C = 300000
a = -0.07
The correct interpretation of x is OD. The variable x represents the number of years after 2000.
Answer:
Step-by-step explanation:
The exponential decay formula for this situation is
[tex]y=300,000(.93)^x[/tex]
where 300,000 is the initial value, .93 is decay rate (100% - 7% = 93% which is .93 as a decimal), and x represents the number of years after the year 2000. B is your answer.
On parallelogram ABCD below, if A(1, 1), B(8, 5), C(5,-5) and D(-2,-9), what are the coordinates of point E?
The coordinates of point E on the parallelogram are given as follows:
(3, -2).
How to obtain the coordinates of point E?The coordinates of point E are obtained considering that the point E is the midpoint of segment AC, hence it's coordinates are the mean of the coordinates of A and C.
Then the x-coordinate of point E is obtained as follows:
x = (1 + 5)/2 = 3.
The y-coordinate of point E is obtained as follows:
y = (1 - 5)/2 = -4.
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PLS HELP ASAP - algebra 2
India is studying microbiology and is doing an experiment with bacteria. She notices that one of her colonies is dying at a rate of 5% per day. if the original number of colonies was 2757, answer the following:
a. write the equation to model the data that India is witnessing
b. sketch a graph of your equation from part a.
An equation to model the data that India is witnessing is f(x) = 2757(0.95)^x.
A graph of this exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since her colonies is dying at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 5 = 95% = 0.95.
Substituting the parameters into the exponential equation, we have the following;
f(x) = 2757(0.95)^x
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How do you find the range of Class 6?.
The range is calculated as follows by combining the lowest and highest values. Organize the information in ascending or descending order first, then calculate the maximum and minimum values.
The range of a particular data set is the distinction between those maximum and minimum values. Range = Maximum Value–Minimum Value
The range of a set of data is the differential between the collective's maximum and minimum values.
Domain and range are keywords in relations and functions. The range is the set of all potential dependent values produced by a relation from a domain value.
To identify the range, first, arrange the data in ascending or descending order to gain a clear picture of the data's Maximum and Minimum terms.
Then, to get the data range, subtract the lowest value from the largest value in the collection.
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What is 1 4 of a circle in degrees?.
1 in 4 angle of slope in degree is 90°.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.
The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.
So to find the 1 in 3 angle we have to put the value 1/3 in arctan function
which is tan inverse function.
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What is the y coordinate of the solution of the following system 3x 2y 7y − 3x 11?.
So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.
To find the y-coordinate of the solution of a system of equations, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use substitution method.
The system of equations is:
3x + 2y = 7
y - 3x = 11
We can solve for y in the second equation and get:
y = 3x + 11
Now we can substitute this expression of y into the first equation:
3x + 2(3x + 11) = 7
3x + 6x + 22 = 7
9x + 22 = 7
9x = -15
x = -5/3
Now we can substitute this value of x into the second equation:
y = 3(-5/3) + 11
y = -5 + 11
y = 6
So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.
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An isosceles triangle has base angles that each measure x degrees. The measure of the third angle is 72 degrees. Write an equation that can be used to determine x, the measure of each base angle of the isosceles triangle.
Answer:
lol i don't know this
Step-by-step explanation:
lol= laugh out loud
What is ten more than 99?.
The answer of 10 more than 99 is 109.
The answer of 10 more than 99 is 109 which can be derived using simple mathematical calculations.
To find 10 more than 99, you can add 1 to the original number 99.
10 + 99 = 109
It's a simple arithmetic operation where you add a specific number, in this case, 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 99 is 109.
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I need to know the surface area for this shape please
Answer:
87cm²
Step-by-step explanation:
surface area =l×w all round since there is no square, we begin with the first part
6×3×2=36
3×2×2=12
6×2×2=24
4×1×2=
3×1×2=
1×1=1
Then add them all =87cm²
How do you find the inverse of a function in vertex form?.
