ANSWER
Average Rate of Change
[tex] = \frac{f(b) - f(a)}{b - a} [/tex]
EXPLANATION
To find the average rate of change of y=f(x) from x=a to x=b means finding the slope of the secant line joining the points
(a,f(a)) and (b,f(b))
The slope of the secant line joining these points is
[tex] = \frac{f(b) - f(a)}{b - a} [/tex]
This gives the average rate of change of the function.
To find the average rate of change of a function, you need to subtract the function values at two different points and divide by the difference in the input values.
Explanation:To find the average rate of change of a function, you need to calculate the change in the function's output divided by the change in its input. This can be done by subtracting the function values at two different points and dividing by the difference in the input values. For example, if you have a function f(x) and want to find the average rate of change between x = a and x = b, you would use the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
This will give you the average rate at which the function is changing over the interval from a to b.
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#SPJ12
What is the value of x?
A.30 B.45 C.85 D.90
Answer:
45°
Step-by-step explanation:
This is the inscribed angle, in which the angle is 1/2 of the opposite arc. The opposite arc for this question measures at 90°. Divide by 2.
90/2 = 45
45, or B)45° is your answer.
~
A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
First brand: ____ gallons
Second brand: ___ gallons
Answer:
First brand(45%): 90 gallons
Second brand(70%): 60 gallons
Step-by-step explanation:
"The first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
First brand: ____ gallons
Second brand: ___ gallons"
We know that 70 is 15 away from 55, and 45 is 10 away, making this a 10: 15 ratio of 70 to 45 (because the 70 can only counteract the 45 by 10, and the 45 can only counteract the 70 by 15 unless they want to overshoot the 55% average ).
This means that .4*150 is 70% and .6*150 is 45%
This means there is First brand: 90 gallons
Second brand: 60 gallons
Need Help ASAP!!
What’s the future value of a $1,000 investment compounded at 8% semiannually for five years?
Answer:
$1480.24
Step-by-step explanation:
This will be solved by the formula:
[tex]FV=I(1+r)^t[/tex]
Where
FV is the future value (what we are looking for)
I is the initial amount (which is $1000)
r is the rate of interest per period (8% is annual interest, but the period is SEMI-ANNUAL, that's 6 months, half of yearly. So r would be half of 8%, which is 4% or r = 0.04)
t is the times compounding occurs in the whole time (The whole time period is 5 years, but compounding occurs semi-annually, so 5*2 = 10 times. Thus, t = 10)
plugging the info into the formula we will get our answer.
[tex]FV=I(1+r)^t\\FV=1000(1+0.04)^{10}\\FV=1000(1.04)^{10}\\FV=1480.24[/tex]
Answer:
C. $1,480
Step-by-step explanation:
Plato
Explain what type of function is the best model for the data set and justify your choice. Help???????
Answer:
The function is linear
Step-by-step explanation:
* Lets check from the table the type of the function
- At first check if it is linear or not
- The points are:
(165 , 198) , (168 , 201.6) , (170 , 204) , (172 , 206.4) , (175 , 210)
* Find the slope for each two points if the value of the slop is
constant, then the function will be linear
∵ The slop = (y2 - y1)/(x2 - x1)
∴ m1 = (201.6 - 198)/(168 - 165) = 1.2
∴ m2 = (204 - 201.6)/(170 - 168) = 1.2
∴ m3 = (206.4 - 204)/(172 - 170) = 1.2
∴ m4 = (210 - 206.4)/(175 - 172) = 1.2
∵ m1 = m2 = m3 = m4
# Note: You can use any to points to find the slope you will
have the same value
∴ The graph of the points is a line with slope 1.2
* The function is linear
Answer:
A linear function is the best model.
The ratio of y to x for the ordered pairs is constant, so the relationship is a direct variation. A direct variation is a type of linear function.
When the data set is plotted, it forms a line.
Step-by-step explanation:
Distributive property 7(2n+3)
its 14n+21. 7×2n is 14n, and 3×7 is 21
Answer:
[tex]7(2n+3)=14n+21[/tex]
Step-by-step explanation:
[tex]7(2n+3)=(7*2n)+(7*3)\\\\ 7*2n=14n\\ 7*3=21\\ \\ 7(2n+3)=14n+21[/tex]
One half the difference of the cube of a number, x, and three
Answer:
(1/2)(x³ - 3)
Step-by-step explanation:
That would be (1/2)(x³ - 3).
The expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].
Let the number be [tex]x[/tex].
The cube of the number is [tex]x^3[/tex].
Difference of the cube of the number with [tex]1[/tex] is [tex]x^3 - 1[/tex].
Now, one-half difference of a number cubed and one is represent as,
[tex]\frac{1}{2} (x^3 - 1)[/tex].
So, the expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].
Learn more about expressions here:https:
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Choose the TRUE statements.
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 49 units to the left of zero on a number line is −49.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.
Answer:
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.by-step explanation:
Correct:
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.
Wrong:
The absolute value of 49 units to the left of zero on a number line is -49.
This answer is wrong because when u use absolute value, ur final number is always going to be positive, but i this case it’s negative so it wrong.
Have a good day! Hope this helped!!❤️❤️
Which shows the numbers $5.25, $0.69, $123.46 rounded to the nearest dollar? A) $5.25, $.70, $124 B) $5.00, $1.00, $123 C) $5.00, $1.00, $124 D) $6.00, $.1.00, $123
Answer:
B) $5.00,$1.00,$123
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What percent is represented by the shaded area
Answer:
the answer is 25%
Step-by-step explanation:
100% : 4 =25
prime factorization of 52
Answer:
The first prime factor we test is 2:
52 / 2 = 26
26 / 2 = 13
13 is a prime number so the prime factorization is
2 * 2 * 13 = 52
Step-by-step explanation:
52 is a composite number. 52 = 1 x 52, 2 x 26, or 4 x 13. Factors of 52: 1, 2, 4, 13, 26, 52.
Use the bar graph. Describe how the amount of practice time changed from Week 1 to Week 4
there is no bar graph here
3n-7/6=2n+5/3 n=what
[tex]\frac{3n-7}{6}=\frac{2n+5}{3}[/tex] Multiply 3 and 6 on both sides to get rid of the fraction (or cross multiply)
[tex]\frac{3n-7}{6}(3)=\frac{2n+5}{3} (3)[/tex]
[tex]\frac{3n-7}{6}(3)(6)=(2n+5)(6)[/tex]
3(3n - 7) = 6(2n + 5) Distribute/multiply 3 into 3n-7, and 6 into 2n+5
(3)3n - (3)7 = (6)2n + (6)5
9n - 21 = 12n + 30 Subtract 9n on both sides
-21 = 3n + 30 Subtract 30 on both sides
-51 = 3n Divide 3 on both sides
-17 = n
Answer:
n = 17/6 = 2.833
Step-by-step explanation:
Step by step solution :
Step 1 :
5
Simplify —
3
Equation at the end of step 1 :
7 5
(3n - —) - (2n + —) = 0
6 3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2n 2n • 3
2n = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2n • 3 + 5 6n + 5
—————————— = ——————
3 3
Equation at the end of step 2 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 3 :
7
Simplify —
6
Equation at the end of step 3 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
3n 3n • 6
3n = —— = ——————
1 6
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
3n • 6 - (7) 18n - 7
———————————— = ———————
6 6
Equation at the end of step 4 :
(18n - 7) (6n + 5)
————————— - ———————— = 0
6 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 1 1 1
Product of all
Prime Factors 6 3 6
Least Common Multiple:
6
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (18n-7)
—————————————————— = ———————
L.C.M 6
R. Mult. • R. Num. (6n+5) • 2
—————————————————— = ——————————
L.C.M 6
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(18n-7) - ((6n+5) • 2) 6n - 17
—————————————————————— = ———————
6 6
Equation at the end of step 5 :
6n - 17
——————— = 0
6
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
6n-17
————— • 6 = 0 • 6
6
Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
6n-17 = 0
Solving a Single Variable Equation :
6.2 Solve : 6n-17 = 0
Add 17 to both sides of the equation :
6n = 17
Divide both sides of the equation by 6:
n = 17/6 = 2.833
One solution was found :
n = 17/6 = 2.833
Help me please anyone!
Answer:
1) 13(2) + 2m = A
2) 70
Step-by-step explanation:
The answer in the there:
the 7 in 72 represents how many times the value of the 7 in 78
Answer:
1
Step-by-step explanation:
Knowing what place values are, we know that since both of those numbers have the 7 in the tens place, it represents 70. So both of those number are 70 plus another number (under 10)
Answer:
1
Step-by-step explanation:
1
Find the solution to the system of equations. You can use the interactive graph below to find the solution.
{21x + 7y = 42
{-5x + 5y = 10
X =
Y =
X=1 and
Y=3
Look at the image attached to see what I did
X = 1
Y = 3
Hope this helps!
About how many feet of fencing are needed to enclose a rectangular garden with a 30 foot pond side and a 40 foot long diagonal
Answer:
140
Step-by-step explanation:
30+30=60
40+40=80
60+80=140
Answer: Hello there!
If you want to enclose a rectangular garden, then the feet of fencing that you need are equal to the perimeter of the rectangle, this is, the sum of all the sides of the rectangle.
We know that the rectangle has a 30ft pond side and a 40ft long diagonal.
this 40ft diagonal is the hypotenuse of a triangle rectangle where the cathetus is the sides of the rectangle; we know that one of the sides are of 30 ft, and we want to find the other:
Using the Pythagorean theorem; we know that:
[tex]40^{2} = 30^{2} + x^{2}[/tex]
where x is the length of the other side that we don't know yet.
[tex]x = \sqrt{40^{2} - 30^{2} } = 26.5ft[/tex]
Then your rectangle has a 30ft side, and a 26.5ft side (and has two of both)
Then the perimeter is:
30ft + 30ft + 26.5ft + 26.5ft = 113ft
What are two numbers that multiply to -90 but add up to 1?
I'm so bad at facts ;-;
10 and -9. 10 times -9 equals -90 and 10+ -9 equals 1
what is the value of x, 6x +2=180
Answer: [tex]x=\frac{89}{3}[/tex] or [tex]26\frac{2}{3}[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\6x+2-2=180-2\\6x=178[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{178}{6}\\[/tex]
[tex]x=\frac{89}{3}[/tex]
Hope this helps and have a great day!!!
Answer: there are three answers. the exatct, decimal, and mixed. i will give them all!
exact: X= 89/3
decimal: x= 29.6
mixed: x= 29 2/3
Step-by-step explanation:
What are the solutions to the equation? x^2−12x+36=4
x1=
x2=
(not multiple choice)
Answer:
x1=4
x2=8
Step-by-step explanation:
1- Factor the equation.
2- solve a Single Variable Equation
3- Parabola, Finding the Vertex
What should I type here? Will give Brainliest and 25 points Help ASAP!
Answer:
6+10=16 That is your length.
Step-by-step explanation:
Answer:
POINTSS
Step-by-step explanation:
I WANT POIITNS
in triangle ABC, what is the measure of angle C
It is any fraction except 0 of 180°.
Answer:
36 degrees
Step-by-step explanation:
Please help
Me need help
Erode 12 am
answer is 42000(1-.08)^6
Answer:
5)[tex]y=42000(1-0.08)^6[/tex]
6) 25467
Step-by-step explanation:
5) Use the formula;
[tex]y=y_0(1-r\%)^t[/tex]
where [tex]y_0=42000[/tex] dollars is the initial value of the car.
[tex]r\%=0.08[/tex]
and
t=6 years.
We plug in these values to obtain;
[tex]y=42000(1-0.08)^6[/tex]
Third choice is correct
6) The expected value of the car after 6 years is
[tex]y=254666.910[/tex]
We round to the nearest tenth to obtain;$ 25467
A basketball coach claims that the team's players commit, on average, no more than 10 fouls per game. Let µ represent the team's average number of fouls per game. Another coach thinks that these players create more fouls.
What is the null hypothesis, H0, for this situation?
(B) u ≤ 10
What is the alternative hypothesis, Ha, for this situation?
(B) u > 10
What type of significance test should be used for this situation?
A right-tailed test
These are the correct answers but I don't know the explanations for them someone help me out
Answer:
H0: u ≤ 10
Ha: u > 10
A right-tailed test
Step-by-step explanation:
In hypothesis testing there are two types of hypotheses;
The null hypothesis, H0 and the alternative hypothesis, Ha. The null hypothesis is the hypothesis of no difference and as such it always has an equality sign;
=, ≤, ≥
On the other hand the alternative hypothesis complements the null hypothesis meaning that if the null hypothesis is rejected then we take the alternative hypothesis to be true.
In order to identify the null and alternative hypothesis we look out for specific key words that will provide us with information on the type of inequality sign. In this scenario, the coach claims that the average number of fouls committed per game is no more than 10. Since µ represents the team's average number of fouls per game, this statement can be written in mathematical symbols as;
u ≤ 10, that is u is no more than 10; average number of fouls committed per game is no more than 10.
This statement will be our null hypothesis since it contains an equality sign.
H0: u ≤ 10
The complement of this statement will enable us deduce the alternative hypothesis. The complement of this statement can be found in the claim of the second coach who thinks that these players create more fouls, to be specific more than 10 fouls. In mathematical notation this claim can be written as;
u > 10, more than 10 fouls.
This statement will be our alternative hypothesis since it complements the null hypothesis;
Ha: u > 10
The type of significance test to be carried out in hypothesis testing emanates from the inequality sign of the alternative hypothesis. The following are the key points to note, if the alternative hypothesis contains;
≠, then this automatically becomes a two tailed test
<, then this automatically becomes a left tailed test since the inequality sign is pointing towards the left.
>, then this automatically becomes a right tailed test since the inequality sign is pointing towards the right.
Our alternative hypothesis contains >, hence this will be a right-tailed test .
Answer:
Answer is B
Step-by-step explanation:
Jenny will roll a number cube, numbered 1-6, twice. What is the probability of rolling an odd number, then an even number?
Answer:
1/2
Step-by-step explanation:
1,3,5: 3/6
2,4,6: 3/6
6/12
A cookie recipe requires 3/4 cup of flour to make 1.5 dozen cookies. How much flour is needed to make 1 dozen cookies
Answer:
half a cup of flower -> 1/2
Step-by-step explanation:
i used a proportion to figure this out.
suppose the probability of success in a binomial event is 0.15. what is the probability of failure
Answer:
Step-by-step explanation:
85
I haven’t done area in a while and now we have to do with algebra, can anyone please help me with this? Thanks!
Answer: The area of the triangle is:
____________________________________________________
→ " (4x² + 6x) cm³ " .
____________________________________________________
Step-by-step explanation:
____________________________________________________
The formula for the "Area, "A" ; of a triangle is:
A = (1/2) * (baselength) * (perpendicular height) ;
→ that is:
→ A = (1/2) * b * h ;
____________________________________________________
The Area, "A" ; should be in "cubic units" ; in our case, "cubic centimeters" ;
or; " cm³ " .
____________________________________________________
Given: baselength: "b" = " 4x " ;
perpendicular height: " h = (2x + 3) " ;
____________________________________________________
Plug in these values into the equation/formula:
A = (1/2) * b * h ;
→ A = (1/2) * (4x) * (2x + 3) ;
→ (1/2) * 4x = 2x ;
→ A = 2x (2x + 3) cm³
____________________________________________________
→ 2x (2x + 3) = ?
____________________________________________________
Note the "distributive property" of multiplication:
→ a(b + c) = ab + ac .
____________________________________________________
As such:
→ 2x (2x + 3) = 2x(2x) + (2x)(3) ;
= 4x² + 6x ; ____________________________________________________
The area of the triangle is: " (4x² + 6x) cm³ " .
________________________________________________
Hope this helps!
Best wishes in your academic endeavors
— and within the "Brainly" community!
____________________________________________________
Find the slope and y-intercept of the line. y=-x+7
Answer:
slope = - 1, y- intercept = 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 7 ← is in slope- intercept form
with slope m = - 1 and y- intercept c = 7
The slope of the line y = -x + 7 is -1, and the y-intercept is 7.
To determine the slope and y-intercept of the line given by the equation y = -x + 7, we first recognize that it is in slope-intercept form, which is y = mx + b.
Identify the slope (m): In the equation y = -x + 7, the coefficient of x is -1. Thus, the slope of the line is -1.
Identify the y-intercept (b): The constant term in the equation is 7. Thus, the y-intercept is 7, meaning the line intersects the y-axis at the point (0, 7).
The slope of the line y = -x + 7 is -1, and the y-intercept is 7.
One serving of vegetables has 60 calories. Write the unit rate as a ratio. Then write an equivalent ratio.
Answer:
1:60, 2:120
Step-by-step explanation:
In one serivng there are 60 calories, i.e. 60 calories per serving. This is 1:60, an equivalent is 2:120
1:60, 9:540
Hope this helps!
Convert z = 8cos72° + 8isin72° from polar form to rectangular form.
Answer:
The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)
Step-by-step explanation:
* Lets revise how to change from polar form to rectangular form
- Cartesian Coordinates (x , y) and Polar Coordinates (r , θ)
- Where x = r cosФ , y = r sinФ
* To convert from Polar Coordinates (r , θ) to Cartesian Coordinates (x , y)
# x = r × cos( θ )
# y = r × sin( θ )
* In the problem
∵ z = 8 cos72° + 8 sin72°
∴ r = 8
∴ Ф = 72°
∵ x = r cosФ
∴ x = 8 cos72° = 2.5
∵ y = r cosФ
∴ y = 8 sin72° = 7.6
* The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)