joe bought g: gallons of gasoline for $2.85 per gallon and c: cans for oil for 3.15 dollars.

Part A:what expression can be used go determine the total amount joe spent on gasoline and oil?

part B:if he bought 8.4 gallons of gasoline and 6 cans of oil, how much will he have spent in all?


please help! thank you :D​

Answer:

Their mass at the start was 400 kg.

Step-by-step explanation:

Given:

The tyres on a car during a grand prix race are reduced in mass by 3%. Their mass is 388 kg at the end of the race.

Now, to find the mass at the start.

Let the mass at the start be [tex]x[/tex].

According to question:

[tex]x - 3 \%ofx= 388[/tex]

⇒[tex]x-\frac{3}{100}\times x = 388[/tex]

⇒[tex]x-0.03x =388[/tex]

⇒[tex]0.97x=388[/tex]

Dividing both sides by 0.97 we get:

⇒[tex]x=400[/tex]

Therefore, their mass at the start was 400 kg.

To find the original mass of the tyres before the 3% decrease,  we make a simple percentage calculation. By setting up the equation 97/100 * x = 388, we find that the original mass of the tyres was 400 kg.

The question posted is a mathematics problem related to understanding percentages and its application to real-life situations such as a Grand Prix race.

Given that the tyres at the end of the race have a mass of 388 kg, which is 97% of their original mass (since they lost 3%), we can find their original mass by setting up a simple percentage equation. We denote the original mass as 'x' and set up the equation: 97/100 * x = 388. To solve for 'x', we divide both sides of the equation by 97/100, which is equivalent to multiplying by its reciprocal, 100/97.

The solution to the problem is then calculated as following: x = 388 * (100/97) = 400 kg.

Hence, the original mass of the tyres was 400 kg.

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Answer:

[tex]5^{10}+8^3[/tex]

[tex]5^{10}=9765625[/tex]

[tex]8^3=512[/tex]

[tex]=9765625+512[/tex]

[tex]=9766137[/tex]

OAmalOHopeO

Answer:

here  you go If the slope is undefined, it means that it is a vertical line.  This means that it passes through all points in the y direction.  Since the x value is -4, and the line is vertical, that's the only x value on that line.  So you just say the equation of the line is x=-4  

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

y-y1=m(x-x1)

m=0

y-8=0(x-(-4))

y-8=0(x+4)

y-8=0

y=0+8

y=8

Answer:

-33

Step-by-step explanation:

x-6b when b=5 and x=-3

-3-6(5)=-3-30=-33

Answer:

2750

Step-by-step explanation:

As there are 11 players on the field, each averaging 250 pounds, this means that we can add 250 11 times, 1 for each player. Another way to say this would be to multiply 250 and 11, as we are adding 250 11 times. Our answer is then 250*11 = 2750.

Answer: =28r−27

Step-by-step explanation:

Answer:

= 25r - 32-r

Step-by-step explanation:

5(1+4r)-8(4-r)

= 5 x 5r - 32-r

= 25r - 32-r

If r was 2, (example),

= 25 x 2 - 32 - 2

= 50 - 30

= 20

Answer:

there are 306 in total

Step-by-step explanation:

Answer: the answer is 40

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x ----> the number of horses

y ---> the number of sheep

In this problem the relationship between the variables, x, and y, represent a proportional variation.

Remember that, if the linear equation represent a proportional variation then it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

we have

For x=1, y=3

Find the value of the constant of proportionality k

[tex]k=\frac{3}{1}=3\ \frac{sheeps}{horse}[/tex]

substitute

[tex]y=3x[/tex]

using a graph tool

The graph in the attached figure

Answer:

1980°

152.3°

3780°

164.35°

180°

360°

Step-by-step explanation:

The sum of all the interior angles of a polygon  is given by (n - 2)180° where n is the number of sides.

So, the sum of all interior angles of a 13-gon is (13 - 2) 180° = 1980° (Answer)

As the 13-gon is regular, so each angles will be same. Assume each angle is x°.

