The Rawlins family has travelled 600 km on their vacation. This has taken them 8 hours. If they continued at the same rate, how long will it take them to complete their journey if the total distance to be travelled is 2100 km?
A. 20 hours
B. 28 hours
C. 26 hours
D. 12 hours

Answer:

Proportion states that the two ratio or fractions are equal.

Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.

To find how many grains of sand are there in 6300 kg of sand.

Let x be the number of grains of sand in 6300 kg of sand.

Using conversion :

1 kg = 1000 g

6300 kg = 6300000 g

Then, by using proportion method, we have;

[tex]\frac{1}{7\times 10^{-5}}= \frac{x}{6300000}[/tex]

[tex]\frac{10^5}{7} = \frac{x}{6300000}[/tex]

By cross multiply we get;

[tex]6300000 \times 10^5 = 7x[/tex]

or

[tex]63 \times 10^5 \times 10^5 = 7x[/tex]

[tex]63 \times 10^{5+5} = 7x[/tex]  [using [tex]x^a \cdot x^b = x^{a+b}[/tex]]

[tex]63 \times 10^{10} = 7x[/tex]

Divide both sides by 7 we get;

[tex]x = \frac{63 \times 10^{10}}{7} = 9 \times 10^{10}[/tex]

Standard form is a way of of writing down very large or very small numbers easily.

Therefore, [tex]9 \times 10^{10}[/tex] grains of sand are there in 6300 kg of sand.

If there are 4 yellow pencils for each blue one, then this is the answer. If not then comment and tell me.

Blue   Yellow

5        20

7        28

9        36

11        44

13       52

The required number of yellow and blue pencils are 44 and 11 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
As Shawan has 4 yellow pencils for every blue pencil,
Let the number of blue pencils be b,
Now,
Yellow pencil (y) = 4 × b
Now,
put b = 5,7,9,11, or 13
So y = 20, 28, 36, 44, or 52

Now,
b + y  = 55
when b = 11 and y = 44 sums of the pencil would be 55.

Thus, the required number of yellow and blue pencils are 44 and 11 respectively.

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Answer:

4.66 years

Step-by-step explanation:

Let us assume that it will take 't' years for him to repay the money that he would borrow.

We can use monthly cashflow formula:

[tex]C=Pr\frac{(1+r)^{12t}}{(1+r)^{12t}-1}[/tex]

Here, we have been given:

Monthly cashflow C=425

Loan amount P=20000

Interest rate AMR = 7.5%. Therefore, we have [tex]r=\frac{0.075}{12}[/tex]

Upon substituting these values in the formula, we get:

[tex]425=20000\cdot \frac{0.075}{12} \frac{(1+\frac{0.075}{12})^{12t}}{(1+\frac{0.075}{12})^{12t}-1}[/tex]

Upon simplifying, we get:

[tex]425=125 \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t}-1}[/tex]

[tex]425=125 \frac{(1.00625)^{12t}}{(1.00625)^{12t}-1}[/tex]

Upon solving this equation using a calculator, we get:

[tex]t=4.66[/tex]

Therefore, correct answer is 4.66 years. That is, second choice from the given options.

Answer:

[tex]m<A=125\°[/tex]

[tex]m<B=35\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

[tex]m<A+m<B+m<C=180\°[/tex]

substitute the values and solve for x

[tex](6x-1)\°+20\°+(x+14)\°=180\°[/tex]

[tex]7x=180\°-33\°[/tex]

[tex]7x=147\°[/tex]

[tex]x=147\°/7=21\°[/tex]

step 2

Find the measure of angle A

[tex]m<A=(6x-1)\°=6(21)-1=125\°[/tex]

step 3

Find the measure of angle C

[tex]m<C=(x+14)\°=21+14=35\°[/tex]

Answer:

C

Step-by-step explanation:

Since GK bisects ∠FGH then ∠FGK = ∠KGH, hence

6v - 2 = 4v + 4 ( subtract 4v from both sides )

2v - 2 = 4 ( add 2 to both sides )

2v = 6 ( divide both sides by 2 )

v = 3 → C

Answer:

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]

Step-by-step explanation:

First, we need to rearrange the equation to make it y = mx + c

4x - y = 3

y + 3 = 4x

y = 4x -3

So the slope of the line is 4.

