prove that: [tex]tan20+4sin20=\sqrt{3}[/tex]

Answer:

1,406

Step-by-step explanation:

p = a(1 + r)^t

p = 1,236(1.013)^10

p = 1,406.4131692427

p = 1,406

Answer:x=−2±√119

Step-by-step explanation:

Answer:

24.4

Step-by-step explanation:

Given the data :

Month (X) : 0, 1, 2, 4, 6

Weight (Y) : 7.2, 9.4, 10.5, 13.2, 15.9

To obtain the predicted weight at 1 year, we fit the data to obtain the regression model. Using technology, the regression model obtained is :

y = 7.6 + 1.4X1

Substituting x = 1 year into the regression model, we obtained the predicted weight at 1 year ;

1 year = 12 months, hence, x = 12

y = 7.6 + 1.4(12)

y = 7.6 + 16.8

y = 24.4

Answer:

24

Step-by-step explanation:

18/ 3/4=24

Answer:

the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )

Step-by-step explanation:

Given the data in the question;

sample mean x' = 700

sample size n = 64

the standard deviation σ = 100

99% confidence interval for the true mean number of mosquitos caught in all mosquito traps = ?

significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01

∝/2 = 0.01 / 2 = 0.005

Z-critical [tex]Z_{\alpha /2[/tex] = 2.575 { from table }

So, to get the 99% confidence interval;

⇒ x' ± [tex]Z_{\alpha /2[/tex] ( σ / √n )

we substitute

⇒ 700 ± 2.575 ( 100 / √64)

⇒ 700 ± 2.575( 12.5 )

⇒ 700 ± 32.1875

⇒ ( 700 - 32.1875 ), ( 700 + 32.1875 )

⇒ ( 667.81, 732.19 )

Therefore,  the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )

Answer:

C(min)   =  8763.4 $

Step-by-step explanation:

Area =  24000 ft²

In a rectangle,    A =  x * y            x  is the base side and  y the height side

Cost of low and upper side   (x)  is 20 $ per foot

Cost of east and west sides  ( y)  is  10 $per ft

total cost is:

C(r)  =  2 * 20* x  +  2*  10* y

from  A =  x * y      y  =  A / x        y  =  24000 / x

And by substitution in C(r) we get:

C(x)  =   2 * 20* x  +  2*  10* 24000 / x

C(x)  =  40 * x  + 480000 / x

Tacking derivatives on both sides of the equation:

C´(x)  =  40  -  480000 / x²

C´(x)  =  0                40   -   480000/x²   = 0

40* x²  -  480000  = 0

x²  =  480000 / 40

x²  =  12000

x  =  √ 12000   =  109,54 ft

and  y  =  24000 / 109,54

y  =  219,09  ft

Chequing for second derivative

C´´(x)  =   480000 / x⁴     is always positive so we have a minimum of C at the value  x  =  109,54

Minimum cost C (min)  =  40* 109,54 +  20 * 219,09

C(min)   =  4381.6  +  4381.8

C(min)   =  8763.4 $

Answer:

7263

Step-by-step explanation:

Using technology, the quadratic regression function which models the data in the form ax² + bx + c is written thus ;

The quadratic regression function is a polynomial of degree 2. Where, x represents the widget selling price and y represents the total profit earned.

The predicted profit made on a widget selling price of $10.25 can be calculated by substituting x = 10.25 into the equation :

f(10.25) = -147.30(10.25)² + 3231.00(10.25) - 8213.66

f(10.25) = 9428.38

Therefore, the widget selling price is $9428.38

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Answer:

21.142

Step-by-step explanation:

not sure it's correct

Answer:

The expected value of the money she selects is 6.65.

Step-by-step explanation:

Expected value:

Sum of each outcome multiplied by its probability.

We have:

8 + 5 + 4 + 3 = 20 total bills.

8 are ones, so P(X = 1) = 8/20 = 0.4.

5 are fives, so P(X = 5) = 5/20 = 0.25.

4 are tens, so P(X = 10) = 4/20 = 0.2

3 are twenties, so P(X = 20) = 3/20 = 0.15.

What is the expected value of the money she selects?

[tex]E(X) = 0.4*1 + 0.25*5 + 0.2*10 + 0.15*20 = 6.65[/tex]

The expected value of the money she selects is 6.65.

4x + x = 1200

5x = 1200

x = 12 × ( 100 ÷ 5 )

x = 12 × 20

x = 240

______________________________

Larger : 4 × 240 = $ 960

lower : 1 × 240 = $ 240

Answer:

the ratio of white tiles to blue tiles is 48

Step-by-step explanation:

The scale factor does the company need to use for the family size box is 1.56.

A scale factor is the number by which all the components of an object are multiplied in order to create a proportional enlargement or reduction.

According to the question

A food company is designing boxes for several products. Each box is a rectangular prism.

The family size box will be a dilation of the single serving 1.2-ounce box.

It must contain 18.75 ounces of cereal.

For finding scale factor divide 18.75 by 12

= [tex]\frac{18.75}{12}[/tex]

= 1.56

Hence, the scale factor does the company need to use for the family size box is 1.56.

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Answer:

y = 115.0977+12.2992X

91.59%

Step-by-step explanation:

Given :

DLH(X) ILE(Y)

20 361_0

25 400

22 376

23 384

20 361_0

19 360

24 427.2

28 458.4

26 450_8

29 475.2

DLH (X) : Direct Labor Hours

ILE (Y) : Indirect Labor Expense

The regression model obtained by fitting the data using technology is :

y = 115.0977+12.2992X

Where ;

Intercept = 115.0977 ;

Slope = 12.2992

The Coefficient of determination, R² gives the proportion of explained variance due to the regression line.

For the data given above, the Coefficient of determination R² obtained using the Coefficient of determination calculator is 0.9159 ; which means that (0.9159 * 100%) about 91.59% of the variation in indirect labor expense is explained by the regression line while 8.41% is due to other factors.

Answer:

Let base = b

Given height, h is 4inches less than base. So h = b - 4

[tex]Area = \frac{1}{2} \times base \times height\\\\112 = \frac{1}{2} b \times(b-4)\\224 = b(b -4)\\b^2 - 4b -224 = 0\\\\b= \frac{4 \pm \sqrt{16 - (4\times -224)} }{2} \\\\\\b= \frac{4 + \sqrt{16 +896 } }{2} , b= \frac{4 - \sqrt{16 +896} }{2} \\\\\\b = 17.099 , -13.099[/tex]

Since length can't be negative, we take b = 17.099inches

Height ,h = b - 4 = 13.099 inches ≈ 13.1 inches

Answer:

450 foe

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

she needs 4 pounds of pluma to make 6 pounds of jelly.

so 4 pounds of pluma x 4 = exactly 24 pounds of jelly. 4×4=16

Answer:

30% of total students chose snowboarding as their favorite sport.

Step-by-step explanation:

We know that;

=> Total people = 500

=> Snowboarding people = 105

=> Percentage = unknown, so we can say it as x

So we can set up the equation;

x% · 500 = 105

[tex]\frac{x}{100}[/tex] · 500 = 105

x · 5 = 105

x = 105/5

x = 30

So 30% of total students chose snowboarding as their favorite sport.

Hope this helps!

Answer:

twenty-four nights

Step-by-step explanation:

597 divided by 25 will give you 23.88 which i rounded up to 24.

Answer:

7 1/9

Step-by-step explanation:

because I know i'm right

Answer:

Answer in Improper fraction: 64/9

Answer is Mixed number: 7 1/9

In decimal form: 7.11111111111111111111111111111111111111 (Forever, you get the picture)

Step-by-step explanation:

Improper fraction form:

8/3*8/3= 64/9

Hope this helps!

Answer:

Step-by-step explanation:

let a number be x

let another number be x+1

x+x+1=20

2x=20-1

x=19/2

x=9.5

therefore one number is 9.5 and another number is x+1=9.5+1=10.5

[tex]\huge{ \mathrm{  \underline{ Answer} \:  \:  ✓ }}[/tex]

Let the Consecutive odd numbers be x and x+2

Therefore, the numbers are :

______________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer: $4045.43

Step-by-step explanation: I just took the test.

The amount of money Ida will make in all over 5 weeks will be $4556.25.

The amount of money earned by any seller on the cost price is called the profit. It is given that Ida's ice-cream stand has increasing profits each week during the hot summer months. Ida finds that each week during the summer her profits increase by 15% over what they were the previous week.

The amount will be calculated as follows:-

A    =   600 ( 1.15 ) ⁵

A    =   $4556.25

Therefore the amount of money Ida will make in all over 5 weeks will be $4556.25.

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Answer:

7.5 hours

Step-by-step explanation:

The key here is to find out how much can be done in the same amount ot time

the least common multiple of 5 hrs and 3 hrs is 15hrs

In 15 hours:

- At 5 hours per lawn Norton could mow 15/5 = 3 lawns

- At 3 hours per lawn together thay could mow 15/3 = 5 lawns

In 15 hours Jesse would mow 5 - 3 = 2 lawns

15 hours/ 2 lawns = 7.5 hours per lawn

7.5 hours

--------------------

Here's the math

1 lawn/5hrs + x = 1 lawn / 3hrs

1/5 + x = 1/3

Subtract 1/5 from both sides

x = 1/3 - 1/5

x = 5/15 - 3/15

x = 2/15

x = 2lawns/15 hrs

15hrs/2lawns = 7.5 hrs per lawn

7.5 hours

Answer:

-10a^4 + 17a^2s - 6s^2

in other words, your answer is the first one

Answer:

-10a^4 +17a^2s-6s^2

Step-by-step explanation:

see Image below:)

Answer and Step-by-step explanation:

To find the value of x, set the sides BC and AD equal to each other (we can do this because we are told that the figure is a parallelogram, and those sides are congruent as stated in the properties of a parallelogram).

16x - 15 = 30 + 11x

Subtract 11x from both sides of the equation.

5x - 15 = 30

Add 15 to both sides of the equation.

5x = 45

Divide both sides of the equation by 5.

x = 9

So, the answer is 9, which is equal to x.

#teamtrees #PAW (Plant And Water)

Answer:

x = 1.67

Step-by-step explanation:

We know that in a parallel, opposite sides are parallel and congruent, therefore we can solve for x, by:

(BC) = (AD)

16x - 15 = 30 - 11x

(+11x) + 16x - 15 = 30

27x - 15 = 30

27x = 45

x = 45/27

x = 1.67

Therefore, x = 1.67

Hope this helps!

Answer:

103/25

Step-by-step explanation:

412% = 4.12 = 103/25

Answer:

4.12

Step-by-step explanation:

remove the '%' sign and then move the decimal two places to the left

other examples:

5% = .05

4.5% = .045

123% = 1.23

.9% = .009