The exponential growth formula is 3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet is 63.16 years.
What is the exponential growth formula?The exponential growth formula usually has this form:
FV = P (1 + r)^n
FV = Future growth P = Present growth R = rate of growthN = number of years3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet = (In 1,000,000,000 / 3,400,000) / 0.09 = 63.16 years
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C
27 cm
A) 18.9 cm
C) 20.8 cm
74°
A
9 cm
B
B) 26 cm
D) 22.7 cm
The length of other side is 20.8 in the given triangle.
What is a triangle ?
triangle can be defined in which it consists of three sides and three angles and sum of all the angles is always 180 degrees .
Given in the triangle ,
AC = 27 cm
AB = 9 cm
CAB = 74 degrees
a2 = b2 + c2 – 2bc cos ∠x
a2 = 27*27 + 9*9 - 2*27*9*cos74
a2 = 529 + 81 - 486*0.27
a2 = 610-486*0.27
a2 = 610-131.22
a2 = 479
a= [tex]\sqrt{479}[/tex]
a = 20.8 (approximately)
Hence the length of other side is 20.8 in the given triangle.
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Jada has challenged herself to do at least 100 full push-ups this week On Sunday, she does 30 push-ups Her arms are sore, so she decides to do fewer push-ups on the remaining days of the week She wants to do the same number of push- ups each day for the rest of the week. Write and solve an inequality for the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups Which answer choice best interprets the solution in the context of the problem?
A. Jada needs to do at least 11 and 2 thirds
B. Jada needs to do push-ups for at least 12 more days to meet her goal
C. Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal
D. Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal
a) The inequality showing the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups for the week is 30 + 6x ≥ 100.
b) The solution to the inequality shows D. Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal
What is inequality?Inequality is a mathematical statement that two or more mathematical expressions are unequal and not equivalent.
Inequalities are depicted in the following ways:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total number of full push-ups for the week = 100
The number of push-ups done on Sunday = 30
The remaining number of push-ups for 6 days = 70 (100 - 30)
Inequality:30 + 6x ≥ 100
6x ≥ 70
x ≥ 12
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(Factoring Algebraic Expressions LC)
Rewrite 8a + 32ab using a common factor.
A: 8ab(1 + 32ab)
B: 8ab(0 + 4)
C: 8a(1 + 4b)
D: 8a(0 + 4b)
Answer:
The answer is option c.
Please could you give me brainliest
Kristy made 33 cookies for a bake
sale. She is putting the cookies in
packages to sell. Each package will
hold 4 cookies. How many complete
packages of cookies can she make?
how do i do this and whats the answer
Answer:
3 - 1
12 - 4
21 - 7
Step-by-step explanation:
Answer:
youd start and see that you can divide 12/3 this gives you 4 you then divide 4/4 and find 1 so he can do 3 lawns in 1 hour thus you just mutiplltiply each side by 7 so it'd be 21 and 7
Step-by-step explanation:
should look like this
3 1
12 4
21 7
Whats 35 divided by 375?
Answer:0.093333333333
Step-by-step explanation:
Find the exact circumference of each circle
By dividing the circle's diameter by, you may determine a circle's circumference (pi). By dividing 2radius by pi, or 3.14, you may also determine the circumference.
What is Circle’s Circumference?The diameter of a circle, also known as its circumference or perimeter, is the measurement of the circle's edge. As opposed to this, a circle's area indicates the space it occupies. The circumference of a circle is its length when we cut it open and draw a straight line from it. Units like centimeters or meters are typically used to measure it.The circle's radius is taken into consideration when applying the formula to determine the circumference of the circle. Therefore, in order to calculate the circumference of a circle, we must know its radius or diameter.The perimeter (or circumference) of a circle is equal to two R.where,R denotes the circle's radius.
The mathematical constant has a value that is around 3.14 (to the nearest two decimal places).Again,
As the ratio of any circle's circumference to diameter, pi () is a unique mathematical constant.and C = D
C represents a circle's circumference.D represents the circle's diameter.Calculate the circle's circumference, for instance, if its radius is 4 cm.Radius is given as 4 cm.Circumference = 2r
= 2 x 3.14 x 4
= 25.12 cm
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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
[tex]2^{4x} = 2^{3(x - 3)}[/tex]
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
[tex]2^{4x} = 8^{x - 3}[/tex]
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
[tex]8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}[/tex]
Meaning that the correct option is given by the fourth option.
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ANYONE GOOD AT MATH PLEASE I BEG OF YOU FOR HELP!
