The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms.
Answers
The solution to the system of linear equations shows that the cost of 1 kg of turnips is £ 1.1 and the cost of 1kg of mushrooms is £ 2.9.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
First, you should convert the text of the problem into equations, thus you can write:
2m + 2.5t = 8.55 (1)
3m + 4t = 13.10 (2)
where: m = mushrooms and t = turnips
For solving this question, you can apply the addition method. Thus, you should follow the steps below:
Multiply equation 1 by 3 and equation 2 by -2, thus you can rewrite the equations as shown below6m + 7.5t = 25.65 (1)
-6m -8t = -26.20 (2)
Sum equations 1 and 2 and find t-0.5t = -0.55
0.5t = 0.55
Finding mFrom equation 1, you have 6m+7.5t=25.65 . If t= 11/10, you have
6m + 7.5*11/10 = 25.65 * (100)
600 m + 825 = 2565
600 m = 2565 -825
600 m = 1740
m = 1740/600
m=29/10
m=2.9
From the previous steps, you have the answers for the letter a ( £ 2.9 ) and the letter b ( £ 1.1).
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Related Questions
7. $3500 is invested at 3.6% for 4 years. Calculate the value of the investment after 4 years, if interest is: a) compounded semi-annually b) compounded quarterly
Answers
After 4 years, with a semi-annual compounding frequency, the investment of $3500 at an annual interest rate of 3.6% will grow to approximately $4047.47.
a) The value of the investment after 4 years, compounded semi-annually, can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $3500, the annual interest rate (r) is 3.6% or 0.036 as a decimal, the number of times interest is compounded per year (n) is 2 (semi-annually), and the number of years (t) is 4.
Using these values in the formula, we can calculate the future value (A):
A = 3500(1 + 0.036/2)^(2*4)
A ≈ 3500(1 + 0.018)^(8)
A ≈ 3500(1.018)^(8)
A ≈ 3500(1.156424812)
A ≈ 4047.47
Therefore, the value of the investment after 4 years, compounded semi-annually, is approximately $4047.47.
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ou have three submissions for each question except the multiple choice questions 4. [-15 Points ] Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x+y+z=3.
Answers
The volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + y + z = 3 is 27.
We can use the following steps to solve the given problem:
Step 1: Consider the given plane equation x + y + z = 3.
Step 2: Now, find the intercepts of the plane on the axes, as follows:Putting x = 0 and y = 0 in the equation x + y + z = 3, we get z = 3.So, the z-intercept is 3.Putting x = 0 and z = 0 in the equation x + y + z = 3, we get y = 3.So, the y-intercept is 3.Putting y = 0 and z = 0 in the equation x + y + z = 3, we get x = 3.So, the x-intercept is 3.Therefore, the intercepts of the plane x + y + z = 3 on the three axes are 3, 3, and 3.
Step 3: Let the rectangular box be of dimensions l, b, and h, respectively, and one of its vertices be (0, 0, 0).So, the other three vertices of the box will be (l, 0, 0), (0, b, 0), and (0, 0, h).Also, the coordinates of the vertex of the rectangular box on the plane x + y + z = 3 will be (3, 0, 0), (0, 3, 0), and (0, 0, 3).Hence, l = 3, b = 3, and h = 3.Substituting these values in the formula for the volume of a rectangular box, we get:V = l × b × h= 3 × 3 × 3= 27Therefore, the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + y + z = 3 is 27.
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Conservative change function is given in terms of dimensionless variables as:
-dg/dt + (1-g^2)dg/dx =0, - [infinity]0
a) Which condition must g provide for function to oppose the traffic rules.
b) What is vehicles’ maximum velocity (Umax)=?
c) inital condition is given as: g(x,0)= 1-x. Find the value of g(1,1)=?
Answers
To oppose the traffic rules, the function g must satisfy |g(x)| > 1. The maximum velocity of the vehicles is Umax = 0. Finally, the value of g(1,1) is 0 based on the given initial condition.
a) For the function g to oppose the traffic rules, it must satisfy the condition |g(x)| > 1. In other words, the absolute value of g must be greater than 1. This condition indicates that the function represents a vehicle moving in the opposite direction of traffic flow.
b) To determine the maximum velocity of the vehicles (Umax), we can analyze the equation -dg/dt + (1-g^2)dg/dx = 0. By setting dg/dx = 0, we can find the critical points where the velocity is maximum. In this case, when g = ±1, the term (1-g^2) reaches its maximum value of 0. Therefore, the maximum velocity of the vehicles is Umax = 0.
c) Given the initial condition g(x,0) = 1 - x, we can find the value of g(1,1) by substituting x = 1 into the function. Thus, g(1,1) = 1 - 1 = 0. Therefore, the value of g(1,1) is 0.
