The table shows the age and grade level of a sample of children in a club.

Create a scatter plot that represents the data that is shown in the table. The x-axis represents the child's age, and the y-axis represents the child's grade level.

The first four terms of the sequence defined by the formula an = -221 + 200n are: -21, 179, 379, and 579.

To find the first four terms of the sequence defined by the formula an = -221 + 200n, we can substitute the values of n from 1 to 4 into the formula and evaluate the expression.

When n = 1:

a1 = -221 + 200(1)

a1 = -221 + 200

a1 = -21

So, the first term of the sequence is -21.

When n = 2:

a2 = -221 + 200(2)

a2 = -221 + 400

a2 = 179

The second term of the sequence is 179.

When n = 3:

a3 = -221 + 200(3)

a3 = -221 + 600

a3 = 379

The third term of the sequence is 379.

When n = 4:

a4 = -221 + 200(4)

a4 = -221 + 800

a4 = 579

The fourth term of the sequence is 579.

Therefore, the first four terms of the sequence defined by the formula an = -221 + 200n are: -21, 179, 379, and 579.

Each term in the sequence is obtained by substituting the corresponding value of n into the formula and evaluating the expression. As n increases, the terms of the sequence increase by 200 each time.

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The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer: D

Step-by-step explanation:

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.

Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).

To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.

After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.

In conclusion, it is represented by the equation y = -x + 3.

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Answer:

Step-by-step explanation:

a + c = 257

12a + 8c = 2576

-12a - 12c = -3084

12a  + 8c = 2576

-4c = -508

c =  127 children tickets

a + 127 = 257

a = 130 adult tickets

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Step-by-step explanation:

we need the greatest or largest common factor (LCF) to find how many bags.

method prime factorization :

beginning with 2 we divide the number as often as possible by the current prime number until there is a remainder. then we use the next higher prime number and do the same.

when we reach 1 as final result, the process ends.

135 ÷ 2 not possible, going to 3

135 ÷ 3 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 not possible, going to 5

5 ÷ 5 = 1 end

135 = 3×3×3×5

495 ÷ 2 not possible, going to 3

495 ÷ 3 = 165

165 ÷ 3 = 55

55 ÷ 3 not possible, going to 5

55 ÷ 5 = 11

11 ÷ 5 not possible, going to 7

11 ÷ 7 not possible, going to 11

11 ÷ 11 = 1 end

495 = 3×3×5×11

315 ÷ 2 not possible, going to 3

315 ÷ 3 = 105

105 ÷ 3 = 35

35 ÷ 3 = not possible, going to 5

35 ÷ 5 = 7

7 ÷ 5 not possible, going to 7

7 ÷ 7 = 1 end

315 = 3×3×5×7

the LCF is the longest sequence of prime factors the numbers have in common.

so, again, the numbers as prime factors in comparison :

135 = 3×3×3×5

495 = 3×3×5×11

315 = 3×3×5×7

they have in common

3×3 and 5

the LCF = 3×3×5 = 45

so, she can make max. 45 treat bags.

each bag will contain

135/45 = 3 pieces of candy A

495/45 = 11 pieces of candy B

315/45 = 7 pieces of candy C

you notice, how these numbers are exactly the remaining factors of the prime factoring ? it is not a coincidence ...

notice that 45 is the maximum number of treat bags.

following the prime factor combinations she could also create fewer treat bags (but with correspondingly more content).

she could create also

1 or

3 or

5 or

9 or

15

treat bags.

By using Pythagoras theorem we get the height of the roof of dog house is 21 inches.

The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. 

This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. born. 

According to the question:

Given, Hypotenuse(h) = 29 inches

           Base(b) = 40/2 = 20 inches

Using Pythagoras theorem, we get

h² = b² + p²

⇒ 29² = 20² + p²

⇒ p² = 29² - 20²

⇒ p² = 841 - 400

⇒ p² = 441

⇒ p = √441

⇒ p = 21

∴ The height of the roof of dog house is 21 inches.

