Solve: 5(x + 2) = 3x + 5

The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

It is given that,

f(x) = 200 × [tex](1.098)^x[/tex]

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0   2   4   6   8   10

f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200

f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241

f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291

f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350

f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423

f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509

So,

(x, f(x)): (0, 200)  (2, 241)  (4, 291)  (6, 350)  (8, 423)  (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × [tex](1.098)^t[/tex]

⇒ [tex](1.098)^t[/tex] = 2

⇒ log[tex](1.098)^t[/tex] = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

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The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

The given parameters are:

Initial = 350

Final = 375

The rate is calculated as:

Rate = Final/Initial - 1

So, we have:

Rate = 375/300 - 1

Evaluate

Rate = 1.25 - 1

This gives

Rate = 0.25

Express as percentage

Rate = 25%

Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

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By critically observing the graph above, the amount of water in this pond at 0 hour is equal to 2,660 liters.

Similarly, the amount of water in this pond at 1 hour is equal to 3,225 liters.

Next, we would determine the rate of increase:

Rate = Δy/Δx

Rate = (3225 - 2660)/(1 - 0)

Rate = 665.

The amounts given in parts (b) and (c) are not equal because because the line doesn't pass through the origin (0, 0) of the graph.

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The equations that are true for x = –2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16

Given the solution to a quadratic equation to be -2 and 2, the equation is expressed as:

(x-(-2))(x -2) = 0
(x+2)(x - 2) = 0

Expand

x^2 - 2x + 2x - 4 = 0

x^2 - 4 = 0

Hence the equations that are true for x = –2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16

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Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8

Step-by-step explanation:

The maximum height of the ball after its third bounce is equal to 3.568 feet.

In this question we are aware that the maximum height reached by the ball decreases linearly after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:

n = 0

a₀ = 10 ft

n = 1

a₁ = 0.85 · 10 - 1

a₁ = 8.5 - 1

a₁ = 7.5 ft

n = 2

a₂ = 0.85 · 7.5 - 1

a₂ = 5.375 ft

n = 3

a₃ = 0.85 · 5.375 - 1

a₃ = 3.568 ft

The maximum height of the ball after its third bounce is equal to 3.568 feet.

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The first one is 10 feet.
The second one is 6.141 feet.

Step-by-step explanation: Edge 2023

Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of [tex]R = 10^{12}[/tex].

The equation is:

[tex]L = 10\log{R}[/tex]

In which:

For this problem, we have that L = 120, hence the relative intensity is found as follows:

[tex]120 = 10\log{R}[/tex]

[tex]\log{R} = 12[/tex]

[tex]R = 10^{12}[/tex]

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Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].

What are equivalent expressions?

Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].

      [tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]

                    [tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]

Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]

                     [tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]

Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]

                     [tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]

                [tex]$\sqrt{8}=2 \sqrt{2}$[/tex]

                     [tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]

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The complete question is :

Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot

The distance between the points (-8, -3) and (-2, -5) is √40 units

Using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Therefore, using (-8, -3) and (-2, -5).

x₁ = -8

x₂ = -2

y₁ = -3

y₂ = -5

d =  √(-2 + 8)² + (-5 + 3)²

d = √(6)² + (-2)²

d = √36 + 4

d = √40

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Option B. ($99,242.00, $100,758.01)

a) For n - 1 = 49 degrees of freedom, we have form t distribution tables:

P( t < 2.010) = 0.975

Therefore, P(-2.010 < t < 2.010) = 0.95

Therefore the confidence interval here is obtained as:

X +₋ t 8/√ⁿ

100 \pm 2.010*\frac{2}{\sqrt{50}}

100 \pm 0.5685

(99431.61, 100568.39)

Therefore A is the correct interval here.

Q2) From t distribution tables, we have here:

P(-2.680 < t < 2.680) = 0.99

Therefore the confidence interval here is obtained as:

100 \pm 2.010*\frac{2}{\sqrt{50}}

100 \pm 0.7580

(99242, 100785)

1) A university wants to determine the average salary of its graduating computer science majors. The university asks the graduating classes of 50 students to share their starting salaries when hired. The 50 students had an average salary of $100,000 with a standard deviation of $2,000. Find a 95% confidence interval for the average starting salary of computer science majors from the university.

a - ($99,431.61, $100,568.39)

b - ($99,445.64, $100,554.36)

c- ($99,982.26, $100,017.74)

d - The salaries are not normally distributed so we cannot compute a confidence interval

2) Find a 99% confidence interval for the previous problem.

a - ($99,271.44, $100,728.56)

b - ($99,242.00, $100,758.01)

c - ($99,996.46, $100,003.55)

d - The salaries are not normally distributed so we cannot compute a confidence interval

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You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.

Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.

The slope of the line is then

[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]

which means that 1 in ≈ 2.5 cm.

So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)

[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]

Using an exponential function, it is found that 14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]

In which:

In this problem, the parameters are:

A(0) = 135, h = 10.75, t = 12532/365 = 34.334.

Hence the amount is:

[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]

[tex]A(t) = 135(0.5)^\frac{34.334}{10.75}[/tex]

A(t) = 14.75.

14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.

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i. Line BD = 6√2 cm

ii. Perimeter = 3 (π + 4) cm

iii. Area = 18 ( π - 2) cm

Let the length of BD = x

Since B is the midpoint of the arc AC, then ∠BOC = 15°

In ΔBDB

Let's use the trigonometric ration, tan

[tex]Tan 45 = \frac{BD}{CD}[/tex]

CD = x

Then, using the Pythagorean theorem

[tex]x^2 + x^2 = 12^2[/tex]

[tex]2x^2 = 144[/tex]

[tex]x^2 = \frac{144}{2}[/tex]

[tex]x = \sqrt{72}[/tex]

[tex]x = \sqrt{36 *2}[/tex]

[tex]x = 6\sqrt{2}[/tex]

Thus, line BD is [tex]6\sqrt{2}[/tex] cm

ii. Perimeter = BC + BD + CD

= 2πr/8 + x + r -  x

= π(12)/4 + r

= 3π + 12

= 3 ( π + 4) cm

iii. Area of shaded area = Area of BOC + Area of BOD

⇒ πr^2/8 × 1/2x^2

= π144/8 × 1/2(72)

= 18π - 36

= 18 ( π - 2) cm²

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Answer:

1/3 and -1/2

Step-by-step explanation:

You can use the factoring method to identify the solutions of x

6x^2+x-1

2 numbers have to multiply to 6 and subtract to 1 because x is the same as 1x

So, you get 3x and 2x

since you know that -1x1 is -1 you will get

(3x-1)(2x+1)=0

Now, since (3x-1) and (2x+1) multiply to get 0, if either (3x-1) or (2x+1) is 0 the statement will be valid

3(1/3)-1=0

2(-1/2)+1=0

So, your answers are 1/3 and -1/2

Answer:

Step-by-step explanation:

hello :

the perimeter of triangle is : P= (x-z+yx)+( z+x+xz)+A

given  P=x+y+xy  calculate the third side  A

x+y+xy = (x-z+yx)+( z+x+xz) so :  A=x+y+xy -x+z-yx-z-x-xz....continu

a=

If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

The perimeter of the triangle park is x + y + xy meter. The length of the two sides are x - z + yx meter and z + x + xz meter.

Let the third side be 'A'. Then the third length of the triangle is given as,

x + y + xy = (x - z + xy) + (z + x + xz) + A

x + y + xy = x - z + xy + z + x + xz + A

y = x + xz + A

A = y - x - xz

If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.

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Step-by-step explanation:

Find lower quartile first: 1/4 (61)th term which equals to 15.25th term. Use your graph to estimate where 15.25 is and draw a line till it meets tne curve. As soon as it touch the curve, continue the line downward and you'll get LQ in kg. Secondly, find upper quartile: 3/4(61)th term which equals to 45.75th term. Proceed the same thing I mentioned above for lower quartile. Then the formula for interquartile range is upper quartile minus lower quartile and you'll get the answer in kg.

Option C

The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.

The volume of the hemisphere is calculated by using the formula,

= [tex]\frac{2}{3}[/tex] × π × r³ cubic units

where r is the radius of the hemisphere.

It is given that,

A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.

So, the volume of the bowl is

V =  [tex]\frac{2}{3}[/tex] × π × (1)³

  =  [tex]\frac{2}{3}[/tex] × π cubic feets

The volume of each smaller hemisphere-shaped mold =  [tex]\frac{2}{3}[/tex] × π × r³ cubic units

So, for 27 molds, the volume = 27 × [tex]\frac{2}{3}[/tex] × π × r³ cubic units

All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.

Then,

[tex]\frac{2}{3}[/tex] × π = 27 × [tex]\frac{2}{3}[/tex] × π × r³

⇒ r³ = 1/27

⇒ r = 1/3 ft

Therefore, the required radius of each of the smaller molds is 1/3 foot.

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Answer:

Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)

Step-by-step explanation:

The question doesn't specify which leg is under question.  Is it the adacent leg or the opposite leg?  I'll assume adjacent.

We can use the acronym

SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions.  For an angle other than the right angle, the following relationships are defined.

SOH:  S is sine = Opposite/Hypotenuse

CAH:  C is cosine = Adjacent/Hypotenuse

TOA:  T is tangent = Opposite/Adjacent

For a side adjacent (A) to the 36° angle, we can use

Cosine = Adjacent/Hypotenuse

Since we know the hypotenuse (12) we can find A:

Cosine(36) = A/12

A = Cosine(36)*12

A = (0.809)*12

Adjacent = 9.71

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

If the opposite leg is calculated, we would use

Sine= Opposite/Hypotenuse

Sine(36) = Opposite/12

O = (0.5877)*12

Opposite = 7.053

Answer:

90 is the right answer

Step-by-step explanation:

because it give the value pf o is tan o

There might be 18 colored papers.

colored papers to white papers:

3:8

48 white papers

8x6 = 48

Then 3x6= 18

There might be 18 colored papers.

Ratios evaluate numbers, normally through dividing them. in case you are evaluating one facts factor (A) to another statistics factor (B), your formulation might be A/B. this indicates you are dividing data A by using information B. for example, if A is 5 and B is 10, your ratio will be 5/10.

In mathematics, a ratio indicates how many times one quantity incorporates some other. for instance, if there are 8 oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6. further, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the full amount of fruit is 8:14.

Ratios can be absolutely simplified just like fractions. To simplify a ratio, divide all the numbers in the ratio through the same wide variety until they can not be divided anymore.

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Answer:

(3, 2 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (4, 1 ) , then

midpoint = ( [tex]\frac{2+4}{2}[/tex] , [tex]\frac{3+1}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{4}{2}[/tex] ) = (3, 2 )

Total distance travelled = (x.a + 2x -10) miles .

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

The whole trip can be divided into two parts

Part 1 :- Speed = x mph  and time =  a hours

        ∴ Distance = x .a miles

Part 2 :- Speed = x -5mph  and time =  2 hours

        ∴ Distance =(x-5).2 = (2x -10)miles

Total distance = (x.a + 2x -10) miles

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Answer:

Step-by-step explanation:

(a)

      1 - Simplify 4 - 9 to -5.

         ⇒ | - 5 |

      2 - Simplify.

       ⇒ 5

  (b)  

   1 -  Simplify

 ⇒ -5

The sum of the areas of circle C and circle D is 98 units square. Option D

It is important to note that the if the circles overlap each other, then the most have the same radius

Also, the formula for area of a circle is given as;

Area = [tex]\pi r^2[/tex]

For Circle C

The value for π = 3. 142

radius = 7cm

Substitute the values into the formula

We have

Area = π × 7 × 7

Area = 49 π units square

For Circle D

Substitute the values into the formula

Area = [tex]\pi r^2[/tex]

Area = π × 7 × 7

Area = 49 π units square

Sum of the areas of circle C and circle D = area of circle C and area of circle D

Sum of the areas of circle C and D = 49π + 49 π

= 98 units square

The sum of the areas of the circles is 98 units square

Thus, the sum of the areas of circle C and circle D is 98 units square. Option D

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The measure of angle D in the convex pentagon ABCDE is 132°

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the measure of angle D, hence:

angle A = x - 40.

∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)

3(x - 40) + 2x = 540

x = 132°

The measure of angle D in the convex pentagon ABCDE is 132°

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Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.

The general formula for finding the angle between the minute hand and the hour hand is

M = [tex]\frac{2}{11}[/tex] (H × 30 ± θ)

It is given that,

Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.

So,

M = [tex]\frac{2}{11}[/tex] (H × 30 - θ)

   = [tex]\frac{2}{11}[/tex] (6 × 30 - 110)

   = [tex]\frac{2}{11}[/tex] (180 - 110)

   = [tex]\frac{2}{11}[/tex] × 70

   = 140/11

So, he left after 6:12 p.m

Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.

M = [tex]\frac{2}{11}[/tex] (H × 30 + θ)

   = [tex]\frac{2}{11}[/tex] (6 × 30 + 110)

   = [tex]\frac{2}{11}[/tex] (180 + 110)

   = [tex]\frac{2}{11}[/tex] × 290

   = 580/11

So, he returned before 6:52 p.m

Then,

The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.

Therefore, he took 40 minutes to return home.

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The quadratic equation given in the graph can be represented in these two following ways:

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this graph, the roots are [tex]x_1 = 0, x_2 = 4[/tex], hence the factored form of the polynomial is:

f(x) = ax(x - 4).

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = 5a(5 - 4)

5a = 10

a = 2.

Hence the factored form of the polynomial is:

f(x) = 2x(x - 4).

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:

y = a(x - 2)² - 8

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = a(5 - 2)² - 8

9a = 18

a = 2.

Hence the equation in vertex-form is:

y = 2(x - 2)² - 8

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