Question: Margo Xavier makes a deposit at
an ATM. She has a paycheck for $375.42 and
a refund check for \$24.95. She would like to
receive $45.00 in cash and deposit the
remaining amount. What is her total deposit?

The numeric value of the derivative at x = 3 is given as follows:

C. 0.5.

The quotient function has the format given as follows:

(f/g)(x).

The derivative of the function is obtained applying the quotient rule, as follows:

(f/g)'(x) = [f'(x)g(x) - f(x)g'(x)]/[g(x)]².

Then at x = 3, the derivative is given as follows:

(f/g)'(3) = [f'(3)g(3) - f(3)g'(3)]/[g(3)]².

Replacing the values from the table, we have that:

(f/g)'(3) = [3 x 2 - 1 x 4]/2².

(f/g)'(3) = 2/4

(f/g)'(3) = 0.5.

Meaning that the correct option is given by option C.

More can be learned about the quotient rule at https://brainly.com/question/29232553
#SPJ1

Answer: v=-19

Step-by-step explanation:

We can multiply by 7 on both sides which cancels out 7 on both sides. He new equation would be v=-19 which is our answer.

The simplification of the given expression above would be = x⁵

The exponential laws in mathematics states that to multiply two exponential functions with the same base, we simply add the exponents.

The second law states that to divide two exponential functions with the same base, we subtract the exponents.

From the expression given above;

x⁷/x² = X(7-2) = x⁵

Therefore, in conclusion, the simplification of the given expression above while following the guide of the exponential laws would be = x⁵

Learn more about exponents here:

https://brainly.com/question/30475430

#SPJ1

The value of the indefinite integral in the context of this problem is given as follows:

B. [tex]\cosh{(e^x + 5)} + C[/tex]

The indefinite integral in the context of this problem is defined as follows:

[tex]\int e^x \sinh{(e^x + 5)} dx[/tex]

We can use substitution to solve the integral, hence:

[tex]u = e^x + 5[/tex]

[tex]du = e^x dx[/tex]

[tex]dx = \frac{du}{e^x}[/tex]

Hence the integral as a function of u is given as follows:

[tex]\int \sinh{u} du[/tex]

The result of the integral is of:

cosh(u) + C.

In which C is the constant of integration.

As a function of x, the integral is given as follows:

[tex]\cosh{(e^x + 5)} + C[/tex]

More can be learned about indefinite integrals at https://brainly.com/question/22008756

#SPJ1

Five-number summary for data set A is: 21, 23.5, 27, 31.5, 34

Five-number summary for data set B is: 21, 22.5, 24.5, 28.5, 35

the five-number summary of a data set consists of:

The minimum or the lowest value

First quartile (Q1), that is the middle of the first part of the data set when ordered.

Median, that is the center of the data set.

Third quartile (Q3), that is the middle of the second part of the data set when ordered.

Maximum value or largest value.

The five-number summary is written from the least to the largest value.

Five-number summary for data set A:

Given, 24, 31, 30, 32, 23, 25, 34, 32, 25, 21, 22, 29;

Minimum: 21

First Quartile: 23.5

Median: 27

Third Quartile: 31.5

Maximum: 34

Five-number summary for data set B:

Given, 35, 33, 32, 21, 22, 23, 24, 25, 24, 22, 25, 25;

Minimum: 21

First Quartile: 22.5

Median: 24.5

Third Quartile: 28.5

Maximum: 35

Learn more about Five-number summary on:

https://brainly.com/question/24809873

#SPJ1

Her savings would be $12.72 ($760 - $744.80 - $2.48).

The difference in the final payment is therefore $221.50 - $150 = $71.50.

a. The printer's price after the trade discount is $760 ($860 - $100). If Janet takes the 2% cash discount, she'll pay $744.80 ($760 * 98%).

If she borrows this amount at 6% for 20 days (the difference between 30 days credit and 10 days cash discount), her interest cost will be $2.48 ($744.80 * 6% * 20/360).

Therefore, her savings would be $12.72 ($760 - $744.80 - $2.48).

b. For choice 1, Janet would pay $150 for 17 months and then the remainder ($4,020 * 75% - $150 * 17) in the 18th month.

For choice 2, the monthly payment is $221.50, calculated by using the formula for an installment loan.

The difference in the final payment is therefore $221.50 - $150 = $71.50.

Read more about monthly payments here:

https://brainly.com/question/28106777
#SPJ1

The total area of the figure is 50.13 square units.

We can decompose the figure into a rectangle of 12 by 3 units, and a semicircle whose radius is 3 units.

Remember that the area of a rectangle is equal to the product between its dimensions, then the area of the rectangle we will get.

A = 12*3 = 36 square units.

For a semicircle of radius R, the area is:

a = 0.5*3.14*R²

Here the radius is 3 units, then.

a =  0.5*3.14*3² = 14.13 square units.

Adding that we will get:

total area = 36 square units + 14.13 square units.

total area = 50.13 square units.

Learn moer about area at:

https://brainly.com/question/24487155

#SPJ1

The specific measurements or Dimensions of the cone and cylinder (such as the radius and height).

The volume of the component part consisting of a cone on top of a cylinder,  the volumes of the individual shapes and sum them together. the part consists of a cone and a cylinder/

1. Volume of the cone:

The volume of a cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

2. Volume of the cylinder:

The volume of a cylinder can be calculated using the formula V_cylinder = π * r^2 * h, where r is the radius of the base and h is the height of the cylinder.

the given diagram and determine the necessary measurements. without the specific measurements or dimensions (such as the radius and height of the cone and cylinder), I am unable to calculate the volumes.

the specific measurements or dimensions of the cone and cylinder (such as the radius and height).

To know more about Dimensions .

https://brainly.com/question/28749362

#SPJ11

Answer:

       0      1      2      3      4      5      6      7

       |      |      |      |      |      |      |      |

     2/3   1     2.7    3.4         7      |

                         |_____________|

                               |

                             3 3/4

Answer:

82 in^2

Step-by-step explanation:

Total Surface Area (TSA) = 2 × Base Area + Base Perimeter × Height

TSA = 2× (7×2) + (7+7+2+2) ×3

= 2 × 14 + 18 × 3

= 82 in^2

Hello,

150 - 1/3% of 150

= 150 - 33,33% x 150

= 150 - 50

= 100

approximately 100

Example: 33 1/3% = 1/3. 1/3 of $150.00 = $50.00, so discounted price is: $150.00 - $50.00 = $100.00

The value of f(3) in the function is undefined

The given function are f(x)= x³+18x²+104x+192 for x≤-3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)=√x²-9

We have to find the value of f(3)

The 3 lies in the interval -3< x≤3

So we use function f(x)= 3x-9/x³-2x²-5x+6 to find f(3)

f(x)= 3(3)-9/(3)³-2(3)²-5(3)+6

=0/27-18-15+6

=undefined

Hence, the value of f(3) in the function is undefined

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

The hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

The half-life of cobalt-60 is 5.24 years, which means that after 5.24 years, the radioisotope activity will have decreased to 50% of its initial level. Since the hospital needs to replace the cobalt when the radioisotope activity has decreased to 45% of its initial level, this means that the cobalt needs to be replaced after slightly less than one half-life has passed.
To find out how long this is, we can use the formula:
t = (ln(0.45) / ln(0.5)) x 5.24
where t is the time in years since the cobalt was first used.
Using a calculator, we find that:
t ≈ 2.16 years
Therefore, the hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

For more such questions on whole number , Visit:

https://brainly.com/question/30199892

#SPJ11

Answer:

Step-by-step explanation:

You want to find the values of cos(x), tan(x), and sin(x) in right triangle DEF as shown in the figure.

The relationships between trig functions and sides of a right triangle are summarized in the mnemonic SOH CAH TOA. This tells you ...

  Cos = Adjacent/Hypotenuse

  cos(x) = f/e

  Tan = Opposite/Adjacent

  tan(x) = d/f

  Sin = Opposite/Hypotenuse

  sin(x) = d/e

<95141404393>

Answer:

Step-by-step explanation:

You want the left sum and the right sum of the four subinterval areas under the curve f(x) = √(x+3) on the interval [-1, 1].

The Riemann sum is the sum of the subinterval areas. The area of each subinterval is the height of the rectangular area, multiplied by its width. Here, the interval width is (1 -(-1))/4 = 0.5.

The heights of the intervals of interest will be the function values f(-1 +0.5n) for f(x) = √(x+3) and n = 0 .. 3 for the left sum and 1 .. 4 for the right sum.

The attached calculator display shows the function values for n=0 .. 4. The expression Total(Most( )) adds the first four function values; while the expression Total(Rest( )) adds the last four function values of these five. Multiplying by the interval width (1/2) gives the left- and right-Riemann sums, respectively.

__

Additional comment

The actual integral value is about 3.44772.

<95141404393>

Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

The inequality that best describes the included values of x is x < 8

From the question, we have the following parameters that can be used in our computation:

The number line

On the number line, we have the following

The above means that we make use of the less than symbol

This is because the open circle uses < or > while arrows pointing left means <

So, we have

x < 8

Hence, the inequality that best describes the included values of x is x < 8

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

1. The final velocity is 8.3 m/s and the distance covered is 16.8 m.

2. The acceleration is  34.7  and it would travel  58.9 m.

Acceleration is a physical quantity that describes the rate of change of an object's velocity over time. In other words, it is the rate at which the speed or direction of motion of an object changes.

Using;

v = u + at

v = ?

u = 2.9 m/s

a = 1.8 m/s2

t = 3 s

Then;

v = 2.9 + (1.8 * 3)

v = 8.3 m/s

Also;

[tex]v^2 = u^2 + 2as\\s = v^2 - u^2/2a\\s = (8.3)^2 - (2.9)^2/2 * 1.8[/tex]

s = 68.89 - 8.41/3.6

= 16.8 m

2)

[tex]v^2 = u^2 + 2as\\a = v^2 - u^2/2s\\a = (27)^2 - 0^2/2 * 10.5[/tex]

a = 34.7[tex]m/s^2[/tex]

Using;

[tex]s = ut + 1/2at^2\\ut = 0\\s = 1/2at^2\\s = 0.5 * 34.7 * (2)^2\\s = 69.4 m[/tex]

It would travel; 69.4 - 10.5 = 58.9 m

Learn more about acceleration:https://brainly.com/question/12550364

#SPJ1

The amount more in income tax that Cho pays than Helen each month would be £56.

Here, we have,

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

Find out more on income tax at

brainly.com/question/20704728

#SPJ1

complete question:

You can use these steps to work out the amount of income tax you pay each month.

Work out

monthly salary - 987.5

Work out

answer to Step 1 +5

Step 1

Step 2

Cho has a salary of £24 000 per year.

Helen has a salary of £1720 per month.

How much more income tax does Cho pay than Helen each month?

Answer:100

Step-by-step explanation:

The number of balloons needed to fill the room is given as follows:

5729 balloons.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions of the room are given as follows:

15 ft, 25 ft and 8 ft.

Hence the volume is given as follows:

V = 15 x 25 x 8

V = 3000 ft³

The volume of a sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

V = 4πr³/3.

The balloon has a radius of 0.5 ft, hence it's volume is given as follows:

V = 4π x 0.5³/3

V = 0.5236 ft³.

Then the number of balloons is obtained as follows:

3000/0.5236 = 5729 balloons.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

The value of the hypotenuse AB is 4.73 units.

Given is right triangle, we need to find the measure of side AB,

So, we know that the Sine of an angle is the ratio of the perpendicular side to the hypotenuse of the triangle,

So,

Sin A = BC / AB

Sin 25° = 2 / AB

AB = 2 / Sin 25°

AB = 4.73

Hence the value of the hypotenuse AB is 4.73 units.

Learn more about trigonometric ratios click;

https://brainly.com/question/25122825

#SPJ1

Answer:

1/6

Step-by-step explanation:

1 x 1/6 = 1/6

Any number multiplied with one is that number itself.

