Answer:
x = -8 and x= 7
Step-by-step explanation:
recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.
Hence the asymptototes will occur in x-locations where the denominator , i.e
(x+8)(x-7) = 0
solving this, we get
(x+8) = 0 ----> x = -8
or
(x-7) = 0 ------> x = 7
hence the asymptotes occur x = -8 and x= 7
Answer:
x = -8 and x = 7.
Step-by-step explanation:
The vertical asymptotes are lines that the function will never touch.
Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.
[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The vertical asymptotes are at x = -8 and x = 7.
Hope this helps!
hey guys can you please help me with this. i’m really desperate please help anything helps. thank u :(
Answer:
- 29 / 20
Step-by-step explanation
The cosec (x) = 1 / sin(x)
There are 2 ways to do this:
Either using a calculator:
sin^-1(20 / 29) = 43.60281897
so inputting into 1/sin(-x) where x = 43.6.....
This gives: -29 / 20
OR
1 / sin(x) = cosec ( x)
so cosec (x) = 1/(20/29)
= 29/20
By observing the cosec(x) graph, we see that to get cosec (-x), all we need to do is to minus our answer seeing as the graph is symmetrical across the axes. Therefore x = -29/20
In the news, you hear “tuition is expected to increase by 7% next year.” If tuition this year was $1200 per quarter, what will it be next year?
Answer: $1284 per quarter
Step-by-step explanation:
Answer:
$5136
step by step:
this year tuition-1200
in a year there are 4 quarters
so total this yr is 1200×4=4800
Next year
tuition is 100%+7%per 4months
so
1.07×1200=1284per month
per year 1284×4=5136
These two polygons are similar.
Answer:
[tex]\huge\boxed{z=3}[/tex]
Step-by-step explanation:
If two polygons are similar, then corresponding sides are in proportion.
The corresponding sides:
4 → x
y → 15
3 → w
2 → 6
z → 9
therefore:
[tex]\dfrac{z}{9}=\dfrac{2}{6}[/tex] cross multiply
[tex](z)(6)=(9)(2)[/tex]
[tex]6z=18[/tex] divide both sides by 6
[tex]z=3[/tex]
Answer:
Step-by-step explanation:
k/4 + 3= 14 k = pls help
Answer:
k = 44
Step-by-step explanation:
k/4 + 3 = 14
k/4 = 11
k = 44
Answer:
[tex]\boxed{\sf k=44}[/tex]
Step-by-step explanation:
[tex]\sf \frac{k}{4} +3=14[/tex]
Subtract 3 from both sides.
[tex]\sf \frac{k}{4} +3-3=14-3[/tex]
[tex]\sf \frac{k}{4}=11[/tex]
Multiply both sides by 4.
[tex]\sf \frac{k}{4}(4)=11(4)[/tex]
[tex]\sf k=44[/tex]
In the figure below, which term best describes point L?
Explanation:
The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.
A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.
Answer: B.) Circumcenter
Step-by-step explanation:
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
Given the equation (x−13)2+y2=64, identify the center and radius. Do not enter any spaces when typing your answers.
Answer:
centre = (13,0)
radius = 8
Step-by-step explanation:
The standard equation of the circle is
(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)
where
(x0,y0) is the centre,
r is the radius.
For
(x-13)^2 + y^2 = 64 ..............(2)
we rewrite (2)
(x-13)^2 + (y-0)^2 = 8^2 ...............(3)
and compare (3) with (1)
to identify
x0 = 13, y0 = 0, and r = 8
Therefore
centre = (13,0)
radius = 8
A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The 90% confidence interval for the true average age of all students in the university is
Answer:
The 90% confidence level is [tex]19.15< L < 20.85[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 64[/tex]
The mean age is [tex]\= x = 20 \ years[/tex]
The standard deviation is [tex]\sigma = 4 \ years[/tex]
Generally the degree of freedom for this data set is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 64 - 1[/tex]
[tex]df = 63[/tex]
Given that the level of confidence is 90% the significance level is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =[/tex]10 %
[tex]\alpha = 0.10[/tex]
Now [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]
Since we are considering a on tail experiment
The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as
[tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]
The margin for error is mathematically represented as
[tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]
[tex]MOE = 0.85[/tex]
he 90% confidence interval for the true average age of all students in the university is evaluated as follows
[tex]\= x - MOE < L < \= x + E[/tex]
substituting values
[tex]20 - 0. 85 < L < 20 + 0.85[/tex]
[tex]19.15< L < 20.85[/tex]
A basketball coach is curious about the heights of players in the league. Let the proportion of basketball players who are over 72 inches be p. If the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%, what are the null and alternative hypothesis? Select the correct answer below: H0: p=0.85; Ha: p<0.85 H0: p>0.85; Ha: p=0.85 H0: p=0.85; Ha: p>0.85 H0: μ=0.85; Ha: μ>0.85
Answer:
H0: p=0.85;
Ha: p>0.85
Step-by-step explanation:
What was being tested is that:
the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%.
