Hello, precalc, need help on finding csc
Recall the double angle identity for cosine:
[tex]\cos(2x) = \cos^2(x) - \sin^2(x) = 1 - 2 \sin^2(x)[/tex]
It follows that
[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2 \implies \sin(x) = \pm \sqrt{\dfrac{1-\cos(2x)}2} \implies \csc(x) = \pm \sqrt{\dfrac2{1-\cos(2x)}}[/tex]
Since 0° < 22° < 90°, we know that sin(22°) must be positive, so csc(22°) is also positive. Let x = 22°; then the closest answer would be C,
[tex]\csc(22^\circ) = \sqrt{\dfrac2{1-\cos(44^\circ)}} = \sqrt{\dfrac2{1-\frac5{13}}} = \dfrac{\sqrt{13}}2[/tex]
but the problem is that none of these claims are true; cot(32°) ≠ 4/3, cos(44°) ≠ 5/13, and csc(22°) ≠ √13/2...
Annie's rectangular garden is 5 feet long and 3 feet wide. What is the area of her garden?
we know that
the dimensions of the first garden are------> 5 ft x 3 ft
perimeter first garden=2*[5+3]-----> 16 ft
the dimensions of the second garden are---> (5*2) ft x (3*2) ft
10 ft x 6 ft
perimeter second garden=2*[10+6]-----> 32 ft
so
The answer is
32
Draw the image of quadrilateral ABCD under a translation by 2 units to the left and 3 units up.
The image of the quadrilateral after the translation is added as an attachment
How to determine the image of the quadrilateral?The given parameter represents the quadrilateral ABCD on the graph.
On this graph, we have the coordinates of ABCD to be:
A = (2, -3)
B = (-1, 3)
C = (-1, -3)
D = (-4, -4)
The translation is given as
2 units to the left and 3 units up.
Mathematically, this can be represented as
(x, y) = (x - 2, y + 3)
So, we have
A' = (0, 0)
B = (-3, 6)
C = (-3, 0)
D = (-6, -1)
Next, we plot the above coordinates on the graph (See attachment)
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Answer:
look at the photo
Step-by-step explanation:
it just is
Someone help me with this
A water dunking tank at a carnival is in the shape of a right circular cylinder. Its height is 5 feet, and the radius of each base is 3 feet, as shown in the picture below.
Answer:
141.37 ft^3
Step-by-step explanation:
No question was asked, but based off of the given information, I will assume you want to know the volume of the circular cylinder.
The volume of a circular cylinder is: v=(π)(r^2)(h)
r=3
h=5
v=(π)(3^2)(5)
v = 141.37
10, the shorter side equals 7 and the longer side equals 14.
Angle A is the angle created by the hypotenuse and the longer side.
Angle C is the right angle. Draw the triangle and label all sides and
angles.
Answer:
I have no idea I am so sorrt
When Josiah buys a ticket at the local movie theater, he receives 100 reward points to use toward future purchases. He is offered a scratch-off card instead of the points, which will allow him to try for a higher point value. The three possible point awards on the scratch-off card are 25, 100, and 120. There is an equal number of cards for each point award in the stack he chooses the card from.
Which statement is true?
A
The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points.
B
The best option is to take the scratch-off card because two of the three possible point values on the card are the same or greater than the 100 points.
C
The best option is to take the scratch-off card because the 120-point value that is on the card is greater than 100 points.
D
The best option is to take the 100 points because the probability of being awarded more than 100 points on the scratch-off card is zero.
The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Since, there is an equal number of cards of point 25, 100, and 120
P(x =25) = P(x =100) = P(x =200) = 1/3
x: 25 100 120
P(x): 1/3 1/3 1/3
The expected value is:
E(x) = 25×(1/3) + 100×(1/3) + 125×(1/3)
E(x) = 245/3 < 300/3 = 100
Thus, the best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.
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Cate and Elena were playing a card game. The stack of cards in the middle had 28 cards in it to begin with. Cate added 8 cards to the stack. Elena then took 13 cards from the stack. Finally, Cate took 3 cards from the stack. How many cards were left in the stack?
Answer:
20
Step-by-step explanation:
28 + 8 = 36
36 - 13 = 23
23 - 3 = 20
If f(x) = 3x² and g(x) = x+2, find (f•g)(x)
Answer:
Step-by-step explanation:
3x^2(x +2) = 3x^3 + 6x^2 is the answer
Darren is making veggie burgers for his family. He will use all the burgers mix he made to form 4 burgers of equal weight. The recipe only makes 32 oz burger mix but Darren made more than that to make extra big burgers
Answer:
4 > 32
Step-by-step explanation:
The variable x represents how much each of Darren's burgers will weigh. Since he will form 4 burgers of equal weight, the expression 4x represents the total weight of the burgers.
And, since Darren will use more than 32 ounces of burger mix, 4x must be greater than 32.
This inequality shows the relationship.
4x > 32
Now, solve for x.
4x > 32
4x/4 32/4
divide 32 by 4
So the answer is x > 8
how to get the perimeter and area.
13. Given that y varies as x^2 and that y = 36 when x=3, find:
a) k
b) the value of y when x=2
c) the value of x when y= 64
Answer:
K=4
Y=16
X=4
Step-by-step explanation:
[tex]y = kx {}^{2} \\ finding \: k \: when \: y= 36 \: and \: x = 3 \\ 36 = k(3) {}^{2} \\ 36 = 9k \\ dividing \: through \: by \: 9 \\ \frac{36}{9} = \frac{9k}{9} \\ 4 = k \\ k = 4 \\ findnig \: y \: when \: x = 2 \\ y = 4(2) {}^{2} \\ y = 4 \times 4 = 16 \\ finding \: x \: when \: y = 64 \\ 64 = 4 \times x \\ 64 = 4x \\ dividing \: through \: by \: 4 \\ \frac{64}{4} = \frac{4x {}^{2} }{4} \\ 16 = x {}^{2} \\ square \: root \: bothsides \\ \sqrt{16} = x {}^{2} \\ 4 = x \\ x = 4[/tex]
Noah was given an assignment to build a rectangular prism with a volume of at least 32 cubic centimeters. If the area of the base is 4 squared centimeters, which inequality could represents the possible heights?
Answer:
h ≥ 8 cm
Step-by-step explanation:
Solving :
V ≥ 32 cm³
a = 4 cm²
h ≥ 32/4
h ≥ 8 cm
How am I supposed to do this? I WILL GIVE BRAINLEST!
Answer:
D. 28.Step-by-step explanation:
Students with 1 to 3 pairs of shoes:
About 32. Just say 32.Students with 13 - 15 pairs of shoes:
4. Just say 4.Solve 32 - 4:
32 - 4= 28.28 is your answer.What is the approximate volume of a soda can
that is 5 inches tall and has a 2 inch diameter?
3
The length of an arc is equivalent to its degree measure
a) True b) False
Answer:
The police caught the bank robbers(passive)
Answer:
1. it's False because the radian measure of an angle is the length..
Transcribed image text: h of the following statements as true or false. replace lace the underlined word(s) or expression to produce a true statement. The radian measure of an angle equals the length of the arc it intercepts.on the Any degree measure can be converted to radians 180 by by _. To construct the inverse of a trigonometric function, the function must be restricted to a domain on which the function is either always increasing or The length of an arc intercepted by an angle is proportional to the radius; therefore, a central angle of - in a circle with radius k will intercept an an with length kt A triangle with side lengths 7, 11.and 14 has an area of 120-21 Area : Jlo (16-706-Ingen llo
Step-by-step explanation:
Thanks don't forget to follow me brainly
Busi has a bag containing 20 balls. There are twice as much yellow balls than blue balls, but yellow balls are only a third of red balls. The green balls are the same number as the blue balls. How many of each of the ball
Answer:
12 red balls
4 yellow balls
2 blue balls
2 green balls
Step-by-step explanation:
set no. of yellow, blue, red and green ball as y, b, r, g respectively
y=2b
r=3y
g=b
y+b+r+g = 20 (translate all of them into b (smallest in qty)
2b + b + 3(2b) + b = 20
10b = 20
b =2
y = 4, r = 12, b =2, g =2
find the equation of circle (5,1) diameter 4 square root 5
Answer:
[tex](x-5)^2+(y-1)^2=20[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Given:
center = (5, 1)diameter = 4√5Diameter = 2r (where r is the radius)
⇒ r = 4√5 ÷ 2 = 2√5
Substituting these values into the equation:
[tex]\implies (x-5)^2+(y-1)^2=(2\sqrt{5})^2[/tex]
[tex]\implies (x-5)^2+(y-1)^2=20[/tex]
NO LINKS!!! Please help me with this graph
Find vertex
f(0)=(0)So
(0,0) is the vertexThe graph shifted 3 units right.
So new translation
g(x)=|x-3|Find y intercept
g(0)=|-3|=3But it's at (0,1) approximately
So compression factor
1/3Now last equation
g(x)=1/3|x-3|Accurate oneTake (-4,2)Find value
g(-4)=|-7|=7So compression factor
2/71/3.5So accurate equation is
1/3.5|x-3|Answer:
[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
The vertex of the parent function is at (0, 0) as [tex]f(0)=|0|=0[/tex]
From inspection of the graph, the vertex of the transformed function is at (3, 0). Therefore, there has been a translation of 3 units right:
[tex]\implies g(x)=f(x-3)=|x-3|[/tex]
(There has not been any vertical translation since the y-value of the vertex of the parent function and the translated function is the same)
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies g(x)=a\:f(x-3)=a|x-3|[/tex]
The line goes through points (10, 2) and (-4, 2).
Substituting one of these points to find a:
[tex]\implies a|10-3|=2[/tex]
[tex]\implies 7a=2[/tex]
[tex]\implies a=\dfrac{2}{7}[/tex]
Therefore,
[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]
PROOF find the correct statements and reasons to complete the two column proof
Given: B is the midpoint of AC
D is the midpoint of BE
BC = BD
Prove: AC = BE
Answer: ac bd be 2bd
Step-by-step explanation: addion
P(S) = 5/8
P(T) = 1/8
If S and T are mutually exclusive events, find P(S or T),
Answer:
P(S ∪ T) = 3/4
Step-by-step explanation:
Given:
P(S) = 5/8P(T) = 1/8For mutually exclusive events S and T,
P(S ∪ T) = P(S) + P(T)
Therefore,
P(S ∪ T) = (5/8) + (1/8)
= 6/8
= 3/4
NO LINKS!!! Exponential Growth and Decay Part 1
Problem 1
a = 2500 = starting amount
b = 1 + r = 1 + 0.035 = 1.035 = growth factor
The equation is [tex]y = 2500*1.035^x[/tex] as it is in the form [tex]y = a*b^x[/tex]
Plug in y = 5000 and solve for x.
[tex]y = 2500*1.035^x\\\\5000 = 2500*1.035^x\\\\1.035^x = 5000/2500\\\\1.035^x = 2\\\\\log(1.035^x) = \log(2)\\\\x\log(1.035) = \log(2)\\\\x = \log(2)/\log(1.035)\\\\x \approx 20.148792\\\\x \approx 21\\\\[/tex]
I rounded up to get over the hurdle. This is because plugging x = 20 will lead to y being smaller than $5000, so we must use x = 21.
Answers:The function is [tex]y = 2500*1.035^x[/tex]It takes about 21 years to reach $5000=========================================================
Problem 2
a = 4.22 = starting amount
b = 1 + r = 1 + 0.031 = 1.031 = growth factor
The equation goes from [tex]y = a*b^x[/tex] to [tex]y = 4.22*1.031^x[/tex]
Plug in y = 9.33 and solve for x.
[tex]y = 4.22*1.031^x\\\\9.33 = 4.22*1.031^x\\\\1.031^x = 9.33/4.22\\\\1.031^x \approx 2.21090047393365\\\\\log(1.031^x) \approx \log(2.21090047393365)\\\\x\log(1.031) \approx \log(2.21090047393365)\\\\x \approx \log(2.21090047393365)/\log(1.031)\\\\x \approx 25.9882262216245\\\\x \approx 26\\\\[/tex]
Answers:The function is [tex]y = 4.22*1.031^x[/tex]It takes about 26 years for the ticket to reach the price of $9.33=========================================================
Problem 3
a = 400 = initial value
b = 1 + r = 1 + 0.25 = 1.25 = growth factor
The template [tex]y = a*b^x[/tex] updates to [tex]y = 400*1.25^x[/tex]
Plug in y = 3000 and isolate x.
[tex]y = 400*1.25^x\\\\3000 = 400*1.25^x\\\\1.25^x = 3000/400\\\\1.25^x = 7.5\\\\\log(1.25^x) = \log(7.5)\\\\x\log(1.25) = \log(7.5)\\\\x = \log(7.5)/\log(1.25)\\\\x \approx 9.029627\\\\x \approx 10\\\\[/tex]
Like with the first problem, I rounded up to the nearest whole number. If you tried out x = 9, then y = 2980 approximately which is short of the goal of 3000. Trying x = 10 leads to y = 3725 approximately, which is now over the goal we're after.
Answers:The function is [tex]y = 400*1.25^x[/tex]It takes about 10 days for 3000 people to get infected.[tex]\\ \rm\Rrightarrow P=P_o(1+r)^t[/tex]
[tex]\\ \rm\Rrightarrow 5000=2500(1+0.035)^t[/tex]
[tex]\\ \rm\Rrightarrow 2=1.035^t[/tex]
[tex]\\ \rm\Rrightarrow log2=log1.035^t[/tex]
[tex]\\ \rm\Rrightarrow log2=tlog1.035[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log2}{log1.035}[/tex]
[tex]\\ \rm\Rrightarrow t=20.15[/tex]
We can't take 20 as it can cause depict in price .
So t=21years#2
[tex]\\ \rm\Rrightarrow 9.33=4.22(1+0.031)^t[/tex]
[tex]\\ \rm\Rrightarrow 9.33=4.22(1.031)^t[/tex]
[tex]\\ \rm\Rrightarrow 1.031^t=2.21[/tex]
[tex]\\ \rm\Rrightarrow log1.031^t=log2.21[/tex]
[tex]\\ \rm\Rrightarrow tlog1.031=log2.21[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log2.21}{log1.031}[/tex]
[tex]\\ \rm\Rrightarrow t=25.97\approx 26[/tex]
#3
[tex]\\ \rm\Rrightarrow 3000=400(1+0.25)^t[/tex]
[tex]\\ \rm\Rrightarrow 30/4=1.25^t[/tex]
[tex]\\ \rm\Rrightarrow 7.5=1.25^t[/tex]
[tex]\\ \rm\Rrightarrow log7.5=log1.25^t[/tex]
[tex]\\ \rm\Rrightarrow log7.5=tlog1.25[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log7.5}{log1.25}[/tex]
[tex]\\ \rm\Rrightarrow t=9.03[/tex]
Same like first case
t=101234
Equivalent Fractions Whole Number
8
4
=
4
2
=
?
4
1
=
8
2
=
?
6
2
=
3
1
=
?
6
6
=
3
3
=
?
Answer:
1) 2
2) 4
3) 3
4) 1
Step-by-step explanation:
8/4 is 2
8/2 is 4
3/1 is pretty simply 3
And lastly (and kind of least)...
3/3 is 1
Hope this helped you out!
For the following system of equations, the value of x is
The system of equation is x + 3y = 6
6x — бу = 4
Answer:
32/22
Step-by-step explanation:
X+3Y= 6--------(1) ×6
6X-6Y=4--------(2)×1
6X+18Y=36---------(3)
6X-6Y= 4-----------(4)
subtracting equation(4)from (3)
22X = 32
x= 32/22
Answer: a
Step-by-step explanation:
Use your shapes to create a new shape with an area of 1 square unit that is not a square. Trace your shape.
A new shape with an area of 1 square unit that is not a square can be formed by combining two small triangles
How to determine the new shape?The given parameters are:
Area of square = 1 square unitLarge triangles = 2Medium triangles = 1Small triangles = 4The area of each small triangle is:
Area = 0.5 square unit
Multiply both sides by 2
2 * Area of triangle = 1 square unit
Substitute Area of square = 1 square unit
2 * Area of triangle = Area of square
This means that a new shape can be formed by combining two small triangles
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Convert this repeating decimal to a fraction: 0.75757575....
Answer:
25/33
Step-by-step explanation:
Answer:
[tex]\frac{25}{33}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.7575..... (1) ← multiply both sides by 100
100x = 75.7575... (2)
subtract (1) from (2) thus eliminating the repeating digits
99x = 75 ( divide both sides by 99 )
x = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex] ← in simplest form
Last year direct marketing had $122,222 in sales. This year direct marketing's sales are down by 9%. What are direct marketings sales this year
First, i will multiply 122,222 x 0.09 which is equal to 10,999.98 Then, i will subtract 10,999.98 from 122,222 which is equal to 111,222.02. so the direct marketing sales this year are 111,222.02.
Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used.
Find the proportion in a t-distribution less than −1.4 if the samples have sizes n1=30 and n2=40.
Enter the exact answer for the degrees of freedom and round your answer for the area to three decimal places.
Using the t-distribution, it is found that the proportion in a t-distribution less than −1.4 if the samples have sizes n1=30 and n2=40 is of 0.083.
How to find a proportion in a t-distribution?The proportion is found using a calculator, with three inputs:
The tail of the test, if it is left, right, or two-tailed.The test statistic.The amount of degrees of freedom.In this problem, we have a left-tailed proportion, as we want the proportion that is less than a value, with test statistic t = -1.4 and 30 + 40 - 2 = 68 df, hence the proportion is of 0.083.
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( 9 × 10 2 ) + ( 7 × 10 3 )
Answer:
2/5 or 0.4
Step-by-step explanation: i'm smart
if a rhombus has an area of 264 square units. If DB=12 units, find AC
Using the formula for calculating the area of a rhombus, the length of /AC/ is 44 units
Calculating the area of a RhombusFrom the question, we are to determine the length of AC
The area of a rhombus is given by
[tex]A = \frac{pq}{2}[/tex]
Where A is the area
p and q are the diagonals
Then, for the given diagram,
[tex]A = \frac{/DB/ \times /AC/}{2}[/tex]
From the given information,
A = 264 square units
/DB/ = 12 units
∴ [tex]264 = \frac{12\times /AC/}{2}[/tex]
[tex]264 = 6\times /AC/[/tex]
[tex]/AC/ = \frac{264}{6}[/tex]
/AC/ = 44 units
Hence, the length of /AC/ is 44 units
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