based on the number of mice that took part in the experiment, the total number of mice that had at least one effect is 20 mice.
how many mice had a health effect?15 mice had at least 1 tumor while 4 mice had both a tumor and respiratory failure.
the number of mice with just a tumor is:
= 15 - 4
= 11 mice
the number of mice with respiratory failure alone is:
= 9 - 4
= 5 mice
the mice that had at least one symptom is:
= 11 + 5 + 4 mice with both
= 20 mice
question is:
what are the number of mice with at least one effect?
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To graph the inequality y < 2x - 1, you would draw a solid line. A true B false
True
Personally, when I see the line underneath the equality sign, I know I've got to draw a dotted line. That's how I remember the difference between drawing a solid / dotted line.
Hope this helps!
need help on this problem
Using an exponential function, it is found that:
For Country A, the doubling time is of 43 years.For Country B, the growth rate is of 1.9% per year.What is the exponential function for population growth?The exponential function for population growth is given as follows:
[tex]P(t) = P(0)e^{kt}[/tex]
In which:
P(t) is the population after t years.P(0) is the initial population.k is the exponential growth rate, as a decimal.t is the time in years.For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{0.016t}[/tex]
[tex]e^{0.016t} = 2[/tex]
[tex]\ln{e^{0.016t}} = \ln{2}[/tex]
[tex]0.016t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.016}[/tex]
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{36k}[/tex]
[tex]e^{36k} = 2[/tex]
[tex]\ln{e^{36k}} = \ln{2}[/tex]
[tex]36k = \ln{2}[/tex]
[tex]k = \frac{\ln{2}}{36}[/tex]
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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find an angle measure of angle A and B
A (5y-3)
C (3y+27)
The measure of angle A and C will be 94.5° and 85.5°.
How to calculate the angle?(5y - 3) + (3y + 27) = 180
Collect like terms
5y + 3y - 3 + 27 = 180
8y = 180 - 27 + 3
8y = 156
y = 156/8 = 19.5
(5y - 3) = (5 × 19.5) - 3 = 94.5
(3y + 27) = (3 × 19.5) + 27 = 85.5
Therefore, the measure of angle A and C will be 94.5° and 85.5°.
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(1)
Determine the equation of the line passing through the point (0; -1) and
parallel to the -axis. Do you remember what the gradient of this line is?
(2)
Determine the equation of the line passing through the point(-1;0) and
parallel to the -axis. Do you remember what the gradient of this line is?
We know that,
slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]
Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )
So,
Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]
Now,
The required line equaqtion is given by,
==> y−y 1 = m(x-x1)
==> y−1=1(x−0)
==> y−1=x
==> y=x+1
will give brainliest !!!!
Finding the inverse function of [tex]f(x) = 5\sqrt{x + 3} - 2[/tex], it is best described by graph B.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
[tex]f(x) = 5\sqrt{x + 3} - 2[/tex]
[tex]y = 5\sqrt{x + 3} - 2[/tex]
Exchanging x and y:
[tex]x = 5\sqrt{y + 3} - 2[/tex]
Working through the function to isolate y:
[tex]5\sqrt{y + 3} = x + 2[/tex]
[tex]\sqrt{y + 3} = \frac{x + 2}{5}[/tex]
[tex](\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2[/tex]
[tex]y + 3 = \frac{(x + 2)^2}{25}[/tex]
[tex]y = \frac{(x + 2)^2}{25} - 3[/tex]
[tex]f^{-1}(x) = \frac{(x + 2)^2}{25} - 3[/tex]
Which is best represented by graph B.
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what is the sum of .74+.19+3.09+1.98=
Answer:
6
Step-by-step explanation:
no calculator at hand ?
really ? you are using us a simple calculator ?
Answer:
6
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
0.74+
0.19+
3.09+
1.98=
-----------------
6
Need help ASAP
I will mark Brainleist
Need help part A, B and C
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
3. Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.
Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Answer:
Part A
1. A third degree polynomial has exactly three zeros. This is because its highest power (or degree) is 3. Ray would only be correct in saying that a polynomial can have 4 zeros if it is a 4th degree polynomial. Since in this case, a 4rd degree polynomial is being discussed, Kelsey is correct.
2. Function chosen: g(x) = (x + 2)(x - 1)(x - 2)
End behaviour: x —> ∞, g(x) —> ∞
x —> - ∞, g(x) —> -∞
Zeros/x intercepts of the function: -2, 1, 2
y intercept: g(x) = (x + 2)(x - 1)(x - 2)
g(x) = (0 + 2)(0 - 1)(0 - 2)
g(x) = (2)(-1)(-2)
g(x) = 4
3. See Graph 1
Part B
4. f(x) = (x + 5)(x + 3)
Direction: opens upward
Zeros/x intercepts: -5, -3
y intercept: 15
5. See graph 2
Part C
You can draw the roller coaster yourself using the graphs below
There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
The experiment is not a binomial experiment.
What is a binomial experiment?
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.
The conditions for a binomial experiment include:
1. Each trial should be classified either as a success or a failure.
2. There are a fixed number of observations
3. The trials are independent.
4. The number of trials are fixed.
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Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
A. 8 hours
B. 9 hours
C. 16 hours
D. 19 hours
Answer: B. 9 hours
Step-by-step explanation:
Question analysis (Optional if you can understand the question)
Since they are 1170 miles apart, with their speed, the question is asking how long would it take them to travel 1170 miles together.
In other words, the distance that Jo and Jan together add up to 1170 miles.
Given information
Total distance = 1170 miles
Jo's rate = 60 mph
Jan's rate = 70 mph
Set variables
Let x be the time they took to meet each other
Set equation
60x + 70x = 1170
Solve equation
130x = 1170
Divide 130 on both sides
130x / 130 = 1170 / 130
[tex]\boxed{x=9 \: hrs}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
need help with this asap
The converse, inverse and contrapositive of each conditional statement include:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.What is a conditional statement?
A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.Read more on conditional statement here: brainly.com/question/16951916
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Write the trig form of the complex number
18i
The trigonometric form of the complex number given in the task content is; 18(isin(π/2)).
What is the trigonometric form of the complex number?If follows from the task content that the complex number whose trigonometric representation is to be determined is; 18i.
Hence, It follows that the trigonometric form is;
= 18(cos(π/2) + isin(π/2)). where; cos(π/2) = 0.
Hence, we have;
= 18(isin(π/2)).
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Find the sum of the geometric series given a1=−1, r=2, and n=7
A. -127
B. -116
C. 1
D. -118
Answer:
A
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex] , then for n = 7
S₇ = [tex]\frac{-1(2^{7}-1) }{2-1}[/tex] = [tex]\frac{-1(128-1)}{1}[/tex] = - 1 (127) = - 127
(giving brainlyst) Question 2(Multiple Choice Worth 2 points) (13.03 LC) Which statement best describes the expression (5 x 3-12) x 87 O Subtract the product of 5 and 3 from the product of 12 and 8. O Multiply the difference of 12 and 8 by the product of 5 and 3. O Multiply the difference of 5 and 3 by 8, then subtract 12. O Subtract 12 from the product of 5 and 3, then multiply by 8. k
Answer:
See below
Step-by-step explanation:
Using PEDMAS:
O Subtract 12 from the product of 5 and 3, then multiply by 87
Sarah had three times as many quarters as nickels. She had $3.20 in all. How many quarters did she have?
A. 12
B. 15
C. 4
Answer:
A. 12
Step-by-step explanation:
If she had 12 quarters, then she would have to have 4 nickels according to the problem.
12 * .25 = $3 (money in quarters)
4 * .05 = $.2 ( money in nickels)
Adding those 2 together, we get $3.2.
She have 12 quarters
what is unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
There are two situation in Unitary method:
There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
If she had 12 quarters, then
12 * .25 = $3 ( quarters)
4 * .05 = $.2 ( in nickels)
Hence, she have 12 quarters.
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A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 4 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
1 thousand
2 thousand
3 thousand
5 thousand
The quantity of product that would result in the same profit is 1 thousand. Option A
How to determine the function
Given the polynomial function as;
P(t) = –2t³ + 8t² + 2t
Where;
P(t) is the company's profit = $8 milliont is the number of skincare profitLet's equate the values
–2t³ + 8t² + 2t = 8
–2t³ + 8t² + 2t - 8 = 0
Factorize the expression
(-2t³ + 8t²) + ( 2t -8) = 0
- t² ( 2t - 8) + (2t -8) = 0
We take the similar factor
2t - 8 = 0
2t = 8
t = 8/2
t = 4
But we have that the company produced 4 thousand products for $8 million profit, so we have
= 4/ 4
= 1 thousand
Thus, the quantity of product that would result in the same profit is 1 thousand. Option A
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Beginning with the graph of f(x) x2, what transformations are needed to form g(x) = 3(x + 2)2 - 1?
O The graph of g(x) is narrower than f(x) and S shifted to the right 2 units and down 1 unit.
O The
graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the right 2 units and down 1 unit.
Answer: The graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
Step-by-step explanation:
See attached image.
The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
What are graph transformations ?By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.
According to the given question given a graph f(x) = x² and g(x) is 3(x+2)² - 1.
Let us break transformations of g(x) one by one.
g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.
Now, g(x) = 3(x+2)² implies the graph is shifted towards left by 2 units as x + 2 = 0 is x = -2.
Now, g(x) = 3(x+2)² - 1 implies that the whole graph has been shifted 1 units down along the y axis.
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b. What is another composition of rigid motions that maps A GHJ to A KLM?
Another rigid motions that maps Δ GHJ to ΔKLM is ΔGHJ winding point J rotates 180° in the counterclockwise direction. It then transits south by 10 units and to the right by two units. See the attached image.
What is Rigid Motion?Rigid Motion is any method of moving all the points in the plane in such a way that.
the relative distance between sites remains constant andthe relative location of the points remains constant.There are four forms of rigid motions:
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Please help me with this i need big help in this
The value of the angle TSU is.97°. Therefore, none of the given options are correct.
How to calculate the angle?From the information given, the value of UZ will be:
= YZ - YU
= 63 - 26
= 37°
UZ = TZ = 37°
Therefore, the value of TSU will be:
= 23° + (37° × 2)
° 23° + 74°
= 97°
In conclusion, the correct option is E.
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cual es el valor de 10=z-6
Answer:
z=16
Step-by-step explanation:
10=z-6
10+6=z-6+6
16=z
Answer:
10=z-6
or, z= 10+6
or, z = 16
the vale of y is 16
A washer and a dryer cost $737 combined. The washer costs $37 more than the dryer. What is the cost of the dryer
Answer: $350
Step-by-step explanation:
$700 divided by 2 is 350
josh is looking to get a new car because he decided he was spending too much on gas. over the past year he found that he drove 7,700 miles. at current gas prices [ youll need to actually consider your current cost for gasoline ]. he was getting about 27 miles per gallon. if he bought a vehicle that realizes 33 miles per gallon. what might be a reasonable estimate of monthly gas costs?
Josh's monthly fuel expenses are $1,050.
PricesGiven that Josh is looking to get a new car because he decided he was spending too much on gas, and over the past year he found that he drove 7,700 miles, and at current gas prices of $4.5 he was getting about 27 miles per gallon, To determine, if he bought a vehicle that realizes 33 miles per gallon, what might be a reasonable estimate of monthly gas costs, the following calculation must be made:
27 = 10033 = X3300 / 27 = X122.22 = X122.22 = 100100 = X10000 / 122.22 = X81.81 = X(7700 / 33) x 4.5 = X233.33 x 4.5 = X1050 = XTherefore, Josh's monthly fuel expenses are $1,050.
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Answer:Josh's monthly fuel expenses are $1,050.
Step-by-step explanation:
What is the classification of each system?
Answer:
inconsistentconsistent independentconsistent dependentStep-by-step explanation:
Consistent Independent = exactly ONE solution
Consistent Dependent = INFINITELY many solutions
Inconsistent = NO solution
Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. Integrate c ln(x+y)dx-x^2 dy where C is the rectangle with vertices (1,1), (3,1), (1,4), and (3,4).
Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30
How to evaluate an Integral with Green's Theorem?
The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.
Green's Theorem can be applied as follows:
∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA
The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).
Applying Green's Theorem to the given function gives;
∮_c (ln x + y) dx - x² dy
= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy
= ∫₁⁴∫₁³ (-2x - 1) dx dy
= -3·[x² +x]₁³
= -30
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What is the measure of
Find the equation of an ellipse satisfying the given conditions.
Foci: (-4, 0) and (4, 0); length of major axis: 14?
The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
How to determine the ellipse equation?The given parameters are:
Foci: (-4, 0) and (4, 0)Length of major axis = 14The above means that:
c = 4 and
The semi-major axis, a = 7 i.e 14/2
Calculate b using
[tex]b = \sqrt{c^2 + a^2[/tex]
So, we have:
[tex]b = \sqrt{4^2 + 7^2[/tex]
[tex]b = \sqrt{65[/tex]
Square both sides
[tex]b^2 = 65[/tex]
The standard form of the ellipse is represented as:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
This gives
[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]
Evaluate
[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
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Write the expression as a polynomial:
(a-2)(4a³-3a²)
Answer:
[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]
How do you work this equation? x² + x - 30 = 0
Answer:
x = 5 , x = - 6
Step-by-step explanation:
First we factor using factorisation method :
We need 2 numbers that multiply to give +1 and add to give -30 :
To find these numbers we write out all the factors of 30 :
1, 30
2 , 15
3 , 10
5 , 6 ----> These must be the numbers as -5+6 = 1
Now we split +x into -5x and +6x :
x² -5x + 6x -30 = 0
Factor the first 2 terms together and the last two terms :
x(x-5) + 6(x-5) = 0
Keep 1 bracket and terms outside the brackets collect them into one:
(x-5)(x+6) = 0
We know that 1 of these brackets must be equal to zero as anything multiplied by zero = 0
Either x - 5 =0 OR x + 6 = 0
So x = 5 x = - 6
These are our final answers
Hope this helped and have a good day
Answer:
(x-5) (x+6)
x=5
X=-6
Step-by-step explanation:
x²+x-30=0
factorizing
x²-5x+6x-30=0
x(x-5)+6(x-5) =0
(x-5)(x+6)=0
now solve individually
x-5=0
send 5 to the other side
x=5
x+6=0
send 6 to the other side
x=-6
hope you understand the procedure
A line has the equation 32 - 2y = 1 What is the equation of
parallel line going through the point (-6,
- 10)?
The equation is given by Ar + By = C where
Answer:
A = 3; B = -2; C = 2
Step-by-step explanation:
Original line:
3x - 2y = 1
Slope of original line:
-2y = -3x + 1
y = 3/2 x - 1/2
slope = m = 3/2
Parallel lines have equal slopes, so we need the equation of the line with slope 3/2 that passes through the point (-6, -10)
y = mx + b
y = (3/2)x + b
Substitute -6 for x and -10 for y and solve for b.
-10 = (3/2)(-6) + b
-10 + 9 = b
b = -1
Equation: y = (3/2)x - 1
2y = 3x - 2
3x - 2y = 2
if Jill's age is 84 and johns age is 21 how many years ago was Jill 10 times older than john
Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2^x– 4, (Consider domain, range, x-intercepts, and y-intercepts.)
The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function given in the problem is:
f(x) = x³ + x² – 3x + 4
The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.
The second function given in the problem is:
g(x) = 2x – 4
The highest degree (power) of this function is 1. Thus, this function is a type of linear function.
Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).
Thus, the first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
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