The proportion of people in the area who would purchase food from the restaurant is greater than 60%.
Hypothesis testing is used to determine if the proportion of people in a particular area that would purchase food from a particular restaurant is greater than 60%. The null hypothesis, denoted by H0, is that the proportion of people who would purchase food from the restaurant is 60%, or p=0.6. The alternative hypothesis, denoted by H1, is that the proportion of people who would purchase food from the restaurant is greater than 60%, or p>0.6.
To conduct the test, we can use a one-sample proportion test, which is a type of statistical test that compares an observed proportion to a hypothesized proportion. To calculate the test statistic, we can use the formula:
Test statistic = (observed proportion - hypothesized proportion) / (standard error of the proportion)
In this case, the observed proportion is 320/500 = 0.64 and the hypothesized proportion is 0.6. Therefore, the test statistic is:
Test statistic = (0.64 - 0.6) / (square root of (0.6 * (1 - 0.6) / 500))
Test statistic = 0.04 / (square root of (0.6 * 0.4 / 500))
Test statistic = 0.04 / 0.0341
Test statistic = 1.17
The test statistic is 1.17, which is greater than the critical value of 1.645. Therefore, we can reject the null hypothesis and conclude that the proportion of people in the area who would purchase food from the restaurant is greater than 60%.
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Substitute x = 2 into each equation. Which two equations have the solution x = 2?
Answer:
Step-by-step explanation:
The two equations that have the solution x = 2 when x is substituted for 2 are:
Equation 1: 2 + 3x = 10
2 + 3(2) = 10
2 + 6 = 10
8 = 10
Equation 2: 2x + 4 = 10
2(2) + 4 = 10
4 + 4 = 10
8 = 10
Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. Do not add any spaces when typing in the equation.
The equation showing the total cost for purchasing x tickets is given as y = 12.5x + 7
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total cost for x tickets.
From the table, using the points (2, 32) and (6, 82):
y - 32 = [(82 - 32)/(6 - 2)](x - 2)
y - 32 = 12.5(x - 2)
y = 12.5x + 7
The equation is given as y = 12.5x + 7
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The equation C = 50m represents the monthly cost of membership at Jane’s current gym. The equation C= 35m represents the monthly cost of membership at a different gym, named Gym City
It can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.
What are expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the equation C = 50m, that represents the monthly cost of membership at Jane’s current gym. The equation C = 35m represents the monthly cost of membership at a different gym, named Gym City
The equation for direct variation is -
y = Kx
where -
{K} denotes the rate of change
Now -
For Jane’s current gym, the equation that represents the monthly cost of membership is C = 50m. This means it costs $50 per month as a membership fee.For Gym City, the equation that represents the monthly cost of membership is C = 35m. This means it costs $35 per month as a membership fee.Therefore, it can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.
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raquel wants to make a rectangular garden with a area of 12m, but using the least amount of fencing. Each has to be a whole (ie not decimals). What will the dimensions of the garden be?
Answer:
Step-by-step explanation:
The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.
We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.
We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.
Therefore, the dimensions of the garden are 4m by 3m.
A square and a regular heptagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of exterior angle $BAC$
The degree of the measure of the exterior angle is 141 3/7°.
the term exterior angle in triangle is defined as angles that are parallel to the inner angles of a polygon but lie on the outside of it
Here we know that A square and a regular heptagon are coplanar and share a common side AD.
And then here we need to find each of the interior angle of the regular heptagon.
As we all know that here we have to use the formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.
According to the given formula here we have a regular heptagon's interior angle measures is calculated as
=> 180(7-2)/7 = 128 4/7.
Here we also know that the angle A and D would be 128 4/7 degrees.
Here the next step is to Find angle BAC.
For that here we have to know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees.
Now we have to subtract those from 360 degrees to find angle BAC then we get the expression like the following,
=> Angle BAC = 360 - (angle A + 90)
=> 360 - (128 4/7 + 90)
When we simplify this one then we get the resulting value as,
=> 360 - 218 4/7 = 141 3/7 degree
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Pls help will get grounded if I fail ☹ Write the rule for the linear. Remember a function rule written using f(x).
which of the following shows the correct first step to solve x^2-16x=-21 by completing the square? I'LL GIVE YOU BRAINLLEST PLEASE HELP ASAP!!!!!!!!!!!!!!!!!
Answer: B. [tex]x^{2} - 16x + 64 = -21 + 64[/tex]
Step-by-step explanation:
What is the value of the expression below when w= 5 and x=9? 7w-x=
Answer:
Step-by-step explanation:
Given that w=5 and x=9, we can substitute these values into the expression to find the value of the expression:
7w-x
= 7(5) - 9
= 35 - 9
= 26
So the value of the expression when w=5 and x=9 is 26
Find the total amount in an
account to the nearest cent after 3
years if the interest is compounded
annually on an investment of $5600 at
7.65%.
The total amount in an account to the nearest cent after 3 years if the interest is compounded annually on an investment of $5600 at 7.65% is $6,986.02
To find the total amount in the account after 3 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the total amount, P is the initial investment (principal), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $5600, r = 0.0765, n = 1 (because the interest is compounded annually), and t = 3. Plugging these values into the formula gives:
A = 5600(1 + 0.0765)^3
A = $6,986.02
So, the total amount in the account after 3 years, to the nearest cent, would be $6,986.02
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medians are drawn from point $a$ and point $b$ in this right triangle to divide segments $\overline{bc}$ and $\overline{ac}$ in half, respectively. the lengths of the medians are 6 and $2\sqrt{11}$ units, respectively. how many units are in the length of segment $\overline{ab}$?
The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
What is right triangle ?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.
We know that the medians are 6 and $2\sqrt{11}$ units, respectively.
Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$
so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$
so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.
Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
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Please help me with this problem!!
Check the picture below.
find the vector, not with determinants, but by using properties of cross products. (i × j) × k
(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.
What is cross product?The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.
A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.
As we know,
i × j = | i | × | j | × sin 90° × k
or, i × j = 1 × 1 × 1 × k
or, i × j = k
thus, (i × j) × k = k × k
or, (i × j) × k = 0
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1) Rustam has three times as many carrots as Pio. Rustam has 5 fewer carrots that Claudine.
Form an equation relating the number of carrots that Pio has compared to Claudine.
b. Use your equation to find out how many carrots Pio has, if Claudine has 20?
C. Use your equation to find out how many carrots Claudine has, if Pio has 10?
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Rustam has three times as many carrots as Pio
R=3P
Where is Rustam, P is Pio and C is Claudine.
Rustam has 5 fewer carrots that Claudine.
R=C-5
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.
Now let us find the number of carrots Pio has when Claudine has 20
3P=20-5
3P=15
Divide both sides by 3
P=5
Pio has 5 carrots when Claudine has 20.
Now if pio has 10 then the number of carrots with Claudine
3(10)=C-5
30+5=C
35=C
Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
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work out the value of r in the equation below
5.8/r=tan 19
give your answer in 1d.p.
Answer: 16.8
Step-by-step explanation:
[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]
Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answer:
Step-by-step explanation:
The correct answer is: 4x4 + 8x2y2 – 3x3y – 7xy3. This is the standard form for the polynomial, where the terms are written in descending order. The terms in this polynomial are the 4x4 term, the 8x2y2 term, the -3x3y term, and the -7xy3 term.
what is the least positive integer value of $x$ such that $(2x)^2 2\cdot 37\cdot 2x 37^2$ is a multiple of 47?
The least positive integer value of x is 1
We can start by expressing the expression (2x)^2 2372x 37^2 as a multiple of 47.
47 | (2x)^2 2372x 37^2
Since 47 is a prime number, we can use the property that a multiple of a prime number is a number that can be divided by that prime number without leaving a remainder.
So, we need to find the least positive integer value of x such that (2x)^2 2372x 37^2 is divisible by 47.
We can start by assuming (2x)^2 2372x 37^2 as (2x)^2 2372x 37^2 = 47*k, where k is any integer.
We can start testing values of x starting from 1,
x=1 : (21)^2 * 23721 * 37^2 = 4 * 74 * 1369 = 47 * 2028,
x=2 : (22)^2 * 23722 * 37^2 = 16 * 148 * 1369 = 47 * 6912,
and so on.
So the least positive integer value of x such that (2x)^2 2372x 37^2 is a multiple of 47 is x=1.
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8 = c − –3
c =
what does C equal?
[tex]8 = c - - 3 \\ 8 = c + 3 \\ c = 8 - 3 \\ c = 5[/tex]
Answer:
it is c=5
Step-by-step explanation:
here is how you get the answer
8=c−−3
8=c+3
c=8−3
c=5
Draw the line of reflection that reflects quadrilateral ABC D onto quadrilateral A' B'C'D'.
Therefore , solving the provided quadrilateral question we can say that - (x,y) -> (x,y) is the formula for a reflection across the y-axis.
Describe a quadrilateral.In geometry, a four-sided object having four corners is referred to as a quadrilateral. The word comes from either the Latin quad or portfolio of innovative (meaning "side"). Four corners, four states, and four corners are the three dimensions of a rectangle. Concave and convex surfaces come in essentially two varieties. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, angles, rhombuses, and squares.
Here,
The ordinate and abscissa are other names for the y-axis and x-axis, respectively.
The Y-axis is a line drawn from the bottom to the top of the graph. This axis runs parallel to the coordinates that need to be measured.
The numbers on the y-axis are referred to as y-coordinates.
When writing sorted pairs, the x-coordinate and then the y-coordinate are included in parenthesis.
(x, y).
A' ( -1, 1 ) ⇒ A"(-1, -1)
B' (-2, 2) ⇒ B"(-2, -2)
C' (-2, 3) ⇒ C"(-2, -3)
and D' (-1, 4) ⇒ D" (-1, -4)
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Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number
The bacteria count after 5 hours, given the initial bacteria count and the rate that the bacteria are disappearing is 59 bacteria
How to find the bacteria count ?First, find the rate at which the bacteria are disappearing from the culture dish every hour. This rate is:
= 100 % - 90 %
= 10 %
This means that every hour, 10% of the bacteria are removed from the culture dish on account of the antibiotic.
In five hours therefore, the bacteria count on the culture dish would be:
= Starting number of bacteria x ( 1 - rate of decrease per hour) ^ number of hours
= 100 x ( 1 - 10 %) ⁵
= 100 x 90 %⁵
= 59 bacteria
In conclusion, after 5 hours of the antibiotic working on the culture dish, the number of bacteria left would be 59 bacteria.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
In a paint factory, an old conveyer line has filled 22 barrels of paint and is filling more at a rate of 1 barrel per minute. A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled? How long will that take?
It takes 10 minutes for the two lines to have filled an equal number of barrels
How many barrels will each line have filled?Each line will have filled 90 barrels
Let “x” be the number of minutes
The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute
Thus, a equation is framed as follows:
Old conveyor: 20 + 7(number of minutes)
Old conveyor: 20 + 7x ------- eqn 1
A worker just switched on a newer line that can fill 9 barrels per minute
Thus, a equation is framed as follows:
New conveyor: 9(number of minutes)
New conveyor: 9x -------- eqn 2
In a little while, the two lines will have filled an equal number of barrels.
Thus, eqn 1 must be equal to eqn 2
Thus it takes 10 minutes for the two lines to have filled an equal number of barrels
Substitute x = 10 in any one of equations
Substitute in eqn 2
9x = 9(10) = 90
Thus each line will have filled 90 barrels
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what is the answer for this question? answer ASAP
Answer:
1÷(5/2×(2×(8-2/5)-1))
1÷(5/2×(2×(6/5)-1))
1÷(5/2×(12/5-1))
1÷(5/2×7/5)
1÷(35/10)
1÷35/10
1×10/35
10/35
2/7
find the quotient
324÷0.6
Answer:540
Step-by-step explanation:
Answer:
540
Step-by-step explanation:
When multiplying two numbers and one is a decimal you multiply both of them by 10 to keep whole number denominators.
[tex]\frac{324}{0.6}[/tex]
[tex]10* \frac{324}{0.6}[/tex]
[tex]\frac{3240}{6}[/tex]
[tex]\frac{3240}{6} = 540[/tex]
hello everyone, i need help can someone help me here please! thankyou
Answer:
1. 37, 44, 51
2. 24, 19, 14
3. 36, 49, 64
Step-by-step explanation:
The first rule is add 7
The second rule is subtract 5
The third rule is add 2 to every difference
Given:2x-3y+z=03x+2y=354y-2z=14Which of the following is a solution to the given system?(2, 3, 5)(3, 2, 0)(1, 16, 0)(7, 7, 7)
The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.
First, add the first equation to the second equation to eliminate the y-term:
5x + z = 7
Next, add the third equation to the first equation to eliminate the x-term:
3y + z = 3
Finally, substitute the expression for z into the expression for x and solve for y:
y = 3
Now that we have the values for x and y, substitute them into one of the original equations to solve for z:
2(2) - 3(3) + z = 0
z = 5
The solution is (2, 3, 5).
Three fathers-Paul, Johnson, and Nicolas have between them a total of 15 children of which 9 are boys. Paul has 3 girls and Johnson has the same number of boys. Johnson has 1 more child than Paul who has 4 children. Nicholas has 4 more boys than girls and the same number of girls as Paul has boys. How many boys each do Nicolas and Paul have?
Answer:
Nicholas has 5 boys, and Paul has 1 boy
Step-by-step explanation:
We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:
[tex]p + j + n = 15[/tex] (1st Equation)
[tex]p_{g} = j_{b} = 3[/tex] (2nd Equation)
[tex]j = p + 1 (p = 4)[/tex] (3rd Equation)
[tex]n_{b} = n_{g} +4[/tex] (4th Equation)
[tex]n_{g} = p_{b}[/tex] (5th Equation)
Whew! That was a lot. We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:
b = g + 4 and b + g = 6
So, we substitute the first equation into the second equation, giving us:
g + 4 + g = 6
2g = 2
g = 1
So, Nicholas has one girl, meaning he has 5 boys.
So, Nicholas has 5 boys, and Paul has 1 boy.
Hope this helped!
Describe the discontinuity of the graphed function. Be sure to indicate the location of each discontinuity and identify the type of discontinuity.
function f(x) is said to be discontinuous at a point ‘a’ of its domain D if it is not continuous there. The point ‘a’ is then called a point of discontinuity of the function.
he function of the graph which is not connected with each other is known as a discontinuous function.
A function f(x) is said to have a discontinuity of the first kind at x = a,
if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.
f(x) is said to have a discontinuity of the first kind from the left at x = a,
if the left hand of the function exists but not equal to f(a)
There are three types of discontinuity.
Jump Discontinuity
Infinite Discontinuity
Removable Discontinuity
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What is the equation of a circle with a center (−3, −2) and radius of 5?
HELPPPPPPP!!!!!!
(x − 3)2 + (y − 2)2 = 25
(x − 3)2 + (y − 2)2 = 5
(x + 3)2 + (y + 2)2 = 5
(x + 3)2 + (y + 2)2 = 25
Which option distinguishes the element that needs to be adjusted on the chart in the following scenario?
Donna just completed her demographic chart for her final social studies project on population growth. Her
teacher returns it and says her independent variable is incorrect and needs to be changed.
title
O y-axis value
O legend
Ox-axis value
833
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Jan 16
An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.
What are the types of variables?In an experiment, there are two (2) main types of variables and these include the following:
Dependent variable.Independent variable.What is an independent variable?In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.
In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.
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how do you think the cartesian product you read about is related to the cartesian coordinate system we use for graphing
The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.
The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.
When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.
In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.
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Why is 1 A common factor of every number?
A number multiplied by 1 is the number itself. So,1 is a factor of every number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself. Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.Every number other than 1 has at least two factors, namely the number itself and 1.To know more about common factors:
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