The total revenue the previous year is $20,000
How to calculate the total revenue ?This year the total revenue of the small business is $14,200
This amount is 29% less than the total revenue in the previous year
Therefore the total revenue in the previous year can be calculated as follows
100 - 29
= 71
= 71/100
= 0.71
Total revenue= 14,200/0.71
= 20,000
Hence the total revenue the previous year is $20,000
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4. A pizza company is interested in the average number of pizzas eaten each year by
people. They send out 30 volunteers to conduct research by collecting random
samples of 25 people each and determine the number of pizzas that the people in
the group ate in the previous year. After looking at the sample means, the company
estimates that the mean number of pizzas eaten is 6.4 with a margin of error of 1.3.
Based on these values, what interval is likely to contain the true mean number of
pizzas eaten in the previous year by the population?
Based on these values, the interval that likely to contains the true mean number of pizzas eaten in the previous year by the population is :5.1-7.7
What does a margin of error mean?
The margin of error of 1.3 means that the interval that contains the true mean of the people sampled is the mean plus or minus the margin of error, in other words, the mean of 6.4 could either be greater by 1.3 or less by 1.3
interval containing the true mean number=mean± marginal of error
upper limit of the mean interval=6.4+1.3
upper limit of the mean interval=7.7
lower limit of the mean interval=6.4-1.3
lower limit of the mean interval=5.1
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what is the domain and the range of the following relation? show work
{(2,-5) , (4,31), (11,-11), (-21,3)}
The domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}
What is the domain and the range of a function?The domain and the range of a function are the set of input values and output values of the graph
How to determine th domain and range of the function?We have the following ordered pairs of the function
(x, y) = {(2,-5) , (4,31), (11,-11), (-21,3)}
Remove the y values to determine the domain
x = {2, 4, 11, -21}
Remove the x values to determine the range
y = {-5, 31,-11,3}
Hence, the domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}
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An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
Answer:
wait first of all where did they put grandma?
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
Answer:
W = 11/8 or 1 3/8
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
W=(1/4)(L)
width is 1/4 length
if the length is 5 1/2 ft
5 1/2 is equivalent to 11/2
W= (1/4)(11/2)
Multiply across.
W = 11/8 or 1 3/8
ppppppllllllssss hhhhheeeeellllppppp
Answer: 10^-5 = 1/10^5
Step-by-step explanation: Every time you see a negative exponent, it would be 1/10^ (exponent number)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{10^{-5}}\\\\\mathsf{= \dfrac{1}{10\times10\times10\times10\times10}}\\\\\mathsf{= \dfrac{1}{100\times100\times10}}\\\\\mathsf{= \dfrac{1}{10,000\times10}}\\\\\mathsf{= \dfrac{1}{100,000}}\\\\\mathsf{= \dfrac{1}{10^5}}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{1}{10^5}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Fiona is heating water for a science experiment the temperature of the water increases 4/5 of a degree every 2/5 of a minute how much is the temperature of the water increasing per minute.
Answer needed ASAP
thanks
The temperature that water is increasing per minute is 2 degrees.
What is the increase in temperature per minute?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.
The first step is to determine what 2/5 of a minute is equivalent to in seconds.
1 minute = 60 seconds
2/5 x 60 = 24 seconds
The formula that can be used to determine the temperature that water is increasing per minute is :
Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute
(4/5 x 60) / 24 = 2 degrees
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igcse math (quadratic functions)
given the equation: x^2 + 5x - 14
use the discriminant to decide if there are two real and different roots, two equal roots or no real roots
Answer:
2 real different roots
Step-by-step explanation:
Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:
[tex]\displaystyle{D = b^2-4ac}[/tex]
The formula is derived from a quadratic formula which is:
[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The expression inside the square root is discriminant. The discriminant says that:
There are 2 real different roots if the discriminant (D) is greater than 0. (D > 0)There is 2 real double roots (same roots) if the discriminant (D) is equal to 0. (D = 0)There are no real roots (imaginary or complex roots) if the discriminant (D) is less than 0. (D < 0)From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:
a = 1b = 5c = -14Therefore, substitute the coefficients’ values in the discriminant:
[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]
Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.
Can someone help me on this question and explain the process?
