Question 1
B. Set of whole numbers
Eliminate A and C because negative integers are in those sets.Question 2
A. Set of real numbers
The equation represents a line, which has a domain of all real numbers.If the perimeter of the square is 4x then the domain of the function will be set of rational numbers and the domain of the function y=3x+8(3-x) is set of real numbers.
Given The perimeter of the square is f(x)=4x and the function is y=3x+8(3-x)
We will first solve the first part in which we have been given that the perimeter of the square is 4x and we have to find the domain of the function.
First option is set of rational numbers which is right for the function.
Second option is set of whole numbers which is not right as whole number involves 0 also and the side of the square is not equal to 0.
Third option is set of integers which is not right as integers involve negative number also and side of square cannot be negative.
Hence the domain is set of rational numbers.
Now we will solve the second part of the question
f(x)=3x+8(3-x)
we have not told about the range of the function so we can put any value in the function and most appropriate option will be set of real numbers as real number involve positive , negative and decimal values also.
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if 3t -7 = 5t, then 6t =
Answer:
21
Step-by-step explanation:
[tex]3t-7=5t[/tex]
subtract 3t from both sides
[tex]-7 = 2t[/tex]
multiply both sides by 3
[tex]-21 = 6t[/tex]
so 6t = -21
Suppose Jenny places 9500 in an account that pays 13% interest compounded each year. Assume that no withdrawals are made from the account.
tell me your the greatest but once you turn they hate us
Please help! Please help with all sections
The number of hours spent playing video games is the independent variable and cumulative grade point average is the dependent variable.
What is an independent variable?An independent variable simply means the variable that's changed to test the effect on the dependent variable.
Here, the number of hours spent playing video games is the independent variable and cumulative grade point average is the dependent variable.
This is because the number of hours is being used to predict cumulative grade point average.
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The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006? Round your answer to the nearest integer.
The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
What are percentages?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?
The number of the employees in 2006 will be calculated as:-
Number of employees decreased = 0.5% x 8110
Number of employees decreased = (0.5/100) x 8110
Number of employees decreased = 40.55
The number of the employees in 2006 will be
N = 8110 - 40.55 = 8069.45
Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
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The point A(0,3) and point B(4,19) lie on the line L.
Find the equation of line L
Answer: The equation is y = 4x+3
Slope = 4
y intercept = 3
========================================================
Explanation:
Let's start off by finding the slope.
[tex]A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\[/tex]
The slope is 4.
The y intercept is 3 because of the point (0,3)
We go from y = mx+b to y = 4x+3
m = slope
b = y intercept
---------------
Check:
Plug in x = 0 and we should get to y = 3
y = 4x+3
y = 4(0)+3
y = 0+3
y = 3
That works out. Now try x = 4. It should lead to y = 19
y = 4x+3
y = 4(4)+3
y = 16+3
y = 19
The answer is confirmed.
Question 6b
6b of 6
The width of a rectangle is 15 centimeters less than its length. If the area of the
rectangle is 100 square centimeters, find the length and the width using the formula
A = lw.
O Length = 25 centimeters and Width = 10 centimeters
○ Length = 20 centimeters and Width = 5 centimeters
O Length = 115 centimeters and Width = 100 centimeters
○ Length = 5 centimeters and Width = 20 centimeters
Answer:
○ Length = 20 centimeters and Width = 5 centimeters
Step-by-step explanation:
Let the length = L
Then the width is L - 15
A = lw
100 = L(L - 15)
L² - 15L - 100 = 0
(L - 20)(L + 5) = 0
L - 20 = 0 or L + 5 = 0
L = 20 or L = -5
Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.
L = 20
width = L - 15 = 20 - 15 = 5
Answer: ○ Length = 20 centimeters and Width = 5 centimeters
what is 190 divided by 2/3
After divide, the solution of the expression is, 285
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
190 divided by 2/3.
Now, We can simplify as;
⇒ 190 ÷ 2/3
⇒ 190 × 3/2
⇒ 95 × 3
⇒ 285
Thus, The solution of the expression is, 285
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The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
y = x^3 - 4
y = (x - 4)^3
y = (-x - 4)^3
y = (-x)^3 - 4
Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven-dollar games could he buy with the money he had left?
Answer:
three
Step-by-step explanation:
60 - 39 = 21
21/7 = 3
If you drive 72 miles and use 6 gallons of gas, what is your rate
Answer:
Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.
Help me please help help
[tex]\angle P = \angle S \Rightarrow \angle S = 42 &^\circ\\\angle Q = \angle T \Rightarrow \angle S = 86 &^\circ\\\angle R = \angle U\\[/tex]
Sum of all angles in a triangle equals 180:
[tex]\angle R = 180 - (86 + 42) = 180 - 128 = 52[/tex]
Answer:
[tex]U = 52 &^ \circ[/tex]
PLEASE HELP!!!!!!!!!
The equivalent expression to ∑n(n+1) is ∑n²+∑n.
What is Equivalent expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression;
∑(n(n+1))
= ∑ (n² + n)
= ∑n²+∑n
Thus, the equivalent expression to ∑n(n+1) is ∑n²+∑n.
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Two dice are rolled. What is the probability of getting a sum equals 5?
Probability = (Round to 4 decimal places)
What is the median of these figure skating ratings?
5.0 6.0 7.0 7.5 8.0 9.0 10.0
Answer:
5.0 6.0 7.0 7.5 8.0 9.0 10.0
arranging the following
5.0 , 6.0 , 7.0 , 7.5 , 8.0 , 9.0, 10.0
7.5 is the median..
3y + 9x = 21 Graph A On a coordinate plane, a line goes through (negative 3, negative 2) and (0, 7). Graph B On a coordinate plane, a line goes through (0, negative 7) and (3, 2). Graph C On a coordinate plane, a line goes through (0, 7) and (3, negative 2). Graph D On a coordinate plane, a line goes through (negative 3, 2) and (0, negative 7). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
Answer:
Graph C
Step-by-step explanation:
Graph A (-3, -2) (0, 7)
3(7) + 9(0) = 21
21 = 21 ✓
3(-2) + 9(-3) = 21
-6 - 27 = 21
-33 = 21 ✖
Graph B (0, -7) (3,2)
We know from above that (0, 7) is a point on the line 3y + 9x = 21, therefore point (0, -7) cannot be on that line.
3(2) + 9(3) = 21
6 + 27 = 21
33 = 21 ✖
Graph C (0, 7) (3, -2)
We know from above that (0, 7) is a solution.
3(-2) + 9(3) = 21
-6 + 27 = 21
21 = 21 ✓
Since both points on graph C is a solution to the equation of the line given, it is the answer (looking at graph D is not necessary unless you want to double check your answer).
log(2t+4)=log(14-3t)
Answer:
t = 2
Step-by-step explanation:
[tex]2t + 4 = 14 - 3t[/tex]
[tex]5t = 10[/tex]
[tex]t = 2[/tex]
Checking:
[tex] log(2(2) + 4) = log(8) [/tex]
[tex] log(14 - 3(2)) = log(8) [/tex]
Which function is graphed below?
The graph of the function is y = arcsec(x).
In a recent year (365 days), a hospital had 5705
births.
a. Find the mean number of births per day.
b. Find the probability that in a single day, there are 17
births.
c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births?
Using the Poisson distribution, it is found that:
a) The mean is of 15.63.
b) The probability is of 0.0911 = 9.11%.
c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes.e = 2.71828 is the Euler number.[tex]\mu[/tex] is the mean in the given interval.Item a:
The mean is given by:
[tex]\mu = \frac{5705}{365} = 15.63[/tex]
Item b:
The probability is P(X = 17), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]
The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
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Using the Poisson distribution, it is found that
a) The mean is 15.63.
b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.
c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]
The parameters are
x is the number of successes.
e = 2.71828 is the Euler number.
[tex]\mu[/tex] is the mean in the given interval.
Item a:The mean is given by:
[tex]\:\mu =\frac{5705}{365}[/tex]
Item b: The probability is P(X = 17), hence:
[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:The probability is P(X = 0), hence:
[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]
The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,
hence 0 births in a single day would be a significantly low number of births.
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Given the diagram below, what is cos(45)?
A. √2
B.1/√2
C. 3√2
D. 1/√3
Using the cosine ratio, the value of cos(45) in the diagram is: B. 1/√2.
How to Find the Cosine Ratio?Cosine ratio is, cos ∅ = adjacent length/hypotenuse length of a right triangle.
The triangle is a 45-45-90 triangle, thus, the two legs will be the same length, which is: 9 units each.
Hypotenuse = √(9² + 9²) = √162 = 9√2 units
∅ = 45°
Adjacent = 9 units
cos 45 = 9/9√2 = 1/√2
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How can I solve this? Thank you
The labeled angles are both equal to c by the corresponding angles theorem.
