A car travels about 46 feet in one second. At this speed,
about how many feet will the car travel in 2 seconds?
A
920 feet
B
48 feet
480 feet
D
92 feet

Answer:

b,c,e

Step-by-step explanation: a: 5+0=5

b:15x0 =0

c: 1.4+2.7=4.1

d:2/3 x 5/9

e:4& 2/3 =5-1/3

Answer:

  a. 16.9 m

  b. 4.082 seconds

  c. no

  d. 2.041 seconds

  e. 21.41 m

Step-by-step explanation:

A graphing calculator can help you answer these questions quickly and easily. The graph is attached.

__

Evaluate the function at t=3.

  h(t) = -4.9t^2 +20t +1

  h(3) = (-4.9×3 +20)×3 +1 = 5.3×3 +2 = 16.9

The baton will be at a height of 16.9 meters after 3 seconds.

__

The axis of symmetry of quadratic ax^2+bx+c is located at x=-b/(2a). The point of release and the later point at the same height will be symmetrically located about the axis of symmetry. The peak height will be on the axis of symmetry of the graph. That value of time is ...

  tpeak = -20/(2(-4.9)) = 20/9.8 ≈ 2.041 . . . seconds

The baton will be at the release height again after 2×2.041 = 4.082 seconds.

__

As we saw in part (b), the maximum height will be when t=2.041 seconds. That height is found by evaluating the function for that value of t.

 h(2.041) = (-4.9(2.041) +20)(2.041) +1 = 21.41 . . . meters

The baton will not reach a height of 25 meters.

__

We found this answer in part (b): 2.041 seconds to reach the maximum height.

__

We found this answer in part (c): 21.41 meters is the maximum height.

_____

Additional comment

The time at maximum height is 20/9.8 seconds = 100/49 = 2 2/49 seconds. In general, the answer values shown here are rounded to 4 significant figures. The graphing calculator rounds to 3 decimal places.

Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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Answer:

348

Step-by-step explanation:

A=2(wl+hl+hw)

2(6·9+8·9+8·6)=348

Answer:

2. The rate of change in the table is -6

3. The slope of the line is \(\frac{3}{2}\) ⇒ d

Step-by-step explanation:

Let us start with no. 2

∵ The rate of change is the constant ration between x and y

∴ The rate of change is the slope of the line represents the table

∵ (1, -3) and (2, -9) are two points on the line

∴ x1 = 1 and y1 = -3

∴ x2 = 2 and y2 = -9

→ Substitute them in the rule of the slope above

∴ \(m=\frac{-9-(-3)}{2-1}=\frac{-9+3}{1}=\frac{-6}{1}\)

∴ m = -6

∴ The rate of change in the table is -6

Let us solve no.3

∵ The rule of the slope is \(m=\frac{y2-y1}{x2-x1}\) , (x1, y1) and (x2, y2) are two points

   on the line

→ Choose from the graph any two points on the line

∵ (0, 0) and (4, 6) are two points on the line

∴ x1 = 0 and y1 = 0

∴ x2 = 4 and y2 = 6

→ Substitute them in the rule of the slope above

∴ \(m=\frac{6-0)}{4-0}=\frac{6}{4}=\frac{3}{2}\)

∴ m = \(\frac{3}{2}\)

∴ The slope of the line is  \(\frac{3}{2}\)

Answer:

0.9876

Step-by-step explanation:

Given a normal distribution :

Mean(m) of distribution = 5V

Standard deviation (sd) = 0.02 V

Lower voltage specification = 4.95

Upper voltage specification = 5.05

Using the Zscore formula :

(x - m) / sd

x = 4.95

(4.95 - 5) / 0.02

-0.05 / 0.02 = -2.5

P(Z ≤ -2.5) = 0.0062

x = 5.05

(5.05 - 5) / 0.02

0.05 / 0.02 = 2.5

P(Z ≤ 2.5) = 0.9938

P(Z ≤ 2.5) - P(Z ≤ -2.5)

0.9938 - 0.0062 = 0.9876

Answer:

Step-by-step explanation:

17*12+11=45

Answer:

The answer is A.

To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.

Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.

Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.

Hence, in this case, since there are 100 items, then there will be 100 numbers of values.

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Answer:

10 dollars

Step-by-step explanation:

5 + 5

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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Answer:

Step-by-step explanation:

1. x is inversely proportional to y

x=k/y

k is the constant of proportionality

x =60/y

2. x=60/y

x=60/12

x=5

Answer:

True

Step-by-step explanation:

Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17

A group of numbers or variables coupled with the operations +, -,, or form an expression.

Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.

The given algebraic expression is 35.1 = 12.9 + 10.2x

solving for x

35.1 - 12.9 = 10.2x

10.2x = 22.2

x = 22.2/ 10.2

x = 2 3/17 as a mixed number in simplest form

the value of x is 2 3/17

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Answer:

A volcano ejected with an initial velocity of 304 feet per second.

The height in feet is given by the equation H=-16t^2+ 304t where t is the time in seconds.

We will use the equation that traces the path of the projectile to determine the following information:

1) The time it takes the projectile to reach its maximum height (using the vertex formula: t=-b/2a)

The equation; H = -16t^2 + 304t, a=-16; b=304

t = -304/2°(-16)

t = 9.5 sec to reach max height

2) The maximum height of the projectile (use the result from part 1 to find the maximum height of the projectile)

t = 9.5

H = -16(9.5^2) + 304(9.5)

h = = -1444 + 2888

h = 1444 ft is the max height

3) Find the time it takes the projectile to return to the ground. Assume that the projectile starts at height H=0.

-16t^2 + 304t = 0

factor out -16t

-16t(t - 19) = 0

t = 19 sec to reach the ground

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

40*5 is 200. 200 cents is $2

Answer: 7 units

Step-by-step explanation:

Using the distance formula, the square root of (X2 - X1)^2 + (Y2 - Y1)^2 is equal to the distance between two points.

5-(-2) = 7 9^2 equals 49

-3-(-3) = 0

The square root of 49 plus 0 is 7, so the answer is 7 units.

The mean number of dogs per household in a small town is 1.8, with a variance of 2.64 and a standard deviation of approximately 1.62.

To calculate the mean of the probability distribution, we multiply each possible number of dogs by its corresponding probability, and then add up the products:

Mean = (0 x 0.3) + (1 x 0.2) + (2 x 0.15) + (3 x 0.1) + (4 x 0.1) + (5 x 0.15) = 1.8

So the mean number of dogs per household in this small town is 1.8.

To find the variance of the probability distribution, we first need to calculate the squared deviation of each possible number of dogs from the mean, weighted by its probability:

\((0 - 1.8)^2 x 0.3 + (1 - 1.8)^2 x 0.2 + (2 - 1.8)^2 x 0.15 + (3 - 1.8)^2 x 0.1 + (4 - 1.8)^2 x 0.1 + (5 - 1.8)^2 x 0.15 = 2.64\)

Therefore, the variance of the probability distribution is 2.64.

Finally, the standard deviation is the square root of the variance:

Standard deviation = sqrt(2.64) ≈ 1.62 (rounded to two decimal places)

So the standard deviation of the probability distribution is approximately 1.62.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

its 1900 Bc. Because BC stand for before chirst

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

(-3)4

-3*4

-12

Elaborate ur question about - 34

Answer:

plz

Step-by-step explanation:

thx

Answer:

its 4 hours

Step-by-step explanation:

Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

The value of b is solved using square root is found to be b = 2√ac.

The section of a quadratic formula following the square root symbol, b²-4ac, is the discriminant. If we have two solutions, single solution, or none at all, the discriminant informs us.

The given equation is:

b²- 4ac = 0

Separating unknown value from the equation:

b² = 4ac

Taking square root both side.

√b² = √4ac

Simplifying

b = 2√ac

Thus, the value of b is solved using square root is found to be b = 2√ac.

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Answer:

10

Step-by-step explanation:

A) The Slope is: 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is: y = 2x + 4

The general form of equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the given graph, we can see that the slope is gotten from the formula:

A) Slope = (y₂ - y₁)/(x₂ - x₁)

Thus:

Slope = (10 - 4)/(3 - 0)

Slope = 6/3

Slope = 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is:

y = 2x + 4

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Answer: The equation for the decrease in water is given by:

W = -0.414t + 129.549

To find after about how many minutes the water level would be less than or equal to 64 cups, we can set W to 64 and solve for t:

64 = -0.414t + 129.549

-65.549 = -0.414t

t = 158.1

Rounding to the nearest 10 minutes, we get:

t = 160

Therefore, after about 160 minutes, the water level would be less than or equal to 64 cups.

Regarding the values of a and b, we can see that they are not relevant to this problem since they are not given in the equation for the decrease in water. So, none of the given options is correct.

Step-by-step explanation: