The person doesn't need to stop for gas as the gas will be able to travel the journey.
How to calculate the value?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
Since the gas tank is 1/4 for your tank as it holds 12 gallons of gas. The full gas will be:
= 12 × 4
= 48 gallons
Since your destination is 90 miles away and it uses 25 mph. The number of hours will be:
= 90 / 25
= 3.6 hours.
The number of gallons needed will be:
= 3.6 × 12
= 43.2
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 10,000
3%
10,001 - 50,000
5%
50,001 - 100,000
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
To calculate the state income tax owed on a $50,000 per year salary, we need to apply the progressive tax rate based on the income range.
What does money interest mean?
You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.
The first $10,000 of the salary will be taxed at 3%, the next $40,000 (from $10,001 to $50,000) will be taxed at 5%, and the remaining $0 will be taxed at 5.5%
Tax on first $10,000 = $10,000 x 3% = $300
Tax on next $40,000 = $40,000 x 5% = $2,000
Tax on remaining $0 = $0 x 5.5% = $0
Total tax owed = $300 + $2,000 + $0 = $2,300
Therefore, the state income tax owed on a $50,000 per year salary is $2,300.
Learn more about interest
brainly.com/question/25793394
#SPJ1
The population of River City in the year 2000 was 400. Assume the
population increase at a rate of 6.75% per year. What's the populati
2020?
The population of the River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.
what is percentage ?A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.
given
population increase at a rate of 6.75% per year
then divide that number by the initial population and multiply by 100.
The population of the River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
Write and expression using only positive exponents for the width w of the rectangle
Area= 72 X^7Y^2 and L= 24 X^2Y^3
Answer:
[tex]\boxed{W = \dfrac{3X^5}{Y}}[/tex]
Step-by-step explanation:
Area A = [tex]72 X^7Y^2[/tex]
Length L = [tex]24 X^2Y^3[/tex]
A = L x W where W = width
W = A/L
[tex]\dfrac{72 X^7Y^2}{24 X^2Y^3}\\\\\\= 3X^{(7-2)}Y^{(2-3)}\\\\= 3 X^5Y^{-1}\\\\\\[/tex]
[tex]\textrm{Using the identity }x^{-1} = \dfrac{1}{x}\\\\[/tex]
we get
[tex]W = \dfrac{3X^5}{Y}[/tex]
Find the 2 two-digit numbers that divide 179 with a remainder of 4.
The two digit number that will make a remainder of 4 when it divides 179 is 35
How to find the two digit numberThe number 179 is a prime number hence it's only factors are 1 and 179.
For the number to have a remainder of 4, it means that subtraction 4 from 179 will give a number that will divide it without remainder
The subtracted 4 will serve as the remainder
179 - 4 = 175
factors of 175: 1, 5, 7, 25, 35 and 175.
175 / 35 = 5
because of this we can say that (175 + 4) / 35 will give a remainder of 4.
Learn more about subtraction at:
https://brainly.com/question/13378503
#SPJ1
the value of which of these expressions is closest to e?
The value of e is closest to the (1+1/22)^22 .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables , constants and exponents.
Given, expressions
the expression whose value is closest to e
we know that , the Value of e is 2.718
[tex](1+1/19)^{19}[/tex] = [tex]( 19+1/ 19 )^{19}[/tex] = (20/19 )^19 = 2.65
(1+1/22)^22 = (22+1/22)^19 = (23/22)^19 = 2.659
(1+1/20)^22 = (20+1/20)^22 = (21/20)^22 = 2.653
(1+1/21)^21 = (21+1/21)^21 = (22/21)^21 = 2.656
Therefore, The value 2.659 is the closest to the value of e.
So, option B. is correct.
To learn more about Algebraic expression from the given link.
https://brainly.com/question/953809
#SPJ1
i need help with #5 pleaseee
Answer:
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function: g(x)=√x
Horizontal Shift: None
Vertical Shift: Up 3 Units
Reflection about the x-axis: Reflected
Vertical Stretch: Stretched
Find the growth/decay rate given the exponential function.
g(x) = 6(.83)
Answer:
Decay Rate = 17 percent
Step-by-step explanation:
1.00 - 0.83 = 0.17
The number 1500 can be said correctly as "one-thousand five hundred" or as "fifteen hundred."
Write out at least four different ways to say 743.
The four words are Seven hundred forty-three, Seven-four-three, Seven four three, Seven hundred and forty-three.
What is number?Number is a mathematical object used to count, label, and measure. It is a fundamental concept in mathematics and is used in many different ways. Numbers can be used to represent anything from quantities of objects to ideas and concepts. Additionally, numbers are used to describe relationships between different objects or concepts. Numbers are also used to represent positions in space, as well as represent data in a graph or table.
1. Seven hundred and forty-three
2. Seven four three
3. Seven fourty-three
4. Seven hundred forty-three.
To know more about number click-
https://brainly.com/question/24644930
#SPJ1
solve the equation 3(1/6x + 9) = 1/2x(x-54)
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Exact Form: x = 55 + √ 3241 2 , 55 − √ 3241 2
Decimal Form: x =
55.96489065… , −0.96489065…
The pentagons and are similar.
Find the length of .
B
E
A
4
2
4
3
5
C
K
N
J
4.8
x
4.8
3.6
6
L
The value of x that is the measure of LM is 2.8 units.
What is similar polygons?
Two polygons with the same shape but different sizes are said to be similar polygons. Comparable polygons have corresponding sides that are proportional and corresponding angles that are congruent.
If the corresponding sides have a constant ratio and the corresponding angles are congruent, two polygons are said to be similar.
Let the pentagons ABCDE and JKLMN are similar.
Means their shape is same but differ in size.
Each side of pentagon JKLMN is 0.8 units greater than the pentagon ABCDE.
The measure of CD is 2 units.
⇒ The measure of LM = 2 + 0.8 = 2.8
Hence, the value of x that is the measure of LM is 2.8 units.
To know more about similar polygons, click on the link
https://brainly.com/question/1108275
#SPJ1
WILL GIVE BRANIST
What is the shape of the front of the Mexican tote bag? Use the drop-down menus to describe the shape. ➡ Click the arrows to choose an answer from each menu. The shape of the front of the tote bag is a trapezoid of sides that are perpendicular two pairs because it has
The shape of the front of the Mexican tote bag can be described as a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides and the other pair of non-parallel sides.
In this case, the sides of the trapezoid are perpendicular two pairs, meaning that one pair of non-parallel sides is perpendicular to the other pair of non-parallel sides.
The front of the Mexican tote bag typically has a wider top and a narrower bottom, which creates the parallel sides of the trapezoid. The wider top provides a larger opening for easy access to the contents of the bag, while the narrower bottom helps maintain the bag's shape and stability.
This trapezoidal shape is commonly seen in tote bags as it offers practicality and functionality. The wider top allows for convenient storage and retrieval of items, while the narrower bottom helps distribute the weight evenly and prevents the bag from sagging.
The trapezoidal shape of the front of the Mexican tote bag combines both style and functionality. It not only provides an aesthetically pleasing design but also offers practicality in terms of storage capacity and easy access to the bag's contents.
For more such questions on trapezoid visit:
https://brainly.com/question/1463152
#SPJ8
DUE SOON! PLEASE HELP!
Answer:
C
Step-by-step explanation:
You have to work the math
Answer:
B
Step-by-step explanation:
900mm is the current size of the pawn
The original size was 30mm which means we divide 900mm by 30mm
So,
900 ÷ 30 = 30
Which means b is the answer
C can't be the answer because if the original size of the pawn was 30mm and you say it was enlarged by 450mm, it means the current size will have to be 30 × 450 = 13500mm, and this is not the case
Write 94/4 as a percent.
(Round to 3 decimal places if necessary.)
Answer:
2350%
Step-by-step explanation:
In percentage:
94/4 x 100% = 2350%
(Converting from fraction to percentage, simply multiply the fraction by 100)
There is no need to round off the answer to 3 decimal places as the answer is already a pure whole number with no decimal places.
Given that 2p=5q, work out the ratio p : q
Therefore, the ratio of 5:2 is the p:q ratio of 2p=5q. When two quantities are proportionate, one rises and the other follows suit.
what is proportionality ?Relationships that have the same ratio over time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear relationship between two numbers or variables. When the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities stays the same at all values.
given
2p=5q
p/q = 5/2
Therefore, the ratio of 5:2 is the p:q ratio of 2p=5q. When two quantities are proportionate, one rises and the other follows suit.
To know more about proportionality visit:
https://brainly.com/question/29126727
#SPJ1
Evaluate the expression for w=2 and x=2 2w+12 ÷(2x)
Answer: The expression is (22) +12/(22) = 4 + 12/4 = 4 + 3 = 7.
Step-by-step explanation:
To evaluate the expression 2w+12 ÷ (2x) for w=2 and x=2, we need to substitute the given values into the expression and simplify.
First, we substitute the value of w=2 into the expression, giving us 2(2)+12 ÷ (2x).
Next, we simplify the expression by multiplying 2 and 2, getting 4+12 ÷ (2x).
Then we add 4 and 12, getting 16 ÷ (2x).
Finally, we substitute the value of x=2 into the expression, giving us 16 ÷ (2(2)) = 16 ÷ 4 = 4.
So the final value of the expression 2w+12 ÷ (2x) for w=2 and x=2 is 4.
Martin has 6,150 in doctor bills for the year his deductible is 500. His policy pays 80% once he has met his deductible for the year how much in all did Martin pay including his deductible
Answer:
1630
Step-by-step explanation:
You want to know what Martin paid to cover 1650 in doctor bills when his insurance pays 80% after a deductible of 500 has been met.
CopaymentWhen insurance pays 80% of the amount over 500, Martin pays the other 20%. Martin's share of the bill is ...
500 + 0.20(6150 -500)
= 500 +0.20(6150) -0.20(500) = 400 +0.20(6150)
= 400 +1230 = 1630
Martin paid 1630 in all, including the deductible.
When do we flip the Inequality Signs?
Show All Steps
Explanation: Inequalities can be solved just like equations can, with one important caveat if you multiply or divide by a negative number, you have to flip the direction of the inequality sign.
Definitions if don't know what some words mean :D
Inequalities- different in size
caveat- A warning
Example
I hope this helps
(Laplace transform)
Use the convolution property to solve
(18s)/(s^2+36)^2
[tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)² using convolution property.
What is convolution property?Convolution is a mathematical operation on two functions (f and g) that results in a third function (f×g) that expresses how the shape of one is altered by the other. It is a mathematical operation on two functions (f and g) in mathematics, more specifically in functional analysis.
Convolution is a term that describes both the method of computing a function and its result. Its definition states that it is the integral of the product of the two functions after one of them has been shifted and reflected about the y-axis. The result of the integral remains unchanged regardless of which function is chosen to be reflected and shifted before it (see commutativity). The convolution function is created by evaluating the integral across all shift values.
[tex]\begin{aligned}& =\frac{1}{a} \int_0^t \cos a u \sin a(\mathrm{t}-\mathrm{u}) \mathrm{du} \\& =\frac{1}{a} \int_0^t[\cos a u \sin (a \mathrm{t}-a u)] \mathrm{du} \\& =\frac{1}{a} \int_0^t\left[\frac{\sin (a \mathrm{t}-a u+a u)+\sin (a \mathrm{t}-a u-a u)}{2}\right] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\\end{aligned}[/tex]
[tex]\begin{aligned}\\& =\frac{1}{2 a}\left[(\sin \mathrm{at}) \mathrm{u}+\left(\frac{-\cos a(\mathrm{t}-2 \mathrm{u})}{-2 a}\right)\right]_0^t \\& =\frac{1}{2 a}\left[(\sin a t) \mathrm{u}+\frac{\cos a(\mathrm{t}-2 \mathrm{u})}{2 a}\right]_0^t \\& =\frac{1}{2 a}\left[t \sin \mathrm{at}+\left(\frac{\cos a t}{2 a}\right)-\left(0+\frac{\cos a t}{2 a}\right)\right] \\& \therefore L^{-1}\left[\frac{s}{\left(\mathrm{~s}^2+\mathrm{a}^2\right)^2}\right]=\frac{1}{2 a} t \sin \mathrm{at}\end{aligned}[/tex]
Thus, [tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)² using convolution property.
Learn more about this convolution here:
https://brainly.com/question/28167424
#SPJ1
Find the distance between (-2, 6) and (1, 3).
Answer:
3√2
Step-by-step explanation:
Distance (d) = [tex]\sqrt{((1 - -2)^2 + (3 - 6)^2)}[/tex]
= [tex]\sqrt{((3)^2 + (-3)^2)}[/tex]
= √18
= 3√2
CAYMAN Sleep Couch PRICE Was R2-699 (including VAT) PRICE Now R1 999 (excluding VA Use information above to answer the questions that follow. 2.1 Show that the couch's original price excluding VAT was R2 346.96. 2.2 Show with calculation that a customer is expected to pay R2 299 incl nouding VAT when purchasing the couch at SALE price.
Given: cost of CAYMAN sleep couch with VAT is R2 699
cost without VAT is R1 999
What are the answers for 2.1 and 2.2 questions?2.1 To calculate the original price of the couch excluding VAT, we can use the following formula:
Price including VAT / 1 + (VAT rate / 100) = Price excluding VAT
In this case, the VAT rate is 15% (since it is included in the original price), so the formula is:
R2,699 / 1 + (15 / 100) = R2,346.96
2.2 To calculate the expected price of the couch including VAT at the sale price, we can use the following formula:
Price excluding VAT * (1 + (VAT rate / 100)) = Price including VAT
In this case, the VAT rate is still 15% and the sale price is R1,999 (excluding VAT), so the formula is:
R1,999 * (1 + (15 / 100)) = R2,299
To learn more about VAT refer to:
brainly.com/question/20628016
#SPJ1
2. Triangle XYZ is rotated 90° clockwise about the origin to form triangle
XYZ.
Y
N
у
6
L
3
N
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
N
12
3 4 5
X
67
X
Which state ment is true
Answer:
21 because 21x2 is 21 rrrr
Solve the inequality
Show clear algebraic working.
m² + 3> 21
—————
4
Therefore , the solution of the given problem of inequality comes out to be m > 4.24.
What is inequality, exactly?In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.
Here,
Given :
=> m² + 3> 21
=> m² > 21-3
=> m² > 18
=> m > √18
=> m > 4.24
Therefore , the solution of the given problem of inequality comes out to be m > 4.24.
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
the sum of 5 consecutive numbers is 100 what is the 1st number
Answer:
18
Step-by-step explanation:
Please help me with this math question! Thank you!
The expression that illustrate the diagram below is f(x) = 47-2x
What are linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
In the diagram, the total no of box is 45 and 2 boxes are missing on the second box. Therefore the constant in the the expression is 45+2 = 47. Let x be the variable.
Therefore f(x) = 47-2x
when it is pattern 1
x= 1
f(1) = 47-2 = 45
when it's pattern 2
f(x) = 47-2×2 = 43
when it's pattern 3
f(x) = 47- 2×3 = 41
therefore the expression that can illustrate the diagrams is f(x) = 47-2x
learn more about linear expression from
https://brainly.com/question/2030026
#SPJ1
Explain how solve 4^x + 3 = 7 using the change of base formula . Include the solution for x in your answer. Round your answer to the nearest thousandth.
By algebra properties and base change formula, the value of x of the exponential function 4ˣ ⁺ ³ = 7 is equal to 1 / ㏒₇ 4 - 3
How to solve an exponential function by means of change base formula
In this question we find an exponential function that must be solved, this can be done by combining algebra properties and base change formula. Change base formula is a property that changes the base of a logarithm into another, defined below:
㏒ₐ x = ㏒ₙ x / ㏒ₙ a
Where:
n - Original basea - Resulting baseFirst, write the entire expression:
4ˣ ⁺ ³ = 7
Second, use logarithm operators on both sides:
㏒₄ 4ˣ⁺³ = ㏒₄ 7
Third, use logarithm properties to simplify the expression:
(x + 3) · ㏒₄ 4 = ㏒₇ 7 / ㏒₇ 4
x + 3 = 1 / ㏒₇ 4
Fourth, clear x within the expression by algebra properties:
x = 1 / ㏒₇ 4 - 3
To learn more on base change formula: https://brainly.com/question/30237855
#SPJ1
which expression is equal to 1/64?
Answer: There are many but these are some of them
2/128
4/256
6/384
8/512
Step-by-step explanation:
Question 4
Solve by Completing the Square: x² + 12x + 21 = 0
O {-12 ± √15}
O {-6± √15}
O {6 ± √15}
O {-6 ± √57}
answers to the equation as the Completing the Square: x = 6 ± √15 ≈ {2.13, 9.87} as x² + 12x + 21 = 0 .
what is square ?According to Euclidean geometry, a square has four equal sides and four equal angles, making it an equilateral quadrilateral. Another name for it is a rectangle with two adjacent sides that are the same length. An equilateral quadrilateral is one that has four equal sides and four equal angles, like a square. Angles that are 90 degrees or straight are square angles. The square's diagonals are also split at a 90-degree angle and are evenly spaced. a rectangle with two equal sides that is adjacent. a quadrilateral with four equal sides and straight angles on all four sides. a parallelogram with two adjacent sides that are equal and create a right angle. rhombus with straight sides.
given
the square can be completed by adding the square of half the x-coefficient: (-12/2)² = (-6)² = 36.
x² -12x +36 = -21 +36
(x -6)² = 15 . . . . . . . . the form you want for your answer template
Taking the square root gives ...
x -6 = ±√15
answers to the equation as the Completing the Square: x = 6 ± √15 ≈ {2.13, 9.87} as x² + 12x + 21 = 0 .
To know more about square visit:
https://brainly.com/question/14198272
#SPJ1
WILL GIVE BRAINLIEST
In kite WXYZ, m
Answer Here
Answer:
What atre u asking me to solve?
Step-by-step explanation:
(x-3)^2= -3
ANSWER BY FINDING THE SQUARE ROOT PROPERTY?
Tracy, a political campaign organizer, realizes that the number of hours needed to get out a mailing for her candidate is inversely proportional to the number of campaign workers she has. If she uses the information in the accompanying graph, how many hours would it take to do the mailing if 125 workers are used?
Answer: It is impossible for me to answer this question as I do not have access to the accompanying graph that Tracy is using. The graph would be needed to determine the relationship between the number of hours needed to get out a mailing and the number of campaign workers used. Without this information, it is not possible to determine how many hours it would take to do the mailing if 125 workers are used.
Step-by-step explanation: