Answer:
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Step-by-step explanation:
From the information given :
An exit poll of 200 voters finds that 94 voted for the referendum.
How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
This implies that ;
the Sample size n = 200
the probability p = 0.52
Let X be the random variable
So; the Binomial expression can be represented as:
X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)
Mean [tex]\mu[/tex] = np
Mean [tex]\mu[/tex] = 200 × 0.52
Mean [tex]\mu[/tex] = 104
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]
The standard deviation [tex]\sigma[/tex] = 7.065
However;
P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .
The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5
Now;
x = 94.5
Therefore;
[tex]z = \dfrac{x- \mu}{\sigma}[/tex]
[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]
[tex]z = \dfrac{-9.5}{7.065}[/tex]
z = −1.345
P(X< 94.5) = P(Z < - 1.345)
From the z- table
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
ACEG is a paralellogram. BKD, HJF and CKJG are straight lines. Find the values of x and y
Answer:
[tex]\boxed{\mathrm{x=53\° \: \: \: y=33\°}}[/tex]
Step-by-step explanation:
Apply these rules to solve:
• Angles on a straight line add up to 180 degrees.
• Angles in a triangle add up to 180 degrees.
• Opposite angles in a parallelogram are equal.
• Angles in a quadrilateral add up to 360 degrees.
What is the result of subtracting the second equation from the first? \begin{aligned} -2x+7y &= 10 \\\\ 3x+7y &= 2 \end{aligned} −2x+7y=10 3x+7y=2
Answer:
-5x = 8
Step-by-step explanation:
The result is shown here. The y-terms cancel.
[tex]\begin{array}{rccc}& -2x+7y &= &10 \\-&(\ \,3x+7y &= &2)\\\cline{1-4}&-5x+0y&=&8 \end{array}[/tex]
The simplified result is ...
-5x = 8
Answer:
The result is that 5x = -8
Step-by-step explanation:
Here, we want to subtract 3x + 7y = 2 from -2x + 7y = 10
Mathematically that would be;
(-2x+7y)-(3x+7y) = 10-2
-2x + 7y -3x -7y = 8
-2x -3x + 0 = 8
-5x = 8 or 5x = -8
Which shows the rational expression written using the least common denominator?
x+1/4x^2 + x+1/x^2
A) x+1/4x^2 + 4(x+1)/4x^2
B) x+1/x^2 + x+1/x^2
C) x+1/x^2 + 4(x+1)/x^2
D) x+1/4x^2 + x+1/4x^2
Answer:
(x + 1)/4x² + 4(x + 1)/4x²
Step-by-step explanation:
x+1/4x² + x+1/x²
The above can be simply as follow:
Find the least common multiple (LCM) of 4x² and x². The result is 4x²
Now Divide the LCM by the denominator of each term and multiply the result with the numerator as show below:
(4x² ÷ 4x²) × (x + 1) = x + 1
(4x² ÷ x²) × (x + 1) = 4(x + 1)
x+1/4x² + x+1/x² = [(x + 1) + 4(x + 1)]/ 4x²
= (x + 1)/4x² + 4(x + 1)/4x²
Therefore,
x+1/4x² + x+1/x² = (x + 1)/4x² + 4(x + 1)/4x²
Answer: A
Step-by-step explanation:
The point (2, 3) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work.
Answer:
[tex]Sin \theta = \frac{Perpendicular}{Hypotenuse}=\frac{3}{\sqrt{13}}[/tex]
[tex]Cos \theta = \frac{Base}{Hypotenuse}=\frac{2}{\sqrt{13}}[/tex]
[tex]Tan \theta = \frac{Perpendicular}{Base}=\frac{3}{2}[/tex]
Step-by-step explanation:
We are given that The point (2, 3) is on the terminal side of angle Θ, in standard position
First Draw a vertical line from the point(2,3) to the x axis.
So, Length of vertical line is 3
The intersection of the line with the x axis is at x=2.
So, now we have obtained a triangle with the horizontal side of length 2, the vertical side of length 3
To Find hypotenuse we will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2\\Hypotenuse^2=3^2+2^2\\Hypotenuse=\sqrt{9+4}\\Hypotenuse=\sqrt{13}[/tex]
[tex]Sin \theta = \frac{Perpendicular}{Hypotenuse}=\frac{3}{\sqrt{13}}[/tex]
[tex]Cos \theta = \frac{Base}{Hypotenuse}=\frac{2}{\sqrt{13}}[/tex]
[tex]Tan \theta = \frac{Perpendicular}{Base}=\frac{3}{2}[/tex]
please hellppp ......
Answer:
BC = 11.9Step-by-step explanation:
To solve for BC we use sine
sin ∅ = opposite / hypotenuse
From the question
AC is the hypotenuse
BC is the opposite
So we have
sin 58 = BC / AC
sin 58 = BC / 14
BC = 14 sin 58
BC = 11.87
BC = 11.9 to one decimal place
Hope this helps you
Answer:
[tex]\boxed{BC = 11.9 \ cm}[/tex]
Step-by-step explanation:
Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]
Where A = 58°, Opposite = BC and AC = 14 cm
Sin 58 = [tex]\frac{BC}{14}[/tex]
BC = 0.848 * 14
BC = 11.9 cm
What is 37 ÷ 100 × 9 =
Answer: 3.33
Step-by-step explanation:
Multiplication and division should be solved left to right.
[tex]37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33[/tex]
Hope it helps <3
Answer:
=37/100×9=.
=divide 37 by 100
=0.37 ×9
=3.33
ASAP! PLEASE help me with this question!
Answer:
The last graph is the correct answer
Step-by-step explanation:
Here, we are interested in picking the correct graph that best answers the question.
Before we pick any of the graphs as our answer, it will be appropriate to solve the inequality.
-4h + 42 <34
-4h < 34-42
-4h < -8
Now divide both side by -4; kindly note that when dividing an inequality by a negative number, the sign will change
h > -8/-4
h > 2
So which of the graph best showcases this?
The correct answer is the last graph
What is the domain of F(x) = In (x)?
A: all real numbers except 0
B: all real numbers
C: all real numbers less than 0
D: all real numbers greater than 0
Answer:
the answer is B
Step-by-step explanation:
In terms of symbols, we would write [tex]x > 0[/tex]
The natural log function, or any log function, is not defined for x = 0 or any negative x value.
Consider the form [tex]\log_b(y) = x[/tex] which is equivalent to [tex]y = b^x[/tex] and notice how the y value slowly approaches zero but never actually gets there. That is one way to see why the inputs of any log function must be larger than 0.
Does any wonderful person want to be so kind and give your girl a hand? I am talking about the math question down below:)
Answer:
The last one, The Hypotenuse Leg Theorem, or HL Theorem,
Step-by-step explanation:
Answer:
HL theorem
Step-by-step explanation:
If any 2 right angled triangles have same length of hypotenuse then both are congruent by HL theorem
please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8
Answer: THE ANSWER IS A
Step-by-step explanation:
5-(3/2)^3
=13/8
im a math god
what happens to 5/x + 5 as x decreases from a large positive number to a small positive number? does it increase, decrease, or stay the same?
Answer:
Increases
Step-by-step explanation:
It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.
According to an article by George Will (San Jose Mercury News, Feb. 28, 2002), the average U.S. consumption per person per year of French Fries is 28 pounds. Suppose that you believe that the average in Santa Clara County is not 28 pounds. You randomly survey 50 people in this county. The sample average is 24 pounds with a sample standard deviation of 10 pounds. Conduct an appropriate hypothesis test. The p-value for this test is:________.
a. 0.0068
b. 0.0034
c. 0.0136
d. 0.0047
Answer: d. 0.0047
Step-by-step explanation: The p-value is the calculated value used to compare to the significance level to determine if you reject or fail to reject the null hypothesis.
To find p-value, first find the z-score:
z = [tex]\frac{x-\mu}{SE}[/tex]
x is sample mean
μ is population mean
SE is standard error calculated by [tex]\frac{s}{\sqrt{n} }[/tex]
SE = [tex]\frac{10}{\sqrt{50} }[/tex]
SE = 1.414
z = [tex]\frac{24-28}{1.414}[/tex]
z = - 2.83
The hypotheses ([tex]H_{0}, H_{a}[/tex]) are if sample mean is equal or different from the average given, so, p-value will be the value of z from z-table multiplied by 2:
p-value = 0.00233*2
p-value = 0.0047
The p-value for this test is 0.0047
Allison accumulated $7,000 in credit card debt. If the interest rate is 15% per year and she does not make any payments for 3 years, how much will she owe on this debt in 3 years for quarterly compounding? Round your answer to two decimal places.
Answer:
Allison will owe $10,888.50 in 3 years
Step-by-step explanation:
FV=PV(1+r/n)^nt
Where,
PV=$7000
r=15%=0.15
n=quarterly=4
t=3 years
FV=PV(1+r/n)^nt
=7000(1+0.15/4)^4*3
=7000(1+0.0375)^12
=7000(1.0375)^12
=7000(1.5555)
=10,888.50
To 2 decimal places=$10,888.50
Allison will owe $10,888.50 in 3 years
Answer:
$10,888.20
Step-by-step explanation:
Order of Operations: BPEMDAS
Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ
A = Final Amount
P = Initial Amount
r = rate
a = Compounded number
b = time
Step 1: Define
P = 7000
r = 15% = 0.15
a = 4
b = 3 years
Step 2: Solve for A
Substitute: A = 7000(1 + 0.15/4)⁴⁽³⁾Parenthesis: A = 7000(1.0375)⁴⁽³⁾Exponents: A = 7000(1.0375)¹²Exponents: A = 7000(1.55545)Multiplication: A = 10888.20At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.
Simplify.
N4 x N7 over n5
Answer:
[tex]n^6[/tex].
Step-by-step explanation:
[tex]n^4 * \frac{n^7}{n^5}[/tex]
= [tex]n^4 * n^{7 - 5}[/tex]
= [tex]n^4 * n^2[/tex]
= [tex]n^{4 + 2}[/tex]
= [tex]n^6[/tex].
Hope this helps!
Determine the equation of the line that is parallel to y=23x+4 and passes through the point (3,7).
Answer: y = 23x - 62
Step-by-step explanation:
Parallel lines have the same slope.
y = 23x + 4
m=23 b=4
Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m). I will choose the latter.
y = mx + b
7 = 23(3) + b
7 = 69 + b
-62 = b
m = 23, b = -62 --> y = 23x - 62
Please help pleaseee give first person to answer brainlest A system of equations is shown below: Equation A: 3c = d − 8 Equation B: c = 4d + 8 Which of the following steps should be performed to eliminate variable d first? A : Multiply equation A by −4. B : Multiply equation B by 3. C : Multiply equation A by 3. D : Multiply equation B by 4.
Answer:
Multiply the first equation by -4
Step-by-step explanation:
Equation A: 3c = d − 8
Equation B: c = 4d + 8
We want to eliminate variable d
Multiply the first equation by -4
-4( 3c = d − 8)
-12c = -4d +32
Add this to the second equation
-12c = -4d +32
c = 4d + 8
================
-11c = 0d + 40
Answer:
A : Multiply equation A by −4
Step-by-step explanation:
3c = d - 8
Multiply the equation by -4.
-12c = -4d + 32
-12c = -4d + 32
c = 4d + 8
Add equations.
-11c = 0d + 40
-11c = 40
The d variable is eliminated.
(2.5)
(1,1)
Write a rule for the linear function shown in the graph
Answer:
I guess y=2x+5
help me plz its math and if u help i will give brainlest
Answer: the correct answer is 40
Step-by-step explanation:
All angles in a triangle equal 180.
180-100=80
the question says the other two angles are equal. So we will divide by 2
80/2=40
Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches.
Answer:
[tex]\sqrt{16}[/tex] = 4
[tex]\sqrt{25}[/tex] = 5
16x^2 - 40x + 25
= (4x - 5)^2
Hope this helps!
Answer:
4x-5, B
Step-by-step explanation:
EDGE 2020
Which situation can be represented by 80x > 150 + 50x?
Answer:
All numbers greater than 5, i.e., [tex]x>5[/tex] .
Step-by-step explanation:
The given inequality is
[tex]80x>150+50x[/tex]
Isolate variable terms on one side to find the solution.
Subtract 50x from both sides.
[tex]80x-50x>150+50x-50x[/tex]
[tex]30x>150[/tex]
Divide both sides by 30.
[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]
[tex]x>5[/tex]
It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.
A standard deck of of 52 playing cards contains 13 cards in each of four suits : diamonds, hearts , clubs and spades. Two cards are chosen from the deck at random.
Answer:
Probability of (one club and one heart) = 0.1275 (Approx)
Step-by-step explanation:
Given:
Total number of cards = 52
Each suits = 13
FInd:
Probability of (one club and one heart)
Computation:
Probability of one club = 13 / 52
Probability of one heart = 13 / 51
Probability of (one club and one heart) = 2 [(13/52)(13/51)]
Probability of (one club and one heart) = 0.1275 (Approx)
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
Please help me, im in desperate need of help for these questions
Answer:
For the first one, answer is dilation of 2
Step-by-step explanation:
you see the coordinates for triangle A'B'C' are all doubled the coordinates of triangle ABC
if (x)= 2x square minus 1,then f(-3)
Answer:
17.
Step-by-step explanation:
f(x) = 2x^2 - 1
f(-3) = 2(-3)^2 - 1
= 2 * 9 - 1
= 18 - 1
= 17
Hope this helps!
Hope it will help u....
PLEASE HELP
A hire purchase agreement offers gym equipment, with a marked price
$897, for $87 deposit and $46.80 a month payable over 2 years.
Calculate :
a) the total hire-purchase price
b) the amount of
amount of interest charged
Answer: a) $1,210.20 b) $313.20
Step-by-step explanation:
a) $87 down + $46.80(24 months) = $1,210.20 total paid
b) $1,210.20 - $897.00 = $313.20 interest paid
Use cubic regression to find a function that fits the following points.
Answer:
Step-by-step explanation:
To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.
Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is
[tex]-2x^3+2x^2-4x+3[/tex] with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.
In the picture down below
Answer:
b
Step-by-step explanation:
trust me
Answer:
A
Step-by-step explanation:
HELP ASAP PLEASE!!!
A) The range for this function is the set
B)the domain of this function is all real numbers
C) The domain for this function is the set 3
D)All real numbers are in range of this function
E) it’s in the picture
Answer:
A and C
Step-by-step explanation:
The line is at 3, and no number is within reach except 3. So the answer is A and C.
21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?
Answer:
83
Step-by-step explanation:
f(x) = 7x - 1
Put x as 12.
f(12) = 7(12) - 1
f(12) = 84 - 1
f(12) = 83
EF is a median of trapezoid ABCD. What is the value of x?
Answer:
x = 4
Step-by-step explanation:
The midsegment ( median is equal to half the sum of the parallel bases, that is
[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values
[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2
7x - 2 = 26 ( add 2 to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
3. A CD costs £9.50 in London and
cheaper, in British money, is the CD when bought in the US?
4. An MP3 player costs €20.46 in Spain and £12.60 in the UK. Which is
the cheaper in dollars, and by how much?
in Nou Delhi is 32860 rupees.
Step-by-step explanation:
Only Q4 has clear details
therefore, solving Question 4,
1 euro = $1.17
then, €20.46 =20.46×1.17 = $23.93.
1 pound =1.28 dollars.
then, £12.60 = 12.60×1.28 =$16.128
therefore, MP3 in pound is cheaper in dollar by $7.81.
