using pascals triangle, find the 5th power of 25
Answers
The image below shows the pascal triangle.
The pascal triangle shows until the fifth power, where a = 25 and b = 0.
[tex]25^5=25^5+5\cdot25^4\cdot0+10\cdot25^3\cdot0^2+10\cdot25^2\cdot0^3+5\cdot25\cdot0^4+0^5=9,765,625[/tex]Hence, the answer is 9,765,625.
Related Questions
12⋅(1/4+1/3)to the 2nd power+2/3
Answers
Answer: 19/4 or 4 3/4 or 4.75
Step-by-step explanation:
calculate the sum
12(7/12)^2+(2/3)
use the properties of exponents
12x(49/144)+(2/3)
simplify the expression
(49/12)+(2/3)
calculate the sum
19/4 or 4 3/4 or 4.75
have a GREAT day!!
True or False: It does not matter which side you get the variable as stated by the symmetric property.
Answers
Answer: True
Step-by-step explanation: As the Symmetric property states you can put a variable on either side of a problem, or an equation.
the net of a rectangular prism is shown below each Square represents one square unit what is the total surface area of the cone
Answers
Given:
Area of each sqaure = 1 square unit
Let's find the total surface area of the net image.
From the image, the total number of squares we have is = 52.
The total surface area will be the total number of squares since each square represents one square unit.qu
We have 52 squares in total.
Therefore, the total surafce area of the rectangular prism is 52 square units.
ANSWER:
B. 52 square units
EO GEOMETRYVolume of a sphereThe diameter, D, of a sphere is 19.8 m. Calculate the sphere's volume, V.Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.
Answers
Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=19.8/2=9.9 m -----> the radius is half the diameter
pi=3.14
substitute given values
[tex]V=\frac{4}{3}\cdot3.14\cdot9.9^3[/tex]V=4,062.3 m3Final and of the unknown side rania answer to the nearest whole number 7 mm to 7 mm what is the answer
Answers
Round to the nearest whole number means round the tenth digit to the one digit, so
Divide 1 by 2
1/2 = 0.5, so we will add 0.5 and subtract 0.5 from 7
7 - 0.5 = 6.5
7 + 0.5 = 7.5, so
[tex]6.5\text{ }\leq\text{ 7 mm <7.5}[/tex]You can choose any number between them
[tex]6.5\approx\text{ 7}[/tex][tex]7.49\approx\text{ 7}[/tex]At a dinner table, the meal cost $22 and a sales tax of $1.87 was added to the bill. How much would the sales tax be on a $66 meal? What is the tax rate for the meals in this city?
Answers
Calculate the percentage for the tax rate
using this analysis
[tex]1.87\cdot\frac{100}{22}=8.5[/tex]The tax rate for meals in this city is 8.5%
Calculate the tax for the $66 meal.
[tex]66\cdot0.085\cdot=5.61[/tex]The tax for a $66 meal should be $5.61
Simplify the expression [tex]\sqrt[3]{32a^{7} }b\fracx^{9}[/tex] . Assume a ≠ 0 and b ≠ 0.
Enter the correct answer in the box.
Answers
The result obtained when we simplify the expression ³√(32a⁷b⁹) is ³√(2⁵ × a⁷) × b³
How to simplify ³√(32a⁷b⁹)The simplification of ³√(32a⁷b⁹) can be obatined as illustrated below:
³√(32a⁷b⁹)
We shall simplify the individual term. This is shown below
³√32 = ³√2⁵
³√a⁷ = ³√a⁷
³√b⁹ = b^(9/3) = b³
Combining the above, we have
³√(32a⁷b⁹) = ³√2⁵ × ³√a⁷ × b³
³√(32a⁷b⁹) = ³√(2⁵ × a⁷) × b³
From the above illustration, we can conclude that simplifying ³√(32a⁷b⁹) results in ³√(2⁵ × a⁷) × b³
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1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hoursto complete the book?
Answers
We have:
That in 1/4th of 24 hours someone reads 1/3rd of a book, in other words:
[tex]h=\frac{24}{4}\Rightarrow h=6[/tex]So in 6 hours someone reads 1/3rd of a book, now:
If in 6 hours someone reads 1/3 of a book, then how many hours will it take to read the whole book.
In order to solve for the ammount of hours to read the whole book, we multiply the ammount of hours it takes to read 1/3rd of the book (6h) times the total of the book (1 book) and divide by the ammount of book that is read in 6 hours (1/3rd); that is:
[tex]T=\frac{6\cdot1}{(\frac{1}{3})}\Rightarrow T=18[/tex]Therefore the total ammount of time it will take to read the whole book are 18 hours.
rewrite the expression in standard form (use the Fewest number of symbols and characters possible) a. 5g + yh
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a) 5y
b) 7de
c) 20yz
d) 90d
Explanation:[tex]1a)\text{ }5\times y=5y[/tex][tex]b)\text{ }7\times d\times e=7de[/tex][tex]\begin{gathered} c)\text{ }5\times2\times2\times\times y\times z \\ 5\times2\times2=20 \\ \text{ }y\times z\text{ = yz} \\ 5\times2\times2\times\times y\times z\text{ = 20yz} \\ \end{gathered}[/tex][tex]\begin{gathered} d)\text{ }3\times3\times2\times5\times d\text{ } \\ 3\times3\times2\times5\text{ = 90} \\ 3\times3\times2\times5\times d=\text{ 90d} \end{gathered}[/tex]The average life span in years of different species of zoo animals are shown: 35, 16, 12, 8, 14, 8, 5, 8, 1, 121. Indentify the number summary. Using 1.5 interquartile ranges up from Q3 and down from Q1, identify any outliers. Min:Max:Q1:Q2:Q3:IQR:Outliers:2. Sketch and label a box-and-whisker plot of the data. Use an appropriate scale.<-----I-----I-----I-----I-----I-----I-----I-----I-----I-----I-----I----->3. What is the mean average life span?Mean:4. What is the MAD for the average life span?MAD:5. Explain what the MAD means in the context of the data
Answers
1)First, lets arrange our data in ascending order:
[tex]1,5,8,8,8,12,12,14,16,35[/tex]notice that we have the following:
[tex]\begin{gathered} \min =1 \\ \max =35 \end{gathered}[/tex]now, since we have ten elements in your data set, we can find the median by adding the two central elements. In this case we have:
[tex]\begin{gathered} \operatorname{median}=\frac{8+12}{2}=\frac{20}{2}=10 \\ \operatorname{median}=10 \end{gathered}[/tex]Next, notice that we can divide our data set in two equal parts:
[tex]\mleft\lbrace1,5,8,8,8\mright\rbrace,\mleft\lbrace12,12,14,16,35\mright\rbrace[/tex]the median in these two subsets are going to be or first and third quartile, therefore, we have that:
[tex]\begin{gathered} Q_1=8 \\ Q_2=10 \\ Q_3=14 \end{gathered}[/tex]Now we can find the IQR:
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \Rightarrow IQR=14-8=6 \\ \text{IQR}=6 \end{gathered}[/tex]Finally, the outliers are the following for 1.5 interquantile:
[tex]\begin{gathered} 1.5\cdot\text{IQR}=(1.5)(6)=9 \\ \Rightarrow Outliers\colon Q_1-9=8-9=-1 \\ Q_2+9=14+9=23 \end{gathered}[/tex]2)The box and whisker plot would be the following:
3)We can find the mean with the following formula:
[tex]\operatorname{mean}=\frac{\sum ^n_{i=1}x_i}{n}[/tex]In this case, the mean is:
[tex]\begin{gathered} \operatorname{mean}=\frac{1+5+8+8+8+12+12+14+16+35}{10}=\frac{119}{10}=11.9 \\ \operatorname{mean}=11.9 \end{gathered}[/tex]therefore, the average life span is 11.9
$)We can find the mean absolute deviation (or MAD), with the following expression:
[tex]\text{MAD}=\frac{\sum ^{}_{}|x_i-\operatorname{mean}|}{n}[/tex]with this expression we can find out the variability of the dataset.
In this case, we have the following:
[tex]\begin{gathered} \text{MAD}=\frac{|1-11.9|+|5-11.9|+|8-11.9|+|8-11.9|+|8-11.9|+|12-11.9|+|12-11.9|+|14-11.9|+|16-11.9|+|35-11.9}{10} \\ =\frac{10.9+6.9+3.9+3.9+3.9+0.1+0.1+2.1+4.1+23.1}{10} \\ =\frac{59}{10}=5.9 \\ \text{MAD}=5.9 \end{gathered}[/tex]We have that the MAD for the average lifespan is 5.9
5) Since the mean absolute deviation is 5.9, we can estimate that the values of the dataset are approximately 5.9 units away from the mean. therefore, there is a high variability in the life span of the animals
A shirt is on sale for 25% off. Sandy paid $7.50 for the shirt. What was the shirt's regular price?
Answers
Ik cause I took the quiz
Hello! I need answer 1 solved, for geometry this is a question sheet!
Answers
1) We have to solve for x.
We have a right triangle, so we can apply the Pythagorean theorem to relate the side lengths.
As x is the hypotenuse, we can write:
[tex]\begin{gathered} x^2=9^2+15^2 \\ x^2=81+225 \\ x^2=306 \\ x=\sqrt{306} \\ x\approx17.5 \end{gathered}[/tex]Answer: x = 17.5
Convert 1.6 x 10-2 to standard notation.
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Recall that:
[tex]b\times a^{-x}=\frac{b}{a^x}.[/tex]Therefore:
[tex]1.6\times10^{-2}=\frac{1.6}{10^2}=\frac{1.6}{100}.[/tex]Simplifying the above result we get:
[tex]\frac{1.6}{100}=0.016.[/tex]Answer: 0.016.
A 95% confidence interval for the mean hours freshmen spent on social media per day was calculated to be (2.5 hr,3.1 hr). The confidence interval was based on an SRS of
size n=50 and was calculated using a Normal distribution. The population standard
deviation is (show all work).
Answers
The standard deviation of the population is 1.0823
Given
95% confidence interval
Mean fresh men hours on phone 2.5 hr, 3.1 hr
ME is calculated as follows:
Margin of Error = Z a/2 * (sd/ [tex]\sqrt{n}[/tex]) = (Upper
Where sd = standard deviation
n = size of population
interval - Lower Interval) / 2 = (3.1 - 2.5) / 2 = 0.3
Where,
x = Mean
Standard Deviation
(Confidence Level/100) - 1
Z = a/2× ([tex]sd/\sqrt{n}[/tex]), where
([tex]sd/\sqrt{50}[/tex]) = 0.3 = 1.96
Standard deviation equals [tex]0.3\sqrt{\frac{50}{96} }[/tex],
which is 1.0823
Hence the population standard deviation is 1.0823
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Convert the following phrase into a mathematical expression. Use x as the variable. Combine like terms when possible.A number multiplied by - 9, subtracted from the sum of 15 and two times the numberThe expression is(Simplify your answer.)
Answers
Given:
A number multiplied by - 9, subtracted from the sum of 15 and two times the number.
Let the number = x
A number multiplied by - 9 ⇒ -9x
The sum of 15 and 2 times the number ⇒ 15 + 2x
So, the expression will be ⇒ 15 + 2x - (-9x) = 11x + 15
So, the answer will be ⇒ 11x + 15
you are buying one flower for each member of the swim team to wear at an awards tonight there are 19 members on the team you have decided to buy pink roses and yellow roses the pink roses cost $3 and the yellow roses cost $2 you will spend $50 Let x represent pink roses and y represent yellow roses . If there's a solution graph them
Answers
Let:
x = Number of pink roses
y = Number of yellow roses
there are 19 members on the team, so:
[tex]x+y\le19[/tex]the pink roses cost $3 and the yellow roses cost $2 you will spend $50, so:
[tex]3x+2y\le50[/tex]so:
[tex]\begin{gathered} y\le19-x \\ y\le\frac{1}{2}(50-3x) \end{gathered}[/tex]Options1. is -2, -1, 2, 52. is subtract 25/2, add 25/2, subtract 25/4, add 25/4 and the second box is the same thing.6. is -5/2, -11/2, 5/2, 11/2.
Answers
Given the equation:
[tex]7=-2x^2+10x[/tex]Step 1: Factor -2 out of the variable terms
[tex]7=-2(x^2-5x)[/tex]Step 2: Divide both sides by -2.
[tex]\frac{7}{-2}=x^2-5x[/tex]5. Order from least to greatest -1/5, 10.5], 0.25, 5/10
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-1/5, 10.5, 0.25, 5/10
Step 02:
-1/5 = -0.2
5/10 = 0.5
from least to greatest
- 1/5 , 0.25 , 5/10 , 10.5
That is the solution.
The retail price for Jamaican allspice is $4.69 per ounce. You buy 8 ounces of allspice on sale for $4.62 per ounce. How much money do you save?
Answers
Answer:
Step-by-step explanation
56 cents
Explanation: The deal is 7 cents less per ounce, you need to buy 8 ounces, multiply 7 by 8, equaling 56 cents
The function f(x) is a cubic function and the zeros of f(x) are −2, 1 and 2. The y-
intercept of f(x) is -8. Write the equation of the cubic polynomial in standard
form.
Answers
In linear equation, p(x) = -2x³ - 6x² - 12x - 8 is the equation of the cubic polynomial in standard form.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written
p(x) = a( x - x₁ ) ( x - x₂) ( x - x₃ )
Where a is the leading coefficient.
We know the three roots of the polynomial −2, 1 and 2.
p( x ) = a( x + 2) ( x + 1 ) ( x + 2 )
Since the y-intercept of the polynomial is y= - 8 when x=0
- 8 = a( 0 + 2 ) ( 0 + 1 ) ( 0 + 2 )
- 8 = a * 4
- 8 = 4a
a = -8/4
a = -2
The polynomial is
p( x ) = -2( x + 2) ( x + 1 ) ( x + 2 )
We must write it in standard form, so we have to multiply all of the factors as follows
p(x) = -2 ( x + 1 )² ( x + 1 )
p(x) = -2 ( x² + 4 + 2x ) ( x+ 1 )
p(x) = -2 ( x₃ + 3x² + 6x + 4 )
p(x) = -2x³ - 6x² - 12x - 8
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Carol says that 83 + 96 + 74 is greater than 300.
Is Carol correct? Why or why not?
Answers
Answer:
that girl is wrong because if you add 83+96+74 it equals 253, and that is not greater than 300
Step-by-step explanation:
The length of a rectangle is 17 meters and the width is 12 meters. What is the perimeter of the rectangle? Do not include units in your answer.
Answers
We have that the perimeter is the addition of all the sides of the rectangle, so we have that
[tex]\begin{gathered} p=2\cdot l+2\cdot w \\ p=2\cdot17+2\cdot12 \\ p=34+24=58 \end{gathered}[/tex]I got 58 for my answer
Simplify: 3(s + 5)3s + 153s + 58s18s
Answers
The given equation is 3(s + 5)
and it will be simplified as
3(s + 5) = 3s + 15
So option A is correct
Two students were competing to have the
highest amount of sales at a bake sale.
Together they made $132. If each
student had made $15 more in sales, one
student would have made twice as much
as the other student.
How much money did the winning
student make, in dollars?
Answers
Amount of money made by thee winning student as per the given conditions is equal to $93.
As given in the question,
Let x dollars be the money made by winning student
And y be the amount made by other student
As per given conditions:
x + y = $132 ___(1)
x + 15 = 2(y+15)
⇒ x +15 = 2y +30
⇒ x-2y =15 ____(2)
Multiply (1) by 2 and add it to (2)
2x +2y = 264
x - 2y = 15
3x = 279
⇒x =$93
Hence, y = 132 -93
= $39
Therefore, amount of money made by thee winning student as per the given conditions is equal to $93.
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about 7 out of 20 homes have a dishwahser on a street with 60homes, how many would you expect to have?
Answers
On a street with 60 homes, about 7 out of 20 have a dish washer, and 21 expect to have one.
Explain about the equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A ratio can be used to resolve this 7/20=x/60 is the ratio.
20x=420
x=21
The answer is 21
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Greg bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7.5% per year, and for the laptop it was 8% per year. The total finance charges for one year were $400. How much did each computer cost before finance charges?
Answers
the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
From the question above, we can see that the laptop costs $350 more than the desktop, therefore, we say:
let x represent the cost of the laptop ;
then x-350 will be the cost of the desktop .
We can also see that the total finance charge of $400 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as follows:
400 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
252 26.75 = 0.155x
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that:
cost of desktop = x -350
therefore:
1,798- 350 = 1448
cost of laptop = $1798
cost of desktop = $1448
Thus, the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
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The question is below! I think the answer is: 10(8-i)
Answers
Notice that the GCD between 80 and 10 is 10. Therefore, we can factor the expression as following:
[tex]80-10i\rightarrow10(8-i)[/tex]The radius of a circle is 10 centimeters. What is the area?Give the exact answer in simplest form. _____ square centimeters (pi, fraction)
Answers
The radius of the circle can be computed using the equation
[tex]A=\pi r^2[/tex]The radius of the circle is provided in the problem, which is 10 cm. Just plug it in on the equation above and compute, we get
[tex]A=\pi(10cm)^2=100\pi cm^2[/tex]The exact answer is 100π square centimeters.
I am having trouble with this equation & how to correctly use the [ & ) when it comes to writing in interval notation.
Answers
We need to solve the inequality:
[tex]4\left(2-x\right)>\left(5x-7\right)-\left(x-10\right)[/tex]In order to do so, we can expand the expressions on each side, then apply the same operations on both sides of the inequality until we isolate the variable x and find the solution.
By expanding the expression, we obtain:
[tex]\begin{gathered} 4(2)+4(-x)>5x-7-x-(-10) \\ \\ 8-4x>5x-x-7+10 \\ \\ 8-4x\gt4x+3 \end{gathered}[/tex]Now, adding 4x to both sides, we obtain:
[tex]\begin{gathered} 8-4x+4x>4x+3+4x \\ \\ 8>8x+3 \end{gathered}[/tex]Subtracting 3 from both sides, we obtain:
[tex]\begin{gathered} 8-3>8x+3-3 \\ \\ 5>8x \end{gathered}[/tex]Then, dividing both sides by 8, we obtain:
[tex]\begin{gathered} \frac{5}{8}>\frac{8x}{8} \\ \\ \frac{5}{8}>x \\ \\ x<\frac{5}{8} \end{gathered}[/tex]Notice that x must be less than 5/8. Thus, 5/8 does not belong to the solution set. We represent this using (..., ...) for interval notation (open interval). Also, since there is no beginning to the interval solution, we write -∞ in replacement of the left boundary of the set.
Therefore, the solution set is:
Answer
[tex]\left(-\infty,\frac{5}{8}\right)[/tex]It says to find the area of the figure. Round to the nearest hundredth where necessary. Please Help!
Answers
Answer:
309.76 mm²
Explanation:
The given figure is a square with:
• Side length, s = 17.6 mm
The area of a square with side length, s is found by using the formula:
[tex]A=s^2[/tex]Therefore:
[tex]\begin{gathered} \text{The area of the figure}=17.6^2 \\ =17.6\times17.6 \\ =309.76\; mm^2 \end{gathered}[/tex].The area of the figure is 309.76 mm².
