Answers
The number of sick days an employee takes per year is believed to be about 12.
The mean purpose of null hypothesis is to verify or disprove the proposed statistical assumptions, also is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
If you wish to test the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the null hypothesis is "the mean number of sick days an employee takes per year is equal to 12 days".
Then, the correct null hypothesis is:
[tex]H_0\colon\mu=12\text{ days}[/tex]The alternative hypothesis is an alternative to the null hypothesis, then if you want to check the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the alternative hypothesis is "mean number of sick days an employee takes per year is not equal to 12 days".
Then, the correct alternative hypothesis is:
[tex]H_a\colon\mu\ne12\text{ days}[/tex]Related Questions
Maria's earnings vary directly with the number of hours she works. Suppose that she worked 6 hours yesterday and earned
$96. If she earned $144 today, how many hours did she work today?
Answers
Answer:
9 hours
Step-by-step explanation:
96÷6 =16
So she earns 16 for 1 hour so 144÷16=9 so she worked 9 hours
The table shows the busiest airports, shipping ports, and rapid rail systems in the United States. Suppose you are doing a report in which you have to research one entry from each column. You have no preference for any choices over any other choices. What is the probability that you would select Chicago O’Hare Intl. Airport, the port of Houston, Texas, and the Boston MBTA?
Answers
Ok, so
First of all, we're going to research one entry from each column.
In the first column, we want to know what's the probabili
I need help please, find the distance between (8 ,6) and (3 -6)
Answers
Answer:
distance = 13
Explanation:
The distance between two points (x1, y1) and (x2, y2) can be calculated as
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing (x1, y1) = (8, 6) and (x2, y2) = (3, -6), we get that the distance between these points is
[tex]\begin{gathered} d=\sqrt{(3-8)^2+(-6-6)^2} \\ \\ d=\sqrt{(-5)^2+(-12)^2} \\ \\ d=\sqrt{25+144} \\ \\ d=\sqrt{169} \\ \\ d=13 \end{gathered}[/tex]Therefore, the distance between the points is 13.
How many degrees would this octagon need to be rotated clockwise around its center to get point K to point G
Answers
In the image below you can observe that we have to rotate four times.
Where each rotation is 45 degrees. So,
[tex]45\times4=180[/tex]Hence, the right answer is A. 180°.15. The number of snowboarders + skiers at a resort per day and the amount of new snow the resort reportedthat morning are shown in the table. Graph the paired data below for the five days listed, and then draw anddetermine the equation of the line of best fit through the data. (1/2 point)Amount of NewSnow (in inches) (x)Number ofSnowsliders (y)2+Equation for Line of Best Fit:468101146 1556 1976 2395 2490Number of Snowsliders25002000150010005000ty14 8 12New Snow (in.)16. If the resort reports 15 inches of new snow, how many skiers and snowboarders would you expect to be atthe resort that day? You should use your equation from the previous problem. (1/2 point)
Answers
To determine the equation of theline of best fit, we will be needing a few things. First, we need to calculate the average (mean) of the x-values.
To find the mean, we simply add all of the x-values, then divide it by the number of addends.
The mean x-value is 6, calculated as follows:
[tex]\frac{2+4+6+8+10}{5}=6[/tex]Then, we also do the same for the y-values; wee look for the mean.
[tex]\frac{1146+1556+1976+2395+2490}{5}=1912.6[/tex]The mean y-value is 1,912.6.
We will use theses means t osolve for the slope m using the equation:
[tex]m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}[/tex][tex]\begin{gathered} m=\frac{(2-6)(1146-1912.6)+(4-6)(1556-1912.6)+(6-6)(1976-1912.6)+(8-6)(2395-1912.6)+(10-6)(2490-1912.6)}{(2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2} \\ \\ m=176.35 \end{gathered}[/tex]So m = 176.35.
Finally, we solve for b using the equation:
[tex]b=\bar{y}-m\bar{x}[/tex][tex]\begin{gathered} b=1912.6-176.35(6) \\ b=854.5 \end{gathered}[/tex]So b = 854.5.
Now we can write the full equation of the best-fit line:
y = 176.35x + 854.5
If the resort reports 15 inches of new snow, then we use x = 15 to solve for y using the equation of the best-fit line to approximate the number of snowsliders.
[tex]\begin{gathered} y=176.35x+854.5 \\ y=176.35(15)+854.5 \\ y=3499.75 \end{gathered}[/tex]We round off this value to 3,500 since we are looking for number of people.
The answer is 3,500.
Lori has purple and red flowers in groups of 6. She has x groups of purple flowers and y groups of red flowers. Select an expression that shows the total number of flowers that Lori has?
Answers
Given
the number of group of purple as x
the number of group of red as y
The sum total of the flowers in group of 1 will be x+y
Since we are to find the total number of flowers she will have in group of 6, we will multiply the sum of the flower by 6 as shown;
6(x+y)
Open the parenthesis
= 6(x)+6(y)
= 6x+6y
The correct option is B
What is the diameter of a circle with circumference 24 pi ft?
Answers
Answer:
24 ft
Explanation:
The circumference of a circle is equal to:
[tex]C=d\cdot\pi[/tex]Where d is the diameter of the circle. So, replacing c by 24π feet, we get:
[tex]24\pi=d\cdot\pi[/tex]Dividing both sides by π, we get:
[tex]\begin{gathered} \frac{24\pi}{\pi}=\frac{d\cdot\pi}{\pi} \\ 24=d \end{gathered}[/tex]Therefore, the diameter is 24 ft
Jessica is a professional baker. She bakes 113 cupcakes in 2 hours How many cupcakes will she make in 6 hours? Jessica can make cupcakes in 6 hours How long will it take her to make 791 cupcakes? It will take Jessica 791 cupcakes hours to make The equation that represents this situation is y Time (hour) Cupcakes 113 2 791
Answers
You know that Jessica can bake 113 cupcakes in 2hours, using this relationship you can calculate the number of cupcakes she can bake in 6 hours using cross multiplication:
2hours_____113cupcakes
6hours_____xcupcackes
[tex]\begin{gathered} \frac{113}{2}=\frac{x}{6} \\ (\frac{113}{2})\cdot6=x \\ 339=x \end{gathered}[/tex]She can bake 339 cupcakes in 6 hours.
*-*-*-*-*-*-*
To determine how much time it will take to make 791 cupcakes you can also apply cross multiplication, this time you know the amounts of cupcakes and neet to calculate the time:
So if the can make 113 cupcakes in 2 hours,
Then she will make 791 cupcakes in x hours:
113 cupcakes_____2hours
791 cupcakes_____xhours
[tex]\begin{gathered} \frac{2}{113}=\frac{x}{791} \\ (\frac{2}{113})\cdot791=x \\ 14=x \end{gathered}[/tex]It will take her 14 hours to make 791 cupcakes.
*-*-*-*-*-*-*
To determine an equation that represents this situation, first determine the variables.
In this case:
y → will represent the number of cupcakes made
x → will represent the time she spent coocking the cupcakes
Next is to determine how many cupcakes she makes in one hour:
If she makes 113 cupcakes in 2hours, in half the time she will make half the cupcakes, that is
[tex]\frac{113}{2}=56.5[/tex]She makes 56.5 cupcakes per hour, since each passing hour se adds 56.5 cupcakes then this number will represent the coefficient of variation (or slope) of the equation and must multiply x.
Then the equation that represents this relationship is
[tex]y=56.5x[/tex]How long will it take for the ball to hit the ground? Round to the nearest hundredth.
Answers
Given:
[tex]h(t)=-16t^2+95t+3[/tex]Find-:
How long will it take for the ball to hit the ground?
Explanation-:
To hit the ground height is zero.
