The pattern tells that the amount raised by Robert in 26th mile is $90.
What is a pattern?
A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.
The amount of money raised by Robert for first mile = $5
The amount of money raised by Robert for second mile = $6
The amount of money raised by Robert for third mile = $7.2
The difference between amount raised in first and second mile = $1
The difference between amount raised in second and third mile = $1.2
Similarly, the difference between amount raised in third and fourth mile will be = $1.4
Similarly, the difference between amount raised in fourth and fifth mile will be = $1.8
Following this pattern the difference between 25th and 26th mile will be = (26 × 0.2) + 0.4 = $5.8
Now, the amount raised in 26th mile = 84.2 + 5.8 = 90
Therefore, the amount raised is $90.
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Solve the following:
a) 2(x + 3) = x - 4
b)
4(5x - 2) = 2(9x + 3)
Answer:
a. x= –10
b. x= 7
Step-by-step explanation:
a. 2(x+3)=x–4
2x+6=x–4
C.L.T
2x–x= –6–4
x= –10
b.4(5x–2)=2(9x+3)
20x–8=18x+6
C.L.T
20x–18x=6+8
2x=14
divide both sides by 2
x= 7
Please Help!!
(use the figure to answer questions 8,9 and 10)
The height ( in feet) of a ball thrown by a child is given by
= −^2 + 6 + 7,
where is the horizontal distance ( in feet) from where the ball is thrown ( see figure).
8. How high is the ball when it leaves the child’s hand? (Justify your answer)
9. What is the maximum height of the ball? ( must show work)
10. How far from the child does the ball strike the ground? ( must show work)
The ball is 7 feet high when it leaves the child’s hand
The maximum height is 16 feetIt lands 7 feet from the childHow high is the ball when it leaves the child’s hand?Given that
h(x) = -x^2 + 6x + 7
When it leaves his hand, we have
x = 0
This gives
h(0) = -(0)^2 + 6(0) + 7
Evaluate
h(0) = 7
What is the maximum height of the ball?Here, we have
h(x) = -x^2 + 6x + 7
Differentiate and set to 0
-2x + 6 = 0
So, we have
x = 3
The maximum height is
hmax = -3^2 + 6(3) + 7
hmax = 16
How far from the child does the ball strike the ground?This means that h(x) = 0
So, we have
-x^2 + 6x + 7 = 0
This gives
x^2 - 6x - 7 = 0
Expand
x^2 + x - 7x - 7 = 0
Factor
x(x + 1) -7(x + 1) = 0
So, we have
(x - 7)(x + 1) = 0
Solve for x
x = 7 or x = -1
Hence, the distance is 7 feet
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A restaurant customer left $0.70 as a tip. The tax was 4% and the tip was 10% of the cost including tax.
Answer: The tip is 20% of the cost including tax. Thus .20 * X=3.50.Divide both sides of the equation by .20..20 divided into .20 = 1, so “X” = 1.And 3.50 divided by .20 = 17.50 So X = 17.50, cost of the meal plus the tax.The tax is .07, so we know that 100% of the meal cost PLUS 7% of the meal cost is 107% of the meal cost. That is 1.07 * Meal without tax = 17.50. Divide 17.50 by 1.07 and you get 16.355. Round up to 16.36.Is that right? Let’s see:7% tax on meal at 16.36 is 16.36 * .07 = 1.1452. Round up to 1.15.$1.15 + 16.36 = 17.51.And 20% (the tip) of 17.51 is .20 * 17.51 = 3.50Cost of the whole meal; food, tax and tip is 16.36+1.15+3.50 = 21.01.
Step-by-step explanation: my big brain
find (-7x +1) + (4x-5)
Answer:
-3x -4
Step-by-step explanation:
(-7x +1) + (4x-5)
= -7x +1 + 4x-5 (brackets are unnecessary due to the commutative law of addition)
= -3x -4
In the triangle below, x= ?
round to nearest tenth
The measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
For the tangent of X equal, we can make x the subject by finding the tan inverse of opposite divided by the adjacent side as follows:
tan X = 8/10 {opposite/adjacent}
X = tan⁻¹(0.8)
X = 38.6598
Therefore, the measure of the angle X is equal to 38.7° to the nearest tenth using the trigonometric ratio of tangent of X.
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The store sells 2-64 oz. bottles of liquid dish soap for $8.39 or 3 - 40 oz. bottles at $7.20. Which is the better buy?
It is better to buy 2-64 oz bottles of liquid dish soap for $8.39.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Given that, the store sells 2-64 oz bottles of liquid dish soap for $8.39 or 3 - 40 oz bottles at $7.20.
2 pounds = 32 oz
So, 32+64=96 oz
Now, 8.39/96
= $0.087 per oz
Here, 3 - 40 oz = 88 oz
Unit rate = 7.20/88
= $0.081 per oz
Therefore, it is better to buy 2-64 oz bottles of liquid dish soap for $8.39.
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You are building an entertainment center with shelves that are x inches deep by x inches long. The height of the unit will be twice the depth. If the volume of the unit will be 8,192 inches cubed, what is the height, in inches, of the entertainment center?
The height, in inches, of the entertainment center is 32 inches while other dimensions are 16 inches.
The volume of the unit will be the product of length, depth and height. Now the depth will be 2x. Based on this, performing the calculation to find the value of x.
Volume = length × depth × height
8192 = x × x × 2x
Performing multiplication on Right Hand Side of the equation
8192 = 2x³
Rewriting the equation according to x
x³ = 8192/2
Performing division on Right Hand Side of the equation
x³ = 4096
Taking cube root on Right Hand Side of the equation
x = [tex] \sqrt[3]{4096} [/tex]
x = 16 inches
Height = 2×16
Performing multiplication on Right Hand Side of the equation
Height = 32 inches
Thus, length and depth are 16 inches and height is 32 inches.
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i have a question.
0,2 2,3 4,4 6,5 8,6 10,7
(coordinates ^)
Q. first, complete the table of x and y coordinates.
x. y
----------
3. _
5. _
7. _
Answer:
x | y
0 | 2
2 | 3
3 | 4
4 | 5
5 | 6
6 | 7
7 | 8
So, completing the table:
x | y
3 | 4
5 | 6
7 | 8
Step-by-step explanation:
Please study well it is a very easy question
23 equals x minus 9; x minus 14
The value of 'x' satisfying the statement is x = 32 or x = 27.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A statement 23 equals x - 9, x - 14 which can be numerically expressed as, 23 = x - 9 or 23 = x - 14.
Therefore,
x - 9 = 23 or x - 14 = 23.
x = 23 + 9 or x = 23 + 14.
x = 32 or x = 37.
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2. What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C 12, 4), D(5,2)?
parallelogram
rhombus
quadrilateral
rectangle
3. What is the most precise name for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C (8, 8), D (8,5)?
parallelogram
rhombus
square
kite
i’m giving 25 points
The most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C 12, 4), D(5,2) is A. parallelogram.
The most precise name for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C (8, 8), D (8,5) is A. kite
How to explain the quadrilateralSince the lengths of all sides are equal and the opposite sides are parallel, because the slopes of two parallel lines are equal. Therefore, ABCD is a parallelogram because opposite sides are parallel and congruent.
Also, since, the two disjoint pairs of consecutive sides are congruent as AB=DA and BC=CD. Thus, by definition of kite, that Two disjoint pairs of consecutive sides are congruent, the given quadrilateral is a kite.
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The pair of points lies on the same line with the given slope. Find x.
(3,1), (x,11); slope=2
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{x}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 2 }\implies \cfrac{10}{x-3}=2\implies 10=2x-6 \\\\\\ 16=2x\implies \cfrac{16}{2}=x\implies \boxed{8=x}[/tex]
Help……………………………………..
Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x)
what is function ?Volumes and their variations, mathematics and supporting structures, types and their placements, and locations where they can be collected are all included in the study of mathematics. This same relationship between a group of inputs, each of which produces going support, is referred to as a "function.". Every function has a territory and a codomain, usually known as a scope. F is typically used to denote operations (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one operations, several more functions, within functions, and also on functions.
given
According to the table, the function's value at x = 10 is:
h(10) is not defined.
the values of the function change as x exceeds x = 10 to:
h(x+) = 18.5......
When roughly speaking, we have:
h(x+) = 18.5
Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x) .
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The complete question :-
What is Limit of h (x) as x approaches 10 plus?
I need help with this last step.What do I put in the circles I'll give 50 points and brainliest for the first answer.
Answer: IS easy you only need to put your answer that you got when you multiply the numbers:)
Step-by-step explanation:
a bag of fertilizer covers 2500 square feet of lawn how many bags of fertilizer should be purchased to cover a rectangular lawn 410 by 65 feet
Answer: 11
Step-by-step explanation:
410 * 65 = 26,650 sq ft
26,650/2500 = 10.66 bags
Answer:
11 bags.
Step-by-step explanation:
We know that the area is 410 x 65 = 26650
Now, we need to divide to find how many bags is needed.
26240/2500 = 10.66, which we round up cause we can't have a half bag.
The first time Account # 1: was 1 year
account number # 2: was 10 years
Now just double it. Need help asap, thank you!!
What is the LCD of 16/25, 24/30, and 3/4
Answer:
2900
Step-by-step explanation:
16/25+24/30+3/4
=25*30*4=2900
suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. what is the expected value of his or her total winnings for the four spins?
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. The expected value of his or her total winnings for the four spins is $800.
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again.
We have to determine the expected value of his or her total winnings for the four spins.
Total winning depends on the fourth term.
Outcome Skunk 100 200 500
Probability 1/4 1/4 1/4 1/4
Total Winning 0 900 1000 1300
Expected Total Winning = 1/4 (0 + 900 + 1000 + 1300)
Expected Total Winning = 1/4 × 3200
Expected Total Winning = 800
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The complete question is:
Contestants on a game show spin a wheel like the one shown in the figure above. Each of the four outcomes on this wheel is equally likely and outcomes are independent from one spin to the next.
The contestant spins the wheel.
If the result is a skunk, no money is won and the contestant's turn is finished.
If the result is a number, the corresponding amount in dollars is won.
The contestant can then stop with those winnings or can choose to spin again, and his or her turn continues.
If the contestant spins again and the result is a skunk, all of the money earned on that turn is lost and the turn ends.
The contestant may continue adding to his or her winnings until he or she chooses to stop or until a spin results in a skunk.
Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. What is the expected value of his or her total winnings for the four spins?
What is the solution to the following inequality
-8<4(8-2x)
The solution of the inequality is x < 5
How to determine the solution to the inequalityInequalities are defined as unequal comparison between two expressions, numbers or equations on the basis of their sizes on the number line.
From the information given, we have that;
-8<4(8-2x)
expand the bracket
-8 < 32 - 8x
collect like terms
-8 - 32 < -8x
subtract the like terms
-40 < - 8x
Make 'x' the subject of formula, we have to divide both sides by the coefficient of x, we get;
-40/-8 < -8x/-8
Divide the values
x < 5
Hence, the value is x < 5
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What is the product of and ? Write your answer in standard form.
(a) Show your work.
(b) Is the product of and equal to the product of and ? Explain your answer.
Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]
Product of an Equation:
In mathematics, a product is a number or quantity obtained by multiplying two or more numbers. Example: 4 × 7 = 28, where the number 28 is said to be the product of 4 and 7. Another example: 6 times 4 is 24, so 6 multiplied by 4 is 24. The product of two positive numbers is a positive number, as if the product of two negative numbers is also positive (e.g., -6 × -4 = 24).
Now,
(A) We need to find the product of two given expressions.
[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]
To multiply two given expressions, first multiply the first term in the first parenthesis by the entire expression in the second term, then do the same for the second term in the first parentheses.
[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]
⇒ [tex]\frac{1}{2x} * [5x^{2} -2x +6] - \frac{1}{4} * [5x^2 - 2x +6][/tex]
⇒ [[tex]\frac{1}{2x} * 5x^2[/tex] - [tex]\frac{1}{2x} *2x[/tex] + [tex]\frac{1}{2x}* 6[/tex] ] - [ [tex]\frac{1}{4} * 5x^2 + \frac{1}{4} * 2x - \frac{1}{4}*6[/tex]]
Now, simplify the equation:
[tex]\frac{5x}{2} -1 + \frac{3}{x} - \frac{5x^2}{4} +\frac{x}{2} +\frac{3}{2}[/tex]
Rearranging the equation:
[tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]
Thus, the product of the two expressions is [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex].
