If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have
[tex]V = tr[/tex]
It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains
[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]
of liquid.
If it's emptied at 500 gal/min, it would take
[tex]13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}[/tex]
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.24 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.4 liter when constructing a 99% confidence interval
At least 832 teenagers must be interviewed.
It is given that the standard deviation is of 1.24 liters.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2}[/tex] = 0.005
Now, we have to find z in the Ztable as such z has a p-value of [tex]1-\alpha[/tex].
So it is z with a p-value of [tex]1-0.005 = 0.995[/tex], so [tex]z= 2.575[/tex]
Now, find the margin of error M as such
[tex]M = Z * \frac{SD}{\sqrt{n} }[/tex]
In which SD is the standard deviation of the population and n is the size of the sample.
How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liters when constructing a 99% confidence interval?
At least n teenager must be interviewed.
n is found when M = 0.1.
We have that SD = 1.12
So
[tex]0.1 = 2.575*\frac{1.12}{\sqrt{N} }[/tex]
[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]
[tex]n = 831.7[/tex]
So rounding up to at least 832 teenagers must be interviewed.
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Line K has a slope of -5. Line J is perpendicular to line K. What is the slope of line K?
If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.
NEED HELP ASAPP PLEASEE
Answer:
22.25
Step-by-step explanation:
take the two values away
the sector is the full address , the triangle is in it. the segment is the bit left near the circumference
Your friend is helping to raise money for a local charity by participating in a cartwheel-a-thon. Your
friend is 70 inches tall with your friend's arms raised in the air. Your friend is able to complete a
cartwheel in 15 seconds. The charity sponsor supplies a wristband to each participant to assist in
counting the number of cartwheels completed. The wristband is 4 inches from the end of your friend's
arm. Write a model for the height h (in inches) of the wristband as a function of the time (in minutes)
given that the wristband is at the highest point when + = 0.
The height of 70 inches, and location of the wristband as well as the period of 15 seconds gives the function for the height of the wristband as the equation;
h = 31•sin((8•π)•t + π/2) + 35How can the height of the wristband be modelled?The model for the height can be derived from the general form of the sine function as follows;
y = A•sin(B•t - C) + DMaximum point = 70 - 4 = 66 at t = 0
Minimum point = 4
Amplitude, A = (66 - 4) ÷ 2 = 31
D = 4 + 31 = 35
At t = 0, we have;
66 = 31 × sin(B × 0 - C) + 35
31 = 31 × sin(- C)
sin(- C) = 1
C = -π/2
1 minute = 60 seconds
1 second= 1 minute/60
15 seconds = (15/60) minutes
Period = 15 seconds = 15/60 minutes
Period = 2•π/B
Therefore;
15/60 = 2•π/B
1/4 = 2•π/B
B = 2•π/(1/4) = 8•π
y = Height of the function
Let h represent the height of the wristband.
The equation for the height is therefore;
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When you rewrite the general Standard form equation in slope-intercept form, y = mx + b, you can see
that the slope of a standard form equation is
m
and the y-intercept is
b
BC-A
The procedure to rewrite the standard form in slope intercept form is as shown below.
How to rewrite an equation in Slope Intercept Form?The standard form of the equation of a line is;
ax + by + c = 0
Slope intercept form is;
y = mx + c
Intercept form is;
x/p + y/q = 1
To Convert ax + by + c = 0 into y = mx + c
1) Move ax and c to the right hand side to get;
by = -ax - c
Divide both sides by b to get;
y = - ax/b - c/b
Comparing to slope intercept form, we can say that;
Slope = -a/b
y-intercept = -c/b
If we are using y = mx + b as slope intercept form, this will also be accurate because we will just switch c with b in the standard form to arrive at same answer.
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Enter the first 4 terms of the sequence defined by the given rule. assume that the domain of each function is the set of whole numbers greater than 0. f(n) = (2n + 2)2 the first 4 terms of the sequence are , , , and .
The first four terms of the sequence are 8,12,16 and 20.
What is a Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions. An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.Given the function is f(n) = (2n+2)2
Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:
f(1) = (2*1+2)2 = 8
f(2) = (2*2+2)2 = 12
f(3) = (2*3+2)2 = 16
f(4) = (2*4+2)2 = 20
Hence, The first four terms of the sequence are 8,12,16 and 20.
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(score for question 3: ... of 10 points) 3. the table shows the test scores and the sleep averages of several students. test score (%) 88 75 76 92 96 94 83 90 99 65 7788 82 83 94 97 7 6.5 average sleep (h) 6 7.5 8 7 6.5 8 8.5 5 7 8 9 9 9 8.5 8.5 (a) write the least squares regression equation that models the data. let x = the test score and y = average sleep. (b) use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. show your work. answer: 1
The linear regression model obtained by fitting the data points is Y = 0.0914X1 - 0.3741.
How to illustrate the regression?x = test score
y = average sleep
Slope = 0.0914
intercept = - 0.3741
The test score of a student that sleeps 8 hours
y = 8
8 = 0.0914X1 - 0.3741
8 + 0.3741 = 0.0914X1
X = 8.3741 / 0.0914
X = 91.62
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HELP MATES, HELP!
Mustafa was asked whether the following equation is an identity:
Answer: Mustafa is incorrect. He made a mistake in step 2.
Step-by-step explanation: Mustafa was certainly correct in step 1 that x(9x+3) + 3(x+3) is 9x^2 + 6x + 9. However when he was factoring, he made a mistake.
(3x + 3)^2 is NOT equal to 9x^2 + 6x + 9. Rather, (3x + 3)^2 is equal to 9x^2 + 18x + 9. If you want to double check this, use FOIL.
The correct factoring of 9x^2 + 6x + 9 is actually 3(3x^2 + 2x + 3). So, Mustafa made a mistake in step 2.
Help me with answer to these questions and sorry that it is in spanish.
The computation of the decimals are illustrated below.
How to calculate the values?1. 7/4 + √5
= 1.75 + 2.24
= 3.99
2. -✓2 + 9
= -1.41 + 9
= 7.59
3. 2 - 5/4
= 2 - 1.25
= 0.75
4. 7.93 + 1/7
= 7.93 + 0.14
= 8.07
5. π + ✓5
= 3.14 + 2.24
= 5.38
6. ✓2 + 13/4 - 3
= 1.41 + 3.25 - 3
= 1.66
7. 8.5 - 12.65
= -4.15
8. 4 + ✓3 - 11/3
= 4 + 1.73 - 3.67
= 2.06
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f(x)=x(4x+9)(x-2)(2x-9)(x+5) has zeros at x = -5, x = -9/4, x=0, x=2, and x =9/2. what is the sign of f on the interval 0
Answer:
Just look at the other answer
Step-by-step explanation:
Answer:
f is always positive on the interval.
Step-by-step explanation:
Determine whether the following is a statistical question.
How old are you?
PLEASE HELP ME
Answer:
A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school? and "how old are you?" are statistical questions.
Step-by-step explanation:
Evaluate the expression 9 - z when z = 4.
Answer:
its 5 5+4=9
Step-by-step explanation:
Area=
Help me please!! Thanks :)
Answer:
80π
Step-by-step explanation:
Circle O with radius IO:
large radius = IO = 12 = R
Circle O with diameter JK
IJ = JK = KL = 2 × IO = 24
IJ = JK = KL = 24/3 = 8
small radius = 8/2 = 4 = r
The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.
That is the same as
1 semicircle of radius 12 plus 1 semicircle of radius 4
A = πR²/2 + πr²/2
A = π(12² + 4²)/2
A = 160π/2
A = 80π
What is the y-value of the solution to the system of equations {3x+4y=42x−4y=6?
The value of y for the system of equation is -1/2 .
What is a System of Equation ?A system of equation is a set of equation that have common solution
The set of equation given is
3x+4y=4
2x−4y=6
To solve the system , Elimination method will be used
Add equation 1 and 2 to eliminate y
5x = 10
x = 2
Substitute the value of x in equation 1 to determine y
3x +4y = 4
6 + 4y = 4
4y = -2
y = -1/2
Therefore the value of y for the system of equation is -1/2 .
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What is the relationship between a and b?
Answer:
A
Step-by-step explanation:
If LM = 3x + 5, MN = 4x, and LN
=
11x7, select all that are true
a. x=3
b. x=7
c. lm = 14
d. lm = 28
e. ln = 26
f. ln =54
We have that x = 3, LM = 14 and LN = 2. options A, C and E
How to determine the value
We known that the three sides are on a straight line
LM + MN = LN
Let's substitute the values, we have
3x + 5 + 4x = 11x - 7
Collect like terms
3x + 4x - 11x = -7 -5
-4x = -12
x = -12/ -4
x = 3
LM = 3x + 5 = 3(3) + 5 = 14
LN = 11x - 7 = 11(3) -7 = 33 -7 = 26
Thus, we have that x = 3, LM = 14 and LN = 2. options A, C and E
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Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12
Kaylen earned $14.87 selling cookies and $7.76 selling
lemonade. then she bought 2 pizzas for $5.00 each.
how much money does she have left?
lemovade
declerc
students, draw anywhere on this slide!
Answer: $12.63
Step-by-step explanation:
$14.87 + $7.76 = $22.63
2pizzas x $5 = $10
$22.63 - $10 = $12.63
which factor tree for the graph the function below? Check all that apply.
f(x)= 4•5^x
The statements that are true are B, C, and F.
Which facts are true about the exponential function?
Here we have the exponential function:
[tex]f(x) = 4*5^x[/tex]
We can see that the initial value is 4, and the base is 5. Because the base is larger than 1, this is an exponential growth function.
The statements that are true are:
B: The domain of an exponential function is always the set of all real numbers.
C: Is an exponential growth, so yes, it is increasing.
F: The y-intercept is given by evaluating the function in x = 0, when you do that, you get the initial value, which is 4. So the y-intercept is (0, 4).
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Using the Addition Method, solve for x in the following system of linear equations.
2y + x = 4
y – 3x = 2
a.)
x = 1
b.)
x = 2
c.)
x = 8
d.)
x = 0
Answer:
x = 0
Step-by-step explanation:
if 2y + x = 4
we can assume that y = 2
if y - 3x = 2
it means 2 - 0 = 2
therefore x = 0
Solve x ^ 2 - 3x = - 8 using the quadratic formula.
Answer: [tex]\frac{3 +- \sqrt{23}i}{2}[/tex] If using complex numbers, or undefined if using all real numbers
Step-by-step explanation:
Moving -8 to the left side of the eq by adding both sides by 8=
x^2-3x+8=0
The quad formula:[tex]\frac{-b +- \sqrt{b^2-4ac}}{2a}[/tex]
a=1 b=-3 c=8
Inserting a b c values into formula: [tex]\frac{-(-3) +- \sqrt{(-3)^2-4(1)(8)}}{2(1)}[/tex]
Simplifying: [tex]\frac{3 +- \sqrt{9-32}}{2}[/tex]
[tex]\frac{3 +- \sqrt{-23}}{2}[/tex] Since the square root of a negative number doesn't exist in the set of real numbers, the equation is undefined.
OR
[tex]\frac{3 +- \sqrt{23}i}{2}[/tex] Using complex numbers i, to replace the negative number created by subtracting 9-32.
The data show the heights in feet of 14 roller coasters. find the mean, median, midrange, and mode for the data.
The mean of the heights of roller coaster is 27.92 feet, median is 21, mode is 16 and mid range is 35.5.
Given heights in feet of 14 roller coaster 11,12,13,14,16,21,25,26,31,40,51,55,60.
We have to calculate the mean, median, mid range and mode for the data.
Mean is the sum of numbers divided by the numbers.
Mean=∑X/n
∑X=11+12+13+14+16+21+25+26+31+40+51+55+60
=391
n=14
Mean=391/14
=27.92 feet.
Median is the central value of the data given.
Median=(n/2)th term ,when n is even, ( n/2)th term, (n+1)/2th term when n is odd.
Median=14/2th term=7th term which is 21.
Mode is the number which has higher frequency.
Mode is 16 because it comes 2 times.
Mid range is the sum of upper value and lower value of data divided by 2.
Mid range=(11+60)/2==35.5.
Hence the mean is 27.92 feet, median is 21 feet, mid range is 35.5 feet, mode is 16 feet.
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Question is incomplete as the values of height should be included as under:
11,12,13,14,16,16,21,25,26,31,40,51,55,60.
If you could answer this thank you!
Answer: 55°
Step-by-step explanation:
Hi!
since an angle bisector splits it in half,
110°, being the entire angle divided by 2 = 110/2 = 55°
mark the congruent parts of the triangles and complete the proof
1) given
2) definition of an angle bisector
3) reflexive
4) [tex]\triangle ABD \cong \triangle CBD[/tex] (ASA)
5) [tex]\angle A \cong \angle C[/tex] (CPCTC)
Select the two expressions equal to the area of this figure in square centimeters.
Answer:
1.(6*4) + (18*6) + (6*4)
1.(6*10) + (6*6) + (6*10)
Step-by-step explanation:
there are two ways to break this shape into three rectangles:
1.Top right rectangle, Top left rectangle, Bottom long rectangle
2. Left rectangle, Middle square, Right rectangle.
Can someone help me out in these geometry fill in the blanks? It’s urgent, gotta have answers fast
Answer:
Vertical angles are equal
Step-by-step explanation:
-
[tex]vertical \: angles \: are \: equal[/tex]
[tex]3y = 150[/tex]
The sum of two supplementary angles equals 180 degrees
Therefore 6x +150=180
Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?
T
Step-by-step explanation:
The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to [tex]\frac{\pi}{2}[/tex]
Answer:
Step-by-step explanation:
Comments
You need to get the radian measure of the circle.
The radian measure of the entire circle is 2 * pi
To get the radian measure of 1/4 of the circle, just divide by 4.
2 pi / 4 = pi/2
The central angle is = to 1/4 of the circumference of the circle.
So the central angle is also pi/2
Answer: pi/2
What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
slope is change in y / change in x
change in y is -5 bc y decreases by 5
change in x is 10 bc x increases by 10
-5/10 simplifies to -1/2
Figure AAA is a scale image of figure BBB.
Figure AAA maps to figure BBB with a scale factor of \dfrac{2}{7}
7
2
start fraction, 2, divided by, 7, end fraction.
What is the value of xxx?
Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the increase or decrease in the size of a figure.
Figure A maps to figure B with a scale factor of 4/9, hence:
4/9 * x = 16
x = 54
Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54
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Please help!!! Having some trouble with this! Tom, Jim, and Matt want to build a castle next to their swing set. The castle is as wide as the swing set, and 6 feet long. The additional play area is enlarged to yield the following layout:|
Length = 7 + 2x [L]
Breadth = 6 + x [B]
So, Area = L × B
=> Area = (7 + 2x) (6 + x)
=> Area = 7 × 6 + 7x + 2x × 6 + 2x²
=> Area = 42 + 7x + 12x + 2x²
=> Area = 2x² + 19x + 42
Option B is correct.
Any questions, you may ask.
Answer: b.) 2x² + 19x + 42
Area of rectangle:
⇒ Length × Width
⇒ (6 + x) × (7 + 2x)
apply distributive method: (a + b)(c + d) = ac + ad + bc + bd⇒ 6(7) + 6(2x) + x(7) + x(2x)
simplify
⇒ 42 + 12x + 7x + 2x²
arrange
⇒ 2x² + 19x + 42