17. The prevalence of a disease is 12% in population X (n = 10,000). Two screening tests have been developed for this disease. Individuals first undergo screening test 1, which has a sensitivity of 85

100.48 square inches make up half of the cookie cake. The solution has been obtained by using area of circle.

What is area of circle?

The territory that a circle's circumference encloses or includes is referred to as its area. The square is its unit of measurement.

We are given that the diameter of a circular cookie cake is 16 inches.

Area of circle = π \(r^{2}\)

The radius (r) = 8 inches

So, from this we get

⇒ Area of circle = π \(8^{2}\)

⇒ Area of circle = 64 * 3.14

⇒ Area of circle = 200.96 square inches

So, half cookie cake = 100.48 square inches

Hence, 100.48 square inches make up half of the cookie cake.

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Answer:

i guess your new grade would be 88%. If you past 100%, you might pass for that grade. Even if you get a 90%, you'll still be able to pass.

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

1L=1000

6L=?

6×1000= 6000ML

a soup can hold 200ML

6000/200

= 30

Step-by-step explanation:

Jaden has made a total of 6000 ML (6 L x 1000 ML/L = 6000 ML) of corn soup.

To find out how many bowls he can fill, we need to divide the total amount of soup by the amount of soup that can fit in one bowl.

6000 ML ÷ 200 ML/bowl = 30 bowls

Therefore, Jaden can fill 30 bowls with his 6 L of corn soup.

The simplified form of the given expression is 9b

From the question, we are to simplify the given expression

The given expression is 3√b^2

This expression can be properly written as

(3√b)²

To simplify the expression,

First, we will expand the expression by applying one of the rules of exponents

(3√b)²

Applying the rule of exponent

3² × (√b)²

9 × b

= 9b

Hence,

The simplified expression is 9b

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To solve this problem, we need to find the intersection of the circle with a 61-mile radius centered at the transmitter and the straight line connecting the two cities.

First, let's draw a diagram of the situation:

r

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T (transmitter)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

C1      C2

Here, T represents the transmitter, C1 represents the city 68 miles north of the transmitter, and C2 represents the city 81 miles east of the transmitter. We want to find out how much of the straight line from C1 to C2 is within the range of the transmitter.

To solve this problem, we need to use the Pythagorean theorem to find the distance between the transmitter and the straight line connecting C1 and C2. Then we can compare this distance to the radius of the transmitter's range.

Let's call the distance between the transmitter and the straight line "d". We can find d using the formula for the distance between a point and a line:

scss

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d = |(y2-y1)x0 - (x2-x1)y0 + x2y1 - y2x1| / sqrt((y2-y1)^2 + (x2-x1)^2)

where (x1,y1) and (x2,y2) are the coordinates of C1 and C2, and (x0,y0) is the coordinate of the transmitter.

Plugging in the values, we get:

scss

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d = |(81-0)*(-68) - (0-61)*(-68) + 0*0 - 61*81| / sqrt((81-0)^2 + (0-61)^2)

 = 3324 / sqrt(6562)

 ≈ 41.09 miles

Therefore, the portion of the straight line from C1 to C2 that is within the range of the transmitter is the portion of the line that is within 61 miles of the transmitter, which is a circle centered at the transmitter with a radius of 61 miles. To find the length of this portion, we need to find the intersection points of the circle and the line and then calculate the distance between them.

To find the intersection points, we can solve the system of equations:

scss

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(x-0)^2 + (y-0)^2 = 61^2

y = (-61/68)x + 68

Substituting the second equation into the first equation, we get:

scss

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(x-0)^2 + (-61/68)x^2 + 68(-61/68)x + 68^2 = 61^2

Simplifying, we get:

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(1 + (-61/68)^2)x^2 + (68*(-61/68))(x-0) + 68^2 - 61^2 = 0

Solving this quadratic equation, we get:

makefile

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x = 12.58 or -79.23

Substituting these values into the equation for the line, we get:

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y = (-61/68)(12.58) + 68 ≈ 5.36

y = (-61/68)(-79.23) + 68 ≈ 148.17

Therefore, the intersection points are approximately (12.58, 5.36) and (-79.23, 148.17). The distance between these points is:

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sqrt((12.58-(-79.23))^2 + (5.36-148.17)^2)

≈

Answer:

135 in

Step-by-step explanation:

convert inches to feet

11*12=132

135>132

135 inches are longer

Answer:

Step-by-step explanation:

Factorize both numbers:

Common factors are:

So HCF is:

\(\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid\)

As per Euclid Division Algorithm.

