Answer:
Step-by-step explanation:
(a) The estimate for the difference in population means is 6.000.
(b) The standard error for the difference in population means is 3.208.
Conclusion:
Based on the given data, the 95% confidence interval for the difference in population means between this year's sales and last year's sales is between -0.608 and 12.608. This suggests that the population mean for this year's sales is likely to be higher than the population mean for last year's sales. This is supported by the fact that the estimate for the difference in population means is 6.000, which is greater than 0.
5. A type of bacteria doubles in number every 25 minutes. Find the constant k
for this type of bacteria, then write the equation for modeling this exponential
growth.
To find the constant k for this type of bacteria, we can use the formula for exponential growth:
N(t) = N0 * e^(kt)
where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.
We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:
N(25) = 2 * N0
Substituting this into the formula, we get:
2 * N0 = N0 * e^(k*25)
Dividing both sides by N0 and simplifying, we get:
2 = e^(25k)
Taking the natural logarithm of both sides, we get:
ln(2) = 25k
Solving for k, we get:
k = ln(2)/25 ≈ 0.0278
Therefore, the equation for modeling the exponential growth of this type of bacteria is:
N(t) = N0 * e^(0.0278t)
*IG:whis.sama_ent
the tables show the cost of bagels at four different bakeries. choose two bakeries with the same unit cost.
Answer:The diagram shows the market demand and supply curves for the bread market. You know that there are 250 identical bakeries operating in the market
Step-by-step explanation:
What is 7months as a fraction of 2years 3months
Step-by-step explanation:
2 years and 3 months = 27 months ( there is 12 months in a year)
7 months of this would be THIS fraction:
7/27
Determine whether the following statements are TRUE or FALSE (do not write down the statements
just state TRUE or FALSE). [7 marks]
a. () ≥ 1 for any event .
b. () = 1 where is the Sample space.
c. If {} is any finite or infinite sequence of disjoint events, then (⋃
=1 ) = ∑ ()
=1 .
d. If ⊆ where and are two events in a sample space, then () ≤ ().
e. If and are two events in a sample space, then ( ∪ ) = () − () + ( ∩ ).
f. If and are two independent events in a sample space, then ( ⁄ ) = (∩)
() .
g. Mutually exclusive events are not independent
a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE
How to determine whether the following statements are TRUE or FALSEa. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.
b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.
c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.
d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.
e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.
f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.
g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.
Learn more about set theory at https://brainly.com/question/28916593
#SPJ1
I need help with this please
Answer:
thats 4th grade math... 0_0 but the answer is 414 ft².
Step-by-step explanation:
So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo
Research and find out the 10 countries where the population. is growing fastest and the 10 countries where it is the slowest growing. Explain how this information is related to the concept of percentage increase and decrease. You can either present this on a chart or have someone film you are explaining it.
Given this equation what is the value of y at the indicated point?
Using curves, we can find that the value of y at the indicated point on the curve is √3.
What is the definition of curves?
A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.
Here in the question,
Given equation:
x = y² - 2
As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:
1 = y² - 2.
Adding 2 on both sides:
1 + 2 = y² - 2 + 2
⇒ 3 = y²
⇒ y = √3.
Therefore, the value of y at the indicated point on the curve is √3.
To know more about curves, visit:
https://brainly.com/question/6436086
#SPJ1
tigate
b) The construction of a tangent to a circle given a point outside the circle can be justified using the
second corollary to the inscribed angle theorem. An alternative proof of this construction is shown
below. Complete the proof. (5 points)
Given: Circle C is constructed so that CD = DE = AD; CA is a radius of circle C.
Prove: AE is tangent to circle C.
1.
2.
3.
4.
5.
C
A
Statements
CD=DE
D
Circle C is constructed so that CD = DE = AD;
CA is a radius of circle C.
CD DE LAD
AACD is an isosceles triangle;
AADE is an isosceles triangle.
m/CAD+mzDCA+mzADC = 180º;
mzDAE+mzAED+mZEDA=
180°
E
1.
2.
3.
4.
Given
Reasons
Definition of congruence
Isosceles triangle
Substitution property
5. Isosceles triangle theorem
The proof that AE is tangent to circle C is given below:
What is the angle addition postulate?The angle addition postulate is a fundamental concept in geometry that states that the measure of an angle formed by two adjacent angles can be obtained by adding the measures of the two angles.
More specifically, given two adjacent angles with measures A and B, the measure of the angle formed by the two adjacent angles (denoted as AOB) can be found by adding the measures of the two angles:
A + B = AOB
This postulate is often used in geometric proofs and can be applied to any adjacent angles, including those formed by intersecting lines, parallel lines, or polygons.
