The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.
Given information:
A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.
Each rat will be given a different dosage of the drug.
The oncologist will then measure the growth rate of the cancerous tumor.
Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.
The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.
Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.
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OLVE
(a) 3^2x+1=9^
2x-1
Answer:
x=2
Step-by-step explanation:
you first have to make the bases the same
3^2x+1=9^2x-1
3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9
3^2x+1=3^4x-2
2x+1=4x-2
2x-4x=-2-1
-2x/-2=-4/-2
x=2
I hope this helps
I want to know how to solve this equation
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
:
The width of a rectangle is 5 cm more than triple its length. The perimeter of the
rectangle is 240 cm. What is the length and width of the rectangle?
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Answer:
length: 28.75 cmwidth: 91.25 cmStep-by-step explanation:
Let L represent the length of the rectangle. Then the width is W=5+3L, and the perimeter is ...
P = 2(L+W)
240 = 2(L +(5 +3L))
120 = 5 +4L
115 = 4L
115/4 = L = 28.75 . . . . cm
W = 5+3L = 5 +3(28.75) = 91.25 . . . . cm
The length and width of the rectangle are 28.75 cm and 91.25 cm.
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
Graph the complex numbers in the complex plane
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Answer:
see attached
Step-by-step explanation:
The imaginary value is plotted on the vertical axis in the same way that the y-coordinate would be for an ordered pair (x, y). Similarly, the real value is plotted on the horizontal axis.
__
I find it helpful to think of the complex number a+bi as equivalent to the ordered pair (x, y) = (a, b) when it comes to graphing.
John is building a fence for his dog. He knows that he wants to make the width 3 feet longer than twice the length. Find the area of the fence.
Write the answer in standard form.
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answer:
28 seconds ..............
A large bag contains 29 balls of different colors. The balls are of the same size, weight, surface, such that besides the color they cannot be differentiated. Among the 29 balls, 8 are green, 4 are yellow, 6 are red, 5 are blue, and 6 are black.
(a) What is the probability of getting exactly 1 green, 1 yellow and 2 red when pulling 8 balls? number (rtol=0.01, atol=0,0001)
(b) What is the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls? number (rtol=0.01. atol=0.0001)
(c) What is the probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls? (Note: If there are remaining balls, they need to be either blue or black) number (rtol=0.01, atol=0.0001)
(d) What is the probability of getting 2 blue and 2 non-blue when pulling 4 balls? number (rtol=0.01, atol=0.0001)
(e) Recalculate part (d) using a binomial distribution. number (rtol=0.01, atol=0.0001)
Answer:
White
6
Red
9
Green
Total number of balls =5+6+9
=20
(i) Probability =
Total cases
favourable cases
P(Green) =
20
9
(ii) P(White or red) =
20
5+6
=
20
11
(iii) P(neither green nor white) = P(Red)
=
20
6
=
10
3
The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15
Total favorable outcomes = 8 x 7 x 15 = 840
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= favorable outcomes / possible outcomes
= 840 / 2,765,905
= 0.000303
Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
(b) Total number of balls = 29
Total number of balls to be pulled = 6
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10
Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3
Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680
Total possible outcomes = C(29, 6) = 593,775
Probability
= favorable outcomes / possible outcomes
= 1,680 / 593,775
= 0.00283
Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose the first green = C(8, 1) = 8
Number of ways to choose the last green = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15
Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6
Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10
Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= 50,400 / 2,765,905 ≈ 0.0182
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Find the missing side lengths leave your answer as a racials simplest form
Answer:
m=[tex]7\sqrt3[/tex]
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]
In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7
And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]
Hope this helps!
in a standard normal model which values of z cut off the middle 96
Answer:
-2.053 to 2.053 is ± .48 from z=0
Step-by-step explanation:
HELP PLS ! ! !
What is |1 − 8i|?
A) √-65
B) 65
C) √65
D) √13
Answer:
C) SQRT(65)
Step-by-step explanation:
the magnitude of 1-8i is given by the following:
sqrt(a^2+b^2)
sqrt(1^2+8^2)
=sqrt(1+64)
=sqrt(65)
It is to be noted that the magnitude of |1 − 8i| is √(65) (Option C)
What is the computation of the above?To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.
Using the formula, we have -
|1 - 8i| = √(1² + (-8)²)
= √(1 + 64)
= √65
Hence, the magnitude of 1 - 8i is √65.
So the correct answer is C) √65.
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What is the greatest common factor of 10 and 13?
ANSWER IN LESS THEN 3 MINS AND I'LL GIVE BRAINLIEST
Answer:
the answer for this would be 1
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
What is the value of the 2 in 4.502?
Answer:
0.002
Step-by-step explanation:
2 in 4.502 is in the thousandths place
Value is 0.002
The word "theory" is composed of the letters of the split alphabet. Three cards are taken out at random and stacked in a row one after another in order of appearance. How many possible compounds can be made up of the letters of this word?
Answer:
There would be [tex]120[/tex] of them.
Step-by-step explanation:
There are [tex]6[/tex] distinct letters in the word "[tex]\verb!theory![/tex]".
Hence, there would [tex]6[/tex] possible choices for the first letter that was selected.
Since the chosen card won't be placed back in the pool, there would be only [tex](6 - 1) = 5[/tex] possible choices for the second letter.
Likewise, there would be [tex](6 - 2) = 4[/tex] choices for the third letter.
[tex]6 \times 5 \times 4 = 120[/tex]. In other words, there are [tex]120[/tex] possible ways to draw three cards out of [tex]6[/tex] one after another.
Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "[tex]\verb!the![/tex]" and "[tex]\verb!het![/tex]" from the number of combinations.
i need help with this question asapppppp
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Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
In a clinical trial of a certain drug, 17 subjects experience headaches among the 221 subjects treated with the drug. Construct a 95% (Wald) confidence interval estimate for the proportion of treated subjects who experience headaches.
a. Find the best point estimate of the population proportion.
b. Identify the value of the margin of error E.
c. Construct the confidence interval.
d. write a statement that correctly interprets the confidence interval.
Solution :
Given :
n = 221
x = 17
a). [tex]$p=\frac{17}{221}$[/tex]
= 0.076
b). At the 95 confidence interval
Value of z = 1.96
Margin of error
[tex]$=1.96 \times \sqrt{\frac{p(1-p)}{n}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$[/tex]
= 1.96 x 0.017
= 0.03332
c). confidence interval
= ( 0.076-0.033, 0.076+0.033)
= ( 0.043, 0.109 )
d). The confidence interval does not contain null value, so it is significant.
Jessica has 28 coins. One fourth of them are quarters. Two thirds of the rest of the coins are dimes. The remaining ones are nickels. How many quarters, dimes, and nickels does he have? How much money does he have in coins? If he wants to buy 2 packs of cards, with each pack $1.35, how much money would he have left?
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Answer:
7 quarters, 14 dimes, 7 nickels total $3.50$0.80 will remainStep-by-step explanation:
a) 1/4 of 28 = 28/4 = 7 coins are quarters.
2/3 of (28 -7) = (2/3)(21) = 14 coins are dimes
The remaining 28 -7 -14 = 7 coins are nickels
__
b) The amount of money in coins is ...
7×$0.25 +14×$0.10 +7×$0.05 = $3.50 . . . in coins
__
c) 2 packs of cards at $1.35 each will cost 2×$1.35 = $2.70. After the purchase, the remaining money would be ...
$3.50 -2.70 = $0.80 . . . remaining
A scale drawn on the map shows that 1 inch represents 40 miles. If tuo cities
are 25 inches apart on the map, what is the distance between them in real
life?
Answer:
Im pretty sure its 1,000 miles (dont forget the unit)
Step-by-step explanation:
Determine if this problem is a inverse variation or direct variation problem! This means that:
equation would be:
1=40
25=x
cross multiply*
x=25*40
x=1,000 miles apart! (dont forget the unit)
If this doesnt work then try this equation!
1=40
25=x
Multiply 1*40 and 25 *x
40=25x......
40/25= 1.6
x=1.6! (Extra step)
Cheers!
Answer: 100 Miles
Step-by-step explanation: took the miles and got it correct.
(Also it's 2.5 inches apart, not 25.)
The length of a rectangle is five times its width. If the perimeter of the rectangle is 108 in, find its area.
Answer:
Step-by-step explanation:multiple 5 times 108 and that gives you your answer..
f(x) = - 2x
g(x) = 8x^2 - 5x + 7
Find (f • g)(x).
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Answer:
(f•g)(x) = -16x^3 +10x^2 -14x
Step-by-step explanation:
(f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)
Use the distributive property:
(f•g)(x) = -16x^3 +10x^2 -14x
Which ordered pair would form a proportional
relationship with the points in the graph?
O (44)
O (69)
O (9,6)
O (8,5)
Kesley works at a nursery she has 157 beads that she wants to share equally between 16 children for a necklace making activity.
How many beads will each child have and how many beads will be left over
Each child will get 9 pieces with 13 pieces left.
What is division?
'Division is a method of distributing a group of things into equal parts.'
According to the given problem,
Number of beads Kesley has = 157
Number of children to be shared between = 16
Number of beads in possession of each child = 157 ÷ 16
= 9
Number of beads divided equally = 144
Remaining beans = 157 - 144
= 13
Hence, we can conclude that out of 157 beans, 144 is divided equally among 16 children with each child getting 9 pieces.
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Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean
(a) Find endpoints of a t-distribution with 5 % beyond them in each tail if the sample has size n = 12.
(b) Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20.
Answer:
a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.
b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.
Step-by-step explanation:
Here the answer is given as follows,
A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario? Question 23 options: |x + 18| ≤ 4 |x – 18| ≤ 4 |x – 4| > 18 |x + 18| > 4
Answer:
the correct answer is |x – 18| ≤ 4
just took the test
Step-by-step explanation:
write your answer in simplest radical form.
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Answer:
√3
Step-by-step explanation:
The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...
1 : 1 : √2
This means ...
p·√2 = √6
p = (√6)/(√2) = √(6/2)
p = √3
I NEED HELP PLEASE AND THANK YOU!!! ASAP
Answer:
71
Step-by-step explanation:
Initial angle lies in 4th quadrant
equation that passes 1,3 and slope of 2 in point slope form
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
