For each graph, f(x) is the parent function and g(x) is a transformation of f(x). Use the graph to determine the equation of g(x).
Answers
The equation of g(x) when the parent function f(x) = 3^x is transformed is g(x) = 3^{x - 4} + 5.
The equation of g(x) when the parent function f(x) = 2^x is transformed is g(x) = 4(2)^{x - 3}.
The equation of g(x) when the parent function f(x) = 4^x is transformed is g(x) = -2(4)^{x + 1} + 3.
How to determine the equation of g(x) by using the graph?By critically observing the graph of the exponential function f(x) = 3^x, we can reasonably and logically deduce that f(x) is vertically translated (k) by 5 units up and horizontally translated (h) by 4 units to the right. Therefore, the equation of g(x) is given by:
g(x) = 3^{x - h} + k
g(x) = 3^{x - 4} + 5.
Based on the graph of the exponential function f(x) = 2^x, we can reasonably and logically deduce that f(x) is compressed by a scale factor (a) of 4 units and horizontally translated (h) by 3 units to the right. Therefore, the equation of g(x) is given by:
g(x) = a(b)^x - h}
g(x) = 4(2)^{x - 3}
Based on the graph of the exponential function f(x) = 4^x, we can reasonably and logically deduce that f(x) is reflected across the x-axis and expanded by a scale factor (a) of 2 units, followed by a translation of 1 units left and 3 units up:
where; a = -2, h = -1, and k = 3.
g(x) = a(b)^x - h} + k
g(x) = -2(4)^{x - (-1)} + 3
g(x) = -2(4)^{x + 1} + 3
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Related Questions
Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F. What was the temperature at 6 pm?
Answers
The temperature at 6 P.M. would be - 29 °F.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F.
Temperature at 9 A.M. = - 10.4°F.
At noon, the temperature would be = - 10.4°F + 10°F = - 0.4°F
At 3 P.M., the temperature would be = - 0.4°F - 10°F = - 10.4°F
At 6 P.M., the temperature would be = - 10.4°F - 18.6°F = - 29 °F
Therefore, the temperature at 6 P.M. would be - 29 °F.
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Marquis used the steps below to find the solution to the inequality Negative 5.6 greater-than-or-equal-to x + 3.6.
Step 1 Subtract 3.6 from both sides of the inequality.
Negative 5.6 greater-than-or-equal-to x + 3.6. Negative 5.6 minus 3.6 greater-than-or-equal-to x + 3.6 minus 3.6. Negative 9.2 greater-than-or-equal-to x.
Step 2 Interpret the results.
x greater-than-or-equal-to negative 9.2
x is greater than or equal to –9.2.
Step 3 Draw a number line.
A number line going from negative 9.5 to negative 8.8. A closed circle is at negative 9.2. Everything to the left of the circle is shaded.
Which describes the first step in which Marquis made an error?
In Step 1, Marquis should have added 3.6 to each side of the inequality.
In Step 2, Marquis should have interpreted the results as x less-than-or-equal-to negative 9.2, which means that x is less than or equal to –9.2 .
Marquis should have used an open circle at –9.2 in Step 3.
Marquis should have shaded the number line to the right of –9.2 in Step 3.
Answers
Answer:
x greater-than-or-equal-to negative 9.2
Step-by-step explanation:
Step by step in math notation here is what Marquis solved
Starting with -5.6 ≥ x + 3.6
Step 1
Subtract 3.6 from both sides of the inequality.-5.6 - 3.6 ≥ x + 3.6 - 3.6-9.2 ≥ x
Step 2: Interpret the results
-9.2 ≥ x
is
x ≤ -9.6 The correct interpretation is x less -than-or-equal-to negative 9.2
Since the question is asking only for the first step where the error was made, the rest of the actions taken have no relevance
Let A= and B=.What value(s) of k , if any , will make AB = BA ? Select the correct choice below and. if necessary fill in the answer box within your choice. A. k = D (Use a comma to separate answers as needed.) B. No value of k will make AB = BA
Answers
The value of k = −8 for which AB = BA.
[tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]
Now,
[tex]AB = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right] \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] = \left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] \left[\begin{array}{ccc}2&3\\-1&-1\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]
Thus, in order for AB = BA, we must have that
[tex]\left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]
Equate the values, and we get
18 + 3k = -6
3k = -6 - 18
3k = -24
k = -8
and 2 = -6 - k
k = -6 - 2
k = -8
Therefore we can say that it is easy to see that these equations are satisfied if and only if k = −8, and thus k = −8 is the (unique) value for which AB = BA.
--The given question is incomplete; the complete question is
"Let [tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]. What value(s) of k, if any, will make AB = BA?"--
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3/4 + x < 1/6.
Please help!!!!!
Answers
Original Equation:
[tex]\frac{3}{4} + x < \frac{1}{6}[/tex]
1) Subtract 3/4 from both sides:
[tex](\frac{3}{4}+x)-\frac{3}{4} < \frac{1}{6}-\frac{3}{4}[/tex]
2) Simplify:
[tex]x < \frac{1}{6}-\frac{3}{4}[/tex]
Find a common denominator for both fractions (I will use 12)
[tex]x < \frac{2}{12} -\frac{9}{12}[/tex]
Simplify:
[tex]x < \frac{-7}{12}[/tex]
We cannot simplify the expression anymore, therefore this is the answer!
From 60 cm to 90cm.
% i need help
Answers
Answer:
90 is 150% of 60
OR
90 is 50% greater than 60
Step-by-step explanation:
To find the percentage increase between two values, the first step is to find the difference between the final and initial value.
Final value: 90cm
Initial value: 60cm
Difference = 90 - 60 = 30cm
Next, you need to divide the difference between the two values by the initial value.
30 / 60 = 0.5
Lastly, you need to take the value previously found and multiply it by 100 to convert it from a decimal to a percentage.
0.5 * 100 = 50%
This value will be your percentage increase.
If you want to know what percentage the final value is of the initial value, you can take the percentage you have and add 100% to it.
50% + 100% = 150%
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Have a GREAT day!!!
Answer: 150%
Step-by-step explanation:
First, ask yourself what the difference between the two is: 90-60=30.
Secondly, 30 is 1/2 of 60. 1/2=50%.
You also need to add the hundred percent because we are adding 60 and 60 is 100% of 60. It increases by 50 and then 100. so 150%.
50% + 100% = 150%
Please help me answer this trigonometry question. 10 POINTS AND BRAINLIEST available.
Answers
Answer:
Step-by-step explanation:
sin(YZX)=opposite/hypotenuse
sin(YZX)=7.5/22.3
then apply sin inverse to find angle Z
In a city of exactly 100,000 people, 90% can expect to live to (at least) age 60 and 60% can expect to live to (at least) age 80. What is the probability that a resident of this city who is 60 years old will survive until they are 80?
my work:
The probability that a resident of the city who is 60 years old will survive until they are 80 is 0.6 * 0.9 = 0.54.
is this correct?
Answers
The probability that a resident of this city who is 60 years old will survive until they are 80 will be 0.54 l.
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.
In this case, in the city of exactly 100,000 people, 90% can expect to live to (at least) age 60 and 60% can expect to live to (at least) age 80.
The probability that a resident of this city who is 60 years old will survive until they are 80 will be:
= 90% × 60%
= 0.54
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On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0).
Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"?
Answers
The rule that describes the composition transformation that maps ABCD to A''B''C''D'' is;
''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The given coordinates of parallelogram ABCD are;
⇒ (3, 5), (6, 5), (4, 1), (1, 1)
The coordinates of the parallelogram A'B'C'D' are;
⇒ A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)
The coordinates of the parallelogram A''B''C''D'' are;
⇒ D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)
The image of the point (x, y), following a reflection about the x-axis is the point (x, -y).
And, The difference in the coordinates of the parallelogram ABCD and A'B'C'D' is the change in the sign of the y-coordinates
Therefore, the transformation that gives the parallelogram A'B'C'D' from the parallelogram ABCD is a reflection about the x-axis
Thus, The difference between the coordinates of the vertices of the parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the x-value by (-6), and a change in the y-value by (+1)
Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation of 1 unit, x in the y-direction.
Which gives;
The composition transformation that maps the pre-image ABCD to the final image A''B''C''D'', (given that in a composition transformation, the transformation to the right is done first) are; which is the option;
''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.
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set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curves y = 1/(1 x2), y = 0, x = 0, and x = 2 about the line x = 2.
Answers
Answer: a
Step-by-step explanation: add 2 + 3 +28
An integral for the volume of the solid obtained by rotating the region bounded by the curves y = 1/(1 x2), y = 0, x = 0, and x = 2 about the
line x = 2 is v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx
we will use the method of cylindrical shells here as per the limits given to calculate the volume,
let us first find the volume of a cylindrical shell with thickness dx at a distance of x from y axis,
dV = 2.pi(2-x).y.dx
where (x,y) is a point on the curve y=1/1+[tex]x^{2}[/tex]
v = 2.pi.(2-x)(1/1+[tex]x^{2}[/tex]).dx
Therefore the total volume would be,
v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx
v = 2.pi.[2tan-1 x -(1/2).ln(1+[tex]x^{2}[/tex])] at 0,2
v = 2.pi.[2tan-1(2) - ln 5/2]
v = 4 .pi.tan-1(2) - pi.ln5
therefore volume = 8.8 approximately.
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PLEASE HELP !!
Question: what do means indicate about the vegetables weight?
Tomatoes are typically ____ (lighter or heavier) than cucumbers since the mean weight for tomatoes is ___ (less or greater) than the mean weight for cucumbers.
Answers
Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.
Answer:
Lighter, less
Step-by-step explanation:
The mean is also known as the average. This means that it is the sum of all values divided by the total number. Therefore it is said that on average, tomatoes weigh less than cucumbers.
A muic treaming ervice charge a flat monthly fee plu a per ong charge for each ong downloaded. It cot $11 to download 2 ong during the month and $14 to download 8 ong during the month. Write an equation in the form y = mx b for thi function
Answers
"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month."
The equation in the form y = mx b for this function is:
y = (1/2)x + 10
To write an equation in the form y = mx + b for this function, we can use two sets of data points, (x, y), to find the slope (m) and the y-intercept (b) of the line.
Let x be the number of songs downloaded and y be the cost in dollars.
First data point: (2, 11)Second data point: (8, 14)We can use the slope formula to find m:
m = (y2 - y1) / (x2 - x1) = (14 - 11) / (8 - 2) = 3 / 6 = 1/2Next, we can use one of the data points and the slope to find b:
b = y - mx = 11 - (1/2) * 2 = 11 - 1 = 10Therefore, the equation of the line is: y = (1/2)x + 10
This equation represents the cost y in dollars of downloading x number of songs, given the flat monthly fee and per song charge.
Complete Question:
"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month. Write an equation in the form y = mx + b for this function."
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Find the circumference of a circle with a radius of 3 miles
Answers
The circumference of the circle with radius 3 miles is 18.85 miles.
What is a circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The following are some of the circle's crucial characteristics:
If the circles have equal radii, they are said to be congruent.The longest chord in a circle is its diameter.In the center of a circle, equal chords subtend equal angles.The chord is divided in half by the radius drawn perpendicular to the chord.Circles with various radii are comparable.A circle can encircle a kite, triangle, square, trapezium, rectangle, and more.You may encircle a square, triangle, or kite with a circle.Equal in length are the chords that are equally spaced from the center.The longest chord's (diameter) distance from the circle's center is equal to zero.As the chord length rises, the perpendicular distance from the circle's center decreases.The tangents are parallel to one another if they are drawn at the diameter's end.The radii connecting the ends of a chord to the center of a circle create an isosceles triangle.The radius of the circle is 3 miles
Circumference of the circle 2π(radius) = 2*π*3 = 18.85 miles.
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the quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least ? grounds per mile, minimum.
Answers
The quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least 4 grounds per mile.
A utility cooperative is a specific kind of cooperative that is responsible for providing its members with a public utility, such as power, water, or telecommunications. Profits are either distributed to members as "patronage" or "capital credits," which are dividends paid on a member's investment in the cooperative, or they are reinvested for infrastructure.
Every consumer is a shareholder and a member of the company. This means that, in contrast to investor-owned utilities where the amount of individual authority is determined by the number of shares held, all members have the same level of personal authority. Many utility cooperatives operate their business in accordance with a set of ideals based on the Rochdale Principles, just like cooperatives active in other industries.
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Describe the inverse operation that will undo the given operation adding -6
Answers
Answer:6
Step-by-step explanation:
What is the arithmetic sequence if the first term is 40 and the common difference is -12
Answers
Answer:
40,28,16,4, -8,-20... keep going
Step-by-step explanation:
use 40-12, then 40-2*12, so forth
The cost of basketball was $38 last week. This week, the cost fell to $33 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
HELPPPP. ILL GIVE YOU 100 POINTS:))
if you dont the problem i js give yu the points
Answers
Answer: 13.2%
Step-by-step explanation:
To find the percentage we need to use the formula: (original cost-new cost)/original cost *100
Plugging in the numbers: (38-33)/38*100=0.131578947368421*100=13.2%
Help please with graphing and the solution !
Answers
The weight of gift is 5 pound extra with medium size of box.
What is the weight of items?In science and engineering, the weight of an object is the force acting on the object due to gravity.
Let the weight is W
The first company charged “$15 to ship a medium box, plus an additional $1 per pound”.
So, that the amount of certain weight is F = $15 + $1*W
The second company charged “$10 to ship a medium box, plus an additional $2per pound”.
So, that the amount of certain weight is S = $10 + $2*W
The two shipping methods will cost the same amount
so that, F = S
$15 + $1*W = $10 + $2*W
$5 = $1*W
W = 5 pound.
So that the weight of gift is 5 pound extra with medium size of box.
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A sprinkler sends the water out in a circular pattern.How many feet away from the sprinkler can it spread water if the area forked by the watering pattern is 706.50 square feet? Use 3.14 for pie
Answers
The number of feet away from the sprinkler where it could spread water would be the radius of the circle in which it is spraying.
The area of the circle is
[tex]\pi[/tex]r²=706.50
(3.14)r²=706.50
r²=706.50÷3.14
r²=225
Now, the square root will shift from LHS to RHS.
r=(225)²
r=15
Therefore, the sprinkler can spread the water 15 feet away .
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The grocery tore ha bulk pecan on ale, which i great ince you're planning on making 5 pecan pie for a wedding. How many pound of pecan hould you buy?
Firt, determine what information you need to anwer thi quetion, then click here to diplay that info (along with other info). You will need to buy how many pound of pecan
Answers
Answer: You should buy 7.5 pounds of pecan.
Step-by-step explanation: Each pecan pie needs 1.5 pounds each and 1.5 x 5 = 7.5
the sum of two positive integers is 28. when the smaller integer is subtracted from three times the larger, the result is 36. find the two integers.
Answers
The two integers required in the question are; 16 and 12
How to solve Algebraic word problems?We are told that the sum of two positive integers is 28. Now, if the two integers are x and y, then we have;
x + y = 28 ------(1)
When the smaller integer is subtracted from three times the larger, the result is 36. Thus;
3x - y = 36 ------(2)
Add eq 1 and eq 2 to get;
4x = 64
x = 64/4
x = 16
16 + y = 28
y = 28 - 16
y = 12
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A loss of 15% is incurred by selling an article at Rs 10200. At what price should one sell it in order to make a profit of 15%?
Answers
Answer:
13800
Step-by-step explanation:
First we suppose the cost price is X, so 15%x is lost
x-15%x=10200
85%x=10200
x=12000
Now want 15% profit, so 100%+15%=1.15
12000x1.15=13800
you have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get at least 14 heads. what is the probability that you will get heads more than 14 times?
Answers
The probability of getting at least 14 heads when flipping a fair coin 20 times is 0.25.
This can be calculated using the binomial distribution formula which states that the probability of obtaining exactly x successes in n trials is given by
P(x) = (n choose x) * p^x * (1-p)^(n-x),
where n is the total number of trials, p is the probability of success, and x is the number of successes.
For this problem, n=20, p=0.5, and x=14, so the probability of getting at least 14 heads is P(x) = (20 choose 14) * 0.5^14 * 0.5^6 = 0.25.
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Consider the exponential function f(x)=(15). What is the value of the growth factor of the function?
23/1/2
23/
05
O 15
Answers
On solving the provided question, we can say that here, the function is f(x) = 1/5(15^x) and growth factor is 15.
What is function?
The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
For given question
the function is
f(x) = 1/5(15ˣ)
when f(x) = aˣ
then the growth factor of function = a
Then for f(x) = 1/5(15ˣ)
Growth factor = 15
Therefore the growth factor of function is 15.
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The drama club i elling ticket to their play to raie money for the how' expene. Each tudent ticket ell for $4. 50 and each adult ticket ell for $8. The auditorium can hold no more than 84 people. The drama club mut make at leat $560 from ticket ale to cover the how' cot. If 29 tudent ticket were old, determine all poible value for the number of adult ticket that the drama club mut ell in order to meet the how' expene. Your anwer hould be a comma eparated lit of value. If there are no poible olution, ubmit an empty anwer
Answers
If 29 student tickets were sold, then all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses are 54 and 55 .
the price for each student ticket is $4.50 and adult is $8 ;
The number of people auditorium can hold is = no more than 84 people ;
the number of children tickets sold is = 29 tickets ;
Let "x" be number of adult tickets sold.
The total revenue from ticket sales = $4.50×29 + $8×(x)
⇒ $130.5 + $8x.
The total revenue must be at least $560,
So , $130.5 + $8x ≥ $560.
Subtracting $130.5 from both sides, we get $8x ≥ $429.5 ;
Dividing both sides by 8, we get x ≥ 53.69 ;
Since the number of adult tickets sold must be an integer, the minimum number of adult tickets that must be sold is 54.
The maximum number of people allowed in the auditorium is 84, so the maximum number of adult tickets that can be sold is 84 - 29 = 55.
Therefore, the possible values for the number of adult tickets that must be sold are 54, 55.
The given question is incomplete , the complete question is
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4.50 and each adult ticket sells for $8. The auditorium can hold no more than 84 people. The drama club must make at least $560 from ticket sales to cover the show's costs. If 29 student tickets were sold, determine all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses.
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a. suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is 0.3, whereas the probability that the father is a current smoker is 0.4. what is the probability that both the father and mother are current smokers?
Answers
The probability that both the father and mother are current smokers is 0.12.
The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.
The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.
Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.
P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)
P(Father and Mother are current smokers) = 0.4 × 0.3
P(Father and Mother are current smokers) = 0.12
The required probability is 0.12.
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Solve the equation:
x + 5(x + 2) = 4
Pls show steps helppp
Answers
x + 5x + 10 = 4
6x + 10 = 4
6x = 4 -10
6x = -6
x = -1
I hope this helps :))
Solve the equation? I really don't get it.
P = __
Answers
Answer:
Step-by-step explanation:
P = x
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Quetion 1
You have $50 in your aving account and plan to depoit $10 each week. Your friend ha $25 in her aving account and plan to alo depoit $10 each week. Let $x$ repreent the number of week and let $y$ repreent the total amount of money in the account
Answers
The equation for your savings account can be represented as:
y = 50 + 10x
The equation for your friend's savings account can be represented as:
y = 25 + 10x
where x is the number of weeks and y is the total amount of money in the account.
Savings Account EquationsThe equation for the savings account can be determined by taking the initial amount of money and adding the weekly deposit over a certain number of weeks. The initial amount of money in your savings account is $50, and you plan to deposit $10 each week, so each week your balance will increase by $10.
Starting from the initial balance, after the first week, the balance will be $50 + $10 = $60. After the second week, the balance will be $60 + $10 = $70, and so on. We can represent this pattern using an equation:
y = 50 + 10x
where y is the balance after x number of weeks.
Similarly, for your friend's savings account, the initial balance is $25 and the weekly deposit is $10. So, each week the balance will increase by $10. Using the same pattern, the equation for your friend's savings account can be represented as:
y = 25 + 10x
where y is the balance after x number of weeks.
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A weather station on the top of a mountain reports that the temperature is currently
0'C and has been falling at a constant rate of 3°C per hour. If it continues to fall
this rate, find each indicated temperature. Explain or show your reasoning.
Answers
The needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.
How to solve this?A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.
We must discover,
What will the temperature be in 2 hours, 5 hours, and half an hour if it continues to plummet at current rate?
In response to the question,
A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.
The temperature drops by 3°C in one hour = 0 – 3 = -3°C
The temperature drops in two hours = (2)(-3°C) = -6°C
Temperature drop in 5 hours = (5)(-3°C) = -15°C
In half an hour, the temperature drops = (0.5)(-3°C) = -1.5°C.
As a result, the needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.
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The required temperature will drop further at this rate in 2 hours at -6 °C, 5 hours at -15 °C, and 30 minutes at -1.5 °C.
What is the weather station on the top of a mountain?A weather station on a mountaintop says that the temperature is now 0 °C and has been dropping at a consistent pace of 3 °C every hour.
A weather station is a place equipped with tools for measuring atmospheric conditions, gathering data for weather forecasts, and researching the weather and environment.
The temperature drops by 3 °C in one hour = 0 – 3 = -3 °C. The temperature drops in two hours = (2)(-3 °C) = -6 °C
Temperature drop in 5 hours = (5)(-3 °C) = -15 °C
In half an hour, the temperature drops = (0.5)(-3 °C) = -1.5 °C.
Therefore, the needed temperature continues to decline at this pace in 2 hours -6 °C, 5 hours -15 °C, and half an hour -1.5 °C.
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Hint: The 103 degree angle is corresponding to angle 3x + 1.
Answer: x = Answer
Answers
The measure of value of x for the given set of parallel lines is found as:
x = 34.
Define the term alternate exterior angles?The pair of angles that lie outside the parallel lines yet on the other side of the transversal are known as alternate exterior angles. When two lines are split in a third line, called transversal, the phrase alternating exterior angles is frequently used. According to the Alternative Exterior Angles Theorem, pairs of alternative exterior angles become congruent if any lines k and l are parallel.From the definition of alternate exterior angles:
3x + 1 = 103°
3x = 103 - 1
3x = 102
x = 34
Thus, the measure of value of x for the given set of parallel lines is found as: x = 34.
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