ANSWER:
a) -37
b) 9
Given:
f(x)=-x-8 and g(x) = x² + 8x − 15
a) f(1) + g(–3)
f(1) = 1 - 8 = -7
g(-3) = -3² + 8(-3) - 15 = 9 - 24 - 15 = -30
f(1) + g(–3) = -7 + (-30)
= -7 - 30
-37
b) g(−9) − f(–7):
g(-9) = -9² + 8(-9) - 15 = 81 - 72 - 15 = -6
f(-7) = -7 - 8 = -15
Thus,
g(−9) − f(–7) = -6 - (-15)
= -6 + 15
= 9
What is the value of this expression?
5 (912−14 )+ 0.5
Enter your answer, in simplest form, in the box.
Answer:
4490.5
Step-by-step explanation:
5(898)+0.5
=4490.5
Sample Data48262191036984391035414135264238472947512227421220143514138142710482529331220229149943521413Computations(Round the mean and sample standard deviation to values to FIVE decimal places)Sample Mean = 25.42Sample Standard Deviation = 14.25724(Round the lower/upper limits and margin of error to THREE decimal places). #1. 80% Confidence Interval: 80% Confidence Interval Margin of Error:What does this confidence interval mean given the data?#2. 95% Confidence Interval:95% Confidence Interval Margin of Error: #3. 99% Confidence Interval:99% Confidence Interval Margin of Error:#4. Make up YOUR OWN Interval.50% Confidence Interval:50% Confidence Interval Margin of Error:
The given information is:
- Sample mean = 25.42
- Standard deviation = 14.25724
Part 1.
We have a confidence interval (C.I.) of 80%.
We need to find the z-score for this C.I., so, let's see a diagram:
We have a two-sided confidence interval. So, we need to find the z-score for a cumulative probability of 80+10=90%=0.9.
By using a standard normal table, we can see that z-score for 0.9 is:
By using an online calculator, we find the exact z-score is 1.282.
The confidence interval is given by the formula:
[tex]C.I=\bar{x}\pm z_c\frac{s}{\sqrt{n}}[/tex]Where x is the mean of the sample, Zc is the z-score for the given confidence level, s is the standard deviation and n is the number of elements in the sample n=50.
By replacing the known values, we obtain:
[tex]\begin{gathered} 80\%C.I.=25.42\pm1.282\frac{14.25724}{\sqrt{50}} \\ \\ C.I.=25.42\pm1.282\times2.016 \\ C.I.=25.42\pm2.585 \end{gathered}[/tex]So, the lower and upper limits are:
[tex]\begin{gathered} lower:25.42-2.585=22.835 \\ upper:25.42+2.585=28.005 \end{gathered}[/tex]The margin of error is equal to half the width of the entire confidence interval, and it is also the value we add and subtract to the mean to find the confidence interval, so the margin of error is 2.585.
At a New Car Dealership, a particularmodel comes in 4 different trim levels(CX, DX, EX, and Si). The same modelcomes in 5 different colors (Night Black,Pearl White, Evening Blue, Sandy Red,and Forest Green). The model of car alsohas 3 different interior options (GreyCloth, Tan Cloth, Black Leather). Howmany different versions of this model canbe created from these options?
solution
diferent trim levels = 4
different colors = 5
different interior options = 3
then:
[tex]4\cdot5\cdot3=60[/tex]answer: 60 different versions of this model
I would love if someone can please help me on this algebra problem??
SOLUTION
From this question, it means that
[tex]\begin{gathered} y=\sin x\text{ was translated to} \\ y=4\sin x \end{gathered}[/tex]To be sure the required translation, let us see a quick look at the graph of the function and it's image
[tex]y=\sin x[/tex]And
[tex]y=4\sin x[/tex]Now, we can see that the image is an enlarged form of the original function
Therefore this is a dilation. And since the increase in size is vertical, that is across the y-axis, It is a Vertical dilation.
Hence the correct answer is Vertical dilation.
Amount of Water (ml) 5 8 8.5 8 8.ŏ 8 8 8 10 I → 0 1 2 3 4 5 6 7 8 9 Days What information does the intercept provide A The amount of water in the beaker decreased by 40 ml. B. The water was gone by the eighth day.
First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40
The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q9
For the given function,
Vertical Asymptote:- x =-3
Horizontal asymptote:- y =20
Oblique asymptote :- No oblique asymptote
Asymptote:
A vertical asymptote is found by letting the denominator equal zero. A horizontal asymptote is found by comparing the leading term in the numerator to the leading term in the denominator. The degree of the numerator is greater than the degree of the denominator, so there is no horizontal asymptote.
Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator
given,
R(x) = [tex]\frac{20x}{x+3}[/tex]
Vertical Asymptote:-
Equate denominator to zero
x +3 = 0
x = -3
Horizontal asymptote:-
Here degree on x in numerator and denominator is same,
so horizontal asymptote will be,
y= 20/1
y = 20
Oblique asymptote:-
There won't be any slant asymptote, because degree in numerator is equal to the degree in denominator.
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Question 21 (1 point)Find the power function that the graph of f given below resembles, but is shifted tothe left by 3 units.f(x)=(x − 3)³Oy=x³Oy=x-27Oy=x⁹Oy=x-³
STEP - BY - STEP EXPLANATION
What to find?
The power function that the given graph resembles.
Given:
f(x)=(x − 3)³
First, we need to note that;
If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).
Let q=3
[tex]f(x)=(x-3)^3[/tex][tex]f(x)=(x-3+3)^3[/tex][tex]f(x)=x^3[/tex]ANSWER
y=x³
Use the given information to determine the lateral and surface areas of thesolid. Round your answer to the nearest unit.
Here, we want to use the given information to calculate the lateral and the total surface area
To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism
Now, we will make the shape lie on its side
This mean the triangles will represent the base
Mathematically, the perimeter of a triangle is the sum of its side
We need the last side of the triangle
We can get this by the use of Pythagoras' theorem
As we can see, the side measure 5 is the hypotenuse as it faces the right angle
The square of the hypotenuse equals the sum of the squares of the two other sides
3,4 and 5 are a Pythagorean triple
This means that, the measure 3 is the last side of the triangle
So the perimeter is;
[tex]3+4+5\text{ = 12 in}[/tex]The height is the measure 8 inches
Thus, the lateral area is;
[tex]12\text{ }\times8=96in^2[/tex]Now, we want the total surface area, but firstly, we need the area of the base
The area of the base is the area of the triangle
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\times b\times h \\ \\ B\text{ = }\frac{1}{2}\times4\times3=6in^2 \end{gathered}[/tex]two times this is 12 in^2
The total suface area is thus;
[tex]96in^2+12in^2=108in^2[/tex]??????????????????????The answers got cropped out they are ; 9, 8, 7, 6.
Given that the baker has a total of 18 cups of flour, you know that the baker needs:
- This amount of flour for a batch of banana pancakes:
[tex]1.75\text{ }cups[/tex]- This amount of flour for a batch of apple pancakes:
[tex]0.6\text{ }cups[/tex]You know that the baker makes 8 batches of banana pancakes.
Let be "x" the greatest number of whole batches of apple pancakes that the baker can make.
You can set up this equation using the given data:
[tex]1.75x+(0.6)(8)=18[/tex]Now you need to solve for "x", in order to find its value:
[tex]1.75x+4.8=18[/tex][tex]1.75x=18-4.8[/tex][tex]x=\frac{13.2}{1.75}[/tex][tex]x\approx7.5[/tex]Since the number of cups cannot be greater than 18 cups, you need to round down:
[tex]x\approx7[/tex]Hence, the answer is: Third option.
a local business club has 7 exclusive board members and 31 General members and how many committees of five members can be chosen so that only general managers are included
We need to choose 5 members from the general only
The number of general members = 31
As the arrangement is not required
So, the number of committees will be:
[tex]31C5=\frac{31!}{(31-5)!\cdot5!}=169,911[/tex]so, the answer will be 169,911 committees
In your own words, explain what you know about a number that satisfies theequation x2 = -1.
The number that satisfies the equation is
[tex]x^2=-1[/tex]Doing the square root on both sides
[tex]x=\pm\sqrt{-1}[/tex]On complex number we use the definition:
[tex]i=\sqrt[]{-1}[/tex]Therefore, the number that satisfies the equation is
[tex]x=\pm i[/tex]That means that a solution is a complex number.
Complex numbers have two parts, the complex part and the real part:
[tex]z=a+bi,\quad a,b\in\mathbb{R}[/tex]Look that a and b are real coefficients, but z is a complex number because we have b multiplying i, the complex unit.
But why complex numbers are so important?
• Complex numbers can be used to solve polynomial equations, that we couldn't solve before
,• Complex numbers can connect exponential function with trigonometric functions
[tex]e^{ix}=\cos (x)+i\sin (x)[/tex]Complex numbers are a powerful set that we can use to solve many complex problems in physics and mathematical, it may seem hard but they actually make things easier, sometimes working with complex numbers is way easier than working with real numbers.
Can you help me solve this? And step by step please?
Given the sequence:
1/2, 3/4, 9/8, 27/16, ..........
We are to find the recursive formular
A recursive geometric formular has a pattern:
An = An - 1 * r
Where r is the common ratio. But before we write the formular, we need to look for the value of r.
This r value has to be the same between each consecutive number in the series.
Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:
x/2 = 3/4 where x/2 is the same as 1/2 x.
Cross multiply to get 4x = 6 and x = 3/2.
That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.
3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:
An = An - 1 * 3/2
Therefore, the crrect optio is B.
im gonna send a photo of the problem
You have the following interval:
(-∞,-2]
the previous interval can be written as follow:
x ≤ -2 as an inequality
and on the number line you have:
What is the equation of the horizontal asymptote of the graph of y = 1/x+5 – 4?
We can find the horizontal asymptote of this kind of functions using the limit:
[tex]\begin{gathered} \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{\infty}-4=-4 \\ \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{-\infty}-4=-4 \end{gathered}[/tex]Therefore the equation of the horizontal asymptote is:
[tex]y=-4[/tex]Please help I only have the first given answer.
By the property of congruency of triangles, the following conclusions are taken from the figure
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
What is congruency of triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.
There are five axioms of congruency
They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom
Here,
In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
So,
[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]
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Given the diagram below, whereAB||CD, find the measure of xand y.
Notice that there are two triangles between the parallel lines.
Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.
[tex]160+y=180[/tex]We solve for y.
[tex]\begin{gathered} y=180-160 \\ y=20 \end{gathered}[/tex]On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.
[tex]x=30[/tex]Therefore, x = 30° and y = 20°.A small yoga studio offers two plans for sessions.•Plan A: Pay a $320 yearly fee and then $5 per session. • Plan B: Pay no yearly fee and $15 per session. Complete each statement. Both plans will cost the same for __?__ sessions. To attend one session each week for a year, plan _?__ will be cheaper.
1) Firstly, let's express each plan by using linear equations.
Plan A:
5x+320
Note that the $320 payment is done once, then 5 per session.
Plan B
15x
2) To get to know when opting for plan A or Plan B is not relevant, we need to equate both equations and solve it for x (x stands for the number of sessions)
[tex]\begin{gathered} 5x+320=15x \\ 5x-15x=-320 \\ -10x=-320 \\ 10x=320 \\ \frac{10x}{10}=\frac{320}{10} \\ x=32 \end{gathered}[/tex]So if you attend 32 sessions then, doesn't really matter which plan is it.
3) Now, let's figure out which plan is more interesting to take:
[tex]\begin{gathered} C_A(x)=5x_{}+320 \\ C(1)=5(1)+320 \\ C(1)=325 \\ --- \\ C_B(x)=15x \\ C_B(1)=15(1) \\ C_B(1)=15 \end{gathered}[/tex]So the plan B is cheaper to attend 1 session
Y=x^2 how does Y= (x-4^2) andY = (x+3) differ from theParent function and each other?what causes this to change?
The parent function is:
y = x²
This is a quadratic function
The child functions are:
y = x - 4² whcih can be written as
y = x - 16
The second child function is
y = x + 3
The two child functions are linear functions while the parent function is a quadratic function.
The parent and child functions also differ in their ranges and domains
For y = x²Domain = ( -∞ , ∞ )
Range = [0 , ∞ )
For y = x - 4² and y = x + 3:Domain = ( -∞ , ∞ )
Range = (-∞ , ∞ )
The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .
For y = x - 4², the y - intercept is -16
For y = x + 3, the y - intercept 3
This change is due to transformation (basically translation) on the x and y axes
Britta is preparing a budget. What does this task MOST likely involve?A. She is looking at her credit card bills to predict her credit score.B. She is not allowing herself to spend any money for 30 days.C. She is allotting a set amount of money for her expenses.D. She is determining which investments are the best fit for her goals.
From the question we are to determine Britta most likely task in preparing a budget.
First let's know what a budget is.
A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.
So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.
Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.
