The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is 0.607.
How to determine the proportionThe proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is given by the formula:
P(18 < X < 28) = P(Z < (28 - 21)/5.5) - P(Z < (18 - 21)/5.5)
We can then calculate the z-scores for the lower and upper bounds of the range as follows:
Z1 = (28 - 21)/5.5 = 1.27Z2 = (18 - 21)/5.5 = -0.55
Using a z-table or calculator, we can find the probabilities associated with these z-scores:
P(Z < 1.27) = 0.898P(Z < -0.55) = 0.291
Therefore,P(18 < X < 28) = P(Z < 1.27) - P(Z < -0.55) = 0.898 - 0.291 = 0.607
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Los clientes de una compañía telefónica pueden elegir entre dos planes de servicio para hacer llamadas de larga distancia. Con el primer plan, hay una tarifa
mensual de $28 y cobran $0.07 por cada minuto que hablen. Con el segundo plan, hay una tarifa mensual de $11 y cobran $0.12 por cada minuto que hablen.
¿Cuántos minutos se tendría que hablar por teléfono para que los dos planes cuesten lo mismo?
minutos
Answer:
132 seconds aka 2.2 minutes
Step-by-step explanation:
they met at 132 seconds then converted to minutes which is 2.2 minutes
12,24,36,48,60,72,84,96,108,120,132
11,22,33,44,55,66,77,88,99,110,121,132
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To model the given data points, we can use a linear function of the form y = mx + b.
First, we need to find the slope (m) of the line:
m = (y2 - y1) / (x2 - x1)
m = (-6 - (-2)) / (1 - 0)
m = -4/1
m = -4
Now, we can use the slope and one of the points to find the y-intercept (b):
y = mx + b
-2 = (-4)(0) + b
b = -2
Therefore, the linear function that models the given data is:
y = -4x - 2
I need help plsss!!
Tell whether x and y are proportional.
x 123
y 789
yes
no
The ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.
What is ratio and proportion?Ratio and proportion are two mathematical concepts that are closely related.
A ratio is a way of comparing two or more quantities by dividing one quantity by another. It expresses the relative size or magnitude of two quantities. Proportion, on the other hand, refers to the equality of two ratios. It states that two ratios are equal. Proportions can be used to solve problems involving unknown quantities.
Equation:To determine whether x and y are proportional, we need to check if the ratio of corresponding values of x and y is always the same.
Let's find the ratio of y to x for each corresponding value:
y/x for x=1: 7/1 = 7
y/x for x=2: 8/2 = 4
y/x for x=3: 9/3 = 3
Since the ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.
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M∠V=(2x+2) ∘ , and m ∠ W = ( 3 x + 4 ) ∘ m∠W=(3x+4) ∘. Find m ∠ V. M∠V
the measure of angle V is approximately 21.87 degrees. To find the measure of angle V, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:
m∠V + m∠W + m∠X = 180
where angle X is the third angle in the triangle formed by V, W, and X. We know that m∠W is (3x+4) degrees, and we can see that angle X is adjacent to angle V, so we can use the fact that the sum of adjacent angles is equal to the total angle to write:
m∠V + m∠X = (2x+2) degrees
Now we can substitute this expression for m∠X into the first equation to eliminate m∠X:
m∠V + (2x+2 - m∠V) + (3x+4) = 180
Simplifying and solving for x, we get:
5x + 6 = 180
5x = 174
x = 34.8
Now we can substitute this value of x back into our expression for m∠V + m∠X to find m∠V:
m∠V + (2(34.8)+2 - m∠V) = 71.6
Simplifying and solving for m∠V, we get:
3m∠V = 65.6
m∠V = 21.87 (rounded to two decimal places)
Therefore, the measure of angle V is approximately 21.87 degrees.
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Please help! Please check my work and help me with the explanations! (I’m in k12)
Answer:
To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:
Step 1: Find the amplitude
The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.
Step 2: Find the period
The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.
Step 3: Find the midline
The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.
