Answer:
Step-by-step explanation:
Based on the information given, we can calculate the change in the depth of the river between the years 1846, 1847, and 1848.
Change in depth between 1846 and 1847:
The depth of the river dropped from 5 feet in 1846 to 4.9 feet in 1847. The change in depth can be calculated as:
Change in depth = 4.9 - 5 = -0.1 feet
So, the depth of the river dropped by 0.1 feet between 1846 and 1847.
Change in depth between 1847 and 1848:
The depth of the river rose from 4.9 feet in 1847 to 6.4 feet in 1848. The change in depth can be calculated as:
Change in depth = 6.4 - 4.9 = 1.5 feet
So, the depth of the river increased by 1.5 feet between 1847 and 1848.
2. The mean age of a family of five is 22 years. The median is 13, the mode is 42, and the
range is 39 years. Find the ages of the five family members.
The ages of the five family members as required are; 3, 10, 13, 42 and 42.
What are the ages of the five family members?As evident, in the task content, let a, b , c , d , e represents the ages of the family members in ascending order.
Since the median of the ages is; 13, it follows that the the third term, c = 13.
Also, since the mode is 42, it follows that; d = e = 42.
Also, since the range of the ages is 39, it follows that; 42 - a = 39 and consequently a = 3.
Finally, since the mean age is 22; it follows from the mean formula that;
22 = ( 3 + b + 13 + 42 + 42 ) / 5
110 = b + 100
b = 10.
Ultimately, the ages of the five family members as required are; 3, 10, 13, 42 and 42.
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Shopping Preferences Visitors to a shopping mall in Atlanta, Georgia, were surveyed to determine their preference for shopping in wholesale warehouse stores. The following information was determined.
58 shopped in BJ’s Wholesale Club.
49 shopped in Sam’s Club.
45 shopped in Costco.
15 shopped in BJ’s Wholesale Club and Sam’s Club.
16 shopped in BJ’s Wholesale Club and Costco.
12 Shopped in Sam’s Club and Costco.
5 shopped in all three stores.
17 did not shop in any of the three stores.
How many participants shopped in ….
BJ’s Wholesale Club only
Costco only
Sam’s Club only
Exactly one of these warehouse stores.
Exactly one of these warehouse stores.
BJ’s Wholesale Club and Costco.
BJ’s Wholesale Club and Sam’s Club.
Sam’s Club and Costco.
None of these warehouse stores.
The number of participants that shopped in:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17
To answer this question, we can use a Venn diagram to visualize the data and find the number of participants that shopped in each category.
First, we'll create a venn diagram with three circles, one for each store (BJ's Wholesale Club, Sam's Club, and Costco). Then, we'll fill in the data from the question.
1. Start with the center of the venn diagram, where all three circles overlap. This represents the 5 participants who shopped in all three stores.
2. Next, fill in the overlapping sections between two circles. These represent the participants who shopped in two of the stores, but not the third.
- BJ's Wholesale Club and Sam's Club: 15 - 5 = 10
- BJ's Wholesale Club and Costco: 16 - 5 = 11
- Sam's Club and Costco: 12 - 5 = 7
3. Finally, fill in the sections that do not overlap with any other circles. These represent the participants who shopped in only one of the stores.
- BJ's Wholesale Club only: 58 - 10 - 11 - 5 = 32
- Sam's Club only: 49 - 10 - 7 - 5 = 27
- Costco only: 45 - 11 - 7 - 5 = 22
Now, we can use the venn diagram to answer the questions:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 32 + 22 + 27 = 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17
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A bike shop in Belleville bought a mountain bike for $723 and marked it up 50% from the original cost. Later on, Andy purchased the mountain bike and paid Belleville sales tax of 14%. How much, including tax, did he pay for the mountain bike? You must include a $ sign and you must round to the nearest cent
The tax money given by Andy is equivalent to $151.83.
What is tax?Tax is a type of financial charge imposed by governmental organization on the individual to fund government spending and various public expenditures.
Given is that a bike shop in Belleville bought a mountain bike for $723 and marked it up 50% from the original cost.
Total cost of bike after marking it up -
{x} = $723 + ${50% of 723}
{x} = $723 + ${50/100 x 723)
{x} = $723 + $361.5
{x} = $1084.5
Money given by Andy as tax -
{t} = 14% of 1084.5
{t} = 14/100 x 1084.5
{t} = $151.83
Therefore, the tax money given by Andy is equivalent to $151.83.
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Rectangle jklm is congruent to a 4 inch by 7 inch rectangle. How many different values are possible for the length of ?.
Two different values are possible for the length of Rectangle jklm.
When we say that two rectangles are congruent, we indicate that their sides are equal. The rectangles' lengths and widths have to be comparable. It's feasible that jm will be 4 or 7 inches long given that one rectangle has dimensions of 4 and 7. Two lengths are conceivable as the solution. The length and breadth make up the rectangle shape. A rectangle has four sides, and its opposing sides are all the same length. You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle.
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A bee population is measured each week and the results are plotted on the graph.
Fill in the blanks to the answers below:
What is the bee population when it is first measured?
The bee population when it is first measured is ___ bees.
Is the bee population growing by the same factor each week? Yes or No
If you answered yes to question 2, then what is the growth factor?
The growth factor is ____
The population of the bees when it was first measured was 500 bees
The bees are growing by the same factor each week. The answer is yes
How to find the population of the beesAt the fist time the bees where measured, we have to measure from the origin of the graph.
The first point on the graph is at the population of 500
2. To get if the growth is by the same factor, we have to observe how the growth is taking place weekly
In the first week, it grew from 500 to 1000
1000 / 500 = 2
In the second week, the growth is from 2000 to 1000
2000 / 1000 = 2
In the third week. the growth is from 2000 to 4000
4000 / 2000 = 2
Hence there is a growth constant of 2 across the weeks
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need help with this, problem shown below show work
Answer:
Step-by-step explanation:i cant see words need closer view
In 6 and 7, construct a line plot for each data set.
133
2'4' 41,1,0,
113
2' 2'4
6.
According to the information, the line plots of points 6 and 7 have several values that are repeated more than once as shown in the graphs.
How to make a line plot?To make a line plot we must identify the values that we must locate on the number line. Once we know the values we must place a point or symbol above the corresponding numerical value. For each number we must put a point, so we can count the frequency of different values.
Based on the above, we can infer that the line plots of points 6 and 7 would look like this:
attached images
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what is 23.5 cm to inches ?
1 cm is defined as 1/100 of a meter. One foot is defined as 1/3 of a yard or 12 inches in length. We know that, 1 inch = 2.54 cm and therefore, 23.5 centimeter = 9.252 inches
Centimeters :
The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and equals approximately 39.37 inches. It is defined as 1/100 of a meter.
The centimeter is based on the SI unit of measurement and is equal to one hundredth of a meter as indicated by the prefix "centi". The metric prefix ranges from 10-18 to 1018 in decimal, and the base (metric in this case) has no prefix and a modulus of 1. Exploring the most commonly used metric prefixes such as kilogram, mega, giga, tera, centi, milli, micro, and nano can be useful for quickly navigating metric units.
Inch:
Inches is a unit of length or distance in several systems of measurement, including traditional American units and British Imperial units. An inch is defined as 1/12 of a foot, so 1/36 of a yard. By modern definition, 1 inch equals 25 exactly 4 mm.
The term "inch" comes from the Latin unit "uncial", equivalent to "1/12" in Roman terms. There were several standards for inches in the past and the current definition is based on international yards. One of the earliest definitions of an inch was based on a barley grain, where an inch equals the length of three dry round grains of barley laid end to end. Another version of the inch is believed to be derived from the width of a person's thumb, where length was obtained by averaging the widths of three thumbs (small, medium, and thumb).
By multiplying the value in centimeters by the conversion factor 0.3937007874021.
So, 23.5 centimeters = 23.5 × 0.39370078740213
= 9.25196850395 inches.
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where did Goku die nnnnnnnnnnnnnnnnnnnnnnnn
Answer:
Goku died you I just started watching
Question 3(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following graphs represents a linear function?
coordinate plane with a graph that passes through the points negative 3 comma 0 and negative 1 comma negative 4 and 1 comma 0
coordinate plane with a graph drawn that passes through the points negative 4 comma 0 and 0 comma negative 4 and 4 comma 0 and 0 comma 4
coordinate plane with a graph drawn that passes through the points negative 4 comma negative 2 and negative 4 comma negative 1 and negative 4 comma 0
coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2
The second and fourth graphs represent linear functions.
What is a linear function?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
To determine which of the given graphs represents a linear function, we need to check whether the graph is a straight line.
The first graph passes through the points (-3, 0), (-1, -4), and (1, 0). We can plot these points and see that they do not lie in a straight line. Therefore, the first graph does not represent a linear function.
The second graph passes through the points (-4, 0), (0, -4), (4, 0), and (0, 4). We can plot these points and see that they do lie on a straight line. Therefore, the second graph represents a linear function.
The third graph passes through the points (-4, -2), (-4, -1), and (-4, 0). We can plot these points and see that they lie on a vertical line. Therefore, the third graph does not represent a linear function.
The fourth graph passes through the points (-4, 0), (-2, -1), and (0, -2). We can plot these points and see that they do lie on a straight line. Therefore, the fourth graph represents a linear function.
Therefore, the second and fourth graphs represent linear functions.
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Answer: It is the second one
Step-by-step explanation:
Because It makes the most sense
Use an algebraic equation to find the measure of each angle that is represented in terms of x.
Answer:
Step-by-step explanation: 9.17
Hans can choose Plan A or Plan B for his long distance charges.
The plan that costs less if Hans makes 300 minutes of long distance calls is Plan A by $ 4.
The number of long distance minutes till the plans cost the same is 350 minutes.
If the time spent on long distance calls is more than this amount, the plan that costs less is Plan B.
How to find the plan cost ?The cost per plan can be seen on the graph. At 300 minutes of long distance calls, Plan A costs $ 24 and plan B costs $ 28 so the cheaper plan is Plan A by :
= 28 - 24
= $ 4
The number of minutes till they cost the same is 350 minutes which is where they intercept and after this, Plan B will cost less.
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Is 0 0 is infinity or indeterminate form?
In calculus, 0^0 is an indeterminate form. It is not equal to infinity. But 0x0 is equal to zero.
Some of the indeterminate forms 0/0, 0×∞,∞/∞, ∞ −∞, ∞/0, [tex]0^{0}[/tex].
An unknown value is referred to as being "indeterminate." Even after inserting the limits, we are still unable to determine the original value, according to the indeterminate form of mathematics. When two functions are considered as a ratio, the indeterminate form frequently appears when both functions go closer to 0 in the limit. The term "indeterminate form 0/0" refers to these circumstances. The indeterminate form can also be created, much as addition, subtraction, multiplication, and exponential operations. If the limiting behavioral of separate components of the provided expression cannot identify the overall limit, a limit is said to be indeterminate.
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Which hill is the steepest
Answer:
Liberty Hill
Step-by-step explanation:
To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:
|m|= |Slope (or gradient)|
= |[tex]\frac{VerticalDistance}{HotizontalDistance}[/tex]|
The hill with the greatest absolute value of m is the steepest:
|[tex]m_{Dixie} = |\frac{40}{80}|[/tex]
= 0.5
[tex]|m_{Bell}| =|\frac{20}{80}|[/tex]
= 0.25
[tex]|m_{Liberty}| = |\frac{60}{80}|[/tex]
= 0.75
Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest
A scientist conducts an experiment on the growth of a certain bacteria culture.
The variable t represents the number of hours since the beginning of the experiment.
When t=0 (that is, at the beginning of the experiment), there were 50 bacteria in the culture.
Every 1 hour, the number of bacteria in the culture increases by a factor of 2.
The number of bacteria in the culture, N, can be modeled as a function of t by an exponential growth function N (t).
(Recall that an exponential growth function N (t) is a function of the form N(t)= ab', where a and b are positive constants.)
The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the number of bacteria in the culture at a given time be N ( t )
The culture increases by a factor of 2
So , the value of r = 200 % , r = 2
Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50
So , the exponential equation is
N ( t ) = N ( 0 ) ( 1 + r )^t
Substituting the values in the equation , we get
N ( t ) = 50 ( 1 + 2 )^t
N ( t ) = 50 ( 3 )^t
On simplifying the equation , we get
N ( t ) = a ( b )^t , where a = 50 and b = 3
Hence , the exponential equation is N ( t ) = 50 ( 3 )^t
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A floor plan of Gail’s bedroom and closet is shown.
Which expression could be used to determine the total area of the bedroom and closet in square meters?
The bedroom has a surface space of 17.4225 m² and the closet has a surface area of 2.5875 m².
What is area?In mathematics, the area is a measure of the amount of two-dimensional space taken up by a shape. It is a scalar quantity, meaning it has only magnitude and no direction. The unit of measurement used for area depends on the units used for the length of the sides of the shape. Common units used to measure area include square centimeters, square meters, square inches, and square feet. The formula for finding the area of a shape depends on the specific type of shape. For example, the area of a rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. The area of a triangle is given by the formula A = (1/2)*bh, where b is the base and h is the height of the triangle.
Here,
area of bedroom=l*w
l=5.05 m
w=3.45 m
area of bedroom=5.05*3.45
=17.4225 m²
area of closet=l*w
l=0.75 m
w=3.45 m
area=0.75*3.45
=2.5875 m²
The area of the bedroom is 17.4225 m² and that of closet is 2.5875 m².
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Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.
Answer:
There is exactly one solution: (1, 2).
Step-by-step explanation:
For this, it's already in slope intercept form so all you have to do is graph the two and see at what point do these two lines cross, which is (1, 2).
Hope this helps!
passes through the point (4, 5);
slope = -1/4
The equation of line is y= -1/4x+ 6.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
passes through the point (4, 5);
slope = -1/4
Using the slope intercept form
y = mx + b
y= -1/4x + b
As the point passes through (4, 5) then
5 = -1/4 (4) + b
5 + 1 = b
b= 6
So, the equation of line is y= -1/4x+ 6.
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Given m lil n, find the value of x and y
The numerical values of x and y are 14 and 54 respectively.
What is the numerical value of x and y?The sum of angles on a straight line is equal to 180 degrees.
From the diagram, angle (9x + 2)° and angle (5x - 18)° are on a straight line,
Since the sum of angles on a straight line is equal to 180 degrees.
(9x + 2)° + (5x - 18)° = 180°
Solve for x
9x + 2 + 5x - 18 = 180
14x - 16 = 180
14x = 180 + 16
14x = 196
x = 196/14
x = 14
Now, angle (9x + 2)° and angle (2y + 20)° are corresponding angles.
Since corresponding angles are congruent.
(9x + 2)° = (2y + 20)°
Plug in x = 14 and solve for y
9( 14 ) + 2 = 2y + 20
126 + 2 = 2y + 20
128 = 2y + 20
128 - 20 = 2y
108 = 2y
2y = 108
y = 108/2
y = 54
Therefore, the value of x is 14 and y is 54.
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I really need help with this question
Answer: Can't help I tried to figure it out, but it was wrong.
Step-by-step explanation: I'm sorry.
John is a quarterback. This year, he completed
350 passes, which is
70percent of all the passes he's attempted this year.
How many passes has John attempted this year?
The number of passes that John has attempted this year will be 500.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
John is a quarterback. This year, he completed 350 passes, which is 70% of all the passes he's attempted this year.
Let 'y' be the total passes that John attempted. Then the equation is given as,
0.70 = (350 / y)
y = 350 / 0.70
y = 500
The number of passes that John has attempted this year will be 500.
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Identify the solution of -4/3x+4/9=x^2
Mr. Phil had a boatload of money he decided to leave it to his family but wanted to make sure his goldfish was taken care of today he decided to give 1/2 of his estate to his wife, 30,000 to his daughter half of what was left over to his butler, half of what was left to his goldfish. he realized he had $8000 remaining so he donated to charity. what was the original value of his estate?
Answer:
208,000
Step-by-step explanation:
7 - Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 4 1 −2 −5 −8
x −2 −1 0 1 2
y 4 1 0 1 4
x 2 2 0 2 2
y −2 −1 0 1 2
x 0 1 2 3 4
y −2 1 0 1 −2
A linear function has a constant rate of change, which means that the change in the value of y is proportional to the change in the value of x. This means that if we plot the points (x,y) for a linear function, they will fall on a straight line.
To determine which of the tables represents a linear function, we can calculate the rate of change between the points. If the rate of change is the same for all pairs of points, then the table represents a linear function.
For the first table:
Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3
Rate of change between (−1,1) and (0,−2) = (−2−1)/(0−(−1)) = −3
Rate of change between (0,−2) and (1,−5) = (−5−(−2))/(1−0) = −3
Rate of change between (1,−5) and (2,−8) = (−8−(−5))/(2−1) = −3
Since the rate of change is constant (equal to −3) for all pairs of points, the first table represents a linear function.
For the second table:
Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3
Rate of change between (−1,1) and (0,0) = (0−1)/(0−(−1)) = 1
Rate of change between (0,0) and (1,1) = (1−0)/(1−0) = 1
Rate of change between (1,1) and (2,4) = (4−1)/(2−1) = 3
Since the rate of change is not constant (it changes from −3 to 1 to 3), the second table does not represent a linear function.
For the third table:
Rate of change between (2,−2) and (2,−1) is undefined since x does not change.
Rate of change between (2,−1) and (0,0) = (0−(−1))/(0−2) = 0.5
Rate of change between (0,0) and (2,2) = (2−0)/(2−0) = 1
Rate of change between (2,2) and (2,−2) is undefined since x does not change.
Since the rate of change is not constant (it changes from undefined to 0.5 to 1 to undefined), the third table does not represent a linear function.
For the fourth table:
Rate of change between (0,−2) and (1,1) = (1−(−2))/(1−0) = 3
Rate of change between (1,1) and (2,0) = (0−1)/(2−1) = −1
Rate of change between (2,0) and (3,1) = (1−0)/(3−2) = 1
Rate of change between (3,1) and (4,−2) = (−2−1)/(4−3) = −3
Since the rate of change is not constant (it changes from 3 to −1 to 1 to −3), the fourth table does not represent a linear function.
Therefore, the only table that represents a linear function is the first one.
Suppose a population of cells starts at 200 and triples every day. Let p equal the cells and d equal the number of days since the 200 cells were observed. True or False: You could use the equation the equation below to model this situation.
p = 200 · 3d
True
False
The model [tex]p = 200.3^d[/tex] satisfies the statement, A population of cells starts at 200 and triples every day.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex]
Given, A population of cells starts at 200 and triples every day.
Where 'p' is the number of cells and 'd' is the number of days.
The situation is represented by [tex]p = 200.3^d[/tex].
Now, Three times 200 is 600 and Nine times 200 is 1800.
At d = 1.
[tex]p = 200.3^1[/tex].
[tex]p = 600[/tex].
And,
At, d = 2.
[tex]p = 200.3^2[/tex].
[tex]p = 1800[/tex].
So, The model satisfies the statement and it is true.
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Need help with math. Need now
Answer:
Step-by-step explanation:
the volume of top triangular prism :
(16x21)/2x15=2520 yd^3
the volume of bottom:
22x16x15=5280 yd^3
so the volume of the figure:
2520+5280=7800 yd^3
Noah wrote that 6+6=12. Then he wrote that 6+6-n=12-n. Are his equations balanced?Explain
Answer: Yes
Step-by-step explanation:
We don't know the value of n and you are subtracting it from both sides.
Fifteen friends are playing Duck, Duck, Goose. The friends sit equally spaced in a circle. There are three people between Stanley and Frank.
What is the measure of the major arc along the perimeter of the circle between Stanley and Frank?
Enter your answer in the box.
The measure of the major arc along the perimeter of the circle between Stanley and Frank is 264°.
What is an arc measure?A circle's arc, or circumference, is a section of the circle. The difference between an arc length and an arc measure is the angle the arc creates with the circle's center. It is possible to measure this arc in radians or degrees.
Given:
Fifteen friends are playing Duck, Duck, and Goose.
The friends sit equally spaced in a circle.
So, 360/15 = 24° is the angle measure of an arc.
There are three people between Stanley and Frank.
That means there are 11 people between Stanley and Frank.
So, 11 x 24 = 264° is the measure of the major arc.
And the perimeter of the major arc is 264°
Therefore, the perimeter of the major arc is 264°
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Does someone mind helping me with this? Thank you!
The equation of the line that has a slope of -4 and passes through the point (4, -1) is y = -4x + 15.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of a line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
An equation,
y = x/4 - 2.
The slope of the line that is perpendicular to the line y = x/4 - 2 is,
= -(1/1/4)
= -4.
The equation of the line that has a slope of -4 and passes through the point (4, -1) is,
y + 1 = -4(x - 4)
y = -4x +16 -1
y = -4x + 15
Therefore, the equation is y = -4x + 15.
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Find the length of Segment AB and Segment CD. How did you determine the lengths?
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~4 - 1~~)^2 + (~~2 - 5~~)^2} \implies \implies AB=\sqrt{( 3 )^2 + ( -3 )^2} \\\\\\ AB=\sqrt{ 9 + 9 } \implies AB=\sqrt{ 18 }\implies AB\approx 4.24[/tex]
now, we could do the same thing for CD, however, notice, the y-coordinates are the same, meaning is just a horizontal line, we can just count the units off the grid, from 2 to 6, 4 units.