Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

The solution to the initial value problem is:y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t).

The characteristic equation of this linear second order ordinary differential equation is:

m^2 - 2m + 5 = 0

The roots of this characteristic equation are m = 1 ± 2i, which means the general solution to the homogeneous equation is:

y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t)

To find the particular solution, we can use the method of undetermined coefficients and guess that yp(t) = Ae^(-t) cos(2t) + Be^(-t) sin(2t).

Substituting this into the differential equation, we get:

2Ae^(-t) cos(2t) - 2Ae^(-t) sin(2t) + 5Ae^(-t) cos(2t) - 5Be^(-t) sin(2t) = 12e^(-t) cos(2t)

Comparing coefficients, we have:

2A - 2A + 5A = 12

7A = 12

A = 12/7

-5B = 0

B = 0

So the particular solution is:

yp(t) = (12/7)e^(-t) cos(2t)

The general solution to the non-homogeneous equation is then:

y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t) + (12/7)e^(-t) cos(2t)

Using the initial conditions, we can find the values of c1 and c2:

y(0) = 10 = c1 + (12/7)

c1 = 10 - (12/7)

y'(0) = 0 = c2e^(0) sin(0)

c2 = 0

Therefore, the solution to the initial value problem is: y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t)

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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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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:

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]

Answer:60

Step-by-step explanation:

10+5=15

15x4=60

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.

The solution to the system of equations is x = 7/8 and y = 71/8

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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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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The true statements bout Gretchen's adjusted data set are (1), (4), and (5).

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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The perimeter of the triangle is (30+x) cm

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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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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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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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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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

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

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

Answer:

I believe the answer is b??

Answer: 63.125

Step-by-step explanation: I got it correct ;)

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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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 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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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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Answer:324234

Step-by-step explanation:

Answer:

The mean of the data set is 7.

2 + 9 + 10 + 6 + 8

= 35

35 ÷ 5

= 7

Step-by-step explanation:

You're welcome

The vat rate is 13%

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:

Add VAT:

d² - 2d + 195 = 0

Solving the quadratic equation we get:

d = 15

Then

VAT rate = 15 - 2 = 13%

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Answer:200%

Step-by-step explanation: A different way of saying that a number has doubled is by saying it has increased by 200%.

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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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.

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:

A function statement is contained within the function block. A function block is a set of instructions within a program that defines what the function should do when it is called.

It is generally surrounded by curly braces and contains one or more lines of code.

A function statement usually contains a formula and calculation. The formula is an expression that specifies the calculation that should be performed when the function is called. The calculation is the result of the formula, which is the value that will be returned when the function is called.

For example, if we have a function that calculates the area of a circle, the formula might be A = πr^2 and the calculation would be A = 3.14 * r^2. The formula describes how the area of a circle is calculated and the calculation is the result of that formula. When the function is called, the calculation will be performed and the result will be returned.

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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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