A mathematics teacher wanted to see the correlation between test scores and homework The homework grade (x) and test grade (y) are given in the accompanying table: Write the linear regression equation that represents this set of data rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade; to the nearest integer, for student with homework grade of Homework Grade (x) Test Grade (y) 79 68 78 79 89 82 59 73 85 72 63 90 74 87 79 Copy Vulues for Calculator Open Stalistics Cakculator Regression Equation: Final Answer: Sabmnlt Aniwrer

A 98% confidence interval for Americans' average daily eating and drinking time is (64.172, 82.228)

Given data,

How long do Americans spend drinking or eating? Let's say that, for a representative sample of 101 Americans, the daily average for eating or drinking is 73.2 minutes, with a straightforward standard deviation of 39 minutes. Create and analyze a 98% confidence interval for Americans' average daily eating and drinking time.

Let,

c = 98% = 0.98

n = 101

Mean μ = 73.2

Standard Deviation σ = 39

Now,

To analyze a 98% confidence interval for Americans' average daily eating and drinking time, we have;

CI = μ ± Z * σ/√n

CI = 73.2 ± 2.326 * 39/√101

    = 73.2 ± 9.028

    = 64.172, 82.228

Hence, the average daily calorie intake for Americans is within a 98% confidence zone (64.172, 82.228).

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The hypotheses are:

Null hypothesis: the average test scores are the same for the different teaching methods.

Alternative hypothesis: the average test scores are different for the different teaching methods.

To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample.

Hence we get the required answer.

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8/5 mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

It is given that a mini fruit juice box contains 4 fluid ounces of juice, we need to find how many mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

What is 1 quart?

A unit of the US customary system used in liquid measure, equal to 2 pints or 32 ounces

4 divided by 2 1/2

4 divided by 5/2

4 × 2/5

8/5

Therefore, 8/5 mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

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let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be  0 ≤ h ≤ 3

If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.

Let m is a vector space over a field F,  a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .

L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)

L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)

A subset h⊆ m which satisfy (1) and (2) is a subspace of v

Dimension of Vector space and a subspace :

According to linear algebra theorem,

The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .

If m is spanned then here, dim m = 3

h ⊆ subs m <===> dim h < dim m

If h is subspace of m and dim m = 3 then,

dim h = h with 0≤ h ≤3

If h is zero, the dimension of improper subspace , h = {0}

If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,

Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3

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The five things when two parallel lines are cut by a transversal are the corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

Here we have to find the five things that happen when two parallel lines are cut by a transversal.

When two parallel lines are cut by the transversal line it will form five angles.

Corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

From the given figure:

Corresponding angle:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

consecutive angle:

∠3 and ∠6

∠4 and ∠5

alternate interior angle:

∠3 and ∠5

∠4 and ∠6

alternate exterior angle:

∠2 and ∠8

∠1 and ∠7

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Using disk scheduling algorithm,

Total distance ( head movement) for following algorithms is 120.

Disk Scheduling Algorithm

Disk scheduling is performed by the operating system to schedule I/O requests to arrive at the disk. Disk scheduling is also called I/O scheduling.

we have given that

Total cylinders on a disk drive = 100 , numbered from 0 to 99.

The queue order is 10, 20, 50, 70, 80 .

Current disk position = cylinder 40

Starting from current head position.

We have to calculate the total distance (head movement) for the following algorithm.

Since, disk moving towards zero.

Now , Total distance = |40-10| + | 10-0| + |0-20| +

|20-50| + |50-70| + |70-80|

= 30 + 10 + 20 + 30 + 20 + 10

= 120

Hence, the required distance is 120.

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There will be 80 chairs and 10 tables to furnish a school cafeteria

What exactly is a two-variable linear equation?

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Detailed explanation:

There are 8 chairs around each table. 8×40$ =320$

Each table cost $200.

Each table and chair combination is

200 + 320= 520

The total amount the school may spend is $5,200.

So, 5200 minus 520 equals 10.

Therefore, there are ten sets of table and chairs.

There are thus 10 tables.

Eight plus ten chairs total 80.

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The answer choice which represents an expression which is equivalent to the given expression; √-36 is; Choice D; 6i.

It follows from the task content that the expression which is equivalent to the given expression be determined.

Since the given expression is; √-36.

The square root of a negative number is undefined but can however be evaluated as follows;

√-36

= √-1 × √36

= √-1 × 6

However, the square root of -1; √-1 = i.

= 6i

Ultimately, the required equivalent expression is; Choice D; 6i.

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The probability that is lower than 63 grams is 95%

Given that,

X~ Normal ( 67 grams, 5 grams ) , n = 5

=> E( x ) = 67 grams , Var( X ) =5 grams

* ~ Normal ( 67 grams , 1 grams )

We know that, if X~ Normal ( E ( x) = a . Val (x ) = b)

Then X~ Normal ( E(x) = a, √Var (x)/n = √b/n)

E(x) = a, Var (x)/ = √b/n

Probability that sample mean X , is blw 65 and 70 grams

P ( 65< X<70 ) =

= P(Z<1. 76 ) - P(Z≤-2.65)

Using standard normal table values represent area

left of the Z- score, we get

= 0.96080 - 0.00402

= 0 .95678

=0.9568

So,The probability that is lower than 63 grams is 95%

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The probability that the drawn marble is green is 5/9.

What do you mean by an intersection in probability?

P(A∩B) denotes the probability of A and B occurring together, also known as the likelihood of A intersecting with B, or the likelihood of two occurrences occurring concurrently, or the probability of two events occurring simultaneously.

We define the intersection of two events as the set of all results that occur for any two events A and B. In other words, if both A and B happen, the intersection will happen. A and B are crossed when A∩B is used as a symbol.

Solution Explained:

Total number of white marbles = 6

Total number of black marbles = 2

Total number of green marbles = 10

Marbles in total = 6 + 2 + 10 = 18

A marble is drawn on random

Therefore, the probability of the marble being green P(G) = 10/18 = 5/9

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Answer: 92°

Step-by-step explanation:

The triangle is an isosceles triangle, since two sides are equal. That means the two opposite angles are also equal. Hence m∠N = m∠M = 44°.

Since all interior angles of a triangle adds up to 180°, m∠L can be calculated as:

[tex]180-2(44)=180-88=92[/tex]

The inequality could be used to determine the number of subscriptions that Jennifer needs to sell is 2x+x≥90.

In mathematics, an inequality is a relationship that results from a non-equal comparison of two integers or other mathematical expressions. It is most typically used on a number line to compare the sizes of two numbers. There are several notations for various sorts of inequalities:

The symbol a < b indicates that an is less than b.

The symbol a > b indicates that an is greater than b.

These are known as strict inequalities, because an is strictly less than or strictly bigger than b. Equivalence is not allowed.

Given,

Carol intends to sell twice the number of magazine subscriptions as Jennifer..

And also given that,

Carol and Jennifer needs to sell at least 90 subscriptions in all

Let Carol sell 2x magazines then Jennifer sell x

So, they need to sell at least 90

x+2x ≥ 90

∴2x+x ≥ 90

Hence, the answer is  option 4

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The length in cm of any one of its interior diagonals is √14 D.

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The present age of the son is 12 years and the present age of the father is 36 years.

What is the age problem?

Age problems are algebra word problems that deal with the ages of people currently, in the past, or in the future.

Let the present age of the son be 'x'

Then, the present age of the father will be '3x'

According to the question,

The age of the son after 12 years = (x+12) years

And the age of the father after 12 years = 2(x+12) years

Therefore,

or, 3x+12=2(x+12)

or, 3x+12=2x+24

or, x=12

And, the father's age = 3*12 = 36 years

Hence, the present age of the son is 12 years and the present age of the father is 36 years.

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The required area is 10.3 square units.

Area of triangle= 12 /(a* b)

Area of a triangle using trigonometric area formula = 1/2( a * b) sin(c)

here, base = a , height = b*sin(c)

Given ,

Only the sine of the included angle, whose two side lengths are specified, can be used despite the two angle measurements that have been provided. The EF and DF sides of our triangle's angle, which measures 31 degrees, are also provided.

On putting the values given in the formula we get,

Area = 1/2* 8 * 5sin(31)

        = 20 * 0.51503807491

         ≈ 10.3

Therefore, the area of the triangle DEF is 10.3 square units.

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2,042,040 alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

Given that,

Consider that you have 17 employees under your management and that you must organize three teams to work on various tasks. Assume that every employee will be part of a team and that they all possess the same credentials and abilities to ensure that everyone has an equal chance of being selected.

We have to find how many alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

We know that,

Assume we have k groups to place the n interchangeable objects in, with n₁ + n₂ +... + nₐ = n objects in each group. The multinomial coefficient, or (n!) / [(n₁!) (n₂) ... (nₐ!)], measures the number of possible ways to accomplish something.

Since all of the employees in this situation have the same credentials and skills, we have n = 17 people and k = 3 groups to place them in.

Additionally, we have n₁ = 6, n₂ = 3, and n₃ = 8 (remember that 6 + 3 + 8 = 17).

