The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Answers
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex]Related Questions
Given that A = {1, 2,2 3} and B = {4, 6}, then find B×A
Answers
The solution for set B × A is {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Given,
The sets,
A = {1, 2, 3}
B = {4, 6}
We have to find B × A.
Here,
Consider the Cartesian product:
The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B is referred to as the Cartesian Product of sets A and B in mathematics. For instance, the Cartesian Product of A and B is (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), and (2, 5) if A = [1, 2] and B = [3, 4, 5].
The Cartesian product of B × A = {(b, a) | b € B, a € A}
So,
B × A = {4, 6} × {1, 2, 3}
B × A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Learn more about Cartesian product here:
https://brainly.com/question/24372634
#SPJ1
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark ( 1 ) for the fraction bar.
Answers
Consider that the coordinates of the mid-point of a line segment is given by the formula,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]The given diagram represents the line segment between the points (-3,4) and (-6,-1).
So the corresponding mid-point is given by,
[tex]\begin{gathered} x=\frac{-3+(-6)}{2}=\frac{-9}{2} \\ y=\frac{4+(-1)}{2}=\frac{3}{2} \end{gathered}[/tex]Thus, the mid-point of the given line segment is ( -9/2 , 3/2 ) .
Karen wants to buy a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 4%, charged as simpleInterest. They lend her $8000 for 6 years. She makes no payments except the one at the end of that time.Answer the following questions. If necessary, refer to the list of financial formulas.х5?(a) How much total interest will Karen have to pay?s0(b) What will the total repayment amount be (including Interest)?s[]
Answers
Answer:
a) $1,920
b) $9,920
Explanation:
Step 1. Gather all of the information.
The amount borrowed will be the principal or starting amount P:
[tex]P=8,000[/tex]The interest rate will be r:
[tex]r=4\text{ percent}[/tex]We will need the interest rate in decimal form, for that, divide the percentage amount by 100:
[tex]\begin{gathered} r=\frac{4}{100} \\ \downarrow \\ r=0.04 \end{gathered}[/tex]And the time of the loan is 6 years, this will be the value of t:
[tex]t=6[/tex]Step 2. To solve part a, we use the following formula to calculate the interest:
[tex]I=p\times r\times t[/tex]Substituting all of the known values:
[tex]I=8,000\times0.04\times6[/tex]The result is:
[tex]I=1,920[/tex]The total interest that Karen will have to pay is $1,920.
Step 3. To solve part b, we need to find the total repayment amount.
To find this, we add the interest and the principal amount:
[tex]T=P+I[/tex]Where T represents the total amount.
Substituting P and I:
[tex]\begin{gathered} T=8,000+1,920 \\ \downarrow \\ T=9,920 \end{gathered}[/tex]The total amount she will have to repay is $9,920.
Answer:
a) $1,920
b) $9,920
Which statement is equivalent to ~p? p: Even numbers are divisible by 2.
Answers
The statement ~p is "Even numbers are not divisible by 2."
Given statement:-
p: Even numbers are divisible by 2.
We have to find ~p for the statement p.
We know that ~p means negation of p.
Hence, we will negate the statement by adding "not" in the statement.
Hence, the statement will become,
Even numbers are not divisible by 2.
Negation of a statement
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written ~P or -P.
It is interpreted intuitively as being true when P is false, and false when P is true.
To learn more about negation, here:-
https://brainly.com/question/22787240
#SPJ1
At a coffee shop, there is a pot that has a volume of 5.4 L. Find how many cubic centimeters of coffee will completely fill the pot
Answers
Given:
Total volume = 5.4 L.
We know that 1 L is equivalent to 1000 cubic centimetres; hence:
[tex]5.4L\times\frac{1000cm^3}{1L}[/tex]ANSWER
5400 cm³ of coffee will completely fill the pot
(-1,2) and (3,32)
For each of the following, find the formula for an exponential function that passes through the two points given.
Answers
The required exponential function f(x) = (4)(2)ˣ which is passes through the two points (-1,2) and (3,32).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Let the formula for an exponential function would be as
⇒ f(x) = abˣ
The exponential function passes through the two points (-1,2) and (3,32).
f(-1) = 2
f(3) = 32
2 = ab⁻¹
2b = a
32 = ab³
Substitute the value of a = 2b in the above equation,
32 = 2b×b³
32 = 2b⁴
b⁴ = 16
b⁴ = 2⁴
b = 2
Substitute the value of b = 2 in the equation a = 2b,
So a = 2×2 = 4
⇒ f(x) = (4)(2)ˣ
Therefore, the required exponential function f(x) = (4)(2)ˣ
Learn more about exponential function here:
brainly.com/question/11487261
#SPJ1
Triangle ABC is inscribed in the circle with arcs shown. find X and the measures of angle A, angle B, Angle C
Answers
The total circumference of a circle = 360°
Therefore,
[tex]\text{arc AB + arc BC+ arc AC}=360^0[/tex]Where,
[tex]\begin{gathered} \text{arc AB=(6x+10)}^0 \\ \text{arc BC=(x+15)}^0 \\ \text{arc AC=((8x-40)}^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} (6x+10)^0+(x+15)^0+(8x-40)^0=360^0 \\ 6x^0+x^0+8x^0+10^0+15^0-40^0=360^0 \\ 15x^0-15^0=360^0 \\ 15x^0=360^0+15^0 \\ 15x^0=375^0 \\ \text{divide both sides by }15 \\ \frac{15x}{15}=\frac{375^0}{15} \\ x=25^0 \end{gathered}[/tex][tex]\begin{gathered} \text{arc AB=(6x+10)}^0=(6\times25+10)^0=150^0+10^0=160^0 \\ \text{arc BC=(x+15)}^0=(25^0+15^0)=40^0 \\ \text{arc AC=(8x-40)}^0=(8\times25^0-40^0)=200^0-40^0=160^0 \end{gathered}[/tex]To calculate
[tex]\begin{gathered} \angle A,B,\angle C \\ We\text{ will use the theorem,} \\ \text{The measure of an insribed angle in a circle equals half the measure of the intercepting arc} \\ \end{gathered}[/tex][tex]\begin{gathered} \angle A=\frac{arc\text{ BC}}{2} \\ \angle A=\frac{40^0}{2}=20^0 \end{gathered}[/tex][tex]\begin{gathered} \angle B=\frac{arc\text{ AC}}{2} \\ \angle B=\frac{160^0}{2}=80^0 \end{gathered}[/tex][tex]\begin{gathered} \angle C=\frac{arc\text{ AB}}{2} \\ \angle C=\frac{160^0}{2}=80^0 \end{gathered}[/tex]Hence,
x = 25°
∠ A=20°
∠ B=80°
∠ C=80°
Please help me solve. I also need help on what ratios to put in the two boxes before the answer. Do I just choose any of them?
Answers
Explanation
By metric conversion
[tex]\begin{gathered} 1\text{ mile =}1.61km \\ 1\text{ hour = 60 mins} \end{gathered}[/tex]Therefore;
[tex]\frac{57mi}{1hr}\times\frac{1.61}{1}\times\frac{1}{60}=1.5295\frac{km}{\min }[/tex]Answer:
[tex]\begin{gathered} \text{Box 1= }\frac{\text{1.61}}{1} \\ \text{Box 2=}\frac{1}{60} \\ \text{Box 3=}1.53 \end{gathered}[/tex]66. WORKER EFFICIENCY An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled f(x) = -x³ + 6x² + 15x television sets x hours later. How many sets will such a worker have assembled by 10:00 A.M.? [Hint: At 10:00 A.M., x = 2.] b. Ilow many sets will such a worker assemble between 9:00 and 10:00 A.M.?
Answers
Step-by-step explanation:
use differential calculus
Consider the right triangle shown below where a=8.09, b=9.4, and c=12.4. Note that θ and ϕ are measured in radians.What is the value of cos(θ)?cos(θ)= What is the value of sin(θ)?sin(θ)=What is the value of tan(θ)?tan(θ)= What is the value of θ?θ=
Answers
By definition
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hipotenuse}}[/tex]From the picture
[tex]\begin{gathered} \cos (\theta)=\frac{a}{c} \\ \cos (\theta)=\frac{8.09}{12.4} \\ \cos (\theta)=0.65 \end{gathered}[/tex]By definition
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hipotenuse}}[/tex]From the picture:
[tex]\begin{gathered} \sin (\theta)=\frac{b}{c} \\ \sin (\theta)=\frac{9.4}{12.4} \\ \sin (\theta)=0.76 \end{gathered}[/tex]By definition
[tex]\tan (angle)=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]From the picture
[tex]\begin{gathered} \tan (\theta)=\frac{b}{a} \\ \tan (\theta)=\frac{9.4}{8.09} \\ \tan (\theta)=1.16 \end{gathered}[/tex]Isolating θ from the previous equations:
[tex]\begin{gathered} \theta=\arccos (0.65)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arcsin (0.76)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arctan (1.16)=49.24\text{ \degree}\approx49\text{ \degree} \end{gathered}[/tex](The difference between the values is caused by rounding errors)
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
Answers
By evaluating the equation in x = 2040, we can estimate the price to be $1507.7.
How to evaluate the equation?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Given that,
We know that the equation:
y = 1.83*x - 2225.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2040
we will get
y = 1.83*2040 - 2225.5 = 1507.7
Hence, The price will be 1507.7, in dollars, of a game in the year 2040.
To learn more about model from the given link:
https://brainly.com/question/28858291
#SPJ13
will send image. select the expression. that is not equivalent to 10 + 10p
Answers
We have that
[tex]\begin{gathered} 5(10\text{ + p +p) = 5(10 + 2p)} \\ =\text{ 50 + 10p }\ne\text{ 10 + 10 p} \end{gathered}[/tex]So the answer is the first one.
9×2=2×9 what is the property of this problem?
Answers
The property involved is called "commutative property of product"
SInce we are flipping the oerder of the factors and arrive at the same result.
The "flipping is called "commuting" in Math terms.
Which of the following tests should be administered to see if an experimental medicine lowers blood pressure among hypertensive patients? A. two-tailed test OB. right-tailed test OC. alternative test OD. left-tailed test
Answers
We have to select the appropiate test to see if an experimental medicine lowers blood pressure among hypertensive patients.
In this case, we want to test if the mean for the blood pressure after the treatment is significantly lower than the blood pressure mean without treatment.
Then, for the blood pressure to be significantly different it has to be to the left of a critical value.
Then, it is a left-tailed test.
Answer:
Evaluate the expression.If x=12, y=8, and z=3x3 + y + z3
Answers
We need to find the value of
[tex]x^3+y+z^3[/tex]Where x = 12, y = 8, and z = 3
Substitute these values in the expression above
[tex](12)^3+8+(3)^3[/tex]12^3 = 1728
3^3 = 27
Then
[tex]1728\text{ + 8 + 27 = 1763}[/tex]The value of the given expression is 1763
Number of adult tickets sold = Number of child tickets sold =
Answers
Given:
Total ticket = 321
Total collection = $3535
Adult ticket price = $15
Child ticket price = $5
Find-:
(1)
Number of adult tickets sold
(2)
Number of child tickets sold
Explanation-:
Let the number of adult tickets = x
Let the number of child tickets = y
If the total ticket is 321 then,
[tex]x+y=321........................(1)[/tex]Price for adult ticket is:
[tex]=15x[/tex]The price for child ticket is:
[tex]=5y[/tex]total price is $3535 then,
[tex]15x+5y=3535...................(2)[/tex]From eq(1)
[tex]\begin{gathered} x+y=321 \\ \\ 5x+5y=1605..............(3) \end{gathered}[/tex]So eq(2) - eq(3) is:
[tex]\begin{gathered} (15x+5y)-(5x+5y)=3535-1605 \\ \\ 15x-5x+5y-5y=1930 \\ \\ 15x-5x=1930 \\ \\ 10x=1930 \\ \\ x=\frac{1930}{10} \\ \\ x=193 \end{gathered}[/tex]Put the value in eq(1) then,
[tex]\begin{gathered} x+y=321 \\ \\ 193+y=321 \\ \\ y=321-193 \\ \\ y=128 \end{gathered}[/tex]So,
Number of adult tickets = 193
Number of child tickets = 128
5. a) Look at the number grid below. Shade the Multiples of 4, 1 2 3 4 5 6 7 00 8 9 10 11 12 13 14 15 16 17 17 18 19 20
Answers
We need to find the multiples of 4 using the next given set:
The multiples of 4 are given by
4*1 =4
4*2 = 8
4*3= 12
4*4=16
4 *5 =20
Then:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.
Mr Gregory drives a furniture delivery truck 4 days each week the table below shows the driving record for 1 week find the difference in meters between the distance Mr Gregory traveled on Wednesday and Thursday
Answers
ANSWER:
6150 meters
STEP-BY-STEP EXPLANATION:
To calculate the difference between the two days we must calculate the subtraction of the values corresponding to the days Wednesday and Thursday.
[tex]80.75\text{ km}-74.6\text{ km}=6.15\text{ km}[/tex]Now, we convert this value in kilometers to meters, knowing that 1 kilometer is equal to 1000 meters:
[tex]6.15\text{ km}\cdot\frac{1000\text{ m}}{1\text{ km}}=6150\text{ m}[/tex]Picture explains it all
Answers
Reason
The question gave you a 90 degree angle.
We know the straight angle would be 180 degrees.
So the second half is another 90 degrees.
Half of that (45) added to 90 = 135 degrees.
Picture attached shows it’s at 45 degrees on the second half or you can assume it’s half of 90.
an object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) =
Answers
GIVEN
The function of the object's velocity is given as follows:
[tex]v(t)=-2\sin t[/tex]Also given:
[tex]s(0)=0[/tex]SOLUTION
To get the position's function (s(t)), the velocity function needs to be integrated:
[tex]s(t)=\int v(t)dt[/tex]Therefore:
[tex]\begin{gathered} s(t)=\int(-2\sin t)dt \\ \mathrm{Take\:the\:constant\:out}: \\ s(t)=-2\cdot\int\sin\left(t\right)dt \\ \mathrm{Use\:the\:common\:integral}:\quad \int \sin \left(t\right)dt=-\cos \left(t\right) \\ s(t)=-2\left(-\cos\left(t\right)\right) \\ \mathrm{Simplify}\text{ and add a constant to the solution} \\ s(t)=2\cos\left(t\right)+C \end{gathered}[/tex]Recall that s(0) = 0. Therefore:
[tex]\begin{gathered} s(0)=2\cos(0)+C=0 \\ \therefore \\ C=-2 \end{gathered}[/tex]Hence, the position function is:
[tex]s(t)=2\cos t-2[/tex]The THIRD OPTION is correct.
A French restaurant used 808,870 ounces of cream last year. This year, due to a menu update, it used 90% less. How much cream did the restaurant use this year?
Answers
Answer:
80,887
Step-by-step explanation:
808,870 x (1 - 0.9)
808,870 x 0.1
80,887
9b 9a) Use the slope formula to determine the rate of change eq y- and find the y-intercept "5" by substituting the x and y values into y=mx + b
Answers
A) We need to find the rate of change of the function first.
The rate of change or slope of the line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Where x and y are the coordinates of a point in line.
In order to calculate the slope we can take the poinst:
x1 = -6, y1 = 4
x2 = -2, y2= 1
Using the formula of above we find that the slope is:
[tex]m=\frac{1-4}{-2-(-6)}=-\frac{3}{4}[/tex]Now, in order to find the value of y-intercept of the line we can use formula:
[tex]y=m\cdot x+b[/tex]Which is the function of the line. From the formula of above we don't know the value of b (the y-intercept).
But we know that the formula must be valid for a point in the line. We can find the value of b replacing the coordinates of a point in the line, let's choose: x = -6 and y = 4, so:
[tex]4=\text{ m}\cdot(-6)+b[/tex]Now we use the value of m of above:
[tex]4=(-\frac{3}{4})\cdot(-6)+b[/tex]And from the last equation we can see that:
[tex]b=4-\frac{3}{4}\cdot6=4-\frac{9}{2}=\frac{8}{2}-\frac{9}{2}=-\frac{1}{2}[/tex]So, the equation of the line is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]And the y-intercept is obtain replacing x = 0, so the y-intercept is: y = -1/2
b) From the stepts of above we already know an equation that represents the function! It is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]c) Now, we need to use the last equation to find y = n in the table. We know from the table that the value x for that value of y is x = 3, so we replace that value in the equation of the line:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot3-\frac{1}{2}=-\frac{9}{4}-\frac{1}{2}=-\frac{9}{4}-\frac{2}{4}=-\frac{11}{4}[/tex]So the value of n is:
[tex]n\text{ = -}\frac{\text{11}}{4}[/tex]Which of the following choices are correct ways to name the line in the figure below?
Answers
line VK and line TV
Explanation:
To name the lines, we pick the points on the line.
The points on the line: K, T, and V
We can name the line towars the right or towards the left.
The lines using the points:
line KV or line VK
line TV or line VT
line KT or line TK
The line with two arrows at the end represent a line.
The line with one arrow represent a ray
from the options, the correct ways to name the line in the figure below:
line VK and line TV
KV is a ray not a line
Therefore, the correct ways to name the line in the figure below : line VK and line TV
the figure shows a net for a three-dimensional figure. the net includes three squares.a) what is the three dimension figure. b) what is the surface area of the digure.
Answers
(b).
The area of the figure is equal to the sum of the area of the three squares and 2 triangles.
The area of the square is
[tex]2\operatorname{cm}\times2\operatorname{cm}=4\operatorname{cm}^2[/tex]The area of the triangle is
[tex]\frac{1}{2}\times1.7\operatorname{cm}\times2\operatorname{cm}=1.7\operatorname{cm}^2[/tex]Hence, two triangles and three squares have a total area of
[tex](4\operatorname{cm}\times3)+(2\times1.7cm)=15.4\operatorname{cm}^2[/tex]LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Answers
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
Where do the graph shifted if the function changes from Y=x^2 to Y=(x+h)^2
Answers
The independent variable x is shifted (x + h). This is a value of h units to the right since it is the sum to the variable x.
So, the graph to find where the graph shift, we need to find the difference between these two values:
[tex](x+h)^2-x^2=x^2+2hx+h^2-x^2=2hx+h^2[/tex]Then, the graph is shifted
[tex]2hx+h^2[/tex]A flower bed is in the shape of a rectangle. It measures7 yd long and 4 yd wide. Chris wants to use mulch tocover the flower bed. The mulch is sold by the squarefoot. Use the facts to find the area of the flower bed insquare feet.2ftX 5?Conversion facts for length1 foot (ft)1 yard (yd)1 yard (yd)===12 inches (in)3 feet (ft)36 inches (in) i need help with this math problem.
Answers
Answer
252 ft²
Step-by-step explanation
1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 7 yd is:
[tex]\begin{gathered} 7\text{ yd =}7\text{ yd}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ \text{ Simplifying the units:} \\ 7\text{ yd =}\frac{7\cdot3}{1}\text{ ft} \\ 7\text{ yd }=21\text{ ft} \end{gathered}[/tex]Similarly, the equivalence of 4 yards is:
[tex]\begin{gathered} 4\text{ yd }=4\text{ yd}{}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ 4\text{ yd }=4\cdot3\text{ ft} \\ 4\text{ yd}=12\text{ ft} \end{gathered}[/tex]Therefore, the length of the bed is 21 ft and the width is 12 ft.
Finally, the area of the bed (a rectangle) is calculated as follows:
[tex]\begin{gathered} A=legnth\cdot width \\ A=21\cdot12 \\ A=252\text{ ft}^2 \end{gathered}[/tex]Please help with this problem my son is having problems showing his work an understanding how. Solve x2 – 6x = 16 using the quadratic formula method. Show your work. Then describe the solution.
Answers
Solution
We are given the quadratic equation
[tex]x^2-6x=16[/tex]We want to solve by using the quadratic formula method
Note: Given a quadratic equation
[tex]ax^2+bx+c=0[/tex]The formula method is given
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From
[tex]\begin{gathered} x^2-6x=16 \\ x^2-6x-16=0 \\ \text{Comparing with the general form of a quadratic equation} \\ a=1 \\ b=-6 \\ c=-16 \end{gathered}[/tex]Substituting the parameters intot the quadratic formula
and
Therefore,
[tex]x=8,-2[/tex]Solve the problem15) 21 and 22 are supplementary angles. What are the measures to the nearest hundredth) of the two angles?5x - 92I
Answers
∠1 is 31.5°
∠2 is 148.5°.
Given:
∠1 = x
∠2 = 5x-9
The measure of ∠1 and ∠2 are supplementary angles.
First, the value of x can be calculated as,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=\frac{189}{6} \\ x=31.5 \\ x=\angle1 \end{gathered}[/tex]Substitute the value of x in ∠2.
[tex]\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}[/tex]Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.
For Hox)=2x– 9 and 96 = ; « +9), find (10 g)(x) and (gof)(x). Then determine whether (f = 9/8)= (4 * H(X).What is (fog)x)?(10 g)x)=0
Answers
Given the functions;
[tex]\begin{gathered} f(x)=2x-9 \\ g(x)=\frac{1}{2}(x+9) \end{gathered}[/tex]We want to find the composite functions;
[tex]undefined[/tex]