the following stem-and-leaf plot shows scores on a statistics midterm exam. the instructor decided to give an f to the 10th percentile or below. what is the highest score with an f grade?

The zeros of a polynomial are the values of x for which the polynomial is equal to 0.

What is polynomial?

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a non-negative integer power. It is an algebraic expression that can involve constants, variables, and exponents.

To find the rational zeros of a polynomial, use the Rational Zero Theorem. This theorem states that if the polynomial is written in standard form, ax^n + bx^n-1 + cx^n-2 + ... + k = 0, then the possible rational zeros are any rational number that can be expressed as p/q, where p is a factor of k (the constant) and q is a factor of a (the leading coefficient).

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Complete question is:

How to Find All Possible Rational Zeros Using the Rational Zeros Theorem With Repeated Possible Zeros?

The area of the rectangle will be equal to 11 square units.

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.

The area of the rectangle is calculated by finding the determinant of the matrix as below,

[tex]A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right][/tex]

A = ( 6 - ( -5 )

A = 6 + 5

Area = 11 square units

Hence, the value of the area of the rectangle is 11 square units.

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Katie spent approximately $285.544 on fuel during her vacation in Australia.

The Average Cost is the per unit cost of the product received by dividing the total cost (TC) by the total output (Q). By per unit cost of production, we mean that all the fixed and variable costs are considered for calculating the average cost. Thus, it is also called Per Unit Total Cost.

Symbolically, the average cost is expressed as:

AC = TC/Q

To estimate how much Katie spent on fuel, you need to multiply the number of gallons of gas she used (56 gallons) by the average cost of gas per gallon ($5.099):

56 gallons × $5.099/gallon = $285.544

So, Katie spent approximately $285.544 on fuel during her vacation in Australia.

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Correct option is D, using area of playground the length and width of the playground is length = 10 yd, breadth = 2 yd.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy. A plane figure's area is the space that its perimeter encompasses. The area of a closed figure is the total number of unit squares covering its surface. Area is measured in square units like cm2 and m2.

The area of a shape is the area enclosed by its perimeter or boundary.

A = b × h is the formula for calculating the area, A, of a square or rectangle.

The playground's length is 5 times more than its breadth,

thus l=5w.

However, 10=2 x 5 allows us to write

l=5w, and

area = 20

=l x w

= (5x2) x 2

=20.

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Complete question -

The area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground.

length = 1 yd, width = 20 yd

length = 2 yd, width = 10 yd

length = 10 yd, width = 2 yd

length = 20 yd, width = 1 y

An equation of the function graphed above include the following: f(x) = 2∛x - 4.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Additionally, a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate of the pre-image or parent function.

By critically observing the graph of the function shown above, we can logically deduce that it is a cube root function that has been vertically shifted by a scale factor of 2 units and then translated downward by 4 units. Therefore, this can be modeled by this equation as follows;

f(x) = 2∛x - 4.

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The value of x in the triangle is 17 .

The perimeter of the triangle ABC is 86 units.

Triangle Proportionality Theorem states that If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Therefore, let's use the theorem to find the value of x in the triangle.

Hence,

20 / 4 = 2x - 4 / 6

cross multiply

120 = 4(2x - 4)

120 = 8x - 16

120 + 16 = 8x

136  = 8x

divide both sides by 8

x = 136 / 8

x = 17

Hence, let's find the perimeter of the triangle ABC.

perimeter of the triangle ABC = 24 + 26 + 2(17) - 4 + 6

perimeter of the triangle ABC = 50 + 30 + 6

perimeter of the triangle ABC = 86 units

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Answer:

%6, 1/2, 0.6, 6/5

Step-by-step explanation:

Answer:

Bottom left option

Step-by-step explanation:

The four numbers present in this order are:

[tex]\frac{1}{2} = 0.5[/tex]

0.6

[tex]\frac{6}{5} = 1.2[/tex]

[tex]6 percent = \frac{6}{100}[/tex] = 0.06

The order of the numbers from least to greatest are:

6%, [tex]\frac{1}{2}[/tex], 0.6, [tex]\frac{6}{5}[/tex]

Answer:

i hope this helpes

Step-by-step explanation:

(a) To find the time necessary to type 50 words per minute, we need to solve the equation:

157/1 + 5.4e^-0.12t = 50

Rearranging the equation to isolate e^-0.12t and using the natural logarithm, we can find t:

ln(N - 157) = ln(5.4) - 0.12t

-ln(N - 157) = 0.12t - ln(5.4)

0.12t = ln(5.4) + ln(N - 157)

t = (ln(5.4) + ln(N - 157)) / 0.12

Plugging in N = 50, we get:

t ≈ 11.52 weeks

(b) To find the time necessary to type 75 words per minute, we follow the same steps as above:

157/1 + 5.4e^-0.12t = 75

ln(N - 157) = ln(5.4) - 0.12t

-ln(N - 157) = 0.12t - ln(5.4)

0.12t = ln(5.4) + ln(N - 157)

t = (ln(5.4) + ln(N - 157)) / 0.12

Plugging in N = 75, we get:

t ≈ 9.32 weeks

Answer:

For 50 wpm : 7.7 weeks approximately

For 75 wpm : 13.3 weeks approximately

Step-by-step explanation:

Given the relationship between N, the typing speed and t, the number of weeks of lessons as:

[tex]\mbox{\large N= \dfrac{157}{1+5.4e^{-0.12t}}}[/tex]

To solve for t for a particular N

cross-multiply the left side with the right side denominator to get

[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{N}}[/tex]

For N= 50 this works out to

[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{50}}[/tex]

[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157}{50} - 1}\\[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157-50}{50} } = \dfrac{107}{5} = 2.14[/tex]

Divide by 5.4 both sides:

[tex]\mbox{\large e^{-0.12t } = \dfrac{2.14}{5.4}} = 0.3963\\[/tex]

Take natural logs on both sides

[tex]\mbox{\large \ln(e^{-0.12t}) = \ln(0.3963)\\}[/tex]

[tex]\mbox{\large \ln(e^{-0.12t}) = -0.12 \;\textrm{since $ln(e^x)$ = x}}[/tex]  since ln(eˣ) = x

ln(0.3963) = -0.9256

Therefore

[tex]t = \dfrac{-0.9256}{-0.12} = \dfrac{0.9256}{0.12} = {7.7133 \;weeks\approx \mbox{\large \boxed{7.7 \;weeks}}[/tex]

For N = 75, follow the same strategy and you will end up with

[tex]1+5.4e^{-0.12t}=\dfrac{157}{75} \\\\\\1+5.4e^{-0.12t}= 2.0933\\\\5.4e^{-0.12t} = 2.0933 - 1 = 1.0933\\\\e^{-0.12t} = \dfrac{1.0933}{5.4} = 0.2025\\\\[/tex]

Taking logs on both sides
[tex]-0.12t =-1.5971[/tex]

[tex]t = \dfrac{-1.5971}{-0.12} = 13.3097 \;weeks \approx \boxed{\mbox{\large 13.3 \;weeks}}[/tex]

Answer:

15,19,26

Step-by-step explanation:

second side of a triangular deck is 4 feet longer than the shortest​ side,

shortest​ side = x

second side = x+4

third side = 2x-4

perimeter = 60 = x+x+4+2x-4 =4x

x=15

second side = x+4 =19

third side = 2x-4 =30-4 =26

Answer:

negative two and five eights

Step-by-step explanation:

It usually helps to break down the equation like this:

-1 - 1 = -2

1/4 = 2/8

2 - 3 = 5, therefore 2/8 - 3/8 = 5/8.

Put it all together,

-1 1/4 - 1 3/8 = -2 5/8

The result of 626362737287387287373 times 77474747743874837847348734463763786837 represented in scientific notation is 4.80498727057566113882339366151788673587 × 10⁹⁵.

The number you provided in your question can be represented in scientific notation. Scientific notation is a way of expressing numbers in a compact form that is especially useful for very large or very small numbers. The number you provided in your question can be represented in scientific notation as:

7.7474747743874837847348734463763786837 × 10⁷⁷

And 626362737287387287373 can be represented as:

6.26362737287387287373 × 10¹⁸

The product of these two numbers can be calculated as follows:

(7.7474747743874837847348734463763786837 × 10⁷⁷) × (6.26362737287387287373 × 10¹⁸) =

= (7.7474747743874837847348734463763786837 × 6.26362737287387287373) × (10⁷⁷ × 10¹⁸) =

= 48.0498727057566113882339366151788673587 x 10⁹⁵

So, the result of 626362737287387287373 times 77474747743874837847348734463763786837 in scientific notation is:

4.80498727057566113882339366151788673587 × 10⁹⁵

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30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point fomeasuring elevation and depth, and which can vary depending on the location.

Sea level is the average level of the surface of the ocean, which is used as a reference point for measuring elevation and depth. The term "sea level" can also refer to the specific measurement of the height of the ocean's surface at a specific location.

30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level. This means that the location is 30 degrees lower in elevation than the reference point of the average surface of the ocean. This can be measured in either meters or feet, depending on the unit of measurement being used.

One way to think about 30 degrees below sea level is to imagine a point 30 degrees below the level of the water in a swimming pool. This would be considered a very deep point in the pool, and would be much lower than the surface of the water. Similarly, a location that is 30 degrees below sea level is much lower in elevation than the average sea level.

It's important to note that the concept of sea level can vary depending on the location, as sea level can vary due to factors such as ocean currents, tides, and the shape of the ocean floor. Therefore, the reference point for sea level can be different in different locations.

In summary, 30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point for measuring elevation and depth, and which can vary depending on the location.

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Answer:

$ 481.50

Step-by-step explanation:

Discount:

    Discount = 25% of retail price of TV

                    = 0.25 * 600

                    = $ 150

   Price after discount = Retail price - discount

                                     = 600 - 150

                                     = $ 450

Tax:

Tax = 7% of 450

        = 0.07 * 450

        = $ 31.50

Amount to be paid:

Amount needs to be paid = price after discount +  tax

                                           = 450 + 31.50

                                            = $ 481.50

The probability that at least one tag is lost is 0.75.

The probability that exactly one tag is lost is equal to the probability of the left tag being lost and the right tag being kept, plus the probability of the right tag being lost and the left tag being kept.

Using the formula for the probability of the union of two events, the probability that at least one tag is lost is:

P(A1 or A2) = P(A1) + P(A2) - P(A1 and A2) = 0.4 + 0.4 - 0.16 = 0.64

The probability of the left tag being lost and the right tag being kept is:

P(A1 and not A2) = P(A1) × (1 - P(A2)) = 0.4 × (1 - 0.4) = 0.24

The probability of the right tag being lost and the left tag being kept is:

P(A2 and not A1) = P(A2) × (1 - P(A1)) = 0.4 × (1 - 0.4) = 0.24

So, the probability of exactly one tag is lost, given that at least one tag is lost, is:

P(exactly one tag is lost | at least one tag is lost) = P(A1 and not A2 or A2 and not A1) / P(A1 or A2) = (0.24 + 0.24) / 0.64 = 0.75

Rounding to two decimal places, the answer is 0.75.

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27 gallons of water is used outside everyday.

Given is that of the 90 gallons a average person uses a day, 30% is used out doors.

Let the amount of water used outside be {x} gallons. Then, we can write -

{x} = 30% of 90

{x} = (30/100) x 90

{x} = 27

Therefore, 27 gallons of water is used outside everyday.

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Answer:

Second option

Step-by-step explanation:

Given inequality
[tex]-8t\:+\:2\:\dfrac{1}{4}\ge 42\dfrac{1}{4}[/tex]

Convert mixed fractions to improper fractions:
[tex]2\dfrac{1}{4}=\dfrac{9}{4}[/tex]

[tex]2\dfrac{1}{4}=\dfrac{169}{4}[/tex]

The inequality becomes

[tex]-8t+\dfrac{9}{4}\ge \dfrac{169}{4}[/tex]

Multiply throughout by 4

[tex]-32t + 9 \ge 169[/tex]

[tex]\rightarrow -32t \ge 169-9\\\\-32t \ge 160\\\\-t \ge \dfrac{160}{32}\\\\-t \ge 5\\\\[/tex]

Multiply throughout by -1 (the inequality is reversed):

[tex]t \le -5[/tex]

The second option correctly represents this inequality

Option #1: Solve the inequality and graph the solution set.

Option #2: Test out the options to see which has solutions.

Let's do Option #2:

The first possible answer shows t < -5, so if we pick t = -10, we'd be in that interval.  Let's test if t = -10 is a solution:

      [tex]\begin{aligned}-8(-10) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]80 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]82\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]

That checked!

So this alone tells us that the bottom two answers are not possible answers, since they do not include -10 in their sets.

But now we need to decide between the top answer or the one right below it.  The only difference between the two number lines is that the top one does NOT include x = -5, while the second one does.  So we need to test out if x = -5 is a solution, just like we did for x = -10.

     [tex]\begin{aligned}-8(-5) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]40 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]42\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]

Because of the "or equal to" in the inequality, this does check.

Our answer is the second number line, with a closed circle at x = -5 and the shading to the left.

If you wanted to do this by solving the inequality, that work would look like this:

     [tex]\begin{aligned}-8t + 2\frac{1}{4} &\geq 42\frac{1}{4}\\[0.75em]-8t + 2\frac{1}{4}-2\frac{1}{4} &\geq 42\frac{1}{4}-2\frac{1}{4}\\[0.75em]-8t &\geq 40\\[0.75em]\dfrac{-8t}{-8}~ &{\boldsymbol{\leq}}~ \dfrac{40}{-8}\\[0.75em]t &\leq -5\end{aligned}[/tex]

Note that the inequality flipped because we divided both sides of the inequality by a negative number.

1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

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

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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We split a given vector by its magnitude to get a unit vector that has the same direction. Consider the vector v = (1, 4), which has a magnitude of |v|. The unit vector uv, which is in the same direction as v, is obtained by dividing each component of the vector v by |v|.

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Answer:

win=16, lose=12

Step-by-step explanation:

total is 28, and win to lose is 4:3

so 4+3=7 , which means we put them into 7 part

and 28/7=4, each part equal to 4

so the win= 4 time 4=16

            lose = 3 time 4= 12

The solution of the integral  ∫sin ( x ) cos³( x )dx is equal to ( cos⁴(x) / 4 ) + c , where 'c' is the constant.

Solution of the integral is solved by substitution method :

∫∫sin ( x ) cos³( x )dx ___( 1 )

Let us consider cos ( x ) = t  ____( 2 )

Now differentiate both the side we get,

-sin (x ) dx = dt  

⇒ sin (x ) dx = -dt  ____( 3 )

Substitute the value of ( 2 ) and ( 3 )  in ( 1 ) we get,

∫ t³ ( -dt )

= - ∫ t³ dt

= - t⁴ / 4  + c

Where 'c' is the integral constant .

Relace t = cos (x)

= - cos⁴ ( x ) / 4 + c

Therefore, the integral of the ∫sin ( x ) cos³( x )dx is equal to

( cos⁴(x) / 4 ) + c .

The above question is incomplete, the complete question is:

solve each integral using the information : ∫sinx cos³x dx

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Answer:

Yes because there all the same shape the size dosent effect the shape of it.

Step-by-step explanation:

Answer:

101.  ΔABC congruent to ΔDEF

102. ΔJKL not congruent to ΔMNO

Step-by-step explanation:

Q 101

Triangle ABC has 3 sides equal  to each of the three sides of DEF

The corresponding two angles of ABC and DEF are also equal

So the third angle of ABC ∠B must be equal to the third angle of DEF so we have three sides equal, three angles equal, hence congruent

ΔABC congruent to ΔDEF

Q 102

We have JL = MP = 1.9

m∠J = m∠M = 24°

The other two angles are not correspondingly equal

This only makes one side equal and one angle equal. Not sufficient to make it congruent

Hence ΔJKL not congruent to ΔMNO

When two variables' ratios are equivalent, proportional relationships between them emerge.The right response is option c.A $50 membership fee plus a $20 monthly cost is required to use a gym.

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Answer: -1/x-17        -1-17x

Step-by-step explanation:

Answer:

Step-by-step explanation: First, do the multiplication inside the parenthesizes so 8x5 is 40, and 40+2 is 42. 120-42=78

8n=78

n=9.75

Answer:

Step-by-step explanation:

7877

Answer:

180 gallons is needed.

Step-by-step explanation:

The time taken to fill a 275-gallon hot​ tub is 69 minutes.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A hose fills a hot tub at a rate of 3.99 gallons per minute.

This means,

3.99 gallons = 1 minute

Multiply 275/3.99 on both sides.

275 gallons = 275/3.99 x 1 minute

275 gallons = 69 minutes

Thus,

It will take 69 minutes to fill a 275-gallon hot​ tub

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Answer:

5/21

Step-by-step explanation:

2 x 5 = 10

--------

7 x 6 = 42

10 / 42 in simplest form is 5/21

Answer: it is  Konnachair,  dm me there

Step-by-step explanation:

The board in shape of rectangle must be at least 6.4 feet.

What is a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.

Perimeter, P = 2 (Length + Width)

Area of Rectangle=Length*Breadth

Now,

Given length of board they want to cut=1 3/5 feet=8/5 feet.

No. of board they want to cut=4

so, length of rectangular board must be at least=4*8/5 feet

=32/5=6.4 feet

Hence,

            The board in shape of rectangle must be at least 6.4 feet.

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1. Companywide break-even point in dollar sales = $910,000

2. Break-even point in dollar sales for the East region = $391,667

3. Break-even point in dollar sales for the West region = $225,000

Companywide break-even point in dollar sales: Total fixed expenses / Contribution margin ratio = $189,000 / (273,000/910,000) = $910,000

Break-even point in dollar sales for the East region: Traceable fixed expenses / Contribution margin ratio = $70,000 / (182,000/650,000) = $391,667

Break-even point in dollar sales for the West region: Traceable fixed expenses / Contribution margin ratio = $63,000 / (91,000/260,000) = $225,000

New segmented income statement based on the break-even dollar sales:

Total Company

Sales $910,000

Variable expenses 637,000

Contribution margin 273,000

Traceable fixed expenses 133,000

Segment margin 140,000

Common fixed expenses 56,000

Net operating income $ 84,000

Total East

Sales $391,667

Variable expenses 258,250

Contribution margin 133,417

Traceable fixed expenses 70,000

Segment margin 63,417

Total West

Sales $225,000

Variable expenses 154,500

Contribution margin 70,500

Traceable fixed expenses 63,000

Segment margin 7,500

Net operating income in the new segmented income statement: $84,000

Yes, Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region as these expenses benefit both regions and affect the profitability of each region.

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