Expand the target expression:
A sin(x + ϕ) = A (sin(x) cos(ϕ) + cos(x) sin(ϕ)) = -2 sin(x) + 4 cos(x)
Then we have
A cos(ϕ) = -2
A sin(ϕ) = 4
Recall that sin²(x) + cos²(x) = 1 for all x. Then
(A cos(ϕ))² + (A sin(ϕ))² = (-2)² + 4²
A² (cos²(ϕ) + sin²(ϕ)) = 4 + 16
A² = 20
A = √20 = 2√5
Also recall that tan(x) = sin(x)/cos(x) by definition. Then
(A sin(ϕ)) / (A cos(ϕ)) = 4 / (-2)
tan(ϕ) = -2
ϕ = arctan(-2) = -arctan(2)
Enter and solve an equation to find the complement of an angle that measures 38º.
Use x as your variable.
An equation is
The measure of x is
Answer:
52°
Step-by-step explanation:
The sum of an angle and its complement is 90°.
__
The sum of 38° and its complement, x, is 90°:
38 +x = 90 . . . . . an equation to find the complement of 38°
x = 90 -38 . . . . subtract 38 from both sides
x = 52 . . . . degrees
The measure of x is 52°.
Year Population
2011 - 118,000
2017 - 138,000
a. To the nearest hundredth
of a percent, what is the
percent of change from
2011 to 2017?
The percent of change is about a
___% increase.
Answer:
16% or 16.9492% I'm going to be honest I'm not 100% sure though
A rectangular tarp is 2 times as long as it is
wide. Its width is 8 yards. What is the area
of the tarp?
24 sq. yards
hope it helps...!!!
X Find the length and width of a rectangle whose width is 10 cm shorter
than its length and whose area is 200 cm squared. What is the SUM of
the length and width?
Answer:30
Step-by-step explanation: length is 20, Width is 20-10 =10
Area = 20×10=200
The manager of a restaurant chain wants to know how many times per month diners come to his restaurant. The table shows the number of visits in one month for three samples of 10 randomly chosen diners.
A table with three rows. Title. Text that reads: Number of visits to restaurant in one month. Row one. Text that reads: Sample 1. 5, 2, 6, 4, 4, 7, 2, 1, 2, 3. Total = 36. Row two. Text that reads: Sample 2. 2, 6, 1, 3, 4, 5, 2, 1, 5, 4. Total = 33. Row three. Text that reads: sample 3. 3, 3, 6, 4, 1, 5, 3, 4, 4, 5.
Answer the questions to find the means, compare the samples, and make a prediction.
1. What are the means of Samples 1 and 2? Show your work. (3 points)
2. What is the mean of Sample 3? Show your work. (3 points)
3. Based on the data, would you predict that, in one month, the average diner would visit the restaurant fewer than 3 times, 3 or 4 times, or, about 4 times? Explain your reasoning. (4 points)
The means of samples 1 and 2 is 3.45. The mean of sample 3 is 3.8. Based on the data, the average diner would visit the restaurant 3 or 4 times.
What is the mean of a sample?The mean of a sample is the average of all the data sets given in the sample. The mean of a sample is useful in calculating population averages, central tendency, standard deviation, etc.
Mathematically, the mean of a sample can be expressed as:
[tex]\mathbf{\overline X =\dfrac{sum \ of \ the \ terms }{no \ of \ terms } }[/tex]
[tex]\mathbf{\overline X =\dfrac{\sum X}{N} }[/tex]
The mean of sample 1 is given = 36The mean of sample 2 is given = 33Thus, the means of samples 1 and 2 is:
[tex]\mathbf{\overline X =\dfrac{36+33}{20} }[/tex]
[tex]\mathbf{\overline X =3.45}[/tex]
The mean of sample 3 is:
[tex]\mathbf{\overline X =\dfrac{3+3+6+4+1+5+3+4+4+5}{10} }[/tex]
[tex]\mathbf{\overline X =3.8}[/tex]
Based on the data, the average diner would visit the restaurant 3 or 4 times, because the mean of the samples lies between 3 to 4.
