Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
Answer:
C. 325.
Step-by-step explanation:
The last term a5 = 85
a1 = 45
Sum of n terms = n/2 (a1 + l)
So here we have n = 5, a1 = 45 and the last term l = 85
= (5/2)(45 + 85)
= 5/2 * 130
= 325.
The required sum of the arithmetic series is 325.
Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.
The sum of the nth term of an arithmetic sequence is expressed as:
[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:
n is the number of terms
a is the first term
l is the last term
Given the following
a = 45
n = 5
an = l = 85
Substitute the given values in the formula above:
[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]
Hence the sum of the arithmetic series is 325
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The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is normal, what percent of students study between 22.9 and 25.7 hours
Answer:
Approximately 68% of students study between 22.9 and 25.7 hours.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 24.3 hours, standard deviation of 1.4 hours.
What percent of students study between 22.9 and 25.7 hours?
22.9 = 24.3 - 1.4
25.7 = 24.3 + 1.4
Within 1 standard deviation of the mean, so:
Approximately 68% of students study between 22.9 and 25.7 hours.
please help with math
Answer:
98
Step-by-step explanation:
2, 10, 18, 26, 34, 42, 50... 98
Hope this helps. Have a great day!
write an absolute value equations to satsify the given solution set shown on a number line -1/2 1/2 and a
Plz help fast
9514 1404 393
Answer:
|x| = 1/2
Step-by-step explanation:
Perhaps the simplest equation is ...
|x| = 1/2
__
You could get more elaborate:
|2x| = 1
3 -|6x| = 0
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
What is the correct way to read 43.106
Step-by-step explanation:
Forty three thousand one hundred and six
Answer:
Forty three AND one hundred six thousandths
Step-by-step explanation:
If there is a comma ( , ) between the two numbers, you are correct.
If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals. Those are the "th" numbers. 1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.
If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six" or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".
the mubrer
2. The first term in a sequence is 3.
The rule for the sequence is to multiply by 3 then add 2
Write the next 3 terms in the sequence
Answer:
3, 11, 35.
Step-by-step explanation:
The first 3 terms of the sequence can de written as:
n, 3n + 2, 3(3n + 2) + 2
So when n = 3 the first 3 terms are
3, 3(3) + 2, 3(3(3) + 2)) + 2
= 3 , 9 + 2, 33 + 2
= 3, 11, 35.
Five trucks are to be transported on a ship. Each one weighs 3200 kg and comes
with 8 tyres which weigh 125 kg each. what is the total weight
Total No of trucks: 5
Weight of trucks: 3200Kg
Total weight of trucks: 3200×5
= 16000kg
Total no of tyres = 5 ×8
= 40
Weight of each tyre = 125kg
Total weight of tyres = 125 × 40
= 5000Kg
The total weight of trucks and tyres: 16000 + 5000
= 21000Kg
Answered by Gauthmath must click thanks and mark brainliest
hawkville's population is 2500 people. next year the town clerk expects the population to grow by 1.2%, how many new residents will hawkville have next year?
Answer:
30 new residents
Step-by-step explanation:
Find how many new residents they will have by finding 1.2% of the current population.
2500(0.012)
= 30
So, Hawkville will have 30 new residents
Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m = 8 normal subjects was 1.71 mm, and the sample standard deviation was .53; for n = 10 CTS subjects, the sample mean and sample standard deviation were 2.53 and .87, respectively.
Required:
a. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects?
b. State and test the relevant hypotheses using a significance level of 0.01.
Answer:
Hence, data does not suggest the true average gap detection threshold for CTS subjects exceeds that for normal subjects.
Step-by-step explanation:
H0 : μ1 = μ2
H1 : μ1 < μ2
Given :
m = 8 ; x1 = 1.71 ; s1 = 0.53
n = 10 ; x2 = 2.53 ; s2 = 0.87
The test statistic :
(x1 - x2) / √(s1²/m + s2²/n)
(1.71 - 2.53) / √(0.53²/8 + 0.87²/10)
-0.82 / √0.1108025
Test statistic = - 0.82 / 0.3328700
Test statistic = - 2.463
The degree of freedom using the conservative approach :
Smaller of (10 - 1) or (8 - 1)
df = 7
TCritical value(0.01, 7) = 2.998
Decision region :
Reject H0 if |Test statistic| > |critical value|
Since, 2.463 < 2.998 ; WE fail to reject H0 ; Hence result is not significant at α = 0.01
Determine a scalar c so that the angle between a = i + cj and b = i + j is 45°.
Answer:
c=0
Step-by-step explanation:
ATQ a.b=|a||b|sin(45)
1+c=sqrt(1+c^2)*sqrt(2)*1/sqrt(2)
1+c=sqrt(1+c^2)
(1+c)^2=(1+c^2)
2c=0, c=0
The required simplified value of c is zero for which the angle between a and b is 45°.
What is a vector?Vector is defined as the quantities that have both magnitude and direction are called a vector quantity and the nature of the quantity is called a vector.
Here,
scaler product is given as,
a . b = |a|.|b|cos45
(i + cj). (i + j) = √[1² + c²] . √[1²+1²] × 1/√2
1 + c = √1 + c²
Squaring both sides
(1 + c)² = 1 + c²
1 + c² + 2c =1 + c²
2c = 0
c = 0
Thus, the required simplified value of c is zero for which the angle between a and b is 45°.
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The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
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What is the remainder when (2x^3 + 4x^2 – 32x + 18) = (x + 3)?
