Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. How many gallons can Joe's tank hold?

[tex]\bold{Given : 2^2^x^-^2 - 2^x^-^1 = 2^x - 2}[/tex]

[tex]\bold{\implies (2^2^x) (2^-^2) - (2^x)(2^-^1) = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{(2^2^x)}{(2^2)} - \frac{(2^x)}{(2^1)} = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{(2^2^x)}{4} - \frac{(2^x)}{2} = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{[2^2^x - (2^x)(2)]}{4} = 2^x - 2}[/tex]

[tex]\bold{\implies [2^2^x - (2^x)(2)] = (4)(2^x) - 8}[/tex]

[tex]\bold{\implies 2^2^x - (2^x)(2) - (4)(2^x) + 8 = 0}[/tex]

[tex]\bold{\implies (2^x)^2 - (2^x)(6) + 8 = 0}[/tex]

[tex]\bold{Let\;us\;take : (2^x) = Z}[/tex]

[tex]\bold{\implies Z^2 - 6Z + 8 = 0}[/tex]

[tex]\bold{\implies Z^2 - 4Z - 2Z + 8 = 0}[/tex]

[tex]\bold{\implies Z(Z - 4) - 2(Z - 4) = 0}[/tex]

[tex]\bold{\implies Z = 4\;\;(or)\;\;Z = 2}[/tex]

[tex]\bold{But : Z = 2^x}[/tex]

[tex]\bold{\implies 2^x = 4\;\; (or) \;\; 2^x = 2}[/tex]

[tex]\bold{\implies 2^x = 2^2\;\; (or) \;\; 2^x = 2^1}[/tex]

[tex]\bold{\implies x = 2\;\;(or)\;\; x = 1}[/tex]

Answer:

15/5= x. x=3.

Step-by-step explanation:

Miles ran in total divided by days spent running equals miles ran each day.

Answer:

This is a direct variation where the constant of variation is 5/9

Step-by-step explanation:

The equation for direct variation is y = kx

5x-9y =0

Lets try to get this equation in the above form

Add 9y to each side

5x-9y +9y = 9y

5x = 9y

Divide each side by 9

5/9 x = 9y/9

5/9x = y

This is in the form y = k x where k =5/9

Answer:

The unit price is $2.33 per gallon

Step-by-step explanation:

To find the unit price, we take the price and divide by the amount

$6.99 / 3 gallons

$2.33 per gallon

The unit price is $2.33 per gallon

Answer:

[tex]8.05 * 10^{5}[/tex]

Step-by-step explanation:

Thinking process:

the population of Park Crest Middle School = 400 children

The population in the state = 806, 240 children

The difference:

[tex]806240 - 400\\= 805840[/tex]

Expressing the difference in standard form gives:

8.05 × 10⁵

Final answer:

To find Tamia's age, an equation was set up based on the relationship between Jay and Tamia's ages. Jay is 20 years old and 4 years younger than three times Tamia's age. Solving the equation shows that Tamia is 8 years old.

Explanation:

Jay is 4 years younger than three times Tamia's age. Given that Jay is 20 years old, we can use this information to find out how old Tamia is. Let's denote Tamia's age as T. The relationship between their ages can be represented by the equation: Jay's age = 3 × Tamia's age - 4. Since Jay's age is 20, we can substitute this into the equation, giving us 20 = 3T - 4.

To solve for T, we first add 4 to both sides of the equation, which gives us 24 = 3T. Next, we divide both sides by 3 to find Tamia's age, resulting in T = 8. Therefore, Tamia is 8 years old.

This problem was solved by setting up an equation based on the relationship described between Jay and Tamia's ages, then using basic algebraic steps to solve for Tamia's age.

Answer:

C) 8

Step-by-step explanation:

y = 3x-4

Substitute x=4 into the equation

y = 3*4 -4

y = 12-4

y=8

Put the value of x = 4 to the equation y = 3x - 4:

[tex]y=3(4)-4=12-4=8[/tex]

Answer:

A C B

Step-by-step explanation:

In sequence A. the numbers are being divided by 4.

In sequence B. the numbers are being multiplied by -3

In sequence C. the numbers are being add by 4

So the ratio from least to greatest would be A C B

Answer:

Sequence B, Sequence A, Sequence C

Step-by-step explanation:

Common ratio of a geometric sequence is the ratio of a term and its previous term of the sequence.

Thus, the common ratio of the sequence  A: 160,40,10,2.5,...

[tex]r_1=\frac{40}{160}=\frac{1}{4}[/tex]

The common ratio of the sequence B: -21,63,-189,567,...

[tex]r_2=\frac{63}{-21}=-3[/tex]

The common ratio of the sequence C : 8,12,18,27,....

[tex]r_3=\frac{12}{8}=\frac{3}{2}[/tex]

Since, -3 < [tex]\frac{1}{4}[/tex] < [tex]\frac{3}{2}[/tex]

Thus,

[tex]r_2 < r_1 < r_3[/tex]

Hence, the order the sequences from least common ratio to the greatest common ratio is,

Sequence B, Sequence A, Sequence C

Answer:

2700 cookies.

Step-by-step explanation:

A dozen is a grouping of twelve, that is a dozen = 12.

If there are 225 dozen cookies in the bakery, then there are

[tex]225\cdot 12=2700[/tex] cookies in the bakery.

there are 2700 cookies in total

Since there are 225 dozen cookies in the bakery, we need to determine the total number of cookies.

To convert dozen to individual units, we multiply the number of dozens ( 225 )  by 12, as there are 12 cookies in each dozen :

225 dozen * 12 cookies / dozen = 2700 cookies

Therefore, there are 2700 cookies in total. By multiplying the number of dozens by 12, we account for the fact that each dozen contains 12 cookies. This calculation allows us to determine the precise quantity of cookies in the bakery.

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In combinatorics, we use the combination formula to calculate the number of ways Mrs. Wong can choose 2 books out of 14. The result is 91 ways.

The subject of this question is combinatorics, a topic in mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those specified in this question. In this case, Mrs. Wong has 14 special objects (books) and wants to choose 2 out of them.

We use the combination formula in this scenario. The combination formula is given by C(n, r) = n! / [(n-r)!*r!], where n represents the total number of objects, r is the number of objects to choose, and '!' denotes factorial.

Substituting n as 14 and r as 2 into the formula, we get: C(14,2) = 14! / [(14-2)!*2!] = 91.

Therefore, Mrs. Wong can choose 2 books out of 14 in 91 different ways.

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The question is about combinations in mathematics. Using the formula for combinations, we find that Mrs. Wong can choose 2 books out of 14 in 91 different ways.

This is a problem of combinations in mathematics. Mrs. Wong can choose two out of 14 unread books in a certain number of ways, and we're tasked to find that number.

Considering that order of selection does not matter, we can use the formula for combination: nCr = n! / r!(n-r)!. Here, 'n' is the total number of items, 'r' is the items to be chosen.

So the combinations she can make, denoted as 14C2, can be calculated like this:

14C2 = 14! / 2!(14-2)! = (14*13) / (2*1) = 91 ways

Therefore, Mrs Wong can choose 2 books out of 14 in 91 ways.

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Answer: Bradley would expect 94 times to get a blue or green gumball.

Step-by-step explanation:

Since we have given that

Number of blue gumballs = 15

Number of yellow gumballs = 12

Number of green gumballs = 2

Number of purple gumballs = 16

Total number of all gumballs = 45

Probability of getting either a blue gumball or green gumball be

[tex]\frac{15}{45}+\frac{2}{45}=\frac{17}{45}[/tex]

So, Expectation of getting a blue gumball or green gumball if a gumball was taken out 250 times :

[tex]\frac{17}{45}\times 250=94.4[/tex]

Since we know that it must be less than 94.4.

So, the nearest smallest integer will be 94 times .

Hence, Bradley would expect 94 times to get a blue or green gumball.

Answer:

b+9

Step-by-step explanation:

(b + 3) + 6 = b + (3 + 6) = b + 9

Answer:

70, 105, 140

Step-by-step explanation:

Answer:

We have the following given

mileage = 70 miles per gallon

distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so

60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is

37.5 mi / (70 mi/gal) = 0.54 gallon

Answer:

B

Step-by-step explanation:

70 miles * [1.6 km/mile] = 112 km

Notice when you multiply by km/mile by miles the miles cancel out.

1 gallon will get 112 km

x gallon will get 60 km

Answer:

All explanations are correct

Step-by-step explanation:

In triangle ABC, CD is the perpendicular bisector of AB, thus using ΔADC and ΔBDC,

AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)

∠ADC=∠BDC=90°(CD perpendicular AB)

CD=CD( Reflexive property)

therefore, by SAS rule of congruency,

ΔADC≅ ΔBDC,

Also, In the same triangles, AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)

CD=CD( Reflexive property)

AD=BD (D is the midpoint and divides AB into two equal halves)

Thus, by SSS rule of congruency,

ΔADC≅ ΔBDC,

Thus, all the three explanations are correct.

In the given case, we can conclude that All explanations are correct

In triangle ABC, let CD be the perpendicular bisector of AB. We can use the properties of triangles to demonstrate that ΔADC is congruent to ΔBDC.

AC=BC: This holds true because CD is perpendicular to AB, making point C equidistant from both A and B.

∠ADC=∠BDC=90°: Since CD is perpendicular to AB, both angles ADC and BDC are right angles.

CD=CD: This is a reflexive property, stating that any line segment is equal to itself.

By applying the SAS (Side-Angle-Side) rule of congruency using the above properties, we can conclude that ΔADC is congruent to ΔBDC.

Furthermore, we can establish that in these congruent triangles:

AC=BC (since C is equidistant from A and B due to CD being perpendicular to AB).

CD=CD (reflexive property).

AD=BD (as D is the midpoint of AB).

Hence, using the SSS (Side-Side-Side) rule of congruency, we can also conclude that ΔADC is congruent to ΔBDC.

Therefore, all three explanations correctly demonstrate the congruence of these triangles.

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Answer:

0.49 m²

Step-by-step explanation:

The area (A) is calculated using A = πr² ( r is the radius )

A = external area - internal area

external radius = [tex]\frac{1.2}{2}[/tex] = 0.6

internal radius = [tex]\frac{0.9}{2}[/tex] = 0.45

A = π(0.6² - 0.45²)

   = π(0.36 - 0.2025) = 0.1575π ≈ 0.49 m²

Final answer:

The area of the washers is 0.49m².

Explanation:

To find the area of the washers, we need to find the areas of the outer and inner circles and then subtract the smaller area from the larger one. The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the external diameter is 1.2m, so the radius is half of that, or 0.6m. The area of the outer circle is A₁ = π(0.6)² = 1.13m². Similarly, the radius of the inner circle is 0.45m, and the area of the inner circle is A₂ = π(0.45)² = 0.64m². Finally, the area of the washer is the difference between the two areas: A = A₁ - A₂ = 1.13m² - 0.64m² = 0.49m².

Answer:

I Think It Is 0.12*2

Because I See Both Of The Shadings Colored Differently And Each One Has 12 That Is The Reason For Me Thinking This.

Answer:

7/10 x 2/5 = 14/50 = 7/25

Step-by-step explanation:

mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.

Answer:

7/10 x 2/5 = 14/50 = 7/25

Step-by-step explanation:

mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.

Answer:

The answer is A because if you subtract the 1 you get y=1 and the line of A is at the point 1 on the y-axis

Step-by-step explanation:

The percentage of its capacity is the large container​ filled will be 87.5%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

A large container has a maximum capacity of 64 ounces.

And, The container is filled with 8 ounces less than its maximum capacity.

Now,

Calculate the percent of its capacity is the large container​ filled as;

Percent = (64 - 8) / 64  x 100

            = 56/64 x 100

            = 87.5%

Thus, The percentage of its capacity is the large container​ filled will be 87.5%.

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The complete question is this;

A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. To what percent of its capacity is the large container​ filled?

Answer:

is your answer $3250

Step-by-step explanation:

so we dont know our I (interest) but :

P (principal) = 10000

R (rate) = 6.5%  we'll have to turn it into the decimal which is 0.065

T (time) = 5 years

and our basic formula of finding I is I = PxRxT   so :

I = 10000 x 0.065 x 5

I = 3250

Answer:

Volume of tray =[tex]4x^{3} -60x^{2} +216x[/tex]

Step-by-step explanation:

The Dimensions of rectangular cardboard is given by 12 inches by 18 inches

Length of the rectangular cardboard = 18 inches

Width of the rectangular cardboard = 12 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2 (side of the square )

                               = [tex]18-2x[/tex]

Width of the tray = width of cardboard - 2( side of square)

                            = [tex]12-2x[/tex]

height of tray = sides of square

                       = x

volume of tray = Length × width × height

Volume of tray = [tex]x(18-2x)(12-2x)[/tex]

first we multiply (12-2x) and (18-2x)

Volume of tray =[tex]x(18(12-2x)-2x(12-2x))\\[/tex]

                         =[tex]x(216-36x-24x+4x^{2})[/tex]

                         =[tex]x(4x^{2}-60x+ 216)[/tex]

                         =[tex]4x^{3} -60x^{2} +216x[/tex]

Hence the volume of tray =[tex]4x^{3} -60x^{2} +216x[/tex]

The volume of the Tray is given by the equation [tex]4x^3-60x^2+216x[/tex] and this can be determined by using the given data.

Given :

If the square is cut from each corner of the cardboard and folded to make a tray, then according to the given data:

Tray length = 18 - 2x

Tray width = 12 - 2x

Tray height = x

Now, the volume of the tray is given by the expression:

The volume of Tray = [tex]x(12-2x)(18-2x)[/tex]

Simplify, the above expression.

[tex]\rm Volume = (12x - 2x^2)(18-2x)[/tex]

[tex]\rm Volume = 216x -24x^2-36x^2+4x^3[/tex]

[tex]\rm Volume = 4x^3-60x^2+216x[/tex]

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Brian rented the book for 12 days.

Brian rented a book with the condition that the shop charges $2 for the first day and $3 from the second day onwards. He paid a total of $35 upon returning the book. To determine how many days he kept the book, we must calculate the cost for each day and subtract the initial $2 from the total amount paid.

Steps to Calculate the Number of Days:

Therefore, Brian kept the book with him for 12 days.

the cheap answer is, we divide 500 by (2+3+5+10) and then distribute accordingly.

[tex]\bf \cfrac{500}{2+3+5+10}\implies \cfrac{500}{20}\implies \cfrac{25}{1}\implies 25 \\\\\\ \stackrel{2\cdot 25}{2}~~:~~\stackrel{3\cdot 25}{3}~~:~~\stackrel{5\cdot 25}{5}~~:~~\stackrel{10\cdot 25}{10}\qquad \implies \qquad 50~~:~~75~~:~~125~~:~~250[/tex]

Answer:

Answer is: A

Step-by-step explanation:

Because it is.

Answer:

A. $17.00

Step-by-step explanation:

$5.10 for 6 quarts.

Unit cost: ($5.10)/(6 qt) = $0.85/qt

Price for 5 gallons:

1 gallon = 4 quarts

5 gallons = 5 * 4 quarts = 20 quarts

Price for 5 gallons = unit price * number of quarts

Price for 5 gallons = $0.85/qt * 20 qt = $17.00

Answer: A. $17.00

[tex]i=\sqrt{-1}-\text{the imaginary number}\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrt{-1}=\boxed{6i}[/tex]

Answer:

The correct option is 1. The image of (2,4) is (4,-8).

Step-by-step explanation:

The given rule is

[tex]R_x{\circ}D_{o,2}:(2,4)[/tex]

The transformations perform from right to left. [tex]D_{o,2}[/tex] means dilation with scale factor 2 and center of dilation is origin.

The given rule defines the dilation with scale factor 2 and center of dilation is origin followed by reflection across x-axis.

If a figure dilated by scale factor k and the center of dilation is origin, then

[tex](x,y)\rightarrow (kx,ky)[/tex]

The scale factor is 2,

[tex](x,y)\rightarrow (2x,2y)[/tex]

[tex](2,4)\rightarrow (4,8)[/tex]

If a figure reflected across x-axis, then x-coordinate remains the same but the sign of y-coordinate is changed.

[tex](x,y)\rightarrow (x,-y)[/tex]

[tex](4,8)\rightarrow (4,-8)[/tex]

Therefore image of (2,4) is (4,-8) and option 1 is correct.

Answer:

180 degrees in radians is π

Step-by-step explanation:

0° = 0 radians

90°= π/2

180 °= π

270°= 3π/2

360° = 2π

and so on