The probability that the sample proportion of the Republicans will differ from the population by more than 4% is 95.56%
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of difference a sample, X is from the standard deviation
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
population mean, μ = p = 50% = 0.5
sample size, n = 629
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.50(1 - 0.50)) / 629}
= √{(0.50 * 0.50) / 629}
= 0.0199
Differ by more than 4% is differ by 50% + 4%
X = 50% + 4% = 54% = 0.54
The probability of more than 54% P = P(p > 54%) = P(p > 0.54)
P(p > 0.54) = 1 - P(p < 0.54)
Z score for z < 0.54
z = (X - μ) / σ
= (0.54 - 0.50) / 0.0199
= 2.01
p value for z < 2.01 = 0.0444
P(p > 0.54) = 1 - P(p < 0.54)
= 1 - 0.0444
= 0.9556
= 95.56%
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A harbor seal dives 35 meters below the ocean's surface. Then it dives down an additional 12 meters Determine the seal's new position relative to the surface of the ocean
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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What is the image of (0, -4) after a dilation by scale factor of 2 centered at the
origin?
The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)
What is the scale factor?
A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased
We are given a point (0,-4)
Which is to be scaled by the factor of 2 at the center position
As the value is greater than 1 the size increase
We multiply the coordinate to find the new coordinates
We get (0,-8)
Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)
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David is three time as old as Joseph after 3 years David will be only twice as old as process will be there find their present ages
Answer:
Joseph's present age=3 yrs
David's present age=9 yrs
Step-by-step explanation:
Let Joseph's present age be x.
David's present age=3x
__________________
Ater 3 yrs,
Joseph's age=x+3
David's age=2(x+3)
Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.
Now, balance them.
3x+3=2(x+3)
3x+3=2x+6
x=3
D"s prsent age=9
J's present age=3
Please solve I do not understand it
The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.
The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as
[tex](\frac{1}{4^{-3 } } )^{2}[/tex]
What is expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)
Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]
using law of indices,
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]
4⁻⁶ = 1 / 4⁶ = 1 / 4096
Hence,
1 / 4096 = 0.00024414062
Therefore, the value is less than 1.
Let's change one sign to make the expression greater than 1.
Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]
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pls i will give top rating
A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.
The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
How to find the value of x?Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.
From the given information, we get
x - y = 6 ...............(1)
"if five times the smaller number is two times the larger number"
from the above information, we get
5y = 4x + 2
5) To simplify the value of y:
y = (4x +2) / 5 ...............(2)
Substitute y = (4x +2) / 5 in (1), then we get
x - (4x + 2) / 5 = 6
5x / 5 - (4x + 2) / 5 = 6
simplifying the above equation, we get
(5x - 4x - 2) / 5 = 6
x - 2 = 5 x 6
x -2 = 30
x = 32
Substitute the value of x in (2)
y = 4(32) + 2 / 5
simplifying the above equation, we get
y = 130 / 5
y = 26
From (1), we get
x - y = 6
substitute the value of x and y in the above equation,
32 - 26 = 6
6 = 6
6) T is the 10s digit
X is the one's digit
The two digit number is 10T + X
It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits
10T + X = 7(T+X)
By using distributive law
10T + X = 7T + 7X
10T + X - 7T - 7X = 0
simplifying the above equation, we get
3T - 6X = 0
3(T - 2X) = 0
T - 2X = 0
T = 2X
The tens digit is 3 more than the one's digits, so
T = X + 3
Then we have
T = 2X = X + 3
Subtracting X from both sides,
T - 3 = X + 3 - 3
X = 3
The Tens digit is 6.
The number is 63.
The sum of the digits is 9.
9 × 7 = 63.
Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
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what is 1357 mm in cm
You want to be able to withdraw $20,000 each year for 20 years. Your account earns 9% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
a) The amount of money in the account at the beginning is $222,222.222.
b) The total amount of money withdrawn from the account is $400,000.
c) The amount of interest earned is $177,777.778.
It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".
A = $20,000*20 = $400,000
Let the amount of money in the account at the beginning be represented by the variable "P".
A = P*R*T
400,000 = P*0.09*20
400,000 = P*1.8
P = 222,222.222
The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".
I = A - P = $400,000 - $222,222.222 = $177,777.778
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Suppose that the Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16. What is the probability that a student's mark is more than 75? In a class of 50 students, how many students should have a mark of more than 75?
The probability that a student's mark is more than 75 is 0.0947 and in a class of 50 students, 5 students should have a mark of more than 75.
In the given question,
The Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16.
We have to find the probability that a student's mark is more than 75.
In a class of 50 students, we also have to find how many students should have a mark of more than 75.
From the question the mean = 54
Standard Deviation = 16
So the probability that a student's mark is more than 75.
Using the normal distribution
z = (x−mean)/Standard Deviation
P(x>75) = P(z>(x−mean)/Standard Deviation)
P(x>75) = 1−P(z<(75−54)/16)
Simplifying
P(x>75) = 1−P(z<21/16)
P(x>75) = 1−P(z<1.3125)
From the standard z table value
P(x>75) = 1−0.9053
P(x>75) = 0.0947
Hence, the probability that a student's mark is more than 75 is 0.0947.
Now finding in a class of 50 students, how many students should have a mark of more than 75.
Total student = 50
So the student having mark of more than 75 = Total student * probability that a student's mark is more than 75
The student having mark of more than 75 = 50 * 0.0947
The student having mark of more than 75 = 4.735
The student having mark of more than 75 ≈ 5
Hence, in a class of 50 students, 5 students should have a mark of more than 75.
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Dylan has a bag of 1256 rubber balls to hand out as prizes at a town festival. There are 13 games at the festival. About how many rubber balls should he give each game?
Answer The answer is 96 but as a fraction 96 8/13
Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.
What is the value of (−13)4
Answer: -52
Step-by-step explanation: multiply by breaking apart a factor (-13) x 4
Answer:
28561
Step-by-step explanation:
Find the Exact Value:
Raise -13 to the power of 4.
28561 is the answer.
If a certain stock has a historical 10-year CAGR (compounded annual growth rate) of -2.3% and
currently sells for $83.80 a share, how much did the stock sell for 10 years ago?
Stock used to sell for $105.81 ten years ago.
[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]
Here, CAGR = Compounded Annual Growth Rate = -2.3%
EV = Ending Value = x
BV = Beginning Value = $83.80
n = No. of years = 10
Putting the values in the equation,
[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]
[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]
[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]
[tex]\frac{83.80}{x}=0.792[/tex]
[tex]x = \frac{83.80}{0.792}[/tex]
x = 105.81
Hence, the beginning value is $105.81.
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WILL GIVE BROANLYEST 80 POINTS!!!!!!! What is the volume of a rectangular prism with a length of twenty-two and one-half feet, a width of 12 feet, and a height of 13 feet?
7,800 ft3
3,510 ft3
1,755 ft3
five hundred sixty-two and one-half ft3
Answer:7,800
Step-by-step explanation:
Answer:
Option B (3,510ft) would be correct.
Step-by-step explanation:
The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
A
Step-by-step explanation:
In the diagram a person who is ft tall is standing on the ground ft away from point . A line segment drawn from the top corner of the building to point creates two similar triangles.
The height of the building, using similar triangles, is given by:
36 feet.
What are similar triangles?Similar triangles are two triangles that share these two features, which are listed as follows:
Same angle measures.Proportional side lengths.The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.
From the similar triangles, the equivalent side lengths are presented as follows:
3 ft and 18 ft.6 ft and h ft.Hence the proportional relationship that models this situation is presented as follows:
3/18 = 6/h.
Applying cross multiplication, the height of the building is obtained as follows:
3h = 18 x 6
h = 6 x 6 (simplifying by 3)
h = 36 feet.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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Shamar belongs to a movie club that deducts $14 every month from his bank account. What is the change in Shamar's bank account after 7 months of paying for the movie club?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The change in Shamar's bank account after 7 months is
x - 98.
Where x is the amount in the account initially.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the account = x
Amount deducted every month = $14
The change in the account after 7 months.
= x - 7 x 14
= x - 98
Thus,
The change in Shamar's bank account after 7 months is
x - 98.
Where x is the amount in the account initially.
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A spinner is spun 800 times.
The probabilities it lands on each colour
are shown below.
The probability it lands on red is the same
as the probability it lands on yellow.
Colour Red Green Brown Yellow
Probability. 0.3. 0.54
How many times would you expect it to
land on each colour?
Red: 0
Brown: Yellow:
O
Green:
0
Answer:
green 45 times or 40 a note
If V is the midpoint of WY, VY=29-4x, and WY=5x+19, find WV.
The value of WV is 9x - 10
What is line segment?A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.
From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.
We have;
VY=29-4x WY=5x+19This is represented as;
WV + VY = WY
Then;
WV = WY - VY
substitute the values
WV = 5x + 19 - (29 - 4x)
expand the bracket
WV = 5x + 19 - 29 + 4x
collect like terms
WV = 9x - 10
Hence, the value is 9x - 10
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Twelve less than 9 times a number is equal to 8 minus 4 times the number
Answer:
If you let 'n' to represent a number then '-9 times a number' can be written as -9n
'less then' means subtraction: 12 less then -9 times a number becomes -9n - 12 (the subtraction in the equation is written in the opposite way as written in words)
'8 minus 4 times the number ' becomes 8 - 4n
So, the equation is: -9n - 12 = 8 - 4n
Get all the variables to one side. If you add 9n to both sides:
-9n + 9n - 12 = 8 - 4n + 9n
-12 = 8 + 5n
Subtract 8 from both sides:
-12 - 8 = 8 - 8 + 5n
-20 = 5n
Divide both sides by 5:
-20 ÷ 5 = 5n ÷ 5
-4 = n
Now, check the answer: -9n - 12 = 8 - 4n
-9(-4) - 12 = 36 - 12 = 24 8 - 4(-4) = 8 + 16 = 24 They check!
Step-by-step explanation:
Hope this helps! :)
what is the distance between 2 + x and 2?
Answer:
The difference is the what the sum of 2+x is
Step-by-step explanation:
suppose x=3 2+3 = 5
the difference between 5 and 2 is 3
What is the b-value?
Answer:
3
Step-by-step explanation:
y-intercept = b
The slope-intercept = y=mx+b
y=-2/5x+3
m=-2/5
b=3
If the equation was something like y=-2x-3, then the b would be -3 because you are subtracting 3.
Traveling with the current certain boat went 9 mph against the same boat it only went 1 mph what is the speed of the current how fast would the Bogo if there were no current
If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current is 4km/h and no current is 5km/h.
How to determine the speed?Let b represent the speed of the boat
Let c represent the speed of the current
Downstream:
b + c = 9
Upstream:
b - c = 1
Subtraction
2c = 9-1
2c = 8
Divide both side by 2c
c = 8/2
c = 4 km/h (current)
No current
b = 9 - 4
b = 5 km/h
Therefore the speed is 4km/h and no current is 5km/h.
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A line of best fit was drawn for 5 data points. What is the maximum number
of these data points that may not actually be on the line?
A. 5
B. 3
C. 2
D. 4
Answer:
Step-by-step explanation:
Correct answer is A 5
Please help me I NEED HELP
Answer:
Step-by-step explanation:
ABC = the draw of the square means that the angle is right
We can now say that the other two angles are acute because the sum of the interior angles of a triangle is 180 degrees
BCA = acute
CAB = acute
If y vaires directly with x and y= 12 when x= 15. What is the value of x when
y=16?
The value of x=20, according to the given question.
What is meant by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to the given data in the question,
We know that y varies directly with x like that,
y=kx..................(1)
y=12 when x=15.
Now, we have to find the value of x when y=16.
Then, putting the given values of x & y in the eq. (1), and determine the value of k.
12=k(15)
[tex]k=12/15\\k=4/5\\[/tex]
Now, putting the value of k in the second statement in eq.(1), where only y's value is given.
[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]
Hence, the value of x=20.
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In a poll of 489 adults, 132 of then said they have a tattoo. Find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.
Using the probability of adults of having tattoo, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)
In the given question,
In a poll of 489 adults, 132 of then said they have a tattoo.
We have to find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.
From the question
Total number of adults = 489
The adults that have tattoo = 132
So the proportion in the sample is
p = 132/489
p = 0.269
p ≈ 0.27
Now finding the proportion of adults not having tattoo.
q = 1−p
q = 1−0.27
q = 0.73
Now finding the critical value(z).
The value of z from the standard table for 95% confidence interval.
We can write 95% as 0.95
Z = [tex]z_{\alpha /2}[/tex]
Z = [tex]z_{0.95 /2}[/tex]
Z = [tex]z_{0.475}[/tex]
From the standard table of z
Z = 1.96.
Now finding the margin error.
Margin Error(E) = [tex]Z\times\sqrt{\frac{pq}{n}}[/tex]
As we know that Z = 1.96, p = 0.27, q = 0.73, n = 489
Now putting the value
E = [tex]1.76\times\sqrt{\frac{0.27\times0.73}{489}}[/tex]
Simplifying
E = [tex]1.76\times\sqrt{\frac{0.1971}{489}}[/tex]
E = [tex]1.76\times\sqrt{0.000403}[/tex]
E = 1.76×0.0201
E = 0.0353
Now finding a 95% confidence interval for the proportion of all adults that have a tattoo.
Confidence Interval = p−E< P < p+E
Confidence Interval = 0.27−0.0353< P < 0.27+0.0353
Confidence Interval = 0.2347< P < 0.3053
Hence, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)
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PLS HURRY I NEED THE ANSWER FAST!!!!!!
Paula makes purses. The materials cost $2.25 per purse. She sells them for $5.00 each. Paula wants to invest $5000 for some new equipment. Which of these could be used to determine x, the number of purses Paula must sell to pay for the new equipment?
A 5.00x - 2.25x = 5000
B 5.00x + 2.25x = 5000
C 5.00x = 5000
D 2.25x = 5000
The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;
A. 5.00x - 2.25x = 5000
How to solve equation word problems?We are told the materials costs $2.25 per purse.
She sells the materials for $5 each.
If the number of materials she purchased was x, it means that;
Selling price - Cost price = 5.00x - 2.25x
Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.
Since the formula for profit is;
Profit = Selling Price - Cost Price
Then, we will have;
5.00x - 2.25x = 5000
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Answer: 5.00x - 2.25x = 5000
Step-by-step explanation:
Write an equation of the parabola that passes through the point (-3, -8) and has x-intercepts -7 and -4.
An equation of the parabola is y =
The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).
Equation of a parabolaIt follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.
Since the equation of a parabola in the factored form usually takes the form;
y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.
Therefore, we have; y = a (x - (-4)) (x - (-7))
y = a (x + 4) (x + 7)
Hence, to find the value of a, we set y = -8 and x = -3 so that we have;
-8 = a (-3 + 4) (-3 + 7)
-8 = 4a
a = -2.
Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).
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Given: ST=3x+3 and TU= 2x+9
What is the value of TU?
The value of TU is 21
From the question, we have
ST=3x+3 and TU=2x+9
ST = TU
3x + 3 = 2x + 9
3x - 2x = 9 - 3
x = 6
substituting the value, we get
TU = 2x + 9
= 2 (6) + 9
= 12 + 9
TU = 21
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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1. A cone-shaped filter has a diameter of 10 inches and a height of 4 inches.
What is the volume of liquid the filter can hold? Round your answer to
the nearest hundredth.
The volume of liquid contained by cone is 105 inches cube.
What is volume?
It can be defined as the total content which can be held inside a container.
Main body:
the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] , where r = radius and h = height of cone
diameter = 10 , so radius = d/2 = 5 inches
V = [tex]\frac{1}{3}\pi 5*5*4[/tex]
V = 3.14 *5*5*4*1/3
v≈105 inches cube
Hence the volume is 105 inches cube.
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During December, Far Eas Services makes a credit sale of $2,800 (before sales taxes). The state sales tax rate is 6% and the local sales tax rate is 2.5%.
Record sales and sales tax payable.
The credit sale after state and local tax payable is 2562$.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The credit sale before sales taxes = 2800$,
The rate of state sale tax = 6%,
And rate of local sale tax = 2.5%
The sale after state tax = 2800-2800×6/100=2800-168=2632,
The sale after local tax=2800-2800×2.5/100=2800-70=2730
The credit sale after state and local tax= 2800-168-70=2562.
The required credit sale =2562$.
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