help quickly!!
A grocery store receives a shipment of 700 oranges. The manager randomly selects 25 oranges to weigh. In that sample, 2 oranges weigh 5 ounces. How many oranges in the shipment can the manager predict weigh 5 ounces?

14

56

644

698

Sum of first 7 terms of an AP = 49.

Sum of first 17 terms = 289

the sum of first 30 term

We know that,

Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]

Hence,

→ 7/2 * [ 2a + (7 - 1)d ] = 49

→ 2a + 6d = 49 * 2/7

→ 2( a + 3d ) = 14

→ a + 3d = 14/2

→ a + 3d = 7 -- equation (1)

Similarly,

→ 17/2 * [ 2a + 16d ] = 289

→ 17/2 * 2 * (a + 8d) = 289

→ a + 8d = 289 * 2/17 * 1/2

→ a + 8d = 17 -- equation (2)

Subtract equation (1) from (2).

→ a + 8d - (a + 3d) = 17 - 7

→ a + 8d - a - 3d = 10

→ 5d = 10

→ d = 10/5

→ d = 2

Substitute the value of d in equation (1).

→ a + 3 * 2 = 7

→ a = 7 - 6

→ a = 1

Now,

Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]

→ S(30) = 15 (2 + 58)

→ S(30) = 15 * 60

→ S(30) = 900

Therefore, the sum of first 30 terms of the given AP is 900.

I hope it will help you.

Regards.

answer refer in pic siso

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Answer:

4.5732 %

Step-by-step explanation:

Answer:

Bet $100 and remove all non-face cards.

Step-by-step explanation:

Each option may be answered on the basis of the ratio of face cards to non-face cards, which we'll say is R.

a. removing all of the black cards  No.  The vale of R does not change.  R is the same for both black and red cards, so removing one color does not change R.

b. removing all non-face cards  Yes.  The only cards left are face cards.  The odds of drawing 2 face cards in a row from this modified deck is 100%

c. removing all kings  No.  Face cards are being removed and will thus lower the probability of picking one.

d. removing all of the red cards  No.  Same reasoning as in (a.).

The equation for the plane tangent to each surface - -10x + 6y + z - 5 = 0

What is Plane Tangent?

a tangent is a line that touches a curve at exactly one point without intersecting it. Similarly, a plane tangent is a plane that touches a surface at only one point without intersecting it further. This concept is commonly used in calculus and differential geometry to study the behavior of curves and surfaces.

We usually use partial derivatives of the equation of the surface to find the equation of the plane tangent to the surface at a point. The normal vector to the surface at that point is obtained by taking the cross product of the partial derivatives evaluated at that point. Then, using the coordinates of the point and the normal vector, we can determine the equation of the plane using the point-normal form or the general form of the plane equation.

It is important to note that the tangent plane equation depends on the specific point on the surface where the tangent plane is desired. Different points on the surface will have different tangent planes associated with them.

To find the equation for the plane tangent to the surface z = f(x, y) at a point (a, b, c), we need to use the partial derivatives of f with respect to x and y at the point (a, b) to find the normal vector to the plane.

Then we can use the point-normal form of the equation of a plane to write the equation.

First, we need to find the partial derivatives of f(x, y) = x^2 + y^3 - 6xy with respect to x and y:

fx = 2x - 6y

fy = 3y^2 - 6x

Then we can evaluate these partial derivatives at the point (1, 2) to get the normal vector:

n = <fx(1, 2), fy(1, 2)> = <2(1) - 6(2), 3(2)^2 - 6(1)> = <-10, 6>

So the equation of the plane tangent to the surface z = f(x, y) = x^2 + y^3 - 6xy at the point (1, 2, 3) is:

-10(x - 1) + 6(y - 2) + (z - 3) = 0

Simplifying, we get:

-10x + 6y + z - 5 = 0

So the equation of the plane tangent to the surface z = x^2 + y^3 - 6xy at the point (1, 2, 3) is -10x + 6y + z - 5 = 0

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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Answer: 1) (0, -3) & 2) (0,0)

Step-by-step explanation:

Answer: Songhai

explanation:

Answer:

Songhai

Step-by-step explanation:

Answer:

Step-by-step explanation:

The 100th term in the sequence 5, 9, 13, 17,.. is term 401.

The arithmetic sequence:

5, 9, 13, 17,...

To find,

Which term of the arithmetic sequence 5, 9, 13, 17,...is 401​.

Concept,

For a given A.P. sequence if the first term is 'a', the common difference is 'd', then the aₙth term is given by:

aₙ = a + (n - 1)d....(1)

Calculation,

Here in the given sequence:

5, 9, 13, 17,..

a = 5, d = 9 - 5 = 4, and aₙ = 401, n = n, substitute in equation (1)

401 = 5 + (n - 1)4

⇒ 396 = (n - 1)4

⇒ n - 1 = 99

⇒ n = 100

Therefore, the 100th term in the sequence 5, 9, 13, 17,.. is term 401.

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The amount of tickets earned by friends playing an arcade game  is 1 ticket .

what is meaning of term   amount ?

The term "amount" generally refers to a quantity or a sum of something, often related to a numerical value. It can refer to the total value or quantity of something, such as the amount of money in a bank account

what is arcade game?

An arcade game is a type of video game that was originally designed to be played in public places, such as arcades, malls, and restaurants. These games has  gameplay mechanics

In the given question,

To regroup the amounts so that each person has the same amount, we need to find the total number of tickets earned and divide by the number of friends.

