the sample data supports the claim that the politician's chance of being elected is less than 70%.
To test whether the politician's claim is valid, we can perform a hypothesis test using the null hypothesis that the true probability of the politician being elected is 0.7 and the alternative hypothesis that the true probability is less than 0.7.
Let p be the true probability of the politician being elected. We have:
Null hypothesis: H 0 : p = 0.7
Alternative hypothesis: H a : p < 0.7 (one-tailed test with alpha = 0.05)
We can use the sample proportion, denoted by p, to estimate the true proportion p. The test statistic for testing the above hypotheses is given by:
z = (p - p) / √(p×(1-p)/n)
where n = 500 is the sample size. Under the null hypothesis, the test statistic follows a standard normal distribution. Using the given sample proportion p = 0.6, we can compute the test statistic as follows:
z = (0.6 - 0.7) / √(0.7×(1-0.7)/500) = -3.05
The corresponding p-value for this test statistic is P(Z < -3.05) = 0.0012 (using a standard normal distribution table or calculator).
Since the p-value (0.0012) is less than the significance level (0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true probability of the politician being elected is less than 0.7. In other words, the sample data supports the claim that the politician's chance of being elected is less than 70%.
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what is 164.8 cm height in feet?
The height of 164.8 centimeter after conversion to feet is equivalent to 5.41 feet .
The various measurements units that are used in measuring the height of an object are , centimeter (cm) , meter (m) , feet , inches .
We have to convert the height of 164.8 cm to feet ;
we know that , 1 centimeter is = 0.0328 feet ;
So , we multiply the units given in centimeter by 0.0328 ,
On multiplying 164.8 cm by 0.0328 ;
We get ;
⇒ 164.8 centimeter = 164.8 × 0.0328 ;
⇒ 164.8 centimeter = 5.40544 feet ≈ 5.41 feet ;
Therefore , 164.8 cm is approximately equal to 5.41 feet .
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3x+5=50 , can anyone help me solve that ! . Tysm , also its not high school . its middle but wtv
Answer: x=15
Step-by-step explanation:
3x+5=50
3+5=50
Subtract the numbers
3x+5-5=50-5
3x/3=45/5
x=15
a guy wire runs from the top of a cell tower to a metal stake in the ground. rashon places a 6-foot tall pole to support the guy wire. after placing the pole, rashon measures the distance from the stake to the pole to be 4 ft. he then measures the distance from the pole to the tower to be 9 ft. find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot is 23 feet.
How to calculate the length of the guy wire?Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;
CD = 6 ft.DE = 4 ft.BD = 9 ft.Additionally, the corresponding sides of similar triangles are equal;
AB/CD = BE/DE
AB/6 = (9 + 4)/4
AB/6 = 13/4
AB = 19.5 feet.
By applying Pythagorean' theorem, side AE is given by:
AE = √(AB² + BE²)
AE = √(19.5² + 13²)
AE = 23.44 ≈ 23 feet.
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What is the value of X and Y?
The length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangle, we shall calculate for the length x and y by application of the trigonometric ratio of sine and cosine for the angle 45°.
sin 45° = y/9√2 {opposite/hypotenuse}
by cross multiplication
y = 9√2 × sin 45°
recall that sin 45° = √2/2
y = 9√2 × √2/2
y = 9m
cos 45° = x/9√2 {adjacent/hypotenuse}
by cross multiplication
x = 9√2 × cos 45°
recall that cos 45° = √2/2
x = 9√2 × √2/2
x = 9m
Therefore, the length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°.
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what is multiplying polynomials calculator?
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.
The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.
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The width of a rectangle is 10 feet, and the diagonal length of the rectangle id 32.5 feet. What us the measure of the length if the rectangle in feet? round yo the nearest tenth
Answer:
about 30.9 feet
Step-by-step explanation:
Using the Pythagorean Theorem:
[tex] {l}^{2} + {10}^{2} = {32.5}^{2} [/tex]
[tex] {l}^{2} = 956.25[/tex]
[tex]l = 30.9[/tex]
a radioactive substance has a decay rate of 0.044 per hour. how many grams of a 100 gram sample will remain radioactive after 2 hours? round the answer to the nearest tenth of a gram, and do not include the unit in your answer. if necessary, include a leading 0 with any decimals less than 1. for example, 0.4 instead of .4. note: the formula for radioactive substance is w
91.6 grams of a 100 gram sample will remain radioactive after 2 hours. The solution has been obtained by using the concept of radioactive decay.
What is Radioactive decay?
Radioactive decay is the spontaneous destruction of an atomic nucleus in a radioactive substance that causes the emission of radiation from the nucleus. A parent nuclide in a radioactive process is one that decays, and a daughter nuclide is one that is created in the radioactive process.
We are given that a radioactive substance has a decay rate of 0.044 per hour.
Using the radioactive decay formula,
N(t) = N₀ [tex]e^{-kt}[/tex]
Initially, N = 100
k = 0.044
t = 2
So,
⇒N(t) = 100 * e⁽⁻⁰°⁰⁴⁴ ˣ ²⁾
⇒N(t) = 91.5761
⇒N(t) = 91.6
Hence, 91.6 grams of a 100 gram sample will remain radioactive after 2 hours.
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Let A be a matrix with linearly independent columns. Which one of these statements must be true? You have only three attempts at this problem. A. The equation Az b always has a solution for all b B. The equation Ab has a solution for all b precisely when it has more rows than columns. O C. There is no easy way to tell if Ax-b has a solution for all b D. The equation Az -b has a solution for all b precisely when it has more columns than rows. OE. The equation Ax -b never has a solution for all b F. The equation Az-b has a solution for all b precisely when it is a square matrix. G. none of the abovePrevious question
If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.
Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:
A. The equation Az=b always has a solution for all b.
This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.
B. The equation Ab has a solution for all b precisely when it has more rows than columns.
This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.
C. There is no easy way to tell if Ax-b has a solution for all b.
This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.
D. The equation Az-b has a solution for all b precisely when it has more columns than rows.
This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).
E. The equation Ax-b never has a solution for all b.
This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).
F. The equation Az-b has a solution for all b precisely when it is a square matrix.
This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).
Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.
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(Please help!!) Leslie creates designer bracelets with gemstones. Her most recent order included a total of 6 bracelets. It takes 12 stones to make one bracelet.
Write and solve an equation that represents how many stones were used for the order.
6s = 12; s = 2 stones
s + 6 = 12; s = 6 stones
s − 6 = 12; s = 18 stones
s divided by 12 equals 6; s = 72 stones
Leslie used a total of 128 stones for the order.
What is an arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics.
It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
The correct equation that represents how many stones were used for the order is:
total number of stones = number of bracelets x stones per bracelet
Let's use "s" to represent the total number of stones Leslie used for the order:
s = 8 x 16
s = 128
Hence, Leslie used a total of 128 stones for the order.
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what is rhombus angle sum
Answer:
360 degrees
Step-by-step explanation:
I remember learning this in Math class. The rhombus angle sum will make 360 degrees.
A politician wants to know what percentage of the voters supports her position on the issues of forced busing for integration. What size voter sample should be obtained to determine with 90% confidence the support level to within 4%?
The politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.
What is the proportion?
A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.
To determine the sample size needed to estimate the proportion of voters supporting a certain position within a certain margin of error and level of confidence, we can use the following formula:
n = (Z² * p * (1 - p)) / E²
where:
n is the sample size
Z is the z-score corresponding to the desired level of confidence (in this case, 90%, which corresponds to a z-score of 1.645)
p is the estimated proportion of voters supporting the politician's position (we don't have an estimate, so we'll use 0.5, which maximizes the sample size and provides the most conservative estimate)
E is the desired margin of error (in this case, 4%, which is equivalent to 0.04)
Substituting the values given, we get:
n = (1.645² * 0.5 * (1 - 0.5)) / 0.04²
n = 601.5625
We need to round up to the nearest whole number since we can't have a fractional sample size, so the minimum sample size needed is 602 voters.
Therefore, the politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.
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Determine the equation of the ellipse with center (6, -6), a vertex at (13, -6), and a co-vertex at (6, 0).
The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.
How to derive of the equation of an ellipse
In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.
