The sum of t+4/t+5 and 9/t-1 with a common denominator is (t²+12t+41)/[(t+5)(t-1)].
To find a common denominator for the given expressions t+4/t+5 and 9/t-1, we need to determine the least common multiple (LCM) of the denominators (t+5) and (t-1):
The prime factorization of t+5 is (t+5).
The prime factorization of t-1 is (t-1).
Therefore, the LCM is (t+5)(t-1).
To convert t+4/t+5 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t-1):
t+4/t+5 = (t+4)(t-1)/[(t+5)(t-1)] = (t²+3t-4)/[(t+5)(t-1)]
To convert 9/t-1 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t+5):
9/t-1 = 9(t+5)/[(t+5)(t-1)] = (9t+45)/[(t+5)(t-1)]
Now both fractions have the same denominator, so we can add them:
(t²+3t-4)/[(t+5)(t-1)] + (9t+45)/[(t+5)(t-1)] = (t²+3t-4+9t+45)/[(t+5)(t-1)]
Simplifying the numerator gives:
t²+12t+41
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A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. Answer the following questions. Question 7 Select the least number of socks that he must take out to be sure that he has at least two socks of the same color. 12 4 Question 8 Select the least number of socks that he must take out to be sure that he has at least two black socks. 3
For Question 7, the man must take out 4 socks to be sure that he has at least two socks of the same color. This is because he could potentially take out 3 brown socks and 3 black socks before getting a matching pair, but with 4 socks, there must be at least two of the same color.
For Question 8, the man must take out 3 socks to be sure that he has at least two black socks. This is because he could potentially take out all 12 brown socks before getting a black one, but with 3 socks, there must be at least one black sock and then a potential for a second.
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(Chapter 14) If f(x,y) --> L as (x,y) --> (a,b) along every straight line through (a,b), then limit as (x,y) approches (a,b) = L
Yes, the statement is true. This is a restatement of the definition of the limit of a function of two variables.
Formally, we say that the limit of f(x,y) as (x,y) approaches (a,b) is L if and only if for every number ε > 0, there exists a number δ > 0 such that if the distance between (x,y) and (a,b) is less than δ, then the distance between f(x,y) and L is less than ε. In symbols:
For every ε > 0, there exists a δ > 0 such that if 0 < sqrt((x-a)^2 + (y-b)^2) < δ, then |f(x,y) - L| < ε.
The condition that f(x,y) approaches L along every straight line through (a,b) is equivalent to saying that the limit of f(x,y) as (x,y) approaches (a,b) along any path is also L. This is a stronger condition than the usual definition of the limit, and implies that the limit exists and is equal to L.
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Hiya can someone pls help me ty due in few days thanks! <3
The distance from the wall, that the ladder slipped during the day, would be 21 cm.
How to find the distance ?First, use the Pythagorean theorem to find the original height of the ladder from the wall:
50² + b² = 300²
2, 500 + b ² = 90, 000
b ² = 90, 000 - 2, 500
b = √ 87, 500
b = 295. 8 cm
We can then find the new distance from the wall to be :
= 50 + 70
= 120 cm
The new height of the ladder to show the slip would be:
120² + b² = 300²
14,400 + b ² = 90, 000
b ² = 90, 000 - 14, 400
b = √ 75, 600
b = 275 cm
The distance slipped is:
= 295. 8 - 275
= 21 cm
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modeling with mathematics a web browser is open on your computer screen. a rectangular computer screen is shown displaying a rectangular web browser. the length of the computer screen is labeled x plus 7 inches. the length and width of the web browser are labeled x inches and x minus 2 inches respectively. a. the area of the browser window is 24 square inches. find the length of the browser window $x$ . in. b. the browser covers $\frac{3}{13}$ of the screen. what are the dimensions of the screen? length: in. width: in.
The dimensions of the screen are:
length = L = 12 inches
width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches
a. The area of the browser window is given by:
area = length * width
24 = x(x-2)
Simplifying and solving for x, we get:
[tex]x^2[/tex] - 2x - 24 = 0
(x - 6)(x + 4) = 0
Since the length cannot be negative, we take x = 6. Therefore, the length of the browser window is x = 6 inches.
b. Let L and W be the length and width of the computer screen, respectively. We are given that:
length of browser = x inches = L - 7 inches
width of browser = x - 2 inches
The area of the browser is:
area of browser = x(x-2) = (L-7)(L-9)
We are also given that the browser covers 3/13 of the screen, so:
area of browser = (3/13) * area of screen
x(x-2) = (3/13) * L * W
Substituting x = L - 7 and simplifying, we get:
(L-7)(L-9) = (3/13) * L * W
Expanding and simplifying, we get:
13L[tex]^2[/tex] - 182L + 546 = 3LW
Since L and W are positive, we can divide both sides by 3L to get:
W = (13L - 182) / 3
We also know that the browser covers 3/13 of the screen, so:
area of browser = (3/13) * area of screen
x(x-2) = (3/13) * L * W
6(4) = (3/13) * L * ((13L-182)/3)
24 = (L/3) * (13L-182)
8 = L(13L-182)/3
24 = L(13L-182)
13L^2 - 182L - 24 = 0
(L - 12)(13L + 2) = 0
Since the length cannot be negative, we take L = 12. Therefore, the dimensions of the screen are:
length = L = 12 inches
width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches
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a sailfish can travel as fast as 68 miles per hour. at that rate, how far would a sailfish travel in 45 minutes
Therefore, a sailfish would travel 51 miles in 45 minutes if it maintained a speed of 68 miles per hour in the equation.
To calculate the distance traveled in a given time, we can use the formula distance = rate x time, where rate refers to the speed of travel and time refers to the duration of travel. In this scenario, we are given a rate of 68 miles per hour and a time of 45 minutes.
To use the formula, we first need to convert the time to hours since the rate is given in miles per hour. We do this by dividing the time by 60, since there are 60 minutes in an hour. In this case, 45 minutes divided by 60 minutes per hour gives us 0.75 hours.
Now, we can plug in the values for rate and time into the formula and solve for distance. Multiplying 68 miles per hour by 0.75 hours gives us a distance of 51 miles.
45 minutes / 60 minutes per hour = 0.75 hours
Then, we can use the formula: distance = rate x time
distance = 68 miles per hour x 0.75 hours
distance = 51 miles
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Solution:
20. RAINFALL The amount of rainfall on Monday
and Thursday is shown in the table. If the same
amount of rain that fell on Monday fell for 3 days
and the same amount that fell on Thursday fell for
2 days, how much rain would fall over those 5
days?
Day
Rain (in.)
Equation:
Monday
0.50
Thursday
0.25
4. If W has a chi-square distribution with v degrees of freedom, find E(W) and V(w). if X, i = 1, 2,..,n is a random sample from a normal distribution with mean y and variance o, find E(S) and V(s).
Since S is the average of the random sample, the expected value (E(S)) and variance (V(S)) are: E(S) = µ and V(S) = σ² / n
For W with v degrees of freedom, we know that E(W) = v and V(W) = 2v.
Now, let's consider the random sample X = (X1, X2, ..., Xn) from a normal distribution with mean y and variance o. The sample variance S^2 is defined as:
S^2 = (1/n-1) * sum(i=1 to n) (Xi - y)^2
where y is the sample mean.
Using properties of the normal distribution, we can derive that E(S^2) = o * (n-1)/n and V(S^2) = (2o^2 * (n-1)^2)/(n(n-2)).
To find E(S) and V(S), we take the square root of E(S^2) and V(S^2) respectively. Thus:
E(S) = sqrt(o * (n-1)/n)
V(S) = sqrt((2o^2 * (n-1)^2)/(n(n-2)))
First, let's discuss the chi-square distribution. If W has a chi-square distribution with v degrees of freedom, the expected value (E(W)) and variance (V(W)) are as follows:
E(W) = v
V(W) = 2v
Now let's consider the random sample from a normal distribution. If X, i = 1, 2,...,n is a random sample from a normal distribution with mean y (µ) and variance σ², we can find the sample mean (S) as:
S = (ΣX_i) / n
Since S is the average of the random sample, the expected value (E(S)) and variance (V(S)) are:
E(S) = µ and V(S) = σ² / n
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a study of two kinds of photocopying equipment shows that 61 failures of the first kind of equipment took on the average 80.7 minutes to repair with a standard deviation of 19.4 minutes, whereas 41 failures of the second kind of equipment took on the average 88.1 minutes to repair with a standard deviation of 18.8 minutes. construct a 98% confidence interval for the ratio of the variances of the two populations sampled.
To construct a confidence interval for the ratio of the variances of the two populations sampled, we can use the F-distribution. The formula for the F-statistic is: F = (s1^2 / s2^2) / (n1 - 1) / (n2 - 1) Where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Using the given data, we have:
s1 = 19.4
s2 = 18.8
n1 = 61
n2 = 41
The F-statistic is then:
F = (19.4^2 / 18.8^2) / (61 - 1) / (41 - 1) = 1.399
To find the confidence interval, we need to look up the critical values of the F-distribution with degrees of freedom (df) of (n1 - 1) and (n2 - 1) at the 1% level of significance.
Using a table or calculator, we find that the critical values are 0.414 and 2.518.
Thus, the confidence interval for the ratio of the variances is:
1 / (2.518 / sqrt(F)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(F))
1 / (2.518 / sqrt(1.399)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(1.399))
0.266 < σ1^2 / σ2^2 < 2.083
Therefore, we can be 98% confident that the ratio of the variances of the two populations sampled lies between 0.266 and 2.083.
To construct a 98% confidence interval for the ratio of the variances of the two populations sampled, we will use the F-distribution and the following formula:
CI = (s1^2 / s2^2) * (1 / Fα/2, df1, df2, F1-α/2, df1, df2)
Here, s1 and s2 are the standard deviations of the first and second kinds of equipment, and df1 and df2 are the degrees of freedom for each sample. Fα/2 and F1-α/2 are the F-distribution critical values at the α/2 and 1-α/2 levels, respectively.
Step 1: Calculate the variances (s1^2 and s2^2).
Variance1 = (19.4)^2 = 376.36
Variance2 = (18.8)^2 = 353.44
Step 2: Calculate the degrees of freedom (df1 and df2).
df1 = n1 - 1 = 61 - 1 = 60
df2 = n2 - 1 = 41 - 1 = 40
Step 3: Find the F-distribution critical values (Fα/2, df1, df2, F1-α/2, df1, df2) for a 98% confidence interval (α = 0.02).
F0.01, 60, 40 = 0.4611
F0.99, 60, 40 = 2.1080
Step 4: Calculate the confidence interval using the formula.
CI = (376.36 / 353.44) * (1 / 0.4611, 2.1080)
Lower limit = (376.36 / 353.44) * 0.4611 = 0.5925
Upper limit = (376.36 / 353.44) * 2.1080 = 2.2444
The 98% confidence interval for the ratio of the variances of the two populations sampled is (0.5925, 2.2444).
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What is the surface area of a rubik's cube in cm² with side that measures 14cm?
The surface area of the Rubik's cube is 1176 cm².
Surface area is a measurement of the overall space occupied by an object's surface. Often, it is expressed in terms of square measurements like square meters (m²) or square feet (ft²).
A Rubik's cube has six faces, each of which is a square with sides equal to the length of a side of the cube. Therefore, the surface area of a Rubik's cube is six times the area of one of its faces.
The area of one face of the cube with a side of 14 cm is:
14 cm x 14 cm = 196 cm²
So, the total surface area of the Rubik's cube is:
6 x 196 cm²= 1176 cm²
Hence, the area will bed 1176 cm².
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Given: ΔABC m∠1=m∠2 D∈ AC , BD = DC m∠BDC = 100°
Find: m∠A, m∠B, m∠C
The measures of angles are m∠A = 80°, m∠B = 50°, and m∠C = 50°, concluding that the triangle is an isosceles triangle.
Based on the given information, we can start by using the fact that the angles in a triangle sum to 180 degrees. Let's label the unknown angles as m∠A, m∠B, and m∠C:
m∠A + m∠B + m∠C = 180
We also know that m∠1 = m∠2, which means that triangle ABD is similar to triangle CBD by the Angle-Angle (AA) similarity theorem. This implies that the ratios of corresponding sides in these triangles are equal:
AB/BD = BD/DC
Since BD = DC, we have AB = DC.
Therefore, triangle ABC is isosceles with AB = AC. This means that m∠B = m∠C.
Now let's use the given information that BD = DC and m∠BDC = 100° to find the measure of m∠B. We can draw the perpendicular bisector of BC to point D, which will bisect angle BDC into two equal angles of measure x degrees.
Since triangle BDC is isosceles, we know that:
m∠DBC = m∠DCB
= (180 - m∠BDC)/2
= 40°.
