A shipping carton has the shape of right triangular prism. Thelength of the carton is 4 times the longer lag of the righttriangular base. The shorter leg of the base is 1/2 of the longerleg. If the volume is 5832 cubic inches what is the length of thecarton?

Answer:

D

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{\frac{5\pi }{8} }{2\pi }[/tex]

   = π × 12.8² × ([tex]\frac{5}{8}[/tex] ÷ 2)

   = π × 163.84 × [tex]\frac{5}{16}[/tex]

   ≈ 160.8 cm² ( to the nearest tenth )

we have the function

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

the vertex of the given function is the point

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

therefore

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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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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Answer:

Step-by-step explanation:

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

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°

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:

t=-132

Step-by-step explanation:

multiply -12 on both sides.

-12x11=t

t=-132

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

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

The limits of the range for the length of time that Act 3 could last is 33.6

The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category. In general, integrals are divided into two categories: definite integrals and indefinite integrals.

A 24-hour period was predicted for Act 3 of the 2003 Leonid meteor shower. This prediction had a 0.7-day error window. How long could Act 3 potentially last, in the range

Lower Limit: 24-0.7(24) = 0.3(24) = 7.2 hrs

Upper Limit: 24+0.7(24) = 40.8 hrs

Range = Upper Limit - Lower Limit

= 40.8 - 7.2

=33.6

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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)

Answer:

it’s 20 feet

Step-by-step explanation:

just took the test

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]

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]

1.

2.

3.

In the figure of the second exercise there is one block which is not visible.

4.

We can see that the figure is made with 8 blocks

5.

The maximum length of the figure would be 6. You need 3 blocks to get a heigth of 3 units. Then you can add the other 5 blocks to the one which is in the base to make the figure with a length of 6 units.

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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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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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 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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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:

y=1.4x+5.8

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

IT HAS TO BE X=0 BECAUSE YOU ADD 8 TO X-8 THAT REMOVES THAT 8 THEN THE ADD 8 TO THE OTHERSIDE OF THE EQUAL SIGN

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:

Step-by-step explanation:

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