The total number of teams that can be selected is therefore (17!) / [(6!) (3!) (8!)], which equals 2,042,040.

Therefore, 2,042,040 alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

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There are four common types of transformations -

translation

rotation

reflection

 dilation.

x=[tex]\frac{y+1o}{4}[/tex] is the solution of the eqution y=4x+10.

An liner equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

From the question  y=4x-10

add 10 both side

y+10=4x

Divide both side with 4

                x = [tex]\frac{y+1o}{4}[/tex]

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NOTE: The given question is incomplete on the portal. Here is the complete question.

Question: What is the solution to the system of equation y = 4x - 10 ?

Using Magnetic field,

a) Magnetic force acting on loop is 2.59 ×10⁻⁴ N

b) Torque acting on loop is zero.

We have given that,

Each side of square loop wire , L = 2.00 cm

Square loop carring current , I₂ = 0.230 A

Solenoid , has n= 30 turns/cm

Current Carrying in solenoid, I₁ = 15.0 A

Magnetic field inside solenoid , B = μ₀ n I₁

where, μ₀---> susceptibility of free space

μ₀ = 4π×10⁻⁷A/m

pulgging all known values in above formula,

B = (4π×10⁻⁷ A/m) 30 turn/cm × 100cm /1m (15.0 A)

= 5.6 ×10⁻² T

Now, the magnitude of magnetic force on one side of loop , F = B× L× I₂× sinθ

=> F = ( 5.6 ×10⁻² T )(0.02 m)(0.230 A) sin90°

=> F = 0.02599 × 10⁻² N

=> F = 2.59 ×10⁻⁴ N

The force acting on one side of loop lie in the plane of loop, are prependicular to the all sides and directed away from interior of the loop. Thus, these force strech the loop do tends to rotate it.

So, if loop is not rotate then there is not torque associated. Hence, Torque acing on loop is zero.

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Complete question:

A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.230A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30.0 turns/cm and carries a clockwise current of 15.0 A. Find (a) the force on each side of the loop and (b) the torque acting on the loop.

According to the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

It is given to us that -

Amount of time a person experiences cold virus symptoms are normally distributed with

a mean of 7.5 days

and, a standard deviation of 1.5 days

We have to find out the proportion of cold sufferers that experience symptoms for more than 8 days.

Now, from the given information, we have

Mean = μ = 7.5

Standard deviation = σ = 1.5

and, X = 8

Now, the proportion of cold sufferers that experience symptoms for more than 8 days can be represented as -

P(X > 8)

= P{[(X-μ)/σ] > [(8-7.5)/1.5]}

=P(Z>0.33)

Looking at the z-score values, we find out that

P(Z>0.33) = 0.129 = 12.9%

Thus, from the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

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Answer:

y= mx+b

y= 4x+b

-1=4(1)+b

-1=4+b

-4 -4

-5=b

y = 4x -5

Step-by-step explanation:

The Option b and e are correct they are the actual relationship between salary raises and performance rating is linear and  if the mean performance rating is 1.2, then the mean raise is $3800.

Given that,

The relationship between the magnitude of annual wage increases and the performance evaluations given to employees of a certain organization is described by a set of data. The least squares regression equation is y = 1400 + 2000x, where x is the performance rating and y is the raise amount (in dollars).

We have to find which of the following suppositions has to be accurate.

We know that,

[tex]\hat{y}[/tex]= 1400+2000x

Where,

[tex]\hat{y}[/tex] is predicted raise amount,

x is performance rate

Now,

If we compare the given equation with general form of simple linear regression equation i.e. y = a + b²

Option-B is correct.

Now,

For x=1.2 ,

[tex]\hat{y}[/tex] =1400+2000*1.2=3800

So, that option e) is also correct Option.

Therefore, The Option b and e are correct they are the actual relationship between salary raises and performance rating is linear and  if the mean performance rating is 1.2, then the mean raise is $3800.

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Answer: 1 1/6

Step-by-step explanation:

(P.S: Everthing in italics are either fractions. mixed numbers, or numbers.

And there ya' go! The answer is 1 1/6! You're welcome!

The correct option for the t test for the difference between the means of 2 independent populations is sample variances are equal.

The Autonomous samples t Test analyzes the method for two free gatherings to decide if there is factual proof that the related populace implies are essentially unique. The Free samples t Test is a parametric test. This test is otherwise called: Free t Test.

The t test for the difference between the means of 2 independent populations when standard deviations are unknown, we must assume that sample variances are equal.

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The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

Given that,

In the picture we can see the full question.

