Answer:
Step-by-step explanation:
Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.
From the first mixture, we have:
12x + 3y = 39
From the second mixture, we have:
16x + 6y = 58
We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:
16x + 6y = 58
(24x + 6y = 78)
-8x = -20
Dividing both sides by -8 gives:
x = 2.5
Substituting this value of x into the first equation, we get:
12(2.5) + 3y = 39
Simplifying, we get:
30 + 3y = 39
Subtracting 30 from both sides gives:
3y = 9
Dividing both sides by 3 gives:
y = 3
Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.
Find the average rate of change of g(x) = 3x² + 3 on the interval [ - 9, 4].
Answer:
-15
Step-by-step explanation:
You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].
Average rate of changeThe average rate of change is defined as ...
AROC(g) = (g(b) -g(a))/(b -a)
We can evaluate this directly, or we can simplify it a bit first.
AROC = ((3b² +3) -(3a² +3))/(b -a)
= (3b² -3a²)/(b -a)
= 3(b -a)(b +a)/(b -a)
= 3(b +a)
Interval [-9, 4]The AROC on the interval [a, b] = [-9, 4] is then ...
AROC = 3(4 +(-9)) = 3(-5)
AROC = -15
__
Additional comment
In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.
Jeremy sees a jacket that he wants that is on sale for $44.95. The original price was
$68.49. Estimate how much Jeremy can save by buying the jacket on sale. (1pt)
Answer:
$25
Step-by-step explanation:
You round 44.95 to 45 and 68.49 to 70. 70 - 45 = 25.
3. On a state math exam the scores were normally distributed with a mean of 72 and a standard deviation of 8. Use bell curve with standard deviations to help you complete the problem.
b. What percentage of students will score less than 72?
C. What percentage of students will score above 80?
The mean is 72, which is the center of the distribution, 50% of the students will score less than 72. The area to the right of z = 1, so approximately 15.87% of students will score above 80.
a) Since the mean is 72, and we want to know the percentage of students who scored less than 72, we need to find the area under the normal distribution curve to the left of the z-score that corresponds to 72. Since the standard deviation is 8, the z-score is:
z = (72 - 72) / 8 = 0
Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0 is 0.5. Therefore, 50% of students scored less than 72.
b) To find the percentage of students who scored above 80, we need to find the area under the normal distribution curve to the right of the z-score that corresponds to 80. The z-score is:
z = (80 - 72) / 8 = 1
Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1 is 0.1587. Therefore, approximately 15.87% of students scored above 80.
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Write an equation for the word problem below.
"The YMCA summer camp charges registration fee of $40 and then charges $100 per week of camp."
Y = [blank] x + [blank]
Y = MX + B
Answer:
The equation is in slope-intercept form, Y = MX + B, where M is the slope and B is the y-intercept. In this case, the slope is 100 and the y-intercept is 40.
I hope that helps!
Step-by-step explanation:
The equation for the word problem is Y = 100x + 40.
Where Y is the total cost of the summer camp, x is the number of weeks of camp, 100 is the cost per week of camp, and 40 is the registration fee.
Please help to solve this problem
When event 1, 6, and 8 are checked, probability P(X) equals 3/8.
When event 2, 3, 4,5, and 7 are checked, P(not X) equals 5/8.
Describe probability.Simply put, probability is the likelihood that something will occur. The study of events with a probability distribution is called statistics.
There are eight balls in the bag, numbered one to eight.
Five balls are grey, while the remaining ones are all white.
2,3,4,5, and 7 are the gray-colored balls.
The white coloured balls are 1, 6, and 8, and the probability of getting a grey ball is P(not X).
P(not X) = Chance of receiving a grey ball a) Calculate P(X) and P (not X)
1, 6, and 8 are verified for event X, and P(X) equals 3/8.
2,3,4,5, and 7 are tested for the event "not X," and P(not X) = 5/8.
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The line plot above shows the amount of olive oil, in ounces, used in 13 different pizza recipes. Isabella wants to make one pizza from each of the recipes. Will she have enough olive oil to make the pizzas if she buys a 16-ounce bottle of olive oil? Explain or show your reasoning.
