a rancher plans to use 170 yards of fencing to enclose a rectangular corral and to divide it into two parts with a fence parallel to the shorter sides of the corral. find the dimensions of the corral if its area is to be 1200 square yards.

8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.

As, the largest perfect square that divides 12! is

2^10 * 3^4 *5^2 = 2073600.

Now, the square root of the number 2073600 is,

1440

Now, we have to find the prime factorization of 1440

1440 = 2×2×2×2×2×3×3×5

Now, in the prime factorization of 1440

the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.

So, the sum of the exponents of the prime factors be 5+2+1 = 8

Hence, 8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

Learn more about Prime Factorization here https://brainly.com/question/18187355

#SPJ4

Answer:

no because 60+48+36 is 144

Step-by-step explanation:

please mark brainliest

The total number of people is 144. The data is not consistent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.

The total number of the people in the party,

60+48+36 is 144

But it is given in the question that there are 100 in the party.

Therefore, the total number of people is 144. The data is not consistent.

To know more about an expression follow

https://brainly.com/question/23941117

#SPJ2

The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.

A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

To know more about scatterplot,

https://brainly.com/question/25280625?referrer=searchResults

#SPJ4

The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:

From the given graph, we have the following:

(h, k) = (3, 5) [the vertex]

Substitute the values into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:

6 = a|2 - 3| + 5

6 = a|-1| + 5

6 = a + 5

6 - 5 = a

1 = a

a = 1

To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:

y = 1|x - 3| + 5

y = |x - 3| + 5

Learn more about equation of absolute value function on:

https://brainly.com/question/25290500

#SPJ1

Answer:

X=

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−84=108x

Step 1: Subtract 108x from both sides.

2x−84−108x=108x−108x

−106x−84=0

Step 2: Add 84 to both sides.

−106x−84+84=0+84

−106x=84

Step 3: Divide both sides by -106.

−106x

−106

=

84/−106x=−42/53

The solution is 1790 grams

The amount of bismuth left after 10 days if the half life is 5 days will be

1790 grams

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the half life of the element be represented as t½

The value of t½ = 5 days

Now , the initial amount of bismuth N₀ = 7160 grams

The number of days t = 10 days

The amount of bismuth left after 10 days = N( t )

Now , the value of N( t ) is given by the formula ,

N( t ) = N₀ ( 1/2 )^ t/ t½

Substituting the values in the equation , we get

N( t ) = 7160 ( 1/2 )^10/5

N( t ) = 7160 ( 1/2 )²

N( t ) = 7160 / 4

N( t ) = 1790 grams

Therefore , the value of N( t ) is 1790 grams

Hence , the amount of bismuth left is 1790 grams

To learn more about half life click :

https://brainly.com/question/29301147

#SPJ2

The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle has interior angles are:

(2x)°, (3x)° and (4x)°

As we know that the sum of interior angles is 180 degrees in the triangle.

According to the given figure,

(2x)° + (3x)° + (4x)° = 180°

Apply the addition operation in the above equation,

9x = 180

x = 180/9

x = 20°

Thus, The triangle has interior angles are:

(2x)° = 2 × 20° = 40°

(3x)° = 3 × 20° = 60°

(4x)° = 4 × 20° = 80°

Learn more about the triangles here:

https://brainly.com/question/17997149

#SPJ1

The interquartile range of the reaction times is 0.528 or 52.80%

A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:

The interquartile range is x = 1.45 and x = 1.75

For x = 1.45

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z=(1.45-1.5)/0.18

 = -0.28

For x = 1.75

Z=(1.75-1.5)/0.18

 = -1.39

From the normal distribution table,

P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)

                            = P(z < 1.39) - P(z< - 0.28)

                            = 0.9177 - 0.3897

                           = 0.528

                          = 52.8%

To learn more about normal distribution, visit:

https://brainly.com/question/16710304

#SPJ4

Thus, the number of ways in which  to choose 4 letters, without replacement, from 17 distinct letters is 57,120.

Total distinct letters are 17.

There are 17 alternatives for the initial letter if there are 17 letters.

There are just 16 alternatives left once you remove the letter.

Each time you remove a letter, the bag contains one fewer letter.

Number of ways = 17 x 16 x 15 x 14

Number of ways =  57,120

Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.

To know more about the permutation, here

https://brainly.com/question/1216161

#SPJ4

Answer:

See below

Step-by-step explanation:

Horizontal lines have ZERO slope

Vertical lines have 'undefined' slope

for this example  x = 1/2    includes the point and has undiefined slope

The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.

A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.

n = 50 makes up the sample size.

Furthermore, the sample variance is s² = 20

The following is the formula for both the variance confidence interval:

σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]

Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.

The 90% confidence interval's lower bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)

= 32.54

The 90% confidence interval's upper bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)

= 96.86

Consequently, the confidence level for the distribution's variance is (96.86, 32.54).

Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).

Learn more about confidence intervals at

https://brainly.com/question/22985950?referrer=searchResults

#SPJ4

Answer:

[tex]{ \boxed{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}[/tex]

- \theta = 25°

- opposite = x

- hypotenuse = z

[tex]{ \tt{ \sin(25 \degree) = \frac{x}{z} }} \\ [/tex]

Answer: x/z

Step-by-step explanation:

sin25 uses soh from sohcahtoa

sin25 = opposite/hypotenuse = x/z

There was 110%  percent increase in the number of visitors.

Percent:

Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.

Given,

p x 3,700=4,070

There was a % percent increase in the number of visitors.

Here we need to find the increase in the percentage.

