At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours. Find the average speed of the lorry on the return journey.​

Answer: They will each get 6 and there will be 1 left over.

Step-by-step explanation:

6*4 is 24. 25-24=1

a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073

A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.

Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.

μ=22

σ=2

X≈N(22,2)

a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)

=1-P(Z≥2)

=1-P(Z<2)

=1-0.97725

=0.02275

b) Let a is the 71th percentile of X,

P(X≤a)=0.71

P((X-μ)/σ)≤(a-μ)/σ)=0.71

P(Z≤z)=0.71

From the standard normal table by calculating with z value, we get

a=24.073

Therefore,

a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073.

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according to the question

given data in the question,

the type of sample-

random stratified sampling

The usage of satisfied sampling may be required for a variety of distinct features.

The population is first split into two or more strata or subgroups in this kind of random sampling. Beginning with the sampling procedure, each unit is assigned to one stratum based on the unit's historical performance. Following that, separate random samples are chosen using a basic random sampling technique from each stratum, which contains a percentage of the population. that is, they are both mutually and jointly exhaustive.

The traits that we are evaluating are distinct from those of members of another stratum and similar to those of the sample unit stratum.

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the type of sample that proportionately reflects the relevant diversity of opinions in the population from which it is drawn is random stratified sampling

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

The sample size in statistics is a measurement of the total number of samples utilized in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It's also known as sample statistics.

Considering the query

the information in the query

a sample's type-

stratified sampling at random

For a number of unique traits, satisfied sampling may be necessary.

In this type of random sampling, the population is initially divided into two or more strata or subgroups. Each unit is categorized into a stratum at the start of the sampling process depending on its prior performance. A basic random sampling approach is then used to select distinct random samples from each stratum, which represents a portion of the population. they are mutually and jointly exhaustive, in other words.

The characteristics that we are examining are different from those of members of one stratum and comparable to those of the stratum that contains the sample unit.

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The required value of PQ is 18.5 inches in the given triangle PQR.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

As per the given question, let's call the length of side PR (the hypotenuse). Since we know that PR = 37 inches and angle R = 30°, we can use the sine rule to write the following equation:

sin R = perpendicular/hypotenuse

sin R = PQ/PR

sin 30° = PQ/37  

1/2 = PQ/37  

PQ = 37/2

Apply the division operation, and we get

PQ = 18.5

Therefore, the required value of PQ is 18.5 inches.

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In a triangle PQR, right-angled at Q, PR = 37 inches and angle R =

30°. Find: PQ

The equation of the line passing through point P(4,-6) and perpendicular to the line y = -3 is x = 4.

A number that identifies the direction and steepness of a line is its slope or gradient. The slope of the straight line is written as y=mx+c where m is the slope and c is the y-intercept.

Given the equation of a line is y = -3 and point P(4,-6).

From the given equation, we can say that y is a horizontal line. The line perpendicular to this horizontal line will be a vertical line. The equation of the line perpendicular to y is of the form x = n where n is the x-coordinate of the point passing through this line.

Here, the x-coordinate is 4 from the point (4,-6). Then, the required line is x=4.

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Answer:

I'm sorry I can't really help but I'll try. I'm only a middle schooler T^T.

The diagram that models the ratio in the story is circled on the image given at the end of the answer.

If the students used 12 rolls of blue streamers, the number of rolls of yellow streamers that the students used was of:

8 rolls.

A ratio between two amounts a and b is given by the division of the amount a by the amount b.

The group used 3 rolls of blue paper streamers for every 2 rolls of yellow paper streamers, hence the ratio is given as follows:

blue streamers/yellow streamers = 3/2.

If the students used 12 rolls of blue streamers, the amount of yellow streamers is found applying the proportion as follows:

12/x = 3/2.

Applying cross multiplication, we have that:

3x = 2 x 12

3x = 24

x = 24/3

x = 8 rolls of yellow streamers.

The problem is given by the image shown at the end of the answer.

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The vertex of the absolute function g(x) = − |x + 3| − 4 will be at (-3, -4).

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as,

f(x) = | x - h| + k

The function is given below.

g(x) = − |x + 3| − 4

The vertex of the absolute function g(x) = − |x + 3| − 4 will be at (-3, -4).

The absolute function is drawn below.

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Answer:

Q+R+S=180

30°+R+129°=180

R=180-159

R=21..

is the answer

Consecutive integers are a set of positive whole numbers which follows one another respectively. Thus the required proof to the question is as explained below:

The theorem states that:[tex]/hypotenuse/^{2}[/tex] = [tex]/adjacent/^{2}[/tex] + [tex]/opposite/^{2}[/tex]Thus a set of consecutive numbers which represent each side of a right angled triangle must obey the Pythagorean theorem.

Consecutive integers are a set of positive whole numbers which follows one another respectively. Examples are; 20, 21 and 22, 2, 3 and 4 etc.Therefore, the three consecutive integers that are also Pythagorean tribble are 3, 4 and 5.

So that let the adjacent side be 3, and the opposite side 4, then;[tex]/hypotenuse/^{2}[/tex] = [tex]/adjacent/^{2}[/tex] + [tex]/opposite/^{2}[/tex]                       = [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16                       = 25

hypotenuse = [tex]\sqrt{25}[/tex] = 5

Therefore the common three consecutive integers that are Pythagoras tribble are 3, 4 and 5.

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Answer:

Step-by-step explanation: 1/2 is the slope of the line

Applying the trend in the table the population in 2023 is predicted to be

Exponential function  is a type of function that are of 3 main parts

Considering the given problem,  f(x) = 80(b)^x

the starting = 80

the base = b

the exponents = x

f(x) = 80(b)^x using the table again

132 = 80b

b = 132/80

b = 1.65

after 2023 the exponents will be

x = 2023 - 2016

x = 7

The predicted population

= 80(b)^x

= 80(1.65)^7

= 2898

the predicted population is 2898

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x = - 3 / 4Y

y = - 117 + 4Y / 9

Slope-intercept form with slope and y-intercept can be written as y = mx + b.

The slope-intercept form of a straight line is one of the most common ways to show the equation of a line. The slope-intercept formula can be used to derive the equation of a line when the y-intercept and slope of the straight line are known.

Consider a straight line with y-intercept "b" and slope "m." The slope-intercept form equation of a straight line is given by y = mx + b. For example, the equation of the line with a y-intercept = 5 and slope = -1 is written as y = -x+5.

When two points (x1, y1) and (x2, y2) are given, then the slope-intercept form is written as (y2 - y1)/(x2 - x1).

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Answer:

See below.

Step-by-step explanation:

We can find three points by picking values of one of the variables and calculating the other.  I'll pick a few values of x:  -2, 0, 2, 4.  Now calculate the values of y with the equation x-y = 0.  We can rearrnage this to -y = -x, or y = x.  This tells us that y equals x, so the data points would be:

(-2,-2)

(0,0)

(2,2)

(4,4)

Plot these points on graph paper and then draw a straight line through them.  Or use an online graphing utility, such as the free DESMOS.  The graph is attached.

Steady state vector represent the long term market share of both groceries i.e WB and ZA. The long term market share of ZA is 0.727...

The steady-state behavior of a Markov chain is the long-term probability that the system is in each state. In other words, no matter how many transitions are applied to the system, it does not affect the state vector.

We have, WB and ZA are two competing grocery stores.

Probability that a customer who shops this week at WB will shop again here next week , p₁= 64% = 0.64

Probability(not shop again from WB) = 1-p₁

= 1 - 0.64 = 0.36

Probability that a customer who shops this week at ZA will shop again here next week , p₂ = 76% = 0.76

P(not shop again from ZA) = 1- p₂= 1 -0.76

= 0.24

Let market share of WB and ZA be "x" and "y" respectively, So, steady state vectors , s = [x y]

and x + y = 1 ---(*)

The Transition matrix, P=[1- p₁ p₁ ; 1-p₂ p₂]

P = [ 0.36 0.64 ; 0.24 0. 76 ]

we have to determine the value of x and y . So, we solve the following matrix equation, s[ I - P] = 0

matrix where I is identity matrix of 2×2

=> s([ 1 0 ; 0 1 ] - [0.36 0.64 ; 0.24 0. 76 ] ) = [0 0 ; 0 0 ]

=> s[1- 0.36 0- 64 ; 0 - 0.24 1 -0.76]

=[0 0 ; 0 0]

=> s[ 0.64 - 0.64 ; - 0.24 0.24] = [0 0;0 0]

=> [ x y] [0.64 -0.64 ; -0.24 0.24] = [0 0; 0 0]

Matrix multiplication,

=> [ 0.64x - 0.24y ; - 0.64x + 0.24y ]

= [ 0 0 ; 0 0]

equating the LHS and RHS

0.64x - 0.24y = 0 --(1)

- 0.64x + 0.24y = 0 --(2)

If we multiply equation (1) by -1 then we get equation(2). So, both equations are identical and we can collpase them in one equation for further calculation. Now, we have to equations

0.64x - 0.24y = 0 --(3)

x + y = 1

we can solve these equations either matrix method or substitution. We use here substitute

x = 1- y in equation (3) we get

0.64x - 0.24y = 0=> 0.64(1 - y) - 0.24 y = 0

=> 0.64 - 0.64y - 0.24 y = 0

=> 0.64 = 0.88y

=> y = 0.64/0.88 = 8/11 = 0.727

from equation (*) , x = 1 - 8/11 = 3/11 = 0.272

So, Market share of grocery ZA is y i.e 0.727.

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Unit Rate: 3

11 movie tickets: $33

Step-by-step explanation:

$24/8 = 3

The unit rate is 3

3 x 11 = $33

$33 for 11 movie tickets

By using the concept of conversion of unit, it can be calculated that

There are 12075 milligrams in 12 grams 75 milligrams

What is conversion of unit?

The process of changing a value from one unit to the equivalent measurement in other unit is called conversion of unit.

Conversion of unit is a very important tools and is very much required in physics, maths and chemistry.

There are 1000 milligrams in 1 gram.

In 12 grams 75 milligrams, number of milligrams = [tex]12 \times 1000 + 75[/tex]

                                                                                = 12075 milligrams

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410 milliliters of compound A needed to make 902ml of the drugs.

the link between two or more things in terms of quantity, amount, or size.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

We know the ratio of A to B is 7:4

let x = the multiplier

then

7x = amt of compound A

and

4x = amt of compound B

7x + 4x = 902

11x = 902

x = 902/11

x = 82 is the multiplier

therefore

5(82) = 410 milliliters of compound A needed

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Answer:

Those must-haves should include food, clothing, housing and insurance. And it also should include emergency and retirement savings, Luber said.

Step-by-step explanation:

hope this helped:)

brainliest for the brains:)

a) The height of the rectangular shower stall is ( 3x - 2 )

b) The volume of the shower stall when x = 4 is 240 feet³

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

a)

Let the width of the rectangular shower stall be W = x

Let the length of the rectangular shower stall be L = ( x + 2 )

Let the height of the rectangular shower stall be H = H

Now , the equation will be

The volume of the rectangular shower stall is V = 3x³ + 4x² - 4x

And ,

Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

3x³ + 4x² - 4x = x ( x + 2 ) H

On simplifying the equation , we get

3x³ + 4x² - 4x = ( x² + 2x ) H

Dividing by ( x² + 2x ) on both sides of the equation , we get

H = ( 3x - 2 )

Therefore , the value of L is ( 3x - 2 )

On substituting the value for H in equation for volume of rectangular stall ,

Volume of rectangular shower stall = x ( x + 2 ) ( 3x - 2 )

Volume of rectangular shower stall = ( x² + 2x ) ( 3x - 2 )

Volume of rectangular shower stall = 3x³ + 4x² - 4x

Therefore , the height of the shower stall is ( 3x - 2 )

b)

The volume of rectangular shower stall = 3x³ + 4x² - 4x

when the value of x = 4

Substitute the value for x = 4 in the equation , we get

Volume of rectangular shower stall = 3x³ + 4x² - 4x

Volume of rectangular shower stall = 3 ( 4 )³ + 4 ( 4 )² - 4 ( 4 )

Volume of rectangular shower stall = 3 x 64 + 4 x 16 - 16

Volume of rectangular shower stall = 192 + 64 - 16

Volume of rectangular shower stall = 240 feet³

Therefore , the volume of the rectangular shower stall is 240 feet³

Hence , a) The height of the shower stall is ( 3x - 2 )

b) The volume of the shower stall when x = 4 is 240 feet³

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A person who invests $3,500 in a bank paying 6.75% interest compounded quarterly, must leave it for a period of 53 quarters (13 years) to reach a future value of $8,500.

The future value is the product of the compounded present value at an interest rate for some periods.

Compounding involves charging interest on the accumulated interest and principal, unlike the simple interest system.

When we are given the interest rate, and present and future values, we can determine the period from an online finance calculator as follows:

I/Y (Interest per year) = 6.75%

PV (Present Value) = $3,500

PMT (Periodic Payment) = $0

FV (Future Value) = $8,500

Results:

N (# of periods) = 53.023

Total Interest = $5,000.00

Thus, the investor needs 53 quarters (13 years) to accumulate a future value of $8,500.

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The equation of the line through (1, 2) so that the segment of the line intercepted between the axes is y+2x=4.

Let's use the slope-intercept form to find the equation of the line,

Hence the equation of the line would be of the form y=mx+c,

now the point at which the line intersects X-axis is (a,0), and the point at which it intersects Y-axis is (0,b).

⇒ m×a+c = 0

⇒a= − c/m

​and b=c+0 ⇒ b=c

Now, (1,2) is the midpoint of (a,0) and (0,b)

ie. 2=(0+b)/2​ ⇒ c/2 ​=2

                  ⇒c = 4

and  1=(a+0)/2​ ⇒ 1= −c/2m​

                       ⇒ m= −c​/2

                       ⇒ m= −2

∴ The equation of the line is given by y+2x=4.

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The complete question is-

What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is?

Answer: No.

Step-by-step explanation: In order for a motion to be considered "rigid", it must undergo a transformation or rotation in which the distance between the vertices does not change. The distance between the vertices becomes larger in the image, meaning this is not a rigid motion.

Good luck!

385 Sample size is necessary is the 95% confidence Interval for p .

Sample Size:

Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population. Sampling is the process of selecting a subset of individuals from a population to estimate characteristics of the population as a whole. The number of entities within a subset of the population is selected for analysis

According to the Question:

The Necessary Sample Size is calculated as follows:

Necessary Sample Size =

(Z-score)² * Std Dev*(1-StdDev) / (margin of error)²

For example, given a 95% confidence level, 0.5 standard deviation, and a margin of error (confidence interval) of +/- 5%. Necessary Sample Size =

= (1.96)² x 0.5(0.5)) / (0.05)²

= (3.8416 x 0.25) / .0025

= 0.9604 / 0.0025

= 384.16

So in order to get 95% confidence level, with confidence interval of +/- 5%, and standard deviation of 0.5, I have to survey 385 samples.

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By using trigonometry, it can be concluded that

sin 60° = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{\sqrt{3}}{2}[/tex]

cos 60° = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{1}{2}[/tex]

tan 60° = [tex]\frac{BC}{AC}[/tex] = [tex]\sqrt{3}[/tex]

cot 60° = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{1}{\sqrt{3}}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin \theta, cos \theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}[/tex]

[tex]cos\theta = \frac{base}{hypotenuse}[/tex]

[tex]tan\theta = \frac{perpendicular}{base}[/tex]

[tex]cot\theta = \frac{base}{perpendicular}[/tex]

[tex]sec\theta = \frac{hypotenuse}{base}[/tex]

[tex]cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here, [tex]\Delta ACB[/tex] is a right angled triangle whose base is AC, Perpendicular is BC and hypotenuse is AB

By using Trigonometry,

sin 60° = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{\sqrt{3}}{2}[/tex]

cos 60° = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{1}{2}[/tex]

tan 60° = [tex]\frac{BC}{AC}[/tex] = [tex]\sqrt{3}[/tex]

cot 60° = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{1}{\sqrt{3}}[/tex]

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The graph increasing over the given entire interval: -3 < x < 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=2x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=2 and b=5.

A function can be classified as:

The question gives the entire interval where the function increases. Thus, from the graph is possible to see that the function increases when x is between –3 and 0 because the values of y increase with the increasing of x-values.

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An equation that has 3 variables is called a cubic equation.

In mathematics, the general form of a cubic equation is ax³+ bx² + cx + d=0. Here, a is the co-efficient of the cube of x, b is the co-efficient of the square of x and c is the co-efficient of x. We also have the constant term d.

This is also referred to as a trinomial equation.

The degree of a cubic equation is 3. The degree of an equation is the highest power the equation has. As we can clearly see that the degree here will have to be 3. It also has 3 roots namely, α, β, and γ.

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Answer:

linear

Step-by-step explanation:

equal slope throughout