Explain why the​ t-distribution has less spread as the number of degrees of freedom increases

Answer and explanation:

To find : Match the following items.

Solution :

We arrange all steps by steps,

Step 1 - Given

[tex]2x + x + 4 = -17[/tex]

Step 2 -  Combine like terms,

[tex]3x+ 4 = -17[/tex]

Step 3 - Subtract 4 both side,

[tex]3x=-21[/tex]

Step 4 - Divide by 3 both side,

[tex]x=-7[/tex]

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The following are matched:

1. 2x + x + 4 = -17  ------------ ( Given )

2. 3x + 4 =-17 ----------(combine like terms)

3. 3x =- 21 -----------( subtraction )

4. x = -7 -------------( division )

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Given,

2x + x + 4 = -17

We will combine the like terms.

3x + 4 = -17

We will subtract 4 on both sides.

3x = -17 - 4

3x = -21

Divide both sides by 3.

x = -21/3

x = -7

Thus,

1. 2x + x + 4 = -17  ------------ ( Given )

2. 3x + 4 =-17 ----------(combine like terms)

3. 3x =- 21 -----------( subtraction )

4. x = -7 -------------( division )

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Answer:

Rajan must climb down 15 feet to return to the bottom of the climbing wall.

Step-by-step explanation:

Rajan climbed to a height of 10 ft from the bottom of a climbing wall.

He then climbed up an additional 5 ft.

So, in total he climbed [tex]10+5=15[/tex] feet

If Rajan wants to return to the bottom, he must climb down 15 feet.

Answer:

Rajan must climb down 15 feet to return to the bottom of the climbing wall.

Answer:

The correct Answer is 19

The number of people who will receive the chocolate will be equal to 19.

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the provided data in the question,

Total boxes of chocolate = 13/2

Chocolate received by each person = 1/3 of a box

Then, the number of people who receive the chocolate is,

13/2 ÷ 1/3 = 19.5 or,

A total of 19 people will receive the chocolate.

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A line has the following standard equation form:

y = m x + b

where m is the slope and b is the y intercept

So if Ariel cannot find the slope, then this would only mean that m = 0, there is no slope. And hence the line is either a straight vertical line or straight horizontal line.

Answer:

There is no slope

Given only the information that a line has x and y intercepts and a positive slope, Ariel cannot directly calculate the slope without knowing the exact values of the intercepts. Knowledge of two distinct points on the line is necessary for calculating the slope.

Ariel was told the x intercept and the y intercept of a line with a positive slope. Yet, it was impossible for Ariel to find the slope of the line. What can you conclude about this line? If given only the x and y intercepts without the exact numeric values or additional points, determining the slope directly is challenging because the slope formula, Δy/Δx (change in y over change in x), requires knowledge of at least two distinct points on the line (other than the intercepts without their exact values). However, knowing that a line has both an x and a y-intercept implicitly indicates it is neither vertical nor horizontal, and stating it has a positive slope provides a general direction of the line's angle relative to the axes.

To find the slope, you generally need the coordinates of two distinct points on the line. For instance, if the y-intercept is given as (0, b) and the x-intercept as (a, 0), the slope m can be found by the difference in y values divided by the difference in x values, or (0 - b) / (a - 0) = -b/a. But without knowing a and b's exact values, Ariel cannot calculate the numeric value of the slope. This indicates a limitation in calculating slope with incomplete information about the intercepts' exact numerical values but not an inherent impossibility of the line to have a determinable slope if such values were known.

Answer: Using operations with fractions, John uses 10 gallons from work and errands.

Solution:

Jack purchases 12 gallons of gas on Monday.

He uses 2/3 of the amount purchased commuting to and from work during the week:

(2/3)(12)=(2/3)(12/1)=(2*12)/(3*1)=24/3=8

Then John uses 8 gallons commuting to and from work during the week.

And an additional 2 gallons running errands.

