Answer:
x = +1
x = -1
Step-by-step explanation:
x^4-1=0
x^4=+1
fourth root of x^4= fourth root of +1
x = +1
x = -1
Which of the following slopes of a line pass through points (1, -3) and (0, 2)?
m=5
m = -5
m = undefined
None of these choices are correct.
The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.
What is the Slope of a Line?Slope (m) = rise / run = change in y / change in x.
Given the points, (1, -3) and (0, 2):
Slope (m) = (-3 - 2)/(1 - 0)
Slope (m) = -5/1
Slope (m) = -5
Therefore, the slope of the line is: B. m = -5.
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What data collection
used in face-to-face
or written questionnaires?
method is
interview
O A. survey
O B. observation
O C. experiment
O D. publication
Answer:
survey (A)
A questionnaire (or someone asking questions) is considered to be a survey. It is "surveying" someone's opinion on data.
hope this helps!!
Find the inverse of the function.
y=x+8
Answer:
y^-1= x +8
Step-by-step explanation:
this may be helpful for you
Select the correct answer from each drop-down menu.
Consider functions hand k.
h(t) = 5r2 – 1
k(x) = √5x + 1
For > 0, the value of h(k(x)) is
0, functions hand k
For
the value of k(h(r
inverse functions.
Answer:
h(t)= 5r2-1
That the answer for the question
Skylar models the volume of a popcorn box as a right rectangular prism and the box can hold 69 cubic inches of popcorn when it is full. Its width is 33 in and its height is 5 3/4 in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer:
4/11 of an inch (about .4 of an inch)
Step-by-step explanation:
[tex]l \times 33 \times 5.75 = 69[/tex]
[tex]189.75l = 69[/tex]
[tex]l = \frac{69}{189.75} = \frac{4}{11} = .3636[/tex]
So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.
On December 13, 2007, one British pound was worth 2.04 U.S. dollars.
(a) On that date, how many pounds was 10.79 dollars worth?
Round your answer to the nearest hundredth of a pound.
pounds
(b) On that date, how many dollars was 178.98 pounds worth?
Round your answer to the nearest hundredth of a dollar.
dollars i need help with this problem.
Answer:
a) 5 pounds
b) 365 dollars
Which expression is equivalent?
Answer:
Last one/D 9^9/5/5^9/10
Step-by-step explanation:
I will give lots of points please help
Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
Part (a)The cake can be modeled as a cylinder with:
diameter = 9 inheight = 4 in[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]
If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.
[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]
Part (c)The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:
[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]
Part (d)Probability is approximately 10.6% (see above for calculation)
Part (e)If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
Bacteria colonies can increase by 73%
every 2 days. If you start with 55 bacteria
microorganisms, how large would the
colony be after 10 days?
Future Amount = [?] microorganisms
←time
Hint: Future Amount = 1(1+r) periods
↑
initial growth
amount rate
Round to the nearest whole number.
The size of the colony after 10 days is 852.
What is the size of the colony after 10 days?The growth rate of the colony can be represented with an exponential equation with the form:
FV = P(1 + r)^n
Where:
p = present population r = rate of growth n = growth factor = 10 days / 2 days = 555(1.73)^5 = 852
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If you currently makes 425 What is the gross they will earn If they work every week If the year
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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Enlarge the shape on scale factor 0
Answer:
Multiply with 2 to the original sides
What to do when forget the pasword to the account?
Answer:
usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"
For a fair coin, suppose you toss the coin 100 times.
What is the probability of getting more than 66 heads?
Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.
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.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For the binomial distribution, the parameters are given as follows:
n = 100, p = 0.5.
Hence the mean and the standard deviation of the approximation are given as follows:
[tex]\mu = np = 100(0.5) = 50[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5[/tex]Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.5 - 50}{5}[/tex]
Z = 3.3
Z = 3.3 has a p-value of 0.9995.
1 - 0.9995 = 0.0005.
0.0005 = 0.05%
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Can y’all help me with ! I need correct anwsers ! Please
Answer:
-0.875
Step-by-step explanation:
So you have the points -4.25 and 2.50. To find the midpoint you simply add the two and then divide by 2. This results in (-4.25 + 2.50) / 2 = -0.875
Last year over 10,000 students took an entrance exam at a certain state university. Ivanna's score was at the 36th percentile. Aldo's score was at the 19th percentile.
Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Last year, over 10,000 students took an entrance exam at a certain state university.
Let the maximum score be 100.
Ivanna's score was at the 36th percentile, will be
⇒ [(10,000 – 36) / 10,000] x 100
⇒ 99.64
Aldo's score was at the 19th percentile, will be
⇒ [(10,000 – 19) / 10,000] x 100
⇒ 99.81
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Solve, finding all solutions in [0, 2(pi)]
Answer:
x = π/12, 5π/12
Step-by-step explanation:
We can work this problem a couple of ways. We can convert it to single trig function, shifted horizontally. Or we can convert it to a double-angle equation.
__
horizontal shiftWe recall the sum of angles formula is ...
sin(x+y) = sin(x)cos(y) +cos(x)sin(y)
Using this, we can rewrite the left side of the equation using some angle offset y, and some scale factor k.
k·sin(x +y) = k·sin(y)·cos(x) +k·cos(y)·sin(x) = 2cos(x) +2sin(x)
finding the shift
Equating coefficients of cos(x) and sin(x), we can solve for k and y:
k·sin(y) = 2
k·cos(y) = 2
The ratio of these equations is ...
(k·sin(y))/(k·cos(y)) = 2/2
tan(y) = 1 ⇒ y = π/4
k = 2/sin(π/4) = 2√2
shifted equation
So, our original equation becomes ...
2√2·sin(x +π/4) = √6
Dividing by √2 and using the inverse sine function, we have ...
x +π/4 = arcsin((√3)/2) = π/2 ±π/6
x = π/4 ±π/6
x = π/12, 5π/12
__
double-angle equationIf we square both sides of the original equation, we get ...
(2sin(x) +2cos(x))² = (√6)²
4sin²(x) +8sin(x)cos(x) +4cos²(x) = 6
2sin(x)cos(x) = (6 -4)/4 = 1/2 . . . . use sin² +cos² = 1, subtract 4, divide by 4
Using the trig identity 2sin(x)cos(x) = sin(2x), we can find ...
2x = arcsin(1/2) = π/2 ±π/3 +2kπ . . . . k = an integer;
x = π/4 ±π/6 +kπ . . . . for integer k
x = {π/12, 5π/12, 13π/12, 17π/12}
We know that squaring the equation can introduce extraneous solutions, so we need to try these out. For x in the third quadrant, the sine and cosine values are both negative, so the only useful solutions here are ...
x = π/12, 5π/12
_____
Additional comment
Based on the above, we now know that any trig expression of the form ...
a·sin(x) +b·cos(x)
can be rewritten to the form ...
(√(a² +b²))·sin(x +arctan(b/a)) . . . . . a scaled and shifted sine function
The arctangent will have to take the signs of 'a' and 'b' into account in order to get the angle quadrant right.
Tìm số dư trong phép chia 3^{2020} chia cho 13
Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].
Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].
Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,
[tex]3^{12} \equiv 1 \pmod{13}[/tex]
Now, observe that 2020 = 168×12 + 4, so that
[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]
and since 3⁴ = 81 = 6×13 + 3, we end up with
[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
What must be added to -31 to get 12
Answer:
43
Step-by-step explanation:
31+12=43
Therefore adding 43 to -31 should give the answer 12.
Hii!
____________________________________________________________
Answer:
43
Step-by-step explanation:
We can find an answer to this question by setting up an equation.
-31+x=12
x is the unknown amount we should add to -31 to obtain 12.
Now, to solve it for the variable, x, we need to add 31 to both sides.
Upon doing this we obtain.
x=43
∴, 43 should be added to -31 to get 12
--
Hope that this helped! Best wishes.
--
Find the length of the side labeled . Round intermediate values
to the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth.
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!PLEASE DON'T HESITATE TO ASK WHERE YOU DON'T UNDERSTAND.Expression Math problem...help and get 15 pts!
When h = 0 , [f(x + h) - f(x)]/h = 2x +2 for the given expression.
The missing expression is f(x) = x² + 2x.
What is formula of difference quotient ?f(x+h)-f(x)/h is called the formula of difference quotient.
When h---> 0 ,
the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line
Here the the expression is
f(x) = x² + 2x
Determining f(x + h) by substituting x = x + h on both sides of the given f(x).
Then f(x + h) = (x + h)² + 2(x + h)
= x² + 2xh + h² + 2x + 2h
the difference f(x + h) - f(x).
f(x + h) - f(x) = [x² + 2xh + h² + 2x + 2h] - [x² + 2x]
= 2xh + h² + 2h
Divide the difference from h as in the formula of difference coefficient
[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h
= 2x + h + 2
So, when h = 0 , [f(x + h) - f(x)]/h = 2x +2
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(x^4) (3x^3-2) (4x^2+5x)
Answer:
12x^7+15x^6
Step-by-step explanation:
Change 3x^3-2 to 3x
(x^4)(3x)(4x^2+5x)
Multiply your single terms
(3x^5)(4x^2+5x)
Then distribute
12x^7+15x^6
Out of 310 racers who started the marathon, 289 completed the race, 18 gave up, and 3 were disqualified. What percentage did not complet
Answer:
7.1%
Step-by-step explanation:
Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%
As a unit price, a half-dozen for
$6.00 is
a. $36.00 each
b. $6.00 each
c. $0.50 each
d. $1.00 each
Considering only the values of β for which (1+cosβ)(1−cosβ)sinβ is defined, which of the following expressions is equivalent to (1+cosβ)(1−cosβ)sinβ?
Select the correct answer below:
sinβ
sin3β
secβ
1
sec2β
The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β
What are Trigonometric Ratios ?In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.
The trigonometric expression given in the question is
(1+cosβ)(1−cosβ)sinβ
(a+b)(a-b) = a² - b²
( 1 - cos²β)sinβ
By the trigonometric Identity
1-cos²β = sin² β
sin² β x sin β
sin³β
Therefore Option B is the correct answer.
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NEED HELP ASAP PLEASEE
Answer:
2nd one is the correct
a u.s dollar bill remains in circulation about 1 1/4 years. A u.s coin is in circulation about 22 1/2 times longer. About how long is a coin circulation brainly
Answer:
28.125
Step-by-step explanation:
22.5×1.25=28.125
Answer:
28 1/8
Step-by-step explanation:
1.25 x 22.5 = 28.125
Giving a test to a group of students, the grades and gender are summarized below
Grades vs. Gender
A B C
Male 17 18 5
Female 12 3 14
If one student was chosen at random,
find the probability that the student was female.
Probability = (Round to 4 decimal places)
Figure ABCD is a rhombus. Find the value of x.
58°
x = [ ? ]°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 32°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Diagonals of a Rhombus bisect each other at 90°
[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]
[ Sum of interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]
[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.
Figure ABCD is a rhombus.
Its diagonals intersect at right angle.
Let the another angle be x. Then we have
x + 58° + 90° = 180°
x + 148° = 180°
x = 32°
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please help with this problem
thanks so much
Answer:
5/17
Step-by-step explanation:
If we do the multiplication first, we get:
[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]
If we do the division next, we get:
[tex]\frac{4+1}{13+4} = 5/17[/tex]
Complete the remainder of the
table for the given function rule:
y = ²x + 4
X-6 -3 03 3 6
y 0 [?] [] [] []
Answer: 2, 4, 6, 8
Step-by-step explanation:
Just plug x into the equation for each one.
x = -3
[tex]y=\frac{2(-3)}{3} +4\\y=\frac{-6}{3} +4\\y=2[/tex]
With this one, you can see it is a linear equation and for every increase of 3 on x, y in increased by 2.
x -6 -3 0 3 6
y 0 2 4 6 8