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Similar Shapes and Scale Drawings
Practice and Problem Solving: C
100 points pls :/ Using the two-way table, what percentage of the students that like to travel out of state do not like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
30%
33%
36%
41%
Answer:
41%
Step-by-step explanation:
step one to determine what the fraction would be you just read the question: first you have to see what they want to calculate the percentage of. In this case it's students who like traveling out of state but don't like camping. 88 students like traveling out of state and 36 of those students don't like camping so the fraction you have to use is 36/88 step two next you multiply your fraction by 100 to calculate your percentage 36/88×100= 40.9% step three since you have to round to the nearest whole percent your answer would be 41%
What is a scenario for y= 4x+2
Answer:
a club has 2 dollar down payment and 4 $ per week how much money is owed after 2 weeks
Step-by-step explanation:
20 POINTS!!!! ill mark brainliest! The hypotenuse of the triangle measures 18, what is the radius of circle A? Is the radius the same all around?
Answer:
The radius is 3 and it is the same all around
Step-by-step explanation:
Since The hypotenuse equals the two other sides squared, let's find out what those are.
[tex]\sqrt{9} + \sqrt{9} = \sqrt{18}[/tex]
Now, let's find the square root of those 9s.
[tex]\sqrt{9} = 3[/tex]
Those other sides we talked about (more specifically the base of the triangle) are the radius of the circle because of how they extend to the exterior of the circle, which means since their length is 3, the radius is also 3.
The radius is always constant so it is supposed to be the same all around.
Thang decided to borrow $5000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 9%. How much interest will Thang pay?
Answer:
$1350
Step-by-step explanation:
Simple Interest = Deposit ×Rate/100×Time
SI=5000×9/100×3
=$1350
Compare the process of solving |x – 1| 1 < 15 to that of solving |x – 1| 1 > 15.
The final answer of the solution is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15] and x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
For |x - 1 | + 1 < 15 , we should first break the modulus function .
Two cases are possible for this inequality ,
case 1 - when x ≥ 1
x - 1 + 1 < 15 ⇒ x < 15
putting the number line both x ≥ 1 and x≤ 15
Then, x∈ [1, 15)
case 2 - when x < 1
-x + 1 + 1 < 15
⇒ -x + 2 < 15
⇒ -x < 13 ⇒ x > -13
putting the number line both x > -13 and x < 1
then, x∈ (-13, 1)
now, answer is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15]
Again, for |x - 1| + 1 > 15
Similarly z there are two cases possible for this
case 1 :- when x ≥ 1
x - 1 + 1 > 15 ⇒ x > 15
Putting the number line both x ≥ 1 and x > 15
then, x ∈ [1, ∞)
case 2 - when x < 1
-x + 1 + 1 > 15 ⇒ x < -13
putting the number line both x < 1 and x < -13
Then, x∈ (-∞, 1)
hence, final answer is x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R
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HELP HEELP
The diagram shows a cone of height 8 units and base radius 6 units.
What is the surface area of its side?
Answer:
Option A :- if finding lateral surface area
Other information
radius r = 6 m
height h = 8 m
slant height s = 10 m
volume V = 301.592895 m3
lateral surface area L = 188.495559 m2
base surface area B = 113.097336 m2
total surface area A = 301.592895 m2
Step-by-step explanation:
Using the formulas
A=πrl+πr²
l=√r²+h²
Solving forA
A=πr(r+√h²+r²)=π · 6 · (6+√8²+6²)≈301.59289
What is the value of loge 36?
O
-6
-2
2
6
Answer:
B) -2
Step-by-step explanation:
[tex]log_{6} \frac{1}{36}[/tex] ORIGINAL
[tex]log_{6} 6^{-2}[/tex] REWRITE 1/36
-2 LOG RULE - 6's CANCEL
Hope this helsp!
Is my answer correct?
Answer:
[tex]\displaystyle (x,y) \longrightarrow (x+3, y+1)[/tex]
Step-by-step explanation:
We want to write a rule for the transformation shown.
We can see that ΔA'B'C' is the figure ΔABC shifted rightwards 3 units and upwards 1 unit.
In other words, all x-coordinates of ABC is increased by 3, and all y-coordiantes of ABC is increased by 1.
