Alexander's hobby is dirt biking. On one occasion last weekend, he accelerated from rest to 10.3m/s in 5.98 seconds. He then maintained this speed for 7.92 seconds. Seeing a coyote cross the trail ahead of him, he abruptly stops in 4.33 seconds. Determine Alexander's average speed for this motion.

The dimensions of the deck would be increased by 1 feet.

Area of a rectangle = length x width

Initial area of the deck = 3 x 8 = 24 feet²

Area of the deck when it is increased = (1 + 0.50) x 24  = 36 feet²

Length of the deck after it is increased = 3 + x

Width of the deck after it is increased = 8+ x

Area of the new deck : (3 + x) + (8 + x) = 36

24 + 3x + 8x + x² = 36

x² + 8x + 3x + 24 - 36 = 0

x² + 11x - 12 = 0

The solutions of the quadratic equation are -1 and 12

-1 + x = 0

x = 1

or

12 + x = 0

x = -12

Thus, the dimension of the deck would be increase by 1 feet.

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Answer:D

Step-by-step explanation:

Step 1

Let the length in minutes of Tika's class be m

His class had lasted already for 18 minutes

His class had 37 more minutes to end.

Step 2

Get the equation

Hence the answer is option B ------ ( m - 37 = 18)

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]

The fraction of coefficient factor out is 3/8.

What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals. The numerator and denominator of positive common fractions are natural numbers.

The given expression is , 3/8d+3/4

From this, we have to eliminate the fraction for that we have to make common denominators like that,3/8 d + (3 * 2) / (4 * 2)=> 3/8 d + 6/8

Next, take out the common value i.e, 3/8=> 3/8 ( d + 2)

Therefore, the coefficient factor out is 3/8.

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A. The formula for h is h = V / πr².

B. The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches is 8 inches.

The volume of a cylinder is calculated thus:

= πr²h.

where π = 3.142

r = radius

h = height

Therefore, the height will be:

V = πr²h

We have to make h the subject of the formula. This will be:

h = V / πr²

The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches will be:

h = V / πr²

h = 56.52 / (3.142 × 1.5²)

h = 56.52 / 7.0695

h = 8

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The equation of the sequence is xₙ = 4n + 17 and the 11th term is 61

From the question, we have the sequence to be

17, 21, 25, 29, 21

The form of the sequence is given as

xₙ = cn + d

From the question, we have the first term to be 17

This means that

d = 17

So, we have

xₙ = cn + 17

When n = 1, we have x = 21

So, we have

21 = c + 17

Evaluate

c = 4

Substitute c = 4 in xₙ = cn + 17

xₙ = 4n + 17

This means that

n = 11

So, we have

x₁₁ = 4 * 11 + 17

Evaluate

x₁₁ = 61

Hence, the value is 61

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Answer:

x= −3/10

y= 3/7

Step-by-step explanation:

She make mistake in her first step. She plot a point at (3,2) instead of (3,−2).

Sandra is using the point-slope form [tex]y - y_{1} = m(x-x_{1})[/tex] to graph the equation [tex]y+2=(x-3)[/tex].

She completed the following steps.

1) Firstly she plot a point at (3,2)

2) Then she plot a point 5 units up and 4 units left from (3,2), at (−1,3).

3) Then she connect the points with a line.

She using the point slope for to graph the equation.

The point slope form is [tex]y - y_{1} = m(x-x_{1})[/tex].

The equation is [tex]y+2=(x-3)[/tex].

Now we compare the given equation to the point slope form.

After comparing we get

[tex]y_{1}[/tex] = -2 and [tex]x_{1}[/tex] = 3

So we have to plot a point at (3,-2) but she plot point at (3,2).

She make mistake in her first step.

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Answer: The Pink one

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

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.

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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The function has the vertex value of (-1, -1)

From the question, the definition of the functuion is given as

y = 2x² + 4x + 1

Start by differentiating the function

This is done as follows

y' = 4x + 4

Next, we set the differentiated equation to 0

So, we have the following equation

4x + 4 = 0

This gives

4x = -4

Divide by 4

x = -1

Next, we substitute x = -1 in the given equation y = 2x² + 4x + 1

So, we have the following equation

y = 2(-1)² + 4(-1) + 1

Evaluate

y = -1

Recall that

x = -1 and y = -1

So, we have

(-1, -1)

Hence, the vertex of the function is (-1, -1)

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The vertex of the given function y = 2x² + 4x+1 is (-1, -1) which is the correct answer would be an option (B).

The function is below given by,

y = 2x² + 4x + 1

Differentiate with respect to x to get the derivative of the above function,

y' = dy/dx = d/dx (2x² + 4x + 1)

y' = 4x + 4

Equating the derivative of the function to zero

y' = 0

4x + 4 = 0

4x = -4

Divide by 4 into both sides of the equation,

x = -1

Substitute x = -1 in the given function y = 2x² + 4x + 1

y = 2(-1)² + 4(-1) + 1

y = 2(1) - 4 + 1

y = -1

Therefore, the vertex of the given function is (-1, -1).

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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:

Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.

The entirety of a basketball game is composed by:

4 quarters.

Hence the mid-point of the game is calculated as follows:

0.5 x 4 quarters = 2 quarters.

This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.

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After simplification of the given expression -5w /9 =30 , value of w is equal to -54.

As given in the question,

Given expression is equal to :

-5w / 9 = 30

Simplification of the given expression to get the value of w is :

-5w / 9 = 30

Multiply both the side of the given expression by 9 we get ,

-5w = 30 × 9

Divide both the side of the given expression by -5 we get,

-5w /-5 = ( 30 × 9 ) / -5

⇒ w = -(6 × 9 )

⇒ w = -54

Therefore, after simplification of the given expression -5w /9 =30 , value of w is equal to -54.

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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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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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Answer: y=-1/2x+1

Step-by-step explanation: plug in numbers to find y intercept (b).

-1=-1/2(4)+b

-1=-2+b

b=1

y=-1/2x+1

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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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]

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

:]

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 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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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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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."

Answer: 18

Step-by-step explanation:   it is the smallest one in both tables.

1x6=6 2x6=12 3x6=18

1x9=9 2x9=18

hope this helped