Thus, a+b=c by the exterior angle theorem.
evaluate 7/8+1/4÷6/7
Step-by-step explanation:
[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]
[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]
[tex] = \frac{7}{8} + \frac{7}{24} [/tex]
[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]
[tex] = \frac{21}{24} + \frac{7}{24} [/tex]
[tex] = \frac{28}{24} [/tex]
[tex] = \frac{7}{6} [/tex]
7/8+(1/4÷6/7)
1/4 ÷ 6/7 = 7/24
7/8 + 7/24 = 7/6 = 1 1/6
solve the equation 7m^2-4m+1=0. fully simplify all answers, including non-real solutions
m=
Answer:
m is not an element of real number
What is the exact value of sin (- 105)?
Answer:
Just put it into a calculator
0.97053528353
[tex]\text{Let's find the sine of -105 degrees}\\\text{Start by typing -105 into our calculator}\\\text{and click the sin button}\\\text{It gives us an irrational number, which is the sine of -105 degrees}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The value is end less, it would take an eternity to type it here,}\\\text{ but I will round it to the nearest 100th}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{-0.97}[/tex]
If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
(f + g(x)>3 for all values of x
(f + g)(x)<3 for all values of x
(f + g)(x)>6 for all values of x
(f + g)(x)<6 for all values of x
Answer: for all values of x
Step-by-step explanation:
[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]
Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.
At the beginning of a snowstorm, Amadou had 2 inches of snow on his lawn. The snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was melting, how much snow would Amadou have on his lawn 4 hours after the snow began to fall? How much snow would Amadou have on his lawn after tt hours of snow falling
Answer:
4 inches
Step-by-step explanation:
Given information:
2 inches of snow on the lawnRate of snow falling = 0.5 inches per hourSnow did not meltLet y = height of snow on the lawn
Let t = time in hours
⇒ y = 2 + 0.5t
To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:
⇒ y = 2 + 0.5(4)
⇒ y = 2 + 2
⇒ y = 4 inches
Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.
After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.
After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:
Snow accumulation = Initial snow + (Snowfall rate × Time)
Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)
Snow accumulation = 2 inches + 2 inches
Snow accumulation = 4 inches of snow.
After t hours of snow falling, the amount of snow on Amadou's lawn would be:
Snow accumulation = Initial snow + (Snowfall rate × Time)
Snow accumulation = 2 inches + (0.5 inches/hour × t hours)
Snow accumulation = 2 + 0.5t inches of snow.
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What is the measure of complemnt angle 42
Answer:
Complemetry angle = 90° - 40°
= 50°
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex]
Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complement of 90 by setting up an equation; (let x be the unknown angle).
[tex]\implies[/tex] 42+x=90
Subtract 42 from both sides
x=48
--
Hope that this helped! Best wishes.
--
Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x-values in order from least to greatest (read the graph from left to right). Then, state the domain and range of the function.
The points are follows as (0, -3), (-1, -2), (-2, -1) and (-3, 0).
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The Graph shows the line function;
When the value of x is 0, y will be -3.
When the value of x is -1, y will be -2.
When the value of x is -2, y will be -1.
When the value of x is -3, y will be 0.
The points are (0, -3), (-1, -2), (-2, -1) and (-3, 0).
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1.
Which of the following is the given function's
average rate of change on the interval
-3
Answer: -2
Step-by-step explanation:
[tex]g(-3)=0\\\\g(-2)=-2\\\\\frac{g(-3)-g(-2)}{-3-(-2)}=\frac{0-(-2)}{-1}=\boxed{-2}[/tex]
The legs of a 90-45-45 triangle are 3 and 7. What is the hypotenuse?
Answer:
The hypotenuse is [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
Taking the square root of each side
[tex]\sqrt{58} = \sqrt{c^2}[/tex]
[tex]\sqrt{58} =c[/tex]
Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area =
angle of sector
360
tor) πr²
Sector Area = [?] cm²
Round to four decimal places.
14 cm
46°
14 cm
The area of the shaded part is 8.1447cm²
Area of a sectorThe formula to calculate the area of the shaded region is expressed as:
Area of the shaded region = Area of sector - Area of triangle
Determine the area of the sector
Area of sector = r²β/2
Area of sector = 14²(46π/180)/2
Area of sector = 78.64 cm²
Determine the area of triangle
Area of triangle = 1/2r²sinβ
Area of triangle = 1/2(14²sin46)
Area of triangle = 140.99/2
Area of triangle = 70.49 cm²
Area of shaded part = 78.64 cm² - 70.49 cm²
Area of shaded part = 8.1447cm²
Hence the area of the shaded part is 8.1447cm²
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