Answer:
110 billion or 1.10x10^8 to the nearest 10th.
Step-by-step explanation:
The population, P, that results from a constant yearly increase from a starting value (S) at a rate (R, as a decimal)) for x years is given by the expression:
P(x) = S*e^(1+R)x
P(40) = (35x10^6)*(1.03)^40
P(40) = (35x10^6)*(1.03)^40
P(40) = (35x10^6)*3.26
P(40) = 1.14x10^8
The popultion will be 114,000,000 [114 billion or 1.14x10^8)
110 billion or 1.10x10^8 to the nearest 10th.
At what y points on the curve xy = 25 is the tangent line parallel to 5x + y = 0?
The point at which =the curve xy = 25 is the tangent line parallel to 5x + y = 0 is y = ± 5√5 so, option A is correct.
What is line?
A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.
Given:
the curve xy = 25 and the equation of the line is 5x + y = 0,
The equation of line parallel to line 5x + y = 0 will be,
y = mx + c
y = -5x + c (y = -5x)
The line will be in the curve as it is tangent, so,
xy = 25 and y = -5x + c line have a solution,
Solve the above equation as shown below,
y = ± 5√5
Thus, the point y = ± 5√5 the line is tangent to the curve.
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find the domain of the function
The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }
What is Domain of function?
A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.
According to question
⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]
⇒ x² + y² - 1 ≥ 0
⇒ x² + y² ≥ 1
Hence, the Domain of f(x, y) is { (x, y) ∈ R² | x² + y² ≥ 1 }
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The sum of 18 and a number, x, equals negative 40.
Answer:
x = -58
Step-by-step explanation:
18 + x = -40
-18 -18
x = -58
a ferris wheel 50 ft in diameter makes one revolution every 40 sec. if the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground
So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.
Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
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Suppose that the relation S is defined as follows.
S= {(4,n), (8,q), (4,m)}
Give the domain and range of S.
Write your answers using set notation.
Domain=
Range=
The domain of the relation is {4,8} and the range of the relation is {n,q,m}.
What is domain?A function or relation's domain is the set of all potential independent values that it can have.
Suppose that the relation S is defined as follows.
S= {(4,n), (8,q), (4,m)}
The first term at the point represents the input and the second term at the point represents the output.
So,
the input values are 4,8 and 4 and their respective outputs are n, q and m,
The collection of all conceivable independent values that a function or relation may take is known as its domain.
So, the domain is {4,8}.
The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.
So, the range is {n,q,m}
Therefore, the domain is {4,8} and the range is {n,q,m}.
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Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r. Then write a sentence to explain your answer.
Explanation:
x = amount she travels on each of those three remaining days
3x = total amount traveled over those three remaining days
3x+24 = total amount traveled over the four days
3x+24 = 120 miles total
This equation is in the form px+q = r where:
p = 3q = 24r = 120Let's solve for x. We follow PEMDAS in reverse to undo what's happening to x, so we can isolate it.
3x+24 = 120
3x+24-24 = 120-24 .... subtract 24 from both sides
3x = 96
3x/3 = 96/3 .... divide both sides by 3
x = 32
Triana must travel 32 miles per day for those remaining three days.
Doing so means she travels 3x = 3*32 = 96 miles over those three remaining days. Then add on those 24 miles traveled on the first day to get 96+24 = 120 miles total. This helps confirm the answer.
Another way to confirm the answer is to plug x = 32 into 3x+24 = 120. After simplifying both sides, you should get 120 = 120 which is a true statement.
Select the correct answer from each drop-down menu.
In a particular year, the population of Dallas, TX, was approximately 1 × 10^6 people. If the population of Los Angeles, CA, was approximately three times that of Dallas, there were about ______ x _______ ^6 people living in Los Angeles that year.
The population of Pittsburgh, PA, was approximately 3 × 10^5 people during the same year, which was about ______times that of Dallas.
Answer:
Step-by-step explanation:
Dallas = 1 x 10^6
Los Angeles = 3 times Dallas = 3 [ 1 x 10^6] = 3 x 10^6
Pittsburgh / Dallas = [ 3 x 10^5 ] / [ 1 x 10^6] = 3 / 10 that of Dallas
find the value of y² when y=-9
Answer:
81
Step-by-step explanation:
y = -9
y² = (-9)² = 81
[tex]5 x^2-2x-6=-x^2+6x[/tex]
i just need help with the steps please <3
Answer:
x = -1
Step-by-step explanation:
To solve this equation, you can use the process of polynomial algebra.
