Simon drives 75 km at an average speed of 120 km/h and then 9 km at 70 km/h without stopping. What is the average speed for the whole journey to 1 dp?​

Answer:

  tan(θ) = 2/3

Step-by-step explanation:

You want the tangent of the angle θ between the x-axis and the line connecting the origin to point (3, 2).

The tangent ratio is given by ...

  Tan = Opposite/Adjacent

In the attachment, you can see that the side opposite the angle of interest is the y-coordinate of the point. The side adjacent is the x-coordinate. That means ...

  tan(θ) = y/x

  tan(θ) = 2/3

__

Additional comment

In general, the tangent of the angle a line makes with the x-axis is the slope of the line. Your line has slope 2/3, and that is the tangent of the angle it makes with the x-axis.

Answer:d

Step-by-step explanation:

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

Given,

Number of smokers; Sample size, n = 40

Mean of the sample, μ = 172.5

Standard deviation, σ = 119.5

We have to find the 90% confidence interval estimate of the mean cotinine level of all smokers.

Here,

The confidence interval is given as;-

x − E < μ < x + E

E is the margin of error.

Margin of error,

E = zα/₂ σ/√n

E = 1.644854 119.5/√40

E = 31.07887

Then,

The confidence interval is;

x − E < μ < x + E

141.4211 < μ < 203.5789

That is,

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

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The value of x in the inverse variation is  x = 4

Inverse variation is express mathematically by; y = k/x

where,  y and x = variables

k = constant of variation

We solve for 'x' in the variation using standard form for inverse variation:

y = k/x

Given; y = 3, x = 24

We now use the given information to find k.

Step 1: Substitute the given in to equation y= k/x; to

3 =k/24

Cross multiply

k = 3 * 24

k = 72

Step 2; The inverse relation for is y = 72/x since we have gotten k=72

For y = 18, we get

18 = 72/x

Cross multiply

18x = 72

x = 72/18

X=4

Therefore, the value of  x = 4.

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Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Step-by-step explanation:

Took the test

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Answer:

m∠5 = 91° (sorry if i got it wrong i tried my best)

Answer:

9.47

Rounded to the nearest 0.01 or

the Hundredths Place.

Explanation

9.4725

You rounded to the nearest hundredths place. The 7 in the hundredths place rounds down to 7, or stays the same, because the digit to the right in the thousandths place is 2.

9.47

When the digit to the right is less than 5 we round toward 0.

9.4725 was rounded down toward zero to 9.47

Hope this helps!

The car B was 10 miles east of Car A.

A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.

Where A and B are the coefficient and C is the constant.

Speed of car A = 45 miles per hour and the direction of car A is East.

The distance of car B from Johnstown after 2 hours is 100 miles, east

The distance of car B from Johnstown is given on the graph.

So , the initial distance of car A from Johnstown will be,

= 100 - 2 × 45

=100 - 90

= 10 miles

As seen from the graph, the initial distance, east, of car B from Johnstown is 20 miles.

So, the difference between the cars will be 20-10= 10 miles that means car B was 10 miles east of Car A.

Therefore, the car B was 10 miles east of Car A.

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it's 23% because 46 (ppl who do not like running but like swimming) divided by 200 (the total for everything) is 0.23 which is 23%

Answer:

Line A and C

Step-by-step explanation:

The perpendicular slope of another line is the negative reciprocal of the other slope.

For example, we have line [tex]x_{1}[/tex].

y = x

The line that is perpendicular to it is:

y= [tex]-\frac{1}{x}[/tex]

Lets tranform all of these equation to slope intercept form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Divide 2 on both sides to simplify line a into slope intercept form.

[tex]\frac{2y}{2} = \frac{8x+10}{2}[/tex]

Simplify.

y = 4x + 5

Now it is in slope-intercept form. Slope of 4 and y-intercept of 5.

Line B

Isolate y on both sides by subtracting 3x on both sides.

6y + 3x - 3x = 12 - 3x

6y = 12 - 3x

Divide 6 on both sides.

[tex]\frac{6y}{6} = \frac{-3x+12}{6}[/tex]

Simplify.

y = -1/2x + 2

Now it is in slope-intercept form. Slope of -1/2 and y-intercept of 2.

Line C

Divide both sides by 8.

[tex]\frac{8y}{8} = \frac{-2x-16}{8}[/tex]

Simplify.

y = -1/4x - 2

Line A has a slope of 4. Line C has a slope of -1/4x. Line C is the negative reciprocal of Line A as multiplying Line A by -1 and flipping the fraction simple gets you Line C. (and vice versa).

The measure of angle ABD is 118 degree.

An equation is an expression that shows the relationship between two or more numbers and variables.

WE have been given that the angles are;

(3x +10)° and 2x

WE need to solve the value of x then we use the linear pair;

(3x +10)° + 2x = 180

Solving;

(3x +10)° + 2x = 180

5x + 10 = 180

5x = 180 - 10

5x = 170

x = 36

Angle ABD = (3x +10)° = 3(36) + 10

= 108 + 10

= 118

Hence, the measure of angle ABD is 118 degree.

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The required solution to the given expression is 2 - 6y/x which is determined by the distributive property of multiplication.

The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.

The expression is given in the question

⇒ (y² - 3y³x⁻¹)2m°y⁻²

∵ m° = 1

⇒ (y² - 3y³x⁻¹)2y⁻²

Apply the distributive property of multiplication,

⇒ y² × 2y⁻² - 3y³x⁻¹  × 2y⁻²

⇒ 2y²⁻²- 6y³⁻²x⁻¹

⇒ 2y° - 6y x⁻¹

∵ y° = 1 and x⁻¹ = 1/x

⇒ 2 - 6y/x

Therefore, the required solution to the given expression is 2 - 6y/x.

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The diagram which represents Mason's ratio of made throws and missed throws in the story is option A.

The following are answers to like terms collected respectively

The following expressions are equivalent

If Mason made 20 free throws

Equate missed throws ratio made throws

2 : 5 = x : 20

2/5 = x/20

cross product

2 × 20 = 5 × x

40 = 5x

divide both sides by 5

x = 40/5

x = 8

Total free throws Mason attempted = Number of throws Mason missed + Number of throws Mason made

= 8 + 20

= 28 free throws

If Jennifer made 16 bracelet with neon

Equate neon made bracelet ratio pastel made bracelet

4 : 3 = 16 : x

4/3 = 16/x

cross product

4 × x = 3 × 16

4x = 48

divide both sides by 4

x = 48/4

x = 12

Combine the like terms

4d + 5d

= 9d

8r + 6 + 9r - 3

= 8r + 9r + 6 - 3

= 17r + 3

6r - r + 4

= 5r + 4

Determine if the following expressions are equivalent

3 + 4 = 2 + 5

7 = 7

4(2 + x) = 8 + 4x

8 + 4x = 8 + 4x

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The dimensions of the dumpster that will minimize its surface area are Length = 4.43 yds ,Width  = 2.215 yds and Height  = 2.956 yds

since l = 2w.

Now, the formula for a cube's surface area is;

S = 2lw + 2lh + 2wh.

Changing 2w to l yields;

S = 4wh + 4w² + 2wh.

S = 4w² + 6wh

in the meantime, the formula for a cube's volume is;

V = lwh

add 2w for l to receive;

V = 2w²h

h = V/2w²

In the SA equation, substitute V/2w² for h to get;

SA = 4w² + 6w(V/2w²)

SA = 4w² + 3V/w

V is stated to equal 29 yd3.

Thus;

S = 4w² + 87/w

Let's find the first derivative of S as we want to reduce the surface area;

S' = 8w - 87/w²

At S' = 0;

8w - 87/w² = 0

8w = 87/w²

w³ = 87/8

w = ∛(87/8)

w = 2.215 yds

L = 2 x 2.215= 4.43

since, l = 2w.

l = 4.43 yds

h = V/2w²;

h = 29/(2 × 2.215²)

h = 2.956 yds

Hence, The dimensions of the dumpster that will minimize its surface area is l = 4.43 yds, w = 2.215 yds and h = 2.956 yds

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The length of time till the value of the car is at $9, 600, given the depreciation rate of the car per year is 7.98 years.

The car started off with a value of $17, 500, which was its purchase price. The length of time till the car is is $9, 600 can be found by using the NPER function on spreadsheet. This function shows the length of time till a value becomes another value.

The figures going into the formula are:
Rate = -7.25%

PV = $17, 500

FV = $9, 600

The number of years for the car to depreciate would be 7.98 years.

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Answer:

hello as midpoint is (4,-3)

and an ending point is (8,-5)

there are 4x and 2y among them

so you need to subtract 4x and 2y from the midpoint

which the answer is going to be (0,-1)

i.e. C option

good luck

Answer:

[tex]y=-\frac{1}{3}x +4[/tex]

Step-by-step explanation:

slope= 1-7/9- -9= -1/3

y-intercept: 7 = -1/3(-9)+b, b=4

Answer: -4

Step-by-step explanation:

The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are two figures is shown in figure.

Now,

In first figure;

By using definition of proportional as;

⇒ 4 / 2 = 6 / (x - 2)

Solve for x as;

⇒ 2 (x - 2) = 6

⇒ x - 2 = 3

⇒ x = 3 + 2

⇒ x = 5

Thus, The value of variable in first figure will be;

⇒ x = 5

In second figure;

By using definition of proportional as;

⇒ y / 6 = 12 / 9

Solve for y as;

⇒ y / 6 = 4 / 3

⇒ y = 4 x 6 / 3

⇒ y = 24 / 6

⇒ y = 4

Thus, The value of variable in second figure will be;

⇒ y = 4

Therefore, The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

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The strategy for different scenarios are;

a) Voluntary response

b) Poor sampling

c) Stratified sampling

d) Stratified sampling with follow-up

Given Information;

The school board is debating whether to implement a new rule that would require primary pupils to pass a test in order to advance to the next grade in a large city school system with 20 elementary schools. The pta is interested in learning whether parents support this strategy. Here are a few of the suggestions made for data collection. Indicate the type of sampling technique being used for each and any potential biases that might arise.

a) If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter?

→ Only those who volunteer to answer will participate so, bias is due to the use of a voluntary response sample.

b) If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?

→ If we choose just one school, then the answers may not be independent, so under-coverage bias due to a poor sampling frame.

c) Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?

→ As there are natural groups, and we get a sample from each group, then it is stratified sampling.

d) randomly select 20 parents from each elementary school. send them a survey, and follow up with a phone call if they do not return the survey within a week.

→ Stratified sampling with follow-up, should be unbiased.

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Answer:

Step-by-step explanation:

-19y=-13x -14 to y=-13/-19 - -14/-19

Random sampling: It is a type of probability sampling in which the researcher randomly selects a subset of participates from the population.

Biased Sample: Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower and higher sampling probability than other.

The population generalized in this case, is almost random, the only problem here is that people that want to participate will participate so is likely that the sample is not totally randomized and that there is huge number of people that regularly exercises.

b) This case is less random than the previous , here all the people in the sample regularly do exercise and these people can choose is they prefer to work with a partner or not. So the sample is biased.

In method 01 we can conclude that the result apply to the whole population , whole in method 02 we can't conclude that just because the sample is biased.

Method 01: - Recruit volunteers who are willing to participate. Randomly assign each participate to exercise with a training partner or exercise alone.

So there are people who wants to participate but people don't necessarily do exercise normally day to day life. People also can't choose to work out in a team or alone.

Method 02:  Select a random sample of people from all the people who exercise at a community fitness center. ask each person in the sample whether they use a training partner, and use the response to create the two groups.

The members in the sample are people who exercises regularly and we ask them if they work alone or with a partner then, we create two groups. so this is more biased sample.

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The following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the equation is,

y − 8 = 15 (x + 5)

y=15(x+5)+8

y=15x+75+8

y=15x+83

A linear equation has the form y = mx + b in the slope-intercept format.

Thus, the following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

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Answer:

26

Step-by-step explanation:

18 + (6 - 2) x 2

18 + (4) x 2

18 + 8

= 26