(B) To compare the two expressions we will find the value of the two given expressions,
[tex]\frac{1}{2x} -\frac{1}{4} * 5x^{2} -2x +6[/tex] = [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]
For the value of:
[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]
simplifying the equation:
[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]
⇒ [tex][\frac{1}{4x} * (5x^{2} -2x +6)] - [\frac{1}{2} * (5x^{2} -2x +6)][/tex]
⇒ [tex]-\frac{5x^2}{2} + \frac{9x}{4} + 3.5 +\frac{3}{2x}[/tex]
As you can see, the result of the product of the two expressions is different.
Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]
Complete Question:
What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form.
(A) show your work.
(B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer
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The data plan on your family's cell phone costs more if your family uses more than 5 GB in a month. Write an inequality to show how much data your family can use without being charged more.
please help
The inequality of the statement is x <= 5
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
The data plan on your family's cell phone costs more if your family uses more than 5 GB in a month
Represent the data plan with x
This means that the inequality is
x <= 5
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Can somebody please help me??
Answer:
8.2%
Step-by-step explanation:
To find the sales tax percentage, we need to determine how much of the total price was due to sales tax. To do this, we can subtract the price of the cupboard from the total price:
$92.82 - $85.78 = $7.04
So the sales tax was $7.04. We can then divide the sales tax by the price of the cupboard and multiply by 100% to find the sales tax rate as a percentage:
$7.04 / $85.78 * 100% = 8.2%
Rounding to the nearest tenth, the sales tax rate was 8.2%.
Answer:
8.2% (rounded to the nearest tenth)
Step-by-step explanation:
$92.82-$85.78= $7.04
100%= $85.78
1%= $85.78÷100
= $0.8578
$7.04÷$0.8578= 8.2% (rounded to the nearest tenth)
A map of a highway has a scale of 2 inches = 45 miles. The length of the highway on the map is 8 inches. There are 17 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch =30 miles. How far apart are the rest stops on the new map?
The distance apart is given as 1/3 inches
How to solve for the distance apartSince the original scale was 2 inches = 45 miles, the highway length on the original map was 8 inches * 45 miles/2 inches = 180 miles.
So, each of the 17 rest stops was spaced 180 miles / (17 - 1) = 10 miles apart on the highway.
With the new scale of 1 inch = 30 miles, each inch on the map represents 30 miles on the highway.
Thus, each rest stop on the new map is 10 miles / 30 miles/inch = 10/30 inches = 1/3 inch apart.
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What would the polynomial be?
The options are:
monomial
binomial
trinomial
none of the above
Answer:
Trinomial
Step-by-step explanation:
A trinomial is an algebraic expression with three, unlike terms.
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Measured in meters, the wavelength of red light is about 8x10 to the -7 power, and the wavelength of violet light is 8x10 to the -7 power. The wavelength of red light is how many times longer than the wavelength of violet light
The wavelength of red light is exactly the same as the wavelength of violet light, so it is not longer or shorter.
1. First, we need to identify the wavelengths of red light and violet light.
2. Red light has a wavelength of 8x10 to the -7 power meters and violet light has a wavelength of 8x10 to the -7 power meters.
3. Since both wavelengths are the same, the wavelength of red light is not longer or shorter than the wavelength of violet light.
The wavelength of light is measured in meters, and the wavelength of red light is 8x10 to the -7 power meters, while the wavelength of violet light is 8x10 to the -7 power meters. This means that both the wavelengths are exactly the same and the wavelength of red light is not longer or shorter than the wavelength of violet light. This is because the wavelength of light is a fundamental property that determines the color of light and the wavelength of red light and violet light are both the same.-
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At a basketball game a team made 51 successful shots. They were a combination of 1- and 2- point shots. The team scored a total of 84 points in all.
If the equation be x + 2(51 - x) = 83 then the value of x be 19.
What is meant by expressions?A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.
Let x be the number of 1 point shots.
51 - x be the number of 2 point shots
Let the equation be x + 2(51 - x) = 83
Expanding the above equation as
x + 2(51 - x) = -x + 102
simplifying the above equation, we get
-x + 102 = 83
-x = -19
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-19}{-1}[/tex]
x = 19
Therefore, the value of x be 19.
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PLS Help ASAP
Solve for x
-(-2-52)+(-2)=18
O z=-90
0 z=-2/2
0 z=¹/
X=90
Answer:
(c) x = 18/5
Step-by-step explanation:
You want the solution to -(-2 -5x) +(-2) = 18.
SolutionEliminating parentheses, we have ...
2 +5x -2 = 18
5x = 18 . . . . . . . simplify
x = 18/5 . . . . . . divide by 5
Mr. Thurgood gave his students a math quiz last Friday. Each question on the quiz was worth 3 points, and the quiz was worth 45 points in all.
The number of questions on the math quiz, given the points per question and the total points, in the quiz, was 15 questions.
How to find the number of questions ?To find the number of questions in the quiz, you can use the formula :
= Number of total points in the quiz / Number of points per question
Number of total points in the quiz = 45 points
Number of points per question
The number of questions given in the quiz by Mr. Thurgood is:
= 45 / 3
= 15 questions
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The full question is:
Mr. Thurgood gave his students a math quiz last Friday. Each question on the quiz was worth 3 points, and the quiz was worth 45 points in all. How many questions were in the quiz?
PLS HELP I WILL GIVE BRAINIEST IF CORRECT I NEED HELP ASAP
An urn contains 8 red and 7 black balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are black? Round your answer to three decimal places.
Answer:
Step-by-step explanation:
Since the balls are drawn with replacement, the probability of drawing a black ball on any single draw is 7/15. The probability of drawing 6 black balls in succession is the product of the probabilities of each individual draw being a black ball. Therefore, the probability is:
(7/15)^6 ≈ 0.019
Rounding to three decimal places, the probability is 0.019.
Answer:
0.003
Step-by-step explanation:
The probability of drawing a black ball on any given draw is 7/15, since there are 7 black balls and 15 total balls in the urn. Because the balls are replaced after each draw, the probability of drawing a black ball on each of the 6 successive draws is (7/15) x (7/15) x (7/15) x (7/15) x (7/15) x (7/15) = (7/15)^6.
Therefore, the probability of drawing 6 black balls in succession is:(7/15)^6 = 0.0028 (rounded to three decimal places)
So the probability that all 6 balls drawn from the urn are black is approximately 0.003.
solving 2x^2+x-4=0 using the quadratic formula
The answer to the quadratic equation is x=1±√33/4.
A quadratic equation is what?In mathematics, a quadratic equation is one of degree 2, which means that its maximum exponent is 2. A quadratic has the formula y = ax2 + bx + c, where a, b, and c are all integers and a cannot be zero.
Use the quadratic formula to find the solutions.
−b±√b²−4(ac)/2a
Substitute the values a=2, b=−1, and c=−4 into the quadratic formula and solve for x.
1±√(−1)²−4⋅(2⋅−4)/2⋅2
Simplify.
Simplify the numerator
Raise −1 to the power of 2.
x=1±√1−4⋅2⋅−4/2⋅2
Multiply −4⋅2⋅−4.
Multiply −4 by 2.
x=1±√1−8⋅−4/2⋅2
Multiply −8 by −4.
x=1±√1+32/2⋅2
Add 1 and 32.
x=1±√33/2⋅2
Multiply 2 by 2.
x=1±√33/4
The result can be shown in multiple forms.
x=1±√33/4
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a certain group of women have a .92% rate of red/green colorblindness. if a woman is randomly selected, what is the probability that she dies not have red/green colorblindness?
The probability that a randomly selected woman does not have red/green colorblindness is 0.98 (98%).
The probability of not having red/green colorblindness is the inverse of the probability of having colorblindness. The probability of having red/green colorblindness is given as 0.92%. To calculate the probability of not having red/green colorblindness, subtract the probability of having colorblindness from 1. 1 - 0.92 = 0.08. This means that the probability of not having red/green colorblindness is 0.08, or 8%. To convert this to a percentage, multiply by 100. 0.08 x 100 = 8%. The probability of not having red/green colorblindness is 8%. This can also be written as 0.98 (98%).
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