50 Points! Multiple choice algebra question. Find the domain and range of the function whose graph is shown. Photo attached. Thank you!
Answers
Answer:
"B". Domain is all real numbers, and the Range is all positive real numbers
Step-by-step explanation:
It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.
Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).
The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.
The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.
Since "a" is positive, the Range is positive numbers only.
Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.
Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero". There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0". So, the Range is written as { y | y>0 }.
Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.
Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"
Related Questions
collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community
Answers
Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion x 360° = 0.6 x 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
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Select the incorrect phrases in the paragraph.
Given:
is a right angle
is a right angle
Prove:
Four lines M A, M B, M C, and M D that starts from point M are drawn such that angle A M C equals 90 degrees, and angle B M D equals 90 degrees.
1. Angle A M C is a right angle. It leads to angle A M B and angle B M C are complementary 2. Angle B M D is a right angle. It leads to angle B M C and angle C M D are complementary. 1 and 2 lead to Angle A M B which approximately equals angle C M D.
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
is a right angleis given.
is a right angleis also given.Since
is a right angle,
and
are complementary.Since
is a right angle,
and
are complementary.By the Congruent Complements Theorem,
.
Answers
Note that in the proof stated above, there is no incorrect statement.
How is this so?The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.
The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.
The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.
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pls help very much appreciate it
Answers
use synthetic division
PLEASE HELP 30 PTS
Answers
Answer:
The quotient is
[tex]8 {x}^{2} + 15x - \frac{1}{8} [/tex]
and the remainder is
[tex] \frac{63}{64} [/tex]
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects.
Before treatment, 23 subjects had a mean wake time of 105.0 min. After treatment, the 23 subjects had a mean wake
time of 82.1 min and a standard deviation of 23.3 min. Assume that the 23 sample values appear to be from a
normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a
population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before
the treatment? Does the drug appear to be effective?
Answers
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
what is mean ?In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.
given
For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
When we enter the provided values, we obtain:
s = 23.3
n = 23
t0.025,22 = 2.074
The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:
82.1 ± 2.074 * (23.3/√23)
which is equivalent to:
(71.4, 92.8)
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
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Write an equation in standard form
Answers
The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0) is: y² = -8x
The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3) is: (x - 1)² = -4 (y - 3)
How to write the equation of parabola with directrix of x = 2 and vertex of (0, 0)Quadratic equation when the directrix is at x direction is of the form:
(y - k)² = 4P (x - h)
OR
standard vertex form, x = a(y - k)² + h where a = 1/4p
The vertex
v (h, k) = (0, 0)
P in this problem, is the distance between the vertex and the directrix
P = 0 - 2 = -2
substitution of the values into the equation gives
(y - k)² = 4P (x - h)
(y - 0)² = 4 x -2 (x - 0)
y² = -8x
Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (1, 3)
P in this problem, is the distance between the vertex and the directrix
P = 3 - 4 = -1
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - 1)² = 4 * -1 (y - 3)
(x - 1)² = -4 (y - 3)
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If the profit function for a product is
P(x) = 2800x + 85x^2 − x^3 − 109,000
dollars, selling how many items, x, will produce a maximum profit?
Find the maximum profit.
Answers
The maximum profit that for the equation p(x) = 2800x - 85x² - x³ - 109000 is $672500
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Given the profit function:
p(x) = 2800x - 85x² - x³ - 109000
The profit is maximum at:
p'(x) = 0
p(x) = 2800 + 170x - 3x²
2800 + 170x - 3x² = 0
x = 70
p(70) = 2800(70) - 85(70)² - (70)³ - 109000 = 672500
The maximum profit is $672500
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he table of values represents a quadratic function.
Write an equation of the function in standard form.
Answers
The equation of the quadratic function in standard form is f(x) = 5x² - 3x - 7
To write an equation for a quadratic function in standard form, we need to use the general form of the equation, which is: f(x) = ax² + bx + c where a, b, and c are constants that determine the shape and position of the graph of the function.
Let's choose the points (-2, -16), (-1, -15), and (0, -12) from the table. Substituting these values into the equation above, we get:
-16 = 4a - 2b + c -15 = a - b + c -12 = c
We can use the third equation to solve for c, which is -12 in this case. Substituting this value into the first two equations, we get:
-16 = 4a - 2b - 12 => 4a - 2b = 4 -15 = a - b - 12 => a - b = 3
Now we have two equations in two unknowns, which we can solve by substitution or elimination. Let's use substitution to solve for b first:
a - b = 3 => b = a - 3
Substituting this into the first equation, we get:
4a - 2(a - 3) = 4 => 2a = 10 => a = 5
Now we can substitute the values of a and b into one of the original equations to find c:
-15 = 5 - b + c => -15 = 5 - (5 - 3) + c => c = -7
Therefore, the equation of the quadratic function in standard form is:
f(x) = 5x² - 3x - 7
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What the correct answer??
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The angle of the turn at Deer Trail is of 105 degrees.
What is the angle of the turn?Notice that both of the lines that go up to the left are parallel, thus, the angles formed betwen the intersections are all equal (for the respective lines).
Now, also know that two adjacent angles in an intersection should add up to 180°.
We can see that the angle to the right of deer trail has a measure of 75°, then the angle to the left (which is adjacent) must have a measure M such that:
M + 75° = 180°
M = 180° - 75°
M = 105°
That is the angle of the turn.
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A diamond ring was bought a number of years ago for R3 180,00. The value of the ring increases by 4% per year. Answer the following questions: a. Determine the exponential function that describes the value of the ring after t years. b. Determine the value of the ring nine years after it was bought Choose the correct answers. Select one: a. C. a. V(t) = 3 180,00(1,4)* b. a. V(t) = 3 180,00 × (1+0,04)* b. R4 352,04 d. a. V(t) = (3180,00 × 1,04)* b. R4 526,13 a. V(t) = 3 180,00 x 1,04 b. R4184,66 b. R4526,13
Answers
V(t) = 3 180,00 × (1+0,04)^t
b. To determine the value of the ring nine years after it was bought, we can substitute t = 9 into the exponential function:
V(9) = 3 180,00 × (1+0,04)^9
V(9) = 3 180,00 × 1,04^9
V(9) = R4 526,13
Therefore, the correct answer is b. R4 526,13.
Find the next three numbers in the pattern: 2,0,6,−4,10,−8,
Answers
The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.
To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.
The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.
The pattern is as follows : 2 - (2×1) = 0,
0 + (2×3) = 6,
6 - (2×5) = -4,
-4 + (2×7) = 10,
10 - (2×9) = -8,
Using this rule, we can find the next three numbers in the pattern as follows:
Add 22 because : -8 + (2×11) = 14,
Subtract 26 because : 14 - (2×13) = -12,
Add 30 , because : -12 + (2×15) = 18,
Therefore, the next three numbers in the pattern are 14, -12, and 18.
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The speed limit on the Princes Highway in Victoria is 100km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
Answers
The speed limit for the highway in rounded to the nearest whole is 33 mi/h.
Unit ConversionThe speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.
There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and yards (yd).
For solving this exercise, you need to know the relation between the given units for distance and time.
The question gives - 100 km/h. The kilometer (km) is a multiple of the standard unit of distance - the meter (m) and the hour is a submultiple of the standard unit of time - the second (s)
For solving this question, it is necessary that you know the relation between km/h and mi/h. See below.
[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]
Now you can solve the question from a math tool - Rule of three. Thus,
[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]
[tex]100 \ \text{km/h}= \text{x mi/h}[/tex]
[tex]\text{x}= 100 \times 0.6[/tex]
[tex]\text{x}=33 \ \text{mi/h}[/tex]
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What is the base pic attached below
Answers
Answer: 2.5
Step-by-step explanation:
the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5
hope it helped:)
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 28.4 units of niacin and 37,335 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.11 unit of niacin and 190 units of retinol per gram. Food B contains 0.35 unit of niacin and 95 units of retinol per gram. How many grams of each food does she feed this group of rats each day?
Answers
The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.
Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the two equations on the basis of the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)
We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x
x = 80
Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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I need the best answer to this question complete sentences (I will give 20 points for the full question answered how it says to do it.)
Answers
The three types of rock are igneous, sedimentary, and metamorphic.
What are the three types of rock?There are three types of rocks as explained below.
Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.
Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.
Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.
The rock cycle is the process by which one type of rock can be changed into another type of rock.
The rock cycle involves three main processes:
Weathering and erosionDeposition and lithificationMelting and solidificationTherefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.
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Find the areas of the trapezoids.
Answers
The areas of the trapezoids is,
A = 48 sq units.
Since, The formula to find the area of a trapezoid of a trapezoid is,
⇒ A = 1/2(b₁ + b₂ )h.
Hence, it is stated that the height of each unit is 2.
Now let's substitute the variables in the formula with the actual bases and heights as;
A = 1/2(8 + 4)8,
A = 6 × 8,
A = 48 sq units.
Thus, the areas of the trapezoids is,
A = 48 sq units.
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Which of the following values are solutions to the inequality -8- 4x > 1?
4
I. - 10 II. - 1
O None
O II only
O I and II
O II and III
O I only
O III only
○ I and III
O I, II and III
III. 6
Submit Answer
Answers
Answer:
the answer is:l only
because -10 only states the true statement while -1 and 6 gave False Staments...
What is the solution set for −4x−38<2
Answers
The solution set for the inequality is x < -10
What are inequalities?The different signs for representing inequalities are;
< represents the sign for less than> represents the sign for greater than≥ represents greater than or equal to≤ represents less than or equal toFrom the information given, we have that;
−4x−38<2
To solve for the value of x, take the steps;
collect the like terms
-4x> 2 + 38
Add the values
-4x> 40
Divide both sides by the coefficient of x, we have;
x > -10
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What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
Answers
Answer:
the surface area of the rectangular prism is 572cm².
Step-by-step explanation:
The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:
2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²
So the surface area of the rectangular prism is 572 square centimeters.
PLEASE HELP ILL GIVE BRAINLIEST
What is the difference in what you have as a balance in your check register versus your online statement by 11/18?
your answer goes here
Answered
What is the combined total of the two translation they have in common
Answers
The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.
The combined total of the 2 transactions they have in common is $206.99.
How to calculate the valueUse the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.
Check Register:
Total = 397.45 - 50.32 - 16.32 + 190.67
Total = 521.48
Online Statement:
Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67
Total = 556.26
Difference = online - check register
Difference = 34.78
On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answers
Answer:
Step-by-step explanation:
To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.
The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.
The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.
Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.
Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answers
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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Help asap!! Please help I don’t get this
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The value of arc CD is 110⁰.
The value of arc AD is 120⁰.
What is the measure of the angle?The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)
angle DEC = ¹/₂ (360 - 200)
angle DEC = 80⁰
The value of arc CD is calculated as follows;
80 = ¹/₂ (CD + 50) (intersecting chord theorem)
2 x 80 = CD + 50
160 = CD + 50
CD = 110⁰
Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)
arc AD = 120⁰
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help please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answers
The conjecture that can be made about the other number is option A: the other number is odd.
Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.
Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.
So, we have the equations:
x + y = 2a (since the sum of two even numbers is even)
6 + z = 2b (since the sum of 6 and another number is even)
We can subtract 6 from both sides of the second equation to get:
z = 2b - 6
Now, we can substitute this expression for z into the first equation:
x + y = 2a
And we get:
x + y + z - 2z = 2a
x + (y + z) - 2z = 2a
x + (2b - 6) - 2z = 2a
x + 2b - 2z - 6 = 2a
This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).
So, we can conclude that the other number (z) is odd. Option A is the correct answer.
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The Blue Whale is the largest animal to have ever lived. As an adult it is as long as three school buses added together. A 170,000 kg Blue Whale cruises along at a modest pace. If it has 890,000 Joules of kinetic energy, what is its cruising speed?
Answers
the cruising speed of the blue whale is approximately 3.16 meters per second.
What are velocity?
a velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).
Rearranging the formula, we get:
v = √(2 * KE / m)
Plugging in the values we know, we get:
v = √(2 * 890000 J / 170000 kg)
Simplifying this expression, we get:
v = √10 = 3.16 m/s
Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.
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Tyler, just letting you can do and then let it burn all the way down to nothing the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h right in equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit.
Answers
The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t
Given the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h
L(t) is a function of time, t:
L(t) = 15 in - (1.25 in/hr)t
Note that when the candle has burned down to nothing, L(t) = 0.
Set 15 in - (1.25 in/hr)t equal to zero and solve for t:
(1.25 in/hr)t = 15 in, or
t = 15/ 1.25 in/hr
t = 12 hrs
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Gruden Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:
Answers
Answer:
$140,000
Step-by-step explanation:
7*20,000 = 140,000
PLEASE HELP SO CONFUSING PLEASE HELP WITH THE WHOLE PROBLEM THOUGH‼️‼️
Answers
When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.
The probability that the student got A in the first semester will be 0.15.
How to calculate the probabilityWhen a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.
The probability that the student got A in the first semester will be:
= 46 / 300
= 0.15
The probability for the last question will be:
= 14 / 148
= 0.095.
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8. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. (i) What is the car's angular speed in radians per hour? (ii) What is the car’s linear speed in miles per hour?
Answers
Answer:
the car's angular speed is 72,000π radians per hour.
the car's linear speed is approximately 100.53 miles per hour.
Step-by-step explanation:
To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.
The formula for angular speed is:
ω = 2πf
where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.
In this case, the wheel is spinning at a rate of 10 revolutions per second, so:
ω = 2π(10) = 20π radians per second
To convert this to radians per hour, we can multiply by the number of seconds per hour:
20π radians per second × 3600 seconds per hour = 72,000π radians per hour
To find the car's linear speed in miles per hour, we can use the formula:
v = rω
where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.
The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:
9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles
Now we can substitute the values we have found:
v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)
v ≈ 100.53 miles per hour
Answer:
(i) 10 revolutions = 10(2π) = 20π radians
10 revolutions/sec =
(20π radians/sec)(3,600 sec/hr) =
72,000π radians/hr
(ii) C = 18π inches
10 revolutions × 18π inches =
180π inches
(180π in./sec)(3,600 sec/hr) =
(648,000π in./hr)(1 mi./63,360 in.)
= 225π/22 miles/hour
= about 32.13 miles/hour
An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage. The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $34, with 90% coverage for the first $500 in prescription costs, then 80% coverage for all prescription costs over $500. What is the total out-of-pocket expense for one month?
$120
$154
$696
$764
Answers
the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .
What is the total out-of-pocket expense?To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.
Step 1: Calculate the deductible
The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.
In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:
Average cost per prescription = Total prescription costs / Number of prescriptions
Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]
Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $ [tex]500 - $450 = $50.[/tex]
Step 2: Calculate the coinsurance
After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining [tex]20[/tex] %.
To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:
Coinsurance = (Total prescription costs - Deductible) x 0.2
Coinsurance = [tex]($850 - $500) \times 0.2[/tex]
Coinsurance = $ [tex]70[/tex]
Step 3:
Calculate the total out-of-pocket expense
The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:
Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance
Total out-of-pocket expense = $ [tex]34 + $50 + $70[/tex]
Total out-of-pocket expense = $154
Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .
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