MODELING REAL LIFE You collect S234 selling small and large smoothies. You sell a total of 46 smoothies. How many of each size did you sell?
20 small smoothies
26 large smoothies
Answers
By solving simultaneous equation conditions, there are 26 small smoothies and 20 large smoothies.
What is the simultaneous equation?
Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.
Given, total selling = $234
Let, x be the number of small smoothies sold
y be the number of large smoothies sold
Then, from the given condition,
x + y = 46 ⇒ x = 46-y ........... (i)
4x + 6.5y = 234 ................. (ii)
Now, substituting the value of x from (i) in (ii), then
4(46-y) + 6.5y = 234
or, 184 - 4y + 6.5y = 234
or, 184 + 2.5y = 234
or, 2.5y = 234 - 184 = 50
or, y = 50/2.5 = 20
and, x = 46-20 = 26
Hence, 26 small smoothies and 20 large smoothies.
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Related Questions
Prior to the current period, Benjamin Rubinek, whose tax return filing status is single, had earnings subject to Medicare tax of $199,500. During the current week, Benjamin has gross earnings of $2,900, and he requests that 7% of gross earnings be contributed to a 403(b) plan. Benjamin's employer will withhold $ in Additional Medicare Tax for this period.
Answers
Benjamin's employer will withhold $42.05 in Additional Medicare Tax for this period.
How much will be withheld by the Medicare Tax?To calculate the amount withheld by Benjamin's employer in Medicare tax, we apply the proportion of the Medicare tax to his total earnings.
The parameters for this problem are given as follows:
Medicare Rate: 2.9%, however, only 1.45% of this is withheld by the employee.Benjamin's weekly earnings: $2,900.Then the amount withheld by the employee for the Medicare Tax is calculated with the multiplication of the decimal equivalent of 1.45%, which is of 0.0145, by Benjamin's gross earnings of $2,900 as follows:
Amount = 0.0145 x 2900 = $42.05.
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Katy has 5 white flowers, x red flowers and (2x+1) yellow flowers.
She picks a flower at random.
The probability that it is white is 1/12
Find the probability that it is yellow.
Answers
Answer:
5/12
Step-by-step explanation:
Total 12 flowers
5 are white
12-5=7
red + yellow = 7
x+2x+1 = 7
3x+1=7
3x=6
x=2
white : 5
red : 2
yellow : 5
12 flowers in total, 5 yellow flowers, probability that yellow is picked is 5/12
13.
Graph f(x)=4x(1/2)^x
Answers
start by plugging values for x into the function
a) f(1) = 4 (1/2)^1
f(1) = 2
the first coordinate point is (1,2)
b) f(0) = 4(1/2)^0
f(0) = 4
(0,4)
this method will help you find the coordinate points and where to plot.
The Stock Market Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? PLS HELP
Answers
$50,700 he make in commission in 2011.
How to calculate the commission?According to the commission rate, a commission is a proportion of all sales. Multiply the commission rate by the total sales to get the commission on a sale. Recall to convert the commission rate from a percent to a decimal first, just as we did for computing the sales tax.%Earns= 13% commission/week
Last week sold = $7,500
In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:
$Earns = 0.13 (decimal form)*$7,500
Earns = $975
Last week, he made $975 in commission.
If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year
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subtract and reduce to lowest terms
Answers
Answer:
Below
Step-by-step explanation:
To add or subtract fractions ( or numbers with fractions in them) you HAVE to put the fractions into a common denominator form .....
Common denominator for 5 and 7 is 35
3 3/7 = 120/35
2 1/5 = 77/35
120/35 - 77/35 = ( 120 - 77) / 35 = 43/35 = 1 8/35
. Cell Phone Models A particular cell phone company
offers 4 models of phones, each in 6 different colors and
each available with any one of 5 calling plans. Howy
many combinations are possible?
:C
Answers
120 many combinations are possible.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.
It is represented as: [tex]^nC_r[/tex]
where, n = total number of objects in the set
r = number of choosing objects from the set
Given that,
Cell Phone Models A particular cell phone company offers:
4 models of phones
each in 6 different colors
each available with any one of 5 calling plans
Thus, possible combination numbers are:
= (No. of models) × (No. of colors) × (No. of calling plans)
= (4)× (6)× (5)
= 120 possibilities
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In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is which?