Let's call the entire angle between the 10 and 5 sides to be x
Applying to cosine rule:
[tex]9 {}^{2} = 10 {}^{2} + 5 {}^{2} - 2(10)(5)cos(x) \\ 81 = 100 + 25 - 100cos(x) \\ 100cos(x) = 125 - 81 \\ cos(x) = \frac{44}{100} = 0.44 \\ x = arccos(0.44)\approx63.9[/tex]
We can conclude that the angle inside the small triangle is half of x, which i will denote by y
[tex]y = \frac{x}{2} = \frac{63.9}{2} = 31.95[/tex]
Similarly to find the angle which i will denote by z at the right lower corner of the small or large triangle, apply the cosine law again:
[tex]10{}^{2} = 5 {}^{2} + 9 {}^{2} - 2(9)(5)cos(z) \\ 100 = 25 + 81 - 90cos(z) \\ 90cos(z) = 106 - 100\\ cos(z) = \frac{6}{90} = 0.06666 \\ z = arccos(0.06666)\approx86.2[/tex]
The last angle in our small triangle which i will denote by w, will be 180 minus z and y
[tex]w = 180 - (y + z) \\ w = 180 - (31.95 + 86.2) \\ w = 61.85[/tex]
Let t be our missing side,
applying the law of sines:
[tex] \frac{5}{sin(w)} = \frac{t}{sin(y)} \\ t = \frac{5sin(y)}{sin(w)} = \frac{5sin(31.95)}{sin(86.2)} [/tex]
[tex]t \approx2.652[/tex]
Find each real root. 4√810,000
The simplified form of the real root 4√810,000 is 3600.
To simplify simply means to make something easier. In mathematics, simplifying an expression, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
By considering the given root
4√810,000
=4x 900
=3600
Making something simpler means making it less complicated or cluttered. When you explain a complex mathematical concept to a child in terms they can easily understand, you are simplifying. When you eliminate many of the activities that were keeping you busy and stressed out, you have simplified.
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What is the value of (−12)4?
Answer:
-48
Step-by-step explanation:
[tex](-12)4\\(-12) \times 4\\= -48[/tex]
Answer: -48
Step-by-step explanation:
negative x negative x negative x negative = negative
12 x 4 = 48
remember the answer needs to be a negative
(-12)4 = -48
Solve. √6-3 x -2=0
Value of x = 2/3.
✓(6 - 3x) - 2 = 0
Adding 2 to both sides of the equation
✓(6 - 3x) - 2 + 2 = 0 + 2
✓(6 - 3x) - 2 = 2
Now, tor remove the square root from the Left Hand Side of the equation, square both the sides of the equation.
(✓(6 - 3x))² = 2²
6 - 3x = 4
3x = 6 - 4
3x = 2
x = 2/3
Thus, the value of x is 2/3.
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What is the equation of the line that passes through the point (6,-2) and has an
undefined slope?
keeping in mind that a line with an undefined slope is always a vertical line, check the picture below.
now, we could use those two points from that line and check its slope
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{6}}} \implies \cfrac{4 +2}{0}\implies \cfrac{6}{0}\implies und efined[/tex]
can someone help me find the answer to this??
The correlation coefficient (r) is 0.9168.
The correlation coefficient can be improved by ignoring the bill for the month of July.
What is the correlation coefficient of the data set?The correlation coefficient for the plotted regression data should be around 0.9168 using the estimated data point taken from the attached graph. This indicates that there is a strong positive correlation between the electricity bill ($) and the amount of time spent at home because the obtained correlation coefficient is very close to 1.How close the R-value is to either -1 or 1 serves as a gauge of the strength of a relationship using the correlation coefficient.The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.
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Simplify. 2√12 -4√27
The value of the simplified expression is 8√3
What is simplification?Simplification is a process of reducing terms to expressions, which do not generate changes or values.
RationalizationRationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
Expression: 2√12 -4√27Since there are no denominators, we will only decompose the square root into factors for simplicity
√12 = √2×2×3 = √2²×3 = 2√3√27 = √3×3×3 = √3×3² = 3√32(2√3) - 4(3√3)
4√3 - 12√3
8√3
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After simplifying 2√12 -4√27 the answer will be -8√3.
For simplicity, we should basically convert the square root into its factors.
Now we know that the prime factorization of 12 is, 12 =1×2×2×3.
and for 27 it is 27=3×3×3.
Now 2√12 =2[tex]\sqrt{2^2.3}[/tex]=4√3.
And, 4√27 = 4[tex]\sqrt{3^2.3}[/tex]=12√3.
∴2√12 - 4√27
=4√3 - 12√3
=-8√3 .
∴2√12 - 4√27 =-8√3 .
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Solve m² = 0.04.
m=?
Answer:
M=0.00671
Step-by-step explanation:
[tex] \sqrt{m} = 0.04[/tex]
[tex] \sqrt{m {}^{2} } = \sqrt{0.04} [/tex]
[tex]m = 0.0067082039[/tex]
would suggest rounding off
Jeremiah uses 15 pages out of an exercise book containing 75 pages. What fraction of the exercise book has been used?
I need this word problem translated into a inequality expression
One-fourth multiplied by sum of t and 9 is at most 9
Answer:
[tex]\frac{1}{4}[/tex] (t + 9) ≤ 9
Step-by-step explanation:
One-fourth multiplied by sum of t and 9 is at most 9
One-fourth [tex]\frac{1}{4}[/tex]
sum of t and 9 = t + 9
at most 9 = ≤ 9
The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120ft² to a depth of 3in., how many bags do you need to mulch 200ft² to a depth of 4in ?
To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
What do we mean by depth?The depth of an object is defined as the distance between its nearest and farthest ends in mathematics. The vertical magnitude of an object is measured by its height. Depth is also a measure of an object's vertical magnitude. These two terms appear to represent the same quantity.So,
When z "varies jointly" with x and y, the following formula can be used to describe it:
z = kxy
Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.
The information provided allows us to calculate the value of k.
n = kad10 = k·(120)(1/4)10/30 = k = 1/3 (divide by the k coefficient)Now we can fill in the blanks with the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9n = 22(2/9)Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
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Which relation is a function?
Using the vertical line test, we conclude that the relation that is a function is the bottom right one.
Which of the graphed relations is a function?
A relation is a function only if all the inputs are mapped into a single output.
If we have the graph of a relation, it only will be a function if it passes the vertical line test.
This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.
With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.
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In the first quadrant, you start at (6, 3)
and move 2 units left
What point will you end up on?
Answer: the answer is (6,1)
Step-by-step explanation:
Answer:
(4, 3)
Step-by-step explanation:
If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.
A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)
PLEASE HELP 40 POINTS !!!!
Use function notation to write the equation of the line.
Answer:
Step-by-step explanation:
Its not that hard.. just use your brain or wait for someone else.
The ages of Lily, Oscar, Hana and Albie add
up to 80 years.
The ratio of Lily's age to Oscar's age to Hana's
age to Albie's age is 7:3:6:4.
How many years old is Hana?
Answer:
Hana is 16
Step-by-step explanation:
Total is 80. Ratio is 7:3:6:4. Ratio adds to 20. 80÷20=4. Hana is last in Ratio which is 4. 4×4= 16.
Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
g(x)-f(x)
The domain of the function [tex]g(x) - f(x)[/tex] for [tex]f(x)=2 x+5[/tex]and [tex]g(x)=x^2-3 x+2[/tex] is [tex]g(x) - f(x)[/tex] = [tex]x^2-4x-2[/tex]. The domain will be all real numbers for x, ( ∞,-∞)
What is the domain of the function [tex]g(x) - f(x)[/tex] ?The domain will be all real numbers for x, ( ∞,-∞)
As there are no values that can be substituted for x that can possibly make the function undefined.
Therefore,
[tex]g(x)=x^2-3 x+2 .[/tex]
[tex]f(x)=2 x+5[/tex]
[tex]g(x) - f(x)[/tex] = ([tex]x^2-3 x+2[/tex]) - ([tex]2 x+5[/tex])
[tex]g(x) - f(x)[/tex] = [tex]x^2 - 4x-2[/tex]
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Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (h⁰g)(0)
The value of the expression ( h o g)(0) is 5.
When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.
Consider the two functions,
g(x) = 5x - 2 and h(x) = x² + 1
So,
( h o g)(x) = h(g(x))
( h o g)(x) = ( 5x - 2 )² + 1
( h o g)(x) = 25x² - 20x + 4 + 1
( h o g)(x) = 25x² - 20x + 5
( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1
( h o g)(0) = 0 - 0 + 4 + 1
( h o g)(0) = 5
The value of the expression ( h o g)(0) is 5.
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The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 of the animals in the habitat you are studying.
a. Write a function that models the change in the animal population.
The function that models the change in the animal population is
[tex]F(x) = x ( 1+ r)^{t}[/tex]
According to the question we have been given that
population decreases = 3.5% per year
Number of animals counted = 80
The formula to be used is
[tex]F(x) = x (1 + r)^{t}[/tex] (1)
where, F(x) = amount of animals counted after t years
x = initial amount of animals
r = decrease or increase rate of animal species.
t = time
Now according to the question,
r = -0.035
x = 80
Putting the required values in equation (1) we get
[tex]F(x) = 80 (1 - 0.035)^{t}\\ F(x) = 80 (0.965)^{t}[/tex]
Thus above is the required function that models the change in the animal population.
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Question 10: Neil writes down four numbers with a sum of 50.
All the numbers have two decimal places and no two numbers are the same.
Write down four possible numbers Neil could have written down.
Answer:
15-10-11-14
Step-by-step explanation:
15+10= 25
25+11= 36
36+14= 50
The slope of the car is ________
Answer:
y = 60x
slope: 6 0 probably
Step-by-step explanation:
Dunnno
Answer:
y = 60x
slope: 6 0
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $66. A season ski pass costs $400. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
$74.95 ladder; 6.5% tax
Answer:
11.5307692308
Step-by-step explanation:
Answer:
Around $79.88
Multiply and simplify. √8 x² . √2 x²
The simplest form of the expression is 4 x² .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean editing an analogous math expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, and then inside the simplified expression, we tend to are about to be alone left with not like terms that cannot be reduced any.We have given an expression √8 x² . √2 x² . .....(1)
On multiplying , we get
√8 x² . √2 x² = √16 x⁴
On simplifying , we get
√16 x⁴ = √ 4 × 4 × x² × x²
= 4 x²
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