1/6

Step-by-step explanation: Anything multiplied by 1 equals itself, therefore, the answer is 1/6. Hope this helps, and please give me Brainliest! :)

13

5^2+12^=169

square root of 169=13

if the triangle wasnt a right angled triangle it would equal to 13 and would give u something else

When we apply Gauss- Jordon elimination method to solve the system of equation, it becomes;

[tex]\left[\begin{array}{cccc}1&0&0&6\\0&1&0&2\\0&0&1&-6\end{array}\right][/tex]

To solve the augment matrix that represents a system of linear equation using Gauss- Jordon elimination method, we reduce every value to 0's and 1's to get the values in the fourth column.

-5   -3    -4   -12

0    -2    -7    38

0      1     4    -22

    R₁ ÷ -5                                   R₂ ÷ -2

1    3/5     4/5  12/15             1    3/5    4/5   12/15

0    -2    -7    38                   0     1       7/2   -19

0      1     4    -22                  0      1     4    -22          

R₁ - 3/5R₂                                   2R₃

1      0   -13/10   69/5              1      0   -13/10   69/5

0     1      7/2     -19                 0     1      7/2     -19

0     0     1/2      -3                   0     0     1         -6

 R₂ + 13/10R₃                                  R₂ - 7/2R₃

1      0     0     6                             1      0     0     6  

0     1      7/2  -19                          0     1      0      2

0     0     1         -6                         0     0     1      -6

Find more exercises on Gauss- Jordon elimination method;

https://brainly.com/question/1216774

#SPJ1

Answer:

To find the x-intercepts, we set y = 0 and solve for x:

f(x) = (x+9) (x+9) (x-8) = 0

The solutions are x = -9 (double root) and x = 8.

To find the y-intercept, we set x = 0:

f(0) = (0+9) (0+9) (0-8) = -583.

Therefore, the y-intercept is (0, -583).

Answer:

Step-by-step explanation:

chill

If x > 5, then x - 3 > 0 since x is greater than 3. Therefore, |x - 3| = x - 3.

a) The equation of the plane is 2y + z - 2 = 0.

b) The equation of the plane Π1 that is parallel to Π and passes through (2,2,2) is 2y + z - 6 = 0.

c) The distance between the planes Π and Π1 is 4 / √6.

Given data ,

The given line has the parametric equations:

x = 1 + 2t

y = -1 + 3t

z = 4 + t

By comparing the coefficients of t, we can identify a point on the line, which is (1, -1, 4) when t = 0.

To find the normal vector to the plane Π, we use the fact that it is parallel to the vector ⟨0, 2, 1⟩. Since the normal vector is perpendicular to the plane, any vector parallel to the plane can serve as the normal vector. Therefore, we can take the vector ⟨0, 2, 1⟩ as the normal vector.

Now we have a point (1, -1, 4) on the plane Π and a normal vector ⟨0, 2, 1⟩.

The equation of the plane Π can be written as:

0(x - 1) + 2(y + 1) + 1(z - 4) = 0

Simplifying the equation gives:

2y + z - 2 = 0

So, the equation of the plane Π is 2y + z - 2 = 0.

(2)

To find the equation of the plane Π1 that is parallel to Π and passes through (2, 2, 2), we can use the same normal vector ⟨0, 2, 1⟩.

The equation of the plane Π1 can be written as:

0(x - 2) + 2(y - 2) + 1(z - 2) = 0

Simplifying the equation gives:

2y + z - 6 = 0

So, the equation of the plane Π1 is 2y + z - 6 = 0.

(3)

We can take the point (1, -1, 4) on the plane Π and find the perpendicular distance from this point to the plane Π1 using the equation of Π1.

The distance between the two planes is given by the formula:

Distance = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)

Using the point (1, -1, 4) and the equation of Π1: 2y + z - 6 = 0, we can substitute the values into the formula:

Distance = |(2)(-1) + (1)(4) - 6| / √(2² + 1² + 1²)

= |(-2) + 4 - 6| / √(4 + 1 + 1)

= |-4| / √6

= 4 / √6

Hence , the distance between the planes Π and Π1 is 4 / √6.

To learn more about distance between point and plane click :

https://brainly.com/question/14442366

#SPJ1