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Answer and Step-by-step explanation:

The answer would be

CB ≅ AB

Because these parts of the shape match up and are proven congruent by CPCTC. And, if you were to look at the other pairs of sides given as answer choices, they don't look nearly the same.

#teamtrees #PAW (Plant And Water)

Area of base triangle = 1/2×base×height

Area of base= 8×6×1/2= 24cm²

Area of prism = Bh = 24 × 12 = 288cm³

Answer:

Solution given:

base[b]=6cm

height [h]=8cm

length[l]=12cm

volume of a prism=area of triangle *length

=½*b*h*l=½*6*8*12=288cm³

is a required answer.

If we round up, we get x = 12, which means that 12 students took history and 36 students took mathematics.

A Venn diagram is a graphical representation of sets, often used to show relationships between different sets of data. It consists of one or more circles, where each circle represents a set. The circles are usually overlapping to show the relationships between the sets. The region where the circles overlap represents the elements that belong to both sets. The non-overlapping parts of each circle represent the elements that belong to only one of the sets.

Here,

A. To illustrate the data on a Venn diagram, we need to draw two overlapping circles, one for history and one for mathematics. We can label the regions as follows:

The region where the circles overlap represents the students who took both history and mathematics.

The region outside both circles represents the students who did not take either history or mathematics.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history.

In this diagram, let's assume that x students took history and 3x students took mathematics. Then the total number of students who took the examination is x + 3x = 4x. We can label the regions on the diagram accordingly:

The region where the circles overlap represents the students who took both history and mathematics. Since there are 3x students who took mathematics, and all of them are included in the overlap region, the number of students who took both is 3x.

The region outside both circles represents the students who did not take either history or mathematics. Since there are 46 students in total, and 4x of them took the examination, the number of students who did not take either is 46 - 4x.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics. Since x students took history, and 3x took mathematics, the number of students who took history but not mathematics is x - 3x = -2x. However, since we cannot have a negative number of students, we can assume that this region is empty.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history. Since there are 3x students who took mathematics, and some of them also took history, the number of students who took mathematics but not history is 3x - 3x = 0. Therefore, this region is also empty.

B. We know that the total number of students who took the examination is 46. Therefore, we have:

x + 3x = 46

4x = 46

x = 11.5

However, since x represents the number of students who took history, it must be a whole number. Therefore, we can round x up or down to the nearest whole number. If we round down, we get x = 11, which means that 11 students took history and 33 students took mathematics.

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The set of values of k for which the curve y = (k + 1) x² - 3x + (k + 1) lies below the X axis is k > 1/2 and k < -5/2.  

Quadratic functions are polynomial functions of second degree.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given function is y = (k + 1) x² - 3x + (k + 1).

If the curve lies below the X axis, then the curve will not touch the X axis.

This means that, there will be no zeroes for the quadratic function.

So the discriminant will be negative.

Discriminant = \(\sqrt{b^{2}-4ac }\) , for f(x) = ax² + b x + c.

So, for the function given,

Discriminant = \((-3)^{2} -[4*(k+1)*(k+1)]\)

                     = \(9-4(k+1)^{2}\)

                     = 9 - 4(k² + 2k + 1)

                     = 9 - 4k² - 8k - 4

                     = -4k² - 8k + 5

-4k² - 8k + 5 < 0

4k² + 8k -5 > 0

Find the zeroes of 4k² + 8k - 5.

Zeroes are, k = [ -8 ± \(\sqrt{8^2-(4*4*-5)}\) ] / (2 × 4)

                      = [ -8 ± \(\sqrt{144}\) ] / 8

                      = [-8 ± 12] / 8

Zeroes are k = 4/8 = 1/2 and k = -20/8 = -5/2

4k² + 8k -5 = 0 when k = 1/2 and k = -5/2

4k² + 8k -5 > 0, when k > 1/2 and k < -5/2

Hence the values of k are k > 1/2 and k < -5/2 for which the function lies below the X axis.