By adding all the numbers in the line plot, we conclude that she will have enough olive oil.
Will she have enough olive oil for the 13 recipes?To check this, we just need to add the 13 numbers and see if it is more than 16.
Each point above the line plot means how many times that number will apear in our sum, then the sum will be:
(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))
Now we need to solve that:
(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))
= 2 + 9/4 + 3 + 1 + 1/4
= 2 + 3 + 1 + 9/4 + 1/4
= 6 + 10/4
= 6 + 8/4 + 2/4
= 6 + 2 + 1/2
= 8 + 1/2
That is the amount of ounces of oil that she needs for the 13 recipes, it is less than 16 ounces, so she will have enough oil.
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What is the center and radius of a circle with the following equation
Answer:
Center: (1, -3); radius: 2
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - 1)² + (y + 3)² = 4
(x - 1)² + (y - (-3))² = 2²
Center: (1, -3); radius: 2
please help me fast please
Step-by-step explanation:
Substituting the given values, we get:
a + b/c = 24 + 36/4
= 24 + 9
= 33
Therefore, a + b/c = 33 when a = 24, b =36, and c = 4.
How do you write y = 6 in slope intercept form
I need help on this. Can you help me?
The expressions that are polynomials include the following: E. 13x²² + x²³ + 7x¹⁹ + 12x²
What is a polynomial function?In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value.
Generally speaking, all of the variables with respect to a polynomial function would always have positive (non-negative) integer exponents. Additionally, a polynomial function does not have variables or numerical value under a radical, in its denominator, or as its argument (non-polynomial function).
In this context, we can reasonably infer and logically deduce that all of the given expression except 13x²² + x²³ + 7x¹⁹ + 12x² does not a polynomial function.
In conclusion, the polynomial function 13x²² + x²³ + 7x¹⁹ + 12x² has only positive (non-negative) integer exponents.
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The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:
A(t) = A0 * (1/2)^(t/8)
where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.
Substituting the given values, we get:
A(t) = 7 * (1/2)^(t/8)
b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:
A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)
Simplifying, we get:
A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)
c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:
A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)
75% of the people in a small city have car insurance with the company Geico. This unusually high amount is due to the amount of advertising withing the city and social media ads. If 10 people are selected at random from this city, what is the probability that at least 8 of them have car insurance with Geico?
Answer:
Step-by-step explanation:
This is a binomial distribution problem, where each person either has car insurance with Geico or doesn't have.
Let's denote the probability of a person having car insurance with Geico as p = 0.75, and the probability of not having car insurance with Geico as q = 0.25.
The probability of getting exactly k people out of n people who have car insurance with Geico is given by the binomial distribution formula:
P(k) = (n choose k) * p^k * q^(n-k)
where (n choose k) is the number of ways to choose k items out of n items, which is calculated by the formula:
(n choose k) = n! / (k! * (n-k)!)
where n! denotes the factorial of n.
We need to find the probability of getting at least 8 people out of 10 who have car insurance with Geico, which is the same as the probability of getting 8, 9, or 10 people who have car insurance with Geico. So, we can calculate this probability by adding the probabilities of these three cases:
P(at least 8) = P(8) + P(9) + P(10)
P(8) = (10 choose 8) * 0.75^8 * 0.25^2 = 0.002
P(9) = (10 choose 9) * 0.75^9 * 0.25^1 = 0.054
P(10) = (10 choose 10) * 0.75^10 * 0.25^0 = 0.056
Therefore, the probability of at least 8 people out of 10 having car insurance with Geico is:
P(at least 8) = P(8) + P(9) + P(10) = 0.002 + 0.054 + 0.056 = 0.112
So, the probability that at least 8 people out of 10 have car insurance with Geico is 0.112 or approximately 11.2%.
The two top concert tours in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B. Three tickets for concert B cost a total of $687. How much did an average ticket cost for each tour?
The average ticket cost for each concert is given as follows:
Concert A: $188.83.Concert B: $95.67.How to obtain the ticket costs?The ticket costs are obtained by a system of equations, for which the variables are given as follows:
Variable a: cost for Concert A.Variable b: cost for Concert B.It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:
6a + 6b = 1707
a + b = 284.5.
Three tickets for concert B cost a total of $687, hence the cost for concert B is of:
3b = 687
b = 287/3
b = $95.67.
Replacing into the first equation, the cost for concert A is given as follows;
a = 284.5 - 95.67
a = $188.83.
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4) It has been known that 18% of victims of financial fraud know the perpetrator of the fraud
personally. If a sample of 156 people were victims of fraud, what is the mean number of those
victims that know the perpetrator of the fraud personally?
Answer:
If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.
Lauren’s age is half of Joe’s age. Emma is four years old than Joe. The sum of Lauren, Emma, and Joe’ age is 54. How old is Joe?
Extended sheet of paper in Europe is 21.0 CM wide and 29.7 cm long which has a greater area the standard sheet of paper with using stage or the standard sheet of paper in Europe explain and show your reasoning
the extended sheet in Europe has a greater area than the standard letter size paper. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.
What is area of rectangle ?area of rectangle = length * breath
The standard sheet of paper commonly used in the United States and Canada is known as "Letter" size paper, which measures 8.5 inches by 11 inches (21.59 cm x 27.94 cm). To compare the area of this paper to the extended sheet of paper used in Europe, we need to convert the dimensions to centimeters.
So, the area of the standard letter size paper in centimeters would be:
21.59 cm x 27.94 cm = 603.78 square cm
On the other hand, the extended sheet of paper in Europe measures 21.0 cm by 29.7 cm. Therefore, its area would be:
21.0 cm x 29.7 cm = 623.70 square cm
the extended sheet of paper in Europe has a greater area than the standard letter size paper used in the United States and Canada. The difference in area between the two is about 20 square cm, it can make a difference in certain applications.
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The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error?
The individual actually had the disease
Yes
No
Positive
320
9
Negative
12
1160
Question content area bottom
Part 1
The probability is enter your response here.
(Round to three decimal places as needed.)
The probability to three decimal places is 0.036 and the unfavorable consequence of this result will be that the patients who tested negative will not be treated and as such will spread the disease.
How to solve the probabilityTo find the probability of an event, we often use divide the total number of possible results by the total results. In this case, we are told to find the total number of persons who tested negative for the disease by the total number of positive cases. 320 + 12 persons tested positive for the disease. The sum is 332.
The total number of negative cases recorded from this sum is 12. Thus, the probability will be 12/332 = 0.036. An unfavorable consequence of this error will be that the subjects who tested negative will not be treated and can thus spread the disease.
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Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!
State the principle of mathematical induction
The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.
It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:
Let P(n) be a statement involving an integer n
Base Case: P(m) is true for some m
Induction Hypothesis: Assume P(k) is true for some k>m.
Induction Step: Show that P(k+1) is true.
Therefore, P(n) is true for all n>m
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Below is data for people visiting the 'Starry eyes' exhibition for the last 13 days. Calculate the Mean, Median and Mode and drag the correct answer into the table.
OPTIONS:
No Mode | 51.63 | 54 | 45.63 | 43 | 30 | 55.18 | 57 | 34 | 39.09 | 38.81| 47.5 | 42.9 | 50 | 29 | 46
The following values are in No Mode: 51.63, 54, 45.63, 43, 30, 55.18, 57, 34, 39.09, 38.81, 47.5, 42.9, 50, 29 and 46. There is no Mode; the Median is 45.63; the Mean is approximately 44.99.
In order to determine the Mean, Median, and Mode for the provided data set:
Sort the information in ascending order:
29, 30, 34, 38.81, 39.09, 42.9, 43, 45.63, 46, 47.5, 50, 51.63, 54, 55.18, 57
Mean:
The mean is calculated as follows:
Mean is the average of all values (number of values)
Mean = (29 + 30 + 34 + 38.81 + 39.09 + 42.9 + 43 + 45.63 + 46 + 47.5 + 50 + 51.63 + 54 + 55.18 + 57) / 15
Mean ≈ 44.99
Median:
When the values are organised in order, the median is the middle value in the data set. The median is the value in the middle when there are an odd number of values. The median is the average of the two middle values when there are an equal number of values.
The median is the eighth value in the data set because there are 15 values total:
Average = 45.63
Mode:
The most prevalent value in a data set is referred to as the mode. There is no mode in this instance because no value appears more than once.
As a result, there is no Mode and the Mean is roughly 44.99, while the Median is 45.63.
No Mode | 51.63, 54, 45.63, 43, 30, 55.18, 57, 34, 39.09, 38.81, 47.5, 42.9, 50, 29 and 46.
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NEED HELP WILL GIVE BRAINLIEST AND 5 STARS ITS DUE IN 20 min
In this question, f is a one-to-one function and f(0)=7. Thus, f⁻¹(7)=0.
As we already know that f(0)=7,
then (f(0))⁻¹ = f⁻¹(7)=0.
Thus, (f(0))⁻¹=0.
What is one-to-one function?These are important as they can be used to show the existence of an inverse function. A one-to-one function is a type of mathematical function that maps one element of its domain to exactly one element of its codomain. This means that for every element of the domain, there is a unique element of the codomain.
f⁻¹(7)=0
The inverse of a one-to-one function f is denoted by f⁻¹, and it is defined as the inverse of the function f.
In this question, f is a one-to-one function and f(0)=7.
This means that the inverse of f, f⁻¹, maps 7 to 0.
Thus, f⁻¹(7)=0.
(f(0))⁻¹=0
Since the inverse of a one-to-one function f is denoted by f⁻¹, then (f(0))⁻¹ is the inverse of f(0).
As we already know that f(0)=7, then (f(0))⁻¹ = f⁻¹(7)=0.
Thus, (f(0))⁻¹=0.
To summarize, f⁻¹(7)=0 and (f(0))⁻¹=0 since f is a one-to-one function and f(0)=7.
This is because the inverse of a one-to-one function f is denoted by f⁻¹ and it maps 7 to 0.
Thus, f⁻¹(7)=0 and (f(0))⁻¹=0.
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Choose all the functions that are NOT linear.
A. y = 5 (2x - 1)
B. y = x (3 - x )
C. y= -2x+4
D. y = 1/3x - 5
E. y =5
Answer:
B
Step-by-step explanation:
y = x ( 3-x) = 3x - x^2 the ' x^2 ' makes it nonlinear
Whats the Surface area?
Answer:
118.4cm2
Step-by-step explanation:
Surface area of square :5×5=25
Surface area for one triangle:
square root of 9²+2.5²=9.340770846
Area of triangle 0.5×5×9.340770846=23.35192712
As there is 4 triangle do 23.35192712×4=93.40770846
After
25+93.40770846=118.4077085
1dp= 118.4cm²
A triangle has sides with lengths of 8 meters, 15 meters, and 17 meters. Is it a right triangle?
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
From the given side lengths, let a = 8, b = 15, c = 17 (c cannot be less than a or b)
[tex]a^2 + b^2 = (8)^2 + (15)^2[/tex]
[tex]a^2 + b^2 = 64 + 225 = 289[/tex]
[tex]c^2 = (17)^2 = 289[/tex]
[tex]a^2 + b^2 = c^2 \ (289 = 289)[/tex]
Therefore, a Triangle with side lengths of 8, 15 and 17 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(8, 15, 17) = 1, they are a primitive Pythagorean Triple.
A capsule of paracetamol is made of a cylinder and a hemisphere at each end. The total length of the capsule is 20 mm and the width is 6 mm.
Calculate:
(a) What is the length of the cylinder? (b) Find the volume of the cylinder, to 3 significant figures
(c) Find the volume of the two hemispheres
(d) What is the total volume of the capsule?
Answer:
Step-by-step explanation:
To solve this problem, we can use the following formulae for the volume of a cylinder and a hemisphere:
Volume of a cylinder = πr²h
Volume of a hemisphere = 2/3πr³/2
where r is the radius of the cylinder or hemisphere, and h is the height of the cylinder.
(a) To find the length of the cylinder, we can subtract the combined length of the two hemispheres from the total length of the capsule:
Length of cylinder = Total length of capsule - 2 × radius of hemisphere
Length of cylinder = 20 mm - 2 × 3 mm (radius of hemisphere)
Length of cylinder = 14 mm
(b) To find the volume of the cylinder, we need to know the radius and height. Since the width of the capsule is given as 6 mm, and we know that the cylinder runs the full length of the capsule, we can use the following formula to find the radius of the cylinder:
Width = 2 × radius of hemisphere + diameter of cylinder
6 mm = 2 × 3 mm + diameter of cylinder
Diameter of cylinder = 6 mm
Radius of cylinder = 3 mm
Now we can use the formula for the volume of a cylinder to find the volume of the cylinder:
Volume of cylinder = πr²h
Volume of cylinder = π(3 mm)² × 14 mm
Volume of cylinder ≈ 395.8 mm³ (to 3 significant figures)
(c) The radius of each hemisphere is 3 mm (since they have the same radius as the cylinder), so we can use the formula for the volume of a hemisphere to find the volume of each hemisphere:
Volume of hemisphere = 2/3πr³/2
Volume of hemisphere = 2/3π(3 mm)³/2
Volume of hemisphere ≈ 56.55 mm³ (to 3 significant figures)
(d) To find the total volume of the capsule, we can add the volumes of the cylinder and the two hemispheres:
Total volume of capsule = Volume of cylinder + 2 × Volume of hemisphere
Total volume of capsule ≈ 509.9 mm³ (to 3 significant figures)
Therefore, the length of the cylinder is 14 mm, the volume of the cylinder is approximately 395.8 mm³, the volume of each hemisphere is approximately 56.55 mm³, and the total volume of the capsule is approximately 509.9 mm³.
what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).
How to obtain the coordinates of point P?The coordinates of point P are obtained applying the proportions in the context of the problem.
P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:
P - A = 2/3(B - A)
Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:
x - 9 = 2/3(-6 - 9)
x - 9 = -10
x = -1.
The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:
y + 8 = 2/3(7 + 8)
y + 8 = 10
y = 2.
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A box of granola bars measures 22 centimeters long by 5 centimeters wide by 15 centimeters high. A box of fruit bars measures 24 centimeters long by 3 centimeters wide by 26 centimeters high. Which box has the greater volume? How much greater?
Question content area bottom
Part 1
Select the correct choice below and fill in the answer box to complete your choice.
(Type a whole number.)
A.
The box of granola bars has a greater volume. It is
210 cubic centimeters greater than the fruit bars box.
B.
The box of fruit bars has a greater volume. It is
enter your response here cubic
Answer: The box of fruit bars. It is 76 cm greater.
Step-by-step explanation:
Find what percentage of $6500 is $4250
Step-by-step explanation:
To find the percentage that $4250 represents of $6500, we can use the following formula:
percentage = (part / whole) x 100%
where "part" is $4250 and "whole" is $6500.
Substituting these values into the formula, we get:
percentage = (4250 / 6500) x 100%
percentage = 0.6538 x 100%
percentage = 65.38%
Therefore, $4250 represents 65.38% of $6500.
Answer: It is approximately 65%
Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%
Draw a conclusion based upon true statements (i) and (ii).
(i) If two triangles are congruent, then they are similar.
(ii) △ ABC is not similar to △ DEF
Based οn the true statements (i) and (ii), we can cοnclude that △ ABC is nοt cοngruent tο △ DEF.
Statement (i) tells us that if twο triangles are cοngruent, then they are similar. This means that cοngruence implies similarity. Hοwever, statement (ii) tells us that △ ABC is nοt similar tο △ DEF. This means that there is nο similarity between the twο triangles.
Therefοre, we cannοt cοnclude that the twο triangles are cοngruent, because cοngruence implies similarity and we have been given that there is nο similarity between them. In οther wοrds, the fact that △ ABC is nοt similar tο △ DEF means that we cannοt cοnclude anything abοut their cοngruence, because we dο nοt have enοugh infοrmatiοn tο determine whether they are cοngruent οr nοt.
To knοw mοre about congruent
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