Answer:
X= -5.3 & Y= -2.34
X= 0.49 & Y= 3.49
X= 2.85 & Y=5.85
Step-by-step explanation:
To find the intersection you would need to graph it and locate where both lines will intersect.
Question 2
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>
B 0.67/1
The measure of one angle of a right triangle is 0° more than the measure of the smallest angle.
Find the measures of all three angles, and separate your answers with commas.
9514 1404 393
Answer:
45°, 45°, 90°
Step-by-step explanation:
If the difference of two angles is 0°, then they are congruent, and the triangle is isosceles.
The angle measures of the isosceles right triangle are 45°, 45°, 90°.
Slope 0; through (-5, -1)
with steps please.
Step-by-step explanation:
0 slope means it has in x.
so the equation is y=-1, because that is the coord for the points'y axsis
7. Find the missing side. Round to the nearest tenth
Hi there!
[tex]\large\boxed{x \approx 19.6}[/tex]
We can use right triangle trigonometry to solve.
We are given the angle's adjacent side and are trying to solve for the hypotenuse, so:
Use cosine: cos Ф = A / H
Thus:
cos 30° = 17 / H
Simplify:
0.866 = 17 / H
Isolate for H:
H · 0.866 = 17
H = 17 / 0.866
H = 19.63 ≈ 19.6
Answer:
x = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = 17/x
x cos 30 = 17
x = 17/cos 30
x=19.62990
To the nearest tenth
x = 19.6
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
Answer:
[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]
Step-by-step explanation:
Express 80 inches in standard notation using feet and inches.
80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
The solution to the given problem is to use some standard conversion units that are:
1 foot = 12 inches1 inch = 0.8333 feetSolution:
As mentioned above that one inch is equal to 0.8333 foot therefore
1 foot = 12 inches
then,
80 inches would be equal to
= [tex]\frac{80}{12}[/tex] ft
= [tex]\frac{20}{3}[/tex] ft
= 6ft 8 inches
= 6' 8"
Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
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Graph the compound inequality on the number line. x > 7 or x < -4
OSEAMENTE no se la respuesta
7,25 x (y+5,6)=58 vậy y =
Answer:
y=2,4
Step-by-step explanation:
7,25x( y+5,6)=58
7,25y+ 40,6=58
7,25y=58-40,6
y=17,4:7,25
y=2,4
x
A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.
Lower endpoint______ Upper endpoint__
Answer:
it simple as look
Step-by-step explanation:
He y I a m r a v I t ha n k S
Wowowowowowowowowk
answer this now please :)
9514 1404 393
Answer:
E. 384 cu ft
Step-by-step explanation:
The sum of length and width is half the perimeter, so the width is ...
(40/2) -12 = 8 . . . feet
The depth is half that, so is 8/2 = 4 feet.
The volume is ...
V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³
Find the measure of TU
A. 8
B. 12
C. 14
D. 11
Answer:
D. 11
Step-by-step explanation:
First apply the secant-secant theorem to find the value of x.
Thus,
VU(TU + VU) = VW(BW + VW) (secant-secant theorem)
Substitute
(7)(x + 4 + 7) = (9)(-2 + x + 9)
7(x + 11) = 9(7 + x)
7x + 77 = 63 + 9x
Collect like terms
7x - 9x = 63 - 77
-2x = -14
Divide both sides by -2
x = 7
✔️Find TU
TU = x + 4
Substitute get value of x
TU = 7 + 4 = 11
Answer:
11
Step-by-step explanation:
Question 24 of 58
Four classmates collect data by conducting a poll. They
ask students chosen at random how many books they
have to read for English class.
• Kevin interviews 25 students.
• Mary interviews 92 students.
• Sydney interviews 24 students.
• Caleb interviews 31 students.
Whose results are probably the most trustworthy?
O A. Mary's
OB. Sydney's
C. Kevin's
D. Caleb's
SUBMIT
In how many distinct ways can the letters of the word MAMAS be arranged?
Answer:
120 ways
Step-by-step explanation:
There are 5 letters.
5! = 5*4*3*2*1
= 20*6
= 120
Answer:
The answer is 30. You cant repeat letters. Ther are 5 letters, the M and A are repeat letters so 5-2=3 5!/3! = 30
Step-by-step explanation:
What is the slope of the line that passes through the points (9, -1) and (4, -11)?
Write your answer in simplest form.
Answer:
2
Step-by-step explanation:
We have two points so we can find the slope
m = ( y2-y1)/(x2-x1)
= ( -11 - -1)/( 4 -9)
= (-11+1)/( 4-9)
-10/ -5
= 2
write the first 10 multiplies of 6 and 8 pairs of numbers and find this LCM
↪[tex] \huge\rm{answer: } \: \boxed{ \purple{24 }}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
M(6)= {0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ...}
M(8) = {0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...}
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge\boxed{ \boxed{ \rm{Hope \: this \: helps }}}[/tex]
Answer:
6=0,6,12,18,24,30,36,42,48,54,60
8=0,8,16,24,32,40,48,56,64,72,80
HCF=24,48
LCM=0,6,12,18,,30,36,42,48,54,60,8,16,24,32,40,,56,64,72,80
Translations _______ side lengths of the figure.
A. change
B. alter
C. preserve
D. all of these
Answer:
C. preserve
Step-by-step explanation:
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
rút gọn :
(x+2)^2+(3-x)^2= ?
Step-by-step explanation:
=x^2+2x+4+9-6x+x^2
=2x^2-4x+13
Do number three plz triangle theorem
Answer:
AA
Step-by-step explanation:
We know that all three angles are similar as shown by the markings
I would use AA, or the Angle Angle theorem