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Answer:

5w^2 + 6w - 32

Step-by-step explanation:

Subtract as needed and combine like terms

(-2w^2 + 6w - 19) - (-7w^2 +13) dont forget to distribute the negative

so you get this:

-2w^2 + 7w^2 = 5w^2

6w

-19 - 13 = - 32

your answer is 5w^2 + 6w - 32

hope this helps :)

Hi :)

Let's solve by combining like terms

Combining like terms means you add or subtract

Solve by combining like terms

\(\implies\darkblue\sf{-2w^2+6w-19-(-7w^2+13)}\\\implies\darkblue\sf{-2w^2+6w-19+7w^2-13}\\\implies\darkblue\sf{-2w^2+7w^2+6w-19-13}\\\implies\darkblue\sf{\underline{5w^2+6w-32}}\)

\(\tt{Learn\:More;Work\:Harder}\)

:)

Answer:

7.19 per pair

Step-by-step explanation:

Take the total cost and divide by the number of pairs of gloves

$21.57/3 pairs

7.19 per pair

Answer:

$7.19

Step-by-step explanation;

The collective price of the gloves of 21.57. Assuming there is no additional cost for packaging, one will simply have to divide the collective price of the gloves by the amount of gloves to find the unit price of the gloves.

21.57 / 3 = 7.19

Answer:

26

explination

10^2+24^2=26^2

Answer:

15 Hours

Step-by-step explanation:

259miles = 7 hours

555miles = x

Cross Multiply

259x = 555×7

259x = 3885

Divide Both sides by 259

x = 3885 ÷ 259

x = 15 hours

It would take the driver 15 hours to get to Atlanta

Answer:

Flower Bed A is the 3rd on down

C=10pi,  A = 25pi

Flower Bed B is the 5th one down

C=12pi, A=36pi

9514 1404 393

Answer:

  A) 10π ft; 25π ft²

  B) 12π ft; 36π ft²

Step-by-step explanation:

The circumference is given by ...

  C = πd = 2πr . . . . . . . . . . for radius r or diameter d

The area is given by ...

  A = πr² = (π/4)d²

__

A) For a diameter of 10 ft, the circumference is π(10 ft) = 10π ft.

The area is (π/4)(10 ft)² = 25π ft².

__

B) For a radius of 6 ft, the circumference is 2π(6 ft) = 12π ft.

The area is π(6 ft)² = 36π ft².

Answer:

D

Height of marble from the ground

Explanation:

Dora wanted to see whether the position of the marble on the ramp (which would be the height) has an effect on the kinetic and potential energy of the marble, then the height would be the independent because it is what is being changed. An independent variable is the variable in an experiment that you change to see if it has an effect on the dependent variable.

The dependent would be the kinetic and potential energy and the constant would be the type of marble.

Answer:hiofhcjcuchc

Step-by-step explanation:

Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

Answer:

Option D

Step-by-step explanation:

We have that:

csc(x) = 1/sin(x)

Then:

csc(  tan(√(17)/8)^-1 )

To use the inverse tangent function, you can go to the "inv" button in your calculator, and then use go to the "tan" button.

This is equal to:

= csc( 27.26°)

= csc(27.26°)

= 1/sin(27.26°) = 2.18

And we know that:

(9*√17)/17 = 9/√17 = 2.18

Then the correct option is D.

To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.

The volume of the house can be found by multiplying the square footage by the ceiling height:

1,400 sq ft x 9 ft = 12,600 cubic feet

Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

Two polygons are similar if the ratio of their corresponding sides are in the same proportion. Hence:

Similarity ratio of STUV to GFIH = TU / GH = 5 / 1

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

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Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

Mason recieved 15 points for answering the question correctly so that means that he had -15 points before. The points would be at -15 and 0.

0 and -15 because he is at 0 after the question so he would have been in the negatives before the question. He would have been at -15 before the question.

Answer:

option D

Step-by-step explanation:

\(sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1\)

Explanation:

\(sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\\)

            \(=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1\)

Therefore ,

               \(sin^2( \frac{3\pi}{2}) = ( - 1)^2\)