The missing number in a given integer array of 1 to 100 can be found using the PHP array_diff() function.
This function compares two array and returns the difference. To find the missing number, we first need to create an array that contains all numbers from 1 to 100. We then create another array with the given integers. Using array_diff(), we can compare the two arrays and the difference will be the missing number.
To use the array_diff() function, we first need to create the two arrays. For example,
$array1 = range(1,100);
$array2 = array(1,2,3,4,5,6,7,8,9);
The first array is containing all numbers between 1 and 100 and the second array is containing the given integers.
The next step is to use the array_diff() function. The syntax for this is
$diff = array_diff($array1, $array2);The result of this will be an array containing the missing integer.
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What are the 3 types of solutions and examples?
PLEASE HELP ASAP! 40 POINTS!
The talent show committee is anticipating selling 300 tickets to the talent show. They expect 180 adults to attend, and 120 children to attend. They hope to raise $1,440 from ticket sales to purchase classroom supplies. Adult tickets will be twice as expensive as child tickets. For what prices should the committee sell adult tickets and child tickets to the show?
Step-by-step explanation:
The committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.
Let x be the price of adult tickets in dollars and y be the price of child tickets in dollars. We can set up the following system of equations to represent the given information:
x + y = 300 (the total number of tickets sold)
180x + 120y = 1440 (the total amount of money raised)
x = 2y (the price of adult tickets is twice the price of child tickets)
Substituting the third equation into the first equation, we get:
2y + y = 300
3y = 300
y = 100
Substituting this value for y into the third equation, we get:
x = 2*100
x = 200
Substituting these values for x and y into the second equation, we get:
180200 + 120100 = 1440
This equation is true, so the solution x = $200 and y = $100 is valid. Therefore, the committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.
How do you find the mean and standard deviation of a random variable?
Random variable contains the random outcome of an event in probability, The mean and standard deviation are calculated in terms of expected values E(x) in case of random variable.
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is mean and standard deviation?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
for a random variable, we use expected value for mean and standard deviation.
mean = E(X)
Standard deviation = [tex]\sqrt {variance} =\sqrt {E(X^{2})-(E(X)^{2})}[/tex]
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The bridge that leads to honeymoon island state park only allows cars and motorcycles. The toll for the bridge is 50 cents for motorcycles and one dollar for cars and trucks. One Saturday, the tollbooth attendant collected a total of $150, and the vehicle counter recorded 170 vehicles crossing the bridge. How many motorcycles and how many cars and trucks crossed the bridge that day?
A car travels 62 miles per hour. At this rate, how far will the car travel in 7 hours?
Answer:
372 miles
Step-by-step explanation:
You need to multiply 62 and 6
Answer:
The car will travel 434 miles in 7 hours.
Step-by-step explanation:
To get the answer you simply need to multiply 62, which is the speed of the car, by 7 hours, how long it will travel.
Therefore, the answer is 434 miles.
Compute The Following. (A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.
The values of the expressions are P 9, 3 = 504, C 9, 3 = 84, P 8, 8 = 40320 and C 9, 9 = 1
How to compute the expressionsFrom the question, we have the following parameters that can be used in our computation:
(A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.
The above expressions are permutation and combination expressions
The combination formula is ⁿCᵣ = n!/(n - r)!r!The permutation formula is ⁿPᵣ = n!/(n - r)!Using the above as a guide, we have
Expression (A) P9, 3
Apply the permutation formula
P n, r = n!/(n - r)!r!
So, we have
P 9, 3 = 9!/6!
Evaluate
P 9, 3 = 504
Expression (B) C 9, 3
Apply the combination formula
C n, r = n!/(n - r)!r!
So, we have
C 9, 3 = 9!/(6! * 3!)
Evaluate
C 9, 3 = 84
Expression (C) P8, 8
Apply the permutation formula
P n, r = n!/(n - r)!r!
So, we have
P 8, 8 = 8!/0!
Evaluate
P 8, 8 = 40320
Expression (D) C 9, 9
Apply the combination formula
C n, r = n!/(n - r)!r!
So, we have
C 9, 9 = 9!/(9! * 0!)
Evaluate
C 9, 9 = 1
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A water tank is built in the form of a right rectangular prism, with dimensions that measure 17.7 ft by 6.8 ft by 6.7 ft. How many cubic feet of water would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
it's a rectangular box with dimensions, 17.7 x 6.8 x 6.7 = 806.412
806.4 [tex]ft^{3}[/tex] to the nearest 10th
Guided practice (page 4)
Previous page
Distance from the ground in floors
11+
10+
of
8+
74
1
...
C
8 9 10
Which of the following statements are true about the elevator? Select all that apply.
Elapsed time in seconds
The elevator stayed 3 floors above the ground initially, then went to a lower floor.
The elevator stayed 3 floors above the ground initially, then went to a higher floor.
The elevator appeared to be moving faster when going up than when going down.
The elevator stayed 7 floors above the ground for 2 seconds.
Hint
Submit Answer
The correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is the distance of the elevator from the ground in floors.
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.Therefore, the correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.To solve more questions on functions, expressions and polynomials, visit the link below -
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Sort the following steps into ones that are required, and ones that are not required, to show that △abc ≅ △dbc.
Each corresponding side of the two triangles is equal, we can conclude that △abc ≅ △dbc.
Required:
1. Show that angles ∠A and ∠D are equal.
2. Show that angles ∠B and ∠D are equal.
3. Show that sides AB and BD are equal.
Not Required:
1. Show that angles ∠C and ∠D are equal.
2. Show that sides AC and CD are equal.
To show that △abc ≅ △dbc,
we need to use the Side-Side-Side (SSS) Congruence Theorem. This theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.
Therefore, to show that △abc ≅ △dbc, we have to show that each corresponding side of the two triangles is equal. Additionally, we have to show that the angles opposite of the corresponding sides are equal. This can be done using the Angle-Angle-Side (AAS) Congruence Theorem. This theorem states that if two angles and the side between them in one triangle are equal to the same two angles and the side between them in another triangle, then the two triangles are congruent.
To show that △abc ≅ △dbc, we must show that angles ∠A and ∠D are equal, angles ∠B and ∠D are equal, and sides AB and BD are equal. The other steps (showing that angles ∠C and ∠D are equal and sides AC and CD are equal) are not required, since they are implied by the equal angles and sides already established.
Once all of these equalities have been established, we can conclude that △abc ≅ △dbc.
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At 8 a.m., the hobbit left Beorn's and headed towards the Misty Mountains at 3 mph. 2
hours later, Gandalf left Beorn's and headed in the same direction. If Gandalf was 5 miles
ahead at noon, what was his speed?
Answer:
8.5 mph
Step-by-step explanation:
First find how far Hobbit traveled in 4 hrs (8AM - Noon)
3 mph x 4 hr = 12 miles
Now find Gandalf's speed:
Galdalf traveled the same 12 miles that Hobbit did PLUS 5 more miles in 2 hours (10AM -Noon) for a total of 17 miles
Speed = 17 mi / 2 hr = 8.5 mph
Given the arithmetic sequence:
5, 9, 13,...
Part A: What is the common difference AND how do you find it?
Part B: What are the 4th and 5th terms of this sequence?
Part A: The common difference is 4.
Part B: The 4th term is 17 and the 5th term is 21 of this sequence.
What do you mean by arithmetic sequence?
The difference between each term in an arithmetic sequence is a constant. To put it another way, we just add the same value repeatedly, indefinitely.
According to the given question,
We have the given information:
The arithmetic sequence:
5, 9, 13,...
Now, we need to find the common difference and we will find it in this way,
The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.
d = t2 - t1
= 9-5 = 4
So, the common difference is 4.
Then, we need to find the 4th and 5th terms of this sequence,
t4 = t3 + d
= 13+4
= 17
t5 = t4 + d
=17 + 4
=21
Therefore, the 4th term is 17 and the 5th term is 21.
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The common difference of this arithmetic sequence is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.
What in mathematics is an arithmetic sequence?Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a geometric sequence is raised by either multiplying by or dividing by a certain constant, k.
Briefing:Part A:
The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.
Therefore, the common difference (d) is equal to 9 - 5 = 4.
The 4th and 5th terms of this sequence are
Part B:
Using Arithmetic progression formula,
aₙ = a + (n- 1)d
where
n = nth term
a (first term = 5
d = common difference = 4
4th term of the sequence
a₄ = a + (n- 1)d
a₄ = 5 + (4 - 1)4
a₄ = 17
5th term of the sequence
a₅ = a + (n- 1)d
a₅ = 5 + (5 - 1)4
a₅ = 21
Hence the 4th and 5th term of this arithmetic sequence is 17 and 21.
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This figure is made up of a rectangle and half a circle find perimeter of the figure to the nearest 10th show your work please use 3.14 for pi
The required perimeter of the given figure will be 60.84 m.
We have been given the figure which is made up of a rectangle and half a circle.
We have to determine the perimeter of the given figure.
