Class: 1,2,3,3,4,4,4,4,5,3
First, order from lowest to highest
1,2,3,3,3,4,4,4,4,5
Median = (1,2,3,3) 3, 4,(,4,4,4,5) = (3+4)/2 = 3.5
Find the median of the first and last half:
Q1 = 1,2,3,3,3.5 = 3
Q3 = 3.5,4,4,4,5 = 4
Then for the interquartile: Q3- Q1 = 4 -3 = 1
I need to know how to do the whole thing and understand it.
We are given the data on the number of candies handed by neighborhood A and neighborhood B.
Let us first find the mean and variance of each neighborhood.
Mean:
[tex]\bar{x}_A=\frac{\sum x}{N_1}=\frac{12}{6}=2[/tex][tex]\bar{x}_B=\frac{\sum x}{N_2}=\frac{20}{6}=3.33[/tex]Variance:
[tex]s_A^2=\frac{\sum x^2}{N_1}-\bar{x}_A^2=\frac{28}{6}-2^2=0.667[/tex][tex]s_B^2=\frac{\sum x^2}{N_2}-\bar{x}_B^2=\frac{80}{6}-3.33^2=2.244[/tex]A. Null hypothesis:
The null hypothesis is that there is no difference in the mean number of candies handed out by neighborhoods A and B.
[tex]H_0:\;\mu_A=\mu_B[/tex]Research hypothesis:
The research hypothesis is that the mean number of candies handed out by neighborhood A is more than neighborhood B.
[tex]H_a:\;\mu_A>\mu_B[/tex]Test statistic (t):
The test statistic of a two-sample t-test is given by
[tex]t=\frac{\bar{x}_A-\bar{x}_B}{s_p}[/tex]Where sp is the pooled standard deviation given by
[tex]\begin{gathered} s_p=\sqrt{\frac{N_1s_1^2+N_2s_2^2}{N_1+N_2-2}(\frac{N_1+N_2}{N_1\cdot N_2}}) \\ s_p=\sqrt{\frac{6\cdot0.667+6\cdot2.244}{6+6-2}(\frac{6+6}{6\cdot6})} \\ s_p=0.763 \end{gathered}[/tex][tex]t=\frac{2-3.33}{0.763}=-1.74[/tex]So, the test statistic is -1.74
Critical t:
Degree of freedom = N1 + N2 - 2 = 6+6-2 = 10
Level of significance = 0.05
The right-tailed critical value for α = 0.05 and df = 10 is found to be 1.81
Critical t = 1.81
We will reject the null hypothesis because the calculated t-value is less than the critical value.
Interpretation:
This means that we do not have enough evidence to conclude that neighborhood A gives out more candies than neighborhood B.
The radius of a circle is 6 feet. What is the area of a sector bounded by a 66° arc?Give the exact answer in simplest form. ____ square feet. (pi, fraction,)
where:
r= radius = 6 ft
Θ = angle = 66°
Replacing:
[tex]A=\frac{66\cdot\pi}{360}\cdot6^2[/tex]A= 33/5 π
Innings in his latest game,
The equation for the expression is given by
[tex]x+6\frac{2}{3}>82\frac{1}{3}[/tex]To get the value for x
Step 1: Subtract
[tex]\begin{gathered} 6\frac{2}{3} \\ \text{from both sides} \end{gathered}[/tex][tex]x+6\frac{2}{3}-6\frac{2}{3}>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]x>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]\begin{gathered} 82\frac{1}{3}=\frac{247}{3} \\ \\ 6\frac{2}{3}=\frac{20}{3} \\ \\ x>\frac{247}{3}-\frac{20}{3} \end{gathered}[/tex]Simplifying further
[tex]\begin{gathered} x>\frac{247-20}{3} \\ \\ x>\frac{227}{3} \end{gathered}[/tex][tex]\begin{gathered} x>\frac{227}{3}\text{ } \\ or \\ x>75\frac{2}{3} \end{gathered}[/tex]Ill send you the pictures of my question, it isnt allowing me to put them here
A is the correct option
what principal will amount to $1750 if invested at 3% interest compounded quarterly for 5 years
The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
Where
A is the total amount after t years
P is the principal or initial amount invested
r is the interest rate
n is the number of compouding periods in a year
t is the number of years
From the information given,
A = $1750
r = 3% = 3/100 = 0.03
t = 5
n = 4 because it was compounded quarterly
By substituting these values into the formula, we have
1750 = P(1 + 0.03/4)^4 * 5
1750 = P(1 + 0.03/4)^20
1750 = P(1.0075)^20
Dividing both sides by (1.0075)^20, it becomes
P = 1750/(1.0075)^20
P = 1507.0822
Approximating to the nearest whole number,
Principal = $1507
find the difference between the mode and median of the distribution of data
Step 1: Rewrite the dot plot in tabular form
Step : Compute the mode
From the table, we can see that the numer appears most ( that is the number with the highest frequence, f) is 4.
Therefore,
mode = 4
Step 3: Find the median
First arrange the data in ascending order. In this case, the data is already in ascending order.
If ∑f is odd, the median is the middle value which is at position
[tex]\frac{\sum f+1}{2}[/tex]If ∑f is even, the median is the average of the two values at positions
[tex]\frac{\sum f}{2}\text{ and }\frac{\sum f}{2}+1[/tex]In this case, ∑f = 12 is even.
Therefore, the median is the average of the numbers at position 6 and 7
number at position 6 is 3
number at position 7 is 4
Hence, the median is given by
[tex]\frac{3+4}{2}=\frac{7}{2}=3.5[/tex]median = 3.5
Step 4: Find the difference between the median and mode
The difference is given by
[tex]4-3.5=0.5[/tex]Hence the difference is 0.5
what is 5.37 with 15% discount
Answer
5.37 with 15% discount = 4.5645
Explanation
5.37 with 15% discount
= 5.37 - (15% of 5.37)
= 5.37 - 0.15(5.37)
= 5.37 - 0.8055
= 4.5645
Hope this Helps!!!
Answer:
Step-by-step explanation:
15% off 5.37 is 4.56.
The difference is 0.81
What two numbers multiply to -25 adds up to 2
8) Find the volume of a cylinder that has a radius of 9 cm and a height of 15 cm. 15 cm 9 cm
In order to find the volume of the given cylinder, use the following formula:
V = π·r²·h
where:
r: radius of the cylinder = 9 cm
h: height of the cylinder = 15 cm
π = 3.1415
replace the previous values of the parameters into the formula for V:
V = (3.1415)(9 cm)²(15 cm)
V = 3,816.92 cm³
Hence, the volume of the given cylinder is 3,816.92 cm³
“Rewrite the following expression so there are no negative exponents. Do not simplify”
The rule of the negative exponent is given below:
[tex]X^{-a}=\frac{1}{X^a}[/tex]Hence, the expression:
[tex]\frac{yx^3.-2x^{-2}y^{-2}}{-3x^{-1}y^{-4}.-3y^3}[/tex]can then be re-written, without the negative exponent, as:
[tex]\frac{yx^3\text{ . }\frac{-2}{x}\frac{1}{y^2}}{\frac{-3}{x}\frac{1}{y^4}.-3y^3}[/tex]2) The expression:
[tex]\begin{gathered} \frac{x^3y^{-1}}{3x^4y^{-2}.2x^2y^2} \\ \end{gathered}[/tex]can be re-written, without the negative exponent, as:
[tex]\frac{x^3\times\frac{1}{y}^{}}{3x^4\times\frac{1}{y^2}.2x^2y^2}[/tex]Bath and Body works is having a sale. Their Body Mists are 65% off. If the original price is $14.50, how much would you spend if you bought 5 body mists? Write an equation(s) to represent the problem and solve.
Body mists are 65% off
The original price is $14.50
So, the 60% of 14.50 is
[tex]\begin{gathered} 60\text{ percent of 14.50 dollars is =}\frac{60\times14.50}{100} \\ 60\text{ percent of 14.50 dollars is}=8.7\text{ dollars} \end{gathered}[/tex]Since the 8.7 dollars is off so, the net price is 14.50-8.7
The prics of one body mists after 60% off is $5.8
Let the x is the amount spend in the 5 body mists
Since the prics of 1 body mists is $5.8
So, the price of 5 body mists is : 5 times of $5.8
[tex]\begin{gathered} \text{The price of 5 body mists =5}\times5.8 \\ \text{The price of 5 body mists=}29\text{ dollars} \\ \text{ Since we assume that the price of the 5 body mists is x } \\ So,\text{ x = 29 Dollars} \end{gathered}[/tex]Answer : x = $29
A line passes though two points A(-2, 2). B(-1, 2). What is the slope:
The slope of the line that passes through points (-2, 2) and (-1, 2) is 0.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point A(-2, 2)
x₁ = -2y₁ = 2Point B( -1, 2 )
x₂ = -1y₂ = 2To determine the slope, plug the given x and y coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 2 - 2 )/( -1 - (-2) )
Slope m = ( 0 )/( -1 + 2 )
Slope m = ( 0 )/( 1 )
Slope m = 0
Therefore, the slope of the line is 0.
Learn more about slope formula here: brainly.com/question/24578307
#SPJ1
There are 360° in a circle graph. If 50° of the graph represents rent and 7° of the graph represents savings, what fractional portion of the whole graph is not represented by rent and savings?
