Answer:
2.5
Step-by-step explanation:
The radius of a cylinder formula is
R = √(V / π × h)Plug in
R = √(200 / 3.14 × 10)So . .
R = √(6.4)R = 2.5
( I rounded to the tenth decimal place so you know!)
Factor the polynomial completely. 14a^4 b^2 - 21a^3 b^2
Answer: [tex]b^{2}(1-21a^{3})[/tex]
Step-by-step explanation:
[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]
A box contains 14 books & 7 pieces of dusters. Each piece of duster weighs 0.2 pounds each book weighs 1.1 pounds. The box & its contents together weigh 18.25 pounds. How much does the empty box weigh?
Answer:
1.45
Step-by-step explanation:
weight of all books= 14×1.1= 15.4
weight of all duster=7×0.2= 1.4
weight of books and duster= 15.4+1.4=16.8
weight of the empty box = 18.25-16.8=1.45
Julia has 42 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 180 square meters. List each set of possible dimensions (length and width) of the field.
The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.
Area of a rectanglearea of rectangle = lw
where
l = lengthw = widthTherefore,
perimeter = 2w+ l
42 = 2w + l
l = 42 - 2w
Hence,
area = w(42 - 2w)
180 = 42w - 2w²
-2w² + 42w - 180 = 0
-w² + 21w - 90 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1b = 21w = - 21 / 2 × -1
w = 10.5 meters
Then,
l = 42 - 2w
l = 42 - 2(10.5)
l = 21 meters
Therefore, the dimensions are 10.5 meters and 21 meters.
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The average score for the statistics exam was a 75 with a standard deviation of 8. A student was told that they received a
score 1.45 standard deviations below the mean. What was their score?
A mean is an arithmetic average of a set of observations. The score of the student is equal to 63.4.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Given the mean score was 75, while the standard deviation was 8. Therefore, the score of the student is,
Scre of the student = μ - 1.45σ = 75 - 1.45(8) = 63.4
Hence, the score of the student is equal to 63.4.
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The rule for a pattern is subtract 4. The first number of the pattern is 41. Which choice is true about this pattern?
A.The numbers in the pattern are even.
B.The numbers in the pattern are odd.
C. The numbers alternate between even and odd.
Answer:A
Step-by-step explanation:
the correct choice is: B. The numbers in the pattern are odd.
To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:
First number: 41
Second number: 41 - 4 = 37
Third number: 37 - 4 = 33
Fourth number: 33 - 4 = 29
As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.
So, the correct choice is:
B. The numbers in the pattern are odd.
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The square root of X+6= X-6
Answer:
x = 10
Step-by-step explanation:
I assume you mean
sqrt(x + 6) = x - 6
let's square the whole equation :
x + 6 = (x - 6)² = x² - 12x + 36
x² - 13x + 30 = 0
the general solution to a quadratic equation is
x = (-b ±sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -13
c = 30
x = (13 ±sqrt(13² - 4×1×30))/(2×1) =
= (13 ±sqrt(169 - 120))/2 = (13 ±sqrt(49))/2 =
= (13 ± 7)/2
x1 = (13 + 7)/2 = 20/2 = 10
x2 = (13 - 7)/2 = 6/2 = 3
for x = 10 we get for the original equation
sqrt(10+6) = 10-6 = 4
sqrt(16) = 4
4 = 4
so, x = 10 is a valid solution.
for x = 3 we get
sqrt(3 + 6) = 3 - 6 = -3
sqrt(9) = -3
3 = -3
so, this (x = 3) counts as an invalid solution, because most teachers nowadays expect the square root symbol operation to deliver only the positive solution.
although a square root is actually representing both : the positive AND the negative solution, because the negative number multiplied by itself is the same result as the positive number multiplied by itself.
so, actually
sqrt(9) = -3
± 3 = -3
is still correct and valid. but not what your teacher expects most likely.
in my younger days only the square root of a negative number counted as invalid operation (in the space of Real numbers, of course), and therefore only a solution leading to a square root of a negative number was an invalid solution.
PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.
1.156÷106
Please help
Will give 20 points whoever gets this right
Thank you :)
Answer:
0.0109056604
that is the answer, I used a calculator
The product of a number and 7 less than the number is 260. Find the numbers.
Answer: 20,-13
Step-by-step explanation:
We can rewrite the problem as an equation. This equation is x(x-7)=260 (x being the mystery number). We can simply this into x^2 -7x=260. We can then rewrite this as x^2 -7x -260=0. We need to find the roots of this quadratic, which are -13 and 20. You can find this by factoring the quadratic.
Help me out with this math problem for 50 points!!!
Answer:
see attached for a graph-1, -2.6, -497Step-by-step explanation:
The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.
__
Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.
The graph will be a solid dot at x=-1, and shading to its left.
__
Possible solutions are any values less than or equal to -1. Some are ...
-1
-1.073
-429
Rewrite the equation below so that it does not have fractions:
3/4x - 2 = 5/12
Do not use decimals in your answer.
Answer:
Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]
First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2
Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]
Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29
—-
Have a nice day!!
NEED HELP ON THIS
If z=-1-i, find z^10 in rectangular form.
The polar form of this problem is 3cis90degrees, what’s the rectangular form?
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].
Hence, we must first convert from rectangular to polar form:
[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]
Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:
[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]
Therefore, [tex]z^{10}=32i[/tex] in rectangular form.
Problem 2
[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]
Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.
A population about which we want to get some information is called?
A population about which we want to get some information is called the sample.
What is a sample in a population study?This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.
Therefore from the definition above the answer to the question is the population sample.
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Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
Increase £180 by 25%
please thank you so much!!!
Answer:
£225
Step-by-step explanation:
[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]
100 + 25 = 125%
[tex]\frac{125}{100}[/tex] × 180 = £225
a) Fill in the gaps below to describe the transformations.
clockwise/anticlockwise about (-1,0) to give
triangle A'.
Triangle A' is then reflected in the line
to give triangle A".
b) What type of single transformation maps triangle A onto triangle A"?
A"
Triangle A is rotated
O
-4
A
a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.
Triangle A' is then reflected in the line y=0 to give triangle A''.
b) Rotation
a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.
b) Rotation
Given,
Triangles A , A' , A'' .
Here,
The triangles are rotated and reflected to get different triangles .
Firstly ,
Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .
To get A'' triangle A' is reflected from horizontal axis.
Triangle A maps into triangle A'' by rotation .
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Composition of the functions is
commutative.
Answer:
The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).
when A complete 1/3 part of any work B can complete 1/4 part of that same work. Similarly when B complete 1/5 part of that work C can complete 1/2 part of that same work. if A can complete that work in 20 hours, then in how many hours can C complete that work.
Answer:
10.672hrs ( maybe)
Step-by-step explanation:
A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs
B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs
B can complete the 1/5 part of work in 26.67/5=5.336hrs
according to question C can complete 1/2part of work in same time then the whole work can complete in
2*5.336=10.672hrs
Solve this pls explain all steps for 22.5 = 1.5x
22.5 = 1.5x
x = 22.5/1.5
x = 15
hope it helps...!!!
Answer:
x = 15
Step-by-step explanation:
1.5x = 22.5
x = 22.5/1.5
assuming your finding x
PLEASE HELP ME ANSWER THIS AAAA
Volume of a Rectangular Prism = length x width x height
Volume = 20
Length = 2
Width = 2
Height = d
20 = 2 x 2 x d
20 = 4 x d
d = 5
Answer: d = 5 centimeters
Hope this helps!
Answer:
d = 5 cm
Step-by-step explanation:
Volume of a rectangular prism: L*W*H
L = 2 cmW = 2 cmH = d cmV = 20 cm³Substitute the values above into the formula:
V = L*W*H
20 = 2*2*d
20 = 4d
/4 /4
5 = d
Therefore, the value of d is 5 cm.
Hope this helps!
Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [?
Answer:
so the next 2 sequences would be 60 and 62
Step-by-step explanation:
The next two terms in the given arithmetic sequence are 60 and 62.
The arithmetic sequence is given as follows:
20, 32, 42, 50, 56, ?
To find the next two terms in the sequence, let's analyze the pattern:
The sequence increases by the following increments:
12, 10, 8, 6
We can observe that the increments are decreasing by 2 each time.
To find the next two terms, we can continue this pattern:
Increment: 4 (6 - 2)
Increment: 2 (4 - 2)
Adding the increments to the previous terms:
56 + 4 = 60
60 + 2 = 62
Therefore, the next two terms in the arithmetic sequence are 60 and 62.
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help will mark Brainliest
Answer:
4.03 < 16.5
Step-by-step explanation:
Four and three hundreths = 4.03
sixteen and five-tenths = 16.5
4.03 < 16.5
is -0.25 rattional or irrational
given the right triangle ABC, find tan A
The tangent is the ratio of the perpendicular and the base of the right triangle. Then tan A will be x/y.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The right-angle triangle ΔABC is given.
The angle ∠C is 90°.
And the perpendicular is x, the base is y, and the hypotenuse is z.
Then the value of the tangent of angle ∠A will be
The tangent is the ratio of the perpendicular and the base of the right triangle.
tan A = x/y
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Select the correct answer.
The graph of function fis shown.
Which statement correctly compares the two functions?
OA. They have the same end behavior as x approaches -
B. They have the same end behavior as x approaches -
OC. They have different end behavior as x approaches -
165 divided by 11 =
154 divided by 14 =
306 divided by 17 =
322 divided by 14 =
Answer:
165 divided by 11 = 15
154 divided by 14 = 11
306 divided by 17 = 18
322 divided by 14 = 23
The sum of four consecutive even numbers is 60. Find the smallest of the four number.
Answer:
answer = 12
Step-by-step explanation:
Let the smallest number be x
So
X+(x+2)+(x+4)+(x+6)=60
4x+12=60
4x=48
X=12
Respond
1. Describe a real-life situation that can be modeled by a function (a relation in which every input
value corresponds to only one output value). The situation must be different from the examples
provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your
relation does, in fact, represent a function.
2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example.
3. Identify the domain and range of your function, using proper mathematical notation.
4. Cite any sources you may have used in
formulating your response.
A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.
What is a function?It should be noted that a function simply means an expression that shows the relationship between the variables.
In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.
The function will be:
= 20 + 5w
where w represents the number of weeks.
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The price of a tv was decreased by 20% to £1440. What was the price before the decrease?
Answer:
€ 1800
Step-by-step explanation:
x - 20% of x = 1440
x - 20x/100 = 1440
x - x/5 = 1440
(5x - x)/5 = 1440
4x/5 = 1440
therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]
x = 360 × 5
= € 1800
[tex](sinx^{2} theta)\frac{x}{y}(1+costheata)[/tex]
The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
How to evaluate the expression?The expression is given as:
[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]
Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].
So, we have:
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]
Open the bracket
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
Express 1 as cos°(Ф)
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
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