The null hypothesis which we are testing against would be that the proportion of basketball players who are over 72 inches is 85%.
H0: p=0.85;
Ha: p>0.85
Select the type of equations. Consistent. Equivalent. Inconsistent
Answer:
Consistent.
Step-by-step explanation:
Since there is one solution ( the lines intersect), the equations are consistent
They would be inconsistent if the lines do not intersect
The would be equivalent if they are the same line
The answer would be consistent.
Step-by-step explanation:
In the graph shown here, there is only one solution
because the lines intersect at the point (5, 3).
In order for the lines to be inconsistent, the lines would have to not
meet or intersect each other but notice that this is not the case here.
The would be equivalent if they are the same exact line
so it would look like there would just be one line.
what is the domain and range of the relation shown?
Answer:
A.
{-4 ≤ x ≤ 4}
{-4 ≤ y ≤ 4}
Step-by-step explanation:
We’ll domain is the amount of x values,
Range is the amount of y values
_______________________________
Domain:
Starts from -4 to 4
{-4 ≤ x ≤ 4}
I made the sign less than or equal to because the circle lines are solid.
Range:
This starts from -4 to 4 also.
{-4 ≤ y ≤ 4}
Thus,
answer choices A. is correct
Hope this helps :)
Hey there! I'm happy to help!
Note that this is not a function because some inputs can have more than one output, that's why they say relation, not function! :D
DOMAIN
The domain is all of the possible x-values of the relation. We see that the lowest x-value is -4, while the highest is 4. If you plug in these two or any number in between, there will be at least one corresponding output.
This domain can be written as -4 ≤ x ≤ 4.
RANGE
The range is all of the possible outputs or y-values. We see that the minimum y-value is -4 and that the highest is 4. Therefore, we will just write it the same as the domain but use a different variable.
-4 ≤ y ≤ 4.
This matches with Option A.
I hope that this helps! Have a wonderful day!
Compute the following values when the log is defined by its principal value on the open set U equal to the plane with the positive real axis deleted.
a. log i
b. log(-1)
c. log(-1 + i)
d. i^i
e. (-i)^i
Answer:
Following are the answer to this question:
Step-by-step explanation:
The principle vale of Arg(3)
[tex]Arg(3)=-\pi+\tan^{-1} (\frac{|Y|}{|x|})[/tex]
The principle value of the [tex]\logi= \log(0+i)\ \ \ \ \ _{where} \ \ \ x=0 \ \ y=1> 0[/tex]
So, the principle value:
a)
[tex]\to \log(i)=\log |i|+i Arg(i)\\\\[/tex]
[tex]=\log \sqrt{0+1}+i \tan^{-1}(\frac{1}{0})\\\=\log 1 +i \tan^{-1}(\infty)\\\=0+i\frac{\pi}{2}\\\=i\frac{\pi}{2}[/tex]
b)
[tex]\to \log(-i)= \log(0-i ) \ \ \ x=0 \ \ \ y= -1<0\\[/tex]
Principle value:
[tex]\to \log(-i)= \log|-i|+iArg(-i) \\\\[/tex]
[tex]=\log \sqrt{0+1}+i(-\pi+\tan^{-1}(\infty))\\\\=\log1 + i(-\pi+\frac{\pi}{2})\\\\=-i\frac{\pi}{2}[/tex]
c)
[tex]\to \log(-1+i) \ \ \ \ x=-1, _{and} y=1 \ \ \ x<0 and y>0[/tex]
The principle value:
[tex]\to \log(-1+i)=\log |-1+i| + i Arg(-1+i)[/tex]
[tex]=\log \sqrt{1+1}+i(\pi+\tan^{-1}(\frac{1}{1}))\\\\=\log \sqrt{2} + i(\pi-\tan^{-1}\frac{\pi}{4})\\\\=\log \sqrt{2} + i\tan^{-1}\frac{3\pi}{4}\\\\[/tex]
d)
[tex]\to i^i=w\\\\w=e^{i\log i}[/tex]
The principle value:
[tex]\to \log i=i\frac{\pi}{2}\\\\\to w=e^{i(i \frac{\pi}{2})}\\\\=e^{-\frac{\pi}{2}}[/tex]
e)
[tex]\to (-i)^i\\\to w=(-i)^i\\\\w=e^{i \log (-i)}[/tex]
In this we calculate the principle value from b:
so, the final value is [tex]e^{\frac{\pi}{2}}[/tex]
f)
[tex]\to -1^i\\\\\to w=e^{i log(-1)}\\\\\ principle \ value: \\\\\to \log(-1)= \log |-1|+iArg(-i)[/tex]
[tex]=\log \sqrt{1} + i(\pi-\tan^{-1}\frac{0}{-1})\\\\=\log \sqrt{1} + i(\pi-0)\\\\=\log \sqrt{1} + i\pi\\\\=0+i\pi\\=i\pi[/tex]
and the principle value of w is = [tex]e^{\pi}[/tex]
g)
[tex]\to -1^{-i}\\\\\to w=e^(-i \log (-1))\\\\[/tex]
from the point f the principle value is:
[tex]\to \log(-1)= i\pi\\\to w= e^{-i(i\pi)}\\\\\to w=e^{\pi}[/tex]
h)
[tex]\to \log(-1-i)\\\\\ Here x=-1 ,<0 \ \ y=-1<0\\\\ \ principle \ value \ is:\\\\ \to \log(-1-i)=\log\sqrt{1+1}+i(-\pi+\tan^{-1}(1))[/tex]
[tex]=\log\sqrt{2}+i(-\pi+\frac{\pi}{4})\\\\=\log\sqrt{2}+i(-\frac{3\pi}{4})\\\\=\log\sqrt{2}-i\frac{3\pi}{4})\\[/tex]
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7
Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate planes, using triple integrals.
First,
[tex]9x+15y+15z=45\implies 3x+5y+5z=15[/tex]
The volume is given by the integral (one of 6 possible combinations),
[tex]\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}[/tex]
Find X.
Round to the nearest tenth.
Law of Cosines : c2 = 22 + b2 - 2ab cos C
Answer:
70.5°
Step-by-step explanation:
22² = (20)²+(18)² - 2(20)(18) cos X
484 = 400 + 324 - 720 cos X
-240 = -720 cosx
1/3 = cos X
[tex]cos^{-1}(\frac{1}{3})[/tex] = X
X = 70.52877937
6th grade math, help me please:)
Answer:
21
Step-by-step explanation:
Just like a dilation you want to find some sort of scale factor. Now when 7/2 is simplified it then becomes 3.5. Now multiply that by 6 since we are trying to find the ratio. when multiplied by 6 it becomes 21 so the ration of wins to losses is 21/6
Please! help and tell me the answers, or help me figure out these answers for 20 points? please! And please help me. Can anybody help me?
Answer:
1. Pattern (rule) : y = x-6
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
Step-by-step explanation:
Note: question number correspond to your order of questions.
1. Pattern (rule) : y = x-6
for missing parts, see attached table.
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
Which of the following inequalities is not true?
A) -2/2 < 3
B) |-1| ≥ 0
C) |-9| ≠ |9|
D) -7 ≤ -5
Answer:
C) |-9| != |9|
Step-by-step explanation:
The definition of absolute value is simply the non-negative value of the argument without regards to the sign. With this in mind, let's walk through these options.
A) -2/2 < 3 ==> -1 < 3 which is True
B) |-1| >= 0 ==> 1 >= 0 which is True since 1 is > 0
C) |-9| != |9| ==> 9 != 9 which is False since 9 == 9
D) -7 <= -5 which is True since -7 is < -5
Cheers
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answer:
69 meters
Step-by-step explanation:
Answer:
Please privately chat to us why you chose to cheat during online class, otherwise we will contact your parents and kick you out of our program for the reason stated.
Step-by-step explanation:
Please contact your Quantitive Reasoning teacher at her email, as stated in Google Classroom.
Which relation is a function?
Answer:
A
Step-by-step explanation:
A function is that of which has only one x value. Therefore you are looking for the graph that does not have multiple x values. Doing a vertical line test to see whether there is more than one point on a line of the graph will show you that A is the only one that has one answer for each x value that is given. All the other graphs have two points for some of the x's, which makes them not a function.
An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How many groups of 3 participants can
be chosen, assuming that the order in which the participants are chosen is irrelevant?
Answer: 680
Step-by-step explanation:
When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given: Total participants = 17
From these, a group of 3 participants is to be tested under a special condition.
Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]
[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]
Hence, there are 680 groups of 3 participants can be chosen,.
Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width what is the largest possible length
Answer:
Largest possible length is 21 inches.
Step-by-step explanation:
Given:
Total material available = 60 inches
Length to be 3 more than twice of width.
To find:
Largest possible length = ?
Solution:
As it is rectangular shaped frame.
Let length = [tex]l[/tex] inches and
Width = [tex]w[/tex] inches
As per given condition:
[tex]l = 2w+3[/tex] ..... (1)
Total frame available = 60 inches.
i.e. it will be the perimeter of the rectangle.
Formula for perimeter of rectangle is given as:
[tex]P = 2 \times (Width + Length)[/tex]
Putting the given values and conditions as per equation (1):
[tex]60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch[/tex]
Putting in equation (1):
[tex]l = 2\times 9+3\\\Rightarrow l = 21\ inch[/tex]
So, the answer is:
Largest possible length is 21 inches.
A merchant had a batch of 120 face shields. If you sold 5/6 of the lot yesterday, how many protectors do you have to sell?
Answer:
Step-by-step explanation:
lot = 120 face shields
sold 5/6 of 120 =
5 × 120 ÷ 6 =
600 ÷ 6 = 100 sold of the lot.
then: 120-100 = 20
They need to sell 20 protectors.
Answer:
20 face shields.
Step-by-step explanation:
You have 120 face shields.
You sell 5/6 of them. That means that you still have to sell 1 - 5/6 = 1/6 of the lot.
120 * (1/6) = 20 * 1 = 20 face shields to sell.
Hope this helps!
Fifty students are enrolled in a Business Statistics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90. a) Determine the standard error of the mean
Answer:
The standard error S.E of the mean is 5
Step-by-step explanation:
From the given data;
Fifty students are enrolled in a Business Statistics class.
After he first examination, a random sample of 5 papers was selected.
Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90
The objective of this question is to determine the standard error of the mean
In order to achieve this ; we need to find the mean and the standard deviation from the given data.
TO start with the mean;
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]
Mean [tex]\overline X[/tex] = 0.2(375)
Mean [tex]\overline X[/tex] = 75
On the other hand; the standard deviation is :
[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]
[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]
[tex]s = \sqrt{125}[/tex]
s = 11.18
Finally; the standard error S.E of the mean is:
[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]
[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]
[tex]S.E = \dfrac{11.18}{2.236}[/tex]
[tex]S.E = 5[/tex]
The standard error S.E of the mean is 5
Edit: I figured it out, it's 14+7(sqrt sign) 2
A square piece of paper is folded once so that one pair of opposite corners coincide. When the paper is unfolded, two congruent triangles have been formed. Given that the area of the original square is $49$ square inches, what is the number of inches in the perimeter of one of these triangles? Express your answer in simplest radical form.
Answer:
[tex]Perimeter = 14 + 7\sqrt{2}[/tex]
Step-by-step explanation:
Given:
Area of the square = 49 in²
Required
Determine the perimeter of the one of the congruent triangles
First, we'll determine the length of the square;
[tex]Area = Length * Length[/tex]
Substitute 49 for Area
[tex]49 = Length * Length[/tex]
[tex]49 = Length^2[/tex]
Take Square root of both sides
[tex]7 = Length[/tex]
[tex]Length = 7[/tex]
When the square is divided into two equal triangles through the diameter;
2 sides of the square remains and the diagonal of the square forms the hypotenuse of the triangle;
Calculating the diagonal, we have;
[tex]Hypotenuse^2 = Length^2 + Length^2[/tex] -- Pythagoras Theorem
[tex]Hypotenuse^2 = 7^2 + 7^2[/tex]
[tex]Hypotenuse^2 = 2(7^2)[/tex]
Take square root of both sides
[tex]Hypotenuse = \sqrt{2} * \sqrt{7^2}[/tex]
[tex]Hypotenuse = \sqrt{2} * 7[/tex]
[tex]Hypotenuse = 7\sqrt{2}[/tex]
The perimeter of one of the triangles is the sum of the 2 Lengths and the Hypotenuse
[tex]Perimeter = Length + Length + Hypotenuse[/tex]
[tex]Perimeter = 7 + 7 + 7\sqrt{2}[/tex]
[tex]Perimeter = 14 + 7\sqrt{2}[/tex]
Two ballpoint pens are selected at random from a box that contains3 blue pens, 2 red pensand 3 green pens. If X is the number of blue pens
Answer: 3/(28) ≈ 10.7%
Step-by-step explanation:
3 blue + 2 red + 3 green = 8 total pens
First pick and Second pick
[tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]
slope=4/3 find the equation of the parallel line through (5,5)
Answer:
[tex]y=\frac{4}{3}x-1.75[/tex]
Step-by-step explanation:
If the slope of a line is 4/3,
and we wanna find the equation of a line that is parallel to it and crosses through (5,5).
So we already have the slope because the slope of 2 parallel lines are the same.
y = 4/3x
Look at the image below↓
So now we just need to find the y-intercept.
After some numbers we got,
[tex]y=\frac{4}{3}x-1.75[/tex]
Look at the other image below↓
Thus,
the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].
Hope this helps :)
Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 4.5 m^3. Syrus isn't sure if the tent will be tall enough for him to stand inside. What is the height of the tent?
Answer: 2neters
Step-by-step explanation: I also recently did it on Khan academy
The height of the tent of the figure is H = 2 m
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
Let the volume of the tent be represented as V
Now , the value of V is
V = 4.5 m³
Let the height of the prism be H
Now , the base of the triangle B = 1.5 m
And , the length of the tent L = 3 m
So , Volume of Prism = B x h
4.5 = ( 1/2 ) x 1.5 x H x 3
On simplifying , we get
4.5 = 2.25H
Divide by 2.25 on both sides , we get
H = 2 m
Hence , the height of the tent is 2 m
To learn more about volume of prism click :
https://brainly.com/question/11336446
#SPJ3
The complete question is attached below :
Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 4.5 m^3. Syrus isn't sure if the tent will be tall enough for him to stand inside. What is the height of the tent?
Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among 2160 passenger cars in a particular region, 243 had only rear license plates. Among 358 commercial trucks, 55 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.05 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval.
Answer:
For 0,90 of Confidence we reject H₀
For 0,95 CI we reject H₀
Step-by-step explanation:
To evaluate a difference between two proportion with big sample sizes we proceed as follows
1.-Proportion 1
n = 2160
243 had rear license p₁ = 243/2160 p₁ = 0,1125
2.Proportion 2
n = 358
55 had rear license p₂ = 55/ 358 p₂ = 0,1536
Test Hypothesis
Null Hypothesis H₀ ⇒ p₂ = p₁
Alternative Hypothesis Hₐ ⇒ p₂ > p₁
With signficance level of 0,05 means z(c) = 1,64
T calculate z(s)
z(s) = ( p₂ - p₁ ) / √ p*q ( 1/n₁ + 1/n₂ )
p = ( x₁ + x₂ ) / n₁ + n₂
p = 243 + 55 / 2160 + 358
p = 0,1183 and then q = 1 - p q = 0,8817
z(s) = ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160 + 1 / 358)
z(s) = 0,0411 /√ 0,1043*0,003256
z(s) = 0,0411 / 0,01843
z(s) = 2,23
Then z(s) > z(c) 2,23 > 1,64
z(s) is in the rejection region we reject H₀
If we construct a CI for 0,95 α = 0,05 α/2 = 0,025
z (score ) is from z- table z = 1,96
CI = ( p ± z(0,025*SE)
CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )
CI = ( 0,1536 ± 1.96*0,01843)
CI = ( 0,1536 ± 0,03612 )
CI = ( 0,11748 ; 0,18972 )
In the new CI we don´t find 0 value so we have enough evidence to reject H₀
What is the quotient? URGENT!!
Answer:
The answer is A.
Step-by-step explanation:
You have to multiply by converting the second fraction into upside down :
[tex] \frac{4x + 1}{6x} \div \frac{x}{3x - 1} [/tex]
[tex] = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} [/tex]
[tex] = \frac{(4x + 1)(3x - 1)}{x(6x)} [/tex]
[tex] = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } [/tex]
[tex] = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } [/tex]