study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 3 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.
The probability that their hospital stay is greater than 6 days is equal to 0.67724 and the probability that their hospital stay is from 5 to 6 days is equal to 0.108
Mean (μ) = 7.37
Standard deviation (σ) = 3
we need to calculate probability that their hospital stay is from 5 to 6 days i.e.
⇒ P(5 < X < 6) = P(X < 6)-P(X < 5)
Here we will use standard normal distribution where,
Z-score = (X -μ )/ σ = (6 - 7.37)/3 = -0.46
Z-score = (5 - 7.37)/3 = -0.79
from Z table we found p-value
⇒P(5<X<6) = P(X<6) - P(X<5) = 0.32276 - 0.21476 = 0.108
So there is 0.108 probability that their hospital stay is from 5 to 6 days.
we need to calculate probability that their hospital stay is greater than 6 days i.e.
We get: P(X > 6) = 1 − P(X < 6)
Here we will use standard normal distribution where,
Z-score = (X - μ)/σ = (6 - 7.37)/3 = -0.46
from Z table we found p-value
P(X > 6) = 1 - P(X<6) = 1 - 0.32276 = 0.67724
So there is 0.67724 probability that their hospital stay is greater than 6 days.
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2x+14= -21-5x
Need to find out what x is but a step by step explanation please
Answer:
Step-by-step explanation:
solve for x
2x+14=-21-5
2x+14=-26
subtract 14 from both sides
2x+(14-14)=-14-26
2x=-14-26
2x=-40
divide both sides of 2x = -40 by 2
[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]
2/2=1
x=[tex]\frac{-40}{2}[/tex]
x= -20
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
The following investments were done:
Metal account: $ 1,500Glass account: $ 3,000Paper account: $ 3,500How much money has a person invested in three accounts?
In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:
Metal: x
Glass: 2 · x
Paper: 8,000 - 3 · x
And the yield function is equal to:
280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)
280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x
120 = 0.08 · x
x = 1500
The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.
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A pet hotel charges $25 per night to keep a dog. When the dog arrives, there is a mandatory $15 examination fee. Part A: Write a function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days. Part B: How much would a 6 night stay cost? Part C: Does a 3 night stay cost half as much as a 6 day stay since it is half the time? Explain in detail!
A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15
B) The total cost to stay for 6 nights is; $165
C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.
How to solve algebra word problems?We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.
A) If the number of nights spent is n, then the function rule here for the total cost is;
T = 25n + 15
B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;
T(6) = 25(6) + 15
T(6) = $165
C) The cost of 3 nights would be;
T(3) = 25(3) + 15
T(3) = $90
This is more than half of the cost of 6 nights.
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3. there are 27 tasks available. you will be randomly assigned 12 of them. there are 10 of them that you want to do. (a) what is the probability that you will be assigned none of the tasks that you want? (b) what is the probability that you will be assigned exactly 7 of the tasks that you want? (c) what is the probability that you will be assigned at least 1 of the tasks that you want? (d) what is the probability that you will be assigned at least 7 of the tasks that you want?
On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049
a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %
b) The probability that I am assigned exactly 7 of the tasks that I want
p = 10C7 * 17C5 / 27C12 = 0.0427 = 4.27%
c) The probability that I am assigned at least one of the tasks I want
p = 1 - 17C12 / 27C12 where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.
Thus, p = 1 - (7/19665) = 0.9996
d)Probability that I am assigned at least 7 of the tasks I want
p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12
⇒ p = 17 / 345 = 0.049 = 4.9%
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Simplify one over x raised to the negative eighth power.
Answer:
1/x to the -8 power simplified would be x^8
Step-by-step explanation:
When there is a negative exponent you put the fraction under 1
[tex]\frac{1}{\frac{1}{x^{8} } }[/tex] and its the same as x^8
The simplified expression is [tex]x^8[/tex].
What is exponent?Exponent is the power of the variable or constant to which it is raised.
The expression 1 over x is denoted by 1/x.
The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].
The exponents of the denominator change from negative to positive when they move from denominator to numerator.
[tex]\frac{1}{x^{-8}}=x^8[/tex]
Thus, the simplified expression will be x raised to the power 8.
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in a basketball game Tatiana May 23 baskets each of the baskets was worth either two or three points and Tatiana scored a total of 53 points let x represent the number of two-point baskets she made and why represent the number of three-point baskets she made.part a write a system of equations represent the situation.part b would you use graphing or substitution to solve the system and determine the number of 2.3 point baskets Tatiana made? explain.part c use the method you chose in part b to solve the system and find out how many two point and 3-point baskets Tatiana made.
Part A
start by naming the variables you will be using in the system of equation
x= number of two-point baskets
y= number of three-point baskets
since she did 23 baskets the first equation representing the number of baskets she made will be
[tex]x+y=23[/tex]the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.
[tex]2x+3y=53[/tex]Part B
Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.
However both methods could be used.
Part C
[tex]\begin{gathered} x+y=23 \\ 2x+3y=53 \end{gathered}[/tex]How tall is a building that casts a 71-ft shadow when the angle of elevation of the sun is 29 degrees.Round to the nearest foot
Solution
We will draw a diagram to illustrate the information
Using the concept of SOHCAHTOA
We are given adjacent and we want to find opposite
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan29=\frac{H}{71} \\ cross\text{ multiply} \\ H=71tan29 \\ H=39.35594265 \\ H=39ft \end{gathered}[/tex]Therefore, the answer is
[tex]undefined[/tex]Emily is designing a t-shirt logo for her company. The t-shirt printing company offers 11 colors to choose from for the logo design. If any number of colors can be chosen, how many different color combinations are possible?
39,916,800 color combinations are possible
Here, we want to get the possible number of color combinations possible.
Since any number of colors can be chosen, there are no restrictions here
That means the number of possible color combinations will be;
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations
26. HOW DO YOU SEE IT?
The graph represents the height / of a
projectile after / seconds.
Height of a Projectile
Height (feet)
20
15
10
5
0
0.5 1 1.5 2 2.5
Time (seconds)
a. Is h a function of t? Explain.
b.
Approximate the height of the projectile after
0.5 second and after 1.25 seconds.
c. Approximate the domain and range.
d. Is t a function of h? Explain.
We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.
(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.
(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.
(c)The domain of the function is [0,2.5] and the range of the function is [0,30].
(d) t is not a function of h.
Therefore a) h is a function of t. (b) Approximate height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.
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The equation for line s can be written as x - y = -2. Line t is perpendicular to lines and passes through (-4, 1). What is the equation of line t?
=========================================================
Explanation:
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.
So Bx-Ay = D will update to -x-y = D
Plug in the coordinates of (-4,1) to find D.
-x-y = D
D = -x-y
D = -(-4)-1
D = 4-1
D = 3
We go from -x-y = D to -x - y = 3
Then multiply both sides by -1 to end up with x + y = -3
Solve for x to the nearest tenth.
Answer:
x = 11,2 inchs
Step-by-step explanation:
I infer that the units are in inches.
8-3 = 5
Then:
By the Pythagorean Teorem:
x² = 10² + 5²
x² = 100 + 25
x² = 125
√x² = √125
x = 11.18
to the nearest tenth:
x = 11.2 inches
The PayDay loan company lends you $500. After 2 weeks pay you pay back $520. What is the simple interest rate? Note that the times is a fraction of a year.
Answer:
Explanation:
• Loan Amount = $500
,• Time = 2 weeks
,• The amount paid pack = $520
We want to determine the simple interest rate.
First, find the amount paid as interest:
[tex][/tex]x^2-8x+9
find x using the quadratic formula
Answer:
[tex]x = 4 \pm \sqrt7[/tex]
Step-by-step explanation:
Hello!
Standard form of a Quadratic: [tex]ax^2 + bx + c= 0[/tex]
Given the Equation: [tex]x^2 -8x+9=0[/tex]
a = 1b = -8c = 9Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex]
Solve by substituting the values into the Quadratic Formula.
Solve for x[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex][tex]x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(9)}}{2(1)}\\[/tex][tex]x = \frac{8 \pm \sqrt{64 - 36}}{2}\\[/tex][tex]x = \frac{8 \pm \sqrt{28}}{2}\\[/tex][tex]x = \frac{8 \pm 2\sqrt{7}}{2}\\[/tex][tex]x = 4 \pm \sqrt7[/tex]The solution to the quadratic is [tex]x = 4 \pm \sqrt7[/tex].
a. Plot the data for the functions f(x) and g(x) on a grid.
b. Identify each function as linear, quadratic, or exponential, and use complete sentences to explain your choices.
c. Describe what happens to the function values in each function as x increases from left to right.
d. At what value(s) of x are the function values equal? If you cannot give exact values for x, give estimates.
For the given tables, we have that:
a. The grids are given at the end of the answer.
b. The functions are classified as follows: f(x) exponential, g(x) linear.
c. When x increases by one unit from left to right, we have that:
f(x) is multiplied by 4.g(x) is increased by 1.d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.
Exponential and linear functionsThe difference between exponential and linear functions is in the rate of change, as:
Linear functions change by a constant amount when x changes by 1.Exponential functions change by a common ratio when x changes by 1.Hence the functions are classified as follows:
f(x) exponential: when x increases by 1, y is multiplied by 4.g(x) linear: when x increases by 1, y increases by 1.We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:
At x = 1, g(x) > f(x).At x = 2, f(x) > g(x).This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.
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what is 3b= 39 can you pleasee help me
Answer: b=13
Step-by-step explanation:
b=39/3
b=13
Answer: its 13
Step-by-step explanation
a farmer needs to enclose three sides of a meadow with a fence (the fourth side is a cliff wall). the farmer has 34 feet of fence and wants the meadow to have an area of 140 sq-feet. what should the dimensions of the meadow be? (for the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). additionally, the length should be as long as possible.)
The dimensions are Width = 7 feets ; length = 20 feets
As given,
Meadow area is 140 square feet.
Height = W (smaller dimension and 2 sides)
Height = L (longer dimension and 1 side)
Fence yards equal 34 feet;
Hence,
L + W = 34
L + 2W = 34
L = 34 - 2W - - - (1)
Recall:
Area = L * W = 140
Substitute value of L
140 = (34 - 2W) * W
140 = 34W - 2W²
2W² - 34W + 140 = 0
W² - 17W + 70 = 0
W² - 10W - 7W + 70 = 0
W(W - 10) - 7(W - 10) = 0
(W - 10) = 0 or (W - 7) =0
W = 10 or W = 7
We choose the shorter width because length should be as long as possible:
W = 7
L + 2W = 34
L = 30 - 14
L = 20 feets
Therefore, The measurements are 7 feet wide and 20 feet long.
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Help me with these two question please!!!
Question 10
Lines a and b by the converse of the consecutive interior angles theorem
Question 11
Lines e and f by the converse of the alternate interior angles theorem
=What is 623 divided by 7
623 / 7 = 89
Result = 89
Find the quotient of 0.744 by 6
[tex]0.744\div6[/tex]
Simplify:
[tex]\frac{0.744}{6}[/tex]
[tex]=0.124[/tex]
with pic. Which of the following functions is graphed below?
The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)
How to derive the absolute function associated with the picture
Absolute values are functions defined by the following piecewise function:
f(x) = |x| = x for x ≥ 0.f(x) = |x| = - x for x < 0.The function in the picture is the consequence of the following rigid transformations:
Horizontal translation 5 units in the + x direction.Vertical translation 4 units in the - y direction.Now we proceed to obtain the image of f(x):
Horizontal translation
f'(x) = |x - 5|
Vertical translation
g(x) = |x - 5| - 4
The picture is represented by the function g(x) = |x - 5| - 4.
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-6 = -2/5y solve for y and simplify your answer as much as possible
Answer: y = 15
Step-by-step explanation:
Combine multiplied terms into a single fraction
-6 = -2y/5
Then, multiply both sides by 5 to get:
-30 = -2y
Last, you divide both sides by -2 to get:
15 = y or y = 15
Hope this helps!
Draw of a modelled object
A truck rental company charges $90 plus $20 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 5, and what does it represent?
Of(h) = 20h + 90
$470, which is the total charge in dollars for renting a truck for 5 hours
Question 6 of t
Of(h) = 90+20h
$190, which is the total charge in dollars for renting a truck for 5 hours
Of(h) = 20 +90h
$470, which is the total charge in dollars for renting truck for 5 hours
Of(h) = 90h + 20
$190, which is the total charge in dollars for renting a truck for 5 hours / pls help lol
The function that represents the total charge for renting a truck for a certain number of hours is f(h) = 90 + 20h What is the value of the function for an input 5 represent : $190, which is the total charge in dollars for renting a truck for 5 hours.
How to find the total charges?Given data :
Charges = $90 + $20 per hour
Value = 5
Now let formulate an equation
f(h) = 90 + 20h
Where,
h = 5
So,
Total charge = 90+ 20 ×5
Total charge = 90 + 100
Total charge =190
Therefore the correct option is B.
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a salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b. altogether, how many forms did he use?
The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.
Given that,
A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b
A = 50
B = 4A + 0.5C = 200+ 0.5C .......... (i)
C = A + 0.5B = 50 + 0.5 B .......... (ii)
multiply (ii) with 2
B = 2C -50 .......... (iii)
B = 0.5C + 160 ...........(i)
subtract (i) from (iii)
0 = 1.5C -210
C = 420/3 = 140
put in (i)
B = 200 + 0.5(140) = 270
Total forms = A+B+C = 50 + 270 + 140 = 460
Therefore, he used 460 forms altogether.
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Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. The speed of the tennis ball is...
The speed of the tennis ball is 6.2 metres per seconds.
How to find the speed of the tennis?Speed is measured as the ratio of distance to the time in which the distance was covered.
Therefore, speed can be represented mathematically as follows;
speed = distance / time
Hence, the table tennis travels 12.4 metres south in 2 seconds.
The speed of the tennis can be computed as follows:
distance = 12. 4 metres
time = 2 seconds
Therefore,
speed = 12.4 / 2
speed = 6.2 meters per seconds.
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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given that,
Katie and her best friend Liam play tennis every Saturday morning.
When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.
The speed of the tennis can be found by using formula
speed=distance/time
distance = 12. 4 metres
time = 2 seconds
Now speed=12.4/2
speed=6.2
Hence speed of the tennis ball is 6.2m/s
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Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 89 km/h slower than the other. If the two planes are 3254 kilometers apart after 2 hours, what is the rate of each plane?
Answer:
769 and 858
Step-by-step explanation:
Every hour, the distance between the two planes increases by 2x + 89
2 hours = 4x + 178
3254 = 4x + 178
4x = 3076
x = 769
Hi, can you help me to solve this problem please!!!
The Solution:
Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.
An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.
From the given graph of f(x), the function f(x) is ODD.
The degree of the function f(x) is odd since the f(x) itself is odd.
2x-4<6
what is the solution to this inequlity
Answer:
x < 5
Step-by-step explanation:
[tex]2x - 4 < 6[/tex]
[tex]2x < 10[/tex]
[tex]x < 5[/tex]
.........................................................
Please help.
Is the answer ASA, SSS, AAS, or HL
Answer:
SSS
Step-by-step explanation:
We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.
Find the coordinates of the vertices of each figure after a reflection over the given axis.
triangle ABC with vertices A(2,3)B(4,-5), and C(-1,2); x-axis
The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
Given,
A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)
To find the coordinates of the vertices of each figure after a reflection over the given axis.
Now, According to the question:
We should know that:
You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin = (-x, y)
So here's our set of points.
A(2,3) , B(4,-5), and C(-1,2)
Here's those points reflected over the x axis.
A' (2, -3) B' (4, 5) and C' (-1, -2)
Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
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