As per the given figure, the required solution would be as:
The required perimeter = 2 × (rectangle's length) + rectangle's width + circumference of half a circle
The required perimeter = 2 × 15 + 12 + π × 6
The required perimeter = 30 + 12 + 3.14 × 6
The required perimeter = 30 + 12 + 18.84
Apply the addition operation, and we get
The required perimeter = 60.84 m
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consider the following hypothesis test: h0: ha: m $ 20 m , 20 a sample of 50 provided a sample mean of 19.4. the population standard deviation is 2. a. compute the value of the test statistic. b. what is the p-value? c. using a 5 .05, what is your conclusion? d. what is the rejection rule using the critical value? what is your conclusion?
As a result, the test is significant and we can draw this conclusion that the population mean is less than 20.
A test statistic is what?A test statistic is a statistic used for testing statistical hypotheses. A test statistic, which is a tally of a data set that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.
a) Here, the test statistic is calculated as:
Z= [tex]\frac{p'-p}{\sqrt{(p(1-p)/n} }[/tex]
Z=[tex]\frac{19.4-20}{\sqrt{(20(1-20)/50} }[/tex]
Z= -2.12
Therefore -2.12 is the required test statistic value here.
b) Given that this is a one-tailed test, the following p-value was calculated using standard normal tables: p = P(Z -2.12) = 0.0169
The necessary p-value in this case is therefore 0.0169.
c) The test is significant in this case, and the null hypothesis can be rejected because the p-value is 0.0169 0.05, which is the level of significance. This means that there is enough data to conclude that the mean is less than 20.
d) For a significance level of 0.05, we have the following data from normal standard tables:
P(Z < -1.645) = 0.05
Therefore, the following is the rejection criteria in this case: Reject H0 if Z -1.645.
We can reject the null hypothesis here and draw the same conclusion as in the previous section because the test statistic value is -2.12 -1.645. As a result, the test is significant and we can draw this conclusion that the population mean is less than 20.
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Determine the domain of the following graph
Answer:
-1
Step-by-step explanation:
I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)
please help mee solve it, i would rlly appreciate it
Answer:
For question 6 & 8, the answers are shown on the pictures!For question 7, the answers are on the explanation.Step-by-step explanation:
Paul's Pizzeria: y = 15x
Leo's Pizzeria: y = 12x
Therefore, Paul's Pizzeria takes in more money per pizza <3
Find the characteristic polynomial and the eigenvalues of the matrix. 6 3 3 6 The characteristic polynomial is □ (Type an expression using λ as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice 0 A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) B. The matrix has no real eigenvalues.
The characteristic polynomial is P(λ) = λ² - 12λ + 27.
The real eigenvalues of the matrix are 3, 9. Answer A.
The full question is in the attachment. The characteristic polynomial from a matrix is P(λ) = |A - λI|
[tex]Matrix\:A\:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right)[/tex]A - λ
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \lambda \left(\begin{array}{cc}1&0\\0&1\end{array}\right)[/tex]
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \left(\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right)[/tex]
[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6 \:-\: \lambda&3\\3&6 \:-\: \lambda\end{array}\right)[/tex]
If matrix P [tex]\left(\begin{array}{cc}a&b\\c&d\end{array}\right)[/tex] than determinant of matrix P = |P| = ad - bc
P(λ) = |A - λI
P(λ) = (6 - λ) (6 - λ) - (3 × 3)
P(λ) = 36 - 12λ + λ² - 9
P(λ) = λ² - 12λ + 27
The eigenvalues
P(λ) = 0
λ² - 12λ + 27 = 0
(λ - 3) (λ - 9) = 0
λ - 3 = 0 or λ - 9 = 0
λ₁ = 3 λ₂ = 9
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URGENT!
in how many ways can 7 books be arranged in a shelf if three particular books must stay together?
Answer:
5040 ways
Step-by-step explanation:
We need to place 3 particular books so that they are always together.
let 3 books are one books
we have 5 books
these can be arranged in ⁵P5 = 5! = 12O
total books = 3 × 2 = 6
Required no. of books are 120×6 = 720.
The area of a right triangle with two equal sides of length s is 1/2s². Kelsey is making flags for
her favorite team's next hockey game. The flags are shaped like right triangles with two 8-
inch sides.
What is the area of each flag?
The area of the flag is 32 in²
Isosceles right triangle:The right-angled triangle that has two equal sides is known as the Isosceles right triangle. In other words, if an Isosceles triangle has two equal sides then the triangle is said to be an Isosceles right triangle.
The formula for the Area of an Isosceles right triangle is given by
Area = s²/2Where x is the equal sides of the triangle.
Here we have
The equal side of a right-angle triangled Flag is 8 inches
=> As we know Area right-angle triangle = x²/2
Area of the flag = 8²/2
= 64/2 = 32 inch²
Therefore,
The area of the flag is 32 in²
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What is an advantage of using a stem-and-leaf plot instead of a histogram? What is a disadvantage? O A. Stem-and-leaf plots show data clusters where histograms do not O B. Stem-and-leaf plots contain original data values where histograms do not. O C. Stem-and-leaf plots.easily organize data of all sizes where histograms do not O D. Stem-and-leaf plots graph qualitative data where histograms do not.
Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.
What is stem and leaf?The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.
The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.
The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.
Therefore, option B is the correct answer.
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Devon is considering taking out a 75000 loan for a 15 year period. How many monthly payments he has to make for the life of the loan?
Devon's monthly payment will be about 416.6
To make for the life of the loan.
What is interest ?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. The three types of interest include simple (regular) interest, accrued interest, and compounding interest.
Have given,
He considered to take lone about 75,000 for a 15 year period,
In 1 year he will be paid [tex]\frac{75,000}{15}[/tex] = 5000
Then in 1 month he will be paid [tex]\frac{5000}{12}[/tex] = 416.6
Devon's monthly payment will be about 416.6
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What are the 6 angle types?
Angles are 6 types.
What are different types of angles?1.Acute Angle: An acute angle is any angle that is less than 90 degrees and is between 0 degrees and 90 degrees.
2.Obtuse Angle: Opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90 degrees and less than 180 degrees. It is the angle that is between 90 degrees and 180 degrees.
3. Right Angle: A right angle is always 90 degrees in length. Acute angles are those that are less than 90 degrees, whereas obtuse angles are those that are higher than 90 degrees.
4. Straight Angle: A straight angle has a measured angle of 180 degrees. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line.
5.Reflex angle: The arms make an acute angle because this measurement is less than 90 degrees. What about the angle on the opposite side, though? What is the name of the larger angle that complements the acute angle? It is referred to as a reflex angle.
A reflex angle is any angle having a dimension higher than 180 degrees but less than 360 degrees (which corresponds to 0 degrees).
6.Complete Rotation: Entire rotation or full angle refers to an angle with a value of 360 degrees. When one of the arms extends completely, it is created.
Angles are 6 types.
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3. Mary is a real estate agent. One month she sold 7 houses at these prices: $171 000, $165 000, $178 000, $161 000, $174 000, $168 000, $240 000
3.a) What is the median price of the houses she sold?
3.b) Do you think the mean price is greater than or less than the median price of the houses sold that month? Why?
3.c) Which average do you think better represents a typical price of houses she sold that month? Why?
The median price of the houses sold will be equal to $171000 and yes, the mean price is greater than the median price of the houses.
What is Mean?Mean in mathematics is a quantity that falls somewhere between the extremes of a set. There are different types of meanings, and how they are calculated relies on the connection that is known about or is believed to control the other members.
a.
The median of given prices will be,
Let's arrange the given prices in ascending order,
161000, $165000, $168000, $171000, $174000, $178000, $240000
Then, the middle term is the median,
So, median = $171000
b.
Number of terms = 7
The mean of the given prices will be,
(171000 + 165000 + 178000 + 161000 + 174000 + 168000 +240000)/7
= 1257000/7
Mean = 179571.4286
Comparing mean and median, the mean price is greater than the median.
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Is 3x² a polynomial?
The expression given in question is not a polynomial because it could not satisfy the criteria for polynomial.
What is polynomial?The algebraic expression that contains two or more terms having different power of the same variables along with subtraction, addition or multiplication sign is termed as polynomial.
such as x² - 4x+7
In the above expression, there are different power of same variable x,
or x³+ 3x²+x-5
The terms are separated by either addition or subtraction sign.
What is the degree of a polynomial?We know that a polynomial expression contains different terms in where there is different power of same variables. The highest power is called the degree of polynomial.
As example, 4x³+2x²-3x+2
we have highest power 3 so this is called 3-degree polynomial.
What are the criteria of polynomial?We stated earlier that an expression can be said a polynomial whenever two or more terms which contain numbers and variables along with addition or subtraction operator. From the question we have a term 3xA² that contain a number and two variable x and A. There is no addition or subtraction sign. So, the term could not satisfy the criteria for polynomial. It is called monomial.
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In which triangle all the sides are equal and all the angles are also equal *?
When dividing 456.3 by 100, how should the decimal point be moved?
