Answer:
The 99% confidence interval is
[tex]37.167< \= x < 44.833[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 29[/tex]
The sample mean is [tex]\= x =[/tex]$41
The sample standard deviation is [tex]\sigma =[/tex]$8
The level of confidence is [tex]C =[/tex]99%
Given that the confidence level id 99% the level of confidence is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Next we evaluate the margin of error which is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]
[tex]MOE = 3.8328[/tex]
The 99% confidence level is constructed as follows
[tex]\= x - MOE < \= x < \= x + MOE[/tex]
substituting values
[tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]
[tex]37.167< \= x < 44.833[/tex]
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. nequals=5353, pequals=0.30.3, and Xequals=20
Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = [tex]\left[\begin{array}{ccc}n\\X\end{array}\right][/tex].[tex]p^{x}.(1-p)^{n-x}[/tex]
P(20) = [tex]\left[\begin{array}{ccc}53\\20\end{array}\right] .(0.3)^{20}.(1-0.3)^{33}[/tex]
P(20) = [tex]\frac{53!}{33!.20!}.3.5.10^{-11}.7.7.10^{-6}[/tex]
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = [tex]\sqrt{n.p.(1-p)}[/tex] = 3.34
Find the z-score:
z = [tex]\frac{x - mean}{sd}[/tex] = [tex]\frac{20-15.9}{3.34} = 1.23[/tex]
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
Simplify the expression:
(4k – 4) + ( –9k – 5)
Answer:
The answer is
- 5k - 9Step-by-step explanation:
(4k – 4) + ( –9k – 5)
Remove the bracket and simplify
That's
4k - 4 + - 9k - 5
4k - 4 - 9k - 5
Group like terms
4k - 9k - 4 - 5
We have the final answer as
- 5k - 9
Hope this helps you
We can use FOIL to solve:
(4k - 4) + (-9k - 5)
(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)
-36k - 20k + 36k + 20
-20k + 20
Best of Luck!
There were 3 squirrels and 18 acorns on Josh’s back porch. What was the ratio of squirrels to acorns? Enter your answer in reduced form. (100 points!!)
Answer:
1:6
Step-by-step explanation:
Answer:
Step-by-step explanation:
1:6
From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?
Answer: 0.18
Step-by-step explanation:
P(1 unit is defective)= C2 1* P^1*Q^1
C2 1= 2!/(1!*(2-1)!)=2
P=0.1 - probability that items from a production line are defective
Q=1-0.1=0.9 - probability that items from a production line are functional.
P(1 unit is defective)= 2*0.1*0.9=0.18
Find the area of this shape
Answer:
12.5
Step-by-step explanation:
(7.5+2.5)x2.5/2
Answer:
12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 2.5+ 7.5) *2.5
= 1/2 ( 10) * 2.5
=12.5 units ^2
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
How many 4-digit numbers divisible by 5, all of the digits of which are even, are there?
Answer:
There are a total of 100 numbers!!
Step-by-step explanation:
Basically you have to do
4*5*5*1 because there are 4 even numbers 2,4,6,8 that can be in the beginning of a number, 5 even numbers 0,2,4,6,8 that can be in the middle and only 1 number at the end that will make it divisible by 5 which is zero.
Hope this helps!!!
Evaluate the given algebraic expressions replacing x with −2 and y with 1. 3x2
Answer:
No solutions
Step-by-step explanation:
3x^2=y
3(-2)^2=1
Follow P.E.M.D.A.S.
3(4)=1
12=1
A rectangular prism has a length of 9 cm, a width of 5 cm, and its volume is 180 cubic centimeters. What is the height of the prism?
Answer:
Right rectangular prism
Solve for height
h=4cm
l Length
9
cm
w Width
5
cm
V Volume
180
cm³
Answer:
Step-by-step explanation:
volume of rectangular prism=l×w×h
9×5×h=180
h=4 cm
where h is the height of prism.
Graph f(x) = \xi.
Click on the graph until the graph of f(x) = \xi appears.
Answer:
The graph of IxI is:
y = x for values of x ≥ 0
y = -x for values of x ≤ 0
Then you will see a "V", with the arms pointing up and the vertex in the point (0, 0)
(Something like in the image, but with the arms pointing upside instead of downside)
The actual graph is:
Circle A has center of (4,6) and a radius of 5, and circle B has a center of (1,0) and a radius of 15. What steps will help show that circle A is similar to circle B? Dilate circle Dilate circle A by a scale factor of 3. translate Circle A using the rule (x - 3, y + 6). Rotate circle A 180° about the center. reflect circle A over the y-axis.
The answer is A. Dilate circle A by a scale factor of 3
I took the test :)
WILL MARK BRAINLIST----- A particular map shows a scale of 1 cm:5 km. What would the map distance be (in cm) if the actual distance to be represented is 14 km?
Answer:
The map distance would be 2.8 cm
Step-by-step explanation:
Use the proportion given by the following relationship, where you use "x" as the unknown value in cm:
[tex]\frac{1\,\,cm}{5\,\,km} =\frac{x}{14\,\,km} \\\frac{1\,\,cm\.\,(14\,\,km)}{5\,\,km} =x\\x=2.8\,\,cm[/tex]
Which of the these angles is congruent to <5? Yes or no
Hello!
Answer:
A) Yes.
B) No.
C) Yes.
D) Yes.
Step-by-step explanation:
To find the correct solutions to this question, we can go through each choice and check for their congruency:
A) Yes. ∠8 is congruent to ∠5 because ∠5 and ∠8 are vertical angles.
B) No. ∠5 is not congruent to ∠6 because ∠5 and ∠6 are supplementary to each other.
C) Yes. ∠5 is congruent to ∠1 because corresponding angles are congruent.
D) Yes. ∠5 is congruent to ∠4 because alternate exterior angles are congruent.
A) The angle 8 should be congruent so it should be Yes.
B) The angle 6 should be congruent so it should be No.
C) The angle 1 should be congruent so it should be Yes.
D) The angle 4 should be congruent so it should be Yes.
What are congruent angles?The congruent angles are those angles in which the corresponding sides and angles should be of equal measure.
A) Yes. ∠8 is congruent to ∠5 since ∠5 and ∠8 are vertical angles.
B) No. ∠5 is not congruent to ∠6 since ∠5 and ∠6 are supplementary to each other.
C) Yes. ∠5 is congruent to ∠1 since corresponding angles are congruent.
D) Yes. ∠5 is congruent to ∠4 since alternate exterior angles are congruent.
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Which linear inequality is represented by the graph?
Answer:
A. y ≤ 1/2x + 2
Step-by-step explanation:
Well look at the graph,
It is a solid line with it shaded down,
meaning it is y ≤,
So we can cross out B. and D.
So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.
now the slope can be found by seeing how far away each points are from each other,
Hence, the answer is A. y ≤ 1/2x + 2
The equation of a line is y = 1.5x_2. What are it’s slope and y- intercet
Answer: the slope is 1.5 and the y-intercept is -2.
Step-by-step explanation:
Assuming you meant 1.5x-2 and accidentally pressed shift to turn - into _.
This equation is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Thus, the slope is 1.5 and the y-intercept is -2.
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]Slope = 1.5\\\\Y-intercept = -2[/tex]
▹ Step-by-Step Explanation
(I'm assuming the underscore was meant as a minus sign)
[tex]Slope \\equation \\\\ y = mx + b\\\\[/tex]
mx represents the slope and b represents the y-intercept.
Therefore:
1.5 is the slope, and -2 is the y-intercept.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Which of the following is true? |−8| < 6 |−6| < |−8| |8| < |−6| |−6| < −8
Answer: The second choice
Step-by-step explanation:
Absolute value is the distance a number is from 0 on the number line. Thus, the absolute value of -8 is 8, which is greater than the absolute value of -6, or 6.
Hope it helps <3
Answer:
Step-by-step explanation:
the second option, |-6| < |-8|.
I need help with this one!
Answer:
[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]
Step-by-step explanation:
The easiest way to remember sine, cosine, and tangent ratios is to use SOH-CAH-TOA as an acronym.
SOH - Sine: Opposite over hypotenuse
CAH - Cosine: Adjacent over hypotenuse
TOA - Tangent: Opposite over adjacent
Note that these are referring to the position of the sides relative to the angle you are looking at. In this case, that is angle A. Since it's tangent, we have:
[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]
This Question: 1 pt
Solve the system of equations by the substitution method.
12x + 3y = 22
- 4x = y + 8
Soloct the correct choice helow and if necessary fill in the answer box to complete your choice
Answer:
no solution
Step-by-step explanation:
use the second equation because y is already by itself
-4 x = y + 8
y = -4x - 8
substitute:
12x + 3(-4x - 8) = 22
distribute the 3:
12x -12x - 24 = 22
0 - 24 = 22
-24 ≠ 22
Explain how to write an equivalent expression using the
associative property.
