Type the correct answer in each box. Use numerals instead of words. If necessary, use / for fraction bar(s)
f(x) {____if -1_< x _<1
____if 3_< x _<5
Answer: f(x) = 4 if -1 ≤x ≤ 1
f(x) = x - 1 if 3≤ x ≤ 5
Step-by-step explanation:
if -1 ≤x ≤ 1
We can see that in this range the function is constant, f(x) = 4
if 3≤ x ≤ 5
In this region we can see a linear relationship, with the points (3, 2) and (5, 4)
as the extremes, we can find the slope of this linear equation as:
s = (4 - 2)/(5 - 3) = 2/2 = 1
So our equation is
f(x) = 1*x + b
to find the value of b we can evaluate our function in the first point, we know that when x = 3, y = 2, so we have:
2 = 1*3 + b
b = 2- 3 = -1
then f(x) = 1*x - 1
Then we have:
f(x) = 4 if -1 ≤x ≤ 1
f(x) = x - 1 if 3≤ x ≤ 5
Compute the amount of interest earned in the following simple interest problem. A deposit of $4,500 at 5% for 3 years:
$67.50
$6.75
$675.00
$6,750.00
Answer:
$675.00
Step-by-step explanation:
4500 x 0.05 x 3 = 675
Stir-fry is Gabe's favorite food to cook, but it always makes a lot of smoke! Gabe needs to know the volume of his kitchen so he can buy a fan that is the right size. Gabe's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of Gabe's kitchen?
Answer:
The volume of Gabe's kitchen is 680 ft^3
Step-by-step explanation:
The volume of the kitchen can be derived by multiplying the floor area of the kitchen by the height.
Volume = floor area × height
Given;
Floor area = 85 ft^2
Height = 8 ft
Substituting the given values into the equation;
Volume = 85 × 8 = 680 ft^3
The volume of Gabe's kitchen is 680 ft^3
Which is the slope of the line that passes through the points (3, 17) and
(7.25)?
Find the distance between (-10,12) and (-6,-14). Round to the nearest hundredth
Answer:
26.31 units
Step-by-step explanation:
Given: Points [tex](-10,12),(-6,-14)[/tex]
To find: Distance between the given points
Solution:
Let [tex](x_1,y_1)=(-10,12)\,,\,(x_2,y_2)=(-6,-14)[/tex]
The distance formula is used to find the distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex]
According to distance formula,
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(-6+10)^2+(-14-12)^2}\\ =\sqrt{16+676}\\ =\sqrt{692}\\ =26.31[/tex]
So, distance between the given points is 26.31 units
A rhombus has side lengths of 25. What could be the lengths of the diagonals?
A. 22 and 40
B. 26 and 36
C. 26 and 48
D. 30 and 40
Answer:
The correct option is;
D. 30 and 40
Step-by-step explanation:
Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be
2 × 25×sinθ and 2 × 25× cosθ
Therefore tanθ = (2 × 25×sinθ)/(2 × 25× cosθ) = (sinθ)/(cosθ)
Therefore, the root of the sum squares of both diagonals = 50
Therefore, we analyze each of the options as follows
For A. we have √(22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For B. we have √(26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For C. we have √(26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For D. we have √(30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
(x + 5) (x - 7)
Step-by-step explanation:
To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:
[tex]x^2[/tex] - 2x - 35
[tex]x^2[/tex] - 7x + 5x - 35
Group:
([tex]x^2[/tex] - 7x) (5x - 35)
Take out GCF (Greatest Common Factor):
x(x - 7) 5(x - 7)
(x + 5) (x - 7)
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
19.5 in²
Step-by-step explanation:
Area of rhombus tile = side × height
Area = 3 × 6.5
Area = 19.5 in²
A rhombus, like any parallelogram, has area equal to base times height,
that's 3×6.5 = 19.5 square inches
Answer: 19.5
What number is 4 time another. The sum of the reciprocals is 15/4. find the numbers
Answer:
3/4 , 3
Step-by-step explanation:
Let one number = x
Other = 4x
Sum:
x + 4x = 15/4
5x = 15/4
x = 3/4
Thus the numbers are 3/4 , 3
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What population parameter is being tested
Answer: 4
Step-by-step explanation:
Mr. Khan went for a trip in his car, which travels 14.5km/h on 1 liter petrol. The
reading of a speedometer was 19034.0 km when he started his journey and read
19396.5 km after he had completed his journey. How many liters of petrol are
consumed?
