Answer:
15.47 degrees
Step-by-step explanation:
What is the value of f(x) when x = 4 in the piecewise function f(x) =
2x² when x>4 …….. 4x when x < 4
The question asks the value of f(x) when x = 4 in the equation
x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}
Solving for f(x):
4(4)=16
16 is the answer!
Hope it helps!
if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places.
x y
2 73
3 77
4 85
5 101
6 133
A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706
The regression equation is (d) log(y) = 0.064x + 1.706
How to determine the regression equation?The table of values is given as:
x 2 3 4 5 6
y 73 77 85 101 133
Calculate the logarithm of the y values.
So, we have:
x 2 3 4 5 6
log(y) 1.86 1.89 1.93 2 2.12
Next, we enter the above values in a regression calculator.
From the calculator, we have the following summary:
Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63The regression equation is then represented as:
log(y) = bx + a
Where:
b = SP/SSX = 0.64/10 = 0.064
a = MY - bMX = 1.96 - (0.064*4) = 1.706
So, we have:
log(y) = 0.064x + 1.706
Hence, the regression equation is (d) log(y) = 0.064x + 1.706
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Answer: D. log(y) = 0.064x + 1.706
Step-by-step explanation: I got it right on my test
complete the flow chart to prove
someone pls help me pls pls asap
The attached figure represents the complete flowchart.
How to complete the flowchart?The given statement is:
∠1 ≅ ∠2
To prove
∠3 ≅ ∠4
By vertical angle theorem, we have:
∠2 ≅ ∠4
By transitive property of congruence, we have:
∠2 ≅ ∠3
By transitive property of congruence, we have:
∠1 ≅ ∠3
By vertical angle theorem, we have:
∠3 ≅ ∠4
See attachment for the complete flowchart.
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30 245x-1) (x³+3) 30 245x - 1 ) ( x³ + 3 )
Answer:
30245x⁴ - x³ + 90735x - 3
Step-by-step explanation:
1. Expand the expression
(30245x - 1)(x³ + 3)
2. Multiply
30245x x x³ + 30245x x 3-(x³ + 3)
3. Determine the sign
304245x⁴ + 90735x - (x³ + 3)
4. Rewrite the expression
30425x⁴ + 90735x - x³ - 3
= 30245x⁴ - x³ + 90735x - 3
(brainliest will be appreciated :)
Ibsan want to buy a chicken from one of two supermarkets around his house. the two supermarkets contain 20 local and 25 imported chickens respectively. how many possible chickens are there to choose from
Answer:
Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.
How to solve exercise 1
Answer:
[tex]period \: of \: sin(2x) = \pi \\ period \: of \: cos \frac{x}{4} = 8\pi \\ period \: of \: tan \frac{x}{3} = 3\pi[/tex]
Step-by-step explanation:
Hello !
[tex]periodicity \: of \: a.sin(bx + c) + d = \\ \frac{periodicity \: of \: sin(x)}{ |b| } \\ periodicit \: of \: sin \: (x) \: is \: 2\pi = \\ \frac{2\pi}{2} \: simplify = \pi \\ periodicity \: of \: a.cos(bx + c) = \\ \frac{periodicity \: of \: cos(x)}{ |b| } \\ periodicit \: of \: cos \: (x)is \: 2\pi = \\ \frac{2\pi}{1\frac{1}{4} } \: simplify \: = 8\pi \\ periodicity \: of \: a.tan(bx + c) = \\ \frac{periodicity \: of \: tan(x)}{ |b| } \\ periodicity \: of \: tan(x) \: is \: \pi \\ \frac{\pi}{} \frac{1}{3} [/tex]
A printer designs a tag in the shape of a circle with a smaller circle cut out. She cuts her prototype from a 5 in. by a 7 in. index card. The cut edges of the tag will be printed with gold leaf. What is the approximate amount of gold leaf on a tag?
The circumference of the larger circle is about ____ inches. The circumference of the smaller circle is about ____ inches. So, the total length of gold leaf on a tag is approximately
____ inches.
The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.
How to illustrate the circle?The circumference will be:
= 2πr
= 2 × 3.14 × 2
= 12.57 inches.
The circumference of the smaller circle will be:
= 2πr
= 2 × 3.14 × 0.5
= 3.14
The total length will be:
= 12.57 + 3.14
= 15.71 inches.
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Explain what the slope and y-intercept of the equation represents in this situation y=14x+9
Answer:
slope: 14
y intercept: (0,9)
Step-by-step explanation:
in the form y = mx + b, the slope is m: 14
to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.
here is a gauge for the fuel tank of a car the fuel tank hols 52 litres of fuel when the tank is full the tank is 1/4 full of fuel
work out how many more litres of fuel are needed to fill the tank
Why is it most logical to let x represent Dianna’s current age?
Answer:
In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Choose the most logical value for the variable to represent.
x= Diana's age now
This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)
However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.
3: Morgan Cruise earns net self-employment income of $221,600. She works a second job from which she receives FICA taxable earnings of $111,300.00.
Self-Employment tax =
137,700 cap
Based on the amounts that Morgan Cruise is getting paid, her self-employment tax will be $22,916.63.
How much does Morgan pay in self-employment tax?taxable earnings from self-employment:
= 92.35% x 221,600
= $204,647.60
Self-employment tax is:
= (12.4% x 137,700 limit) + (2.9% x 200,000 limit) + (0.9% x (204,647.60 - 200,000)
= 17,074.80 + 5,800 + 41.83
= $22,916.63
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Type the correct answer in each box. Use numerals instead of words.
Functions f and g are represented in the table and the graph.
The values of the functions from the graph and table are; (f ° g)(4) = 4 and x = 0 at (g ° f)(x) = 1
How to solve function inputs?1) We want to find the value of (f ° g)(4). This can also be expressed as;
f(g(4))
Now, from the given graph, g(4) = 2. Thus;
f(g(4)) = f(2)
From the table, f(2) = 4. Thus;
(f ° g)(4) = 4
2) We are given; (g ° f)(x) = 1
This is also expressed as;
g(f(x)) = 1
From the graph g(x) = 1 is at x = 1. Thus;
f(x) = 1 and from the tabe;
x = 0 at f(x) = 1
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I am a 3-digit odd number.
The sum of my digits is 9.
My tens digit is twice that if my hundreds digit.
What am I?
Answer:
Step-by-step explanation:
let the number at unit place=x
ten's place=y
hundred's place=z
x,y,z are integers.
x+y+z=9
also digit=100z+10y+x
y=2z
x+2z+z=9
x+3z=9
x=1,3,5,7,9
for x=1
1+3z=9
3z=9-1=8
z=8/3 (rejected as z is an integer.)
when x=3
3+3z=9
3z=9-3=6
z=6/3=2
z=2
y=2z=2×2=4
so number=100×2+10×4+3=200+40+3=243
Jeff places a 13 ft ladder against a wall. The base of the ladder is 5 ft from the wall. How high on the wall does the ladder reach?
Work Shown:
[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]
I used the pythagorean theorem.
I need help asap. ive tired a lot and cant get it
In a catalog, movies are identified by an ID number—2 letters followed by 3 digits.Repetitions are permitted. How many catalog numbers can be made?What is the probability that the ID number is divisible by 5? (Include the 2 letters in the ID number.)
Using the Fundamental Counting Theorem, it is found that:
676,000 catalog numbers can be made.There is a 0.2 = 20% probability that the ID number is divisible by 5.What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:
[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]
Hence the number of catalog numbers is:
[tex]N = 26^2 \times 10^3 = 676000[/tex]
The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:
[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]
There is a 0.2 = 20% probability that the ID number is divisible by 5.
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What was the percent increase of China's
population from 1970 to 1995?
56.25%
45%
156.25%
9.405%
China's Population
Population
(billions)
0.7
Year
1965
1970
1975
1980
1985
1990
1995
2000
0.8
0.92
0.98
1.08
1.14
1.25
1.26
The percentage increase China's population from 1970 to 1995 is: 56.25%.
How to Calculate Percentage Increase?Percentage increase = (Final Value - Original Value)/Original value × 100.
Given the following:
Original value = 0.8 billion
Final Value = 1.25 billion
Final Value - Original Value = 1.25 - 0.8
Final Value - Original Value = 0.45
Percentage increase = 0.45/0.8 × 100 = 56.25%.
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Suppose you have 7 red cards, 9 green cards, and 12 blue cards. The cards are well shuffled, and you randomly draw one card How many elements are there in the sample space?
Find the probability of drawing a green card
How many elements are there in the sample space?
There are 28 elements in the sample space and the probability of a green card is 9/28
The elements in the sample space?The given parameters are:
Red = 7
Green = 9
Blue = 12
The elements in the sample space is:
Elements =7 + 9 + 12
Evaluate
Elements = 28
Hence, there are 28 elements in the sample space
The probability of green?This is calculated as
P =Green/Elements
So, we have:
P = 9/28
Hence, the probability of a green card is 9/28
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(a) Using the digits 0 to 7 exactly once each, form a collection of positive integers whose sum is 100.
(b) Find a second solution to (a) which has a different number of integers in the sum.
(c)Show that in any solution (a), the sum of the digits in the units places is 20.
(d)Find, with reasons, the smallest possible value of the largest integer in a solution to (a).
A) The collection of positive integers whose sum is 100 are: 23, 17, 6, 54, 0.
B) Another collection of positive integers whose sum is 100 are: 13, 27, 4, 56, 0.
C) Due to the fact that the units can be commuted, their sum is always equal to 20.
D) The smallest possible value is 0 and the largest is 57.
What is the sequence of positive integers?A) The formation of a collection of positive integers can be done by trial and error. For example, only using the digits {0, 1, 2, 3, 4, 5, 6, 7}.
For example, we can have;
23 + 17 + 6 + 54 + 0 = 100
Where the numbers used are: 23, 17, 6, 54, 0.
B) Another example is;
13 + 27 + 4 + 56 + 0 = 100
C) If we add the units digits of these 5 numbers, we get:
3 + 7 + 6 + 4 + 0 = 20
Now, if we compute the units digits between the different numbers, to get for example: 27, 13, 6, 54, 0
The sum is still equal to 100, and the units digits are the same ones, so we still have that the sum of the units digits is equal to 20.
d) The smallest integer that we use is 0.
For the largest we just commute the tens and units digits so we make the larger integer possible, which is:57.
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San is currently three times Harry's age. Sam's age is also 10 more than twice Harry's age. the following systems of equation models this scenario. x=3y, x=10+2y
Step-by-step explanation:
so, what do we need to do ?
just solve these equations and find Sam's age (and Harry's) ?
x = 3y
x = 10 + 2y
so, we simply use the first equation in the second :
3y = 10 + 2y
y = 10
x = 3y = 3×10 = 30
Sam is currently 30 years old, Harry is 10.
Type your answer into the box. 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres, the length is 7.3 metres and the height is 4.2 metres. Dulce Livramento 4.2 m What is the volume of the cuboid? Type your answer into the box . 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres , the length is 7.3 metres and the height is 4.2 metres . Dulce Livramento 4.2 m What is the volume of the cuboid ?
The volume of the cuboid is 183.96 m³
What is the volume of a cuboid?A cuboid is a plane shape with a six-faced solid called a hexahedron. The volume of a cuboid is Length × width × height
From the information given:
The length of a cuboid is = 7.3 metresThe width = 6 metresThe height = 4.2 metresThe volume of the cuboid is;
= (7.3 × 6 × 4.2) m³
= 183.96 m³
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Justin‘s gas tank is 3/10 full after he buys 14 gallons of gas it is 4/5 full how many gallons can Justin‘s tank hold
Answer:
I can help, its 45
what is the constant of variation?
Answer:
constant (unchanged) ratio of two variable quantities
Step-by-step explanation:
y = k x ( or y = k x )
y = 15 when x = 24, find x when y = 25. find the constant of variation.
Algebra
Help me with this question
Answer:
SORRY I CAN NOT HELP YOU
please solve it?
1. 3q4 × 2q5 ÷q3
2. 4-²
3. 16^1/2
4.4°
Brainliest to whoever answers accurately
Answer: [tex]a_{n}=5000(1.02)^{n-1}[/tex]
Step-by-step explanation:
to get the rate do:
5100/5000 to get 1.02
Also for geometric sequence, the exponent 'n' is always subtracted by 1
Therefore, your answer is:
[tex]a_{n}=5000(1.02)^{n-1}[/tex]
help me help me help help help me
Answer:
b. 0
c. 4
d. 2
e. [tex]\frac{76}{35}[/tex]
Step-by-step explanation:
b.) When translated it will become this expression 10 - [(2x15)/3] = 0
c.) It will become [tex]\frac{4(12-7)}{5}[/tex]
d.) This will transform to [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]
e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]
f(x) = x/2 - 3 and g(x) = 3x² + x − 6, find (f+ g)(x)
Answer:
3x^2+3x/2-9
Step-by-step explanation:
collect like term
When a numberis decreased by 20% of itself the result is 64
Answer:
80Step-by-step explanation:
100% - 20% = 80% = 64
so
64 : 80 * 100 = 80
check
80 - 20% = 64
a line of best fit was drawn for 15 data points. what is the maximum number of these data points that may not actually be on the line?
The maximum number of the data points that may not actually be on the line is 15
How to determine the number of data points?The number of points is given as:
Points = 15
A line of best fit implies that the model is a regression model
In a regression model, all the data points may not pass through the line of best fit.
This means that the maximum number of the data points that may not actually be on the line is 15
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