tan( 20 ) + 4 Sin( 20 ) =
( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =
Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =
Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =
Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =
Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =
Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =
Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =
________________________________
2 × Cos( 30 + 20 ) =
2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =
2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =
√3 Cos(20) - Sin(20)
_________________________________
Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =
Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =
Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =
0 + √3 Cos(20) / Cos(20) =
√3 Cos(20) / Cos(20) =
Cos(20) simplifies from the numerator and denominator of fraction
√3 × 1 / 1 =
√3
And we're done ....
the average number of mosquitos caught in 64 mosquito traps in a particular environment was 700 per trap . the standard deviation of mosquitos caught in the entire population of traps is 100 mosquitos. what is the 99% condidence interval for the true mena number of mosquitos caught in all mosquito traps
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 )
Norton can mow the large lawn in about 5 hours. When he works with
Jesse, they can mow the same lawn together in about 3 hours. Which of
the following equations can be used to determine how long it would
take Jesse to mow the lawn by himself?
total. jobs
job. A
time. together time time
job. B
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
Which of the following statements is not true regarding the function y = 2"?
A. The function is an exponential function.
B. The function has a domain of all real numbers.
C. As the value of x gets very large, the value of y gets close to zero.
D. As the value of x increases by one, the value of y doubles.
What is the larger amount when $1200 is divided in the ratio 4: 1?
4x + x = 1200
5x = 1200
x = 12 × ( 100 ÷ 5 )
x = 12 × 20
x = 240
______________________________
Larger : 4 × 240 = $ 960
lower : 1 × 240 = $ 240
a rectangular area of 24000 square feet is to be fenced on all four sides. fencing east and west sides cost $10 per foot fencing for the other two sides cost $20 per foot. what s the cost of least expensive
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 $
Find the value of x for the right triangle. Round your answer to the nearest hundredth.
450
19
Answer:
450 foe
Step-by-step explanation:
Corvert 412% in a fraction
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
HELP
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. In her first week of business, her profits were $600. How much money will she make in all over 5 weeks?
Enter your answer, rounded to the nearest dollar, in the box.
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.
What is Profit?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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I need help can someone help me and please explain it
Question 6
1 pts
A baby weighed 7.2 pounds at birth. Her weight was recorded at each of her infant
doctor appointments. The records for her appointments from birth to six months are
shown in the table below. Use the line of best fit to estimate the baby's weight at 1
year (12 months)?
Months
Weight (lbs)
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
The triangular pyramid represented below has a triangular base of 15 centimeters and a triangular height of 20 centimeters. The height of the pyramid is 18 centimeters. What is the volume in cubic centimeters of the pyramid?
A company want to find out if there is a linear relationship between indirect labor expense (ILE), in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 10 months are given. Approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived?
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
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.
QUESTION IN PICTURE thx <3
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!
A shirt requires 3/4 of a yard of material. How many shirts can be made from 18 yards of material?
Answer:
24
Step-by-step explanation:
18/ 3/4=24
PLEASE HELP! I WILL GIVE BRAINLIEST!?!
find the area and perimeter of the rectangular image with length 12 cm and width 11 cm
Emily has plum trees in her backyard.
Eeach year she uses the fruit to make jelly.
Here are the ingredients for her recepie.
4 pounds of pluma
3 pounds of sugar
1 cup of water
This recepie makes 6 pounds of jelly.
How many pounds of plums will she need to make 24 pounds of jelly?
Show how you figured this out.
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
Find the amount after the specified time. A population of 1,236 grows 1.3% per year for 10 years.
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
plwjahajsjwjjee helppppp!!
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!
Convert the following angle from degrees to radians. Express your answer in simplest form. 120
The height of the triangle is 4 inches less than four times its
base. The area of the triangle is 112 in2. What is the height of
the triangle?
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
NEED HELP DUE IN 2 MINUTES!!!!
A food company is designing boxes for several products. Each box is a rectangular prism.The company also wants to offer a family size box of cereal. The family size box will be a dilation of the single serving 1.2-ounce box. It must contain 18.75 ounces of cereal. What scale factor does the company need to use for the family size box?
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.
What is a scale factor?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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What is the product (-2a^2+s)(5a^2 -6s)
PLS HELP
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:)
URGENT!
Find the value of x for which ABCD must be a parallelogram.
3
9
1
41
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!
find the roots of y = x^2 + 4x-115
Answer:x=−2±√119
Step-by-step explanation:
Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. What is the expected value of the money she selects
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.
if the sum of two consecutive odd number is 20 find the number
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
[tex]x + x + 2 = 20[/tex][tex]2x = 20 - 2[/tex][tex]2x = 18[/tex][tex]x = 9[/tex]Therefore, the numbers are :
[tex]x = 9[/tex][tex]x + 2 = 11[/tex]______________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
5) If Gwen's book has 597 pages and she plans to read 25 pages each night, how many nights will it take her to finish reading the book?
Answer:
twenty-four nights
Step-by-step explanation:
597 divided by 25 will give you 23.88 which i rounded up to 24.
Company X tried selling widgets at various prices to see how much profit they would
make. The following table shows the widget selling price, x, and the total profit earned
at that price, y. Calculate the quadratic regression equation for this set of data. Using
this equation, find the profit, to the nearest dollar, for a selling price of 10.25 dollars.
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 ;
f(x) = -147.30x² + 3231.00x - 8213.66Profit earned on $10.25 is $9428.38The 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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Workings please......
Answer:
21.142
Step-by-step explanation:
not sure it's correct