Total number of tickets earned = 0 + 0 + 0 + 1 + 1 + 2 + 3 = 7

Number of friends = 7

Each person will have the same amount of tickets if we divide the total number of tickets earned by the number of friends:

7 tickets ÷ 7 friends = 1 ticket per person

Therefore, each person should receive 1 ticket.

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Answer:

c = 10 / x

Step-by-step explanation:

3(cx - 7) = 9

value in terms of c

c = 10 / x

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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Given:

Angles A and B are vertical angles.

The measure of angle A is 8x + 1 and angle B is 21 – 2x.

To find:

The measure of each angle.

Solution:

We know that vertically opposite angles are always equal.

Angles A and B are vertical angles.

\(m\angle A=m\angle B\)

\(8x+1=21-2x\)

Isolate variable terms.

\(8x+2x=21-1\)

\(10x=20\)

Divide both sides by 10.

\(x=\dfrac{20}{10}\)

\(x=2\)

Now,

\(m\angle A=8x+1\)

\(m\angle A=8(2)+1\)

\(m\angle A=16+1\)

\(m\angle A=17\)

And,

\(m\angle B=21-2x\)

\(m\angle B=21-2(2)\)

\(m\angle B=21-4\)

\(m\angle B=17\)

Therefore, the measure of angle A and angle B is 17 degrees.

Answer:

-4

Step-by-step explanation:

x2 is x*2.

If x=-2, then the equation would be -2*2 which is -4.

Answer:

-4

Step-by-step explanation:

x2 when x=-2

-2 (2)

-2 · 2

-4

The required bigger triangle is dilated with a scale factor of 3/7 to form a smaller triangle.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
To determine the scale factor for the given figure we have to determine the ratio of any corresponding sides,

So,
Scale factor = 12/28
Scale factor = 3/7

Thus, the required bigger triangle is dilated with a scale factor of 3/7 to form a smaller triangle.

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The image in the question is missing, so the image attached is the suggested image of the solution given above.

Answer:

option 2 I think it's right

Answer:

≈39.27 units

Step-by-step explanation:

To find the area of a semi circle, you use the formula for finding the area of a circle, which is \(\pi\)\(r^{2}\), and then you divide that by 2 since it is half of a circle.

In this case, \(\pi\)\((5)^{2}\) ≈ 78.54

\(\frac{78.54}{2}\) = 39.27

Answer:

To put this equation in standard form, you need to complete the square for both the x's and the y's.

First, complete the square for the x's by adding and subtracting (16/2)^2 = 16^2/2^2 = 32/2 = 16.

4x² - 16x + 16 - 16 - 5y² - 30y - 9 = 0

4x² - 16x + 16 - 5y² - 30y - 9 = 0

Now, complete the square for the y's by adding and subtracting (30/2)^2 = 30^2/2^2 = 900/2 = 450.

4x² - 16x + 16 - 5y² - 30y + 450 - 450 - 9 = 0

4x² - 16x + 16 - 5(y² - 15y + 225) - 9 = 0

Now, you can simplify the expression inside the parentheses by completing the square for y.

4x² - 16x + 16 - 5(y - 15)^2 + 5*225 - 9 = 0

Now, divide everything by -5 to get the equation in standard form:

-4/5x² + 16/5x - 16/5 - (y - 15)^2 = 0

The standard form of the equation is:

(-4/5)x² + (16/5)x - 16/5 - (y - 15)^2 = 0

Answer:

4 \(\frac{3}{10}\)

Step-by-step explanation:

woiwowikio;salkf,cpods;klxgc,powe;dcxkvg,sd;

Answer:

270 per year so 6 years is 1620 and add that with 6000=7620

Answer:

there is no question but i think out of a,b,c and e i think b or c

Step-by-step explanation:

sorry

Answer:  24 points

Work Shown:

k = amount of points Katrina scored

k = 8

s = amount of points Sarah scored

s = 3k, since she scored three times as many

s = 3*8

s = 24 points

The quadrilateral that has diagonals that always bisect its angles and also bisect each other is a (1) rhombus.

In a Rhombus, the diagonals are perpendicular bisectors of each other, and they bisect each other at their point of intersection, dividing the rhombus into four congruent triangles.

Each angle of a rhombus is = 180° divided by number of sides, so each angle of a rhombus is 90°.

In a rectangle, the diagonals bisect each other, but they do not necessarily bisect the angles of rectangle.

In a parallelogram, the diagonals bisect each other, but they do not necessarily bisect the angles of parallelogram.

In an isosceles trapezoid, the diagonals do not bisect each other.

Therefore, the correct answer is option (1) rhombus.

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The given question is incomplete, the complete question is

Which quadrilateral has diagonals that always bisect its angles and also bisect each other?

1) rhombus

2) rectangle

3) parallelogram

4) isosceles trapezoid.

The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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Answer:

Option B.

Step-by-step explanation:

The given function is

\(f(x)=-2\sqrt{x-7}+1\)

The above function is defined if (x-7) is greater than 0.

\(x-7\geq 0\)

Add 7 on both sides.

\(x\geq 7\)

It is means domain of the function is \([7,\infty)\). So, -6 is not in domain.

We know that

\(\sqrt{x-7}\geq 0\)

Multiply both sides by -2. So, the sign of inequality will change.

\(-2\sqrt{x-7}\leq 0\)

Add 1 on both sides.

\(-2\sqrt{x-7}+1\leq 0+1\)

\(f(x)\leq 1\)

It is means range of the function is \((-\infty,1]\). So, -6 is in Range.

Since –6 is not in the domain of f(x) but is in the range of f(x), therefore the correct option is B.

Answer:

B

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

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