While we looking into the given question we have identified that,

The Old population = 3700

And the new population  = 4070

So, the value of P is calculated as,

=> p = 4070/3700

=> p = 1.1

When we convert this into percent then we get 110% as increase.

To know more about Percentage here.

https://brainly.com/question/13729841

#SPJ1

Step-by-step explanation:

remember, the circumference of a circle is

2×pi×r

and that is for the full 360° of a circle.

how long will the arc length of 1° be ?

well,

2×pi×r / 360

and how long will the arc length of 78° be ?

well,

78 × 1° = 2×pi×r × 78/360

you see ? that is the whole trick ...

now we only need to enter the value for r (radius).

and that is GH = 9 units.

so, the length of the arc GJ is

2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =

= 12.25221135... ≈ 12.25 units

Answer:

4/7

Step-by-step explanation:

32:56

32÷2=16

56÷2=28

16:28

16÷2=8

28÷2=14

8:14

8÷2=4

14÷2=7

4:7

32:56 ~ 32/56

=4/7

Answer:

2.5991  <  3.7  <  3.706  <  3.76

Step-by-step explanation:

Answer:

The dive lasted approximately [tex] \boxed{\sf 2.76} [/tex] seconds.

Step-by-step explanation:

Given formula: h = 16t²

Where, t is time in seconds and h is the distance in feet traveled by a free-falling body or object.

According to the question,

Height of the cliff from which diver dives (h) = 122 feet.

By substituting the value of height in the formula we get:

[tex]\rm \implies 122 = 16 {t}^{2} \\ \\ \rm \implies {t}^{2} = \dfrac{122}{16} \\ \\\rm \implies {t}^{2} = 7.625 \\ \\ \rm \implies t = \sqrt{7.625} \\ \\ \rm \implies t = 2.76 \: seconds[/tex]

The number of donuts that can be purchased for $10 is 20.

The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.

Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.

The price is directly proportional to the number of donuts purchased.

p ∝ n

We will remove the proportionality sign.

p = k*n

7.5 = k*15

k = 1/2

The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.

p = (1/2)n

10 = (1/2)n

n = 10*2

n = 20

Hence, the number of donuts that can be purchased for $10 is 20.

To learn more about numbers, visit :

https://brainly.com/question/17429689

#SPJ9

The equations that can be used to solve for y, the length of the room

First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:

Area of a rectangle = Length × Width

Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:

y( y - 5) = 750

When this equation is fully expressed, we will get the following equations:

Therefore, options, B, C, and E are correct.

Learn more about the area of a rectangle here:

https://brainly.com/question/2607596

#SPJ1

Answer:

2,156 A. 21.56

Step-by-step explanation:

The lengths of the piece she should cut is = 3  2/3

acc to our question-

hence,The lengths of the piece she should cut is = 3  2/3

learn more about unitary method click here:

brainly.com/question/24587372

#SPJ4

It takes 35 years for the population of West Fremont to double. We have the following condition;

West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.

Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.

According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.

Doubling time = 70 / Growth rate                

= 70 / 2                        

= 35 years

So, it takes 35 years for the population of West Fremont to double.

To learn more about population Growth click here:

https://brainly.com/question/27424886

#SPJ4

Hours taken by Bob and Bill if they work together is 3 1/13.

Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.

We have to find the time taken by both to do the work if done together.

Time ratio of Bob and Bill = 5: 8

Efficiency of Bob and Bill = 8: 5

Total amount of work done = 5× 8 = 8× 5 = 40

The total efficiency of Bob and Bill = 13

Hours took by both bob and bill to do the work if done together = 40/13

                                                                                                              = 3 [tex]\frac{1}{13}[/tex]

Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.

To know more about the work and its efficiency refer to the link given below:

https://brainly.com/question/27870797

Answer:

x^5

Step-by-step explanation:

Answer: 151.8

Step-by-step explanation:
330/100 x 54 = 178.2

330- 178.2 = 151.8

The number of centimeter cubes to be added to make the cuboid is; 30 cubes.

From the given plan, side elevation and front elevation, we can see that the number of cubes needed to make the shape is 18 blocks.

From the front elevation, 12 blocks is required (4 * 3 blocks).

From the side elevation, 6 blocks are required which gives us a total of 18 blocks.

The number of blocks needed to make the given cuboid is;

Volume of cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = Volume cubes - Number of cubes from elevation

The number of cubes to be added = 48 cubes - 18 cubes

The number of cubes to be added = 30 cubes.

Read more about Volume of cuboid at; https://brainly.com/question/27432084

#SPJ1

The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30

Side a + side b + side c ≤ perimeter of the triangle

(2n + 3) + (2n + 2) + n ≤ 30

2n + 3 + 2n + 2 + n ≤ 30

5n + 5 ≤ 30

substract 5 from both sides

5n ≤ 30 - 5

5n ≤ 25

n ≤ 25/5

n ≤ 5 cm

The largest possible lengths of the sides is:

Side a = (2n + 3)cm

= 2(5) + 3

= 10 + 3

= 13 cm

Side b = (2n + 2) cm

= 2(5) + 2

= 10 + 2

= 12 cm

Side c = n cm

= 5 cm

So therefore, the largest possible length of the triangle is 13 cm

Read more on perimeter of a triangle:

https://brainly.com/question/24382052

#SPJ1

Answers:

1st box:  0

2nd box:  67

===============================================

Explanation:

The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours

Plug x = 0 into the equation

y = 2.7x + 67

y = 2.7*0 + 67

y = 67

Or you can note that the equation is of the form y = mx+b

The y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67