What is 2/3-1/2 mathswatch

The exponential function that models this situation is:

[tex]D(t) = 10000(1.045)^t[/tex]

Using the function, in 2050, she will have $37,453.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

For this problem, the parameters are:

A(0) = 10000, r = 0.045.

Hence the equation is:

[tex]D(t) = 10000(1.045)^t[/tex]

2050 is 30 years after 2020, hence the amount is:

[tex]D(30) = 10000(1.045)^{30} = 37453[/tex]

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Answer: 1/45

Step-by-step explanation: 10 total marbles. 4 are blue 3 are red 2 are green and 1 is yellow. The chance of drawing a green is 2/10 or 1/5. Then there are only 9 marbles left in the bag. So the chance of a yellow marble is 1/9. 1/5 x 1/9 = 1/45.

Answer:

$ 7.52

Step-by-step explanation:

Find charge per minute

 59 - 23 min = 36 minutes   cost   16.32 - 10.56 = $ 5.76

      or   $5.76 / 36 min = 16 cents per min

   from 59 to 78 = 19 more minutes        x .16/min =  $ 3.04

            so from 59 to 78 will leave 10.56 - 3.04 = $7.52

The equation of the line of best fit is y = 1.7x  - 58

We start by drawing the line of best fit (see attachment)

From the attached graph, we have the following points

(x, y) = (70, 75) and (61, 60)

The slope (m) is:

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

This gives

m = (60 - 75)/(61 - 70)

Evaluate

m = 1.7

The line of best fit is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.7(x - 70) + 61

This gives

y = 1.7x - 119 + 61

Evaluate

y = 1.7x  - 58

Hence, the equation of the line of best fit is y = 1.7x  - 58

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Answer:

21:14:8

Step-by-step explanation:

X:Y=3:2

Y:Z=7:4

X:Y=21:14

Y:Z=14:8

X:Y:Z=21:14:8

Answer-4,5

Step-by-step explanation:

The total possible number of outcomes for the season record is [tex]2^{33}[/tex].

An event that may be given a mathematical probability is known as an outcome in mathematics (an outcome of an experiment). The amount of potential outcomes for a particular experiment determines the probability assigned to each result.The result of an experiment is a number of outcomes.

According to the question,

The basketball team at a college will play 33 games next winter. There are only two possible outcomes for each game: a win or a loss.

So, the total number of possible outcomes for the season record=[tex]2^{33}[/tex].

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Answer:

First function:

Zeros = 6 and -6. Y-intercept = (0,72). X-intercepts = (6,0) and (-6,0).

Second function:

Zeros = 3 and -3. Y-intercept = (0, -27). X-intercepts: (3, 0) and (-3, 0).

Step-by-step explanation:

The zeros are x-intercept numbers.

The y-intercept can be found when the function is in standard form. Plug in 0 for x, then solve.

Hope this helps!

Answer:

1. x₁ = 6, x₂ = -6

2. x₁ = 3, x₂ = -3

Step-by-step explanation:

Given functions:

[tex]1)\ f(x) = -2(x-6)(x+6)[/tex]

[tex]2)\ f(x)=(x-3)(3x+9)[/tex]

..................................................................................................................................................

Zero Product Property: If m • n = 0, then m = 0 or n = 0.

Standard Form of a Quadratic: ax² + bx + c = 0.

..................................................................................................................................................

1. f(x) = -2(x - 6)(x + 6)

Step 1: Set the function to zero.

[tex]\implies 0 = -2(x-6)(x+6)[/tex]

Step 2: Divide both sides of equation by [tex]-2[/tex].

[tex]\implies \dfrac{0}{-2} = \dfrac{-2(x-6)(x+6)}{-2}[/tex]

[tex]\implies 0=(x-6)(x+6)[/tex]

Step 3: Apply the Zero Product Property.

[tex]x_1 \implies x-6=0[/tex]

[tex]x_2 \implies x+6=0[/tex]

Step 4: Solve for x in both equations.

[tex]x-6+6=0+6 \implies \boxed{x_1 = 6}[/tex]

[tex]x+6-6=0-6 \implies \boxed{x_1 = -6}[/tex]

The zeros (x-intercepts) of this function are: [tex]x_1=6,\ x_2=-6[/tex].

.................................................................................................................................................

2. f(x) = (x - 3)(3x + 9)

Step 1: Set the function to zero.

[tex]\implies 0 = (x - 3)(3x + 9)[/tex]

Step 2: Apply the Zero Product Property.

[tex]x_1 \implies x-3=0[/tex]

[tex]x_2 \implies 3x + 9=0[/tex]

Step 3: Solve for x in both equations.

[tex]x-3+3=0+3 \implies \boxed{x_1 = 3}[/tex]

[tex]3x=-9 \implies \dfrac{3x}{3}=\dfrac{-9}{3} \implies \boxed{x_1 = -3}[/tex]

The zeros (x-intercepts) of this function are: [tex]x_1=3,\ x_2=-3[/tex].

..................................................................................................................................................

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Answer:180 °

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.

Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45

45x2= 90

Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.

The answer is 90

The surface area of the composite figure shown in the figure attached is 233.6 cm²

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

The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²

The surface area of the composite figure shown in the figure attached is 233.6 cm²

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Answer:

- 11 < x < 8

Step-by-step explanation:

inequalities of the type | x | < a have solutions of the form

- a < x < a

then

| 2x + 3 | < 19

- 19 < 2x + 3 < 19 ( subtract 3 from each interval )

- 22 < 2x < 16 ( divide each interval by 2 )

- 11 < x < 8

The value of the given division operation is 3/7

From the question, we are to determine the quotient of the given division operation

The given division operation is

-3/2÷-7/2

[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]

[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]

[tex]=\frac{-3}{-7}[/tex]

[tex]=\frac{3}{7}[/tex]

Hence, the value of the given division operation is 3/7

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Answer:

30

Step-by-step explanation:

Since ABC is isosceles, BC = CA.

So, AB = 9(3)+3 = 30.

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is [tex]2w+6[/tex].

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

[tex]A=w(2w+6)[/tex]

We can also substitute 40 in for A as it's given in the question.

[tex]40 = w(2w+6)[/tex]

Distributing w by multiplying it by both terms in the parentheses, we get

[tex]40 = 2w^2+6w[/tex]

We can make the equation simpler by dividing both sides by 2.

[tex]20 = w^2+3w[/tex]

Subtracting both sides by 20 will make the left-hand side 0.

[tex]0=w^2+3w-20[/tex]

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]

[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]

[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]

Since the second solution results in a negative number, it cannot be the length of w.

[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

[tex]l=2(3.217)+6[/tex]

[tex]l=12.434[/tex]

The length of this rectangle is 12.434 cm.

[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]

[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]

Answer: The function is even because [tex]f(x)=f(-x)[/tex].

Step-by-step explanation:

[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]

So, the function is even.

The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

From the information given, we have the following proofs;

Length, l = 2x + 30 - 49

Length = 2x - 19

The formula for perimeter of a rectangle is given as;

Perimeter = 2( length + width)

Substitute the expressions into the formula

Perimeter =  2 ( x+ 15 + 2x - 19 )

Perimeter = 2 (3x - 4)

Perimeter = 6x - 8

We have that the area is  162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163

Area = 27(6x-8) + 162

Expand the bracket

Area= 162x - 216 + 162

Area = 162x - 54

But we know that

Area = length × width

Substitute the expressions

Area = (x+15)(2x-19)

Area =  2x² - 19x +30x - 285

Area = 2x² + 11x - 285

Equate the two formulas for area

162x - 54 = 2x² +11x - 285

Collect like terms

2x² + 11x - 285 - 162x + 54 = 0

2x²  - 151x - 231 = 0

Solve the quadratic equation

(2x + 3)(x-77) = 0

Let's solve for x

x - 77 = 0

x = 77

The expression for the width;

Width = x+15

Width = 77 + 15

Width = 92 feet

The expression for the length

Length = 2(x+15) - 49

Length = 2 ( 77 + 15) - 49

Length = 154 + 30 - 49

Length = 184 - 49

Length = 135 feet

Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

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Answer:

2x⁴-45x-8

Step-by-step explanation:

The area of the paper that remains is 391.04 cm²

From the question, we are to calculate the area of the remaining part of the paper

Area of the paper that remains = Area of rectangle - 2×Area of semicircle

Area of the paper that remains = (l×w) - 2(πr²/2)

Area of the paper that remains = (l×w) - (πr²)

Where l is the length of the paper

w is the width if the paper

and r is the radius of the semicircle

From the given information,

l = 37 cm

w = 16 cm

r = w/2 = 16/2 = 8 cm

Putting the parameters into the equation,

Area of the paper that remains = (37×16) - (3.14(8)²)

Area of the paper that remains = 592 - (3.14×64)

Area of the paper that remains = 592 - 200.96

Area of the paper that remains = 391.04 cm²

Hence, the area of the paper that remains is 391.04 cm²

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The percentage error of the given estimation is 17.7%.

The percentage error of any estimation is calculated as:

Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.

In the question,

The estimated value is given to be 40 marbles.

The actual value is given to be 34 marbles.

We are asked to find the percentage error of this estimation.

We know that:

Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.

Substituting the values, we get:

Percentage error = {(|34 - 40|)/34}*100%,

or, Percentage error = 6/34*100%,

or, Percentage error = 17.6470 % = 17.7% (Rounding to the nearest tenth, that is, up to one decimal place).

Thus, the percentage error of the given estimation is 17.7%.

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First, find the supplement of the angle that is 105 degrees.

105 + 75 = 180

Now, we can find complete the lower left triangle's angles.

39 + 75 + ? = 180

? = 66 degrees

The 66 degree angle of the lower left triangle and angle x are vertical angles. Vertical angles are congruent.

Therefore, the measure of angle x is 66 degrees.

Hope this helps!

The Outcome of event A and B is simply the intersection of both sets written as A ∩ B is; C: {seagull, crow}

From the image, we are given the animals namely; Pig, Penguin, Seagull, Tiger, Crow, Bat, Mosquito.

Now, these animals are classified as either a bird or can fly.

Animals that are birds are; Penguin, Seagull, Crow

Animals that can fly are; Seagull, Crow, Bat, Mosquito.

Now, we are told that;

Event A is the animal is a bird. Thus, the set notation that represents this event A is written as;

A = {Penguin, Seagull, Crow}

Event B is that the animal can fly and again the set notation that represents event B is written as;

B = {Seagull, Crow, Bat, Mosquito}

Now, Outcome of event A and B is simply the intersection of both sets. Thus; A ∩ B = {seagull, crow}

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Answer:

B

Step-by-step explanation:

Cos(0)=1

since the diagram shows x as (1,0)

Answer:

6

Step-by-step explanation:

The arc length is (2)(pi)(27)(40/360)=6pi.

So, k=6.

The graph of a function f exists the set of all points in the plane of the form (x, f(x)).

The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.

Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]

Substitute the values in the function, we get

t = -2, h(t) = 0.05859375

t = -1, h(t) = 0.1875

t = 0, h(t) = 0.6

t = 1, h(t) = 1.92

t = 2, h(t) = 6.144

t = 3, h(t) = 19.6608

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Answer: 32

Step-by-step explanation:

The line is straight meaning 180 angle. When finding B you subtract 148 by 180 which would be 32.

Monthly interest payment is $100.

According to the statement

balance in account = $100

APR = 12%

we use the formula Balance formula to solve this problem.

So, BALANCE * [APR / 12 month] to find monthly interest payment

Here balance is the starting amount in the bank account

And APR is the type of interest rate applied on the amount

And 12 month is the time period for which APR is applicable.

So, substitute the values in it then

Monthly interest payment = 100 * [12/12]

After solving the equation become

Monthly interest payment = 100*1

Monthly interest payment = 100$

So, Monthly interest payment is $100.

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abc =32 ft³  is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.

A rectangle with all equal sides, commonly known as a square.  Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,

The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0  we wish to optimize V= abc.

L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)

The four partial derivatives are zero at an ideal position, so:

δLδa=bc−λ(b+2c)=0

δLδb=ac−λ(a+2c)=0

δLδc=ab−λ(2a+2b)=0

Plus the restriction. The first two enlighten:

λ=bcb+2c=aca+2c

Consequently,  b(a+2c)=a(b+2c)  implies to b=a. The third partial, where b=a, now informs us that   a2=4aλ  and so  λ=a/4  nd by using this information in the second partial, we obtain  4c=a+2c  which informs us that c=a/2 .

Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex]  which means that a=4 feet, b=4 feet, and c=2 feet.

The maximum volume is therefore, abc=32 ft³

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The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8

This are constants that is used to enlarge of diminish a given figure of sides of a figure

We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2

From the given figure;

scale factor = radius of cone 2/radius of cone 1

Given the following parameters

radius of cone 2 = 2 ft

radius of cone 1 = 2.5ft

Substitute

scale factor =  2/2.5

scale factor = 0.8

Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8

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