Find the area of the shaded region. Show all of your work.
3 in
6 in
9 in
12 in
18 in

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

Answer:

B

Step-by-step explanation:

From the information available, 4 sandwiches are EQUALLY shared by 5 people.

If for example the sandwiches were to be shared among 2 persons, then we would have;

In the same manner if 4 sandwiches were to be shared equally among 5 people, then we would have;

ANSWER:

Each student would get 4/5 of a sandwich. This is because the total number of sandwiches is less than the total number of persons sharing. That is the reason why each peron cannot get a whole sandwich to himself/herself. Each person can only get four-fifths of a sandwich.

Based on the fact that sales tax in Connecticut is 6.35%, the price of a single pack of gum can be shown by the function, p(g) = 4g + 0.254g

The price of a single pack of gum is g and Sarah bought 4 packets.

The total cost of her purchase is:
= (4 x price of single pack) x ( 1 + Sales tax rate)

When expressed in terms of g, the function is:

= 4g x (1 + 6.35%)

p(g) = 4g + 0.254g

Find out more on functions at https://brainly.com/question/25638609

#SPJ1

The final value of the integral as   \($\frac{191}{60}$\)   which represents the total "volume" of \($f(x,y)=7x+6y$\) over the region\($D$.\)

The given double integral can be rewritten as:

\(\iint_D 7x \, dA + \iint_D 6y \, dA\)

where  \(D$ is the region bounded by $y=\sqrt{x}$ and $y=x^2$.\)

To evaluate this integral, we first check the intersection points of the two curves:

\(\sqrt{x} = x^2 \quad \Right arrow \quad x = 0 \text{ or } x =1\)

Therefore, the region  D is shown in the figure below:

region D

Next, we can choose to integrate with respect to \(x$ or $y$\). Since the lower boundary of  D is given by \($y=\sqrt{x}$\)which is a function of \(x$,\) we choose to integrate with respect to x first:

\(\begin{aligned} \iint_D 7x \, dA &= \int_0^1\int_{\sqrt{x}}^{x^2} 7x \, dydx \\ &= \int_0^1 7x(x^2-\sqrt{x}) \, dx \\ &= \frac{56}{15} \end{aligned}\)

Similarly, we can evaluate the other integral:

\(\begin{aligned} \iint_D 6y \, dA &= \int_0^1\int_{\sqrt{x}}^{x^2} 6y \, dydx \\ &= \int_0^1 6\left(\frac{x^4-\sqrt{x}}{2}\right) \, dx \\ &= \frac{49}{20} \end{aligned}\)

Therefore, the value of the given double integral is:

\(\iint_D (7x+6y) \, dA = \frac{56}{15}+\frac{49}{20} = \frac{191}{60}\)

In summary, we evaluated the given double integral by splitting it into two integrals, integrating with respect to x  first and then with respect to y , over the region bounded by \(y=\sqrt{x}$ and $y=x^2$\). By doing so, we obtained the final value of the integral as \(\frac{191}{60}$,\) which represents the total "volume" of \($f(x,y)=7x+6y$\) over the region D.

To know more about double integral  click here:

brainly.com/question/30217024

#SPJ4

Answer:

\(m=\frac{-23}{3}\)

\(m=-7.6666666667\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-1.25, -18.5)

Point (0.25, -30)

Step 2: Find slope m

Answer:

  7. inverse relationship; equation: y = 16/x

  8. no relationship; no equation

Step-by-step explanation:

The attachment shows the support for the conclusions. The relationship can be chosen from those offered by looking at differences, ratios, or products of y-values for sequential x-values.

__

In the first problem, we note that the relationship between y-values varies inversely as the relationship between x-values: when x goes up by a factor of (n+1)/n, the value of y goes down by its inverse factor: n/(n+1). That same relationship is observed by noting that the product of x and y is a constant, 16.

 relationship: inverse

  y = 16/x

__

As we looked at the table, we thought this might be an exponential function. Each y-value seemed to be twice the one before—until we got to x=5. As x went from 4 to 5, the y-value increased by a factor of 16, not 2. This means there is no simple relationship between x and y, and no simple equation that will describe the sequence of y-values.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 7

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values are calculated by dividing 16 by the x-value.

\(\sf y=\dfrac{16}{x}\)

Question 8

As the x-value increases, the y-value increases.  

The y-value increases by a factor of 2 for each x-value increase of 1 unit from 1 ≤ x ≤ 4 and 5 ≤ x ≤ 6.

\(\sf y=2^x \ for \ 1\leq x\leq 4\)

\(\sf y=2^{(x+3)} \ for \ 5\leq x \leq 6\)

These are separate exponential relations for restricted domains.

So there doesn't appear to be one relationship for a non-restricted domain.

Based on the time the clock is set to, and the minutes lost every hour, the time the clock would show the next day at 10 am is 8:57 am

To find the time that the clock would show the next day, first find the difference between the 1 pm and 10 am the next day:

This difference is:

= 10 am the next day - 1 pm

= 10 + (12 - 1)

= 10 + 11

= 21 hours

The number of minutes lost is:

= 21 x 3 minutes per hour

= 63 minutes

The time the clock would be showing is:
= 10 am  - 63 minutes

= 8:57 am

Find out more on correct time at https://brainly.com/question/13993250

#SPJ1

Answer:

I = (2350)(0.0277)(6)

Step-by-step explanation:

We're told the principal, rate, and time so we just plug in.

We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277

We need for the resulting equation to have no solution.

For the equation to have no solution, we should have the same number of x on both sides of the equation.

In this case, on the left side, we have 8x-3x-x which results in 4x, so we should also have 4x on the right:

This is so that when we try to solve for x, all of the terms with x will cancel each other, and thus have no solution.

Now, for the second blank space, we can have any number from 0 to 9. I will put 5 but it can be any number (except 2 because its already on the left side):

Answer: 8x-3x+2-x = 4x+5

Answer:

m∠A = 59°

Explanation:

In a Quadrilateral, which is inscribed in a circle, tends to have opposite sides sum up to 180°

so solve:

m∠A + m∠C = 180°

m∠A + 121° = 180°

m∠A = 180°- 121°

m∠A = 59°

Answer:

∠A = 59°

Step-by-step explanation:

This is a cyclic quadrilateral, since every vertex of the quadrilateral touches the circumference of the circle.

The opposite angles in a cyclic quadrilateral add up to 180°

∠A is opposite to ∠C

⇒ ∠A + ∠C = 180

⇒ ∠A + 121 = 180

⇒ ∠A = 180 - 121

⇒ ∠A = 59°

Step-by-step explanation:

Slope is 1/3 while the intercept is 10/3

Answer:

20.18

Step-by-step explanation:

do ten times two and six times three, then when done take first answer and put it in front of the other one but put a period in the middle of the two. hopes this helps. :)

The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

\(\text{A} = \pi \text{r}^2\)

The circumference of a circle is expressed mathematically as;

\(\text{C} = 2\pi \text{r}\)

Given that the area of the circle is 20π cm², we determine the radius of the circle.

\(\text{A} = \pi \text{r}^2\)

\(20\pi \ \text{cm}^2 = \pi \times \text{r}^2\)

\(\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }\)

\(\text{r}^2 = 20 \ \text{cm}^2\)

\(\text{r} = \sqrt{20 \ \text{cm}^2}\)

\(\text{r} = 4.47 \ \text{cm}\)

Now, we determine the circumference of the circle.

\(\text{C} = 2\pi \text{r}\)

\(\text{C} = 2 \times \pi \times 4.47 \ \text{cm}\)

\(\text{C} = 8.94 \ \text{cm}\times\pi\)

\(\text{C} = 8.94\pi\)

Therefore, the circumference of the circle is 8.94π centimeters.

Learn more about circles here: brainly.com/question/11952845

Answer:

B

Step-by-step explanation:

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many pairs οf sunglasses must be sοld tο cοver the fixed and variable cοsts in οrder tο reach the break-even pοint.

Assume that X sunglasses must be sοld tο break even.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=>  $9.44 X = $748,374 + $2.19 X

=>  $9.44 X - $2.19 X = $748,374

=>  $7.25 X = $748,374

=>  X = $748,374 / $7.25

=>   X = 103,184

Therefοre, fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

To know more about unitary method visit:

brainly.com/question/28276953

#SPJ1

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

Explanation:

Here, we want to get the percentage of the gross pay is the take-home pay

Mathematically, we have to divide the take-home pay by the gross pay and multiply it by 100%

Her take-home pay is the difference between her gross pay and her deductions

We have this as:

We have this as:

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

Learn more about trigonometric ratios at:

brainly.com/question/1836193

#SPJ1

The temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

The formula to convert the temperature from Celcius to Fahrenheit is:

\(\textdegree F = (\textdegree C * 1.8) + 32\)

We need to calculate the temperature change of \(6 \textdegree C\) in Fahrenheit:

\(\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8\)

The temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

We can calculate the  Fahrenheit temperature of the water and the desired temperature in Fahrenheit:

\(^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2\)

\(^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77\)

The current temperature of the pool is \(66.2 ^{\circ} F\) and the desired temperature is \(77 ^{\circ} F\).

Therefore the temperature needs to be increased by:

\(\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F\)

which is the same temperature change we calculated earlier in Fahrenheit.

Therefore, the temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

Learn more about Temperature change at:

https://brainly.com/question/25677592

#SPJ1

Answer:

Ben is 4 meters below the surface area.

Answer:

Below

Step-by-step explanation:

Earnings, e, will be divided by 4  friends to equal 12

e/4 = 12      multiply both sides of the equation by 4

4 * e/4 = 12 * 4

    e = 48

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

By using the coordinates of the labeled point, the point-slope equation of the line include the following: D. y + 5 = -3(x - 3)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

0 5 2 -2

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 5)/(0 - 3)

Slope (m) = -9/3

Slope (m) = -3

At data point (3, -5) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 3(x - 3)  

y + 5 = -3(x - 3)

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

A one-to-one correspondence between the set of all positive integers and the set of all rational numbers exists.

By definition, any rational number can be expressed as a fraction a/b, where a and b are integers and b is nonzero. Since any positive integer can be expressed as the fraction a/1, each positive integer can be associated with a rational number a/1.

Thus, there is a one-to-one correspondence between the set of all positive integers and the set of all rational numbers. Furthermore, since any rational number a/b can be expressed as the product of a and b, it can also be associated with the product of two positive integers a and b.

Thus, there is also a one-to-one correspondence between the set of all rational numbers and the set of all positive integers.

For more questions like Positive integers  click the link below:

https://brainly.com/question/29770528

#SPJ4

After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

For similar question on free fall formula.

https://brainly.com/question/3522016

#SPJ11

The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.

The formula to find the slope between two coordinates is expressed as:

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of each line above the x-axis are:

Slope 1 = (5 - 0)/(5 - 8)

Slope 1 = -1.7

Slope 2 = (5 - 5)/(5 - (-2))

Slope 2 = 0

Slope 3 = (5 - 0)/(-2 - (-5))

Slope 3 = 5/3 = 1.7

Read more about slope between two coordinates at: https://brainly.com/question/3493733

#SPJ1