Question 6(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation MC)
How many times larger is 8 x 105 than 4 x 10³?
2,000
200
20
2.0

The input value x in the function k( x ) = 6x - 12 when k( x ) = 15 is 9/2.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the value of x, equate the function to 15 and solve for x.

k( x ) = 6x - 12

k( x ) = 15

15 = 6x - 12

Rearrange the equation

6x - 12 = 15

Collect like terms

6x = 15 + 12

6x = 27

Divide but sides by 6

6x/6 = 27/6

x = 27/6

x = 9/2

Therefore, the input value (x) is 9/2, this forms an ordered pair of ( 9/2, 15 ).

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By solving a linear equation, we will see that the points are vertical only if the value of x is -2.

We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:

x₁ = x₂

y₁ ≠ y₂

In this case, the two points are:

F(3-2x, 12) and G(x+9, 7)

The y-component is different, so we only need to have:

3 - 2x = x + 9

This is a linear equation, below I will solve it:

3 - 2x = x + 9

3 - 9 = x + 2x

-6 = 3x

-6/3 = x

-2  =x

The points are vertical if x = -2.

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Hence, the survey of professor will be representative survey.

A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole.

Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.

The survey of professor will be representative survey.

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Using the half life of palladium, mass seven weeks after start was 0.7931 gm.

The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.

The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.

The  half life of palladium 100 = 4 days

after 24 days sample has reduced to a mass of 5mg

standard exponential function is

[tex]P = P_o e^{kt}[/tex]

plugging P = P₀ /2

[tex]P_o/2 = P_o e^{4k }[/tex]

[tex]1/2 = e^{4k }[/tex]

ln (1/2) = 4k

k = -0.1733

function becomes

[tex]P = P_o e^{- 0.1733 t }[/tex]

plugging P = 5 and t = 24

[tex]5 = P_o e^{( - .1733\times 24 ) }[/tex]

P₀ = 320.10

In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.

For the second part of the problem:

7 weeks = 5 × 7 =49 days

plugging t = 49

[tex]P = 320.10 e^{(-.1733 * 35 ) }[/tex]

mass 7 weeks after = 0.7431 mg

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The value of p that we get by solving the inequality given in the question is [tex]p\geq \frac{-20}{3}[/tex]

The given inequality is

[tex]\frac{3}{4}p+8\geq 3[/tex]

⇒[tex]\frac{3}{4}p\geq 3-8[/tex]                              (subtracting 8 on both sides)

⇒[tex]3p\geq -5*4[/tex]                             (multiplying both sides by 4)

⇒[tex]p\geq \frac{-20}{3}[/tex]                                  (dividing both sides by 3)

⇒[tex]p\geq -6.667[/tex]

Therefore the value of p must be greater than or equal to -20/3 or -6.667

That is, [tex]p\geq -6.667[/tex]

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The fraction that are female in the company is 227/256

The given parameters are

Male staff = 58

Total number of staff = 512

Start by calculating the number of female staffs

So, we have

Female staff = Total number of staff - Male staff

Substitute the known values in the above equation

So, we have

Female staff = 512 - 58

Evaluate the like terms

Female staff = 454

The fraction that are female is

Fraction = Female staff/Total number of staff

This gives

Fraction = 454/512

Simplify

Fraction = 227/256

Hence, the fraction is 227/256

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The value of x is 54.

If a transversal meets two parallel lines, each pair of same-side interior angles is supplementary (their sum is 180°), according to the theorem for the "same-side interior angle theorem."

The given angles in the figure are 2x + 42° and x - 24°, which are interior angles formed on the same side of the transversal.

By Same Side Interior Angles Theorem,

2x + 42° + x - 24° = 180°

3x + 18° = 180°

3x = 180° - 18°

3x = 162°

x = 54

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Answer:

x > 9

Step-by-step explanation:

60 cents is 20% of $3.

In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."

Given Data

60 cents as a percent of $3

1 dollar = 100 cents

$3 dollar = 300 cents

Percentage:

[tex]\frac{Value}{Total value}[/tex] × 100

[tex]\frac{60}{300}[/tex] ×100

20%

60 cents in 20% of $3.

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The complete question is:
"60 cents is what percent of $3."

It is shown that if a parallelogram's diagonals are perpendicular, the parallelogram is a rhombus.

A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal).

A rhombus is a quadrilateral with all of its sides equal. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.

We must demonstrate that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Let ABCD be a  parallelogram .

Consider Δ AOD and Δ COD

Since, a parallelogram's diagonals bisect each other we can say that,

AO = CO

∠AOD = ∠COD = 90°

DO = OD

Δ AOD ≅ Δ COD [SAS rule]

∴ AD = CD

Because the parallelogram's adjacent sides are equal, we can conclude that all four sides are equal.

As a result, it is demonstrated that if the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.

