Final answer:
The y-intercept in the equation y=0.10x+9.50 represents an initial financial value of $9.50, such as a fixed charge or baseline cost, before any variable amounts are factored in.
Explanation:
In everyday English, the financial meaning of the y-intercept in the equation y=0.10x+9.50 refers to the initial amount or fixed cost that does not depend on the quantity represented by x. In other words, when x, which might represent the quantity of goods sold or the number of hours worked, is zero, the y-intercept indicates a starting value of $9.50. This could be a baseline charge, a fixed fee, or some kind of initial cost before any additional variables are added to the equation.
Use numerals instead of words. If necessary use/ for the fraction bar
Answer:
10
Step-by-step explanation:
Range=big-small=34-16=18
Interquartile range=big number in box-small number in box= 29-21=8
The different between the two is 18-8=10
Answer:
The difference of range and interquartile range is 10.
Step-by-step explanation:
Consider the provided information.
From the box plot we can identify:
The lowest value is 16
The first quartile is 21
The 2nd quartile or median is 26
The 3rd quartile is 29
The highest value is 34
Range is the difference of the highest value and lowest value of the data set.
Range = 34 - 16 = 18
Interquartile range is the difference of the 3rd quartile from the 1st quartile.
IQR: 29 - 21 = 8
Thus, the difference of range and interquartile range is:
18 - 8 = 10
Hence, the difference of range and interquartile range is 10.
use natural logarithms to solve the equation 5e^3x+7=21
Answer:
5e^(3x+7)=21
e^(3x+7)=4.2
(3x+7)lne=ln4.2
lne=1
3x+7=1.435
3x= -5.565
x= -1.855
To solve the equation [tex]5e^{3x}+7=21[/tex], isolate the exponential term, take the natural logarithm of both sides, and then solve for x. This results in x ≈ 0.3362.
To solve the equation [tex]5e^{3x}+7=21[/tex], follow these steps:
First, isolate the exponential term by subtracting 7 from both sides:
[tex]5e^{3x} = 14[/tex]
Next, divide both sides of the equation by 5:
[tex]e^{3x} =\frac{14}{5}[/tex]
Now, take the natural logarithm (ln) of both sides:
[tex]ln(e^{3x}) = ln(\frac{14}{5})[/tex]
Since the natural logarithm and the exponential function are inverse operations, the left side simplifies to:
[tex]{3x} = ln(\frac{14}{5})[/tex]
Finally, solve for x by dividing by 3:
[tex]x =\frac{1}{3}\times ln(\frac{14}{5})[/tex]
Using a calculator, this results in:
x ≈ 0.3362
Rationalize the denominator and simplify. 6 /5-3
Final answer:
To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.
Explanation:
To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.
The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.
Therefore, the simplified expression is 3/1 = 3.
Find the additive inverse of 6+4i
[tex]0-(6+4i)=0-6-4i=-6-4i[/tex]
The additive inverse of the complex number 6+4i is -6-4i because it negates both the real and imaginary parts, resulting in a sum of zero when added to the original number.
The additive inverse of a complex number is a number that, when added to the original number, yields a sum of zero. For the complex number 6+4i, its additive inverse is found by changing the sign of both the real and the imaginary parts. Therefore, the additive inverse of 6+4i is -6-4i.
evaluate x -2 y 0 / x 3 y -2 when x = 2 and y = 5
Answer:
5/8
Step-by-step explanation:
first plug in for x & y, then solve. you should get 5/8
2 -2 +5 +0 / 2 +3 +5 -2
5/8
Answer:
125/32
Step-by-step explanation:
solve 30% of what = 60 step by step
Answer:
200
Step-by-step explanation:
Of means multiply and is means equals
30% * W = 60
Change to decimal form
.30 * W = 60
Divide each side by .30
.30W /.30 = 60/.30
W = 200
Roger and his brother work similar jobs, earning the same amount per hour. Roger earns $3,240 per month working hours, and his brother works 20
hours more than Roger and earns $5,400 per month.
