HelloI’m having trouble on the *calculus* portion on my ACT PREP GUIDEI need help solving this

The data on the attempts and distances of the science experiment on the launch of a ball by a catapult, presented in a tabular form gives the following;

a. The five attempts have an average distance of 50.58

b. The distance the sixth ball has to travel so as to give an average distance traveled of 50.9 meters is 52.5 meters

An average is a descriptive statistics that tends to describe the values in a dataset. An average or the mean of a dataset is obtained by summing the data values and dividing the result by the number of data points

Please find attached, the Attempt to Distance table obtained from a similar question online

a. The formula for average, [tex] \bar{x} [/tex] of a set of data or observations is presented as follows;

[tex] \displaystyle{\bar x = \frac{Sum \: of \: observations}{Number \: of \: observations}} [/tex]

Mathematically, we have;

[tex] \displaystyle{\bar x = \frac{\sum x}{N}} [/tex]

Which gives from the attached table;

[tex]\displaystyle{\sum {x} =50.7+49.4 +52.3 + 48.9 + 51.6 = 252.9}[/tex]

N = 5

Which gives;

[tex] \displaystyle{\bar x = \frac{252.9}{5} = 50.58}[/tex]

b. The distance, d, the ball has to travel on the sixth attempt to get an average of 50.9 meters is found as follows;

The new total number of attempts, N = 6

Which gives;

[tex] \displaystyle{\bar x = 50.9 = \frac{d + 252.9}{6} }[/tex]

6 × 50.9 = d + 252.9

Therefore;

d = 6 × 50.9 - 252.9 = 52.5

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It will take about 8.7 hours until there are 350 bacteria present using exponential growth.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

The formula is as follows:

P = [tex]initial (rate)^x[/tex]

Given that 260 bacteria are placed in a petri dish.

initial value = 260

growth factor = 2

growth factor's associated time period = 26 hours

Exponential growth equation can be written as

[tex]n = 260(2^(t/26))[/tex]

For n=350, we can put the value and take log on both sides.

[tex]350=260(2^{(t/26)} )[/tex]

[tex]1.3 = 2^{t/26}[/tex]

log 1.3 = (t/26) log(2)

26×log(1.3)/log(2) = t

t ≈ 8.7 hours

Therefore, it will take about 8.7 hours until there are 350 bacteria present.

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The simplified form of the given expression is 25 x² y ²⁶.

What is the simplified form of the expression?

Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.

What are the exponent rules?

The different Laws of exponents used to solve the above mentioned question are:

[tex]x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }[/tex]

According to the given question.

We have an expression (5xy⁷)²(y⁴)³

To simplify the above expression we use the exponent rules.

Therefore,

(5xy⁷)²(y⁴)³

(5² x² y²×⁷) (y ⁴׳)

(25 x² y¹⁴ ) (y¹²)

25 x² y¹⁴⁺¹²

25 x² y ²⁶

Therefore, the simplified form of the given expression is  25 x² y ²⁶

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The best approximate solution to the linear system is  x= 3/4 y = -1

What is linear system?

linear system are system of equations in which the variables are never multiplied with each other but only with constants and then summed up.

Reorder the equation:2x-y =5/2

2x-2y = 7/2

Subtract the two equations:

2x-y -(2x-2y)=5/2 - 7/2

Remove parentheses:

2x-y -2x +2y =5/2-7/2

Cancel one variable:

-y +2y =5/2-7/2

Combine like terms:

5/2-7/2

Write the numerators over common denominator:

Y= 5-7/2

Calculate the sum or difference:-2/2

Rewrite the fraction:-2/2

Cross out the common factor:-1

Substitute into one of the equations:2x-(-1)=5/2

Remove the parentheses:2x+1=5/2

Multiply both sides of the equation by the common denominator:2x×2+2=5×2/2

Reduce the fractions:2x×2+2=5

Rearrange unknown terms to the left side of the equation:4x=5-2

Calculate the sum or difference:4x=3

Divide both sides of the equation by the coefficient of variable:

The solution of the system is:x=3/4

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The equation for a line parallel to y = 3x + 2 that passes through the point (2, 1) is y = 3x - 5.

The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a given angle and passes through a given point.

Depending on the information available, the equation of a line can be found using a variety of methods. Among the methods are:

The given equation of line is y = 3x + 2.

We need to find the equation of line parallel to the given line and it passes through the point (2, 1).

Slope of line y = 3x + 2 is given as:

By comparing the given equation with y = mx + c, we can say that the slope(m) = 3

Let, a point with coordinates (x, y) be on the line parallel to given line.

Finding slope again we get,

[tex]\frac{y-1}{x-2}[/tex] = 3

y-1 = 3x - 6

∴ y = 3x - 5

As a result, a line parallel to y = 3x + 2 that passes through the point (2, 1) has the equation  y = 3x - 5.

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Answer:

Option 1:

Explanation:

In order for f(x) to be concave up in an interval, the graph of the derivative would have to be increasing in that interval.

In the given graph, from x=-1.5 to x=1.5, the graph of the derivative is decreasing, therefore, the statement that "f is concave up from x=-1.5 to x=1.5" is false.

Next, for f to have an inflection point at any x-value the slope of the derivative, f'(x) must change signs at that x-value. Therefore, the statement "f has an inflection point at x=1.5" is true.

Finally, for f(x) to have a relative minimum at x=2, the value of the derivative must be 0, which is as seen on the graph.

Therefore, the first option is False.

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

 where

a

=

7

and

b

=

3

x

.

(

7

+

3

x

)

(

7

−

3

x

)

Answer: -(3x - 7)(3x + 7)

Step-by-step explanation:

1. Rewrite the formula:

-[tex]9x^{2} + 49[/tex]

2. Factor -1 out of [tex]-9x^{2} + 49[/tex]

[tex]-(9x^{2} - 49)[/tex]

3. [tex]9x^{2} - 49 = (3x)^{2} - 7^{2}[/tex]

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

4. Factor the difference of two squares. [tex](3x)^{2} - 7^{2} =[/tex]

[tex](3x-7)(3x+7)[/tex]

5. Add back negative:

Answer: [tex]-(3x-7)(3x+7)[/tex]

Using given function, we conclude that it will take 3 seconds the ball to reach a height of 45 meters.

In this question, we have been given a function h = 30t - 5t²

This function is used to find the height (h) of the ball in meters after 6 seconds.

We need to find the amount of time required to reach ball to a height of 45 meters.

here, height h = 45 meters

to find : time t

h = 30t - 5t²                          ........................(Given function)

45 = 30t - 5t²

30t - 5t² - 45 = 0

5t² - 30t + 45 = 0

t² - 6t + 9 = 0

(t - 3)² = 0

t - 3 = 0

t = 3 seconds

Therefore, it will take 3 seconds  the ball to reach a height of 45 meters.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the Angle-Arc relationship

STEP 2: Interpret the given image

STEP 3: Find the required angle

By substitution

Hence, the answer is 50°

we have the function

f(x)=1/2Ix+4I-3

the vertex of the given function is the point

(-4,-3) ---------> III quadrant

therefore

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A rectangle has a perimeter of 60 feet. The rectangle's length is four times its width. The area of rectangle is 144 square feet.

Given that,

A rectangle has a perimeter of 60 feet.

The rectangle's length is four times its width.

We have to find the area of rectangle.

Let us take length as x

The width will be 4x

The perimeter =2(4x+x)

2(4x+x)=60

4x+x=60/2

5x=30

x=30/5

x=6

The length will be 6.

The width will be 4×6=24.

The area of rectangle is length×width

=6×24

=144 square feet.

Therefore, the area of rectangle is 144 square feet.

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Answer:

3/2, 1.5

Step-by-step explanation:

When you put 36 cookies divided amongst 24 students, each student cookies one and a half cookies

Applying precedence of operations, the parenthesis on the operations are inserted as follows:

The acronym PEMDAS defines the precedence of operations, from highest to lowest, as follows:

For the first item, we want a result of 29, hence the expression will be of:

(6+9)/3+(16-4)*2.

As the equivalent result will be of:

(6+9)/3+(16-4)*2 = 15/3 + 12 x 2 = 5 + 24 = 29.

For the second item, we want a result of 2, hence the expression will be of:

36/(4 + 2) - 4.

As the equivalent result will be of:

36/6 - 4 = 6 - 4 = 2.

For the third item, we want a result of 28, hence the expression will be of:

(5-3)*2 + 8*(5 - 2)

As the equivalent result will be of:

(5-3)*2 + 8*(5 - 2) = 2 x 2 + 8 x 3 = 4 + 24 = 28.

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Solving a system of equations, we will see that Suvinder bought 60 of the £0.20 stamps and 40 of the £0.35 stamps.

We know that Suvinder spent £26 on 100 postage stamps, defining:

Then we can write the system of equations:

x + y = 100

x*0.20 + y*0.35 = 26

Isolating x on the first equation we get:

x = 100 - y

Replacing that in the other equation we get:

(100 - y)*0.20 + y*0.35 = 26

Solving that for y, we get:

20 - y*0.20 + y*0.35 = 26

20 + y*0.15 = 26

y*0.15 = 26 - 20 = 6

y = 6/0.15 = 40

Then:

x = 100 - y = 100 - 40 = 60

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Answer:

y=1.4x+5.8

You have to do y2-y1 over x2-x1.

Answer:

[tex]x = - 0.25[/tex]

Step-by-step explanation:

[tex]12x + 3[/tex]

[tex]12x = - 3[/tex]

[tex] \frac{12x}{12} = \frac{ - 3}{12} [/tex]

[tex]x = - \frac{1}{4} \: or \: - 0.25[/tex]

The measure of the angle 15 is 97°

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles.

The parallel lines are e and f. These parallel lines are cut across by the transversal lines c and d. The transversal line d is the line that forms the angle 15 with the parallel lines e and f.

Therefore, the angle 97 degrees and the angle 15 are alternate exterior angles.

Alternate exterior angles are congruent.

Therefore,

∠15 = 97 degrees.

Hence, the measure of ∠15 is 97 degrees.

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Answer: 1/12

step by step equation:

The ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.

According to the question,

We have the following details:

The average age of the Bear family is 58 years.

Now, let's take Tom's age to be x years, Lisa's age to be y years and  John's age to be z years.

So, we have the following expression:

(x+y+z)/3 = 58

(x+y+z) = (58*3)

(x+y+z) = 174 .... (1)

Now, John is two years younger than Tom, so we have:

z = (x-2) ....(2)

Lisa is 16 years older than John. So, we have:

y = (z+16) ....(3)

Now, putting the values of y and z in equation 1,

x+z+16+x-2 = 174

Now, again putting the value of z from equation 2,

x+x-2+16+x-2 = 174

3x+12 = 174

3x = 174-12

3x = 162

x = 162/3

x = 54 years

Now, putting the value of x in equation 2,

z = x-2

z = (54-2) years

z = 52 years

Now, putting the value of z in equation 3,

y = z+16

y = (52+16)

y = 68 years

Hence, the ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.

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Answer:

it’s 20 feet

Step-by-step explanation:

just took the test

1 kg = 1000g

Hence,

This implies that,

Answer:

Midpoint, M is (5,8)

Step-by-step explanation:

To find the midpoint, average the x's (add and divide by2) then average the y's.

The x's are the first numbers (2+8)/2 is

10/2 which is 5.

The y's are the second numbers in the parentheses, (9+7)/2 is 16/2 which is 8.

So the x of the midpoint is 5 and the y is 8.

The midpoint is (5,8)

The maximum value in this range is 8.3 girls. The range of a set of numbers is the difference between its highest and lowest values. To find it, subtract the lowest number from the highest in the distribution.

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Step-by-step explanation:

the initial distance is 2 2 /5mile or 2.4 mikes and the final is 8 1/10 or 8.1 mile . Therefore total distance to hike is

Distance=8.1 - 2.4 = 5.7miles

since they will trek at 3 miles per hour the time needed is : 5.7 MILE/ 3MILES PER hour

time: 1.9HOURS

since they started at 10am and there is 2 HOURs ALLOWANCE from noon ,THEREFORE they will reach the marker by noon 0.10 hour left

THAT'S ALL MISS

Answer:

Step-by-step explanation:

Equation: 7x - 9 = 5 (x+2) 7x - 9 = 5x + 10 2x = 19 x = 9.5