The interval estimate for the true population proportion is 45.25% to 64.75% and we can conclude that the majority of the community supports water rationing
How to determine the error margin?The given parameters are:
p = 55% = 0.55n = 100Confidence level = 95%The error margin is calculated using:
[tex]E = z * \sqrt{\frac{p* (1 - p)}{n}}[/tex]
Where z is the critical value.
At 95% confidence level, the critical value is:
z = 1.96
So, we have:
[tex]E = 1.96 * \sqrt{\frac{0.55 * (1 - 0.55)}{100}}[/tex]
Evaluate
[tex]E = 1.96 * \sqrt{0.002475}[/tex]
Evaluate
E = 0.0975
Hence, the error margin is 0.0975
How to determine the interval estimate for the true population proportion?This is calculated using:
I = p ± E
So, we have:
I = 0.55 ± 0.0975
Expand
I = (0.55 - 0.0975, 0.55 + 0.0975)
Evaluate
I = (0.4525, 0.6475)
Express as percentage
I = (45.25%, 64.75%)
Hence, the interval estimate for the true population proportion is 45.25% to 64.75%
How to interpret the estimate?From the simulation,
Lowest sample p = 45% Highest sample p =66%The values are approximately the interval estimates.
i.e.
45.25% ≈ 45% and 64.75% ≈ 65%
Hence, we can conclude that the majority of the community supports water rationing
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Solve the following equation for b.
13b = 6b + 14
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\textsf{\textbf{\underline{Given question:-}}}[/tex]
Solve the following equation for b.
13b=6b+14
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
❖ First of all, we need to make sure that all the variables are on one side (the left-hand side, LHS) and numbers are on the right-hand side, RHS.
Here we have variables on the right-hand side, so we can move that term to the left-hand side, making sure to use the opposite operation:-
13b=6b+14 Subtract 6b on both sides, which results in:-
7b=14 Divide by 7 on both sides, which results in:-
b=2 We've found the value of b. Now, we need to check our solution by replacing b with the value of b, 2, and seeing whether or not we end up with a true statement:-
13(2)=6(2)+14 Multiply.
26=12+14 Now add.
26=26 Since the left-hand side does equal the right-hand side, we conclude that our solution, b=2, is correct.
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
help please <33 i’m struggling if anyone sees this please help this girl <3333
Answer:
2 15/28
Step-by-step explanation:
First we will convert both mixed fractions into improper fractions.
5 1/4 becomes 21/4
2 5/7 becomes 19/7
21/4 - 19/7 does not work, so we must make the denominator the same
147/28 - 76/28 = 71/28
Now we convert back to a mixed number:
2 15/28
Answer: [tex]-11\frac{15}{28}[/tex]
Step-by-step explanation:
Convert to Improper fractions
[tex]5\frac{1}{4} = \frac{21}{4} \\2\frac{5}{7} = \frac{19}{7} \\[/tex]
Find a lowest common multiple
lcm(4,7) = 28 (7 * 4)
since they are just multiplying each other, we can cross multiply
[tex]\frac{(21*7) - (19*4)}{4*7} = \frac{147-76}{28} \\= \frac{71}{28} \\=2\frac{15}{28}[/tex]
The number of cable TV systems recently decreased from 20, 000 to 8.500 Find the percent of decrease Round to the nearest tenth of a percent.
A: 8.1%
B: 12.5%
C: 75%
D: 81.1%
Answer:
B: 12.5%
Step-by-step explanation:
You take the 20.000- 8.500 the number decreased with= 11.5.
You then round of your answer to the nearest 10th, the number 11,5 will change to 12,50.
Solve the following systems of equations:
[tex]1.& \left\{\begin{matrix} 5x-3y-z=1&\\ x+4y-6z=-1& \\ 2x+3y+4z=9& \end{matrix}\right.\\ \ \\ 2.& \left\{\begin{matrix} x+y=7& \\ x\times y=12& \end{matrix}\right.\\ \ \\ 3.& \left\{\begin{matrix} x^2+y^2=169& \\ x+y=17& \end{matrix}\right.\\ \ \\ 4. & \left\{\begin{matrix} y^2-2y+1=x & \\ \sqrt{x}+y=5 & \end{matrix}\right. \end{align*}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 1) \ \left\{\begin{matrix} 5x-3y-z=1&\\ x+4y-6z=-1& \\ 2x+3y+4z=9& \end{matrix}\right. \end{gathered}$}[/tex]
The coefficient matrix associated with the system is constructed and the columns and rows are reduced.
[tex]\left ( \begin{array}{ccc|c} 5 & -3 &-1 &1\\ 1 & 4 & -6 &-1\\ 2 & 3 & 4 & 9 \end{array} \right ) \begin{array}{c} \xrightarrow[\textup{F}_3- 2\textup{F}_2]{\textup{F}_1 - 5\textup{F}_2} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & -5 &16 & 11 \end{array} \right )\\ \ \\ \ \\ \begin{array}{c} \xrightarrow[]{23\textup{F}_3 - 5\textup{F}_1} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & 0 & 223 & 223 \end{array} \right )[/tex]
So, z=1. Translating the last matrix to the associated system of equations, we have that x=1, y=1, since:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} y&=\dfrac{6-29}{-23}=\dfrac{-23}{-23}=1\\ x = -1+6-4=1 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{2) \ \left\{\begin{matrix} x+y=7& \\ x\times y=12& \end{matrix}\right. } \end{gathered}$}[/tex]
Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ y=7-x \quad \Longrightarrow \quad 12=x(7-x)=7x-x^2 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 0=x^2-7x+12=(x-4)(x-3); } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{3) \ \left\{\begin{matrix} x^2+y^2=169& \\ x+y=17& \end{matrix}\right. } \end{gathered}$}[/tex]
Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ y=17-x \quad \Longrightarrow \quad 169=x^2 +(17-x)^2=x^2+x^2 -34x+289 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ 0=2x^2-34x+120=2(x^2-17+60)=2(x-12)(x-5); } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{4 \ \left\{\begin{matrix} y^2-2y+1=x & \\ \sqrt{x}+y=5 & \end{matrix}\right. } \end{gathered}$}[/tex]
Substitute the expression that represents x into the second equation. Then both sides of the equation are squared and solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ \sqrt{y^2-2y+1}+y=5\quad \Longrightarrow\quad \left ( \sqrt{y^2-2y+1} \right )^2=(5-y)^2 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y^2-2y+1=y^2-10y+25\quad \Longrightarrow\quad 8y=24; } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y=6 \qquad x=4 } \end{gathered}$}[/tex]
Ciara bought four burgers.
She paid with a £20 note and got £6 change.
a
How much did each burger cost?
£3.50 for each burger
3.50×4= 14 left over is 6 from the 20 pound note
what is -3(4+(-7) + (-2( 5) -17) with examples pls
Answer:
2
Step-by-step explanation:
-3 (4 - 7) + (2 x 5 - 17)
-3 (4 - 7) + (10 - 17)
-3 x (-3) + (-7)
9 + (-7)
9 - 7
=2
Factorise X squared add 4X
Answer:
[tex]\huge\boxed{\sf x(x + 4)}[/tex]
Step-by-step explanation:
Given expression:
x² + 4x
Take x common
x(x + 4)
[tex]\rule[225]{225}{2}[/tex]
I need help! A flagpole casts a shadow 25 feet long and the angle of elevation of the sun is 72 degrees. Find the height of the flagpole to the nearest foot.
Answer:
From the diagram you can see that we have constructed a right triangle, with height A and base 15.Length of shadow = 15 feet.Height of flagpole = A.We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.tan(40∘)=oppositeadjacent=A15∴tan(40∘)=A15Rearranging:A=15tan(40∘)By calculator:A=12.59 feet. ( 2 d.p.)
I will give brainliest to whoever gives me the correct answer once I figure out how
In this figure: the value of “y” that makes the quadrilateral “A B C D” a parallelogram is:
Answer:
y = 10
Step-by-step explanation:
if the figure is to be a parallelogram, then
∠ ACB and ∠ DAC are alternate angles and are congruent , that is
5y - 13 = 7 + 3y ( subtract 3y from both sides )
2y - 13 = 7 ( add 13 to both sides )
2y = 20 ( divide both sides by 2 )
y = 10
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 33 feet up. The ladder makes an angle of 74 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
HOPE IT HELP (≧▽≦)(≧▽≦)(≧▽≦)
Answer:
Step-by-step explanation:
the answer is wrong its 34.3
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 2 or 5 on your next turn, you win the game. What is the probability of winning on your next turn? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
The probability of winning the game on your next turn is; 14%
How to find the Probability of Winning?The sample size of the two number cubes, when rolled is:
n = 36
The number of outcomes that give a sum of 2 or 5 is 5,
And the outcomes are (1, 1) (2, 3) (3, 2) (1, 4) (4, 1)
The probability is the quotient of the number of outcomes of the sum of 2 or 5 and the total outcomes.
Thus,
Probability = 5/36 * 100% = 13.89% ≈ 14%
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To join the game club, you must pay $7 a month plus
$3 per game (x) that you download. Write an
expression to show the total cost per month to be a
member of the game club.
Answer: Total cost/month = 7 + 3x
Step-by-step explanation:
This is only the total cost per month that is why it is only 7 and 3x since the number of downloaded games is not given.
I'm not sure about my answer but I hope that it helps.
please help meh I give brainliest
Work out the angle x
2x
3.
Answer:
x = 30
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+2x+3x = 180
Combine like terms
6x= 180
Divide each side by 6
6x/6 = 180/6
x = 30
What critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 21 observations
To find the degrees of freedom in the given question, we have to take into consideration of the confidence interval as well as degrees of freedom. The critical t-value in this data set is 2.086
What is Confidence Interval?This is the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
We can also say that it is a range of values so defined that there is a specified probability that the value of a parameter lies within it.
Data;
sample size (n) = 21degree of freedom (df) = n-1 = 21 - 1 = 20At a 95% confidence level, the t is
α = 1 - 0.95
The critical t-value in this data set is 2.086
Learn more on t-value here;
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Please awnser two more questions after this
Answer:
J(-9,-5)
K(-9,3)
L(0,-2)
M(0,-5)
. What number decreased by 5% of itself equals 703?
Answer:
The number is 740
Step-by-step explanation:
Hello!
Let the number that we want to solve for be x.
100% of x is x, but a decrease of 5% if 95% of x.
Solve for x95% of x = 7030.95x = 703x = 703 ÷ 0.95x = 740The number is 740.
Check5% of 740 0.05(740) = 37740 - 37 = 703The solution is correct.
What is the specific heat of a material that gains 600 joules of energy when a 0.25 kg object increases in temperature by 3C?
Group of answer choices
800 J/kgC
1200 J/kgC
300 J/kgC
450 J/kgC
Answer:
Step-by-step explanation:
800 J/kgC
What is the specific heat of a material that gains 600 joules of energy when a 0.25 kg object increases in temperature by 3C?
it is 800 J/kgC
PLEASE SOLVE FOR X AND Y!!!! I WILL MARK BRAINLIEST!!!!
opposite sides and diagonals of a parallelogram are equal
+ diagonals of a parallelogram meet eachother in the middle so:
10x+14=x+77
10x-x=77-14
9x=63
x=63÷9
x= 7
y+8=4y-19
y-4y=-19-8
-3y=-27
y=-27÷-3
y=9
2z+3=37
2z=37-3
2z=34
z=34÷2
z=17
PLS HELP ME IT IS DUE TODAY
For each value of , determine whether it is a solution to
-28 < 4w - 8.
Step-by-step explanation:
reduce -28<4w-8
-7<w-2
add +2
-7+2<w-2+2
-5<w
w>-5
Answer:
See below ~
Step-by-step explanation:
Solving the inequality :
-28 < 4w - 84w > -20w > -5Evaluating the given numbers :
-5
-5 > -5No5
5 > -5Yes-9
-9 > -5No-1
-1 > -5YesThe table lists the measures of center and measures of dispersion for a data set.
mean median mode range standard deviation
65.8 63.5 65 11 3.9
find the mean, median, mode, range, and standard deviation when each value of the data set is increased by 8.
Answer:
it's difficult , sorry
Step-by-step explanation:
ask easily one
The doctor told my dad he should drink 72 ounces of water every day.
How many cups of water should he drink per day? (There are 8 ounces in a cup.) Write and solve an equation to represent this problem.
How many quarts of water is that? Write and solve an equation to represent this problem.
Answer: 9 cups
Step-by-step explanation: 8 multiply it by 9 .
PLEASE HELP 100 POINTS AND BRAINLIEST
Answer:
I did the work and uploaded the answers i hope it helped!!
Can someone please help me with this please and thankyou
Answer:
∠ABC = 55°
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line (AC) intersects a set of parallel lines (m and n) in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
⇒ ∠BAC = ∠DCA
⇒ ∠BAC = 50°
The interior angles of a triangle sum to 180°
⇒ ∠BCA + ∠BAC+ ∠ABC = 180
⇒ 75 + 50 + ∠ABC = 180
⇒ ∠ABC = 180 - 75 - 50
⇒ ∠ABC = 55°
SOMEONE PLS HELP
Find the arc length of the partial circle.
Either enter an exact answer in terms of te or use 3.14 for at and enter your answer as a decimal.
units
Answer:
9.42
Step-by-step explanation:
Since the angle shown is 90 degrees we can deduce that the rest of the arc is 270 degrees therefore we can make the fraction:
270/360; 360 being the total angle measurement of a circle
270/360 simplifies to 3/4
The fraction represents how much of the circle that arc covers
Now we have to find the circumference which would be
2(3.14)r
r = 2 therefore: 2(3.14)2 = 12.56
Now that we have the circumference of the WHOLE circle we multiply it by 3/4 to find out the arc length
Which gives us 9.42
Multiply.
[tex]\frac{\sqrt{2}}{6}cis (\frac{3\pi }{5})[/tex]·[tex]\frac{\sqrt{6}}{4}cis (\frac{2\pi }{3})[/tex]
A.[tex]\frac{\sqrt{3}}{12}cis(\frac{19\pi }{15})[/tex]
B. [tex]\frac{\sqrt{3}}{12}cis(\frac{2\pi }{5})[/tex]
C. [tex]\frac{\sqrt{2}}{8}cis(\frac{2\pi }{5})[/tex]
D. [tex]\frac{\sqrt{2}}{8}cis(\frac{19\pi }{15})[/tex]
Multiply the moduli and add the arguments:
√2/6 cis(3π/5) × √6/4 cis(2π/3)
= (√2/6 × √6/4) cis(3π/5 + 2π/3)
= √3/12 cis(19π/15) … [A]
In a school, 60% of students have access to the internet at home. A group of 8 students is chosen at random. Find the probability that at least 6 students have access to the internet.
write 0.009 as a fraction. (Its a refresh I need pls answer it bc I forgot how to do this!)
Answer:
9/1000
Step-by-step explanation:
When writing decimals into fractions, you first take the last digit, (in this case 9), and place it as your numerator, then count how many decimal places there are after 0. <---- in our case we have 3 decimal places which means our denominator has 3 zeros. Hence it is 1000.
HELP ME PLEASEEEEE
Answer:
x = 4
Step-by-step explanation:
x(x + 8) = 48
x² + 8x = 48
x² + 8x - 48 = 0
times into -48
add into 8
(x - 4)(x + 12) = 0
x - 4 = 0
x = 4
or
x + 12 = 0
x = -12
A length cannot be a negative number therefore x = 4