We have to find what is the probability of selling more than 3 radios.

We know that,

In the picture there is a table

We have to first find the table then we get the probability of selling more than 3 radios.

First,

Given data is 100 weeks of sales data

Probability is number of weeks/ 100 weeks

x=0, number of weeks is 3

P=3/100=0.03

x=1, number of weeks is 20

P=20/100=0.2

x=2, number of weeks is 50

P=50/100=0.5

x=3, number of weeks is 20

P=20/100=0.2

x=4, number of weeks is 5

P=5/100=0.05

x=5, number of weeks is 2

P=2/100=0.02

The probability table we get,

x term are 0,1,2,3,4,5

P(x)    |0.03 | 0.2 |  0.5 |  0.2 |0.05| 0.02|

The probability of selling more than 3 radios is sum of the probability of selling 4 radios and 5 radios

P(x>3)=P(x=4)+P(x=5)

P(x>3)= 0.05+0.02

P(x>3)= 0.07

Therefore, The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

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We can identify key terms in word problems that can tell use what math symbols or operations to use:

There are other key terms that can help us, including:

We're given:

11 is more than twice x:

Less than 44:

Combine all of these to get the inequality:

11 + 2x < 44

The equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

The slope-intercept form is just a means of formulating a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are clearly visible. This form is frequently referred to as the y = mx + b form. This line form is one of the most prevalent in algebra classes.

A line's slope-intercept form is y = mx + b, where m is its slope and b is its y-intercept.

The equation of the line which is passing through two points is:

y₂-y₁ / x₂-x₁

(6-7)/(-3+6)=-1/3

A line's slope-intercept form is y =mx +b, where m is the slope and b is the y intercept.

y = -1/3 x +b. We must now calculate b, the y intercept. To find b, plug one of the given points into the previous equation and solve for b.

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

b = 5

y = -1/3x +5

Therefore, the equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

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Cubic units are used to measure volume. Length, width, and height formula for a rectangular prism that represents its volume: The lengths of a rectangular prism's three distinct dimensions (length, width, and height) are multiplied together to determine the volume of the object. So, V = lwh is one volume formula for rectangular prisms.

What is Volume?

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.

What is rectangular prisms?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Length, width, and height formula for a rectangular prism that represents its volume: The lengths of a rectangular prism's three distinct dimensions (length, width, and height) are multiplied together to determine the volume of the object. A volume formula for rectangular prisms is as follows:

                                         V = lwh

The prism's base is a rectangle with the dimensions (l, w) and (h), and the height (h) is the separation between the two bases at a perpendicular angle.

Rectangular prism volume formula based on base area and height: The area of a rectangular prism's one side can be used to determine the prism's base, or area B. B divided by the prism's height will yield the dimension of the prism. Thus, the following is a second formula for a rectangular prism's volume:

                                    V = Bh

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She needs to add 4 liters of the 8% acid solution when a chemist wants to combine a 4% acid solution.

Given that,

A chemist wants to combine a 4% acid solution. She has 8 liters of 2% acid on hand and wants to mix with some 8% acid to get the needed 4% acid solution.

We have to find she needs to add how much of the 8% acid solution.

We know that,

Assuming she wants to use all 8 liters of the 2% acid, you can set up the solution as follows:

x = required liters of the 8% acid

(2%)(8) + (8%)x = (4%)(x + 8)

2(8) + 8x = 4(x + 8)

16+8x=4x+32

8x-4x=32-16

4x=16

x=16/4

x=4 liters

Therefore, she needs to add 4 liters of the 8% acid solution when a chemist wants to combine a 4% acid solution.

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The correct option is option( A).

Using the property of Obtuse Triangle, the triangle with sides { 8, 10, 14 } is an Obtuse Triangle.

Obtuse Triangle:

An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In geometry, a triangle is represented as a closed 2D figure with three sides of equal or unequal length and three angles of equal or unequal measurements.

Obtuse triangle property:

we have given the sides of triangle so, we use the fourth property for check the triangle formed by given sides are obtuse triangle or not .

8² + 10² = 164; 14² = 196 -> obtuse

9² + 12² = 225; 15² = 225 -> not obtuse

10² + 14²= 296 ; 17²= 289 --> not obtuse

12² + 15² = 369; 19²= 361 --> not obtuse

Hence, the required triangle is triangle with sides 8, 10, 14.

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Complete Question:

which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle

A. 8, 10, 14

B. 9, 12, 15

C. 10, 14, 17

D. 12, 15, 19

Answer: the answer is A 8, 10, 14.

Step-by-step explanation: it show below.