Joe made a scale drawing of the community pool in his town.
​The scale drawing is shown below.
​If the scale factor is 1in : 7 m

What is the perimeter of the actual pool

Answer:

x=25

Step-by-step explanation:

√x−1−4=0

√x−5=0

√x=5

√x^2=5^2

x= 25

The answers are :

1. a) 10^-5 relates to the hundred-thousandths place. The number 3 will be in the hundred thousandths place followed by 0 which is in ten thousands place. The places before 3 will each hold digit 0.

b) The standard form will be 0.000032.

2. The standard form will be 0.000007

3. The standard form will be 0.0000875

What is the standard form ?

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

It is given that the number is 3.2 × 10^-5.

Let's simplify it. So , we get ;

= [tex]\frac{3.2}{10^5}[/tex]

= [tex]\frac{3.2}{100000}[/tex]

= 0.000032

1.

a)

10^-5 in standard form will be :

= 0.00001

So , we can conclude that 10^-5 relates to the hundred-thousandths place.

When we write 3.2 × 10^-5 in the standard form it will be equal to 0.000032.

The number 3 will be in the hundred thousandths place followed by 0 which is in ten thousandths place.

The places before 3 will each hold digit 0.

b)

The standard form of 3.2 × 10^-5 will be 0.000032.

2.

Diameter of an atom in gold is about 7 × 10 ^-6.

Let's express this to standard form.

So ,

7 × 10 ^-6

= [tex]\frac{7}{10^6}[/tex]

= [tex]\frac{7}{1000000}[/tex]

= 0.000007

3.

Average mass of one flea which is 8.75 × 10^-5. Let's represent this in standard form :

8.75 × 10^-5

= [tex]\frac{8.75}{100000}[/tex]

= 0.0000875

Therefore , the answers are :

1.

a) 10^-5 relates to the hundred-thousands place. The number 3 will be in the hundred thousands place followed by 0 which is in ten thousands place. The places before 3 will each hold digit 0.

b) The standard form will be 0.000032.

2. The standard form will be 0.000007

3. The standard form will be 0.0000875

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Answer:

Step-by-step explanation:

I would have to go with b

The value of y such that the amount of fencing needed is 260 meters is 80 meters

The perimeter of a rectangular field is the sum of the side lengths of the field

For all regular quadrilaterals, you add up the side lengths to determine the perimeter

The given parameters are

Width = 50 m

Amount of fencing = 260 m

Length = y

The amount of fencing is the perimeter of the fence

And perimeter is calculated as

P = 2 * (Length + Width)

So, we have

2 * (y + 50) = 260

Divide both sides by 2

So, we have

y + 50 = 130

Subtract 50 from both sides

So, we have

y = 80

Hence, the value of y such that the amount of fencing needed is 260 meters is 80 meters

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Answer:

-1/8

Step-by-step explanation:

So to start you already have the denominator equal, which helps a lot. So you do whatever operation is on top which in this case would be 5 + -7. Which you end up with -2/16. Then you simplify and end up with -1/8. Hope this helps. Have a great night. :)

Answer:

x = 7

x = -1

Step-by-step explanation:

2x - 6 = 8  Add 6 to both sides

2x = 14  Divide both sides by 2

x = 7

2x -6 = -8  Add 6 to both sides

2x = -2  Divide both sides by 2

x = -1    

The equation in slope-intercept form is y = x - 6.

What is in slope-intercept form?

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line p is

y = 8x + 2

Comparing with the slope intercept form, slope = 8

If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8

To determine the y intercept, we would substitute m = 8, x = - 1 and

y = -2 into y = mx + c. It becomes

-2 = 8 × - 1 + c

-2 = - 8 + c

c = - 8 + 2 = -6

The equation becomes

y = x - 6

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Answer:

7

Step-by-step explanation:

3 goes into 21 7 times leaving no remainder which means: 3 x 7 = 21

Answer:

7/8 or 0.875

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

[tex]3\frac{1}{2} = \frac{3*2+1}{2} = \frac{7}{2} \\\\\frac{7}{2} \div 4=\frac{7}{2}*4=7*2=14[/tex]

The two numbers which satisfy the condition that the difference between them be; 16 as required in the task content are; 17 and 1.

It follows from the task content that the two numbers whose difference amount to 16 are to be determined as required in the task content.

Given the numbers in discuss as; x and y such that;

x - y = 16

To find:

The numbers x and y.

Therefore, the possible numbers are such that; x = 17 and y = 1.

Ultimately, the two possible combination of number such that their difference is 16 are; 17 and 1.

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Answer:

you to get my number 3 whole thing together

Answer:Let x = the unknown number

The product of a number and 5:  5x

is =

four times the sum of that number and 10:  4*(x+10)

5x = 4(x+10)

5x = 4x + 40

Step-by-step explanation:

The value of the indicated probability P(A or B) is 0.85

The probabilities are given as

P(A) = 0.55

P(B) = 0.5

P(A and B) = 0.2

The indicated probability is given as

P(A or B)

This is calculated using the following equation

So, we have

P(A or B) = P(A) + P(B) - P(A and B)

So, we have

P(A or B) = 0.55 + 0.5 - 0.2

Evaluate the like terms

P(A or B) = 0.85

Hence, the value of the indicated probability P(A or B) is 0.85

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Answer:

138.75 lb

Step-by-step explanation:

75% as a percentage is 0.75.

185(0.75) = 138.75

The equation of the obtained inverse function is y=x/4 - 1/2.

The given function is f(x)=4x+2.

The inverse function is represented [tex]f^{-1}[/tex] with regard to the original function [tex]f[/tex] and the domain of the original function becomes the range of the inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

The inverse function f(x)=4x+2 can be solved as follows:

Now, f(x)=4x+2

⇒y=4x+2

⇒x=4y+2

⇒x-2=4y

⇒y=(x-2)/4

The graph of the function and inverse function is plotted as given below.

From the graph, the coordinates are (0, -0.5) and (2, 0).

Slope = m = (y2-y1)/(x2-x1)

=(0+0.5)/(2-0)

=0.5/2

=1/4

Put, m=1/4 and (2, 0) in y=mx+b

We get, 0=1/4 (2)+b

b=-1/2

Then, the equation is y=x/4 - 1/2

Therefore, the equation of the obtained inverse function is y=x/4 - 1/2.

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Answer:

323

Step-by-step explanation:

Integer = whole number

.6 always rounds upwards

Area of rectangle is length times of width. Thomas is painting the wall at a warehouse blue. He painted in 6 hours of area 240 square feet.

Area of rectangle is length times of width.

Area=Length*width.

From the given figure the length is 12 ft and width is 5 ft in 1.5 hrs.

area he covered painting= 12ft*5ft

=60 square feet.

In 1 and half hour he painted 60 square feet.

Now for 6 hours we have to calculate.

4*(1 and half hrs)=6 hrs

So we have to multiply 4 with 60 to get the area in 6 hours.

4*60=240square feet.

Therefore 240 square feet area Thomas painted.

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2+2=4-1=3 quick maths

Step-by-step explanation:

f(g(x)) means g(x) is embedded in f(x) as the argument or input value for f(x).

therefore,

f(g)x)) = 4(x² - 1) - 7 = 4x² - 4 - 7 = 4x² - 11

c. is the right answer

g(f(x)) is now the other way around. now f(x) is the only value for g(x) :

g(f(x)) = (4x - 7)² - 1 = 16x² - 56x + 49 - 1 = 16x² - 56x + 48

a. is the right answer

Answer:

-16

Step-by-step explanation:

pretty sure its the right answer, we did this a week ago in class so it may be wrong.

so first u gotta find the derivative of s(t) to get the vel equation. the derivative of s(t):

s(t)'= -4t, which is the vel equation

s(t)'=v(t)

v(4)=-4(4)

which equals -16

The instantaneous velocity of the ball at t = 4 seconds is -16 feet per second.

To find the instantaneous velocity of the ball at t = 4 seconds, we need to calculate the derivative of the given function s(t) with respect to t, and then evaluate it at t = 4.

Given that s(t) = -2t² - 2, we can find the velocity function v(t) by taking the derivative of s(t):

v(t) = d/dt (-2t² - 2)

v(t) = -4t

Now, we can find the instantaneous velocity at t = 4 by substituting t = 4 into the velocity function:

v(4) = -4(4)

v(4) = -16

This means that at that specific moment, the ball is moving downward with a velocity of 16 feet per second. The negative sign indicates the direction of motion.

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The liters of the 5% and the 40% solutions is

x= 4.3L

This is further explained below.

You have been tasked with creating a solution with a concentration of 20% in a volume of 10 liters by combining solutions of 5% and 40%. It seems as if there may be more than one response to this question. If you assume that the combined volume of the 5% and 40% solutions equals 10L, then you may calculate the required volume of solution. The formula ought to go as follows:

10 L= 40% solution volume+ 5% solution volume

10 L= x + 5% solution volume

5% solution volume= 10l-x

In conclusion, The formula for calculating volume would look like this then:

Volume 0.2*concentration 0.2= volume 0.4*concentration 0.4 + volume 0.05*concentration 0.05

10 * 0.2= x *0.4 + (10- x) *0.05

10l * 0.20= x  * 35% + 10*0.05

x *35 = 10l * 20 - 10 *5= 10 *15

x = 10l *15/35

x= 4.28 L

x= 4.3L

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The projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that : the baggage weight projected was 2,182 1/4 lbs and the actual weight of all bags totaled 2,095 1/3 lbs.

Now, to find out by how much was the projected weight overstated we subtract weight projected with actual weight of baggage :

weight overstated = weight projected - actual weight

weight overstated = 2,182 1/4 lbs  - 2,095 1/3 lbs

weight overstated = 87 - 1/12 lbs

weight overstated = 86(11/12) lbs

Therefore, the projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.

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There is enough information to find the surface area of the​ pyramid

A polyhedron formed by connecting a polygonal base and a point, called the ape-x is known as a pyramid.

The formula for calculating the volume of a pyramid is expressed as:

Volume = BH/3

From the given question, the pyramid is square based. Since we are given the length of the base to be 4.8m and the  height of each triangular face of the pyramid is 6m, we can simply determine the height of the pyramid using Pythagoras theorem and then calculate the volume.

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Answer:

[tex]K^{2}[/tex]

Step-by-step explanation:

[tex]\frac{K^{-4} }{K^{-6} } \\= \frac{K^{6} }{K^{4} } \\= K^{6-4} \\= K^{2}[/tex]

There are 4 bags left after completing one step

The number of bags left after completing one step can be calculated as follows

The amount of trail mix into the bags is 2 1/4

= 9/4

The total amount of trail mix in the bag is 2/3

The first step is to calculate the number of bags

= 9/4 ÷ 3/8

= 9/4 × 8/3

= 36/12

= 6

There are 2/3 bags of trail

= 2/3 × 6

= 4

Hence 4 bags of trail mix are left after completing one step

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It's a little hard to determine what the picture says considering it is slightly blurred, however if you are trying to subtract the following, then after simplifying the expression, the solution written in Scientific Notation would be:

[tex]1.702[/tex] × [tex]10^5[/tex]

Hope this helps!

The correct safe-breaker code is given by 6437346.

It is given that the number is palindrome. Palindrome is a combination of letters or symbols which when written in reverse order gives the same combination of letters or symbols when written in normal order. Let the seven-digit code be given by abcdefg. As it is palindrome therefore, a=g, b=f, c=e, and d=d. Also, first digit is double than third digit that is a=2c.

According to question d=7, c=f-1 and,

b=7-3 = 4.

Since the number is palindrome so b=f. Therefore f=4.

Now, c=f-1 => c = 4-1 = 3, and c = e = 3.

Also, a=2c => a=6.

Thus, the numbers are a=6, b=4, c=3, d=7, e=3, f=4, g=6 and the combination is 6437346.

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The correct combination of the safe is 241742

We can solve the problem following a few steps. Let's assume the third number is x

So, the first digit is 2x according to the question.

Thus the fourth number is 7,

Now we can conclude that , 4 = x + 3  ( second number = sixth number , as mentioned earlier )

4 = x + 3

or , x = 4 - 3

or , x = 1  

After solving this equation we can use the value of x  as 1

∵  Hence the numbers are,

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