To estimate a proportion of students with a grade point average of 3.7 and higher in a college, a random sample of 200 students was taken and the number of successes counted to be 35. The 95% confidence interval for a population proportion is:
Answer: \((0.1481323,\ 0.2018677)\)
Step-by-step explanation:
The confidence interval for population proportion :
\(\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\) , where n= sample size, \(\hat{p}\) = sample proportion , z*= Critical z-value.
Let p = population proportion of successes.
Given: n= 200 , \(\hat{p}=\dfrac{35}{200}=0.175\)
Critical z value for 95% confidence = 1.96
The 95% confidence interval for a population proportion is:
\(0.175\pm (1.96)\sqrt{\dfrac{(0.175)(1-0.175)}{200}}\\\\=\ 0.175\pm (1.96)\sqrt{0.000721875}\\\\= 0.175\pm (1.96)(0.0268677)\\\\=(0.175-0.0268677,0.175+0.0268677)\\\\= (0.1481323,\ 0.2018677)\)
Required confidence interval: \((0.1481323,\ 0.2018677)\)
At which points is the function continuous?
The function is continuous in the domain x ≥ 3/4
At which points is the function continuous?Here we have a root function:
f(x) = ⁴√(4x - 3)
This is an even degree root function, so we have problems when the argument is negative.
Then the allowed values (where the function is defined, and thus, continuous) are:
4x - 3 ≥ 0
4x ≥ 3
x ≥ 3/4
There the function is continuous.
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5.3 MATHEMATICS HOLIDAY PACKAGE-TERM 2(2023) Instructions: Attempt ALL items 1. Your family has seven siblings; peter, John, Sarah, Joy, Ali, Mary and Ivan. There is an interval of 2 years between the ages of the children from Ivan to peter. Ivan is three years old. Task: Using an arrow diagram, explain the information about your family.
Consider the relation “nine more than seven times a number is equal to seven more than six times the number” Using n to represent the unknown number, form a equation that represents this relation. Then solve the equation. I WILL MARK BRAINLIEST
Answer:
The number is n = - 2------------------------------------------
The number is n.
The equation we can set:
nine more than seven times a number ⇒ 7n + 9is equal seven more than six times the number ⇒ 6n + 7It is 7n + 9 = 6n + 7Solve it:
7n + 9 = 6n + 77n - 6n = 7 - 9n = - 2133.5 divided by 5 show work
Answer:
26.7
Step-by-step explanation:
Use a c a l c u l a t o r :P
Can somebody solve this?
Answer:
8 months
Step-by-step explanation:
if you can get 120 per month then 950/120 = ~8
Answer:
She needs $350.
Step-by-step explanation:
120 x 5 = 600
$950 - $600 = $350
slope of the line with points (4,-2) and (24,-17)
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1
-17+2 divided by 24-4
-15/20
-3/4
Answer:
-3/4
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (-17- -2)/(24-4)
= (-17+2)/(20)
= -15/20
=-3/4
The sales tax rate is 4.5%. How much sales tax will you pay on a $125 purchase?
Work Shown:
4.5% of 125 = 0.045*125 = 5.625
That rounds to 5.63
Answer:
5.625
Step-by-step explanation:
find the area of the shaded figure below round your answer to one decimal place
This is a complex figure, you have to calculate the area of the shaded figure.
If you look at the figure, you have to decompose it into simpler geometrical shapes first
The shape is composed of a rectangle and a semicircle. To calculate the shaded area, you have to calculate the area of the rectangle and the area of the semicircle. Then you have to subtract the area of the semicircle from the area of the rectangle to determina the area of the shaded portion.
\(A_T=A_R-A_C\)"T" represents the shaded portion
"C" represents the semicircle
"R" represents the rectangle
First calculate the area of the rectangle
\(\begin{gathered} A_R=w\cdot l \\ A_R=8\cdot18 \\ A_R=144 \end{gathered}\)Next calculate the area of the semicircle, to do so you have to calculate the area of the circle and divide it by 2
\(\begin{gathered} A_C=\frac{\pi r^2}{2} \\ A_C=\frac{\pi4^2}{2} \\ A_C=8\pi \end{gathered}\)The area of the shaded part is
\(\begin{gathered} A_T=A_R-A_C_{} \\ A_T=144-8\pi_{} \\ A_T=118.867\cong118.9 \end{gathered}\)The area of the shaded portion is 118.9
I WILL GIVE BRAINLIEST.
Find the lateral surface area of a cylinder with a diameter of 21 inches and a height of 15 inches.
Answer:
Step-by-step explan
21
Ben is an activity leader.
He is planning a team-building event for a group of people.
Ben has this part of a map.
Key: 1 cm on the map is 1000 m on the ground
The group will start at point A and walk directly to point B.
Ben needs to write instructions to give to the group.
The instructions need to include the
. bearing
. distance to be walked.
(a) Write the instructions for the group.
Remember to give units with your answer.
Diagram drawn
accurately
Suppose you are flying a kite at the park on a windy day. You notice that the height of the kite, h, is
affected by the speed of the wind, w. You decide to measure the height of the kite at different wind
speeds to determine the relationship between the two variables. After some experimentation, you
measure the height of the kite at three different wind speeds: 10 mph, 15 mph, and 20 mph. You
measure the height of the kite to be 50 feet at 10 mph, 75 feet at 15 mph, and 100 feet at 20 mph.
Determine the equations that relate the height of the kite to the speed of the wind.
The equation that relates the height of the kite to the speed of the wind is: h = 5w.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
To determine the relationship between the height of the kite and the speed of the wind, we can use linear regression to fit a line to the data points we have measured. The line will take the form y = mx + b, where y is the height of the kite, x is the speed of the wind, m is the slope of the line, and b is the y-intercept.
Using the three data points we have, we can calculate the slope of the line as follows:
m = (y2 - y1) / (x2 - x1)
= (75 - 50) / (15 - 10)
= 25/5
= 5
Therefore, the equation for the line is y = 5x + b. To find the value of b, we can use one of the data points.
For example, using the point (10, 50):
50 = 5(10) + b
b = 0
So the equation that relates the height of the kite to the speed of the wind is:
h = 5w
where h is the height of the kite in feet, and w is the speed of the wind in mph.
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6. Determine the system of equations based on the following relationships and then solve
for the two integers.
a. Fourteen more than twice the first integer gives the second integer
b. The second integer increased by one is the square of the first integer
Answer: (-3,8) and (5,24)
The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).
To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.
According to the given information:
a. Fourteen more than twice the first integer gives the second integer:
This can be expressed as: 2x + 14 = y
b. The second integer increased by one is the square of the first integer:
This can be expressed as: y + 1 = x^2
Now, we have a system of equations:
1) 2x + 14 = y
2) y + 1 = x^2
To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):
2x + 14 + 1 = x^2
2x + 15 = x^2
Rearranging the equation, we have:
\(x^2 - 2x - 15 = 0\)
Factoring the quadratic equation, we get:
(x - 5)(x + 3) = 0
Setting each factor equal to zero:
x - 5 = 0 --> x = 5
x + 3 = 0 --> x = -3
Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':
For x = 5:
2(5) + 14 = y
10 + 14 = y
y = 24
For x = -3:
2(-3) + 14 = y
-6 + 14 = y
y = 8
Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).
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A home buyer is debating between two different mortgages for $167,800. The options are: option a: 20-year fixed rate loan at 7. 45% with a total of $323,198. 36 paid in principal and interest over the life of the loan option b: 15-year fixed rate loan at the same rate. How much more total principal and interest will the buyer pay for the 20-year loan versus the 15-year loan? a spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
The 20-year loan will cost the customer around $46,058.24 more in total principal and interest than the 15-year loan.
From the given information:
Option A: The loan term is 20 years, fixed rate of 7.45%, with a total of $323,198.36 paid in interest and principal.
Option B: 15-year fixed rate loan at the same rate.
We require the principal sum in order to calculate the total amount repaid for the 15-year loan. The primary sum is determined by the information provided to be $167,800.
Determine the total principal and interest difference:
The total principal and interest paid for the 20-year loan is $323,198.36.
We must determine the total amount paid in principle and interest for the 15-year loan. We may use a spreadsheet containing the loan amount, interest rate, and period to do this or a mortgage calculator.
We calculate the principle and interest payments for a 15-year loan to be $277,140.12 by plugging in the values: loan amount = $167,800, interest rate = 7.45%, and loan duration = 15 years.
Find the difference by subtracting the total paid for the 15-year loan from the total paid for the 20-year loan:
\(323,198.36 - 277,140.12 = \$46,058.24\)
As a result, the 20-year loan will cost the customer around $46,058.24 more in total principal and interest than the 15-year loan.
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plz help me will br
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.
The average rate of change is given by the rate of change of both variables.
"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:
Δy/Δx
("Δ" means "change").
We want to analyze the change over the interval 3 ≤ x ≤ 9.
Step 1: change of x (Δx)The change from x = 3 and x = 9 is
Δx = 9 - 3 = 6
Step 2: change of y (Δy)We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.
The change from y = 28 to y = 4 is
Δy = 4 - 28 = -24
Step 3: rate of changeThen, the average rate of change is:
Δy/Δx = -24/6 = -4
Answer: -4
Given square ERTN, what is the length of NT ?
Answer:
|NT| = 25
Step-by-step explanation:
The four sides of this square all have the same length. Thus, 5x = 10x - 25, which, in turn, becomes 25 = 5x, giving us x = 5. The length of NT is 5(x), or |NT| = 25.
help please! need it asap
Answer:
\(x = 6\)
Step-by-step explanation:
These right triangles are similar due to the Angle Angle Similarity Theorem.
This means their side lengths are proportional
We need to find the corresponding sides of the inner triangle and full right triangle.
7 corresponds with 7 and 3.5
4 corresponds with x.
Set up proportion.
\( \frac{4}{7} = \frac{x}{7 + 3.5} \)
\( \frac{4}{7} = \frac{x}{10.5} \)
\(42 = 7x\)
\(x = 6\)
the sum of three numbers is 112. the third number is 3 times the first. the second number is 7 more than the first. what are the numbers?
Answer:
all the would need water becouse water is the main reason to get live
How do you solve this? Without going into anything to complicated as this should be Year 10 maths
Given : ABCD is a square with each side 5cm .
To Find : The area of the shaded region .
Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .
If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.
Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;
\(\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}\)
Here radius will be equal to 5cm .
⇒ Area = πr² / 4 .
⇒ Area = π (5cm)² / 4 .
⇒ Area = 22/7 × 25 × 4 cm².
⇒ Area = 19.64 cm² .
So , total area of both quadrants = 39.28 cm² .
Also , area of square will be :
\(\large\boxed{\bf{\red{Area_{square}=(side)^2}}}\)
⇒ Area = 5cm × 5cm .
⇒ Area = 25 cm².
Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².
Similarly area of other white region = 5.36cm² .
And the areas sum will be = 5.36cm² × 2 = 10.72cm² .
Now , from the figure it's clear that ,
⇒ Area of unshaded region + Area of shaded region = 25cm².
⇒ 10.72cm² + ar( Shaded region ) = 25cm².
⇒ ar ( Shaded region ) = 25cm² - 10.72cm².
⇒ ar ( Shaded region ) = 14.28 cm².
Hence the area of shaded region is 14.28 cm².
\(\large\boxed{\red{\bf Answer = 14.28cm^2}}\)
Roland has built a circuit, and is using a device called an
ammeter to measure how quickly electrical current is flowing
through the circuit. He calculates that the current should be
0.180 amps, but he measures the current as 0.173 amps. What
is Roland's percent error?
Roland's percent error is approximately 3.889%.
This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.