[tex]h(t)=0[/tex][tex]\begin{gathered} h(t)=-16t^2+95t+3 \\ \\ -16t^2+95t+3=0 \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} -16t^2+95t+3=0 \\ \\ \end{gathered}[/tex]Use quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]So, the value of "t" is:
[tex]\begin{gathered} -16t^2+95t+3=0 \\ \\ t=\frac{-95\pm\sqrt{95^2-4(-16)(3)}}{2(-16)} \\ \\ t=\frac{-95\pm\sqrt{9025+192}}{-32} \\ \\ t=\frac{-95\pm96.005}{-32} \\ \\ t=5.969,t=-0.03 \end{gathered}[/tex]So, after 5.969 second ball to hit the ground.
Find the volume of the figure. Use 3.14 for ñ If necessary, round your answer to the nearest tenth.
Answers
The given figure is a cone. The formula for calculating the volume of a cone is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
radius = 6.5
height = 14
pi = 3.14
By substituting these values into the formula, we have
Volume = 1/3 x 3.14 x 6.5^2 x 14
Volume = 619.1 m^3
heather is six years younger than her husband ryan the sum of their ages is 5w how old is ryan a)23b)29c)31d)46
Answers
Please help will mark brainlessness
Answers
Answer:
f(x) y-intercept: 7
f(x) x-intercept: -7/2 or -3.5
g(x) y-intercept: 21
g(x) x-intercept: -7/2 or -3.5
Step-by-step explanation:
The y-intercept of any function can be found, by substituting in 0 as x. The reason for this is because anywhere on the y-axis, the x-value will be equal to zero. So we know the x-value is going to be zero, we just need to solve for the y-value.
So to find the y-intercept of "g", we simply calculate g(0):\
[tex]g(0) = 3(2(0) + 7)\\\\g(0) = 3(7)\\\\g(0) = 21[/tex]
so the y-intercept of the function is 21. Now to find the y-intercept of f, we do the same thing:
[tex]f(0) = 2(0)+7\\\\f(0)=7[/tex]
Now to find the x-intercept, we use a similar method. Anywhere on the x-intercept, the y-value is zero, and the x-value may vary. In function notation, the f(x) and g(x) represent the y-value, so we simply substitute it as zero.
To find x-intercept of g, just set g(x) equal to zero:
[tex]0 = 3(2x+7)[/tex]
now from here, we usually would have two solutions. Since if one of the factors equals zero, then the entire thing is zero, regardless of the other value.
So let's set the factor (x+7) equal to zero: [tex]2x+7 = 0\implies 2x = -7\implies x=-\frac{7}{2}[/tex]
let's set 2 equal to zero: [tex]2=0[/tex], which is of course never true, so we only have the one solution of x = -7
To find the x-intercept of f, do the same process:
[tex]2x+7=0\implies 2x=-7\implies x=- \frac{7}{2}[/tex]
What is the exact value of cosine of the quantity pi over 3 question mark
Answers
We are required to find the value of the cosine of pi over 3.
The cosine of an angle is a ratio of the side adjacent to the angle to the hypothenuse side
Our approach is to first plot a triangle that will help us give values to this side and get our ratio.
Fortunately, pi over 3 is a special angle as we will see.
We can convert it to degrees via the formula:
[tex]\frac{\pi}{3}\times\frac{180^o}{\pi}=60^o[/tex]Recall that the sum of angles in an equilateral triangle of sides' ratio 2:2:2 is 180 degrees and each angle is 60 degrees.
We can find side o through Pythagoras Theorem as:
[tex]o=\sqrt[]{2^2-1^2}=\sqrt[]{4-1}=\sqrt[]{3}[/tex]The cosine of the angle is a ratio of the adjacent side, o and hypothenuse, 2.
[tex]\cos 60^o=\cos \frac{\pi}{3}=\frac{\text{adj}}{\text{hyp}}=\frac{1}{2}[/tex]OPTION B
(2x+50) (5x-10) lines p and q are parallel solve x
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |P|=2x+50 \\ |Q|=5x-10 \end{gathered}[/tex]|P| & |Q| are parallel lines: |P| = |Q|
Since |P| & |Q| are parallel lines, we equate both of them to solve for x, we have:
[tex]\begin{gathered} |P|=|Q| \\ 2x+50=5x-10 \\ \text{Put like terms together} \\ \text{Subtract 2x from both side, we have:} \\ 2x-2x+50=5x-2x-10 \\ 50=3x-10 \\ \text{Add 10 to both sides} \\ 50+10=3x-10+10 \\ 60=3x\Rightarrow3x=60 \\ \text{Divide both side by 3, we have:} \\ \frac{3}{3}x=\frac{60}{3}\Rightarrow x=20 \\ x=20 \end{gathered}[/tex]answer in standard form and contain only positive(x+2) (2x^2-x-9)
Answers
(x+2) (2x^2-x-9)
Apply distributive property:
x(2x^2)+x (-x) + x (-9) + 2 (2x^2) + 2 (-x) + 2 (-9)
2x^3 - x^2 - 9x + 4x^2 - 2x - 18
Combine like terms:
2x^3 -x ^2 + 4x^2 - 9x -2x -18
2x^3 + 3x^2 - 11x - 18
4. I The coordinates of ΔLMN are L(0,-3), M(2,1) and N(7,0). Right the coordinates of L’,M’, and N’ when ΔLMN is under a translation 2 units to the left and 4 units up
Answers
Given: The coordinate of triangle LMN as
[tex]\begin{gathered} L(0,-3) \\ M(2,1) \\ N(7,0) \end{gathered}[/tex]To Determine: The coordinates of the image, L'M'N' under the translation 2 units to the left and 4 units up
The translation rule for a translation of of a units to the left is
[tex](x,y)\rightarrow(x+a,y)[/tex]The translation rule for translation of b units up is
[tex](x,y)\rightarrow(x,y+b)[/tex]Therefore, the translation rule of a units to the left and b units up is
[tex](x,y)\rightarrow(x+a,y+b)[/tex]Applying the rule to given translation of 2 units to the left and 4 units up would be
[tex](x,y)\rightarrow(x+2,y+4)[/tex]Now, we apply the rule to get the coordinates of the image as shown below
[tex]\begin{gathered} L(0,-3)\rightarrow L^{\prime}(0+2,-3+4)=L^{\prime}(2,1) \\ M(2,1)\rightarrow M^{\prime}(2+2,1+4)=M^{\prime}(4,5) \\ N(7,0)\rightarrow N^{\prime}(7+2,0+4)=N^{\prime}(9,4) \end{gathered}[/tex]Hence, the coordinate of the image is
L'(2,1)
M' (4,5)
N' (9,4)
You randomly draw a marble, put it back, and then randomly draw a marble.What is the probability of drawing a yellow marble and then drawing a green marble? Write answer as a fraction.
Answers
Given:
The total number of marbles =7.
The number of yellow marbles = 2.
The number of green marbles =2.
The marbles are replaced after being drawn.
To find:
We need to find the probability of drawing a yellow marble and then drawing a green marble.
Explanation:
The probability of drawing yellow marble P(Y).
[tex]P(Y)=\frac{The\text{ number of yellow marbles}}{The\text{ total number of marbles}}[/tex][tex]P(Y)=\frac{2}{7}[/tex]The probability of drawing green marble P(G).
[tex]P(G)=\frac{The\text{ number of gr}een\text{ marbles}}{The\text{ total number of marbles}}[/tex][tex]P(G)=\frac{2}{7}[/tex]The probability of drawing a yellow marble and then drawing a green marble is
[tex]=P(Y)\times P(G)[/tex][tex]=\frac{2}{7}\times\frac{2}{7}[/tex][tex]=\frac{4}{49}[/tex]Final answer:
The probability of drawing a yellow marble and then drawing a green marble is 4/49.
Solve Each System by Elimination:-3x-5y=14-5x+7y=8
Answers
(-3, -1)
1) Solving this system by Elimination method:
Let's eliminate the x variables firstly:
-3x-5y=14 x -5 Multiply by the factor that yields the LCM (3,5) =15
-5x+7y=8 x 3 Multiply by the factor that yields the LCM (3,5) =15
15x +25y =-70
-15x +21y =24 Add both equations simultaneously
-----------------------
46y= -46 Divide both sides by 46
y= -1
2) Plug y=-1, into the smaller coefficients equation, just for convenience
-3x -5y = 14
-3x -5(-1) = 14
-3x +5=14 Subtract 5 from both sides
-3x = 9
x= -3
3) So the answer to this Linear System is (-3, -1)
diana has gift box that is 11 inches long, 8 inches wide and 6 inchers she has a sheet of wrapping paper that is 4 feet long by 1 foot wide does she have enough wrapping paper to wrap the box? justify your anwser
Answers
For this problem we need the paper sand to be enough to cover the surface of the box.
now we calculate the surface area of the box finding the area of each face
Surface
frontal face and bottom
the area is
[tex]\begin{gathered} A=6\times11 \\ A=66 \end{gathered}[/tex]the area of frontal face and bottom is
[tex]\begin{gathered} A=66+66 \\ A=132 \end{gathered}[/tex]left and right face
the area is
[tex]\begin{gathered} A=6\times8 \\ A=48 \end{gathered}[/tex]area of both sides
[tex]\begin{gathered} A=48+48 \\ A=96 \end{gathered}[/tex]upper and lower face
[tex]\begin{gathered} A=8\times11 \\ A=88 \end{gathered}[/tex]and the are of both face is
[tex]\begin{gathered} A=88+88 \\ A=176 \end{gathered}[/tex]Total Surface is the sum of the area of all faces
[tex]\begin{gathered} S=132+96+176 \\ S=404 \end{gathered}[/tex]Total surface of the box is 404 squre inches
Area of the paper
first we change the feet per inches to do the comparison with the surface area of the bos
[tex]\begin{gathered} 4ft\times12=48in \\ 1ft\times12=12in \end{gathered}[/tex]the paper is
and the area of the paper is
[tex]\begin{gathered} A=12\times48 \\ A=576 \end{gathered}[/tex]the area of the paper is 576square inches
[tex]576>404[/tex]the are of the paper is greater than the suface area of the box, the paper will be enough
which of the following statements correctly compares the tow functions f(x) and g(x)?.
Answers
We have two functions and we have to find which statements are true.
They both have a maximum value of 1.
f(x) has a minimum and not a maximum, so this statement is not true.
The graphs of both functions cross the x-axis at 0.
f(x) does not cross the x-axis, so this statement is not true.
The graphs of both functions cross the y-axis at 1.
This is true for f(x).
For g(x), we have to calculate g(0) to find at which value of y the function cross the y-axis:
[tex]g(0)=-4\cdot0^2+1=0+1=1[/tex]This statement is true.
Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
This is true for f(x).
For g(x), the maximum value happens when x=0, because for all other values of x, the quadratic term becomes more negative.
In the previous statement we calculate g(0)=1, so 1 is the maximum value of g(x).
This statement is true.
They both have a minimum value of 1.
g(x) does not have a minimum value. This statement is not true.
Answer: The statement that are true:
- The graphs of both functions cross the y-axis at 1.
- Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
11. Using the diagram below, classify the angle pairs as corresponding. alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.a. < 6 and < 7
Answers
• 1 and 3.
,• 9 and 11.
,• 2 and 4.
,• 10 and 12.
,• 5 and 7.
,• 13 and 15.
,• 6 and 8.
,• 14 and 16.
,• 1 and 5.
,• 2 and 6.
,• 9 and 13.
,• 10 and 14.
,• 3 and 7.
,• 4 and 8.
,• 11 and 15.
,• 12 and 16.
The alternate interior angles are• 9 and 4.
,• 10 and 3.
,• 13 and 8.
,• 14 and 7.
,• 2 and 13.
,• 10 and 5.
,• 4 and 15.
,• 12 and 7.
The alternate exterior angles are• 1 and 12.
,• 2 and 11.
,• 5 and 16.
,• 6 and 15.
,• 1 and 14.
,• 9 and 6.
,• 3 and 16.
,• 11 and 8.
The consecutive interior angles are• 9 and 3.
,• 10 and 4.
,• 13 and 7.
,• 14 and 8.
,• 2 and 5.
,• 10 and 13.
,• 4 and 7.
,• 12 and 15.
The consecutive exterior angles are• 1 and 11.
,• 2 and 12.
,• 5 and 15.
,• 6 and 16.
,• 1 and 6.
,• 11 and 16.
,• 9 and 14.
,• 11 and 16.
Therefore, angles 6 and 7 are none of the choices.HU Pon estos numeros en orden de menor a mayor: 5, 8,-1,-3. nine 8, 5, -3,-1 O O O 0 -1,3,5,8 0 -3, -1, 5,8
Answers
The given numbers are,
[tex]5,8,-1,-3[/tex]As we know, -3 < -1 < 5 < 8 therefore we can arrange the number in the order from least to the greatest as,
[tex]-3,-1,5,8[/tex]Solve the following system of equations and state whether the system is dependent, independent, or inconsistent.4x+3y=12And4x-3y=12
Answers
Given:
[tex]\begin{gathered} 4x+3y=12 \\ 4x-3y=12 \end{gathered}[/tex]Required:
To solve the system of equation using graph and to state whether the system is dependent, independent, or inconsistent.
Explanation:
Consider the equation
[tex]4x+3y=12[/tex]When x=0,
[tex]\begin{gathered} 0+3y=12 \\ 3y=12 \\ y=\frac{12}{3} \\ y=4 \end{gathered}[/tex]When x=3,
[tex]\begin{gathered} 12+3y=12 \\ 3y=12-12 \\ 3y=0 \\ y=0 \end{gathered}[/tex]Now consider the equation
[tex]4x-3y=12[/tex]When x=0,
[tex]\begin{gathered} 0-3y=12 \\ -3y=12 \\ y=-\frac{12}{3} \\ y=-4 \end{gathered}[/tex]When x= 3,
[tex]\begin{gathered} 12-3y=12 \\ -3y=12-12 \\ -3y=0 \\ y=0 \end{gathered}[/tex]The graph of the given system of equation is,
The blue graph is graph of 4x+3y=12 and the black graph is graph of
4x-3y=12.
The two line crosses at the point (3,0).
Therefore the solution is
[tex]\begin{gathered} x=3 \\ y=0 \end{gathered}[/tex]Here the solution is one.
Therefore the consistent system has exactly one solution, it is independent .
Final Answer:
The solution of the given system of equation is
[tex]\begin{gathered} x=3 \\ y=0 \end{gathered}[/tex]The consistent system has exactly one solution, it is independent .
The graph of =yfx is shown below.Draw the graph of =y12fx.
Answers
Multiplying f(x) by 1/2 meant that the function is being compressed by a factor of 1/2. This means that the function gets closer to the x-axis.
Based on the graph, the slope of the linear function is -1/2. See the illustration below to see why.
If we multiply the slope -1/2 by the factor 1/2, the slope changes to -1/4.
Also, the y-intercept that is at y = -3 after multiplying by a factor of 1/2, the y-intercept changes to -1.5.
Hence, the graph of y = 1/2f(x) will have a y-intercept at y = -1.5 and has a slope of -1/4. The graph of y = 1/2f(x) is shown below. (blue line)
I understand this, but, I’m not having the best of luck with this problem, I need a quick breakdown please.
Answers
Answer:
The period of the given graph is approximately 13 hours;
[tex]13[/tex]Explanation:
Given the graph in the attached image.
The period of a graph is the horizontal distance between two points over which a complete cycle occurs;
As shown in the figure below;
The two lowest points are at points;
[tex]\begin{gathered} (6,2.02) \\ \text{and} \\ (19,2.00) \end{gathered}[/tex]The period will be the horizontal distance between the two points;
[tex]\begin{gathered} P\approx19-6 \\ P\approx13 \end{gathered}[/tex]Therefore, the period of the given graph is approximately;
[tex]13[/tex]The half-life is blank years. Round to one decimal place as needed
Answers
SOLUTION
The formula to apply is
[tex]\begin{gathered} A=A_oe^{-\lambda t} \\ Where\text{ A = amount of substance remaining = 0.5, after half decayed} \\ A_o=1 \\ \lambda=0.051 \\ t=\text{ time in years } \end{gathered}[/tex]Putting in the values into the formula, we have
[tex]\begin{gathered} 0.5=1\times e^{-0.051t} \\ 0.5=e^{-0.051t} \\ Taking\text{ ln of both sides, we have} \\ ln0.5=-0.05t \\ t=\frac{ln0.5}{-0.051} \\ t=13.59112 \end{gathered}[/tex]Hence the answer is 13.6 years to 1 d.p
Solutions to EquationsDetermine which of the following are true statements. Check all that apply
Answers
First question.
We must subtitute w=-13 into the given equation:
[tex](-5(-13)-6)-(-4(-13)+7)=14[/tex]then, we have
[tex]\begin{gathered} (65-6)-(52+7)=14 \\ 59-59=14 \\ 0=14\text{ its an absurd !!} \end{gathered}[/tex]so, the answer is false.
Second question.
We must substitute c=-3 into the given equation:
[tex]-(-3)-3=-2(-3)-6[/tex]which gives
[tex]\begin{gathered} 3-3=6-6 \\ 0=0\text{ thats correct !!} \end{gathered}[/tex]so, the answer is true.
Third question.
We must substitute z=12 into the given equation:
[tex]4(6(12)+7)=2(5(12)+98)[/tex]which gives
[tex]\begin{gathered} 4(72+7)=2(60+98) \\ 4(79)=2(158) \\ 316=316\text{ thats correct!!} \end{gathered}[/tex]so, the answer is true.
Fourth question.
We must substitute y=-5 into the given equation:
[tex]3(-5)+2=4(-5)+7[/tex]which gives
[tex]\begin{gathered} -15+2=-20+7 \\ -13=-13\text{ thats correct !!} \end{gathered}[/tex]so, the answer is true.
Problem 2: Find mZH. H 89° 5.r-7 Exterior angle: D and Remote angles: Equation:
Answers
The exterior angle is
Remote angles are ; 70° and 50°
Exterior angle is equal to the sum of the opposite interior angles
Hence;
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Answer:
A,B, D
Step-by-step explanation:
the slope is undefined since this line is vertical
and since it is vertical and endless it will have all y values
There is no y intercept since it’s off to the side of the y axis but there is an x intercept which is at -2 since that is the only x value on the line
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Answer: A,B,D
Step-by-step explanation:
It is B and D because the x intercept is -2 because since it is only x=-2 it is undefined slope because it can be any y number, but can only be x=-2 which gives you B and D
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(c) Does f (x) have any holes? If so, where are they? (just the x-coordinate is suffi- cient)(d) Does f (x) have any x-intercepts? If so, what are they?
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f(x) is not defined where the term of the denominator is zero.
This happens when x = 4, x = -5 or x = -1
The x-intercepts is the points where f(x) = 0
this happens when x = -7 and x = 3
Notice that x = -1 can't be a x-intercept because the function is not defined at this point.