Betty decides to set aside $200/month. If her monthly 401(k) savings are earning 5.4% APR compounded monthly, what will the balance be in her account after 40 years? 10. Over the 40-year period, how much total money did Betty deposit into the 401(k)? 11. Over the 40-year period, how much less money did she receive in her paychecks?

Answer:

4 and 5/12

Step-by-step explanation:

Answer:

(1, -3)

Step-by-step explanation:

Set the line equations equal to each other:

-3x = 5x - 8

Solve for x:

-3x = 5x - 8

-8x = -8

x = 1

So, the lines will intersect at the x coordinate of 1.

Plug in 1 as x into one of the equations, to solve for the y coordinate:

f(x) = -3x

f(1) = -3(1)

= -3

So, the y coordinate of the intersection point is -3.

The point of intersection between the lines is (1, -3)

Answer:

Yes, she is. The exact product of 602 and 341 is 205,282.

Step-by-step explanation:

To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.

So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.

Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.

So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.

Answer:

9/4

Variables in inverse proportion have a constant product.

\(xy=(9)(3)=27 \\ \\ xy=12x=27 \\ \\ x=\frac{9}{4}\)

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:

770,400

Step-by-step explanation:

770,400 seconds

Answer:

both

Step-by-step explanation:

Answer:

true! :)

Step-by-step explanation:

Answer:

C: 1/2x +7

Step-by-step explanation:

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer: A) 7,200

Step-by-step explanation:

Answer:7200

Step-by-step explanation:

2+2=7200

Answer: there you go :)

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Step-by-step explanation:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

We set up our equations:

35x+40y = 1850        eq1

x+y = 50                   eq2

Substituting eq 2 into eq 1,

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

  x = 30

Substitute value of x into eq 2.

x+y = 50

30+y = 50

     y = 20

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Answer:

3/12

Step-by-step explanation:

The weighted average length of a nail from the carpenter's box is 3.5 centimeters.

Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:

Short nail: 2.5 cm x 70.5%= 1.7625 cm

Medium nail: 5.0 cm x (19% = 0.95 cm

Long nail: 7.5 cm x 10.5% = 0.7875 cm

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

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The sky appears blue because of Rayleigh scattering while water appears blue due to selective absorption and scattering of light.

The blue color of the sky is a result of Rayleigh scattering which occurs when the Earth's atmosphere scatters shorter wavelengths of light (blue and violet) more efficiently than longer wavelengths (red and orange).

When sunlight enters the atmosphere, the blue light is scattered in all directions by the molecules and tiny particles present in the air creating the blue appearance of the sky.

Similarly, water appear blue due to selective absorption and scattering of light. Water molecules selectively absorb colors from the visible light spectrum and absorb longer wavelengths (such as red) more effectively than shorter wavelengths (such as blue).

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answer

Equilateral Triangle

Answer:

equilateral triangle

Step-by-step explanation:

Answer: f is Parralel to g

Step-by-step explanation:

Answer:

You gave us no choices

Step-by-step explanation:

h is not parallel f

Answer:

k = -3

k =5

Step-by-step explanation:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\\)

\(5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\\)

\(\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3\)

A = (-1, 1) and B = (2, k) so:

\(d(A,B)=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(2-(-1))^2+(k-1)^2}=\\\\=\sqrt{3^2+(k-1)^2}=\sqrt{9+k^2-2k+1}=\sqrt{k^2-2k+10}\\\\\\d(A,B)=5\\\\\sqrt{k^2-2k+10}=5\quad|(\ldots)^2\\\\\big|k^2-2k+10\big|=25\\\\k^2-2k+10=25\qquad\vee\qquad k^2-2k+10=-25\\\\k^2-2k-15=0\qquad\vee\qquad k^2-2k+35=0\\\\\\\Delta_1=(-2)^2-4\cdot1\cdot(-15)=64>0\qquad\text{two solutions}\\\\\Delta_2=(-2)^2-4\cdot1\cdot35=-136<0\qquad\text{no solutions}\\\\\\k_1=\dfrac{2-\sqrt{64}}{2}=\dfrac{2-8}{2}=\dfrac{-6}{2}=\boxed{-3}\)

\(k_2=\dfrac{2+\sqrt{64}}{2}=\dfrac{2+8}{2}=\dfrac{10}{2}=\boxed{5}\)

The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.

Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.

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The sum of the interior angles in a triangle is 180 degrees. Therefore, if we add up all of these angles, they must be equal to 180.

64 + 85 + (4x + 27) = 180

176 + 4x = 180

4x = 4

x = 1

Let's check our answer!

4(1) + 27 = 31

31 + 85 + 64 = 180

180 = 180

Hope this helps!! :)

Answer:

x=1

Step-by-step explanation:

The sum of the angles in a triangle is 180

64+ 85+ 4x+27 = 180

Combine like terms

4x+176=180

Subtract 176 from each side

4x+176-176 =180-176

4x = 4

Divide by 4

4x/4 = 4/4

x=1

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

Answer:

g(x) = x + 3

Step-by-step explanation:

A composite function is a function that is written inside another function which means substituting one function into another function.

Ex: (fоg)(x) is a composite function, where x of f(x) is substituted by g(x)

∵ h(x) = (fоg)(x)

∵ \(h(x)=\sqrt{x+5}\)

∵ \(f(x)=\sqrt{x+2}\)

→ Substitute x of f(x) by g(x)

∴  (fоg)(x) = \(\sqrt{g(x)+2}\)

→ Equate (fоg)(x) by h(x)

∴ \(\sqrt{g(x)+2}=\sqrt{x+5}\)

→ Cancel the roots from the two sides

∴ g(x) + 2 = x + 5

→ Subtract 2 from both sides

∴ g(x) + 2 - 2 = x + 5  - 2

∴ g(x) = x + 3

Answer:

\( - 3 \frac{5}{7} x - 2\ \frac{1}{2} \)

\( \frac{ - 26}{7} - \frac{5}{2} \)

LCM of 7 and 2 is 14

Multiplying (-26/7) with 1/2 (to make the denominator 14) and -5/2 with 1/7

\( \frac{ - 26}{7} \times \frac{1}{2} - \frac{5}{2} \times \frac{1}{7} \)

\( \frac{ - 26}{14} - \frac{5}{14} \)

\( \frac{ - 26 - 5}{14} \)

\( - \frac{31}{14} \)

Answer is A. 101°

Step-by-step explanation:

The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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Answer:

Which one is at the bottom? if the one at the bottom is 0 then the answer is 0. If its not then its related to pemdas or something else

Step-by-step explanation:

Answer:

? = 4

4 is the answer

Step-by-step explanation:

heart = 21

rainbow = 7

unicorn horn = 9

so, we have

heart + rainbow + rainbow = 35

21 + 7 + 7 = 35

heart + unicorn horn + rainbow = 37

21 + 9 + 7 = 37

rainbow + unicorn horn + unicorn horn =25

7 + 9 + 9 = 25

unicorn horn + unicorn horn + rainbow - heart = ?

9 + 9 + 7 - 21 = 4

Both representations are equivalent and describe the same function.the function rule for this table is:   f(x) = -1/2 x 2

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.

To write a function rule for a given array, we need to determine how the values ​​in the output column (y) relate to the values ​​in the input column (x).

Looking at the given data, we notice that the output values ​​decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .

The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values ​​decrease by 1 every time the input values ​​increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.

Therefore, the function rule for this table is:

f(x) = -1/2 x 2

where x is the input value and f(x) is the output value.

Alternatively, we can also represent the function in table entries, for example:

f(0) = 2

f(2) = 1

f(4) = 0

f(6) = -1

Both representations are equivalent and describe the same function.

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The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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