The slope of a line perpendicular to an equation is:

[tex]\frac{-1}{gradient}[/tex]

So the slope of the perpendicular line is:

[tex]\frac{-1}{4}[/tex] = -0.25

Now to find the equation of a line you can use the following equation:

y - y₁ = m(x - x₁)

Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:

y₁ = 6

x₁ = -5

m = [tex]\frac{-1}{4}[/tex]

y - 6 = [tex]\frac{-1}{4}[/tex](x - - 5)

To get rid of the fraction we need to multiply the whole equation by 4:

4y - 24 = -1(x - - 5)

The two negatives cancel out:

4y - 24 = -1(x + 5)

Multiply the brackets out:

4y - 24 = -x + 5

Now, to rearrange the formula back into y = mx + c

Move the -24 over to the other side making it a +24:

4y = 2x + 5 + 24

4y = 2x + 29

Divide everything by 4:

y = [tex]\frac{2}{4}x + \frac{29}{4}[/tex]

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]

Answer:

68

Step-by-step explanation:

Since this is an isosceles triangle the bottom 2 angles are equal.  So both bottom angles are 56 degrees.  The three angles of a triangle add to 180 degrees.

56+ 56+ x = 180

Combine like terms

112 +x =180

Subtract 112 from each side

112-112+x = 180-112

x =68

There are many ways to answer this. Here is one answer shown below

AB/WX = BC/XY

On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.

On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.

It might help to line up ABC over top WXY so you can pick out the corresponding sides. I show this in the attached image below.

Answer: There are many ways to answer this.

Step-by-step explanation:

On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.

On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.

Answer:

5 : 3

Step-by-step explanation:

the ratio of length : width

= 10 : 6 ← divide both parts of the ratio by 2

= 5 : 3 ← in simplest form

Answer:

The family formed by these numbers is 3x where x is any integer number.

Step-by-step explanation:

We have been given 3 9 12

We can see that given numbers are multiple of 3 so, we can say that the given numbers are from the family of 3x

Where x is any integer number when multiplied by 3 will give the multiple of 3.

Answer:

B. <1 and <5

Step-by-step explanation:

they look exactly the same

Answer:

Correct answer is B. <1 and <5

Step-by-step explanation:

Answer:

47 squared units.

Step-by-step explanation:

Multiply the probability by the cost of the accident:

14,886.05 x 0.071 = 1056.91

Now add the overhead cost:

1056.91 + 110 = 1166.91

The closest answer to this is number D.

Answer:

D. $1165.49

Step-by-step explanation:

We have that the probability of a driver getting into an accident = 7.1% i.e. 0.071.

Now, the average cost of an accident = $14,886.05

Then, the expected cost of an accident =  $14,886.05 × 0.071 = $1056.91

As, the overhead cost for insurance = $110

Therefore, the driver's insurance premium = $1056.91 + $110 = $1166.91

Since, the closest option to $1166.91 is option D.

Hence, the driver's insurance premium will be $1165.49.

Final answer:

The number in question is 70, found by solving the equation 1/2 * x - 25 = 10.

Explanation:

To find a number where half of that number, subtracted by 25, equals 10. We can set up an equation to represent this: 1/2 * x - 25 = 10, where 'x' is the number we are trying to find. To solve for 'x', we first add 25 to both sides of the equation, which gives us 1/2 * x = 35. Then, to isolate 'x', we multiply both sides by 2, resulting in x = 70. Therefore, the number is 70.

Final answer:

To find the number, isolate the variable by performing inverse operations. The number is 70.

Explanation:

To find the number, we need to translate the given information into an equation. Let's assume the number is x. The equation can be written as:

1/2x - 25 = 10.

To isolate the variable x, we first add 25 to both sides of the equation:

1/2x - 25 + 25 = 10 + 25.

This simplifies to 1/2x = 35.

