x width=82x38 =3116the formula for the perimeter is always length+length+width+width=82+82+38+38 =240Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}\circ\leftharpoonup}}[/tex]
Pelet'rimeter =
Area = 3116 cm^2
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}\circ\leftharpoonup}}[/tex]
[tex]\bullet[/tex] Let's work out the perimeter
[tex]\twoheadrightarrow\sf P=2(a+b)[/tex]. a=length & b=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf P=2(82+38)[/tex]
[tex]\bullet[/tex] Perform the addition operation
[tex]\twoheadrightarrow\sf P=2\cdot120[/tex]
[tex]\bullet[/tex] Multiply and obtain the perimeter
[tex]\twoheadrightarrow\sf P=240cm[/tex]
[tex]\bullet[/tex] Now let's find the area
[tex]\twoheadrightarrow\sf A=lw[/tex] l=length w=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf A=82\cdot38[/tex]
[tex]\bullet[/tex] Multiply and obtain the area
[tex]\twoheadrightarrow\sf A=3116cm^2[/tex]
--
Hope that this helped! Best wishes.
[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]
--
Can someone please help me? I’ll give brainliest to the first person who gets it right
Answer:
128 degrees
Step-by-step explanation:
B = D
B = 128
Therefore, D = 128
This shape has these characteristics:
⇒ there are two sets of parallel sides
⇒ This shape is a parallelogram
Since this shape is a parallelogram:
⇒ meaning that angles opposite to each other
⇒ equal in measure
Since ∠B and ∠D are opposite each other
⇒ ∠D = 125°
Answer: ∠D = 125°
Hope that helps!
I need a walk through please 1
Answer:
[tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]
Step-by-step explanation:
You work in the order you have: you start with your number x, so your first step will be [tex]f_0(x)=x[/tex]. then you add 2: [tex]f_1(x) =x+2[/tex]. Then you take the square root of what you have in the previous step: [tex]f_2(x) = \sqrt {x+2}[/tex]. Finally, you divide by 9: [tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]
Find the jacobian of the vector valued function F(v) = [3x*2y, 5xx, 9yy]
Answer:
F(v)=0
Step-by-step explanation:
F(v) = [3x*2y, 5xx, 9yy]
Calculate the product
F(v) =[tex]\frac{d}{dv\\}[/tex] [3x*2y, 5x*x, 9y*y]
The derivative of a constant is always 0
F(v) =[tex]\frac{d}{dv\\}[/tex]((6xy,5[tex]x^{2}[/tex],9[tex]y^{2}[/tex]))
f(v)=0
find in factord form -9n+n^2=0
Answer:
n(-9+ n) =0
Step-by-step explanation:
-9n+n^2=0 Kind of use 'reverse distributive' property
n (-9 + n) = 0
7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains, she also uses 1.2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form. 7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains , she also uses 1.2 cm of white fabric . Express the amount of white fabric to coloured fabric as a ratio in its simplest form
Answer:
amount of coloured fabric in mm = 48
amount of white fabric in mm = 12
ratio = white fabric : coloured fabric = 12 : 48 = 1:4
16. You found a shortcut to school that saves 5 minutes off of taking the freeway. About 1 in every 10 trips
you get stuck behind a bus and it ends up taking you 20 minutes longer than the freeway. What is the expected
value of the shortcut?
Answer:
it saves 2.5 minutes
Step-by-step explanation:
The expected value of a random variable is the sum of products of possibilities and the probability of each.
Here, you have a probability of 0.9 of saving 5 minutes, and a probability of 0.1 of adding 20 minutes.
__
The expected value of the shortcut is ...
0.9(-5) +0.1(20) = -4.5 +2.0 = -2.5
The shortcut is expected to save 2.5 minutes on average.
_____
Additional comment
The probability of 0.9 comes from the 9 of 10 trips that result in a time saving.
Mirele needs to buy fencing to completely surround her backyard pool. How much fencing should she buy?
A pool has a length of 31.74 feet and a height of 14.85 feet.
Answer:
93.18 feet
Step-by-step explanation:
Length of backyard pool = 31.74 feet
Height of backyard pool = 14.85 feet
To find = Use the formula for the perimeter of a rectangular pool.
