Using Function Notation
The mapping diagram shows a functional relationship.
Domain
Range
82
I WINDO
11
4
43
12
Complete the statements.
f(4) is
f(x) = 4 when x is

[tex]Answer:\ a_n=34-8n[/tex]

Step-by-step explanation:

26, 18, 10, 2

18-26=-8

10-18=-8

2-10=-8

This is an arithmetic progression:

[tex]a_n=a_1+(n-1)d,\\a_1=26\ \ \ \ \ d=-8\ \ \ \ n=1,\ 2,\ 3,\ 4\\a_n=26+(n-1)(-8)\\a_n=26+(n)(-8)+(-1)(-8)\\a_n=26-8n+8\\a_n=34-8n[/tex]

ΔJKL has 53.28 units of side length.

So,

The formula for the perimeter of the side of a triangle: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, each side of the triangle will be: 53.28 units

Therefore, ΔJKL has 53.28 units of side length.

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The solution of t in 100 t=70 /240 is t= 7/2400

The equation is given as

100 t=70 /240

Divide both sides of the equation by 100

So, we have

t=70 /240 * 1/100

Evaluate

t= 7/2400

Hence, the solution of t in 100 t=70 /240 is t= 7/2400

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Answer:

see explanation

Step-by-step explanation:

1

(5p² - 3) + (2p² - 3p³) ← remove parenthesis

= 5p² - 3 + 2p² - 3p³ ( collect like terms , largest exponent first )

= - 3p³ + 7p² - 3

2

(a³ - 2a²) - ( 3a² - 4a³) ← distribute second parenthesis by - 1

= a³ - 2a² - 3a² + 4a³ ( collect like terms, largest exponent first )

= 5a³ - 5a²

3

(- 4[tex]k^{4}[/tex] + 14 + 3k²) + (- 3[tex]k^{4}[/tex] - 14k² - 8) ← remove parenthesis

= - 4[tex]k^{4}[/tex] + 14 + 3k² - 3[tex]k^{4}[/tex] - 14k² - 8 ← collect like terms, largest exponent first

= - 7[tex]k^{4}[/tex] - 11k² + 6

4

(3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex]) - (- 6[tex]n^{4}[/tex] - 3n - 8[tex]n^{5}[/tex]) ← distribute second parenthesis by - 1

= 3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex] + 6[tex]n^{4}[/tex] + 3n + 8[tex]n^{5}[/tex] ( collect like terms, largest exponent first )

= 2[tex]n^{5}[/tex] - 2[tex]n^{4}[/tex] + 3n + 3

5

(y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex]) + (- 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] ) - (  [tex]x^{4}[/tex]y³ + 6[tex]x^{4}[/tex][tex]y^{4}[/tex])

remove parenthesis from first 2 and distribute third by - 1

= y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] - [tex]x^{4}[/tex]y³ - 6[tex]x^{4}[/tex][tex]y^{4}[/tex]

collect like terms

note the term with the largest exponent is [tex]x^{4}[/tex][tex]y^{4}[/tex]

= (- 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 6[tex]x^{4}[/tex][tex]y^{4}[/tex] ) + (- 10[tex]x^{4}[/tex]y³ - [tex]x^{4}[/tex]y³) + (y³ + 6y³)

= - 13[tex]x^{4}[/tex][tex]y^{4}[/tex] - 11[tex]x^{4}[/tex]y³ + 7y³

The foci are placed 4 feet apart from the ellipse's center. Then the distance between the foci of the ellipse will be separated by 8 feet.

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

A major axis of 32 ft and a minor axis of 14 ft.

The major axis 2a of the ellipse will be

2a = 10 feet

a = 5 feet

The minor axis 2b of the ellipse will be

2b = 14

b = 7 feet

We must utilize the following connection to get the foci's coordinate:

b² = a² - c²

3² = 5² - c²

c² = 25 - 9

c² = 16

c = ± 4

As a result, the foci are placed 4 feet apart from the ellipse's center. As a result, the foci are separated by 4 + 4 = 8 feet.

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Given parallelogram LMNO with diagonals intersecting at point P, OP is equal to 23.

A parallelogram is a two-dimensional figure with two pairs of parallel sides. A parallelogram's pair of opposite sides are of equal length and its opposite angles are of equal measure.

The diagonals of a parallelogram bisect each other, divides each other into two equal lengths.

If the diagonals of parallelogram LMNO intersects at point P, then MP is equal to OP. If MP = 2x + 5 and OP = 3x − 4, solve for x.

MP = OP

2x + 5 = 3x − 4

5 + 4 = 3x - 2x

x = 9

Substitute the value of x to solve for OP.

OP = 3x − 4

OP = 3(9) - 4

OP = 27 - 4

OP = 23

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Answer:

All answers in explanation

Step-by-step explanation:

Step 1: Unknown
Unknown is the number of refills purchased

Step 2 Key Information
Cost of souvenir cup, price per refill and total money spent

Step 3: Strategy (equation)
Define a variable x that represents the number of refills bought

The souvenir cup cost $14.25

Each refill costs $1.25

So x refills will cost 1.25x

Total cost = 14.25 + 1.25x

We are told she spent $23

So the equation is
14.25 + 1.25x = 23

Step 4: Solution
Equation is
14.25 + 1.25x = 23

a) Isolate the x term by subtracting 14.25 on both sides

14.25 - 14.25 + 1.25x = 23 - 14.25

1.25x = 8.75

b) Divide both sides by 1.25:
1.25x/1.25 = 8.75/1.25

x = 7

Solution is 7 refills

Step 5: Check your answer
Plug x = 7 back into the left side of the equation and check if it works out to 23
14.25 + 1.25 (7) = 14.25 + 8.75 = 23

So our answer is correct

The total number of band members and dancers in the halftime show in all rows were 276.

A row is an arrangement of things in a straight line next to each other.

if there are n rows and each row has m members then total number of members = m* n

Given that marching band was in 3 sections and each section has 8 rows of  8 players , then players in each section of marching band  = 8 *8 = 64

As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192

Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.

Then, dancers in each section of  dancers = 6*7 =42

As there are two such sections, then the total dancers = 2* 42 = 84

total no of band members and dancers = 192+84 = 276

Therefore, The total number of band members and dancers in the halftime show were 276.

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Here the conjecture we can made is :

The sum of interior angles i.e. ∠A and ∠B is equal to the exterior angle at C.

The exterior angle of any triangle is defined as the angle which is at the outside boundaries of that triangle. whereas, the interior angle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle for that triangle.

In mathematics, the two angles are called as adjacent angles if they have a common vertex or we can say they are angle of a common vertex in the triangle.

we can define the adjacent angle as the angles which have common side and common vertex and they don't overlap.

According to the exterior angle property, if a side of a triangle is made, then the exterior angle formed is always equals to the sum of  two interior angles opposite to each other in the triangle.

Thus on the basis of exterior angle property we can make the conjecture that, "the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles".

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There is not enough evidence

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

For  1.5 moles substrate concentration per liter

Reaction ( n2 ) = 15 runs

average velocity ( x2 ) = 7.5 micromoles per 30 minutes

standard deviation ( s2 ) = 1.5

For 2.0 moles substrate concentration per liter

Reaction( n1 ) = 12 runs

(x1) = 8.8 micromoles on average per 30 minutes

standard deviation ( s1 )  = 1.2

Show Reason to believe that this increase in substrate conc causes an increase in mean velocity

Hypothesis test

H0 : μ1 - μ2 = 0.5

H1 : μ1 - μ2  > 0.5

significance level ( ∝) = 0.01

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Answer:

0.66 with a bar

Step-by-step explanation:

It would take the test administrator 48 seconds to allow for the performance of the task

So, if we want 97.5 percent, we must look it up in our z table. So I need to find the z score that is closest to.975, which is 1.96.

The 97.5th percentile point of the standard normal distribution is a quantity often used in probability and statistics for statistical computations. This figure is around 1.96, which means that 95% of the area under a normal curve is within 1.96 standard deviations of the mean.

As a result, the z score for the 97.5th percentile would be multiplied by the class standard deviation. As a result, we obtain;

1.96*6 = 11.76

Then, this new time gotten would be added to the first mean of the class,

As a result, we have 36+11.76 = 47.76 which is approximately 48

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The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.

Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.

If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.

n = (42.60 + 49.24)/2

n = 91.84/2

n = 45.92 seconds

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Answer:

11

Step-by-step explanation:

[tex]6+2(2+3)/2[/tex]

[tex]6 + \frac{2 * (2+3) }2}[/tex]   Cancel out 2* and the bottom 2

[tex]6+2+3[/tex]     6+2=8

 ⬇️

   8 + 3

    = 11

Answer:

50 ohms.

Step-by-step explanation:

Volts = current * resistance

110 = 2.2 * r

R = 110 / 2.2

  = 50 ohms.

Answer:

There is 2121.80 in the account after 2 years.

Step-by-step explanation:

Use the formula A = P(1 + r)^t  where P = initial amount, A = amount after t years and r = the rate (as a decimal).

So, for this problem:

Amount after 2 years = 2000(1 + 0.03)^2

= £2121.80

If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

Given that B is midpoint of AC and C is the midpoint of BD.

We are required to prove that AB is equal to CD.

Midpoint is the point which divides the line segment into two equal parts.