Answer:
25L
Step-by-step explanation:
19396.5 km - 19034.0 km = 362.5 km travled
362.5 km / 14.5 km/L = 25L
Water is leaking out of an inverted conical tank at a rate of 8200.08200.0 cm3/min cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 11.0 m11.0 m and the the diameter at the top is 4.5 m4.5 m. If the water level is rising at a rate of 16.0 cm/min16.0 cm/min when the height of the water is 3.0 m3.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Answer: cm3/min
Answer:
I' = 197,474.47 cm^3/min
the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min
Step-by-step explanation:
Given;
Tank radius r = d/2 = 4.5/2 = 2.25 m = 225 cm
height = 11 m
Change in height dh/dt = 16 cm/min
The volume of a conical tank is;
V = (1/3)πr^2 h .....1
The ratio of radius to height for the cone is
r/h = 2.25/11
r = 2.25/11 × h
Substituting into equation 1.
V = (1/3 × (2.25/11)^2)πh^3
the change in volume in tank is
dV/dt = dV/dh . dh/dt
dV/dt = ((2.25/11)^2)πh^2 . dh/dt ....2
And change in volume dV/dt is the aggregate rate at which water is pumped into the tank.
dV/dt = inlet - outlet rate
Let I' represent the rate of water inlet and O' represent the rate of water outlet.
dV/dt = I' - O'
Water outlet O' is given as 8200 cm^3/min
dV/dt = I' - 8200
Substituting into equation 2;
I' - 8200 = ((2.25/11)^2)πh^2 . dh/dt
I' = ((2.25/11)^2)πh^2 . dh/dt + 8200
h = 3.0 m = 300 cm (water height)
Substituting the given values;
I' = ((2.25/11)^2)×π×300^2 × 16 + 8200
I' = 197,474.47 cm^3/min
the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min
What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120
Answer:
B. 20
Step-by-step explanation:
5P2 is equal to 20 using the permutation formula.
Find cos(a) in the triangle.
Choose 1 answer
Answer:
the correct answer is 35 / 37
Line p passes through (8, -6) and is perpendicular to the line 2x + y = -7. The slope of line p is . The equation of line p is y = 1/2x + ?.
Answer:
y = (1/2) x -10
Step-by-step explanation:
Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !
2x + y = -7 rewrite in form y=
y = -7 -2x
slope of this line is -2
perpendicular lines are opposite reciprocals so the line p has a slope = 1/2
line p passes through (8, -6) so plug in point into equation of p and get ?
y = 1/2 x +?
-6 =1/2(8) +?
-6 =4 + ? subtract 4 from both sides
-6-4 = ?
-10 = ?
y = (1/2) x -10
g Which one of the following best describes an advantage of using a Poisson distribution (Model 1) over the distribution in Model 2 to model X? It allows us to model the data continuously. It allows individuals to have an arbitrarily large number of siblings. It reduces the amount of unknowns needed for modeling.
Answer:
It reduces the amount of unknowns needed for modeling.
Step-by-step explanation:
Let's first look at the characteristics of poisson distribution.
The Poisson distribution has the following characteristics:
1. It is a discrete distribution.
2. The occurrences in each interval can range from zero to infinity.
3. Each occurrence is very independent of the other occurrences.
4. It helps describes discrete occurrences over an interval.
5. It reduces the amount of constant and unknown needed for modeling an equation.
There are five families that each have one child. Each of them hires Riley as a babysitter. Because the children she babysits are different ages, Riley charges each family a different amount. To visualize her earnings, Riley recorded and plotted her pay from each job. Using the scatterplot, calculate her average rate of pay.
Answer:
Average Rate of Pay = $ 5.23 /hr
Step-by-step explanation:
We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:
x (Hours) = 12 13 16 17 20
y ($) = 54 56 65 64 100
The statistical data calculated is:
∑x = 78, ∑x² = 1258, ∑y = 339, ∑xy = 5504, n = no. of data points = 5
Now, we use linear regression model to fit a straight line to this data.
y = a + bx --------- eqn (1)
where,
b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]
b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]
b = 5.23
and,
a = (∑xy - b∑x²)/∑x
a = [5504 - (5.23)(1258)]/78
a = -13.83
Therefore, eqn (1) becomes:
y = -13.83 + 5.23x
The graph plot of this straight line fit is provided in the attachments.
Now, we derivate the equation with respect to x, to get the average rate of pay:
Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)
Average Rate of Pay = $ 5.23 /hr
A footbridge has a span of 54 feet. A sign is
to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge?
Answer:
27
Step-by-step explanation:
Because if it is halfway, that means
halfway=1/2
1/2=1/2 of 54
54/2 or 1/2 of 54=27
PLS MARK ME BRAINLIEST I NEED IT PLEASE
The center of the sign will be 27 feet apart from both ends of the bridge.
Given that,
A footbridge has a span of 54 feet. A sign is to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Since the bridge is 54 feet long,
Now at the center of the bridge, a sign is placed,
So the distance of sign from both ends is equal to half of the total length of the bridge. i.e.
