A truck carrying 9.35 pounds of sand travels to a construction yard and loses 4.6 pounds of sand along the way. How much sand does the truck have when it arrives at the yard?

The radius and volume of the cylinder are 4 cm and 754 cm³ respectively and volume of the cone is 216 cm³.

What the volume of a cone and cylinder?

Volume of cone and cylinder is V = (1/3)πr²h and V = (1/3)πr²h respectively

where r is the radius of the base of the cone, h is the height of the cone, and π is the mathematical constant π (approximately equal to 3.14).

For cone:

To use this formula, we first need to find the radius of the base of the cone. We know that the diameter of the base is 12 cm, so the radius is half of that:

r = d/2 = 12/2 = 6 cm

Now we can plug in the values we have into the formula:

[tex]V = \frac{1}{3} \pi {r}^{2} h \\ V = \frac{1}{3} π( {6}^{2} )(19) \\ V = ( \frac{1}{3} )π(36)(19) \\ V = ( \frac{1}{3} )(3.14)(36)(19) \\ V = 216.24 cm³[/tex]

So, volume of the cone is 216.24 cm³ or 216 cm³ ( approximately)

For cylinder:

We are given the diameter of the cylinder as 8 cm, so we can find the radius as half of that:

r = d/2 = 8/2 = 4 cm

We are also given the height of the cylinder as 15 cm.

Now we can plug in these values into the formula:

[tex]V = π {r}^{2} h\\ V = π( {4}^{2} )(15) \\ V = π(16)(15) \\ V = 240π \\ V ≈ 753.98 \: cubic \: centimeters[/tex]

Therefore, the volume of the cylinder is approximately 753.98 cubic centimeters or 754 cm³ (approximately).

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The identity using the Pythagorean Identity:

[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex]  , Hence proved

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

the Fundamental Pythagorean Identity: sin²(x)+cos²(x)=1

Verify the identity using the Pythagorean Identity:

[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex]

To prove this take the right-hand side of the given identity.

We know that,

[tex]\frac{sinx}{1+cosx}*\frac{1-cosx}{1-cosx}\\\\=\frac{Sinx(1-cosx)}{1-cos^2x}\\\\=\frac{1-cosx}{sinx}[/tex]

Hence the left-hand sides.

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Answer:

90°

Step-by-step explanation:

Given the vectors:

[tex]\displaystyle{\vec v = \langle -6, -3\rangle \ \: \text{and} \ \: \vec u = \langle 4, -8 \rangle}[/tex]

You can find the angle between two vectors by solving for θ in the equation:

[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}[/tex]

Where:

[tex]\displaystyle{\vec v \times \vec u = v_xu_x + v_yu_y}\\\\\displaystyle{|\vec v| = \sqrt{v_x^2 + v_y^2}}\\\\\displaystyle{|\vec u| = \sqrt{u_x^2+u_y^2}}[/tex]

Therefore:

[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}\\\\\displaystyle{(-6)(4)+(-3)(-8) = \sqrt{(-6)^2+(-3)^2} \cdot \sqrt{4^2+(-8)^2} \cos \theta}\\\\\displaystyle{-24+24=\sqrt{36+9}\cdot \sqrt{16+64}\cos \theta}\\\\\displaystyle{0=\sqrt{45}\cdot \sqrt{80}\cos \theta}\\\\\displaystyle{\dfrac{0}{\sqrt{45}\cdot \sqrt{80}}=\cos \theta}\\\\\displaystyle{0=\cos \theta}\\\\\displaystyle{\theta = 90^{\circ}}[/tex]

Therefore, the angle between two vectors is 90 degrees.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. If the width is changed by a scale factor of 1/3, then the new width is (1/3)w. The length and height remain the same. Therefore, the new volume of the rectangular prism is:

V' = l(1/3w)h

Multiplying both sides by 3 to simplify the expression, we get:

3V' = lw(3h)

Since the original volume of the rectangular prism is 768 ft3, we have:

V = lwh = 768

Multiplying both sides by 3 to simplify the expression, we get:

3V = lw(3h)

Substituting 3V for lw(3h), we get:

3V' = 3V(1/3w) = Vw

Therefore, the new volume of the rectangular prism is:

V' = Vw = (768 ft3)(1/3) = 256 ft3

So, the volume of the same shape if the width is changed by a scale factor of 1/3 is 256 ft3.

Answer:

Let's start with the fixed cost, which is the cost to rent the room: $150. This is the y-intercept of the equation. Now, for each child attending the party, there is an additional cost of $5. We can represent the number of children attending with the variable x. Therefore, the equation in slope-intercept form is: y = 5x + 150 So the correct answer is D) y = 5x + 150

There is 53.5 cubic feet of space left for water in the aquarium.

The volume of three-dimensional space occupied by an object or substance alone is referred to as volume.

The aquarium's total volume can be found by multiplying its dimensions:

Volume = Length x Width x Height

Volume = 6 ft x 3 ft x 3 ft

Volume = 54 cubic feet

However, Ms. Collins has already filled the bottom of the tank with gravel that takes up 0.5 ft of space. Therefore, the remaining space for water is:

Remaining space = Total volume - Gravel volume

Remaining space = 54 cubic feet - 0.5 cubic feet

Remaining space = 53.5 cubic feet

So, there is 53.5 cubic feet of space left for water in the aquarium.

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This is called random sampling.

What is random sampling?

Random sampling is commonly used in research and statistical analysis, as it helps to reduce the potential for bias in the sample selection process. There are several techniques for conducting random sampling, such as simple random sampling, stratified random sampling, and cluster sampling, each with its own specific method of selection.

Random sampling is an important tool in statistical inference and research. By selecting a random sample from a population, researchers can obtain an estimate of the population parameters (such as the mean or proportion) with a known level of precision and confidence.

There are several techniques for conducting random sampling:

Simple random sampling: In this technique, each member of the population has an equal chance of being selected. This can be done by assigning each member of the population a unique number and using a random number generator to select the sample.

Stratified random sampling: In this technique, the population is divided into subgroups (strata) based on some characteristic (such as age or gender). A random sample is then selected from each stratum.

Cluster sampling: In this technique, the population is divided into clusters (such as neighborhoods or schools). A random sample of clusters is then selected, and all members within those clusters are included in the sample.

Random sampling has several advantages over non-random sampling methods, such as convenience sampling or purposive sampling. First, it helps to ensure that the sample is representative of the population, reducing the potential for bias in the sample selection process. Second, it allows for the calculation of sampling error, which is the degree of error that is inherent in any sample due to chance variation. Finally, random sampling allows for the use of inferential statistics, which enables researchers to make inferences about the b based on the sample data.

However, random sampling also has some limitations. It can be expensive and time-consuming to select a truly random sample from a large population. Additionally, it may be difficult to ensure that all members of the population are included in the sampling frame, which could result in some members being excluded from the sample. Finally, the sample size must be large enough to ensure a sufficient level of precision in the estimates of the b parameters.

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Answer: N=4

Step-by-step explanation:

Answer: n = 4

Step-by-step explanation:

subtract 9 from both sides simplify subtract 11n from both sides then combine like terms, simplify, divide both sides by the same factor, then simplify then boom :)

As the size of a sample increases, the mean of the distribution of sample means increases always. - False

The mean of the distribution of sample means does not always rise as sample number rises. The population mean is not changed by increasing the sample number because the population mean is equivalent to the mean of the distribution of sample means. The variation of the distribution of the sample means does, however, decline as the sample number rises.

The distribution of sample means approximates normality with a mean equal to population mean and a standard deviation equal to population standard deviation divided by square base of the total sample size. This is known as the central limit theorem. As a result, the distribution of sample means becomes more tightly focused around the community mean and less variable as the sample number rises.

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Step-by-step explanation & Answer

———-———-———-———-———-———-———-———-———-———-———-——

Page 1

So first we need to multiply the small packages by 5 because he needs to said 5 of them which is:

5 x 2.80 = 14 Which is our answer for the first part of the question.

Next we need to multiply the big/large packages by 4 because he is going to send 4 of them.

4 x 3.80 = 15.2 / ( money terms ) = 15.20

[tex]\left \{ {{small= 14} \atop {big=15.20}} \right.[/tex]

———-———-———-———-———-———-———-———-———-———-———-——

Page 2

We can them add them up or we can leave it at this but just in case lets add them up:

15.20 + 14 = 29.20 Which is the answer.

[tex]\left[\begin{array}{ccc}An&sw&r\\&=&\\22&.&9\end{array}\right][/tex]

The side length of each square is √225 in = 15 inches so the option B is correct

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9. The square root of 16 is 4 because 4 multiplied by 4 equals 16. The square root of a number is always a positive number, although it can be irrational (a non-repeating, non-terminating decimal) for some numbers.

The formula to find the length of one side of a square, s, when given the area, A, is:

s = √(A)

So, for the square with A = 225 in², the side length would be:

s = √(225) in

s = 15 inches

Therefore, the side length of the square with an area of 225 in² is 15 inches.

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Answer:

Step-by-step explanation:

The statement that is not true for the function notation of the volume of a cube, V(s) = s3, is not specified. Please provide the statement you are referring to.

This statement implies that the daily high temperature in the town in Alaska has been below -4°F (minus four degrees Fahrenheit) for three consecutive weeks.

Answer:

47

Step-by-step explanation:

Given: 94 decreased by 50%

First, we will change the percentage to a decimal, by moving the decimal two nodes to the left.

50% = .50

Next, we will multiply the decimal with the number.

94 · .50 = 47

check attached image for further explanation

The overall classification accuracy of this model on the test set is 0.179

The overall classification accuracy of the model can be calculated by dividing the number of correctly classified instances (the sum of true positives and true negatives) by the total number of instances in the test set

Accuracy = (TP + TN) / (TP + TN + FP + FN)

where TP = True Positives, TN = True Negatives, FP = False Positives, and FN = False Negatives.

From the confusion matrix given

True Positives (TP) = 124

True Negatives (TN) = 116

False Positives (FP) = 77

False Negatives (FN) = 851

Plugging these values into the formula, we get

Accuracy = (124 + 116) / (124 + 116 + 77 + 851)

Accuracy = 0.179

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The given question is incomplete, the complete question is:

The following classification confusion matrix shows the results of a model's classifications on a test set: Test Set Results Model Prediction FALSE TRUE FALSE 116 TRUE 77 124 851 (The rows refer to the model's classifications, and the columns to the actual results in the test set.) a. What is the overall classification accuracy of this model on the test set?

 so it is 2o bevuse

hi

The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.

Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:

tan(26.8°) = h/x ----(1)

tan(19.5°) = h/(x + 43.9) ----(2)

From equation (1), we have x = h/tan(26.8°)

Substituting this value of x in equation (2) and solving for h, we get:

h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))

Plugging in the values, we get:

h ≈ 62.4369 feet

Therefore, the height of the building is approximately 62.4369 feet.

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Let a = 10, b = 6, c = 12, and d = x

ab=cd

x = ab/c

x = 10(6)/12

x = 5

The number that should be added to both sides of this quadratic equation to complete the square is (-3/2)² .

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

We can solve quadratic equations that lack a factor by completing the square.

In order to make the left side of the formula a perfect square trinomial, the equation's form must be adjusted.

The given  quadratic equation:

1 = x² - 3x

This can be written as:

x² - 3x - 1 = 0

a = 1, b = -3 and c = -1.

using the formula: (b/2)² = (-3/2)²

The number added both side is:

(-3/2)² + 1 = x² - 3x + (-3/2)²  (required equation);

On simplification:

9/4 + 1 = (x -3/2)²

13/4 = (x -3/2)²

Thus, the number that should be added to both sides of this quadratic equation to completing square is (-3/2)² .

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Answer:27

Step-by-step explanation:First you find 10% of 30 which is 3 then you subtract 30-3=27

The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: [tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex] ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

[tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex]

To prove this take the right-hand sides

[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx[/tex]

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Answer:

B  only

Step-by-step explanation:

The correct answer is B only.

The distributive property states that a multiplication of a number by a sum or difference can be rewritten as the sum or difference of the products of the number with each term in the sum or difference. In other words, a(b + c) = ab + ac and a(b - c) = ab - ac.

Option A, 5 x 2 + 3 = 5 X (2 + 3), does not use the distributive property correctly. It tries to distribute the 5 over the sum 2 + 3, which is not possible.

Option B, 5 x 2 + 3 = 5 x (2) + 5 x (3), correctly applies the distributive property by distributing the 5 over each term in the sum 2 + 3.

Therefore, the valid application of the distributive property is B only.

The answer is A. 1/4.

The probability that the waiting time is greater than 5 minutes is 0.3012

Given that the waiting time at a drive-through window has an exponential distribution with a mean of 6 minutes.

The probability density function of an exponential distribution is given by

f(x) = (1/μ) × e^(-x/μ)

where μ is the mean of the distribution.

Therefore, the probability that the waiting time is greater than 5 minutes is

P(X > 5) = ∫[5, ∞] f(x) dx

= ∫[5, ∞] (1/6) × e^(-x/6) dx

= [-e^(-x/6)]_[5, ∞]

= e^(-5/6)

Using a calculator, e^(-5/6) is approximately 0.3012.

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It is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change.

What is speed?

she should always be aware of her speed and adjust it as necessary to stay within the legal limit.

Yes, this is an inequality problem. We can use an inequality to represent the situation:

David's speed ≤ Speed limit + 7 mph

Let's substitute the given values:

David's speed ≤ 60 mph + 7 mph

David's speed ≤ 67 mph

If David's speed is less than or equal to 67 mph, then she will not get a ticket, because she is within the allowable limit of going 7 mph over the speed limit. However, if David's speed is greater than 67 mph, then she will be going too fast and is at risk of getting a ticket.

Since David is driving on cruise control, it is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change. Therefore, she should always be aware of her speed and adjust it as necessary to stay within the legal limit.

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Based on the given information, Lola used 9/8 cups of rice for the rice pudding.

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another. It consists of two numbers separated by a horizontal line called a fraction bar or a vinculum. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator.

Lola has 4 1/2 cups of rice, which is equivalent to 9/2 cups of rice.

She uses 3/4 of the rice to make sushi rolls for dinner. So, the amount of rice she uses for the sushi rolls is:

(3/4) x (9/2) = 27/8 cups of rice

To find the amount of rice she uses for the rice pudding, we need to subtract the amount she used for the sushi rolls from the total amount she had:

9/2 - 27/8 = 36/8 - 27/8 = 9/8

So Lola used 9/8 cups of rice for the rice pudding.

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A = π r² is the formula

r is the radius

Hope it helps ✨

Answer:

Step-by-step explanation:

[tex]A=\pi \times r^2[/tex]          where r is the circle's radius

Thus, the approximate area of lake whose shape is taken on the square of the grid is 8 sq. unit.

A grid area is a rectangular area just on grid that is made up of one or more grid cells. When you define an area using named grid areas or when you place an object using line-based placement, grid areas are produced.

By dividing the supplied figure in square grids and counting how many of these there are, it is easiest to determine the area of a typical two-dimensional shape.

For the following question:

Thus,

Total area = 4*1 + 8*(1/2)

Total area = 4 + 4

Total area = 8 sq. unit

Thus, the approximate area of the lake whose shape is taken on the square of the grid is 8 sq. unit.

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The amounts of Alex's transactions in order are $50.00, $40.00, $24.00, $35.00, $149.00, and $98.67.

The amounts of Alex's transactions can be listed in the following order:

The amount he received from selling his bike: $50.00

The amount he deposited into his savings account, which is 80% of $50.00: $40.00

The first deposit he made of $24.00

The second deposit he made of $35.00

The total amount he had in his account before withdrawing 2/3 of it: $149.00 (which is the sum of $50.00, $40.00, $24.00, and $35.00)

The amount he withdrew to buy the used skateboard, which is 2/3 of $149.00: $98.67

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