20b - 16 Factor the expression completely

The value of the expression, [9(10 - 2)] ÷ [2 + (5 × 2)], found using PEMDAS order of operations is 6

A mathematical expression is a mathematical statement which consists of two or more numbers or variables that are linked by mathematical operators.

The possible expression in the question is presented as follows;

[9(10 - 2)] ÷ [2 + (5 × 2)]

The above expression can be evaluated using the order of operations convention, which is a set of rules used in mathematics and computer programming, that indicates the procedure which comes first when evaluating a mathematical expression.

The rules can be memorized using mnemonics like PEMDAS that represents;

PEMDAS indicates that operations within a parentheses is to be performed first, before exponents, which comes before multiplication, followed by division then addition before subtraction.

The convention aims to remove ambiguity, such that the expression 1 + 2 × 3 = 1 + (2 × 3)

To evaluate the given expression, we therefore have;

[9(10 - 2)] ÷ [2 + (5 × 2)]

Performing operations within the parentheses gives;

[9(10 - 2)] ÷ [2 + (5 × 2)] = [9(8)] ÷ [2 + (10)]

[9(8)] ÷ [2 + (10)] = [9×8] ÷ [2 + 10]

[9×8] ÷ [2 + 10] = 72 ÷ 12

There are no exponents, (E), or further multiplication, (M), outside the parentheses, therefore performing the, division, (D) gives;

[tex]\displaystyle{ 72 \div 12 = \frac{72}{12} =6}[/tex]

The value of the expression is therefore;

[9(10 - 2)] ÷ [2 + (5 × 2)] = 6

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Answer:

your mom

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No 3.674 is not equal to 6.764

What is equality?

We say that two values, numbers , expression are equal if they have = sign in between them, Two value or number are said to be same if every digit from both the number is same and in same order. in other words if the difference between them is zero

We are given two numbers 3.674 and 6.764

We take the difference of them

We get

6.764- 3.674= 3.09

Which is not equal to zero

Hence the two numbers are not equal.

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We need to simply find the difference in height to solve this problem. The person standing at an elevation of 15 feet is closer to the basement.

The elevation of the basement is said to be 12 feet and the elevation of the roof is 32 feet. The person is standing at an elevation of 15 feet. Inorder to find whether the person is closer to the basement of the roof we need to find the difference in height of the person from the basement and from the roof. The difference in height between the person and the basement is 15-12=3 feet and the difference between the height of the person and the roof is 32-15=17 feet. Since 3 is less than 17 the person is closer to the basement.

Therefore the person standing at an elevation of 15 feet is closer to the basement.

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The 205th term of the sequence is 768 with a common difference of 4.

So, the sequence is:

-48, -44, -40, -36, -32,... +4

The common difference is: -48 + 4 = - 44 ⇒ 4

Formula: aₙ = a + (n - 1)d

Now calculate as follows:

aₙ = a + (n - 1)d

aₙ = -48 + (205 - 1)4

aₙ = -48 + (204)4

aₙ = -48 + 816

aₙ = 768

Therefore, the 205th term of the sequence is 768 with a common difference of 4.

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y = -5x -25 is the equation in​ slope-intercept form of the line that passes through the given point (-5,-5) and is parallel to the given equation ​ y = -4x+1.

The standard form of an equation of a line in​ slope-intercept form is

y = mx + c

where m represents the slope of the line and c represents the y intercept.

The equation of the parallel line is

y = -4x + 1

Here the slope of the line is -4 and the intercept is +1.

Two line that are parallel to each other have same slope.

So, the slope of the line passing through the point(-5, -5) and is parallel to the line y = -4x + 1 is -4.

putting the point given in the standard form

y  = m(x) + c

-5 = -4(-5) + c

-5 = 20 + c

c = -25

The equation of line is y = -5x -25

Therefore, y = -5x -25 is the equation in​ slope-intercept form of the line that passes through the given point (-5,-5) and is parallel to the given equation ​ y = -4x+1.

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The rate of miles per gallon is 24.5 miles/gallon and an equation for the  proportional relationship is 1 : 24.5 and we can drive 1592.5 miles on 65 gallons of gas.

In proportionality, Algebra demands that two ratios be equal. A/B = C/D denotes the ratio of a and b to c and d. When using a proportion to solve a word problem, one of the four quantities is usually unknown.

It can be resolved by multiplying one numerator by the opposing denominator, adding the resulting number, and then solving for the other numerator and denominator.

Proportionality refers to any relationship that consistently has the same ratio. For instance, the number of trees in an orchard and the quantity of apples in a crop are determined by the average number of apples per tree.

It is given that,

A test of a new car shows it can drive 357.7 miles on 14.6gallons of gas.

We need to find how far you could drive on 65 gallons of gas.

14.6 gallons of gas = 357.7 miles

miles per gallon =  357.7 miles/14.6 gallons

                           = 24.5 miles/gallon

For 65 gallons of gas

65 gallons = 24.5 × 65 miles

                  = 1592.5 miles

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We are given the following equation: y = 5/4x - 7/4 and we are asked to identify the slope.

To answer the question, we must recall the slope-intercept form of a linear equation:

y = mx + b where m is the slope and b is the y-intercept.

Using this format, we know that m = 5/4 and b = - 7/4.

Therefore, the slope of the equation is 5/4.

(C) "A dollar's value is impacted by ongoing inflation" best demonstrates an exponential decay.

So, only one of the options in this case—the dollar value being affected by constant inflation—seems to exhibit exponential decay.

Therefore, (C) "A dollar's value is impacted by ongoing inflation" best demonstrates an exponential decay.

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The correct question is given below:

Which of the following scenarios demonstrates an exponential decay?

A. Value of a dollar invested in a savings account

B. Value of a dollar affected by constant deflation

C. Value of a dollar affected by constant inflation

D. None of the above

Considering a 0.05 significance level, there is enough evidence to conclude that the resting heart rate of men aged 18 to 25 who exercise regularly is less than that of men who do not exercise regularly.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the resting rate is less, hence:

[tex]H_0: \mu_1 \geq mu_2[/tex]

Then:

[tex]H_0: \mu_1 - \mu_2 \geq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the rate is less, hence:

[tex]H_1: \mu_1 - \mu_2 < 0[/tex]

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences are given as follows:

The test statistic is given according to the following equation:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence the value of the test statistic is given by:

t = -8/0.27

t = -29.63

Considering a left-tailed test, as we are testing if the parameter is less than a value, and using a t-distribution calculator, with t = -29.63 and 30 + 40 - 2 = 68 df, the p-value of the test is of 0.

Since this p-value is less than the significance level, there is enough evidence to conclude that the resting heart rate of men aged 18 to 25 who exercise regularly is less than that of men who do not exercise regularly.

The problem is given by the image at the end of the answer, and we have to test the claim using a significance level of 0.05.

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Answer:

D. 135 degrees

Step-by-step explanation:

Angle x = 180 - 45

             = 135 degrees,   (adjacent angles are supplementary).

The price of iphone in £ will costs £825 in London, £848.21 in Paris and  £839.16 in New York .The lowest value of iphone in London which costs  £825.

We had given the following information that An iphone costs £825 in London, €950 in Paris and $1,200 in New York.

We have to find the lowest price of iphone among the given iphone prices

We had to find the lowest price in £ .

Therefore we have to convert all the given prices into £.

For the conversion of prices we had given that  £1 = €1.12 and £1 = $1.43.

Now In Paris iphone costs €950. Converting €950 into £ will be as follows

 £1 = € 1.12.

∴ £x = € 950.

∴ x = £848.21.

Now In New York iphone costs $1,200. Converting $1,200 into £ will be as follows

£1 = $1.43.

∴ £x = $1,200

∴ x = £839.16.

Now the price of iphone in £ will costs £825 in London, £848.21 in Paris and  £839.16 in New York.

Therefore by comparison we get the lowest value of iphone in London which costs  £825.

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The solution of the equation is not extraneous.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

⇒ Square root of quantity 2x plus 8 end quantity equals 6.

Now,

Since, The algebraic expression is,

⇒ Square root of quantity 2x plus 8 end quantity equals 6.

Hence, The mathematical expression is,

⇒ √2x + 8 = 6

Solve for x as,

⇒ √2x + 8 = 6

Take square both side, we get;

⇒ 2x + 8 = 36

⇒ 2x = 36 - 8

⇒ 2x = 28

⇒ x = 14

So, The value of x = 14

Since, The solutions of an equation are known as extraneous solutions if they are invalid.

Hence, Substitute x = 14 in above equation, we get;

⇒ √2x + 8 = 6

⇒ √2 × 14 + 8 = 6

⇒ √36 = 6

⇒ 6 = 6

Thus, The solution is not extraneous.

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The value of the angle y in the quadrilateral is 90° .

There are four sides, four vertices, and four angles in a closed quadrilateral.