Complete the equation or inequality you would use to find how many hours each brother works in a month
how many
* + 20
x 20
x-20 2
3
3,240
50
5,400
Answer:
Roger works 30 hours and his brother works 50 hours
Step-by-step explanation:
Let
x ---->the number of hours Roger works in a month
y ---->the number of hours his brother works in a month
step 1
Find out how much they earn per hour
5,400-3,240=$2,160 -----> amount earned by 20 hours of work
$2,160/20=$108 per hour
step 2
Find out how many hours each brother works in a month
Roger
108*x=3,240
x=3,240/108=30 hours
His brother
y=x+20
y=30+20=50 hours
Answer:
i dont know
Step-by-step explanation:
Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?
1box = 1400/7 = 200
200×3=600
1400+600=2000
Answer:
2000
Step-by-step explanation:
Given :Workers have packed 1,400 glasses in 7 boxes.
To Find :If they pack 3 more boxes, how many glasses will they have packed in all?
Solution:
Workers packed no. of glasses in 7 boxes = 1400
Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]
Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]
= [tex]600[/tex]
So, initially they packed 1400 glasses
If they pack 3 more boxes so, the pack 600 glasses more
So, The total no. of glasses have packed by workers = 1400+600 = 2000
Hence they have packed 2000 glasses in all.
What is the solution to the inequality X squared <49
[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation below.
If we divide both sides by -2, we have
[tex]bx-5 = -8 \iff bx = -3 \iff x = -\dfrac{3}{b}[/tex]
So, if you choose b=3, you have x = -3/3=-1
a)
The value of x in terms of b is:
[tex]x=\dfrac{-3}{b}[/tex]
b)
The value of x when b is 3 is:
[tex]x=-1[/tex]
Step-by-step explanation:We are given a equation in terms of x and b as follows:
[tex]-2(bx-5)=16-----------(1)[/tex]
a)
Now on simplifying the equation i.e. we solve for x i.e. we find the value of x in terms of b as follows:
On dividing both side of the equation by -2 we get:
[tex]bx-5=-8[/tex]
Now on adding both side by 5 we get:
[tex]bx=-8+5\\\\\\bx=-3[/tex]
Now, on dividing both side of the equation by b we get:
[tex]x=\dfrac{-3}{b}------------(2)[/tex]
b)
when b=3 in equation (2) we have:
[tex]x=\dfrac{-3}{3}\\\\\\x=-1[/tex]
A family is planning a wedding celebration in a gazebo. They want to know the area so that they can determine how many people can comfortably fit inside. They take some measurements and find that each side is 8 ft long and the apothem is 9.7 ft. What is the area of the enclosed gazebo?
Answer:
The area of the enclosed gazebo is [tex]310.4\ ft^{2}[/tex]
Step-by-step explanation:
I assume that is a regular octagon (eight equal aides)
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}(P)(a)[/tex]
where
P is the perimeter of the polygon
a is the apothem
Find the perimeter P (the octagon has 8 sides)
[tex]P=8(8)=64\ ft[/tex]
[tex]a=9.7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(64)(9.7)[/tex]
[tex]A=310.4\ ft^{2}[/tex]
x+4/6=2/3+x-1/4 slove for X
Answer:
No solution
Step-by-step explanation:
x + 2/3 = 2/3 + x - 1/4
x = x - 1/4
0 ≠ -1/4
Which geometric object is defined as the set of all points in a plane that are equidistant from two points ?
A. Line Segment
B. Circle
C. Parabola
D. Line
A geometric object which is defined as the set of all points in a plane that are equidistant from two (2) points is: D. Line.
What is a line?A line can be defined as a geometric object which comprises the set of all points in a plane that are all equidistant from two (2) points.
This ultimately implies that, a line is a one-dimensional geometric object that is straight and forms the shortest distance between two (2) points because it extends endlessly in both directions.
Read more on line here: https://brainly.com/question/1655368
Answer:
a line
Step-by-step explanation:
fourteen of the 100
digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?
Answer:
0.14
Step-by-step explanation:
Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. It means that the probability that a randomly selected item is defective is: [tex]\frac{14}{100} = 0.14[/tex].
Please help!!!!! Thanks
Answer:
Look to the attached file
Step-by-step explanation:
A farmer wants to put a fence around a garden in the shape of a square. The fence posts are placed every 2 meters. One side of the garden is 10m long. How many posts does the farmer need?
Answer:
The farmer would need 80 posts.
Step-by-step explanation:
If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.
The scores on a test are normally distributed with a mean of 80 and a standard deviation of 16. What is the score that is 2 standard deviationsdeviations aboveabove the mean?
The deviation from 80 of about 16 is normal.
So the lowest is usually 80 - 16 = 64 and the highest is 80 + 16 = 96
But now we have a "deviation" that is 2 standard deviations above the mean score.
So 80 + 16 + 16 = 112 is this score.
Hope this helps.
r3t40
Final answer:
To calculate the score that is 2 standard deviations above the mean of 80 with a standard deviation of 16, you add 2 times the standard deviation to the mean, resulting in a score of 112.
Explanation:
To find the score that is 2 standard deviations above the mean on a test with a mean of 80 and a standard deviation of 16, we use the formula:
Score = Mean + (Number of Standard Deviations × Standard Deviation)
So, plugging in the numbers we get:
Score = 80 + (2 × 16)
Score = 80 + 32
Score = 112
The desired score is therefore 112, which is 2 standard deviations above the mean of 80.
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month.
The simultaneous Equations for both total costs are;
Company A: y = 45x + 150
Company B: y = 50x + 125
Thus, both companies charge the same amount of money for food truck permits for 5 months
How to find the equation of the total charges?
We are told that;
Company A charges a one time fee of $150 and $45 per month.
Company B charges a one time fee of $125 and $50 per month.
Thus, using the concept of the equatiom of a line In slope intercept form, we have:
Company A: y = 45x + 150
Company B: y = 50x + 125
let's use the number 5 for x as an example
45(5) + 150 = 375
50(5) + 125 = 375
So both companies charge the same amount of money for food truck permits for 5 months.
Complete question is;
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation
what is the area of the triangle? (sorry if its sideways)
Answer:
6
Step-by-step explanation:
2 x 6 = 12/2 = 6
Answer:
A = 6 units ^2
Step-by-step explanation:
The area of a triangle is found by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 (6) *2
A = 6 units ^2
How are trapezoids and parallelograms related?
Both are rhombuses.
Both have two pairs of congruent sides.
Both have supplementary angles.
Both have parallel sides.
Trapezoids and parallelograms both feature parallel sides, with a trapezoid having one pair and a parallelogram having two pairs. Parallelograms always have supplementary consecutive angles and congruent opposite sides, which is not necessarily the case for all trapezoids.
Trapezoids and parallelograms are related by the characteristic that they both have parallel sides. Specifically, a trapezoid has one pair of parallel sides known as the bases, whereas a parallelogram has two pairs of parallel sides.
Moreover, the consecutive angles in a parallelogram are supplementary, meaning that any two angles next to each other add up to 180 degrees. While trapezoids do not have this property for all four of their angles, the angles adjacent to the bases (the non-parallel sides) may also be supplementary, depending on the specific shape of the trapezoid.
It is important to note that while all parallelograms are quadrilaterals with opposite sides that are congruent and parallel, not all trapezoids share these properties. The key distinction between the two shapes lies in the number of parallel sides.
Additionally, comparing them with rhombuses, parallelograms can be rhombuses if all sides are congruent, but trapezoids cannot be rhombuses as they lack the two pairs of parallel sides.
5. (03.02)
If g(x) = x2 + 3, find g(4). (2 points)
16
19
8
11
Answer:
19
Step-by-step explanation:
g(x)=x^2+3
g(x)=(4^2)+3
g(x)=16+3=19
if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19
Answer:
option(B) g(4) =19.
Step-by-step explanation:
Given:If g(x) = [tex]x^{2}[/tex] + 3.
To find: g(4).
Solution: We have given that
g(x) = [tex]x^{2}[/tex] + 3.
for x=4.
g(4) = [tex]4^{2}[/tex] + 3.
g(4) = 16+3
g(4) =19.
Therefore, option(B) g(4) =19.
Sketch the graph of y = (x - 3)2 - 25, then select the graph that corresponds
to your sketch.
Answer:
Option C. Graph C
Step-by-step explanation:
we have
[tex]y=(x-3)^{2}-25[/tex]
This is the equation of a vertical parabola open upward (vertex is a minimum)
The vertex is the point (3,-25)
therefore
The graph is C
The graph in the attached figure
Answer:c
Step-by-step explanation:
What is the chance that a person randomly selected off the street was born in May
8%
12%
20%
30%
Answer: Eight percent.
Step-by-step explanation: In order to find this, we have to use the probability formula, which is:
The Event We Are Looking For/All of the Events.
In this case, plugging the numbers into the formula we get
May(1)/All the months in the year, including May (12).
Diving this, our answer will be 0.08333..., or rounded up to 0.8
However, since we are only looking for one specific event, we can take the number 100, and divide it by all the events. 12/100 is 8.333..., or rounded to 8.
Final answer:
The chance that a person randomly selected off the street was born in May is about 8%, assuming birth rates are evenly distributed throughout the year.
Explanation:
The question, "What is the chance that a person randomly selected off the street was born in May?" is one that pertains to the subject of probability in Mathematics. Since there are typically 12 equally likely months that a person could be born in, and assuming there is no significant variation in birth rates by month, the chance that someone chosen at random off the street was born in May is 1 out of 12 months.
Thus, to calculate the probability, you would divide 1 by 12, which equals approximately 0.0833. To express this as a percentage, we multiply by 100, yielding an 8.33% chance. Therefore, the closest answer among the provided options is 8%.
What is the point-slope form of a line with slope 2 that contains the point (1,3)?
A. y-1 = 2(x-3)
B. y+ 3 = -2(x - 2)
c. y + 3 = 2(x+1)
D. Y-3 = 2(x - 1)
solve for x in the equation
I need help ASAP
Answer:
D
Step-by-step explanation:
Given
2x² + 3x - 7 = x² + 5x + 39
Subtract x² + 5x + 39 from both sides
x² - 2x - 46 = 0 ← in standard form
with a = 1, b = - 2, c = - 46
Solve for x using the quadratic formula
x = (- (- 2) ±[tex]\sqrt{(-2)^2-(4(1)(-46)}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{4+184}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{188}[/tex] ) / 2
= ( 2 ± 2[tex]\sqrt{47}[/tex] ) / 2
= 1 ± [tex]\sqrt{47}[/tex]
Pam is playing with red and black marbles. The number of red marbles she has is three more that twice the number of black marbles she has. She has 42 marbles in how. How many red marbles does Pam have?
Answer:
29 red marbles
Step-by-step explanation:
Call R the number of red marbles and B the number of black marbles.
According to the second sentence, R = 2B + 3.
According to the third sentence, R + B = 42.
Now we have 2 equations, 2 unknowns. Sub the first into the second since it already has R isolated:
2B + 3 + B = 42
3B = 39
B = 13
Now sub this into either of the original equations (I'll use the first):
R = 2(13) + 3
R = 29
Which unit of measure would be appropriate for the volume of a cylinder that is 8 meters tall and has a radius of 4 meters
Answer: cubic meters : m³
Step-by-step explanation:
Cylinder volume is the product of area of the base by height.
Area of the base is the product of π·radius² = square meters : m²
Volume = square meters·meters = m²·m = cubic meters : m³
[tex]\textit{\textbf{Spymore}}[/tex]
Which of the following is a factor of 2x^4 + 20x^3 + 50x^2?
A. 2x^3
B. x^4
C. x+4
D. x+5
Answer:
D. x + 5
Step-by-step explanation:
2x^4 + 20x^3 + 50x^2
= 2x^2 (x^2 + 10x + 25)
= 2x^2 (x + 5)^2
= 2x^2 (x + 5) (x + 5)
Answer
D. x + 5
For this case we have the following expression:
[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]
It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:
[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]
If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.
Rewriting the expression we have:
[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]
Thus, one of the factors of the original expression is[tex]x + 5[/tex].
Answer:
Option D
What’s the value of x
Answer:
x = 25
Step-by-step explanation:
The 2 given angles form a straight angle and are supplementary, that is
2x + 2 + 5x + 3 = 180
7x + 5 = 180 ( subtract 5 from both sides )
7x = 175 ( divide both sides by 7 )
x = 25
Use long division to find the quotient below.
(15x^3+2x^2-75)÷(3x-5)
Answer:
5x^2 + 9x + 15.
Step-by-step explanation:
There is no term in x so we add one (0x).
5x^2 + 9x + 15 <------------Quotient.
--------------------------------------
3x - 5 ) 15x^3 + 2x^2 + 0 x - 75
15x^3 - 25x^2
--------------------
27x^2 + 0x
27x^2 - 45x
------------------
45x - 75
45x - 75
..........