At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?

b) How far from Town X did each vehicle travel when they passed each other?

Answer:

45

Step-by-step explanation:

Answer:

1. C

2. B

Step-by-step explanation:

A. A(-2,5) => A' (-2 + 2, 5) or A' (0,5)

B. A(-2,5) => A' (- -2, 5) or A' (2,5)

The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

Learn more about Translation here:

https://brainly.com/question/27425612

#SPJ1

Answer: 11

Step-by-step explanation:

Answer:

Simplify = 7x/6 - 3/28

Reciprocal = 6x/7 - 28/3

Step-by-step explanation:

Add x to the top of the first fraction to combine them.

To find the reciprocal you flip the numbers. So the numerator is the bottom and the dominator is the top.

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

More can be learned about the mean of a data-set at brainly.com/question/1156334

#SPJ1

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

To know more about Integral.

https://brainly.com/question/27419605

#SPJ8

Answer:

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

Step-by-step explanation:

The image point is in the 3rd quadrant, and the pre-image point is in the first quadrant. This means there has been any of ...

The only answer choice involving the appropriate rotation is ...

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

__

Checking this, we have

  (x, y) ⇒ (x -2, y +2) . . . . translation left 2, up 2

  (x -2, y +2) ⇒ (-y -2, x -2) . . . . followed by 90° CCW rotation

  J(9, 1) ⇒ J'(-3, 7) . . . . . consistent with the given image point

Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

Answer:

i am so sorry i dont get the question

Step-by-step explanation:

Answer:

We reject H₀, we find that the  current level of mercury uptake in the Everglades has decrease

Step-by-step explanation:

We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)

Test Hypothesis:

Null hypothesis             H₀          μ   =  μ₀

Alternative hypothesis Hₐ          μ   <  μ₀

Sample size 25             then n < 30 we will use t-student table

Population mean : μ₀ = 15 ppm

sample mean :  μ  = 14,6 ppm

sample standard deviation:   s = 1 ppm

Sample size n :  25

degrees of freedom   df = n - 1         df = 24

We will develop the test for CI 90%  then  α = 10%      α = 0,1   α/2 = 0,05

For that values in t student table we find:

t(c) = 1,711    by symmetry t(c) = - 1,711

To compute ts

t(s) =  ( μ - μ₀ ) / s/√n

t(s) = 14,6 - 15 / 1 /√25

t(s) = - 0,4*5 / 1

t(s) = - 2

Comparing t(c)and t(s)

|t(s)| > |t(c) |      and t(s) < t(c)         -2 < -1,711

Therefore t(s) in in the rejection region, we reject H₀  

Answer: Its A

Step-by-step explanation:

Herb spent 55 hours at the library.

Fractions defines a part of a whole and are represented as a numerical value. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Total time spent in the Library = 1/6 + 1/4 + 1/2

Total time spent = 11/12 x 60 mins

Total time spent = 55 hours

Learn more about fractions here: https://brainly.com/question/78672

#SPJ1

Answer:

<2≅<3   Given

<2≅<1     verbally opposite angle are equal

<3≅<1    since <2≅<3

<4≅<3    verbally opposite angle are equal

<1≅<4      since <3≅<1

Step-by-step explanation:

have a nice day/night bye!!!

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Finding the inverse of the cube of a bijective function is an important step in understanding the properties of functions. To prove that f-cube is a bijection if f is a bijection, we can use the fact that for any two real numbers x and y, if x = y, then x1/3 = y1/3. This means that if f(x) = f(y), then (f(x))3 = (f(y))3, or f-cube(x) = f-cube(y). Since f is a bijection, this means that x = y, so f-cube is also a bijection.

To find the inverse of f-cube, we can use the fact that for any real number x, x1/3 is a well-defined real number. This means that if we have f-cube(x) = y, we can take the cube root of both sides to get f(x) = y1/3. Since f is a bijection, it has an inverse function f^-1, so we can apply this inverse to both sides to get x = f^-1(y1/3). This means that the inverse of f-cube is f^-1(y1/3).

In conclusion, if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Learn more about Bijection

brainly.com/question/13012424

#SPJ11

Answer:

y₁ - y₂ = (-7/9)(x₁ - x₂)

Step-by-step explanation:

The general structure for an equation in point-slope form is:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.

Point 1: (4, -3)                   Point 2: (-5,4)

y₁ - y₂ = m(x₁ - x₂)                                  <---- Original equation

-3 - 4 = m(4 - (-5))                                 <---- Plug values in for "x" and "y"

-7 = m(4 - (-5))                                      <---- Simplify left side

-7 = m(9)                                               <---- Simplify within parentheses

-7/9 = m                                              <---- Divide both sides by 9

I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:

y₁ - y₂ = (-7/9)(x₁ - x₂)  

It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.

The loss of the farmer is $828.64 after selling two horses. Although the selling price of two horses is the same. The percentage of loss 2.25%.

What is profit?

The profit formula aids in determining the gain in any financial transaction as well as the profit made by selling a specific product, which is typically done in a business. When the selling price exceeds the cost price, a profit can be determined. So, the equation to calculate the profit is:

Selling price (S.P.) minus cost price equals profit (C.P.)

Given that a farmer sold two horses for $18,000.

Assume that the cost price of a horse is x that is sold at 15% profit.

The cost price of another horse is y that is sold at 15% loss.

The profit after selling first horse is x × 15% = 15x/100

The selling price of the horse is x + 15x/100 = (100x + 15x)/100 = 115x/100

The loss after selling second horse is y × 15% = 15y/100

The selling price of the horse is y - 15y/100 = (100y - 15y)/100 = 85y/100

The selling price both horse is $18000.

Therefore,

115x/100 = 18000 ....(i)

85y/100 = 18000 ....(ii)

Solve equation (i)

115x/100 = 18000

115x = 1800000

x = 1800000/115

x = 15652.17

Solve equation (ii)

85y/100 = 18000

85y = 1800000

y = 1800000/85

y = 21176.47

The profit after selling first horse is (18000 - 15652.17) = 2347.83.

The loss after selling second horse is (21176.47 - 18000) = 3176.47

The loss is greater than profit.

The loss is  3176.47 - 2347.83 = $828.64

The percentage of loss is 828.64/(21176.47 + 15652.17) = 2.25%

To learn more percentage loss, click on below link:

https://brainly.com/question/16947160

#SPJ1

Answer:

OPTION B SHOULD BE CORRECT

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

For such more question on equation

https://brainly.com/question/29174899

#SPJ8

z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

             Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

                z score =(550-500)/100  = 0.5

So, z score for value 660 is;

                z score = (660-500)/100  = 1.6

So, z score for value 500 is;

                z score = (550-500)/100  = 0

So, z score for value 440 is;

                z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

                z score = (270-500)/100  = -2.3

To learn more about the standard deviation from the given link

https://brainly.com/question/12402189

#SPJ4

z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

            Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

               z score =(550-500)/100  = 0.5

So, z score for value 660 is;

               z score = (660-500)/100  = 1.6

So, z score for value 500 is;

               z score = (550-500)/100  = 0

So, z score for value 440 is;

               z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

               z score = (270-500)/100  = -2.3

To learn more about the standard deviation from the given link

brainly.com/question/12402189

#SPJ4

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

for more such question on mean visit

https://brainly.com/question/1136789

#SPJ8

Out of Maria's total expenses, the proportion of expenses for her car would be 0. 57 .

To find the proportion, the formula would be :

= Maria total car expenses / Maria total expenses for the month

Maria total car expenses = $ 290. 02

Maria total expenses for the month =  $ 507. 59

The proportion of expenses for her car would be :

= 290. 02 / 507. 59 x 100 %

= 0. 57 x 100 %

= 57 %

In conclusion, Maria's car alone takes over 0. 57 or 57 % of her total expenses.

Find out more on proportion at https://brainly.com/question/27538904

#SPJ1

Answer:

a) 20%

b) 50%

c) -75%

Step-by-step explanation:

Mathematically, percentage change is;

(new value -old value)/old value * 100%

(i) (90-75)/75 * 100%

= 15/75 * 100% = 20%

ii) (60-40)/40 * 100%

= 20/40 * 100% = 50%

iii) (5-20)/20 * 100% = -15/20 * 100% = -75%

SOLUTION:

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Therefore from the question, the integers are:

The number line is shown below

The value of the product of the number as given in the task content is; Choice B; 1.

It follows from the task content that the numbers whose product are to be determined are; ¾ and 1⅓.

To effectively multiply, we must convert the mixed number to a fraction as follows;

1⅓ = 4/3.

Hence, the product is; 4/3 × 3/4 = 12/12 = 1.

Read more on product of numbers;

https://brainly.com/question/10873737

#SPJ1

The properties of angle bisector of triangle are as follows:

Angle Bisector:-

The angle bisector of an angle in a triangle is a straight line that divides the angle into two equal or congruent angles. Every triangle has three angle bisector. The point in a triangle where these three angle bisectors intersect is known as its incenter.

Angle Bisector's Properties:-

Thus, these are the properties of angle bisector of a triangle.

To learn more about angle bisector refer here

https://brainly.com/question/13880193

#SPJ4

According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.

To illustrate this value on an abacus we must find the number of this operation as shown below:

Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:

Learn more about abacus in: https://brainly.com/question/13385199

#SPJ1