We know that from the properties of parallel line x = 70° as the angles are alternate angles.

Again the interior angle adjacent to the 70° angle is equal to

180° - 70° = 110°

Given another interior angle is 90°.

We know sum of all the four angles of a quadrilateral is 360°.

Therefore

70 + 90 + 110 + y = 360°

Hence we will find the value of y.

y = 360° - 270°

or, y = 90°

Therefore the value of y is 90° .

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The lower bound for the length of the remaining ribbon is 13.8 cm, and the upper bound is 15.8 cm.

Here,

To work out the lower and upper bounds for the length of the remaining ribbon, we need to consider the possible scenarios that would result in the smallest and largest remaining lengths.

Given:

Original length of ribbon = 23 cm (correct to the nearest cm)

Length of the piece cut off = 87 mm (correct to the nearest mm)

First, let's convert the length of the piece cut off to centimeters:

1 cm = 10 mm

So, 87 mm = 87 / 10 cm = 8.7 cm (correct to the nearest mm)

Now, let's calculate the upper bound for the remaining ribbon length:

Upper bound = Original length - Length cut off + Tolerance

Upper bound = 23 cm - 8.7 cm + 0.5 cm (maximum possible rounding error for 87 mm)

Upper bound = 23 cm - 8.7 cm + 0.5 cm = 15.8 cm

Next, let's calculate the lower bound for the remaining ribbon length:

Lower bound = Original length - Length cut off - Tolerance

Lower bound = 23 cm - 8.7 cm - 0.5 cm (maximum possible rounding error for 87 mm)

Lower bound = 23 cm - 8.7 cm - 0.5 cm = 13.8 cm

So, the lower bound for the length of the remaining ribbon is 13.8 cm, and the upper bound is 15.8 cm.

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ANSWER :

d. cot θ

EXPLANATION :

Note that the reciprocal of tangent is cotangent.

If reciprocals are multiplied with each other, the result is 1.

From the problem, we have :

Since the result of the product is 1, the tangent function must be multiplied by its reciprocal.

That will be cotangent.

Or we can just simply divide the equation by tan θ.

Answer:

Step-by-step explanation:

To solve for x, isolate it on one side of the equation.

Use a distributive property.

a(b+c)=ab+ac

a(b-c)=ab-ac

2(x-14)

2*x=2x

2*14=28

=2x-28

-5x>2x-28

Subtract by 2x from both sides.

-5x-2x>2x-28-2x

Solve.

-7x>-28

Multiply by -1 from both sides.

[tex]\sf{\left(-7x\right)\left(-1\right) < \left(-28\right)\left(-1\right)}[/tex]

Solve.

-7x*-1=7x

-28*-1=28

7x<28

Divide by 7 from both sides.

7x/7<28/7

Solve.

Divide these numbers from left to right.

28/7=4

[tex]\Rightarrow \boxed{\sf{x < 4}}[/tex]

Therefore, the final answer is b. x<4.

I hope this helps, let me know if you have any questions.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{-5x > 2(x-14) } \end{gathered}$}}[/tex]

Use distributive property to multiply 2 by x−14.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{-5x > 2x-28 } \end{gathered}$}}[/tex]

Subtract 2x on both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{-5x-2x > -28 } \end{gathered}$}}[/tex]

Combine −5x and −2x to get −7x.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{-7x > -28 } \end{gathered}$}}[/tex]

Divide both sides by −7. Since −7 is <0, the direction of inequality is changed.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{x < \dfrac{-28}{-7} } \end{gathered}$}}[/tex]

Divide −28 between −7 to get 4.

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{x < 4 } \end{gathered}$}}}[/tex]

Janae will have $ 95 in her account after 10 days.

A sequence of numbers that has a fixed common difference between any two consecutive numbers is called an arithmetic progression (A.P.)

Given,

Amount in Janae's account = $ 50

Amount she wishes to save for 10 days = $ 5

This scenario models an arithmetic progression(A.P)

In an A.P,

a _n = a + (n-1)d

where a _n = nth term, a is the first term, n is the no. of terms and d is the common difference.

In this question, a = 50, n = 10, d = 5 and we have to find out a _n

Therefore, a _n = 50 + (10-1)x5

                         = 50 + 45 = 95

Answer:- Janae will have $ 95 in her account after 10 days.

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The coordinates points of intersection of the circle and the parabola are (1,6) and (-1,6).

