Answer:
4450878
Step-by-step explanation:
Finding Side Lengths in a Right Triangle
What is the value of s?
15 units
С
5
B
15
S
D
Answer:
maybe it's 10.because c is 10,b is 10,and so as s.
hence s is 10 also.
Express the product of z1 and z2 in standard form given that [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + isin(\frac{2\pi }{5})][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2}) + isin(\frac{-\pi }{2})][/tex]
Answer:
Solution : 5.244 - 16.140i
Step-by-step explanation:
If we want to express the two as a product, we would have the following expression.
[tex]-6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right]\cdot 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Now we have two trivial identities that we can apply here,
( 1 ) cos(- π / 2) = 0,
( 2 ) sin(- π / 2) = - 1
Substituting them,
= [tex]-6\cdot \:2\sqrt{2}\left(0-i\right)\left(\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right)[/tex]
= [tex]-12\sqrt{2}\sin \left(\frac{2\pi }{5}\right)+12\sqrt{2}\cos \left(\frac{2\pi }{5}\right)i[/tex]
Again we have another two identities we can apply,
( 1 ) sin(x) = cos(π / 2 - x )
( 2 ) cos(x) = sin(π / 2 - x )
[tex]\sin \left(\frac{2\pi }{5}\right)=\cos \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]
[tex]\cos \left(\frac{2\pi }{5}\right)=\sin \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex]
Substitute,
[tex]-12\sqrt{2}(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}) + 12\sqrt{2}(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4})[/tex]
= [tex]-6\sqrt{5+\sqrt{5}}+6\sqrt{3-\sqrt{5}} i[/tex]
= [tex]-16.13996 + 5.24419i[/tex]
= [tex]5.24419i - 16.13996[/tex]
As you can see option d is the correct answer. 5.24419 is rounded to 5.244, and 16.13996 is rounded to 16.14.
If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4
Answer:
The correct answer is c
Step-by-step explanation:
Answer:
C.) 3/2
Explanation:
PLATO
-3(y-5)+6y-2 simplify using distributive property and then combine like terms ANOTHER ONE PLEASE
Answer:
3y+13
Step-by-step explanation:
-3(y-5)+6y-2
Distribute
-3y +15 +6y-2
Combine like terms
-3y+6y +15-2
3y +13
[tex]\bf \large{\purple{ \implies}} \tt \: - 3(y - 5) \: + \: 6y \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 15 \: + \: 6y \: - 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 6y \: + \: 15 \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: 3y \: + \: 13[/tex]
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Years in which U.S. presidents were inaugurated
Answer:
Interval Level of Measurement
Step-by-step explanation:
The Interval level of measurement highlights the distances between two measurements. These distances are meaningful and could be rated as low intervals or high intervals. Intervals also indicate class and order between measurements. The inauguration of the United States President is an event that occurs 72 to 78 days after the presidential election. It is usually done as a private and public oath-taking ceremony on January 20, four years after the last presidential election. So, even if the president is on a second term, this event must be held.
The last U.S presidential election occurred on January 20, 2017, and the next one will be held on January 21, 2021. So there is an interval of four years between the last and next U.S presidential inauguration ceremony.
Which of the following situations describe the expression 3 / (4/5)?
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW
Answer:
Choice D
Step-by-step explanation:
3 ÷ 4/5
We need to have 3 of something and divide it into 4/5
This eliminates choices B and C because those have 4/5 of something
Choice A is giving away which is subtracting
Choice D is 3 lbs divide into 4/5 lb groups
A ball thrown upwards hits a roof and returns back to the ground.
The upward movement is modeled by a function [tex]s=-t^2+3t+4[/tex]
s= −(t^2)+3t+4
and the downward movement is modeled by [tex]s=-t^2+3t+4[/tex]
s= −2(t^2)+t+7, where s is the distance (in metres) from the ground and t is the time in seconds.
Find the height of the roof from the ground.
Answer: 6 m
A ball thrown upwards from the altitude 4 m,
hits a roof and returns back to the ground.
upward movement: s= −t²+3t+4
downward movement: s=-2t²+t+7
Step-by-step explanation:
Let's calculate the intersection:
[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]
Sorry, i have forgotten the picture.
10/7p+13/8+15/2p=909/56 i NEED THiS solving multi step equations w fractions and #8 PLEASE
Answer:
P= 2
Step-by-step explanation:
10/7p+13/8+15/2p=-909/56
Combine like terms
10/7p+15/2p=-909/56-13/8
20p+105p/14=-909-13*7/56
125/14p=-909-91/56
125/14p= -1000/56
125/14p*14/125= -1000/56*14/125
simplify
P= 8/4=2
And for #8 n =1 I answered this question it
Search
Savannah used 2 quarts of paint on a summer project. She still had 5.
quarts of paint left when she was finished. How much paint did Savannah
have at first?
la cloud
Answer:
7 quarts
Step-by-step explanation:
total paint = paint used + paint left
total paint = 2 +5
total paint 7
An angle is 100° angle. how many degrees will you add it to make it a linear pair ?
Answer:
80
Step-by-step explanation:
linear pair = 180
Now,
100 + 80 = 180
The mathematics teacher proposes to his students that whoever determines their years of Experience as a teacher will have an extra point, for this they will have to solve the following expression
-5 + {4 * 6 + 3 + 1 + (3- (4-8) + (3-2)]}
How many years of experience does the teacher have?
Answer:
29 years of experience.
Step-by-step explanation:
So let's take the expression step by step. Remember that you need to follow the order of precedence here for the operations. Parentheses, exponentials, multiplication, and addition.
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( 4 - 8 ) + ( 3 - 2 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( -4 ) + ( 1 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 + 4 + 1 ] }
-5 + { 4 * 6 + 3 + 1 + [ 8 ] }
-5 + { 24 + 3 + 1 + 8 }
-5 + { 36 }
29
So the teacher has 29 years of experience.
Cheers.
The perimeter of the isoceles triangle is 54. The ratio of the leg to the base is 7:4. Find the length of the base
9514 1404 393
Answer:
12 units
Step-by-step explanation:
The ratio of the base to the other sides is ...
4 : 7 : 7
The perimeter is a total of 4 +7 +7 = 18 ratio units, so each ratio units stands for 54/18 = 3 length units.
The base length is then ...
(4 ratio units)(3 length units/ratio unit) = 12 length units
A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 10 minutes there are 140 bacteria, after how many minutes will there be 40 bacteria remaining? Round your answer to the nearest whole number.
Answer:
18 minutes
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the time,
and T is the half life.
A = 140 when t = 10. Solve for the half life:
140 = 700 (½)^(10 / T)
0.2 = ½^(10 / T)
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31
When A = 40, t is:
40 = 700 (½)^(t / 4.31)
0.057 = ½^(t / 4.31)
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8
Rounded to the nearest whole number, it takes 18 minutes.
The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
The half-life decay formula is given as,
N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]
Where T is half-life while t is the time taken.
N₀ is the initial amount,
As per the given,
N(t) = 140 when t = 10.
140 = 700 [tex](1/2)^{(t / T)}[/tex]
Take log both sides,
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31 minutes
Put N(t) = 40
40 = 700[tex](1/2)^{(t / 4.31)}[/tex]
Take log both sides,
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8 ≈ 18 minutes
Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".
For more about exponential function,
https://brainly.com/question/15352175
#SPJ2
Bianca took a job that paid $150 the first week. She was guaranteed a raise of 6% each week. How much money will she make in all over 8 weeks? Round the answer to the nearest cent. please answer with the reasoning, I want to learn how to solve this and not just get the answer. Thank you.
Answer:
$225.54 (hope it help)
Step-by-step explanation:
for 2nd week
$150 for the first week and a raise of 6% each week
which means 150+6%
6% of 150 is 9 (150x0.06)
150+9=159
and it repeats
for 3rd week
6% of 159 is 9.54 (159x0.06)
159+9.54=168.54
for 4th week
6% of 168.54 is 10.1124 (168.54x0.06)
168.54+10.1124=178.652
for 5th week
6% of 178.652 is 10.71912 (178.652x0.06)
178.652+10.71912=189.37112
an easier to do it is to just do 178.652 + 6% on your calculater
and I'll skip all the way to the 8th since you know the formula
212.777390432+6%=225.544033858
225.544033858≈225.54
What is the conjugate of 3+6i?
A -3 - 6i
B 3 - 6i
C 3 + 6i
D 9i
Answer:
B
Step-by-step explanation:
A conjugate is a term that has the same real part of its original but opposite terms of the second sign
Look at
[tex]3 + 6i[/tex]
The real part is 3 so B and C are the only possible answer.
The conjugate has the opposite sign of the second sign so the answer is
B
[tex]3 - 6i[/tex]
Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A
Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
This pattern follows the rule add 9. What are the next 3 terms?
An image of a pattern. Term one has 9 triangles, term two has eighteen triangles, term three has twenty seven triangles.
Answer:
Next three terms after 27 are 36, 45 and 54. I hope this will help .
The graph below represents which of the following functions?
Answer:
D
Step-by-step explanation:
The correct answer is D, try graphing them on desmos.
8. If 30 cents out of every 1 dollar goes to taxes and the rest is net income, what's the
ratio of taxes to net income?
d
A. 30 : 7
B. 3:10
C. 30 : 1
D. 3:7
Answer:
D. 3:7Step-by-step explanation:
1 dollar = 30 cents tax + 70 cents net income
The ratio of taxes to net income:
30 : 70 = 3 : 7Correct choice is D
If 30cents are out then net income=100-30=70
ratio:-
[tex]\\ \rm\Rrightarrow \dfrac{30}{70}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3}{7}[/tex]
[tex]\\ \rm\Rrightarrow 3:7[/tex]
How to simplify this expression??
Answer :
[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]
Step-by-step-explanation :
I did the explanation in the picture.
rate = 45 mph time=4 hours distance =
━━━━━━━☆☆━━━━━━━
▹ Answer
180 miles
▹ Step-by-Step Explanation
Distance = mph * hours
Distance = 45 mph * 4 hrs
Distance = 180 miles
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
A. 13
B. 52
C. 208
D. 104
Answer:
D. 104
Step-by-step explanation:
[tex]y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } [/tex]
when y is 26, x is 4:
[tex]26 = \frac{k}{ {(4)}^{2} } \\ k = 416[/tex]
when x is 2:
[tex]y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104[/tex]
Answer:
D; 104
This is the correct answer
[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]
In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.
The number of times that each prime divides the original integer becomes its exponent in the final result.
In here, Prime number 2 to the power of 2 equals 4.
[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]
First, We need to add fractions-
Rule:-
[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]
LCD = [tex]7 \cdot 2^{2}[/tex]
[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]
[tex]x=2[/tex]
OAmalOHopeO
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answer:
[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]
Step-by-step explanation:
Given that:
1) x ∝ √y
2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]
Combining the proportionality
=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
Where k is the constant of proportionality.
the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi
Answer:
James town is 5 meters higher than Takoradi .
Step-by-step explanation:
Given:
Height of James town = 2 meters below sea level
Height of Takoradi town = 7 meters below sea level
To find:
How much higher is James town that Takoradi = ?
Solution:
As we can see the standard of height is how much the town is below the sea level.
So, the height of town having lesser value will be at a higher level.
Value of Height of James town is lesser than that of Takoradi town.
Therefore, James town is at a higher level.
Difference of height = 7 meters - 2 meters = 5 meters
So, the answer is:
James town is 5 meters higher than Takoradi.
Which decimal is equivalent to
15/100?
A- O 0.015
B- 0.15
C-o 1.5
D- 0.0015
Answer:
D
Step-by-step explanation:
0.0015
hope this helps
Find the zeros of the function in the interval (-2 pie, 2 pie). f(x) = 3 cos x
Answer:
Roots are -π/2 and π/2
Step-by-step explanation:
[tex]{ \bf{f(x) = 3 \cos(x) }}[/tex]
when x is -2π:
[tex]{ \sf{f( - 2\pi) = 3 \cos( - 2\pi) }} \\ { \sf{ = 3}}[/tex]
hence -2π is not a zero of the function
when x is 2π:
[tex]{ \sf{f(2\pi) = 3 \cos(2\pi) }} \\ { \sf{ = 3}}[/tex]
hence 2π is not a zero of the function
when x is π/2:
[tex]{ \sf{f( \frac{\pi}{2}) = 3 \cos( \frac{\pi}{2} ) }} \\ { \sf{ = 0}}[/tex]
Hence ±π/2 is the zero of the function.
Labour costs, totalling $47.25, account for 63%
of a car repair bill. Calculate the total bill.
Answer:
75
Step-by-step explanation:
Let x = total bill
x*63% = 47.25
x *.63 = 47.25
Divide each side by .63
x*.63/.63 = 47.25/.63
x=75
Translate this sentence into a equation. 42 decreased by Jose’s savings is 16. Use the variable j to represent Jose’s savings.
Answer:
[tex]42-j=16[/tex]
Step-by-step explanation:
"Decreased by" means subtraction.
The information says 42 decreased "by Jose's savings", which is represented by j.
"Is" means equal to.
Put it all together:
[tex]42-j=16[/tex]
:Done
Answer:
j - 42 = 16
Step-by-step explanation:
J = Jose Savings
42 = the amount decreased
16 = the left amount
J-42 = 16
j = 16+42
J = 58
Jose's savings was $58.
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.
a) Conduct the appropriate hypothesis test using a 0.1 level of significance.
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
i. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
ii. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
iii. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
iv. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
Answer:
Step-by-step explanation:
99% =2.58
xbar / Point Est. 50.67
µ 50
σ 3.9
n 36
Confidence Interval
50-> (48.9,52.44) -> Fail to Reject H0
Test Statistic 1.0308
P-Value 0.1549