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Answer:

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The wingspan of the actual aeroplane is 80 feet.

Given, that the model of an aeroplane has a wingspan of 20 inches and the scale factor is 1 inch = 4 feet.

We need to find what is the wingspan of the actual aeroplane.

The scale factor is a way to compare figures with commonly described but differing scales or measurements.

The wingspan of the actual aeroplane = The wingspan of the model aeroplane × Scale factor.

⇒The wingspan of the actual aeroplane = 20 × 4 feet = 80 feet.

Therefore, the wingspan of the actual aeroplane is 80 feet.

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Answer:

yes

Step-by-step explanation:

The value of cos(A+B) is 36/325.

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

=  120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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Answer:

leaning at 3 degrees off of normal (to the nearest whole degree)

Step-by-step explanation:

To visualize, let's assume the tower is leaning to the right, (as viewed by us).

If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.

The height and base of the triangle are given

Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles).  If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°.  Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°.  So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.

Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]

Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.

[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]

Answer:

See below.

Step-by-step explanation:

19.

The spinner has 12 equal-sized sections.

1/3 of 12 = 4

A number that appears in exactly 4 sections has a probability of 1/3. The number 3 appears exactly 3 times.

A number that appears more than 4 times has a probability greater than 1/3. The number 0 appears exactly 5 times.

A number that appears fewer that 4 times has a probability of less than 1/3.

Both 1 and 2 appear fewer than 4 times.

Answer:

Probability greater than 1/3: 0

Probability equal to 1/3: 3

Probability less that 1/3: 1, 2

20.

The amount of concentrate is 12 gallons.

The total amount of drink is 40 gallons.

The fraction of the concentrate out of the total is 12/40.

12/40 = 0.3

0.3 of each gallon is concentrate.

Color the bottom up to 0.30

The line represent the amount of money in the line of the account will be x + y = 45.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Alina has $20 in her account she wants to purchase a purse, shoes that cost $45.

If the line makes the purchase, Then the line represent the amount of money in the line of the account will be

x + y = 45

where x be the price of purse and y be the price of shoe.

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The stock worth now, to the nearest cent is  $90.75.

The current worth of stock = initial price of stock+increase in the price of stocks

If you bought stock last year for a price of $103, and it has risen 13.5% since then,

Let X be the worth of stock;

103 ×  100 = (13.5% + 100%) × X

10300 = 113.5X

X = 10300/113.5

X = 90.74889868

X = $90.75

Hence, The stock worth now, to the nearest cent is  $90.75.

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If he picks 1965, then the Gross earning will be $85.55.

The missing part of the question is given below.

If he picks 1965, then Calculate the Gross earning.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Calculate the gross earning for an apple picker based on the following differential pay scale:

     1 – 1000: $0.03 each

1001 – 1600: $0.06 each

  over 1600: $0.07 each

Total apples picked by Lindbergh = 1965

So, for 1000 apples, he will get =1000 × 0.03 = $30

Now, remaining apples = 1965 – 1000 = 965

Now for next 600 apples (from 1001-1600), he will get = 600 × 0.05 =$30

Now, remaining apples = 965 – 600 = 365

So, for remaining 365 (above 1600) apples, he will get = 365 × 0.07 = $25.55

So, total gross earning = $30 + $30 + $25.55

⇒ $85.55 is total gross earning

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Answer:

48 cents

Step-by-step explanation:

Divide 2.88 by 6 to determine the value of a single pudding.

2.88/6 = 0.48

Hence, each pudding is worth 48 cents.

Hope this helps!

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.

Gilberta adds 7 spoonfuls of salsa for every 5 eggs.

Then the scrambled eggs have a stronger salsa taste will be

Lashawn's eggs = 3/2 = 1.5

Gilberta's eggs = 7/5 = 1.4

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.

Then the correct option is A.

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Answer:

a. 61.25

b. 70

c. 212

Step-by-step explanation:

a. What is your cost if you travel 57 miles?

The cost is $ .

y=47+0.25x

y=47+0.25(57)

y=47+14.25

answer: 61.25

b. If your cost was $64.50, how many miles were you charged for traveling?

You were charged for traveling miles.

64.50-47=0.25x

17.50=1/4x

17.50*4

answer 70=x

c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

The maximum number of miles you could travel is miles.

100-47

53=1/4x

answer : x= 212

Step-by-step explanation:

the perimeter is

2×length + 2×width = 1030 ft

length + width = 515 ft

length = width + 181

now we use that in the first equation :

(width + 181) + width = 515

2×width + 181 = 515

2×width = 334

width = 167 ft

because of

length = width + 181

length = 167 + 181 = 348 ft

The width and length of the rectangular field are 165.5 ft and 346.5 ft respectively.

Concept: Perimeter is the sum of the length of all sides of a figure/solid.

Given: Length = 181+width

Let width be equal to 'width' ft

Perimeter= 1030 feet

In a rectangle there are 2 length and 2 width so the perimeter of a rectangle is equal to 2*(181+ width) + 2width = 362 + 2width + 2 width = ⇒362 + 4width =1030 ft

4width = 662 ( on transposing)

width= 165.5 ft

length= 181+ 165.5 ft

length = 346.5 ft

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Answer:

For a principle amount of $1600 and rate 5.4%, the effective annual yield is 5.55% if interest is compounded annually.

Step-by-step explanation:

Concept: The annual percentage yield (APY) or the effective annual yield is the real rate of return earned on an investment, taking into account the effect of compounding interest.