John uses in total from work and errands= 8 gallons+2 gallons

John uses in total from work and errands= 10 gallons

we have

[tex]2y-x\leq -6[/tex]

we know that

if a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A) [tex](0,-3)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-3)-0\leq -6[/tex]

[tex]-6\leq -6[/tex] -------> Is True

therefore

the ordered pair [tex](0,-3)[/tex] is a solution of the inequality

case B) [tex](2,-2)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-2)-2\leq -6[/tex]

[tex]-6\leq -6[/tex] -------> Is True

therefore

the ordered pair  [tex](2,-2)[/tex] is a solution of the inequality

case C) [tex](1,-4)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-4)-1\leq -6[/tex]

[tex]-9\leq -6[/tex] -------> Is True

therefore

the ordered pair  [tex](1,-4)[/tex] is a solution of the inequality

case D) [tex](6,1)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(1)-6\leq -6[/tex]

[tex]-4\leq -6[/tex] -------> Is False

therefore

the ordered pair  [tex](6,1)[/tex] is not a solution of the inequality

case E) [tex](-3,0)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(0)-(-3)\leq -6[/tex]

[tex]3\leq -6[/tex] -------> Is False

therefore

the ordered pair  [tex](-3,0)[/tex] is not a solution of the inequality

therefore

the answer is

[tex](0,-3)[/tex]

[tex](2,-2)[/tex]

[tex](1,-4)[/tex]

The recursive sequence is:[tex]T_n = \frac 14T_{n-1}[/tex] and there are 25 contaminants left after the third hour of the experiment

The initial number  of contaminant is 400.

If 3/4 contaminants are filtered out, there are 1/4 contaminants left.

So, the recursive sequence is:

[tex]T_n = \frac 14T_{n-1}[/tex]

Where T1 = 400

This means that n = 3.

So, we have:

[tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_2 = \frac 14 * T_1[/tex]

Substitute [tex]T_2 = \frac 14 * T_1[/tex] in [tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_3 = \frac 14 * \frac 14 * T_1[/tex]

Substitute 400 for T1

[tex]T_3 = \frac 14 * \frac 14 * 400[/tex]

Evaluate

[tex]T_3 = 25[/tex]

Hence, there are 25 contaminants left after the third hour of the experiment

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Final answer:

A recursive sequence can be formulated to model the number of grams of contaminants after "n" hours. After plugging in the values, the amount of contaminants after the third hour is 168.75 grams.

Explanation:

A. To formulate a recursive sequence modeling the number of grams after "n" hours, we can start with the initial amount of contaminants of 400 grams and then multiply it by three-fourths each hour. This can be represented by the formula: an = (3/4) * an-1. This formula tells us that to find the amount of contaminants after "n" hours, we multiply the amount after the previous hour by three-fourths.

B. To calculate the amount of contaminants after the third hour of the experiment, we can use the recursive formula. Let's plug in the values: a0 = 400 grams, a1 = (3/4) * a0 = (3/4) * 400 = 300 grams, a2 = (3/4) * a1 = (3/4) * 300 = 225 grams, a3 = (3/4) * a2 = (3/4) * 225 = 168.75 grams.

Therefore, the amount of contaminants after the third hour of the experiment is 168.75 grams.

Answer:Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.

Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.

If P is a an intersection point of these diagonals

Then we can say that, AP=PC and BP=PD ( by the property of bisecting)

So, In quadrilateral ABCD,

Let us take two triangles, [tex]\triangle BPA[/tex]  and  [tex]\triangle DPC[/tex].

Here, AP=PC

BP=PD,

[tex]\angle APB=\angle DPC[/tex] ( vertically opposite angles.)

So, By SAS postulate,[tex]\triangle BPA\cong \triangle DPC[/tex]

Thus AB=CD  ( CPCT).

Similarly, we can prove, [tex]\triangle APD\cong \triangle BPC[/tex]

Thus, AD=BC (CPCT).

Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.

Therefore, quadrilateral ABCD is a parallelogram.

Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.

The congruence of triangles BPA and DPC, proven through the Side-Angle-Side postulate or other congruency postulates, can be used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another.

The statement used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another is that triangles BPA and DPC are congruent. The congruence of these triangles can be shown through the Side-Angle-Side (SAS) postulate or other congruency postulates depending on a given figure, and this property that diagonals bisect each other is a defining trait of a parallelogram. Therefore, by showing the congruence of triangles BPA and DPC, we can deduce that ABCD is a parallelogram.

Answer:

29 more workers are needed.

Step-by-step explanation:

Let us assume that the 10 workers, working at their normal rate would finish the job in exactly 8 days.

The rate of working for 1 worker is:

[ 1/10 of the job ] / [ 8 days ] = [ 1 job ] / [ 80 days ]

This is also [ 1/80 of the job ] / [ 1 day ]

In 2 days, the fraction of the job that gets done is:  

[tex]2\times \frac{1}{80}=\frac{1}{40}[/tex]

Job left = [tex]1-\frac{1}{40} =\frac{39}{40}[/tex]

Now the rate has to be :

[tex]\frac{\frac{39}{40} }{2} =\frac{39}{80}[/tex]

Now, let w be the additional number of workers needed.

We get:

[tex]\frac{10+w}{80}=\frac{39}{80}[/tex]

Solving for w;

[tex]10+w=39[/tex]

[tex]w=39-10[/tex]

w = 29

Therefore, 29 more workers are needed.

-------------------------------------------------------------------------------------

There can be another approach as well.

Fraction of the job done by 10 workers in 2 days = 1/4

Remaining fraction = 1-1/4 = 3/4

Lets say W workers are needed more.

So, we can say that 3/4 of the work is to be done by 10+W workers.

Hence, it will take a total of 30 workers to complete the job.

Making it additional 20 workers.

Answer:

B) 2m+6=24 m=9 ; each ticket cost $9.

Step-by-step explanation:

Given: Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24.

Here "m" represents the cost of each movie ticket.

Now let's form an equation.

2m + box of popcorn = $24

Box of popcorn cost $6

So,

2m + 6 = 24

Now, we have to solve for m.

Subtract 6 from both sides, we get

2m + 6 - 6 = 24 - 6

2m = 18

Dividing both sides by 2, we get

2m/2 = 18/2

m = 9

So, the cost of movie ticket is $9 each.

Therefore, the answer is B) 2m+6=24 m=9 ; each ticket cost $9.

Answer:y−8=−[tex]{\frac{3}{7}[/tex](x−5)

Step-by-step explanation:

For a rectangle with a fixed perimeter P, the one with maximum area has dimensions L = P/4 and W = P/4 obtained by optimizing the area expression.

To find the rectangle with the maximum area given a fixed perimeter P, we can use optimization techniques. Let L represent the length and W represent the width of the rectangle. The perimeter is given by P = 2L + 2W, and the area is given by A = LW.

Since P is fixed, we can express one of the variables in terms of the other using the perimeter equation. Solving for L, we get L = (P/2) - W. Substituting this expression into the area equation, we have A = ((P/2) - W)W.

To find the dimensions that maximize A, we take the derivative of A with respect to W, set it equal to zero to find critical points, and check for endpoints (since we are dealing with real-world dimensions).

(dA/dW) = (P/2) - 2W = 0.

Solving for W, we get W = P/4. Substituting this value back, we find L = P/4.

Therefore, the rectangle that maximizes the area for a fixed perimeter P has dimensions L = P/4 and W = P/4.

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The question probable may be:

What are the dimensions of the rectangle with the maximum area given a fixed perimeter P?

Final answer:

The statement about cubic polynomial functions rising to the left and falling to the right is false; the behavior of a cubic function's graph depends on the sign and magnitude of its coefficients, particularly the leading coefficient.

Explanation:

The statement that a graph of a cubic polynomial function that rises to the left must necessarily fall to the right is false. While this behavior is common for many cubic functions, it's not a definitive rule. Cubic functions are defined by the equation f(x) = [tex]ax^3 + bx^2[/tex] + cx + d, where a, b, c, and d are constants, and a ≠ 0. The sign and magnitude of these constants, especially the leading coefficient 'a', influence the end behavior of the function.

For example, if 'a' is positive, the right end of the cubic function's graph will rise, and depending on the signs and magnitudes of the other coefficients, the left end might also rise or fall. Similarly, if 'a' is negative, the right end will fall, and the left end's behavior can vary. Cubic graphs can also exhibit turning points where the function's direction changes, which is dictated by the local minima and maxima.

Therefore, while many cubic polynomials may display the behavior of rising to the left and falling to the right, others with different coefficients could have a completely different end behavior or shape, such as rising on both ends or falling on both ends. Two-dimensional (x-y) graphing tools and learning about graphing polynomials can provide visual understanding of these concepts.

Answer: The correct options for blank 1,2 and 3 are B, F and C respectively.

Explanation:

It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.

The two angles are called supplementary angles if they are  lies on the same arc of a straight line and their sum is 180 degree.

Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.

[tex]\angle PQR+\angle RQS=180^{\circ}[/tex]    .... (1)

Therefore, the correct option for first blank is option B.

