A box has a base of 3 inches by 4 inches and a height of 12 inches. What is the length of the interior diagonal of the box, in inches?

answear 12x

Step-by-step explanation:

6.5x-3.6x=

30x-18x=

12x

When about 60.2 liters of fuel are added to each car, the two vehicles will have the same mass.

Let x be the number of liters of fuel needed for the two vehicles to have the same mass.

The first vehicle's total mass with fuel is: 1295 + 0.737x

The total weight of the second vehicle with gasoline is: 1290 + 0.820x

We want the two masses to be equal so that we may equalize the two expressions and solve for x:

295 + 0.737x = 1290 + 0.820x

0.083x = 5

x = 60.24

Therefore, the two vehicles will have the same mass when approximately 60.2 liters of fuel have been added to each vehicle.

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The requried class average is 83.2 points.

To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.

The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.

The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.

The total number of points earned by all the students is 960 + 704 = 1664 points.

The total number of students is 12 + 8 = 20.

To find the class average, we divide the total number of points by the total number of students:

average = total points / total students

average = 1664 / 20

average = 83.2

Therefore, the class average is 83.2 points.

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The fish tank requires 7900 square cm of glass.

First, choose three fish for our tank. Let's choose a neon tetra, a guppy, and a corydoras catfish.

According to the guideline given, each fish requires 4,000 cubic centimeters of water for every inch of a fish's length. Determine the total length of the three fish to calculate the required water volume.

Assuming the neon tetra is 1 inch long, the guppy is 2 inches long, and the corydoras catfish is 3 inches long, the total length of the fish is 1+2+3=6 inches.

To accommodate these three fish, we need 6 inches x 4,000 cubic centimeters of water per inch = 24,000 cubic centimeters of water.

To design the fish tank. Make it a rectangular prism shape with the dimensions of 50 cm x 30 cm x 40 cm (length x width x height).

To calculate the amount of glass necessary to build the tank, to find the surface area of the glass required. There are five sides to the tank (four sides and the base), find the area of each and add them up.

The front and back sides each have an area of 50 cm x 40 cm = 2000 square cm.

The two side walls each have an area of 30 cm x 40 cm = 1200 square cm.

The base has an area of 50 cm x 30 cm = 1500 square cm.

So, the total surface area of glass required is:

2(2000 square cm) + 2(1200 square cm) + 1500 square cm = 7900 square cm.

Therefore, 7900 square cm of glass is needed to build our fish tank.

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Answer:

7

Step-by-step explanation:

7, 7, 7, 11, 15, 18

The mode is the number that appears most.

Answer: 7

Answer:

7

Step-by-step explanation:

The mode is the most frequently occurring value in a set of data. In this case, the number 7 occurs twice, which is more than any other number, so the mode is 7. It is worth noting that if there were no values that occurred more than once, then there would be no mode for the data set. In this case, the data set has a single mode, but it is possible for a data set to have multiple modes if there are multiple values that occur with the same highest frequency.

Answer:

120/30*29*28*27

Step-by-step explanation:

Answer: 18º

Step-by-step explanation:

a + 126º = 180º (adj.  ∠s on st. line)

a = 54º

Let the adjacent angle next to b be c.

a + c = 180º (int. ∠, AB//CD)

54º + c = 180º

c = 126º

108º + x = 126º (ext. ∠ of Δ)

x = 18º

The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

Both the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.

A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.

Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.

In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

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The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

We have,

From the given quadratic function,

We see that,

The x-values are -∞ to ∞

The y-values are from 3 to ∞

Now,

The x-values are called the domain.

The y-values are called the range.

Thus,

The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

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Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

We have,

The amount of tax applied to the bill is 6% of the subtotal, or 0.06x.

The total bill (including tax) is.

x + 0.06x = 1.06x

To find the amount of tip Wyatt left on the total bill, we need to multiply the total bill by 17% (or 0.17):

0.17(1.06x) = 0.1802x

The expression in terms of xx that represents the total amount that Wyatt paid is:

= x + 0.06x + 0.1802x

Simplifying the expression by combining like terms.

Total amount = 1.2422x

Thus,

Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

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Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

We have,

The null and alternative hypotheses to determine if the females who read the "great sense of humor" description gave the potential partner an average attractiveness rating that was higher than neutral (μ = 4) can be written as:

Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

Thus,

The null hypothesis states that the mean attractiveness rating of males who are described positively and with a great sense of humor is not significantly different from a neutral rating of 4.