Read more about angle addition postulate here:
https://brainly.com/question/24746945
#SPJ1
The principal at Orchard Ridge High School signs each graduate's diploma by hand. It takes him 30 seconds to sign 4 diplomas. What do I put in the table
The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.
What is proportion?Two ratios are said to be equal when a proportion is stated. Ratios, which can be written as a fraction or a colon, are used to compare two objects or values. For instance, a class might have a boy to girl ratio of 2:3 or 2/3. A percentage is an equation proving the equality of two ratios. The formula is a/b = c/d, where a, b, c, and d are all numerical values or variables. Numerous branches of mathematics, science, and daily life, including banking, engineering, and cookery, require proportions.
Given that, it takes the principal 30 seconds to sign 4 diplomas.
Setting the proportion we have:
30 seconds / 4 diplomas = x seconds / y diplomas
x = 7.5y
Substituting the values of x and y from the table we have:
For y = 12
x = 7.5(2) = 90
Similarly, for y = 20:
x = 7.5(20) = 150
For x = 210:
210 = 7.5y
y = 28
The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.
Learn more about proportion here:
https://brainly.com/question/29774220
#SPJ1
The complete question is:
please bold the answers and show work aswell
The number of packs of peanut m&m's did they sell that day is 378 packs.
The distance traveled by the plane is 1,008 miles.
The time taken by the plane is 7.78 hours.
How many packs of peanut m&m's did they sell that day?Let
Number of peanut sold = x
Ratio of peanut to plain
7 : 10 = x : 540
7/10 = x/540
7 × 540 = x × 10
3,780 = 10x
divide both sides by 10
x = 3,780 / 10
x = 378
When t = 2.8 hours
d = 360t
d = 360(2.8)
d = 1,008 miles
Therefore, the time taken for the plane to fly 2800 miles is;
d = 360t
2800 = 360t
divide both sides by 360
t = 2,800/360
t = 7.78 hours
Read more on ratio and proportion:
https://brainly.com/question/12024093
#SPJ1
Use the graph to answer the questions
WILL MARK BRAINLIEST!!
The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;
1. The vertex point is (50, 630)
2. The solution point are; (20, 0), and (80, 0)
3. Vertex form; f(x) = -0.7·(x - 50)² + 630
4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)
What is a quadratic equation?A quadratic equation is an equation of the form f(x) = a·x² + b·x + c
1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)
The vertex point is; (50, 630)
2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;
The solutions are; (20, 0), and (80, 0)
3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
Therefore;
(h, k) = (50, 630)
f(20) = 0 = a·(20 - 50)² + 630
a·(20 - 50)² = -630
a = -630/((20 - 50)²) = -630/900 = -7/10
a = -7/10 = -0.7
The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630
4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)
r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7
The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)
Learn more on the factored form of a quadratic equation here: https://brainly.com/question/25094938
#SPJ1
Find the area of the circle with a circumference of
. Write your solution in terms of
.
Area in terms of
: ______
Answer:
circumference of a circle is
[tex]2\pi\:r[/tex]
And the area of the circle is
[tex]\pi \: r {}^{2} [/tex]
4p + 1 < −11 or 6p + 3 > 39
The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.
What is compound inequality?A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.
According to question:Let's solve each inequality separately:
4p + 1 < −11
Subtracting 1 from both sides, we get:
4p < -12
Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:
p > -3
So the solution to the first inequality is:
p > -3
Now let's look at the second inequality:
6p + 3 > 39
Subtracting 3 from both sides, we get:
6p > 36
Dividing both sides by 6, we get:
p > 6
So the solution to the second inequality is:
p > 6
Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:
p > 6 or p > -3
This can be written more simply as:
p > -3
To know more about compound inequality visit:
https://brainly.com/question/30307684
#SPJ1
7. The distance covered by a biker is denoted by 6x² - 13x - 15 and the time
is denoted by x-3. Find the speed at x = 9.
Hiya, I need help on a few questions URGENTLY
Boris has a coin collection that contains US, Euro and British coins.If the ratio of US to Euro coins is 5 to 2 and the ratio of Euro to British coins is 5 to 1. What is the ratio of US to British coins?
Amanda works at the local cafe and gets paid £10 per hour (h) and a fixed sum of £50 for a month. Write a formula for the money (m) that she will receive in a month?
A holiday package costs £190, plus £50 a day. What. formula shows the cost of the holiday, C for d days?
The ratio of US to British coins is 25 to 4.
The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
How to solve the Problem?1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.
First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.
Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.
Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.
25 : 10 :: 10 : 2
Multiplying both sides by 2, we get:
50 : 20 :: 10 : 2
Simplifying, we get:
The ratio of US to British coins is 25 to 4.
2. To calculate Amanda's monthly pay, we can use the formula:
m = 10h + 50
where m is the total money Amanda receives in a month, and h is the number of hours she works.
The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
3. To calculate the cost of the holiday package for d days, we can use the formula:
C = 190 + 50d
where C is the cost of the holiday package, and d is the number of days.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
Learn more about fixed cost here: https://brainly.com/question/30641520
#SPJ1
Find the area of the trapezoid 11 yd 11 yd 7 yd
Answer:
Step-by-step explanation:
A=1/2(b1+b2)h
=1/2 (11yd+11yd)(7yd)
=1/2(22yd)(7yd)
=(11yd)(7yd)
=77yd
Please help me i really need this done
Answer:
Step-by-step explanation:
4-10(9m-7)
4-90m+70
74-90m
56x+24/8
8(7x + 3)/8
7x + 3
24r + 16
8(3r + 2)
is 2m-3 same as 4(1/2m-3)
2m-3 = 2m-12
: no
-2(10-15x) same as 14x-20+16x
-20+30x = -20+30x
: yes
please help me fill these boxes
The measurements for area of Jacobs yard are;
Part A = 6m x 3m = 18m
Part B = 4.5m x 3m = 13 m
Part C = 1/2 x 3m x 3m = 4.5 m²
Total area = 18m² + 13.5m² + 4.5m² = 36m²
How do you identify sections that would help in calculating area?To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.
Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.
For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.
Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?
Part A = .............. x ........... = ...........m
Part B = + .............. x ............. = ............ m
Part C = 1/2 x ................. x ............ = ............... m²
Total area = ................... + ..................... + .................. = ..............m
Find more exercises on calculating area;
https://brainly.com/question/30656333
#SPJ1
Find any solution(s) (refer to attachment) of and select the correct statement.
A. The equation has no solution.
B. The equation has two solutions.
C. The equation has one solution.
D. The equation has one solution and one extraneous solution.
1. a^2 – 3a + 2
2. b^2 + 4b + 3
3. c^2 +6c + 5
4. x^2 +8x + 7
5. y^2 +10y + 9
6. r^2 +12r +11
7. m^2 + 5m +4
8. a^2 -8a + 7
9. x^2 -12x +11
10. x^2 + 11x +10
11. t^2 -18t + 72
12. r^2 -16r + 60
13. z^2 -20z + 100
14. y^2 + 4y -5
15. b^2 -2b -8
16. x^2 – 3x – 40
17. 2x^2 – 5x +2
18. 3x^2 + 10x + 3
19. 2x^2 + 11x + 5
20. 2x^2 + 7x + 6
Please Write Your Answer Below:
Answer:
1. (a-1)(a-2)
2. (b+1)(b+3)
3. (c+1)(c+5)
4. (x+1)(x+7)
5. (y+1)(y+9)
6. (r+1)(r+11)
7. (m+1)(m+4)
8. (a-1)(a-7)
9. (x-1)(x-11)
10. (x+1)(x+10)
11. (t-6)(t-12)
12. (r-6)(r-10)
13. (z-10)^2
14. (y+5)(y-1)
15. (b-4)(b+2)
16. (x-8)(x+5)
17. (2x-1)(x-2)
18. (3x+1)(x+3)
19. (2x+1)(x+5)
20. (2x+3)(x+2)
You draw a card at random from a deck that contains
3
33 black cards and
7
77 red cards.
What is
P(draw a black card
)
P(draw a black card)start text, P, left parenthesis, d, r, a, w, space, a, space, b, l, a, c, k, space, c, a, r, d, end text, right parenthesis?
If necessary, round your answer to
2
22 decimal places.
The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.
Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.
Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.
The total number of cards in the deck is:
Total number of cards = number of black cards + number of red cards = 33 + 77 = 110
The probability of drawing a black card is given by:
P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110
Therefore, the probability of drawing a black card is:
P(draw a black card) = 0.3 or 30%
To know more about card visit:
https://brainly.com/question/14611704
#SPJ9
Let's get this party started!
Warm Up Time!
Graph a relationship in which the value of y is 5 less than half the value of x.
Select two points on the coordinate grid. A line will connect the points.
2
3
Step 1: Write the equation (Translate from
words to a number sentence)
Step 2: Graph using Slope Intercept Form
What is the Y-intercept? Plot this point first!
What is the slope? Use the slope to plot a 2nd point
The slope of the equation is 1/2 and the y-intercept is -5.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
Step 1:
The relationship between x and y can be expressed as:
y = (1/2)x - 5
This equation says that y is equal to half of x, with 5 subtracted from that value.
Step 2:
To graph this equation using the slope-intercept form (y = mx + b), we can identify the slope and y-intercept.
The slope of the equation is 1/2, which means that for every increase of 1 unit in x, y increases by 1/2 unit.
The y-intercept is -5, which is the point where the line crosses the y-axis.
To graph the equation, we can start by plotting the y-intercept, which is the point (0, -5).
Next, we can use the slope to find another point on the line. Since the slope is 1/2, we can move up 1 unit and right 2 units (since the slope is rise over run, or change in y over change in x). This gives us the point (2, -4).
We can now draw a line that connects these two points, which represents the relationship between x and y.
The two points are:
(0, -5)
(2, -4)
The graph of the equation is in the attached image.
Hence, The slope of the equation is 1/2 and the y-intercept is -5.
To learn more about the slope visit:
https://brainly.com/question/3493733
#SPJ1
At Amy's Pizza Palace, the cost of a pizza depends on the number of toppings. The graph shows this relationship.
247
21
Cost of Pizza
(in $)
18-
15-
12-
9
6-
3-
1
2
6
3 4
Number of Toppings
7
TURUDANY
According to this graph, what is the meaning of the v-intercept?
The cost of pizza with no toppings is $6. So correct option is C.
Describe Graph?A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.
There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.
Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.
Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.
To know more about intercept visit:
https://brainly.com/question/31350827
#SPJ1
The complete question is:
Explain what the constant of proportionality means in the equation 1 over 2 x + y
In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.
What is constant of proportionality?If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.
The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.
The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.
A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.
If x = 0
Then,
1/2(0) + y = c
y = c
The proportionality constant, c, can be seen in the equation
1 over 2 x + y = c.
This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.
The slope of the line connecting the two variables is another name for the constant of proportionality.
Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that
are being compared are represented by these variables.
In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.
To know more about constant proportionality, visit:
https://brainly.com/question/27598477
#SPJ1
The Complete questions as follows-
Explain what the constant of proportionality means in the equation 1 over 2 x + y = c
Work out sheet below please
Answer:
-4 + 8 = 4
-2 + 6 = 4
-1 + 5 = 4
So the three pairs are -4 and 8; -2 and 6; and -1 and 5.
Help please i need this asap!! I'll give 100 points
The range is expressed in interval notation as (-1, ∞)
How to find the function (f+g)(x)?To find the linear function f(x), let us use the table given.
A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):
[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]
Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:
a = -6, g(a) = 16, b = -3 and, g(b) = 10
Therefore g(x)
[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]
now find the (f+g)(x).
[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]
(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1
The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:
[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]
Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.
As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.
The range is expressed in interval notation as (-1, ∞)
Learn more about function here:
https://brainly.com/question/12431044
#SPJ1
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 56.923 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 14 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:
x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923
Using the formula for the sum of a geometric series, we have:
x(1 - (1.1)^7)/(1 - 1.1) = 56.923
x(1 - 1.1^7)/(-0.1) = 56.923
x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles
Therefore, the hiker traveled approximately 4 miles on the first day.
The equation for Sn, the sum of the first n terms of the sequence, is:Sn = x(1 - r^n)/(1 - r)
where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.
Using the equation for Sn from Part B, we can find the total number of miles the hiker will travel in 14 days:S14 = x(1 - 1.1^14)/(1 - 1.1)
S14 ≈ 167.63
Therefore, the hiker will travel approximately 167.63 miles in 14 days.
More on geometric series can be found here: https://brainly.com/question/4617980
#SPJ1
What is 47/ 30 in mixed numbers I'm giving 10 points must hurry
Answer:
1 17/30.
Step-by-step explanation:
you can find this out by seeing how many 30s go into 47 which is 1.
Then subtract to find how much is leftover still over 30.
47 - 30 = 17
So 1 and 17/30
The daily profit, P(x), of an oil refinery is given by P(x) = 8x -0.02x², where x is the
number of barrels of oil refined.
a. How many barrels should be refined to maximize the profit?
b. What is the maximum profit?
Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.
P(x) = 8x - 0.02x²
P'(x) = 8 - 0.04x
Setting P'(x) = 0, we get:
8 - 0.04x = 0
Solving for x, we get:
x = 200
Therefore, 200 barrels should be refined to maximize the profit.
b. To find the maximum profit, we substitute x = 200 into the profit function P(x):
P(200) = 8(200) - 0.02(200)²
P(200) = 1600 - 800
P(200) = 800
Therefore, the maximum profit is $800.
Step-by-step explanation:
Write Percent as a decimal 42.15%
Answer:
42.15 as a decimal is 0.4215 and you can multiply 0.4215 by a number to get 42.15 percent of that number.
Step-by-step explanation:
So the answer is 0.4215
Hope this helps! =D
Answer:0.4215
Step-by-step explanation:
42.15%÷100=0.4215