A candy box is made from a piece of cardboard that measures 29 by 16 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?

Answer:

4

Step-by-step explanation:

When you fold it to make it a cube, the number opposite to 1 is 4

In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

Read more about exponents here:

https://brainly.com/question/13669161

#SPJ1

The Question in English

What does a^2 mean in mathematics

The 98% confidence interval for the mean of the repeated measurements of the weight, with the sample size of 5, is approximately (5.3503, 14.6515).

To get the confidence interval, first let's see what we know:

To calculate the standard deviation, we'll use the sample mean as an estimate for the population standard deviation:

Standard Deviation = SD = x / √n

SD = 10.0009 / √5 ≈ 4.4721

Now we can calculate the margin of error:

Margin of Error = 2.326 * (SD/ √n) = 2.326 * (4.4721 / √5) ≈ 4.6506

Finally, we can calculate the 98% confidence interval:

Confidence Interval = (x - Margin of Error, x + Margin of Error) = (10.0009 - 4.6506, 10.0009 + 4.6506) ≈ (5.3503, 14.6515)

Learn more about confidence intervals at:

https://brainly.com/question/20309162

#SPJ4

Answer:

10 - (-2) = 12, 10 + 2 = 12

Step-by-step explanation:

10 - (-2) = 12

10 + 2 = 12

Answer:

66.67 in^3

Step-by-step explanation:

volume of a cylinder = nr^2h

Volume of a cone =  1/3(nr^2h)

n = 22/7

r = radius

the volume of a cone is 1/3 that of a cylinder

volume of the cone = 1/3 x (200) = 66.67 in^3

The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

The measure of an inscribed angle is equal to half the measure of its intercepted arc. Since angle QTR intercepts arc QR, the measure of angle QTR is half the measure of arc QR. Therefore, to find the measure of angle QTR, we need to determine the measure of arc QR.

1. To find the measure of arc QR, we can use the fact that tangents are perpendicular to the radius at the point of tangency. This means that angle QSR (formed by the tangent PQ and the radius QS) is a right angle. Since angle QSR is a right angle, arc QR is a semicircle, which has a measure of 180 degrees. Therefore, the measure of angle QTR is half of 180 degrees, which is 90 degrees.

2. The measure of angle QTR is 90 degrees. This is determined by recognizing that angle QTR is an inscribed angle intercepted by the tangent line PQ and the secant line PR. The measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the tangent PQ forms a right angle with the radius QS, making arc QR a semicircle with a measure of 180 degrees. Therefore, angle QTR, intercepted by arc QR, has a measure of 90 degrees.

Learn more about intercepted arc here: brainly.com/question/29886231

#SPJ11

Answer:

7

Step-by-step explanation:

42/6=7

Answer:

D. 7

Step-by-step explanation:

4 power 1/2 =x -5

2 = x - 5

2+5 = x

x = 7

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

Learn more about money

brainly.com/question/2696748

#SPJ11

Answer:

Blue marble: 1/3

Step-by-step explanation:

There are 3 marbles as a of 9 total marbles. Divide 3 by 9 and the simplify 3/9 into 1/3 as both are divisible by

We can conclude that there is no measurable effect of immersing them in water or dropping them. Thus, we cannot conclude that the treatment has any significant effect.

To answer whether there appears to be any measurable effect of immersing the devices in water or dropping them, we have to compare the average scores of each group before and after submerging them in water or dropping them.

The null and alternative hypotheses are stated as follows:

Null Hypothesis H0:

µ1 = µ2 = µ3

Alternative Hypothesis Ha:

µ1 ≠ µ2 ≠ µ3

The level of significance is α = 0.05.

ANOVA table helps us to calculate the test statistic.

The calculated F-value of 1.56 is less than the critical F-value of 3.05 at the 0.05 level of significance.

Since the calculated F-value is less than the critical F-value, we fail to reject the null hypothesis.There is no significant difference in the scores between the groups.

Learn more about null hypothesis at:

https://brainly.com/question/32572205

#SPJ11

Answer: The answer is 3/8.

Learn how to add and subtract fractions

Khan Academy Video: Adding and subtracting fractions

The value of expression in fraction form is,

⇒ 3/8

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ 7/8 - 1/2

Now, We can simplify as;

⇒ 7/8 - 1/2

⇒ (7 - 4) / 8

⇒ 3 / 8

Thus, The value of expression in fraction form is,

⇒ 3/8

Learn more about the subtraction visit:

https://brainly.com/question/17301989

#SPJ5

a. The most economical speed for a trip is v = 35 mph. and b. The largest value of M is M = 87.5 miles.

a. To find the most economical speed for a trip, we need to maximize the value of M, which represents the number of miles the automobile can travel on one gallon of gasoline.

Given equation: M = -(1/30)v² + (5/2)v

Take the derivative of M with respect to v using the power rule for derivatives:

dM/dv = -(2/30)v + (5/2)

Set the derivative equal to 0 and solve for v to find the critical point:

-(2/30)v + (5/2) = 0

-(2/30)v = -(5/2)

v = (5/2) * (30/-2)

v = 35

Since v must be less than 70 according to the given range, the most economical speed for the trip is v = 35 mph.

b. To find the largest value of M, we can substitute the given expression for M into the equation and evaluate it for the given range of v, which is v < 0 < 70.

Given equation: M = -(1/30)v² + (5/2)v

Substitute v = 70 into the equation to find the largest value of M:

M = -(1/30)(70)² + (5/2)(70)

M = -4900/30 + 350/2

M = -163.33 + 175

M = 11.67

Therefore, the largest value of M is M = 87.5 miles. (rounded to two decimal places)

To know more about speed, refer here:

https://brainly.com/question/17661499#

#SPJ11

4/9

hope it helps...!!!

Answer:

\( \frac{4}{9} \)

Step-by-step explanation:

\( \frac{80 \div 10}{180 \div 10} = \frac{8 \div 2}{18 \div 2} = \frac{4}{9} \)

Hope this help you out =)

Answer:

C. 10.0 m

Step-by-step explanation:

\(C=2\pi r\)

radius is half of diameter

\(r = \frac{d}{2} \\r=\frac{3.2}{2} \\\)

\(C= 2 (3.14) \frac{3.2}{2}\)

\(C= (3.14)3.2\\C=10\)

Answer:

To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.

Step-by-step explanation:

This is a continuation of the question on the recipe for making salad. The initial recipe from her grandmother is stated below (found on brainly, ID 6786167).

The fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape.

Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit.

Number of cups required for each fruit in the original recipe:

apple = 1 cup , orange = 1 cup, strawberry = 4cups, cherry = 2cups, grape = 3cups

Original ratios of the cup of fruit respectively = 1:1:4:2:3

Total number of cups required in the original recipe: 1+1+4+2+3 = 11 cups

Now for this question, 3 cups of apples are remaining. And we want to find number of other fruits she needs in order to use up the remaining apples.

To do this we would use the ratios of the cup of fruit.

When we had 1 apple, the ratio was = 1

Now we have 3apples, the new ratio = 3×original ratio

=3×1 = 3

This means we would multiply each of the fruit ratios by 3

For orange, new ratio = 3×1 = 3

For strawberries, new ratio = 3×4 = 12

For cherry, new ratio = 3×2 = 6

For grape, new ratio = 3×3 = 9

To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.

Answer:

Priscilla uses one part orange, four parts strawberry, two parts cherry, and three parts grape for every one part apple. So, to use three times the quantity of apples, she will have to use three times the quantity of the other fruits as well. She needs three parts orange, twelve parts strawberry, six parts cherry, and nine parts grape for three parts apple.

Step-by-step explanation:

plato/edmentum answer

The general solution to the homogeneous equation is:

\([\vec{y}_C(t) = c_1 e^{-5t}\begin{bmatrix}2 \ -3\end{bmatrix} + c_2 e^{3t}\begin{bmatrix}2 \ 1\end{bmatrix}]\)

where (\(c_1\)) and (\(c_2\)) are constants.

To find the complementary solution to the homogeneous equation \((\vec{y}'=\begin{bmatrix}1 & 4 \\\ 3 & -3\end{bmatrix}\vec{y})\), we first need to find the eigenvalues and eigenvectors of the coefficient matrix.

The characteristic equation is:

\(\left|\begin{matrix} 1-\lambda & 4 \\\ 3 & -3-\lambda \end{matrix}\right| &= (1-\lambda)(-3-\lambda) - 4\cdot 3 \&= \lambda^2 + 2\lambda - 15 \&= (\lambda+5)(\lambda-3)\end{align*}\)

So the eigenvalues are (\(\lambda_1 = -5\)) and (\(\lambda_2 = 3\)).

To find the eigenvectors, we solve the system\(((A-\lambda I)\vec{x} = \vec{0})\) for each eigenvalue. For (\(\lambda_1 = -5\)), we have:

\(\begin{bmatrix} 1-\lambda_1 & 4\\ \ 3 & -3-\lambda_1 \end{bmatrix}\begin{bmatrix}x_1 \ x_2\end{bmatrix} &= \begin{bmatrix}0 \ 0\end{bmatrix} \\Rightarrow \begin{bmatrix}6 & 4\\ \ 3 & 2\end{bmatrix}\begin{bmatrix}x_1 \ x_2\end{bmatrix} &= \begin{bmatrix}0 \ 0\end{bmatrix}\end{align*}\)

Solving this system, we get the eigenvector:

\([\vec{v}_1 = \begin{bmatrix}2 \ -3\end{bmatrix}]\)

For (\(\lambda_2 = 3\)), we have:

\(\begin{bmatrix} 1-\lambda_2 & 4\\ \ 3 & -3-\lambda_2 \end{bmatrix}\begin{bmatrix}x_1 \ x_2\end{bmatrix} &= \begin{bmatrix}0 \ 0\end{bmatrix} \\Rightarrow \begin{bmatrix}-2 & 4 \\\ 3 & -6\end{bmatrix}\begin{bmatrix}x_1 \ x_2\end{bmatrix} &= \begin{bmatrix}0 \ 0\end{bmatrix}\end{align*}\)

Solving this system, we get the eigenvector:

\([\vec{v}_2 = \begin{bmatrix}2 \ 1\end{bmatrix}]\)

Therefore, the general solution to the homogeneous equation is:

\([\vec{y}_C(t) = c_1 e^{-5t}\begin{bmatrix}2 \ -3\end{bmatrix} + c_2 e^{3t}\begin{bmatrix}2 \ 1\end{bmatrix}]\)

where (\(c_1\)) and (\(c_2\)) are constants.

Learn more about " homogeneous equation " : https://brainly.com/question/14926412

#SPJ11

Answer:

A.

\( \frac{12}{5} \)

Step-by-step explanation:

tan ? = \( \frac{front}{side} \)

In picture, we know tan F = tan R

the length of side;

= √oblique² - front²

= √13² - 12²

= √169 - 144

= √25

side = 5 cm

So, tan R = \( \frac{front}{side} \)

= \( \frac{12}{5} \)

So, the answer is A

Given :-

To find:-

Answer:-

Since here the given two triangles are similar, therefore,

Hence ,

\(\implies \dfrac{DE}{DF}=\dfrac{CA}{AR}\\\)

\(\implies \tan F = \tan R \dots (1) \\\)

Now in ∆DEF ,

So on using Pythagoras theorem we have,

\(\implies DE^2 + EF^2 = DF^2 \\\)

\(\implies DE^2 = (13ft)^2-(12ft)^2\\\)

\(\implies DE^2 = 169ft^2-144ft^2\\\)

\(\implies DE^2 = 25ft^2 \\\)

\(\implies DE =\sqrt{25 ft^2} \\\)

\(\implies \underline{\underline{ DE = 5\ ft.}} \\\)

Now again we know that ,

\(\implies \tan\theta =\dfrac{perpendicular}{base}\\\)

And here ,

\(\implies \theta = \angle F \\\)

So ,

\(\implies \tan F = \dfrac{DE}{EF} \\\)

\(\implies \tan F =\dfrac{5ft}{12ft}=\boxed{\dfrac{5}{12}} \\\)

Hence from equation (1) , we have;

\(\implies \underline{\underline{\tan R =\dfrac{5}{12}}} \\\)

and we are done!

