four vehicles are traversing a 1-km segment of a highway and the following observations are made: vehicle a: 1.2 min vehicle b: 1.5 min vehicle c: 1.7 min vehicle d: 1.4 min what is the space-mean speed?

The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³ thus option (C) will be correct.

Density or mass density is the mass of any object per volume.

For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.

Density can be uniform or non-uniform.

Density is the division of mass and volume and the mass must be for the quantity of the volume only.

Given that,

Mass = 10 g

Volume = 2.5 cm³

Density = 10/2.5 = 4 g/cm³

Hence "The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³".

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The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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Answer: 1,2L

Step-by-step explanation:

10 cm ------------ 0.75 L

16 cm ------------ ?

?= (16 x 0.75) : 10

?= 12 : 10

?= 1,2 L

The equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

In this question we have been given a point (6, 3) and slope m = 2

We need to find an equation of line passing through (6, 3) with slope m = 2

Using formula of the point-slope form:

(y - y1) = m(x - x1)

(y - 3) = 2(x - 6)

y - 3 = 2x - 12

y = 2x - 12 + 3

y = 2x - 9

This is slope-intercept form of equation of line.

slope = 2

y-intercept = -9

Therefore, the equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

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The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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There would be 1024 possible outcomes on a 5 question test with each question having 4 possible answers.

Based on the given information, there are 4 possible ways for each of the 5 questions.

4 possible ways to answer Question # 1

4 possible ways to answer Question # 2

4 possible ways to answer Question # 3

4 possible ways to answer Question # 4

4 possible ways to answer Question # 5

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is

4 x 4 x 4 x 4 x 4 = 1024

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By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.

The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.

Then let us round each of the given fiqures into 1 significant fiqure as instructed:

6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated

21.5 to 1 significant figure will be  20

Then (6000*20) =120000

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The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

Both t tests and F tests (also known as analyses of variance, or ANOVAs) are based on the premise that the population variances (i.e., the distribution, or "spread," of scores around the mean) of two or more samples are identical. The independent samples t-test and ANOVA employ the t and F statistics, which, provided that group sizes are equal, are often resistant to breaches of the assumption. A ratio of less than 1.5 between the largest and smallest group can be used to identify equal group sizes.

The independent samples t-test and ANOVA make the assumption of homogeneity of variance, which states that all comparison groups have the same variance. The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

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Slope between the points (-10, 5) and (14,-3) is -1/3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find slope between points (-10, 5) and (14,-3)

m=-3-5/14+10

m=-8/24

m=-1/3

Hence, slope between the points (-10, 5) and (14,-3) is -1/3.

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With the help of probability we can say that there are 1140 ways.

acc to our question-

Hence,we can say that there are 1140 ways.

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Answer:

2,156 A. 21.56

Step-by-step explanation:

Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

The equations are

3(x+2) = 18

x + 2 = 6

Part A

Consider the first equation

3(x + 2) = 18

Divide both side of the equation by 3

3(x+2) / 2 = 18/3

x + 2 = 6

We will get equation B from equation A, if we divide both side of the equation by 3

Part 2

The first equation

3(x+2) = 18

x + 2 = 6

x = 6-2

x = 4

The second equation

x+2 = 6

x = 6-2

x = 4

Both the equation has same solution

Hence,

Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

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A monomial function that has a minimum value is y = 5x^10

In this question, we have been given four monomial functions.

y = 5x^10

y = -4x^11

y = -x^12

y = 6x

we need  to find a monomial function that has a minimum value.

For function y = 5x^10, as x > 0 increases, f(x) increases. And as x < 0 decreases, f(x) increases.

We know that for even, positive monomial function if coefficient > 0 and exponent is even then a monomial has a minimum value.

Therefore, a monomial function that has a minimum value is y = 5x^10

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The total number of athletes, the football club has is 180.

Given, In the football club, 36 footballers are Latvian, while there are 4 times the footballers of other nationalities.

as, footballers that are Latvian = 36

now, footballers of other nationalities = 4×36

footballers of other nationalities = 144

so the total number of footballers = 144 + 36 = 180

Therefore, the total number of athletes, the football club has is 180.

Hence, the total number of athletes, the football club has is 180.

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When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

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The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the​ population, A, of a country in​ millions, t years after 2003.

The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.

Here,

A = 384. 7e^0. 018t

513=384. 7e^0. 018t

513/384.7= e^0.018t

ln(513/384.7) = 0.018t

ln(513/384.7)/0.018 =t

t=15.9895575229 years

t=16 years

2003+16= 2019

In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.

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Answer:

39.94

Step-by-step explanation:

Ask? :)

Answer:40,000        porque dice que redondees a la centecima mas cercana              

In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.

A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.

Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.

Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.

We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.

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Blair received 15 bars as the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients.

The weighted average is calculated by adding up all the variables, multiplying by their weight, and dividing by the sum of the weights. Instead of treating each item equally, a weighted average or mean multiplies each item being averaged by a number based on its relative importance. The weights or weightings correspond to including that many comparable items of the same value in the average.

Here,

The average weight of the bars given to Brennan (light), Blair, and Maya was higher than the average weight of the bars given to the other two recipients (heavy).

Let X represent the combined weight of all the bars.

The weight of the bars Brennan was given was equal to 45% of X, or 0.45X.

Maya was given bars that weighed 26% of X, or 0.26X.

The weight of the bars Claire was given was the rest, or 29% of X, or 0.29X.

Brennan received bars with an average weight of 0.45 x/ 24.

The weight of the Maya-received bars, on average, is 0.26X/13.

Similar to the previous example, if Blair receives B bars, then their average weight is 0.29X/B.

Similarly, the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients. So blair received 15 bars.

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Answer:

50

Step-by-step explanation:

The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.

What is the slope of a line?

The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis. It signifies the rise in the y-variable for a unit change in the x-variable.

If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).

(2, 3) representing the purchase by Logan,

(5, 7.5) representing the purchase by Lin,

(3, 4.5) representing the purchase by Chita.

The unit price can be calculated by the slope of the line;

m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.

Hence, The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.

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Answer:

The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.

Answer:

L=12, W=6

Step-by-step explanation:

L=2W

(L+2L)=36

3L=36

2L=12

L=6

Answer:

The slope of y = 5x - 4 is 5.

Notice that the equation, y = 5x - 4, of the line is written in the form y = mx + b. Thus, it is in slope-intercept form. When the equation of a line is in slope-intercept form, we know that the slope of the line is equal to m, the coefficient of x.

In y = 5x - 4, the coefficient of x is 5. Thus, the slope of the line, y = 5x - 4, is 5.

The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.

The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.

Amount needed for vacation = $50 USD = $7,740 JMD

Each souvenir is priced at 200 Jamaican dollars.

One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.

50 US dollars = 154.8 × 50

= 7,740 Jamaican dollars

Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir

= 7,740 Jamaican dollars ÷ 200 Jamaican dollars

= 38.7 souvenirs.

As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.

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Answer:

y = -5/3 - 3

Step-by-step explanation:

Since it's given a graph, we can use rise over run to figure it out

We pick 2 points that are integers on the graph , which means two points on the graph that the line goes through

Example- I picked (-3, 2) and (0, -3), you can indicate them so you don't forget or anything

We now draw a triangle formed by those two points (a line that goes from (-3, 2) to (-3, -3) and a line from (0, -3) to (-3, -3)

Rise (Which is the height of the triangle you just drew) is 5 units, but it's going down, so -5

The base (Run) is 3 units. Using rise/run, the slope is -5/3

The y-intercept, which is at the point where the graph crosses the y-axis, is -3.

The slope intercept form is y=mx+b, where m = slope and b = y-intercept, so the equation of the graph is y = -5/3x -3

The inequality describing oil and tyre change within 180 minutes is 3x + 4y > 60.

Taking each information seperately followed by summing them for a complete equation.

1 oil change taken amount of time = 9 minutes

So, x oil change will take amount of time = 9x

Similarly, y number of tire changes will take amount of time = 12y

Adding these values to form the equation -

Number of oil and tyre changes in less than 180 minutes

Keep the value of each and symbol for 'less than'

9x + 12y > 180

Dividing the inequality by 3

3x + 4y > 60

Hence, the required inequality is 3x + 4y > 60.

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We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

L.H.S=(cosA−sinA+1)/(cosA-sinA-)

dividing by sinA

=cotA+1−cosecA/cotA−1+cosecA

​=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A

=(cotA+cosec)²-1/2cotA

=cotA+cosecA(R.H.S)

​Hence the above trigonometric function is proved.

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When one lists their ages and their heights as ordered pairs (age, height), the statement that is true is D. It is both a relation and a function.

A relation between two sets is a collection of ordered pairs that each contain one object from the other set. If the ordered pair (x,y) is in the relation and the object x is from the first set and the object y is from the second set, the objects are said to be related. A relation is a type of function.

A function is a relation that states that there should be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be associated with only one y-value.

It should be noted that based on the information, only one value can be attributed to each person. Therefore, the correct option is D.

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