we know that [tex]r[/tex]
area of the circle is equal to
A= [tex]\pi[/tex] × [tex]r^{2}[/tex]
solve for [tex]r[/tex]
[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]
for A=60cm2
[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]
we know that
[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5
=2[tex]\sqrt{15}[/tex]
so,
[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]
2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex] × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]
= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm
this means the answer is-
2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]
A, B, C, D, E, F, G & H form a cuboid.
AB= 5.4 cm, BC = 3.4 cm & CG = 6.7 cm.
Find HC rounded to 1 DP.
Refer to the attachment for the diagram:
The length of HC rounded to 1 DP = 9.3 cm²
What is a cuboid?
A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.
From the figure,
length (l)= 5.4 cm = AB
width (w)=3.4 cm = BC
height (h)= 6.7 cm = CG
Formula:
Length of diagonal = √(l²+w²+h²) = √(5.4²+3.4²+6.7²) = 9.25 cm²
Rounded to 1 decimal point:
9.3 cm²
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a simple random sample of 40 items resulted in a sample mean of 25. the population standard deviation is 5. what is the standard error of the mean? (round your answer to two decimal places).
The standard error of the mean is approximately 0.79 (rounded to two decimal places).
Define standard error ?
The standard error is a statistical term that measures the variability of a sample mean or an estimate of a population parameter from its true value. It is the standard deviation of the sampling distribution of the mean. In simpler terms, the standard error measures how much the sample mean varies from the true population mean. A smaller standard error indicates that the sample mean is more likely to be representative of the population mean, while a larger standard error suggests that the sample mean may not be as reliable.
The formula for the standard error of the mean is:
[tex]SE = \frac{\sigma }{\sqrt{n}}[/tex]
Where σ is the population standard deviation and n is the sample size.
Substituting the given values:
[tex]SE =\frac{5}{\sqrt{40}}[/tex]
SE ≈ 0.79
Therefore, the standard error of the mean is approximately 0.79 (rounded to two decimal places).
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A school of 38 teachers has 15 married women. If 6 of the teachers are couples, how many of the teachers are neither married nor have their spouses not in the school?.
Answer:
17
Step by step explanation
15-6=21
38-21=17
what is the inequality
Answer:-4<x<=5
Step-by-step explanation:
The white dot is above -4 and the filled in dot is above 5. Put that together plus the correct inequality signs and you get -4<x<=5
Answer: [tex]-4 < x\leq 5[/tex]
Step-by-step explanation:
The inequality ends at 4 and it is colored white so x must be greater than -4 therefore the first expression is x > -4 or -4 < x.
The other side of the inequality ends at 5 and it's colored black so x is less than or equal to 5. Therefore the second expression is [tex]x\leq 5[/tex].
if we merge the two equations together than we would get [tex]-4 < x\leq 5[/tex].
I hope that helped you.
:)
Question 6(Multiple Choice Worth 1 points)
(05.07 MC)
A scatter plot is made to model the amount of money left to pay on a car loan. The data used for the scatter plot are shown in the table:
Number of Months 3
Money Owed $19,500 $18,500 $21,500 $20,000 $22,000 $19,000
5
1
What does the y-intercept of the model represent?
O The monthly payments
The original amount of the loan
2
O The number of months it takes to pay off the loan
The amount of the loan that has been paid that month
0
4
Correct option is third option - " the original amount of the loan "
What is linear equation ? A linear equation, a first-order polynomial, that is, H. The sum of a series of terms, each of which is the product of a constant and a variable to the first power, equals the constant. In particular, linear equations in n variables have the form a0 + a1x1 + ... + anxn = c. where x1,...,xn are variables, coefficients a0,...,an are constants, and c is a constant. With multiple variables, the equation may be linear in some variables and non-linear in others. So the equation x + y = 3 is linear in both x and y, but x + y2 = 0 is linear in x but not in y. An equation of two linear variables represents a straight line in Cartesian coordinates. If the constant term c = 0, the line passes through the origin. A linear equation is an algebraic equation of the form y=mx+b. The above is sometimes called a "linear equation in two variables" where y and x are variables.Calculationx value would be the time in months and y value would be the loan amount that is left.
The y-intercept is basically the point where x is 0. So, we can say the y-intercept would be when time is 0.
That's basically when the loan started and the y-value represents the full loan amount., which is $22,000.
correct option is third option -- "the original amount of the loan".
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a=4,n=8,7=2,x=10
do anybody know
what the answer
is;l
Answer: The answer to this question would either be 8 or it would be 7.
Which expression is equivalent to 5m - (2m - 8) + 12 + 6m?
[tex]=5m-2m+8+12+6m\\=5m-2m+6m+8+12\\=3m+6m+20\\=9m+20[/tex]
The answer is 9m+20,it is equivalent to the expression in the question.
i need help asap show your work
Answer:
G. 12
Step-by-step explanation:
Step 1: Use PEMDAS to start solving
Start solving by following the following:P: ParenthesesE: ExponentsM: Multiplication [or]D: DivisionA: Addition [or]S: Subtraction*Note: After solving any exponents, you solve from left to right. Also, when solving from left to right multiplication or division can be solve; it depends on which one occurs first. The same goes for addition and subtraction; if subtraction occurs before addition, then you subtract first.Step 2: Solve the problem
*Note: Absolute value is considered the same as parentheses.[tex]5-|7-9|+3^{2}[/tex][tex]5-|-2|+3^{2}[/tex]*Note: Absolute value is the distance a number is from zero, so it is always positive.[tex]5-2+3^{2}[/tex][tex]5-2+9[/tex][tex]3+9[/tex][tex]=12[/tex]HELP ASAP!!
Match each equation on the left to its solution on the right.
Some answer choices on the right will be used more than once.
2(6+4x)= 8x + 6
2(4x − 2) = 10x – 6
7+x=2x+6
2x+2=-2(1-x)
x = all real numbers
x = 1
no solution
Answer:
I believe that these are the answers.
Step-by-step explanation:
1. 2(6+4x)=8x+6 No Solution
2. 2(4x − 2) = 10x – 6 x=1
3. 7+x=2x+6 x=1
4. 2x+2=-2(1-x) No Solution
Hope this helps
Answer:
Step-by-step explanation:
2(6 + 4x) = 8x + 6
12 + 8x = 8x +6
12 -6 + 8x = 8x + 6 -6
6 + 8x = 8x
6 + 8x - 8x = 8x -8x
6 = 0
no solution
2(4x -2) = 10x -6
8x -4 = 10x -6
8x - 4 +4 = 10x -6 +4
8x = 10x - 2
8x - 10x = 10x -10x -2
-2x = -2
-2x/-2 = -2 /-2
x = 1
7 + x = 2x +6
7 -6 + x = 2x +6 -6
1 + x = 2x
1 + x -x = 2x -x
1 = x
2x + 2 = 2(1 - x)
2x + 2 = 2 - 2x
2x +2 -2 = 2 -2 - 2x
2x = -2x
2x + 2x = -2x + 2x
4x = 0
4x/4 = 0/4
x = 0
I could not get x = all real numbers for any of the equations.
examples of one solution
Answer:I can’t see image on mobile
Step-by-step explanation:
h
pamala's age is 2 * jiri's age the sum of their ages is 48 what is Jiri's age
Answer:
16
Step-by-step explanation:
p = 2j
p+j = 48
2j + j = 48
3j = 48
3/3 j = 48/3
j = 16
Please help me with this and also remember your answer has to be step by step
The two figures above are congruent. Find the measure of the angle that isn't labeled on either figure.
The measure of the angle that isn't labeled are:
∠B = 100
∠K = 100
∠L = 41
∠M = 86
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
Two congruent figures.
Each figure's total sum of the angles must be 360.
The figures are congruent so the corresponding angles must be equal.
From the first figure we get,
∠A = 133 ( Corresponding angles )
∠A + ∠B + ∠C + ∠D = 360
133 + ∠B + 41 + 86 = 360
∠B = 360 - 260
∠B = 100
Now,
∠k = ∠B = 100
∠L = ∠C = 41
∠M = ∠D = 86
Thus,
The measure of the angle that isn't labeled are:
∠B = 100
∠K = 100
∠L = 41
∠M = 86
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what is the probability of getting heads twice in a row at some point during three coin flips? assume it is a fair coin where heads and tails are equally likely.
The probability of getting heads twice in a row at some point during three coin flips is 1/8.
Given info;
Assume that a fair coin has an equal chance of coming up heads or tails.
What is the likelihood that three coin flips will result in two consecutive heads at any point?
There is a three-coin flip. The potential results are;
(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)
1 is the number of successful results.
Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8
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Mario purchases a prepaid phone plan for 50$. Each minute he uses costs $0.13. How many minutes can Mario talk on this plan
Answer:
49.87
Step-by-step explanation:
Carlos paid $150.95 for Luxury Vinyl Flooring for his Family Room
which is 121 Square feet. He purchased a 1 square foot sample at Lowes to take home to see if the flooring will match his fireplace
in the Family room.
Based on this price, what is the cost of the
sample?
$1.25
$0.95
$1.00
$1.20
Step-by-step explanation:
121 ft² cost $150.95
1 ft² costs then 150.95/121 = $1.247520661... ≈
≈ $1.25
Graph the linear inequality below.
y ≤ x -5
To see the attachment of graph of linear inequality.
Given,
In the question:
The linear inequality is given as:
y ≤ x -5
To graph the above inequality.
Now, According to the question:
What is linear inequality?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Math. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Math are polynomial inequality, rational inequality, absolute value inequality.
Hence, To see the attachment of graph of linear inequality.
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Given the definitions of f(x) and g(x) below, find the value of (gof)(-2).
f(x) = 3x² – 3x – 7
-
g(x) = -3x - 10
Answer:
(g.f)(-2) = -44
Step-by-step explanation:
Given:
f(x) = 3x² - 3x - 7
g(x) = -3x - 10
[tex] \rm \implies(g.f)( - 2) = [3 {( - 2)}^{2} - 3( - 2) - 7][ - 3( - 2) - 10] \\ \\ \rm \implies(g.f)( - 2) = [3 (4) + 6 - 7][ 6 - 10] \\ \\ \rm \implies(g.f)( - 2) =(12 - 1)( - 4) \\ \\ \rm \implies(g.f)( - 2) =11 \times ( - 4) \\ \\ \rm \implies(g.f)( - 2) = - 44[/tex]
what do integers added or subtracted from the function do to the graph?
The addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.
Let a quadratic function be f(x) = 2x^2.
Let c be the positive constant.
It is now necessary to determine what will happen if we add or subtract a constant to the function.
The function f(x) = 2x^2 is a parabola opening upwards.
Now, if we add the positive constant c, then the graph of the function will shift upwards by c units and nothing will change. If we subtract the positive constant c, then the graph of the function will shift downwards by c units.
Thus, the addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.
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The rise and run of the line, state the slope in simplest form
Answer:
it is called horizon simple question simple answer
translate (1,-2) 4 left
The new coordinate after the translation of 4 point left is (-3, -2)
Translation
Translation is done by moving the vertices of the figure the prescribed number of spaces on a coordinate plane and then drawing the new figure.
Given,
Here we have the points (1, -2).
Now, we have to translate this point by left side by 4 point.
In order to translate the given point we have to take the value of the x coordinate and then we have to subtract the translation point from it,
So, the calculation for this one is look like
Here the value of the x coordinate is 1
And now we have to subtract 4 from it,
So,
=> 1 - 4
=> -3
Therefore, the new coordinate after the translation is (-3, -2).
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Answers ? Help pls ):
ONLY ANSWER IF YOU REALLY KNOW IT ! NO LINKS !
Answer:
Break even 126 units
105x - (90x + 1890) Profits will be revenue minutes expenses.
The second answer.
Step-by-step explanation:
105x = 90x +1890 Subtract 90x from both sides
15x = 1890 Divide both sides by 15
x 126
They need to sell 126 units to break even.
105(91) -[90(91) + 1890]
9555-8190-1890
9555 - 16380
-6825
Selling 91 units will produce a loss of 6825
Which division setup matches this question? Dr. Bender feeds her dog ½ of a cup of dog food each day. How long will 5 ¾ cups of dog food last?
Answer:
5 days
Step-by-step explanation:
you need to make 5 3/4 into an improper fraction
(5x40)+3/4= 23/4
make all fractions have a common denominator
1/2 = 2/4
you multiply numerator and denominator by 2 to get a denomintator of 4
23/4 ÷ 2/4
to divide a fraction you turn the second fraction into a reciprocal
2/4 in a reciprocal is 4/2
then you multiply the fractions together
23x2/2x4
simlplify to get
46/8 = 23/4
make into a mixed number by dividing by 4
5 3/4
sara takes wedding pictures. for each picture, she has 1/4 chance that everyone looks at the camera. how many pictures must she take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera?
For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.
Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,
= 1 - (1 - p)ⁿ ≥ P
= (1 - p)ⁿ ≤ 1 - P
= n ≥ ln(1-P)/ln(1-p)
= n ≥ ln (0.2) / ln (0.75)
=5.6
Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.
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x divided by 12; x= 2/3
Answer:
1/18
Step-by-step explanation:
Since x=2/3, we can plug in 2/3 for x, and we have 2/3 divided by 12.
Based on what we know about fractions, we can say that dividing by 12 is the same as multiplying by 1/12.