F (x) +5 x-2 Someone pls help me I’m crying
Given the function:
[tex]f(x)=2x^2+5\sqrt[]{x-2}[/tex]to find f(3), we have to make x = 3 and substitute on the function, to get the following:
[tex]\begin{gathered} f(3)=2(3)^2+5\sqrt[]{3-2}=2(9)+5\sqrt[]{1}=18+5=23 \\ \end{gathered}[/tex]therefore, f(3)=23
Trapezoid ABCD is shown on the coordinate plane.Trapezoid formed by ordered pairs A at negative 4 comma 1, B at negative 3 comma 2, C at negative 1 comma 2, D at 0 comma 1.If trapezoid ABCD is reflected over the x-axis and then reflected over the y-axis, which final step would carry the trapezoid onto itself?Group of answer choicesRotate 180°Rotate 90° clockwiseReflect over the x-axisReflect over the y-axis
Given: The coordinates of a trapezoid as below
[tex]\begin{gathered} A(-4,1) \\ B(-3,2) \\ C(-1,2) \\ D(0,1) \end{gathered}[/tex]To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis
Solution
Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis
The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.
So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps
We have step 1: Reflection over the x-axis, then
Step 2: Reflection over the y-axis
Hence, the final step is reflection over the y-axis
Writing an equation of a probably given the vertex and focus
The equation of the vertical parabola in vertex form is written as
[tex]y=\frac{1}{4p}(x-h)^2+k[/tex]Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
[tex]p=1-6=-5[/tex]Using this value for p and (3, 1) as the vertex, we have our equation
[tex]y=-\frac{1}{20}(x-3)^2+1[/tex]Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
1. The 90% confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019 is given as follows:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.D. Independently sampled pairs.What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 50 - 1 = 49 df, is t = 1.6766.
The remaining parameters are given as follows:
[tex]\overline{x} = 12.9, s = 5.52, n = 50[/tex]
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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5)For positive values of x, which expression isequivalent toSquare root 16x2*x2/3+square root 8x^5/3
The answer is option B
Given:
/16x^2 + x^2/3 + 3/8x^5
You need to simplfiy the expression given which will give you
6 3/x^5 or the second option
[tex]6\sqrt[3]{x^5}[/tex]i need to show work pls
The table shows the grading scale for one of your classes. Tell the letter grade that you earn for each score.a. You earn 14 out of a possible 20 points on a quizz.b. You earn 66 out of a possible 80 points on a test.c. You earn 216 out of a possible 250 points for a report.
a.
[tex]\frac{14}{20}=\frac{7}{10}=0.7[/tex]Therefore, your score would be 70% then you will get a C
b.
[tex]\frac{66}{80}=\frac{33}{40}=0.825[/tex]Your score would be 82.5%, then you will get a B
c.
[tex]\frac{216}{250}=\frac{108}{125}=0.864[/tex]Your score would be 86.4%, then you will get a B
which of these situations cannot be represented by the number -10 ?A) A loss of 10 yeards.B) 10 degrees below zero.C) A withdrawal of $10.D) gaining 10 points.
The correct option is D
gaining 10 points cannot be represented by the number -10
Explanation:-10 can represent all the given situations except gaining 10 points.
Because that will be an increase (+10), and not a decrease (-10)
Answer is: A withdrawal of $10.
the center of the circle is at O. determine the measure of angle ABC
If the center of the circle is at O.then the measure of angle ABC is 28 degree
The measure of angle ABC can be calculated by using central angle theorem
What is central angle theorem
The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.
The angle ABC = 1/2 angle AOC
the angle ABC = 1/2 x 56
the angle ABC is 28
Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree
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Hii I really need help right now I don’t understand.
The function is given as,
[tex]y=4^x[/tex]For x = -1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^{-1} \\ y\text{ = }\frac{1}{4} \\ y\text{ = 0.25} \end{gathered}[/tex]For x = 0 , the value of y is calculated as,
[tex]\begin{gathered} y=4^0 \\ y\text{ = 1} \end{gathered}[/tex]For x = 1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^1 \\ y\text{ = 4} \end{gathered}[/tex]For x = 2, the value of y is calculated as,
[tex]\begin{gathered} y=4^2 \\ y\text{ = 16} \end{gathered}[/tex]Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
_______________________
The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.
x + (x + 9) + (x + 4) = 2x + (4x - 2)
_____________________
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__________________
x + (x + 9) + (x + 4) = 2x + (4x - 2)
3x + 13 = 6x -2
6x - 3x = 13 + 2
3 x = 15
x = 15/3 miles
x = 5 miles
___________________________
5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)
28 = 28
________________________
on Wednesday
x=5
x+ 4 = 9
_________________
Answer
On Wednesday he ran 9 miles
_________________
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