Based on the circle graph and portions that are represented by rent and savings, the fractional portion of the graph that is not represented by rent and savings is 84.2%
How to find the fractional portion?First, find the degrees in the circle graph that is not represented by rent and savings. This is:
= Total number of degrees in circle graph - degrees represented by rent and savings
= 360 - 50 - 7
= 303 °
The fractional portion which isn't represented by either rent or savings is:
= Degrees not represented by rent or savings / Total number of degrees x 100%
= 303 / 360 x 100%
= 84.2%
Find out more on fractional portions at https://brainly.com/question/915216
#SPJ1
In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown. a. What is a function that relates the sales and the number of muffins?b. How many muffins would you have to sell to make at least $175.000 in sales?a. Write the function.s= ______. (Type and expression using m as the variable.)
The function is S = N*1.75. The number of muffins that must be sold to earn $175 is 100.
The number of muffins sold and the amount of sales in a bake sale are shown in the given table. The number of muffins sold is 12, 14, 17, and 18. The amount of the sale is $21, $24.5, $29.75, and $31.5. We can write these in the form of coordinates as (12, 21), (14, 24.5), (17, 29.75), and (18, 31.5).
We should first determine if the ratio is constant. The ratio is the division of the sales amount by the respective number of muffins sold. We find that the ratio of all the pairs is the same and is equal to 1.75. We can form an equation as given below :
S = N*1.75
The variables "S" and "N" represent the sales amount and the number of muffins, respectively. We need to find the number of muffins that need to be sold to earn $175.
S = N*1.75
175 = N*1.75
N = 100
To learn more about equations, visit :
brainly.com/question/10413253
#SPJ9
need answer asap ty
multiplying integers
(-5) (-12) =
-9 × (-6) =
(-7) (8) =
11 × -8 =
(-12) (4) =
question 1 =60
2=54
3=-56
4=-88
5=-48
-2/5y=4 what is y???????
Answer:
-10
Step-by-step explanation:
solve for y by simplifying both sides of the equation, then isolating the variable.
please help. i don’t under any of this and it’s due today
GIVEN:
We are given the exponential relationship as shown below;
[tex]g(x)=4(0.6)^x[/tex]Required;
To determine the characteristics of the graph as indicated.
(1) The range of the function; The range of the function is determined as follows;
[tex]\begin{gathered} For\text{ }the\text{ }function;\text{ }c\times n^{ax+b}+k \\ \\ Range=g(x)>k \end{gathered}[/tex]In this question, the value of k is nil or zero. Therefore, we have
[tex]\begin{gathered} Range: \\ \\ g(x)>0 \\ \\ That\text{ }is; \\ \\ y>0 \end{gathered}[/tex]Going to store for Quetion‘s 9X -7 equals -7
The polynomial 9x-7=-7. The value is x=0.
Given that,
The polynomial 9x-7=-7
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. We are able to perform mathematical operations on polynomial expressions such addition, subtraction, multiplication, and positive integer exponents but not division by variables.
The terms Poly (meaning "many") and Nominal (meaning "terms") make form the word polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. So-called polynomial degrees are polynomial equations with one variable having the largest exponent.
9x-7=-7
9x=-7+7
9x=0
x=0
Therefore, The value is x=0
Complete question: The polynomial 9X -7 = -7. Find the value of x.
To learn more about polynomial visit: https://brainly.com/question/11536910
#SPJ1
I need help with Slopes!
we know that
To find out the slope of the line, we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]we need two points
Looking at the graph
we take the points
(1,3 ) and (2,5)
substitute in the formula above
[tex]\begin{gathered} m=\frac{5-3}{2-1} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]therefore
the slope of the line is 2Urgent!!! Long division
So, we know the bus can hold 20 people in 15 minutes, so the rate per hour is:
20/15m
60m/15m
4
20/15 x 4/4m
80/60m (80 per hour)
4/1 = 4
80/60m x 4/4
320/240m
320/4h
320 people could ride the bus in 4 hours.
Based on the table below, find the range of f(x) x 137911f(x) 8175209Range = {
The range of the functions is the set made of the f(x) values. Therefore the range is:
[tex]\lbrace8,17,5,20,9\rbrace[/tex]homework help
give two examples of when you might estimate differences in everyday life.
Some examples of the use of estimates in our everyday lives are given below:
Making an estimate when shopping so as not to exceed budgetMaking an estimate of the number of shoppers in a shopping mallWhat is an Estimate?This refers to the rough calculation that is done to judge the value of a thing or the data outcome of a proposition.
Hence, when it comes to estimation or rough calculation of values or numbers, it is important that it is done as accurately as possible within the limits of current available data or data projections.
Read more about estimates here:
https://brainly.com/question/107747
#SPJ1
Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total $306, working 12 hours as a cashier and 10 hours as a cook. The next week, sheworked 14 hours as a cashier and 22 hours as a cook, earning $512. How much doesshe earn per hour as a cashier?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the terms with a variable
Let x be the amount she earns per hour as a cashier
Let y be the amount she earns per hour as a cook
STEP 2: Interpret the statements in the question as seen below:
[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]STEP 3: Solve the simultaneous equation using elimination to get x and y
[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]STEP 4: Solve any of equation to get the value of x
[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier
can someone help me
The answer is f(-2) = 30
The question requires us to substitute the value of x into the function.
if the function is:
[tex]f(x)=-2x^3+2x^2-2x+2[/tex]then f(-2) means we only need to substitute -2 for x into the equation given.
[tex]\begin{gathered} f(-2)=-2(-2)^3+2(-2)^2-2(-2)+2 \\ (-2)^3=-8_{} \\ (-2)^2=4 \\ -2(-2)=4 \\ \\ f\mleft(-2\mright)=-2\mleft(-8\mright)+2\mleft(4\mright)+4+2 \\ f(-2)=16+8+4+2 \\ f(-2)=30 \end{gathered}[/tex]Therefore,
The final answer is f(-2) = 30
multiply the question
EXPLANATION:
In order to multiply correctly we must follow the following steps:
-Multiply the numbers that are not in power of 10 and finally add the powers of 10.
The exercise is as follows:
[tex]undefined[/tex]what are the domain and range of this exponential functions y=4×+8
The given function is
[tex]y=4^{x+8}[/tex]The domain of the function would be all real numbers.
But the range would be all real numbers greater than zero because the function approximates to y = 0 but it doesn't go through.
Hence, the answer is the first option.At a restaurant, you order a moal that costs $12. You leave a 15% tip. The sales tax is 9%. What is the total costof the meal In dollars
SOLUTION:
Case: Percentages
Given:
Meal cost= $12
tip= 15%
sales tax= 9%
Method:
To find the Total cost of the meal,
We calculate the actual cost of the tip
[tex]\begin{gathered} 15\%\times12 \\ \frac{15}{100}\times12 \\ \frac{180}{100} \\ 1.8 \end{gathered}[/tex]The actual cost of the tip was $1.80
We then calculate the actual cost of the sales tax
[tex]\begin{gathered} 9\%\times12 \\ \frac{9}{100}\times12 \\ \frac{108}{100} \\ 1.08 \end{gathered}[/tex]The cost of sales tax is $1.08
The total cost of the mean is:
[tex]\begin{gathered} 12+1.80+1.08 \\ =14.88 \end{gathered}[/tex]Final answer:
The total cost of the meal is $14.88
Nate is 22 years old. Karina is 13 years old. How many years ago was Nate's age 4 times Karina'sage?
Nate current age = 22 years
Karina current age = 13 years
let
x = the years ago
[tex]\begin{gathered} 4(13-x)=22-x \\ 52-4x=22-x \\ 52-22=-x+4x \\ 30=3x \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]The answer is 10 years ago.
Quadrilateral DEFG has vertices D(-1,2), E(-2, 0), F(-1,-1) and G(1, 3). A
translation maps quadrilateral DEFG to quadrilateral D'E'F'G'. The image of D is D'(-2,-2).
What are the coordinates of E, F, and G′ ?
Answer:
E' = (-3, -4)
F' = (-2, -5)
G' = (0, -1)
Step-by-step explanation:
Given vertices of quadrilateral DEFG:
D = (-1, 2)E = (-2, 0)F = (-1, -1)G = (1, 3)A translation is a type of transformation and moves a figure left, right, up or down.
Every point on the original figure is translated (moved) the same distance in the same direction.
Therefore, to calculate the mapping rule that translates DEFG to D'E'F'G', compare the coordinates of D with the coordinates of D'.
D = (-1, 2)D' = (-2, -2)The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Therefore, the mapping rule is:
(x, y) → (x-1, y-4)To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
find the area of the trapezoid __ m squared simplify the answer
A trapezoid is given with base lengths of 10m and 14m, and a height of 9m.
It is required to find the area of the trapezoid.
Recall that the area of a trapezoid with base lengths b₁, b₂, and height h is given by:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]Substitute b₁=14, b₂=10, and h=9 into the formula:
[tex]\begin{gathered} A=\frac{1}{2}(14+10)\cdot9 \\ \Rightarrow A=\frac{1}{2}\cdot24\cdot9=108 \end{gathered}[/tex]Hence, the required area is 108 m².
The answer is 108 m².
