The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.
The confidence interval for the difference of the population mean is calculated as,
CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2
= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82
=6.4 ± 1.199
=(v5.201 , 7.599)
therefore , approximately 5.20 , 7.60 .
Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.
The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.
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Given the function f(x) = x² - x - 8, determine the average rate of change of the
function over the interval –4 < x < 3.
Answer:
Average Rate = -14/7
Step-by-step explanation:
f(3) = 3^2 - 3 - 8 = -2
f(-4) = (-4)^2 - (-4) - 8 = 12
interval: [-4, 3]
Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]
= [(-2) - 12] / [3 - (-4)]
= -14/7
A circle has a diameter of 7.6 feet. What is the circumference of the circle in feet? Round to the nearest TENTH.
Answer:
23.88 feets
Step-by-step explanation:
C=2π2
=2×3.142×3.8
=23.8792 feets
rounded to the nearest TENTH
=23.88 feets
The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers
The required two numbers are 9 and 41.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let x be the lesser number, and y be the greater number.
From the question, we know that:
x + y = 50 (Equation 1: The sum of the two numbers is 50)
y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)
The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.
Then, two numbers are x = 9 and y = 41.
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Solve the following equation by first writing the equation in the form a x squared = c: 3 a squared minus 21 = 27 a. a = 4 b. a = plus-or-minus 4 c. a = plus-or-minus 16 d. a = 16 Please select the best answer from the choices provided A B C D
The best answer from the choices provided is a = plus-or-minus 16 . Option C
What is a quadratic equation?A quadratic equation can be defined as an equation that can be rearranged in a standard form
Such that;
x represents an unknown value or variableThe variables, a, b, and c represent known numbersThe variable, a ≠ 0These quadratic equation are also described as polynomial equation having its highest degree as 2.
From the information given, we have that;
3a² - 21 = 27
collect like terms
3a² = 27 + 21
Add the values
3a² = 48
Divide both sides by 3
a² = 48/3
a² = 16
Hence, the value is a² = 16
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Which ordered pair is the solution to the following system? y = x - 2 and 4x + y = 23
Answer:
x=5, y=3
Step-by-step explanation:
y=x−2;4x+y=23
Step: Solve y=x−2 for y:
Step: Substitute x−2 for y in 4x+y=23:
4x+y=23
4x+x−2=23
5x−2=23(Simplify both sides of the equation)
5x−2+2=23+2(Add 2 to both sides)
5x=25
5x/5 = 25/5(Divide both sides by 5)
x=5
Step: Substitute 5 for x in y=x−2:
y=x−2
y=5−2
y=3(Simplify both sides of the equation)
Please help me find x and y. May you also tell me the steps in which to do so.
Answer:
x=
y=31
Step-by-step explanation:
hope this helps
help help help miiiiiiiiiiiio plzzzzzzzz
Answer:
[tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]
Step-by-step explanation:
Inverse of a matrix is given by,
[tex]\begin{bmatrix}a & b\\ c & d\end{bmatrix}=\frac{1}{ad-bc}\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}[/tex]
By using this property,
[tex]\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^{-1}=\frac{1}{(5\times 2-4\times 3)}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]
[tex]=-\frac{1}{2}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]
Therefore, inverse of the given matrix will be [tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]
What is the measure of angle ADC?
angle ADC equals 74 degrees
Given points V(10;2) and N (-7;9).
Determine the coordinates of vectors VN and NV
VN =( ; )
NV = ( ; )
Are 6 8 and 9 12 equivalent?
Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.
Let's first try to understand what is a fraction.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
A fraction would be 5/10, for instance.
Here, the numerator is 5 and the denominator is 10.
6/8 is a fraction.
6/8 can be simplified further.
6/8 = 3/4
9/12 is also a fraction.
9/12 can be simplified further.
9/12 = 3/4
To compare 2 fractions first we try to make the same denominator.
we have the same value. so they are equivalent.
Given question is incomplete complete the question here:
Are 6/8 and 9/12 equivalent?
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how many solutions does y = 5x - 8 and y = 9x - 8 have
The equation y = 5x - 8 and y = 9x - 8 have one solution at
(0, -8)
How to find the solution of the equationThe equation is solved simultaneously by elimination method as follows
y = 5x - 8
y = 9x - 8
subtraction the equations
0 = -4x - 0
-4x = 0
x = 0
substituting x = 0 into y = 5x - 8
y = 5x - 8
y = 5 * 0 - 8
y =0 - 8
y = -8
The solution of the equation is at the point (0, -8)
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A financial analyst wants to set up a hypothesis test to determine if the mean yearly salaries of teachers, tutors, and professors are the same. What would be the correct setup for the null and alternative hypotheses for this test
Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.
Which null and alternative hypotheses are correct?The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.
Identify the null and alternative hypotheses.
As well as the sample size, specify.
Choose a suitable statistical test.
Gather information (note that the previous steps should be done prior to collecting data)
Based on the sample data, compute the test statistic.
Examine the null hypothesis, usually indicated by H0.
Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).
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I don’t know what to do for these whatsoever
Gillian feeds the goats the same amount of hay each day. On May 3, she has 72 pounds of hay left. On May 5, she has 60 pounds of hay left.
Based on the information and the graph provided, how many ponds of hay does Gillian most likely have left on the day that she has most likely 3 pounds of grain left? Provide evidence to support your answer. Include algebraic representations for each situation as part of your support
Answer:56
Step-by-step explanation:
Let ttt be the initial number of trees.
Hint #22 / 5
MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.
The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.
Hint #33 / 5
Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:
\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790
Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.
Hint #44 / 5
\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}
210(t−5)
210
210(t−5)
t−5
t−5+5
t
=41790
=
210
41790
=199
=199+5
=204
divide both sides by 210
add 5 to both sides
Hint #55 / 5
The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point
MacDonald's farm initially had 204204204 orange trees.
Related content
Please answer! Whoever does is a lifesaver and I wish they have a blessed day
Answer:
C = 31
Step-by-step explanation:
always do the parenthesis first so (2+4) = 6
3² + 4(6) x 6 ÷ 8 + 4 (Use PEMDAS)
9 + 4(6) x 6 ÷ 8 + 4, multiply 4 and 6
9 + 24 x 6 ÷ 8 + 4, multiply 24 and 6
9 + 144 ÷ 8 + 4, divide 144 and 8
9 + 18 + 4, now just add
31.
Answer:
c) 31
Step-by-step explanation:
9 + 4(6) * 6 / 8 + 4
9 + 24 * 6 /8 + 4
9 + 144 / 8 + 4
9 + 18 + 4
= 31
What is the length of side AB as shown on the coordinate plane? On a coordinate plane, a rectangle has 4 points. Point A is (negative 2, 1), point B is (4, 1), point C is (negative 2, negative 3), and point D is (4, negative 3). 2 units 4 units 6 units 8 units please help???
Answer:
Step-by-step explanation:
Answer is 6 units
Answer:
6 units fs
Step-by-step explanation:
Solve the following system of equations using elimination:
-x+5y=8
And
3x+7y=-2
Answer:
x=-3, y=1. (-3, 1).
Step-by-step explanation:
-x+5y=8
3x+7y=-2
----------------
3(-x+5y)=3(8)
3x+7y=-2
--------------------
-3x+15y=24
3x+7y=-2
------------------
22y=22
y=22/22
y=1
-x+5(1)=8
-x+5=8
-x=8-5
-x=3
x=-3
carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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4. Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take care to earn 25 cents?
5. A car that travels 20 miles in 1/2 hour at consent speed travels at the same rate as a car that travels 30 miles in 3/4 hour at a constant speed.
6. Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend.
20 POINTS!!! HELP ASAP!! What are the domain and range of the function graphed below?
Darnel uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he make with 1 pint of lemon juice?
Answer:
16 ounces = 1 pint, 8 times 2 = 16
Step-by-step explanation:
Answer in explanation:
1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.
(8 x 2 = 16
your answer is 2
Hope this helps!
Tamika is ordering a taxi from an online taxi service. The taxi charges $3. 50 just for the pickup and then an additional $0. 75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Cost for 5 miles:
Cost for m miles:
If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25 and cost for riding m miles is $[tex]3.50+0.75m[/tex] .
The pickup charge that taxi service charges is = $3.50 ;
the additional charge for per miles driven is = $0.75 ;
we have to find the cost for riding 5 miles ;
So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;
substituting the values , the total cost equation becomes ;
[tex]Total Cost = 3.50 + 0.75\times5[/tex]
= [tex]3.50+3.75[/tex]
= 7.25
So , the cost for 5 miles is = $7.25 ;
to find cost for driving "m" miles ,we substitute the number of miles = m;
[tex]Total Cost = 3.50+0.75\times m[/tex]
= [tex]3.50+0.75m[/tex]
Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .
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Triangle ABC has coordinates A(3,2), B(1,6), C(5,5). The triangles is rotated 180 degrees clockwise and then translated 5 units up. What are the coordinates of C''(after both transformations have occurred)?
A. (-10, -5)
B. (-5, 0)
C. (0, -5)
Answer: First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.
The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)
Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)
So the coordinates of C'' are (-5,0)
Therefore the answer is B.
Step-by-step explanation:
The height, h in feet, of a tennis ball that a player hit upward can be modeled by the equation h = 80t – 16t² , where t is time in seconds.
a) What is the maximum height of the ball?
b) How long does it take to reach the maximum height?
c) How long does it take for the ball to land?
Here's link[tex]^{}[/tex] to the answer:
bit.[tex]^{}[/tex]ly/3gVQKw3
A rectangular cake pan is 13 inches by 9 inches by 2 inches. A round cake pan has a diameter of 8 inches and a height of 2 inches. Which will hold more batter, one rectangular pan or two round pans?
What is the distance apart (-6, -4.7) and (-6, 4.1)
Answer:
8.8
Step-by-step explanation:
Normally, to find the distance between two points, you would use the distance formula, but these two points have the same x-coordinate, meaning they will form a vertical line when connected. To find the length of a vertical line you find the distance between the y-coordinates, in this case -4.7 and 4.1. Finding the distance is the same as finding the absolute value of the difference:
|4.1 -(-4.7)|
|4.1 + 4.7|
|8.8|
8.8
Erin combined 1 17/18 pounds of peanuts with 1 5/6 pounds of M&M's to create trail mix, then evenly distributed the mix in 8 bags. how many pounds of trail mix are in each bag?
There are 17/36 pounds of trail mix in each bag.
Finding out how much pounds of trail mix are in each bagTo find out how many pounds of trail mix are in each bag,you need to first add the weight of the peanuts and M&M's together.
1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) = [tex]\frac{35+33}{18}[/tex] =[tex]\frac{68}{18}[/tex]
which can be simplified to 3 [tex]\frac{14}{18}[/tex]
So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.
To find out how many pounds of trail mix are in each bag, you will divide the total weight of the trail mix by the number of bags.3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =
[tex]\frac{68}{18}[/tex] ÷ [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]
which can be simplified to [tex]\frac{17}{36}[/tex]
So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.
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Solve the equation by completing the squares.
x^2−10x = 11
x= __ and __
Answer:
x = 11 and x = -1
Step-by-step explanation:
We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.
To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:
Half of -10 is -5, and the square of -5 is 25.
x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11
Rewrite x^2−10x + 25 as the square of a binomial: (x - 5)^2.
Then we have (x - 5)^2 - 25 = 11. Solve this for x -5:
(x - 5)^2 = 36. Taking the square root of both sides, we get
x - 5 = ±6
Then x = 11 and x = -1
In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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When x²+(1/x)=3 find x⁴-2x³-x²-2x+1=
(without using calculator)
so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
we can start by squaring the equation x²+(1/x)=3
so we have x⁴ + 2x² + (1/x)² = 9
x⁴ + 2x² + 1 = 9x²
x⁴ - 7x² + 1 = 0
Now we can factor it
(x²-1)(x²-1) = 0
so x² = 1
now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1
x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1
= x⁴-2x³-2x-1
= (x⁴-2x³) - (2x+1)
= x⁴-2x³-2x-1
= (x²-x)² - (2x+1)
= (x-1)² - (2x+1)
so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
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