First, you can rearrange the terms on the left side of the equation so that all the terms with an x^2 coefficient are on one side and all the other terms are on the other side. You can do this by adding x^2 to both sides of the equation:
5x^2 - 2x - 6 + x^2 = -x^2 + 6x + x^2
This gives you:
6x^2 - 2x - 6 = 6x
Now, you can rearrange the terms on the right side of the equation in the same way:
6x^2 - 2x - 6 = 6x^2 - 6x
To solve for x, you can now use the process of polynomial algebra to combine like terms on each side of the equation. This gives you:
6x^2 - 2x - 6 = 6x^2 - 6x
Combining like terms on the left side of the equation gives you:
6x^2 - 6x - 6 = 6x^2 - 6x
Combining like terms on the right side of the equation gives you:
6x^2 - 6x - 6 = 6x^2 - 6x
Now, you can subtract 6x^2 - 6x from both sides of the equation to obtain:
-6x - 6 = 0
Dividing both sides of the equation by -6 gives you:
x + 1 = 0
Finally, you can solve for x by subtracting 1 from both sides of the equation, which gives you:
x = -1
Therefore, the solution to the original equation is x = -1.
Evaluate. Remember Order of
Operations! (PEMDAS)
4-(7+2)÷3= [?]
Answer: 1
Yessssssssssssssss
10 points if you answer his question
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.
Which relationships have the same constant of proportionality between yyy and xxx as the following table?
x y
7 24.5
9 31.5
Choose 3 answers
Answer:
A,D,E
Step-by-step explanation:
A:
14/4 = 3.5
D:
7/2 = 3.5
E: 14/4 = 3.5
The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.
Explanation:To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.
Now, we need to find the relationships that have the same constant of proportionality.
For example, if we have a table with the following values:
x1 y1
x2 y2
x3 y3
and the constant of proportionality is k, then we have the following equations:
x1/ y1 = k
x2/ y2 = k
x3/ y3 = k
So, any other table that satisfies these equations will have the same constant of proportionality as the given table.
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What is the solution to the system of equations graphed below ?
Answer: (6, -1)
Step-by-step explanation:
<3
The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
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Which matrix can be multiplied to the left of a vector matrix to produce another vector matrix?
The matrix that can be multiplied to the left of a vector matrix to produce another vector matrix given as follows:
A. [2;5].
What is a vector matrix?A matrix is also called a vector matrix when it has either only one row or only one column.
In multiplication of matrices, the rows of the left matrix are multiplied by the columns of the right matrix, and the dimensions are given as follows:
the number of rows of the left matrix.the number columns of the right matrix.The matrix in this problem that we are going to multiply is the right matrix, meaning that we want a matrix with one column, and more than one row, which is given by option A.
(a matrix with only one element, as is the case for option D, is not considered a vector matrix).
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arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. based on the results, she reports that 44% of the people in her state bike to work. why is this statistic misleading?
Sample is biased. Based on her findings, Arianna revealed the percentage in her state after polling 600 residents of her city. Thus, the sample fails to accurately reflect the population. Option (4) is correct.
When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. What makes sampling bias significant? Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population. When some population members have a higher or lower sampling probability than others, the sample is biased.
This includes choosing or sampling people according to their hobbies, gender, or age. Therefore, a fair or impartial sample must be representative of the entire population under investigation. When a research study design fails to gather a representative sample of a target population, the phenomenon known as sampling bias takes place. This usually happens as a result of the respondents' selection criteria not capturing a broad enough sampling frame to include all points of view.
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Correct Question:
Arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. Based on the results, she reports that 44% of the people in her state bike to work. Why is this statistic misleading?
Select the correct answer below:
1. The statistic contains a calculation error.
2. The sample is self-selected.
3. The data contains an outlier.
4. The sample is biased.
please help meee!!!!
The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,
What is the linear pair angles?
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
We have,
Angles:
6x° + 35°
z°
8x° + 51°
To find the values of x and z
from the given figure
Linear pair angles:
6x° + 35° + 8x° + 51° = 180
14x° + 86° = 180
14x° = 180° - 86°
14x° = 94°
x° = 94°/14°
x° = 6.71°
Vertically opposites angles are equal
6x° + 35° = z°
z° = 6( 6.71°)° + 35
z° = 40.26 + 35
z° = 75.26°
Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.
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For a sample size of 85 and a population parameter of 0.2, what is the standard error of the sampling distribution?
Answer:
0.043
Step-by-step explanation:
I hope this helps you! Let me know if you have any questions! :)
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
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Harry owns a rare baseball card that is valued at $13.00. If he originally purchased the card for $5.00, by what percentage has its value increased?
The value of baseball card has increased by 160(%) percentage.
What is the percentage?
A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.
Increase = New Number - Original Number
Then: we divide the increased number by the original number and multiply by 100.
Therefore, % increase = (Increase ÷ Original Number)× 100.
Given, the new price of a baseball card = $13
The original price of a baseball card = $5
Then from the above definition,
Increase = 13-5 = 8
% increase = (8/5)*100 = 160%
Hence, its value has increased by 160 percentage.
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Rewrite 20x4y3 − 30x3y4 using a common factor. 2x4y4(10 − 15x) 2x3y3(10y − 15x) 5x4y3(4 − 6y) 5x3y3(4x − 6y)
The expression which represents the correctly rewritten form of the given expression; 20x⁴y³ - 30x³y⁴ is; 5x³y³ ( 4x - 6y ).
Which expression correctly represents the rewritten form of the expression 20x⁴y³ - 30x³y⁴?It follows from the task content that the expression which correctly represents the rewritten form of the given expression be determined.
On this note, since the given expression is;
20x⁴y³ - 30x³y⁴
The greatest common factor of both terms in the expression is; 10x³y³ .
On this note, the expression can be factorised completely as follows;
10x³y³ ( 2x - 3y )
However, the expression which is equivalent to the expression above among the answer choices is;
5x³y³ ( 4x - 6y )
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There is a line whose y-intercept is 10 and whose slope is 0. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in
simplest form.
Answer:
Below
Step-by-step explanation:
A line with slope = 0 is a horizontal line
for y = mx + b form this would be
y = (0)* x + 10
y = 10
A speed skater goes around a turn with a 25 m radius. The skater has a velocity of 15 m/s and experiences a centripetal force of 720 N. What is the mass of the skater?
Answer:
80 kg
Step-by-step explanation:
To find the mass of the skater, you can use the formula for centripetal force:
F_centripetal = m * v^2 / r
Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
Plugging in the values you know, you get:
720 N = m * (15 m/s)^2 / 25 m
Solving for m, you find that the mass of the skater is:
m = 720 N * 25 m / (15 m/s)^2
= 720 N * 25 m / 225 m^2/s^2
= 80 kg
So the mass of the skater is approximately 80 kilograms.
When Landon overdrafts from his checking account, his bank moves $50 from his savings account into his bank account and charges him $5 (from his checking account) as a penalty each time it happens. If Landon had $75.32 in his checking account and he wrote a check for $113.85, how much money would he have in his checking account after the check is cashed and the bank handles his overdraft?
Answer:
Landon would have -$43.53 in his checking account after the check is cashed and the bank handles his overdraft.
Step-by-step explanation:
let g be a polynomial function of x where g(x) = 2x^3 + 5x^2 - 28x - 15 Given (x - 3) is a factor of g, what is the reminder of g(x) + (x - 3)?
The remainder of polynomial g(x) divides (x - 3) that is g(x) / (x - 3) is 0.
What is polynomial?
A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.
Given: g(x) = 2x^3 + 5x^2 - 28x - 15
(x - 3) is a factor of g(x).
We have to find the remainder of g(x) / (x - 3).
Consider,
2x^2 + 11x + 5
[tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]
- 2x^3 -6x^2
____________________________
11x^2 - 28x
- 11x^2 - 33x
____________________________
5x - 15
- 5x - 15
_______________________________
0
Hence, the remainder of polynomial g(x) divides (x - 3) that is
g(x) / (x - 3) is 0.
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A student rewrites the expression 12⋅16−s as another equivalent expression. Which expression could the student write?
The equivalent expression could be 4×3·4×4−s
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.
Let's now have a look at some expressions with variables, such 5x+2.
It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.
The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.
When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.
Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
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The equivalent expression could be 4×3·4×4−s.
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.Let's now have a look at some expressions with variables, such 5x+2.It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
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5. A student surveyed 100 adults who took either vitamin C, zinc, or echinacea
supplements to prevent getting a cold. The adults were asked if they had a cold or no
cold in the last 30 days. The results are shown in the table.
vitamin C
zinc
no cold cold
41
echinacea
total
12
21
74
15
5
6
total
26
56
17
27
100
a. What proportion of adults in the survey took echinacea?
b. What proportion of adults who took vitamin C reported having a cold in the last
30 days?
c. What proportion of adults who reported having a cold took zinc?
The proportions for this problem are given as follows:
a) Took echinacea: 0.27.
b) Having a cold in the last 30 days, of those who took Vitamin C: 0.2679.
c) Took zinc, of those having a cold: 0.1923.
How to calculate the proportions?The proportions are calculated as the division of the number of desired outcomes by the number of total outcomes.
The survey is composed by 100 adults, and of those, 27 took echinacea, hence the proportion is of:
27/100 = 0.27.
56 adults took vitamin C, and of those, 15 reported a cold in the last 30 days, hence the proportion is of:
15/56 = 0.2679.
26 students had a cold in the last 30 days, and of those, 5 took zinc, hence the proportion is calculated as follows:
5/26 = 0.1923.
Missing InformationThe table is given by the image shown at the end of the answer.
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Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .
Answer:We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
Step-by-step explanation:A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
8 The graph shows four ordered pairs that represent ratios. Which
ordered pair represents a ratio that is not equivalent to the others?
A (2,12)
B (3,18)
C (5,24)
D (6,36)
C (5,24) ordered pair represents the ratio that is not equivalent to the others.
What is a ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Consider first pair A, the ratio is given by
2/12 = 1/6
Consider next pair B, the ratio is given by
3/18 = 1/6
Consider next pair C, the ratio is given by
5/24 is not equat to 1/6
Consider next pair D, the ratio is given by
6/36 = 1/6
Hence, the ordered pair represents a ratio that is not equivalent to the others is C (5,24).
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