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Heath had the longest jump of 6 meters in the competition.

Comparison theory is a psychological theory that proposes that people use social comparisons to better understand their own value and place in society. According to this hypothesis, people compare themselves to others in order to assess themselves, typically focusing on the traits that they have and the qualities that other people have. Individuals utilise the comparison to estimate their own value and how they should conduct in order to achieve approval and acceptance from their peers.

This question requires the use of the Comparison Theory.

This theory states that when presented with two or more items, we can compare them to determine which is larger, smaller, longer, shorter, etc.

In this case, we need to compare the distances of each jump for each teammate in order to determine which one had the longest jump.

Step 1: Look at the distances of each jump for Heath.

Step 2: Look at the distances of each jump for Amari.

Step 3: Compare the distances of each jump for both Heath and Amari.

Step 4: Determine which jump was the longest - Heath's 6 meter jump.

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Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.

The open seats in the front row can be filled by the remaining 5 students in 5! ways.

The open seats in the back row can be filled by the remaining 5 students in 5! ways.

So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400

Step-by-step explanation:

By means of angle properties and algebra properties, the measure of the missing angle equals 136°.

In this problem we find the representation of two consecutive angles, whose sum of measures equals 180°. The measure of an angle is equal to 44° and the measure of the other one must be determined by using the following algebraic expression:

m ∠ x + 44° = 180°

Now we proceed to solve the expression by algebra properties:

m ∠ x = 180° - 44°

m ∠ x = 136°

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The ratio of their shares is 1:2:3 and amount is 180.5, 3564, 5371.5 respectively.

To find the amount each received:

Atta received 13.5*(51+110) = 1807.5

Abena received 27*(51+110) = 3564

Kojo received 40.5*(51+110) = 5371.5

The total amount shared is 51 + 110 = 161

The ratio of their shares is 1:2:3, meaning Atta receives 1/6 of the total amount, Abena receives 2/6 of the total amount, and Kojo receives 3/6 of the total amount.

To find the amount each received, we multiply their respective share (1/6, 2/6, and 3/6) by the total amount (161)

Kojo received 3 times as much as Atta, and Atta received 1/2 times as much as Abena.

Atta received 1/6 of the total amount, which is (51 + 110)/6 = 81/6 = 13.5

Abena received 2/6 of the total amount, which is (51 + 110)*2/6 = 162/6 = 27

Kojo received 3/6 of the total amount, which is (51 + 110)*3/6 = 243/6 = 40.5

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Size of x = 102°

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

Given,

In triangle ABC

Sum of interior angles is 180°

∠CAB + ∠ABC + ∠BCA = 180°

87° + ∠ABC + 36° = 180°

123° + ∠ABC = 180°

∠ABC = 180° - 123°

∠ABC = 57°

In triangle DBG

Exterior angle is equal to sum of two opposite interior angles.

DGF = GDB + DBG

DGF = GDB + ABC

DGF = 45° + 57°

DGF = 102°

DGF and EFC are alternate angles made by EF and DG on BC

∴ EFC = DGF

x = 102°

Hence, 102° is size of x.

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The value of x  when y = 10 and Z = 16, in the given joint variation is: 1120.

If X varies jointly with Y and Z, then we can use the formula X = k * Y * Z, where k is the constant of proportionality.

Using the given information, we can find k by plugging in the values of Y, Z, and X and solving for k:

14 = k * 2 * 4

k = 14 / (2 * 4)

k = 7/2

Now that we know the value of k, we can use it to find the value of X when Y = 10 and Z = 16:

X = k * Y * Z

X = (7/2) * 10 * 16

X = 70 * 16

X = 1120

So the value of X when Y = 10 and Z = 16 is 1120.

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According the diagram, Alyssa trying to solve the problem 4 5/8 - 1 7/8. So the option C is correct.

Alyssa draws the following model to solve a problem.

We can see on the diagram that there have lock of two colors red and black. Some block are cut in both colors.

The total block of red color = 3

The total block of black color = 13/8

So the total block = 3 + 13/8

The total block = (24 + 13)/8

The total block = 37/8

The total block = 4 5/8

The block cut in color red = 1

The block cut in color black = 7/8

Total cut block = 1 + 7/8

Total cut block = (8 + 7)/8

Total cut block = 15/8

Total cut block = 1 7/8

So the problem should be

= The total block - Total cut block

= 4 5/8 - 1 7/8

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The complete question is given below:

Step-by-step explanation:

A right triangle is a triangle that has one angle that measures 90 degrees. Based on the information provided, the following triangles are right triangles:

Triangle A - OA. 55° and 70° are not right angles

Triangle B - OB. 30° and 60° are not right angles

Triangle C - O C. 45° and 45° form a right angle

Triangle D - OD. 60° and 60° form a right angle.

SAA is a mnemonic for solving the triangle, not a triangle itself

24°, 45°, and 126° are not angles that form a triangle as the sum of all angles in a triangle is 180.

Step-by-step explanation:

The f O U r M U la is 72inc hes

Designs have the same fractions o black and white is 16/2

Given,

Four student, each with 2 distinct colors, and no two subsequent flag may share the same color. Hence, the first stripe may be colored in any of 4 different ways.

The second student can be colored in 4 different ways after it is not the same color as the first.

The third flag should not be the same color as the second; it can be colored in 4 different ways.

The fourth flag should not be the same color as the third, allowing for a total of 4 different color combinations. total = 4 * 2  * 2 = 16

designs have the same fractions o black and white is 16/2

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Answer:

Shown Below

Step-by-step explanation:

The difference between the two polynomials 3x^2-4x-5 and 2x^2-7x-3 is the result of subtracting the second polynomial from the first one.

3x^2 - 4x - 5 (first polynomial)

(subtraction operator)

2x^2 - 7x - 3 (second polynomial)

= x^2 - 3x - 2 (difference)

So the difference between 3x^2-4x-5 and 2x^2-7x-3 is x^2 - 3x - 2

This is a polynomial with a degree of 2 (quadratic) and the coefficient of x^2 is 1, x is -3 and the constant is -2.

Answer: 30

Step-by-step explanation: 600/20=30 so each inch on the scale represents 30 feet in real life.

Answer:

12 inches

Step-by-step explanation:

Use a proportion.

1 inch is to 8 yards as x inches is to 96 yards

1/8 = x/96

Cross multiply.

8x = 96

x = 12

Answer: 12 inches

Answer:

11.6%

Step-by-step explanation:

First, we have to find how much it increases

48 - 43 = $5

We know it increases by $5

Then we take

5 divided by 43, then times 100 = 11.6%

So, it increases 11.6%

There are 6 possible outcomes for this experiment.

The total number of outcomes possible for an experiment of drawing two balls one after the other without replacing the first ball, depends on the number of possible outcomes for the first draw, multiplied by the number of possible outcomes for the second draw, given that the first ball was not replaced.

The total number of ways to choose one ball out of three is 3, and the number of ways to choose the second ball out of two remaining balls is 2. Therefore, the total number of outcomes possible for this experiment is 3 x 2 = 6.

The possible outcomes are:

(Red, Purple), (Red, Blue), (Purple, Red), (Purple, Blue), (Blue, Red) and (Blue, Purple)

It's important to notice that this method is called the Multiplication Rule for counting the total number of outcomes of two or more independent events.

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After applying the sales tax, the expression for the total price of the phone is 1.03p.

What is sales tax?

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.

The amount for phone is represented as - p dollars and cents

The sales tax percentage is - 3% = 0.03

The sales tax applied on the phone is - 0.03p

The total price of the phone is denoted by the expression -

Total Price = Price of phone + Sales Tax

Total Price = p + 0.03p

Total Price = 1.03p

Therefore, the total price is obtained as 1.03p.

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Answer:

c, 64 percent

Step-by-step explanation:

3+3+10+9=25

25-9(yellow)=16

25/16=64

Answer: D: 64%

Step-by-step explanation: 3 + 3 + 9 + 10 = 25, 3 + 3 + 10 = 16 (Alternative: 25 - 9) 16 / 25 = 64. So the answer is 64%

Answer: A function that increases by a factor of 10 over every unit interval in x and starts at f(0)=1 could be represented by the function rule f(x) = 10^x.

This function starts at f(0) = 10^0 = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. For example:

f(1) = 10^1 = 10

f(2) = 10^2 = 100

f(3) = 10^3 = 1000

and so on.

Another possible function rule could be f(x) = 10x +1 it starts at f(0) = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. for example:

f(1) = 101 +1 = 11

f(2) = 102 +1 = 21

f(3) = 103 +1 = 31

and so on.

Both functions have similar behavior and answer the given conditions.

Step-by-step explanation:

The cost of making 60 triangular flags with base 3.5feet and height 2.5 feet with making charges of $0.40per square foot  is equal to $105.

Flag is triangular in shape.

Base of the flag = 3.5 feet

Height of the flag = 2.5feet

Area of the flag = ( 1/2) base × height

                          = ( 1/2 )× ( 3.5 ) × ( 2.5)

                          = 4.375 square feet.

Cost of one square foot flag = $0.40

Cost of making one flag = $ ( 0.40 ×  4.375 )

                                        = $ 1.75

Cost of making 60 flags =  $ ( 1.75 × 60 )

                                        = $ 105.

Therefore, the cost of making 60 triangular flag is equal to $105.

The given question is incomplete, I answer the question in general according to my knowledge:

You make and sell triangular flags. Each flag has a base of 3.5 feet and a height of 2.5 feet. Fabric for the flags costs $0.40 per square foot. What is the cost to make 60 flags?

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Answer: b) ? · 2 5= 4

d) 4 ÷ 2 5= ?

e) ? ÷ 2 5= 4

The equations that represent the situation are b) ? · 2 5= 4 , d) 4 ÷ 2 5= ?, e) ? ÷ 2 5= 4

The question is asking for an unknown quantity and it is asking to find it by using the 4 and 25, so the equations that represent the situation are the ones that have 4 and 25 in them and have the unknown quantity on one side of the equation and the known quantity 4 on the other side.

a) 4 · 2 5= ? is not a valid equation as it is asking to multiply 4 and 25, which is known and doesn't have any unknown quantity.

c) 2 5÷ 4 = ? is also not a valid equation as it is asking to divide 25 by 4 and doesn't have any unknown quantity.

Step-by-step explanation:

By simplifying  45y/30y (7x+49)  this  we get 3 / 2(7x + 49).

45y/30y (7x+49)

45y / 30y(7x +49) : 3 / 2(7x + 49)

45y / 30y(7x + 49)

45y / 30(7x + 49)

Factor the number :45 = 15 . 3

=15.3 / 30(7x + 49)

Factor the Number : 30 = 15 . 2

15.3 / 15.2(7x + 49)

Cancel the common factor : 15

= 3 / 2(7x + 49).

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You may not cross a single broken white or yellow line, when doing so would interfere with traffic unless it is safe to do so and without interfering with traffic.  

The yellow line on the road serves as a barrier between opposing lanes of traffic as a traffic safety measure. It is intended to alert drivers to the fact that they are moving in the opposite directions and should keep a safe distance while driving.

The yellow line is typically placed in the centre of the road to indicate the separation of traffic. On highways and interstates, the yellow line is frequently used to mark the separation between two lanes of traffic moving in the same direction.

Drivers should always follow the yellow line and never cross it because doing so can be risky and result in accidents. The yellow line can also be used to show when passing other vehicles is dangerous.

On the driver's side, it is prohibited to pass other cars when a yellow line is interrupted by a solid line. Overall, the yellow line is an important safety measure for drivers to be aware of and obey when on the road.

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Answer:

A quadratic equation of the form ax^2 + bx + c = 0 has solutions (or roots) that are either real or complex. The solutions of the equation vanish (or become equal to zero) when the equation is equal to zero.

For the equation x^2 (2p-4)x-(3q5)=0 to have a solution that vanishes, the discriminant (b^2 - 4ac) must be equal to zero.

Therefore, the roots of the quadratic equation x^2 (2p-4)x-(3q5)=0 vanish when p = 4 and q = 0

The resulting equation: 3x - 2 = 3x - 5

This equation does not have any true answer, meaning either the question asked is wrong or you have typed this equation wrong.

The only answer you could write for this is No Solution.

Yes I can receive the radio signals.

The graph that represents the situation is given in the attached image.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A gymnast joined a yoga studio to improve his flexibility and balance.

He pays a monthly fee and a fee per class he attends.

The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

The graph of the linear equation is given in the attached image.

And the graph that is equivalent to the graph is also given in the attached image.

Therefore, the equivalent graph is given in the attached image.

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Volume of the cone with height 18 meters and radius 'r' is given by :

a. Equation to represents the volume of the cone is 6πr²( cubic meters).

b. Three possible examples:

r    (meters )         :       2        4        6

V (cubic meters ) :     24π     96π    216π

Height 'h' of the cone is 18meters.

Radius of the cone is 'r' meters.

a. Equation to represents volume of a cone as function 'r'

Volume 'V' of the cone is = ( 1 / 3 )π ×r² × h

Substitute value h = 18 meters we get,

V = ( 1 / 3 )π ×r² × 18

⇒ V = 6πr² cubic meters

b. Three possible examples for different values of 'r'

When r = 2

V = 6π × ( 2)²

⇒ V = 24π cubic meters

When r = 4

V = 6π × ( 4)²

⇒ V = 96π cubic meters

When r = 6

V = 6π × ( 6)²

⇒ V = 216π cubic meters

Therefore, the required volume of the cone with radius 'r' and height 18meters is:

a. Equation to represents volume is 6πr².

b. Table completion:

r    (meters )         :       2        4        6

V (cubic meters ) :     24π     96π    216π

The above question is incomplete , the complete question is:

There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.

a. Write an equation that represents the volume V as a function of the radius r.

b. Complete this table for the function, giving three possible examples.

r :  2     _    _

V: ?     ?      ?

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Period of deferral in the deferred annuity = 3 periods or 3 quarters.

Given: Quarterly payment of 300 for 9 years that will start 1 year from now.

To find the Period of deferral in the deferred annuity.

A deferment period is an agreed-upon time during which a borrower does not have to pay the lender interest or principal on a loan.

Solution: Formula for Period of deferral

K = nt - 1

K- Period of deferral

n- number of times compounded

t- time of start

K= nt - 1

K= 4(1) - 1

K= 3

Period of deferral = 3 periods / 3 quarters.

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Answer:

hypotenuse = 14.8

Step-by-step explanation:

Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

[tex]3.2^2 + 14.4^2 = c^2\\10.24 + 207.36 = c^2\\\sqrt{217.6} = c\\c = 14.751...\\c = 14.8[/tex]

Answer:2x

Step-by-step explanation:

Answer: the correct answer would be 2x

Step-by-step explanation: