Answer:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\cos(x)\tan(x)=\cos(x)[/tex]
On the interval [0, 2π).
First, we can subtract cos(x) from both sides:
[tex]\cos(x)\tan(x)-\cos(x)=0[/tex]
Factor:
[tex]\cos(x)\left(\tan(x)-1\right)=0[/tex]
Zero Product Property:
[tex]\cos(x)=0\text{ or } \tan(x)-1=0[/tex]
Solve for each case:
[tex]\cos(x)=0\text{ or }\tan(x)=1[/tex]
Using the unit circle:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{5\pi}{4}, \frac{3\pi}{2}\right\}[/tex]
However, since tangent isn't defined for π/2 and 3π/2, we remove them from our solutions. Hence:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
Hyo spent $48.84 for a gold-plated trophy that costs $37 per pound. How much did the trophy weigh?
In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were assigned to each of the three methods. The time required to complete the task was recorded. The following information is provided: MSTR = 45.89 and MSE = 6.27. What is the critical value of F if we want to determine whether the means of the three populations are equal at the 5% level of significance?
Answer:
The answer is "3.35".
Step-by-step explanation:
Treatment independence degree
[tex]= 3 - 1 \\\\= 2[/tex]
Grade of error independence
[tex]= 30 - 3 \\\\= 27[/tex]
[tex]\alpha = 0.05[/tex]
F is the critical value[tex]= 3.35[/tex]
with the use of the critical value table F or the Excel command [tex]FINV(0.05,2,27)[/tex]
Binomial distributions
The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 52.5%. What is the probability that in a random sample of 430 voters, less that 49.6% say they will vote for the incumbent?
Answer: the vote will get 82.45%
Step-by-step explanation:
1) Kyle puls $740 in the
bank for 5.5 years with a
27% interest rate. How
much money does he
have in the bank all
together after 5.5
years
Answer:
1,838.90
Step-by-step explanation:
Annual interest rate 27%=0.27 per year.
Solving our equation:
A = 740(1 + (0.27 × 5.5)) = 1838.9
A = $1,838.90
When Victoria goes bowling, her scores are normally distributed with a mean of 130 and a standard deviation of 11. What is the probability that the next game Victoria bowls, her score will be between 123 and 130, to the nearest thousandth?
Answer:
0.239 = 23.9% probability that the next game Victoria bowls, her score will be between 123 and 130
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 130 and a standard deviation of 11.
This means that [tex]\mu = 130, \sigma = 11[/tex]
What is the probability that the next game Victoria bowls, her score will be between 123 and 130?
This is the p-value of Z when X = 130 subtracted by the p-value of Z when X = 123. So
X = 130
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 130}{11}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
X = 123
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{123 - 130}{11}[/tex]
[tex]Z = -0.64[/tex]
[tex]Z = -0.64[/tex] has a p-value of 0.2611
0.5 - 0.261 = 0.239
0.239 = 23.9% probability that the next game Victoria bowls, her score will be between 123 and 130
I Jen has an account balance of more than $15. Is her account balance greater than or less than a debt of $20? Fully explain your reasoning in writing.
Solve for x.
9
2x-111
X
= [?]
Answer:
x=94
Step-by-step explanation:
I hope I'm correct. Here's my explanation: x+9 and 2x-111 would equal 180, hence the line (supplementary). So x+9+2x-111=180
x=94
hope this helps.
Step-by-step explanation:
x+9=2x-111( being corresponding angles )
x=2x-111-9
x-2x=-120
-x=-120
x=120
Last week, the daily low temperatures for a city, in degrees Celsius, were 5, 8, 6, 5, 10, 7, and 1. What was the average low temperature? Show your reasoning.
What is the first step in evaluating the expression shown below? (12 ÷ ( 7 . 4 − 3 . 6 ) + 8 − 2) A. Subtract 7 . 4 − 3 . 6 . B. Divide 12 ÷ 7 . 4 . C. Add 3 . 6 + 8 . D. Subtract 8 − 2 .
Answer:
A
Step-by-step explanation:
(12 ÷ ( 7 . 4 − 3 . 6 ) + 8 − 2)
Follow the order of operations, the first thing to do would be the parenthesis.
7.4 - 3.6 = 3.8
So, your answer would be A, Subtract 7 . 4 − 3 . 6.
Have a wonderful day!
Answer:
A hope you get it right
(☞ﾟヮﾟ)☞ ¯\_(ツ)_/¯
find the midpoint of (-1,2) (-4,-9)
Answer:
use this info to help answer it
Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.
20. Solve for x.
25
12
20
Answer:
x = 9.6
Step-by-step explanation:
25x = 12 x 20
25x = 240
x = 9.6
Jonah wants to make a one-sample
z
zz interval using
99
%
99%99, percent confidence to estimate what proportion of silicon wafers at his factory are defective. He wants the margin of error to be no more than
3
%
3%3, percent. A previous study suggests that about
6
%
6%6, percent of these wafers are defective.
If we assume
p
^
=
0.06
p
^
=0.06p, with, hat, on top, equals, 0, point, 06, what is the smallest sample size required to obtain the desired margin of error?
Answer:
416
Step-by-step explanation:
Kahn Academy
10 • (0.15 +q) for q= 2.6
Answer:
27.5
Step-by-step explanation:
Please let me know if you want an explanation for why this is the answer (comment on this answer). A lot of people don't actually read the explanations, so I wouldn't want to waste my time. However, if you would like it I would be more than happy to type one out for you. Thanks!
Which expression is equivalent to 7t + 2)?
1. 7t + 14
2. 7t +9
3. t+9
4. t+14
Answer:
1.
Step-by-step explanation:
7 * t = 7t
7 * 2 = 14
7(t+2) = 7t + 14
Add and check 5,655+7,978
Answer: 13,633
Step-by-step explanation: 5,655+7,978=13633
Check: 13,633- 5,655=7,978
Select the correct answer. Consider functions fandg f(3) = 5.2.1, for 3 + 2 and = + -6 4:2 – 16: + 16 96) = 4+ 48, for : * -12 Which expression is equal to 10) (+? OA . OB. 1 Ос. OD. 5+2 6
Answer:
A
Step-by-step explanation:
The slope of the line below is -2. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
Answer:
y=-2x-3
Step-by-step explanation:
Since the slope is -2, we can make an equation : y=-2x+b
Now plug in the point given to find b.
1=-2(-2)+b
1=4+b
b=-3
so, the equation is y=-2x-3
The Sine Function
Your sine regression model for a given problem is
y = 0.500 sin (0.222x - 1.509) + 0.521.
Use your model to predict y(95). Round your answer to the nearest hundredth.
a. y(95) = 0.27
b. y(95) = 0.47
c. y(95) = 0.17
d. y(95) = 0.85
Please select the best answer from the choices provided
Answer:
D. y(95) = 0.85
Step-by-step explanation:
I calculated it logically
Plz help me well mark brainliest if correct!!
What is the midline equation of y = -4sin (2x - 7) + 3?
Step-by-step explanation:
Thank you this is your answerPlz help me well mark brainliest if correct!.,....
Answer:
6cm
Step-by-step explanation:
I did 24 divided by 4 since a square has 4 sides
Help me on this question please
We need to split it into 2 + 3 + 5 = 10 'parts', meaning each 'part' is 18 KD.
Thus, Ahmed receives 18(2) = 36 KD, Qasim receives 18(3) = 54 KD, and Omer receives 18(5) = 90 KD
3. Calculate the value of x in the figure to the right: (2 Points)
Answer:
x = 12
Step-by-step explanation:
When two chords intersect each other inside a circle, the products of their segments are equal.
------------------
2x = 6 * 4
2x = 24
Divide both sides by 2
x = 12
Simplify: −2x−y−2z+4x−2y+3z
Answer:
2x - 3y + z
Step-by-step explanation:
hope this helped :]
Solve for line segment AB
Answer:
AB = 32
Step-by-step explanation:
Given:
AD = 40
CD = 9
Required:
Find the length of segment AB
Solution:
BC and CD are radius of the circle. Therefore,
BC = CD = 9
AB = AC - BC
AB = AC - 9
We need to find AC
Since AD is tangent, CD is perpendicular to AD, this means that <D is a right angle. This makes ∆ADC a right triangle.
Therefore, we can apply Pythagorean theorem to find AC.
Thus:
AC² = AD² + CD²
AC² = 40² + 9²
AC² = 1,681
AC = √1,681
AC = 41
Let's find BC:
AB = AC - 9
Plug in the value of AC
AB = 41 - 9
AB = 32
In the triangle below,
y = [? ] cm. Round to the
nearest tenth.
15 cm
X
35°
909
Answer:
12.3
Step-by-step explanation:
You will use cosine to solve for y because you are given the hypontenuse and need to find the adjacent side.
cos 35 degrees = adjacent/hypontenuse
cos 35 = y/ 15
15( cos35 ) = y
y=12.287
=12.3
What value of X makes the equation true -7x - (-5-x) = -9(2x-1) -
Answer:
x=17/9
Step-by-step explanation:
-7x-(-5-x)=-9(2x-1)
= -7x+5x+x= -18x+9
= -x= -18x+9
+18x +18x
=17x=9
x= 17/9
Hope this helps!
Answer:
-7x -(-5-x)=9(2x-1)
-7x+5x+x=18x+9
-x=-18x+18x
17x=9
x=17/9
Step-by-step explanation:
hopes this help
The table below shows the values for the function
y = f(x).
Complete the table for the
function
y = f(1/5x).
Given:
The table of values of function [tex]y=f(x)[/tex] is given.
To find:
The table of values of function [tex]y=f(\dfrac{1}{5}x)[/tex].
Solution:
The horizontal stretch is defined as:
[tex]g(x)=f(ax), 0<a<1[/tex]
Here, f(x) is horizontally stretched by factor a to get g(x).
The given function is:
[tex]y=f(\dfrac{1}{5}x)[/tex]
It means the function [tex]y=f(x)[/tex] is horizontally stretched by factor [tex]\dfrac{1}{5}[/tex] to get [tex]y=f(\dfrac{1}{5}x)[/tex].
So, we need to multiply the given x-values by 5 to get the required table of values.
Therefore, the required table of values is:
x y
-20 7
-5 -2
0 3
15 -4
30 5
PLEASE HELP ASAP!!!!
If two angles are adjacent and add up to 130º and one angle is 89º, what is the measure of the other angle?
Answer:
41
Step-by-step explanation:
130-89= other angle whic is 41
Consider the sequence of steps to solve the equation: 3(x - 4) + 5x 9x - 36
Given => 3(x-4)+ 5x 9x - 36
Step 1 = 3x - 12 + 5x-9x - 36
Step 2 -> 3x + 5x - 12-9x - 36
Step 3 8x - 12 - 9x - 36
Step 48x - 8x - 12 - 9x - 8x - 36
Step 5 => 0 - 12 - x - 36
Step 6-12 - 36
Step 7-12 + 36 x - 36 + 36
Step 8 = 24 x +0
Step 9 = 24 - x
Which property yields Step 1?
3)
A)
Distributive Property
B)
Multiplicative Identity
Multiplication Property of Equality
Answer:
Distributive Property
Step-by-step explanation:
You are distributing 3 to x and -4