Answer:

zero

Step-by-step explanation:

the slope of a function m: y2-y1/x2-x1

m=-3-(-3)/5-(-5)

m=0/10=0

The slope of the line drawn passing through (- 5, - 3) and (5, - 3) is zero, so option C is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

straight line drawn passing through (- 5, - 3) and (5, - 3)

Calculate the slope of the line as shown below,

\(m = y_2 - y_1 / x_2 - x_1\)

m = slope

m = -3 - (-3) / 5 - (-5)

m = 0 / 10

m = 0

Therefore, the slope of the line drawn passing through (- 5, - 3) and (5, - 3) is zero.

To know more about the line:

https://brainly.com/question/2696693

#SPJ6

Answer:

A. ( x + 2y = ( y - 3 ) = 7

maaf kalo salah

74=p×38 is the percent equation that can be used to solve the following problem 38 What's is the percent of 74

To find the percent of a number, we need to divide the part (38) by the whole (74) and then multiply by 100 to convert the decimal to a percentage.

So the percent equation is:

38/74 = p/100

We can cross-multiply to solve for p:

74p = 38 × 100

p = (38 × 100) / 74

p = 51.35

Therefore, the percent of 38 in 74 is approximately 51.35%, option B is correct

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

To determine the number of seconds it took for the cannonball to hit the ground, we need to look for the point in the table where the height is equal to zero.

From the given data, we can see that at 5 seconds, the height is 0 feet. Therefore, the cannonball hit the ground 5 seconds after it was dropped.

So the answer is: 5

Learn more about feet here:

https://brainly.com/question/15658113

#SPJ11

The number of students that leave by bus or car is given as follows:

5801 students.

The union and intersection sets of multiple sets are defined as follows:

The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.

Hence the number of students that leave by bus or car is given as follows:

3232 + 2549 = 5801 students.

More can be learned about union and intersection at brainly.com/question/4699996

#SPJ1

Answer:

-1 |4  |-7|6

-6|5  |0 |3

8| -5|2 |-3

1|-2  |7 | -4

Hope this helps

Step-by-step explanation:

Answer:

7066.66666667

Step-by-step explanation:

Sorry if i'm wrong

while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent​

Let

x ------> amount that Curtis spent

we have that

10=2x-26 ------> equation that represent this situation

solve for x

2x=10+26

2x=36

x=$18

therefore

Answer:

  095

Step-by-step explanation:

You want the bearing from C to D, given that the bearing from D to C is 85° west of north.

The bearing from C to D will be the opposite of the bearing from D to C.

Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.

  180° +(-85°) = 95°

The 3-digit bearing of D from C is 095.

So, the system of equations representing this situation is: n + d + q = 95; 0.05n + 0.10d + 0.25q = 13.70; q = d + 11.

To represent this situation with a system of equations, we can use the following equations:

The total number of coins: n + d + q = 95

The total value of the coins in dollars: 0.05n + 0.10d + 0.25q = 13.70

The relationship between the number of quarters and dimes: q = d + 11

The first equation represents the total number of coins, which is given as 95.

The second equation represents the total value of the coins in dollars, which is given as $13.70. The values of each coin (nickel, dime, quarter) are multiplied by their respective quantities (n, d, q) and summed up to obtain the total value.

The third equation represents the relationship between the number of quarters (q) and dimes (d), which states that there are 11 more quarters than dimes.

To know more about equations,

https://brainly.com/question/20499926

#SPJ11

Answer:

x > - 8

Step-by-step explanation:

Given

48 > - 6x

Divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity.

- 8 < x , thus

x > - 8

Answer:

x >-8

48>−6x

Step 1: Flip the equation.

−6x<48

Step 2: Divide both sides by -6.

\(\frac{-6x}{-6}\)< \(\frac{48}{-6}\)

x>−8