1. Move the decimal point three places to the right.
2. Move the decimal point two places to the right.
3. Move the decimal point three places to the left.
4. Move the decimal point two places to the left.
When dividing 456.3 by 100, how should the decimal point be moved is:
Add three places to the left of the decimal point.What is meant by decimal point ?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point. 12.5 is a decimal number, for instance.
In mathematics, the decimal system—also known as the Hindu-Arabic number system or the Arabic number system—is a positional numeral system that uses 10 as its base and calls for the use of 10 different numbers, including 0, 1, 2, 3, 4, 5, 6, 7, and 8. To indicate decimal fractions, a dot (decimal point) is also necessary.
We use decimals on a daily basis when dealing with things like money, weight, and length. Decimal numbers are used when higher accuracy is required than full numbers can provide.
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1. Find the altitude of an isosceles triangle with base 12 and congruent sides of length 10.
On solving the provided function, we can say that altitude of the given isosceles triangle is 6.63 unit.
What is an isosceles triangle?A triangle with two sides that have the same length is said to be isosceles. Let's carry out a little exercise to better comprehend this. Fold the corners of a rectangular piece of paper in half.
An isosceles triangle has the following characteristics: two equal sides and two equal angles. The two equal sides are referred to as the legs of the triangle, and the angle between them as the vertex angle or apex angle.T he base and the apex angle are divided by the perpendicular from the apex angle. The isosceles triangle is divided into two congruent triangles by the perpendicular, which is sometimes referred to as its line of symmetry.
[tex]12 ^2=10^2 +(a/2)^2\\ 144 -100 = a^2\\ 44 = a^2\\ a^2 =44 ; a =\sqrt{44} =6.63\\[/tex]
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What is SSS SAS AAS ASA?
Answer:
it is the conditions to show the triangle congruentStep-by-step explanation:
SSS:side,side,sideSAS:side,angle,sideAAS: angle, angle,sideASA: angle,side, anglea normal population has a mean of 59.8 and a standard deviation of 18.0. a sample of 10 will be taken. find the probability that the sample mean will be greater than 59.8. a) calculate the z score. (round your answer to 2 decimals.) b) find the probability that the sample mean will be greater than 59.8. (round your answer to 4 decimals.)
The z-score is 0 and the probability that the sample mean will be greater than 59.8 is 0.5000
How to determine the probability?From the question, the given parameters about the distribution are
Mean value of the set of data = 59.8Standard deviation value of the set of data = 18.0The actual data value = 59.8The z-score
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (59.8 - 59.8)/18.0
Evaluate
z = 0
The probability
The probability that the sample mean will be greater than 59.8 is then calculated as:
P(x > 59.8) = P(z > 0)
From the z table of probabilities, we have;
P(x > 59.8) = 0.5
Hence, the probability is 0.5000
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The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic inche) when x i meaured in feet. Write a rule for W. Then find W(2)
The rule for transformed function W(x ) = V(12x) is, W(x) = 1728 x³ - 864 x² and the value of W(2) is 10368 in³.
What is transformed polynomial function?Transforming a function means that the curve representing the graph "moves left, right, up and down" or "stretches " or "mirrors". For example, the graph of the function f(x) = x² + 3 can be obtained by simply shifting the graph of g(x) = x² up by 3 units. We have , function of Volume of box in cubic inches, V(x) = x³- 6 x² --(1)
also, an another function, W(x) = V(12x) repreent the volume (in cubic feet ) when x is meaured in inches. Now , understand the problem,
We are a function V whose inputs are in inches and whose outputs are in cubic inches . We are provide an another function W whose inputs are in inches and whose outputs are in cubic feet., W(x) = V(12x) makes sense because there are 12 inche in 1 feet. We are asked to write a rule for W and interpret the output for an input. Write the transformed function W(x) ,
W(x) = V(12x)
=> W(x) = (12x)³ - 6 (12x)²
=> W(x) = 1728 x³- 6× 144 x²
=> W(x) = 1728 x³ - 864 x²
Now, calculate W(2)
W(2) = 1728 (2)³ - 864 (2)²
=> W(2) = 13824 - 3456
=> W(2) = 10368 in³
When x is 2 feet , the volume of the is 8100 cubic inches.
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Complete question:
The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic feet) when x i meaured in inches. Write a rule for W. Then find W(2)
f(x) = -3 |x-1| +5; Find f(3)
Answer: f(3) = -1
Step-by-step explanation:
f(x) = -3 |x-1| +5
f(3), we just need to put 3 in for both the x
f(3) = -3 |3-1| +5
f(3) = -9 + 3 +5
f(3) = -1