Therefore, the rule for the x-coordinate is:
[tex]\displaystyle x \longrightarrow x + 3[/tex]
And the rule for the y-coordinate is:
[tex]\displaystyle y \longrightarrow y + 1[/tex]
In conclusion, we have that:
[tex]\displaystyle (x,y) \longrightarrow (x+3, y+1)[/tex]
A regular decagon has a radius of 8 cm. what is the approximate area of the decagon? recall that a decagon is a polygon with 10 sides.
The approximate area of the decagon with a side of 8cm is 492.37 cm².
Given side of the regular decagon = 8cm
What is a regular decagon?A decagon is a polygon with 10 equal sides.
We know that area of a regular decagon with side a is given by:
[tex]A=\frac{5}{2} a^{2} \sqrt{5+2\sqrt{5} }[/tex]
So, the area A of the regular decagon with a side of 8cm=[tex]\frac{5}{2} 8^{2} \sqrt{5+2\sqrt{5} }[/tex]
[tex]A=160\sqrt{5+2\sqrt{5} }[/tex]
A=492.37 cm²
Therefore, the approximate area of the decagon is 492.37 cm².
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1335+0540 what is the answer
Answer:
1875
Step-by-step explanation:
1335 + 0540 = 1875
Answer:
1,875
Step-by-step explanation:
[tex]1335 + 540 = 1,875[/tex]
Hope this helps! : )
If PR = 20. then what is PX=
Answer:
PX = 10
Step-by-step explanation:
PR = 20
PX = PR/2 (diagonals of parallelogram bisect eachother)
or, PX = 20/2
so, PX = 10
Tammy received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.41 per pound. After buying the coffee, she had $19.54 left on her card. How many pounds of coffee did she buy?
Total money Tammy has = $70
Money she is left with now = $19.54
Therefore, the money she used on coffee =
70 - 19.54 = $50.46
Now,
1 pound coffee costs $8.41
Pounds of coffee she bought = 50.46 ÷ 8.41
= 6 pounds
The area of a trapezoid is 260 cm2. If the bases have lengths of 12 and 14, what is the height?
a 10
b 15
c 20
d 13
Please, help me. anyone?
Which rules of exponents will be used to evaluate this expression? select three options. startfraction left-brace (negative 8) superscript 4 baseline right-brace superscript negative 5 baseline over (negative 8) superscript 6 baseline endfraction fractional exponent quotient of powers power of a power power of a product negative exponent zero exponent
The 3 rules that we need to use to simplify the expression are:
Exponent of an exponent rule.Quotient of powers.Negative exponent.Which rule of exponents must we use?
As I understand, the expression that we have is:
[tex]\frac{((-8)^4)^{-5}}{(-8)^6}[/tex]
The first rule we need to use, is the exponent of an exponent rule, it says that:
[tex](a^n)^m = a^{n*m}[/tex]
If we apply that to the denominator, we get:
[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6}[/tex]
Now we need to use the quotient of powers:
[tex]\frac{a^m}{a^n} = a^{m - n}[/tex]
Using that we get:
[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-20 - 6} = (-8)^{-26}[/tex]
Finally, we use the rule for a negative exponent:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
So we get the simplified form:
[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-26} = \frac{1}{(-8)^{26}}[/tex]
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Answer:
B, C, and E
Step-by-step explanation:
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level α.
n = 40, α = 0.01
r = 0.402
r = ±0.312
r = 0.43
r = ±0.402
Answer:
r= 0.402
Step-by-step explanation:
It costs the same to produce both packages, so the company wants to reduce the amount of wasted space, or space not taken by the balls. which package should the company choose? the cylinder because it has about 27.5 in.3 less wasted space than the prism the cylinder because it has about 61 in.3 less wasted space than the prism the prism because it has about 22.5 in.3 less wasted space than the cylinder the prism because it has about 67 in.3 less wasted space than the cylinder
The package which the company should choose if it costs the same to produce the two products is the cylinder because it has about 27.5 in.3 less wasted space than the prism.
What is the Cost of Production?The term "cost of production" refers to all the costs that are involved when a company offers a service or manufactures a product.
Costs of production relate to the different expenses that a firm faces in producing a good or service.
This refers to the amount which is used to produce a good.
With this in mind, we can see that there are the given dimensions for the square prism and cylinder from the complete question.
Hence, because they cost the same, choosing the cylinder is the best choice because of the less wasted space than the prism.
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Answer:
It's A
Step-by-step explanation:
Answer number 7 please thank you
Answer:
[tex] \frac{25}{100} \times 1.20[/tex]
A railroad crew can replace 360 meters of rails in 6 days. How many kilometers of rail can they repair in 25days
The railroad crew repair 1500 km in 25 days if the railroad crew can replace 360 meters of rails in 6 days
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
A railroad crew can replace 360 meters of rails in 6 days.
Let's suppose the x kilometers of rail they can repair in 25v days
Per day they repair = 360/6 = 60 km/day
Then the x can be found:
x = 60×25
x = 1500 km
Thus, the railroad crew repair 1500 km in 25 days if the railroad crew can replace 360 meters of rails in 6 days.
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What is the equation in slope-intercept form of the line that passes through the point (2,-2)
and is perpendicular to the line represented by y = x + 2?
2
=X+2?
5
A y = 3x - 7
5
B
y = 2x + 7
+ 7
c y=-zx-3
5
C -2
X
5
D y=-3x + 3
The equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = x + 2 is y = -1/2 - 3
Equation of a lie in slope-interceptThe equation of a line in slope intercept form is expressed as:
y = mx + c
m is the slope
c is the intercept
Given the equation of a line y = x + 2, the slope of the line perpendicular is -1/2. If this line pass through the point (2, -2), the required equation will be
y - (-2) = -1/2(x+2)
2(y+2) = -(x+2)
2y + 4 = -x - 2
2y = -x - 6
y = -1/2 - 3
Hence the equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = x + 2 is y = -1/2 - 3
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Solve for x
3(3x-2)=39
Answer:
3(3x-2)=39
9x-6=39
9x=39-6
9x=33
x=33/9
x=11/3
Answer:
x=5
Step-by-step explanation:
First, distribute the left side. 3(3x-2)=39 3 x 3x=9x 3 x -2=-6 m So, we get 9x-6=39
Next, we add six to both sides. We get 9x=45.
Lastly , we divide both sides by 9 and get x=5.
Plug x=5 into the place where x is to check your work. 3(3(5) - 2)=39
3(15-2)=39 3(13)=39 39=39 Since 39 is equal to 39, the equation is true.
Write the domain and range of the graph below…
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's see what's the domain and range for the given function ~
[tex]\qquad \tt \dashrightarrow \:domain \in [ -5 , 4 ] [/tex]
or
[tex]\qquad \tt \dashrightarrow \: - 5 \leqslant x \leqslant 4[/tex]
Because domain = all values of x between its maximum (4) and minimum (-5) value [ including them ]
[tex]\qquad \tt \dashrightarrow \:range \in[ -4 , 9 ][/tex]
or
[tex]\qquad \tt \dashrightarrow \: - 4 \leqslant y \leqslant 9[/tex]
Because range = all values of y between its maximum (9) and minimum (-4) value [ including them ]
Lamar and Mimi are in the same math class. The table shows their scores on 6 math tests. Lamar Mimi 93 90 97 93 96 90 95 91 94 90 98 100 The best measure of center in this scenario is the , and its values for Lamar’s and Mimi’s data are and , respectively. When comparing the measures of center, we can conclude that generally Lamar’s scores are Mimi’s.
The best measure of centre is the mean , don't take median as we need average of marks here.
Lamar- 93,90,97,93,96,90Mimi:-95,91,94,90,98,100Mean of Lamar
93+90+97+93+96+90/6559/693.16%Mean of Mimi
95+91+94+90+98+100568/694.66%Mimi has been better
Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.
Could ΔABC be congruent to ΔADC by SSS? Explain.
Yes, but only if AB ≅ DC.
Yes, but only if BC ≅ DC.
No, because AB is not congruent to AC.
No, because AB ≅ DA.
Answer:
d
Step-by-step explanation:
god a 100 on edg
ΔABC cannot be congruent to ΔADC by SSS?l because D. No, because AB ≅ DA.
How to depict the triangle?It should be noted that when the three corresponding sides of the figures have the same length, it can be concluded that the triangles are congruent by SSS.
In this case, ΔABC cannot be congruent to ΔADC by SSS?l because AB is not equal to DA.
Therefore, the correct option is D.
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