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Answer: Never, All real numbers, x<0, x>0

Step-by-step explanation:

The function is positive when it is above the x-axis.

The function is negative when it is below the x-axis.

The function is increasing when the graph is going up.

The function is decreasing when the graph is going down.

The depth of the personal submarine is -14.9 meter.

An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

Given that,

The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.

Now,

To find the depth adding the -20.6+5.7

-20.6+5.7

-14.9

Hence, The depth of the personal submarine is -14.9 meter

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Answer:

all real numbers

Step-by-step explanation:

4(4x+2)+2(9x+4)+3=34x+19

16x+8+18x+8+3=34x+19

34x+19=34x+19

all real numbers

:]

To solve this problem, we will use the following formula for the area of a trapezoid:

where a, and b are the lengths of the bases and h is the height.

Now, we are given that ( we will omit the units to simplify the calculations):

Therefore:

Substituting in the above formula, we get:

Simplifying the above result, we get:

Answer:

Slope intercept form: [tex]y=mx+b[/tex]

We can identify two points on the given graph and solve for the slope and the y-intercept.

Two clear points on the graph are (6,0) and (0,6).

First, we can solve for the slope by using the slope equation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

⇒ Plug in the points (6,0) and (0,6):

[tex]m=\dfrac{0-6}{6-0}\\\\m=\dfrac{-6}{6}\\\\m=-1[/tex]

Therefore. the slope of the line is -1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-x+b[/tex]

Now, we can find the y-intercept. It is the value of y when the line crosses the y-axis.

In this case, we can see on the graph that this is 6.

[tex]y=-x+6[/tex]

[tex]y=-x+6[/tex]

[tex] - {k}^{2} + 3k = 28 - 2 {k}^{2} \\ - {k}^{2} + 2 {k}^{2} + 3k - 28 = 0 \\ {k}^{2} + 3k - 28 = 0 \\ (k + 7)(k - 4) = 0 \\ \\ k + 7 = 0 \\ \\ ork - 4 = 0 \\ \\ k = - 7 \\ \\ or \\ \\ k = 4[/tex]

ATTACHED IS THE SOLUTION

I GROUPED THE LIKE TERMS TOGETHER FIRST AFTER THAT THEN FACTORISED.

well, the change was 8 bucks.

if we take 20 to be the 100%, what is 8 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 8& x \end{array} \implies \cfrac{20}{8}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2}=\cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]

Answer:

Step-by-step explanation:

What is the answer:

4(3x+2)-2=

12x + 8 - 2 =

12x + 6

To solve for y we will have to simply replace the value of x and the solution we write it in the equivalent palce for y, that is:

For x = -5:

For x = -2:

For x = 0:

For x = 3:

The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.

What is an expression?

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

Given that;

The expression is;

(4.617 × 10³ ) ÷ (5,700 ÷ 10² )

Now, Solve the expression by using BODMAS rule;

= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )

= 4,617 ÷ 57

= 81

Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.

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Answer: The Pink one

Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.

Answer:

KM

KL

LM

Step-by-step explanation:

The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.

What is translation and reflection?

In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.

According to the question, the given expression for the translation as well as for the reflection are as follows:

h(x)=a |b(x) + c| + d

g(x)=1/3 | x + 3| - 4

And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.

Translation expression: h(x+7)=a |b(x+7) + c| + d

Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4

Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.

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y -intercept #4 the starting value

(1 , 7.5) #3 the value after 1 year

because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.

The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given Data

x coordinate = 4

y coordinate = 7

Slope = y-coordinate/ x-coordinate

Slope = 7/4

The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.

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The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.

The test hypothesis is as follows:

H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.

Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.

We will apply a t-test for a single mean because the population standard deviation is unknown,

It is assumed that the sample means  [tex]\bar{x}[/tex] = 91.

The adjusted sample presented is:

S = { 62, 78, 89, 95, 95, 137}

Calculate the sample standard deviation as follows:

[tex]\bar{x}[/tex] = 62 + 78 + 89  + 95 + 95 + 137 =80

[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]

s =28.66

[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]

Thus, the test statistic value is 0.94.

Compute the p-value of the test as follows:

p-value = p(tₙ₋₁ < t)

p-value = p(t₆₋₁ < t)

p-value = p(t₅ < t)

*Make use of a t-table.

As a result, the test has a p-value of 0.1515.

Rule of decision:

The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.

p-value = 0.1515 > α = 0.05

At 5% significance, the null hypothesis will not be rejected.

As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.

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Answer:

532

Step-by-step explanation:

Sum of the first n terms of an arithmetic series:

[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]

Where:

Given terms:

Substitute the given terms into the formula to create an equation for the nth term:

[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]

[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]

[tex]\implies S_n=38n[/tex]

To find S₁₄, substitute n = 14 into the found equation:

[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]

Answer:D

Step-by-step explanation: