A decrease in smoking in the United States has resulted in lower death rates caused bylung cancer. The number of death rates per 100,000 people y can be expressed byy = - 26x2 - .55x + 91.81, where x represents the number of year after 2000.
Answers
Given the equation:
[tex]y=-0.26x^2-0.55x+91.81[/tex]Where x represents the number of years after 2000.
Let's solve for the following:
a.) Calculate the number of deaths per 100,000 for 2015 and 2017.
• For 2015, we have:
Number of years between 2015 and 2000 = 2015 - 2000 = 15
Substitute 15 for x and solve for y:
[tex]\begin{gathered} y=-0.26(15)^2-0.55(15)+91.81 \\ \\ y=-0.26(225)-8.25+91.81 \\ \\ y=-58.5-8.25+91.81 \\ \\ y=25.06\approx25 \end{gathered}[/tex]The number of deaths per 100,000 for 2015 is 25.
• For 2017:
Number of years between 2017 and 2000 = 2017 - 2000 = 17 years
Subustitute 17 for x and solve for y:
[tex]\begin{gathered} y=-0.25(17)^2-0.55(17)+91.81 \\ \\ y=7.32\approx7 \end{gathered}[/tex]The number of deaths oer 100,000 for 2017 is 7.
• b.) Let's solve for x when y = 50 using the quadratic formula.
Apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{(b^2-4ac)}}{2a}[/tex]Now, subsitute 50 for y and equate to zero:
[tex]50=-0.26x^2-0.55x+91.81[/tex]Subtract 50 from both sides:
[tex]\begin{gathered} 50-50=-0.26x^2-0.55x+91.81-50 \\ \\ 0=-0.26x^2-0.55+41.81 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Apply the general quadractic equation to get the values of a, b and c:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Hence, we have:
a = -0.26
b = -0.55
c = 41.81
Thus, we have:
[tex]\begin{gathered} x=\frac{-(-0.55)\pm\sqrt[]{-0.55^2-4(-0.26\ast41.81)}}{2(-0.26)} \\ \\ x=\frac{0.55\pm\sqrt[]{0.3025+43.4824}}{-0.52} \\ \\ x=\frac{0.55\pm6.617}{-0.52} \\ \\ x=-13.78,\text{ 11.}67 \end{gathered}[/tex]Since the number of years cannot be a negative value, let's take the positive value 11.67
Therefore, the value of x is 11.67 when y = 50.
Related Questions
i need these answered , i am very confused The options for them are:constant rational square root exponential growth cube root linear absolute value cubic logarithmic quadratic
Answers
Based on the question and the options provided, we have that:
[tex]7)\text{ The name of the parent function for g(x) = 3}\sqrt[]{x}\text{ is a square root}[/tex][tex]8)\text{ The name of the parent function for f(x) =}2^{x^{}}+5\text{ is exponential growth}[/tex][tex]9)\text{ The name of the parent function for f(x)=}\frac{5}{4}\sqrt[3]{x}\text{ is cube root}[/tex][tex]10)\text{ The name of the parent function for h(x) =}8x\text{ is linear}[/tex][tex]11)\text{ An example of an absolute value equation is: y = }\lvert x+5\rvert-3[/tex]Convert 6 kg per inch to g per m 6 points
Answers
We can do this conversion in this way:
[tex]\frac{6\operatorname{kg}}{i}\cdot\frac{1000gr}{\operatorname{kg}}\cdot\frac{1i}{0.0254m}=23622.047g/m[/tex]Then, the answer is 23622.047g/m.
In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of 1/2, reflected4 across the x-axis, and movedthrough the translation [? ].
Answers
We have to identify the translation.
We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.
We can then find the translation in each axis from the image as:
Triangle is DEF is translated 3 units to the left (and none in the vertical axis).
We can express this translation as this rule:
[tex](x+3,y+0)[/tex]Answer: (x+3, y+0)
Hey need your help it’s the one about the %
Answers
Answer:
[tex]\text{\$}$219.27$[/tex]Explanation:
We were given that:
Pamela bought an electric drill at 85% off the original price (she bought it at 15% of the original price)
She paid $32.89 for the drill
The regular price is calculated using simple proportion as shown below:
[tex]\begin{gathered} 15\text{\%}=\text{\$}32.89 \\ 100\text{\%}=\text{\$}x \\ \text{Cross multiply, we have:} \\ x\cdot15\text{\%}=\text{\$}32.89\cdot100\text{\%} \\ x=\frac{\text{\$}32.89\cdot100\text{\%}}{15\text{\%}} \\ x=\text{\$}219.27 \\ \\ \therefore x=\text{\$}219.27 \end{gathered}[/tex]Therefore, the regular price was $219.27
Find the area of the yellow region. Round to the nearest tenth. 7.53cm
Answers
The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]Calculating:
[tex]A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2[/tex]The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
[tex]A_s=\frac{d^2}{2}[/tex]Calculating:
[tex]\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}[/tex]The required area is:
A = 178.13 - 113.40 = 64.73 square cm
circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
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The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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Use the quadratic formula to solve for X 5x^2 +2x=2
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Given:
[tex]5x^2+2x=2[/tex]To solve for x using the quadratic formula, we simplify the given equation first:
[tex]\begin{gathered} 5x^2+2x=2 \\ 5x^2+2x-2=0 \end{gathered}[/tex]Next, we use the quadratic formula of the form ax^2+bx+c=0:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where:
a=5
b=2
c=-2
We plug in what we know:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2^{}-4(5)(-2)}}{2(5)} \\ \text{Simplify} \\ x_{1,2}=\frac{-2\pm\sqrt[]{44}}{10} \\ x_{1,2}=\frac{-2\pm2\sqrt[]{11}}{10} \end{gathered}[/tex]We separate the solutions:
[tex]x_1=\frac{-2+2\sqrt[]{11}}{10}=\frac{-1+\sqrt[]{11}}{5}=0.46[/tex][tex]x_2=\frac{-2-2\sqrt[]{11}}{10}=-\frac{1+\sqrt[]{11}}{5}=-0.86[/tex]Therefore,
[tex]x=0.46,-0.86[/tex]what is the substitution for f7=3(x)^2+2(x)-9
Answers
Given a function f(x), whenever you want to evaluate the function, you simply change the variable for the value you where you want to evaluate the function at, and then perform the mathematical operations the function tells you to do.
In our case f(x) = 3x^2 + 2x -9
If we evaluate f(x) at x=7, then
[tex]f(7)=3(7)^2+2(7)\text{ -9 = 3 }\cdot\text{ 49 + 2}\cdot\text{ 7 - 9 = 152}[/tex]So f(7) = 152.
Let w be defined as 2 more than the number of digits in the integer w. For example, 15* = 4 (2 digits in 15 + 2). If whas 7000 digits, then what is the value of (w)*?
Answers
The number of digits in 7000 is 4
The number of digits in w=7000
[tex](w)^{\cdot}=\text{ the number of digits in w+2}[/tex][tex](w)^{\cdot}=\text{7000+2}[/tex][tex](w)^{\cdot}=7002[/tex]Hence the required value is 7002.
9Which is the best name for a quadrilateral with vertices at A(5,-2), B(2,2), C(1,-5), and D(-2,-1)?A parallelogramB squarerhombusD rectangle
Answers
Parallelogram. Option A is correct
Explanations:In order to determine the best name for a quadrilateral with the given vertices, we will find the measure of the distance AB, BC, CD, and AD using the distance formula as shown;
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y^{}_1)^2}[/tex]For the measure of AB with coordinates A(5,-2), B(2,2);
[tex]\begin{gathered} AB=\sqrt[]{(5-2)^2+(-2-2^{}_{})^2} \\ AB=\sqrt[]{3^2+(-4)^2} \\ AB=\sqrt[]{9+16} \\ AB=\sqrt[]{25} \\ AB=5 \end{gathered}[/tex]For the measure of BC with coordinates B(2,2) and C(1, -5)
[tex]\begin{gathered} BC=\sqrt[]{(2-1)^2+(2-(-5^{}_{}))^2} \\ BC=\sqrt[]{1^2+7^2} \\ BC=\sqrt[]{50} \\ BC=5\sqrt[]{2} \end{gathered}[/tex]For the measure of CD with coordinates C(1,-5), and D(-2,-1);
[tex]\begin{gathered} CD=\sqrt[]{(1-(-2))^2+(-5-(-1^{}_{}))^2} \\ CD=\sqrt[]{3^2+(-4)^2} \\ CD=\sqrt[]{9+16} \\ CD=\sqrt[]{25} \\ CD=5 \end{gathered}[/tex]For the measure of AD with coordinates A(5, -2), and D(-2,-1);
[tex]\begin{gathered} AD=\sqrt[]{(5-(-2))^2+(-2-(-1^{}_{}))^2} \\ AD=\sqrt[]{(5+2)^2+(-2+1)^2} \\ AD=\sqrt[]{7^2+(-1)^2} \\ AD=\sqrt[]{50} \\ AD=5\sqrt[]{2} \end{gathered}[/tex]For the slopes;
Check if the length AB is perpendicular to AD
[tex]\begin{gathered} m_{AB}=\frac{2+2}{2-5} \\ m_{AB}=-\frac{4}{3} \end{gathered}[/tex]For the slope of AD
[tex]\begin{gathered} m_{AD}=\frac{-1+2}{-2-5} \\ m_{AD}=-\frac{1}{7} \end{gathered}[/tex]Since AB is not perpendicular to AD, hence the quadrilateral is not a rectangle and also not a square or rhombus since all the sides are not equal.
From the given distances, you can see that opposite sides are equal (AB = CD and BC = AD ), hence the best name for a quadrilateral is a parallelogram.
what is 2.939 radian measure to degree measure
Answers
The answer is 168.5 degrees
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|
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Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
{x|x ≤ - 6}
Write written interval motion and graph the interval
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The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
What exactly is interval notation?
The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.Interval Notation x<-6. x<−6 x < - 6.
Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
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Find d the side length of a square given the area of the square
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Area of a square = side length ^2
Given: A= 20.25
Replacing:
20.25 = s^2
√20.25 = s
s = 4.5 m
what is the slope formula of (4,2) and (7, 6.5)
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Suppose the given coordinates are represented as,
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}[/tex]Then, the formula for slope can be expressed as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}[/tex]Solving it,
[tex]m=\frac{4.5}{3}=1.5[/tex]The slope is 1.5.
The formula of (10, 8) anjd (-5,8) is
[tex]m=\frac{8-8}{-5-10}[/tex]help in this question pls
Answers
an environmental scientists is conducting research on a particular type of air pollutant. She collects air samples over time and determines the average number of micrograms (ug) of the pollutant in a cubic meter (m^3). Her data are shown in the table below.Which Function models the scientists data?A. F(×)=1.12t +50B. F(×)=50 · 1.12tC. F(×)=50 - 6tD. F(×)=50 · 0.88^t
Answers
If we graph the points of the table in a coordinate system we'll see that they line up like a line function, so option D is not possible.
If we also add the graphs for the other 3 options, we get:
The points don't line up perfectly but they are much closer to the line in blue than the red or black lines.
Therefore answer is option C f(t) = 50 - 6t
Americans who are 65 years of age or older make up 13.2% of the total population. If there at 30.3 million american in this age group, find the total u.s. population
Answers
Given:
Americans who are 65 years of age or older make up 13.2% of the total population.
Required:
The total u.s. population
Explanation:
Let the total population of u.s be x.
According to the given condition.
[tex]13.2\text{ \% of x = 30.3 billion}[/tex]Therefore,
[tex]\begin{gathered} \frac{13.2}{100}\text{ }\times\text{ x = 30.3} \\ x\text{ = }\frac{30.3\text{ }\times\text{ 100}}{13.2} \\ x\text{ = 229.55 billion} \end{gathered}[/tex]Answer:
Thus the total population of u.s is 229.55 billion.
OA.y> -22² +10z - 8OB. y<-2x² +102-8OC. y2-22² +10r - 8OD. y ≤-22² +10z - 8
Answers
Solution:
Using a graph plotter,
The correct answer that satisfies the graph is OPTION C.
Martin finds an apartment to rent for $420 per month. He must pay a security deposit equal to one and a half months' rent. How much is the security deposit? Alexis earns $31,350 per year. According to the banker's rule, how much money can she afford to borrow for a house?
Answers
if one month is $420
and the security deposit is one and a half month= 1.5*$420
1.5*420=630
So the answer is: 630
The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
2 x cubed + 13 x squared + 18 x
2 x cubed + 5 x squared minus 18 x
2 x squared + 13 x + 18
2 x squared + 5 x minus 18
Answers
Answer:
2 x squared + 5 x minus 18
Step-by-step explanation:
Hope this helps sorry if not right
Answer: D
Step-by-step explanation: EDGE
triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary
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To answer this question, we have that, if two triangles are similar, they maintain the same proportion on their corresponding sides.
We have that the corresponding sides are QP and TS, OP and RS, and QO and TR, so we can write:
[tex]\frac{TS}{QP}=\frac{RS}{OP}=\frac{TR}{QO}[/tex]Then, since we have the values for QP, TS, and OP, we can find RS using the above proportion:
[tex]\frac{TS}{QP}=\frac{RS}{OP}\Rightarrow\frac{41.4}{11}=\frac{RS}{8}\Rightarrow RS=\frac{41.4\cdot8}{11}=\frac{331.2}{11}\Rightarrow RS=30.109090\ldots[/tex]Then, we have that we can round this value to 30.11 units, and if we round the answer to the nearest tenth, we finally have that RS = 30.1 units.
Answer:
x = 30.1 (round 30)
Step-by-step explanation:
being similar we can solve with a simple equation
11 : 8 = 41.4 : x
x = 8 × 41.4 : 11
x = 331,2 : 11
x = 30.1 (round 30)
Which cosine function has maximum of 2, a minimum of –2, and a period of 2pi/3 ?
Answers
Given:
maximum = 2, minimum = -2
period = 2π/3
Find: the cosine function having those attributes stated above
Solution:
Cosine equations follow the pattern below:
[tex]y=Acos(B(x-C))+D[/tex]where A = amplitude, B = 2π/period, C = horizontal shift, and D = vertical shift.
Since the only given information is the period, let's calculate for the value of B.
[tex]B=\frac{2\pi}{period}\Rightarrow B=\frac{2\pi}{\frac{2\pi}{3}}=3[/tex]Out of the choices, only y = 2cos 3θ has the value of B which is 3. Hence, y = 2cos 3θ is the cosine function that has a maximum of 2, a minimum of –2, and a period of 2pi/3. (Option 3)
Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answers
Answer: 16 or 4
Step-by-step explanation:
-6-10=-16
10-6=4
Question : Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 6% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
The Furniture Barn pays the same as The Furniture Warehouse if my sales are $
Answers
The amount to be sold in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse is $7000.
How to calculate the value?Lat the amount of sales be represented as x.
Since the Furniture Barn offers you a job that pays straight commission of 6% of the sales. This will be:
= 6% × x = 0.06x
Also, the Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. This will be:
= 350 + (1% × x)
= 350 + 0.01x
The equation will be expressed as:
0.06x = 350 + 0.01x
Collect like terms
0.06x - 0.01x = 350
0.05x = 350
Divide
x = 350 / 0.05
x = 7000
The sale is $7000.
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Find the real part and the imaginary part of the following complex number. (sqrt(6) - sqrt(6i))/4
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
(√6 - √6i) / 4
Step 02:
complex numbers:
[tex]\frac{\sqrt{6}-\sqrt{6}i}{4}=\frac{\sqrt{6}}{4}-\frac{\sqrt{6}i}{4}[/tex]real part:
√6 / 4
imaginary part:
- √6i / 4
That is the full solution.
i do not understand what i am getting wrong for the 3rd question
Answers
ANSWER:
-4.1201
SOLUTION
[tex]\log _b\frac{1}{4}=\log _b1-\log _b4[/tex]this is also equivalent to
[tex]\log _b\frac{1\times7}{4\times7}=\log _b\frac{7}{28}=\log _b7-\log _b28=5.7833-9.9034=-4.1201[/tex]passes through (1,3) and parallel to y=-x
Answers
The equation of a line parallel to y=-x and passes through (1,3) is x+y=4
What is the relationship between coordinates and the equation of a line?The coordinates of a line pass through the equation of a line.
What is the relationship between two parallel lines?Two parallel lines make the same angle with respect to the x-axis ie. make the same slope.
We have been given that the line is parallel to y=-x or x+y=0
Thus, they will be having the same slope which is -1.
Since, in the equation Ax+By+C=0, the slope is equal to -A/B
So putting the values in the equation y=mx+c where m is the slope and c is the constant
y=-x+c
Now we know that the equation passes through (1,3)
So, putting values 1=-3+c which gives c=4
Therefore, the equation of the line is y=-x+4 or x+y=4.
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I just want to go to sleep but I need the answer to this question
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The average rate of change of a function f(x) from x1 to x2 is given by:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case we need the first three seconds so x1=0 and x2=3.
Calculate the values of the function at x=0 and x=3 to get:
f(0)=150 and f(3)=0.
Substitute these values into the formula for average rate of change:
[tex]\begin{gathered} \frac{f(3)-f(0)}{3-0} \\ =\frac{0-150}{3} \\ =\frac{-150}{3} \\ =-50 \end{gathered}[/tex]Hence the avearage rate of change of the function for the first three seconds is -50.
Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).
ABCD is a rectangle. Find the length of AC and the measures of a and f.
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SOLUTION
Consider the diagram
We need to obtain the value of length AC
Using the pythagoras rule, we have
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