The standard form of the ellipse is shown below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Center of the ellipsea - Length of the major semiaxis.b - Length of the minor semiaxis.Now we proceed to derive the equation of the ellipse:
Major semiaxis:
A = (13, - 6) - (6, - 6)
A = (7, 0)
a = 7
Minor semiaxis:
B = (6, 0) - (6, - 6)
B = (0, 6)
b = 6
Equation of the elipse:
(x - 6)² / 49 + (y + 6)² / 36 = 1
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The function f(x) = x + 5 represents the length of a rectangle, and the function g(x) = 7x − 2 represents the width of the rectangle. What is the area of the rectangle if x = 3? 56 27 285 152
Answer: 152
Step-by-step explanation:
Length: f(x) = x+5
Width: g(x) = 7x-2
Area: A= f(x) *g(x)
A= (x+5)(7x-2)
= 7x^2 -2x + 35x -10
= 7x^2 +33x -10 // Substitute 3 in for x
=7(3)^2 +33(3) -10
=7(9) +99 -10
=63+99-10
=152
Answer:
152
Step-by-step explanation:
took the test xx
what is maximum and minimum calculator online
Minimum and Maximum Calculator is an online widget that helps you find the max and min values of a function.
The maximum value is the point at which the function has the highest value of all other values, while the minimum value is the lowest value in the entire function.
The calculator returns the global maximum and minimum of the function along with a graph on the Cartesian plane as the solution. A min-max calculator is an online calculator that can be used to find the maximum and minimum values of a mathematical function.
Finding the extreme values of a function is also known as optimization. Feature optimization is a central concept in engineering, business, and machine learning.
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The annual rate of growth in population of a certain city is 8%. If its present population is 1,96,830 then what was the population three years ago?
Answer: The population three years ago was 156250.
Step-by-step explanation:
Let 3 years ago, the population of a city = P
Rate of growth (R) = 8% p.a.
Present population (P) = 1,96,830.
Therefore,
[tex]A=P(1+R100)n[/tex]
P = A÷(1 + 8/100)³
196830 ÷ (1+2/25)³
=156250.
3 years ago, the population of the city = 156250.
Find the value x given angles?
Answer:
x=60
Step-by-step explanation:
180 is the some of the angle of an triangle
in the left triangle the angle is = 180-70-75=35
in the right triangle the angle is=180-35-60=85
x=180-80-45=60
Answer:
Step-by-step explanation:
Remember: The three interior angles of a triangle will always add up to 180 degrees.
In order to solve for x, we need to solve for other missing angles
1) Solve for the missing angle on the triangle to the left.
180 - 75 -70 = 35 degrees.
2) Solve for the missing angle on the triangle to the right (not x).
180 - 60 - 35 = 85 degrees
3) Finally, solve for the x angle by subtracting 45 and 85 from 180. x = 50 degrees.
how many sundays in a year
Usually there are 52 Sundays in a year approximately.
There are a total of 52 weeks in a year if we take a rough estimate.
Every week has one sunday in it. So, going by this logic, each year will have about 52 sundays in it.
Now, one thing that we should notice here is that is not certain that there will be definitely 52 sundays. This number of 52 can increase also by a number of one or two because it is possible that the year might not starting from sunday. Because when we do 365/7 we get 52.14 so, this decimal place might include one or two Sundays in it.
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3 = blank X blank X blank = 27
fill in the blanks
Answer:
blank=9
Step-by-step explanation:
what is the secant in trigonometry?
Secant can be defined as the reciprocal of cosine. Secant of angle A will be hypotenuse/adjacent.
There are three basic trigonometric ratios. Sin, Cos and Tan.
Sin = opposite side/ hypotenuse
Cos = adjacent side/ hypotenuse
Tan = opposite side/ adjacent side
Here in the give image, Sin(A) = a/c
Cos(A) = b/c
Tan(A) = a/b
There are reciprocals for each trigonometric functions
Cosecant is the reciprocal of sine. Cosec(A) = c/a
Secant is the reciprocal of Cosine. Sec(A) = c/b
Cotangent is the reciprocal of Tangent . Cot(A) = b/a
So secant is one of inverse trigonometric functions.
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Write the number below as a fraction in its simplest form
answer:
answer:1/8
answer:1/8explanation :
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.hope this helped.
need help please help me fast
The area of the triangular prism is 240 mm²
Right triangular prism:A triangular prism is a prism with three rectangular faces connecting its two congruent triangular faces. It consists of 5 faces, 6 edges, and vertices.
The sum of the areas of all the triangle's faces is the surface area. By using the net of a prim we can determine the area of the prism as given below. Here we calculate the individual parts of the net to get the total area.
Here we have
A right triangular prism and its net
The area of the prism can be calculated by calculating the area of the 2 triangles and the areas of 3 rectangles in the given net
As we know Area of rectangle = Length × Width
Area of rectangle parts = [ 3 × 8 ] + [ 3 × 15 ] + [ 17 × 3 ]
= 24 mm² + 45 mm² + 51 mm²
= 120 mm²
Area of triangle parts = 2 [ 1/2 (15 × 8) ]
= 120 mm²
Total area of prism = 120 mm² + 120 mm² = 240 mm²
Therefore,
The area of the triangular prism is 240 mm²
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what is mean arterial pressure formula
The mean arterial pressure formula is MAP = CO x TPR or MAP = (SBP + 2DBP) / 3.
The mean arterial pressure (MAP) formula is:
MAP = CO x TPR
where:
CO is the cardiac output (how much blood is siphoned by the heart each moment)
TPR is the all-out peripheral resistance (the resistance from the bloodstream in the body's veins)
On the other hand, the mean arterial pressure can also be calculated using the following equation:
MAP = (SBP + 2DBP)/3
where:
SBP is the systolic blood pressure (the highest pressure in the arteries when the heart beats)
DBP is the diastolic blood pressure(the lowest pressure in the arteries when the heart is at rest between beats)
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Find the product of 4 x 3/8
Answer:
1.5
Step-by-step explanation:
Answer: 1.5
Step-by-step explanation:
what is the answer to this, its on khan
Answer:
B) 5
Step-by-step explanation:
AB = 4 units
BC = 3 units
Use Pythagorean theorem to find the length of AC,
AC² = AB² + BC²
= 4² + 3²
= 16 + 9
= 25
[tex]AC = \sqrt{25}\\\\[/tex]
AC = 5 units
When an object is dropped into a liquid, the volume of the displaced liquid is _______ to the volume of the object that is dipped. ( a ) Smaller ( b ) Greater ( c ) Equal ( d ) May be Greater or Smaller
Answer:
C
...................
AC=3x-4 AB=62 BC=x-2 find the x
AC=3x-4 AB=62 BC=x-2, x = 17. This can be solved by using the concept of simplification.
What is straight line?A line is an endlessly long object without breadth, depth, or curvature in geometry. So, despite the fact that they can exist in two, three, or more dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its endpoints in daily life.
The most clear and simple way to calculate depreciation is along a straight line. It is most beneficial when an asset's value declines slowly over time at a pace that is close to constant.
Given that,
AC=3x-4
AB=62
BC=x-2
As we can clearly see in line AB:
AC+BC= AB
=>(3x-4)+(x-2)= 62
=>4x -6 = 62
=>4x = 62+6
=>4x = 68
=>x = 68/4
=>x= 17
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The complete question is as follows:
Use the diagram to complete the statements.
The angle of depression from point R to point S is angle
.
The angle of elevation from point S to point R is angle
.
Angle 2 is the angle of elevation from
.
Angle 1 is the angle of
.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
What is an angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
There is an angle of elevation from point R to S. Thus point R is lie above S.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
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The difference between the high and low temperatures on Sunday was at least 35°F. The low temperature on Sunday was -8°F.
Part A
Select the correct values and symbol to write an inequality that represents the possible high temperatures, t, on Sunday.
t- __ _ __
High temp ≥ Low temp + difference
High temp ≥ -8°F + 35°F
High temp ≥ 27°F
InequalityAn inequality is a relationship between two different quantities or expressions.
An inequality may be expressed by a mathematical sentence that uses the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
≠ is not equal to
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3^8 x 2^3 divided by 3^5
Answer:
216
HOPE THIS HELPS
PLS GIVE BRAINLIEST
In AQRS, q = 99 cm, r = 17 cm and s-96 cm. Find the measure of ZS to the nearest
degree.
The measure of ∠S is 75 degrees
How to find the measure of ∠S to the nearest degree?
The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:
cos(S) = (q² + r² - s²)/2qr
where q, r and s are the lengths and Q, R and S are the angles
Using the formula:
cos(S) = (q² + r² - s²)/2qr
cos(S) = (99² + 17² - 96²)/(2*99*17)
cos(S) = 0.2597
S = cos⁻¹(0.2597)
S = 75 degrees
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