The alternative hypothesis states that the mean attractiveness rating of such males is significantly higher than a neutral rating of 4.

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Step-by-step explanation:

how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .

The solution is given below.

The result of the mixed digits given when expressed as improper fractions are as follows;

3 1/2 = ((2×3)+1)/2 = 7/2

7 4/5 = ((5×7)+4)/5 = 39/5

5 3/4 = ((4×5)+3)/4 = 23/4

4 1/3 = ((3×4)+1)/3 = 13/3

4 2/3 = ((3×4)+2)/3 = 14/3

5 1/5 = ((5×5)+1)/5 = 26/5

8 2/3 = ((3×8)+2)/3 = 26/3

2 3/5 = ((5×2)+3)/5 = 13/5

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complete question:

3 1/2 as a improper fraction7 and 4/5 as an improper fraction5 3/4 as an improper fraction4 1/3 as an improper fraction4 + 2/3 as an improper fraction5 1/5 as an improper fraction8 2/3 as an improper fraction 2 3/5 as an improper fraction

The answers are explained in the solution.

Given are lines drawn in a coordinate plane, we need to identify the equations,

So, we have,

y = 2x – 4 = r

y = 2x + 4 = p

This is because these lines are parallel and have same slope, also the y-intercept is -4 and 4,

y = x = n

y = -x = s

This is also because, the line of y = x passes from origin.

b) We can use a translation to map the line p or r onto the line r or p.

c) We can use an axial symmetry in the y-axis to map the line n or s onto the line s or n.

d) The line s or n is mapped onto itself under central symmetry in the point (0, 0).

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Factorization is a mathematical process of breaking down a number or an expression into smaller numbers or simpler expressions that can be multiplied together to get the original number or expression.

Expressions, which are essentially mathematical statements containing numbers and letters, can be factorized in algebra. For illustration, consider the phrase 2x + 4. Finding the expressions or numbers that are common to each term allows us to factorize the expression. Since 2 appears in both terms, we can remove it by factoring to get 2(x + 2).

Given equation =  [tex]2x^{2} + 7x + 6[/tex]
                         ⇒   [tex]2x^{2} + 4x + 3x + 6[/tex]

                         ⇒ [tex]2x ( x+2) +3(x+2)[/tex]

                         ⇒[tex](2x + 3) (x+2)[/tex]

Therefore the factors of the expression [tex]2x^{2} + 7x + 6[/tex] are [tex](2x + 3) (x+2)[/tex].

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Answer:

Step-by-step explanation:

We can start by drawing a diagram of the situation:

markdown

Copy code

                     *

                    / \

                   /   \

                  /     \

                 /       \

         _______/_________\_______

              4ft         4ft

               |          |

              1ft        h ft

We can see that the distance from the center of the wheel to the white plank is also 4 feet (since the radius of the wheel is 4 feet).

Next, we need to find the height of the white plank after the wheel is rolled forward through an angle of π/3 radians.

To do this, we can use trigonometry. Let's call the height of the white plank after the motion "h". We can use the sine function to relate the angle through which the wheel is rolled and the height of the plank:

sin(π/3) = h/4

Simplifying this equation, we get:

h = 4sin(π/3)

h = 4(√3/2)

h = 2√3

Therefore, the height of the white plank after the motion is 2√3 feet from the ground.

The requried 3 1/2 cups of chocolate chips would be needed for 7 dozen cookies, so the answer is (c).

The ratio of chocolate chips to cookies is 1 1/2 cups for every 3 dozen cookies. To find how much chocolate chips are needed for 7 dozen cookies, we can use the following proportion:

1 1/2 cups / 3 dozen cookies = x cups / 7 dozen cookies

where x is the unknown amount of chocolate chips needed for 7 dozen cookies.

To solve for x, we can cross-multiply and simplify:

(1 1/2 cups) * (7 dozen cookies) = (3 dozen cookies) * x

21/2 cups = 3x

x = 3.5

Therefore, 3 1/2 cups of chocolate chips would be needed for 7 dozen cookies, so the answer is (c).

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Answer:

A(4;-1)

B(4;-5)

S=yB-yA/ xB-xA

= -5+1/ 4-4

=-4/0

impossible

Hello!

To find the equation of the line that passes through the points (0, -8) and (4, -3), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

First, we can find the slope of the line by using the formula:

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

where (x1, y1) = (0, -8) and (x2, y2) = (4, -3). Substituting these values, we get:

m = (-3 - (-8)) / (4 - 0) = 5/4

So the slope of the line is 5/4. Now we can use the point-slope form of the equation with either of the given points. Let's use the point (0, -8):

y - (-8) = 5/4(x - 0)

Simplifying this equation, we get:

y + 8 = 5/4x

Subtracting 8 from both sides, we get the final equation:

y = 5/4x - 8

So the equation of the line that passes through the points (0, -8) and (4, -3) is y = 5/4x - 8.

the domain and range of the inequality are,

x ≥ 1 and y ≥ - 4

The inequality is:

⇒ y ≤ √(x - 1) - 4

Now, To find:

The domain and range of the given inequality.

Solution:

We have,

⇒ y ≤ √(x - 1) - 4

The related equation is:

⇒ y ≤ √(x - 1) - 4

This equation is defined if:

√x - 1 ≥ 0

x ≥ 1

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set.

So, the domain of the given inequality is, x ≥ 1

We know that,

√(x - 1)  ≥ 0

√(x - 1) - 4 ≥ - 4

y ≥ - 4

So, the range of the given inequality is, y ≥ - 4

Therefore, the correct option is C.

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Answer:

1 730.1504 bytes^3

Step-by-step explanation:

6.6 x 6.4 x 6.4 x 6.4 x B x B x B

can be written as:

(6.6 x 6.4 x 6.4 x 6.4) x B^3

where B^3 represents B cubed or B raised to the power of 3.

Therefore, the product using exponents is:

1684.032 x B^3

Answer: C. 96

Step-by-step explanation:

I took 8×3×4=96

Since the height is 5 in and it already took up one inch, that means just 4 more inches to go hence the 4 in the multiplication.

The correct representation of the inequality –3(2x – 5) < 5(2 – x) are :

-6x + 15 < 10 - 5x

x < 5

Given an inequality,

–3(2x – 5) < 5(2 – x)

We have to find the equivalent representation of the inequality.

(-3)(2x) - (-3)(5) < (5)(2) - (5)(x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x < 5

Hence the correct options are -6x + 15 < 10 - 5x and x < 5.

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Answer:

A

Step-by-step explanation:

The opposite of an integer is the number on the opposite side of the number line with the same distance from zero. So, the integers that are opposites are 14 and -14, 17 and -17, 32 and -32, and 15 and -15. This is because these pairs have the same absolute value but different signs. For instance, the absolute value of 14 is 14, and the absolute value of -14 is also 14. Therefore, -14 is the opposite of 14. Similarly, -17 is the opposite of 17 and so on.

Answer:

a

Step-by-step explanation:

got it right on edge

Answer:

215

Step-by-step explanation:

To solve this expression, we must first use the order of operations. We begin with the parentheses and evaluate 23-11, giving us 12. Then, we divide 48 by 12, which equals 4. Finally, we multiply 4 by 38, resulting in 152. We add this to 63, giving us a final answer of 215. Thus, the solution to 63+48÷(23-11)×38 is 215.

Answer:

Elena

Step-by-step explanation:

Sorry we have to see the complement first because it is of 90° jjust let the second w go we will do that later we can find the value of w by choosing elena

Answer: 17/29 As A Fraction! (58.6%)

Step-by-step explanation: Just Divide 17 (Amount Won) By Amount Played (29)

The slope of a linear function of the table of values given above is calculated as: m = 3.

The slope of a linear function is calculated as change in y over change in x. Note that f(x) is also the same as variable "y".

To calculate the slope, pick any two pairs of values from the table given, i.e. (2, 3) and (3, 6):

Slope of the linear function (m) = change in y / change in x = 6 - 3 / 3 - 2

Slope (m) = 3/1

Slope (m) = 3.

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The image is reflected over the y-axis. Then the correct option is B.

Given that:

Point of the polygon VWXYZ, W(2, 4)

Point of the polygon V'W'X'Y'Z', W'(-2, 4)

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

The point W' can be obtained by reflecting the shape across the y-axis.

Thus, the correct option is B.

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The missing diagram is given below.