133.2
13.32
14.8
30.0
Answers
If in an analysis of variance problem involving 3 treatments and 10 observations per treatment, S S E = 399.6. The M S E for this situation is C. 14.8.
How to find the sample variance?We would be making use of this formula to find or determine the MSE which is the variance within the sample.
MSE = S S E / r (c-1)
Where:
MSE represent variance within the sample = ?
SSE represent sum of the squares of error = 399.6
r represent 3 treatment
c represent observation per treatment = 10
Let plug in the formula so as to know the variance within the sample (MSE )
Sample variance ( MSE ) = 399.6 /3 (10 - 1 )
Sample variance ( MSE ) = 399.6 / 3 (9)
Sample variance ( MSE ) = 399.6 / 27
Sample variance ( MSE ) = 14.8
Therefore we can conclude that the correct option is C which is 14.8.
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Which expression is equivalent to the answer and show work pls I am force to write it down :,)
Answers
Answer:
Last option:
[tex]\dfrac{4x^4y^2}{z}[/tex]
Step-by-step explanation:
Original expression is
[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]
Let us eliminate the obvious wrong answers
[tex]\dfrac{12}{3} = 4\\\\[/tex]
so the coefficient in the answer should be 4.
We can eliminate first and third choices
Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]
Second choice is out so the last choice is the correct one.
We can go further with the other terms
[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]
[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]
Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]
19.
Which conclusion is not justified by the prior given statements?
A. Given: If a line is vertical, then it has an undefined slope.
Given: Line / is vertical.
Conclusion: Line / has an undefined slope.
B. Given: If a triangle is isosceles, then it has two congruent sides.
Given: If a triangle has two congruent sides, then it has two congruent angles.
Conclusion: If a triangle is isosceles, then it has two congruent angles.
C. Given: If two angles are vertical, then they are congruent angles.
Given: 21 and 22 are vertical angles.
Conclusion: 21 22
D. Given: If Mark goes fishing, then he will buy a new fishing rod.
Given: If Mark goes fishing, then he will need to buy bait.
Conclusion: If Mark buys a new fishing rod, then he will need to buy bait.
Answers
Answer: the thing is I don’t know
Step-by-step explanation:
Which of the following statements are always true? A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
Answers
(A) If f(t) is increasing, it's not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
(B) f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
Left-Hand Sums and Right-Hand Sums give us different approximations of the area under a curve. If one sum gives us an overestimate and the other an underestimate, then we can hone in on what the actual area under the curve might be. Any left-hand sum will be an under-estimate of the area of R. Since f is increasing, a left-hand sum will use the smallest value of f on each sub-interval. This means any left-hand sum will fail to cover all of R and any right-hand sum will be an over-estimate of the area of R. Since f is increasing, a right-hand sum will use the largest value of f on each sub-interval. This means any right-hand sum will cover R and then some.
A) If f(t) is increasing then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.
B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is concave up then the trapezoid approximation is an overestimate, and the midpoint is underestimated.
So, If f(t) is increasing, it's not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. and if f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t; (1, 0, 1)
Answers
The parametric equations for the tangent line to the given curve is x = 1-7t , y = 6t and z = 1-7t .
In the question ,
it is given that ,
x = [tex]e^{-7t}[/tex]cos(6t), y = [tex]e^{-7t}[/tex]sin(6t), z = [tex]e^{-7t}[/tex] ,
So , the parametric equation of the curve will be ,
r(t) = [ [tex]e^{-7t}[/tex]cos(6t), [tex]e^{-7t}[/tex]sin(6t), [tex]e^{-7t}[/tex] ]
the point given as (1,0,1) implies that ,
[tex]e^{-7t}[/tex]cos(6t) = 1 , [tex]e^{-7t}[/tex] = 0 , sin(6t), [tex]e^{-7t}[/tex] = 1 which implies that ⇒ t = 0 .
So , the point (1,0,1) is the point r(0) .
Now , differentiating x , y and z with respect to t ,
we get ,
r'(t) = [ [tex]-e^{-7t}[/tex][7cos(6t) + 6sin(6t)], [tex]e^{-7t}[/tex][6cos(6t) - 7sin(6t)], [tex]-7e^{-7t}[/tex] ]
substituting , t = 0,
we get ,
r'(0) = [-7 , 6 , -7]
the equation of the tangent line passing through the point (1,0,1) and parallel to the tangent vector r'(0) is
r(t) = r(0) + tr'(0) = (1,0,1) + t(-7,6,-7)
So , r(t) = [ 1 - 7t , 6t , 1 - 7t ]
So , x = 1 - 7t , y = 6t and z = 1 - 7t .
Therefore , the required parametric equations are x = 1 - 7t , y = 6t and z = 1 - 7t .
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Find the terminal point on the unit circle determined by 11π/6 radians. Use exact values, not decimal approximations.
Answers
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.
According to the question, it is provided that,
θ = 11π/6 radians
Now,
x = 1.cos(11π/6)
x = cos(11π/6)
x = cos(330°)
x = [tex]\sqrt{\frac{3}{2} }[/tex]
y = 1.sin(11π/6)
y = sin(11π/6)
y = -0.5
y = - [tex]\frac{1}{2}[/tex]
Then,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
These two represents the terminal points
To find the terminal positions, we merely used the aforementioned equations, equated these two equations, and concluded that the same should be taken into consideration.
It could be figure out by using the x and y points
Therefore
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
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100 POINTS
Choose the equation for the graph below. (please explain, I want to understand the solution)
Answers
The equation of the graph is [tex]-\frac{3x^{2} }{2x +6}[/tex]
How is the equation of the graph found?The asymptotic line is x = -3So, the domain of definition x ≠- 3This eliminates options a, b and c .In option e domain of definition is x ≠ ± 3The domain is defined by the image.So, option d is correct. The equation of the graph is [tex]-\frac{3x^{2} }{2x +6}[/tex]What is an asymptotic line?A boundary between positive and negative curvature on a surface is known as an asymptotic line. They are the surface-traced curves that are perpendicular to one of the asymptotic directions at each location. One of the directions where the curvature is equal to zero, as well as one of the Dupin indicatrix cubic's asymptotes that corresponds to this point, or the axis when it is reduced to two parallel lines.They are the curves that are drawn on the surface with normal curvature, which is the curvature that is always equal to zero in the plane that contains the tangent to the curve and the surface normal.This is the same as saying that the curvature and the geodesic curvature are equal.To learn more about asymptotic line, refer:
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Answer: C
Step-by-step explanation:
due to the slope
PLEASE HELP !!!!!! The time between a flash of lightning and the sound of its thunder can be used to estimate the distance from a lightning strike. The distance from the strike is the number of seconds between seeing the flash and hearing the thunder divided by 5. Suppose you are 17 miles from a lightning strike. Write and solve an equation to find how many seconds there would be between the flash and thunder.
Answers
Answer:
Step-by-step explanation:
12.5663706144
I need a answer using the race method (high school level)
and i will make it worth your time
What do you think you could do to show this statement is true?
How could you manipulate this equation to allow you to state this.
Answers
By using algebraic expression, the proof of
(a + b)(a - b) = a² - b² has been shown below-
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Algebraic expressions are of different types based on number of terms.
They are monomial, binomial, trinomial and so on
Algebraic expression with one term is called monomial
Algebraic expression with two terms is called binomial
Algebraic expression with three terms is called trinomial
The given algebraic expression is
(a + b)(a - b)
a² - ab + ba - b²
a² - ab + ab - b² [Commutative law of addition]
a² - b²
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order the following pair of numbers using <,>or=:-12 _-|12|
Answers
Answer:
-12 _ -|12|
(-12) = (-12)
Thus, Both are equal
Describe the slope of the line.
The slope is positive
Find the slope
m=_______
Answers
The equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
The line on the graph passes through points (0, 3) & (0, 4).
m = (4-3)/(0-0)
m = 1/0
m = ∞
so, the slope is undefined.
Therefore, the equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
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you are designing a rectangular wooden box with width 4 inches greater than its height, and length 3 times its height. the box has wood that is 1 inch thick on each side of the four sides on the top and bottom. a. write a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
Answers
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box
what is polynomial function ?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable)
calculation
outside length are height = x
width = x +4 , length = 3x
volume = l *b * h
o(x) = 3x ( x+ 4 )x
= 3[tex]x^{2}[/tex](x+4 )
= O (x) = [tex]3x^{3} + 12x^{2}[/tex]
there is 1 inch of wood , so lengths of inner sides 2 inch less than outer sides as 1 inch from reduced
length = 3x-2
width = x +4-2 = x+2
height = x -2
volume = l*b*h
=[tex]3x^{3} - 2x^{2} - 12x + 8[/tex]
w(x) = [tex]14(6^{2}) + 12(6) -8\\ 504 + 72 -8 \\568inch^{3}[/tex]
so volume of wood = [tex]568inch^{3}[/tex] for x =6
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
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HW9.4. Algebraic and geometric multiplicity of eigenvalues Observe that -1 is an eigenvalue of A= [-1.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 -2.00 Determine the algebraic and geometric multiplicity of this eigenvalue of A. Algebraic multiplicity integer Geometric multiplicity integer
Answers
The value of algebraic multiplicity will be 1 and geometric multiplicity will be 1
[tex]$$\begin{aligned}& A=\left[\begin{array}{ccc}3 & -2 & 0 \\-2 & 4 & 4 \\1 & 0 & 2\end{array}\right] \\& \Rightarrow A=\left[\begin{array}{ccc}-1 & 1 & 0 \\0 & 0 & 0 \\1 & 1 & -2\end{array}\right]\end{aligned}$$[/tex]
[tex]$$Det(A-\lambda I) = Det A=\left[\begin{array}{ccc}(-1-\lambda) & 1 & 0 \\0 & -\lambda & 0 \\1 & 1 & (-2-\lambda)\end{array}\right]$$[/tex]
[tex]$$-(1+\lambda)\left|\begin{array}{cc}-\lambda & 0 \\1 & -2-\lambda\end{array}\right|-1\left|\begin{array}{cc}0 & 0 \\1 & -2-\lambda\end{array}\right|$$[/tex]
[tex]$$\begin{aligned}& =-(1+\lambda)\left(\lambda^2+2 \lambda\right) . \\& =-\lambda(1+\lambda)(\lambda+2) .\end{aligned}$$[/tex]
So, for [tex]\lambda=-1[/tex], eigen values are [tex]\lambda[/tex]=0,-1,-2.
Hence, the value of algebraic multiplicity=1
[tex]AV=\lambda v \\& \Rightarrow A V=-V\\ \Rightarrow-V_1+V_2=-V_1\\ \Rightarrow V_2=0 \\& v_1+v_2-2 v_3=-v_3\\ \Rightarrow v_1+v_2-v_3=0\\ \Rightarrow v_1=v_3 \\[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad\left[\begin{array}{l}v_1 \\0 \\v_1\end{array}\right] \\& =v_1\left[\begin{array}{l}1 \\0 \\1\end{array}\right]\end{aligned}$$[/tex]
So, the value of eigen vectors are: [tex]& =\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right] \\[/tex]
And the value of geometric multiplicity =1
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A line passes through the points (– 7,– 2) and (– 14,– 7). Which points lie on the same line? Select all that apply.
Answers
Answer:
A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.
The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.
Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).
Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).
GIVING BRAINLIEST!!!!!!!
What is the perimeter of rectangle PQRS?
Answers
Answer: 20 units
Step-by-step explanation:
Since the rectangle is on the graph, we can directly count the units.
Perimeter is the sum of all sides.
4+4+6+6=20
GIVING BRAINLIEST
ANSWER 4 X 4 X 8 X 2
Answers
Answer:
The answer is 256
Step-by-step explanation:
Answer:
256
Step-by-step explanation:
4 · 4 · 8 · 2 = 256
1. Whole milk has 3.25% milk fat in it. If you have 2 cups of milk, how many grams of fat are you
getting? (Remember to convert cups to ml first and get the total amount of milk, or 100%, first)
Answers
Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
What is milk fat?
The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.
Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.
100 grams = 3.25 % of milk fat.
10 grams = x
x = 10 * 3.25 / 100
=0.325 %
Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.
Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
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Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1273 Determine the interval of convergence. (Enter your answer using interval notation.) Need Help? Read It Talk to a Tutor + -12 points SEssCalcET2 8.6.009. Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1 + 16) = 4+ 5 f(x) = 4 + 5 n = 1 Determine the interval of convergence. (Enter your answer using interval notation.)
Answers
A power series representation for the function the interval of convergence is x > -14 .
Given :
a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1273 Determine the interval of convergence.
f ( x ) = 3 / 17 + x
Interval of convergence :
The interval of convergence can be calculated once you know the radius of convergence. First you solve the inequality |x − a| < R for x and then you check each endpoint individually.
3 / 17 + x < 1
3 < 1 * ( 17 + x )
3 < 17 + x
-14 < x
x > -14
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the median is defined as: multiple choice question. the value of the observation that occurs most frequently the arithmetic mean of the values of a set of data the midpoint of the values after they have been arranged in rank order the average of the largest and the smallest value in a data set
Answers
The median is defined as the midpoint of the values after they have been arranged in rank. Option B
What is median?Median is simply defined as the middle value of a given sorted list of numbers or data set.
It is seen as the value that separates the higher half from the lower half of a given data sample, a probability distribution or a population.
For a data set, it is also called "the middle" value.
It also involves ordering the data set or a group of numbers in an ascending order, that is, from least to greater number.
The media is selected from picking the number in the midpoint for an even set of data which does not always occur.
In an odd group of data, after ordering the number from the least to the greatest, the two mid-numbers are taken, added and divided by half to determine the median.
Hence, the median is the midpoint of a set of ordered data.
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What is the freezing point, in C, of a 2.75 m solution of C8H18 in benzene?
Answers
The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.
The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.
To determine the freezing point of a solution, we can use the freezing point depression equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.
To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:
ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C
To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:
5.5 °C - 14.06 °C = -8.56 °C
This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.
Adryanna got a manicure for $35 and a pedicure for $43. If she plans on leaving a 15% tip how much will she pay on total
Answers
The total amount that will be paid will be $89.70.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip
The total amount that will be paid will be:
= ($35 + $43) + (15% × $78)
= $78 + $11.7
= $89.7
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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest
angle
• The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.
• The measure of the largest angle is twice the smallest angle plus 10 degrees.
• The sum of the angles of a triangle can be written as x + y + z = 180.
What are the other equations that represent this system of equations?
Select each correct answer.
Answers
the triangle could represent in a relation as x = 60 - 2(y + z) and x = 2z + 20.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":
x = 60 - 2(y + z) —- (1)
The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:
x = 2z + 20 —- (2)
Hence the triangle could represent in relation as x = 60 - 2(y + z) and x = 2z + 20.
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Graph the system below and write its solution.
x-2 y=2
y={1}/{2} x-3
Note that you can also answer "No solution" or "Infinitely many" solutions.
Answers
The required answer for the given system of linear equations is No solution.
What is a system of linear equation?
A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.
Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get
No solution
The graph of the given system of linear equations is given below
Hence, the required answer for the given system of linear equations is No solution.
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A solution to an equation is a value that, when substituted for the variable, makes the equation true.x+2=75+2=77=7✓Since 5+2=7 is a true statement, we know that 5is indeed a solution to the equation.
Answers
A solution to an equation is a value that, when substituted for the variable, makes the equation true. In the equation x+2=7, the solution is x=5.
This is because if we substitute 5 for x, the equation becomes 5+2=7, which is a true statement. To find this solution, we need to solve the equation by subtracting 2 from both sides, leaving us with x=5. This solution works because it satisfies the equation; when we substitute 5 for x, the equation is true.
In equations, solutions are important because they are the values that make the equation true. Without solutions, equations would remain unsolved and incomplete, which is why it is important to find the solution to an equation.
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