Answers
Answer:
The market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Step-by-step explanation:
To find out how much the market trader needs to sell the remaining 20 packs of muffins, we first need to calculate his total cost and his target revenue.
The cost of the loaves of bread is:
100 loaves x 84p/loaf = £84
The cost of the packs of muffins is:
60 packs x £1.10/pack = £66
Therefore, the total cost for the trader is:
£84 + £66 = £150
To make a 40% profit, the trader needs to make £150 x 40/100 = £60 in profit.
His target revenue is, therefore:
£150 + £60 = £210
The revenue from the loaves of bread is:
100 loaves x £1.20/loaf = £120
The revenue from the 40 packs of muffins sold at £1.60 per pack is:
40 packs x £1.60/pack = £64
So the total revenue from the loaves of bread and the 40 packs of muffins is:
£120 + £64 = £184
This means that the trader needs to make:
£210 - £184 = £26
from the sale of the remaining 20 packs of muffins.
To sell 20 packs of muffins to make £26, he needs to sell each pack for:
£26/20 = £1.30 per pack
Therefore, the market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Related Questions
A surfer recorded the following values for how far the tide rose, in feet, up the beach over a 15-day period. 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24 Which of the following histograms best represents the data collected?
Answers
In this case, we can choose a bin size of 3, starting from 5 to 24, and divide the data into the following bins: 5-7, 8-10, 11-13, 14-16, 17-19, 20-22, and 23-25. Next, we count the number of data points that fall into each bin and represent it using bars.
Looking at the given histogram options, it is clear that only histogram B represents the data accurately. It has bins that cover 5-7, 8-10, 11-13, 14-16, 17-19, 20-22, and 23-25. The height of each bar accurately represents the number of data points in that bin.
Therefore, we can conclude that histogram B best represents the data collected.
7) If a professor can grade 5 essays in 40 minutes, the professor can grade 32 essays in 256 minutes. (10pts)
O True
O False
Answers
Answer:
O True
Step-by-step explanation:
Unit rate of essays/minute:
40 minutes / 5 essays = 8 essays/minute
256 essays / 32 minutes = 8 essays/minute
The unit rates are equal.
Answer: O True
(-6,-4), (0, -4), and (2,-4)
What is the equation of this line?
Answers
Answer: y = -4
Step-by-step explanation:
Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.
This means the equation of the line is:
y = -4
See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.
Solve the following by completing the square or squaring both sides using steps illustrated in the lesson content.. Leave answers in radical (EXACT) form. Do not use decimals. -2x+6=-x^2
Answers
-x^2 + 2x - 6 = 0
Next, we need to complete the square by adding and subtracting (2/2)^2 = 1 from the left-hand side of the equation:
-(x^2 - 2x + 1 - 1) - 6 = 0
Now we can simplify the expression inside the parentheses:
-[(x - 1)^2 - 1] - 6 = 0
Distribute the negative sign:
-[(x - 1)^2 - 1] + 6 = 0
Simplify:
-(x - 1)^2 + 7 = 0
Next, we can square both sides to eliminate the square root:
(x - 1)^2 = 7
Finally, we can take the square root of both sides, remembering to include the plus or minus sign:
x - 1 = ±√7
Adding 1 to both sides:
x = 1 ± √7
Therefore, the solutions to the equation -2x + 6 = -x^2 are x = 1 + √7 and x = 1 - √7.
Answer:
Starting with the equation:
-2x + 6 = -x^2
First, we can rearrange it to put it in standard quadratic form:
x^2 - 2x - 6 = 0
To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:
x^2 - 2x + 1 - 1 - 6 = 0
The first three terms can be written as a perfect square:
(x - 1)^2 - 7 = 0
Add 7 to both sides:
(x - 1)^2 = 7
Now we can take the square root of both sides:
x - 1 = ±√7
Add 1 to both sides:
x = 1 ± √7
So the solutions to the equation are:
x = 1 + √7 or x = 1 - √7
mark me brilliant
Help me please, this assignment is alr past due
Answers
Answer:
Step-by-step explanation:
However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent. Negative version because to get to a decimal you move in the negative direction.
.1 = 1.0 x [tex]10^{-1}[/tex]
.01 = 1.0 x [tex]10^{-2}[/tex]
.001 = 1.0 x [tex]10^{-3}[/tex]
.000001 =,1.0 x [tex]10^{-6}[/tex]
Find the endpoints of the latus rectum of the parabola below.
(y - 1)? = 16(x + 1)
Answers
Answer:
(3, 9) and (3, -7)
Step-by-step explanation:
You want the end points of the latus rectum for the parabola defined by ...
(y -1)² = 16(x +1)
Vertex and scale factorCompare the given equation to the form ...
(y -k)² = 4p(x -h)
we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.
Latus rectumSince the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...
(h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)
__
Additional comment
If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).
On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
Answers
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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Find the equation of the quadratic function g whose graph is shown below.
Answers
The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex and other points, we can determine the value of a as follows:
g(x) = a(x - h)² + k
-13 = a(-7 + 4)² - 4
-13 = a(-3)² - 4
-13 + 4 = 9a
-9 = 9a
a = -1.
Therefore, the required quadratic function is given by:
g(x) = a(x - h)² + k
g(x) = y = -(x + 4)² - 4
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CNNBC recently reported that the mean annual cost of auto insurance is 957 dollars. Assume the standard deviation is 193 dollars. You will use a simple random sample of 58 auto insurance policies. You may assume original population is approximatley normally distributed, and round your answers to three decimals.
Find the probability that a single randomly selected policy has a mean value between 964.6 and 1000.1 dollars.
P(964.6 < X < 1000.1) = ???
Find the probability that a random sample of size
has a mean value between 964.6 and 1000.1 dollars.
P(964.6 < M < 1000.1) = ???
Answers
The probabilities are given as follows:
P(964.6 < X < 1000.1) = 0.071 = 7.1%.P(964.6 < M < 1000.1) = 0.338 = 33.8%How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for this problem is given as follows:
[tex]\mu = 957, \sigma = 193[/tex]
The probability is the p-value of Z when X = 1000.1 subtracted by the p-value of Z when X = 964.6, hence:
Z = (1000.1 - 957)/193
Z = 0.22.
Z = 0.22 has a p-value of 0.5871.
Z = (964.6 - 957)/193
Z = 0.04.
Z = 0.04 has a p-value of 0.5160.
Hence:
0.5871 - 0.5160 = 0.0711.
For the sample of 58, the standard error is obtained as follows:
s = 193/sqrt(58) = 25.34.
Hence:
Z = (1000.1 - 957)/25.34
Z = 1.7.
Z = 1.7 has a p-value of 0.9554.
Z = (964.6 - 957)/25.34
Z = 0.3.
Z = 0.3 has a p-value of 0.6179.
Hence:
0.9554 - 0.6179 = 0.338.
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A group of students worked out the mean and range of their ages. The mean was 12 years and 3 months. The range was 2 years and 7 months. a) What was the mean of the ages of the same group of students exactly one year later? b) What was the range of their ages exactly one year later? Write a sentence to explain each of your answers.
Answers
Exactly one-year later,
(a) Mean of the ages will be 13 years and 3 months.
(b) Range of the ages will be same 2 years and 7 months.
Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.
New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;
So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.
Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.
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Can someone help with this and give the right answer I am on a time limit
Answers
The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers: [tex]k = y/x^a \times z/x^b,[/tex] where a and b are the powers of x in the expressions for y and z, respectively. when [tex]x = -3[/tex] and [tex]y = 4[/tex] , z is equal to -81/16.
What is the constant of variation?In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:
[tex]y = 54 = (8^a) \times k = > a = 3[/tex]
[tex]z = 144 = (8^b) \times k = > b = 2[/tex]
Substituting these values into the formula for k, we get:
[tex]k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64[/tex]
Therefore, the constant of variation is 27/64.
Using the same formula as above, we can solve for z when x = -3 and y = 4:
[tex]k = y/x^a \times z/x^b[/tex]
We need to determine the powers of x in the expressions for y and z:
[tex]y = 4 = (-3)^a * k = > a = -1[/tex]
[tex]z = ? = (-3)^b * k = >[/tex] we don't know b or z yet
Substituting these values into the formula for k, we get:
[tex]k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2[/tex]
Simplifying this expression, we get:
[tex]k = -12z/9 = -4z/3[/tex]
Now we can solve for z:
[tex]-4z/3 = 27/64[/tex]
Multiplying both sides by 3/(-4), we get:
[tex]z = -81/16[/tex]
Therefore, when [tex]x = -3[/tex] and [tex]y = 4, z[/tex] is equal to [tex]-81/16.[/tex]
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1. The rectangle shown is dilated by a scale factor of 3. (a) Calculate the length of each side of the dilated image. (b) Draw the new image and label it .
Answers
According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.
How to calculate the length of each side of the dilated image?To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:
8 / 3 = 2.6615 / 3 = 5According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.
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2x+15-8=14
find the value of x
Answers
Answer:
x = 3.5
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]
Next, isolate the variable, x. First, subtract 7 from both sides of the equation:
[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]
Finally, divide 2 from both sides of the equation:
[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]
x = 3.5 is your answer.
~
Learn more about solving with PEMDAS, here:
https://brainly.com/question/26499272 - See AadhPrit's answer.
Answer:
[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]
Step-by-step explanation:
To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.
We can do this by first combining the constants on the right-hand side of the equation:
[tex]2x+15-8=14[/tex]
[tex]2x+7=14[/tex]
Next, we can isolate x by subtracting 7 from both sides of the equation:
[tex]2x=7[/tex]
Finally, we can solve for x by dividing both sides of the equation by 2:
[tex]x=\frac{7}{2}[/tex]
Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].
Can someone help me with this
Answers
Answer:
x = 23°
Step-by-step explanation:
We Know
The 67° angle + the x must be equal to 90°
Find the x.
Let's solve
67° + x = 90°
x = 23°
If Kayla has a 73% in her history class and she took a test 20% of her grade and got a 60 on it. What would her grade be?
Answers
Answer:
70.4%
Step-by-step explanation:
Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:
New overall grade = (0.80 x 73) + (0.20 x 60)
New overall grade = 58.4 + 12
New overall grade = 70.4
Therefore, Kayla's new overall grade is 70.4%
Answer:
70.4% or a C-.
Step-by-step explanation:
To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.
To calculate Kayla's new grade, you can use the following formula:
New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)
Plugging in the numbers given in the problem, we get:
New grade = (0.73 x 0.80) + (0.60 x 0.20)
New grade = 0.584 + 0.12
New grade = 0.704
Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.
There are 15 tables at a wedding reception,
5 of which have purple centerpieces.
1) What is the probability that a randomly
selected table will have a purple centerpiece?
◄) Write your answer as a fraction or whole
number.
Answers
Answer:
1/3
Step-by-step explanation:
There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.
5/15 is 5 out of 15. 5/15 simplifies to 1/3.
need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
Answers
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24
Answers
1. Pour la première question, si le garçon peut courir une distance de 10 mètres pendant que la voiture en parcourt 0, alors le garçon peut courir la même distance que la voiture en un temps infini, ce qui signifie qu'il peut courir pendant que la voiture parcourt 66 mètres. Par conséquent, la réponse est (A) 0.
2. Pour la deuxième question, nous pouvons utiliser la formule suivante:
Nombre total d'uniformes produits = nombre d'ouvriers x nombre d'uniformes produits par ouvrier
Soit n le nombre d'ouvriers dans l'équipe. Avant l'augmentation de 20%, chaque ouvrier produisait en moyenne 1000 / n uniformes par semaine. Après l'augmentation, chaque ouvrier produit en moyenne (1000 / n) x 1.2 + 50 uniformes par semaine. Par conséquent, nous avons l'équation suivante:
n x [(1000 / n) x 1.2 + 50] = 1200
Simplifiant l'expression, nous obtenons:
1200 = 1200 + 50n / n
50n = 0
Par conséquent, la réponse est (A) 4, ce qui implique qu'il y avait seulement 4 ouvriers dans l'équipe. Cependant, cette réponse est peu plausible, car il est peu probable qu'une équipe de seulement 4 ouvriers puisse produire 1000 uniformes par semaine avant l'augmentation de 20%.
Need help. What is the x value pic attached below
Answers
The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2
Calculating the value of xFrom the question, we have the following equation that can be used in our computation:
f(x) = (1/3)^x - 2
When the value of f(x) is 7, we have
(1/3)^x - 2 = 7
So, we have
(1/3)^x = 9
Take the log of both sides
x = log(9)/log(1/3)
Evaluate
x = -2
Hence, the value of x is -2
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v=? image attached please help
Answers
Answer:
v=12
Step-by-step explanation:
9/v = 6/8
9 = 6v/8
72= 6v
v= 12
Answer:
v = 12
Step-by-step explanation:
Now we have to,
→ Find the required value of v.
Given proportion,
→ (9/v) = (6/8)
Then the value of v will be,
→ (9/v) = (6/8)
→ 9 × 8 = 6 × v
→ 72 = 6v
→ 6v = 72
→ v = 72/6
→ [ v = 12 ]
Hence, the value of v is 12.
NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83
Answers
Step-by-step explanation:
Here is a graph from Desmos....you should be able to see where the function is > 0
i need answer please
Answers
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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What are the values of x and y?
X=
Y=
Answers
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
someone help i really need help with this
Answers
Answer:
29
Step-by-step explanation:
she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.
State whether the decay is linear or exponential, and answer the associated question.
The value of a car is decreasing by 12% per year. If the car is worth $9,000 today, what will it be worth in two years?
Answers
_________________________________
= 12 × 9,000 ÷ 100= 1,080= 1,080 × 2= 2,160= 9,000 - 2,160= $6,840The Car Will Be Worth $6,840 After 2 Years_________________________________
Answer:
$6,840
Step-by-step explanation:
Suppose in an orchard the number of apples in a tress is normally distributed with a mean of 300 and a standard deviation of 30 apples. Find the probability that a given tree has between 300 and 390 apples.
Answers
Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
How the probability is determined:Probability refers to the chance or likelihood that an expected event occurs out of many possible events.
Probability lies between 0 and 1, depending on the degree of certainty.
Mean = 300
Standard deviation = 30
Range = 300 to 390
Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
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A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?
Answers
The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).
The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).
Substituting l = 1 m, we get
T = 2π√(1/9.81)
T ≈ 2.006 s.
In one day, there are
24 hours x 60 minutes/hour x 60 seconds/minute
= 86,400 seconds.
The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes
86,400/2
= 43,200 back-and-forth swings in one day.
The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is
2 x 12 degrees
= 24 degrees
= 0.419 radians.
Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is
1 meter x 0.419
= 0.419 meters.
Multiplying by the number of swings in one day, we get:
0.419 meters/swing x 43,200 swings/day
= 18,115.2 meters/day.
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Please help solve graphs
Answers
The graphs are:
1) not one-to-one
2) one-to-one
3) not one-to-one
Are the graphs one-to-one?A graph represents an one-to-one function only if.
We can't draw a vertical line that touches the graph twice or more.
We can't draw an horizontal line that touches the graph twice or more.
For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.
Similarly forthe third graph, the line y = 0 touches two points-
So these two are not one-to-one.,
For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.
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The electrical signal created by a piece of test equipment at a specific point in time is described by the function v inst(t)=12xsin(360x60x6.3+79). What is the maximum voltage produced by the system?
Answers
The maximum voltage produced by the system is 12 volts.
The function given is:
[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]
To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.
Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.
First, calculate the value of the argument:
360 * 60 * 6.3 + 79 = 136080 + 79 = 136159
Now, substitute this value back into the sine function:
sin(136159)
The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:
136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22
Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.
Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.
So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:
Maximum voltage = 12 * 1 = 12 volts.
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please help! it is matrices, so it should be rlly easy.
Answers
B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.
How to find the determinant of the matrix BWe can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:
|B| = (-2 × -2) - (1 × 5)
|B| = 4 - 5
|B| = -1.
Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.
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