= 54 / 2
= 27
Thus, the center of the sign will be 27 feet apart from both ends of the bridge.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Question 1
Write x2 + 4x – 3x3 + 6 in standard form.
a) – 3x3 + 4x + x2
b) x2 – 3x3 + 4x + 6
c) –3x3 + x2 + 4x + 6
d) 6 + 4x – 3x3 + x2
Answer:
-3x^3 + x^2 + 4x +6
Answer is C
Step-by-step explanation:
Answer: -3x^3 + x^2 + 4x +6
Answer is C
Step-by-step explanation:
how many tenths are in 4600
Answer:
4600 tenths as a Fraction
Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.
4600 tenths as a Decimal
If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.
4600 tenths as a Percent
To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.
4600 tenths of a dollar
First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.
Step-by-step explanation:
Hope this helped!
Stay safe!!!
Answer:
Step-by-step explanation:
To answer this, multiply 4600 by 10: 46000. There are 46000 tenths in 4600.
The graph of a function is shown below.
D
Which statement best describes section D of the graph?
0 А.
linear and increasing
О В.
linear and decreasing
Ос.
nonlinear and increasing
OD
nonlinear and decreasing
What is the measure of angle A?
Answer:
A = 19.47
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin A = 2/6
Take the inverse sin of each side
sin ^-1 ( sin A) = sin ^-1 (2/6)
A =19.47122063
To the nearest hundredth
A = 19.47
Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.
Answer:
Tn = 34-3nStep-by-step explanation:
The formula for calculating the nth term of an arithmetic sequence is given as;
Tn = [tex]a+(n-1)d[/tex]
a is the first term
n is the number of terms
d is the common difference
If two terms of an arithmetic sequence are a12=70 and a30=124 then;
T12 = a+(12-1)d = 70
T12 = a+11d = 70...(1)
T30 = a+(30-1)d = 124
T30 = a+29d = 124...(2)
Solving equation 1 and 2 simultaneously to get a and d;
Taking the difference of both equation we have;
29d - 11d = 124-70
18d = 54
d = 54/18
d = 3
Substituting d=3 into equation 1 to get the value of 'a' we have;
a+11(3) = 70
a+33=70
a = 70-33
a = 37
To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3
Tn = 37+(n-1)3
Tn = 37+3n-3
Tn = 34-3n
This gives the required nth term
· Find (f • g)(x).
f(x) = 3x
g(x) = 5x
Write your answer as a polynomial in simplest form.
(fog)(x) =
The expression of (fog)(x) in the simplest form is [tex](fog)(x)=15x[/tex] and this can be determined by using the arithmetic operations.
Given :
[tex]f(x) = 3x\\g(x) = 5x[/tex]
The following steps can be used in order to determine the expression of (fog)(x):
Step 1 - Write the given function.
[tex]f(x) = 3x\\g(x) = 5x[/tex]
Step 2 - Now, replace 'x' by g(x) in order to determine the expression of (fog)(x).
[tex](fog)(x)=3\;g(x)[/tex]
[tex](fog)(x)=3\times 5x[/tex]
Step 3 - Simplify the above expression.
[tex](fog)(x)=15x[/tex]
The expression of (fog)(x) in the simplest form is [tex](fog)(x)=15x[/tex].
For more information, refer to the link given below:
https://brainly.com/question/5245372
The digit in the ten's place of a two digit number is one less than the digit in the one's place. If we add this number to the number obtained by reversing its digits, the result is 55, find the number.
Answer:
23
Step-by-step explanation:
55 = 23 + 32
14 and 41 came into my d, but 1 and 4 are 3 apart from each other
(would really appreciate the brainliest)
A movie membership costs $10 a month plus an additional $5 for each movie purchased. If you have only budgeted to spend a maximum of $25 this month, how many movies can you purchase?
Answer:
3
Step-by-step explanation:
25-10/3=3
Answer:
3 movies
Step-by-step explanation:
You can pay for 3 movies because
5*3=15 and you have to pay for the membership which is 10 so
10+15=25
Which of the following represents a function?
Answer:
see below
Step-by-step explanation:
A graph is a function if any vertical line intersects points on the graph only once. The graph of A is a function.
__
Ordered pairs represent a function if no x-value is repeated. In the list of B, the x-value -1 shows up twice. The list of B is not a function.
__
As with ordered pairs, a table represents a function if no x-value is repeated. In the table of C, the x-value 3 shows up twice. The table of C is not a function.
__
A mapping diagram represents a function if each x-value is only mapped to one y-value. In the map of D, the x-value 3 is mapped to two different y-values. The map of D is not a function.
Answer:D
Step-by-step explanation:
A number pattern starts with 10 and follows the rule "multiply by 3." What is true
about all of the numbers in this pattern?
What is 1/3 of 5 1/2
Answer:
im so sorry
Step-by-step explanation:
Answer:
(1/3)*(5 1/2) = 1.83333333333 or 1.8
Step-by-step explanation:
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
In the attached file
