Box A has a volume of 512 cubic meters. Box B is similar to box A. To create Box B, Box A's dimensions were divided by 2. What is the volume of Box B? 256 m3 170 m3 128 m3 64 m3

The gas gauge will show a lower reading if the gas tank is less than full when you return home after your trip to the mountains.

The gas gauge will show a lower reading if the gas tank is less than full when you return home after your trip to the mountains. This is due to the increased effort required to drive in mountainous terrain, which necessitates more fuel consumption.The amount of fuel used by the car will be determined by a variety of factors, including the engine, the type of vehicle, and the driving conditions. Since the car was driven in the mountains, it is likely that more fuel was used than usual, causing the gauge to show a lower reading.

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We have found a value of b that makes y(t) = \(e^2t\) [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y. To check if y(t) is a solution of y′ = Ay, we need to substitute it into the differential equation and see if it holds.

Let's start by finding y′:

y′(t) = [\(2e^2t, 8e^2t, 4be^2t\)]

Now, let's find Ay:

Ay = [4 1 3; 2 3 3; −2 −1 −1] [1; 4; b] = [4+4b; 14; -5-b]

We want y(t) = e^2t [1; 4; b] to satisfy y′ = Ay, so we set them equal:

y′ = Ay

[\(2e^2t; 8e^2t; 4be^2t] = [4+4b; 14; -5-b] e^2t\) [1; 4; b]

Expanding this equation, we get:

\(2e^2t\)= (4+4b)\(e^2t\)

\(8e^2t\) = 14 \(e^2t\)

\(4be^2t\)= (-5-b) \(e^2t\)

The second equation is always true, so we can ignore it. For the first equation, we can cancel out \(e^2t\) on both sides to get:

2 = 4+4b

Solving for b, we get:

b = -1/2

Finally, we can substitute b = -1/2 back into the third equation to check if it holds:

4be^2t = (-5-b) \(e^2t\)

-2e^2t = (-5 + 1/2)\(e^2t\)

This equation is true, so we have found a value of b that makes y(t) = \(e^2t\) [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y.

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Answer:

64 dollars

Step-by-step explanation:

1st day= $2

2nd day= $4

3rd day= $8

4th day= $16

5th day= $32

6th day= $64

Answer: she saved $64 on the sixth day (hope this helps! )

Step-by-step explanation:

day 1= $2

day 2=$4

day 3=$8

day 4=$16

day 5=$32

day 6=$64

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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The distributive property for multiplication is given by,

Using the above property, the given polynomial can be simplified as,

Now, comine the like terms and arrange the terms in the desceding order in which the exponents of variables comes.

Answer:

5 × 10 ^ -6

to get the answer move the decimal in 0.000005 to 5 which 6 place forward

which can also be written as 5 × 10 ^ -6

hope it helps

5×10- 6

Step-by-step explanation:

because we are converting decimal into scientific notation

For the given Cuboid, the width will be equal to 4.5 cm.

What exactly is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where opposite faces are equal in size and shape. A cuboid is also known as a rectangular parallelepiped or rectangular prism.

In a cuboid, the three pairs of opposite faces are parallel to each other and perpendicular to the other pair of faces. The cuboid has eight vertices or corners, twelve edges, and six rectangular faces.

Now,

We can use the formula for the volume of a cuboid to find the missing dimension:

Volume = Length x Width x Height

In this case, we are given the length and height of the cuboid, but we do not know its width. Let's assume that the width of the cuboid is "w". Then, we can write the equation:

220.5 = 7 x w x 7

Simplifying this equation, we get:

220.5 = 49w

Dividing both sides by 49, we get:

w = 4.5

Therefore, the third dimension of the cuboid is:

Width = 4.5 cm

So, the cuboid has three dimensions of 7 x 4.5 x 7 cm.

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Answer:

7m ^1÷2

Step-by-step explanation:

see attached joint

hope it helps

The rate change of the function g(x) in the interval [2, -4] is :

r = -1/2.

