A person is putting oranges into a box. The dimensions of the box
are 13 inches by 16 inches by 13 inches. Assuming oranges are
spherical with a 2.8-inch diameter, how many oranges should fit in
the box? (Hint: Packing spheres in a rectangular prism usually takes
up 190% of the volume of the spheres using random packaging.)
Answer:
oranges

Answer:

44

Step-by-step explanation:

20+36+40+80= 176

176/4= 44

Answer:

2 and 5

Step-by-step explanation:

Use the sum-product pattern

3x^{2}{\color{#c92786}{-11x}}-20

3x^{2}+{\color{#c92786}{4x}}{\color{#c92786}{-15x}}-20

2

Common factor from the two pairs

3x^{2}+4x-15x-20

x(3x+4)-5(3x+4)

3

Rewrite in factored form

x(3x+4)-5(3x+4)

(x-5)(3x+4)

Solution

Answer:

54 yd²

Step-by-step explanation:

A = 10 yd × 3 yd + 6 yd × 4 yd

A = 30 yd² + 24 yd²

A = 54 yd²

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Let's practice a little algebra and set the second distance to x.

9/4=270/x

solve

9x=270*4

x=30*4

x=120

The second distance is 120.

Done! any question about this just ask me in the comment.

La expresion que podemos utilizar para encontrar el valor de los lados del cuadrado :

R = \(\sqrt{x^{2}+16x+64}\)

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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Answer:

1.025 is the anwser in decimal form

Answer:

1 1/40

Step-by-step explanation:

so change 5/8 and 2/5 to have a common denominator, which would be 40, so it would change into 25/40 + 16/40, which is 41/40, just add the numerators and simplify. hope this helped a bit

\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

Answer:

Option A.

Step-by-step explanation:

The given expression is,

\([(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}\)

By solving the given expression,

\((64)^{-\frac{1}{2}}=\frac{1}{(64)^{\frac{1}{2}}}\) [Since \(a^{-1}=\frac{1}{a}\)]

           \(=\frac{1}{\sqrt{64}}\)

           \(=\frac{1}{8}\)

Now the expression will be,

\([(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}=(\frac{1}{8})^{-\frac{2}{3}}\)

                 \(=8^{\frac{2}{3}}\)

                 \(={(\sqrt[3]{8})^2}\)

                 = 2²

                 = 4

Therefore, value of the given expression will be 4.

Option (A) will be the answer.

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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The inverse function is \(f^-1(X)=5x+6\),

Given,

\(y=\frac{x-6}{5}\)

To find inverse function, first interchange the variables 'x' and 'y'

\(x=\frac{y-6}{5}\)

solve for y,

\(5x=y-6\\\\5x+6=y\\\\y=5x+6\)

Replace y with \(f^-1(x)\)

\(f^-1(X)=5x+6\)

Thus, the inverse function is \(f^-1(X)=5x+6\)

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The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\(- 2 ( 2 x + 3 ) \leq 26.\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\(- 2 ( 2 x + 3 ) \leq 26\)

Divide both sides by -2. We know that since 2 is negative, it'll be < (less than) 0. So, the direction of inequality will change.

\(2x+3\geq \frac{26}{-2} \\ \)

Divide 26 by -2..we'll get the answer as -13.

\(2x+3\geq -13 \)

Now, subtract 3 from both the sides.

\(2x\geq -13-3 \)

Subtracting -13 by 3..we'll get the answer as -16.

\(2x\geq -16 \)

Divide both sides by 2. We know that since 2 is positive, the direction of inequality will remain the same.

\(x\geq \frac{-16}{2} \\ \)

Divide -16 by 2..we'll get the answer as -8.

\( \huge \boxed{ \boxed{ \bf \: x\geq -8 }}\)

Answer:

Since f′>0, f is strictly increasing, so if f(0)=0, you will have f>0 if x>0 and f<0 if x<0. There is no need to consider the second derivative.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

because 629 × 0 = 0 then f(1) would be 629. etc.

