Answer: 16.16 in
Step-by-step explanation:
10^2 + x^2 = 19^2
100 + x^2 = 361
x^2 = 261
x = 16.16 in
1. Given the data: 12, 14, 21, 19, 25, 29, 26,
21, 15, and 18. Calculate the standard deviation,
the mean, and the interquartile range using the
calculator.
For the data 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18.
the mean is 20
the standard deviation is 3.7
the interquartile is 10
How to solve for the meanFor the data 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18. the mean is calculated as follows
= sum of data / number of data
sum = 200
number of data = 10
mean (x bar) = 200 / 10
= 20
standard deviation
standard deviation is the square root of the ratio of sum of squares to number of samples
sum of squares = (x - x bar)²
= (12 - 20)² + (14 - 20)² + (21 - 20)² + ......+(21 - 20)² + (15 - 20)² + (18 - 20)²
= 274
standard deviation = √(274 / 20) = 3.7
Interquartile range = upper quartile - lower quartile
raw data = 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18
arranged data = 12, 14, 15, 18, 19, 21, 21, 25, 26, 29,
upper quartile = 25
lower quartile = 15
Interquartile range = 25 - 15 = 10
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Which of the following statements is true for all real symmetric matrices Mcq?All the eigenvalues are realAll the eigenvalues are positiveAll the eigenvalues are distinctSum of all the eigenvalues is zero
Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.
Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.
All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.
Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T
Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.
Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.
A=-(A)^T
Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.
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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.
To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.
To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].
The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.
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Consider a game in which each play costs one nickel (1¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?
The expected profit, in cents, for a player who plays 1 game is 5.25 cents.
How to obtain the expected profit?The distribution that models the profit of a player for a single game is given as follows:
P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.
P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.
P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.
P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.
The expected value of a discrete distribution is computed by adding the total of each outcome and multiplying it by its probability, as follows:
E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25
E(X) = 5.25 cents.
Hence, the expected profit is 5.25 cents
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All the gummy machines at a candy factory work at the same rate: Six machines working simultaneously can complete big order in 22 hours. How many hours would it take t0 fill the order if the number of working machines decreased by a factor of 2? er: hours
The numbers of hours taken to fill the order if the number of working machines decreased by a factor of 2 is; 44 hours
How to find the rate of work?We are given;
Numbers of hours a work is complete by 6 machines = 22 hours
Now, we know that the number of hours required to complete a work is inversely proportional to the number of machines used.
Therefore, If the number of working machines decreased by a factor of 2, then the number of hours will be increased twice.
Therefore, we can say that;
The numbers of hours taken to fill the order = (22 * 6)/3
= 44 hours
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Shawna bought an antique writing
desk marked down from $6,116 to
$1,951. What percentage is the
discount?
(round your answer to the nearest percent)
Percent changes are measured by (the change in amount) divided by (the starting amount).
In this case, you'd have
[tex]\dfrac{6116-1951}{6116}=\dfrac{4165}{6116}\approx 0.6810[/tex]
This is about a 68% discount.
Mark’ mother i planning to borrow $25,000 to remodel the retaurant he own. He contacted everal loan companie, and he i comparing two different option. Company 1 offer an interet rate of 5. 25%. Company 2 offer an interet rate of 8. 5%. Both loan option involve imple interet and mut be repaid in exactly 3 year. How much more will mark’ mother pay in interet if he chooe to borrow the money from company 2?
If Mark’s mother borrows the money of $25,000 from company 2 which offers a rate of 8.5% for 3 years, she needs to pay the charge of $6375.
How to calculate the simple interest?Interest is the cost of borrowing or saving money. Simple interest is an easy method to calculate the interest charge on a loan.
As its name, calculating the simple interest is simple and quick. We only multiply the money we borrow or deposit, by the period, then multiply them by the interest rate applied by the bank or any financial institution chosen.
