Answer:
The value of cos Ф is ± [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
sin²Ф + cos²Ф = 1sin²Ф = 1 - cos²Фcos²Ф = 1 - sin²Ф∵ sin Ф = [tex]\frac{\sqrt{3}}{2}[/tex]
∴ sin²Ф = [tex](\frac{\sqrt{3}}{2})^{2}[/tex]
∴ sin²Ф = [tex]\frac{3}{4}[/tex]
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 - [tex]\frac{3}{4}[/tex]
∴ cos²Ф = [tex]\frac{1}{4}[/tex]
→ Take square root for both sides
∴ cos Ф = ± [tex]\frac{1}{2}[/tex]
∴ The value of cos Ф is ± [tex]\frac{1}{2}[/tex]
Which is a correct frost step for solving this equation
Answer:
you have to post the equation
Step-by-step explanation:
F=1.8C+32 solve for given variable
Answer:
Step-by-step explanation:
The formula F = 1.8C + 32 can be used to find the temperature in degrees Fahrenheit F when the temperature is given in degrees Celsius C. For what value is the temperature in degrees Fahrenheit equal to the temperature in degrees Celsius? Justify your reasoning by writing and solving an equation. (Hint: If Fahrenheit and Celsius are equal, they can be assigned the same variable.)
PLS HELP. URGENT
Serena and Derek have 270 stickers in all. Serena has 25% more stickers than Derek. How many stickers does Derek have? (Type out your work and answer)
1. Here is a number line. Write the two missing numbers in the boxes.
0
2
Answer:
The box on the left is 0.4 and the box on the right is 1.8
Benjamin wants to buy a video game that costs $24, but he only wants to spend 40% of his savings. How much must Benjamin save in order to buy the game?
Answer:
14.4 there sorry for the wait
PLEASE HELP!!
The blue dot is at what value on the number line?
Pictrure Below:
2. Paula learned to play a total of 10 pieces over the course of 5 weeks of piano lessons. In all, how
many weeks of piano lessons will Paula need before she will be able to play a total of 18 pieces?
A rancher has a square cow pen with side length x. He decides to change the shape
of the pen while still using the same amount of fencing materials. The equation
(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)
of the pen and its area (in square feet).
a. If 300 represents the area of the new cow pen, what do the expressions
(x + 10) and (x - 10) each represent?
b. Find x, the original side length (in feet) of the square pen. Show your reasoning.
Answer:
a) x+ 10 is the length of the ranch
x - 10 is the width of the ranch
b) 20 feet
Step-by-step explanation:
Area of the square ranch = L²
L is the side length of the ranch
If the equation
(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)
Then we can find x where;
x + 10 is the new length of the ranch
x - 10 is the new width of the ranch
Open the parenthesis
equation
(x + 10)(x - 10) = 300
x²²-10x + 10x - 100 = 300
x² - 100 = 300
x² = 300+100
x² = 400
x = √400
x = 20
Hence the original length of the square pen is 20 feet
The values (x + 10) and (x - 10) represents the length and width of the new pen.
The value of x, the original length of the pen is 20 cm
How to find the side of a square?The pen is a square. It was later reconstructed to form the following expression.
(x + 10)(x - 10) = 300
where
area = 300 feet squaredTherefore,
(x + 10)(x - 10) = 300
x² - 10x + 10x - 100 = 300
x² - 100 = 300
x² = 300 + 100
x² = 400
x = √400
x = 20 ft
Therefore, the original side length of the square pen is 20 ft.
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The concentration of dichlorodiphenyltrichloroethane (DDT - an infamous pesticide) in Lake Michigan has been declining exponentially over many years. In 1971, the DDT concentration was 13.00 ppm (parts per million). In 1984, the DDT concentration was 2.22 ppm.
Using these data points, determine the exponential decay function to model the DDT concentration decline in terms of years, tt, where t=0t=0 represents the year 1971.
A) Write your function as y = Ce^{rt}y=Ce^rt. Round your value of rr to four decimal places.
B) Another way to write the function down is known as the half-life formula, written as y = C(0.5)^{t/H}y=C(0.5)^t/H, where HH is the time required for the concentration to get cut in half. Using the initial two data points, find the value of HH, rounded to 2 decimal places. Show all Algebraic work.
C) The goal was to reduce the DDT concentration to 0.98 ppm by 1995. Was this possible according to your model?
Answer: A) [tex]y=13e^{-0.1359t}[/tex]
B) H = 5.10
C) Yes
Step-by-step explanation: Exponential Decay function is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: [tex]y(t)=Ce^{rt}[/tex]
A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:
[tex]y(t)=Ce^{rt}[/tex]
[tex]2.22=13e^{13r}[/tex]
[tex]e^{13r}=0.1708[/tex]
Using a natural logarithm property called power rule:
[tex]13r=ln(0.1708)[/tex]
[tex]r=\frac{ln(0.1708)}{13}[/tex]
[tex]r=-0.1359[/tex]
The decay function for concentration of DDT through the years is [tex]y(t)=13e^{-0.1359t}[/tex]
B) The value of H is calculated by [tex]y=C(0.5)^{\frac{t}{H} }[/tex]
[tex]2.22=13(0.5)^{\frac{13}{H} }[/tex]
[tex](0.5)^{\frac{13}{H} }=0.1708[/tex]
Again, using power rule for logarithm:
[tex]\frac{13}{H} log(0.5)=log(0.1708)[/tex]
[tex]\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}[/tex]
[tex]\frac{13}{H} =2.55[/tex]
H = 5.10
Constant H in the half-life formula is H=5.10
C) Using model [tex]y(t)=13e^{-0.1359t}[/tex] to determine concentration of DDT in 1995:
[tex]y(24)=13e^{-0.1359.24}[/tex]
y(24) = 0.5
By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.
Wich calculation will ALWAYS have a result greater than 1
Step-by-step explanation:
number less than 1 B.4/9+ a fraction less than 12 C. 1 3/4 - a fraction less than 3/4 D.7/8 a number less than 1
If alice earns 56% more than wallaceAlice's salary is how many times Wally's salary?
Answer:
Alice's salary is 1.56 times Wally's salary
Step-by-step explanation:
Let Wally's salary = x
Alice's salary = x + 56% of x
= x + 0.56x
= 1.56x
= 1.56 * Wally's salary
Answer:b
Step-by-step explanation:
Roxanna has a collection of silver spoons from all over the world.
If the spoons are arranged in sets of 7, there are 5 left over.
If the spoons are arranged in sets of 8, there is 1 left over.
If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
Answer: 89
Step-by-step explanation: 8 x 11 + 1 = 89, 7 x 12 + 5 = 89, 15 x 5 + 14 = 89
A 2.5-meter piece of framing lumber has been used to cut a piece 1.65 meters long. How much of the original piece of lumber remains, in meters?
Answer:
0.85 of the original piece of lumber remains.
Step-by-step explanation:
Well, this lumber piece of lumber started as 2.5 meters long. Then, a 1.65 meter piece was cut off of it. All we need to do is subtract.
2.5 - 1.65 =
2.50 - 1.65 = 0.85.
Therefore, 0.85 of the original piece of lumber remains.
Hope this helps! :)
The rectangle shown as a perimeter of 70 cm and the given area. It’s length is 8 more than twice it’s width. Write and solve a system of equations to find the dimensions of the rectangle.
The length of the rectangle is ___cm and the width of the rectangle is ___cm.
width of the rectangle = b = x
length of the rectangle = l = 8 + 2x
Perimeter of the rectangle = 70cm
Also, perimeter of the rectangle = 2(l + b)
70 = 2[x + (8 + 2x)]
70 = 2(x + 8 + 2x)
70 = 2(3x + 8)
70 = 6x + 16
70 - 16 = 6x
54 = 6x
54/6 = x
9 = x
Therefore, b = x
b = 9cm
l = 8 + 2x
I = 8 + 2×9
I = 8 + 18
I = 26cm
PLS SOLVE!!!!! THANK YOU!!!!!
A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an
approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. What
percentage of filled boxes of rice have a weight between 28 and 29 ounces?
Find the z-table here.
O 33.1%
O 36.7%
O 63.3%
66.9%
Answer:
D
Step-by-step explanation:
I got it right
Using the normal distribution, it is found that 66.9% of filled boxes of rice have a weight between 28 and 29 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by: [tex]\mu = 28.2, \sigma = 0.4[/tex].
The proportion of filled boxes of rice have a weight between 28 and 29 ounces is the p-value of Z when X = 29 subtracted by the p-value of Z when X = 28, hence:
X = 29:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29 - 28.2}{0.4}[/tex]
Z = 2
Z = 2 has a p-value of 0.977.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 28.2}{0.4}[/tex]
Z = -0.5
Z = -0.5 has a p-value of 0.308.
0.977 - 0.308 = 0.669 = 66.9%.
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Please help me, thanks!
Answer:
Algebraic expression for 75 less than twice Mabel's score is 2m-75
Step-by-step explanation:
We need to translate the phrase 75 less than twice Mabel's score into algebraic expression.
Translating into algebraic expression
Let m represent Mabel's score
Twice Mabel's score = 2m
75 less than Twice Mabel's score = 2m-75
So, algebraic expression for 75 less than twice Mabel's score is 2m-75
Pls answer 55-62 I will give brainlist
If Triangle ABC is congruent to Triangle SRT, find the possible value(s) for x
Answer:
x = 2 or x = -3
Step-by-step explanation:
Given that ∆ABC ≅ ∆SRT, it follows that their corresponding side lengths are congruent to each other.
Thus:
[tex] RT = BC [/tex]
[tex] (x^2 + x) = 6 [/tex]
Solve for x
[tex] x^2 + x = 6 [/tex]
Subtract 6 from each side
[tex] x^2 + x - 6 = 6 - 6 [/tex]
[tex] x^2 + x - 6 = 0 [/tex]
Factorise
[tex] x^2 + 3x - 2x - 6 = 0 [/tex]
[tex] x(x + 3) -2(x + 3) [/tex]
[tex] (x - 2)(x + 3) [/tex]
x = 2 or x = -3
factor 2w+6
Please explain? I'd like to understand how you did it so that I can do it myself the next time, thanks a mil :)
Answer:
2( w + 3 )
Step-by-step explanation:
Well first off, since theres no common term to factor out, I had to split 6 in half
so 2 w + 6 becomes 2w + 2 x 3.
I then factored out 2 because it's a common term,
which then leaves: 2( w + 3 )
basically, you have to find a common term to factor out, if you don't see one, you have to do something to a number so there's common terms.
A store sees 138 customers in 8 hours. What is the unit rate (in customers per hour)?
Answer:
Step-by-step explanation:
138/8 = 17.25
All changes saved
4. Calculate the federal income taxes. In 1862, the federal income tax was 3 percent on incomes between $600 and $10,000 per year and 5 percent on incomes
over $10,000 per year. In 1862, you made $750. How much did you pay in income taxes?
O $37.50
O $225
O $22.50
$2,250
Answer:
$22.50
Step-by-step explanation:
My bad lol, I posted the answer under the wrong thing.
-2/3 x 3/4
Please help!
Answer:
-1/2
Step-by-step explanation:
Answer:
-9/8.
Step-by-step explanation:
-3/2 * 3/4
= -3*3 / 2*4
= -9/8.
A rectangle has a length of 12 yards less than 3 times its width. If the area of the rectangle is 135 square yards, find the length of the rectangle.
Answer:
The length is 15 yards
Step-by-step explanation:
Given
Represent the width with W and length with L: So
[tex]Area = 135yd^2[/tex]
[tex]L=3W - 12[/tex]
Required
Determine the length of the rectangle:
Area is calculated as thus:
[tex]Area = L * W[/tex]
Substitute 3W - 12 for L and 135 for Area
[tex]135= (3W - 12) * W[/tex]
[tex]135= 3W^2 - 12W[/tex]
Reorder:
[tex]3W^2 - 12W - 135= 0[/tex]
Divide through by 3
[tex]W^2 - 4W - 45 = 0[/tex]
Expand:
[tex]W^2 - 9W + 5W - 45 = 0[/tex]
[tex]W(W - 9) + 5(W - 9) = 0[/tex]
[tex](W + 5)(W-9) = 0[/tex]
[tex]W + 5 = 0[/tex] or [tex]W - 9 = 0[/tex]
[tex]W = -5[/tex] or [tex]W = 9[/tex]
But width can't be negative
So:
[tex]W = 9[/tex]
Recall that: [tex]L=3W - 12[/tex]
[tex]L = 3 * 9 - 12[/tex]
[tex]L = 15[/tex]
Hence, the length 15 yards
What value of x makes the equation 5(x - 3) + 2x = 41 TRUE?
Answer: x = 8
Step-by-step explanation: PLEASE GIVEBRAINLIEST IT HELPS ALOT
Answer:
x=8
Step-by-step explanation:
Follow the order of operations to simplify the equation:
5(x-3) +2x=41
Start by multiplying into the parenthesis: 5x-15+2x=41
Combine like terms: 5x+2x-15=41 then simplify: 7x-15=41
Add 15 to both sides: 7x=56
Divide both sides by 7 to get x by itself: x=8
Hope this helps! (^-^)
Read the description of f below, and then use the drop-down menus to complete an
explanation of why f is or is not a function,
f relates each student in Mr. Well's history class to their score on a final exam.
Answer:
because a function always gives a determined answer from what was placed into the domain, this is not a function. what is put into the domain (students) may not get the same result through f.
Answer: 1. the students 2. the final exams 3. is- domain- one- range brainliest plzz??
what is 0.125 in a percent
What is the slope of the line that passes through the points (2, -3) and (2, 13)
Write your answer in simplest form.
Answer:
The answer is undefined
Step-by-step explanation:
The slope of the line that passes through points (2, -3) and (2, 13) is not defined.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The line that passes through points (2, -3) and (2, 13)
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Plug the values to find the slope of the line:
m = (13 + 3)/(2-2) = 16/0 = not defined
Thus, the slope of the line that passes through points (2, -3) and (2, 13) is not defined.
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find the slope please :)
Answer:
3/4
Step-by-step explanation:
up 3 over 4
Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for x, the number of minutes it will take Amy to finish typing her paper?
A. 38x- 1,450>76
B. 38(x + 1,450)>4,000
C. 38x> 4,000
D. 38x + 1,450> 4,000