The necessary expression for calculating the average rate of change inside the given function f(x) is given using :
f'(x) = (f(9) - f(2))/7
What is the average change rate?It quantifies how significantly the function changed per unit on average over that time interval. The slope of the single direction connecting every interval's ends on the function's graph is used to calculate it.
What is the distinction between the slope and the average rate of change?As we can see, slope is another way of calculating the average change rate. The average rate of change is calculated by dividing the difference in the dependent (y-term) by the difference inside the independent variable (x-term). The slope, as well as average rate of change are the same thing.
According to the given data:The function is given to f(x)
The interval is given to be [2,9]
Let a = 2 and b = 9
The expression which is used to determine the average rate of change in f(x) is given by
f'(x) = (f(b) - f(a))/b - a
f'(x) = (f(9) - f(2))/7
The necessary expression for calculating the average rate of change inside the given function f(x) is given using :
f'(x) = (f(9) - f(2))/7
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Please awnser this problem and please show work!!
Answer:
111/22 or 5 and 1/22
Step-by-step explanation:
9 and 7/22 equals 205/22
4 and 3/11 equals 47/11
multiply 47/11 times 2/2 to get common denominator
47/11 times 2/2 is 94/22
205/22 minus 94/22 is 111/22 which is also 5 and 1/22
the population standard deviation for the height of college baseball players is 3.0 inches. if we want to estimate 95% confidence interval for the population mean height of these players with a 0.68 margin of error, how many randomly selected players must be surveyed?
The number of players randomly selected is 381 and the standard deviation is 1.96.
What is the standard deviation?The standard deviation is a measurement of how much a group of values varies or is dispersed. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection. The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD. A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
[tex]Z(\alpha /2)=1.96[/tex]
Sample size = n = [tex][Z(\alpha /2 * \sigma/E) ]^{2}[/tex]
n = [1.96 * 3.0 / 0.95]²
n = 381.85
n ≈ 381
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What is the quotient?
1.242 ÷ 1.8 =
Answer: 0.69
Step-by-step explanation:
1.242 ÷ 1.8=
1.242/1.8=0.69
Brooke is buying a tent that is in the shape of a rectangular pyramid. The base is 6 feet by 8 feet. If the tent holds 88 cubic feet of air, how tall is the tent's center pole?
The height of the rectangular pyramid tent's center pole = 5.5 feet.
What is the Volume of a Rectangular Pyramid?Volume of rectangular pyramid = 1/3(length)(width)(height).
Given the following:
Volume of the rectangular pyramid tent = 88 cubic feetLength = 8 feetWidth = 6 feetHeight = ?Substitute
88 = 1/3(8)(6)(height)
88 = 16(height)
88/16 = height
5.5 = height
Therefore, the height of the rectangular pyramid tent's center pole = 5.5 feet.
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a $5.62
b $7.42
At the grocery store, Ruby buys 3 packs of juice for $2.12 each, and 4 bags of popcorn for $3.50 each. What is the total amount that Ruby
spends on the juice and popcorn?
c) $18.98
Line
Guide
$20.36
Answer:
20.36 is the answer
2.12x3=6.36
3.50x4=14
14+6.36=20.36
Answer:
20.36
Step-by-step explanation:
1)3*2.12=6.36
2)4*3.50=14
3)6.36+14=20.36
What's the lcd of 1/3 and 3/9
Answer:
LCD = 9
Step-by-step explanation:
1/3 = 3/9
3/9 =3/9
for how many different digits n is the 3 digit number 14n divisible by n, 14n refers to a three digit number with the unit digit of n
0, 1, 2, 4, 5, and 7.
So that would be 6 digits.
In mathematics, the only single symbol used to represent a number is a digit. For instance, there are two digits in the numbers 89: 8 and 9. As a result, in everyday life, digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, and 0 are employed to represent groups of numbers and perform mathematical operations. A positional numeral system uses a single sign, such as "2," or a set of symbols, such as "25," to represent numbers. The word "digit" derives from the fact that the ten fingers of the hands, or digit in Latin, corresponding to the ten symbols of the decimal system, which uses the base-10 numeral system.
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A car detailing shop charges $30 for materials, plus $50 per hour for labor to paint pinstripes on a car. Which function can be used to find the total cost C(h) to get pinstriping that requires h hours to complete?
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 50h + 30
How to create Cost Function?
We are given the following costs in the car detailing shop as follows;
Cost of Materials = $30
Cost per hour for labor = $50
Since the equation of a line in slope intercept form is; y = mx + c, then we can say that the equation here can also be expressed as;
C(h) = 30 + 50h
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 30 + 50h
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in a large population, 63 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? give your answer as a decimal (to at least 3 places) or fraction.
The probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical summaries of how likely an event is to occur or how likely a proposition is to be true. The likelihood of an event occurring is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.To find the probability that at least one of them has been vaccinated:
In a huge number, 63% of people are vaccinated, leaving 37% unvaccinated. The point of concern for the probability that at least one of the four randomly selected people has been vaccinated. As a result, we must account for the possibility that one, two, three, or four randomly selected people were vaccinated.We use P(1) for only one person; the same reasoning should apply to other subscripts.
P(1) = (63/100)(37/100)(37/100)(37/100) = 0.03089833P(2) = (63/100)(63/100)(37/100)(37/100) = 0.05094049P(3) = (63/100)(63/100)(63/100)(37/100) = 0.08398297P(4) = (63/100)(63/100)(63/100)(63/100) = 0.13845841Adding all these probabilities given 0.3042802.
As a result, the probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
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find the lines slope and point on the line
picture below
The slope is 4 and point on the line is origin (0,0).
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The equation of the line is
y+4=4(x-2)
We have to find the slope and point on the line.
y+4=4(x-2)
y+4=4x-8
Substract 4 from both sides we get,
y=4x-12
Since the equation now is in y = mx + b form, we can identify the slope m=4 and the y-intercept b=-12 and point on the line origin (0,0).
Therefore, the slope is 4 and point on the line is origin (0,0).
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A survey showed that 8 out of 20 homeowners in a neighborhood had cable television. if there were 320 homeowners in the neighborhood, how many could be expected to have cable television?
The number of homeowners in the neighborhood could be expected to have cable television is 128.
Given that, a survey showed that 8 out of 20 homeowners in a neighborhood had cable television.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Now, 8/20 × 320
= 8 × 16
= 128
Hence, the number of homeowners in the neighborhood could be expected to have cable television is 128.
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BRAINLIES AND 30 POINTS PLS HELP
. Why is using iodine helpful when looking at cells?
Answer:
As a biological stain, iodine is useful for studying plant cells because it stains starch blue-black and in animal tissue, it can help in the demonstration of nuclei and cell membranes
Answer: Iodine is also a useful stain. When studying plant cells, iodine is used. Because it is a starch indicator, it reacts with starch and turns blue-black. Iodine can also be used as a stain on animal cells, making the cell membrane and nucleus appear more visible
Step-by-step explanation:
0.5{3x + 4(3 + 2x)}
please simplify!!
Answer:
0,5(3x+12+8x)
0,5(11x+12)
5,5x+6
Answer:
5.5x + 6
Step-by-step explanation:
0.5{3x + 4(3 + 2x)}
Apply the distributive property, multiply 4 by 3 and 4 by 2x.
0.5(3x + 12 + 8x)
Add 3x and 8x
0.5(11x + 12)
Apply the distribdistributive proproperty again and multiply 0.5 by 11x and 0.5 by 12.
The product would be 5.5x + 6.
Mrs. Schott gets a biweekly paycheck of $1,230.90.
What is her annual salary?
Answer:
Step-by-step explanation:
Answer:
biweekly salary =
365/14=
23
then total salary
of her is =$1230.90
*23
=
Step-by-step explanation:
Which expression is equivalent to quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity? negative forty nine over 8 times d minus one tenth forty nine over eight times d minus one tenth negative three eighths times d minus one and three tenths negative three eighths times d minus one tenth
Answer: The Answer would be -49/8d -1/10
Step-by-step explanation: I got it right on the test
have a good day
The answer for the given expression is -49d/8 - 1/10. Thus, the correct option is option A.
The expression can be solved by simple arithmetic operation.
(-3 1d/4 + 3/5) - (2 7d/8 + 7/10)
In the next step simplify the terms and open brackets.
-13d/4 + 3/5 -23d/8 - 7/10
Taking the like terms together.
-13d/4 - 23d/8 + 3/5 - 7/10
Solving the terms by taking L.C.M.
(-104d-92d/32) + (30-35/50)
-196d/32 - 5/50
Simplifying the terms.
-49d/8 - 1/10.
Thus, the value of the expression is -49d/8 - 1/10.
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When finding multiples of a number, you _________ the original number by 1, then 2, then 3 and so on.
Answer:
Step-by-step explanation:
jlfhwfhwfh
Please help for my homework
Answer:
260 m2
Step-by-step explanation:
Simplify the expression 11c+3(−5c+4d)
step by step explanation:
-4c+12d
1. Distribute:
11c+3(-5c+4d)
11c-15c+12d
2. Combine like terms:
11c-15c+12d
-4c+12d
I dont understand what i am supposed to do
Applying the alternate exterior angles theorem, the value of x = 10.
How to Apply the Alternate Exterior Angles Theorem?According to the alternate exterior angles theorem, the following alternate interior angles are congruent to each other:
m<JPM = m<NQK
Given the following:
m<JPM = 125°
m<NQK = (13x - 5)°
Substitute
125 = 13x - 5
125 + 5 = 13x
130 = 13x
Divide both sides by 13
130/13 = 13x/13
10 = x
x = 10
Therefore, applying the alternate exterior angles theorem, the value of x = 10.
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What does x equals to
The value of x is 20°
According to the question we have been given two parallel lines which is cut by a transversal line. There are total 8 angles and given is the measure of
∠4 = 5x + 35° and ∠7 = 45°.
