Question 1 of 10
Identify the type of function represented by f x = 2 1/2
The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function
The function is
f(x) =[tex]2(\frac{1}{2})^x[/tex]
The function is defined as the expression that represents the relationship between one variable and another variable.
The function is in the form of
f(x) = a × [tex]b^x[/tex]
Such functions are called exponential function
Here
The value of a = 2
The value of b = 1/2
If the value of b > 1, the function is called exponential growth function.
If the value of b < 1, the function is called exponential decay function.
Here b < 1
Therefore it is exponential decay function
Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function
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HELPPPP I NEED THIS QUICKLY!!
A) Yes it is a function and f(x)=2.80+3.50x so 2.80 is an independent function and 3.50x is dependent function
B) Domain x = (0,20] and Range y = (2.8,72.8]
A dependent function is what?
A dependent function type is one whose outcome depends on the parameters of the function.
Independent function: What is it?
Independent function (plural independent functions) as a noun (mathematics) any one of a group of functions whose value cannot be inferred from the values of all the others.
Given: The expression y = 3.5x + 2.8 calculates the y (in dollars) cost of an x-mile taxi fare. You have enough cash to take a cab for a maximum of 20 kilometres.
Domain and range to find
Solution:
y = 3.5x + 2.8
cost y (in dollars)
miles, in.
You have enough cash to take a cab for a maximum of 20 kilometres.
0 < x ≤ 20
Therefore, x = [0, 20].
Domain x = [0, 20]
y = 3.5x + 2.8
x = 0
=> y = 0 + 2.8 = 2.8
x = 20
=> y = 3.5(20) + 2.8
=> y = 70 + 2.8
=> y = 72.8
2.8 < y ≤ 72.8
y = (2.8 , 72.8 ]
Range = (2.8 , 72.8 ]
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Find the domain and range of the function f(x)= √9-x² . OR. Let f ...
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Consider this function. f(x) = |x – 4| + 6 If the domain is restricted to
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pls hurry and thanks 40 pts
The angle of x in the triangle is 75 degrees.
How to find the angles of triangle?The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Therefore, the base angles are equal.
The third angle of the triangle is 30 degrees(vertically opposite angles)
Hence,
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150 / 2
x = 75 degrees
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The function f(x) = (x + 5)(x-3) is dilated by x to produce
the function g(x) = x f(x). How many x-intercepts does
3. the function g(x) have?
Function g(x) have 3 x intercepts.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The function f(x) = (x + 5)(x-3) is dilated by x to produce the function
the function g(x) = x f(x).
A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size
g(x)=x(x + 5)(x-3)
=x(x²-3x+5x-15)
=x(x²+2x-15)
x=0, x=-5 and x=3
The function g(x) have 3 x intercepts.
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9. (-1kw-1z-2)-3
- (-1)-³³₂
11, 9-648
h2
These are the questions here is the photo
Using the simplification of power, [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex] and [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex].
In the given question,
We have to simplify the given expression.
Before simplifying the expression we first learn that the negative power can be positive after changing their position from numerator to denominator.
We use the method of adding the power of expression to solve the expression.
(1) The given expression is [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}[/tex].
We firstly simplifying the power after the bracket by multiplying the power to each variable.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-\frac{1}{4})^{-3}(w^{-1})^{-3}(z^{-2})^{-3}[/tex]
Simplifying the expression.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1)^{-3}(\frac{1}{4})^{-3}(w^{-3})(z^{6})[/tex]
Now we make the power positive by changing their position
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1){4}^{3}(w^{-3})(z^{6})[/tex]
Simplifying
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex]
(2) The given expression is [tex]\frac{g^{-6}h^8}{h^2}[/tex].
Simplifying the expression.
As we know that the power with same base get subtracted when they are in division.
So [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{8-2}[/tex]
[tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex]
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Container A has 600 mL of water and is being filled at a rate of 12 mL per minute. Container B has 1500 mL of water and is being drained at 12 mL per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answer:
It will take 37.5 minutes for both containers to reach the same amount of water which is 1050 mL
Step-by-step explanation:
1500 - (12 × 37.5) = 1050
600 + (12 × 37.5) = 1050
Bert keeps honeybees on his farm. When he first started he used a six frame beehive that held 40 pounds of honey. now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive.
How much honey does Bert’s new beehive hold?
If now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive. The amount of honey that Bert’s new beehive hold is 200.
How to find the number of honey?Given data:
Number of frame beehive = 6
Pound of honey = 40
Current Frame beehive = 30
First step is to formulate an equation and then use the formulated equation to find the number of honey
40 × 30 ÷ 6
Hence,
40 × 5
= 200 honey
Therefore the number of honey is 200.
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The area of a rectangle is 110 square units. It’s length measures 11 units. Find the length of diagonal
The diagonal of the rectangle is 14.87 units.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area of rectangle = 110 square units
Length = 11 units
Area of a rectangle = Length x Wide.
110 square units = Length x Wide
110 = 11 x Wide
Wide = 110/11
Wide = 10
Now,
The diagonal of a rectangle.
Using the Pythagorean theorem we get,
Diagonal² = Wide² + Length²
Diagonal² = 10² + 11²
Diagonal² = 100 + 121
Diagonal² = 221
Diagonal = √221
Diagonal = 14.87 units.
Thus,
The diagonal of the rectangle is 14.87 units.
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Sarah has 21.50 to go grocery shopping. On her way to the store, she donates 3.00 to a canvasser for a charity. IF mangoes cost 2.25 at the store that day, how many mangoes can she purchase if she uses up all of her remaining money
Sarah can purchase 8 mangoes with all her remaining money
How to find the number of mangoes she can purchase using her remaining money?Given that:
Sarah has 21.50 to go grocery shopping
She donates 3.00 to a canvasser for a charity (that is subtraction).
Thus, the remaining money = 21.50 - 3.00 = 18.50
If mangoes cost 2.25. In order to know how many mangoes she can purchase if she uses up all of her remaining money, you have to divide the remaining money (18.50) by the cost of the mangoes (2.25). Thus:
Number mangoes = remaining money /cost of mangoes
Number mangoes = 18.50 / 2.25 = 8
Therefore, she can purchase 8 mangoes if she uses up all of her remaining money
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the data set has 80 observations and has mean 30 and standard deviation 5. approximately how many observations lie between 20 and 40?
A minimum of 71 observations must fall inside the interval (20, 40).
Define Chebyshev's theorem.It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Given,
The data set has 80 observations and has mean 30 and standard deviation 5.
Chebyshev's theorem states that for each data set, the proportion (or percentage) of values that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.
x = 30
s = 5
Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).
(30 - 3.5, 30 + 3.5) = (10, 40)
According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of 80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.
A minimum of 71 observations must fall inside the interval (20, 40).
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it is known that 15% of the calculators shipped from a particular factory are defective. what is the probability that exactly four of ten chosen calculators are defective?
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, whereC5 3= 5!/3/2=4*5/2=10p is the probability that one randomly selected calculator is defective= 10%=0.1q is the probability that one randomly selected calculator is non-defective.q=1-p=1-0.1=0.9So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081learn more about probability click here:
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Determine the intercepts of the line
x int
y int
Answer:
Y-int = -45, X-int =-11.25
Step-by-step explanation:
Please read this before moving on :)
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.
We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.
Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
1 - Finding the Slope
2 points; (0,-40), (-10,0)
0-(-40)/(-10)-0 = 40/-10 = -4
2 - Y-INTY=MX+B
Y=MX+(-45)
Y=MX-45
Y-int = -45
3 - X-INTY=MX+B
0=(-4)x+-45
45=-4x
X-int =-11.25
consider the following data set which is the time (in minutes) for students to finish a math test. 34 45 27 33 38 41 45 29 30 39 34 40 28 33 36 50 (a) what is the sample mean? (b) what is the sample standard deviation? (c) construct a 99% confidence interval for the population mean.
a) Sample mean of set is 36.375.
b) Standard deviation of sample is 6.66208.
Define mean and standard deviation.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Given,
a) Mean
Total number of values = 16
= Sum/Total number of values
= 34 +45+ 27 +33 +38+ 41+ 45 +29 +30+ 39 +34 +40 +28 +33 +36+ 50/16
= 582/16
= 36.375
Sample mean of set is 36.375.
b) Sample standard deviation
S² = ∈ (x i - x)²/N-1
S² = 666.75/16-1
S² = 44.383333
S = √44.38333
S = 6.66208
Standard deviation of sample is 6.66208.
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A 850 kg car is moving with a speed of 10 m/s. Which of the following would cause the largest change in momentum?
a. Double the velocity and mass
b. Double the velocity and cut the mass in half
c. Keep the velocity the same and triple the mass
d. Cut the mass and velocity in half
The largest change in momentum will happen when the velocity and mass of the object are doubled( option A)
What is momentum?The momentum of a body is the product of the mass of the body and it's velocity. Momentum is measured in kg/ms^-1. It is a vector quantity. it is represented by p
Momentum of a body is expressed as p= m× v
where m is the mass of the body and v is it's velocity. This means that the higher the mass and velocity of the body the higher it's momentum.
The initial momentum of the body of mass 850kg and velocity 10ms^-1 = 850kgms^-1
When the velocity and mass are doubled , then the new momentum will be 1700× 20= 34000kgms^-1
Therefore the largest change in momentum will be obtained when both mass and velocity are doubled.
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3/8=15/5x-2 please help me find x
Answer x = 19/24
Step-by-step explanation:
In this figure, lines L and M are parallel.
What is the measure of angle w?
60\degree60°
100\degree100°
120\degree120°
128\degree128°
Which parabola below has a maximum value?
a. y = 0.1x2 - 3x
b. y = 4x2 + 24x +23
c. y = 2x - 3x2
d. y = x2 + 2x + 20
In the given parabola equations, the third equation [tex]y = 2x - 3x^{2}[/tex] has a maximum value.
What is the Maximum parabola?
If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).
We have,
[tex]y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20[/tex]
For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).
By Simplifying the third equation we get its leading coefficient is negative (a < 0).
[tex]y = -3x^{2} + 2x[/tex]
Hence in the given parabola equations, the third equation has a maximum value.
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Please Help. The depth at which whales dive, y, in feet, as related to the duration of the dive, t, in seconds, is represented by the linear model y hat equals 4.8 plus 11.23 times t. If the dive duration is 5 seconds, what is the predicted depth of the dive?
0.02 feet
60.95 feet
−60.95 feet
−0.02 feet
Using the linear function, the depth of the dive at 5 seconds is 60.95 feet
Linear FunctionLinear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.
In this question, we can represent the problem using a linear function or equation and plug in the value of our unknown.
y = 4.8 + 11.23t
Using this function, we can find the depth at 5 seconds;
y = 4.8 + 11.23(5)
y = 60.95ft
The depth of the whale at 5 seconds is 60.95 feet
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18=0.125 . Which calculation is NOT a way to find 58?
The calculation that is not a way to find a fraction of 5/8 is:
1 - 0.125.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the numeric value of the fraction 5/8 presented in this problem is given as follows:
5/8 = 0.625.
The calculation that is not a way to find the fraction of 5/8 is the only expression that has a different value than 5/8.
The expression with a different value is of:
1 - 0.125 = 0.875.
As the value of 0.875 is different than the value of 0.625 equivalent to the fraction of 5/8.
Missing InformationThe complete problem is given by the image at the end of the answer.
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If B=x^{2}+ 2 and C=2+2x^{2}find an expression that equals 2B+C in standard form.
The expression that equals 2B+C in standard form is 4x² + 6
How to determine the expression?From the question, we have the following parameters that can be used in our computation:
B = x² + 2
C = 2 + 2x²
The expression to calculate is given as
2B + C
Substitute the known values in the above equation, so, we have the following representation
2B + C = 2x² + 4 + 2 + 2x²
Evaluate the like terms
2B + C = 4x² + 6
Hence, the expression is 4x² + 6
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an important issue facing americans is the large number of medical malpractice lawsuits and the expenses that they generate. in a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the physician insurers association of america). construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed.
About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.
A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.
arbitrary sample size, n = 1228
number of those who were dropped or dismissed, x = 856
The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785
Level of confidence = 0.99
Level of significance α = 0.01
The population proportion's 99% confidence interval estimate is calculated as follows:
p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]
Using the Excel function or the z-distribution table for calculation
[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]
=NORMSINV(0.05)
[tex]z_{0.01/2}[/tex] ≅ ±2.58
The interval's computation is as follows:
0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]
= 0.7785 ± 2.58 * 0.0118
= = 0.7785 ± 0.0306
(0.7479, 0.8091)
As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].
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15. Mindy has $20. She spent $8.64 including tax to buy a new card game. She
needs to set aside $10 to buy lunch. If Lollipops cost $.28 including tax, what is
the maximum number of lollipops that Maya can buy?
Step-by-step explanation:
she can therefore only spend $10 of the $20.
$8.64 are adjust gone for the card game.
that leaves us with
10 - 8.64 = $1.36
to spend on lollipops.
1 lollipop costs $0.28
so, she can buy a many lollipops as times 0.28 fits into 1.36 :
1.36 / 0.28 = 4.857142857...
that means she can buy 4 lollipops max.
she would keep some change, but not enough to buy a 5th lollipops, because then she would have to cut into the $10 reserve she needs for lunch.
for 5 lollipops she would need $1.40 (5×0.28).
Solve the equation x/2 + 1 = 5x
Answer:
9/2
Step-by-step explanation:
X/2+1=5x
(X+2)/2=5x
x+2=10x
2=9x
X=9/2
Write a linear function f with the given values f(0) = 2, f(3) = -1
The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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if the same data are analyzed using a one-way anova and the randomized block design, the sums-of-square between groups (ssb) is:
Using One way ANOVA and Randomized block design, the sum of squares between groups (ssb) is equal to the sum of sum of sum of explantary variable A's sum of squares and errors sum of square.
Statistics uses one-way ANOVA to compare the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means. It is constructed using the sum of squares measure of total variability used in the numerator of the standard deviation, subtracting the mean, squaring the difference, and adding all observations to obtain the total variability Generate a scale. For multiple groups, we focus on decomposing this total variability (total sum of squares) into the variability between means (the sum of squares of the explanatory variable A) and the variability of the residuals or errors (the error sum of squares).
SSTotal = sum of squares = ∑( yᵢ - Y )²
Total variation is assessed by the total mean (the estimated mean of all observations, available from mean-only models).
SSA = Sum of Squares of Explanatory Variable A
Also called treatment, regression, or model sum of squares. ∑∑(yᵢⱼ - Y' )²
SSE = error (residual) sum of squares
Variation of response around group mean.
Also called the sum of squared residuals.
SSE = ∑∑( Y - Y')²
The total sum of squares is always equal to the sum of the sum of the squares of the explanatory variable A and the sum of the squared errors, SST (total) = SSA + SSE. This equation means that if SSA increases, SSE must decrease if SSTotal remains the same. This result is called the sum of squares decomposition formula.
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the number of homes sold by a realtor during a month has the following probability distribution: number sold probability 0 0.20 1 0.40 2 0.40 what is the probability that the realtor sells no more than one house during a month?
The probability that the retailer sells no more than one house in a month is 0.60.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes and how likely they are to happen. The analysis of events governed by probability is called statistics.
The given is a probability distribution. The probability density function or PDF of the probability is defined for the random variable x, where x ranges from 0 less than or equal to x less than or equal to 2 ie the range of x is from 0 to 2 with 0 and 2 inclusive.
x : 0 1 2
p(x): 0.20 0.40 0.40
The probability that the retailer sells no more than one house in a month is given by
P(x less than or equal to one) = P(0) + P(1)
=0.20 + 0.40 = 0.60.
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A hiking guide recommends that a person wear snowshoes when the accumulated snow has a depth of at least 6 inches. At 8:00 a.m., the depth of snow in a certain area is 4 inches. The predicted average rates of change of the depth of snow for different time intervals are shown in the table. For which of the following time periods between 8:00 a.m. and 8:00 p.m. would the guide recommend wearing snowshoes?
A. 8:00 a.m.-10:00 a.m. and 1:00 p.m.-3:00 p.m.
B. 8:00 a.m.-11:00 a.m. and 3:00 p.m.-4:00 p.m.
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
D. 9:00 a.m.-11:00 a.m. and 2:00 p.m.-4:00 p.m.
Considering the average rate of change, the time periods in which snowshoes are recommended are given as follows:
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function (change in the numeric value) divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The initial amount is of 4 inches, hence, considering the rates, the amounts of snow on the ground are given as follows:
11 am: 4 + 3 x 0.75 = 6.25 inches. (>6 at 10 am).3 pm: 6.25 - 4 x 0.25 = 5.25 inches.8 pm: 5.25 + 5 x 0.50 = 7.75 inches. (>6 at 5 pm).Hence the intervals are given by option c.
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HLP ME PLSSSS ITS DUE IN 5 MNS
Answer:
It's either 1:3 or 1:3
Step-by-step explanation:
A scale factor is times, calculate and, a reinduced PEMDAS
out of 150 coins, 90 are quarters. of the remaining coins, 40% are nickels and the rest are dimes and pennies. there are 5 dimes for every penny. how many pennies are there?
There are 6 pennies in a total of 150 coins.
Given that,
Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.
and also,
For every penny, there are five dime.
Total = 150 coins
Out of it, 90 are quarters so the remaining coins are 60
It is said that,
In that 60 coins 40% are nickels which means
40% of 60 is 24
So remaining coins are 36 (by subtracting 24 from 60)
It is said that there are 5 dimes for every penny which means
Using Algebra,
x + 5x = 36
6x= 36
x= 6
Therefore, there are 6 pennies in a total of 150 coins.
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a toy manufacturer inspects boxes of toys before shipment. each box contains 17 toys. the inspection procedure consists of randomly selecting three toys from the box. if one or more of the toys are defective, the box is not shipped. suppose that a given box has two defective toys. what is the probability that it will be shipped? a) 0.1765 b) 0.6691 c) 0.3309 d) 0.0221 e) 0.4341 f) none of the above.
The probability that it toys will be shipped is option b ) 0.6691 .
Hypergeometric Distribution will be used
P ( X = x ) = h ( x , N , n , k ) = [tex]C_{k,x}[/tex][tex]C_{N-k,n-x}[/tex] / [tex]C_{N,n}[/tex]
[tex]C_{n,x}[/tex] = n! / [ x! ( n - x ) !
According to question,
N = 17
k = 2
n = 3
To find : P ( X = 0 ) ,
P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )
= [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]
= 455 / 680
= 0.6691
So there is 66.91 % probability that toys will be shipped .
Hence , option b ) 0.6691 is the correct answer .
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