Answer: 5
Step-by-step explanation: To solve f(x), g(x), or f(g(x)) problems, we place the value of x in the functions with the value that we are given. This value will be f(g(5)) or g(3) or f(27). We plug in the number in the parentheses.
In this problem, we have to first plugin 5 to g(x) then plug g(5) into f(x).
First, we do g(5)=sqrt((5^2)+2). This gives us 3. Then we plug in 3 which is g(5) into f(x). This gives us f(g(5)) or f(3)=sqrt((3^3)-2) which is 5.
Maria makes a fruit salad. The table shows the amounts of different kinds of fruit that she uses. Kind of Fruit Amount Grapes 3 2/3 cups Melon 2 1/4 cups Pineapple 23/4 cups Strawberries? The amount of strawberries that Maria uses is 3/8 times the amount of the other fruits combined. How many cups of strawberries does Maria use?
Proportionately, the number of cups of strawberries that Maria needs to use is 3¹/₈ cups.
What is proportion?Proportion refers to a part of a whole.
Proportion is a ratio of one value to another.
Proportions are depicted as decimals, fractions, or percentages.
In this situation, we know that the amount of strawberries is a fractional value of the combined fruits.
Thus, we can multiply the fraction of strawberries against the combined value of the other fruits to determine the number of cups of strawberries needed.
Kind of Fruit Amount
Grapes 3²/₃ cups
Melon 2¹/₄ cups
Pineapple 2³/₄ cups
Total of other fruits = 8²/₃ cups
Strawberries ?
Strawberries = 3¹/₈ (8²/₃ x ³/₈)
Thus, Maria needs 3¹/₈ cups of strawberries.
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(URGENT) lWhich pair of functions are inverses of each other?
If the two graphs are mirror images of one another across the line y = x, then they are inverse functions.[tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex]
How do you find a pair of inverse functions?As for looking at the graphs, we already knew that. You should keep in mind that inverse functions are represented by two graphs that are mirror images of one another over the line y = x. The broadest definition of an inverse function is one that "reverses" another function.
The inverse, for instance, must take b to an if a function goes from a to b. When the first and second elements of each pair in the original function are switched, a set of ordered pairs is obtained that is known as the inverse of the function. The act of switching the x and y coordinates is known as obtaining an inverse. They aren't opposites. The output of the first function is sent through an inverse function, which then generates an output whose input was the first function.
So, option A) [tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex] is the appropriate response.
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The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. About what percentage of the men are over 70.5 inches tall?
a ----2.5
b-----68
c-----16
d----5
e-----32
Answer:
Step-by-step explanation:
To find the percentage of men who are over 70.5 inches tall, we need to use the standard normal distribution table, which gives the proportion of observations that fall within a given range of standard deviation from the mean.
We first need to standardize the height of 70.5 inches by subtracting the mean (68 inches) and dividing by the standard deviation (2.5 inches) to get (70.5 - 68) / 2.5 = 0.8
This tells us that 70.5 inches is 0.8 standard deviations above the mean.
We can then look up the proportion of observations that fall within this range in the standard normal distribution table, which is approximately 0.1587 or 15.87%. So, the answer is (1-0.1587) = 84.13 or 84.13%.
So the answer is 84.13%
how many groups of 5/3 are in 1
The number of groups of 5/3 are in 1 would be equal to 3/5
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
Division of fraction
Given that groups of 5/3 are in 1
= 1 ÷ 5/3
Then Multiply by the reciprocal of 5/3
The reciprocal of 5/3 is 3/5
1 ÷ 5/3
= 1 × 3/5
= 3/5
Therefore, the number of groups of 5/3 are in 1 is; 3/5
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The function f(x) = 4x + 9 represents the number of animals adopted at one shelter, where x is the number of months.
The function g(x) = x + 2 represents the number of animals adopted at another shelter, where x is the number of months.
Part A: What is (f + g)(x)? Show all necessary steps. (2 points)
Part B: Evaluate (f + g)(5). Show your work. (2 points)
Part C: Explain what your answer represents in terms of the scenario. (2 points)
a. The function, (f + g)(x), is evaluated as: (f + g)(x) = 5x + 11
b. The function (f + g)(5) = 36
c. (f + g)(5) = 36 means in 5 months, the total number of animals adopted at the two shelters is 36.
How to Evaluate Functions?We can evaluate functions just as we solve normal algebraic equations when we plug in the given value of a variable.