\( \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} \)

\(\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \: = \: 270 \: \times \: 3 \: + \: 90\)

\(\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0\)

Again Applying Euclid Division Algorithm

\(\large\bf{\purple{ \hookrightarrow \: }} \tt \: 270 \: = \: 90 \: \times \: 3 \: + \: 0\)

\(\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0\)

As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.

\({\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}\)

Answer:

Step-by-step explanation:

Given equation:

Solve for variables:

Answers:

Answer:

The slope is 6

Step-by-step explanation:

Y2-Y1 / X2-X1

-3-(-9) / -1-(-2)

6

Answer:

m = 6

Step-by-step explanation:

slope (m) = rise / run

rise = y2 - y1 = -3 - (-9) = 6

run = x2 - x1 = -1 - (-2) = 1

slope = 6/1 = 6

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}\)

Okay, here we have this:

Considering the provided inequation, we are going to graph it, following the required steps, so we obtain the following:

1.

The line will be solid as long as there is an equal, and dashed when not, therefore for this case as the inequality has a lesser or equal then it will be solid.

2.

The vertical motion model is h(t) = -16t² + 54t + 3The equation above is in the standard form of a quadratic equation which is given as y = ax² + bx + c.The maximum point of a parabola (quadratic equation) is always at the vertex of the parabola. The formula for finding the x-coordinate of the vertex is given by -b/2a.

Using the above formula to find the time taken to reach the maximum height, we can find the time by finding the x-coordinate of the vertex of the quadratic equation, t = -b/2a.Substitute a = -16, b = 54 into the formula:$$\begin{aligned} t &= \frac{-b}{2a}\\ &= \frac{-54}{2(-16)}\\ &= 1.69 \end{aligned}$$Therefore, the time taken to reach the maximum height is 1.69 seconds (rounded to the nearest tenth).To find the maximum height reached by the object, we need to substitute t = 1.69 into the equation and solve for h(t):$$\begin{aligned} h(t) &= -16t^2 + 54t + 3\\ &= -16(1.69)^2 + 54(1.69) + 3\\ &= 49.13 \end{aligned}$$

Therefore, the maximum height reached by the object is 49.1 feet (rounded to the nearest tenth).Maximum height reached by an object = 49.1 feetTime taken to reach the maximum height = 1.69 seconds

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Answer:

circumference = 31.4 milometers

Step-by-step explanation:

circumference = 5(2)(π)

circumference = 31.4 milometers

Answer:

W=4

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

(-2,1) and (3, -4)

Step-by-step explanation:

(-2,1) and (3, -4) this is where the lines intersect, hence these are the solution.  :) have a great night!

Answer:

a. 2(4*8 + 8*6 + 4*6)

2(32+48+24)

2(104)

208 in^2

b. 4*8*6 = 192 in^3

To find the total percentage decrease, we first need to find the new values of the stocks in Company A and Company B after the decrease.

The new value of the stock in Company A is: $5800 - (1% \times $5800) = $5742

The new value of the stock in Company B is: $7470 - (20% \times $7470) = $5976

To find the total value after the decrease, we add these two values: $5742 + $5976 = $11718

To find the percentage decrease from the original total value ($5800 + $7470 = $13270) to the new total value ($11718), we use the formula:

percentage decrease = [(original value - new value) / original value] x 100%

percentage decrease = [($13270 - $11718) / $13270] x 100%

percentage decrease = 11.7%

Therefore, the total percentage decrease in the investor's stock account is 11.7%.

Answer: congress

Step-by-step

The first step in the legislative process is the introduction of a bill to Congress. Anyone can write it, but only members of Congress can introduce legislation. Some important bills are traditionally introduced at the request of the President, such as the annual federal budget. Planation:

Congress

The US congress is a combination of 2 components called the House of Representatives and the Senate.

Legislative Branch

The US government is made up of 3 branches. Both parts of Congress are a part of the legislative branch. The purpose of the legislative branch is to create laws. The houses of congress create bills and then vote on them to become laws. If a bill passes both the Senate and the House of Representatives, then it is eligible to become a law in the United States.

Differences between the Senate and House of Representative

While both the Senate and House are in Congress, they have slight differences. One of the main differences is the size of the bodies. The senate has 100 senators. Each state in America gets 2 senators. On the other hand, there are 435 representatives in the House. Representation in the House is based on the population of each state.

Answer:

a = 13.3

Step-by-step explanation:

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

15^2 = a^2 + b^2

a^2 = 15^2 - 7^2 = 225 - 49 = 176

a = √176 = 13.26 = 13.3

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

Step-by-step explanation:

When the diver hits the water the height, h(t), becomes zero.  We set h(t) equal to zero and solve the resulting equation for t:

h(t) = -4t^2+ 11t + 3 = 0

The coefficients of this quadratic equation are {-4, 11, 3}, and so the discriminant (needed in the quadratic formula) is -11 - 4(-4)(3) = 47.

                                            -11 ± √37               11 + √37            11 - √37

Therefore the roots are t = --------------, or t = ------------- or t = ---------------

                                                  -8                          8                        8

Both of these results are positive.  Picture the graph as one opening down and intersecting the x-axis in two places.  The diver hits the water (and h becomes zero) at the later time:

       11 + √37

t = ---------------- sec (a little over 2 sec)

              8

The amount he would pay to purchase a laptop today that is the same value as the one he saw in the ad is $390.

Cost price: Cost prize is the price at which the goods and services were purchased.

It is given that,

projected price: $400.00, and the laptop will be out on the market in about one year with 2.5% inflation.

Now, if he pays today for a laptop of the same value as the one in the advertisement, his cost will be 2.5% of $400 less, or as follows:

cost price of laptop = $400 - 2.5& x 400

cost price of laptop = 97.5% x $400

cost price of laptop = $390

As a result, the laptop that he needs right now will cost $390.

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Answer:

Question 1:

\({ \tt{f(x) = {x}^{2} - 10x + 25}}\)

when f(x) is f(10), we substitute for x as 10; x = 10

\({ \tt{f(10) = {10}^{2} - 10(10) + 25 }} \\ { \tt{f(10) = 100 - 100 + 25}} \\ { \boxed{ \tt{ \: f(10) = 25 \: }}}\)

Question 2:

\({ \tt{f(x) = \frac{2 {x}^{3} - 7 }{10} }} \\ \)

when f(x) is f(-1), we substitute for x as -1; x = -1

\({ \tt{f( - 1) = \frac{2 {( - 1)}^{3} - 7 }{10} }} \\ \\ { \tt{f( - 1) = \frac{ - 2 - 7}{10} }} \\ \\ { \boxed{ \tt{ \: f( - 1) = - \frac{9}{10} \: }}}\)

Answer:

B is the answer

Step-by-step explanation:

According to Pythagoras theorem, the value of the third side of the triangle is 38.6mm

In math Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Here we have given that the triangular pendant has two sides of length 23 mm and 31 mm.

And we need to find the possible lengths (in whole mm) for the third side.

Here in the given question, we have the values of the two sides are 23mm and 31mm.

Then we have to apply the values on the Pythagoras theorem formula,

=> hypotenuse² = adjacent² + opposite²

Now, we have to apply the values as opposite and adjacent on it, then we get,

=> hypotenuse²= 23² + 31²

=> hypotenuse² = 529 + 961

=> hypotenuse² = 1490

Therefore, the value of the third side is 38.6mm

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Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

Answer:

  0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

  x^2 +y^2 = -xy

Factoring the expression of interest, we have ...

  x^3 -y^3 = (x -y)(x^2 +xy +y^2)

Substituting for xy using the first expression we found, this is ...

  x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0

The value of x^3 -y^3 is 0.

Answer:

9

Step-by-step explanation:

\(\frac{3}{5} = \frac{x}{15}\)

Cross multiply

\(45=5x\)

Divide both sides by 5

\(\frac{45}{5}=\frac{5x}{5}\)

x = 9

The missing value is 9

~Learn with Lenvy~