The formula for calculating the simple interest is
P x R x T
P means principal or how much money we borrow or save
R means rate or how many percentages of interest applied
T means time or how long we borrow or save the money
By using the formula mentioned before, the simple interest would be
$25,000 x 8.5% x 3 = $6375
Thus, the amount of simple interest paid is $6375 and the total amount paid is $25000 + $6375 = $31,375
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a cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. how much work is done in pumping a full tank of water up to ground level? (the water weighs 9800 newtons per cubic meter.)
The work is done in pumping a full tank of water up to ground level is 470400πNm.
Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities
The radius of the layer = 2m
V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3
Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)
Weight of the water = 9800 frac=9800 m 3 N
So, weight of the layer = 39200 pi Delta y=39200πΔy
distance layer is moved =5-y=5−y
W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy
=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy
=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04
=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.
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21. Calculate the future value of a $7,000 after 9
years, when there is an interest rate of 2.05%
with quarterly simple interest payments.
[A] $7,322.88
[D] $8,419.30
[B] $8,414.35
[E] $7,527.31
[C] $6,148.05
The solution is Option A.
The amount after 9 years with an investment of $ 7000 at a simple interest calculated quarterly at rate 2.05 is $ 7,322.88
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount invested P = $ 7,000
The rate of interest R = 2.05 %
The time period t = 9 years
Since the interest is calculated quarterly , t= T/4
Now , the simple interest is calculated by the formula
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Substituting the values in the equation , we get
Simple Interest I = [ ( 7000 x 2.05 x 9 ) / 4 ] / 100
On simplifying the equation , we get
Simple Interest I = ( 129150 ) / 400
Simple Interest I = $ 322.875
I = $ 322.88
Now , the amount after 9 years = initial amount P + Interest I
Amount after 9 years = 7,000 + 322.88
Amount after 9 years = $ 7,322.88
Hence , the amount after 9 years is $ 7,322.88
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Can anyone please help me out with this question?
a) The percentile rank of a score of 71 on this test is given as follows: 33rd percentile.
b) Victor's score, which is the 60th percentile, is given as follows: 84.
What is a percentile?A measure is said to be in the xth percentile of the data-set if it the bottom separator of the bottom x% of measures of the data-set and the top (100 - x)% of measures, that is, it is greater than x% of the measures of the data-set.
The ordered data-set in this problem is given as follows:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96.
The data-set is composed by 15 scores, and 5 is the 5th score in the data-set, hence the percentile rank of a score of 71 on this test is calculated as follows:
5/15 = 0.33 = 33rd percentile.
The 60th percentile is the score at the position given as follows:
0.6 x 15 = 9th score = 84.
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The ratio of the same side interior angles of two parallel lines is 1:14. find the measures of all eight angles formed by the parallel lines and transversals.
Answer:
x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.
Step-by-step explanation:
The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.
Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.
Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.
Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.
In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.
PLS HELP FOR 100 POINTS PLS
Answer:
it is 3
Step-by-step explanation:
I don't know I would
Answer:
it is 3
Step-by-step explanation:
It Basile 9 divide by 4
PLEASE HELP ASAP
90 students sat a Maths exam. On the way out of the hall, they were asked whether they found it hard, OK or easy. Here are the results:
Show the results on a pie chart. Remember to include full workings, so it is clear how you have calculated each angle.
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
The price of a new phone is $960.00 and the rate of tax is 7.6%.what is the amount of sales tax?
Answer: $72.96
Step-by-step explanation:
7.6% = 0.076
Take 960.00 times 0.076 = $72.96
Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 8cm,15cm
Answer:
hypotenuse is 17cm
Step-by-step explanation:
According to Pythagoras theorem,
AC²=AB²+BC²
AC² = 8²+15²
AC = √64+225
AC =√ 289
AC =17cm
Which division problem can be described using this model?
A. 2÷1/10
B. 2÷1/5
C. 1÷1/10
D. 2÷5
Answer:
I believe that the answer is 2/5 because all of the other answers equal 10 (for b and c) or 20 (for a)
Step-by-step explanation:
Select all the correct answers. which two equations can you use to find the adult and child admission fees for a puppet show? let a represent the fee for adults and c represent the fee for children. adults children admissions collected day 1 45 30 $315 day 2 50 40 $370 45c 30a = 315 45a 50c = 315 45a 30c = 315 50c 40a = 370 50a 40c = 370
The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, two equations can you use to find the adult and child admission fees for a puppet show
Let a represent the fee for adults
Let c represent the fee for children.
On day 1 number of adults = 45
So, fees of 45 adults = 45a
On day 1 number of children= 30
So, fees of 30 children = 30c
Total collection on day 1 = 315
Therefore, equation is 45a + 30c = 315
On day 2 number of adults = 50
So, fees of 50 adults = 50a
On day 2 number of children = 40
So, fees of 40 children = 40c
Total collection on day 2 = 370
So, equation = 50a + 40c = 370
Hence, The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370
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A cell phone is originally priced at $120. The store owner gives a discount and the cell phone is now priced at $90. Find the percentage discount for the cost of the cell phone,.
Answer:
25%
Step-by-step explanation:
To find the percentage discount for the cost of the cell phone, we need to first find the difference between the original price and the discounted price:
$120 - $90 = $30
Then we need to divide this amount by the original price and multiply by 100% to express the result as a percentage:
($30 / $120) * 100% = 25%
Therefore, the percentage discount for the cost of the cell phone is 25%.
Consider the values shown. What
place value must the answer be
reported to?
67.4 +43 +30 + 42.10 =
A. tens place B. ones place
C. tenths place
D. hundredths place
Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar. He found 15% did not have enough peanuts. How many candy bars do not have enough peanuts if the factory produces 20,000 candy bars?.
Here every 50th candy bar is tested . It is a sampling interval .
What does "systematic sampling" mean?
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.
The advantages of simple random sampling can be imitated if the population is arranged randomly.
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.
Here every 50th candy bar is tested . It is a sampling interval .
Therefore he use systematic sampling plan.
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a party store has 54 packs of plates in stock. the packs are either sets of 8 or sets of 12. if the store has 496 total plates in stock, how many plates would a customer but if he or she buys all of the packs of 12 that the store has in stock?
If the customer purchases every pack of 12 which the shop has 192 plates in stock.
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the matching variable, rewrite the value's original equation.Total number of packs of plates = 54.
The set are either sets of 8 or sets of 12.
Let x represent the overall number of 12-plate packets.
There will therefore be in total packs of 8 plates: 54 - x.
Thus,
8(54−x) + 12x = 496
432 − 8x + 12x = 496
4x = 64
x = 16
Thus, there are 16 packs of 12 plates in the store.
So, if a consumer purchases all of the 12-packs of plates, he will ultimately purchase 1216 = 192 plates.
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Write in standard form:
8.254 x 10^6
•Type your answer using commas to show place value.
•Type your answer with NO spaces
The number is the standard from is given by the equation A = 8.254 x 10⁶
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 8.254 x 10⁶
On simplifying the equation , we get
A = 8.254 x 1000000
Multiplying the number , we get
A = 8,254,000
Now , the number can also be written as
A = 8254000
So , the standard form of the number A is given by the equation
A = 8.254 x 10⁶
Hence , the number is A = 8.254 x 10⁶
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Simplify: -3x + 6 - 3x - 24 + 2y
-6x + 2y - 18
2y - 18
6x + 2y - 30
None of these choices are correct.
Answer:
To simplify the expression -3x + 6 - 3x - 24 + 2y, you can start by combining like terms.
-3x and -3x are both negative, so they can be combined to give -6x.
6 and -24 are both constants, so they can be combined to give -18.
So the simplified expression is: -6x - 18 + 2y
If you want to write the expression in standard form, you can rearrange the terms to give: 2y - 6x - 18
CORRECT ME IF I'M WRONGIf ST =
2v 59, RU= -v + 83, and PQ = v, what is the value of v?
Answer:
El valor de la variable b se corresponde con:
a) b = 0,25
b) b = 9
c) b = 125
4 1/7 divided by 2/3
Exact Form: 87/14
Decimal Form: 6.21428571... or 6.21
Answer: 6.21
Step-by-step explanation:
80085
write an equation of the circle with center (-6,8) and radius 9
Answer:
(x + 6)^2 + (y - 8)^2 = 81
Step-by-step explanation:
in need some help. i cant figure this out.
Answer:
x = 1.28
Step-by-step explanation:
Given equation:
[tex]3 \frac{1}{2}x-6=2-2\frac{3}{4}x[/tex]
Add 2³/₄x to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2-2\frac{3}{4}x+2\frac{3}{4}x[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2[/tex]
Add 6 to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6+6=2+6[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x=8[/tex]
Rewrite the mixed numbers as improper fractions:
[tex]\implies \dfrac{3 \cdot 2+1}{2}x+\dfrac{2 \cdot 4+3}{4}x=8[/tex]
[tex]\implies \dfrac{7}{2}x+\dfrac{11}{4}x=8[/tex]
Make the denominators of the fractions the same:
[tex]\implies \dfrac{7 \cdot 2}{2 \cdot 2}x+\dfrac{11}{4}x=8[/tex]
[tex]\implies \dfrac{14}{4}x+\dfrac{11}{4}x=8[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{14+11}{4}x=8[/tex]
[tex]\implies \dfrac{25}{4}x=8[/tex]
Multiply both sides by 4:
[tex]\implies 4 \cdot \dfrac{25}{4}x=4 \cdot8[/tex]
[tex]\implies 25x=32[/tex]
Divide both sides by 25:
[tex]\implies \dfrac{25x}{25}=\dfrac{32}{25}[/tex]
[tex]\implies x=\dfrac{32}{25}[/tex]
Convert the improper fraction to a mixed number:
[tex]\implies x=1 \frac{7}{25}[/tex]
The value of x as a decimal:
[tex]\implies x=1.28[/tex]
points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. is the meaning of _____
Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints is the meaning of perpendicular bisector theorem
The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment ,then it is equidistant from the segment's endpoints.
The perpendicular bisector of a triangle is the line segment that is drawn from a vertex to the opposite side bisecting the side at a right angle. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts. The point at which all the three perpendicular bisectors of a triangle meets is called the circumcenter of a triangle.
It is the meaning of perpendicular bisector theorem.
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In the figure above, is AB || CD?
1. If m 2 5 = 30 and m 2 3 = 150?
A. Yes because angles 5 and 3 are same-side interior angles.
B. Yes because angles 5 and 3 are alternate interior angles.
C. Yes because angles 5 and 3 are vertical angles.
OD. No because angles 5 and 3 are vertical angles.
O E. No because angles 5 and 3 are corresponding angles.
F. No because angles 5 and 3 are alternate interior angles.
Answer:
the answer is yes because angles 5 and 2 are same side interior angles and same side interior angles add up to 180*.
Step-by-step explanation:
Make sure not to be fooled by the "it looks like it" theorem. Teachers will try to trick you by making the lines look not parallel. All you need to look at are if the angles are congruent or supplementary based on the theorems you hopefully were taught in class. Wow what has brainly done I sound like a teacher lol.
45 − (−28) = A) −73 B) −17 C) 63 D) 73
Answer:
(d) 73
- and - are plus so 45+28
Step-by-step explanation:
Answer:
D) 73
Step-by-step explanation:
-)- basically means plus so 45 + 28 is ... 73,so that's your answer!
6(x - 3)2(4x - 3) = 6
0x = 3
0x = -9
0x = 4
0x = 9
The two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
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 equation as follows -
6(x - 3).2(4x - 3) = 6
We have the equation as -
6(x - 3).2(4x - 3) = 6
12(x - 3)(4x - 3) = 6
(x - 3)(4x - 3) = 6/12
(x - 3)(4x - 3) = 1/2
x(4x - 3) - 3(4x - 3) = 1/2
4x² - 3x - 12x + 9 = 1/2
4x² - 15x + 9 = 1/2
2(4x² - 15x + 9) = 1
8x² - 30x + 18 = 1
8x² - 30x + 17 = 0
(x - 0.696)(x - 3.054) = 0
(x - 0.696) = 0 and (x - 3.054) = 0
x = 0.696 and x = 3.054
Therefore, the two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
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