The probability for possibilities of x between P(X>4) and P(6.72<X<10.16) is 0.5987 and 0.2351
X is N(5, 16)
means that, Z=(x-mean)/√variance = (x-5)/√4
=(x-5)/2
that is, Z is standard normal.
Then, by symmetry of the standard normal curve,
P(X>4)=P(X−5>4−5)
=P(X−54>4−54)
= P(Z>−14)
=P(Z>−.25)
=P(Z<.25)
= 0.5987.
Similarly
P(6.72<X<10.16)
= P(6.72−5<X−5<10.16−5)
=P(6.72−54<10.16−54)
=P(0.43<Z<1.29)
=P(Z<1.29)−P(Z<.43)
=.9015−.6664
= 0.2351.
Therefore, The probability for possibilities of x between P(X>4) and P(6.72<X<10.16) is 0.5987 and 0.2351
Complete question - X is a normal random variable with mean=5 and variance=4 What are the possibilities for P(X>4) and P(6.72<X<10.16)?
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If you answer first with the correct answers ill mark you brainlist:)
All the correct values are,
a)⇒ f (0) = - 1
b)⇒ f (1) = 1
c)⇒ f (-1) = - 3
d)⇒ f (a) = 2a - 1
e)⇒ g (0) = - 4
f)⇒ g (-2) = 0
g)⇒ g (3) = 5
h)⇒ g (t) = t² - 4
i)⇒ f (a+5) = 2a + 9
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The function are,
⇒ f (x) = 2x - 1
⇒ g (x) = x² - 4
Now, We can find all the values by substituting as;
a) f (0)
⇒ f (x) = 2x - 1
Put x = 0;
⇒ f (0) = 2×0 - 1
⇒ f (0) = - 1
b) f (1)
⇒ f (x) = 2x - 1
Put x = 1;
⇒ f (1) = 2×1 - 1
⇒ f (1) = 1
c) f (-1)
⇒ f (x) = 2x - 1
Put x = -1;
⇒ f (-1) = 2×-1 - 1
⇒ f (-1) = - 2 - 1
⇒ f (-1) = - 3
d) f (a)
⇒ f (x) = 2x - 1
Put x = a;
⇒ f (a) = 2×a - 1
⇒ f (a) = 2a - 1
e) g (0)
⇒ g (x) = x² - 4
Put x = 0;
⇒ g (0) = 0² - 4
⇒ g (0) = - 4
f) g (-2)
⇒ g (x) = x² - 4
Put x = -2;
⇒ g (-2) = -2² - 4
⇒ g (-2) = 4 - 4
⇒ g (-2) = 0
g) g (3)
⇒ g (x) = x² - 4
Put x = 3;
⇒ g (3) = 3² - 4
⇒ g (3) = 5
h) g (t)
⇒ g (x) = x² - 4
Put x = t;
⇒ g (t) = t² - 4
i) f (a+5)
⇒ f (x) = 2x - 1
Put x = a + 5;
⇒ f (a+5) = 2×(a + 5) - 1
⇒ f (a+5) = 2a + 10 - 1
⇒ f (a+5) = 2a + 9
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find a power series representation for f(x) = arccot(x).
The power series representation for f(x) = arccot(x) is
[tex]\pi /2- \lim_{n \to \infty} (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]
The power series ∑aₙxⁿ is an infinite series and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the geometric series as an example.
The power series is a very important kind of infinite series where the terms contain the powers of a variable. A power series is a series of the general form:
∑aₙ(x-x₀)ⁿ=a₀+a₁(x-x₀)+a₂(x-x₀)²+a₃(x-x₀)³+.........
called a power series centered at x₀
where x is a variable,
x₀ is a real constant, and the
aₙ's are real constants called the coefficients of the series.
The given power series representation is f(x) = arccot(x).
we observe that f '(x)=-1/(1+x²) and find the required series by integrating the power series for -1(1+x²)
arccot(x)=∫-1/(1+x²)dx
⇒∫-(1-x²+x⁴-x⁶+....)dx
⇒C-x+1/3x³-x⁵/5+1/7x⁷-......
To find C we put x=0 and obtain C=arccot(0)=π/2
Therefore,
C=π/2-x+1/3x³-x⁵/5+1/7x⁷-.......
f(x)=π/2- ∑(-1)ⁿₓ x^2n+1/2n+1
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>>
Based on the factor tree, which two numbers are not prime?
6 and 42
3 and 7
7 and 42
3 and 7
The number 1 is called a unit. It has no prime factors and is neither prime nor composite. The number is 6 and 42.
What is unit? Unit is an individual thing or person regarded as single and complete but is also part of a whole or group. We also use the word unit while referring to the unit price of an item. It means the cost per item, per liter or per kilogram.Units are the tools to measure and compare different things. Comparison becomes easy when all the units for the measurement are the same. Different units can be classified depending on their use.A single quantity regarded as a whole in calculation. : a definite quantity (as of length, time, or value) used as a standard of measurement. the dollar is the unit of U.S. money. 3. : a single thing or person or group that is a part of a whole.To learn more about quantity refer to:
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One is referred to as a unit. It is neither prime nor composite and lacks any prime factors. The digits are 6 and 42.
What is meant by factor tree?A number's factors, and more specifically its prime factorization, can be expressed as factor trees. There are factors for each branch of the tree. The branch comes to an end and the number is circled once the factor at the branch's end is a prime number, leaving only itself and one as potential factors.
A factor tree is a technique that enables us to determine the prime factors of a given integer. With this approach, we factorize the inputted number until no further factors can be discovered. Prime factorization is the list of prime factors or numbers that we would multiply together to arrive at the given number.
Therefore, the correct answer is option a) 6 and 42.
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which of the following is true about statistics such as the sample mean or sample proportion?
A. A statistic is a constant.
B. A statistic is always known.
C. A statistic is a paraméter
D. A statistic is a random variable.
The correct option is option D) A statistic is a random variable.
We derive the above answer due to the following reason,
Any statistic is a random variable with its own distribution referred to as the sampling distribution as it is a function of sample values and there may be several samples taken from a given population.
The probability distribution of a statistic that is acquired by the continuous sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or the mode of a variable.
There are three standard types of sampling distributions in statistics:
Sampling distribution of the meanSampling distribution of a proportionT-distributionRead more about Statistics from:
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what will be the value stored in the variable x after the execution of the following code snippet? int a
The result of running the code is that x will be 20.
Therefore, your software is saying:
Place x at 30. (I'm assuming that you don't care about the case here because you wrote an X in capital letters that don't exist anywhere else;)
Place y at 20.
If y is not equal to x-10, ask. "If yes, put x to the value of x-5; if no, set x to the value of y," is the next step.
Your question receives the response "no," and x is then set to the value of y since the values of x and y you selected to result in y being equal to x-10. The result of running the code is that x will be 20.
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Full question
After execution of the following code, what will be the value of x? X = 30; y = 20; if (y ! = (x - 10)) x = x - 5; else x = y;
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.8 cm 2 cm
The length of hypotenuse = 5.2 centimeters.
What is right angle and Pythagorean theorem?The triangle that has at least one angle 90 degrees is called right angle triangle. The largest side length of a right triangle is termed as hypotenuse.
The Pythagorean theorem is applicable for right-angled triangle. The theorem stated that the square of hypotenuse is equal to the sum of the square of the remaining two side lengths. If a right-angled triangle has hypotenuse H and other two side length b and o respectively, then H² = b² + o².
What is the length of hypotenuse in this right-angled triangle?Assume this right-angled triangle is named as ABC, AC is the hypotenuse and AB and BC is the other sides.
As AB = 2 cm and BC = 4.8 cm
then according to the Pythagorean theorem AC² = AB²+ BC²
AC²= 2² + 4.8²
Hypotenuse AC = 5.2 centimeter.
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The nth term of a sequence is 60 - 8n.
Find the largest number in this sequence.
Answer:
The largest term is 52.---------------------------------
Given sequence:
t(n) = 60 - 8nThis is decreasing sequence since the common difference is negative, d = - 8.
Therefore the first term is the largest one:
t(1) = 60 - 8*1 = 60 - 8 = 52How long would it take to spend 1.4 billion dollars if you were to spend $1 a second? Please write your answer in days.
Answer:
[tex]16203[/tex] days
Step-by-step explanation:
There are 60 seconds per minute, so 3600 sec/hour, and 86400 seconds per day, so the answer is about [tex]16203[/tex] days.
Convert into symbolic form.
“Michael does not have the time or money to complete the project.” Each phrase should be declared as a symbol before you put it into symbolic form. (P, Q, R, S)
The statement can be represented symbolically as: (P) ∨ (Q) → (S)
How to represent a statement in symbolic form?
Representing a statement in symbolic form involves using logical symbols and logical operators to create a logical expression that captures the meaning of the statement. Here are some common symbols and operators used in symbolic logic:
Negation (¬ or ~): used to represent "not", e.g. ¬P means "not P"Conjunction (∧): used to represent "and", e.g. P ∧ Q means "P and Q"Disjunction (∨): used to represent "or", e.g. P ∨ Q means "P or Q"Implication (→): used to represent "if-then", e.g. P → Q means "if P, then Q"Bi-Implication (↔): used to represent "if and only if", e.g. P ↔ Q means "P if and only if Q"Parentheses: used to group symbols and indicate the order of operations, e.g. (P ∧ Q) ∨ R means "either (P and Q) or R".To put the statement "Michael does not have the time or money to complete the project" into symbolic form, we first need to identify the key phrases and declare them as symbols. Here are a few possible ways to do this:
(P) Michael does not have the time
(Q) Michael does not have the money
(R) Michael does not have the time or money
(S) Michael can not complete the project
We can put them in different ways, depending on the statement you want to make.
Then the statement can be represented symbolically as:
(P) ∨ (Q) → (S)
This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.
Alternatively, we can use the following representation
(R) → (S)
This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.
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A month later, Mayor Bruns (from Exercise 5-23) picks up the morning edition of the city's leading newspaper, the Sun-American, and reads an exposé of unemployment fraud. In this article, the newspaper claims that out of every 15 unemployment beneficiaries, the probability that four or more have jobs is 0.9095, and the expected number of employed beneficiaries exceeds 7. You are a special assistant to Mayor Bruns, who must respond to these claims at an afternoon press conference. She asks you to find the answers to the following two questions: (a) Are the claims of the Sun-American consistent with each other? (b) Does the first claim conflict with the opinion of the mayor's assistants?
Answer:
Follow me if this helped you
Step-by-step explanation:
a)The claims of the Sun-American are not consistent with each other. The probability that four or more out of every 15 unemployment beneficiaries have jobs is 0.9095, but the expected number of employed beneficiaries exceeds 7, which is more than 4.
Given f(t)=t+3 and g (t) = 2t2 - 3t+ 4, find
(f.g) (t).
Write your answer in standard form.
The value of the solution of (f.g)(t) is 2t^2-3t+7
What is function and example?A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
What are the 3 types of functions?Types of Functions
Many – one function. Onto – function (Surjective Function) Into – function. Polynomial function
In the given equation,
f.g (t) is 2t^2-3t+7
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suppose the mean GPA of BYU-Idaho students is 3.5 and the standard deviation is 0.7. It is well known that this distribution is left-skewed. A random sample of n = 81 students will be drawn.
The shape that represents the sample mean of the 81 students who are selected is; Approximately normal
What is the shape of the sampling distribution?When a distribution of data is defined as skewed, it means that it does not take the normal distribution's bell shape. Rather, it tends to distort with values either to the left or right of the center of the data.
Now, the Central Limit Theorem states specifically that the distribution of sample mean is normally distributed. It goes further to state that if the population values from which the sample originates is not normally distributed, the sample distribution will be normal. This effect will lead to increases as sample size increases.
