Answer: x²-x+6
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Since we are given the values of f(x) and g(x), we can directly subtract them.
x²+1+(5-x) [distribute +1]
x²+1+5-x [combine like terms]
x²-x+6
Answer:
[tex]\huge\boxed{(f+g)(x) = x^2 - x+ 6}[/tex]
Step-by-step explanation:
[tex]\sf f(x) = x^2 + 1\\g(x) = 5-x[/tex]
Adding both functions
[tex]\sf (f+g)(x) = x^2 + 1+ 5 - x\\(f+g)(x) = x^2 - x+ 6[/tex]
It takes 3 gardeners 30 minutes to plant 18 trees. How many gardeners would it take to plant 45 trees in 45 minutes
Answer:
It will take 7.5 gardeners to plant 45 trees in 45 minutes
Step-by-step explanation:
It takes 3 gardeners 30 minutes to plant 18 trees.
Let's determine the rate of this 3 gardeners
Rate= 18 trees/30 minutes
Rate= 2/5 trees per minute
So 3 gardeners= 2/5 trees per minute
But then one Gardner= 2/(3*5) trees per minute
One Gardner=2/15 trees per minute
Let's determine the number of gardeners it will take to plant 45 trees in 45 minutes
One Gardner=2/15 trees per minute
X(22 /3)= 2/15*(22.5/3)
It will take 7.5 gardeners to plant 45 trees in 45 minutes
is -1 a rational number.
Answer:
Yes it is a rational number
Step-by-step explanation:
Rational numbers include positive, negative numbers and 0 that can be ritten as ratio.
Answer:
yes
Step-by-step explanation:
ratio numbers include negatives and positives
Can someone help me out
3/196
Step-by-step explanation:
multiply everything
the sum of two numbers is 87. One of the numbers is 6 more than twice the other. what are the two numbers?
Answer:
27 and 60
Step-by-step explanation:
lets say the first number 'a' and the second number 'b'
1) The question says the sum of two number is 87 which means a + b = 87........given 1
2) we have another given which says one of the number is 6 morethan twice the other which means a = 2b + 6.......... given 2
a + b = 87
2b + 6 + b = 87 (we substitute 'a' with the given 2b + 6)
3b + 6 = 87
3b = 87 - 6
3b = 81
3b = 81
3 3
b = 27 ..... the first number
a = 2b + 6
a = 2 × 27 + 6
a = 54 + 6
a = 60..... the second number
hope u like it ❤️❤️❤️
For any question comment me
3=7-2(3z+2)
How to solve
Answer: z = 0 | Equation is not solvable
Step-by-step explanation:
We have 3 = 7 - 2(3z + 2)
When we distribute the 2, we get: -6z - 4 + 7 = 3
Combine like terms: -6z + 3 = 3
Subtract the left hand side 3 from the right hand side 3: -6z = 0
We can not divide by zero thus the equation is not solvable.
Laura bought a pair of shoes for 20$. The shoes were on sale for 15% off, and she also used a coupon for an extra 20% off. Before sales tax was applied, how much did Laura pay for the shoes?
Answer:
$13.60 before sales tax
Step-by-step explanation:
$20 x .85 (aka 15% off) = $17
then
$17 x .80 (aka 20% off) = $13.60
Use Lagrange multipliers to minimize the function f(x,y,z)=x2 +y2 +z2
subject to the following constraint: x+y+z-24=0
Assume that x, y, and z are positive
Question options :
A)64
B)192
C)128
D)384
Answer:
B)192
Step-by-step explanation:
Please find attachment
5(x + 3) - (9x - 4)
Answer:
-4x + 11
Step-by-step explanation:
Distribute and then Simplify
BD bisects ∠ABC. Find m∠ABD and m∠CBD
Answer:
Since BD bisects angle ABC, the resultant angles, angles ABD and CBD will be equal in magnitude. Since we are not given either the value of ABC nor are we given the figure, the answer we can get to from the given question is
angle ABD = angle CBD
Evaluate. (1/4)^−2−(5^0⋅2)⋅1^−1 Enter your answer in the box. HELP! 100 POINTS!
Answer:
[tex]\Huge \boxed{\mathrm{14}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex](\frac{1}{4} )^{-2} - (5^0) (2)(1^{-1})[/tex]
Solving for exponents and multiplying:
[tex](4 )^{2} - (1) (2)(1)[/tex]
[tex]16-2[/tex]
Subtracting:
[tex]\Rightarrow \ 14[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\huge\boxed{14}[/tex]
Step-by-step explanation:
[tex]\sf (\frac{1}{4} )^{-2} - (5^0 * 2 )* (1^{-1})[/tex]
Using law of exponents [tex]a^0 = 1[/tex] and [tex]1/a^m = a^{-m}[/tex]
=> [tex]4^2 - (1*2)*(1)[/tex]
=> [tex]16 - 2[/tex]
=> 14
what is the distance between the coordinates (2,9) and (10,7) round your answer to the nearest tenth
Answer:
8.2
Step-by-step explanation:
We can use the distance formula: [tex]\sqrt{((x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]\sqrt{(10-2)^2 + (7-9)^2} = \sqrt{8^2 + (-2)^2} = \sqrt{64+4} = \sqrt{68} = 2\sqrt{17} = 8.2[/tex]
For this exercise, use the following set of 16 scores (ranked) that con- sists of income levels ranging from about $50,000 to about $200,000. What is the best measure of central tendency and why? $199,999 $98,789$90,878 $87,678 $87,245 $83,675 $77,876 $77,743 $76,564 $76,465 $75,643 $66,768 $65,654 $58,768 $54,678 $51,354
Answer:
The median = Median = $77,153.5
Step-by-step explanation:
Given the data :
199999 98789 90878 87678 87245 83675 77876 77743 76564 76465 75643 66768 65654 58768 54678 51354
Measures of central tendency are used to describe the center or midpoint of a group of observation. They could include the mean, median and mode.
Mean described the average value of the distribution
Median, the middle observation.
Mode, the observation which occurs most
Using online calculator to save time ;
the mean = 83,111.06
Median = 77153.5
For the mode, all the values have a frequency of 1
Plotting the data on an histogram, it could be observed that the Data is positively skewed and hence, not symmetrical.
Since the distribution is not symmetrical, using the mean isn't the best and the mode is also not usable.
Therefore, the median seems to be the best of the 3 measures
What kind of lines are the edges of the length and the width of a piece of printer paper? A. parallel lines B. perpendicular lines C. neither
Answer:
[tex]\huge\boxed{B. \ Perpendicular \ Lines}[/tex]
Step-by-step explanation:
The edges of length and width of a piece of printer paper perpendicularly intersect each other.
=> Perpendicular Lines are those making an angle of 90 degrees with each other.
Answer:
Perpendicular lines
Step-by-step explanation:
H.
Please help! I need help with part B if 1000 students were surveyed what would the probability be of how many plays sports?
Answer:
188 students would play sports, out of 1,000.
Step-by-step explanation:
If the probability that a random high school student plays a sport is 0.188 (150/800), which means for every 1 high school student 0.188 of them play a sport. Multiply 0.188x1,000 to get 188 students who play a sport.
The area of a sector of a circle is given by the equation uppercase A = StartFraction pi r squared uppercase S Over 360 EndFraction, where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write? 360 uppercase A + pi r squared 360 uppercase A minus pi r squared StartFraction 360 + uppercase A Over pi r squared EndFraction StartFraction 360 uppercase A Over pi r squared EndFraction
Answer:360A/pi ^2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
i got it right
Mic
Point A is at ( – 6. 8) and point B is at (6, -7)
What is the midpoint of line
segment AB?
Answer:
(0, 0.5)
Step-by-step explanation:
Let M is the midpoint of the line
x-coordinate of the midpoint:
xM = ( xA + xB ) / 2 = (-6 + 6) / 2 = 0
y-coordinate of the midpoint:
yM = (yA + yB) / 2 = (8 - 7) / 2 = 1/2 = 0.5
Answer: M (0, 0.5)
Answer:
(0, 0.5)
Step-by-step explanation:
-38--25 +25-50 solve
Answer:
-38Step-by-step explanation:
[tex]-38-25+25-50[/tex]
Follow the PEDMAS order of operation
Add and subtract left (left to right )
[tex]\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\-\left(-25\right)=+25\\\\=-38+25+25-50\\=-13+25-50\\-13+25=12\\=12-50\\12-50=-38[/tex]
Answer: [tex]-38[/tex]
Add parentheses
[tex](-38--25)+(25-50)[/tex]
Subtract
[tex]-38-(-25)=-13\\25-50=-25[/tex]
Add
[tex](-13)+(-25)=-38[/tex]
Divide. 19,432 and 56 pls help me
Answer:
347
Step-by-step explanation:
Which shows a list of the first six prime numbers?
1, 3, 5, 7, 9, 11
1, 2, 3, 5, 7, 9
2, 3, 5, 7, 9, 11
2, 3, 5, 7, 11, 13
Answer:
Step-by-step explanation:
the fourth option shows a list of the first 6 prime numbers
Answer: Option 4. 2, 3, 5, 7, 11, 13
Step-by-step explanation:
Remember, 1 is neither a prime number nor a composite number, it only has one factor.
So, we can exclude the first and second choice.
The third one has 9. But 9 is not a prime number.
Factor of 9: 1, 3, 9
It has 3 factors
So, this is not prime number and it should be excluded.
The fourth one is a complete list of prime numberHope this helps!! :)
Please let me know if you have any question
Use the simple interest formula to determine the missing value. p=?, r=6%, t=9 months, i=81
Answer:
P = 1800
Step-by-step explanation:
The formula to calculate simple interest (I) is
I = [tex]\frac{PRT}{100}[/tex] ( note that time is in years ), thus
9 months = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75 years
Thus
81 = [tex]\frac{P(6)(0.75)}{100}[/tex] ( multiply both sides by 100 )
8100 = 4.5P ( divide both sides by 4.5 )
P = 1800
At walmart, a bar of soap costs $3.96 plus 8% sales tax. What is the total cost of a bar soap? Round to the nearest cent.
$4.27
(3.96) 1.08
4.27
What is the name for a function that can be written in the form y=mx+b, where x is the
independent variable and mand bare real numbers? Hint: Its graph is a line.
Answer: The formula is meant for slope interception.
m = slope
x = the independent variable
y = the dependent variable
idk if this is the answer you were looking for but I hope it helps!!!
On what date did the 16th century begin?
1 January 2016
1 January 1601
1 January 1600
1 January 1501
Answer:
The 16th Century began on January 1st of 1600
Answer:
1 January 1501
hope it helps.
Help plzzz!!Given P(A) = 0.78, P(B) = 0.65 and P(AUB) = 0.873, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
===================================================
Work Shown:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)\\\\P(A \cap B) = 0.78 + 0.65 - 0.873\\\\P(A \cap B) = 0.557\\\\[/tex]
-------------
Side note:
A similar formula is [tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
We can isolate the last term to get the first equation shown above.
Answer:
===================================================
Work Shown:
-------------
Side note:
A similar formula is
We can isolate the last term to get the first equation shown above.
Step-by-step explanation:
Solve 3/5 + 3/2 (Btw it can only be shown as a mixed number)
PLEASEEEEE HELPPP MEEE WITHH THIS QUESTIONN PLEASEEE
Answer: A
Step-by-step explanation:
To find the average rate of change, you use the formula [tex]\frac{f(b)-f(a)}{b-a}[/tex]. The best way to get the correct answer is to plug in each interval to make sure it equals 0.
-1 ≤ x ≤ 2: Correct
[tex]\frac{f(2)-f(-1)}{2-(-1)}[/tex] [solve for f(2) and f(1)]
[tex]\frac{1-1}{3}=\frac{0}{3} =0[/tex]
------------------------------------------------------------------------------------------------------
-3 ≤ x ≤ -2: Incorrect
[tex]\frac{f(-2)-f(-3)}{-2-(-3)}[/tex] [solve for f(-2) and f(-3)]
[tex]\frac{5-11}{1} =\frac{-6}{1}=-6[/tex]
------------------------------------------------------------------------------------------------------
-5 ≤ x ≤ 5: Incorrect
[tex]\frac{f(5)-f(-5)}{5-(-5)}[/tex] [solve for f(5) and f(-5)]
[tex]\frac{19-29}{10} =\frac{-10}{10} =-1[/tex]
------------------------------------------------------------------------------------------------------
2 ≤ x ≤ 3: Incorrect
[tex]\frac{f(3)-f(2)}{3-2}[/tex] [solve for f(3) and f(2)]
[tex]\frac{5-1}{1} =\frac{4}{1} =4[/tex]
------------------------------------------------------------------------------------------------------
After going through all the intervals, we found that A was the only one that has an average rate of change of 0.
A policeman believes that the more text messages drivers send while driving, the greater the likelihood of being in a car accident. Which of the following findings would support his belief?
a) r(30) = .38, p < .05
b) r(40) = .28, p < .01
c) r(30) = -.38, p < .05
d) r(40) = -.28, p > .05
Answer:
The correct option is (a).
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
In this case, a hypothesis test for a significant positive correlation is to be performed to determine whether the claim made by the policeman is true or not.
The hypothesis can be defined as follows:
H₀: There isn't a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ ≤ 0.
Hₐ: There is a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ > 0.
Consider the first option.
The sample correlation computed from 30 samples data is,
r = 0.38
The correlation is positive and the sample size is large enough to rely on the sample data.
The p-value of the test is, p < 0.05.
As the p-value is less than 5% level of significance, the null hypothesis will be rejected.
Thus, concluding that there enough evidence to support the policeman's belief.
Thus, the correct option is (a).
The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother’s Day with a 99% confidence interval and a margin of error within plus or minus $12. Assuming the standard deviation for spending on Mother’s Day is $36, the required sample size is ________. a.) 60 b.)72 c.)97 d.)108
Answer:
a.) 60
Step-by-step explanation:
Margin of Error formula = z × s/√n
z = z score of confidence interval
We are given z score of 99% = 2.58
s = Standard deviation = $36
Margin of Error= ± 12
n= unknown
= 12 = 2.58 × 36/√n
12 × √n = 92.88
√n = 92.88/12
√n = 7.74
Square both sides
(√n)² = 7.74²
n = 59.9076
Approximately n ≈ 60
Therefore, the required sample size = 60
Which shape best describes the distribution of the following data? 1, 15, 36, 6 67,68, 68, 68, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 72 a. normal b.bimodal c.positively skewed d.negatively skewed
Answer: d.negatively skewed
Step-by-step explanation:
1
15
36
6
67
68
68
68
69
69
69
69
70
70
70
70
70
71
71
72
The distribution with the data above is negativey skewed. This was inferred from the histogram plot generated from the data.The output shows a distribution which has a long tail to the left and peaks to the right. This characteristics describes a distribution which is negatively skewed. Diagram of the obtained histogram for the distribution can be found in the attachment below.
1. Find the distance between A (-6, -5) and B (2.0)
9.13
9.43
9.03
9.0
Answer:
B
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula.
The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let's let (-6,-5) be x₁ and y₁ and let (2,0) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(2--6)^2+(0--5)^2}[/tex]
Simplify:
[tex]d=\sqrt{(8^2)+(5)^2[/tex]
Square and add:
[tex]d=\sqrt{64+25}\\d=\sqrt{89}[/tex]
Use a calculator:
[tex]d\approx9.4340[/tex]
Our answer is B :)