Samuel was absent for the last biology test. For those who took the test, the mean was 84.6, the median was 82, and the mode was 88. When Samuel took the test, the class mean went down to exactly 84. His score was different from every other students’ score. What effect, if any, did Samuel’s score have on the class mode?

A: None; the mode stayed the same.
B: It decreased the mode by exactly 1 point.
C: It increased the mode by exactly 1 point.
D: It increased the mode by greater than 1 point.
E: The effect of Samuel’s score on the mode cannot be determined from the given information.

The total number of different combinations is 120.

What is combination and permutation?

We are to find the number of different combinations of classes does Sylvia have to choose from.

We will be using  the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:

  nCr  = n!/r!( n - r )!

Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be

    ⁴C₁ * ²C₁  *  ³C₁  *  ⁵C₁  

= 4!/1!( 4 - 1 )!  × 2!/1! ( 2 - 1 )!  ×  3!/1! ( 3 -1)!  × 5!/1! ( 5 - 1 )!

= 4 × 2 × 3 × 5

= 120

Thus, the total number of different combinations is 120.

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The value of x is 14 °

The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.

In ΔOPQ,

∠O = (2x- 5)°

∠P = (3x-8)°

∠Q= (10x- 17)°

Thus by angle sum property of triangle we know:

∠O+ ∠P + ∠Q = 180

thus 2x - 5 + 3x - 8 + 10x - 17 = 180

15x - 30 = 180

= 15 x = 180 + 30

= 15 x = 210

= x= 210 / 15

= x = 14 .

Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °

∠P = (3x-8)° = 3× 14 - 8 = 44°

∠Q= (10x- 17)° = 10 × 14 - 17 = 123°

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The difference between of the cost of the phones in the USA and the UK is $51. 2

Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.

It is also known as the rate at which a currency is exchanged to another currency

From the information given, we have that;

We also have that;

The exchange rate is expressed as;

£1 = $1.36

Now, let's convert the cost from dollars to euros, we have;

If £1 = $1.36

Then, £920 = $x

cross multiply, we have;

x = 920 × 1. 36

x = $1251. 36

Now, let's find the difference between the cost in the USA and UK, we have;

=  $1251. 36 - $1200

= $51. 2

Hence, the difference is $51. 2

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Answer:

C

Step-by-step explanation:

Since the y-coordinates of both points are -3, the equation is [tex]y=-3[/tex].

The only option with a y-coordinate of -3 is option C.

The distance that the person bike over the past 5 weeks is 7284 feet.

Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered. Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

From the information, the forest trail is 607 feet long and a person biked from one end to the other and back again 6 times in the past 5 weeks.

Therefore, the distance that the person covered will be:

= 2 × 6 × 607

= 7284 feet.

The distance is 7284 feet.

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The circumference of the circle will be given by 62.84 cm.

A circle is a closed figure having a fixed point known as center of the circle and the distance from the center to any point on the boundary of circle is known as the radius of the circle. Circumference is the total length of the boundary of the circle. The circumference of the circle is given by the formula

C = 2πr where r is the radius of the circle and the value of π is given as 3.142.

Now, according to question r = 10cm

C = 2×3.142×10

C = 20×3.142

=> C = 62.84 cm

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Following the descriptions of the relationship existing  between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d

Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.

Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.

Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.

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In the picture there are 4 graphs.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

Given that,

In the picture there are 4 graphs.

We have to find the domain and range of the each function using inequality or set-builder notation.

A function's domain is the set of values that we are allowed to enter into our function.

This set consists of the values of the x-axis for a function like f. (x).

The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

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Answer: I think the answer is $1.21

Step-by-step explanation: Instead of 3 pairs it says 3 dozen. A dozen is 12.

3 x 12 = 36

Then you should do 43.56 / 36

For one pair of gloves it should be $1.21

The contractor got $14.52 because he did a dozen (12) divided by 43.56.

I hope that helps! ^^

The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.

Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.

Where P exists at the origin and line segment is a horizontal one.

The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).

The segment exists not a horizontal or vertical line:

The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].

Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).

where neither P nor Q exists at the origin.

Use the end points of the segment PQ to estimate the components of the directed segment.

[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]

= (6,-4)

The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are

[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]

To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.

Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

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Answer:

J(18)-9

Step-by-step explanation:

j times 18 minus 9

The inequality which correctly represents the fact that the spending limit cannot be exceeded as described in the task content is; 100x ≤ 200.

It follows from the task content that the inequality which correctly represents the spending limit as described be determined.

Since the given spending limit is; $200.

Let, x = the number of figures made.

Therefore, the cost of making x number of figures can be written algebraically as; 100x.

Hence, since it costs $100 to make each figure, it follows that the required inequality is;

100x ≤ 200.

This follows from the fact that each figure costs $100 to make.

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Answer: 12.8x2

Step-by-step explanation:

Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².

The correct answer option is option a.

This is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.

For instance, from the task which is given above;

3.2x and 4x

= 3.2x × 4x

= 12.8x²

In this answer above,

12.8 is the coefficient and

x² is the variable.

In conclusion, 3.2x × 4x will give the result 12.8x².

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Answer:

See below

Step-by-step explanation:

99.87-71 = 28.81     this is   28.81/12 = z-score = +2.4

   corresponding to .9918  ( from z-score table)  =  a score of 99.18%

We have that the area of the infield is 81 in2.

This area is a square, which means it has equal sides, and its area is:

If the area of the square is 81 in2, we have that:

So the side of the infield is 9 inches.

The two column proof of the given angles are;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

Statement 4; x = 28°

Reason 4; Algebra

From the attached image, we can complete the two column proof as follows;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

From statement 3, we can use algebra to find x as;

x + 3x + x + 12 = 152

5x + 12 = 152

5x = 152 - 12

5x = 140

x = 28°

Thus;

Statement 4; x = 28°

Reason 4; Algebra

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Answer:

MP = 19

Step-by-step explanation:

MP = MN + NO + OP

we require to find OP and MN before we can evaluate MP

NO + OP = NP , that is

8 + OP = 15 ( subtract 8 from both sides )

OP = 7

and

MN + NO = M0 , that is

MN + 8 = 12 ( subtract 8 from both sides )

MN = 4

Then

MP = MN + NO + OP = 4 + 8 + 7 = 19

For given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'

Part A:

We need to write the converse to the conditional statement.

The converse of given conditional statement would be:

'If it is a television, then the object has a remote.'

Part B:

We need to write a biconditional statement from the conditional statement.

A biconditional statement of the given conditional statement would be:

'The object has a remote if and only if it is a television.'

Part C:

We need to validate the above biconditional statement.

The biconditional statement is true because the conditional statement and the converse are true.

Therefore, for given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

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The solution set of the given inequality is:

9.52  ≤  x  ≤ 22.22

Or [9.52, 22.22] if we write this as an interval.

Here we have the inequality:

200 ≤ 15.75x + 50 ≤ 400

Which represents Kali's earning potential.

To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:

200 - 50 ≤ 15.75x + 50  - 50 ≤ 400 - 50

150 ≤ 15.75x ≤ 350

Now we need to divide both all by 15.75, so we get:

150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75

9.52  ≤  x  ≤ 22.22

This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]

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After using translation the image of the given points will be at Q( 6 , 6 ) and  M( -2 , -11 ).

What is translation ?

The linear movement of a point relative to its initial position is known as translation. The horizontal position is labeled first and the vertical position is labeled second when describing a point's coordinates with respect to the origin of an x-y coordinate plane.

The translation is given to be (x,y) → (x + 1, y - 3)

The tow points are Q(5,9), M(-3,-8)

using translation  we get,

Q( 5 , 9 ) → (5 + 1, 9 - 3) = Q( 6 , 6 )

M( -3 , -8 ) → (-3+ 1, -8- 3) = M( -2 , -11 )

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The rate of change of the level of the swimming pool is -0.019 inches per hour.

The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.

We know that the change happens between 10 pm and 7:45pm, so the number of hours is:

2 hours + 7 hours + 45 min

Where:

1 hour  = 60 min

45 min = 45/60 hours = 0.75 hour

Then the total time is:

2h + 7h + 0.75h = 9.75h

Then the rate of change is:

R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.

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Answer:

answer is B

Step-by-step explanation:

Sorry if this is incorrect

Answer:

A. -11x + 7y

Step-by-step explanation:

4y - 9x + 3y - 2x

4y + 3y = 7y

-9x - 2x = -11x

-11x + 7y

I hope this helps!

The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.

The formula for the height of the projectile can be used to calculate the hang time as follows;

h = ut - 0.5at²

here;

h is the height of the projectile

u is the velocity = 7.3 m/s

a is the acceleration due to gravity

The standard value of acceleration due to gravity is equal to 9.81 m/s²

The height will be zero both the times when t=0 and when the journey has been completed

Now adding these values to the formula;

h = ut - 0.5at²

0 = 7.3t - 0.5(9.81)t²

Solving for t;

4.905t² = 7.3t

4.905t² / t = 7.3

4.905t = 7.3

t = 7.3 / 4.905

t = 1.49 ≈ 1.5

Therefore; the hang time is calculated to be 1.5 seconds.

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Answer:

Circumference 87.92 ft

Step-by-step explanation:

You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.

14×2=28

28×3.14=87.92