Next, we multiply both sides of the equation by 2 to undo the division by

1/2: 2 × (1/2x) = 2 × 35.

The 1/2 cancels out on the left side, leaving us with x = 70.

Therefore, the number is 70.

Answer:

Rational

Step-by-step explanation:

A rational number is a number that can be written  as a fraction, (or is any real number, positive or negative) Irrational numbers, for example, are numbers that are decimals, but dont terminate or repeat. Such as [tex]\pi[/tex] and [tex] the square root of 2, 3 and 5. may i have brainliest?

Answer:

None of these are equivalent

Step-by-step explanation:

36 + 9 = 45

9(4 – 1) = 9* 3 = 27

 (4 • 9) + (4 • 2) = 36+ 8 = 44

Answer:

13

Step-by-step explanation:

I believe you would take the number of students and divide by the number of members

I'm not sure what you're trying to ask, but if you're trying to find the individual cost;

Solution: Cost of 1 candy bar is $0.91

Explanation: The quotient of 10 and 11 is 0.90909090909, which rounds into 0.91

Hope This Helps!!!

-Austint1414

One chocolate bar costs approximately 0.91 dollars.

Let x be the cost of one chocolate bar.

Given that 11 chocolate bars cost 10 dollars, we set up a proportion:

11 bars / 10 dollars = 1 bar / x dollars

To get cost of one chocolate bar (x), we cross-multiply:

11 * x = 10 * 1

11x = 10

x = 10 / 11

x ≈ 0.91 dollars.

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Full question:

11 chocolate bars cost 10 dollars. How much does 1 chocolate bars cost?

[tex]A(n)=5+(n-1)\left(\dfrac{1}{6}\right)=5+\dfrac{1}{6}n-\dfrac{1}{6}=\dfrac{1}{6}n+\dfrac{30}{6}-\dfrac{1}{6}\\\\A(n)=\dfrac{n+29}{3}\\\\\text{Put n = 1, n = 4 and n  = 10 to the formula:}\\\\A(1)=\dfrac{1+29}{3}=\dfrac{30}{3}=10\\\\A(4)=\dfrac{4+29}{3}=\dfrac{33}{3}=11\\\\A(10)=\dfrac{10+29}{3}=\dfrac{39}{3}=13[/tex]

Answer:How much soy sauce does Bonnie mix with every 1 millimeter of vinegar is 1.5

How much vinegar does bonnie mix with 1 millimeter of soy sauce is .666

Step-by-step explanation: The first is 150 divided by 100 is 1.5

Answers: choice A, choice C

Compute the discriminant (use a = 1, b = 5, c = 11)

D = b^2 - 4ac

D = 5^2 - 4*1*11

D = 25 - 44

D = -19

The discriminant is negative, so the two solutions are complex or imaginary. The -19 will be under the root as choice A and choice C show

Answer:

2

Step-by-step explanation:

evaluate from left to right, substituting the given values into the expression

= [tex]\frac{70}{10}[/tex] + (5 × 3) - (2 × 10)

= 7 + 15 - 20

= 22 - 20

= 2

Substitute the values of a and b to the expression:

[tex]a=3,\ b=10\\\\\dfrac{70}{b}+5a-2b=\dfrac{70}{10}+(5)(3)-(2)(10)\\\\=7+15-20=22-20=\boxed2[/tex]

Answer:

y = -3x+20

Step-by-step explanation:

First we will write the equation in point-slope form,

[tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

We must find the slope.  The formula for slope is

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

Using our two points, we have

m = (8-2)/(4-6) = 6/-2 = -3

We will use the first point and this slope:

y-2 = -3(x-6)