Given the following:
f(x) = 4x + 9 [number of animals at one shelter]
g(x) = x + 2 [number of animals at another shelter
Part A: Find (f + g)(x)
(f + g)(x) = f(x) + g(x) = 4x + 9 + x + 2
Combine like terms:
(f + g)(x) = 5x + 11
Part B: Find (f + g)(5)
Substitute the x = 5 into the function (f + g)(x)
(f + g)(5) = 5(5) + 11
(f + g)(5) = 25 + 11
(f + g)(5) = 36
Part C: It means in 5 months, the total number of animals adopted at the two shelters is 36.
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PART B
Tim's upcoming move will span 250 miles. Which company should he hire? Explain how you found your
answer.
For upcoming trip. Tim should hire company A
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
Given,
Distance to cover = 250 miles
For company A
By the graph line passes through
(200, 200) , (0,150)
equation of the line,
y-150 = [(200-150)/(200-0)](x-0)
y-150 = [50/200] x
y = x/4 + 150
y = 0.25 x + 150
No. of miles = 250
y = 0.25×250 + 150
y = 62.5 + 150
y = $212.5
Price for company B
y' = 0.75x + 50
where x is number of miles
for 250 miles price of company B
y' = 0.75 × 250 + 50
y' = 187.5 + 50
y' = $237.5
∵ y < y'
∴Price of trip with company A is less than company B
Hence, Tim should hire Company A for upcoming trip.
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Evaluate the expression 6x + 4 9/10when x =23.
142 9/10
6*23=138, 138+4 9/10=142 9/10
Which of the numbers below correctly describes 25 A?
The required number below correctly describes 25 A is 0.025 KA. Option A is correct.
What is a unit of measurement?Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
25 A is the unit of current,
Now,
This unit can be further written as,
25 A = 25 × KA / 1000 = 0.025 KA
The required number below correctly describes 25 A is 0.025 KA. Option A is correct.
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Complete question-
which of the numbers below correctly describes 25 A? a) .025 KA, b) .25KA, c) 25,000 uA, d) 2500 mA
What is the sum of the exterior angles for each of the parallelogram and the hexagon?
A) 90°
B) The answer depends on the number of sides of the polygon
C) 180°
D) 360°
Very confused, if you could please explain it to me, that would be great!!
The sum of the exterior angles for a parallelogram is 360°.
What is exterior angle?Exterior angles are angles that are formed outside two lines when they intersect. They are located outside the two lines, on the outside of the shape. They can be found by adding the two interior angles together, whose measurements are always equal to 180 degrees. Exterior angles are also supplementary angles, meaning that the sum of their measurements is always equal to 360 degrees.
This is because the four angles on the outside of the parallelogram are all right angles, and the sum of four right angles is 360°.
Similarly, the sum of the exterior angles for a hexagon is also 360°.
This is because the six angles on the outside of the hexagon are all 120° angles, and the sum of six 120° angles is 360°.
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The measures of the interior angles of a quadrilateral are 2°, 3x", 5x°, and 7x°. Find the measures of all the interior angles.
X= ?
3x= ?
5x= ?
7x= ?
HURRY PLEASE !
Answer:
x = 22.5°
3x = 67.5°
5x = 112.5°
7x = 157.5°
Step-by-step explanation:
You have both 2° and x for the measure of the first angle. I used x°.
Sum of the measures of the interior angles of a polygon
For an n-sided polygon:
(n - 2)180° = 2(180°) = 360°
x° + 3x° + 5x° + 7x° = 360°
16x = 360
x = 22.5°
3x = 67.5°
5x = 112.5°
7x = 157.5°
How do the interior and exterior angles of a polygon relate? *
They are congruent
O They are supplementary
O They are complementary
There is no relationsh
please help! math factorization
Factors of [tex]$$4(x-y)^3-x+y$$[/tex] are [tex]4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y[/tex] and [tex]$16 x^{16}-1$[/tex], respectively, are [tex]\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex].
What do you meant by factorization ?Let's incrementally simplify.
[tex]$$4(x-y)^3-x+y$$[/tex]
Distribute:
[tex]$$=4 x^3+-12 x^2 y+12 x y^2+-4 y^3+-x+y$$$=4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y$[/tex]
Factor [tex]$16 x^{16}-1$[/tex]
[tex]$$\begin{aligned}& 16 x^{16}-1 \\& =\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex]
When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. Each check takes longer on average due to the larger size of our product and the larger size of the numbers we use to verify it.
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Please help!
Graph y= -3/2 x -3.
Answer:there you go
Step-by-step explanation:
use a graphing calc
SALE
50% OFF!
During the sale, Wanda pays $3 for a spinach salad. What was the original price?
Submit
Answer:
$6
Step-by-step explanation:
50% x 2 = 100%
3 x 2 = $6
Use the division or the multiplication property of equality to 927/y = 309 solve . What is the result?
Which has a greater absolute value 10 or -9
Answer:
10
Step-by-step explanation:
10 is 10 units away from 0 on a number line
-9 is only 9 units away from 0 on a number line
The farthest away from 0 would be 10
Solve the system of equations.
3x-2y=3
-4x+5y=-11
The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7). An equation is a proposition that has two equal sides as well as an equal sign .
what is equation ?
It is thought that a number's simplest form is represented by its smallest equivalent fraction. finding the simplest form: what to do. For shared factors, look into the numerator and denominator. Examine a fractional integer to determine if it is a prime number. An equation is a proposition that has two equal sides as well as an equal sign in the middle. In the general form of any equation, the degrees of all the variables are listed in descending order. The common representation of a system of equations is an x + b = 0. x + b y + c = 0 is the general form of a two-variable linear equation (or something similar). Identity or conditional equations are the two categories under which equations fall. An identity holds true regardless of how the variables are valued.
given
Equation substitution is another name for combining the equations. When one variable is added to another equation, this is done.
-8x - 5y = -13
-4x - 5y = 11
Let's make the second equation a one-variable-on-each-side equation.
-5y = 4x + 11
y = -4/5x - 11/5
Put this into your first equation right now.
-8x - 5(-4/5x - 11/5) = -13
Give out the -5 symbol.
-8x + 4x + 11 = -13
Stack similar phrases.
-4x + 11 = -13
-4x = -24
Divide both sides by -4 to isolate x.
x = -24/-4
x = 6
Reintroduce this to either equation now.
y = -4/5(6) - 11/5
Multiply.
y = -24/5 - 11/5
Subtract.
y = -35/5
Simplify.
y = -7
The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7).
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Above are two different models of the same rectangular dog run. If the area of the model on the left is 54 sq cm, what is the area of the model on the right?
Answer:
48 sq cm
Step-by-step explanation:
The smaller square is 3' x 3' = 9 square feet.
The larger square is 9' x 9' = 81 square feet.
9 goes into 81 exactly 9 times (81 / 9 = 9), so we could just multiply the 54 cm by 9 and get your answer in centimetres.
54 x 9 = 486 cm
Can someone help me? Or explain this please I will give all stars!!
Answer:
The slope is 1. It is the number before the x. If we do not see a number, we assume that the number is 1.
Step-by-step explanation:
Answer:
The slope: 1
Step-by-step explanation:
The slope is simply the number in front of the x ONLY in the form y=mx+b, which it is currently in. If it is not in that form, try and manipulate the equation to put it into that form.
Moreover, if it is just x by itself imagine there being a 1 in front of it.
The answer: 1
PLEASEEEEE HELPPPPPP!!!!
The combinations between the linear function g(x) = 4 · x + 1 and the quadratic function g(x) = 4 · x + 1 are f ° g (x) = 16 · x² + 44 · x + 10 and g ° f (x) = 4 · x² + 36 · x + 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) a linear function and a quadratic function, respectively. The composition between two functions is represented below:
f ° g (x) = f [g(x)]
g ° f (x) = g [f(x)]
Where the input of the former function is substituted by the latter function. Now we proceed to find the resulting function:
f(x) = x² + 9 · x
g(x) = 4 · x + 1
f ° g (x) = (4 · x + 1)² + 9 · (4 · x + 1)
f ° g (x) = 16 · x² + 8 · x + 1 + 36 · x + 9
f ° g (x) = 16 · x² + 44 · x + 10
g ° f (x) = 4 · (x² + 9 · x) + 1
g ° f (x) = 4 · x² + 36 · x + 1
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PLEASE ANSWER FAST FOR TEST
Represent the following scenario as a rate and a unit rate.
Write your Unsimplfied Rates as unsimplified fractions.
Write your Simplified Unit Rates as whole numbers or decimals rounded to two decimal places.
Form
Representing Rates and Unit Rates in Multiple Ways
Unsimplified Rate
Simplfied Unit Rate
"per language"
Dawn spent $32.2 on 14 gallons of gas.
Rate of Dollars to Gallons
dollars
gallons
dollars per gallon
Rate of Gallons to Dollars
gallons
dollars
gallons per dollar
The amount per gallon that Dawn will spend is $2.3 per gallon.
How to calculate the value in the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In the information given, it was stated that Dawn spent $32.2 in 14 gallons of gas. The amount per gallon will be:
= Total amount / Number of gallons
= $32.2 / 14
= $2.3
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