Thus, we can conclude that the shape is normally distributed
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Complete question is;
Suppose the mean GPA of School A students is 3.5 and the standard deviation is 0.7 it is well known that this distribution is left-skewed. A random sample of n = 81 students will be drawn. What is the shape of the sampling distribution of the random variable ¯X. which represents the sample mean of the 81 students who are selected.?
- Left- skewed
- right-skewed
- approximately normal
- we cannot determine this from the information given.
please help due soon!!!!
The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.
What is a formula of perimeter of triangle?The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet.
The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.
Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.
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When Alton started his current job, his employer told him that he had one day of paid vacation until he reaches his first year with the company. Then, at the end of the first year, he would have three vacation days. After each year, his number of vacation days would triple up to 27 days of paid vacation. In what year will he have maxed out his vacation days?
After 4 year he will have maxed out his vacation days.
What is Geometric sequence?A geometric sequence is a set of integers that follows a pattern in which the following term is determined by multiplying the previous one by a factor known as the common ratio, or r.
Given:
After first year one day of paid vacation.
After second year 3 day of paid vacation.
So, the sequence is 1, 3, 9,.....
Common ratio, r = 3/1 = 3
maximum paid vacation days , [tex]a_n[/tex]= 27
Using [tex]a_n = a r^{n-1[/tex]
Then, 27 = 1 x [tex]r ^{ (n-1)[/tex]
27 = [tex]3^{n-1[/tex]
3³ = [tex]3^{n-1[/tex]
now, comparing the base
n-1 = 3
n=4
Hence, after 4 year his vacation mxed out.
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okay i retook it sorry it was bad before
Answer: The first orange is the best deal at $0.8 per orange. The second cand is the best deal at $0.45 per candy.
Step-by-step explanation:
First orange: 5 for $4 equals $4/5 per orange, which equals $0.8 per orange.
Second orange: 10 for $9 roughly equals $1.111 per orange
Third orange: $0.82 each
The first orange is the best deal at $0.8 per orange
First candy: 3 for $1.5 equals $1.5/3 per candy, which equals $0.5 per candy.
Second candy: 4 for $1.8 equals $0.45 per candy
Third candy, 10 for $4.6 equals $0.46 per candy
DUE SOON! PLEASE HELP! QUESTION DOWN BELOW!
Answer:
a)not quadratic
b)quadratic
c)quadratic
d)not quadratic
a) x=-3
b) maximum is (-3,4)
c)[tex](-3-\sqrt{2},0)[/tex] and[tex](-3+\sqrt{2},0)[/tex]
d)(0,-14)
e) Domain: (-∞,∞), {xIx∈ℝ}
Range: (-∞,4), {yIy≤4}
Step-by-step explanation:
Hope this helps!
The table and the graph each show a different relationship between the same two variables, x and y:
X
3
4
5
6
100
110
190
Y
200
270
360
450
540
How much more would the value of y be in the table, than its value on the graph, when x = 11? (1 point)
800
640
480
320
160
0
246810p
The value of y will be 90 more than its value on the graph, when x = 11. The solution has been obtained using the linear equations.
What is a linear equation?
The equation is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.
From the given information, we need to initially form the equation
We are given different points
Let us take two points as (3,270) and (4,360)
Using slope-intercept form, we get the equation as
⇒y=90x+0
⇒y=90x
Now, putting x=11, we get
y = 990
Hence, the value of y will be 90 more than its value on the graph, when x = 11.
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A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points one, negative three, and three, zero. What is the slope of the line?
The slope of a given line is m=1.5.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
The coordinate points of a line are (1, -3) and (3, 0).
Substitute, (x₁, y₁) and (x₂, y₂) in m=(y₂-y₁)/(x₂-x₁), we get
m= (0+3)/(3-1)
= 3/2
= 1.5
Therefore, the slope of a given line is m=1.5.
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What am I doing wrong in this problem? List the data in the following stem-and-leaf plot. The leaf represents the tenths digit. 14 15 1447 16 56 17 8 18 366 Separate the numbers in the list by a comma. The list is: 151, 154, 154, 157, 165, 166, 178, 183, 186, 186
It will stand for the 15.1, not The 151.
So therefore here you got almost correct the answer,
but you misunderstood about the leaves because the leaves will stand for the decimal.
The 10th means that after the decimal,
So the foundation must be the 15.1.
15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.
A stem and leaf diagram is a way of displaying a collection of numbers. The ‘stem’ consists of the first part of every number, usually the first digit(s) and the ‘leaf’ consists of the latter part of every number, usually the last digit. We need to know how to draw them and how to use them.
Draw a stem-and-leaf diagram to represent Scott’s data.
Step 1: Figure out what our key will be. The stem will be the first two digits, whilst the leaf will be the last digit. Our key is any number that is in the list, represented in terms of a stem and leaf.
Step 2: Use our key to draw our stem part of the diagram, which will have to include: 15,16,17,18,
Step 3: Rewrite the data in numerical order.
151, 154, 154, 157, 165, 166, 178, 183, 186, 186
Step 4: Fill in the ‘leaf’ values (the last digit of every value) alongside the correct ‘stem’ value, to complete the stem and leaf diagram.
14 15 1447 16 56 17 8 18 366
14
15 1447
16 56
17 8
18 366
151 , 154 , 154 , 157
165 , 166
178
183 , 186 ,186
it will stand for the 15.1, not The 151. So therefore here you got almost correct the answer, but you misunderstood about the leaves because the leaves will stand for the decimal. The 10th means that after the decimal, So the foundation must be the 15.1, 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.
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jon paid $200 for 8 classes at gold dawn yoga studio. the cost, y, is rorportional to the number of classes purchased, x. graph three points and find the slope
The slope of the given data is 25.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Jon paid $200 for 8 classes at gold dawn yoga studio.
the cost, y, is proportional to the number of classes purchased, x
The slope will be cost of each class
200/8=25
So the equation will be y=25x
25 is the slope.
Hence, the slope of the given data is 25.
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4. United Bank offers a 15-year mortgage at an APR of 4.2%. Capitol Bank offers
a 25-year mortgage at an APR of 4.5%. Marcy wants to borrow $120,000.
a. What would the monthly payment be from United Bank?
b. What would the total interest be from United Bank? Round to the nearest
ten dollars.
c. What would the monthly payment be from Capitol Bank?
d. What would the total interest be from Capitol-Bank? Round to the nearest
ten dollars.
e. Which bank has the lower total interest, and by how much?
f. What is the difference in the monthly payments?
uw.nadin
g. How many years of payments do you avoid if you decide to take out the
shorter mortgage?
Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.
What is total interest?
Total interest is determined by the addition of all the interest payments.
what would be the monthly payment and total interest from each bank?
United bank offers mortgage at an APR of 4.2%
APR means annual percentage rate.
mortgage is offered for the period of 15 years.
initial principal amount of Marcy = $120000
we need to determine the monthly payment from United bank.
at first, we will determine the rate of interest per month.
monthly interest rate = (4.2) / (100 × 12) = 0.0035
1 year = 12 months
15 years = 15×12 = 180 months
monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal
monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000
= $1207.70
from united bank monthly payment = $1207.70
Now we calculate the monthly payment from Capitol bank.
APR for capitol bank = 4.5%
number of years for which mortgage is issued = 25 years
number of months = 12×25 = 300.
monthly interest rate = (4.5) / (100×12) = 0.00375
monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000
= 1834.62
monthly payment from Capitol bank = $1834.62
total interest from Capitol bank = principal money × yearly interest rate × time period.
Total interest = 120000 × 4.5/100× 25
= $135000 for the Capitol bank
Total interest from United bank = principal amount × yearly interest × time period
= 120000× 4.2/100 × 15
total interest from united bank = $75600
United bank has lower total interest.
difference in monthly payment = 1834.62 - 1207.70
= 626.92 dollars
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please help, need asap. do 30, and 31....30 points!!!!!!!!!!!!!!!!!
The indicated measures:
m∠ABC = 138° and m∠BCD = 52°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠DAE = 16° and m∠EDC = 64°.
The diagonals of the kite intersect at 90°.
(1).
In ΔAED,
the sum of all the angles of the triangle is 180°.
m∠DAE + m∠ADE + m∠AED = 180°
m∠ADE = 180 - 90 - 16
m∠ADE = 74°
According to the angle addition postulate,
m∠ADE + m∠EDC = m∠ADE
m∠ADE = (74 + 64)°
m∠ADE = 138°
From the property of kites,
m∠ADE = 138° = m∠ABC.
(2). m∠EBC = m∠EDC,
m∠EBC = 64°
In ΔBCD,
the sum of all the angles of the triangle is 180°.
m∠DBC + m∠BCD + m∠CDB = 180°
m∠BCD = 180 - 64 - 64
m∠BCD = 52°
Therefore, 138° = m∠ABC and m∠BCD = 52°.
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if the expression 4x + 2(x - 4) is equivalent to x +2 then what is the value of x?
Answer:
x=2
Step-by-step explanation:
4x + 2(x - 4) is equivalent to x +2
first, distribute. 4x+2x-8
next, combine like terms. 6x-8
6x-8 = x+2
we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)
get rid of the parenthesis. 6x-8+8-x=x+2+8-x
combine like terms. 6x-x-8+8=x-x+2+8
solve. 5x=10
divide both by 5. 5x/5=10/5
x=2
A mixture is made by combining 1.97 lb of salt and 5.37 lb of water. What is the percentage of salt (by mass) in this mixture
The percentage of salt (by mass) in this mixture is calculated to be
26.8%How to find the percentage of salt (by mass) in this mixtureinformation from the problem
A mixture is made by combining 1.97 lb of salt
and 5.37 lb of water
The question is a percentage problem, percentage deals with a fraction hundred.
The percentage of the salt in the mixture is calculated by first finding the mass of the mixture
mass of the mixture = mass of salt used + mass of water that made the solution
mass of the mixture = 1.97 lb + 5.37 lb
mass of the mixture = 7.34 lb
The percentage of salt in the mixture
= 1.97 / 7.34 * 100
= 0.2684 * 100
= 26.8%
The percentage of salt in the mixture is 26.8%
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PLEASE HELP ASAP:
A bag has 1 speckled pen, 3 black pens,
and 7 yellow pens. You randomly pull a pen
from the bag, put it back, and then pull out
another one.
What is the probability of not getting a yellow and then not getting a yellow? Write
your answer as a fraction.
Answer:
[tex]\textrm{P(no yellow on two picks )} = \dfrac{16}{121}[/tex]
Step-by-step explanation:
The total number of pens is 1 + 3 + 7 = 11 out of which 7 are yellow.
(We don't really care what color the other pens are since we are interested only in the yellow pens)
[tex]\textrm{P(yellow on first pick )} = \dfrac{\textrm{Number of yellow pens}}{\textrm{Total number of pens}} = \dfrac{7}{11}[/tex]
The probability of not getting a yellow on first pick is the complement of this probability and is 1 less than the probability of picking an yellow
[tex]\textrm{P(not yellow on first pick )} = 1- \dfrac{7}{11} = \dfrac{4}{11}[/tex]
Since we are putting back the pen after the first pick, the total number of pens as well as pens of each color remain the same.
Therefore the probability of not getting a yellow on second pick is the same as the first pick and is [tex]\dfrac{4}{11}[/tex]
The combined probability of not getting an yellow on both picks is the product of these probabilities
[tex]\textrm{P(no yellow on two picks )} = \dfrac{4}{11}\cdot \dfrac{4}{11} = \dfrac{16}{121}[/tex]
graph
Which of the following statements are true about the function graphed here? Select all that apply.
The mathematical function has an absolute minimum at x = 15.
The domain of the mathematical function shown in the graph is all real numbers.
The average rate of change of the function between x = 20 and x = 25 is 0.
The domain of the mathematical function shown in the graph is all values of x such that 0 ≤ x ≤ 20.
The mathematical function is decreasing for all values of x such that x > 15.
The mathematical function is increasing for all x such that 15 < x < 22.
The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).
What is the linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables..
Given,
The mathematical function has an absolute minimum at x = 15.
The average rate of change of the function between x = 20 and x = 25 is 0.
The mathematical function is increasing for all x such that 15 < x < 22.
The line intersects the y-axis at (0, -6). Then the y-intercept of the line is (0, -6).
The domain of the linear function will be a real number.
And the range of the linear function is also real number.
Hence , The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).
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Identity each of the following statistics as either descriptive or inferential
A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.
What are the examples of descriptive and statistics?Two sets of pupils with scores from various classes are highlighted, Using descriptive statistics, determine the mode of the following data: Using descriptive and inferential statistics, determine the z score for the given data.
Measurements of variability and measures of central tendency make up descriptive statistics (spread). Mean, median, and mode are examples of central tendency metrics. Variability measures include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.
correlation analysis, A set of independent variables and a dependent variable, such as Hypothesis Tests, are related in regression models. To compare entire populations or evaluate the correlations between variables, hypothesis testing is utilised along with samples and confidence intervals.
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The complete question is " Identify the type of data (qualitative/quantitative) and the level of measurement for the
expenses of respondents in a survey?"
A couple is starting a family and decides to have four children. Assume that the probability of having a boy or having a girl are equal. Find the probability model for the number of girls the couple has
Consequently, the probability of producing precisely one girl or exactly one male 0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3; 0.9375 ; 0.5
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.
Due to this:
p = 0.5
Modeling the probability of how many females the couple has:
[tex]P(x =x) is equal to nCx * px * (1 - p) (n - x)\\P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625\\\=P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25\\P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375\\P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25\\P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625[/tex]
likelihood of having at least one female
N = 4 trials in total.
P(x 1) is equal to p(x = 1) plus p(x = 2) plus p(x = 3) plus p(x = 4)
Employing the relation
P(x =x) is equal to nCx * px * (1 - p) (n - x)
use a calculator
P(x ≥ 1) = 0.9375
Chances of getting just one female or exactly one boy
3 females OR 3 boys OR 1 boy
P(x = 1)
P(x =x) is equal to nCx * px * (1 - p) (n - x)
P(x = 1) = 4 * 0.5 * 0.125
P(x = 1) = 0.25
The likelihood of getting one girl and three males or vice versa is 0.25
Consequently, the likelihood of producing precisely one girl or exactly one male
0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3 is 0.9375 ; 0.5
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A consumer purchased a computer after a 30% price reduction. If represents the computer's original price, the reduced price can be represented by
If x represents the computer's original price, the reduced price can be represented by
We want to reduce x by 30%. Thus, the reduced price is:
x - 0.20x = 0.70x
More informally, if you take away 30%, you're left with 70%.
This question is similar to previous one so I used that answer launguage here also
As an object's depth below the surface of a body of salt water increases, so does the pressure
acting on the object due to atmospheric and water conditions. The rate at which pressure
increases is approximately 11 pounds per square inch (psi) for every increase in depth of 25
feet (ft). The pressure at the surface of the water is 15 psi. Rounded to the nearest foot, at
what depth will the pressure acting on the object be 50 psi?
236.5 ft depth will the pressure acting on the object.
Find the depth?The m is the slope, and b is the y-intercept, therefore f(x) = mx + b.
You are given the value of m = 4.44 (lb/in2) for every 10 feet of descent; however, you need f(x) to be a function of the depth in inches, thus you must determine what m is for every inch of fall.
120 inches are equal to 10 feet multiplied by (12 inches per foot).
Every 120 inches of fall, then, gives rise to m = 4.44.
m = 4.44 / 120 = 0.037 for each inch of fall
Consequently, f(x) = 0.037x + b
The fact that f(0) = 15 and b = 15 can be used to find b.
f(x) = 0.037x + 15 is the equation as a result.
Set f(x) = 120 and work out x to obtain the pressure at that point.
120 = 0.037x + 15 0.037x = 105 x, or 105 / 0.037 = 2837.8 inches, or roughly 236.5 ft.
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