It is given that ∠PQR=115°.

Using the substitution property of equality, the equation (1) can be written as,

[tex]115^{\circ}+\angle RQS=180^{\circ}[/tex]

Therefore, the correct option for second blank is option F.

Using the subtraction property of equality, ​​ ∠PQR=65° .

An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.

Since 65 is less than 90, so by the definition of acute angle the ∠RQS ​ is an acute angle.

Therefore, the correct option for third blank is option C.

Answer:

See explanation below.

Step-by-step explanation:

To construct a square using only a compass and a straightedge first we need to:

*Note: To draw a perpendicular line through a segment follow the next steps:

Answer:

B. [tex]\sqrt{16}[/tex]

Step-by-step explanation:

We have been given 4 numbers. We are asked to find the rational number from our given choices.

We know that a number is a rational number, when it could be written as a fraction.

Let us check our given choices one by one.

A. [tex]\sqrt{15}[/tex]

[tex]\sqrt{15}=3.8729833462074169[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{15}[/tex] is not a rational number.

B. [tex]\sqrt{16}[/tex]

[tex]\sqrt{16}=\sqrt{4^2}=4[/tex]

Since our given number is an integer and we can write it as a fraction [tex]\frac{4}{1}[/tex], therefore, [tex]\sqrt{16}[/tex] is a rational number.

C. [tex]\sqrt{17}[/tex]

[tex]\sqrt{17}=4.1231056256176605[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{17}[/tex] is not a rational number.

D. [tex]\sqrt{18}[/tex]

[tex]\sqrt{18}=4.2426406871192851[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{18}[/tex] is not a rational number.

It is to be noted that from the options given, the rational number is √16

A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers.

Among the given numbers, the √16 is a rational number.

The √16 equals 4, which can be expressed as the fraction 4/1.

The square roots of 15, 17, and 18 are irrational numbers because they cannot be expressed as fractions or terminate or repeat in decimal form.

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Answer:  If you have SSA, then the third side determines the triangle. If it is too short to intersect the other side, then it does not form a triangle. The third side can also be just the right length to meet the other side, making one triangle. Finally, the third side might be long enough to intersect the other side at two different points, creating two triangles.

i just took the assignment

There are different rules in mathematics. The explanation is that when a person have SSA, the third side is often used to know the type of triangle and also;

When it  too short to pass through the other side, it rather then not form a triangle. The third side can be the appropriate length to meet the other side, creating one triangle.

Furthermore, the third side can be able to pass through or intersect the other side at two key areas or points, forming two triangles.

Note that;

"SSA" is known to be when one knowns two sides and an angle that is said to be not or not part of the angle between the sides.

The Law of Sines is known to be used first to calculate one of the other two angles.

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Final answer:

Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum. Mathematics plays a crucial role in explaining quantum physics. It has various applications and impacts our understanding of the universe and technology.

Explanation:

Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum. It focuses on understanding the behavior of subatomic particles and the strange submicroscopic world they inhabit. Quantum mechanics, a part of quantum physics, describes the motion of objects that are atomic or subatomic in size and demonstrates wave-particle duality.

Mathematics plays a crucial role in explaining quantum physics. The mathematics of probability is used to describe the behavior of complex quantum systems. Additionally, equations and mathematical models are used to calculate and predict the behavior of subatomic particles.

Quantum physics has many applications and impacts our understanding of the universe and technology. It helps explain phenomena such as why some materials conduct electricity while others do not. It is also vital in areas such as atomic and nuclear physics, where it is used to study and manipulate the behavior of particles and systems at the quantum level.

In an isosceles triangle with one angle measuring 102°, the other two angles are both 39°. The sum of all angles in a triangle is 180°. Therefore, the largest angle is 102° and the smallest are both 39°.

If a triangle is isosceles and one angle measures 102°, we can determine the measures of the other two angles. Since it's an isosceles triangle, two angles are the same. According to the properties of triangles, we know that the sum of all three angles must be 180°. Therefore, we can subtract the known angle from 180° to determine the sum of the remaining two angles.

180° - 102° = 78°

Since the two remaining angles are equal, we divide 78° by 2 to find the measure of each angle.

78° ÷ 2 = 39° each

The measures of the largest and smallest angles in the isosceles triangle are 102° (the largest) and 39° (the smallest).

It really is five roots in e2020