Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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Answer:

f(-2) is 14.

Step-by-step explanation:

We have been given the function:

We have to find f(-2)

That means put x= -2 in the given function we get:

After simplification we will get:

After further simplification we will get the required result:

 Hence, ƒ (-2) is 14

Answer:

the answer is 1 because any expression divide itself equals tp 1

\(\sf \frac{3}{4} \div \frac{3}{4} \)

\(\sf \longmapsto \frac{3}{4} \times \frac{4}{3} \)

\(\sf \longmapsto \frac{3 \times 4}{4 \times 3} \)

\(\sf \longmapsto \frac{12}{12} \)

\(\sf \longmapsto \cancel{ \frac{12}{12}{ } }\)

\(\sf \longmapsto1\)

OR the last 2 steps can also be written as,

\(\sf \longmapsto \frac{12 \div 12}{12 \div 12} \)

\(\sf \longmapsto1\)

Answer:

the answer is -5/2

hope it helps you mate..

please mark me as brainliast

Answer:

\( \sqrt{2} \: \: \: \: \: \: \frac{ \pi}{2} \: \: \: \: are \: \: \: \: the \: \: \: \: answers\)

First In, First Out (FIFO) is an accounting method in which assets purchased or acquired first are disposed of first. It assumes that the remaining inventory consists of items purchased last.

From the question, there are a total of 5 items in the inventory. The first purchase price for 2 items was $50, while the other 3 were purchased at $60 per item.

If one item is sold, under the FIFO method, it was sold for $50. Therefore, the remaining items in the inventory are 1 $50 item and 3 $60 items.

Therefore, the cost will be:

OPTION C is the correct option.

Answer:

With the Pay-As-You-Go Calling Plan, licensed users can call out to numbers located in the country/region where their Microsoft 365 license is assigned to the user based on the user's location, and to international numbers in 196 countries/regions. Unlimited incoming minutes are included.

Answer:

In 1997, the baseball card would be worth $7.46 + $2.52 = $9.98.

In 1998, the baseball card would be worth $9.98 + $2.52 = $12.50.

In 1999, the baseball card would be worth $12.50 + $2.52 = $15.02.

Step-by-step explanation:

In this problem, we are given the value of a baseball card in 1996, which is $7.46. We are also told that the value of the card increases by $2.52 each year since then. This means that in 1997, the value of the card increased by $2.52 compared to its value in 1996, so the value in 1997 would be $7.46 + $2.52 = $9.98. Similarly, in 1998, the value of the card increased by another $2.52 from its value in 1997, so the value in 1998 would be $9.98 + $2.52 = $12.50. In 1999, the value of the card increased by another $2.52 from its value in 1998, so the value in 1999 would be $12.50 + $2.52 = $15.02.

a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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To find the new graph we need to remember the equation of a line in its slope-intercept form

In our case m will represent the charge per hour and b will be the flat fee.

Then the new charge will be described by the equation

The graph of this equation is

4/3 is the value of k that makes the system of linear equations has no solutions .To determine the value(s) of k such that the system of linear equations has no solutions, we need to use the concept of consistency and consistency of a system of linear equations, which is the property that a system of equations has exactly one solution or no solution.

A system of linear equations is consistent if it has exactly one solution and inconsistent if it has no solution. We can use the concept of determinant of a matrix to check the consistency of the system of linear equations. The determinant of a matrix is a scalar value that can be calculated from the elements of a matrix and it tells us whether a matrix is invertible or not. An invertible matrix corresponds to a consistent system of linear equations and a non-invertible matrix corresponds to an inconsistent system of linear equations. To check the consistency of the system of linear equations, we can use Cramer's Rule, which states that the determinant of the coefficient matrix must be non-zero for the system to have a unique solution.

The coefficient matrix of the given system of equations is:

| 1 2 k |

| 3 6 8 |

The determinant of the coefficient matrix is:

|1 2 k|

|3 6 8| = (18) - (26) + (k*3) = 8 - 12 + 3k

If the determinant of the coefficient matrix is non-zero, the system of equations will have a unique solution, if the determinant of the coefficient matrix is zero, the system of equations will have no solution.

So for the system of linear equations to have no solution, the determinant of the coefficient matrix must be zero.

8 - 12 + 3k = 0

3k = 4

k = 4/3

So the value of k that makes the system of linear equations has no solutions is 4/3.

It is worth noting that if there are infinite solutions, the determinant of the matrix is zero but the rank of the matrix (the number of linearly independent rows or columns) is smaller than the number of variables

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

5x+7x=660;

12x=660;

x=660:12;

x=55 (kg).

Then 5x=5×55=275 kg and 7x=7×55= 385 kg.

The required ratio is therefore

660= 275:385.

a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

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Answer:

1023/4

Step-by-step explanation:

shown in the picture

Step-by-step explanation:

x= 15/26 × 30 = 17.3

y= 26/15 × 16.5 = 28.6

Answer: y = 2

Step-by-step explanation: Horizontal means y =

Answer:

○ \(\displaystyle y = 2\)

Step-by-step explanation:

This is a STRAIT HORISONTAL LINEAR EQUATION, therefore sinse every x-coordinate will have the same y-coordinate of \(\displaystyle 2,\) this is the option you would pick.

I am joyous to assist you at any time.

The value of partial fraction decomposition are x^3/(x^2+5x+4) is A/(x+4) + B/(x+1) + Cx/(x+4), 8x+1/(x+1)^3(x^2+3)^2 is A/(x+1) + B/(x+1)^2 + C/(x+1)^3 + D/(x^2+3) + E/(x^2+3)^2, x^4/(x^4 -16) is A/(x+2) + B/(x-2) + C/(x^2+4) and  t^4+t^2+1/(t^2+1)(t^2+7)^2 is A/(t^2+1) + B/(t^2+7) + C/(t+it) + D/(t-it) + E/(t+it)^2 + F/(t-it)^2.

The partial fraction decomposition of x^3/(x^2+5x+4) is

x^3/(x^2+5x+4) = A/(x+4) + B/(x+1) + Cx/(x+1)^2

The partial fraction decomposition of 8x+1/(x+1)^3(x^2+3)^2 is

8x+1/((x+1)^3(x^2+3)^2) = A/(x+1) + B/(x+1)^2 + C/(x+1)^3 + D/(x^2+3) + E/(x^2+3)^2

The partial fraction decomposition of x^4/(x^4 -16) is

x^4/(x^4 -16) = A/(x+2) + B/(x-2) + C/(x^2+4)

The partial fraction decomposition of of numerical value t^4+t^2+1/(t^2+1)(t^2+7)^2 is

(t^4+t^2+1)/((t^2+1)(t^2+7)^2) = A/(t^2+1) + B/(t^2+7) + C/(t+it) + D/(t-it) + E/(t+it)^2 + F/(t-it)^2

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Answer:

A

Step-by-step explanation:

that should be an equal sign

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:

A = 2πr² + 2πrh

If you know the height h, then you can solve the quadratic equation for r.

Solution

For this case we have the followinf:

Triangle ABD is isoceles with base BD, AC perpendicular BD Definition of isosceles triangle

AB congruent to AD: Given

< 1 and < 2 are right triangles definition of perpendicular

AC congruent to AC Reflexive

Triangle ABC and ADC are right triangles Definition of right triangle

Triangle ABC congruent to triangle ADC HL

< BAC = < DAC CPCTC

Answer:

Area of the shaded polygon= 372

Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

Answer:

y = -6x -6

Step-by-step explanation:

The general form of the equation of a line in the slope-intercept form may be given as

y = mx + c where

m is the slope and c is the intercept

Hence given the equation

18x + 3y = -18

subtract 18x from both sides

3y = -18x - 18

Divide both sides of the equation by 3

y = -6x -6

This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept

In a case whereby baseball game receives 3 raffle tickets and a $2 certificate for the team store. A group of people receives 39 raffle tickets the amount of money in certificates the group receive is  $26.

If one baseball game receives 3 raffle tickets and a $2 certificate for the team store, then we can say that each raffle ticket is worth 2/3 dollars ($2 divided by 3 tickets).

So, for 39 raffle tickets, the group would receive (39 x 2/3) = $26

Therefore, the amount of money in certificates the group receive is  $26

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Answer:

Step-by-step explanation: