Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads East at 20 miles per hour. Complete an equation for the distance between the friends after t hours.

Answer:

Step-by-step explanation:

Thus if you are not allowed to repeat a digit the number of possible 4 digit numbers you can construct from 1,2,3,4 is 4 3 2 1 = 24.

The number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

Given that, using only digits 1 and 2 form 4-digit numbers.

Digits are the single symbols used to represent numbers in Maths. For example, in number 89, 8 and 9 are two digits. Hence, the numerals such as 0, 1, 2, 3,4, 5,6,7,8,9, and 0 are the form of digits which are used to represent a combination of numbers and do arithmetic operations in our day to day life.

Here,

For the first digit you are picking from 2 digits.

For the second digit you are picking from 2 digits.

For the third digit you are picking from 2 digits.

For the fourth digit you are picking from 2 digits.

2×2×2×2=16

4-digit numbers

1111, 2111, 1211, 1121, 1112, 1221, 2112, 1122, 2211, 1212, 2121, 2221, 1222, 2122, 2212 and 2222.

Therefore, the number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

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The gas used and miles are proportional for each scooter.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality .

Therefore, let's check whether the scooter A and scooter B shows proportional relationships.

Hence,

For scooter A:

y = kx

where

Therefore,

2 = 150 k

k = 2  /150

k = 1 / 75

Hence,

y = 1 / 75 x

From the table of scooter A, the ratio is constant, therefore, the relationships of gas used and distance covered is proportional for scooter A.

For the Scooter B the graph is also proportional because the ratios of the variables are constant.

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Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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The name of the step in which you check the conditions for the test on a population means in the four-step process is called step 1. Explanation: The hypothesis test for a population mean is a common procedure used in statistics to test claims about population means.

In the hypothesis testing for the population means, there are four major steps that must be followed, these are;

Step 1: State the hypothesis.

Step 2: Set the criteria for a decision.

Step 3: Compute the test statistic.

Step 4: Make a decision.

In the first step, verify the conditions that are necessary for the hypothesis testing process to continue.

One important condition to check for the test on a population mean is to check if the population is normally distributed. Other factors such as sample size and standard deviation should also be considered when conducting a hypothesis test on a population mean.

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Frequency tables are used to show the number of occurrence of each data in a dataset.

The complete frequency table is as follows:

\(\begin{array}{cc}{Trick}&{Years}\\52&0&53&1&54&2&55&1&56&2\end{array}\right]\)

The given data are:

54, 56, 53, 54, 56, 55

To complete the frequency table, we simply count each data element and the number of occurrence (i.e. the frequency).

So, we have:

52 has a frequency of 0

53 has a frequency of 1

54 has a frequency of 2

55 has a frequency of 1

56 has a frequency of 2

So, the complete frequency table is:

\(\begin{array}{cc}{Trick}&{Years}\\52&0&53&1&54&2&55&1&56&2\end{array}\right]\)

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Answer:

1. m = -3, b = 4

2. m = 0, b = 7

3. m = -1.5, b = -4

4. m = 3, b = 0

5. m = 1.5, b = -7

We will determine the area of the green section as follows:

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:

Now, we transform it to radians:

*Second: We replace on the equation:

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

Answer:

A ≈ 43.4 cm²

Step-by-step explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

  given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² × \(\frac{138}{360}\) ( simplify fraction by dividing numerator/denominator by 6 )

   = π × 6² × \(\frac{23}{60}\)

   = 36π × \(\frac{23}{60}\)

   = \(\frac{36\\pi (23) }{60}\)

   ≈ 43.4 cm² ( to the nearest tenth )

If this has a constant, it would travel 13.5 miles in an hour, therefore it would travel 6.75 miles in a half hour.

Answer:

Step-by-step explanation:

Geoff is feeling peckish, so he decides to pop into the shop and grab some snacks. He picks up a packet of crisps for 25p, a can of soup for 68p and a watermelon for £1.47. He wonders why the watermelon is so cheap, but he doesn't question it. He goes to the cashier and hands over a £5 note. The customer behind Geoff wonders "how much change does he get back?"

To figure this out, we need to add up the price of the snacks and take it away from the money Geoff gave. We can use a dot to show the pence as parts of a pound. For example, 25p = 0.25 pounds.

The price of the snacks is:

0.25 + 0.68 + 1.47 = 2.40 pounds

The money Geoff gave is:

5.00 pounds

The change is:

5.00 - 2.40 = 2.60 pounds

So, Geoff gets £2.60 in change and a bargain watermelon.

Answer:

Answer:

2.60

Step-by-step explanation:

25+68+147=240

500-240=260

turn into pounds 2.60

Step-by-step explanation:

The half-life of the radioactive substance is approximately 1.6 hours.

In radioactive decay, the half-life is the time it takes for half of the initial amount of a radioactive substance to decay. In this case, the initial amount of the substance is 2.46 g, and after 9.5 hours, only 0.076875 g remains undecayed.

To determine the half-life, we can compare the remaining amount of the substance to the initial amount. From the given data, we can calculate the fraction of the substance remaining after 9.5 hours by dividing 0.076875 g by 2.46 g. This gives us approximately 0.03125.

Now, we can use the formula for exponential decay: N(t) = N₀ * (1/2)^(t/T), where N(t) is the amount remaining after time t, N₀ is the initial amount, T is the half-life, and ^(t/T) denotes exponentiation.

By substituting the values into the equation and solving for T, we find that T is approximately 1.6 hours. Therefore, the half-life of this radioactive substance is approximately 1.6 hours, indicating that it takes 1.6 hours for half of the substance to decay.

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The measure of the third angle is approximately 18.93 degrees.

To find the measure of the third angle of a triangle, we need to use the fact that the sum of the three angles in any triangle is always equal to 180 degrees.

First, we need to convert the given angles from degrees, minutes, and seconds into decimal degrees. To do this, we can use the following formulas:

decimal degrees = degrees + (minutes/60) + (seconds/3600)

For the first angle, 41° 31' 29", we have:

decimal degrees = 41 + (31/60) + (29/3600)

= 41.5247

For the second angle, 119° 32' 59", we have:

decimal degrees = 119 + (32/60) + (59/3600)

= 119.5497

Now we can find the measure of the third angle by subtracting the sum of the first two angles from 180 degrees:

third angle = 180 - (41.5247 + 119.5497)

= 18.9256 degrees

Therefore, the measure of the third angle is approximately 18.93 degrees.

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It would take 6.3 hours for 10 painters to complete the paint job.

If the time required to paint a house varies inversely with the number of painters, we can use the formula:

T = k/N

where T is the time required to paint the house, N is the number of painters, and k is a constant of proportionality.

To find k, we can use the given information that it takes 7 hours for 9 painters to complete the paint job:

7 = k/9

Solving for k, we get:

k = 63

Now we can use this value of k to answer the question. If there are 10 painters, we can use the formula to find the new time required:

T = 63/N

T = 63/10

T = 6.3

Therefore, it would take 6.3 hours for 10 painters to complete the paint job.

What is paint job?

A paint job refers to the process of applying a layer or layers of paint onto a surface, such as a wall, ceiling, or object, in order to enhance its appearance, protect it from damage, or both. Paint jobs can range from simple touch-ups to full-scale renovations, and they can be done on a wide variety of surfaces, including wood, metal, concrete, and more. Paint jobs are often done by professional painters or DIY enthusiasts, and they can involve a variety of techniques and tools, such as brushes, rollers, sprayers, and paint guns.

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There are ${14 \choose 6}$ ways to select 6 of the babies from the group of 14, including Evie and Ben.

The question is asking how many ways there are to select 6 of the 14 babies from the group if Evie and Ben are included. This can be solved using the formula for combinations, which is ${n \choose r}$, where n is the total number of items and r is the number of items being selected. In this case, n = 14 and r = 6. Therefore, the answer is ${14 \choose 6}$. This means that there are 1001 ways to select 6 of the 14 babies, including Evie and Ben. To solve this, first the formula is used. Then, the total number of items, 14, is plugged into the formula. Finally, the number of items being selected, 6, is plugged into the formula. This yields the final answer of ${14 \choose 6}$.

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Answer:

The ratio is 4:1 school colors to no colors

Step-by-step explanation:

Do 1200/300 = 12/3 =4/1

Answer:

4:1

Step-by-step explanation:

that is the most simplified version of it

unsimplified is 1200:300

The capacities of the other two tins is 1.8 and 2.4litre.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

Three tins of oil with heights 6cm, 10cm, and 15cm are similar.

The medium size tin holds 2 liters of oil

Now,

Capacity of first tine= 6/3.33

=1.8

Capacity of third tin=6/2.5

=2.4

Therefore, by unitary method answer will be 1.8 and 2.4litre.

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answer

x=6, y=-2

explanation

-2x + 8 = y -------equ 1

3x - y = 22 -------equ 2

u can use any of the simultaneous equation method

using elimination method

rearrange first from -------equ 1

-2x+8=y

-y-2x=-8

multiple through by -1

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

rearrange first from -------equ 2

3x-y=22

-y+3=22 ------equ 4

equate 3 and 4, adding them together

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

-y+3=22 ------equ 4

0+5x=30

5x=30

x=6------equ 5

replace 6 for x in any equation

using -------equ 3

y+2x=8

y+2(5)=8

y+10=8

y=8-10

y=-2

Answer:

(x, y)=(6, -4)

Step-by-step explanation:

-2x+8=y

3x-y=22

Substitute the given value of y into the equation 3x-y=22

3x-(-2x=8)=22

Solve the equation for x

x=6

Substitute the given value of x into the equation 3x-y=22

3x6-y=22

Solve the equation for y

y=-4

The possible solution of the system is the ordered pair (x, y)

(x, y)=(6, -4)

Check if the given ordered pair is the solution of the system of equations

-2x6+8=-4

3x6-(-4)=22

Simplify the equalities

-4=-4

22=22

Since all of the equalities are true, the ordered pair is the solution of the system

(x, y)=(6, -4)

The equivalent exponential expression for this problem is given as follows:

A. 4^15 x 5^10.

The exponential expression in the context of this problem is defined as follows:

\(\left(\frac{4^3}{5^{-2}}\right)^5\)

To simplify the expression, we must first apply the power of power rule, which means that when one exponential expression is elevated to an exponent, we keep the base and multiply the exponents, hence:

4^(15)/5^(-10)

The negative exponent at the denominator means that the expression can be moved to the numerator with a positive exponent, hence the simplified expression is given as follows:

4^15 x 5^10.

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The function file 'mysolve.m' takes two inputs a and b, calculates the area of the right triangle using the given formula A = 0.5 * a * h and returns the area as output.

To calculate the area of a right triangle, we use the formula A = 0.5 * base * height or A = 0.5 * a * b where a is the length of the leg and b is the length of the hypotenuse.

The function file 'mysolve.m' to calculate the area of the right triangle is given below:

function [area] = mysolve(a,b)h = sqrt(b^2-a^2);area = 0.5*a*h;end

Explanation: The given function takes two input parameters a and b which are the length of the leg and hypotenuse respectively. We first calculate the height h of the triangle using the Pythagorean theorem which is h = sqrt(b^2-a^2). We then use the formula A = 0.5 * base * height to calculate the area of the right triangle where base is a and height is h. Finally, we return the calculated area as output from the function file 'mysolve.m'.

Conclusion: Thus, the function file 'mysolve.m' takes two inputs a and b, calculates the area of the right triangle using the given formula A = 0.5 * a * h and returns the area as output.

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Answer:

The answer is the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:.80

p-by-step explanation:

Answer:

Step-by-step explanation:

The GCF of 8 and 9 is 1

Divide both terms by the GCF, 1:

8 ÷ 1 = 8

9 ÷ 1 = 9

The ratio 8 : 9 cannot be reduced further by dividing both terms by the GCF = 1 :

This ratio is already in lowest terms.

Therefore:

8 : 9 = 8 : 9

Answer:

it would be like this on a graph

Step-by-step explanation:

theres the picture lemme know if u can't see it

Answer:

(3 x \(x\)) + (3 x 8) = 42

Step-by-step explanation:

3(x+8) = 42

3*x + 3*8 = 42

3x + 24 = 42

3x = 42 -24

3x = 18

x = 18 / 3

x = 6

Hope this helps :)

Answer:

\(3(x+8) = 42\\=>(x+8) = 14\)

\(3(x+8)=126\\=>x+8 = 42\)

\(3(x+8) = 42\\=> 3x +24 = 42\)

\(3(x+8) = 42\\=> 3\cdot x +3\cdot 8 = 42\)

YES              

\(x +8 = 14\\3\cdot x +3\cdot 8 = 42\\3x + 24 =42\)              

NO

\(3(x+8) = 126\\x+24 = 42\\3x+8 =42\)

0.25x^2 - 0.16y^4

Both terms are perfect squares so use the difference of squares formula

A^2 - b^2 = (a+b)(a-b) where a = 5x and b = 4y^2

Answer is 0.01(5x + 4y^2)(5x-4y^2)

Answer:

Solution given:

0.25x^2 - 0.16y^4

[0.5x]²-[0.4y²]²

[Note: Using formula: x²-y²=(x+y)(x-y)]

(0.5x+0.4y²)(0.5x-0.4y²) is a required answer.

Answer:

Half;  twice

Step-by-step explanation:

In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".

Thus,

2r = d

r = d/2

For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.

Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius

Answer:

AB + BC + CA

Step-by-step explanation:

12b-8 + 12b- 8 + 9b+8

33b - 8