Step 4: Find the y-intercept
The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.
Step 5: Sketch the graph
Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:
- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.
- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).
- The graph is symmetric about the midline.
Therefore, the information about the function is:
Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)
Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)
Midline: y = -2 (The horizontal line that the graph oscillates around.)
y-intercept: -2 (The value of the function when x = 0.)
Question 5(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric
The answer of the given question based on the histogram is option (a) IQR, because Sunny Town is symmetric and option (b) IQR, because Beach Town is skewed.
What is Frequency?Frequency refers to the number of times a particular event or value occurs within a given dataset or sample. In statistics, frequency is often used to describe the distribution of a variable, where a frequency distribution shows the number of observations that fall into each category or interval.
The IQR (interquartile range) should be used for both sets of data to determine the location with the most consistent temperature. The IQR is a measure of spread that is not influenced by extreme values or outliers, which is helpful in comparing the consistency of temperatures in different locations. It is appropriate to use the IQR for Sunny Town because the data is roughly symmetric, and for Beach Town because although it is skewed, the IQR is more robust than the range and is not influenced by outliers.
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3. Which translation moves point X so that
its image is on the y-axis?
A (x,y) → (x + 4, y + 8)
B (x,y) → (x-4, y + 8)
C (x, y) → (x+8, y + 4)
D(x, y) → (x+8, y - 4)
In addition, the image's y-coordinate would be , this indicates that we must raise the point by to align it with the y-axis. Hence, D is the right response.
What kind of coordinate is that?Option A moves the point 4 units horizontally and 8 units vertically, but does not move it onto the y-axis.
Option B moves the point -4 units horizontally and 8 units vertically, but does not move it onto the y-axis.
Option C moves the point horizontally by 8 units and vertically by 4 units, but it does not move it to the y-axis.
Option D moves the point 8 units horizontally and -4 units vertically. When we apply this transformation to an x-axis point, its y-coordinate remains unchanged, so the point's image is on the y-axis. As a result, option D is the correct translation:
(x, y) → (x+8, y-4)
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Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000. Which statements regarding function S are true? Select TWO that apply. Responses A. S(10)=S(5) means that there were the same number of students in 2010 as in 2005. B. S(3)= 2,015 means that there were 3 students in the year 2015. C. S(15) − S(10) = −40 means that there were 40 less students in 2010 than there were in 2015. D. S(5)= 2,024 means that there were 2,024 students in the year 2005. E. S(0) = 2,000 means that there were no students in the year 2000.
Answer:
The correct responses are:
A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.
E) S(0) = 2,000 means that there were no students in the year 2000.
B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.
I just want to know what to put in the number line
Answer:
270 students walked to school
30% students walked to school
Step-by-step explanation:
270 /900 is 30%
Answer:
Step-by-step explanation:
first mark the 30% line. then divide 900 by 0.3 to get 30% of the students (270)
Write the absolute value equations in the form |x|=c (where b is a number and c can be either a number an expression) that has the following solution set.
Two solutions x=1/2, x=-1/3
According to the given information, the absolute value is |x - 7/6| = 5/6.
What is an algebraic expression?
A mathematical expression known as an algebraic expression can include variables, integers, and mathematical operations including addition, subtraction, multiplication, and division.
When expressing quantities or values that might change depending on the values given to the expression's variables, algebraic expressions are utilised. Expressions in algebra can include one or more variables and be simple or complex.
Two solutions x=1/2, x=-1/3
|x - 7/6| = 5/6.
We know that the absolute value of (1/2 - 7/6) equals the absolute value of (-1/3 - 7/6) because they are opposites and have the same absolute value. So we need an expression that equals 5/6 when either 1/2 - 7/6 or -1/3 - 7/6 is plugged in for x.
To get an expression that equals 5/6 when 1/2 - 7/6 is plugged in for x, we can subtract 7/6 from 1/2 and take the absolute value of the result:
|1/2 - 7/6| = |-1/6| = 1/6.