= 2 ( length + height )
Length of fencing bought by Mirele:
2 ( 31.74 + 14.85 ) = 2 ( 46.59 ) = 93.18 feet
Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select
one that applies.
Answer:
Yes, No, No
Step-by-step explanation:
The function of an exponential graph is attached below. The first graph fits the look of an exponential graph. The rest do not.
Answer:
Yes, No, No
Step-by-step explanation:
1st graph represents exponential2nd graph represents quadratic3rd graph represents linearThere are 120 students in Year 11 at a school.
Each student studies one language, either French, Spanish, German or Welsh.
21 of the 40 students studying Welsh are male.
18 males and 9 females study French.
12 of the 17 students studying Spanish are female.
Twice as many females study German than males.
How many students in Year 11 are female?
Answer:
80 students are female
Step-by-step explanation:
21 are male meaning 19 are female
9 are female in French
12 are female in Spanish
total = 40
2x + 40 = 120
2x = 80
x = 40
females' = 80
total = 80
How would you know the answer (important)
Answer:
okay so I can't see the last option on ur sheet but when u graph this equation the point that lies on the curve is (2,-3) so that is the vertex but if I move up this curved line it passes through the Y axis at (0,-1), the Last answer that I can't see it wouldn't happen to be (-1,6) would it
A 3-column table with 3 rows. Column 1 is labeled Unit Fraction with entries StartFraction 1 Over 10 EndFraction, one-fourth, c. Column 2 is labeled Fraction with 100 in the denominator with entries StartFraction 10 Over 100 EndFraction, b, StartFraction 50 Over 100 EndFraction. Column 3 is labeled Percent with entries a, 25 percent, 50 percent.
Complete the table by finding the missing equivalent form for each row.
a =
b =
c =
The missing equivalent forms are: a = 10%, b = 25/100 and c = 1/2
Complete questionUnit Fraction Fraction with 100 in denominator Percent
1/10 10/100 a
1/4 b 25%
c 50/100 50%
Complete the table by finding the missing equivalent form for each row.
How to determine the missing equivalent forms?From the above table, we have the following equations
a = 10/100
b = 25%
c = 50/100
The variable a must be in percentage.
So, we have:
a = 10/100
Express as percentage
a = 10%
The variable b must be a fraction with 100 in denominator
So, we have:
b = 25%
Express as fraction
b = 25/100
The variable b must be a unit fraction
So, we have:
c = 50/100
Divide the fraction by 50/50
c = 1/2
Hence, the missing equivalent forms are:
a = 10%, b = 25/100 and c = 1/2
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A theme park had 1099 visitors in 3 days. There were twice as many visitors on saturday than on Friday. There were 234 more visitors on Sunday than on Saturday. How many visitors were there on Saturday?
Answer:
346
Step-by-step explanation:
Visitors on Friday(x)+Visitors on Saturday(2x)+Visitors on Suday(2x+234)
x+2x+2x+234=1099
5x+234=1099
5x=1099-234
5x=865
x=865/5
x=173
So, visitors on Saturday = 2x = 346
The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
Three rectangles are shown, one below the other. The middle rectangle has a width of 6 units, and, along each width, is a triangle with a height of 4 units. The length of the lowermost rectangle is 8 units and its width is 5 units.
104 units2
132 units2
152 units2
168 units2
Here, the surface area, in square units, of the triangular prism is 152 units².
We know that the area of any triangle can be calculated as
Area = 1/2 * base * height
The area of any rectangular figure can be calculated as
Area = length * width
Here, the length of the rectangular portion of the prism is 8 units.
The width of the lowermost rectangle is 5 units.
The area of the uppermost rectangle = the area of the lowermost rectangle = 8 * 5 units² = 40 units²
Again the width of the middle rectangle is 6 units.
So, the area of the middle rectangle = 6 * 8 units² = 48 units²
Now, the height and base of the triangles are 4 and 6 respectively.
So, the area of the left-hand side triangle = the area of the right-hand side triangle = 2 * (1/2) * 4 * (6/2) units² = 1 * 4 * 3 units² = 12 units²
Then the area of the triangular prism = area of rectangular portion + area of triangular portion = (2 * 40 + 48) + (2 * 12) units² = (80 + 48) + 24 units² = 128 + 24 units² = 152 units²
Therefore the surface area, in square units, of the triangular prism is 152 units². So, Option C is correct.
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