A scale diagram of a garden shows the length as 14.5cm. If the scale is 1:150, what is the actual length? The garden is _______m in length.

Answer:

[tex]\large \boxed{\sf \ \ \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }=4 \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to find the following limit.

[tex]\displaystyle \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }[/tex]

First of all, for any x real number different from 4 and positive, we can write

[tex]\dfrac{x-4}{\sqrt{x}-\sqrt{4}} = \dfrac{(x-4)(\sqrt{x}+\sqrt{4})} {(\sqrt{x}-\sqrt{4})(\sqrt{x}+\sqrt{4})}} ==\dfrac{(x-4)(\sqrt{x}+\sqrt{4})}{x-4}=\sqrt{x}+\sqrt{4}[/tex]

so the limit is

[tex]\sqrt{4}+\sqrt{4}=2+2=4[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 0.06x

Step-by-step explanation:

The given statement:  A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex]  [we divide a percentage by 100 to convert it into decimal]

[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]

Hence, the required algebraic expression would be :

0.06x

Answer:

A) P(A|B) = 0.01966

B) P(A'|B') = 0.99944

Step-by-step explanation:

A) We are told that A is the event "the person is infected" and B is the event "the person tests positive".

Thus, using bayes theorem, the probability that the person is infected is; P(A|B)

From bayes theorem,

P(A|B) = [P(A) × P(B|A)]/[(P(A) x P(B|A)) + (P(A') x P(B|A'))]

Now, from the question,

P(A) = 1/400

P(A') = 399/400

P(B|A) = 0.8

P(B|A') = 0.1

Thus;

P(A|B) = [(1/400) × 0.8)]/[((1/400) x 0.8) + ((399/400) x (0.1))]

P(A|B) = 0.01966

B) we want to find the probability that when a person tests negative, the person is not infected. This is;

P(A'|B') = P(Not infected|negative) = P(not infected and negative) / P(negative) = [(399/400) × 0.9)]/[((399/400) x 0.9) + ((1/400) x (0.2))] = 0.99944

Answer:

7/9

Step-by-step explanation:

P(blue or odd) = P(blue) + P(odd) − P(blue and odd)

P(blue or odd) = 4/9 + 5/9 − 2/9

P(blue or odd) = 7/9

Alternatively:

P(blue or odd) = 1 − P(not blue and not odd)

P(blue or odd) = 1 − 2/9

P(blue or odd) = 7/9

Answer:

115 mi

Step-by-step explanation:

speed = distance/time

distance = speed * time

0.5 hours at 50 mph

distance = 50 mph * 0.5 h = 25 mi

1.5 hours at 60 mph

distance = 60 mph * 1.5 h = 90 mi

total distance = 25 mi + 90 mi = 115 mi

Answer:

120 inches long in total becuase 12x10 is 120.

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

Point-slope form:

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= [tex] \frac{5}{6} [/tex]

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]

Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

= -1 ÷ (-⅜)

= -1 ×(-8/3)

= [tex] \frac{8}{3} [/tex]

[tex]y = \frac{8}{3} x + c[/tex]

When x=3, y=3,

[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]

Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].

Answer:

2.25

Step-by-step explanation:

The computation of the number c that satisfied is shown below:

Given that

[tex]f(x) = \sqrt{x}[/tex]

Interval = (0,9)

According to the Rolle's mean value theorem,

If f(x) is continuous in {a,b) and it is distinct also

And, f(a) ≠ f(b) so its existance should be at least one value

i.e

[tex]f^i(c) = \frac{f(b) - f(a)}{b -a }[/tex]

After this,

[tex]f(x) = \sqrt{x} \\\\ f^i(x) = \frac{1}{2}x ^{\frac{1}{2} - 1} \\\\ = \frac{1}{2}x ^{\frac{-1}{2}[/tex]

[tex]f^i(x) = \frac{1}{{2}\sqrt{x} } = f^i(c) = \frac{1}{{2}\sqrt{c} } \\\\\a = 0, f (a) = f(o) = \sqrt{0} = 0 \\\\\ b = 9 , f (b) = f(a) = \sqrt{9} = 3\\[/tex]

After this,

Put the values of a and b to the above equation

[tex]f^i(c) = \frac{f(b) - f(a)}{b - a} \\\\ \frac{1}{{2}\sqrt{c} } = \frac{3 -0}{9-0} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{3}{9} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{1}{3} \\\\ \sqrt[2]{c} = 3\\\\\sqrt{c} = \frac{3}{2} \\\\ c = \frac{9}{4}[/tex]

= 2.25

Answer:

see explanation

Step-by-step explanation:

(1)

2x - 3 ≤ 3 ( add 3 to both sides )

2x ≤ 6 ( divide both sides by 2 )

x ≤ 3

(2)

2 - 3y > 16 ( subtract 2 from both sides )

- 3y > 16

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

y < - [tex]\frac{14}{3}[/tex]

Answer:

[tex]\boxed{\frac{x^2 }{8} }[/tex]

Step-by-step explanation:

The quotient is the result from division.

Let x be that number.

Division between x² and 8.

[tex]\frac{x^2 }{8}[/tex]

The algebraic expression representing the quotient of a number squared and eight is x²/8.

An algebraic expression is a combination of terms formed using mathematical operators (+, -, *, /). The terms are made by the combination of variables and constants.

In the question, we are asked to write an algebraic expression that represents the quotient of a number squared and eight.

We know that an algebraic expression constitutes both variables and constants.

We assume the number in the expression to be x.

The number squared is then represented by x².

The quotient of the number squared and eight can be represented as x²/8.

Therefore, the algebraic expression representing the quotient of a number squared and eight is x²/8.

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Answer:

A) 22 cans required to paint

B) Including 13% tax, cost of painting = $633.93

Step-by-step explanation:

As we check the figure, we have a composite figure.

Cuboid on the base and a pyramid on the top of it.

To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.

And 4 triangular faces of pyramid with Base = 6m and Height 5m.

So, total area to be painted = 4 rectangular faces + 4 triangular faces

Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]

Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]

Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]

A) Area painted by 1 can = 6 [tex]m^2[/tex]

Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]

B)

Cost of 1 can = $25.50

Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561

Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93

So, the answers are:

A) 22 cans required to paint

B) Including 13% tax, cost of painting = $633.93

Answer:

[tex]y(x)=100+0.1x[/tex]

Step-by-step explanation:

Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.

We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.

[tex]y(0)=100[/tex]

As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:

[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]

We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:

[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]

Then, we have the equation for the total fee in function of the vertical distance:

[tex]y(x)=100+0.1x[/tex]

Answer:

a = 6, b = 7, c = 8, d = 7 and e = 6

Step-by-step explanation:

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

Answer:

6, 7, 8, 7, 6

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

1/2= 5/10 - make it an equivalent fraction with the same denominator as the other fraction.

3/5= 6/10

5/10-6/10- subtract

=1/10

Answer:

first we find the slope, m=(4-0)/(4+1)

Step-by-step explanation:

first, we find the slope, m=(4-0)/(4+1)=4/5

y-4=4/5 (x-4), y=(4/5)x+4/5

Answer:

The line of best fit

y = 0.633x + 0.561

Step-by-step explanation:

The coordinates that the dart hit include

(–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6)

The x and y coordinates can be written as

x | y

-5|0

1 | -3

4|5

-8|-6

0|2

9|6

So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.

Σxᵢ = sum of all the x variables.

Σyᵢ = sum of all the y variables.

Σxᵢyᵢ = sum of the product of each x variable and its corresponding y variable.

Σxᵢ² = sum of the square of each x variable

Σyᵢ² = sum of the square of each y variable

n = number of variables = 6

The scatter plot and the line of best fit is presented in the second attached image to this solution

Then the regression analysis is then done

Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]

Intercept b: = [Σyᵢ - m×(Σxᵢ)] / n

Mean of x = (Σxᵢ)/n

Mean of y = (Σyᵢ) / n

Sample correlation coefficient r:

r = [n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}

And -1 ≤ r ≤ +1

All of these formulas are properly presented in the third attached image to this answer

The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.

Hope this Helps!!!

Answer:

a. y = 0.6x + 0.6

Step-by-step explanation:

Answer:

1575 ft

Step-by-step explanation:

Convert 1/10 to decimal to make the math simpler.

1/10 = 0.1

Divide 3.5 by 0.1.

3.5/0.1 = 35

Multiply 35 by 45.

35 × 45 = 1575

The train will travel 1575 feet in 3.5 seconds.

The distance covered by the train in 3.5 seconds will be 1575 feet.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A train travels 45 feet in 1/10 in a second.

Then the speed will be

Speed = 45 / (1/10)

Speed = 45 x 10

Speed = 450 feet per second

The distance covered by the train in 3.5 seconds will be

Distance = 450 x 3.5

Distance = 1575 feet

More about the speed link is given below.

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Answer:

cosΘ = - [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Given that Θ is in the third quadrant then cosΘ < 0

Given

tanΘ = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13

Thus

cosΘ = - [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{12}{13}[/tex]

Answer:

395

Step-by-step explanation:

15.8=d/25

multiply both sides by 25 to remove the denominator

25×15.8=d

d=395

Step-by-step explanation:

Vertex for your equation is (-1, -8)

Answer:

The correct answer that corresponds with that graph is B: y ≤-3x+2.

Step-by-step explanation:

1) First we need to figure out what kind of symbol the line is, greater or less than equations (< , >) then the line are dotted,and if its greater than or equal to or less than or equal to equations ( ≤, ≥) since the line are solid.

2) Now we need to figure out which side should be shaded, if the symbol is a less than or a less than or equal to then the shaded side should be on the left, if the symbol is a greater than or a greater than or equal then the shaded side should be on the right.

In this case we have a solid line and a shaded left side which mean the symbol that been used here is a less than or equal to symbol ( ≤ ).

So our answer is B: y ≤-3x+2.

Remember:

- greater or less than equations (< , >) = dotted line

- greater than or equal to or less than or equal to equations ( ≤, ≥) = solid line

- less than or a less than or equal to = shaded left side

- greater than or greater than or equal to = shaded right side

Answer:

60%

Step-by-step explanation:

We need convert 3/5 into a percent in order to find the answer.

We can convert by first dividing 3 by 5 to find the decimal value.

3/5= .6

Now we need to multiply by 100 to make it a percentage

.6 x 100= 60

60%

Answer:

X= 50°

Y= 70°

Z= 30°

BDE= 30°

2BDE= 60°

Step-by-step explanation:

(2x -70 )+z+(2x+20)=180...(sum of angle on a straight line)

2x -70 = BDE... alternate angles

Y + (2x-70)+(50+x-20) = 180...(sum of angles in a triangle)

X-20 = z ... alternate and opposite angles

(2x -70 )+z+(2x-+20)=180

2x-70 + x-20 +2x +20= 180

5x -70= 180

5x = 250

X= 50°

X-20 = z

50-20= z

30° = z

2x -70 = BDE

2(50) -70 = BDE

100-70 = BDE

30°= BDE

Y + (2x-70)+(50+x-20)

Y + 100-70 +50 +50 -20 = 180

Y + 200-90=180

Y= 70°

2BDE = 2*30

2BDE= 60°

Answer:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]

[tex](f/g)(2)=-4[/tex]

Step-by-step explanation:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]  and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]

Answer:  $323.33

Step-by-step explanation:

($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month

    ↓                ↓              ↓

 price        finance      down payment

Answer:

(D) -2,-3

Step-by-step explanation:

From the origin, we can find the current position of point B by counting.

B is 2 to the left of the y-axis, meaning that it's x value is -2.

B is 3 down of the x-axis, making it's y value -3.

Therefore, the coordinates of point B are -2,-3.

Hope this helped!

Answer: (D) -2,-3

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

35 = 7x

Divide each side by 7

35/7 = 7x/7

5 = x

Answer:

No.

Step-by-step explanation:

Substitute 4 (as x) and 2 (as y) into the 2 equations to see if they fit.

y = x - 2

2 = 4 - 2

2 = 2

The first equation is true for (4,2).

Now try the 2nd one.

y = 3x + 4

2 = 3(4) + 4

2 ≠ 16

So the 2nd equation is not true for (4,2).

Either one not true makes the solution incorrect.

No, (4, 2) is not the solution for system of Equation.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

Equations:

y= x-2 ............(1)

y= 3x+ 4.................(2)

Put the value of y from equation 1 to equation (2), we get

x- 2 = 3x+ 4

x- 3x = 4+ 2

-2x = 6

x= -3

and, y= -3 -2 = -5

So, the solution to the system is (-3, -5)

and, (4, 2) can only satisfy the Equation y= x-2 but does not satisfy y= 3x+ 4.

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