The equations which represents circles that have a diameter of 12 units and a center that lies on the y-axis are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
In which equations is the diameter and center of the circle as described?Recall, the equation of a circle takes the form;
(x - h)² + (y – k)² = r² where r = radius = diameter/2 and (h, k) is the center.
Therefore, if diameter is; 12, the radius of the circle is; 6 so that; r² = 36 and if the center lies on the y-axis, the value of h must be 0.
Ultimately, the equations that satisfy the given conditions are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
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Suppose that a researcher is interested in finding out whether a new math program increases students’ math skills. 36 students participate in the program. After the training, the student’s math skills are measured by an exam that is known to have a µ = 70 and σ = 12. The researcher finds out that students who participated in the program scored an average of 73.6. Can we conclude that the training was successful? Justify and explain your answer.
The hypothesis test conclude that the training program was successful in increasing students' math skills.
As the average exam score of students who participated in the program was significantly higher than the population mean.
Number of students participated = 36
Population mean µ = 70
and σ = 12
To determine whether the math program was successful in increasing students' math skills, we can conduct a hypothesis test.
The null hypothesis denoted as H₀,
There is no difference between mean exam scores of students who participated in math program and population mean µ = 70.
The alternative hypothesis denoted as H₁,
There is a difference between the mean exam scores of the two groups.
Mathematically, the hypotheses as follows,
H₀: µ = 70
There is no difference in the mean exam scores of students who participated in the math program and the population mean.
H₁: µ > 70
The mean exam scores of students who participated in the math program are greater than the population mean.
Use a one-sample t-test to test the hypotheses.
The formula for the t-test statistic is,
t = (X - µ) / (s / √n)
X is the sample mean = 73.6
µ is the population mean = 70
s is the sample standard deviation
s = 12 / √36
= 2
and n is the sample size= 36
Substituting these values into the formula, we get,
t = (73.6 - 70) / (2 / √36)
= 3.6 / (1/3)
≈10.8
To determine whether the t-value is significant,
Compare it to the critical t-value at a chosen significance level α. Assuming significance level of 0.05 and 35 degrees of freedom df=n - 1 .
Critical t-value to be approximately 1.69.
Since calculated t-value 10.8 is greater than the critical t-value 1.69.
Reject the null hypothesis .
Therefore, using hypothesis test conclude that there is sufficient evidence to suggest that the math program was successful in increasing students' math skills.
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Change zero degrees Celsius to Fahrenheit.
Answer: F=32
Step-by-step explanation:formula: F = Celsius*9/5+32
so plug the zero for Celsius, in this case, 0*9/5+32 = 32
PLSSSS LOOK AT ATTACHMENT
Answer:
Step-by-step explanation:
Since they are in a row, add all the measurements
4 ft 10 in
5 ft 6 in add ft with the ft and in with in
3 ft 3 in
12 ft 19 in
There are too many inches. So you can take away 12 of those inches and and turn it into 1 more foot. That would make 13 ft. You'd be left with 7 in.
12 ft + 1 ft 19 in - 12 in
13 ft 7in
How do you write 9.6522 as a percentage
The diagram shows a field. 66 m 140 m 102 m Work out the area of the field.
The area of the field, given that it is a trapezium, would be 7, 986 m ² .
How to find the area ?The field is in the shape of a trapezium which means that the area of the field can be found by the formula :
= ( a + b ) / 2 x height
Side a = 102 m
Side b = 140 m
height = 66 m
The area of the field is therefore:
= ( 102 + 140 ) / 2 x 66
= 121 x 66
= 7, 986 m ²
In conclusion, the area of the field is 7, 986 m ².
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(I NEED THIS RIGHT NOW!! PLEASE GIVE EXPLANATION!!) Millie and her brother, Jack, sold candy baes for the band fund-raiser. Millie sold three times as many candy bars as Jack. If Jack sold 30 candy bars, which equation and solution can be used to represent y, the number of candy bars Millie sold?
A. 3y = 30; y = 10
B. 30 = y/3; y = 103
C. 30 = y/3; y = 90
D. 3y = 30; y = 90
Answer:
C
Step-by-step explanation:
When we do 30=y/3 we get 90 because of the fraction symbol and its says in the problem 3 times as much so more not less so 3x30 equals 90 so we already take out A and B and when there is nothing but a simple equation like 30=3 we dived so it cant be D Ethier so its C
PLS GIVE BRAINLIST
Happy Easter
One leg of a right triangle is 3 inches shorter than the other leg. If the hypotenuse is 7
inches, what are the lengths of the legs? Give the exact answers, not decimal
approximations.
based on an exponential model of the data, what is the predicted value of variable 2 when variable 1=2? round your answer to the nearest whole number.
a. variable 2 ≈ 128
b. variable 2≈ 166
c. variable 2≈ 181
d. variable 2≈ 263
The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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The Hartford offered an annuity that pays 5.5% compounded monthly.
What equal monthly deposit should be made into this annuity in order
to have $100000 in 10 years?
If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.
In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:
Which is : FV = P × [(1 + r)ⁿ - 1]/r,
where:
FV is "future-value" = $100000,
P = monthly deposit
r = monthly interest rate (5.5%/12 = 0.00458)
n = number of months (10 years × 12 months per year = 120 months)
Substituting the values,
We get,
⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,
⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],
⇒ P ≈ $627,
Therefore, an equal monthly deposit is approximately $627.
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Talisa plans a 36-foot deep pond. While digging, she hits rock 30 feet down. How can Talisa modify the radius to maintain the original volume of the pond?
Talisa should make the radius ___ ft
The radius of the pond should be modified to 19.72ft to be able to maintain the original volume of the pond.
How to modify the radius to maintain the original volume?The original shape of the pond is the shape of a cylinder and the formula tye can be used to calculate the volume of a cylinder = πr²h
The volume of the original pond is calculated as follows;
π = 3.14
Radius = 18 ft
height = 36ft
Vol = 3.14×18×18×36
= 36,624.96ft³
The radius of the modified pond is calculated as follows; Volume = 36,624.96ft³
height = 30ft
radius = ?
That is;
36,624.96 = 3.14×r²× 30
r² = 36,624.96/94.2
= 388.8
r = √388.8
= 19.72 ft
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The length of a rectangle is 4 meters less than 3 times the width. The perimeter is 24 meters. Find the width
Answer:
Step-by-step explanation: length of a rectangle is 4 meters less than 3 times the width so we can write L = 3W-4
The formula for the perimeter of a rectangle: P = 2L+2W
Now plug the numbers: P = 2(3W-4)2W
24 = 6W - 8 +2W
24 = 8W - 8
32 = 8W
W = 4
A television show conducted an experiment to study what happens
Answer:
Step-by-step explanation:
[tex]H_o: p = 0.5,H_1:p\neq 0.5[/tex]
[tex]p(\text{buttered side down})=\frac{19}{51}[/tex]
[tex]\pi _o=0.5\\n=51[/tex]
[tex]z=\frac{p-\pi _o}{\sqrt{\frac{\pi _o(1-\pi _o)}{n} } } =\frac{\frac{19}{51}-0.5 }\sqrt{{\frac{0.5(1-0.5)}{51} } }[/tex]
≈ [tex]-1.82[/tex]
a = 0.01 [tex]z_a/z=2.58\\|z| < |z_[ay}}_2|[/tex]
Thus, it cant reject H₀
The toast will land with the buttered side down 50% of the time.
{Hypothesis test}
MARKING AS BRAINLIST PLS HELP
Answer:
The angle of C is 118.6
Step-by-step explanation:
The claim is that for a smartphone carrier's data speeds at airports, the mean is 18.00 Mbps. The sample size is n= 14 and the test statistic is t= -2.645 .
whats the P-value?
According to given information the P-value is approximately 0.016.
What is P-value?In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed results, under the assumption that the null hypothesis is true.
According to given information:To find the P-value for this hypothesis test, we need to use a t-distribution with degrees of freedom equal to n-1 = 14-1 = 13. Since the test statistic is t = -2.645, we need to find the area under the t-distribution curve to the left of t.
Using a t-table or calculator, we can find that the area to the left of t = -2.645 with 13 degrees of freedom is approximately 0.008. This is the probability of observing a t-value less extreme than -2.645, assuming the null hypothesis is true.
Since this is a two-tailed test (we are testing whether the true mean is less than or greater than 18.00 Mbps), we need to double the one-tailed P-value to get the two-tailed P-value. Therefore, the P-value is approximately 0.016 (i.e., 2 x 0.008).
So, the P-value is approximately 0.016.
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Need some help with this khan academy question, thanks.
The relative frequency of the two frequency table is completed as below
less than 2 years 2 or more years row total
college degree 0.26 0.74 1.00
no coll degree 0.70 0.30 1.00
How to fill the tableThe relative frequency table is filled by comparing the values as below
less than 2 years 2 or more years row total
college degree 5/19 14/19 1.00
no coll degree 16/23 7/23 1.00
The row total
5 + 14 = 19 so we have 5/19 (0.26) and 14/19 (0.74)
16 + 7 = 23 o we have 16/23 (0.70) and 7/23 (0.30)
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Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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Supplementary angles
The angles that is supplementary to <HAE is <IAE
What are supplementary angles?Supplementary angles are simply described as a pair of angles whose sum is 180 degrees.
Some properties of supplementary angles are;
The two angles are said to be supplementary angles when they sum up to 180°The two angles together make a straight line, but the angles must not be together in the same place.In a cyclic quadrilateral, opposite angles are said to be supplementaryFrom the information given, we can see that;
<HAE is on a straight line with <IAE , making their sum to be 180 degrees
Then, <IAE is supplementary is <HAE
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Don't know answer please help?
Answer:
104 square meters
Step-by-step explanation:
Make sure all the units are same and consistent!!
The shape of the shaded region = Trapezium
h = Perpendicular height of trapezium
= 16 m
∴Area of shaded region = Area of trapezium
= [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × h
= [tex]\frac{1}{2}[/tex] × [(9 + 4) m] × (16 m)
= [tex]\frac{1}{2}[/tex] × (13 m) × (16 m)
∴Area of shaded region = 104 [tex]m^{2}[/tex]
= 104 square meters
Let x = 7/8 and y = -2/9. If x * z = y, then what is z?
what is the inverse of f(x)=(4x-9)^1/2
The inverse of f(x) = [tex](4x-9)^{1/2[/tex] when the variables of x and y are switched is [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
What is an Inverse of a Function?Inverse of a function is a function which can be reversed into another function. It is also a function that undoes the action of the another function.
How to determine this
When f(x) = (4x-9)^1/2
To determine the inverse, [tex]f(x)^{-1}[/tex]= y
y = (4x-9)^1/2
y = [tex]\sqrt{4x-9}[/tex]
By squaring both sides
y^2 = 4x - 9
By swapping the variables
x^2 = 4y - 9
Subtracting 9 from both sides
x^2 +9 = 4y
divide through by 4
[tex]\frac{x^{2}+9 }{4}[/tex] = 4y/4
y = [tex]\frac{x^{2}+9 }{4}[/tex]
Therefore [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
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7 of 7
Expand:
f(x)=x²-
DONE
+
1
Expanding the function expression f(x) = x^2 - 1, we get f(x) = (x - 1)(x + 1)
Expanding the function expressionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2 - 1
The above expression can be expanded using the difference of two squares
When this theorem is applied, we have
f(x) = (x - 1)(x + 1)
Hence, the function expression f(x) = x^2 - 1 when expanded is f(x) = (x - 1)(x + 1)
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Expanding the function expression f(x) = x^2 - 1, we get f(x) = (x - 1)(x + 1)
Expanding the function expressionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2 - 1
The above expression can be expanded using the difference of two squares
When this theorem is applied, we have
f(x) = (x - 1)(x + 1)
Hence, the function expression f(x) = x^2 - 1 when expanded is f(x) = (x - 1)(x + 1)
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The mass of an oxygen molecule is
5.31×10^-23 grams. The mass of an electron is 9.11×10^-28 grams. How many times greater is the mass of an oxygen molecule than the mass of an electron? Write your answer in standard notation, rounding to the nearest tenth.
The mass of an "oxygen-molecule" is approximately 5.82 × 10⁴ times greater than the mass of an electron, and written in "standard-notation", the answer is 58287.59.
The "Standard-Notation" is defined as a way of writing a number using digits, a decimal point.
The mass of the "oxygen-molecule" is = 5.31×10⁻²³ grams,
The mass of the "electron" is = 9.11×10⁻²⁸ grams,
To find how many times greater the mass of an oxygen molecule is than the mass of an electron, we need to divide the mass of the oxygen molecule by the mass of the electron:
⇒ (5.31 × 10⁻²³)/(9.11 × 10⁻²⁸) = 58287.59 ≈ 5.82 × 10⁴.
Therefore, The mass of oxygen is 5.9 × 10⁴, times greater than electron.
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3x+2=8 what is the value of x
Answer:
x = 2
Step-by-step explanation:
3x + 2 = 8
Subtracting both sides by 2 we get,
=> 3x + 2 - 2= 8 - 2
=> 3x = 6
=> x = 6/3
=> x = 2
There are only red counters, blue counters and green counters in a bag.
number of red counters: number of blue counters: number of green
counters = 1:3:7
A counter is going to be taken at random from the bag.
Complete the table below to show each of the probabilities that the counter will be red or blue or green.
(2 marks)
Answer:
Color Probability
Red 1/11
Blue 3/11
Green 7/11
Step-by-step explanation:
The total number of counters in the bag is 1+3+7=11. The probability of selecting a red counter is 1/11, because there is only one red counter in the bag. The probability of selecting a blue counter is 3/11, because there are three blue counters in the bag. Similarly, the probability of selecting a green counter is 7/11, because there are seven green counters in the bag.
7
An acceleration of 2.5 miles per hour per second
mi/hr
S
feet per hour per second
is closest to which of the following values, in
(1 mile = 5,280 feet)
A) 13,200
B) 2,112
C) 220
D)
1/2,112
The converted acceleration in feet per hour per second is 13200 feet per hour per second
Converting the acceleration from miles per hour per second to feet per hour per secondFrom the question, we have the following parameters that can be used in our computation:
Acceleration = 2.5 miles per hour per second
From the question, we have
(1 mile = 5,280 feet)
Substitute the known values in the above equation, so, we have the following representation
Acceleration = 2.5 * 5,280 feet per hour per second
Evaluate the products
So, we have
Acceleration = 13200 feet per hour per second
Hence, the acceleration = 13200 feet per hour per second
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Identify the law illustrated by the following: 4bracket(3x-7) is equivalent to 12x-28.
What are the values of the "t" column when the rule of the table is 3n + 5.
Answer:
8,11,14,17
Step-by-step explanation:
3n + 5
When n = 1,
3(1) + 5
=> 3 + 5
=> 8
When n = 2,
3(2) + 5
=> 11
When n = 3,
3(3) + 5
=> 14
When n = 4,
3(4) + 5
=> 17
Two cyclists, 64 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist? a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist. b. What is the speed of the faster cyclist?
2. Why was the Constitutional Convention held?
lengte
A. Each state's government was too weak.
B. Americans wanted to win independence from England.
C. The national government was too weak.
D. The states wanted to form the first American government.
Anyone pls
Enter the correct answer in the box.
What is the factored form of this expression?
x² + 6x-16
Substitute numerical values into the expression for p and q.
(0) 101
√O
d'º
+
11
Vo 4
(x+p)(x+q)
<> ≤ 2
TT
aß
A HP
sin cos tan sin-¹ cos¹ tan-¹
CSC sec cot log logo In
The calculated factored form of the expression x² + 6x - 16 is (x - 2)(x + 8)
What is the factored form of the expression?From the question, we have the following parameters that can be used in our computation:
x² + 6x - 16
Expand the expression
So, we have
x² + 6x - 16 = x² + 8x - 2x - 16
Factorize the expression
So, we have the following representation
x² + 6x - 16 = x(x + 8) - 2(x + 8)
Factor out x + 8
So, the expression becomes
x² + 6x - 16 = (x - 2)(x + 8)
Hence, the factored form of the expression x² + 6x - 16 is (x - 2)(x + 8)
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