Given is the function -

g(x) = - (x²/4) + 7

Now, for the interval [2, - 4], we can write -

g(- 2) = - (4/4) + 7 = - 1 + 7 = 6

g(4) = - (16/4) + 7 = - 4 + 7 = 3

The rate change can be given as follows -

r = (3 - 6)/(4 + 2)

r = (-3/6)

r = -1/2

Therefore, the rate change of the function g(x) in the interval [2, -4] is :

r = -1/2.

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The correct option is b. 16.67 acres would the lot next to it contain if it has a 900' frontage and is the same width as the first rectangular lot.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.). The quantity of unit squares that can fit inside a rectangle called its area. Blackboards, painting canvases, laptop monitors, and other flat surfaces are a few instances of rectangular shapes.

Area of a Rectangle = (Length × Breadth) square units.

We know that the Area = Length × Width.

For first lot:

43,560 (sq. ft. in acre) × 25 acres = 1,089,000 sq. ft.

We know that 1,089,000 sq. ft. = Width × 1,350 (length). Therefore width =1,089,000 / 1,350 = 806.67.

From the problem the lots were of the same width.

In second lot: Area =806.67 (width) × 900( length)= 726,000 sq. ft. Therefore:

⇒726,000 (area) / 43,560 = 16.67 acres.

The correct answer is:  b. 16.67 acres

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Answer: (3, -9)

Step-by-step explanation:

The equation of P is \((x-3)^2 +(y+2)^2 =49\)

Substituting the coordinates of each of the points into the equation, we see that only (3, -9) satisfies the equation.

Answer:

I thin B -7 cause its negative and negative goes down.

Step-by-step explanation:

The team had at least one of them playing for 57 minutes in total.

To calculate the total minutes the team had at least one of them playing, we need to consider the individual playing times and the time they played together.

Ann played 19 minutes, Dave played 17 minutes, and Bob played 18 minutes. Together, they played 8 minutes as pairs, and all three played together for 3 minutes.

To determine the total minutes at least one of them was playing, we can sum their individual playing times and subtract the time they played together twice (as pairs) and the time all three played together once.

Total minutes at least one of them was playing = Ann's playing time + Dave's playing time + Bob's playing time - (time played together as pairs) - (time all three played together)

Total minutes = 19 + 17 + 18 - (8 * 2) - 3 = 57 minutes

The team had at least one of Ann, Dave, or Bob playing for a total of 57 minutes.

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The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

B

Step-by-step explanation:

Both C and D solve the equations, so the system must have infinite solutions.

Answer:

rounded to the nearest tenth = 3.7

Answer: 3.7

Step-by-step explanation: because i learn this a book called big fst notbook math by Walbook i recomed it to you

A.  Approximately 34.13% of infants have birth weights between 110 oz and 125 oz.

B. Approximately 14.11% of infants have birth weights between 88 oz and 98 oz.

To find the proportion of infants with birth weights within certain ranges, we need to calculate the area under the normal distribution curve using the z-scores.

A. Birth weights between 110 oz and 125 oz:

To find the proportion of infants with birth weights between 110 oz and 125 oz, we need to calculate the z-scores corresponding to these values and then find the area under the normal curve between those z-scores.

Z1 = (110 - 110) / 15 = 0

Z2 = (125 - 110) / 15 = 1

Using a standard normal distribution table or a calculator, we can find the area under the curve between z = 0 and z = 1, which represents the proportion of infants with birth weights between 110 oz and 125 oz.

P(110 oz ≤ X ≤ 125 oz) = P(0 ≤ Z ≤ 1)

From the standard normal distribution table, the area corresponding to z = 1 is approximately 0.8413, and the area corresponding to z = 0 is 0.5.

P(0 ≤ Z ≤ 1) = 0.8413 - 0.5 = 0.3413

Therefore, approximately 34.13% of infants have birth weights between 110 oz and 125 oz.

B. Birth weights between 88 oz and 98 oz:

Similarly, we can find the proportion of infants with birth weights between 88 oz and 98 oz using the same approach.

Z1 = (88 - 110) / 15 = -1.47

Z2 = (98 - 110) / 15 = -0.8

P(88 oz ≤ X ≤ 98 oz) = P(-1.47 ≤ Z ≤ -0.8)

From the standard normal distribution table, the area corresponding to z = -0.8 is approximately 0.2119, and the area corresponding to z = -1.47 is approximately 0.0708.

P(-1.47 ≤ Z ≤ -0.8) = 0.2119 - 0.0708 = 0.1411

Therefore, approximately 14.11% of infants have birth weights between 88 oz and 98 oz.

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Answer: Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

We must work with linear equations, remember that the general shape is:

y = a*x + b

where a is the slope and b is the y-intercept.

Ok, first we want to find the rate of change (or the slope) of the graphed line:

We know that for a line that passes through the points (x1, y1) and (x2, y2)

The slope is:

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

Then for the graphed function, we can see that it passes through the points:

(0, -2) and (4, 0)

Then the slope is:

a = (0 -(-2))/(4 - 0) = 2/4 = 1/2

Now, the slope of the second line is 15/4.

Let's calculate the difference between the slopes:

15/4 - 1/2 = 15/4 - 2/4 = 13/4

(notice that we are calculating slope2 - slope1)

Then the correct option is:

Function 2 has a greater rate of change by 13/4

Answer:

B) Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

Applying exponential properties, we have that the solution to the given expression is:

\(-\frac{125}{343}\)

When a fraction is elevated to the exponent, we apply the exponent to both the numerator and the denominator.

In this problem, we have that:

Negative base with odd exponent, hence the solution is negative and given as follows:

\(-\frac{125}{343}\)

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Answer:

x = 3

Step-by-step explanation:

<=> 2^x + 2^x + 2^x + 2^x = 32

<=> 4x2^x=32

<=> 2^x = 8

<=> x = 3

Answer:

That's incredible.  I have that exact problem on my website.

Here is my explanation.

My website says probability = 0.131944444444445

https://www.1728.org/occupncy8.htm

Step-by-step explanation:

The quarter is at a height of 258.75 feet when the quarter's height polynomial and the dime's height polynomial are equal at 5/16 seconds.

We can start by setting the two polynomials equal to each other since both the quarter and dime are at the same height at some point.

\(16t^2 + 250 = -16t^2 - 10t + 100\)

By rearranging and simplifying, we can get a quadratic equation in standard form:

\(32t^2 + 10t - 150 = 0\)

Using the quadratic formula, we can solve for t:

t = \((-b \± \sqrt{(b^2 - 4ac))} / 2a\)

where a = 32, b = 10, and c = -150

t =\((-10 \± \sqrt{ (10^2 - 4(32)(-150)))} / 2(32)\)

t = \((-10 \± \sqrt{(2500))} / 64\)

t = \((-10 \± 50) / 64\)

We can discard the negative solution since time cannot be negative. Therefore, t = 5/16 seconds.

To find the height of the quarter at that time, we can substitute t = 5/16 into the polynomial for the quarter:

Quarter: \(16(5/16)^2 + 250\) = 258.75 feet

Therefore, the quarter is at a height of 258.75 feet when the dime and quarter are at the same height.

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The domain and range of F is F={(x, y) Ix+y=10] is: 3. Domain: All Real Numbers Range: All Real Numbers

The given set F={(x, y) | x+y=10} represents a linear equation where the sum of x and y is always equal to 10.

To determine the domain and range of F, we need to consider the

possible values of x and y that satisfy the equation.

Domain: The domain represents the set of all possible values for the independent variable, which in this case is x. Since there are no restrictions on the value of x, the domain is All Real Numbers.

Range: The range represents the set of all possible values for the dependent variable, which in this case is y. By rearranging the equation x+y=10, we can solve for y to get y=10-x. Since x can take any real value, y can also take any real value. Therefore, the range is also All Real Numbers.

The correct answer is: 3. Domain: All Real Numbers Range: All Real Numbers

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The overall distance Tia jumped was 13.358 feet.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

Tia's high jump heights were 4.5, 4.76, and 4.098 feet.