The equation of the given circle is x²+y²=37

The equation of the given parabola is x²=y-5

To find the point of intersection of the parabola and the circle,

Putting the value of x²=y-5 in the equation of circle,

So, we get,

y-5+y²=37

y²+y-42=0

This is a quadratic equation, so using quadratic formula,

y = [-b±√(b²-4ac)]/2a

Here,

a = 1

b = 1

c = -42

y = [-1±√(1²-4(1)(-42))]/2(1)

y = [-1±√(1+168)]/2

y = [-1±13]/2

y = -14/2 and 12/2

y = -7 and 6.

Putting the values of y in x²=y-5,

We get,

x² = 6-5

x = ±1

And,

x²=-7-5

x²=-12

Not possible,

So, when y is 6, the value of x is ±1.

So the coordinate of point of intersection are (1,6) and (-1,6).

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The scientific notation of the whole number 165000 is (1.65 * 10⁵).

As per the question statement, we are provided with a number which is 165000.

We are require to determine the scientific notation of the above mentioned number.

Here, 165000 can be written as (165 * 1000)

Or, 165000 = (1.65 * 100 * 1000)

Or, 165000 = (1.65 * 100000)

Or, 165000 = (1.65 * 10⁵)

That is, the scientific notation of 165000 is (1.65 * 10⁵).

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The quadratic equations are given as follows:

37. y = 1.6(x² - 2x - 3).

38. y = x² - x.

39. y = 0.4074(x² - 12x + 11).

The roots of the quadratic equation are at x = -1 and x = 3, hence it can be written as follows:

y = a(x + 1)(x - 3)

In which a is the leading coefficient.

Hence:

y = a(x² - 2x - 3)

When x = 1, y = -8, hence the leading coefficient a can be found as follows:

-8 = a(1 - 2 - 3)

5a = 8

a = 8/5

a = 1.6

Hence the equation is:

y = 1.6(x² - 2x - 3).

The roots of the quadratic equation are at x = 0 and x = 1, hence it can be written as follows:

y = ax(x - 1)

Hence:

y = a(x² - x)

When x = 2, y = -2, hence the leading coefficient a can be found as follows:

2 = a(2² - 2)

2a = 2

a = 1.

Hence the equation is:

y = x² - x.

The roots of the quadratic equation are at x = 1 and x = 11, hence it can be written as follows:

y = a(x - 1)(x - 11)

Hence:

y = a(x² - 12x + 11)

When x = 2, y = -11/3, hence the leading coefficient a can be found as follows:

-11/3 = a(4 - 24 + 11)

9a = 11/3

a = 11/27

a = 0.4074.

Hence the equation is:

y = 0.4074(x² - 12x + 11).

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The number of freshman who prefer football to basketball is 138 students

It should be noted that the random sample of 50 students found that 12 students prefer football to basketball.

The students that prefer football will be:

= Fraction × Total number of students

= 12/50 × 575

= 6900/50

= 138

There will be 138 students.

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Answer:

     +2

     27

  x 34

+1 238

    68

  =918

Answer:

The right answer choice is the last one

-3x^3 - 3x^2 + 7x + 2

Answer:

The last one is correct

Step-by-step explanation:

multiply -3[tex]x^{2}[/tex] + 3x + 1 by x and the by 2 and then add them together.

x(-3[tex]x^{2}[/tex] + 3x + 1)

-3[tex]x^{3}[/tex] + 3[tex]x^{2}[/tex] + x

2(-3[tex]x^{2}[/tex] + 3x + 1)

-6[tex]x^{2}[/tex] +6x +2

Add the two bold expressions above to find the answer.

-3[tex]x^{3}[/tex] + 3[tex]x^{2}[/tex] + x -6[tex]x^{2}[/tex] + 6x + 2

-3[tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +7x +2

The probability of both balls being red is 2/7

Given that there are four red balls and three green balls in a bag and two of the balls are out of the bag without replacement.

We must find the probability that both balls are red.

Let us consider,

Probability of drawing a red ball = 4 red balls / 7 total balls

1st draw is (4/7)

None are replaced, (put back in the bag) so now there are 3 red balls in a bag of 6 total balls.

2nd draw is 3/6 = (1/2)

Multiply the probabilities together to find the chance of drawing red 2 times in a row.

= (4/7) * (1/2)

= 2/7

Hence, the probability that both balls are red is 2/7

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Answer:

909/1000000

Step-by-step explanation:

Since 0.000909 is 6 places values past the decimal. That is blank out of /1000000. Hence since 909 is the only number other than 0 you put 909/1000000