The 90% confidence interval for the population mean gpa is [2.545,3.114].
The confidence interval for population mean is:
µ ± z* . σ/√n
Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.
The z-score value for 90% confidence interval is 1.645.
The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means
σ² = 0.45
σ = √0.45
σ = 0.67
The 90% confidence interval for population mean is:
2.83 ± 1.645 . 0.67/√15
[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]
[2.545 , 3.114]
Therefore, the 90% confidence interval for the population mean gpa is :
[2.545 , 3.114]
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how large are hamster litters? among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.
We are 90% certain that the average number of hamsters per litter is between 7.1077 and 8.3323.
What exactly is a confidence interval?A confidence interval is a range of values that includes a population value with a high degree of certainty. When a population mean falls between an upper and lower interval, it is frequently expressed as a percentage. The confidence level is the long-run proportion of corresponding CIs that contain the parameter's true value. For example, 95% of all intervals computed at the 95% level should contain the true value of the parameter.
Given, n=47
[tex]\bar{x}[/tex]=7.72
s=2.5
c=90%=0.90
To find the t-value, look in the row that starts with degrees of freedom.
df=n-1
df=47-1
df=46>45 and in the column with c=90% in the table
=1.679
Now, the margin of error is then:
E=[tex]t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}=1.679\times \dfrac{2.5}{\sqrt{47}}\approx 0.6123[/tex]
The confidence interval's boundaries are thus:
[tex]\overline{x}-E[/tex]=7.72-0.6123=7.1077
[tex]\overline{x}+E[/tex]=7.72+0.6123= 8.3323
The average number of hamsters per litter is between 7.1077 and 8.3323, and we are 90% certain of this.
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283x416 in algorithm
Answer:
120,000
Step-by-step explanation:
To estimate the product of 283 × 416, first round each number so that each number contains only 1 non zero digit.
In this case, we will round 283 to the nearest hundred and we will also round 416 to the nearest hundred. To round 283 to the nearest hundred, the number next to two is higher than 5 so we round up. 283 rounds to 300.
416 rounded to the nearest hundred is 400 because the digit to the right of 4 is less than 5 which means we round down. 416 rounds down to 400.
Now we have 300 × 400 which equals 120,000
This means that 283 x 416 is approximately 120,000.
I WILL MARK BRAINLY BE QUICK
Answer:
B
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
Slope: 5
y-intercept: (0,-10)
Answer:
Step-by-step explanation:
The slope is 5
Help quick, State if the two triangles are congruent. If they are state how you know.
The two triangles are congruent and they are congruent by ASA.
How to ascertain if triangles are congruent?Triangles are congruent when they have exactly the same three sides and exactly the same three angles. This simply implies the corresponding sides and angles of the triangles are congruent.
Let's check if the triangles are congruent.
One of the congruent angles in the triangles are vertically opposite angle.
Recall vertically opposite angles are congruent.
In these two triangles, we have a congruent angle pair and a congruent side pair.
Therefore, we can say the triangles are congruent by ASA.
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Need help. I also need to show my work
The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).
We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.
E = x³ - 6x² + 3x + 10
One of the factors in the expression is already given. The given factor is (x + 1).
Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.
E = (x + 1)(x² - 7x + 10)
Now we will factorise the quadratic expression.
E = (x + 1)[x² - 2x - 5x + 10]
E = (x + 1)[x(x - 2) - 5(x - 2)]
E = (x + 1)(x - 2)(x - 5)
We cannot simplify and factorise the expression any further.
Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).
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an experimenter flips a coin 100 times and gets 56 heads. find the 96.5% confidence interval for the probability of flipping a head with this coin. a) [0.355, 0.615] b) [0.375, 0.665] c) [0.455, 0.665] d) [0.505, 0.510] e) [0.455, 0.465] f) none of the above
The probability of the experiment is = 0.375, 0.665.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
probability that first spin is grey = 6/8probability that second spin is blue = 2/8probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16learn more about probability click here:
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Simplify the rational expression by rationalizing the denominator. √12/√8x
3√2x is the simplified form of the given expression by rationalizing the denominator.
What is the justification?In the form p q, where p and q are integers and q0, rational numbers can be expressed. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative.
What does a math denominator mean?In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.
What does common factor mean?A common factor is a whole number that is a factor of at least two other numbers. The greatest common factor is the biggest factor that may be divided into two or more integers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
Make the denominator simpler.
12/2√2x
Reject the 12/2 common factor.
6/√2x
Multiply the numerator and denominator by √2x
(6√2x⋅√2x/√2x)
Combine and make the denominator simpler.
6√2x/2x
= 3√2x
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A shop is having a sale.
All items are reduced by 25%
Work out the sale price of an item normally priced at £90
The sale price of an item normally priced at £90 is £67.5
What is the percentage?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100.
Given :
A shop is having a sale. all items are reduced by 25%.
To Find:
Work out the sale price of an item normally priced at £90.
Price of an item = £90
Price is reduced by 25%
Reduction in price = 25%*90=25/100= 22.5
Reduced price = 90-22.5=67.5
Hence, the sale price of an item normally priced at £90 is £67.5
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write an equation of the line perpendicular to -4x+3y=12 and containing the point (6,8)
The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.
What is a perpendicular line?
Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.
Here,
The slope of ax + by = c is given by m = -a/b
m = -(-4)/3 = 4/3
m = 4/3 for this line.
A perpendicular line will have a slope -1/m = -3/4
The line through (6, 8) with slope -3/4
y = (-3/4)x + b
8 = (-3/4)(6) + b
b = 8 + 9/2 = 25/2
y = (-3/4)x + 25/2
4y = -3x + 50
3x + 4y = 50
Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.
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Please help me (see attachment)
A graph of the given equation (x - y = 6) is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would rewrite the given equation in standard form as follows:
x - y = 6
Adding y to both sides of the equation, we have the following:
x - y + y = 6 + y
x = 6 + y
Rearranging the equation, we have the following:
y = x - 6
By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.
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To find the equation of a regression line, y = ax + b, you need these formulas:
Sy
a=rsa
b =ỹ - ax
A data set has an r-value of 0.793. If the standard deviation of the x-
coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772,
what is the slope of the line to three decimal places?
The slope of the line is 0.393.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").
Given,
A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.
We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:
m = 8ₓ/8ₐ
where m is the slope of the best-fit line.
8ₓ = Standard deviation of the x-coordinates is 5.591,
8ₐ = the standard deviation of the y-coordinates is 2.772.
Slope is:
m = 8ₐ/8ₓ
m = (0.793)(2.772)/5.591
m = 0.393
The slope of the line is 0.393.
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Question 2 of 10 Which of the following is equal to the fraction below? (5/8)
The fraction that is equivalent to the fraction expression given as 5/8 is 40/64
How to evaluate the expression?From the question, we have the following fraction expression that can be used in our computation:
Fraction = 5/8
The above expression is a fraction and at the same time it is a rational number
The denominator of the fraction is 8
So, we start by rationalizing the expression by the fraction
This is represented as
5/8 = 5/8 * 8/8
Evaluate the products of the numerator
So, we have the following representation
5/8 = 40/8 * 1/8
Evaluate the products of the denominator
So, we have the following representation
5/8 = 40/64
The above expression cannot be further simplified
Hence, the equivalent expression of the fraction is 40/64
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Possible question
Which of the following is equal to the fraction below? (5/8)
40/64
0.556
2/5
What Two numbers multiply to get 20 and add to get 17?
Step-by-step explanation:
x + y = 17
x = 17 - y
xy = 20
(17 - y)y = 20
-y² + 17y = 20
-y² + 17y - 20 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =
= (-17 ± sqrt(289 - 80))/-2 =
= (-17 ± sqrt(209))/-2
y1 = (-17 + sqrt(209))/-2 = 1.271583853...
y2 = (-17 - sqrt(209))/-2 = 15.72841615...
the 2 numbers are
1.271583853...
15.72841615...
how many Robin eggs, laid end to end, would be about equal in length to two raven eggs? justify your answer.
Answer:
Step-by-step explanation:
The average length of two raven eggs is about 0.1 m.
Since the average length of a robin egg is about 0.02 m, 5 eggs laid end to end would measure about 0.1 m.
1. The retail price of grapes is $2.17 per pound. if a customer paid $8.68 for grapes, how many pounds did she buy?
help meeeeeeeeeeeeeee pleaseee
The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex = (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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Select all ordered pairs that are a solution to -5x + 3y > 12
options:
(3, 9)
(-5, 5)
(3, -6)
(-2, -5)
(2, 8)
(-6, 0)
The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:
(-5, 5)(2, 8)(-6, 0)How to determine the solution?In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (3, 9), we have:
-5x + 3y > 12
-5(3) + 3(9) > 12
-15 + 27 > 12
12 > 12 (False).
For ordered pair (-5, 5), we have:
-5x + 3y > 12
-5(-5) + 3(5) > 12
25 + 15 > 12
40 > 12 (True).
For ordered pair (3, -6), we have:
-5x + 3y > 12
-5(3) + 3(-6) > 12
-15 - 18 > 12
-33 > 12 (False).
For ordered pair (-2, -5), we have:
-5x + 3y > 12
-5(-2) + 3(-5) > 12
10 - 15 > 12
-5 > 12 (False).
For ordered pair (2, 8), we have:
-5x + 3y > 12
-5(2) + 3(8) > 12
-10 + 24 > 12
14 > 12 (True).
For ordered pair (-6, 0), we have:
-5x + 3y > 12
-5(-6) + 3(0) > 12
30 + 0 > 12
30-5 > 12 (True).
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please help me asap
Answer:
z = 52°
Step-by-step explanation:
Formula we use,
→ A + B + C = 180°
Then the value of z will be,
→ 81° + 47 ° + z = 180°
→ 128° + z = 180°
→ z = 180° - 128°
→ [ z = 52° ]
Hence, the value of z is 52°.
Which equation correctly applies the Associative Property of Addition?
8.9+(6.4 +7.2) (8.9 + 6.4) +7.2
1/6 + 4/6 = 5/6
=
1/3(1/2+3/4)= (1/3 x 1/2) + (1/3 X 3/4)
6-18 = 6 + (-18)
Answer:The equation 8.9+(6.4 +7.2) is correctly applying the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the order in which the numbers are added does not affect the sum.
Tony is decorating a ballroom ceiling with garland. If the rectangular ceiling is 5 meters by 12 meters, how much garland will Tony need to reach from one corner of the ceiling to the opposite corner?
Answer: 13
Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.
Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.
The ceiling of the ballroom is rectangular in structure.
The dimensions of the rectangle are 12 by 5 meters.
So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.
We will use Pythagoras theorem to calculate the length of the diagonal.
12² +5 ² = D²
or, D² = 144 + 25
or, D =√169
or, D = 13
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.
Hence Tony will need 13 meters of garland.
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Little Johnny spent $240 on candy today. If his amount is 2/5 the amount of money his dad gave him, how much did his dad give him orginally
Answer: 600$
Step-by-step explanation:
2/5 of 600 is 240
find the area of the trapezium
Step-by-step explanation:
To find the Area of a Trapezium, we use 1/2(a+b)*h
where a=2.8 and b=4.4, Height=3.5
1/2(2.8+4.4) *3.5
1/2(7.2)*3.5
3.6*3.5
12.6cm2
Answer:
Step-by-step explanation:
Area of a trapezium = 1/2(a + b) x h
1/2 (2.8 + 4.4) x 3.5
1/2 x 7.2 x 3.5
12.6
HOPE IT HELPS YOUPLS RATE AS BRAINLIEST ANSWERWrite 2^40 as a pwer with the following base (2^8)
By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.
How to rewrite a power expression according algebra properties
In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:
Step 1 - Write the original expression presented in the statement.
2⁴⁰
Step 2 - By definition of multiplication between real numbers.
2⁽⁸⁾⁽⁵⁾
Step 3 - By the definition of the power of a power.
(2⁸)⁵
The resulting expression is (2⁸)⁵.
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In 2–3 sentences, describe how you would change the background of a group of cells.
Answer:
We can do it by using the format tab
Step-by-step explanation:
We can change the background of a group of cells by selecting the cell or range of cells we want to format. We should Click Home > Format Cells dialog launcher, or press Ctrl+Shift+F from the keyboard. Then on the Fill tab, under Background Color, we pick the color we want. To use a pattern with two colors, we pick a color in the Pattern Color box, and then pick a pattern in the Pattern Style box. In this tab we can also select gradient or single color
Morgan is 15 years younger than mrs santos. Their shed combined is 44. (Look at picture pls) (D. M+s= 44 and m= s - 10 ; (27, 17); Morgan is 17 and Mrs. Santos is 27.
Answer:
Step-by-step explanation:
To find Mr.Santos's age subtract morgan's age from their combined age
44-15=29
Therefore Mr. Santos age is 29 years
Hope that helps
Solve for x. (10x + 1) (12x-5)°
Arrange the pairs of points in increasing order of the slopes of the lines joining them.
(15, 30) and (20, 40)
(12, 32) and (18, 48)
(27, 12) and (72, 32)
(45, 15) and (60, 20)
(27, 2) and (243, 18)
(18, 63) and (24, 84)
(63, 9) and (84, 12)
↓
↓
↓
↓
↓
↓
The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
How to Arrange the points in increasing order of the slopes of the lines joining them?
Slope is defined as the change in y divided by the change in x. Mathematically:
Slope = (y2 - y1) / (x2 -x1)
To arrange the pair of points. You need to find the slope:
For (15, 30) and (20, 40):
x1 = 15, y1 =30 and x2 =20, y2=40
slope = (40-30)/(20-15) = 10/5 =2
For (12, 32) and (18, 48):
slope = (48-32)/(18-12) = 16/6 = 2.67
For (27, 12) and (72, 32):
slope = (32-12)/(72-27) = 20/45 = 0.44
For (45, 15) and (60, 20):
slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33
For (27, 2) and (243, 18):
slope = (18-2)/(243-27) = 16/216 = 0.07
For (18, 63) and (24, 84):
slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5
For (63, 9) and (84, 12):
slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14
Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
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What is the interquartile range of the data set???
Answer:
14.
Step-by-step explanation:
The interquartile range (IQR) contains the second and third quartiles or the middle half of your data set.
Please give brainliest, will be appreciated.
Answer:
The interquartile range (IQR) measures the spread of the middle half of your data.
graph the following inequality:
Please help thx
The equations y=3+2 and y=2x+1 both will meet at x=3
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.a b asserts that a and b are not equal.If a b, then a must be less than b.When a > b, an is greater than b. (those two are known as strict inequality)If a and b are divided, a must be smaller than or equal to b.When a and b are together, an is greater than or equal to b.Acc to our question-
Given, 3x−2<2x+1⇒3x−2x<1+2⇒x<3orx∈(−∞,3)The lines y=3x−2 and y=2x+1 both will intersect at x=3 Clearly, the dark line shows the solution of 3x−2<2x+1.Hence,The lines y=3x−2 and y=2x+1 both will intersect at x=3
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What is the Value of a,b,c and d?
Answer:A is 7 B is -1 C is -9 D is -13
Step-by-step explanation: I hoped i have helped u! Have a wonderful day!