Which point justifies the shaded area by satisfying StartFraction (y + 1) squared Over 6 EndFraction minus StartFraction (x + 2) squared Over 24 EndFraction greater-than-or-equal-to 1?

(12, 6)
(–2, 6)
(8, –6)
(–1, –2)

Please help asap test is timed!

Answer:x=4 y =1

Step-by-step explanation:

your welcome

Answer:

x = 4, y = 1

Step-by-step explanation:

Substitute the y in the first equation for x-3

X + 2(x-3) = 6

3x -6 = 6

3x = 12

x = 4

Plugging 4 into the second equation

y = 4-3

y = 1

Answer:

24

Step-by-step explanation:

16/12 is 1.333333333

20/15 is 1.333333333

18x1.333333333 is 24

Answer:

Surface area of cubic box = 376 square inch

Step-by-step explanation:

Given:

Using net diagram

Length of cubic box = 10 inches

Width of cubic box = 6 inches

Height of cubic box = 8 inches

Find:

Surface area of cubic box

Computation:

Surface area of cuboid = 2[(lb) + (bh) + (hl)]

Surface area of cubic box = 2[(10)(6) + (6)(8) + (8)(10)]

Surface area of cubic box = 2[60 + 48 + 80]

Surface area of cubic box = 2[188]

Surface area of cubic box = 376 square inch

Answer:

Both sides and they don't even need that kind in. so the fact it does the job and is going out.

Step-by-step explanation:

the problem with it isn't an excuse if it isn't an

Answer:

D

Step-by-step explanation:

given 2 sides of a triangle then the third side SU is in the interval

difference of 2 known sides < SU < sum of 2 known sides , that is

52 - 39 < SU < 52 + 39

13 < SU < 91

Answer:

Part A - i. 0.68 N ii. 1.88 N

Part B - The wagon will move slowly while being raised up off the ground.

Step-by-step explanation:

Part A: Suppose the direction of the force changes from a 48° angle with the floor to a 70° angle with the floor. Determine the effect on the horizontal and vertical components of the force. Give forces to the nearest hundredth of a unit.

Since the force of 2 N is exerted at this new angle of 70°,

i. the horizontal component u = 2cos70° = 0.684 N ≅ 0.68 N and its

ii. vertical component, v = 2sin70° = 1.879 N ≅ 1.88 N

Part B: What implications does this have for pulling the wagon? Explain.

Since we have a horizontal component of 0.68 N and a vertical component of 1.88 N, most of the force is used in raising the wagon off of the ground with less of it moving it forward. So, the wagon will move slowly while being raised up off the ground.

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance  statistic is computed.

What is Analysis of variance ?

What are some instances where ANOVA has been applied?

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Answer:

D

Step-by-step explanation:

to calculate speed ( or v for velocity ) divide the space traveled by the time it took to travel that distance.

v = S/t = 5000m/35min = 143 m/min

The answer of the given question based on the Newton's law is , the scenario demonstrates Newton's third law of motion.

Newton's laws of motion are set of fundamental principles that describe  behavior of a objects in motion. They were formulated by Sir Isaac Newton in the 17th century and are considered to be the foundation of classical mechanics. It consists of three laws of motion they are , Newton's First Law of Motion , Newton's Second Law of Motion , Newton's Third Law of Motion. These laws explain how objects move and interact with one another, and they have numerous applications in physics, engineering, and other fields.

The scenario given describes Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

In this case, the action is the force exerted by the car on the wall, and the reaction is the force exerted by the wall on the car. According to Newton's third law, these forces are equal in magnitude but opposite in direction, which means that the car and the wall exert the same amount of force on each other in opposite directions.

Therefore, the scenario demonstrates Newton's third law of motion.

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Answer:

3/4

Step-by-step explanation:

common denominator is 28

20/28 and 21/28 so 3/4 is greater

5/7 = 0.71

3/4 = 0.75

¾ is greater.

- Toodles!~

Answer:

Daniel has to wait around 5.24 years to withdraw the money.

Step-by-step explanation:

We are given that Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00.

Let the Principal sum of money be represented by 'P'.

The rate of interest be represented by 'R'.

The time period be represented by 'T'.

The final amount of money be represented by 'A'.

Assuming the interest given is compound interest.

So, the formula for calculating the amount of money is given by;

                          \(\text{A} = \text{P} \times (1-\text{R})^{\text{T}}\)

Here, A = $1,150, P = $750, R = 8.5% and let the time he have to wait to withdraw the money be 'n'.

So, putting these values in the above formula we get;

\(\text{A} = \text{P} \times (1+\text{R})^{\text{T}}\)

\(\text{\$1,150} = \text{750} \times (1+\text{0.085})^{\text{n}}\)

\((1+\text{0.085})^{\text{n}} = \frac{\$1,150}{\$750}\)

\((1+\text{0.085})^{\text{n}} = 1.533\)

Taking log on both sides;

\(\text{n} \times ln(1+\text{0.085}) = ln(1.533)\)

\(n = \frac{ ln(1.533)}{ ln(1.085)}\)

n = 5.24 years

Hence, he has to wait around 5.24 years to withdraw the money.

Answer: 68 degrees

Step-by-step explanation:

Let the measure of the angle be x.

The supplement of the angle is 180 - x as supplementary angles add up to 180 degrees.

The complement of the angle is 90 - x as complementary angles add up to 90 degrees.

We can set up an equation.

180 - x = 46 + 3*(90-x)

180 - x = 46 + 270 - 3x

Combine like terms:

2x = 136

Divide both sides by 2:

x = 68

What are supplementary and complementary angles?

The supplement of an angle (180 - x) is [=] 46 more than 3 times the complement (90-x):

180 - x = 3 (90 - x) +46

Now, solve for x:

180 - x = 3 (90 - x) +46

180 - x = 270 - 3x +46

180 - x = 316 -3x

-x = 136 -3x

2x = 136

x = 68

The angle is 68°

1) The line integral value is : ∫F dr = 6

2) The line integral value is : ∫F dr = 6

3) The line integral value is : ∫F dr = 6

Here we are given:

\(F.dr = (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

where\(\vec{F}\) is a conservative field

So,

f(x, y , z) = \(\int\limits (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

f(x , y , z) = (3zx +2yx) + (2xy - 2zy) + (3xz - 2yz) + c(x , y , z)

\(f(x, y, z) = (6xz + 4xy - 4yz) + c(x, y, z)\)

Now substitute the values of x , y ,z ,

1)

Line segment from (0, 0 , 0) to (1,1 ,1)

∫F dr = f(1,1,1) - f(0,0,0)

= |6 + 4 - 4 |- |0 + 0 - 0|

∫F dr = 6

2)

Line segment from (0,0,0) to (0,0,1) to (1,1,1)

First we take (0,0,0) to (0,0,1)

\(\int _c \vec{F}.\vec{dr}=f(0,0,1)-f(0,0,0) =[6(0)(1)+4(0)(0)-4(0)(1)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\)

∫F dr = 0

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+6 [F.dr = 6\)

3)

Line segment from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

First we take (0,0,0) to (1,0,0)

\(\int _c \vec{F}.\vec{dr}=f(1,0,0)-f(0,0,0) =[6(1)(0)+4(1)(0)-4(0)(0)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\int _{c}\vec{F}.\vec{dr}=0\)

Next we take (1,0,0) to (1,1,0)

\(\int _c \vec{F}.\vec{dr}=f(1,1,0)-f(1,0,0) = [6(1)(0) + 4(1)(1) − 4(1)(0)] - [6(1)(0) + 4(1)(0) — 4(0)(0)] = [0+4-0] - [0+0-0]\int _{c}\vec{F}.\vec{dr}=4\)

Lastly we take (1,1,0) to (1,1,1)

\(F.dr = f(1,1,1) ƒ(1,1,0) = [6(1)(1) +4(1)(1) − 4(1)(1)] - [6(1)(0) + 4(1)(1) — 4(1)(0)] =[6+4-4]-[0+4-0]\int _{c}\vec{F}.\vec{dr}=2\)

Adding the three results we get

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+4+2\\\\\int\limits F.dr = 6\)

Therefore we see that the Line integral for the three cases comes out to be same between the initial and final points since it is independent of the path taken.

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Given:

A figure of a circle with radius 8. The central angle of the blue sector is 60 degrees.

To find:

The area of the blue sector.

Solution:

Area of a sector is:

\(A=\pi r^2\dfrac{\theta}{360^\circ}\)

Where, r is the radius and \(\theta \) is the central angle of the sector in degrees.

Putting \(r=8, \theta=60^\circ, \pi=3.14\), we get

\(A=(3.14)\cdot (8)^2\cdot \dfrac{60^\circ}{360^\circ}\)

\(A=(3.14) \cdot (64)\cdot \dfrac{1}{6}\)

\(A=33.49333....\)

Approximate the value to the nearest tenth.

\(A\approx 33.5\)

Therefore, the area of the blue sector is about 33.5 sq. units.

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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If Brain flips a coin 3 times the probability of getting 3 heads is 0.125.

The given statement is Brian flips a fair coin 3 times.

We need to find the probability of getting 3 heads.

Probability refers to possibility. A random event's occurrence is the subject of this field of mathematics. The range of the value is 0 to 1.

The possible outcomes are {HHH, THH, HTH, HHT, TTH, THT, HTT, TTT}.

Total number of outcomes = 8

The number of favourable outcomes =1

So, the probability of getting 3 heads = 1/8 = 0.125

Hence, if Brain flips a coin 3 times the probability of getting 3 heads is 0.125.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer:

t=1

Step-by-step explanation:

2t+t−3=0

2t+t+−3=0

(2t+t)+(−3)=0(Combine Like Terms)

3t+−3=0

3t−3=0

Step 2: Add 3 to both sides.

3t−3+3=0+3

3t=3

Step 3: Divide both sides by 3.

3t

3

=

3

3

t=1

The experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

To find the experimental probability that of 5 students, at least 3 will make a C using the given random-number table, we can use:

Count the number of digits that represent students who make a C, which is 6 out of 10 digits.

Determine the probability of a single student making a C, which is 60% or 0.6.

Use the binomial probability formula to calculate the probability of getting at least 3 students who make a C out of 5 students:

P(X ≥ 3) = 1 - P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = C(5,0) * 0.6^0 * 0.4^5 + C(5,1) * 0.6^1 * 0.4^4 + C(5,2) * 0.6^2 * 0.4^3

P(X < 3) = 0.01024 + 0.07680 + 0.23040

P(X < 3) = 0.31744

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.31744

P(X ≥ 3) = 0.68256

Therefore, the experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

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Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

(4, 32) and (10, 56) are the two ordered pairs that use the data Marshall collected.

To write two ordered pairs that represent the data Marshall collected, we need to consider the given information about the hours rented and the corresponding costs.

First, let's consider the first individual who rented a canoe for 4 hours and paid $32. We can represent this as the ordered pair (4, 32), where 4 is the number of hours and 32 is the total cost.

For the second individual who rented a canoe for 10 hours and paid $56, we can represent this as the ordered pair (10, 56), where 10 is the number of hours and 56 is the total cost.

Therefore, the two ordered pairs that represent the data Marshall collected are:

(4, 32)

(10, 56)

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When a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be standardized.

Standardization refers to the process of establishing norms or standards for a test by administering it to a representative and pretested sample of individuals. This allows for a comparison of an individual's test performance to that of the larger group. When a test is standardized, it means that it has undergone rigorous development and validation procedures to ensure that it is fair, consistent, and reliable.

Standardized tests provide a benchmark for evaluating an individual's performance by comparing their scores to those of the norm group. The norm group consists of individuals who have already taken the test and represents the population for which the test is intended. By comparing an individual's scores to the norm group, it is possible to determine how their performance ranks relative to others.

Therefore, when a person's test performance can be compared with that of a representative and pretested sample of people, it indicates that the test is standardized. Standardization is an essential characteristic of reliable and valid tests, as it ensures consistency and allows for meaningful comparisons among test-takers.

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The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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The length of the fabric which Brandon formed a rectangle, is 11 inches.

To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:

\(L^2 + 5^2 = 13^2\)

where L is the length of the fabric.

Solving for L, we get:

\(L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.\)

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When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.

Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.

The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.

By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.

The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].

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Answer:

26 students

Step-by-step explanation:

We know

The ratio of students failing the test to students passing the test was 2/9

For every 11 students, 2 students fail the test, and 9 passes it.

2:9 = 11

143 students took the test. How many did not pass?

To get from 11 to 143, we time 13. To find how many did not pass, we take

2 times 13 = 26 students did not pass the test.

So, 26 students did not pass the test.

There are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world. We can calculate it in the following manner.

To find how many liters of water are available for human and plant use, we need to multiply the total amount of water in the world (1.4 x 10²¹ liters) by the percentage available for human and plant use (0.26% or 0.0026).

The calculation is:

1.4 x 10²¹ liters x 0.0026 = 3.64 x 10¹⁸ liters

Therefore, there are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world.

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