Answer: all real numbers
Step-by-step explanation:
I assume you meant to write:
Let f(x) and g(x) be functions such that f(x) = x+5 and g(x) = x+4. What is domain of f(x)+g(x)?[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]
Since this is a linear function, the domain is all real numbers.
A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (the Wall Street Journal, May 5, 2010). Suppose a random sample of 100 teen drivers is taken. What is the probability that the sample proportion is within ± 0.02 of the population proportion?
The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
How to determine the probability?The given parameters are:
Sample size, n = 100Population proportion, p = 82%Start by calculating the mean:
[tex]\mu = np[/tex]
[tex]\mu = 100 * 82\%[/tex]
[tex]\mu = 82[/tex]
Calculate the standard deviation:
[tex]\sigma = \sqrt{\mu(1 - p)[/tex]
[tex]\sigma = \sqrt{82 * (1 - 82\%)[/tex]
[tex]\sigma = 3.84[/tex]
Within ± 0.02 of the population proportion are:
[tex]x_{min} = 82 * (1 - 0.02) = 80.38[/tex]
[tex]x_{max} = 82 * (1 + 0.02) = 83.64[/tex]
Calculate the z-scores at these points using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z_1 = \frac{80.36 - 82}{3.84} = -0.43[/tex]
[tex]z_2 = \frac{83.64 - 82}{3.84} = 0.43[/tex]
The probability is then represented as:
P(x ± 0.02) = P(-0.43 < z < 0.43)
Using the z table of probabilities, we have:
P(x ± 0.02) = 0.3328
Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
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The equation of a circle is x² + y²-6y+1=0. What are the coordinates of
the center and the length of the radius of this circle?
(1) center (0,3) and radius 2√2
(2) center (0,-3) and radius 2√2
(3) center (0.6) and radius √35
(4) center (0,-6) and radius √35
Answer:
center (0, 3) and radius 2√2
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex]x^2+y^2-6y+1=0[/tex]
Subtract 1 from both sides:
[tex]\implies x^2+y^2-6y=-1[/tex]
To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:
[tex]\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2+y^2-6y+9=8[/tex]
Factor the trinomial with variable y:
[tex]\implies x^2+(y^2-6y+9)=8[/tex]
[tex]\implies x^2+(y-3)^2=8[/tex]
Factor [tex]x^2[/tex] to match the general form for the equation of a circle:
[tex]\implies (x-0)^2+(y-3)^2=8[/tex]
Compare with the general form of the equation for a circle:
[tex]\implies a=0[/tex]
[tex]\implies b=3[/tex]
[tex]\implies r^2=8 \implies r=2\sqrt{2}{[/tex]
Therefore, the center is (0, 3) and the radius is 2√2
Consider the two regression lines 3x+2y=26 and 6x+y=31, the regression coefficient of y on x is
The regression lines 3x+2y=26 and 6x+y=31 are linear regressions
The mean values are 4 and 7 and the correlation coefficient between x and y is 0.25
The standard deviation of x is 2/13
The mean value and the correlation
We have the equations to be:
3x+2y=26 and 6x+y=31
Make y the subject in the second equation
y = 31 - 6x
Substitute y = 31 - 6x in the first equation
3x+2[31 - 6x] = 26
Expand
3x+ 62 - 12x = 26
Collect like terms
3x - 12x = 26 - 62
Evaluate
-9x = -36
Divide by - 9
x = 4
Substitute x = 4 in y = 31 - 6x
y = 31 - 6 * 4
y = 7
This means that the mean values are 4 and 7
To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.
So, we have:
y = 13 - 3x/2 and x = 31/6 - 1/6y
The above means that:
Bxy = -1/6 and Byx = -3/2
The correlation coefficient is then calculated as:
r^2 = Bxy * Byx
r = -1/6 * -3/2
r = 0.25
Hence, the correlation coefficient between x and y is 0.25
The standard deviation of x
We have:
Var(y) = 4
In (a), we have:
y = 13 - 3x/2
To solve further, we make use of:
Var(y) = Var(ax + b) = a^2Var(x)
This gives
Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)
So, we have:
Var(y) = 13^2 * Var(x)
Substitute 4 for Var(y)
4 = 13^2 * Var(x)
Divide both sides by 13^2
4/13^2 = Var(x)
Express 4 as 2^2
(2/13)^2 = Var(x)
So, we have:
Var(x) = (2/13)^2
Take the square root of both sides
SD(x) = 2/13
Hence, the standard deviation of x is 2/13
1) (b + a) = 4; use a = 1 and b = 3
2) c(b + b); use b = 1 and c = 5
3) 4+ pm; use m = 4 and p =3
4) 5+ pm; use m = 4 and p = 2
5) m(p + 2); use m = 5 and p = 2
6) h+j²; use h = 1 and j = 4
7) y-(x - 5); use x = 5 and y = 6
8) 4xy; use x = 5 and y = 2
9) n(p + 3); use n = 2 and p = 2
10) y +x+x; use x = 3 and y = 5
11) 6+ a-b; use a = 4 and b = 4
Step-by-step explanation:
1). (3+1)=4
2).5(1+11)
5(2)=103).4+3(4)
4+12=16.4).5+2(4)
5+8=135).5(2+2)
5(4)=206).1+4^2
1+16=177).6-(5-5)
6-0=68).4×5×2=40
9).2(2+3)
2(5)=1010).5+3+3=11
11)6+(4-4)
6+0=6.I hope this helps. Pls mark as brainliest like and follow me
Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Select one:
a. (-2, 11)
b. (5.5, -1)
c. (11, -2)
d. (-1, 5.5)
[tex]\left(\frac{-2+13}{2}, \frac{5-7}{2} \right)=\boxed{\left(5.5, -1)}[/tex]
Please hurry:)
Which of the following is equivalent to…
Answer:
D
Step-by-step explanation:
A bronze statue weighs 2400 N and has a base that is 4 m by ½ m. What is the pressure the statue exerts on the floor?
The pressure by the statue exerted on the floor will be 1200 N per square meter.
What is pressure?
The term pressure is defined as the force per unit area.
The formula is igven below.
P = F /A
A bronze statue weighs 2400 N and has a base that is 4 m by ½ m.
Then the base area will be
A = 4 x 1/2
A = 2 square meters
Then the pressure will be
P = 2400 / 2
P = 1200 N per square meter.
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You invest $1000
in an account at 2.5% per year simple interest. How much
will you have in the account at the beginning of the 4th year? Round your
answer to the nearest whole dollar.
A. $1075
B. $1163
C. $3250
• D. $1088
i dont speak English 3456
Write 72 as a product of primes.
Use index notation when giving your answer.
Multiplication is the process of multiplying. The number 72 in terms of the product of primes is described as 2³ × 3².
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The number 72 in terms of the product of primes can be written as,
72 = 2×2×2×3×3×1 = 2³ × 3²
Hence, the number 72 in terms of the product of primes is described as 2³ × 3².
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find the volume of the rectangular prism WILL MARK BRAINLEST
Step-by-step explanation:
volume= l×w×h
1.1/3×1/2×2/3
=1/9
2. 3/4×1/8×13/16
=39/512
3. 1/12×7/8×1/4
=7/384
4. 3/2×1/7×7/8
=3/16
5. 1/5×9/10×2/3
=3/25
6.6/7×7/8×1/2
=3/8
(1)
Mrs Tan had $3756 to spend on furniture. She bought a sofa set for $1195 and 6 chairs at $128 each.
(a) How much did she spend altogether?
(b) How much money did she have left?
(Marshall Cavendish/ Pupil's book My Pals Are Here! Maths 4A 3rd Edition)
Help me with this question please and thank you!!! :):)
Answer:
A intersection B = ( elements which are common in both)
= ( 2,4,7,19)
A union B = ( all the elements which are either in A or in B).
= ( 2, 4, 7 , 13, 14, 19, 20 , 3, 5, 6, 10,11, 12 , 15,17 , 18 , 19 )
In basketball, hang time is the time that both of your feet are off the ground during a jump. The equation for hang time is t = 2 (StartFraction 2 h Over 32 EndFraction) Superscript one-half , where t is the time in seconds, and h is the height of the jump, in feet.
Player 1 had a hang time of 0.9 s. Player 2 had a hang time of 0.8 s. To the nearest inch, how much higher did Player 1 jump than Player 2?
Considering the hang time equation, it is found that Player 1 jumped 0.68 feet higher than Player 2.
What is the hang time equation?The hang-time of the ball for a player of jump h is given by:
[tex]t = 2\left(\frac{2h}{32}\right)^{\frac{1}{2}}[/tex]
The expression can be simplified as:
[tex]t = 2\sqrt{\frac{h}{16}}[/tex]
For a player that has a hang time of 0.9s, the jump is found as follows:
[tex]0.9 = 2\sqrt{\frac{h}{16}}[/tex]
[tex]\sqrt{\frac{h}{16}} = \frac{0.9}{2}[/tex]
[tex](\sqrt{\frac{h}{16}})^2 = \left(\frac{0.9}{2}\right)^2[/tex]
[tex]h = 16\left(\frac{0.9}{2}\right)^2[/tex]
h = 3.24 feet.