The point which represents the cost of 4 pints is:

                     (4,8)        

Step-by-step explanation:

We are given that:

A market sells strawberries for $2.00 per pint.

Then, cost of 4 pints= $ 4×2.00

                                = $8.00

The point on the x coordinate represents number of pints

and the point on the y coordinate represents the cost in dollars

Hence, the point which represents the cost of 4 pints is:

                     (4,8)        

Answer:

c on edg

Step-by-step explanation:

got it right :)

9514 1404 393

Answer:

  = 53(20 +4)  or  =24(50 +3)   or  =(20 +4)(50 +3)

Step-by-step explanation:

Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.

The usual method of multiplication taught in grade school makes use of this sort of rewriting.

53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272

__

Additional comment

We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.

In grade school, we did this digit by digit, so ...

  53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20

  = 12 +60 +200 +1000 = 1272

Answer:

12

Step-by-step explanation:

its either 12 or 18 try 12 first

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

3n-8

Explanation:

multiply n by 3 then subtract 8

Answer:

3 - 8 x n

Step-by-step explanation:

8 less than 3 -> 3 - 8

Times a number, n -> x n

Expression -> 3 - 8 x n

Answer:

Step-by-step explanation:

i think so

The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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Answer:

731

Step-by-step explanation:

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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The method to estimate the y - value from a graph is discussed below.

We have a graph.

We have to estimate how can the graph be used to predict the output (y- value) associated with an input of x = \(3\frac{1}{2}\) = \(\frac{7}{2}\) = 3.5

A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

According to the Question -

Assume that you have a graph plotted for the straight line given by -

y = 2x + 5              ...(1)

(Refer to the figure attached)

The x values are plotted along the horizontal line and the y values are plotted along the vertical axis. You can see in the diagram that for x = \(3\frac{1}{2}\) or 3.5 the corresponding value for y is 6.8. You can repeat the same process for almost any value of x. Similarly, you can find out the value of y without using graph. For x = 5, using Eq (1), we get -

y = 2 x 5 + 5 = 15

Hence, using this way you can predict the y - value for any input.

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Answer:

Present age of A = 16 years

Present age of B = 12 years

Step-by-step explanation:

Let the age of B be x years.

Therefore, age of A = (x + 4) years

Four years ago:

Age of A = (x + 4 - 4) = x years

Age of B = (x - 4) years

According to the given information:

\( \frac{x}{x - 4} = \frac{3}{2} \\ \\ 2x = 3(x - 4) \\ \\ 2x = 3x - 12 \\ \\ 2x - 3x = - 12 \\ \\ - x = - 12 \\ \\ x = 12 \\ \\ x + 4 = 12 + 4 = 16 \\ \\ present \: age \: of \: a = 16 \: yeras \\ \\ present \: age \: of \: b = 12 \: years \\ \)

the solution for \(\theta\) on the interval \((-\pi/2,\pi/2)\) is approximately  \(1.305\)radians.

An interval is a set of real numbers that includes all the numbers between two endpoints. The endpoints can be included or excluded from the interval, depending on whether square brackets or parentheses are used to define the interval.

The equation is:

\(tan(\theta) = 3.804\)

To solve for θ, we can use the inverse tangent function (also known as arctan or tan^-1) on both sides of the equation:

\(\theta = tan^-1(3.804)\)

Using a calculator, we can evaluate this expression and get:

\(\theta \approx 1.305\) radians (rounded to three decimal places)

Therefore, the solution for \(\theta\) on the interval \((-\pi/2,\pi/2)\) is approximately  \(1.305\)radians.

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Step-by-step explanation:

=27/100×160

=43.2

hope it helps.

Answer:

43.2

Step-by-step explanation:

All you have to do is multiply 160 by 0.27. For percentages you always do 0. whatever the percentage is