In summary, to oppose the traffic rules, the function g must satisfy |g(x)| > 1. The maximum velocity of the vehicles is Umax = 0. Finally, the value of g(1,1) is 0 based on the given initial condition.
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0.4 divided by 29 equally is?
Answers
Answer:
72.5 (Not rounded)
Hope this helps!
What will be the 50th term in the sequence defined by an = -11 +5(n − 1)?
Answers
Answer:
234
Step-by-step explanation:
Simplify the expression. an=5n-16. Substitute 50 for n. 5(50)-16= 250-16=234
For problems like this, simplifying the equation helps.
A cell phone company charges $25 per month, plus $0.10 per text message sent. Before taxes, Susie’s bill was $80 for 3 months of service. How many texts did Susie send during those 3 months
Answers
Answer:
50 messages
Step-by-step explanation:
how to find the standard deviation of a binomial distribution
Answers
Answer:
Standard Deviation (σ) = √(n * p * q)
Step-by-step explanation:
To find the standard deviation of a binomial distribution, you can use the following formula:
Standard Deviation (σ) = √(n * p * q)
Where:
n is the number of trials or observations
p is the probability of success in a single trial
q is the probability of failure in a single trial (q = 1 - p)
Here are the steps to find the standard deviation of a binomial distribution:
Determine the values of n (number of trials) and p (probability of success).
Calculate the value of q (probability of failure) by subtracting p from 1 (q = 1 - p).
Multiply n, p, and q together.
Take the square root of the result obtained in step 3.
The final result will be the standard deviation (σ) of the binomial distribution.
Note: The formula assumes that the trials or observations in the binomial distribution are independent and have the same probability of success (p) for each trial.
evaluate the function
Answers
Answer:
-16
Step-by-step explanation:
x = -3 is less than -2, so you should use the first equation 5x-1
thus, 5(-3)-1 = -16
Work out the area of a circle with radius 7.5cm take (pi) to be 3.142 and give your answer to 2 decimal places
Answers
Answer:
The area of this circle is \(176.74cm^2\)
Step-by-step explanation:
The formula for the area of a circle is : \(\pi *radius^2\)
The radius is the length from one side of the circle to the centre.
To work this out you would simply multiply pi by the radius of 7.5. squared. This gives you 176.74.
1) Multiply pi by 7.5 squared.
\(\pi *7.5^2=176.74cm^2\)
In this question pi is to be 3.142
Which of these four different offers gives the biggest price reduction?
Answers
Answer:
We dont see the prices you forgot to attach them
Step-by-step explanation:
1) according a survey found 58% of adults enjoy superhero movies. if eight adults are randomly selected, find the probability that a minimum of seven adults enjoy superhero movies.
Answers
The probability that a minimum of seven adults enjoy superhero movies is P(X ≥ 7) = P(X = 7) + P(X = 8)
You can calculate the specific values using the formulas and then sum them up to find the probability that a minimum of seven adults enjoy superhero movies out of the random sample of eight adults.
To find the probability that a minimum of seven adults enjoy superhero movies out of a random sample of eight adults, we need to calculate the probability of different scenarios: exactly 7 adults, exactly 8 adults, and add them together.
First, let's calculate the probability that exactly 7 adults enjoy superhero movies. We can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k successes,
C(n, k) is the combination formula (n choose k),
p is the probability of success (58% or 0.58 in decimal form),
n is the number of trials (8 in this case), and
k is the number of successes (7).
Using the formula, we can calculate:
P(X = 7) = C(8, 7) * 0.58^7 * (1 - 0.58)^(8 - 7)
Similarly, the probability that exactly 8 adults enjoy superhero movies is:
P(X = 8) = C(8, 8) * 0.58^8 * (1 - 0.58)^(8 - 8)
To find the probability of a minimum of seven adults enjoying superhero movies, we add these two probabilities together:
P(X ≥ 7) = P(X = 7) + P(X = 8)
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Let: L1 = {bb} L2 = {a, ab} L3 = {æ € {a,b}*| |x|≤ 3} = {A, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb} (L1;L2;) ∩ L3 = what?
Answers
The set of strings that are in both languages, which is {bba, bbab}.
How to find the strings of (L₁;L₂;) and L₃?The intersection of the languages specified by (L₁;L₂;) and L₃ is the set of strings that are in both languages.
The language (L₁;L₂;) is formed by concatenating a string from L₁ with a string from L₂. Since L₁ only contains the string "bb", every string in (L₁;L₂;) starts with "bb" and is followed by a string from L₂. Thus, (L₁;L₂;) contains the strings "bba" and "bbab".
The language L₃ contains all strings of length 3 or less over the alphabet {a,b}. Thus, L₃ contains the strings "a", "b", "aa", "ab", "ba", "bb", "aaa", "aab", "aba", "abb", "baa", "bab", "bba", and "bbb".
The intersection of (L₁;L₂;) and L₃ is the set of strings that are in both languages, which is {bba, bbab}.
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Refer to Problems 1-3 to solve Problems 4–6. The first one is done for you. 4. A scale factor between 0 and 1 produces a similar figure that is smaller than the original figure. 5. In Problem 2, YZ = _=4V5, and UV = v=2v5. The ratio of YZ to UV in simplest form is 6. If one polygon can be mapped to another by a series of then the polygons are Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility 218
Answers
The ratio of YZ to UV is 2:1
1) Considering that the distance between YZ is 4√5 and the distance between points U and V is 2√5 the ratio of YZ to UV can be found through this:
\(\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}\)2) Let's rationalize it by multiplying both numerator and denominator by √5 to simplify removing the radicals on the denominator.
\(\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}\cdot\frac{\sqrt[]{5}}{\sqrt[]{5}}=\frac{4\sqrt[]{5^2}}{2\sqrt[]{5^2}}=\frac{4\cdot5}{2\cdot5}=\frac{2}{1}\)3) So the ratio of YZ to UV is 2:1
Diameter of circle o
Answers
Answer:
The diameter of a circle is "2 x radius".
A stock loses $1.50 each day over a five-day period. What is the total change in the value of the stock at the end of five days? (remember to have two numbers after the decimal)
Answers
Given:
A stock loses $1.50 each day over a five-day period.
To find:
The total change in the value of the stock at the end of five days.
Solution:
Stock loses each day = $1.50
We know that, loss or reduction represented as negative change.
So, change in the value of the stock per day = -$1.50
Change in the value of the stock in 5 days = 5×(-$1.50)
= -$7.50
Therefore, the change in the value of the stock at the end of five days is -$7.50. It means, the value of the stock loses $7.50 at the end of five days.
Determine whether the statement is true or false. if it is false, rewrite it as a true statement. class boundaries ensure that consecutive bars of a histogram touch.
Answers
The false statement suggests that class boundaries ensure consecutive bars of a histogram touch, but this is incorrect. Class boundaries are used to define intervals and group data, not to ensure that bars touch.
Class boundaries in a histogram are not designed to ensure that consecutive bars touch. Instead, they are used to define the intervals or ranges into which the data is grouped. The purpose of class boundaries is to establish a clear distinction between adjacent classes, making it easier to interpret the data and create meaningful intervals for analysis.
To clarify, let's consider an example where we have a set of data points ranging from 10 to 30. We want to create a histogram with five bars. We can define the class boundaries as follows:
Class 1: 10 - 14.9
Class 2: 15 - 19.9
Class 3: 20 - 24.9
Class 4: 25 - 29.9
Class 5: 30 - 34.9
In this example, the class boundaries are chosen based on the desired intervals for the histogram. However, it's important to note that the bars representing these classes in the histogram will not touch each other. There will be gaps between them to indicate that they are separate intervals.
The purpose of class boundaries is to create distinct and meaningful intervals for analyzing the data in a histogram.
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In parallelogram LMNOMP is equal to 21MLB is equal to Y plus 3MNP03Y minus 1MNOP is equal to 2X -1 and what are the values of X and Y
Answers
Answer: 3 and 2
Step-by-step explanation:
Answer:
3 & 2
Step-by-step explanation:
A player has 15 hits in 34 times at bat and then gets another hit. Did the batting average increase explain
Answers
Explanation:
BA= H/AB
BA = 15/34 = 0.441
But then he gets another hit:
BA = 16/35 = 0.457
If a baseball is a sphere with a radius of 3.75 cm, what is the surface area of the baseball? use π = 3.14. a. 176.6 cm² b. 725.8 cm² c. 60.5 cm² d. 181.46 cm²
Answers
The surface area of the baseball is 176.6 cm² b.
What is meant by surface area?As a refresher, the surface area of an object is the sum of the areas of all of its faces or the exterior surfaces of its three dimensions. It is calculated in square units.The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area. This is calculated in square units and done using several area formulas.A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.To find the surface area of the baseball:
r=3.75
\(A=4\pi r^{2}\)
\(A=4*\pi *3.75^{2}\)
A=176.6 cm² b.
The surface area of the baseball is 176.6 cm² b.
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A local little league has a total of 60 players, of whom 40% are right-handed How many
right-handed players are there?
Answers
Answer: 24
To get this number, you do 60 x .40, and you get 24 (Amount of right handed people.)
Answer:
24
Step-by-step explanation:
24 because 40% of 60 is 24
given six people how many combinations of three are possible if the order does NOT matter
Answers
Answer:
20 Combos
Step-by-step explanation:
6C3 = 6! / ( 3! * 3!) = 20 COMBOS
A cubic polynomial function has one rational zero and two complex zeros, bí and , where is a rational number. Describe the coefficients of .
A. They are all rational numbers.
B. They are all complex numbers.
C. Some are complex numbers.
D. They cannot be determined.
Answers
Answer:
A+c
Step-by-step explanation:
because common sense
Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C
A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.
A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.
m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°
Answers
Answer: (3)
Step-by-step explanation:
Angles 1 and 4 are supplementary, and their measures thus add to 180 degrees.
Answer:
Step-by-step explanation:
m∠2 + m∠3 = 180°
suzie purchased a dress on sale for 18.74. this is 70% of the original price. what was the original price?
Answers
Answer:
26.7
Step-by-step explanation:
a team of workers is building a 942 foot tall trail. they plan to complete 6 feet per hour. how many hours will take to build he trail
Answers
Using the ratio and proportion method, we can set up a proportion between the height of the trail and the rate of building:
height of trail / rate of building = time to complete trail
We know that the height of the trail is 942 feet, and the rate of building is 6 feet per hour. We can substitute these values into the proportion:
942 / 6 = time to complete trail / 1
Simplifying the left side of the equation, we get:
157 = time to complete trail
Therefore, it will take 157 hours to complete the trail.
To understand why this works, we can think of the ratio between the height of the trail and the rate of building as the number of hours it takes to build one foot of the trail. This ratio is:
height of trail / rate of building = 942 / 6 = 157
So for every 157 hours of work, the workers will have built 942 feet of the trail.
In conclusion, using the ratio and proportion method, we can determine that it will take 157 hours to build each foot of the 942-foot tall trail.
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Find the perimeter. Help please !
Answers
Answer:
2t + 15
Step-by-step explanation:
you add the expressions
\(perimeter=(t+5)+(t)+(10)=2t+15\)
I hope this help you
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
0.96
What is the equivalent fraction?
Answers
Answer:
96% percent and fraction is 24/25
Answer: Down below
Step-by-step explanation:
64 % = 16 / 25
21 / 50 = 0. 42
9 / 25 = 36 %
2 / 5 = 40 %
/ = divide okay
Find an equation in slope-intercept form for the line. Through (5,2) and (3,5) The equation of the line is (Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)
Answers
To find the equation of the line passing through the points (5, 2) and (3, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b the line in slope-intercept form is: y = (-3/2)x + 19/2
First, let's calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points, we have:
m = (5 - 2) / (3 - 5)
m = 3 / (-2)
m = -3/2
Now that we have the slope, we can use one of the given points and the slope to find the y-intercept (b). Let's use the point (5, 2):
2 = (-3/2)(5) + b
2 = -15/2 + b
To find b, we can add 15/2 to both sides of the equation:
2 + 15/2 = b
4/2 + 15/2 = b
19/2 = b
Therefore, the equation of the line in slope-intercept form is:
y = (-3/2)x + 19/2
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I need help explaining
Answers
Answer:
Sure.
Step-by-step explanation:
So X is a variable meaning its a letter that represents a number. When there are a number and a variable (or a letter) like this 2x or 9y it means you are going to multiply the number by the variable. In this case it is 7 times x is equal to 21 so all we have to do is find what times 7 is equal to 21 and that number is 3. So if 7*x=21 is 7*3=21 then x=3. If you have any questions ill be more than open to answering them, hopefully this helped. Have a good day/night.
We can ask, “7 times what equals 21?”
The math family of equations here is
3 x 7 = 21
7 x 3 = 21
21 / 7 = 3
21 / 3 = 7
So to solve for x, or find out mystery number, we have 7x = 21
Whatever we do to one side of the equation, we have to do to the other side to keep it equal. Here, we’ll divide both sides by 7, so that on the left side, x is by itself.
Then we have x = 21/7 which is x = 3
Please ask any questions in the comments
in 250 explain the power of substitutes from porters 5
forces
Answers
The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.
The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.
The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.
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