Using the distributive property, we have

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

y - 2 = -3x--18

y - 2 = -3x+18

Add 2 to each side:

y-2+2 = -3x+18+2

y = -3x+20

Answer:

x = 2

Step-by-step explanation:

check by substituting each given value of x into the function

x = 0 ⇒ y = [tex]\frac{3}{4}[/tex] × 0² = 0

hence (0, 0) is correct

x = 2 ⇒ y = [tex]\frac{3}{4}[/tex] × 4 = 3

hence (2, 4 ) is incorrect

x = 3 ⇒ y = [tex]\frac{3}{4}[/tex] × 9 = 6 [tex]\frac{3}{4}[/tex]

hence (3, 6 [tex]\frac{3}{4}[/tex]) is correct

x = 5 ⇒ y = [tex]\frac{3}{4}[/tex] × 25 = 18 [tex]\frac{3}{4}[/tex]

hence (5, 18 [tex]\frac{3}{4}[/tex]) is correct

Answer: You can get 6 pounds of apples and approximately 19 apples.

Step-by-step explanation:

There are 16 ounces per pound so 6 pounds is 96 ounces

96/5 = 19.2

You can buy 6 pounds of apples for 9, which is approximately 19 apples.

1. First, let's find out how much one pound of apples costs. Since two pounds cost $3.00, one pound would cost half of that, which is $1.50.

2. Now, if one pound costs $1.50, we can find out how many pounds of apples you can buy for $9 by dividing $9 by the cost per pound: [tex]\( \frac{9}{1.50} = 6 \)[/tex]. So, you can buy 6 pounds of apples for $9.

3. Since 1 pound equals 16 ounces, 6 pounds equal [tex]\( 6 \times 16 = 96 \)[/tex]ounces.

4. If one apple is approximately 5 ounces, then the number of apples you can buy for 96 ounces is [tex]\( \frac{96}{5} \).[/tex]

5. Performing the division, [tex]\( \frac{96}{5} = 19.2 \)[/tex]. Since you can't buy a fraction of an apple, you'd round down to the nearest whole number.

6. So, you can buy approximately 19 apples for $9.

Here's the calculation step by step:

1. Cost per pound: [tex]\( \frac{3.00}{2} = 1.50 \)[/tex] dollars per pound.

2. Pounds you can buy for $9: [tex]\( \frac{9}{1.50} = 6 \)[/tex] pounds.

3. Total ounces: [tex]\( 6 \times 16 = 96 \)[/tex] ounces.

4. Apples you can buy: [tex]\( \frac{96}{5} = 19.2 \)[/tex](rounded down to 19 apples).

Answer:

the answer is rectangle

Step-by-step explanation:

To solve the system of equations, isolate x in the second equation and substitute it into the first equation. Simplify the resulting equation and solve for y. Substitute this value of y back into the second equation to find the value of x.

To solve the system of equations:

50 + 10y + 6y = -14

16y = -64

y = -4

Substitute this value of y back into the second equation to find x:

x - 2(-4) = 10

x + 8 = 10

x = 2

Therefore, the solution to the system of equations is x = 2 and y = -4.

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Answer:

y= 1/2 x +11/2

Step-by-step explanation:

To find the slope

m = (y2-y1)/(x2-x1)

  = (8-5)/(5--1)

  = 3/(5+1)

  = 3/6

  = 1/2

Using point slope form of a line

y-y1 = m(x-x1)

y-5 = 1/2(x--1)

y-5 = 1/2(x+1)

Distribute

y-5 = 1/2x +1/2

Add 5 to each side

y = 1/2x + 1/2 + 5

Change 5 to 10/2

y = 1/2x + 1/2 + 10/2

y = 1/2x + 11/2

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

To find the slope, you can use the slope formula and plug in the two points:

(-1,5) = (x₁ , y₁)

(5,8) = (x₂ , y₂)

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{8-5}{5-(-1)}[/tex]

[tex]m=\frac{8-5}{5+1} =\frac{3}{6} =\frac{1}{2}[/tex]

y = 1/2x + b

To find "b", plug in either of the points into the equation:

(5,8)

y = 1/2x + b

8 = 1/2(5) + b

8 = 5/2 + b      Subtract 5/2 on both sides

8 - 5/2 = b         Make the denominators the same in order to subtract them

16/2 - 5/2 = b

11/2 = b

[tex]y = \frac{1}{2}x+\frac{11}{2}[/tex]    

The 3rd option is your answer