Therefore, we have the expression 2/3*1/12.
Next, we get 2/36, which can be simplified into 1/18.
1. Which of the following numbers has factors that
include the smallest factor (other than 1) of 111?
A. 15
B. 22
C. 28
D. 40
The smallest factor (other than 1) of 111 would be 15.
Option (A) is correct.
What is the smallest factor of a number other than 1?
A number can have a maximum of one factor, and only one has that many factors. Every other number has more than one factor.
Prime numbers have two factors, for example, 2,3,5,7,11...,2729...,2927, 9999959999, and so on. Prime numbers have only one factor the number itself.
The factors of 111 are 1, 3, 37, and 111.
for option (A), the factors of 15 are 1, 3, 5, and 15.
for option (B), the factors of 22 are 1, 2, 11, and 22.
for option (C), the factors of 28 are 1, 2, 4, 7, 14, and 28.
for option (D), the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
So if you observe all the options, the smallest factor (other than 1) of 111 would be 15.
Hence, the smallest factor (other than 1) of 111 would be 15.
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um so like hii,, not school related or anyrhing but ill just like to ask anyone if they know the reason why ur phone (samsung) like randomly delted ur music and photos. yah and ill like to know how u could resolve that from happening again
Answer: Can you check the "Recently Deleted" folder? You may find this in the "My Files" app. If this does not work, and you can confirm you have no backups whatsoever, then your photos are as good as gone. This has happened to Android devices in the past (or Samsung devices mostly) where all their media would just disappear. As far as I know, all Samsung themselves say is to restart your phone to try your luck. An app crashing or some form of corrupt media may have caused your photos to go missing. There may, however, still be a small chance that the photos are there, somewhere on your phone, you just can't find them. I advise checking the storage in "Device Care" and see if the Gallery app is using much storage. If it is, I would connect it to a PC and look through the files again.
Step-by-step explanation:
What is the value of x in the equation-2/9x=2/5?
A. -1 4/5
B. -5/9
C. 5/9
D. 1 4/5
The value of x is -1 4/5 i.e, Therefore, the correct option is A
Define Algebraic Expression
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
Given expression,
-2/9 x=2/5
Isolate the variable, x
x = (2 * 9) / ( 5 * -2)
x = - (9/5) or -1 4/5
Hence, the value of x is -1 4/5 i.e, option(A)
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Please someone help me with this question my exams in a few days
Answer:
see explanation
Step-by-step explanation:
(i)
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
(k + x)² = m² + (k - x)² ← expand factors on both sides using FOIL
k² + 2kx + x² = m² + k² - 2kx + x² ( add 2kx to both sides )
k² + 4kx + x² = m² + k² + x² ( subtract k² + x² from both sides )
4kx = m² ( divide both sides by 4k )
x = [tex]\frac{m^2}{4k}[/tex]
----------------------------------------------------------
(ii)
the area A of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = m and h = k - x
A = [tex]\frac{1}{2}[/tex] m (k - x) ← substitute x = [tex]\frac{m^2}{4k}[/tex]
= [tex]\frac{1}{2}[/tex] m ( k - [tex]\frac{m^2}{4k}[/tex] ) ← distribute parenthesis
= [tex]\frac{mk}{2}[/tex] - [tex]\frac{m^3}{8k}[/tex] ← express as a single fraction
= [tex]\frac{4mk^2-m^3}{8k}[/tex] ← factor out m from each term in the numerator
= [tex]\frac{m(4k^2-m^2)}{8k}[/tex] ← factor (4k² - m² ) as a difference of squares
= [tex]\frac{m(2k+m)(2k-m)}{8k}[/tex]
I need help immediately!! It’s subtract mixed numbers with unlike denominators!!
Answer:
C
Step-by-step explanation:
A = 3 11/12
B = 3 2/3
C = 4 1/4
D = 3 3/4
4 1/4 is equivalent to 4 3/12.
The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 16 mph and the Mystic travels at 20 mph. How far apart will they be in 2 hours?
After 2 hours Serenity and Mystic will be 72 miles apart
The speed of the Serenity = 16 mph
The time taken = 2 hours
The speed = Distance / Time
The distance = The speed × time
The total distance traveled = 16 × 2
= 32 miles
The speed of the Mystic = 20 mph
The time taken = 2 hours
The distance = The speed × time
Total distance traveled = 20 × 2
= 40 miles
Total distance = 32 + 40
= 72 miles
Hence, after 2 hours Serenity and Mystic will be 72 miles apart
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