To get an expression that equals 5/6 when -1/3 - 7/6 is plugged in for x, we can subtract 7/6 from -1/3 and take the absolute value of the result:
|-1/3 - 7/6| = |-9/6| = 3/2.
Since both expressions have the same absolute value of 5/6, we can use either one as the absolute value expression in the equation. Thus,
|x - 7/6| = 5/6.
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Jamie is laying stone pavers along his patio and walkway. The walkway is 3.5 feet wide. the patio measures 7 feet from top bottom and 8 feet accross. how much area does jamie need to cover.
84 sq ft area does jamie need to cover.
Describe Area?
The region enclosed by an object's form is referred to as the area. The area of the form is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
A two-dimensional shape's area, which is expressed in square units, is the total surface area it may occupy. The square metre (m2), a derived measure, serves as the area unit in the SI system. On a sheet of paper, draw a square using a pencil. It has two dimensions. Its Area refers to the area that the form occupies on the paper.
the area of the walkway is:
Area of walkway = length x width = 8 ft x 3.5 ft = 28 sq ft
Next, let's calculate the area of the patio. The patio measures 7 feet from top to bottom and 8 feet across. Therefore, the area of the patio is:
Area of patio = length x width = 7 ft x 8 ft = 56 sq ft
Now, to find the total area that Desiree needs to cover, we just add the area of the walkway and the area of the patio:
Total area = area of walkway + area of patio
Total area = 28 sq ft + 56 sq ft
Total area = 84 sq ft
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B(-1;7) , C(x;-1) and D(1;8) : B,C and D are collinear
The coordinates of point C are (17, -1).
how to find slope of line when two points are given ?let say a line have two points A (x1,y1) and B(x2,y2)
slope of line AB = (y2 - y1) / (x2 - x1)
Now given that points B, C, and D are collinear, then they lie on the same straight line. This means that the slope of the line passing through any two of the points will be the same as the slope of the line passing through the other two points. We can use this fact to find the value of x.
The slope which is between points B and C is:
slope of line BC = (y2 - y1) / (x2 - x1) = (-1 - 7) / (x - (-1)) = -8 / (x + 1)
The slope which is between points C and D is:
slope of line CD = (y2 - y1) / (x2 - x1) = (8 - (-1)) / (1 - x) = (9) / (1 - x)
Since B, C, and D are collinear, slope of BC = slope of CD. Therefore:
-8/(x+1) = 9/(1-x)
by solving the x, we get:
-8(1 - x) = 9(x + 1)
-8+8x=9x + 9
x = 17
So, the coordinates of point C are (17, -1).
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pls anwser need helpppp
A recent study1 examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with n=25 in each group: healthy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The data are in FootballBrain where the variable Hipp measures brain size as the volume of the hippocampus (in ml) for each subject.
Let group 1 be the football players with no concussion and group 2 be the football players with a history of concussions.
(a) State the null and alternative hypotheses.
(b) Use StatKey or other technology to find the value of the relevant sample statistic. Round your answer to one decimal place.
(c) Use StatKey or other technology to find the p-value. Round your answer to three decimal places.
(d) Does it appear that this difference in brain size is just due to random chance?
(b) The difference in sample mean is 0.544 ml. (c) Using StatKey, we find the p-value to be 0.046. (d) It is unlikely that this difference is due to random chance alone.
(a) The null hypothesis is that there is no difference in average brain size between football players with no history of concussions (FBNoConcuss) and football players with a history of concussions (FBConcuss). The alternative hypothesis is that the average brain size is larger in FBNoConcuss than in FBConcuss.
H0: μFBNoConcuss = μFBConcuss
HA: μFBNoConcuss > μFBConcuss
(b) The relevant sample statistic is the difference in sample mean between the two groups.
Therefore, the difference in sample mean is 0.544 ml.
(c) Using StatKey, we find the p-value to be 0.046.
(d) With a p-value of 0.046, which is less than the commonly used significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the average brain size is larger in FBNoConcuss than in FBConcuss. It is unlikely that this difference is due to random chance alone.
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B. Find one possible point in the part of
the coordinate plane shown that could
be the fourth Vertex D of the
parallelogram. Give its coordinates.
Answer:(0,-1).
Step-by-step explanation:
As the diagonals of a parallelogram bisect each other, the midpoint of AC is the same as the midpoint of BD. Therefore, the fourth vertex D is (0,-1).
Which angle is an alternate exterior angle to ∠8? ∠3 ∠4 ∠5 ∠6
There is no alternate exterior angle corresponding to ∠8. ∠3 ∠4 ∠5 ∠6 are not an alternate exterior angle to ∠8
We know that alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal,
here, we have,
We have been given a geometrical figure as shown in the image.
Now we know that a pair of alternate exterior angles exist for a pair of parallel lines.
Hence, there is no alternate exterior angle corresponding to ∠8.
Therefore, there is no alternate exterior angle corresponding to ∠8.
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height is normally distributed with a mean of 70 inches and a standard deviation of 4 inches. what percentage of people are shorter than 60 inches?
The likelihood of being over 67 inches tall is 0.127978, or 12.8%.
How does probability work?The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.At the point when this happens, we broadcast that there is plausible that the occasion will happen.
In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.
By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.
5 feet 7 inches equals (5*12 +7) inches, or (60 +7) inches, according to our question.
(67 - 69.1)/(2.65) = -1.136 is the z-score.
The probability of having a height greater than 67 inches is 0.127978, or 12.8%.
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What is the rate of change of Y with respect to X for this function?
Answer:
-7/9
Step-by-step explanation:
its not a complete change to 1 but it is very close to being a 1
A `16`-ounce bottle of orange juice contains `200` milligrams of vitamin C, which is `250\%` of the daily recommended amount (for adults).
On the previous screen, you said the daily recommended amount of vitamin C is `80` milligrams.
Yosef drank `4` ounces of orange juice.
What percent of the daily recommended amount of vitamin C is this?
Since a 16-ounce bottle of orange juice contains 200 milligrams of vitamin C, we can find the amount of vitamin C in 4 ounces by using a proportion:
16 ounces 200 milligrams
4 ounces x milligrams
Solving for x, we have:
x = 50 milligrams
So, Yosef drank 50 milligrams of vitamin C.
To find the percent of the daily recommended amount of vitamin C this represents, we can use another proportion:
80 milligrams 100%
50 milligrams x%
Solving for x, we have:
x = (50/80) * 100 ≈ 62.5%
Therefore, Yosef drank orange juice containing 62.5% of the daily recommended amount of vitamin C.
The following chips are placed in a bucket: 4 red, 1 yellow, 5 blue, and 5 green. One chip is randomly selected from the bucket.
What is the probability that the chip is blue?
Answer:Red
Step-by-step explanation:
Answer:
Step-by-step explanation:
5 blue out of 15 chips
Which of the following are solution’s of the inequality 2.4/n < 6 :0.24 0.4 0.5
The solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.
What is inequality ?
An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequalities express a relationship between two quantities, indicating whether one quantity is less than, greater than, or equal to the other quantity.
We can solve the given inequality as follows:
2.4/n < 6
Multiplying both sides by n (note that n cannot be negative):
2.4 < 6n
Dividing both sides by 6:
0.4 < n
So, any value of n that is greater than 0.4 will be a solution to the inequality.
Out of the given options, only 0.5 is greater than 0.4, so 0.5 is the solution to the inequality.
Therefore, the solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.
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what is the answer to a=4 and b=3 can you help please 100 points right now
Answer:
14
Step-by-step explanation:
Rewrite the equation: 4*4+3-5
Multiply: 16+3-5
Add: 19-5
Subtract: 14
A car loses its value at a rate of 27% each year. How long will it take for its value to halve?
It will take nearly three years for the car's value to be half of its original price.
A circle with radius of \greenD{1\,\text{cm}}1cmstart color #1fab54, 1, start text, c, m, end text, end color #1fab54 sits inside a \blueD{3\,\text{cm} \times 4\,\text{cm}}3cm×4cmstart color #11accd, 3, start text, c, m, end text, times, 4, start text, c, m, end text, end color #11accd rectangle. What is the area of the shaded region? Round your final answer to the nearest hundredth
Given the rectangle's dimensions, its area is 12 cm² and the circle's area is π cm². Thus, the shaded region's area is about 8.57 cm².
The area of the shaded region is equal to the area of the rectangle minus the area of the circle.
The area of the rectangle is given by:
Area of rectangle = length x width = 4 cm x 3 cm = 12 cm²
The area of the circle is given by:
Area of circle = π x radius² = π x (1 cm)² = π cm²
Therefore, the area of the shaded region is:
Area of shaded region = Area of rectangle - Area of circle
Area of shaded region = 12 cm² - π cm²
Area of shaded region ≈ 8.57 cm² (rounded to the nearest hundredth)
Hence, the area of the shaded region is approximately 8.57 cm².
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the missing figure is in the image attached below
Is Joni correct? Explain.
Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.
Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290.
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
What is simple and compound interest?A loan or investment's principle amount is the sole amount used to compute simple interest. Any interest that has been earned on interest that has accrued over time is not taken into account by simple interest.
Contrarily, compound interest is a sort of interest that takes into account both the original principal and any interest that has accrued over time. As a result, the interest gained during one period is added to the principle for the following month, where it continues to earn interest.
Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.
The compound interest is given by the formula:
[tex]A = P (1 + r/n)^{(nt)}[/tex]
Substituting the values we have:
[tex]A = 200(1 + 0.05/1)^{(1*3)}\\A = 200(1.05)^3[/tex]
A = 200(1.157625)
A = $231.53
Hence, Joni will have a total balance of $231.53 after 3 years.
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The complete question is:
what is the probability of selecting a striped marble, not replacing it, then selectinga balck marble?
The probability of selecting a striped marble, not replacing it, then selecting a black marble is 4/15.
The probability of selecting a striped marble on the first draw is 6/10, since there are 6 striped marbles out of a total of 10 marbles in the bag.
After the first marble is drawn, it is not replaced, so there are now 9 marbles left in the bag. Out of these, there are 4 solid marbles and 5 striped marbles. Therefore, the probability of selecting a black marble on the second draw is 4/9.
To find the probability of both of these events occurring together, we multiply the probabilities
P(striped, then black) = P(striped) × P(black | striped not replaced)
P(striped, then black) = (6/10) × (4/9)
P(striped, then black) = 24/90
P(striped, then black) = 4/15
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The given question is incomplete, the complete question is:
There are 10 marbles in a bag (4 solid, 6 striped) .what is the probability of selecting a striped marble, not replacing it, then selecting a black marble?
If a bag of 7 oranges weighs 35 ounces. How much does 1 orange weigh?
Answer:
1 orange weighs 5 ounces.
Divide
35÷7 = 5
so, one orange weighs 5 ounces.
Write a system of equations to fit the situation below. Then solve the system using as many strategies as you can. How many solutions are possible?
Your math class wants to collect money for a field trip, so it decides to sell two kinds of candy bags. The Chocolate Lovers Bag costs
for five chocolate truffles and two caramel turtle candies. The Combusting Caramel Bag costs
for eight caramel turtle candies and two chocolate truffles. How much does each chocolate truffle and caramel turtle candy cost?
All three methods give the same solutions. So, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2).
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It consists of an equal sign between two expressions, which are usually separated by variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
Let x be the cost of a chocolate truffle and y be the cost of a caramel turtle candy. From the given information, we can write the following system of equations:
5x + 2y = C1 (Cost of Chocolate Lovers Bag)
2x + 8y = C2 (Cost of Combusting Caramel Bag)
To solve the system of equations, we can use various strategies. Here are a few:
Method 1: Substitution
We can solve for x or y in one equation and substitute the result into the other equation to eliminate one variable. For example, we can solve for x in the first equation:
5x + 2y = C1
5x = C1 - 2y
x = (C1 - 2y) / 5
Substituting this into the second equation:
2((C1 - 2y) / 5) + 8y = C2
Simplifying and solving for y:
C1/5 - 4y/5 + 8y = C2
y = (5C2 - C1) / 26
Substituting this value of y into the first equation and solving for x:
5x + 2((5C2 - C1) / 26) = C1
x = (3C1 - 10C2) / 65
Therefore, the cost of a chocolate truffle is (3C1 - 10C2) / 65 and the cost of a caramel turtle candy is (5C2 - C1) / 26.
Method 2: Elimination
We can multiply the first equation by 4 and the second equation by -1, and add them to eliminate y:
20x + 8y = 4C1
-2x - 8y = -C2
Adding these equations gives:
18x = 4C1 - C2
x = (4C1 - C2) / 18
Substituting this into the first equation and solving for y:
5((4C1 - C2) / 18) + 2y = C1
y = (9C1 - 20C2) / 36
Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.
Method 3: Matrix algebra
We can write the system of equations in matrix form:
[5 2] [x] [C1]
[2 8] [y] = [C2]
Using matrix algebra, we can solve for the variables:
[x] [C1] [8 -2] [y]
[y] = [C2] [-2 5 ] [x]
Multiplying the matrices, we get:
[x] [8x - 2y] [C1]
[y] = [-2x + 5y] * [C2]
Solving for x and y:
x = (4C1 - C2) / 18
y = (9C1 - 20C2) / 36
Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.
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Please show workkk!!!
Answer:
$104.11
Step-by-step explanation:
To calculate the monthly payment for a loan, we can use the following formula:
Monthly payment = (Pr(1+r)^n) / ((1+r)^n-1)
where:
P = the principal amount (the amount borrowed)
r = the monthly interest rate (annual interest rate divided by 12)
n = the number of payments (total number of years multiplied by 12)
In this case, the principal amount is $3825, the annual interest rate is 15%, and the loan term is 4 years. So we have:
P = $3825
r = 0.15/12 = 0.0125
n = 4*12 = 48
Substituting these values into the formula, we get:
Monthly payment = (38250.0125(1+0.0125)^48) / ((1+0.0125)^48-1)
Monthly payment ≈ $104.11
Therefore, the monthly payment for a $3825 loan at 15% annual interest for 4 years is approximately $104.11.
The wheel of Nguyo's lorry has a radius of 28 cm. The wheel of Kithela's car has a diameter of 42 cm. How many more revolutions does the wheel of Kithela's car make than the wheel of Nguyo's lorry to cover a distance of 770 m? Give your answer to the nearest whole number. (Take л =22/7
we get that the wheel of Kathel's car makes about 146 more revolutions than the wheel of Nguye's lorry to cover a distance of 770 m.
What is circumference?The circumference of a circle is the distance around the outer boundary of the circle. It is the length of the boundary or the "perimeter" of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The circumference is measured in units of length, such as meters or feet.
by the question.
To solve this problem, we need to first find the circumference of each wheel:
[tex]Circumference of Nguyon's lorry wheel = 2πr = 2 x (22/7) x 28 cm = 176[/tex]cm
Circumference of Kathel's car wheel = πd = (22/7) x 42 cm = 132 cm
Next, we can calculate how many revolutions each wheel needs to make to cover a distance of 770 m:
Number of revolutions for Nguyon's lorry wheel = distance ÷ distance covered in one revolution
= 77000 cm ÷ 176 cm ≈ 437.5 revolutions
Number of revolutions for Kathel's car wheel = distance ÷ distance covered in one revolution
= 77000 cm ÷ 132 cm ≈ 583.3 revolutions
Finally, we can find the difference in revolutions between the two wheels:
Difference in revolutions = Number of revolutions for Kathel's car wheel - Number of revolutions for Nguyon's lorry wheel
= 583.3 - 437.5 ≈ 145.8 revolutions
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