The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, e(y) = ?0 + ?1x, is known as

The statement 'Some acute angles are more than 90 degrees' can be proven false using a counterexample because by definition, an acute angle cannot be more than 90 degrees. For a statement to be considered true in mathematics, it must cover all possible cases. If a single exception can be found, we can consider the statement false.

The statement that could be proved false using a counterexample among the choices would be 'Some acute angles are more than 90 degrees'. In Mathematics, an acute angle is defined as any angle that measures more than 0 degrees but less than 90 degrees. Hence, the idea of acute angles being more than 90 degrees is definitely incorrect.

Let's examine each statement:

In conclusion, always remember that for a statement to be true in mathematics, it must cover all possible cases. When a single exception can be found, the statement can be considered false.

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-8 < 8

 since a negative number is below 0 and a positive number is above 0 the first statement is true

Answer:

Rickey keep 2/3 or 0.7 fudge.

Step-by-step explanation:

Consider the provided information.

John made of a pound of fudge and Mary made of a pound of fudge.

Ricky takes the sum of the two amounts of fudge

The sum of the two amounts of fudge is 2 pound.

He divides it into three equal portions.

[tex]\frac{2}{3}=0.\overline6\approx0.7[/tex]

Hence Rickey keep 2/3 or 0.7 fudge.

Region C in the Venn diagram represents students who slept more than 7 hours per night and improved in school performance, as it is the intersection of both sets A and B. The correct option is C.

In the context of the Venn diagram described, where 'A' represents students who slept more than 7 hours per night, and 'B' represents those who improved in school performance, the region 'C' would typically represent the intersection of these two groups.

Therefore, the group of students that region C would represent is option B: students who slept more than 7 hours per night and did improve in school performance. This is because the Venn diagram's intersection area (region C) visually demonstrates where both conditions (sleeping more than 7 hours and improvement in school performance) are met simultaneously.

Answer:

The correct option is C.

Step-by-step explanation:

The given equation of curve is

[tex]y=2x^2+1[/tex]

We need to find the area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints.

We have 4 rectangles in x = 0 to x = 4. So,

[tex]\Delta x=1[/tex]

Left Riemann sum:

[tex]\sum_{i=0}^{n-1}\Delta xf(x_i)[/tex]

Using Left Riemann sum, we get

[tex]\sum_{i=0}^{4-1}(1)f(i)[/tex]

[tex]\sum_{i=0}^{3}(2i^2+1)[/tex]             [tex][\because y=2x^2+1][/tex]

The area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints is

[tex]\sum_{i=0}^{3}2i^2+1[/tex]

Therefore the correct option is C.

Answer:

A. |x| < 3

Step-by-step explanation:

The absolute value of a number is the value that a number has beyond its sign. This means that the absolute value is the numerical magnitude of the number regardless of whether its sign is positive or negative. Formally, the absolute value of any real number x, is defined by:

[tex]|x|=\left \{ {{x,\hspace{3}if\hspace{3}x\geq0} \atop {-x,\hspace{3}if\hspace{3}x<0}} \right.[/tex]

In this sense, to satisfy the inequality [tex]|x|<3[/tex], the domain of x must be:

[tex]-3<x<3\\\\or\\\\(-3,3)[/tex]

Because for [tex]x<-3[/tex] or [tex]x>3[/tex] the inequality is absurd. For example if x=-4

[tex]|-4|=4<3[/tex] which is not true.

and for x=4

[tex]|4|=4<3[/tex] which is not true.

On the other hand  to satisfy the inequality [tex]|x|>3[/tex], the domain of x must be:

[tex]-3>x>3\\\\or\\\\(-\infty,-3)\cup(3,\infty)[/tex]

Because for [tex]x<3[/tex]  the inequality is absurd. For example if [tex]x=2[/tex]

[tex]|2|=2>3[/tex] which is not true.

and for x=-1

[tex]|-1|=1>3[/tex] which is not true.

