FRACTIONS
Understanding equivalent fractions

Answer:

Hydro static force is =18377 N

Step-by-step explanation:

The hydro static force is equals to the hydro static pressure times the area.

The hydro static pressure of a fluid increases as the depth of the fluid increases and the formula of it is given below.

Hydro static Pressure, P = d·g·ρ

Where, d is the depth of the object

g is the gravitational constant

ρ is the density of the fluid

Density of water   ρ = \(1000 kg/m3\)

=1000 kg/m^3 * 9.8m/s^2 which is √(3/2).a below the water level.

Side of the plate  x = 10 m

The hydrostatic force = the pressure at the center x the area =\([sqrt(3)/2 m][1000 kg/m^3 * 9.8m/s^2]\)\([(1/2)(3)(8)(sqrt(3)/2) m^2]\)=18377 N

Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined

Let's factor out

\(\\ \rm\Rrightarrow 64m^2-9n^2\)

\(\\ \rm\Rrightarrow (8m)^2-(3n)^2\)

\(\\ \rm\Rrightarrow (8m-3n)(8m+3n)\)

Done

Answer:

Ans=B.1

Step-by-step explanation:

hope this helps

Using the diameter of the circle, the value of k is 1 + 2sqrt(2).

Since A and C are points on the circumference of the circle with center at (2,1), we know that the radius of the circle is the distance between the center and any point on the circumference.

Therefore, we can find the radius of the circle by finding the distance between the center (2,1) and point A (1,0), which is:

r = sqrt((1-2)^2 + (0-1)^2) = sqrt(2)

Since AC is a diameter of the circle, we know that the distance between points A and C is equal to twice the radius:

AC = 2r = 2sqrt(2)

We also know that the y-coordinate of both points A and C is 0, so the distance between their x-coordinates is equal to the length of the diameter:

k - 1 = AC = 2sqrt(2)

Solving for k, we get:

k = 1 + 2sqrt(2)

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The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, 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:

The given planes are A and B,

A new line, p, is drawn parallel to line l,

Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.

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The image of the remaining question is attached below.

The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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Answer:

252

Step-by-step explanation:

The second and third smallest factors must add to 5. The only possibility is that these factors are 2 and 3.

The second and third largest factors must add to \(462-N\). These factors are \(N/2\) and \(N/3\).

\(462-N=\frac{N}{2}+\frac{N}{3} \\ \\ 462-N=\frac{5N}{6} \\ \\ 462=\frac{11N}{6} \\ \\ N=252\)

Answer: 7

Step-by-step explanation:

The sum of the values is 63, and there are 9 values. Since mean=(sum of values)/(number of values), we get 63/9 = 7.

Answer:

8

Step-by-step explanation:

A(n) =50 - 3(n-1)

Therefore, when is 15, then we will have this,

A(15) = 50 - 3(15-1)

A(15) = 50 - 3(14)

A(15)= 50 - 42

A(15) = 8.

Therefore, the 15th term is 8.

The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

Given:

Radius (r) = 20 inches

Height (h) = 0.7 feet

First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:

Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches

Now, we can substitute the values into the volume formula:

Volume = π * (20 inches)^2 * 8.4 inches

Calculating the volume:

Volume = 3.14159 * (20 inches)^2 * 8.4 inches

≈ 3.14159 * 400 inches^2 * 8.4 inches

≈ 1005.3096 cubic inches

Rounding the volume to the nearest tenth:

Volume ≈ 1005.3 cubic inches

Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

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Answer:

distance = 11.66

Explanation:

The distance between two points (x1, y1) and (x2, y2) can be calculated as:

So, replacing (x1, y1) by (7, 8) and (x2, y2) by (-3, 2), we get:

Therefore, the distance between the points is 11.66 units

Answer:

Step-by-step explanation:

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Answer:

A Toowoomba and Perth

Step-by-step explanation:

its A on e2020

The smallest portion that Ann can cut out of her plans to stay under budget is option A, Toowoomba and Perth, which has a total cost of $291.

To find the smallest portion that Ann can cut out of her plans, we need to calculate the total cost of all cities and see which one is the highest.

Total cost = $161 + $264 + $198 + $130 + $224 + $301 + $277 = $1,555

Since Ann only has $1,265 budgeted for this portion of her trip, she needs to cut out some cities to stay under budget.

Toowoomba and Perth = $161 + $130 = $291

Hobart = $301

Sydney and Newcastle = $224 + $198 = $422

Bendigo = $277

Thus, the correct option is A.

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Answer:

1.6101529

Step-by-step explanation:

Given the following :

Number of samples (n) = 210

Sample mean (x) = 5

Population standard deviation = 0.9

Population mean (m) = 4.9

Since the standard deviation of the population is known, we can use the z statistic

Z = (x - m) / standard error

Standard error = sd / √n

Standard error = 0.9 / √210

Standard error = 0.9 / 14.491376

Standard error= 0.0621059

Z statistic = (5 - 4.9) / 0.0621059

Z statistic = 0.1 / 0.0621059

Z statistic = 1.6101529

Answer:

13

Step-by-step explanation:

3v - w + x

Let w = 6, v =5, and x=4

3 * 5 - 6 + 4

15 - 6+4

9 +4

13

The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.

The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.

The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:

= 5 - 1

= 4

The level of significance would be:

= 1 - 99. 0 %

= 0. 01

The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.

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Answer:

2/3

Step-by-step explanation:

Answer:The answer would be 6a(4b4 +2b3 -3b2)

Step-by-step explanation:All you have to do is take 6a out of each number and put the 6a outside of parenthesis and put the rest of the equation in parenthesis.

The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.

According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.

Ratio of sauce to oregano:

6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano

Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:

8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano

Therefore, for 8 servings, we would need:

8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce

Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

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The two-way frequency table is obtained as follows:

                                              Wore tie          Do not wore tie     Total

Receive compliment                 25                         5                       30

Do not receive compliment       9                         11                       20

       Total                                 34                         16                       50

We know that a two-way frequency table is constructed when we have to deal with two variables ( which is also known as a bivariate data)

Here we have two variables as wore a tie or not and the second variable is: Received compliment or not.

Hence, on the basis of the information provided to us in the question we see that the two-way frequency table is obtained as follows:

                                              Wore tie          Do not wore tie     Total

Receive compliment                 25                         5                       30

Do not receive compliment       9                         11                       20

       Total                                 34                         16                       50

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Complete question

Lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit:

-There were 11 days where she neither wore a tie nor received a compliment.

-There were 30 days in total where she received a compliment.

-There were 16 days in total where she did not wear a tie.

Can you help Lea organize the results into a two-way frequency table?

The probability that the tourist visits atleast one of the two places is 0.90

Probability of cave visit, P(C) = 0.70

Probability of park visit = P(N) = 0.6

Probability of both = P(B) = 0.40

The probability of visiting atleast one of the two places can be defined thus :

Therefore, the probability of visiting atleast one of the two places is 0.90

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The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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Answer:

Step-by-step explanation:

In general, given the function, f(x), its zeros can be found by setting the function to zero. The values of x that represent the set equation are the zeroes of the function. To find the zeros of a function, find the values of x where f(x) = 0.

Answer:

Use the rational root theorem to list all possible rational zeroes of the polynomial P(x) P ( x) .

Evaluate the polynomial at the numbers from the first step until we find a zero. ...

Repeat the process using Q(x) Q ( x) this time instead of P(x) P ( x) . This repeating will continue until we reach a second degree polynomial.

The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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Answer:

the slope is -3/6

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Formula for slope : y1-y2/x1-x2

0-(-3) is 3

6-0 is 6

3/6 = 1/2

The number of integers from 100 to 900 that can be written in base ten without using the digit 7 is 648.

From 100 to 999, all integers are three (3) digit numbers and available digits are (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

It implies that the total number of digits is 9. The next thing to do will be to arrange the 9 digits in three (3) places in such a way that repetition is allowed.

In the first place;

Hence, the first chance is 8 out of 10 chance.

In the second and third place;

∴

The number of integers from 100 to 900 that can be written in base ten without using the digit 7 is:

= 8 × 9 × 9

= 648

Therefore, the number of integers from 100 to 900 that can be written in base ten without using the digit 7 is 648.

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