The inverse of a function in vertex form can be determined by substituting the function in the standard form of a quadratic function
The various steps to find the inverse of a function in vertex form can be noted as -
First, it is required to write the equation in the quadratic function's usual form: y = a(x - h)² + k, where (h, k) is the vertex.The following formula should be changed: x = a(y - k)² + h.Now, by putting y on one side of the equation, solve for y: y = (x - h)/a² + kThe equation can be made simpler by adding -1/a² to the numerator and denominator to get the following result: y = -(x-h)²/a + kThe function will now be in vertex form, with the leading coefficient -1/a, and the vertex (h, k).Read more about vertex form on:
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A
The top of a signal tower is 135 meters above sea level. The angle of depression from the top of
the tower to a passing ship is 20°. How many meters from the foot of the tower is the ship? Round
to the nearest meter.
Answer:
371 meters
Step-by-step explanation:
This is a triangle trigonometry problem. The phase "angle of depression" means the angle looking down to the boat instead of looking straight out from the top of the tower. See image. You can then find the rest of the angle is 70°. Looking at the boat creates one line, the tower is another side, 135m, and the distance to the boat is the third side of a triangle. See image.
Tangent is a trig ratio. It compares the side opposite from the angle to the side next to (adjacent) the angle. We can then write an equation. Unless the teacher/program/text gives you tan 70°, you need a calculator to find it.
tan 70° = x/135
Multiply both sides by 135.
135 tan 70° = x
Put this in a calculator.
135 × tan70°
it comes out a long decimal. But the directions said to round to the nearest meter.
The boat is about 371 meters away from the foot of the tower.
f(x)=(x+1)^2+4
find the zeros, y-int, and vertex.
The zeros, y-intercept and vertex for the given quadratic equation f(x)= (x + 1)² + 4 are respectively,
Zeros- (-1 + 2i)
Y-intercept- 5
Vertex- (-1, 4)
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
f(x) = y = (x + 1)² + 4
y = (x + 1)² + 4
y - 4 = (x + 1)²
So, for vertex
x + 1 = 0
x = -1
y-4 = 0
y = 4
For Zeros, y = 0
y-4 = (x +1)²
(x +1)² = -4
x = -1 + 2i, -1-2i
the zeros are imaginary
For y intercept, x = 0
y-4 = (x +1)²
y = 4 + (1)²
y = 5
Hence, vertex, zeros, and y-int. are respectively (-1, 4), (-1 + 2i), 5
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Kevin had to measure the diameter of a hair strand and the diameter of a grain of sand for his science experiment. He found the diameter of the hair strand to be 0.00006 inches and the diameter of a gain of sand to be 1.3 x 10^-3 inches.
The diameter of the grain of sand is _____ x 10^-3 inches more than the diameter of the hair strand.
What assumption would you make to start the indirect proof of ⊿ ≅ ⊿?.
The assumption we would make to start the indirect proof of AB is congruent to BC is AB + BC.
Indirect Proof:
Step 1 Suppose a right triangle's hypotenuse is not the longest side. That is BC > AB and AC > AB.
Step 2 If BC > AB, then ∠C < ∠A. Since m C = 90, ∠A > 90. So, ∠C + ∠A > 180. By the same
reasoning, ∠C + ∠B > 180.
Step 3 Both connections counter the fact that the sum of the measures of the angles of a triangle equals 180.
Thus, the hypotenuse must be the longest side of a right triangle.
Hence, the correct option is C.
--The given question is incorrect; the correct question is
"What assumption would you make to start the indirect proof that AB is
congruent to BC?
A. A ≠ B
B. B ≠ C
C. AB + BC
D. BA < CB"--
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What is the product of the additive inverse and multiplicative inverse of 3 by 7?.
The additive inverse of 3/7 is -3/7, and the multiplicative inverse of 3/7 is 7/3.
A number that gives 0 after adding with its is called an Additive inverse and it gives 1 after multiplication with its is called a multiplicative inverse.
Here, the given number is: 3/7
Let, x be the additive inverse of the number:
3/7+x=0
x=-3/7
Thus, the additive inverse of 3/7 is -3/7.
Now, let y be the multiplicative inverse of 3/7,
⇒3/7*y
⇒1*y=7/3
Thus, the multiplicative inverse of 3/7 is 7/3.
Hence, the product of additive inverse and multiplicative inverse of minus 3 upon 7
⇒-3/7*7/3
⇒-1
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The area of circle Z is 64 π ft. What is the value of r? r = 4 ft
r = 8 ft
r = 16 ft
r = 32 ft
Answer:
8 ft
Step-by-step explanation:
Area of a circle is given by πr² where r is the radius
Here we are given the area A and asked to find the radius
We have Area :
πr² = 64π
Dividing by π on both sides we get
r² = 64
r = ±√64
r = ±8
We can ignore negative values for radius and state that
r = 8 ft
The formula for the area of the shaded region on the diagram is:
Area of the circle - Area of the square The area of the circle is 78.1c * m ^ 2 rounded to 1 decimal place.
The area of the square is 21.4c * m ^ 2 truncated to 1 decimal place. Write the error interval for the area, a, of the shaded region in the form m < a < n .
The error interval for the area of the shaded region is given as follows:
56.6 < a < 56.8.
How to obtain the error interval?The area of the circle is of 78.1 cm², rounded to one decimal place, hence the interval for the area of the circle is of:
78.05 <= area circle < 78.15.
The area of the square is of 21.4 cm², rounded to one decimal place, hence the interval for the area of the circle is of:
21.35 <= area square < 21.45.
The error formula is:
Area circle - Area square.
The minimum error is when the area of the circle is the greatest and the square is the least, hence:
m = 78.15 - 21.35
m = 56.8.
The maximum error is when the area of the circle is the least and the square is the greatest, hence:
n = 78.05 - 21.45
n = 56.6.
Meaning that the error interval is of:
56.6 < a < 56.8.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
The probability that a student studied for exactly 1 hour is 0.23 Or 23%. The correct option is A.
What is probability?
Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
A table is given where the first column represents the number of hours a student studied math and the second column represents the number of students.
The sum of the second column is 30. So it is the total number of students. And only 7 of them studied mathematics for 5 hours.
Therefore, The probability that a student studied for 5 hours is,
= 7/30.
= 0.23 or 23%.
Therefore, the correct option is A. 23.0.
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The question is incomplete. Your most probably complete question is given below:
23.0
0.70
0.23
0.16
What is the formula of median for class 7?.
The formula of median is Med(x) = X [n=1/2].
The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to consider the entire data set as a representation; in these cases, median is helpful. The median is a simple metric to calculate among statistical summary metrics. Since the data that is in the center of a sequence is used as the median, the median is also known as the Place Average.
Median Formula When n is Odd
Median = [(n + 1)/2] th term
Median Formula When n is Even
Median = [(n/2) th term + ((n/2) + 1) th term]/2
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Suppose that the functions u and w are defined as follows.
u(x) = -x +3
w (x) = 5x+2
Find the following.
(w-u) (-5) = [
(uw) (-5) =
0⁰ 0/6
X
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
What is composite function?Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.
Given:
u(x) = x^2 + 3
w(x) = √x+2
We have to find (w о u)(2) and (u о w)(2).
First to find (w о u)(x)
(w о u) = w(u(x))
= w(x^2 + 3)
(w о u) = √(x^2 + 3) + 2
(w о u)(2) = √(2^2 + 3) + 2
(w о u)(2) = √7 + 2
Now to find (u о w).
(u о w)(x) = u(w(x))
= u(√x+2)
= (√x+2)^2 + 3
= x + 4√x + 4 + 3
(u о w)(x) = x + 4√x + 7
(u о w)(2) = 2 + 4√2 + 7
(u о w)(2) = 9 + 4√2
Hence,
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
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the sum of two numbers is 300. the difference between the two numbers is 40. what are the two numbers
Answer:
170 and 130
Step-by-step explanation:
¿Cuáles son las medidas de un cono (radio, altura) si su volumen es 500 cm3?
The dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the volume of the cylinder as -
V = 500 cm³
We can write -
V = 500
So, we can write -
πr²h = 500
So, we can write -
{r} = √500/πh
{h} = (500/r²)
Therefore, the dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
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{Question in english -
What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}
M,
Lauren has watermelons and oranges in a ratio of 88:14. How many watermelons
does she have if she has 7 oranges?
Answer:
Lauren has 44 watermelons
Step-by-step explanation:
Let us use W to denote the number of watermelons and O to denote the number of oranges
We have
W:O = 88:14
This can be represented as a fraction:
[tex]\dfrac{W}{O} = \dfrac{88}{14}[/tex]
Divide numerator and denominator of [tex]\dfrac{88}{14}[/tex] by 2
[tex]\dfrac{88 \div 2}{14 \div 2} = \dfrac{44}{7}\\\\\\\\\mathrm{So\; \dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]
This means for every 7 oranges there are 44 times that number of watermelons
Since we are given that there are 7 oranges she should have 44 watermelons
Another way of looking at this is from the relation
[tex]\dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]
Putting in O = 7 we get
[tex]\dfrac{W}{7} = \dfrac{44}{7}\\\\[/tex]
Since the denominators are the same the numerators must be the same i.e. W = 44
Lauren has 44 watermelons
Nelly works at an hourly rate of $11. 28 per hour and worked 45 hours last week. She earns overtime for hours exceeding 40 hours. She is paid overtime at a rate of time and a half. What was her gross pay last week?.
Nelly's gross pay is $451.20 + $84.60 = $535.80.
Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.
First, we calculate her regular pay.
She worked 45 hours last week, and her regular hourly rate is $11.28 per hour. Therefore, her regular pay for the week is 40*$11.28 = $451.20. This is the pay she receives for the hours she worked up to 40 hours, which is considered the standard workweek.
Next, we calculate her overtime pay. Nelly worked 45 hours last week, and she is entitled to overtime pay for hours exceeding 40 hours. Therefore, she worked 45-40 = 5 hours of overtime.
Since she is paid time and a half for overtime, her overtime pay is calculated by multiplying her regular hourly rate by 1.5. Therefore, her overtime pay is 5*$11.28*1.5 = $84.60.
Finally, we add her regular pay and her overtime pay to get her gross pay. Her gross pay is the total amount she earns for the week, including both her regular pay and her overtime pay.
Therefore, her gross pay is $451.20 + $84.60 = $535.80.
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How do you know if its inverse?.
The process to identify if the function is inverse is identified through the horizontal line test.
Function in math is known as a correspondence from one value x of the first set A to another value y of the second set B.
Here we need to identify the way to know that whether the given unction is inverse function or not.
By using the horizontal line test that is If any horizontal line intersects the graph of f more than once then the function f does not have an inverse.
Where as If no horizontal line intersects the graph of f more than once, then the function f does have an inverse.
Here we have also have the property of having an inverse is very important in mathematics, and it has a name.
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Find the distance between the points p(8, 2) and q(3, 8). Round to the nearest tenth.
The distance between the given set of points is 7.8 units.
To find the distance between two points in a coordinate plane, we can use the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
In this case, we are given the points p(8, 2) and q(3, 8). Therefore, we can plug in the coordinates of these points into the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((3 - 8)^2 + (8 - 2)^2)
Distance = √((-5)^2 + 6^2)
Distance = √(25 + 36)
Distance = √61
The square root of 61 is approximately 7.8 which rounded to the nearest tenth is 7.8.
Therefore, The distance between the given set of points is 7.8 units.
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Simplify the following polynomial expression.
(5x^4 - 9x^3 + 7x -1) + (-8^4 - 3x + 2) - (-4x^3 + 5x - 1) (2x - 7)
Answer:
[tex]\boxed{\mathrm{Option \;D: 5x^4-37x^3-6x^2+41x-6}}[/tex]
Step-by-step explanation:
You can solve such multiple choice questions using a trick. This especially is useful in a time constrained question
Consider only the coefficients of the terms relating to x⁴ and the constant
If you expand (-4x³ + 5x - 1)(2x - 7) this will work out to
(--4x³) (2x) +..... + (-1)(-7)
This will result in (- 8x⁴ +..... + 7)
Since there is a negative sign before this last term, expanding will change the signs of the terms
-(-8x⁴ + ..... + 7) = 8x⁴ -7
Add the coefficients of the x⁴ terms to get
(5 - 8 + 8)x⁴ = 5x⁴
Add the constants of the individual terms
--1 + 2 - 7 which is -6
So the simplified polynomial is of the form
5x⁴ +....... - 6
Only option D fits these values, so the correct choice is Option D:
[tex]\mathrm{5x^4-37x^3-6x^2+41x-6}[/tex]
ANSWER
--------------------------------------------------------------------------------------------------
If you want to do it the hard way,
First evaluate the last product using FOIL:
[tex]\left(-4x^3+5x-1\right)\left(2x-7\right)\\\\= \left(-4x^3\cdot \:2x-4x^3\left(-7\right)+5x\cdot \:2x+5x\left(-7\right)-1\cdot \:2x-1\cdot \left(-7\right)\right)\\\\= \left(-8x^4+28x^3+10x^2-37x+7\right)\\\\[/tex]
With the negative sign in front of this expression this becomes:
[tex]-\left(-8x^4+28x^3+10x^2-37x+7\right)\\\\= 8x^4-28x^3-10x^2+37x-7\\\\[/tex]
From the original polynomial expression, group like terms:
[tex]\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right)-\left(-4x^3+5x\:-1\right)\left(2x-7\right)\\\\[/tex]
[tex]=\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right) + (8x^4-28x^3-10x^2+37x-7)\\\\[/tex]
Five le than a number i le than or equal to 6 time the number. What inequality can be written to repreent thi tatement?
The inequality statement will be x-5 ≤ 6.
Inequalities are mathematical expressions that contain variables and numerical terms that are separated by the inequality symbol.
An inequality can be derived from a statement of words, which must be correctly interpreted in order to yield the appropriate inequality.
When there are more than and fewer than values in the inequality, we know that the variable must be in the middle.
The inequality symbols are greater than, less than, greater than or equal, and less than, or equal.
There are two conditions given in the question as mentioned below:
1. Five less than a number
2. the number is less than or equal to 6
Let x be the number,
x-5 ≤ 6
So, the inequality statement will be x-5 ≤ 6
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Consider the rectangle with a width of 6 cm and a length of 9 cm. Write a ratio of the length to the width and simplify.
Answer:
Step-by-step explanation:
ttt
How do you simplify 9x?.
To simplify 9x, you need to use the distributive property.
The distributive property states that when you multiply a number by a group of numbers or variables, you can separate the group into individual components, multiply each component by the number, and then add the products together.
For example, 9x can be simplified as follows:
9x = 9x(1)
Using the distributive property, you can separate the 1 into individual components:
9x = 9x(1) = 9x(1 + 0)
Then, you multiply each component by the number:
9x = 9x(1) = 9x(1 + 0) = 9x(1) + 9x(0)
And finally, you add the products together:
9x = 9x(1) + 9x(0) = 9x + 0
Therefore, 9x can be simplified to 9x.
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help me with my ALEKS topics pls, i have 5 left and i need to finish them quick
Answer:
V ≈ 13036 ft³
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here diameter = 19, then r = 19 ÷ 2 = 9.5 and h = 46 , then
V = 3.14 × 9.5² × 46
= 3.14 × 90.25 × 46
≈ 13036 ft³ ( to the nearest whole number )