We need to find the value of x.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
Now using these rules we will solve this problem
Because of corresponding angles , ∠3 = ∠7 = 45°
Also ∠3 and ∠8 make a linear pair and sum of linear pair is 180°.
Therefore , ∠3 + ∠8 = 180°
45° + 5x + 35° = 180°
5x = 180° - 80°
x = 20°
Hence the value of x is 20°
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What is the answer to the.
-2(x - 5) = 6(2- 1/5x) and show me how you solved it
Answer:
x = -2.5
Step-by-step explanation:
6,3.1,9 can it make a triangle
Yes
Step-by-step explanation:We can tell if a triangle can exist based on the relationship between the side lengths.
Side Length Relationships
For a triangle to really exist, the sum of the smaller legs must be greater than the length of the longest leg. This can be expressed with the inequality a + b > c, where a and b are the shorter legs.
Now, we can plug the values we are given into this inequality.
6 + 3.1 > 99.1 > 9Since the inequality is true, this triangle does exist.
Other Examples
One of the most important things to remember is that the sum of the shorter legs must be greater than, not equal to, the longest leg. So take the sides 4, 6, and 10.
4 + 6 > 1010 > 10This statement is not true. 10 is not greater than 10; they are equal. Thus, these sides cannot make a triangle.
Additionally, if the 3 numbers are Pythagorean triples, then it will be a right triangle. For example, the sides 5, 12, and 13 will create a right triangle.
what is the probability that a single card drawn from a standard deck of cards is either an 8 or a heart?
The probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
Probability of an event E denoted by P(E) is defined as (number of favorable outcomes )/( total number of outcomes).
For example : the probability of getting Head in single toss of an unbiased coin. P(H)=1/2.
According to the given question
Total number of cards in a standard deck of cards is 52.
There are 4 suit in a deck each having 13 card each.
number of 8 card in a deck = 4
Number of hearts in a deck = 13-1=12 (-1 because 8 of heart is counted before.)
number of favorable cases of getting either an 8 or a heart is 4+12=16.
The probability of getting either an 8 or a heart is [tex]\frac{16}{52} =\frac{4}{13}[/tex].
Therefore , the probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
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Point P is located 2/5 of the distance from W to Z. Point W is located at (-5, -2) and point P is located at (1, 4). What are the coordinates of point Z?
The coordinates of point Z is (-5/7, 16/7)
Calculating the midpoint of a line using a ratioThe formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:
Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}
Substitute the coordinates and ratios to have;
Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}
Z(x, y) = {-10+5/7, -4+20/7}
Z(x, y) = (-5/7, 16/7)
Hence the coordinates of point Z is (-5/7, 16/7)
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8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables (letters). use the sketch area if needed. combine the like terms and submit your answer. *always combine like terms in alphabetical order and write your constant term last!
When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
Given,
The expression =8+3a+7b-5+2a-7b
Rearrange the terms alphabetical order and combine the like terms
8+3a+7b-5+2a-7b =3a+2a+7b-7b+8-5
=(3+2)a+(7-7)b+(8-5)
=5a+0b+3
=5a+3
Hence, When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
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what is square root 25/49
A. 25/49
B. 5/9
C. 5/7
D. 5/8
Answer: C. 5/7
CALCULATOR
Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
5x+1/3 (3x-6)=10
Answer:
x=2Step-by-step explanation:
5x+1/3(3x−6)=10
Simplify both sides of the equation:5x+1/3(3x−6)=10
5x+(1/3)(3x)+(1/3)(−6)=10 (Distribute)
5x+x+−2=10
(5x+x)+(−2)=10 (Combine Like Terms)
6x+−2=10
6x−2=10
Add 2 to both sides:6x−2+2=10+2
6x=12
Divide both sides by 6:6x/6=12/6
x=2
Evaluate: 3a x 5w (Not simplified)
The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
What is the value of the expression otherwise termed it's simplified form as required that the expression be evaluated?It follows from the task content that the expression which is as given in the task content be evaluated, and hence, expressed in its simplified form.
Given;
3a × 5w
Since, the constants can be multiplied and their product determined, it follows that we have;
(3 × 5) (a × w)
And ultimately, we have the value of the expression to be; 15aw.
Therefore, The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
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can someone help me with the problem?
where is the problem, how can I help you?
i need help with this problem it says
one less than triple a number is the same as six times a number reduced by 7
15 points
Answer:
3x - 1 = 6x - 7
x = 2
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1. To solve it, first get the variable on same side.
3x - 1 = 6x - 7
- 3x - 3x
- 1 = 3x - 7
2. Isolate the variable by doing the inverse operation which is in this case addition (adding 7).
- 1 = 3x - 7
+ 7 + 7
6 = 3x
3. Isolate variable by doing the inverse operation which is in this case division (dividing by 3).
6 = 3x
3 3
2 = x
OR
x = 2
Check:
1. Substitute x with 2 and solve.
3(2) - 1 = 6(2) - 7
6 - 1 = 12 - 7
5 = 5
True statement.