the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.
Why do we use parenthesis next to zero for the range of the exponential parent function?When we write in interval notation, the parenthesis are used to denote that the "ends" of the interval don't belong to the interval.
This means that in (a, b).
a and b don't belong to that interval.
While if instead we wrote [a, b]
In that case, a and b belong.
For the case of the exponential function:
y = a^x
As x tends to really large negative values, the value of y will tend to zero asymptotically. This means that y is really close to zero, but it is never equal to zero.
Then the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.
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a physician orders 16 oz of 25% solution to be made from 10% and 50% stock solutions. how many ml of 50% solution are needed?
180ML of 50% solution are needed.
What is a solution?Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root.
EXPLANATION : To solve this question, we have initial stock solution of 10% and 50% concentration. We need to make final solution of 25% concentration of volume 16oz. [tex](1oz \approx 30ml)[/tex]
To find :- Volume of 50% required
Let us assume we require x oz volume of 50% stock Solution , Then volume of 10% stock added will be (16-x) oz.
Formula used here:- C1V1 + C2V2 = C3V3
Where C1 = 50% = 0.5 , V1 = x oz & C2 = 10%= 0.1 , V2= 16-x oz
C3 = 25% = 0.25 , V3= 16oz
Putting values we have
(0.5*x) + (0.1(16-x)) = 16*0.25
0.5x + 1.6 - 0.1x = 4
x = 6
Hence Volume of 50% solution = x = 6 oz = 6*30 ml = 180ml
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in a game of poker, what is the probability that a five-card hand will contain (a) a straight (five cards in unbroken numerical sequence)
The probability that a five-card hand will contain a straight = 5/1274
There are 52 cards in a deck from which each 13 cards are from 4 different suits (clubs, diamonds, spades and hearts) in a game of poker.
Each 13 cards from high to low are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. So a straight of five cards, i.e., five cards in unbroken numerical sequence would be got only from 10 cards in a sequence.
So the possible ways to get a single straight five from all four suits = [tex]4^5[/tex]
Now as we doesn't need all 5 cards from a single suit, we can ignore 4 ways from the above number. i.e., [tex]4^5-4 = 1020[/tex] ways.
Hence the possible ways to get a straight five from 10 cards from all four suits = 10 x 1020 = 10200 ways
Total number of ways to select 5 cards from 52 cards = 52C5
Thus,
The probability that a five-card hand will contain a straight = 10200 / 52C5
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The graph shows the relationship between the amount of time that a backpacker hikes and the distance traveled.
What does (5,6) represent?
What is the equation of the relationship?
a) The meaning of the point (t, s) = (5, 6) is that the backpacker travels a distance of 5 miles in 6 hours.
b) The equation of the relationship between the distance traveled by the backpacker and time taken is equal to s = (6 / 5) · t.
How to analyze linear equations
According to the image attached aside, we find that the distance traveled by the backpacker (s), in miles, is directly proportional to the time taken (t), in hours. In other words, we have the following relationship:
s ∝ t
s = k · t (1)
Where k is the constant of proportionality, in miles per hour.
a) The meaning of the point (t, s) = (5, 6) is that the backpacker travels a distance of 5 miles in 6 hours.
b) To determine the equation of the relationship, we need to calculate the constant of proportionality. If we know that t = 5 h and s = 6 mi, then the equation of the relationship is:
6 = 5 · k
k = 6 / 5
s = (6 / 5) · t
The equation of the relationship between the distance traveled by the backpacker and time taken is equal to s = (6 / 5) · t.
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This entire concept is difficult for me to understand but I have some grasp of what I’m doing if it’s graphing the equation but doing the reverse, however, is somehow difficult for me. (and yes i need help on all 4 of them)
Find the midpoint of segment CD if C is (1,7) and D is (9, 13).
In 1992, the moose population in a park was measured to be 5200. by 1997, the population was measured again to be 7100 if the population continues to changed linearly find an equation for the moose population p as a function of t the years since 1986
The linear equation for the moose population p as a function of t the years since 1986 is P(t) = 380t + 2920.
What are linear equations in two variables?The equations with two variables where each variable has the largest exponent order of 1 having one, zero, or an infinite number of solutions, and are referred to as linear equations in two variables. A linear equation with two variables has the conventional form ax + by + c = 0, where x and y are the variables. Additionally, the answers can be expressed as ordered pairs, like (x, y).
What are forms of linear equations?Linear equations have three main forms which are as follows:
Y=mx+b, where m is the line's slope and b is the y-intercept, is the formula for slope-intercept form.Ax+By=C is how standard form is expressed, with A, B, and C all being constants.(Y-Y1)=m(X-X1), where m is the slope and (X1, Y1) is a known point on the line, is how the point-slope form is expressed.We will consider x on the graph to be years since 1986 and y on the graph to be the number of Moose.
We have two points on the graph: (6, 5200) and (11, 7100)
Using the slope formula m = (y2 - y1)/(x2 - x1), we can find the slope of this line:
m = (y2 - y1)/(x2 - x1)
m = (7100 - 5200)/(11 - 6)
m = 1900/5
m = 380
Now, that we have the slope of the line, we can use the point-slope formula (y - y1) = m(x - x1) to find the equation for the line. Here, we're using the first point, but either point will produce the same answer.
(y - y1) = m(x - x1)
y - 5200 = 380(x - 6)
y - 5200 = 380x - 2280
y - 5200 + 5200 = 380x - 2280 + 5200
y = 380x + 2920
Since the equation that is being sought is supposed to be in terms of P and t, We will replace y with P and x with t.
Hence, the equation will be P(t) = 380t + 2920.
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I need help on question 2 pls
Answer:
20 gallons after 50 minutes
Step-by-step explanation:
(2gal/5min) * 10 = 20gal/50 min
50/5 = 10
2*10=20
A calculator displays 8.4E9. How do you write 8.4E9 in scientific notation?
According to the given statement 8.4E9 can be written in scientific notation as 8.4 × 10⁹
What is Scientific Notation?Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation.
If a number between 1 and 10 is multiplied by a power of 10, the result is written in scientific notation.
The major benefit of scientific notation is that it enables us to scale down extremely large or extremely small numbers into sizes that are much easier to handle. These numbers are much simpler to work with when they are written in scientific notation.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line on the diagram given is rise/run = 3/4.
How to Calculate the Slope of a Line?The formula for calculating the value of the slope of a line on a coordinate plane is expressed as: change in y / change in x = rise of the line / run of the line.
Slope = rise/run.
Given the line shown in the graph above, we have the following:
The blue line represents the rise of the line = 3 units
The red line represents the run of the line = 4 units
Slope (m) of the line = rise/run = change in y / change in x = 3 units/4 units
Slope (m) = 3/4
Therefore, the slope of the line on the diagram given is rise/run = 3/4.
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Bonjour je galere en maths avec cet exercice de Pythagore qui pour m'aider svp
Answer: utilisez l'équation a^2+b^2=c^2.
Step-by-step explanation: Bonjour, je ne parle pas français donc j'ai utilisé un traducteur pour cela. Pour faire Pythagore, vous utilisez l'équation a^2+b^2=c^2. Donc, d'abord, placez les 2 côtés les plus courts du triangle au carré et additionnez-les. La racine carrée de la réponse pour trouver le côté le plus long. J'espère que cela t'aides.
The wind blew away 28 of your muffins. That was 7/10 of all of them! With how many did you start? As Equation Review
The total number of muffins were 40 and the equation which represnts the given scenarion is (7/10)x = 28.
Let the total number of muffins be x.
According to the given question.
The number of muffins which blew away by wind = 28
And 28 muffins are the 7/10 part of the total muffins.
Therefore, the linear equation in one variable which represents the above scenario is given by
(7/10) × x = 28
⇒ 7x = 280 (multiplying both the sides by 10)
⇒ x = 280/7 (dividing both the sides by 7)
⇒ x = 40
Hence, the total number of muffins were 40 and the equation which represnts the given scenarion is (7/10)x = 28.
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which word or phrase describes a word that has been defined
Three fifth of the T-shirts in a T-shirts shop are blue. Five eights of those T-shirts are on sale.One third of the blue T-shirts that are on sale are size medium. What fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium?
The fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium is 1/ 8
How to determine the fractionFrom the information given, we have the following deductions;
3/5 of the T-shirts are blue5/8 of the T-shirts are on sale1/3 of the blue T-shirts are on sale and medium sizeLet the total number of T-shirts be x
Number of Blue T-shirts that are blue
⇒ x × 3/ 5
⇒ 3x/5
Number of Blue T-shirts on sale
⇒ x × 3/ 5 × 5/ 8
multiply through
⇒ 15x/ 40
⇒ 3x/ 8
Number of Blue T-shirts that are on sale and are of medium size;
⇒ 3x/ 8 × 1/ 3
Multiply through
⇒1/8
Thus, the fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium is 1/ 8
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Select all of the true statements.
Answer:
goooooood luccckkkk.....
For what values of c and d would the rectangles be similar?
By using the definition of similarity and the dimensions of each rectangle, a rectangle with d = 72 and c = 45 fulfills the height to width ratio of 8 / 5. (Correct choice: C)
How to find the dimensions of a rectangle similar to other rectangle
Two rectangles are similar if both hold the same height to width ratio. Mathematically speaking, the two rectangles must fulfill the following requirement:
b / a = d / c (1)
Where:
a - Width of the big rectangle.b - Height of the big rectangle.c - Width of the small rectangle.d - Height of the small rectangle.If a = 50 and b = 80, then the ratio of the second rectangle must be:
d / c = 8 / 5
By direct comparison with any of the four choices, we find that a rectangle with d = 72 and c = 45 fulfills the height to width ratio of 8 / 5.
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A kilogram of dalandan in pure gold costs p55.00. if jessica brought k kilograms, represent the amount paid a as a function
The function of amount paid in terms of kilograms of dalandan is A= 55k.
According to the statement
We have to find that the amount paid in terms of kilograms of dalandan.
So, For this purpose, we know that the
The Amount generally refers to a quantity, sum of two or more quantities.
From the given information:
The Php. 55 cost of dalandan
And then
Let A stands for paid amount
k stands for number of kg of dalandan
Amount = Cost × No. of items
Amount = 55 × k
A = 55 × k
A = 55k
So, The function of amount paid in terms of kilograms of dalandan is A is 55k.
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c. In Euclidean geometry, the interior angles of any triangle add up to 180 degrees. Does this rule apply to triangles in spherical geometry? If not, is there another value that they would always sum to? Explain your answer.
This rule apply to triangles in spherical geometry If there another value that they would always sum to greater than 180 degrees.
What is Euclidean geometry?Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different axioms and theorems.
In spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a spherical triangle exceeds 180 degrees.
Thus, this rule apply to triangles in spherical geometry If there another value that they would always sum to greater than 180 degrees.
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I need help asap!!! (Measurement)
Answer:
the answer is a :)
Step-by-step explanation:
The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the test day, and his score wasn’t included in the calculation. If his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?.
Using the definitions of the mean and of the standard deviation of a data-set, we have that:
The mean would increase.The standard deviation would remain constant.What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.When the measure of 84 is added to the data-set, we have that:
A measure greater than the mean is added, hence the mean would increase.The difference squared between 84 and the mean of 81 is of 9, which is the same as the standard deviation, which would remain constant.More can be learned about the mean and the standard deviation of a data-set at brainly.com/question/26941429
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help me understand this assignment and this one
Answer:
Ok, since this is not a multiple choice question, I'll tell you how I would write it.
Step-by-step explanation:
It stopped snowing for 10 to 12 hours after the storm and then started snowing again. This is because you can see that the y value (amount of snow on the ground in inches) has no change between 10 to 12 hours after the storm began.
For the second part, Think of the independent variable as the cause(its value is independent of other variables) and the dependent variable as the effect, essentially the value that depends on changes in the independent variable. In this case it tells you that the perimeter of a square depends on the length, so that means that the length is independent and the perimeter of the square is dependent. So, the dependent variable is the perimeter, because the perimeter of a square depends on the length.
A function relating these variables is K(x) = y since the dependent variable (y) depends on the independent variable (x)
Now for the last part that says So K(5) = ___ meaning if 5 ___ I don't really understand what it is asking for, since K(x) = y then K(5) would equal whatever y is when x is 5, but k(5) could also equal 5k if we were just evaluating.
If D= the total price. Write an equation for the total price in dollars for the bike including 7.75% sales tax.
Answer:
Step-by-step explanation:
Total Cost = D
D= Price + Price (0.0775)
D= Price (1 +(0.0775)) Factoring the price
D= Price (1.0775)
D= 1.0775 Price
300 people were asked the following question: how many times have you accessed the internet this week? - none - once or twice - three or four times - more than four times which method of displaying the data could be used to display the data produced from that question?
(B) Bar graph method of displaying the data could be used to display the data produced from that question.
What is a bar graph?A bar chart, also known as a bar graph, is a type of chart or graph that displays categorical data using rectangular bars with heights or lengths proportional to the values they represent. The bars can be plotted horizontally or vertically. A vertical bar chart is also known as a column chart.A bar graph compares two or more discrete categories. The chart's one axis represents the specific categories being compared, while the other axis represents a measured value.Some bar graphs show bars clustered in groups of more than one, displaying the values of multiple measured variables.Therefore, (B) bar graph method of displaying the data could be used to display the data produced from that question.
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The correct answer is given below:
300 people were asked the following question: How many times have you accessed the internet this week?
- none
- once or twice
- three or four times
- more than four times
Which method of displaying the data could be used to display the data produced from that question?
(a) Time Plot
(b) Bar graph
(c) Stemplot
(d) Histogram
one side of an isosceles triangle is three times as long as another side of the triangle. If the perimeterof the triangle is 140, then what is the length of the base of the triangle?
Answer:
20
Step-by-step explanation:
P, perimeter of triangle = a + b + c
We're given P = 140 and it is an isosceles triangle.
We can change P to be 2a + b since 2 sides are equal in an isosceles
So, 140 = 2a + b
One side is 3x longer than the other. The equal sides in the triangle can not be 3x longer than each other since it is equal.
And the isosceles sides are longer than the 1 base side.
So if a = our isosceles sides, and b is our base side, than a is 3x our base side which can be written as a = 3b
Now, 140 = 2(3b) + b, and we can now solve
140 = 6b + b => 140 = 7b
20 = b
Our base length is 20.
gym lockers are to be numbered from 1 through 99 using metal numbers to be nailed onto each locker. how many 7s are needed?
The computation shows that there can be 14 7s that will be needed.
How to compute the value?From the information, the gym lockers are to be numbered from 1 through 99 using metal numbers to be nailed onto each locker.
The number of 7s that can be found will be:
= 99/7
= 14
Therefore, there can be 14 7s.
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Two variables are defined, a regression equation is given, and one data point is given.
Hgt
Age
height in inches
age in years of a child
=
Hgt 24 + 2.72(Age)
The data point is a child 12 years old who is 60 inches tall.
Need help on part a
Given the following data:
Age in years of a child = 12 years.Height in inches = 60 inches.What is a residual value?A residual value can be defined as a difference between the measured (given or observed) value from a scatter plot and the predicted value from a scatter plot.
Mathematically, the residual value of a data set can be calculated by using this formula:
Residual value = given value - predicted value
Next, we would determine the predicted value by using the given regression equation as follows:
Hgt = 24 + 2.72(Age)
Hgt = 24 + 2.72(12)
Hgt = 24 + 32.64
Predicted value, Hgt = 56.64 inches.
Now, we can determine the residual value as follows:
Residual value = given value - predicted value
Residual value = 60 - 56.64
Residual value = 3.36 inches.
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All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample
to make a statistical inference about the mean of the normally distributed population from which it was drawn?
Z S
ME= √n.
The margin of error is multiplied by √2.
Given that All else is equal if you cut the sample size in half and to make a statistical inference about the mean of the normally distributed population from which it was drawn ME=(z+s)/√n.
Margin of error (ME) from the mean can be calculated using the formula ME=(z+s)/√n where
z means it is the corresponding statistic of the given confidence level
s means it is the standard deviation of the sample (or of the population if it is known)
N is the sample size
As we know margin of error is proportional with inverse of √N,
If we will cut the sample size in half, the margin of error is multiplied by √2.
Hence, if sample size is cut in half then the margin of error when using the sample to make statistical inferences about the mean of the normally distributed population from which it was drawn is √2.
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please someone answer this ill give you crown if your correct
The slope is 2 exactly.
For each function, identify the vertex, axis of symmetry, y-intercept, and x-intercepts. Then state if each parabola opens upward or downward
13) Vertex = (1, -5)
y - intercept = -6
x - intercept is non - existent
The parabola opens downward.
How to Interpret Parabola function curves?13) We are given the parabolic function;
y = -x² + 2x - 6
x of vertex = x of axis of symmetry: x = -b/2a = -2/(2 * -1) = 1
y of vertex; y = f(1) = -(1)² + 2(1) - 6 = -5
Vertex = (1, -5)
y - intercept = -6
x - intercept is at y = 0 and as such are; (1 + √-5) and (1 - √-5)
Since a < 0, the parabola opens downward.
14) We are given the parabolic function;
y = -3(x - 2)² + 12
y = -3(x² - 4x + 4) + 12
y = -3x² + 12x - 12 + 12
y = -3x² + 12x
x of vertex = x of axis of symmetry: x = -b/2a = -12/(2 * -3) = 2
y of vertex; y = f(2) = -3(2)² + 12(2) = 12
Vertex = (2, 12)
y - intercept = 0
x - intercept is at y = 0 which is x = 4
Since a < 0, the parabola opens downward.
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Mina has £2.40. If she gives half to her brother how much money does she have left
Answer:
she has 1.20 left
Step-by-step explanation:
half of 2.40 is 1.0
Robin drove from his house to Morgan’s house this graph shows the distance robin had left to travel after driving for t minutes
Morgan’s house is located___ miles from Robins house, and it took Robin__minutes to drive that distance
From the intercepts of the given graph, we have that:
Morgan’s house is located 35 miles from Robin's house, and it took Robin 40 minutes to drive that distance.
What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.For this problem, the axis are given as follows:
x: time in minutes.f(x): remaining distance in miles.The intercepts are given as follows:
y = 35, x = 40.
Hence:
Morgan’s house is located 35 miles from Robin's house, and it took Robin 40 minutes to drive that distance.
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