Therefore the correct statement is:

A. |x| < 3

Answer:It's A(45)

Step-by-step explanation:

Got it right on Edge

The required time to run for 9.6 miles is 1.5 hours, as of the given conditions.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
Teresa is going for a run. she runs for 9.6 miles at a speed of 6 miles per hour.
Speed = 6 miles per hour,
Distance = 9.6 miles

As we know,
Time = DIstance/time

Assign the values,
Time = 9.6/6
Time = 1.5 hours

Thus, the required time to run for 9.6 miles is 1.5 hours.

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The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

Given two points,

(12, 10) , (-2, r)

The slope associated with (x₁, y₁) and (x₂, y₂) →

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

So,

m = (r - 10)/(-2-12)

(r - 10)/(-14) = -4

r - 10 = 56

r = 66

Hence "The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66".

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Answer:

Option A is the answer.

Step-by-step explanation:

Table is given as

Year                    2010           2011            2012          2013    

Spring league      68               79              90              101  

Fall league           145             148             151              154

Now as per given table we will analyze each option given

A). Difference in spring league participation increasing every year = 79-68 = 11

Difference in Fall league increasing every year = 148-145 = 3

Therefore option A is true because [tex]\frac{11}{3}>3[/tex] Spring league is increasing more than twice as fast as fall league.

B). This option is not true because participation in the spring league is increasing nearly 4 times of Fall league.

C) False. Spring league participation is more than fall league.

D) False. Same as option C because spring league participation is more than fall league.

The total distance that he drive is:

                     110 miles.

We know that the distance is defined as the product of speed and time.

i.e.

[tex]Distance=Speed\times Time[/tex]

It is given that:

Juan drives 50 mph for 1.5 hours.

This means that at this rate the distance traveled by him is:

[tex]Distance_1=50\times 1.5\\\\i.e.\\\\Distance_1=75\ miles[/tex]

and he travels at the rate of 70 mph for 0.5 hours.

This means that the distance traveled by him at this rate is:

[tex]Distance_1=70\times 0.5\\\\i.e.\\\\Distance_1=35\ miles[/tex]

Hence, the total distance that he drive is:

      [tex]Total\ distance=Distance_1+Distance_2\\\\Total\ distance=75+35\\\\i.e.\\\\Total\ distance=110\ miles[/tex]

Net worth is the calculation of an individual's assets minus their liabilities, while tallying of expenses is a regular tracking of personal spending without considering overall assets or debts. An example of this can be seen in the use of credit cards and savings accounts and their respective interest rates.

The calculation of net worth and the day-to-day or month-to-month tallying of expenses are two different aspects of personal finance. Net worth is a calculation that is made by subtracting a person's liabilities from their assets. In other words, it is your assets (what you own) minus your liabilities (what you owe). On the other hand, tallying of expenses is a way to track your spending habits on a daily or monthly basis, which does not take into account one's assets or debts.

For instance, let's consider a person who owns a house (an asset), but also owes some amount on the mortgage (a liability). Their net worth would be the value of the house minus what's still owed on the mortgage. This is different from keeping track of daily or monthly expenses, which may include the mortgage payment, grocery bills, car payments, and other outgoings.

A common example of the difference is seen in credit card usage. A person might have a $1,000 credit card debt with a 15% interest rate, and simultaneously, a savings account of $2,000 that pays only 2% interest. They are losing money overall because the credit card debt costs more than the savings account earns. To increase their net worth, the rational decision would be to pay off the debt, but this wouldn't necessarily reduce their monthly expenses since they would still need to meet their day-to-day costs.

Calculating net worth is different from day-to-day or month-to-month tallying of expenses. Net worth is a measure of a person's financial wealth, while expense tracking helps monitor spending habits.

Calculating net worth is different from day-to-day or month-to-month tallying of expenses. Net worth is a measure of a person's financial wealth and is calculated by subtracting the total liabilities from the total assets. It provides a snapshot of an individual's overall financial health and is not influenced by short-term spending or expenses.

On the other hand, day-to-day or month-to-month tallying of expenses involves tracking and categorizing the money spent on various items or activities over a specific period. It helps individuals manage their budget, track their spending habits, and make informed financial decisions on a regular basis.

While net worth provides a big-picture view of a person's financial situation, day-to-day expense tracking helps monitor and control spending on a more detailed level to achieve financial goals.

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Answer:

-147

Step-by-step explanation: