Answer:
D. [0,pi/2]
Step-by-step explanation:
when Ф = 0 in radian
r²= 4cos (2(0))
r² = 4 * 1
r² = 4
∴ r = √4 = 2
r = 2.
when Ф = π/2 in radian
r²= 4cos (2(π/2))
r² = 4 * -1
r² = -4
∴ r = 0
Ethan and Layla work at a furniture store. Ethan is paid $235 per week plus 9.5% of his total sales in dollars, xx, which can be represented by g(x)=235+0.095xg(x)=235+0.095x. Layla is paid $53 per week plus 10.5% of her total sales in dollars, xx, which can be represented by f(x)=53+0.105xf(x)=53+0.105x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Answer:
$18,200
Step-by-step explanation:
We want ...
f(x) = g(x)
53 +.105x = 235 +.095x . . . . use given expressions
.01x = 182 . . . . . . . subtract 53+.095x
x = 182/.01 = 18200 . . . . . divide by the coefficient of x
Each must sell $18,200 for their weekly pay to be the same.
From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.
Answer:
The maximum dimension for box will be side length as 26.667 inches and height will be 6.667 inches and volume will be 4741 cu inches.
Step-by-step explanation:
Given:
With dimensions as
40x40 square and sides are folded in square corners.
To Find:
Maximum volume that will yield and maximum dimension for box
Solution:
Consider, a box with 40 x 40 dimensions as follows and
let a x side length square corners are cut and folded up and a new figure is formed .and for that what will be the maximum volume and dimension.
Now,
as the there 2 corner for each side i.e. 2 square on side length
Resultant length will be 40-2x
So volume is given by ,
[tex]V=l^2*h[/tex]
[tex]=(40-2x)^2*x[/tex]
[tex]V=(40^2-2*2x*40+4x^2)*x[/tex]
[tex]V=(1600-160x+4x^2)*x[/tex]
[tex]V=4x^3-160x^2+1600x[/tex]
To get Maximum volume differentiate w.r.t 'x'
[tex]V'=12x^2-320x+1600[/tex]
[tex]V"=24x-320[/tex]
Now solve for x with help of quadratic equation we get ,
12x^2-320x+1600
=4(3x-20)(x-20)
Therefore ,
3x-20=0 or x-20=0
x=20/3 or x=20
x=16.666 or x=20
Now use this values in a 2nd derivative equation,
V"=24(6.667)-320)
V"=160-320
V"=-160 <0 ,................equation(1)[Here maximum volume will be presented]
For X=20
V"=24*20-320
V"=480-320
=160>0 ..................Equation(2)[here minimum volume will presented]
Comparing equation 1 and 2 we get ,
Take as x=20/3 as the folded square length as it is gives minimum value for 2nd derivative.
So
[tex]V=(40-2x)^2*x[/tex]
[tex]V=[40-2(20/3)]^2*20/3[/tex]
[tex]V=[40-40/3]^2*6.667[/tex]
=[tex][26.667]^2*6.667[/tex]
=4740.95
=[tex]4741 cu inches.[/tex]
So side lengths =40-2x=40-2*20/3
=40(1-1/3)
=40(2/3)
=26.667 inches
And the height will be x=20/3=6.667 inches.
Find the number of strings of six lowercase letters from the English alphabet, which satisfies the given conditions. Six lowercase letters contain the letters a and b in consecutive positions with a preceding b, with all the letters distinct.
Answer:
The answer is 1,275,120
Step-by-step explanation:
The goal of this is to determine the number of strings of strings of six lowercase letters from the English alphabet that contain the letters a and b in positions consecutive with a preceding b, with all the letters distinct.
Now,
As the letters a and b are consecutive, the possible string outcomes are in this form:
ab_ _ _ _
_ab_ _ _
_ _ab_ _
_ _ _ ab_
_ _ _ _ ab
As seen here, ab can denoted in five locations as in C (5, 1) = 5 ways
we use the permutation for the order of the letters to be needed.
so,
n= 24, r =4
p (24, 4) = 24ǃ /( 24 - 4)ǃ
= 24ǃ /20ǃ
=255,024
Now, the number of possible strings is 5* 255.024 = 1,275,120.
In conclusion there are 1,275,120 number of strings of six lowercase letters from the English alphabet contain the letters a and b in consecutive positions with a preceding b, with all the letters distinct.
A group of finance managers at a car dealership estimates thatt 23% of all cars purchased last year were leases.If a sample of 800 cars sold last year obtained, what is the that more than 208 cars are going to be leased? Draw and label the appropriate curve. Your work must include caculator commands
Answer:
p = 0.52392
Step-by-step explanation:
Here we have
p = 23% = 0.23
[tex]\hat p[/tex] = 208/800 = 0.26
n = 800
q = 1-p = 0.77
α = 5% = 0.05
Here we have
Z test given by
[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}[/tex]
From which we have
From the Cpdf we have Probability = 0.0219, z = 2.016
Therefore from the z score = 0.0683, p = 0.52392 from z table.
Radiationâ machines, used to treatâ tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3â meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.82.8 âmeters?
Answer:
71.75 milliroentgens per hour
Step-by-step explanation:
The intensity(I) of Radiation varies inversely as the square of the distance (D) from the machine.
This is written as:
[tex]I \propto \frac{1}{D^2} \\$Introducing the constant of Variation k$\\I = \frac{k}{D^2} \\$When D=3 meters, I=62.5 milliroentgens per hour$\\62.5= \frac{k}{3^2}\\k=62.5 X 9 =562.5\\$Substituting K=562.5 into the variation equation$\\I = \dfrac{562.5}{D^2} \\$Therefore, When D=2.8 meters$\\Intensity,I = \dfrac{562.5}{2.8^2}=$71.75 milliroentgens per hour$[/tex]
In order to answer the question correctly, please use the following image below:
Describe the error in finding the angle measure.
Find the correct angle measure.
m∠SUT=(blank)
What is the error in finding the angle measure? What is the correct angle measurement of SUT?
Please show all the work on how you got your answers.(Note: If you are unable to explain your work then it's fine. All that I am asking for is for the work to be shown so I can see how you got your answers)
Answer:
see below
Step-by-step explanation:
The angle where chords cross is the average of the intercepted arcs. Here, that is ...
(37° +46°)/2 = (83°)/2 = 41.5°
Angle SUT is 41.5°.
_____
Comment on the error
The measure of an arc cannot be arbitrarily said to be the same as the angle where the chords cross. It will be the same if (a) the chords cross at the circle center, or (b) the opposite intercepted arc has the same measure. Neither of these conditions hold here.
Answer:
1) A
2) 41.5°
Step-by-step explanation:
SUT would have been 46° if U was the centre
Angle SUT = (37+46)/2
= 83/2
= 41.5
Evaluate the expression 5 exponent 2
Answer:
25
Step-by-step explanation:
5^2
This means multiply 5 two times
5*5
25
40 - 5n = -2 need explanation as well
Answer: n = 8.4
Step-by-step explanation:
40 - 5n = -2
First, subtract 40 from each side of the equation
-5n = -42
Then, divide each side by -5
n = 8.4
The -5 and -42 cancel each other out when dividing, so n = 8.4 is positive.
Answer:
n=8.4
Step-by-step explanation:
To solve, we need to isolate the variable, n
40 -5n =-2
Subtract 40 from both sides
40-40-5n= -2 -40
-5n= -42
Divide both sides by -5
-5n/-5=-42/-5
n=42/5
n=8.4
I need to buy some cardboard to build a box 12 inches long, 8 inches wide and 10 inches high. How much cardboard is needed to build the box
You will need 592 square inches of cardboard to build the box.
To determine how much cardboard is needed to build the box, we calculate the surface area of the box.
The box has six faces: two of each dimension.
Calculating the area of each pair of faces:
Two faces of (12 in x 8 in):
2 x (12 x 8) = 2 x 96 = 192 square inches
Two faces of (12 in x 10 in):
2 x (12 x 10) = 2 x 120 = 240 square inches
Two faces of (8 in x 10 in):
2 x (8 x 10) = 2 x 80 = 160 square inches
Sum the areas of all faces:
192 + 240 + 160 = 592 square inches
50 pounds to 35 pounds
We have to find the percent of change :
50 pounds to 35 pounds
Original amount = 50 pound
New amount= 35 pounds
Since, New amount is less than the original amount,
this is a percentage of decrease.
Change in amount =35 -50 = -15 pound
percentage change= change of amount/original amount x 100
substitute the given values we have:
percentage change= -15/50 x 100
simplify:
percentage change= -30%
Therefore the decrease is 30%
Brainliest????
i need the steps for 26
Answer:
K = 51
Step-by-step explanation:
Since the triangles are similar, the angles are the same measure.
<K = <F
We can find angle F since the angles of a triangle add to 180
D + G + F = 180
59+70 +F = 180
Combine like terms
129+F = 180
Subtract 129 from each side
129-129+F = 180-129
F = 51
K = F = 51
Answer:
51°
Step-by-step explanation:
Angle K corresponds to Angle F
Angle F = 180 - 70 - 59
Angle F = 51°
Growth of Bacteria The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 30 min. (a) If the initial population is 100, determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes).
Answer:
[tex]Q(t) =[/tex] [tex]100(2)^t[/tex]
Step-by-step explanation:
please see the attached files for more details
Aiden put two-fifths of his Money into his piggy bank. He had $15 left in his pocket to buy a toy. How much money did aiden have before he put some into his bank?
Answer:25
Step-by-step explanation:
15x 2/5=25
Answer:
$37.50
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] of Aiden's money is $15. Half of [tex]\frac{2}{5}[/tex] is [tex]\frac{1}{5}[/tex], so you have to find half of $15 to find out what [tex]\frac{1}{5}[/tex] of Aiden's money is.
15/2 = 7.5. [tex]\frac{1}{5}[/tex] of Aiden's money is $7.50.
7.5 × 5 = 37.5, so Aiden had $37.50 before he put some into his piggy bank.
Describe the effect f(1/4x) will have on the function f(x) = x2. The vertical coordinates will increase their distance from the x-axis by a factor of 4. The vertical coordinates will decrease their distance from the x-axis by a factor of 4. The horizontal coordinates will increase their distance from the y-axis by a factor of 4. The horizontal coordinates will decrease their distance from the y-axis by a factor of 4.
Answer:
It is c
Step-by-step explanation:
what is this multiplacation?
Answer:
2 5/18
Step-by-step explanation:
multiply across.
Answer:
improper fraction is 77/18 mixed number form 4 5/18 decimal form 4.27 thank me later
Step-by-step explanation:
find the zero of the polynomial
2x²+9x+4
Answer:
x=-4 or x=-1/2=-0.500
Step-by-step explanation:
Answer:
x= -4 or x= -0.5
Step-by-step explanation:
use a quadratic formula calculator or graph it on desmos
The temperature was very cold then it dropped 10 degrees and then it increased 40 degrees the temperature is now 16 degrees. What is the starting temperature?
Answer:
The initial temperature was To = -14 degrees
Step-by-step explanation:
Solution:-
- We will take the starting temperature to be = Ti
- The final temperature, Tc = 16 degrees
- We are given that there is a drop of 10 degrees from initial temperature To. We can mathematically express this as:
To - 10
- Then there is a rise of 40 degrees after the drop of 10 degrees. The mathematical expression would be:
To - 10 + 40
- The current temperature is Tc. We can equate the expression developed to final temperature:
To - 10 + 40 = Tc
- Solve for To:
To = 16 - 40 + 10
To = -14 degrees
Answer:
-14 degrees
Step-by-step explanation:
In this question, we are asked to calculate the starting temperature if we know what the temperature is now and the kind of temperature change that has happened.
Now, since we do not know the initial temperature , let’s call it x
from the question, it dropped by 10 and increased by 40 and finally with a temperature of 16.
mathematically
x-10+40= 16
x+30 = 16
x = 16-30
x = -14
12. A company charges $8 to make a pattern for an order of t-shirts and $11 for each t-shirt it produced from the pattern. The expression $11n + $8 represents the cost of n t-shirts with the same pattern. Find the total cost for 35 t-shirts with the same pattern.
Answer:
Total cost of t-shirts = $393
Step-by-step explanation:
A company charges a fixed rate of $8 for the printing of pattern on the whole order of t-shirts.
It also charges a variable rate of $11 for each t-shirt.
So the equation for the total cost of the t-shirts becomes,
Total cost of t-shirts = $8 + $11n
Where n is the number of t-shirts.
We are given n = 35 t-shirts
So the total cost of t-shirts are,
Total cost of t-shirts = $8 + $11(35)
Total cost of t-shirts = $8 + $385
Total cost of t-shirts = $393
Figure A is a scale image of Figure B.
What is the value of x?
Answer:
5
Step-by-step explanation:
You see if A is a scale representation of B then 2cm rep 5cm.
thereby, We can say that 1cm rep 2.5cm in the scale.
1cm rep 2.4cm
=12.5cm
12.5 ×1\2.4 =5cm
x=5cm
together preston and horatio have 49 video games. horatio has 11 more then preston. how much does each person have
each person has about 19 each
all you have to do is 49-2=38
38 divided by 2 = 19
Horatio has 30 video games and Preston has 19
Step-by-step explanation:Set up an equation:
x = Games horatio has
Since theres two people we will give x the coefficient of 2
You get 11 from how much more horatio has
49 is the total
The Equation
49 = 2x + 11
Solve
49 = 2x + 11
-11 - 11
38 = 2x
19 = x
Preston has 19 video games and since horatio has 11 more horatio has 30 video games
How many centimeters are in 2.37 meters???
Answer:
237 centimeters
Step-by-step explanation:
A foot = 30 centimeters
We know 1 meter or 1m is equivalent to around 3 feet. The exact measurement of a meter is 3.28 feet. So 1m = 100 centimeters because one foot equals 30 centimeters. .28 of a foot is 10 cm.
2 meter = 200 cm
.37 = 37 centimeters because each 0.01 in a meter = 1 cm. And there are 100 cm in a meter so we can accurately say 2.37 meters are 237 cm.
P.S
Have an Amazing Day! I Hope This Helps and Good Luck!
-Faker/Tosrel
In the figure below, ∠APE and ∠EPD are congruent.
What is the arc measure of AC on circle P in degrees?
Answer:
P = 54 so
arc AC = 150
Step-by-step explanation:
The measure of AC on circle P in degrees is 118degrees
To get the measure of the arc AC on the circle, we will use the formula for calculating the angle at a point.
The sum of the angle at a point is 360 degrees, hence:
arc AB + arcBC + arcCD + arc DE + arcEA = 360
If ∠APE and ∠EPD are congruent, this means that arc DE = arcEA. The equation becomes:
arc AB + arcBC + arcCD + arc DE + arcDE = 360
Substitute the given angles into the expression:
arc AB + arcBC + arcCD +2arcDE = 360
126 + 74 + 42 + 2arcDE = 360
242 + 2arcDE = 360
2arcDE = 360 - 242
2arcDE = 118
arcDE = 118/2
arcDE = 59
arcAC = 2(arcDE)
arcAC = 2(59)
arcAC = 118 degrees
Hence the measure of AC on circle P in degrees is 118degrees
Learn more here: https://brainly.com/question/24356953
To multiply two fractions, multiply the numerator by the
Answer:
Other numerator.
Answer:
multipy the numerator by the other numerator
Narancia out~!
What is the volume of a cube with a side length that measures 112 ft?
Answer:
1,404,928 is the volume of a cube with a side length that measures 112 ft
Answer:
1,404,928 is the volume
Which equation can be used to find the volume of this solid? A triangular prism. The triangular base has a base of 11 inches and height of 7 inches. The height is 9 inches. V = 11 times 9 times 7 V = 11 + 9 + 7
Answer:
V = 11 times 9 times 7
Step-by-step explanation:
To answer this question, a dimensional analysis must be done.
The volume has cube length as a unit, that is, l ^ 3
We analyze each option
V = base * height * height
ignoring what each one means, we know that each one is measured in length therefore:
V = L * L * L = L ^ 3 that is to say that in this way the volume can be found.
The other way is:
V = base + height + height
If we replace, we have to:
V = L + L + L = L, and the volume does not have units of length, therefore this option is not viable.
Which means that the option of V = 11 times 9 times 7 is correct.
I must mention, that the true way to calculate the volume in this case would be:
V = Base area * height
V = (base + height / 2) * height
What is the difference of the rational expressions below?
Answer: A
Step-by-step explanation:
We need to get the denominators to be same first before we can do anything to the numerator.
The LCD (lowest common denominator) is [tex]3x^{3}[/tex]. To find the LCD, multiply the denominators together: [tex]x^{3}[/tex] · [tex]3x[/tex] = [tex]3x^{3[/tex].
Below, we are trying to get the denominators to equal the same or to [tex]3x^{3}[/tex].
[tex]\frac{3}{3} (\frac{4}{x^{3} } ) - \frac{x^{2} }{x^{2} } (\frac{2x-1}{3x} )[/tex]
[tex]\frac{12}{3x^{3} } - \frac{2x^{3}-x^{2} }{3x^{3} }[/tex]
Now that the denominators are the same, we can subtract the numerators from each other.
[tex]\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} } \\[/tex]
[tex]\frac{12-2x^{3} +x^{2} }{3x^{3} }[/tex]
Now, we can just reorganize the variables.
Answer: A or [tex]\frac{-2x^{3} + x^{2}+12 }{3x^{3} }[/tex]
nelson scores 27 out of 40 in a history test. workout his score as a percentage.
Answer:
Step-by-step explanation:
25
Answer:
27 X
__ = __
40 100
cross multiply divide. meaning 27*100 = 40*X. -> 2700 = 40*X. also meaning the answer is 2700 divided by 40 = X.
plug 2700/40 into a calculator. answer 67.5%
Step-by-step explanation:
Evaluate the expression (2a)3
Final answer:
To evaluate the expression (2a)³, we cube the numeric term, resulting in 8, and multiply the exponent of the variable 'a' by 3, which gives us the final result of 8a³.
Explanation:
The expression given, (2a)³, requires us to cubing of exponentials. Cubing in mathematics involves raising a number or expression to the third power. In this case, the number 2 and the variable a are multiplied together first, and then that result is raised to the power of three. To evaluate this expression, you would do the following steps:
Cube the digit term in the usual way, which is 2 cubed or 23, which equals 8.Multiply the exponent of the exponential term by 3. Since the original expression has the variable 'a' to the first power, multiplying the exponent by 3 means 'a' will now have an exponent of 3.Combining these results, the expression (2a)³ becomes 8a³.
Joan, Kylie and Lillian all celebrate their birthdays today. Joan is 2 years younger than Kylie, and Kylie is 3 years older than Lillian. Which of the following could be the combined age of all three birthday celebrants today?A. 51
B. 52
C. 53
D. 54
E. 55
Answer: Option 'B' and 'D' are correct.
Step-by-step explanation:
Since we have given that
Let the age of Lilian be 'x'
Let the age of Kylie be 'x+3'.
Let the age of Joan be 'x+3-2=x+1'.
So, According to question, we get :
Total sum of all three birthday celebrants today would be
[tex]x+x+3+x+1=3x+4[/tex]
If we put 52, we get that
[tex]3x+4=52\\\\3x=52-4\\\\3x=48\\\\x=\dfrac{48}{3}=16[/tex]
If we put 55, we get that
[tex]3x+4=55\\\\3x=55-4\\\\3x=51\\\\x=\dfrac{51}{3}\\\\x=17[/tex]
Hence, Option 'B' and 'D' are correct.
Using algebra, we express each person's age in variables, create a relationship between them, and find that the only option that can represent their combined age as a sum of 3L + 4 is 52. Therefore, option B is the correct answer.
To solve this problem, we can begin by assigning variables to each person's age and then creating equations based on the information provided. Let's let the variable L represent Lillian's age, K represent Kylie's age, and J represent Joan's age.
From the problem, we know that:
Joan is 2 years younger than Kylie: J = K - 2
Kylie is 3 years older than Lillian: K = L + 3
Now, using the second equation, we can express Joan's age in terms of Lillian's:
Substitute the value of K from the second equation into the first: J = (L + 3) - 2
This simplifies to: J = L + 1
Now we can express the combined age of Joan, Kylie, and Lillian:
Combined age: J + K + L
Substitute J and K with the expressions in terms of L: (L + 1) + (L + 3) + L
Add them: 3L + 4
Now, we have to check which option is divisible by 3 when 4 is subtracted from it because the combined age should be in the form 3L + 4. Among the options given:
A. 51 - 4 = 47 (Not divisible by 3)
B. 52 - 4 = 48 (Divisible by 3)
C. 53 - 4 = 49 (Not divisible by 3)
D. 54 - 4 = 50 (Not divisible by 3)
E. 55 - 4 = 51 (Not divisible by 3)
The correct answer is option B, which makes the combined age of Joan, Kylie, and Lillian equal to 52 years.
Hii help I to lazy to do it
Answer:
3 cans
Step-by-step explanation:
We need to find the area of the deck
A = 9 1/9 * 3
Changing to an improper fraction
9 1/9 = (9*9+1)/9 = 82/9
A = 82/9 *3 = 82/3
Changing back to a mixed number
82/3 = 27 1/3
Each can covers 10 m^2
We will need 3 cans
Answer:
3 cans
Step-by-step explanation:
3*9 1/9=27.3 meters^2
the closest number of cans for 27.3 meters^2 is 3 because
1 can=10 meters^2
2 cans=20 meters^2
3 cans=30 meters^2
so by estimating 3 cans would be the closest compared to 20 and 10.