If a man loses 10 percent by selling his watch for 450 then the cost price of the watch would be 500.
Let's assume the cost price of a watch is 100.
So, after selling at a loss of 10 percent, the selling price of the watch is 90.
By comparing the assumed selling price of the watch with the original selling price, 450/90 = 5.
So, the original selling price is 5 times the assumed selling price.
Thus original cost price should also be 5 times of assumed cost price, so the original cost price × 5 = 100 × 5 = 500.
Hence the original cost price of the watch is 500.
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what is the dimension of the solution space if you have 3 linearly independent equations in 5 unknowns?
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2. This is because, when solving a system of equations, the number of equations must match the number of unknowns; otherwise, it is impossible to solve. In this case, the number of equations (3) is less than the number of unknowns (5), meaning that the system is underdetermined. This means that there are infinite solutions, and the dimension of the solution space is 2 (the number of free variables).
In other words, the solution space is a two-dimensional plane where each point represents a possible solution to the system of equations. As the equations are linear, the solution space forms a linear subspace, which means that it is a flat surface.
It is also important to note that the linear independence of the equations is crucial to this solution. If the equations are dependent, then the solution space can have a dimension of 1, 0, or even a negative number. So, the dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
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Which of the following graphs is described by the function below?
[tex]y=x^{2} -6x-7[/tex]
A.) Graph A
B.) Graph B
C.) Graph C
D.) Graph D
The given function [tex]y=x^2 - 6x - 7[/tex] describes the graph A.
What is function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.
We can solve this Function by substituting the 0 for Y.
To find the value of x when y is equal to 0, we can substitute 0 for y in the equation and solve for x:
[tex]0 = x^2 - 6x - 7[/tex]
To solve for x, we can use the quadratic formula:
x = (-b ± [tex]\sqrt{(b^2 - 4ac)}[/tex]) / 2a
In this case, a = 1, b = -6, and c = -7. Substituting these values into the formula, we get:
x = (-(-6) ± [tex]\sqrt {((-6)^2 - 4(1)(-7)}[/tex])) / 2(1)
Simplifying:
x = (6 ± [tex]\sqrt{64}[/tex]) / 2
x = (6 ± 8) / 2
x = 7 or x = -1
Therefore, when y is equal to 0, x can be either 7 or -1.
Therefore the given function describes the graph A.
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the variable socioeconomic status ranges from upper class to lower class and is an example of the select one: a. nominal level of measurement b. ordinal level of measurement c. interval-ratio level of measurement d. ratio level of measurement
The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)
Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.
Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.
However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.
Hence option (c) is correct.
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Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
What is variability?
To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.
To calculate the range, we subtract the smallest value from the largest value:
Largest value: 58
Smallest value: 10
Range = Largest value - Smallest value = 58 - 10 = 48
Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."
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A dog has a mass of 19 kg. What is the mass of the dog in
grams, expressed in scientific notation?
a 1. 9 x 101 g
b 1. 9 x 1038
С
1. 9 X 104
g
d 1. 9 x 10² g
The mass of dog having weight as 19 kg has its mass in grams as 1.9 x 10⁴ grams, option C.
In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.
Measuring units to determine the size, weight, or quantity of any object. Seven fundamental measurement units are utilized in daily life and across the globe.
A dog has a mass of 19 kg
The mass of the dog in grams is:
1 kilogram = 1000 grams
19.5 kg × (10³ g/1 kg) = 1.95 × 10⁴ g.
Thus, the mass of the dog in grams is 1.95 × 10⁴ g.
1000 grammes make to 1 kilogram (kg) (g).
1 kg = 1000 g
The mass m in kilogram (kg) multiplied by 1000 gives the mass m in grams (g)
m(g) = m(kg) × 1000.
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When the equation a – bx = cx + d is solved for x, the result is x = startfraction a. minus b. over c. plus d. endfractionuse the general solution to solve 5 – 6x = 8x + 17.
The solution to the equation 5 – 6x = 8x + 17 is x = -6.
Using the general solution for linear equations, we can rewrite the given equation as x = (a - d)/(c + b). This means that the solution for x is equal to the fraction (a - d) divided by (c + b).
Now let's use this general solution to solve the equation 5 – 6x = 8x + 17. First, we need to identify the values of a, b, c, and d in the equation. From the given equation, we can see that a = 5, b = -6, c = 8, and d = 17.
Next, we can substitute these values into the general solution and simplify:
x = (a - d)/(c + b)
x = (5 - 17)/(8 - 6)
x = -12/2
x = -6
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Answer:-6/7
Step-by-step explanation: got it right on ed
Which of the following values of x is a solution to the system of equations 3x+2y=7 and y=x-5 answers are 7 5/6, 2 3/4, 5 1/3, and 3 2/5 .
The sοlutiοn tο the system οf equatiοns is x = 17/5, which is apprοximately equal tο 3.4. Nοne οf the given answer chοices match this value exactly, sο there is nο sοlutiοn amοng the given chοices.
What is linear equatiοn?A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal plane.
We can sοlve the system οf equatiοns by substituting the secοnd equatiοn intο the first equatiοn and then sοlving fοr x:
3x + 2y = 7 (equatiοn 1)
y = x - 5 (equatiοn 2)
Substituting equatiοn 2 intο equatiοn 1, we get:
3x + 2(x - 5) = 7
Simplifying the equatiοn, we get:
5x - 10 = 7
Adding 10 tο bοth sides, we get:
5x = 17
Dividing bοth sides by 5, we get:
x = 17/5
Therefοre, the sοlutiοn tο the system οf equatiοns is x = 17/5, which is apprοximately equal tο 3.4. Nοne οf the given answer chοices match this value exactly, sο there is nο sοlutiοn amοng the given chοices.
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SOMEONE HELP I WILL GIVE U BRAINLEST PLS 1-10
Answer:
7/4
Step-by-step explanation:
if you divide 7/4, you will get 1.75 which is greater than 1.43.
Answer:
Hi, your answer is 7/4
Step-by-step explanation:
Hope this helps :D
Write an equation of the line that has a slope of 6 and passes through the point (1,-2) in slope-intercept form
Answer:
y=6x-8
Step-by-step explanation:
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.
Point-slope form: y - y1 = m(x - x1)
Substitute the values of m, x1, and y1:
y - (-2) = 6(x - 1)
Simplify the right side:
y + 2 = 6x - 6
Subtract 2 from both sides:
y = 6x - 8
This is the equation of the line in slope-intercept form.
How does the value of a in the function affect its graph when compared to the graph of the quadratic parent function? g(x)=6x^2
Changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
What is function?
A relationship or expression involving one or more variables
The function g(x) = 6x^2 is a quadratic parent function, which means it is the simplest form of a quadratic function.
When we change the value of "a" in the general form of a quadratic function:
f(x) = ax^2 + bx + c
we change the shape of the graph of the function. Specifically, changing the value of "a" stretches or compresses the graph vertically, and changes the direction of the opening of the parabola.
If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The larger the absolute value of "a", the more stretched or compressed the parabola becomes.
In the case of g(x) = 6x^2, "a" is positive and equal to 6, which means the graph is stretched vertically by a factor of 6 compared to the parent function. The parabola opens upwards and is narrower than the parent function.
If we were to change the value of "a" to a different positive value, for example "a" = 3, the graph would still open upwards but would be less stretched than g(x) = 6x^2. On the other hand, if we were to make "a" negative, for example "a" = -6, the graph would open downwards, and be a reflection of the graph of g(x) = 6x^2 about the x-axis.
In summary, changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
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tickets for a raffle cost 5. there were 833 tickets sold. one ticket will be randomly selected as the winner, and that person wins 1400 and also the person is given back the cost of the ticket. for someone who buys a ticket, what is the expected value (the mean of the distribution)?
The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.
In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.
The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.
Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565
The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.
Therefore, the expected value of a ticket is:$5565 / 833 = $6.68
Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.
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A researcher randomly selects 95 high school swimmers and asks them which swim stroke is their strongest and which bathing suit brand they prefer, brand A or brand B. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers brand B and F = the student’s strongest stroke is freestyle.
A 5-column table with 3 rows. Column 1 has entries brand A, brand B, total. Column 2 is labeled breast with entries 15, 18, 33. Column 3 is labeled freestyle with entries 19, 26, 45. Column 4 is labeled butterfly with entries 10, 7, 17. Column 5 is labeled total with entries 44, 51, 95. The columns are titled swim stroke and the rows are titled brand preference.
Which of the following is the correct value and interpretation of P(F|B)?
Answer: 0.51
Step-by-step explanation:
To find the value of P(F|B), we need to use the formula:
P(F|B) = P(F and B) / P(B)
where P(F and B) is the probability that a student prefers brand B and their strongest stroke is freestyle, and P(B) is the probability that a student prefers brand B.
From the given table, we can see that:
P(F and B) = 26/95
P(B) = 51/95
Therefore, we can calculate
:P(F|B) = (26/95) / (51/95) = 26/51 ≈ 0.51
So, the correct value of P(F|B) is approximately 0.51, which can be interpreted as the probability that a student's strongest stroke is freestyle given that they prefer brand B.
a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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0.
Ryan checked out 3 books from the library: one mystery (M), one history book (H), and one biography (B). Which tree diagram shows all the possible orders in which Ryan can read the 3 books?
...
This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.
What is mystery?Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.
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Complete Question is attached below:
Can someone pls help me with this
A. The equation of the line that passes through the point (4,3) and has a slope of -5/2 is y = (-5/2)x + 13.
B. The x-intercept of the equation is x = 26/5 or 5.2
How to Find the Equation of a Line?A. To find the equation of a line that passes through the point (4,3) and has a slope of -5/2, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the given point.
Substituting the values, we get:
y - 3 = (-5/2)(x - 4)
Expanding the right side:
y - 3 = (-5/2)x + 10
Adding 3 to both sides:
y = (-5/2)x + 13
B. To find the x-intercept of this equation, we need to set y = 0 and solve for x:
0 = (-5/2)x + 13
Multiplying both sides by -2/5:
0 = x - (26/5)
Adding (26/5) to both sides:
x = 26/5
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What is the product of (3x+2) and (x - 7) ?
Center of Triangles I please help
The value of angle CI is equal to 40 for the triangle.
What is geometry?
Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that I is the incenter of the triangle AI = 3x+7, BI = 5x-11, and CI = 52-2x.
The value of BI will be calculated as,
AI = BI
3x + 7 = 5x - 11
2x = 18
x = 6
Now for the value of angle CI:
CI = 52 - 2x
CI = 52 - 2 x 6
CI = 52 - 12
CI = 40
Therefore, the value of angle CI is equal to 40 for the triangle.
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A sphere has radius 2. 7cm. What is its surface area to the nearest sqaure cenitmeter
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2.7 \end{cases}\implies SA=4\pi (2.7)^2\implies SA\approx 91.61~cm^2[/tex]
when researching a population where it is impossible or impractical to compile a list of the elements, which sampling technique is appropriate to use?
When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique
Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.
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Rewrite the expression 2(10+12) using the distributive property of multiplication over addition
The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.
The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c
a( b + c ) = ab + ac
Using this property, we can rewrite the expression 2(10+12) as
2( 10 + 12 ) = 2(10) + 2(12)
Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:
2(10+12) = 20 + 24
Simplifying further, we get
2(10+12) = 44
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Determine the domain of the following graph:
Answer:
domain is [-11 , -3]
Step-by-step explanation:
domain is x
range is y
x values are from -11 to -3
Which system has exactly one solution?
A.(y + 4x = -2
y = -4x + 5
B. (6x + 3y = -1
2x + y = 4
C. y = 4x - 5
{ y = -x-5
D.3x - = 2
{y-4 = 3(x-2)
The system of equations that has only one solution is the one where the equations have different slopes, it is the one in option C.
y = 4x - 5
y = -x - 5
Which system of equations has only one solution?A system of linear equations will have only one solution always that the lines are neither parallel nor the same line.
So, one way to check this, is to write both lines in the slope intercept form, and check that the two lines have different slopes.
For example, the first option will give.
y = -4x - 2
y = -4x + 5
These are parallel (same slope different intercept), then this systm has no solutions.
The correct option will be C, where the system is:
y = 4x - 5
y = -x - 5
The slopes are different.
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What is the area of this figure?
Answer: 75 [tex]m^{2}[/tex]
Step-by-step explanation:
5*5 + 5*10 = 25 + 50 = 75
please mark brainliest
e ABC be similar to RST. Find both missing sides t and s.
B
A
5
4
3
R
S
S
9
T
According to the solution we have come to find that, The missing sides are t=ST=9 and s=RT=12.
what is right angle triangle?
A right angle triangle, also known as a right triangle, is a triangle that has one angle measuring 90 degrees, which is also known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is a fundamental property of right triangles. Right triangles are important in mathematics and physics, and they have many applications in geometry, trigonometry, and calculus.
We can use the fact that the two triangles are similar to set up a proportion and solve for the missing sides.
AB/RS = BC/ST = AC/RT
Substituting the given values:
5/RS = 3/9 = 4/s
Solving for RS:
RS = (5/3) * 9 = 15
Solving for RT:
RT = (4/5) * 15 = 12
Therefore, the missing sides are t=ST=9 and s=RT=12.
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Find the area of the figure.
7 cm
11 cm
8 cm
The area is ? square centimeters.
pls help I'll mark brainlisest
Answer:
Area of the figure=126.5cm²
Step-by-step explanation:
As we can see based on the shape of the figure, we can divide it into a;
→ Triangle
→ Rectangle
Formulas that we need are;
⇒ Area of triangle =1/2×base×height
⇒ Area of rectangle =length × width
Let's solve the area of the triangle first;
Area of triangle =1/2 × base × heightArea of triangle=1/2 × 11cm × 7cmArea of triangle=38.5cm²Then the area of the rectangle;
Area of rectangle =length × widthArea of rectangle =11cm × 8cmArea of rectangle =88cm²Finally, we add the triangle and rectangle together-
Area of Triangle + Area of Rectangle = 38.5cm²+88cm²
Area of the figure=126.5cm²
RevyBreeze
What the answer to this problem?
The coordinates of point Q in the parallelogram is (2b + 2a,2c)
1)How to determine the coordinates of Q?The coordinates are given as:
P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)
The parallelogram form of the object indicates that the distances PQ and RS are equal.
The distance RS is calculated as:
RS = ( 2a - 0, 0)
This gives
RS = (2a, 0)
Coordinate Q is calculated as:
Q = P + RS
This gives
Q = (2b,2c) + (2a,0)
Evaluate the sum
Q = (2b + 2a,2c)
Hence, the coordinates of point Q is (2b + 2a,2c)
2)To prove: SQ and PR bisect each otherMidpoint of SQ=(b+ a ,c)
Midpoint of PR=(a+ b, c)
hence, SQ and PR bisect each other.
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a researcher wishes to test the hypothesis that the difference between two population means is zero. if the sample means are 106.4 and 99.2, the standard error of the difference is 6.1, and the critical value needed to reject the null hypothesis is 2.09, what should the researcher decide about the difference between the two populations means?
There is not enough evidence to suggest that the difference between the two population means is statistically significant at the 5% significance level.
To test the hypothesis that the difference between two population means is zero, the researcher can use a two-sample t-test. The test statistic is calculated as the difference between the sample means divided by the standard error of the difference.
In this case, the sample means are 106.4 and 99.2, and the standard error of the difference is 6.1. Therefore, the test statistic is (106.4 - 99.2) / 6.1 = 1.18.
To decide whether to reject the null hypothesis that the difference between the two population means is zero, the researcher needs to compare the test statistic to the critical value. The critical value needed to reject the null hypothesis at a 5% significance level with 2 degrees of freedom (n1 + n2 - 2 = 2) is 2.09.
Since the test statistic of 1.18 is less than the critical value of 2.09, the researcher fails to reject the null hypothesis.
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If there are initially 3500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula. How many bacteria will be present after 5 hours?
The number of bacteria after 5 hours with initial numbers 3500 increased double in each hour is equal to 112,000.
Initially number of bacteria in a culture = 3500
Total hours the number of bacteria double = Each hour
Then the growth rate is equal to 2
As the number of bacteria after each hour is twice the previous numbers.
Formula used for the number of bacteria after t hours ,
N = N₀ x 2^t
where N₀ is the initial number of bacteria.
Time in hours = t hours
And N is the number of bacteria after t hours.
After 5 hours, the number of bacteria present is equal to,
⇒N = 3500 x 2^5
⇒N = 3500 x 32
⇒N = 112,000
Therefore, number of bacteria present after 5 hours is equal to 112,000.
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Lily has a box of candies.
5
6
of the candies are pink.
1
2
of the pink candies are round.
What fraction of the candies are pink and round?
Answer:
1/12
Step-by-step explanation:
Out of the total number of candies, 1/2 of the pink candies are round.
To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:
pink candies = 5/6
round candies among the pink ones = 1/5
Therefore, the fraction of candies that are pink and round is:
(5/6) x (1/2) x 1/5 = 1/12
So, 1/12 of the candies are pink and round.