The missing base for the expression x² = 100 is given by:
± x = 10.
How to find the missing base?The expression in this problem is given as follows:
x² = 100.
The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.
To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:
x = plus/minus square root of 100.
The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:
x = ± 10.
Plus/minus 10 because both of these statements are true:
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[tex]\frac{2}{5} a^{\frac{2}{2} } + C[/tex]
By simplifying 2/5 + [tex]a^{2/2}[/tex] C we get the solution as (2a + 5C) / 5.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.Start by resolving all of the terms enclosed in parenthesis to simplify mathematical equations using the order of operations. The exponents should then be solved, followed by any necessary multiplication. Division problems are next, followed by adding and subtracting to wrap things out.Given equation ,
2/5 + [tex]a^{2/2}[/tex] C
We know that , [tex]a^{2/2}[/tex] = a
So the equation becomes ,
2/5 a + C
By simplifying,
2a / 5 + C
= 2a / 5 + 5C / 5
By combining fractions ,
(2a + 5C) / 5
Thus solution is (2a + 5C) / 5 .
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Simplify the following expressions to simplest form using only positive exponents.
(49x^10y^16)^-5/2
(125x^-18y^9)^5/3
The equivalent expressions using only positive exponents are 1/(7x⁵y⁸)⁵ and (5y³/x⁶)⁵
How to simplify the expressions?Expression 1
From the question, the expression is given as
(49x¹⁰y¹⁶)⁻⁵/²
Express the radicals as roots
So, we have
(49x¹⁰y¹⁶)⁻⁵/² = √[(49x¹⁰y¹⁶)]⁻⁵
Take the square root of each of the factor in the bracket
This gives
(49x¹⁰y¹⁶)⁻⁵/² = (7x⁵y⁸)⁻⁵
Apply the negative exponent rule of indices
So, we have
(49x¹⁰y¹⁶)⁻⁵/² = 1/(7x⁵y⁸)⁵
Expression 2
From the question, the expression is given as
(125x⁻¹⁸y⁹)⁵/₃
Express the radicals as roots
So, we have
(125x⁻¹⁸y⁹)⁵/₃ = ∛[(125x⁻¹⁸y⁹)]⁵
Take the cube root of each of the factor in the bracket
This gives
(125x⁻¹⁸y⁹)⁵/₃ = (5x⁻⁶y³)⁵
Apply the negative exponent rule of indices
So, we have
(125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵
Hence, the equivalent expression is (125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵
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Tell whether the sequence is arithmetic. If it is, identify the common difference.
0, 7, 14, 21, ...
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The sequence is arithmetic and has a common difference of [_]
OmB. The sequence is not arithmetic.
Answer:
A
Step-by-step explanation:
the arithmetic sequence is the one in which the difference between the one and the next term is a constant.
0,7,14,21,28,35,42...
this is an arithmetic sequence with a common difference of [7]
Point A is graphed on the coordinate plane. What ordered pair represents point A?
Answer:
-7,7
Step-by-step explanation:
x-1
3
If-
A) 2
B) 4
C) 9
D) 10
F.
= k and k = 3, what is the value of x ?
Answer:
D
Step-by-step explanation:
Multiply both sides by 3
x − 1 = 9
Add 1 to both sides
x = 10
The circumference of a circle is 19π cm. What is the area, in square centimeters? Express your answer in terms of
When the circumference of a circle is 19π cm the area of the circle is
28.27 square centimeters
How to calculate the area of a circle ?Information given in the question include
The circumference of a circle is 19π cm
Area of a circle is given by
π r^2
where r = radius
π = constant = 3.124
circumference of a circle is given by 2πr
2πr = 19
πr = 9.5
r = 3.024
r = 3 cm
The area is solved as
= π * 3^2
= 28 .27square centimeters
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Choose the
system of inequalities that best matches the graph below.
The system of inequalities that best matches the graph is Option C
Step-by-step explanation:
To find the system of inequalities, we simply need to find the equation of each line.
Thus, let's find the inequality that is represented by each line.
Red Line:
First, let’s determine the slope. To do so, we can use the slope formula:
m = (y₂-y₁) / (x₂-x₁)
We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:
m = (-4+2) / (6-3) = -2/3
Therefore, the slope of the red line is 2.
To write the equation of the red line, we can use the slope-intercept form:
y = mx + c
Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:
y = ((-2/3)x) + (-3)
y = (-2/3)x -3
Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.
And since our line is shaded, our sign will be less than or equal to. Therefore:
y ≤ (-2/3)x - 3
Blue line:
Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:
m = (-3-0) / (3-0) = -3/3 = -1
So, the slope is -1.
We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:
y = -1x + 0
y = -x
Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:
y < -x
Thus, all together, our inequalities are:
y ≤ (-2/3)x - 3
y < -x
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A 12 pack of sodas is priced at $5.40 and a 16 pack of sodas is priced at $6.72. Which is a better buy?
Answer:
Step-by-step explanation:
5.40/12= 0.45
6.72/16=0.42
Answer:
The 16 pack
Step-by-step explanation:
Pack 1: $5.40 for 12
Find the price per soda by dividing the price by 12: $5.40 / 12 = $0.45 per canPack 2: $6.72 for 16
Find the price per soda by dividing the price by 16: $6.72 / 16 = $0.42Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.
70% of the light aircraft that disappear while in flight in a certain country are subsequently found. of the aircraft that are found, 60\`% have an emergency locator, whereas only 10\% of the aircraft not found have such a locator. suppose a light aircraft has disappeared. if the aircraft has an emergency locator, what is the probability that it will not be found? round your answer to three decimal places.
P(The aircraft is discoverd and has no locator) = P(discovered) x P(no locator/discoved =0.28)
Acc to our question-The information is based on the disappearance of the of the light aircraft in the flight in the in a certain country . 70% of the aircraft that disapear while in the flight were discovered . The probability that there is an emergency locator
in the aircraft given that it is discovered is 60% and the probability that the aircraft that has not discovered have an emergenncy locator is 90%.
a) To determine probiblity it wount be discoverd
Calculation
P(the aircraft is discovered and has a locator) = P(discovered) X P(locator/discovered)
= 0.7 x 0.6 = 0.42The probability of the flight discovered and has locator is obatained as given below:
P(The aircraft is discoverd and has no locator) = P(discovered) x P(no locator/discovered)
= 0.7 x 0.4 =0.28The probability of the flight not discovered and has a locator is obatained below.
P(The aircraft is not discovered and has a locator) = P(not discovered) x P (locator | not discorverd) = 1-0
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Randy is 8 years old. His brother is twice as old as Randy. Randy’s sister is three years younger than Randy.
Write an expression to represent the age of Randy’s brother.
Step-by-step explanation:
Randy is 8 years old. His brother is twice as old as Randy. Randy’s sister is three years younger than Randy. Write an expression to represent the age of Randy’s brother.
Randy = R = 8 years
Brother = B
B = 2R
solving:
B = 2R when R = 8
B = 2(8)
B = 16 years old
Answer: Its 16
Step-by-step explanation:
You need to take randy's age twice so you need to calculate 8x2= 16.
Find the value of x so that l//m. State the converse used
For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.
By applying the alternate exterior angle theorem to parallel lines (l//m), we have:
4x - 13 = 2x + 37
4x - 2x = 37 + 13
2x = 50
x = 50/2
x = 25
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how to write as one fraction 7/2a+4/a*a
The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a
What is a fraction?
In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.
Solution Explained:
First, we simplify the equation
= [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]
= [tex]\frac{7}{2a} + 4[/tex]
= [tex]\frac{7 + 8a}{2a}[/tex]
Therefore, the equation can be written as (7 + 8a) / 2a
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Jane is counting the cars going by her house. There are 3 blue cars, 12 white cars, and 1 red car. What is the ratio of white cars to blue cars?
Answer:
4:1
Step-by-step explanation:
12÷3=4
3÷3=1
white to blue
12 : 1
a company that manufactures and bottles apple juice uses a machine that automatically fills 20-ounce bottles. there is some variation, however, in the amount of liquid dispensed into the bottles. the amount dispensed has been observed to be approximately normally distributed with mean 20 ounces and standard deviation 1 ounce. determine the proportion of bottles that will have more than 18 ounces dispensed into them. (round your answer to four decimal places.)
The proportion of bottles that will have more than 18 ounces dispensed into them is 0.0228
Proportion relationship:
Proportion means a relationships between two variables where their ratios are equivalent and it is the way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Given,
A company that manufactures and bottles apple juice uses a machine that automatically fills 20-ounce bottles. there is some variation, however, in the amount of liquid dispensed into the bottles. the amount dispensed has been observed to be approximately normally distributed with mean 20 ounces and standard deviation 1 ounce.
Here we need to determine the proportion of bottles that will have more than 18 ounces dispensed into them and round the answer to the four decimal places.
Here we have to use tables to determine the proportion of bottles that will have more than 18 ounces dispensed into them.
Let us consider X denote the amount of juice dispensed.
Then it can be written as,
P (X >18) = P (Z > (20 - 18)/1)
=> P (X >18) = P (Z > 2)
=> 1 - Ф(2)
=> 1 - 0.9772
=> 0.0228
Hence the proportion of the bottles that will have more than 18 ounces dispensed into them is 0.0228.
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y
y< 2x-3
How would I graph this ?
The graph of the inequality is attached below.
We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.
y < 2x - 3
We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.
y = 2x - 3
We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.
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in how many ways can a community. of five be selected from eight students if two particular students are to be included.
To select the community, there are 20 ways available.
What is Combination?
A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.
Solution:
Since 2 particular students are to be included,
we have to arrange 3 students from 6 students.
nCr = n! / (n-r)!*r!
6C2 = 6!/ (6-3)! 3!
6C2 = 6*5*4*3!/ 3! * 3*2
6C2 = 5*4 = 20
Thereofre, there exists 20 ways of doing the above mentioned.
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Preston goes to the movies with $15 in his wallet. He buys
a ticket for $6.50 and two snacks for $1.75 each. How
much money does he have left?
Select the correct expression.
OA. 15-6.5-1.75
OB. 15-(6.5+ 2.1.75)
O C. 15-2(6.5+ 1.75)
OD. 15-6.5+2.1.75
Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)
What is an Algebraic Expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.
Given,
Total money Preston have = $15
He buys the ticket for = $6.50
And, two snacks = $1.75 each
so the cost of two snacks is = 1.75 * 2 = $3.5
Total cost for ticket and snacks = $3.5 + $6.50 = $10
Now, he spent money on snacks and ticket $10 and he have total money $15 so,
Preston left with = $15 - $10
= $5
Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)
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the school has $925 to spend on new books for the libray .each book costs $9.95. estimate how many books can be bought
The number of books bought by the school is 92.
Here it is given that the school spend $925 to buy new books for the library.
The cost of each book is $9.95
So we have to find the number of books that can be bought.
By dividing the total money spent by the cost of each book we get the number of books bought.
Let n be the number of books bought.
n × 9.95 = Total money spend on the books
As we know the total money spend on the books is $925.
So we get:
925 = n × 9.95
n = 925/ 9.95
= 92
Therefore the total number of books bought is 92.
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12. Choose the correct answer.
t
5/6
7/8
1/2
3/4
l'
m
Answer: angle 1 and 4
Step-by-step explanation:
nevaeh and michael are helping their friend nabhitha move. if nevaeh can move 6 boxes for every 24 boxes that michael moves, then how many boxes can michael move for every box that nevaeh moves? what is the enter
Answer:
Step-by-step explanation: I think it could be 5,0000
Help pls ASAP i am Limited on tile and I need someone to do this I need to do other assignments too
Answer:
78
Step-by-step explanation:
x + 12 = 90
x = 78
The difference between an Arithmetic Sequence and a Linear
Function:
O The Linear Function has a y-intercept.
O All the points on a Linear Function connect.
O The Domain of the Linear Function includes negative numbers.
O All of the above
All the statements about Arithmetic sequence and linear function are correct.
What is Arithmetic sequence and linear function?
When used in mathematics, the term "linear function" describes two different but related ideas: A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.
In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time.
Since the Linear Function has a y-intercept.
Also all the points on a Linear Function connect.
When a line slopes down from left to right, it has a negative slope. This means that a negative change in y is associated with a positive change in x.
That means the Domain of the Linear Function includes negative numbers when the function is decreasing.
Therefore, all the statements are correct.
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Write down the two district properties between parellelograml and trapezium
You can see pic..
Sophia earned $36 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
If you add a prime number to itself, is the sum composite or prime?
Answer: The sum of two prime numbers is always even (which is composite).
Hope this helped :)
The volume of box A is 64 cubic inches. The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches. Can a baseball fit in box A?
Yes, a baseball fit in box A.
What is Volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.
Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.
Given:
The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.
So, the maximum value of Circumference
2πr = 9.5
r= 9.5/ 2 x 3.14
r = 1.472 inch
So, Volume of ball = 4/3 πr³
Volume of ball = 4/3 x 3.14 x (1.472)³
Volume of ball = 13.36 inch³ < 64 inch³
Hence, it will fit inside the box.
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a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. the professor has informed us that 8.75 percent of her students received grades of a. what is the minimum score needed to receive a grade of a?
The minimum score needed to receive a grade of 'a' is 87.92
Given that,
At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.
Mean = μ = 73
Standard deviation = σ = 11
Using the standard normal table,
⇒ P(Z > z) = 8.75%
⇒ 1 - P(Z < z) = 8.75%
= 1 - P(Z < z) = 0.0875
= P(Z < -1.36) =1- 0.0875
= P(Z < 1.3563) =0.9125
∴ Z = 1.3563 ( Using standard normal z-table )
Using z-score formula ;
x= z * σ + μ
x=1.3563 * 11 + 73
x=87.92
So, the minimum score needed to receive a grade of 'a' is 87.92
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Find an equation for the perpendicular bisector of the line segment whose
endpoints are (6, -5) and (-2, -9)
The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.
What is standard form equation?Ax+By=C is the standard form for linear equations in two variables. 2x+3y=5, for example, is a standard linear equation. It is relatively simple to find both intercepts when an equation is given in this form (x and y).In mathematics, a number is written in standard form. The simplest form of decimal numbers is standard form, which can be easily read and written. The standard form of the decimal number 0.007, for example, is 7 10-3. It can be difficult to read or write very large or very small numbers at times. As a result, we write them in standard form.The standard form of numbers (also known as "scientific notation") has different meanings depending on where you are in the world.Therefore,
The coordinates of the end points:
(6, -5) and (-2, -9)
((6, -5) +(-2, -9))/2
= ((6,-9)/2, (-2, -5)/2)
= (1.5, 3.5)
The difference in endpoint coordinates will be;
(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)
Then the ratio of these values, so we need to divide both by the common factor of 2:
(Δx, Δy) = (7, 2)
A line perpendicular to this segment through the point (h, k) can be written as;
Δx·x +Δy·y = Δx·h +Δy·k
7x ,2y = 7(2) 2(4)
7x, 2y = 6 .
Hence the standard form equation for the perpendicular bisector will be; 7x ,2y = 6 .
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light bulbs are packed in boxes of 10. inspectors randomly select 3 of the 10 light bulbs. the box contains exactly 4 defective light bulbs. using a hypergeometric probability distribution, find the following to four decimals. a defective bulb is considered a success. what is the probability that exactly four of the selected is defective? enter the answer as a number to one decimal.
The probability that exactly four of the selected bulbs from the pack of 10 bulbs is defective is 1/120.
Define the hypergeometric probability distribution?When sampling from such a low population without replacement, the hypergeometric distribution represents a discrete probability distribution which determines the likelihood that an event occurs k times in n trials. In terms of the aspect of sampling without replacement, this distribution is equal to the binomial distribution.For the given question;
Total bulbs = 10Defective bulbs = 4Selected bulbs = 3Thus, the probability that exactly four of the selected is defective.
P = ⁴C₄ / ¹⁰C₃
P = 1/120
Thus, the probability that exactly four of the selected is defective is 1/120.
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find the distance between the points (-16,11) and (16,4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]