So, 13x = 1980, ⇒ x = 152.3° (Answer)

Now, the sum of all interior angles for a 23-gon will be (23 - 2) 180° = 3780° (Answer)

Again,as the 23-gon is regular, so each angles will be same. Assume each angle is x°.

So, 23x = 3780, ⇒ x = 164.35° (Answer)

The sum of all the interior angles of a triangle is 180° (Answer)

The sum of all the interior angles of a quadrilateral is 360° (Answer)

The similarity between a square and a rhombus is all the sides of both are same and the difference, between a square and a rhombus is that a square has every angle 90°, but the rhombus has no angle equal to 90°. (Answer)

8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2

Solution:

Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'

Need to find the ratio of a:b

As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.  

For sake of simplicity, let volume of 1 sphere of radius a cm is represented by [tex]V_a[/tex] and volume of 1 sphere of radius b cm is represented by [tex]V_b[/tex]

So volume of 8 solid iron sphere with radius 'a cm' = volume of  1 solid iron sphere with radius 'b cm'

[tex]=>8 \times} \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{b}}[/tex]

[tex]\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{b}}}=\frac{1}{8}[/tex]  ---- eqn 1

[tex]\text {Let's calculate } {V}_{a} \text { and } V_{b}[/tex]

Formula for volume of sphere is as follows:

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Where r is radius of the sphere

Substituting r = a cm in the formula of volume of sphere we get

[tex]V_{a}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi a^{3}[/tex]

Substituting r = b cm in the formula of volume of sphere we get

[tex]V_{b}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi b^{3}[/tex]

[tex]\text { Substituting value of } V_{a} \text { and } V_{b} \text { in equation }(1) \text { we get }[/tex]

[tex]\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}[/tex]

[tex]\begin{array}{l}{=>\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}} \\\\ {=>\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{2}\right)^{3}} \\\\ {=>\frac{a}{b}=\frac{1}{2}}\end{array}[/tex]

a : b = 1 : 2

Hence the ratio of a:b is 1 : 2

Final answer:

The ratio of the radius 'a' of the original smaller spheres to the radius 'b' of the new larger sphere formed by melting the 8 smaller spheres together is 1:2, obtained by equating the volumes and simplifying.

Explanation:

The question pertains to using the concept of volumes of spheres in Mathematics to find the ratio of radii of the original smaller spheres to the new larger sphere formed by melting them together. Given that there are 8 solid iron spheres each with radius 'a cm', and they are melted to form one single sphere with radius 'b cm', we preserve the volume during the melting process.

We know that the volume of a sphere is calculated using the formula [tex]V=\frac{4}{3}\pi r^{3}[/tex]. When combining the volumes of the 8 smaller spheres into one large sphere, the volumes on both sides must be equal since no material is lost during melting. The equation to find the volume of the large sphere is [tex]V=8(\frac{4}{3}\pi a^{3}) = \frac{4}{3}\pi b^{3}[/tex].
Simplifying this equation, we obtain the cubic ratio of radii a³/b³ = 1/8. Taking the cube root of both sides, the simple ratio of the radii is a/b = ∛[1/8], which simplifies to a/b = 1/2. Therefore, the ratio of the radius of the smaller sphere to the radius of the larger sphere, a:b, is 1:2,

Answer:

13. ft per minute is 150. ft per hour is 9,000.

work:

14. x ÷ y = feet per minute.

it is this because the time divided by the depth will equal the time that it took.

15. it would be more reasonable to use feet by minute, because of the accuracy of the answers. with measuring it using feet per hour, your answers will be less precise.

16. the distance will double because the proportional relationship says that the distance is 3 km away if thunder is 9 secs apart from lightning.

will answer next question later

Answer:

3/8, 1/2, 3/4.

Step-by-step explanation:

Now I believe this is asking to set the fractions from least to greatest, but ignore this if im wrong. If so, the answer would be 3/8, 1/2, 3/4. 3/8 is less than 4/8, which is the halfway point for the 8ths, 1/2 is half of a whole, and 3/4 is more than 2/4, the half for 4ths.

Answer:

e-1/25

Step-by-step explanation:

28 tablets will be required for course of therapy.

One tablet is of 400-mg and prescription is for 200 mg for every 6 hours for 14 days. total number of tablets to be find out.

Arithmetic operation are Addition, subtraction, division, and multiply in order to achieve mathematical solution of the statement.

Here, tablet for a day = 200-mg/400-mg x 24 hr/6 hr
                                    =  1/2 x 4
                                    = 2 Tablets a day
Now, for number of tablets for 14 days course,
= 14 x 2
=  28 Tables in 14 days

Thus, 28 tablets will be required for course of therapy.

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Answer:

The average per cost is $19.25.

Step-by-step explanation:

Given:

The fee paid by cat owner = $269.50. Total visits he made that year 14.

Now, to find the average per cost.

So, to get the average per cost we divide the total fee by total visits:  

Average per cost = Total fee ÷  Total visits

                             =  [tex]269.50\div 14[/tex]

                             =  [tex]19.25[/tex]

Therefore, average per cost is $19.25.

Answer:

The Average cost of per visit to the vet  = $ 19.25

Step-by-step explanation:

Here, the total visits to the vet in a  year = 14

Also, the total amount paid to the vet in a year = $269.50

Now, Let us assume the average cost per vet visit = m

So,[tex]\textrm{Average cost of per visit}  = \frac{\textrm{Total amount paid in n visits}}{\textrm{ n visits}}\\ \implies  m = \frac{269.50}{14}  = 19.25[/tex]

or,  m = $ 19.25

Hence, the Average cost of per visit to the vet  = $ 19.25

Answer:

Your answer would be 33.7619047619

Step-by-step explanation:

Answer:

C proportional

Step-by-step explanation:

The answer is c because

proportional means equal

and as u can see in the photo you have represented a proportional relationship because ther line is going in and equal line across the axis and it is increasing at a proportional rate!

and there you go!

There are 165 different subcommittees possible.

To calculate the number of different subcommittees possible, we can use the combination formula. The number of different subcommittees is equal to the number of ways to choose 3 members out of 11. This can be calculated using the formula C(n, r) = n! / (r! (n - r)!), where n is the total number of members and r is the number of members in the subcommittee.

Plugging in the values, we have C(11, 3) = 11! / (3! (11 - 3)!) = 165. Therefore, there are 165 different subcommittees possible.

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Answer: 10.22

Step-by-step explanation:

Standard Deviation = square root of variance 104.44 = 10.22

Final answer:

To find the standard deviation from the variance of 104.4, you take the square root of the variance, resulting in a standard deviation of approximately 10.22.

Explanation:

If the variance for a data set is 104.4, to find the standard deviation, you take the square root of the variance. The formula to calculate the standard deviation (s) from the variance (σ²) is:

s = √σ²

Applying this formula, the standard deviation would be s = √104.4. Using a calculator, you would get:

s ≈ 10.22

Thus, the standard deviation for the data set with a variance of 104.4 is approximately 10.22.

Answer:

46.125 square feet or [tex]46\dfrac{1}{8}[/tex] sq. feet.

Step-by-step explanation:

The rug is shaped like a parallelogram with a base of [tex]\frac{41}{2} = 20.5[/tex] feet. and a height of [tex]2\dfrac{1}{4} = 2.25[/tex] feet.

Now, the area of a parallelogram is given by the product of one side as the base and the perpendicular distance of that side from the opposite parallel side as height.

Now, the area of the given parallelogram is (20.5 × 2.25) = 46.125 square feet. (Answer)

Answer:

Well, we know x has to add up to 180 degrees since a triangle has 180 degrees in it!

63 + 36 = _99__

180 - 99 = 81

81 = x

180 - 81 = 99

99 is z

99 + 13 = 112

180 - 112 = 68

68 is y

Since 13 is an angle measurement. We add to get 180.

68 = y

99 = z

81 = x

good morning,

Answer:

10×(1-0.2ⁿ)

Step-by-step explanation:

1.6/8=0.2

0.32/1.6=0.2

0.064/0.32=0.2

let S represent the sum of n term then S=8×[(1-0.2ⁿ)/(1-0.2)] = 10×(1-0.2ⁿ).

:)

Final answer:

To find the sum of a geometric series, use the formula for the partial sum by identifying the first term and common ratio.

Explanation:

A geometric series is represented by the formula a + ax + ax² + ax³ + ... with a as the first term and x as the common ratio. The sum of the first N terms of a geometric series can be found using the formula of the partial sum.

In the given series 8+1.6+0.32+0.064+..., the first term a = 8 and the common ratio x = 0.2. To find the sum, you can use the formula for the sum of a geometric series: S = a / (1 - x).

Substitute a = 8, x = 0.2 into the sum formula: S = 8 / (1 - 0.2) = 8 / 0.8 = 10. Therefore, the sum of the given geometric series is 10.

Answer:

The number of students who actually went for the skiing is 0.75 times the total number of students .

Step-by-step explanation:

Given as :

Students were surveyed about their wither break plans

The percentage of students who did not go for skiing = 25 %

So, The percentage of students who did not go for skiing =100 % - 25 % = 75%

Let The total number of students = x

So, The number of students actually went for the skiing = 75% of the total number of students

I.e The number of students actually went for the skiing = [tex]\frac{75}{100}[/tex]× x

Or, The number of students actually went for the skiing = 0.75× x

∴ The number of students actually went for the skiing = 0.75 x

Hence The number of students who actually went for the skiing is 0.75 times the total number of students . Answer

Answer:

35

Step-by-step explanation:

Answer:

1. 5417.412

2. 401.13

Step-by-step explanation:

1. First, rewrite

[tex]5\times 10^3+4\times 10^2+1\times 10^1+7\times 10^0+4\times \dfrac{1}{10^1}+1\times \dfrac{1}{10^2}+2\times \dfrac{1}{10^3}[/tex]

as

[tex]5\times 1000+4\times 100+1\times 10+7\times 1+4\times 0.1+1\times 0.01+2\times 0.001[/tex]

So, this is

[tex]5000+400+10+7+0.4+0.01+0.002\\ \\=5417.412[/tex]

2. First, rewrite

[tex]4\times 10^2+1\times 1 \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]

as

[tex]4\times 10^2+1\times 1 +1\times \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]

This is

[tex]4\times 100+1\times 1+1\times 0.1+3\times 0.01[/tex]

So, this is

[tex]400+1+0.1+0.03\\ \\=401.13[/tex]

Answer:

18

Step-by-step explanation:

To find this we must divide 45 by 20 which gives the answer of 2.25. As we know this we now must multiply that by 8 resulting in to 18.

Therefore the answer is 18

Answer:

7x-8y+11z

Step-by-step explanation:

Because this is the only one that doesn't have an equal sign. Therefore, this is an example of an expression, not a equation. All of the other answer choices have an equal sign, they're equations.

Answer:

I guess the question is when her hair will be almost 16cm long.

So she needs to grow hair almost 12 cm of hair. Because 16-4=12

To grow 12cm hair she needs 8 months (12/1.5=8)

So Svetlana needs to cut her hair before 8th month.

The length of playing field is 58.9 feet

Solution:

Given that, the diagonal length of a rectangular playing field is 76 feet,  

And its width is 48 feet.  

To find: length of playing field

Now, we know that, diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse.

So, now, in a right angled triangle  we can use pythagorean theorem to find the length

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, In a right angled triangle ABC we get

[tex]c^2 = a^2 + b^2[/tex]

Where "c" is the length of hypotenuse

"a" is the length of one leg of right angled triangle

"b" is the length of other leg of right angled triangle

[tex]\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}[/tex]

[tex]\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}[/tex]

Hence, the length of the rectangular field is 58.9 feet

Answer:The answer is 3,472

Step-by-step explanation:

I GOT THIS CORRECT TRUST ME!! :)