Is
7 3

a proper, an improper, a mixed number, or a decimal fraction?
a proper fraction
an improper fraction
a mixed number
a decimal number

a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.

b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.

According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.

According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.

a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]

Substitute

m∠AEB = 1/2(53 + 61)

m∠AEB = 57°

b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]

Multiply both sides by 2

2(35) = VW - 36

70 = VW - 36

Add 36 to both sides

70 + 36 = VW

VW = 106°

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The two integers are are mathematically given as

x=3.70

y=13.7

Generally, the equation for the two integers is mathematically given as

x + 10 = y

1/x + 2/y = 2/3

Substitute

1/x + 2/x+10 = 2/3

Multiply by 3

3/x + 6/x + 10 = 2

Multiply by x

2 + 6x/x + 10 = 2x

Multiply by x + 3

2(x + 10) + 6x = 2x(x + 3)

2x+20+6x=2x^2+6x

-2x^2+2x+20=0

x=3.70

hence y

x + 10 = y

3.70+ 10 = y

y=13.7

In conclusion,  the two integers are

x=3.70

y=13.7

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Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].

The range of C(x) is (200, 4,200).

The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.

The maximum capacity is given as 100 items so the domain is:

= [0, 100]

The range is:

When x is 0, the function gives C(x) as:

= 40(0) + 200

= 200

When x is the maximum of 100, the C(x) is:

= 40(100) + 200

= 4,200

Range is:

(200, 4,200)

Full question is:

What is the domain and range of C(x)?

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the information given:

Let's setup an equation for the cost

             [tex]\hookrightarrow Cost = 30 + 0.3x[/tex]

             [tex]30 + 0.3x = 55.2\\0.3x = 25.2\\x=84[/tex]

Ken must have traveled 84 miles

Answer: 84 miles

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This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

The total amount of interest that is paid for the term loan is $383,385.54

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

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Answer:

(a+b)² - 11(a+b) -42

Step-by-step explanation:

Thoughtfully split the expression at hand into groups, each group having two terms,

Group 1:  -11b-11a 

Group 2:  a2+2ab 

Group 3:  b2-42 

Pull out from each group separately :

Group 1:   (a+b) (-11)

Group 2:   (a+2b) (a)

Group 3:   (b2-42) (1)

Looking for common sub-expressions :

Group 1:   (a+b) (-11)

Group 3:   (b2-42) (1)

Group 2:   (a+2b) (a)

final answer:(a+b)² - 11(a+b) -42

Answer:

(a+b+3)(a+b-14)

Step-by-step explanation:

let a+b be x,

= x²-11x-42

=x²-(14-3)x-42

=x²-14x+3x-42

=x(x-14)+3(x-14)

=(x+3)(x-14))

replacing x by a+b,

=(a+b+3)(a+b-14)

Elena's height in centimeters is 142.24 cm.

Elena's height in meters is 1.42 meters.

The mathematical operations that would be used to determine the answers ae division and multiplication.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the operation that is used to determine the product of two or more numbers.

In order to determine the height in centimeters, first determine how many cenitmeters make 1 inch

1 inch = 254 / 100

1 inch = 2.54 cm

Now, convert 56 inches to cm : 56 inches x 2.54 = 142.24 cm

In order to determine the height in meters, first find the unit of conversion of inches to meters

1 inch = 0.0254 meters

0.0254 x 56 = 1.42 meters

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A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₀: μ ≠ 7

Next, we would calculate the t-test as follows:

[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]

t = 0.08/0.0668

t = 1.198.

For the p-value, we have:

P-value = P(t < 1.198)

P-value = 0.1262.

Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.

In conclusion, yes the mean discharge differs from 7 fluid ounces.

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The value of cos(L) in the triangle is Five-thirteenths

Right triangles are triangles whose one of its angle has a measure of 90 degrees

The value of a cosine function is calculated as:

cos(L) = Adjacent/Hypotenuse

The hypotenuse is calculated as

Hypotenuse^2 = Opposite^2 + Adjacent^2

So, we have:

Hypotenuse^2 = 12^2 + 5^2

Evaluate

Hypotenuse^2 = 169

Take the square root of both sides

Hypotenuse = 13

So, we have

Adjacent = 5

Hypotenuse = 13

Recall that

cos(L) = Adjacent/Hypotenuse

This gives

cos(L) = 5/13

Hence, the value of cos(L) in the triangle is Five-thirteenths

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Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

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Answer:

correct

Step-by-step explanation:

dividing both quantities in a ratio by the same non zero number does indeed find an equivalent ratio.

for example

60 : 36 ( divide both parts by 6 )

= 10 : 6 ← equivalent ratio ( divide both parts by 2 )

= 5 : 3 ← equivalent ratio in simplest form

in fact dividing the original by the HCF of the 2 quantities gives the ratio in simplest form immediately , that is

60 : 36 ( divide both parts by 12 )

= 5 : 3

Answer:

y = 2x² − 12x + 8

Step-by-step explanation:

FIRST METHOD :

y = 2x² − 12x + 8

  = (2x² − 12x) + 8

  = 2 (x² − 6x) + 8

  = 2 (x² − 6x + 9 − 9 ) + 8

  = 2 (x² − 6x + 9) − 2×9 + 8

  = 2 (x² − 6x + 9) − 18 + 8

  = 2 (x² − 6x + 9) − 10

  = 2 (x − 3)² − 10

Then ,the equation has a extremum value of (3,-10)

Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0

(2 > 0) , the graph (parabola) opens upward

Therefore ,the extremum (3,-10) is a minimum.

