2/5th of a number is 40% of that number.
In order to calculate the percentage of a given number that is equal to 2/5 of that number, we must first convert the fraction to percentage form, which is as follows:
= 2/3 * 100
= 0.4 * 100
= 40%
We will use the following example to validate the aforementioned process:
Assume that it is 50.
First, 2/5 of 50 equals 2/5 * 50, or 20.
Second, 40% of 50 equals 40/100 * 50 = 0.4 * 50 = 20.
The equality of the two results is evident.
2/5 of a number is therefore 40% of that number.
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The question is incomplete;
\dfrac25 start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?
How many ounces per pound ?
16 ounces is equivalent to 1 pound. In other words, 16 ounces per pound.
What is one pound?
A weight measurement unit: The weight of one pound is roughly equal to 454 grams. A kilogram is equivalent to about 2.2 pounds. One pound contains 16 ounces.
One pound is equal to 0.4535 kilograms and is referred to as an imperial unit of mass or weight measurement.
16 ounces = 1 pound
1 pound (lb) equals 16 ounces (oz)
Pounds To Ounces Conversion Table
1 pound = 16 ounces
2 pounds = 32 ounces
3 pounds = 48 ounces
5 pounds = 80 ounces
6 pounds = 96 ounces
7 pounds = 112 ounces
8 pounds = 128 ounces
9 pounds = 144 ounces
10 pounds = 160 ounces
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What is 50%
percent of 950
Answer:
475
Step-by-step explanation:
475
(50%)%×950= 475.
have a nice day
the diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).
The demand curve graph demonstrates that when prices rise, fewer goods are demanded overall.
The link between price and quantity desired is graphically depicted by the demand curve. It demonstrates how a change in pricing affects how much of an item or service is wanted. The quantity demanded reduces when a good or service's price rises, and vice versa. The quantity demanded falls as the price rises because the demand curve is typically downward sloping. This is due to the fact that when prices are reduced, consumers are more likely to buy products and services. As the price rises, the amount demanded declines, as shown by the hypothetical demand curve that fits this pattern in the diagram to the right. This is a typical pattern observed in the actual world, which is used to guide business and economic decision-making regarding price and output.
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suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. what is the probability that the number will be more than 7 or odd? (enter your probability as a fraction.)
The probability that the number will be more than 7 or odd is 7/10.
The number more than 7 or odd is 1, 3, 5, 7, 8, 9, 10
So probability of 7 number is,
P(A) = number of favorable outcomes of an event / total number of events occurring in a sample
P(A) = 7/10
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
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The temperature was -3, 0, 2, -1, and -3 on five consecutive days. What was the average temperature for those five days?
Answer:
-1 degrees
Step-by-step explanation:
The average = sum of all values/# of values = sum of all temperatures/# of days=
(-3+0+2-1-3)/5= -1
the total cost for baydan and three of her friends to go ice skating can be represented by the expression 4x 36. the four friends pay an amount x to rent the ice skates and an admission fee. how much is the admission fee for one person?
The admission fee for one person is 9.
The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).
Intercept Form of Equation of a Line: x/a + y/b = 1.
Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.
Total cost = 4x +36
It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).
The admission fee for four people= 36
So, the admission fee for one person = 36/4 = 9
Thus, the admission fee for one person is 9.
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The admission fee for one person is 9.
The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).
Intercept Form of Equation of a Line: x/a + y/b = 1.
Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.
Total cost = 4x +36
It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).
The admission fee for four people= 36
So, the admission fee for one person = 36/4 = 9
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Please help I really do need it
Let vector a = a1i + a2j + a3k vector b = b1i + b2j + b3k and vector c = c1i + c2j + c3k be three non-zero vectors such that vector c is a unit vector perpendicular to both the vectors a and vector b. If the angle between vector a and vector b is π/6 then |a1 a2 a3 b1 b2 b3 c1 c2 c3|2 is equal toa 0b 1
The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
Vectors, in Math's, are objects which have both, magnitude and direction. Magnitude defines the size of the vector.
It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
According to the given conditions,
[tex]c1^{2}+c2^{2} +c3^{2} = 1, a.c =0, b.c=0[/tex]
and [tex]cos\frac{π}{6} = \frac{\sqrt{3} }{2} =\frac{a1b1+a2b2+a3c3}{\sqrt{a1^{2} +a2^{2} +a3^{2} } \sqrt{x=b1^{2} +b2^{2} +b3^{2} } }[/tex]
thus, a1c1+a2c2+a3c3=0 , b1c1+b2c2=b3c3=0
and [tex]\frac{\sqrt{3} (a1^{2}+a2^{2} +a3^{2} )^{1/2} (b1^{2}+b2^{2} +b3^{2} )^{1/2} }{2}[/tex] = a1b1+a2b2+a3b3
Now,
[tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right]^{2}[/tex]
= [tex]\left[\begin{array}{ccc}a1&a2&a3\\b1&b2&b3\\c1&c2&c3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right][/tex]
= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) - (a1b1+a2b2+a3b3)^{2}[/tex]
= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) -\frac{3}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
= [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
Therefore, The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]
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Rylan earns $200 for working 16 hours this week.
How much does he earn per hour?
Answer:
Rylan earns $12.50 per hour
Step-by-step explanation:
1. First start by writing the given its always easier when you're able to see the problem.
$200 = 16 hrs
$ x = 1 hr
2. Next divide
[tex]\frac{200}{16}[/tex] = 12.50
who did more one girls did 42 push ups in 6 mins a other 24 in 3 mins
Answer:
The girl who completed 42 push-ups in 6 minutes did more push-ups than the girl who completed 24 push-ups in 3 minutes.
Step-by-step explanation:
Last year, 80 students were in after-school activities. This year, 160 students participated in after-school activities.
What is the percent of change from last year to this year?
Answer:200%
Step-by-step explanation: A different way of saying that a number has doubled is by saying it has increased by 200%.
For circular motion on a circle of radius r, linear speed equals angular speed divided by r. (T/F)
For circular motion on a circle of radius r, linear speed equals angular speed divided by r. This statement is false.
What is angular speed?
The definition of angular speed is the rate at which angular displacement changes, and it is written as follows -
ω = θ/t
where θ is the angular displacement, t is the time and ω is the angular speed.
The statement says that for circular motion on a circle of radius r, linear speed equals angular speed divided by r.
Consider that an object moves around a circle of radius r at a constant speed v.
If s is the distance travelled in time t around the circle then linear speed v is defined as v = s/t.
Also if θ is the angle swept out by this object in time t then the angular speed is defined as ω = θ/t.
Thus, there is some relationship between linear speed and angular speed -
Linear speed = v = s/t
= rθ/t = r(θ/t) = rω
where is ω measured in radians per unit time and for a circle of radius r, a central angle of radians subtends an arc whose length s is s = rθ.
Hence, notice that linear speed is equal angular speed multiplied, not divided, by r.
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solve the equation for x
Answer:
x = 70 , x = 24
Step-by-step explanation:
the measure of a secant- tangent and a tangent- tangent angle is half the difference of the measures of the intercepted arcs.
9
24 = [tex]\frac{1}{2}[/tex] (118 - x) ← multiply both sides by 2 to clear the fraction
48 = 118 - x ( subtract 118 from both sides )
- 70 = - x ( multiply both sides by - 1 ) , then
x = 70
10
61 = [tex]\frac{1}{2}[/tex] (10x + 1 - (5x - 1) ) ← multiply both sides by 2 to clear the fraction
122 = 10x + 1 - 5x + 1
122 = 5x + 2 ( subtract 2 from both sides )
120 = 5x ( divide both sides by 5 )
24 = x
Two sides of the triangle abc has side ab = 22 cm and side ac = 8 cm. Compute the probable perimeter of the triangle.
The perimeter of the triangle is (30+x) cm
What is perimeter of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Perimeter is the distance around the edge of a shape.
To find the perimeter of a triangle , we add all the sides together.
Two sides are 22 cm and 8cm
Represent the other sides of the triangle by x
therefore the perimeter will be calculated as:
22+8+x
P = (30+x)cm
therefore the perimeter of the triangle is( 30+x)cm for any value of x
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Someone answer this
Answer:
I believe the answer is b??
Running bear left the village and traveled 30 miles on a heading of 30° from this point he went 50 miles on a heading of 220° how far did he end up from the village
Running Bear ended up 29.204 miles from the village.
Running Bear left the village and traveled 30 miles in a direction of 30°. Then he went 50 miles in a direction of 220°. To find out how far he ended up from the village, we need to add up the distances he traveled in both directions.
Think of it like putting two arrows end to end on a piece of paper. The first arrow represents the 30 miles he traveled at 30°, and the second arrow represents the 50 miles he traveled at 220°. The total distance from the village to the final point is equal to the length of the combined arrow.
We can represent the two displacements as vectors in a rectangular coordinate system, with the x-axis as the East-West direction and the y-axis as the North-South direction.
The first displacement, 30 miles at 30°, can be written as a vector in the x and y directions using trigonometry:
x1 = 30 cos 30° = 15
y1 = 30 sin 30° = 15
The second displacement, 50 miles at 220°, can be written as a vector in the x and y directions using trigonometry:
x2 = 50 cos 220° = -25
y2 = 50 sin 220° = -43.301
The total displacement from the village to the final point is found by adding the components of the two vectors:
x = x1 + x2 = 15 - 25 = -10
y = y1 + y2 = 15 - 43.301 = -28.301
Finally, we can use the Pythagorean theorem to find the magnitude (distance) of the total displacement:
d = √(-10)^2 + (-28.301)^2 = √851.121 = 29.204 miles
So, Running Bear ended up 29.204 miles from the village.
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Review the equation used in writing a partial fraction decomposition. Startfraction negative 15 x + 10 over (5 x minus 2) squared endfraction = startfraction a over 5 x minus 2 endfraction + startfraction b over (5 x minus 2) squared endfraction which system of equations can be used to determine the values of a and b?.
The equation used in writing a partial fraction decomposition is given as:
Negative 15 x + 10 / (5 x - 2) = a / (5 x - 2) + b / (5 x - 2).
To determine the values of a and b, we can use a system of equations. This system of equations consists of two equations, one for a and one for b. The equation for a is: Negative 15 x + 10 = a * (5 x - 2). The equation for b is: 0 = b * (5 x - 2). We can solve these equations simultaneously to get the values of a and b.
For example, if x = 1, then the equation for a becomes: Negative 15 + 10 = a * (5 - 2), which simplifies to -5 = a * 9. Therefore, a = -5/9. The equation for b becomes: 0 = b * (5 - 2), which simplifies to 0 = b * 3. Therefore, b = 0.
In summary, the system of equations used to determine the values of a and b is:
Negative 15 x + 10 = a * (5 x - 2) and 0 = b * (5 x - 2). By solving these equations simultaneously, we can get the values of a and b.
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Answer:
B!!!
Right on Edge
Step-by-step explanation:
POINTS AND BRAINLIEST
Answer:
On Monday, the baker makes 36 blueberry muffins, so the total number of muffins she makes that day is 36/0.4 = 90.
On Tuesday, the baker makes a total of 60 muffins, so the number of blueberry muffins she makes that day is 60*0.4 = 24.
when you are looking at a figure, when can you say on average? why?
When talking about a figure, you can say "on average" when you are discussing a measure of central tendencies, such as the mean, median, or mode.
This is because these measures represent the "average" point in the data set. For example, if you are looking at a figure that consists of the average monthly temperatures for a given region, the mean would be the average temperature (on average) for that region.
Similarly, if you are looking at a figure that consists of the average daily prices of a certain stock, the mean would be the average daily price (on average) for that stock. In either case, the mean is the "average" point in the data set.
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. using social media in a job search. according to inc, 79% of job seekers used social media in their job search in 2018. many believe this number is inflated by the proportion of 22- to 30-year-old job seekers who use social media in their job search. a survey of 22- to 30-year-old job seekers showed that 310 of the 370 respondents use social media in their job search. in addition, 275 of the 370 respondents indicated they have electronically submitted a resume to an employer. a. conduct a hypothesis test to determine if the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that use social media in their job search. use a 5 .05. b. conduct a hypothesis test to determine if the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer. using a 5 .05, what is your conclusion?
In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:
H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)
Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)
Where p is the true proportion of 22- to 30-year-old job seekers who use social media.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 310/370 = 0.838 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41
Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.
b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:
H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)
Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)
Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:
z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 275/370 = 0.743 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01
Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
Therefore, In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
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In case of (a) Since 3.41 > 1.64485, job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:
H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)
Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)
Where p is the true proportion of 22- to 30-year-old job seekers who use social media.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 310/370 = 0.838 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41
Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.
b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:
H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)
Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)
Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.
We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:
z = (p1 - p) / sqrt(p * (1 - p) / n)
where p1 = 275/370 = 0.743 and n = 370.
Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.
If the calculated z-value is greater than the critical value, we reject the null hypothesis.
z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01
Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.
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parallel, perpendicular,
or neither.
2. AB formed by (3, 7) and (-6, 1)
CD formed by (-6, -5) and (0, -1)
Answer: ez, the answer is Parallel
Step-by-step explanation:
because ab and cd are parallel lines
AB is formed by (3,7) and (-6, 1)
CD is formed by (-6,-5) and (0,-1)
testing the two lines are parallel or perpendicular or neither, is done by determining their gradients
Triangle AB = Gradient of AB = Triangle Y over triangle X = 1-7 over -6-3 = -6 over -9 = 2/3
Triangle CD = Gradient of Triangle CD = Triangle Y over Triangle X = -1 - -5 over 0 - -6 = 1 + 5 over 0 + 6 = 4 over 6 = 2/3
So the two lines AB and CD have the same gradient and thus the two lines are PARALLEL to each other.
What i the area of ΔABC given a = 12 in, b = 24 in, and m∠C = 26°? Round the anwer to three decimal place. 63. 125 in2
93. 156 in2
109. 808 in2
129. 426 in2
Answer: 63.125
Step-by-step explanation: I got it correct ;)
Does someone mind helping me with this problem? Thank you!
Answer:
17.6lbs
Step-by-step explanation:
If 1kg equals 2.2 lbs, therefore multiply the number of pounds per kg by 8:
2.2lbs * 8 = [17.6lbs]
Remove the outlier from Gretchen’s data set, and recalculate the mean, median, standard deviation, and interquartile range. Use the graphing tool to visualize the data.
Question
Which statements are true about Gretchen’s adjusted data set?
The data set is approximately symmetric.
The center moved closer to the center of Manuel’s data set.
The data set is skewed left.
The spread values are closer to the spread values of Manuel’s data set.
The center moved farther from the center of Manuel’s data set.
The spread values are farther from the spread values of Manuel’s data set.
The true statements bout Gretchen's adjusted data set are (1), (4), and (5).
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
It is given that:
Which statements are true about Gretchen's adjusted data set:
The options are:
The data set is approximately symmetric.
The center moved farther from the center of Manuel's data set.
The center moved closer to the center of Manuel's data set.
The spread values are closer to the spread values of Manuel's data set.
The data set is skewed left.
The spread values are farther from the spread values of Manuel's data set.
As we know,
The spread values are more similar to Manuel's data set's spread values, and the data set is roughly symmetric and tilted to the left.
The true statements are:
The data set is approximately symmetric.
The spread values are closer to the spread values of Manuel's data set.
The data set is skewed left.
Thus, the true statements bout Gretchen's adjusted data set are (1), (4), and (5).
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A restaurant charges `\$10` for each burrito and a `\$5` delivery fee. What is the total cost to have `4` burritos deliver
Answer:60
Step-by-step explanation:
10+5=15
15x4=60
For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R
a) basis is [ p , q , r . r ]
b) the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R is 3 for subspace
since the two given equation are in three variable and constants
2q -r= p -----(1)
r= q -s -----(2)
p= q +2r -----(3)
From (2):
r +s= q (+s on both sides)
s= q -r -----(4) (-r on both sides)
Substitute. (3) into (1):
2q -r= q +2r
2q -q= 2r +r
q= 3r -----(5)
Substitute (5) into (4):
s= 3r -r
s= 2r (proved)
hence subspace is [ p , q , r . r ]
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Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water, in inches, minutes after Tyler began to fill the bathtub.
B(0) = 0 Inches of depth are present 0 minutes after filling started, or at time = 0; depth = 0.
B(1) denotes the function one minute into the filling process.
B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.
7 minutes after the filling process began, the feature displays the water depth in inches.
A.) B(0)=0
B(0) = 0 indicates that the depth in inches at time = 0 and depth = 0 is 0 minutes after filling started.
B.) B(1) (1) B(1) denotes the function one minute into the filling process.
C.B(9)=11
B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.
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the marked price of an article is 2080. After allowing d% discount and levying (d-2)% VAT, the cost of the article becomes Rs. 1997.84. Find the discount amount and VAT amount
The vat rate is 13%
What is vat rate?
Vat rate is a consumption tax assessed on the value added in each production stage of a good or service.
Given:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)Add VAT:
2080*(1 - 0.01d) + (d - 2)%2080*(1 - 0.01d) * (1 + (d -2)/100)2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84(1 - 0.01d)(0.98 + 0.01d) = 1997.84/20800.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605- 0.0001d² + 0.0002d + 0.98- 0.9605 = 00.0001d²- 0.0002d - 0.0195 = 0d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Then
VAT rate = 15 - 2 = 13%
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4. ) Jennifer has a new sister named Chloe. Jennifer's mom, who
is a pediatrician, has been tracking Chloe's growth. Assume that
Chloe's growth rate is constant.
d. Use the information from parts(c) and (d) to write an equation representing Chloes growth rate. Let y= height in cm and x= age in months.
c. Use your equation to predict Choles height at 2 years old
The equation for Chloe's growth rate would be y = ax + b, where a is the rate of growth in cm/month and b is the height at age 0.
To predict Chloe's height at two years old, we can plug in x = 24 (representing two years, or 24 months) into the equation.
We would then get y = 24a + b,
Which is Chloe's predicted height at age two. This equation gives us a simple way to predict Chloe's height at any age, as long as we know her rate of growth and her height at age 0.
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plis help
Is (1, 10) a solution to this system of equations?
y = 9x + 1
y = x + 8
yes or no?
The solution to the system of equations is x = 7/8 and y = 71/8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equations be represented as A and B
Now , substituting the values in the equation , we get
y = 9x + 1 be equation (1)
y = x + 8 be equation (2)
On simplifying the equations , we get
x + 8 = 9x + 1
Subtracting x on both sides of the equation , we get
8x + 1 = 8
Subtracting 1 on both sides of the equation , we get
8x = 7
Divide by 8 on both sides of the equation , we get
x = 7/8
Substitute the value of x in the equation (2) , we get
y = 7/8 + 8
y = 71/8
Hence , the equations are solved and the solution is ( 7/8 , 71/8 )
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