Therefore, m∠B = m∠DBC + m∠DCB = 40° + x.
Now we can use the fact that the angles in triangle ABC sum to 180 degrees to solve for m∠A:
m∠A + m∠B + m∠C = 180
m∠A + 2m∠B = 180 (since m∠B = m∠C)
m∠A + 2(40° + x) = 180 (since m∠B = 40° + x)
m∠A + 80° + 2x = 180
m∠A = 100° - 2x
We also know that m∠BDC = 100°, so m∠DBC = m∠DCB = (180 - m∠BDC)/2 = 40°. Therefore, we can write:
m∠A + m∠B + m∠C = 180
m∠A + 2m∠B = 180 (since m∠B = m∠C)
m∠A + 2(40° + x) = 180 (since m∠B = 40° + x)
m∠A + 80° + 2x = 180
m∠A = 100° - 2x
Now we can solve for x by using the fact that m∠A, m∠B, and m∠C must be positive:
m∠A > 0, m∠B > 0, m∠C > 0
100° - 2x > 0
x < 50°
Therefore, the possible values of x are 10°, 20°, 30°, 40°, and 49°. We can use these values to find the measures of m∠A, m∠B, and m∠C:
If x = 10°, then m∠A = 80°, m∠B = 50°, and m∠C = 50°.
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What is the exact number of fractions equivalent to 4/5
The exact number of fractions equivalent to the given fraction is 8/10, 12/15 and 16/20, under the condition that the given fraction is 4/5.
In order to determine the equivalent fractions of 4/5, we are have to multiply the numerator and denominator by same numbers.
Then the exact numbers equivalent to the given fraction is
(4/5) × (2/2) = (4 × 2) / (5 × 2) = 8/10
(4/5) × (3/3) = (4 × 3) / (5 × 3) = 12/15
(4/5) × (4/4) = (4 × 4) / (5 × 4) = 16/20
Then, 8/10, 12/15, and 16/20 are equal to 4/5 when simplified, which means they are equivalent in nature.
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Help
Thanks if you doooo! :)
The circumference of a circle in terms of π with radius 31½ yards is 63π yards ( optionD)
What is circumference of a circle?The circumference is the perimeter of a circle or ellipse. This means that the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment.
The circumference of a circle is expressed as;
C = 2πr
where r is the radius
r = 31 ½ = 63/2 yards
therefore C = 2 × 63/2 × π
C = 63π yards
Therefore the circumference of the circle in term of π with radius 31 ½ is 63π yards
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help i need help super quick
pls help ASAPP v(if u dont know the answer then dont GUESS the answer. and no links please)
the answer is b or the second one
Answer:
Step-by-step explanation:
first do Pemdas and thats it
If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 1 ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1. x=2 If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 21 ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1, x=2 Note: You can eam partial credit on this problem. You have attempted this problem 0 times. You have 3 attempts left before new version will be requested. You have unlimited attempts remaining.
The value at which x does the tangent to the curve y=cosx have a slope of 1 is x = 3π/2.
To find the values of x at which the tangent to the curve y = cos(x) has a slope of 1, if x belongs to the interval [0,2π], we need to find the points where the derivative of the function is equal to 1. The derivative of y = cos(x) with respect to x is -sin(x). So, we need to solve the equation:
-sin(x) = 1
sin(x) = -1
Now, we want to find the values of x in the interval [0, 2π] that satisfy this equation. The sine function takes the value -1 at x = 3π/2. Therefore, x does the tangent to the curve y=cosx have a slope of 1 is x = 3π/2.
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help i need help with the question
The angle which is supplemental to the 6 is the angle 8, which makes option a correct.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
Supplementary angles are a pair of angles that add up to 180 degrees. The angles 6 and 8 lie on a straight line which implies they are supplementary as the sum of angles on a straight line is also 180°
Therefore, the angle which is supplemental to the 6 is the angle 8, which makes option a correct.
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T/F : The solution set of the linear system whose augmented matrix [a1a2a3b] is the same as the solution set of the equation x1a1+x2a2+a3x3=b
True.
the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.
The augmented matrix [a1 a2 a3 | b] corresponds to the system of linear equations:
a1x1 + a2x2 + a3x3 = b
The solution set of this system is the same as the solution set of the vector equation:
[x1, x2, x3] * [a1, a2, a3] = b
which can be written as:
x1a1 + x2a2 + x3a3 = b
Therefore, the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.
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15 The line plot shows the weights of ten eggs laid by one hen. EGGS LAID BY ONE HEN
THE PICTURE
what is the total weight, in onces, of the four heaviest eggs?
A 4
B 7
C 8 1/2
D 8 3/4
Pls tell me the answer again!
Answer:
I believe its 8 3/4
Step-by-step explanation:
297 students are on a school trip
If 4/9 of the boys is equalto 7/9 of the girls
How many more boys than girls are there??
Help.. It got my brain twisted
Step-by-step explanation:
b+g = 297 - eqn1
let the number of boys be b and the number of girls be g
(4/9)*b = (7/9)*g
cross multiply
4x9b = 7x9g
36b=63g - eqn2
from eqn 2
36b = 63g
we can divide both sides by 36 to make b the subject of formula
b=7/4 g
substitute b in eqn 1
b+g=297
7/4 g + g = 297
11/4 g = 297
11g = 297*4
11g=1188
g = 1188/11 = 108
since b+g=297
b+108=297
b=297-108=189
therefore the no of girls is 108 and of boys is 189
189-108 = 81 so there are 81 more boys than the girls
Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
Part A
How many dots will the line plot have in all?
A.
2
B.
6
C.
7
D.
10
Part B
The students will make the line plot using one fractional unit. What fractional unit should the students use so that all of the data can be plotted above a label?
A.
tenths
B.
eighths
C.
fourths
D.
halves
HELP MEEEE
Answer: I don't know, sorry!
Step-by-step explanation:
write the equation of the line that
passes through (2,-6) and is perpendicular to y = 2/3x+4
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+4\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{2} }}[/tex]
so we're really looking for the equation of a line whose slope is -3/2 and it passes through (2 , -6)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{2}) \implies y +6 = - \cfrac{3}{2} ( x -2) \\\\\\ y+6=- \cfrac{3}{2}x+3\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x-3 \end{array}}[/tex]
unfortunately, the virologist has forgotten which two of the three quantities (infected, susceptible, orimmune people) the functions a and b were modeling. using all the differential equations analysisabilities at your disposal, help the virologist conclusively decide what quantities a and b model.be sure to justify your answer (in particular, rule out the alternatives).
Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.
It seems that the specific functions a and b, as well as the differential equations, are not provided in your question. However, I can guide you on how to approach this problem using the given terms and general concepts.
A virologist studies the dynamics of infectious disease using mathematical models. The three quantities of interest are infected people (I), susceptible people (S), and immune people (R). Functions a and b will represent two of these three quantities. To determine which quantities a and b model, we can analyze the given differential equations and follow these steps:
Step 1: Identify the variables and their relationships
Look for the variables (S, I, and R) in the differential equations and analyze how they are related to each other. Determine if there are any rate constants or parameters that link the variables.
Step 2: Analyze the equations' behavior
Study the differential equations' behavior over time, considering different initial conditions. Observe if the equations exhibit any trends, such as an increase or decrease in the quantities.
Step 3: Compare the equations with known epidemic models
Compare the given differential equations with known epidemic models, such as the SIR model or the SEIR model. These models have well-defined equations that describe the rates of change for susceptible, infected, and immune individuals.
Step 4: Rule out alternatives
Based on your analysis, eliminate the alternatives that don't match the behavior exhibited by the differential equations. Ensure that your conclusion is supported by a logical argument.
Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.
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What is the solution to 3ab -9ab +7ab
Answer:
1ab
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
1ab or just ab
Step-by-step explanation:
All 3 parts of the equation have the variables ab at the end, meaning that the solution will also end with ab.
Let's first solve by doing the first property, subtraction:
3ab-9ab=-6ab
Now, we add that sum to 7ab:
-6ab+7ab=1ab
Depending on what they ask, you can either write 1ab or ab, they are the exact same thing.
Write in slope intercept form given the information. slope = -1; y-intercept = 8
i need help with this problem
The Surface Area of Cone is 124.344 cm².
We have,
Diameter= 11 cm
slant height = 7.2 cm
Radius = 5.5 cm
So, Surface Area of Cone
= πrl
= 3.14(5.5)(7.2)
= 124.344 cm²
Thus the Surface Area of Cone is 124.344 cm².
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(-3,6) (-2,9) write the equation in slope intercept form
Answer:
y = 3x + 15
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-3,6) (-2,9)
We see the y increase by 3 and the x increase by 1, so the slope is
m = 3
Y-intercept is located at (0,15)
So, the equation is y = 3x + 15
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Liam said that the following graph shows a positive correlation between ice cream sales and temperature.
A: Is he correct? Why or why not?
B: Liam’s friend Armonte said he believes this represents causation instead of a correlation. Is Liam or Armonte correct? Give at least two reasons to help support your claim.
A: Liam is correct. The graph shows a positive correlation between ice cream sales and temperature. As the temperature increases, ice cream sales also increase.
B: Armonte is not correct. There are a few reasons why the graph represents a correlation and not causation:
Correlation does not imply causation. Just because two variables are correlated, it does not mean that one variable causes the other.
There could be other variables that are affecting both ice cream sales and temperature. For example, if the graph was plotted over a long period of time, there may be seasonal factors that affect both variables, such as summer months having higher temperatures and more ice cream sales.
The graph only shows a relationship between ice cream sales and temperature, but it does not prove causation. To establish causation, a controlled experiment would need to be conducted to show that changes in temperature cause changes in ice cream sales.
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Sarah was mixing up some lemonade to sell for her lemonade stand. The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.
If she has 21 scoops of lemonade mix in the container, how many gallons of lemonade can she make?
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Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.
Given information:
Sarah was mixing up some lemonade to sell for her lemonade stand.
The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.
If 3 scoops of lemonade mix are needed to make 2 gallons of lemonade, then one scoop of lemonade mix can make 2/3 of a gallon of lemonade.
As per the multiplication,
So, with 21 scoops of lemonade mix, Sarah can make:
21 scoops x (2/3 gallon/scoop) = 14 gallons
Therefore, Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.
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when solving a problem that uses the completing the square method, after you complete the square, what would the perfect square trinomial be for this problem: 5x^2 -14x 8
The perfect square trinomial for this problem would be 5(x - (7/5))^2.
The given quadratic equation is:
5x^2 - 14x + 8
To complete the square and find the perfect square trinomial, follow these steps:
1. Make sure the coefficient of x^2 is 1. Divide the entire equation by the coefficient of x^2 (in this case, 5):
x^2 - (14/5)x + 8/5
2. Find the term to complete the square. Take half of the coefficient of the x term, square it, and add it to both sides:
x^2 - (14/5)x + (14/10)^2 = -8/5 + (14/10)^2
3. Rewrite the left side of the equation as the perfect square trinomial:
(x - 7/5)^2 = -8/5 + 49/25
Now, the perfect square trinomial for the given problem is (x - 7/5)^2.
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You have two 5-gallon buckets. One is filled with water but has a slow leak, leaking out water 7 ounces per minute. The other is empty but is being used to catch water from a leaky faucet at a rate of 4 ounces per minute
Based on the mentioned informations, at the time when the first bucket is empty, it is calculated that the second bucket will contain approximately 365.72 ounces volume of water.
The first step is to convert the 5-gallon volume to ounces. There are 128 ounces in one gallon, so 5 gallons is equal to 640 ounces.
The water is leaking out of the bucket at a rate of 7 ounces per minute. Therefore, the amount of water remaining in the bucket after t minutes can be calculated as:
Remaining water in the bucket = 640 - 7t
We want to find out when the remaining water in the bucket reaches zero, so we set the above equation equal to zero and solve for t:
640 - 7t = 0
7t = 640
t = 91.43 minutes
Therefore, it will take approximately 91.43 minutes for the water level in the bucket to reach zero.
At the same time, the empty bucket is being filled with water from the leaky faucet at a rate of 4 ounces per minute. Therefore, the amount of water in the empty bucket after t minutes can be calculated as:
Water in the empty bucket = 4t
We want to find out how much water will be in the empty bucket at the time when the first bucket is empty, so we substitute t = 91.43 into the above equation:
Water in the empty bucket = 4 x 91.43
Water in the empty bucket = 365.72 ounces
Therefore, at the time when the first bucket is empty, the second bucket will contain approximately 365.72 ounces of water.
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The complete question is :
If the bucket that is filled with water initially contained 5 gallons of water and the leak in that bucket started at time zero, how long will it take for the water level in the bucket to reach zero, and how much water will be in the empty bucket at that time assuming that both leaks continue at the same rate of 7 ounces per minute and 4 ounces per minute, respectively?