The positive sign indicates that Roland's measured value is slightly lower than the actual value.
To calculate Roland's percent error, we can use the formula:
Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100
Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:
Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100
Simplifying the expression within the absolute value:
Percent Error = (|-0.007| / 0.180) \(\times\) 100
Since the absolute value of -0.007 is 0.007, we have:
Percent Error = (0.007 / 0.180) \(\times\) 100
Calculating the division:
Percent Error = 0.03889 \(\times\) 100
Percent Error = 3.889%.
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The circle shown has a radius of 4 cm.
Not drawn
to scale
х
What is the length of the diameter of the circle?
cm
Answer:
8 cm
Step-by-step explanation:
4+4=8 To get the diameter, double the radius and add them together.
It costs $145 for 10 people to attend a concert. How much does it cost a group of 8 people?
Answer:
It would cost $116 for a group of 8 people.
Step-by-step explanation:
You would divide 145/10 to find the cost for 1 group (which would be $14.5). Then, you would multiply 14.5x8 to get your answer of $116.
Answer:
$116
Step-by-step explanation:
1. First, let's find how much it costs for 1 person to attend a concert by dividing 145 by 10.
\(\frac{145}{10}\) \(14.5\)2. Next, let's multiply 14.5 by 8.
\(14.5 * 8\) \(116\)Therefore, it costs a group of 8 people $116 to attend a concert.
A elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 27 such doors. If the teacher has 11 sculptures, 10 sketches, and 12 oil paintings, what is the probability that 8 sculptures, 9 sketches, and 10 oil paintings are chosen to be displayed?
Answer:This problem involves using the concept of probability. We can use the formula for probability:
Probability = (number of desired outcomes) / (total number of possible outcomes)
First, let's calculate the total number of possible outcomes. Since there are 27 doors and each door can only have one piece of artwork, there are a total of 27 possible outcomes.
Next, let's calculate the number of desired outcomes. The teacher wants to display 8 sculptures, 9 sketches, and 10 oil paintings. We can choose 8 sculptures from the 11 available in C(11,8) ways (using the combination formula), 9 sketches from the 10 available in C(10,9) ways, and 10 oil paintings from the 12 available in C(12,10) ways. To find the total number of desired outcomes, we can multiply these together:
number of desired outcomes = C(11,8) * C(10,9) * C(12,10)
= (165) * (10) * (66)
= 108,900
Finally, we can plug these values into the formula for probability:
Probability = (number of desired outcomes) / (total number of possible outcomes)
= 108,900 / 27
= 4,033.3 (rounded to one decimal place)
However, probabilities cannot be greater than 1. Therefore, the probability of displaying 8 sculptures, 9 sketches, and 10 oil paintings is 1.
Solve for t.
−18=6t
Options:
a t=−3
b t=−13
c t = 12
d t = 24
Answer:
t = -3
Step-by-step explanation:
To solve, you can divide both side of the equation by 6:
- 18 / 6 = -3
6t / 6 = t
-3 = t
Answer:
Answer = t = -3
please mark as brainliest
how many solutions does 3-2x=5-x+3
Answer:
x-2x=5+3-3
-x=5
x=-5
Step-by-step explanation:
That's the answer
QUESTIONS
You are driving on a multi-lane road and there are bicyclists sharing the road with you. At
intersections,
A: You have the right-of-way when turning right, and bicyclists beside you must yield to you when
you turn
B: Bicyclists ahead of you that want to change lanes must let you pass them first. They must not try to
change lanes in front of you.
CYou should assume that bicyclists are traveling straight unless they signal otherwise, and you must
yield the right-of-way to them if you are turning,
Answer:
C
Step-by-step explanation:
help me fast rapidly is of khan academy:
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTI need help with math I’m not good at it
Answer:
Option 1 should be correct
3×w=12 <- Product ; 3 <- Factor ; w <- other factor
Step-by-step explanation:
hope it helps ^^
find the slope and y - intercept of x = 0
Answer:
When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.
Step-by-step explanation:
trust the process