If B is midpoint of AC then,

2AB=AC-----1

2BC=AC-----2

If C is midpoint of BD then,

2BC=BD-----3

2CD=BD-----4

From 1 & 2

2AB=2BC

AB=BC

Put the value of BC from 3.

AB=BD/2

Now put the value of BD from 4.

AB=2CD/2

AB=CD

Hence proved

Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

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Answer:

120

Step-by-step explanation:

We start with the equation:

[tex]\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40[/tex]

We need to set the fractions into equal denominations so we can sum them all together:

[tex]\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\[/tex]

Now sum the fractions:

[tex]\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40[/tex]

Multiple both sides by 24 to eliminate denominator on left side of equation:

[tex]-8x=-960[/tex]

Divide both sides by -8 to get the value of x:

[tex]x=120[/tex]

Answer:

n=21

Step-by-step explanation:

3n-21=2n

subtract 3n from each side

-21=-1n

two negatives become a positive

Answer: BC=17

Step-by-step explanation:

AC=AB+BC

27=10+BC

27-10=10-10+BC

BC=27-10

BC=17

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.

The number 1.23 as a percentage is 123 %.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Let the number be 1.23

To find percentage multiply it by 100, we get

So, 1.23 × 100 = 123 %

Therefore, the number 1.23 as a percentage is 123 %.

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The elevator finally stopped on the 16th floor.

So, the expression would be:

Now,

Therefore, the elevator finally stopped on the 16th floor.

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Answer:

150

Step-by-step explanation:

[tex]33 = 0.22(x)\\\\\\frac{33}{0.22} =\frac{0.22(x)}{0.22} \\\\\large\boxed{x=150}[/tex]

Answer:

25 + 5x = 30 + 2x

At 5/3s of an hour is when the cost of both tubing companies are the same.

This is when the price of both companies both hit $33.33

Step-by-step explanation:

25 + 5x = 30 + 2x

move variables by subtracting

25 + 3x = 30

move constants by subtracting  

30 - 25 = 5

5 = 3x

x = 5/3

The value of r is 21 when s = -1 , t = 4 and  u = 1/5 for the equation r = 3s² + 5 (t - 2u).

Quadratic Equation:

Quadratic equations are the polynomial equations of degree 2 in one variable of type.

The general form of a quadratic equation is,

f(x) = ax² + bx + c = 0

where a, b, c, ∈ R and a ≠ 0.

‘a’ is called the leading coefficient and

‘c’ is called the absolute term of f (x).

Given,

Equation is,

r = 3s² + 5 (t - 2u).

Here we need to find the value of r when the values of s = -1 , t = 4 and  u = 1/5.

Apply the values on the given equation then we get,

=> r = 3 (-1)² + 5 ( 4 - 2(1/5))

Expand the values,

=> r = 3 (-1)² + 5( [20 -2] /5)

Here the value 5 is getting cancelled then we get,

=> r = 3(-1)² + 18

We know that the value of (-1)² = 1

So,

=> r = 3(1) + 18

=> r = 3 + 18

=> r = 21

Therefore, the value of r is 21.

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Answer: D

Step-by-step explanation:

The weight of the baby increased by a 20%

We know that the initial weight of the baby is 20 pounds, so that will be our 100%, and we can write:

20lb = 100%

Then the weight is 24 lb, so that will represent another percentage X, we can write:

24lb = X

We can solve this for X, taking the quotient between the relations:

(24lb/20lb)  = X/100%

(24lb/20lb)*100% = X = 120%

So we can see that the weight of the baby increased by a 20%

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Answer: d=90 degrees

e=69 degrees

f=111 degrees

Step-by-step explanation:

69+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.

69-69+f=180-69

f=180-69

f=111 degrees

e+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.

e+111=180

e+111-111=180-111

e=180-111

e=69 degrees

d+90=180 ==> if there is a tiny box between an angle, that means that the angle is a right angle which measures 90 degrees.

d-90+90=180-90

d=180-90

d=90 degrees

Therefore, the surface area of the tea bag is 56 cm².

The slant height of the tea bag is l.

l = 5 cm

Each edge of the base of the tea bag = 4 cm

The lateral surface area of tea is L.

The Surface area of the tea bag is S.

The perimeter of the tea bag is p.

The lateral surface of the tea bag is,

[tex]Lateral \: Surface \: Area = \frac{1}{2} \times Perimeter × Slant \: height [/tex]

[tex]L = \frac{1}{2} \times p \times l[/tex]

[tex] = \frac{1}{2} \times 16 \times 5[/tex]

= 40 cm²

The lateral surface area of the tea bag is 40 cm².

Base Area = (4) ²

= 16 cm²

The surface area of the tea bag is,

Surface Area = Lateral surface area + Base area

S= 40 + 16

= 56 cm²

Therefore, the surface area of the tea bag is 56 cm².

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