Answer:
1.5 < x < 34.7
Step-by-step explanation:
You want a compound inequality describing possible lengths (x) for the third side of a triangle with sides 18.1 and 16.6.
Triangle inequalityThe shortest side cannot be any shorter than the difference of the two known sides:
18.1 -16.6 = 1.5
The longest side cannot be any longer than the sum of the two known sides:
18.1 +16.6 = 34.7
The possible lengths of the third side are given by ...
1.5 < x < 34.7
__
Additional comment
If the third side is exactly equal to the sum or the difference, then the "triangle" looks like a line segment. It has zero area. That possibility is usually disallowed. If you want to allow it, then change < to ≤ in the inequality.
In a survey of 120 people who visited a lake, 20% went fishing. Of those who went fishing, 75% also went swimming. Of those who did not go fishing, 50% went swimming.
The two-way frequency table to display the data will be:
Fishing Not Fishing Total
Swimming 15 30 45
Not Swimming 5 45 50
Total 20 75 95
What is the frequency table about?20% of 120 people is 24 people, but since 20% of the people went fishing, we know that 24 people went fishing.
75% of 24 people who went fishing is 18 people.
50% of 96 people who did not go fishing is 48 people.
Total number of people who went swimming is 45 (15+30)
Total number of people who did not go swimming is 50 (5+45)
Total number of people in the survey is 95 (24+71)
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In a survey of 120 people who visited the a lake, 20% went fishing.of those who went fishing,75% also went swimming. Of those who did not go fishing ,50% went swimming. Construct a two-way frequency table to display the data.
Which excerpt from Click It or Ticket Mobilization Media Campaign bet achieve the purpoe of informing people that eat belt law are enforced nationwide?
Click It or Ticket is a nationwide campaign to enforce seat belt laws and increase seat belt use, supported by major organizations.
Nationwide Seat Belt Enforcement CampaignClick It or Ticket is a nationwide mobilization campaign to enforce seat belt laws and increase seat belt use. It is a joint effort of state and local law enforcement, highway safety offices, and the National Highway Traffic Safety Administration and is supported by national and state-level organizations, including:
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let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and "f '(4) = 7". find r'(1). r'(1)
Answer: To find r'(1), we need to use the chain rule of differentiation, which states that:
r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)
In this case, we know that:
h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and f '(4) = 7
Therefore:
r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1) = f'(g(2)) * g'(2) * h'(1) = 7 * 4 * 4 = 112
So, the derivative of r(x) with respect to x at x = 1 is 112
Step-by-step explanation:
a partial relative frequency distribution is given. class relative frequency a 0.22 b 0.18 c 0.40 d (a) what is the relative frequency of class d? (b) the total sample size is 200. what is the frequency of class d? (c) show the frequency distribution. class frequency a b c d total (d) show the percent frequency distribution. class percent frequency a b c d total
The frequency Asked in the problem are listed below in order:
0.2040200100What is a frequency distribution?To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.
Given, a partial relative frequency distribution is given. class relative frequency a 0.22 b 0.18 c 0.40 d
Since all relative frequencies add up to be 1.
So,
0.22 + 0.18 + 0.40 + x = 1
x = 0.20
For b)
total sample size * relative frequency = frequency of a class
200*0.2 = 40
For c)
Frequency distribution is calculated as the frequency of a class = total sample size * relative freq.
A = 44
B = 36
C = 80
D = 40
TOTAL = 200
For d)
Percent frequency is calculated as Percent frequency of a class = 100 * relative freq.
A = 22
B = 18
C = 40
D = 20
TOTAL = 100
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Complete question:
James Harden's 6 year investment of $100,000 accrued 4.2% interest
continuously. About how much money does he expect to receive?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 100000e^{0.042\cdot 6} \implies A = 100000e^{0.252}\implies A \approx 128659.60[/tex]
An automatic filling machine is used to file 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1. 0 liter and a standard deviation of 0. 01 liter. Output is monitored using means of sample of 25 observations. What is the z-value we should use if the control limits will include roughly 97% of the sample means
The UCL and LCL are 1.00434 and 0.99566. The process is not in control and the z-value is 2.17.
We already know that the mean, x = 1.0, and the standard deviation of the process, σ = 0.01.
We already know that according to the central limit theorem, the standard deviation of sample means is equal to the standard deviation of the population divided by the square root of the sample size.
So, it is equal to = 0.01 / √25 ⇒ 0.002
For a sample size of 25. The z value, or the z-score, is about 2.17 for a confidence level of 97 percent.
So, UCL = 1.0 + 2.17 * 0.002 = 1.00434
LCL = 1.0 - 2.17 * 0.002 = 0.99566
Lastly, the process is not in control because the sample means 1.005 and 0.995 are outside the control range.
The complete question that you must be looking for is given below.
An automatic filling machine is used to fill 1-liter bottles of cola. The machine output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.
a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.
b. Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control.
c. What is the z-value we should use if the control limits will include roughly 97% of the sample means?
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For which values of x does the expression √x+11 make sense?
The value of x that best represent this expression √x = 11 is 121.
What is square and square roots?The square root of a number is the part of the number that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents. The portion of a number that yields the original number when multiplied by itself is known as the square root of the number.
Examples of special exponents include squares and square roots. Think about the number 9. Nine is the result of multiplying 3 by itself. This can be expressed as either or 3*3. We refer to this as a square since it has a 2 exponent. When the exponent is now 1/2, the integer's square root is being discussed.
An integer or number (not a fraction) multiplied by itself produces a "Square Number," which is the result. For instance, 3 x 3 = or 3 squared is the result of 3 times 3.
Given:
√x+11 = 0
√x = -11
can be written as
x = -11²
x = 121
The value of x that best represent the expression √x+11 = 0 is 121.
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Correct question:
For which values of x does the expression √x + 11 = 0 make sense?
g soccer fields vary in size. a large soccer field is 108 meters long and 56 meters wide. what are its dimensions in feet? length ft width ft what are its dimensions in inches? length in width in
The dimension of soccer field is 4252.176 in long and 2204.832 in wide.
The power to which the fundamental quantities are elevated in order to express a physical quantity is known as its dimension.
The dimension of soccer field is 108 meters long and 56 meters wide.
The dimension of soccer field in ft is 354.348 ft long and 183.736 ft in width.
As it is given that 1 m =3.28 ft
Therefore the length of the soccer field in ft is
108*3.281 = 354.348 ft
And width of the field is
56*3.281 = 183.736 ft
We know that 1 ft =12 in
Therefore, the length of the soccer field in inches is
354.348 × 12 = 4252.176 in
And width of the field is
183.736 *12 = 2204.832 in
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How to solve 3x+30+x=10+2x+5x+2
After simplification, the value of x is 6.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3x + 30 + x = 10 + 2x + 5x + 2
Now, We can solve as;
⇒ 3x + 30 + x = 10 + 2x + 5x + 2
Combine like terms;
⇒ 4x + 30 = 12 + 7x
Subtract 4x both side,
⇒ 4x + 30 - 4x = 12 + 7x - 4x
⇒ 30 = 12 + 3x
Subtract 12 both side,
⇒ 30 - 12 = 3x
⇒ 18 = 3x
⇒ 3x = 18
Divide by 3;
⇒ x = 6
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Jasmine's average speed was 33 3/4 miles per hour.
How far did she travel if it took her 3½ hours?
jel
A. 79 1/2 miles
B. 89 1/2miles
C. 98 miles
D. 108 miles
Answer:
Step-by-step explanation:
if the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2) Find the vaue of x and y
If the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2), then the values of x = -12 and y = 3.
What is mean by translated by vector?Vector translation is a mathematical concept that describes how an object is moved in space. It involves the use of a vector, which is a quantity that has both magnitude and direction. A vector can represent a displacement, a velocity, an acceleration, or any other physical quantity that has both magnitude and direction.
When an object is translated by a vector, it moves a certain distance in a specific direction. This is usually done by adding the vector to the current position of the object. The magnitude of the vector determines the distance of the translation, while the direction of the vector determines the direction of the translation.
Additionally, the vector can be used to rotate the object. This is done by multiplying the vector by the object’s rotation matrix. The result is the object's new orientation in space, which can be used to orient the object in a different direction.
Vector translation is used in a variety of applications, including computer graphics, robotics, and navigation systems. It i also used in mathematics and physics to represent physical phenomena, such as forces, velocities, or accelerations.
Let the point P(x,5) be translated by the vector t(6,-2).
The image of point P is (x',y') = (x+6,5-2) = (-6,y)
Therefore, x+6 = -6
=> x = -6-6 = -12
Similarly, 5-2 = y
=> y = 5-2 = 3
So the value of x is -12 and y is 3.
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Gabriella has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $34, before discount and tax. After the discount, and before tax, the price is $27. 88. Find the percent discount
The percent discount is 18%.
Now, According to the question:
Based on the given condition:
Formulate:
(34 - 27.88) ÷ 34
Calculate the sum or difference:
= 6.12/34
Convert decimal into fraction:
[tex]=\frac{612}{\frac{100}{34} }[/tex]
Divide a fraction by multiplying its reciprocal:
[tex]\frac{612}{100}[/tex] × [tex]\frac{1}{34}[/tex]
Write as a single fraction:
= 612/ (100 × 34)
Cross out the common factor:
= 18/100
= 9/50
Multiply a number to both numerator and denominator:
[tex]\frac{9}{50}[/tex] × [tex]\frac{2}{2}[/tex]
= 18/100
Rewrite a fraction with denominator equals 100 to a percentage: 18%
Hence, the percent discount is 18%.
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Find the distance between the points (-4,7) and (-4,-5).
Answer: The distance between the points (-4,7) and (-4,-5) is 12.
Step-by-step explanation:
To calculate the distance between two points, we apply the following formula:
[tex]\huge \boxed{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }}[/tex]
The points are:
x₁ = -4y₁ = 7x₂ = -4y₂ = -5To solve the process is:
First we solve what goes inside the parentheses.Then we calculate the result of the parentheses to the power of 2.We add the two results and then we calculate the square root.We substitute the points in the previous formula given, then
[tex]\huge \boxed{\sf{d=\sqrt{(-4-(-4))^2+(-5-7)^2 } }}[/tex]
[tex]\huge \boxed{\sf{d=\sqrt{0^2+(-12)^2 }=\sqrt{0+144} }}[/tex]
[tex]\huge \boxed{\sf{d=\sqrt{144}=12 }}[/tex]
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Conider the line .3x-6y=-8
Find the equation of the line that i parallel to thi line and pae through the point .4,2
Find the equation of the line that i perpendicular to thi line and pae through the point . (4,2)
The equation of the straight line perpendicular to the line 3x - 6y = - 8 is y-2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y=0.
The general equation of a straight line is -
y=mx+c
where -
m is slope of line which tells the unit rate of change of y with respect to x.
c is the y - intercept i.e., the point where the graph cuts the y axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
[tex]y=\frac{-A}{B} x-\frac{C}{B}[/tex]
Given that: -
[tex]3x-6y=8\\\\6y=3x-8\\\\y=\frac{1}{2}x-\frac{4}{3}[/tex]
then,
[tex]m=\frac{1}{2}\\\\c=\frac{4}{3}[/tex]
For a parallel line,
[tex]m=\frac{1}{2}\\and,(4,2)[/tex]
[tex]y-y_{1}=m(x-x_{1})\\\\y-2=\frac{1}{2}(x-4)\\\\2y-4=x-4\\\\y=\frac{x}{2}[/tex]
The equation of parallel line is y=0.5x
For a perpendicular line
[tex]m=2\\\\y-2=2(x-4)\\\\y-2=2x-8\\y-2x=-6\\y-2x+6=0\\[/tex]
Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y -2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y = 0.5x.
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4/9 x 7/8 =7/18 what is 7/8x4/9 how do u know without multiplying?
Answer:
7/18.
Step-by-step explanation:
We know that the result is the same because multiplication is Commutative.
The order of the operation does not matter.
Philip wants to run a total of 3 miles each day. Monday morning, he ran 1 7/8 miles. How many more miles does he still need to run?
On Monday, for completing the daily target Philip needs to travel 9/8 more miles.
As per the question,
As Philip wants to run a total of 3 miles each day.
As on Monday morning, he ran only 1(7/8) miles.
First, we will convert the given mixed fraction in form of improper fractions.
So, converting 1(7/8),
It will become equal to (8*1+7)/8 = 15/8
From above,
We can say, out of the 3 miles he only travel 15/8 miles on Monday.
So, for calculating the required distance we need to subtract the given value 15/8 from 3
Thus we will get it as:
3-15/8 = (24-15)/8 = 9/8 miles.
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need explanation and steps
The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
AB = 6
BC = 6
CG = 6
Then the length of diagonal AC is given as,
AC² = AB² + BC²
AC² = 6² + 6²
AC = 6√2
Then the length of diagonal AG is given as,
AG² = AC² + CG²
AG² = (6√2)² + 6²
AG = 6√3
The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.
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Doctor Jones starts an appointment every 20 minutes.
Doctor Warholm starts an appointment every 35 minutes.
The first appointment for both doctors starts at 8. 30 am.
What is the next time that they have an appointment start at the same time?
The next time that they have an appointment start at the same time is at 10:50 a.m.
Now, According to the question:
Ist Step
For the same time, take LCM of 20 and 35.
20 = 2 × 2 × 5
35 = 5 × 7
IInd Step
HCF (20, 35) = 2 × 2 × 5 × 7
HCF (20, 35) = 140
Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.
Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m. which is the next time that they have an appointment start at the same time.
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114 purple pins 361 yellow pins, what percent of the pins where purple?
Answer: About 31%
Step-by-step explanation:
1. Divide 114 to 361
2. use the pie charts to answer the following questions. a. identify the party that won the highest percentage of votes and seats in 1982. b. describe a change between the percentage of seats won by republicans in 1982 and 2012. c. draw a conclusion about the difference in percentage of votes won and seats
a. The party that won the highest percentage of votes and seats in 1982 is democrat.
b. A change between the percentage of seats won by republicans in 1982 and 2012 is 4%
c. The difference between votes percentage and seats percentage for democrat is 4% and 26% respectively. The difference between votes percentage and seats percentage for republican is 3% and 26% respectively.
The pie chart is given below:
a. We have to identify the party that won the highest percentage of votes and seats in 1982.
We can see that in diagram that gray part of circle shows the vote percentage of democrat and white part of circle shows the vote percentage of republican.
Republican gain votes in 1982 = 52%
Democrat gain votes in 1982 = 49%
So the democrats get the maximum votes in 1982.
b. We have to describe a change between the percentage of seats won by republicans in 1982 and 2012.
In 2012 republican get votes percentage = 48%
In 1982 republican get votes percentage = 52%
So the change between 1982 and 2012 = (52 - 48)% = 4%
c. We have to draw a conclusion about the difference in percentage of votes won and seats.
In 2012 republican get votes percentage = 48%
In 1982 republican get votes percentage = 52%
So, the difference between vote percentage is 4%.
In 2012 republican get seats percentage = 25%
In 1982 republican get seats percentage = 51%
So, the difference between seats percentage is 26%.
In 1982 democrat get votes percentage = 49%
In 2012 democrat get votes percentage = 52%
So, the difference between vote percentage is 3%.
In 2012 democrat get seats percentage = 75%
In 1982 democrat get seats percentage = 49%
So, the difference between seats percentage is 26%.
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(a) Find the first four terms, in ascending powers of x, of the binomial expansion of
(1+12x)^1/2
giving each term in simplest form.
(b) Explain how you could use x=1/36 in the expansion to find an approximation for √12
There is no need to carry out the calculation.
a) The binomial expansion of (1+12x)^1/2 is given by:
(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...
Binomial expression: what is it?
A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.
The first four terms, in ascending powers of x, are:
1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3
b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.
This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .
We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.
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Baumgartner, Prosser, and Crowell are grading a calculus exam. There is a true-false question with ten parts. Baumgartner notices that one student has only two out of the ten correct and remarks, "The student was not even bright enough to have fipped a coin to determine his answers. " "Not so clear," says Prosser. "With 340 students I bet that if they all ?ipped coins to determine their answers there would be at least one exam with two or fewer answers correct. " Crowell says, "I’m with Prosser. In fact, I bet that we should expect at least one exam in which no answer is correct if everyone is just guessing. " Who is right in all of this?
According to Bernoulli's theorem, the success rate for the situation is 0.7173.
In math Bernoulli's theorem is states that that random experiment with exactly two possible outcomes, "success" and "failure" in which the probability of success is the same every time the experiment is conducted.
In order to calculate p we must sum the possible permutations of getting 0 success of 10 trials, 1 success of 10 trials, and 2 successes of 10 trials, and divide this sum by the total possible subsets from 10 elements, then it can be written as,
=> P = (10 1) (10 2) (10 1) / 2¹⁰
When we simplify this one, then we get,
=> P = 56/1024
=> P = 0.0547
When we apply the value on Bernoulli's theorem, then we get,
=> B(340, 0.0547, 0) = ( 340 0 ) x (1/1024) x (1023/1024)³⁴⁰
When we simplify this one then we get,
=> B = 0.7173
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The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
The area of the trapezoid is 42.5 m².
What is trapezium?A trapezium is a quadrilateral with four sides where two sides are parallel to each other.
We have,
Trapezoid:
Short base = 3 m
Height = 5 m
Large base.
= 4 + 3 + 7
= 14 m
Now,
Area of a trapezoid.
= 1/2 x (Short base + Large base) x h
= 1/2 x (3 + 14) x 5
= 1/2 x 17 x 5
= 42.5 m²
Thus,
Trapezoid area is 42.5 m².
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Pop's Cycle Shop sells bicycles and tricycles. The
number of bicycles is 1 less than 4 times the number
of tricycles. All the bicycles and tricycles together have
a total of 174 wheels. How many bicycles are there?
The number of bicycles there is given as follows:
63.
How to obtain the number of bicycles?The number of bicycles and tricycles is obtained using a system of equations, for which the variables are given as follows:
Variable x: number of bicycles.Variable y: number of tricycles.The number of bicycles is 1 less than 4 times the number of tricycles, hence:
x = 4y - 1.
There is a total of 174 wheels, hence:
2x + 3y = 174.
The number of tricycles is obtained as follows:
2(4y - 1) + 3y = 174
11y = 176
y = 176/11
y = 16.
Hence the number of bicycles is of:
x = 4(16) - 1
x = 63.
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find tan theta where theta is the angle shown.
Here we would like to find out the value of given trigonometric ratio . A right angled triangle is given to us with perpendicular= 8 and hypotenuse= 11 . Firstly let's calculate the base using Pythagoras theorem as ,
[tex]\longrightarrow h^2=p^2+b^2\\[/tex]
[tex]\longrightarrow 11^2 = 8^2+b^2\\ [/tex]
[tex]\longrightarrow 121 = 64 + b^2\\ [/tex]
[tex]\longrightarrow b^2=121-64=57\\ [/tex]
[tex]\longrightarrow b =\sqrt{57}=7.54 \\ [/tex]
Now we know that,
[tex]\longrightarrow \tan\theta =\dfrac{p}{b}\\ [/tex]
so substitute the respective values,
[tex]\longrightarrow \tan\theta =\dfrac{8}{7.54}\\ [/tex]
[tex]\longrightarrow\underline{\underline{ \tan\theta = 1.06 \approx \boxed{1}}} [/tex]
and we are done!
Valerie created a table of a proportional relationship that contains the point (3, - 18). which of the tables below could be Valerie’s?
Valerie's table is the table for which the y-value is given by the multiplication of the x-value by -6.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The constant for the relationship in this problem is given as follows:
k = -18/3
k = -6.
Hence the relationship is given as follows:
y = -6x.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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Jolly Roger Peanut Butter cost $3. 59 for a small jar last year. This year the jar costs $4. 19. What is the inflation rate, to the nearest tenth percent?
The inflation rate is 16.71 %
As we know the inflation rate is given by the percentage error.
We know that the formula for the percentage error:
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
Let us assume that A represents the inflation rate of percentage error.
Here, the cost of the Jolly Peanut butter is = $ 3.59
So , the original cost = $ 3.59
The increased cost of Jolly Peanut butter is = $ 4.19
So , the new rate = $ 4.19
Now , the inflation rate is given by the formula of percentage error,
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
A = [ ( 4.19 - 3.59 ) / 3.59 ] x 100
A = ( 0.6 / 3.59 ) x 100
A = 0.16713 x 100
A = 16.71 %
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aldo's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs $4.10 aldo per pound, and type b coffee costs $5.45 per pound. this month's blend used twice as many pounds of type b coffee as type a, for a total cost of $465. how many pounds of type a coffee were used?
The amount of type A used is A=31 lbs.
Assign variables for unknowns.
Let A be the number of pounds of Type A coffee.
Let B be the number of pounds of Type B coffee.
If one pound of Type A costs $4.10 then A pound costs 4.10A
If one pound of Type B costs $5.45 then B pounds cost 5.45B
At this point, you have two equations with A and B as variables. You can use the substitution or elimination method to solve for A.
Equations:
B = 2A----(1)
4.10A + 5.45B = 465.00
4.10A + 5.45(2A) = 465.0
4.10A + 10.9A = 465.00
15A = 465.00
A = 31 lbs (amt. of type A coffee used)
To know the amount of type B coffee used just plug the A value in equation(1) we get:
B=2(31)
B=62.
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What is the area of the triangle?
16 square units
32 square units
8 square units
4 square units
Answer:
8 square units
Step-by-step explanation:
For a triangle,
area = base × height / 2
We need to identify a base and a height for this triangle, and then use them in the area formula above.
Use BC as the base.
A height of a triangle is usually inside the triangle, but not always.
The height of a triangle is a segment that is perpendicular to the a side, or the line containing a side, and intersects the opposite vertex.
In this case, for base BC, the height is a segment from point (-2, 2) to point A. The length of the height is 4.
area = 4 × 4 / 2
area = 8 square units
Gordon irons some shirts for staff at a hotel.
The total weight of these shirts is 9. 5 kg.
Each shirt weighs 190 g.
Gordon charges £38 to iron these shirts.
He sees this advert for ironing in a newspaper.
Ironing Palace
Shirts
90p each
Gordon thinks he charges less to iron these shirts than the Ironing Palace would
charge.
Is Gordon correct?
As per the unitary method, Gordon is correct because the Gordon would charge more than Ironing Palace
In math the term unitary method is defined as the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.
Here we have given that the total weight of these shirts is 9. 5 kg.
And here we have also given that each shirt weighs 190 g.
And Gordon charges £38 to iron these shirts.
And the charges in the Ironing Palace is 90p for each.
Here we have to use the unitary method to calculate the values for each of them,
The Total cost for Gordon is calculated as,
=> 38 x (9.5 / 0.19)
=> 1900
And the total cost for Ironing Palace is calculated as,
=> 90 x 9.5
=> 855
Therefore, while we looking into the values we have identified that Gordon is correct.
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