For a player that has a hang time of 0.8s, the jump is found as follows:
[tex]0.8 = 2\sqrt{\frac{h}{16}}[/tex]
[tex]\sqrt{\frac{h}{16}} = \frac{0.8}{2}[/tex]
[tex](\sqrt{\frac{h}{16}})^2 = \left(\frac{0.8}{2}\right)^2[/tex]
[tex]h = 16\left(\frac{0.8}{2}\right)^2[/tex]
h = 2.56 feet.
The difference is given by:
3.24 - 2.56 = 0.68 feet.
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a. What are the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps?
The distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
Missing informationWhen you walk with a normal stride, the average distance covered in 2 steps is about 5 feet
How to determine the distances?From the question, we have:
Rate = 5 feet per 2 steps
This gives
Rate = 5/2 feet per step
So, we have:
Rate = 2.5 feet per step
The distance is then calculated as:
Distance = Rate * Steps
This gives
Distance = 2.5 * Steps
So, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are
Distance = 2.5 * 4 = 10 feet
Distance = 2.5 * 6 = 15 feet
Distance = 2.5 * 12 = 30 feet
Distance = 2.5 * 30 = 75 feet
Hence, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
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A function, h(x), is defined as shown.
h(x) = StartLayout Enlarged left-brace 1st row 1st column one-fourth x minus 4, 2nd column x less-than-or-equal-to 0 2nd row 1st column one-third x minus 3, 2nd column 0 less-than x less-than-or-equal-to 3, 3rd row 1st column one-half x minus 2, 2nd column x greater-than-or-equal-to 4
Which graph represents h(x)?
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 3) and goes up to a closed circle at (0, 4). The second line starts at (0, 3) and goes up to a closed circle at (3, 4). The third line has a closed circle at (4, 4) and goes up to (6, 5).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 1) and goes up to a closed circle at (3, 0). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).
The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). ....
What is the graph about?Using the piecewise function, one can see that;
In x ≤ 0, the slope of the graph of h(x) = 1/4
In 0 < x ≤ 3, the slope of the graph of h(x) = 1/3
In x ≥ 4, the slope of the graph of h(x) = 1/2
Note that the movement is left to right and the slope of h(x) often increases and the slope of the graph is said to become steeper.
Option B shows the graph of h(x) as it best tells the exact point of various aspect of the function.
Therefore, The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).
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Find the midpoint of the segment with the following endpoints.
(-3,-3) and (1, 2)
[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]
Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
Answer:
Step-by-step explanation:
let the list price=x
93% of x=22,000
x=22,000 ×100/93
≈23,655.91 $
Max is going to order a breakfast platter at The Breakfast Club. He can choose one style of eggs, one type of meat, and one kind of toast. The following table shows the options available to him.
Breakfast platter
Egg options Fried, Scrambled, Poached, Hard boiled
Meat options Bacon, Sausage, Ham, Steak
Toast options White, Wheat, Rye
How many different breakfast platters could Max create?
the answer is 48
Step-by-step explanation:
since there are 4 egg options 4 meat options and 3 bread options. so u multiply this.
4×3×4=48
15. Desde la punta de un edificio el hombre araña lanza una tela a 500 metros, de la base del edificio
con un ángulo de depresión de 60°, ¿Qué altura (h) tiene el edificio?
ayudaaaa
Step-by-step explanation:
the correct answer will be 93
if 300 equals 9 and 500 equals 16 what is the pattern? and what will 7 and 18 equal?
Step-by-step explanation:
hope you can understand
What is the surface area of a square prism with sides that measure 8 units?
O254 units²
O 300 units²
0314 units²
0384 units²
Answer:
384 units²
Step-by-step explanation:
The area of one face is (8)(8)=64.
Multiplying this by the six faces, we get 64(6)=384
Line l and line m intersect.
Prove: ∡1 ≅ ∡3
Answer:
l & m intersect
2 & 3 are supplementary
1 & 3 are congruent
Step-by-step explanation:
The proof of expression"∡1 ≅ ∡3" is given below.
The complete flow chart is given in the attached image.
As per the provided diagram and the given information "Line l and line m intersect", the proof of the required statement can be done in the following steps.
Step 1:
Given: Line l and line m intersect.
Step 2:
∠1 is supplementary to ∠2
From the property of linear pair theorem.
Step 3:
∠2 is supplementary to ∠3
From the property of linear pair theorem.
Step 4:
As per the property of congruent supplements theorem,
∠1 ≅ ∠3
The complete chart is given below.
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The ages of Sonu and Monu are in the ratio 5:7.If Sonu were 9 years older and Monu 9 years younger, the age of Sonu would have been twice the age of Monu .Find their p present age 2 ) The ages of Sonu and Monu are in the ratio 5 : 7.If Sonu were 9 years older and Monu 9 years younger , the age of Sonu would have been twice the age of Monu .Find their present age.
Answer:
Sonu is 15years and Monu is 21 years
Choose the expression that represents a cubic expression
2x + 11
The correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11
The correct question is as given below:-
Need help ASAP. Choose the expression that represents a cubic expression.
a. 2x + 11
b . −3x² − 2x + 11
c . 4x³ − 3x² − 2x + 11
d . 5x⁴ + 4x³ − 3x² − 2x + 11
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The polynomial having a degree of three is called the cubic polynomial which means that the maximum power of the polynomial will be three and the solutions will also be three.
Here in the option, we can see that the maximum power of the polynomial is three and it will have a maximum of three solutions.
The third-degree expression will be:-
E = 4x³ − 3x² − 2x + 11
Therefore the correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11
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Find a solution to dA/dt=-6A if A(0)=6. A(t)=
This equation is separable,
[tex]\dfrac{dA}{dt} = -6A \implies \dfrac{dA}A = -6\,dt[/tex]
Integrate both sides and solve for [tex]A[/tex] :
[tex]\displaystyle \int \frac{dA}A = -6 \int dt[/tex]
[tex]\ln|A| = -6t + C[/tex]
[tex]e^{\ln|A|} + e^{-6t+C}[/tex]
[tex]\implies A(t) = Ce^{-6t}[/tex]
Solve for [tex]C[/tex] using the initial value.
[tex]A(0) = 6 \implies 6 = Ce^0 \implies C=6[/tex]
Then the particular solution is
[tex]\boxed{A(t) = 6e^{-6t}}[/tex]
Section B 13. Amanda produces the newsletter for an editorial club. Each newsletter contains pages printed on both sides in colour and in black. The graphic designer informs Amanda that the upcoming issue of the newsletter will have 4 pages printed in colour and 20 pages printed in black. Every 4 pages printed in colour will cost x cents. Every 4 pages printed in black will cost y cents. (i) Find an expression for the cost of printing one copy of the newsletter. (1 (ii) Each newsletter costs 14 cents to print. Give an example of the cost of printing 4 pages in colour and the cost of printing 4 pages in black. [ An educational institution in Shanghai wants to subscribe to this newsletter. In Singapore, each newsletter costs S$2.20. The conversion rate is ¥1 = S$0.198 45. (iii) Without using a calculator, estimate the price of one newsletter in Y. Each sheet of paper has a mass of 4.5 g. (iv) How heavy is one copy of the newsletter?
Answer:
The answer is 3.2
A. 10%
B.15%
C.28%
D.25%
Answer: 10%
Step-by-step explanation:
She had a total of $16,800. Subtracting the $5700 standard deduction and the $3650 exemption, we get:
[tex]16800-5700-3650=7450[/tex]
Which falls within the 10% tax bracket.
A greedy hamster hoarded two piles of sunflower seeds. Yesterday the ratio of seeds in these piles was 3:4, but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday?
The weight of the each pile yesterday would be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given;
Yesterday the ratio of seeds in these piles was 3:4.
Let it be 3x and 4x.
If the 2 pounds of seeds is added in the bigger pile, then it become
4x + 2
He also ate 1/4 pound from the smaller pile, then
3x - 1/4
Now the quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of the each pie would be
3x = 6 pound
4x = 8 pound
Hence, The weight of the each pile yesterday would be 6 and 8 pounds.
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I need help ASAP please
Which statement is true about whether Z and B are independent events?
A: Z and B are independent events because P(Z | B) =P(Z).
B: Z and B are independent events because P(Z | B) = P(B).
C: Z and B are not independent events because P(Z | B) ≠ P(Z).
D: Z and B are not independent events because P(Z | B) ≠ P(B).
Gabrielle is 10 years older than Mikhail. The sum of their ages is 84. What is Mikhail's age?
Answer:
Hence the age of Mikhail is 37 and the age of Grabrielle is 47
Answer:
Here;
Gabrielle age= 10yrs older that M..= 16 + 10= 26yrs old.
Sum of their age= 84
Now;
100 - 84
16,,