SECOND METHOD :

the graph of a function of the form f(x) = ax² + bx + c

has an extremum at the point :

[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]

in the equation : f(x) = 2x² − 12x + 8

a = 2  ; b = -12  ; c = 8

Then

[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]

Then

[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]

the graph of a function f(x) = 2x² − 12x + 8

has an extremum at the point (3 , -10)

Since the parabola opens up ,then the extremum (3,-10) is a minimum.

Answer:

9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is

55 cm long

28cm wide

cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?

Step-by-step explanation:

Answer:

13. Answer: 0

17. Answer: 3

19. Answer: 2

Step-by-step explanation:

13. f(g(3))

First find g(3) on the right graph.

We see that at x = 3, g(x) = 4

So g(3) = 4

Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer

17.f(f(5))

f(5) = 1

f(f(5)) = f(1) = 3 answer

19. g(g(2))

g(2) = 0

g(g(2)) = g(0) = 2 answer

a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).

a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).

b.i) The Hare runs 31,680 inches per minute (1,900,800/60).

b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).

c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).

In this exercise, the following equivalent values are used for computing the distance and speed:

Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)

Speed of Hare = 30mph

30 miles = 52,800 yards (30 x 1,760)

52,800 yards = 1,900,800 inches (52,800 x 36)

= 880 yards per minute (52,800/60)

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El volumen que queda entre la esfera y el cubo es:  30.49cm^3

El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.

Para el cubo que tiene una arista de 4cm, el volumen es:

V = (4cm)^3 = 64 cm^3

Para la esfera con un diametro de 4cm, el radio es:

R = 4cm/2 = 2cm

Y el volumen será:

V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3

El volumen que queda entre la esfera y el cubo es:

V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3

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there are 12 months in a year, so then 4 months is really 4/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]

Answer: 60

Step-by-step explanation:

Almost everything in this picture is irrelevant to finding the measure of x.

x = 180 - 90 - 30 = 60

Answer:

-32x^5

Step-by-step explanation:

using binomial expression we have (1-2x)^6

a) 88 degrees

b) 44 degrees

Answer:

The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.

'25' above sigma is the upper bound.

In general it means adding 42 from 1 to 25 times.

so 42(25).

Answer:

C. 42(25)

Step-by-step explanation:

Took the unit test review and this was the correct option choice.

Goodluck on your unit test, I am sure that you will do good :)

[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787

From the 2 selected employees, the probability that they will both be females is; C: 4/15

We are given;

Number of male employees = 7

Number of female employees = 8

Total number of employees = 8 + 7 = 15

Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2

Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15

Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:y + a = 180[/tex]

( linear pair )

[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]

[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]

And

[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]

( Exterior angle = sum of opposite interior angles )

[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]

[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]

[tex]\qquad❖ \: \sf \:159 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

slope is 4

Step-by-step explanation:

Slope is rise/run

for every 4 units it rises it runs 1 unit

4/1=4

Answer:

Step-by-step explanation:

12 + 2x + 24 = 27 + x

2x + 36 = 27 + x

x + 36 = 27

x = -9

2(-9) + 24 = -18 + 24 = 6

12 + 6 = 18

27 + (-9) = 18

The dependent variable here is task performance. The independent variable in the question is musical genres.

This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.

The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.

The task performance is what we want to know here. To do so we want to use the genre of music.

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Based on the AED 40,000 net loss that the SoftNet line brings to Hava Racquets company, the incremental effect if the Softnet line is eliminated is that the company would save AED 10,000.

If Hava Racquets Company decides to scrap the Softnet line, then it means that they will no longer be incurring the AED 40,000 net loss that the line had brought to them.

They would instead incur a fixed cost of AED 30,000 which they can apply to their other operations.

This means that in exchange for a AED 40,000 loss, they would instead get  a AED 30,000 loss.

The savings on these losses is:

= 40,000 - 30,000

= AED 10,000

This means that Hava Racquets Company will make a saving of AED 10,000 if they eliminate the line.

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Since there is only one value of x, hence the equation given has only one solution

Equations are expressions separated using mathematical operations. Given the equation below;

2x+5+2x+3x = x

Collect the like terms

2x+2x+3x -x = -2

7x -x = -2

Simplify

6x = -2

x = -2/6

x = -1/3

Since there is only one value of x, hence the equation given has only one solution

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Answer:

All real numbers greater than or equal to 5

Step-by-step explanation:

The range of y=|x| is all real numbers greater than or equal to 0. Adding 5 to this makes the range all real numbers greater than or equal to 5.