Answers
To answer this question we will use the z-score.
Recall that the z-score is given as follows:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]The z-score of 54 is:
[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]The z-score of 56 is:
[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:
[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(0.8Answer: 0.10.Related Questions
Jerome rolls two six-sided number cubes. What is the probability that he rolls doubles, given the sum of the numbers is 8?
Answers
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
hope you get it thats the last pen that works in my house
Answer: There are five possible outcomes with a sum of 8:
2 and 6,
3 and 5,
4 and 4,
5 and 3,
6 and 2.
There is only one outcome, 4 and 4, that is doubles. Therefore, the probability is 1/5.
Step-by-step explanation: Got it right on Edmentum
A parabola opening up or
equation in vertex form.
down has vertex (-1, 4) and passes through (-2, 17). Write its equation in vertex form.
Answers
Equation of parabola in vertex form is 13x² + 26x + 17
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
Given,
vertex (h,k) = (-1, 4)
points (x,y) = (-2, 17)
We know, The equation in vertex form is
y = a(x - h)² + k
put the (h,k) values,
y = a(x - (-1))² + 4
y = a(x + 1)² + 4 --------- eq(i)
Next, find the value of 'a' by plug in the points of (x, y) in eq(i)
y = a(x + 1)² + 4
⇒17 = a(-2 + 1)² + 4
⇒17 = a(-1)² + 4
⇒17 = a + 4
⇒a = 13
Now, substitute 'a' value in eq(i) to find the equation of parabola
y = a(x + 1)² + 4
⇒ y = 13(x + 1)² + 4
⇒ y = 13(x² + 1 + 2x) + 4
⇒ y = 13x² + 13 + 26x + 4
⇒ y = 13x² + 26x + 17
Therefore, equation of parabola in vertex form is 13x² + 26x + 17
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What is the product?(4y − 3)(2y2 + 3y − 5)8y3 + 3y + 158y3 − 23y + 158y3 − 6y2 − 17y + 158y3 + 6y2 − 29y + 15
Answers
We need to find the product of :
[tex]\mleft(4y-3\mright)\mleft(2y2+3y-5\mright)[/tex]So, the result as following:
[tex]\begin{gathered} \mleft(4y-3\mright)\mleft(2y^2+3y-5\mright) \\ =4y\cdot(2y^2+3y-5)-3\cdot(2y^2+3y-5) \\ =8y^3+12y^2-20y-(6y^2+9y-15) \\ =8y^3+12y^2-20y-6y^2-9y+15 \\ \\ =8y^3+6y^2-29y+15 \end{gathered}[/tex]So, the answer is the option 4. 8y3 + 6y2 − 29y + 15
Function A and Function B are linear functions.
Which statement is true?
The y-value of Function A when x = -2 is greater than the y-value of Function B when x = -2.
The y-value of Function A when x = -2 is less than the y-value of Function B when x = -2.
Answers
Answer:
Step-by-step explanation:
The y-value of Function A when x = - 2 is less than the y-value of Function B when x = - 2.
Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Answers
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
[tex]\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}[/tex]Step 3: Simplify the above equation
[tex]\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}[/tex]Hence the equation of the circle is
[tex]x^2+y^2-10x+6y-15=0[/tex]Write an equation of a line in SLOPE INTERCEPT FORM that goes through (-5,-3) and is parallel to the line y = x +5.
Answers
Since the slope of the line y=x+5 is m=1, then if the other line is parallel to y=x+5, then it must have the same slope, this is, m'=1.
Now we can use the point-slope formula to get the equation of the line:
[tex]\begin{gathered} m^{\prime}=1 \\ (x_0,y_0)=(-5,-3) \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-3)=1\cdot(x-(-5))=x+5 \\ \Rightarrow y+3=x+5 \\ \Rightarrow y=x+5-3=x+2 \\ y=x+2 \end{gathered}[/tex]therefore, the equation of the line in slope intercept form that goes through (-5,-3) and is parallel to the line y=x+5 is y=x+2
Find an equation of the tangent line to the graph of y = B(x) at x = 25 if B(25) = −1 and B ′(25) = − 1 5 .
Answers
The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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4. The temperature in Baguio is 18.6℃, while Manila the temperature is 31.5℃. How much warmer is it in Manila than Baguio?A. 12.6℃B. 12.7℃C. 12.9℃D. 13℃
Answers
Given:
The temperature in Baguio is 18.6℃.
The temperature in manila is 31.5℃.
To find:
The differene bin temperature etween imanila and aguio.
Explanation:
The difference between manila and Baguio's temperature s
[tex]31.5^{\circ}C-18.6^{\circ}C=12.9^{\circ}C[/tex]Thus, manila is 12.9 degrees Celcius warmer than Baguio.
Final answer:
anila is 12.9 degrees Celcius warmer than Baguio.
Which of the following data collection methods best describes the situation below?A polling company wants to predict which candidate will win an election. Company employees randomly call 1482 likely voters and ask them how they plan to vote.a. sample surveyb. experimentc. observational studyd. correlation
Answers
Answer
Option A is correct.
Explanation
Sample survey refers to the statistic
HELP ASAP
What is the size of the smallest angle in Triangle A? Give your answer correct to one
decimal place. Show your calculations.
Answers
Answer:
A is an included angle between 3 and 5
a large community college has professors and lectures. total number of facility members is 228. the school reported that they had five professors for every 14 lectures. how many of each type of faculty member does the community college employee?
Answers
a large community college has professors and lectures. total number of facility members is 228. the school reported that they had five professors for every 14 lectures. how many of each type of faculty member does the community college employee?
Let
x -----> number of professors
y ----> number of lectures
we have that
x+y=228
x=228-y -------> equation A
x/y=5/14
x=(5/14)y ------> equation B
equate equation A and equation B
228-y=(5/14)y
solve for y
(5/14)y+y=228
(19/14)y=228
y=228*14/19
y=168
Find the value of x
x=228-168=60
therefore
number of professors is 60number of lectures is 168Solve each system of the equation by elimination. y=-4x+14y=10x-28
Answers
Explanation:
The elimination method consists in substracting one equation from the other, so you eliminate one of the variables and you have only one equation to solve for one variable.
In this case, y has the same coefficient in both equations, so this is the variable we will eliminate.
Substract the first equation from the second:
[tex]\begin{gathered} y=10x-28 \\ - \\ y=-4x+14 \\ \text{ ---------------------} \\ y-y=10x+4x-28-14 \\ 0=14x-42 \end{gathered}[/tex]And solve for x:
[tex]\begin{gathered} 14x=42 \\ x=\frac{42}{14} \\ x=3 \end{gathered}[/tex]Now, we replace x = 3 into one of the equations and solve for y:
[tex]y=-4\cdot3+14=-12+14=2[/tex]Answer:
• x = 3
,• y = 2
Element X decays radioactively with a half life of 14 minutes. If there are 460 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 35 grams?
Answers
Step 1
Given;
[tex]\begin{gathered} Intially\text{ y}_0=460g \\ Half\text{ life, h=14 minutes} \\ y=\frac{460}{2}=230g,\text{ when t=h=14 min} \\ \end{gathered}[/tex]Putting these values in, we have;
[tex]\begin{gathered} 230=a(0.5)^1 \\ a=\frac{230}{0.5}=460g \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=460(0.5)^{\frac{t}{14}}---(1) \\ when\text{ y=35} \\ 35=460(0.5)^{\frac{t}{14}} \end{gathered}[/tex][tex]\begin{gathered} 35=460(0.5)^{\frac{t}{14}} \\ \frac{460\cdot \:0.5^{\frac{t}{14}}}{460}=\frac{35}{460} \\ 0.5^{\frac{t}{14}}=\frac{7}{92} \\ \frac{t}{14}\ln \left(0.5\right)=\ln \left(\frac{7}{92}\right) \\ t=\frac{14\ln\left(\frac{7}{92}\right)}{\ln\left(0.5\right)} \\ t=52.02689 \\ t\approx52.0\text{ minutes to the nearest tenth of a minute} \end{gathered}[/tex]Answer;
[tex]52.0\text{ minutes to the nearest tenth of a minute}[/tex]Rewrite the fraction with a rational denominator:
[tex]\frac{1}{\sqrt{5} +\sqrt{3} -1}[/tex]
Give me a clear and concise explanation (Step by step)
I will report you if you don't explain
Answers
The expression with rational denominator is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]
How to rewrite the fraction?From the question, the fraction is given as
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1}[/tex]
To rewrite the fraction with a rational denominator, we simply rationalize the fraction
When the fraction is rationalized, we have the following equation
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{1}{\sqrt 5 + \sqrt{3} - 1} \times \frac{\sqrt 5 - \sqrt{3} + 1}{\sqrt 5 - \sqrt{3} + 1}[/tex]
Evaluate the products in the above equation
So, we have
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{(\sqrt 5)^2 - (\sqrt{3} + 1)^2}[/tex]
This gives
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{5 - 10 - 2\sqrt 3}[/tex]
So, we have
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3}[/tex]
Rationalize again
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3} \times \frac{- 5+2\sqrt 3}{- 5 +2\sqrt 3}[/tex]
This gives
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{(-5)^2 - (2\sqrt 3)^2}[/tex]
So, we have
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{25 -12}[/tex]
Evaluate
[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]
Hence, the expression is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]
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What kind of polyhedron can be assembled from this net?
Answers
It could be assembled a rectangular prism
and
find the greatest common factor for 8n^3 6n^3
Answers
We determine the greatest common factor as follows:
[tex]8n^3+6n^3[/tex]So, we factor:
[tex]2n^3(4+3)[/tex]So, the greatest common factor is 2n^3.
write the number 1,900 in scientific notation
Answers
Explanation
[tex]1900[/tex]Calculating scientific notation for a positive integer is simple, as it always follows this notation:
[tex]a\cdot10^b[/tex]Step 1
To find a, take the number and move a decimal place to the right one position.
so
[tex]1900\Rightarrow1.900\text{ }[/tex]Step 2
Now, to find b, count how many places to the right of the decimal.
[tex]1900\Rightarrow1.900\text{ ( 3 places)}[/tex]Step 3
finally,
Building upon what we know above,
a= 1.9
b=3 (Since we moved the decimal to the left the exponent b is positive)
replace
[tex]\begin{gathered} a\cdot10^b \\ a\cdot10^b=1.9\cdot10^3 \end{gathered}[/tex]therefore, the answer i
[tex]1.9\cdot10^3[/tex]I hope this helps you
Lemons are sold in bag of six lemons for four dollars If you bought 24 how much would you spend
Answers
Lemons cost $4 for a bag of six, so using the unitary method, which states, "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons.
What is Unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Let x be the cost of 24 lemons.
6 lemons for $4
24 lemons for $x
by unitary method,
cost of 1 lemon=$4/6
cost of 24 lemons,
=24*(4/6)
=$16
Using the unitary method, which states that "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons since a bag of six costs $4.
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A car rental company’s standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 15.75+0.50 M, where M is the number of miles driven. The company also offers an option to ensure the car against damage. The insurance charge I in dollars is given by the function I = 5.70+0.15 M. Let C be the total cost in dollars for a rental that includes insurance. Write an equation relating C to M.
Answers
Answer:
[tex]C\text{ = 0.65 M + 21.45}[/tex]Explanation:
Here, we want to write an equation that relates C to M
From the given question, we have to add the insurance to the standard charge to get the total cost
Mathematically:
[tex]C\text{ = S + I}[/tex]Now, we substitute the values for both S and I
That would be:
[tex]\begin{gathered} C\text{ = 15.75 + 0.50M + 5.70 + 0.15 M} \\ C\text{ = 0.65M + 21.45} \end{gathered}[/tex]Which number can be inserted into the parentheses to make a true statement?-10°C<( )A. -12° CB. -18° CC. -3°CD. -10° C
Answers
Answer:
[tex]-3\degree C[/tex]Explanation:
Here, we want to get the number that could be inserted into the parentheses to make it true
From the logical operator given, we can see that we need a number greater than -10
From the options given, only -3 is greater than -10, which makes it the correct answer choice
A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
Answers
Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.
Who are the individuals on a data-set or on a study?The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.
In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.
Type of the pet.Age of the pet.Weight of the pet.Height of the pet.All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.
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A glassblower makes vases. To prevent them from breaking,each vase's thickness should be 6 millimeters and candeviate by no more than 1 millimeter.Write an inequality to represent this situation, where t is thethickness in millimeters, and solve for the maximumthickness.
Answers
Since each vase should be 6 millimeters and can only deviate by no more than 1 millimeter, the inequality for the thickness would be:
[tex]6\ge t\leq7[/tex]And the maximum thickness would be 7 millimeters.
Select from these metric conversions1 kg = 1000 g1 g = 1000mgand use dimensional analysis to convert 4.59 kg to g.4.59 kg X 1
Answers
Since
[tex]1kg=1000g,[/tex]then:
[tex]1=\frac{1000g}{1kg}.[/tex]Then:
[tex]4.59kg=\frac{4.59kg}{1}\times\frac{1000g}{1kg}=4590g.[/tex]Answer:
[tex]\frac{4.59kg}{1}\times\frac{1000g}{1kg}=4590g.[/tex]An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
An athlete run in 22 minutes is 19.232 laps
Given,
An athlete runs at a speed of 9 miles per hour.
and, If one lap is 349 yards.
To find the how many laps does he run in 22 minutes?
Now, According to the question:
Firstly, Convert the mph into yard per minute,
Remember that:
I mile = 1,760 yard
1hour = 60 minute
Convert the speed in miles/hour to yards/minute
9 [tex]\frac{miles}{hour}[/tex] = 9[tex]\frac{1760}{60}[/tex] = 264 yard/ min
We know that
The speed is equal to divide the distance by the time
Let
s → the speed
d → the distance in yards
t → the time in minutes
Using the formula :
Speed = distance/ time
Solve the distance:
d = speed x time
Speed = 264 yard/ minute
Time = 22 minute
Therefore,
Distance = 264 x 22
Distance = 5,808 yards
Divide the distance by 302 yards to find out the number of laps
= 5,808/ 302 = 19.232 laps
Hence, An athlete run in 22 minutes is 19.232 laps
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help pleaseeeeeeeeeeeeeeeee
Answers
Answer:
b) 28
c) 52
Step-by-step explanation:
f(2) = -2³ + 7(2)² - 2(2) + 12
= -8 + 28 - 4 + 12
= 28
f(-2) = -(-2)³ + 7(-2)² - 2(-2) + 12
= 8 + 28 + 4 + 12
= 52
A rainstorm in Portland, Oregon, wiped out the electricity in 10% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.Answer the following.(a)Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.(b)Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
Answers
Solution
Question A:
[tex]\begin{gathered} Mean=np \\ where, \\ n=\text{ Number of sample values} \\ p=\text{ Probability of mean} \\ \\ n=50 \\ p=10\%=\frac{10}{100} \\ \\ \therefore Mean=50\times\frac{10}{100}=5 \end{gathered}[/tex]- The number of households in the sample that lost electricity is 5
Question B:
[tex]\begin{gathered} \sigma=\sqrt{npq} \\ where, \\ \sigma=\text{ Standard deviation} \\ n=\text{ Number of data points in the sample} \\ p=\text{ Probability of obtaining the mean} \\ q=\text{ Probability of NOT}obtaining\text{ the mean}=1-p \\ \\ n=50 \\ p=10\%=0.1 \\ q=1-0.1=0.9 \\ \\ \sigma=\sqrt{50\times0.1\times0.9} \\ \sigma=2.121320343...\approx2.121 \end{gathered}[/tex]- The standard deviation is 2.121
Final answers
- The number of households in the sample that lost electricity is 5
- The standard deviation is 2.121
Equipment was purchased for $50,000. The equipment is expected to be used 15,000 hours over its useful life and has a residual value of $10,000. In the first two years of operation, the equipment was used for 2,700 hours and 3,300 hours, respectively. Using the activity-based method, what is the equipment’s accumulated depreciation at the end of the second year?
Answers
The equipment’s accumulated depreciation at the end of the second year is $16,000.
What is the accumulated depreciation?Depreciation is the process used in expensing the cost of an asset. The activity based method allocates the depreciation expense using the number of hours the asset was used. Accumulated depreciation is the sum of the depreciation over a period of time.
Depreciation expense using the activity based method = (cost of the asset - residual value) x (number of hours used in a year / total number of hours)
Depreciation expense in year 1 = ($50,000 - $10,000) x (2,700 / 15,000)
$40,000 x 0.18 = $7,200
Depreciation expense in year 2 = ($50,000 - $10,000) x (3,300 / 15,000)
$40,000 x 0.22 = $8,800
Accumulated depreciation = $8,800 + $7,200 = $16,000
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Domain and range from the graph of a piecewise function
Answers
The domain of the given function is:
[tex]\text{Domain}=\lbrack-3,-2\rbrack\cup\lbrack-1,5)[/tex]Because the domain corresponds to the set of all possible inputs, x-axis.
The range of this function is:
[tex]\text{Range}=\lbrack-5,3\rbrack[/tex]Because the range corresponds to the set of all possible outputs, y-axis.
the top ten medal- winning nations in a tournament in a particular year are shown in the table. use the given information and calculate the mean number of gold medals for all nations
Answers
Two ships left a port at the same time. Onetravelled due north and the other due eastat average speeds of 25.5 km/h and 20.8 km/h,respectively. Find their distance apart
Answers
Given:
Two ships left a port at the same time.
One travelled due north at an average speed of 25.5 km/h
And the other ship was due east at average speeds of 20.8 km/h
We will find their distance apart using the Pythagorean theorem.
The distance = Speed * Time
Let the time = t
So, the distance of the first ship = 25.5t
And the distance of the second ship = 20.8t
So, the distance between the ships (d) will be as follows:
[tex]\begin{gathered} d^2=(25.5t)^2+(20.8t)^2 \\ d^2=1082.89t^2 \\ \\ d=\sqrt{1082.89t^2} \\ d=32.907t \end{gathered}[/tex]So, the answer will be:
The distance in terms of time = 32.907t
We will find the distance when t = hours
So, distance = 164.54 km
