Two pairs of shoes and four pairs of socks cost $131, and three pairs of shoes and five pairs of socks cost $190. Find the cost of a pair of socks.
How do I answer this question?
Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?
Final answer:
Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.
Explanation:
We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.
Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:
11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallonSimplifying the first equation:
11r + 7r + $1.75 = $76.99
18r + $1.75 = $76.99
18r = $76.99 - $1.75
18r = $75.24
r = $75.24 / 18
r = $4.18
So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.
Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?
Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___
A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.
Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15
how do write an equation to represent a real world situation?
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground? (s= 16t^2)
Answer:
After 3 seconds the object hit the ground.
Step-by-step explanation:
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.
Given that displacement, s = 16t²
To reach ground displacement should be 144 feet.
That is
s = 16t² = 144
t² = 9
t = 3 seconds.
After 3 seconds the object hit the ground.
What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?
The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
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A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?
In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide
In a glide reflection, the reflection comes first and the glide comes second.
Explanation:In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.
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Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?
Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.
Explanation:The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.
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A certain species of tree grows an average of 4.2 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
Average growth rate = 4.2 cm/week.
So, common difference d = 4.2
The height of the tree a0 = 200 centimeters.
The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)
The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).
The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).
The height of the tree after the end of the nth week an = 200 + 4.2(n).
The equation is a_n = 200 + 4.2(n).
What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?
The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.
Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
A = base * altitude
A = 20 * 8
A = 160 inches square.
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Based on the historical record what is the empirical probability that the city will be hit by a tornado
What are the counting numbers in base 6
In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1 one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we would need:
Base 6 Base 10
1 1
2 2
3 3
4 4
5 5
10 (1 six plus 0 ones) 6
11 (1 six plus 1 one) 7
12 (1 six plus 2 ones) 8
13 9
14 10
15 11
20 (2 sixes plus 0 ones) 12
21 (2 sixes plus 1 one) 13
22 14
23 15
Final answer:
The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.
Explanation:
The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.
The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.
A $28,000 car loan is used to purchase a new car. The loan is for 6 years and has a 5.75% APR. Use the amortization formula to determine the amount of the monthly payments.
“the sum of eight and twice w”
Answer:
the expression is [tex]8+2w[/tex]
Step-by-step explanation:
WE need to write the expression for the given statement
“the sum of eight and twice w”
Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'
Difference represents the subtraction operation.
Sum represents the addition operation.
twice 'w' means 2 times w that is 2w
the sum of 8 and 2w
For sum we use '+'
so ,the expression becomes [tex]8+2w[/tex]
G study find the exact value of each of the remaining trigonometric functions cos theta=4/5 270< theta
Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.
Explanation:The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.
This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.
Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.
Plugging in the given cosine value, we have:
sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5
However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:
sin(theta) = -3/5
For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:
tan(theta) = (-3/5) / (4/5) = -3/4
The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:
sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3
A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rate of the boat in still water.
If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true
Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.
To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.
Raphael paid 636 for camera during a 60% off sale with the cameras regular price
If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to dilute it to a 25% solution?
a culture started with 6,000 bacteria. After 4 hours, it grew to 6,600 bacteria. Predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number.
P = 6,600
A = 6,000
t = 4
k = ?
6600 = 6000e^(4k)
6600/6000 = e^(4k)
1.1 = e^(4k)
Take the natural log of both sides.
ln 1.1 = 4k ln e (remember that ln e = 1)
ln 1.1 = 4k
(ln 1.1) / 4 = k
k = 0.0238
Bacteria after 10 hours.
P = 6000e^(0.0238*10)
= 6000e^0.238
= 7612
Therefore, the bacteria will grow to 7612 after 10 hours.
In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____
arc length = (central angle/360) x 2 x PI x r
= (35/360) x 2 x 3.14 x 25
=15.2638
round answer as needed, you don't say how to round it.
Can someone please solve this ASAP?
surface area = 5ab +5bh
a = 4
b=7
h=18
5*4*7 = 140
5*7*18 = 630
630+140 = 770 square meters
ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?
Answer:
The correct answer is
C 40/41
Step-by-step explanation:
What is the inverse of the function below? F(x) = x - 6
Answer:
f(x)=x+6
Step-by-step explanation:
its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6
a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?
In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
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