The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).
What is interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .
Given exponential function is f(x) = B^x.
A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.
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What is an equivalent function?
Equivalent function has the same domain and range. Equivalent and equal terms are not the same both have different meanings in mathematics.
A function is said to be equal if its Domain and Range are identical. Complete solution, step by step: A and B should be two sets. Now, by function, we mean a rule that guarantees that f(a)=b exists for all a. As a result, set A is referred to as the Domain of File and set B as the Range Off.
Despite being comparable to 1 + 1, 2 is believed to be equal to 2. When two items or amounts are exactly the same, as when 12 is equal to 12, yet 12 is equivalent to 2/4 since they reflect the same value, we can say that they are equal.
In mathematics, an equivalent can be defined in one of two ways. This is thus because there are various definitions for the concept of equivalent in mathematical theory. Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.
Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects.
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MATH PLEASE I NEED ANSWER
Deshaun deposits $4,000 into an account that pays simple interest at an annual rate of 6% . He does not make any more deposits. He makes no withdrawals until the end of 2 years when he withdraws all the money.
After 2 years, Deshaun will have earned $4,000 * 6% = $240 in interest.
The total amount of money in the account at the end of 2 years will be $4,000 + $240 = $4,240. This is the amount Deshaun will withdraw.
4. Nicole uses 2.5 meters of ribbon to decorate
door wreaths. There are 20 meters of ribbon on a
spool. Write an equation that could be used to
determine the number of wreaths that Nicole
could decorate using one spool of ribbon. Solve.
Equation:
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
where W is the number of wreaths, S is the total length of ribbon on the spool, and R is the length of ribbon used per wreath.
Plugging in the given values, we get:
W = 20 / 2.5
Solving for W, we get:
W = 8
So Nicole could decorate 8 wreaths using one spool of ribbon.
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A bookcase is 3 feet high and 3 feet wide. Two braces are going to be built to diagonally cross the back of the case. How long is the piece of wood that is needed to build each brace?
The length of each piece of wood needed to build each brace of the bookcase will be 4.24 feet.
Based on the dimensions, the shape of bookcase is square. So the diagonal of the bookcase will be calculated from the formula -
Diagonal = ✓side² + side²
Keep the values in formula to find the value of diagonal
Diagonal = ✓ 3² + 3²
Taking square on Right Hand Side of the equation
Diagonal = ✓9 + 9
Performing addition on Right Hand Side of the equation
Diagonal = ✓ 18
Finding square root on Right Hand Side of the equation
Diagonal = 4.24 feet
Thus, each diagonal will be 4.24 feet.
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Audrey's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=59+6xy=59+6x, where yy represents the expected quiz score and xx represents hours spent on homework that week. What could the number 59 represent in the equation?
A student's expected quiz score if they spent no time on their homework.
A student's expected quiz score if they spent 65 hours on their homework.
The change in expected quiz score for every additional one hour students spend on their homework.
How many hours a student spends studying all year
The number 59 in the equation represents the following:
"A student's expected quiz score if they spent no time on their homework"
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
y=59+6x
When x=0, y=59+6*0 = 59+0 = 59
This means, y=59 is the student's expected quiz score if they spent no time on their homework.
The number 59 in the equation represents the following:
"A student's expected quiz score if they spent no time on their homework"
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It ha been etimated that about 15% of frozen chicken contain enough almonella bacteria to caue illne if improperly cooked. Suppoe that a upermarket buy 1000 frozen chicken from a upplier. Find an approximate 68% interval (remember empirical rule: approx. 68% of data within 1 tand. Deviation of mean) for the number of frozen chicken that may be contaminated
approximate 68% interval (remember empirical rule: approx. 68% of data within 1 tand. Deviation of mean) for the number of frozen chicken that may be contaminated is (271.02, 328.98) = (271, 329)
Suppose number of trials, n = 1000
And number of defective chickens is within 1 standard deviation of the mean :
Mean = np ; p = 0.3
Mean = 1000 * 0.3 = 300
Standard deviation (s) : sqrt(np(1-p))
s = sqrt(1000 * 0.3 * 0.7)
s = sqrt(210)
s = 14.49
2 standard deviations of the mean: and interval
Mean ± 2s
Lower bound : 300 - 2(14.49) = 271.02
Upper bound : 300 + 2(14.49) = 328.98
(271.02, 328.98) = (271, 329)
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What is the area of the shaded region? Use 3.14 for pi and round your answer to the
nearest tenth.
O
6 cm
10 cm
12.6 cm²
78.5 cm²
50.2 cm²
201.0 cm²
The area of the shaded region is, 201.0 cm².
What is circle?
A circle is a closed, two-dimensional figure in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric around the center for all angles.
In the given figure we have to find the area of the shaded region.
First to find the area of circle with radius 10cm.
Area of circle = [tex]= \pi r^2 = 3.14*(10)^2 = 3.14*100 = 314cm^2[/tex]
Now to find the area of circle with radius 6cm.
Area of circle = [tex]= \pi r^2 = 3.14*6^2=3.14*36 = 113.04 cm^2[/tex]
So, the area of the shaded region is,
[tex]314cm^2 - 113.04cm^2 = 200.96cm^2=201.0cm^2[/tex]
Hence, the area of the shaded region is, 201.0 cm².
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Even more geometry stuff pls help
Answer:
[tex]z=\frac{25}{3}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem, the length of the altitude to the hypotenuse is [tex]\sqrt{5^2-3^2}=4[/tex].
Using the geometric mean theorem,
[tex]4^2=3(z-3) \\ \\ 16=3z-9 \\ \\ 25=3z \\ \\ z=\frac{25}{3}[/tex]
Recall that there are 2π radians in one full rotation and 360 degrees in one full rotation.
Suppose an angle has a measure of 2. 1 radians.
This angle (with a measure of 2. 1 radians) is what percent of a full rotation?
 %
Use your work in part (i) to determine the measure of the angle in degrees.
 degrees
If there are [tex]2\pi[/tex] radians and [tex]360 \textdegree[/tex] in one full rotation and an angle has a measure of [tex]2.1 radians[/tex] then the angle is 33.4 percent of a full rotation , and the measure of the angle in degrees is [tex]120.2\textdegree[/tex] .
we know that in 1 full rotation , the radians is 2π ;
and in 1 full rotation , the degree is 360 degree ;
We know that the relation between the degree and the radian measure is
⇒ [tex]1 radian = \frac{180\textdegree}{\pi }[/tex] ;
Part(i) ;
we have to express the 2.1 radians as a percent of full rotation ;
we get ; ⇒ [tex]\frac{2.1}{2\pi } \times 100\%[/tex]
on simplifying further ,
we get ; [tex]\approx 33.4\%[/tex] .
Part(ii) ;
we have to determine the measure of the angle in degrees.
from part(i) , we find the percent is [tex]33.4\%[/tex] ,
So , [tex]33.4\%\times 360\textdegree[/tex]
On simplifying ,
⇒ [tex]\frac{33.4}{100} \times 360\textdegree[/tex]
[tex]\approx 120.2\textdegree[/tex] .
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Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet. What is the volume of material he must purchase
So Cheng must purchase 32 cubic feet of sculpting material.
Each pyramid has a square base with edge length of 2 feet and a height of 6 feet. The area of the square base is (2 feet)^2 = 4 square feet. The volume of each pyramid is 1/3 * base area * height = 1/3 * 4 square feet * 6 feet = 8 cubic feet.
Since there are four identical pyramids in the sculpture, the total volume of material needed to create the sculpture is 4 * 8 cubic feet = 32 cubic feet. So Cheng must purchase 32 cubic feet of sculpting material.
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Answer:
D
Step-by-step explanation:
Jo ha three metal block. The weight of each block i the ame. When he weighed one block againt 8 gram, thi i what happened
The block weighed 8 grams. The other two blocks average have weighed the same amount as the first block, so they also weighed 8 grams each.
1. Joe has three metal blocks.
2. The weight of each block is the same.
3. Joe weighed one of the blocks against 8 grams.
4. The block weighed 8 grams.
5. The other two blocks must have weighed the same amount as the first block, so they also weighed 8 grams each.
Joe had three metal blocks that all weighed the same. He weighed one of the blocks against 8 grams, and it weighed exactly 8 grams. This meant that the other two blocks must also have weighed 8 grams each, since the weight of all three was the same. Joe was able to determine the weight of all three blocks with just one measurement.
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Solve the Equation.
6x−3(x+8)=9
x=?
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
[tex]6x-3(x+8)=9\\6x-3x-24=9\\3x-24=9\\3x=33\\x=11[/tex]
Answer:
X=11
Step by step:
6x-3(x+8)=9
=6x-3x-24=9
=3x-24=9
+24 +24
=3x=33
=3x/3=33/3
X=11
Expand.
This question is worth 50 points!
Answer:
the answer is (a) x² - 2hx + h²
Step-by-step explanation:
(x-h)² = (x-h)(x-h) = x(x-h)-h(x-h)
x² - hx -hx + h²
= x² - 2hx + h²
Answer:
A) x² - 2hx + h²-----------------------------
Use the identity:
(a - b)² = a² - 2ab + b²Substitute a = x, b = h to get:
(x - h)² = x² - 2hx + h²This is the option A.
Xavier ran 13 miles in 182 minutes. Assume Xavier maintains a constant speed.
Enter the number of minutes it takes Xavier to run 1 mile
Answer:
14 minutes
Step-by-step explanation:
We can represent Xavier's running in the following ratio using the given information:
distance : time
13 miles : 182 minutes
To get the answer to this problem, all we have to do is divide both sides of the ratio by 13, so that the left side is 1 mile.
[tex]13 \textrm{ miles} : 182\textrm{ minutes}\\\overline{\ \ \ \ 13 \ \ \ \: } \ \ \: \overline{\ \ \ \ \ \ \, 13 \ \ \ \ \ \ }[/tex]
1 mile : 14 minutes
It takes Xavier 14 minutes to run 1 mile.
Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
c=⟨–5,8⟩ and d=⟨7,4⟩, find –4c–4d.–4c–4d=
2 The test statistic in a two-tailed test is z=-2. 75 use a 0. 05 significance level to find the P value and state the conclusion about the null hypothesis
The p-value of the test statistic is p-value = 0.006. The null hypothesis will be rejected at 5% level of significance.
What Is Two-Tailed Test?A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining statistical significance. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.
A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.
It is employed in testing the null hypothesis and determining statistical significance.
The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.
Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.
How to calculate the p-value?
Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.
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A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone
The radius of the sphere 1.5 units
The volume of the cone is pi (3)^2 *4 / 3 units^3 = 12pi units^3
The volume of the sphere is (4/3)pi (1.5)^3 units^3 = 4.5 units^3
So ratio of the volume of the sphere to the cone is :
4.5 pi / 12 pi = 4.5 / 12 = (9/2) / (24/2) = 9 / 24 = 3 / 8
What is radius?In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.To learn more about diameter refer to:
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Find the 66th term of the arithmetic sequence 25, 10, -5, ...
On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.
Arithmetic sequence is what?An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.
The given arithmetic sequence is,
25, 10, -5, .....
The sequence's initial word, a, equals 25, while the common difference, d, equals -15.
Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.
66th term =
[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]
The 66th term of the arithmetic sequence is -950.
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Kate bought a circular swimming pool with a diameter of 50 feet. She wanted to know about how
many feet the circumference of her pool is. Which of these is the closest number to the
circumference?
The closest number to the circumference of the circle is 157 feet.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.
Given:
Kate bought a circular swimming pool with a diameter of 50 feet.
We have to find the closest number to the circumference of the circle.
Since,
Circumference = 2πr
where r is the radius of circle.
Here diameter of circle = 50 feet.
⇒ Radius of circle = 25 feet.
⇒ Circumference = 2*π*25 = 157.08
Hence, the closest number to the circumference of the circle is
157 feet.
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Solve 12 (10x + 3 -8y)
Answer:
120x - 96y + 32
Step-by-step explanation:
12 (10x + 3 -8y)
We use the distributive property to solve
120x - 96y + 32
One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is
120x - 96y + 32
Can u please help . ?............
Answer:
See the picture below
Step-by-step explanation:
What is the slope of this line? (5 points)
Show all work.
Answer:
-2,2
Step-by-step explanation:
Is 2x 3 a linear function?
Answer:
yes
Step-by-step explanation:
The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.
8^x/2 divided by 4^x/3 equals 2^-5/2
The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:
x = -6/5.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]
Both 8 and 4 are powers of 2, as follows:
8 = 2³.4 = 2².Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]
The subtraction is obtained as follows:
3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.
(as the least common factor of 2 and 3 is of 6).
Then the simplified expression is of:
[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]
As the exponential function y = 2^x is injective, the solution is obtained as follows:
5x/6 = -5/2.
10x = -12
x = -6/5.
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How do you find the horizontal asymptote of a limit?
The way to find the horizontal asymptote of the limit is evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.
The term asymptote in math is defined as a line that the graph of a function approaches as either x or y go to positive or negative infinity.
Here we have to find the horizontal asymptote of a limit.
The process of finding the horizontal asymptote is the line y = 0 is called the asymptote of the graph, and it also represents the value that f(x) will never quite reach.
Here we can also say that f ( x ) = 1 x is asymptotic to the line y = 0.
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A cube with volume 8 cubic centimeters is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube ? express your answer in simplest radical form.
In simplest radical form as A = 22 = 4 cm2
The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.
Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.
To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.
V = a3
8 cm3 = a3
Taking the cube root of both sides gives us:
a = ∛8
a = 2 cm
Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.
A = l*w
A = 2*2
A = 4 cm2
This can also be expressed in simplest radical form as A = 22 = 4 cm2.
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What is the difference between a problem and an algorithm?
A problem is just a function or even a mapping of inputs to outputs. An algorithm is a recipe for solving a problem with concrete and unambiguous steps.
What is algorithm?In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions used to solve a class of specific problems or perform a computation.
Algorithms are data calculation and processing specifications. More advanced algorithms can use conditionals to divert code execution through various paths (referred to as automated decision-making) & deduce valid inferences (referred to as automated reasoning), eventually achieving automation.
Alan Turing used metaphorical terms like "memory", "search," and "stimulus" to describe machines.
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Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality? A. all whole-number values of n that are at least 1 B.all whole-number values of n that are greater than 1 C.all rational-number values of n that are at least 0.5 D.all rational-number values of n that are greater than 0.5
A statement which correctly describes the solution set of the given inequality include the following: C. all rational-number values of n that are at least 0.5.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.
Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;
5n + 1.5 ≥ 4
Subtracting 1.5 from both sides of the algebraic inequality, we have:
5n + 1.5 - 1.5 ≥ 4 - 1.5
5n ≥ 2.5
Dividing both sides of the algebraic inequality y 5, we have:
n ≥ 2.5/5
n ≥ 0.5
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