1. The domain of [tex]V (h(r))[/tex] is restricted to values of r greater than 0.
2. [tex]V(h(r)) = 3.5\pi r^3[/tex]
3. The volume depends on the radius of the cylinder
Ana must take 11.25 mL of Medicine A daily. She must take 5.5 mL of Medicine B daily. How many more ml of Medicine A than Medicine B must she take
daily?
Answer:
5.75
Step-by-step explanation:
11.25 - 5.5 = 5.75.
So, Ana must take 5.5 more mL of Medicine A than Medicine B.
Hope this helps!
Now change matrix B to a 3 x 3 matrix and enter
these values for B:
B=
1.2 1.4 3.1
2.2 1.1 5.6
3.7 4.2 6.7
The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
What is Matrix?
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object
What is 3×3 Matrix?A 3 x 3 matrix is calculated for a matrix having 3 rows and 3 columns
Given,
B=
1.2 1.4 3.1
2.2 1.1 5.6
3.7 4.2 6.7
Then the 3×3 matrix is
[tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
Hence, The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
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Answer:
Step-by-step explanation:
c11 =
⇒ 56.1
c12 =
⇒ 12.1
c13 =
⇒ 236
(-2)^-3 without exponent
Answer:
-1/8
Step-by-step explanation:
[tex](-2)^-3 \\=\frac{-1}{2}^{3}\\=\frac{-1}{8}[/tex]
Answer:
-1/8
Step-by-step explanation:
[tex]\left(-2\right)^{-3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\left(-2\right)^{-3}=\frac{1}{\left(-2\right)^3}\\\\=\frac{1}{\left(-2\right)^3}\\\\\left(-2\right)^3=-8\\\\=\frac{1}{-8}\\\\=-\frac{1}{8} \\\\\left(\mathrm{Decimal:\quad }\:-0.125\right)[/tex]
16p - 32q + 5 when p= 2 and q = 1
Answer:
0
Step-by-step explanation:
16x2= 32 and 32x1=32 so 32-32=0
In a particular class of 34 students, 16 are men. What fraction of the students in the class are women?
How do you write 1/46 in simplest form.
Answer:
1/46 is already in the simplest form.
Answer:
1/46 is already in its simplest form.
3 πd=12 π
what does d equal?
__________
D = 4
__________
i blelieve this is it.
Answer:
d =4Step-by-step explanation:
[tex]3\pi d = 12 \pi\\\\divide\:both\:sides\:of\:the\:equation\:by\: 3\:\pi\\\frac{3 \pi d}{3\pi} = \frac{12 \pi}{3\pi} \\\\d=4[/tex]
Solve the problem. A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 2.
Answer:
The z-score corresponding to an observed value of x of 2 is 0.215.
Step-by-step explanation:
We are given that a variable x has the possible observations shown below;
Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.
Firstly, we will find the mean and the standard deviation of X, i.e;
Mean of X, ([tex]\mu[/tex]) = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}[/tex]
= [tex]\frac{13}{9}[/tex] = 1.44
Standard deviation of X, ([tex]\sigma[/tex]) = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }[/tex]
= 2.603
Now, the z-score corresponding to an observed value of x of 2 is given by;
z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{2-1.44}{2.603}[/tex] = 0.215.
Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.
Answer:
[tex]y=-0.5x+4.5[/tex]
Step-by-step explanation:
The slope of [tex]y=2x-6[/tex] is:
[tex]2[/tex]The negative reciprocal of that slope is:
[tex]m=-\frac{1}{2}[/tex]So the perpendicular line will have a slope of [tex]-1/2[/tex]:
[tex]y - y_1 = (-\frac{1}{2} )(x - x_1)[/tex]And now put in the point [tex](1,5)[/tex]:
[tex]y-5=(-\frac{1}{2})(x-1)[/tex]And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:
[tex]y-5=-\frac{x}{2}+\frac{1}{2}[/tex][tex]y=-\frac{x}{2}+\frac{11}{2}[/tex][tex]y=-0.5x+4.5[/tex]S. Determine which is the best buy. Show calculations and explain your answer Ed's Bagels 4 for $.89 Best Bagels Only $1.39 for 6
Answer:
eds bageles are $.22 per bagel and best bagels are $.23 per bagel.
Step-by-step explanation:
Which operation would you do third in the following problem?
8 (10-4)
6
addition
subtraction
multiplication
division
Answer:
multiplication
Step-by-step explanation:
it seems the best
what is 67% of 89.5?
Answer:
59.96
Step-by-step explanation:
when 67% if 89.5 is expressed in numbers,
[tex]\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96[/tex]
A total of 438 tickets were sold for the school play. They were either adult tickets or student tickets. There were 62 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
a + s = 394 total tickets sold is 394 s = a - 56 56 fewer student tickets than adult substitute a-56 in place of s in 1st equation and solve for a a + (a - 56) = 394 2a - 56 = 394 2a = 450 a = 225 adult tickets sold s = a-56 = 169 student tickets sold
Hoped I helped
To save for her newborn son's college education, Kelli Peterson will invest $1,500.00 at the end of each year for the next 18 years. The interest rate she expects to earn on her investment is 9%. How much money will she have saved by the time her son turns 18?
Answer:
9% of $1500 is $15 so she gains an extra $15 for each of the 18 years
$1500 in the bank each year for 18 years is $27000 after 18 years
$15 each year as well so that’s an extra $270 in the bank
The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270
Step-by-step explanation:
please help ive been stuck on this for a very long time
By Thales' theorem:
[tex]\[\begin{array}{l}\frac{{18}}{{2x + 2}} = \frac{{24}}{{3x + 1}}\\18(3x + 1) = 24(2x + 2)\\54x + 18 = 48x + 48\\6x = 30\\x = 5\\A.\end{array}\][/tex]
Total employment for metal workers in 2019 is projected to be 210,000. If this is a 5% increase from 2009, approximately what was the total employment in 2009?
Answer:
200,000
Step-by-step explanation:
To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.
210,000 / (1 + .05) = 200,000
I hope this helps!
-TheBusinessMan
Solve M= 2HA + 2HT for H.
Answer:
H = M/(2A +2T)
Step-by-step explanation:
Factor out H and divide by its coefficient.
M = 2HA +2HT
M = H(2A +2T)
M/(2A +2T) = H
H = M/(2A +2T)
Explain How you got that answer
Answer:
[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]
Step-by-step explanation:
Given equation is
[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]
Adding 25 to both sides
[tex]x^2 + y^2 +6x-8y = 25[/tex]
Completing squares
[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]
Both of their "b" is -3 and 4 respectively
So, adding (-3)² => 9 and (4)² => 16 to both sides
[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]
Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.
We get:
Center = (-3,4)
Radius = [tex]5\sqrt{2}[/tex]
On average, a bird visits 1,170 flowers per day for nectar.
Part A: How many flowers does the bird visit in an hour? Round your answer to the nearest whole flower.
Part B: How many flowers does the bird visit in a year?
Which set of points are collinear? P, T, Y D, S, Y H, T, S Y, D, H
Answer: P, T, Y
This is because the points on the line are straight
Option - A is the correct answer.
We have a geometrical figure given in the question.
We have to determine which set of points are collinear.
What are Collinear points?Three or more points are said to be collinear if they lie on a single straight line.
According to question -
It can be seen that only one set of points - (P, T, Y) lie on the same straight line. Of the options mentioned, one is - (P, T, Y)
Hence, the correct option is Option - A.
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the product of a number and 3 of that number and six is the same as the sum
What is the slope of the line?
Answer:
7/4 = 1.75
Step-by-step explanation:
step 1: pick two points on the line that have nice integer coordinates.
--> (3,4) and (-1,-3)
step 2: calculate the y difference and the x difference
--> y difference: 4 - -3 = 7
x difference: 3 - -1 = 4
step 3: the slope is y difference / x difference
--> slope = 7/4
Given h(p)=p^2+2p, Solve h(p)=3
We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:
[tex]p^2+2p=3[/tex].
Subtract 3 from both sides:
[tex]p^2+2p-3=0[/tex].
Then solve for p:
[tex]p^2+2p-3=0[/tex].
[tex](p-1)(p+3)=0[/tex].
So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:
[tex]p-1=0\implies p_1=1[/tex].
Or
[tex]p+3=0\implies p_2=-3[/tex].
Hope this helps.
the perimeter of a rectangle is 12cm. If the length is 2 less than 3 times the width, find the length
Answer:
The length of the rectangle would be 4.
Step-by-step explanation:
We can start by naming the width x.
Therefore, the length would 3x-2.
The perimeter of the rectangle would then be:
2(3x-2+x)
We can set up the given equation
2(3x-2+x)=12
Solve for x.
Divide both sides by 2.
3x-2+x=6
Combine like terms.
4x-2=6
Add 2 to both sides.
4x=8
Divide both sides by 4.
x=2
The width would then be 2.
We can plug that into the expression for length.
3x-2
3(2)-2
6-2
4
The length of the rectangle would be 4.
Suppose Q is the midpoint of PR. Use the information to find the missing value.
11) PQ = 3x + 14 and QR = 7x - 10 x =
Answer:
x = 6
Step-by-step explanation:
Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.
Therefore, PQ = QR. Which is:
[tex] 3x + 14 = 7x - 10 [/tex]
Solve for x. Collect like terms
[tex] 3x -7x = - 14 - 10 [/tex]
[tex] -4x = -24 [/tex]
Divide both sides by -4x
[tex] x = 6 [/tex]
What is mAngleRST in degrees?
Answer:
The measure of angle RST = 120°
Step-by-step explanation:
Answer:
The measure of angle RST = 120°
hope this helps
what is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree.
Answer:
13°
Step-by-step explanation:
The smallest angle in a triangle is the angle opposite the shortest side.
In this case the angle opposite side 9
let the angle be x, then using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{40}[/tex] , thus
x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{40}[/tex] ) ≈ 13° ( to the nearest degree )
a bathtub is filled with 38 1/3 gallons of water. if 2 3/5 gallons splash out, how much water is left in the tub?
Answer:
3/5^3
3/5^3 = 27
125
= 0.216
Step-by-step explanation:
Rules for expressions with fractions:
Fractions - use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter 5/100. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).
Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e., 1/2 : 3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.
Colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2
Calculator follows well-known rules for order of operations. Most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.
Answer:
[tex]\frac{536}{15}[/tex] or [tex]35\frac{11}{15}[/tex] (they're the same)
Step-by-step explanation:
[tex]38\frac{1}{3} - 2\frac{3}{5} = \frac{536}{15} = 35.7333 = 35\frac{11}{15}[/tex]The value of β is:
60º
45º
90º
30º
75º
Answer:
60°
Step-by-step explanation:
The definition of cosine tells you ...
cos(β) = 3/6 = 1/2
β = arccos(1/2) . . . . use the inverse cosine function to find the angle
β = 60°
_____
The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...
1 : √3 : 2
The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.
In what quadrant is cosine negative and cotangent negative?
Answer:
Step-by-step explanation:
cosine is negative in 2nd and 3rd quadrant.
cotangent is negative in 2nd and 4th quadrant.
In the second quadrant, both cosine and cotangent are negative.
What are the signs of each trig function in four quadrants?In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.
We know there are four quadrants in an XY plane.
We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.
tan = (sin/cos).
So, cot = 1/tan = cos/sing.
∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.
∴ In the second quadrant cosine and cotangent, both are negative.
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