The principle amount is $1600, rate is 5.4% and period is 365 days. The formula to find yield is [tex]Y = (1+\frac{r}{n} )^{n} -1[/tex]. All the values are to be inserted in the formula. Here n = 365 and r = 5.4%.

[tex]Y=(1+\frac{0.054}{365} )^{365} -1\\Y=(1.000148)^{365} -1\\Y=5.55%[/tex]

The annual yield is 5.55%.

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Answer:

x<7

Step-by-step explanation:

Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition

⇒"The sum of a number and 3 is less than 10"

Remember the notation of  the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is

⇒ x+3<10

adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore

⇒ x+3-3<10-3

⇒ [tex]x<7[/tex]

In terms of  interval notation

[tex]\implies x\in( -\infty,7)[/tex]

In conclusion

The answer is D) [tex]x < 7[/tex]

Let the number be x

The sum of number and 3

Is less than 10

Lets solve it

Hence

Option D is correct

In 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

P = $30

r = 1% = 0.01

n = 4

[tex]\rm A = 30(1+\dfrac{0.01}{4})^{4\times25}[/tex]

After calculating:

A = $38.51

Thus, in 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.

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Answer:

2 + 2: 4

or 2 + 2: 5 from the dystopian novel 1984.

Answer:

[tex]9600cm^{2}[/tex]

Step-by-step explanation:

Get the area of the triangle and the rectangle, then subtract the triangle's area for the rectangle's

The overhead cost would be assigned to Product J00A using the company's activity-based costing system is $4313.87.

The overhead cost that would be assigned to Product J00A using the company's activity-based costing system will be:

= ($86.50 × 34) + ($4.63 × 105) + ($52.16 × 17)

= $2941 + $486.15 + $886.72

= $4313.87

The overhead cost would be assigned to Product S06U using the company's activity-based costing system will be:

= ($86.50 × 43) + ($4.63 × 812) + ($52.16 × 32)

= $3719.50 + $3759.56 + $1669.12

= $9148.18

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Answer:

[tex]\boxed {192 cm^{2}}[/tex]

Step-by-step explanation:

Find the volume of separate cuboids :

Volume (top cuboid) :

⇒ V = 2 x 6 x (10 - 2)

⇒ V = 12 x 8

⇒ V = 96 cm²

Volume (lower cuboid) :

⇒ V = 8 x 6 x 2

⇒ V = 48 x 2

⇒ V = 96 cm²

Volume (prism) :

⇒ 96 + 96

⇒ 192 cm²

Answer:

-51

Step-by-step explanation:

If the limits are reversed, then place a negative sign in front of the integral.

[tex]\int\limits^a_bf ({x}) \, dx =-\int\limits^b_a f({x}) \, dx[/tex]

[tex]\int\limits^a_3 f({x}) \, dx = 51\\[/tex] where [tex]\alpha =10\\[/tex]

[tex]\int\limits^3_\alpha f( {x}) \, dx =-51[/tex]  where[tex]\alpha =10[/tex]

The value of x that fills the coordinate are 7 or -5

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)² +(y2-y1)²

Substitute the given coordinates

10 = √(15-7)² +(1-x)²

100 = 8²  +(1-x)²

(1-x)² = 100 - 64

(1-x)² = 36

1- x = -6

x = 7 or -5

Hence the value of x that fills the coordinate are 7 or -5

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Complete question

If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.

The answers are as follows:

a) X denotes the number of the california residents that have adequate earthquake insurance

b)  x = 1 ,2 ,3 ......

c) P( X=x ) = 0.3(1-0.3) ^ (x-1)

d)  P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

e) 0.49

f)0.42

g)0.33

It is a branch of mathematics that deals with the occurrence of a random event.

The complete question is

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?

given that 30% of California residents have adequate earthquake supplies.

a) variable X denotes the number of the california residents that have adequate earthquake insurance

b) x = 1 ,2 ,3 ......

c) p=0.3

P( X=x ) = 0.3(1-0.3) ^ (x-1)

d) P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...

e) P( X≥ 3) = 1- P(X<3)

= 1- (P(X=1) + (X=2))

= 1- 0.051

= 0.49.

f) E(X)= 1/P

p is the resident who does not have adequate earthquake supplies

p= 1-0.3

p = 0.7

E(X) = 1/0.7

= 0.42

g) E(X) =  1/q

= 1/0.3

= 3.333

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Because in both graphs the shaded region is above the curve, the correct option is C.

On the graph we can see two parabolas, such that the y-intercepts of these are:

y = 6

y = -4

So we just need to find the pair of options with these y-intercepts, and noticing that for both cases, we must have:

y > parabola.

Because both shaded regions are above the parabolas.

The only option that meets these requirements is option C. Where there is a mistake, as you can see both curves have dashed lines, and always when we have dashed lines we should use the symbols > or <, while in that option we have a ≥ symbol

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Answer:

subract 4 from both sides

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer: d = 40 - 5/2t; 1995

Hope it helps :)

Answer:

All real numbers greater than or equal to 2.

Step-by-step explanation:

To find the range, we look at the y values. Since all the y values never dip under 2 and also keep increasing to infinity, the range is [tex]y\geq 2[/tex].

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

Edge

Answer: [tex]y-3=-4(x+3)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4[/tex]

So, using the point (-3, 3) to substitute into point-slope form, the equation is [tex]\boxed{y-3=-4(x+3)}[/tex]

Answer:

R ,is the Resultant of two forces,

∠ACB +50°=180°

∠ACB=180° -50°

∠ACB=130°

→Cos(130°)=Cos (180°-50°)= -cos 50°= -0.6427

Magnitude of resultant force =70.70 Newtons(Approx)