To find the total number of feet that Tia jumped, you can add up all of her scores.

Her scores were 4.5 feet, 4.76 feet, and 4.098 feet,

So, the total number of feet she jumped is :

⇒ 4.5 feet + 4.76 feet + 4.098 feet

Apply the addition operation to get

⇒ 13.358 feet.

Therefore, the total number of feet she jumped is 13.358 feet.

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Answer:

B: 395

Step-by-step explanation:

Answer:400

Step-by-step explanation:

Total Total revenues will exceed = 8782.01

What is Total Revenue?

Total revenue is the overall sum of money received by a business through the sale of its products and services. Based on demand and price, it measures how successfully a company is generating revenue from its main operations.

Let x - normal (101.15 ,12.15)

where µ = 101.15

σ = 12.15

Mean for 85 customers

µ = 85 * 101.15 =8597.75

standard deviation for 85 customers

σ = \(\sqrt{85}\) * 12.15 = 112.017

P ( x >x₁ ) = 0.05

P ( x-µ/ σ > x₁-8597.75/112.017) = 0.05

P (Z >Z₁) = 0.05

Where

Z₁ = x- 8597.75/112.017

Z₁ = 1.645

Then x = 112.017 *1.645 +8597.75

x = 8782.01

Total total revenues will exceed = 8782.01

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The two congruent base angles' measurements ∠D = 14.36 and

∠E = ∠F = 82.9

A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

As per the data given in the above question are as bellow,

As seen in the picture below, we have D, E, and F as well as sides D, E, and F.

We determine the angle D using the cosine rule.

\(d^2=e^2+f^2-2(e)(f) \cos (D) \\3^2=12^2+12^2-2(12)(12) \cos (D)\)

9=144+144-288 cos(D)

9=288-(288 cos(D))

9-288= -288 cos(D)

-279 = -288 cos (D)

-279/288 = cos (D)

\(D=\cos ^{-1}\left(\frac{279}{288}\right)\)

D=14.26

Triangle DEF is an isosceles triangle, allowing us to calculate E and F using the triangle's angles.

180°-14.36 = 165.64°, rounded to 1 dp;

165.64°2=82.9°

We now get

D = 14.36,

E = 8, and F = 82.9.

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Note: The missing diagram is as bellow.

The smallest angle, angle E, measures is 82 degrees.

Given that DE = DF = 12 and FE = 3, we can see that DE and DF are equal, which means that angles D and F are congruent.

Additionally, EF is the unequal side, so angle E will be the smallest angle in the triangle.

To find the angle measures, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

c²= a² + b² - 2abcos(C)

we know that DE = DF = 12, and EF = 3.

We can set up the equation for angle E:

12²= 12² + 3² - 2 × 12 × 3×cos(E)

Simplifying the equation:

144 = 144 + 9 - 72 × cos(E)

144 = 153 - 72 ×cos(E)

72 × cos(E) = 9

cos(E) = 9 / 72

cos(E) = 1 / 8

To find the measure of angle E, we need to take the inverse cosine (arccos) of 1/8:

E = arccos(1/8)

E = 82.77 degrees (rounded to the nearest degree)

Since the triangle is isosceles, angles D and F are congruent. T

Therefore, each of the base angles (angles D and F) will measure:

D = F = (180 - E) / 2

D = F = (180 - 82) / 2

D = F =98 degrees

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The measure of the other angle in the linear pair is: 118°.

A linear pair is formed by two angles, whose sum equals 180 degrees.

Given that one of the angles of a linear pair is 62 degrees, the measure of the other angle will be its supplement.

Thus:

The other angle = 180 - 62 = 118°

Therefore, the measure of the other angle in the linear pair is: 118°.

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m > 650 miles

A mileage over 650 miles makes company A cheaper than B.

1) Gathering the data

Company A

$127 (unlimited mileage)

Company B

$75 + 0.08m

2) To find out the mileage that makes Company A cheaper than Company B, we can write out the following:

3) Hence when we drive over 650 miles the Company A becomes cheaper than B.