A cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is
2.5 inches. What is the height of the box?​

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:Portion put up on Wednesday =1/12

Step-by-step explanation:

Since we are dealing with fraction

Let the total fence = 1 whole

such that fence put up on Monday = 3/4

and fence he put p on Tuesday = 1/6

Since he put up the rest on Wednesday, To find the portion put up we have that

Portion put up on Wednesday =Total portion of fence - ( Portion put up on Monday and Tuesday)

=1- ( 3/4 + 1/6)

= 1-  18+ 4/ 24

=1- 22/24

= 2/24

Portion put up on Wednesday =1/12

Answer:

Step-by-step explanation:

If the radius of the circle is 6 feet. Then the area of the circle will be 113.097 square feet.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The radius of the circle is 6 feet.

Then the area of the circle will be

Area = πr²

where r is the radius of the circle. Then we have

Area = π × 6²

Area = 36π

Area = 113.097 square feet

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The range of six numbers is 8

According to the question,

Total number of Number = 6

Mean of number = 8

Ratio of numbers = 1 : 1 : 2 : 2 : 3 : 3

Let the common factor in numbers be "x"

Then , sum of number will be x + x + 2x + 2x + 3x +3x

=> 12x

Mean = sum of quantity / Number of quantity

8 = 12x / 6

Calculating the value of x,

12x = 48

=> x = 4

Substituting the value of x,

Number will be : 4 , 4 , 8 , 8, 12 , 12

Range = highest number - smallest number

Here , highest is 12 and smallest is 4

Therefore , Range = 12 - 4

=> 8

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Answer:

We can use the formula for compound interest to find the amount that needs to be deposited:

A = P(1 + r/n)^(nt)

where:

A = accumulated amount

P = principal amount (amount to be deposited)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time in years

In this case, we have:

A = R197 000

r = 0.12 (12% as a decimal)

n = 4 (quarterly compounding)

t = 5 years

Substituting these values into the formula, we get:

R197 000 = P(1 + 0.12/4)^(4 x 5)

Simplifying:

R197 000 = P(1.03)^20

P = R197 000 / (1.03)^20

P = R94 838.36 (rounded to the nearest cent)

Therefore, the amount that needs to be deposited today is R94 838.36.

The actual probability histogram of how frequently we win will roughly follow the normal curve as both the number of games we play and the number of simulations we run increase.

The central limit theorem states that under certain conditions, the probability distribution of the sum (or average) of a large number of independent and identically distributed random variables will approach a normal distribution.

In the case of roulette, if we bet $5 on even numbers and count the number of times we win after a large number of bets, this corresponds to a sum of a large number of independent Bernoulli trials, each with probability p of success (winning on an even number). Therefore, if we want the true probability histogram of the number of times we win to approximately follow the normal curve, we need to ensure that the conditions of the central limit theorem are met.

One way to do this is to increase the number of times we play (i.e., the number of independent Bernoulli trials). As the sample size increases, the distribution of the sample mean (i.e., the proportion of wins) will become more normal.

Another way to achieve this is to increase the number of simulations used to approximate the probability histogram. The more simulations we run, the closer the probability histogram will be to the true underlying distribution. Moreover, as the number of simulations increases, the central limit theorem ensures that the distribution of the sample mean will converge to a normal distribution.

Therefore, both increasing the number of times we play and increasing the number of simulations will have the effect of making the true probability histogram of the number of times we win approximately follow the normal curve.

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The integral distributes over the sum:

\(\displaystyle \int \left(4x^{\frac34} + 2x^{\frac34} + 4x^{\frac12} + 2x + 2\right) \, dx \\\\\\ = \int 4x^{\frac34} \, dx + \int 2x^{\frac34} \, dx + \int 4x^{\frac12} \, dx + \int 2x \, dx + \int 2 \, dx\)

Then just integrate each term using the power rule; if n ≠ -1, then

\(\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C\)

Then your integral is simply

\(\displaystyle \int \left(4x^{\frac34} + 2x^{\frac34} + 4x^{\frac12} + 2x + 2\right) \, dx \\\\\\ = \frac{4x^{\frac34+1}}{\frac34+1} + \frac{2x^{\frac34+1}}{\frac34+1} + \frac{4x^{\frac12+1}}{\frac12+1} + \frac{2x^2}2 + \frac{2x^1}1 + C \\\\\\ = \frac{16}7 x^{\frac74} + \frac87 x^{\frac74} + \frac83 x^{\frac32} + x^2 + 2x + C \\\\\\ = \boxed{\frac{24}7 x^{\frac74} + \frac83 x^{\frac32} + x^2 + 2x + C}\)

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The equation of the line that is parallel to the given line and passes through the point (7,-4) is y = -2x + 10.

The equation of the line that is perpendicular to the given line and passes through the point (7,-4) is y = 1/2x - 15/2.

The equation of a line that is parallel to a given line is calculated as follows;

y = -2x + 6

slope of this line = - 2

Any line that is parallel to this line will also have a slope of -2.

The equation of the line that is parallel to the given line and passes through the point (7,-4):

y - y1 = m(x - x1)

y - (-4) = -2(x - 7)

y + 4 = -2x + 14

y = -2x + 10

The slope of the line perpendicular to the line = 1/2

y - y1 = m(x - x1)

y - (-4) = (1/2)(x - 7)

y + 4 = (1/2)x - (7/2)

y = 1/2x - 7/2 - 4

y = 1/2x - 15/2

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Answer: 1 1/3

Step-by-step explanation: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

Hope this Helps :3

Step-by-step explanation:

Hey there!

Given;

\( = \frac{8}{9} + \frac{4}{9} \)

Adding them.

\( = \frac{8 + 4}{9} \)

\( = \frac{4}{3} \)

Change into mixed number.

\( = 1 \frac{1}{3} \)

Hope it helps....

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

No matter which direction an object is going in, speed is a scalar variable that quantifies how swiftly it is moving. The rate at which an object changes its position in a particular direction is measured by a vector quantity called velocity.

Speed: The amount of time it takes to cover a certain distance is stated in units like meters per second (m/s) or miles per hour (mph). For instance, a car's speed is 60 mph if it covers 60 miles in an hour.

Both the speed and direction of motion are included in the displacement per unit of time, which is stated in terms like meters per second (m/s) or miles per hour (mph). For instance, a car's velocity is 60 mph due north if it drives 60 miles in an hour in that direction.

In other words, velocity informs us on the direction and speed of an object's motion in addition to its speed.

Janet completed a 4 mile run yesterday in 30 minutes. We can calculate her running speed using the following data:

rate = distance/time = 4 miles/30 minutes = 0.1333 miles/minute

Today Janet ran for 45 minutes at the same pace. We can calculate how far she ran today using her rate:

Rate = Distance 45 minutes at a speed of 0.1333 miles per minute equals 6 miles.

Janet completed 6 kilometers of running today.

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Answer:

x = 3/2

Step-by-step explanation:

Since this is an isosceles triangle, the length of two sides would be congruent.

Those two sides are represented with 8x - 1 and 4x + 5 respectively.

We can write the following equation based on the above mentioned information:

8x - 1 = 4x + 5

8x - 4x = 5 + 1

4x = 6

x = 6/4 this can be simplified to 3/2

The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards

= 24÷1/4

= 24× 4

= 96

Hence he can divide the rope into 96 pieces.

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Answer:

12

Step-by-step explanation:

I am in 12th grade and make straight A;s trust me

The company sells all that it produces, the profit function is:-0.5x2+60x-250.

P(x)= R(x)-C(x)      

=-0.5(x-110)2 +6050-(50x+250)

Let Distribute Negative Sign      

P(x)= -0.5(x-110)2 + 6050 +-1(50x+250)

P(x)= -0.5(x-110)2 + 6050 +-1(50x) + (-1) (250)

P(x)= -0.5(X-110)2 +6050 +-50x + -250

Distribute P(x)= -0.5x2+110x+-6050+6050+-50x+-250

Combine Like Terms

P(x)= -0.5x2 +110x+-6050+6050+-50x+-250

P(x)=(-0.5x2) + (110x+-50x) + (-6050+6050+-250)  

P(x)= -0.5x2+60x-250

Therefore the company sells all that it produces, the profit function is:-0.5x2+60x-250.

The missing requirement is:

Assuming that the company sells all that it produces, what is the profit function?

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Answer:

$181.4

Step-by-step explanation:

Note,

Therefore, the store applied a discount price of $181.4 to the set of golf clubs.

a. Length of GK = \(\sqrt{34}\)  and Length of adjacent to GK = \(\sqrt{34}\)

b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. The parallelogram GHJK is Square.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)

a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)

for points G(-3, 6) and K(-6, 1)

Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)

Length of GK = \(\sqrt{34}\)

Length of adjacent side (GH, KJ) to GK =  \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)

Length of adjacent to GK = \(\sqrt{34}\)

b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)

Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)

Slope of GK = \(\frac{5}{3}\)

Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)

Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. All sides are equals to \(\sqrt{34}\)

So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)

and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)

All sides and diagonals are equal then parallelogram GHJK is Square.

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A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

If A = 136 when \(b_{1}\) = 7 and h = 16, find \(b_{2}\)

We are given the equation that we are working with:

A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

We are given certain values that the variables, in this case, are equal to:

A = 136

\(b_{1}\) = 7

h = 16

Substitute the given variables in the given equation for the corresponding numbers:

A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))

We know all the values in the equation except  \(b_{2}\). In order to find  \(b_{2}\) we must isolate it on one side of the equation

136 = 8 (7 + \(b_{2}\))

\(\frac{136}{8}\) = \(\frac{8 (7 + b_{2}) }{8}\)

17 = 7 + \(b_{2}\)

17 - 7 = 7 - 7 + \(b_{2}\)

10 =   \(b_{2}\)

If   \(b_{2}\) is equal to 10 then if we plug it back into the given equation both sides of the equation should equal each other. Remember to use PEMDAS

136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))

136 = \(\frac{1}{2}\) * 16 (7 + 10)

136 = \(\frac{1}{2}\) * 16 (17)

136 = 8 (17)

136 = 136

\(b_{2}\) = 10

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

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The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer:

26 degrees

Step-by-step explanation:

It is the correct solution on delta math

Answer:

Step-by-step explanation:

Use the law of sines:

Answer: If the X is a multiplication symbol then it would be 75

Step-by-step explanation:

10(3^2)−(3)(3)−6

=(10)(9)−(3)(3)−6

=90−(3)(3)−6

=90−9−6

=81−6

=75

Answer:

100x2/3-3x/3-6

Step-by-step explanation:

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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The slope of the line determined by the points (-3,2) and (2,-2) is -0.8. The slope of a line is a measure of the steepness of the line.

To find the slope of a line given two points, you can use the formula:

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

Plugging in the coordinates of the two points given, we get:

slope = (-2 - 2) / (2 - (-3))

= -4 / 5

= -0.8

So, the slope of the line determined by the points (-3,2) and (2,-2) is -0.8.

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- 8r + 14 > 60

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

r  = 23/4  

Interval Notation: ( − ∞ , − 23 4 )

42 + 50 < 58​

Add  

42  and  50 .

92 < 58

I hope its right

Answer:

Not necessarily, because this wasn't an experiment.

Step-by-step explanation:

Making conclusion based on the result of the survey about the happiness of employees due to the fact that they work in a digital workplace is inaccurate.

Statistical tests may not be enough to make generalization about the entire population due to the presence of a possible confounding or third variable unless established using scientific evidence.

Therefore, the lack of scientific evidence means that concluding that working in a digital workplace causes employee happiness is inaccurate.

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Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........