Answer:
The possible distance in miles that Amelia can drive without exceeding her budget is 270 miles
Step-by-step explanation:
Given:
Amelia's budget for renting a car for a day trip = $ 89
Rental cost = $35
cost per mile = $0.20
To Find:
The possible distance in miles that Amelia can drive without exceeding her budget = ?
Solution:
Let M be the number of miles
The equation representing the situation can be
Total budget less than or equal to rental + (number of mile x cost per mile)
That is
[tex]89 \leq 35 +(0.20 \times M)[/tex]
Solving for M, we get
[tex]89-35 \leq 0.20 M\\[/tex]
[tex]54 \leq 0.20M\\[/tex]
[tex]M \leq \frac{54}{0.20}[/tex]
[tex]M \leq 270[/tex]
Amelia's budget: $89. Rental: $35/day + $0.20/mile. Inequality: [tex]\( M \leq 270 \)[/tex] . Amelia can drive ≤270 miles.
let's break it down step by step.
1. Setting up the total cost equation:
We're given that the rental cost is $35 per day plus $0.20 per mile. So, the total cost [tex]\( C \)[/tex] can be represented as:
[tex]\[ C = 35 + 0.20M \][/tex]
Where [tex]\( M \)[/tex] is the number of miles driven.
2. Setting up the inequality:
We're told that Amelia can spend no more than $89. Therefore, we set up the inequality:
[tex]\[ 35 + 0.20M \leq 89 \][/tex]
This inequality represents that the total cost (rental cost plus mileage cost) should be less than or equal to $89.
3. Solving the inequality:
To solve for [tex]\( M \),[/tex] we first subtract $35 from both sides to isolate the term involving [tex]\( M \):[/tex]
[tex]\[ 0.20M \leq 89 - 35 \] \[ 0.20M \leq 54 \][/tex]
4. Dividing both sides by 0.20 to isolate [tex]\( M \):[/tex]
[tex]\[ M \leq \frac{54}{0.20} \] \[ M \leq 270 \][/tex]
5. Interpreting the result:
The inequality [tex]\( M \leq 270 \)[/tex] tells us that Amelia can drive at most 270 miles without exceeding her budget of $89.
So, in detail, Amelia can drive a maximum of 270 miles to stay within her budget. Any distance beyond that would exceed her budget of $89 for the day trip.
Over the last 5 business days, Ross made the following numbers of sales calls: 7,9,6,10, and 8. On average, how many calls
did he make a day?
Answer : 8
7 + 9 + 6 + 10 + 8 = 40
40/5 (5 is the number of sales calls) = 8
A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?
The population of the town in 5 years is 12763
The given parameters are:
Initial value (a) = 10000
Rate (r) = 5%
A population growth model is represented as:
[tex]y = a(1 + r)^x[/tex]
So, we have:
[tex]y = 10000 * (1 + 5\%)^x[/tex]
In 5 years, we have:
[tex]x = 5[/tex]
So, we have:
[tex]y = 10000 * (1 + 5\%)^5[/tex]
Evaluate
[tex]y = 12763[/tex]
Hence, the population in 5 years is 12763
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the greatest common factor 10z-40
Answer:
10 is the greatest common factor
Step-by-step explanation:
Find the prime factors of each term in order to find the greatest common factor (GCF).
10
19=15w-4(3w-1)
What is the answer to this problem
Answer:
w=5
Step-by-step explanation:
First you have to write out the equation. Then you distribute negative 4 to 3w then you distribute -4 to -1 you get 4. Then you need to combine like terms and you get 3W. then you need to subtract four from each side you get 15 equals 3W then divide aside by three and you get W equals five
consider quadrilateral ABCD and point E in the figure below. graph r(135°, E) (ABCD). which graph shows the pre-image ABCD and the image A’ B’ C’ D’ ?
The graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.
What is rotation of figure?Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction.By rotating, a figure changes the point of the figure.
The quadrilateral ABCD and point E in the graphed in the figure below. This quadrilteral is rotated r(135°, E) in order to construct quadrilteral A’ B’ C’ D’ .
The rotation of the figure is 135 degrees. This angle can be break as,
[tex]\theta=135\\\theta=90+45[/tex]
The angle is rotated 90 and 45 degrees. To rotate 90 degree, the angle must be flliped 90 degree clockwise from point E keeping the point c at center.
After this the 45 degree more the figure is rotated. This is shown accurately in the figure A.
Thus, the graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.
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xavier and yolanda have been married for exactly 40 years. yolanda is four years older than xavier now the sum of their ages is 126 how old was yolanda whwn they were married
Yolanda's was 25 years old when they were married.
Step-by-step explanation:
Let,
Age of Xavier = x
Age of Yolanda = x + 4
Combined age = 126
According to given statement;
Xavier's age + Yolanda's age = 126
[tex]x+(x+4)=126\\x+x+4=126\\2x=126-4\\2x=122\\[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{122}{2}\\x=61[/tex]
Yolanda's age = x+4 = 61+4 = 65
Age when married = 65 - 40 = 25
Yolanda's was 25 years old when they were married.
Keywords: word problems, addition
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What is the best definition of arithmetic
Answer:
1a : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them. b : a treatise on arithmetic. 2 : computation, calculation.
Step-by-step explanation:
Final answer:
Arithmetic is a branch of mathematics dealing with numbers, including operations like addition, subtraction, multiplication, and division; it is recognized for its universality and foundational importance in various fields of study.
Explanation:
Arithmetic is a fundamental branch of mathematics that involves the study and manipulation of numbers. It includes the basic operations of addition, subtraction, multiplication, and division. These operations are essential for understanding and working with numbers in both simple and complex mathematical contexts, such as the calculation of quantities, relationships, and patterns. Arithmetic is universally acknowledged for its constant and indubitable truths, such as two plus three always equalling five. This branch of mathematics is not only vital in academic settings but is also crucial in everyday decisions and processes regardless of the period or location. Arithmetic serves as the basis for more advanced mathematical studies and is woven intricately into various fields such as physics, astronomy, and engineering, highlighting its foundational importance in the sciences and beyond.
The solution to which inequality is graphed below?
Answer:
D
Step-by-step explanation:
6b>-18
b>-3
This is shown by the line going from -3 into infinity.
Answer:
6b > -18
Step-by-step explanation:
[tex]6b > -18 \\then \\b >\frac{-18}{6} \\then\\b > -3[/tex]
4 cubed 2 divided by 4
Answer: 32
Step-by-step explanation:
4 cubed 2 divided by 4
Simply is
4 to the power 3 multiplied by 2 divided by 4
4*4*4*2/4
128/4= 32
Does this Series Converge or Diverge? What is the common ratio?
Answer:
Converge
Step-by-step explanation:
Given geometric series
[tex]1,000+200+40+8+\dfrac{8}{5}+...[/tex]
The first term of this geometric series is [tex]a_1=1,000.[/tex]
Next terms can be obtained by dividing by 5 or multiplying by [tex]\frac{1}{5}:[/tex]
[tex]a_2=1,000\cdot \dfrac{1}{5}=200\\ \\a_3=200\cdot \dfrac{1}{5}=40\\ \\a_4=40\cdot \dfrac{1}{5}=8\\ \\a_5=8\cdot \dfrac{1}{5}=\dfrac{8}{5}\\ \\...[/tex]
The sum of this infinite geometric series is
[tex]S=\dfrac{a_1}{1-q}=\dfrac{1,000}{1-\frac{1}{5}}=\dfrac{1,000}{\frac{4}{5}}=1,250[/tex]
Hence, this series is convergent
in the following triangle, what is the length of the hypotenuse, please answer quickly please
Answer:
6
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{hyp}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
hyp = 3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 3 × 2 = 6
What is the answer of (1, 9); slope 4 on a graph?
The point (1, 9) with a slope of 4 on a graph corresponds to the answer of 13.
Explanation:The answer is 13.
To calculate this, we use the formula for the equation of a straight line: y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = 4x + 9. Substituting x = 1 into the equation gives y = 4(1) + 9 = 13.
Therefore, the point (1, 9) has a slope of 4 on the graph.
J divided by 9 is 5 j equal
Answer:
J= 45
Step-by-step explanation:
j ÷ 9 = 5
×9. ×9
J= 45
you multiply by to cancel out the nine. you do it on both sides of the equal sign so it's proportionate
Answer:
j=45
j/9=5
Step-by-step explanation:
j equals fourty five
j over or divided (by) nine equals five
h(x)=0.00004668x^3 find h(x/1.6)
Answer:
0.00019120128
Step-by-step explanation:
1.6x1.6x1.6 x .00004668
Which fraction is bigger
1 1/6 or 1 4/12
Answer:
1 1/6
Step-by-step explanation:
because it takes more to get to 12 than 6
11/6 is bigger because if you convert both into decimal form
11/6=1.83
14/12=1.16
trent has a collection of 198 baseball and basketball training cards. he has 4.5 times as many baseball cards as basketball cards. how many baseball cards does trent have in his collection?
There are 162 base ball cards
Solution:
Let "a" be the number of baseball training cards
Let "b" be the number of basket ball training cards
Trent has a collection of 198 baseball and basketball training cards
Therefore,
a + b = 198 -------- eqn 1
He has 4.5 times as many baseball cards as basketball cards
Number of baseball cards = 4.5(number of basketball cards)
a = 4.5b --------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
4.5b + b = 198
5.5b = 198
b = 36
Substitute b = 36 in eqn 2
a = 4.5(36)
a = 162
Thus there are 162 base ball cards
Trent have 162 baseball cards in his collection.
Trent has a collection of 198 baseball and basketball training cards, with baseball cards being 4.5 times as many as basketball cards. To find out how many baseball cards Trent has, we can set up a system of equations.
Let x be the number of basketball cards.
Since the number of baseball cards is 4.5 times the number of basketball cards, the number of baseball cards is 4.5x.
The total number of cards is 198, so x + 4.5x = 198.
Solving this equation, we find x = 36. Therefore, the number of baseball cards Trent has is 4.5*36 = 162 baseball cards.
simplify: 3x-9+13x-6 show solution
Answer:16x-15
Step-by-step explanation:
3x-9+13x-6
Collect like terms
3x+13x-9-6
16x-15
) On a number line, what is the distance between -5 and -3? Respond in terms of absolute value.
Answer:
2
Step-by-step explanation:
There are 2 units of distance separating -5 and -3.
In the graph of an inequality, the region below a dashed line through the points (4, 3) and (0, 2) is shaded. What inequality does the graph represent?
Answer:
The inequality that represents the graph is y < [tex]\frac{1}{4}[/tex]x + 2
Step-by-step explanation:
i) the region below a dashed line through the points (4,3) and (0,2) is shaded.
ii) first we find the equation of the line passing through the points (4,3) and (0,2)
(y - 3) = [tex](\frac{3 - 2}{4 - 0})[/tex](x - 4) ⇒ y - 3 = [tex]\frac{1}{4}[/tex](x - 4)
⇒ 4y - 12 = x - 4 ⇒ 4y = x + 8 ⇒ y = [tex]\frac{1}{4}[/tex]x + 2
iii) for the area shaded below the line whose equation is given in ii) above the inequality that will represent the shaded region is given by
y < [tex]\frac{1}{4}[/tex]x + 2
The graph represents the inequality y < 1/4x + 2. The inequality was calculated based on the information given: points the line goes through, shading below the line, and the line being dashed all determine the inequality's form.
Explanation:To determine the inequality graphed, we first need to find the equation of the line. The line passes through the points (4, 3) and (0, 2), so we can use these points to find the slope of the line.
The formula for the slope (m) is [tex](y2 - y1)/(x2 - x1).[/tex]. Plug in the coordinates of the two points into this formula: ([tex]3 - 2) / (4 - 0) = 1/4[/tex] So, our slope is 1/4.
Given a slope (m) of 1/4 and the y-intercept (b) of 2, we can write the equation of the line in slope-intercept form (y = mx + b) as y = 1/4x + 2.
One key part of your question is that the region below this line is shaded. In the language of inequalities, shading below the line corresponds to 'y is less than' the line's equation. Also, the line is dashed, meaning that the points on the line are not included in the solution, which we denote as 'less than' rather than 'less than or equal to'.
So, the inequality represented by this graph is y < 1/4x + 2.
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Simplify: (5x^6y^-4)^3(2x^8y^3)
Answer:
see attached picture please
Help!! brainliest
Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a figure for this relationship.
Answer:
B
Step-by-step explanation:
Linc c moving upward will intersect line b
Option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
Lines a, b, and c are coplanar. Lines a and b intersect.
Line c intersects only with line b
As we can see in the picture, the lines are given:
As we know, the coplanar plane is the plane in which all lines or points lie (ie. in the same plane) known as coplanar.
In option (B) the lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
Thus, option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
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32 mm
16 mm
es
Given that the two figures are similar, use a scale factor to find the missing length b.
8 mm
12 mm
16 mm
24 mm
Answer:
scale factor is 4 so it will be 8mm
can someone help me with this problem please
Answer:
The correct option is third one m∠2 =106° , m∠3 =37°.
Therefore,
[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]
Step-by-step explanation:
Given:
Consider ABCD as a Rhombus such that,
∠A = ∠1 = 106°
∠C = ∠2
∠BDC = ∠3
AB=BC=CD=DA
To Find:
∠2 = ?
∠3 = ?
Solution:
ABCD is a Rhombus
∠A ≅ ∠C ............opposite angles of Rhombus are equal. ( property )
Substituting the values we get
∠1 = ∠2
But ∠1 = 106°
∴ ∠2 = 106° ....... Transitive property,
As BC = CD ...Given
ΔBCD is an Isosceles triangle
∴ ∠CBD ≅ ∠BDC = ∠3 ........base angle of Isosceles triangle are congruent.
we know that in a triangle,
Sum of measures of all angles is 180°
in Triangle BCD
[tex]\angle 3 +\angle 2 +\angle 3 =180[/tex]
Substituting the values we get
[tex]2m\angle 3 =180-106=74\\\\\angle 3=\dfrac{74}{2}=37\\\\m\angle 3 = 37\°[/tex]
Therefore,
[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]
What is this percent of change, i'm confused? 1/4 to 1/8
Answer:
Step-by-step explanation:
Percent change= (1/4-1/8)/1/4 × 100%
= {(2 -1)/8} ÷ 1/4 × 100%
= (1/8 ÷ 1/4) × 100%
= 1/8 × 4/1 × 100%
=1/2 × 100%
= 50%
It is 50% change
Answer:
I believe the answer is 50%.
1/4 x 1/2 = 0.125
125/1000
125/1000 <-- divide numerator and denominator by 125
the above fraction simplifies to 1/8
So, one 1/4 is double the value of one 1/8
A bag of Chocolates is labeled to contain 0.384 pounds of chocolate the actual weight of the chocolate is 0.3798 pounds. How much have you or lighter are the chocolates and The started on the label. Show your reasoning
Answer:
The actual weight is 1.1% less (100 - 98.9) than the labeled weight.
Step-by-step explanation:
1. Let's review the information given to us to answer the question properly:
Labeled weight of the bag of chocolates = 0.384 pounds
Actual weight of the bag of chocolates = 0.3798 pounds
2. How much have you or lighter are the chocolates and the stated on the label. Show your reasoning.
Let's find how much we have comparing the labeled weight and the actual weight, using a Direct Rule of Three, this way:
Weight Percentage
0.384 100 %
0.3798 x %
0.384x = 0.3798 * 100
0.384x = 37.98
x = 37.98/0.384
x = 98.9 (Rounding to one decimal place)
The actual weight is 1.1% less (100 - 98.9) than the labeled weight.
The chocolates are 0.0042 pounds lighter than what is stated on the label.
Explanation:The difference in weight between the labeled weight and the actual weight of the chocolates is 0.0042 pounds. This means that the chocolates are 0.0042 pounds lighter than the label indicates.
To calculate this, subtract the actual weight from the labeled weight: 0.384 - 0.3798 = 0.0042 pounds.
So, the chocolates are 0.0042 pounds lighter than what is stated on the label.
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The length of a rectangle is 6 inches more than it’s width. if the perimeter of the rectangle is 24 inches, find the dimensions. create let statement and write equation.
Answer:
The dimensions of the rectangle are;
Width = 3 inches
Length = 9 inches
Step-by-step explanation:
Given;
Perimeter of the rectangle is 24 inches Length is 6 inches more than the widthWe want to determine the dimensions of the rectangle;
Let the width of the rectangle be x inchesThis means, the length of the rectangle will be (x+6) inchesBut, Perimeter = 2(L+W)Forming an equation, we get;
2 ( x + x + 6) = 24
4x + 12 = 24
With the equation we can solve for x
4x = 24 - 12
4x = 12
x = 3
and (x + 6) = 9
Therefore;
Width = 3 inches
Length = 9 inches
The width of the rectangle is 3 inches and the length is 9 inches.
Let's assume that the width of the Rectangle dimensions is represented by 'w' inches.
Since the length is 6 inches more than the width, we can represent it as 'w + 6' inches.
The perimeter of a rectangle is the sum of all its sides.
In this case, the formula for the perimeter is 2(w + l), where w represents the width and l represents the length.
So, for this problem, we have the equation 2(w + w + 6) = 24.
Simplifying this equation, we get 4w + 12 = 24.
Solving for 'w', we find that the width is 3 inches.
Plugging this value back into the equation for the length, we find that the length is 9 inches.
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Mr Edwards buys 2 new knobs for each of his kitchen cabinets. How many knobs does he buy?
Answer:
Step-by-step explanation:
You need to find out how many cabinets it is
Final answer:
To determine how many knobs Mr. Edwards needs to buy for his kitchen cabinets, we need to know the total number of cabinets since he needs 2 knobs for each cabinet.
Explanation:
Mr. Edwards wants to buy new knobs for his kitchen cabinets. To determine how many knobs he needs to buy, we would need to know the exact number of kitchen cabinets he has. However, the information about Chelsea and her trip to Europe, her being a shop-a-holic and physics lover, and the estimation of the number of pairs of shoes that can fit in her closet seem to be unrelated to Mr. Edwards's question. Therefore, to answer Mr. Edwards's query, we need the number of cabinets to calculate the total number of knobs. If there are X cabinets, Mr. Edwards would need to purchase 2X knobs.
A quadrilateral had vertices (2,0) (0,-2) (-2,4) and (-4,2) which special quaderalateral is formed by connecting the midpoints of the sides
Answer:
The special quadrilateral formed by connecting the midpoints of the sides of the original quadrilateral is : a rhombus
Step-by-step explanation:
Look at the photo below for the figure
:)
What is the answer to -2/3x4
Answer
-8/3 (fraction)
or in decimal form it would be -2.6 (the six would be repeating)
Step-by-step explanation:
derivative of tanx? anyone?
Answer:
[tex]\displaystyle \frac{d}{dx}[\tan x] = \sec^2 x[/tex]
General Formulas and Concepts:
Pre-Calculus
Trigonometric IdentitiesCalculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
*Note:
This is a known trigonometric derivative.
Step 1: Define
Identify
[tex]\displaystyle y = \tan x[/tex]
Step 2: Differentiate
Rewrite [Trigonometric Identities]: [tex]\displaystyle y = \frac{\sin x}{\cos x}[/tex]Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{(\sin x)'\cos x - \sin x(\cos x)'}{\cos^2 x}[/tex]Trigonometric Differentiation: [tex]\displaystyle y' = \frac{\cos^2 x + \sin^2 x}{\cos^2 x}[/tex]Rewrite [Trigonometric Identities]: [tex]\displaystyle y' = \frac{1}{\cos^2 x}[/tex]Rewrite [Trigonometric Identities]: [tex]\displaystyle y' = \sec^2 x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The derivative of tanx in calculus is sec^2x, which represents the slope of the curve at any point x for the function tanx.
Explanation:The derivative of a function measures how the function changes as its input changes. In calculus, the derivative is a concept that describes the rate at which a quantity changes.
In the context of your question, the derivative of tanx or tangent x is sec^2x or secant squared x. This is a standard result that is usually memorized in calculus courses and can be derived using the limit definition of the derivative and trigonometric identities.
To put it in simpler terms, if tanx were the equation of a curve, the derivative (sec^2x) would represent the slope of that curve at any point x. This is key to understanding how the function behaves at different points and predicting its future behavior.
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