On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.
How to solve Algebra Word Problems?Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline
Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline
Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon
Then, hybrid car travel, 1 ⁹/₁₁ * x = 1 ⁹/₁₁ * x * 33 = 60 miles per gallon
On 1 gallon of gasoline hybrid car travel 60 miles
On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles
On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
A 10-lb bag of flour costs $3.69. A
5-lb bag costs $1.55. How much can
you save if you buy the big bag
instead of 2 small bags?
$0.29 you save if you buy the big bag instead of 2 small bags .
The unitary method is a strategy that determines the value of many units based on the value of a single unit in addition to calculating the value of a single unit using the values of multiple units.
We must divide the value of one thing by the number of other items we wish to calculate the value of before multiplying that result by one.
From the question,
A huge bag of flour weighing 10 lbs costs $3.69 in total.
Currently, one 5-lb small bag costs $1.55.
Consequently, two 5-lb little bags cost $3.10 each.
Cost difference equals big bag cost minus two small bag expenses.
The price difference is equal to $3.69 minus $3.10.
$0.29 is the cost difference.
By purchasing two small bags of floor instead of one large bag, you will save $0.29.
To learn more about unitary method refer the link:
https://brainly.com/question/16540940
#SPJ1
how does this trick work? why does it always give the correct date of birthday?
The expression can be simplified to:
x + y/100
Where x is the month and y the day. This is why it always works.
Why does the trick always work?Let's define the two variables x and y as the month of your birth and the day of your birth respectively.
Now let's write the expression by following the steps, you should get:
((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100
Now let's simplify the expression we will get:
((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100
(((91x - 13 + y + 3)*11 - x - y)/10 + 11)/100
(((91x - 10 + y)*11 - x - y)/10 + 11)/100
((1001x - 110 + 11y - x - y)/10 + 11)/100
(( 1000x - 110 + 10y)/10 + 11)/100
You already can see what will happen here:
(( 1000x - 110 + 10y)/10 + 11)/100
(100x - 11 + y + 11)/100
(100x + y)/100 = x + y/100
So the expression will do the exact same thing for every values of x and y that you decide to use, it does not depend on your exact date of birthday.
If you want to learn more about expression:
https://brainly.com/question/723406
#SPJ1
Jessica is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Jessica has been adding money. Suppose that x and y are related by the equation =+55030xy.
After differentiating, the amount when x=0 yields starting amount,
300 dollars.
What is diffrentiation?
A technique for determining a function's derivative is differentiation.A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of variation based on a particular variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.In mathematics, differentiation is used to determine change rates.Differentiating the given equation with respect to x,
Given equation,
y= 55x+ 300
[tex]\frac{dy}{dx} =\frac{d(55x+300)}{dx} = 55+0 =$55[/tex] dollars.
The amount when x=0 yields starting amount,
y=55(0)+300=300
Learn more about differentiation here:
https://brainly.com/question/25081524
#SPJ9
Market research was undertaken to determine whether an ad campaign was successful for the software company. 15 men and 75 women were asked if they had seen the company’s latest TV advertisement. Altogether, 2 5 of the people said ‘yes’. 6 15 of the men said ‘yes’. What percentage of women said ‘no’ out of the total survey population?
50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Market research was undertaken to determine whether an ad campaign was successful for the software company.
Total number of people = 15 + 75 = 90
The number of people who said yes = (2/5)90 = 36
The number of people who said no = 90 - 36 = 54
The number of men said yes = (6/15)x15 = 6
The number of men said No = 15 - 6 = 9
The number of women who said no = 54 - 9 = 45
Percentage = (45/90)x100
The percentage of women who said ‘no’ out of the total survey population:
= 50%
Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ1
What is the linear speed in miles per hour of the tip of a lawnmower blade spinning at 2800 revolutions per minute in a lawnmower that cuts a path that is 26 inches wide?
What is the angular speed in degrees per hour?
The linear speed in miles per hour of the tip of a lawnmower blade spinning is 0.0601509076 miles per hour and angular velocity is 293.276 rad/hr.
What is linear speed?The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an item along a straight line. It is the distance traveled along a linear path in the allotted amount of time.
2800 rotations per minute on a lawnmower blade.
Specifically, the frequency of the blade is 2800 revolutions per hour,
f = 2800 / 60, or 46.66.
The angular velocity is
ω = 2πf
where f = frequency
ω = 2 × 3.14 × 46.7
ω = 293.276 rad/hr
The diameter of the circle centered at the blade's middle determines the path's breadth.
26 inches in diameter
radius = 26 / 2 = 13
13 inch = 0.0002051 miles
Velocity is given by -
V = ωR
V = 293.276 × 0.0002051
Velocity = 0.0601509076 miles per hour
To learn more about linear velocity from given link
https://brainly.com/question/2612576
#SPJ9
Use the given point, P, on the unit circle to find the value of sine and cosine of t. Answer exactly.
sin(t)
P is at the point (0, - 1).
cos(t)
=
=
Get Help: eBook
19,731
P
Points possible: 1
This is attempt 1 of 5.
t
SEP 2
6
O)
a
Preview
Preview
♫
tv ♫
17 A
License
2
(((
Value of Sine and Cosine of T is -1 and 0 respectively.
According to the question statement, P is at the point (0,-1)
We are supposed to find the value of trigonometric ratios sine and cosine of T
Let Point P (0,-1)
[tex]x=0, y=-1[/tex] and radius r = 1
[tex]sin(t) = \frac{y}{r}\\sin(t)=\frac{-1}{1} \\sin(t)=-1[/tex]
Therefore, sine of t is -1
[tex]cos(t)=\frac{x}{r} \\cos(t)=\frac{0}{1} \\cos(t)=0[/tex]
Therefore, cosine of t is 0
Trigonometric ratios: Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trigonometric ratios are therefore assessed in relation to sides and angles.To learn more about trigonometric problems, click on the link given below:
https://brainly.com/question/23130410
#SPJ9
12x + 36 -14 -8x +5 =
Answer:
4x + 27
Step-by-step explanation:
12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)
12x + 27 - 8x Combine like terms (12x, -8x)
A student is given this proof.
Given: AOM DON
Prove: CON~ BOM
ZAOM ZDON
given
ZBOM DON
vertical angles
theorem
ZAOM ZBOM
transitive
property of
congruence
ZAOM ZCON
vertical angles
theorem
ZCON BOM
transitive
property of
congruence
The student says that the proof shows that AOM BOM because they
are vertical angles.
Which statement best corrects the student's interpretation?
From the steps below, it has been proved that by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM
How to prove congruent angles?
We are given;
∠AOM ≅ ∠DON
To prove that;
∠CON ≅ ∠BOM
Now, from the image attached, we can say that;
∠BOM ≅ ∠DON because of vertical angles theorem
Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.
Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON
Finally, since ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM
Read more about Congruent Angles at; https://brainly.com/question/3168048
#SPJ1
2/3, ¹/3 =I need to find a LCD less common denominator for this question
In order to answer this issue, I need to identify an LCD, or least common denominator—something that unites all of the group members. We had all previously worked for the same employer, so that was our common denominator.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
Prime number seven.
7*8 = 56
56 is the lowest common factor.
3/7 * 8/8 = 24/56
5/8*7/7 = 35/56
To leaen more about common denominator Visit : https://brainly.com/question/16475052
#SPJ9
Urgent Please!
• What expression would represent the area of a square with side length 10?
—-
•Part C: What expression would represent the area of a square with side length 20?
—-
•Part D: What expression would represent the increase in area caused by changing the side length from 10 to 20?
Answer: B. 100
C. 400
D. 300
Step-by-step explanation:
A=area of square. s=side length of square.
B. A=s^2
A=10^2
A=100
C. A=20^2
A=400
D. I=Increase in Area
I=20^2 -10^2
I=400-100
I=300
Which table had a constant of proportionality between y and x of 1/6
Answer: Table which had a constant of proportionality between y and x of 1/6
is table C
Step-by-step explanation:
The meaning of constant proportionality is very simple and that is
ratio of y and x
here
y/x=1/6;
therefore we have to check various options
checking option C
first part:
3/18=1/6;
second part:
(9/2)/27=1/6;(convert mixed fraction into improper fraction)
third part:
(11/2)/33=1/6;
hence ;
Table which had a constant of proportionality between y and x of 1/6
is table C
Learn more about ratio and proportion here
https://brainly.com/question/28493517
#SPJ9
A rectangle has a length 3x + 1 of and a width of Write an expression for the 3-9
perimeter of the rectangle.
The expression for the perimeter is P = 12x - 16
How to write an expression for the perimeter?The given parameters are
Length = 3x + 1
Width = 3x - 9
The perimeter is calculated as
P = 2 * (Width + Length)
So, we have
P = 2 * (3x + 1 + 3x - 9)
Evaluate
P = 2* (6x - 8)
Expand
P = 12x - 16
Hence, the expression for the perimeter is P = 12x - 16
Read more about perimeter at:
https://brainly.com/question/19819849
#SPJ1
A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,900 per month for the next three years and then $3,800 per month for two years after that. If the bank is charging customers 9.75 percent APR, how much would it be willing to lend the business owner?
The amount will be $141647.55.
we need to use the present value of an annuity formula:
the formula used to determine the present value factor of an annuity is:
present value annuity factor = [1 - 1/(1 + i)ⁿ ] / i
we must divide this into 2 parts:
the first part will deal with the $19,00 monthly payment
the second part deals with the $38,000 monthly payment
i = 9.75% / 12 = 0.8125%
n (first part) = 36
n (second part) = 24
the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)³⁶ ] / 0.8125% = 31.1043
the PV annuity factor for second part = [1 - 1/(1 + 0.8125%)²⁴ ] / 0.8125% = 21.7251
loan = ($219,00 x 31.1043) + ($38,00 x 21.7251)//(1 + 0.8125%)³⁶ = $59092.17 + $82555.38 = $141647.55
hence we get the amount as $141647.55
Learn more about simple interest here:
https://brainly.com/question/25793394
#SPJ9
i need help on this! its due today
Answer:
a) It's growing by 1 Hexagon in each term
b) (Self Explanatory, but if you still font know, just add 1 hexagon on the bottom tail)
c) 1-4
2-5
3-6
4-7
5-8
d) 1 hexagon is added each time
e) Common Difference = a1 - a
= 5 - 4
= 1
f) Consider the equation n + 3
where n is the number of terms.
In this case, n = 12
= 12 + 3
= 15 Hexagons
g) f(n) = 4 + 1(n-1)
f(1) = 4 + 1 ( 1 - 1)
f(1) = 4 + 1 (0)
f(1) = 4 + 0
f(1) = 4
h) (Forgive me, I actually don't know the answer for this one :'( )
Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 253.63 miles on a business trip, what
is his mileage reimbursement?
Answer:
17.75
Step-by-step explanation:
253.63 ×0.07=17.7541
Estimate actual problem by rounding all the way and do actual division: LU 1-1(2), LU 1-3(2)
Actual. Estimate
695)8,950
The actual problem will be 9000 % 700, with the remainder 600 and quotient 12.
Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950 and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple using the round-off rule, here in the dividend 8950, the last two digits are 50, so we can round off it to 9000 and in the divisor 695, the last digit is 5, so we add 1 in the preceding number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.
To know more about the round-off rule refers to the link https://brainly.com/question/28673593?referrer=searchResults.
#SPJ1
Just like Earth, other planets have
seasons. In fact, Neptune's seasons last
for 40 years! How many days would
winter last? (Hint: A year is 365 days).
Winter would last for 14,600 days
How to calculate the number of days that winter would last ?Planet can be described as celestial bodies that move around the sun. The earth and Neptune are typical examples of planets. There are 8 planets in the solar system.
Other planets have different seasons same way as Earth
Neptune's season last for 40 years
Therefore the number of days that winter would last can be calculated by multiplying the number of years which is 40 by the number of days in a year which is 365
1 year is 365 days
Since it 40 years then we multiply by 365
= 365 × 40
= 14,600
Hence Winter would last for 14,600 days
Read more on winter here
https://brainly.com/question/21628517?referrer=searchResults
#SPJ1
Can someone help me with this part and explain me, please?
HELP PLEASE I NEED HELP! Please solve
4(0.5n-6)=n-0.25(12+8n)
Brainiest given
Answer: -21
Step-by-step explanation:
The formula for the nth pentagonal number is
[tex]P_{n}[/tex] = n(3n-1)/2
Use the formula to find the 16th pentagonal number.
The 16th pentagonal number is 376
What is a function?A function can be defined as an expression that explains the relationship between a dependent and an independent variable.
Given the function for the nth pentagonal number as;
Pn = n( 3n -1 )/ 2
To determine the 16th pentagonal number, we need to substitute the value of n as 16
We have;
P16 = 16(3(16) - 1)/ 2
P16 = 16( 48 - 1)/ 2
P16 = 16(47)/ 2
expand the bracket
P16 = 376
Thus, the 16th pentagonal number is 376
Learn more about functions here:
https://brainly.com/question/17043948
#SPJ1
A shipment of 480 bags of coffee beans contains an equal number of 0.75-pound bags,
1.5-pound bags, and 2-pound bags. What is the total weight of the shipment?
A 520 pounds
B 608 pounds
C 680 pounds
D 720 pounds
Answer:680
Step-by-step explanation:
160x.75=120
160x1.5=240
160x2=320
Translate the sentence into an equation.
Five times the sum of a number and 3 equals 7.
Use the variable x for the unknown number.
Answer:
(5x) + 3 = 7
Step-by-step explanation:
Times means 'The answer when you multiply' So we are working in multiplication. ( x )
5x is the multiplication.
It says 'and' which can also mean addition. So we add 3. So far our equation is: (5x) + 3 (Brackets are needed as we are multiplying 5 by x and not multiplying 5 by x+3)
Lastly it says the answer must be 7 so we add that at the end. So the answer is:
(5x) + 3 = 7
A rectangular picture has dimensions of length (2x-1) inches and width (x+7) inches. The area of the picture is 108 in^2. What are the length and width of the picture?
The numerical length and width of the rectangular picture are 9in and 12in respectively.
What are the length and width of the picture?Area of a rectangle is expressed as;
A = length × width
Given the data in the question;
Length = 2x -1Width = x + 7Area = 108in²To determine the numerical length and width of the rectangular picture, first plug the given values into the equation and solve for x.
A = length × width
108 = (2x -1)(x+7)
Expand
108 = 2x² + 14x - 1x -7
108 = 2x² + 13x -7
Reorder
2x² + 13x -7 = 108
2x² + 13x - 7 - 108 = 0
2x² + 13x - 115 = 0
Solve by grouping
(x-5)(2x+23) = 0
x-5 = 0, 2x+23 = 0
x = 5, 2x = -23
x = 5, x = -23/2
x = 5, x = -11.5
But the dimension cannot be negative, hence;
x = 5
Next, determine the numerical length and width.
Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9in
Width = x + 7 = 5 + 7 = 12in
Therefore, the numerical length and width of the rectangular picture are 9in and 12in respectively.
Learn more about area of rectangles here: https://brainly.com/question/27612962
#SPJ1
8/36 = /9 what number is missing to equal 9
Answer:
72
Step-by-step explanation:
I am pretty certain that the answer is 72.
Steps:
[tex]\frac{8}{36}[/tex] [tex]\frac{x}{9}[/tex]
Cross-Multiply and Divide.
8*9 = 72
72 / 36 = 2
2/9 = 0.222222
8/36 = 0.222222
2/9 = 0.2222222
What is the perimeter of a rectangle that has a length of 40 Ft and a width of 17 ft?
Answer:
i think 114ft
Step-by-step explanation:
Answer:
114 FT
Step-by-step explanation:
Perimeter formula: P = 2 (l + w)
P = 2 (40 + 17)
Use distributive property or PEMDAS
Distributive property: P = 80 + 34
P = 114
PEMDAS: P = 2(57)
P = 114
You get 114 either way
Which equation represents the graph of this function?
_
A ) f(x)= √ x −4
____
B) f(x)= √x + 4
____
C) f(x)= √x - 4
_
D) f(x)= √x + 4
Answer:
USE air math
Step-by-step explanation:
hope that helps
For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
x - y = 4
Answer:
Please see picture below.
Step-by-step explanation:
A teacher records your grade points as 197. Your notes say that you have 205 points. What is
your percent error?
The percent error is 8%
How to calculate the percent error ?The formular for percent error is approximate value -exact value/exact value multiplied by 100
The approximate value is 197 points
The exact value is205 points
Percent error = 197 - 205 /205 × 100
= -8/205 × 100
= 0.0390 × 100
= 3.9
Hence the percent error is 8%
Read more on percent error here
https://brainly.com/question/24191505?referrer=searchResults
#SPJ1
What is an equation of the line that passes through the point ( − 3 , − 1 ) (−3,−1) and is perpendicular to the line x − 2 y = 6 x−2y=6?
The equation of the line passing through given points (-3, -10) and perpendicular to other is y + 2x + 7 = 0.
When the equation of line in point-slope form?A line's equation in point slope form is (y - y₁) = m. (x – x₁). As a result, the equation of a line with slope m passing through the origin is: y - 0 = m(x = 0), i.e. y = mx.where m is the line's slope and (x₁, y₁) are the coordinates of a provided point on the line .The equation of the perpendicular line is given as;
x − 2y = 6
Write the equation in standard form;
y = x/2 - 3
Where, slope of the line m₁ is (1/2) and y -intercept is (-3).
The other line passing perpendicular on this line has a slope: m₂.
The relation between slopes of perpendicular lines are-
m₁ × m₂ = -1
m₂ = -1/m₁
m₂ = -1/(1/2)
m₂ = -2
Now, the coordinates of the line are: (-3, -1)
The equation of the line will be;
(y - y₁) = m₂ (x – x₁)
Put the values;
(y - (-1)) = -2(x - (-3))
y + 1 = -2x - 6
y + 2x + 7 = 0
Thus, the equation of line is y + 2x + 7 = 0.
To know more about the point slope form, here
https://brainly.com/question/6497976
#SPJ9
HELP THIS IS DUE TOMORROW!
Algebra 2 question!
Picture attached below
Answer:
[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]
[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]
Multiply by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]
[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]
[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]
Separate the fractions:
[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]
Simplify:
[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]