2+(11 + y)
Answer:
2+(11+y)=(2+11)+y=11+(2+y)
Answer:
Sample Response: The associative property allows you to keep the order of the terms and change the position of the parentheses. So you can rewrite the terms in the same order and then move the parentheses so that the 2 + 11 is now inside. The equivalent expression is (2 + 11) + y.
Step-by-step explanation:
E d g e n u i t y
Help Please! Solve this problem without the law of cosines.
Answer:A
Step-by-step explanation:
Find the number of possible outcomes Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right.
Answer:
120
Step-by-step explanation:
Let's say you put them on the shelf one by one, from left to right.
You can pick 1 of the 5 for the first position.
5
Now you have 4 books left. You pick one out of those 4 for the second position.
5 * 4
There are 3 choices left for the 3rd position.
5 * 4 * 3
2 left for the 4th position.
5 * 4 * 3 * 2
Finally, there is one book left for the 5th position.
5 * 4 * 3 * 2 * 1
Now we multiply:
5 * 4 * 3 * 2 * 1 = 120
a. What is the area and circumference of circle P? Explain how you calculated this answer. b. If the arc measure of arc COD is 100 degrees and the arc measure of arc BSA is 60 degrees, what is the angle measure of angle CRB ? Explain how you calculated this answer.
Answer:
a) 9*π or approx 28.26
b) ∡CRB=100°
Step-by-step explanation:
As known for secants crossing each other inside the circle is coorect the following:
BR*RD=AR*RC
=> 3*RD=4*4.5
RD=6
The diameter of the circle with center P is BD=BR+RD=3+6=9
So the radius of the circle is D/2=9/2=4.5
As known the circumference of any circle can be calculated as
C=2*π*r , where r is the circle's radius
So C=2*4.5*π=9*π= approx 3.14*9=28.26
b) ∡CRB=∡ARD= (arcBC+arcAD), where arcBC and arcAD smaller arcs
BD is the circle's diameter, so arc BD=180°
So arcBC=180°-arcCOD=180°-100°=80°
Similarly arcBD=180°
arcAD=180°-arcBSA=180°-60°=120°
∡CRB= (80°+120°)/2=100°
If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
Answer:
its a postulate
Step-by-step explanation:
The statement represents a geometric postulate.
A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.
In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.
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What is the reciprocal of (17h)/(46j)?
Answer:
I dont give the answer right away so you read what i write and fully understand :D
Step-by-step explanation:
The reciprocal of something is basically when you flip something over. Since 17h/46j is a fraction, the reciprocal is 46j/17h. Remember, a number times the reciprocal is always equal to one.
Answer:
46j over 17h
Step-by-step explanation:
a reciprocal fraction is formed by flipping the fraction around
for example:
2/3
reciprocal= 3/2 or 1.5
HOPE THIS HELPS!!! :)
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Press the hotspot for all that apply.
Answer:
2 and angle that is left of 5
Step-by-step explanation:
Angle 2 is vertical from 110, and vertical angles are congruent. From this, we can figure out that 2 and 3 (they're supplementary) are 70. Angles 5 and 3 are Alternate Interior Angles, and therefore must be congruent. The one to the left of 5 is supplementary to it, and therefore must be 110. Your answers are angle 2 and the angle that is left of 5.
|2x-19| = 4x + 1 helppp
Answer:
x = 9
Step-by-step explanation:
Well to find x we need to use the commutative property which is the moving of numbers and variables to either side of the equation,
|2x - 19| = 4x + 1
-2x to both sides
|-19| = 2x + 1
Absolute value of -19 is 19
19 = 2x + 1
-1 to both sides
18 = 2x
Divide 2 to both sides
x = 9
Thus,
x is 9.
Hope this helps :)
The value of x is -10 when the equation is |2x-19| = 4x + 1
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is |2x-19| = 4x + 1
Mod of two times of x minus nineteen equal to four times of x plus one.
|2x-19| = 4x + 1
2x-19=4x+1
Now add 19 on both sides
2x=4x+20
Subtract 4x on both sides
-2x=20
Divide both sides by 2
x=-10
Hence, the value of x is -10 when the equation is |2x-19| = 4x + 1
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Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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The shape in the figure is constructed from several identical squares. If the side of each square is 1 unit, what is the area and the perimeter of the shape?
Answer:
Area = 7 square units
Perimeter = 14 units
Step-by-step explanation:
The figure shown above consists of 7 squares, each having a side length of 1 unit.
==>Area of shape = area of 1 square × 7
Area of shape = s² × 7.
Where, s = side length = 1 unit
Area of shape = 1² × 7
= 1 × 7
Area = 7 square units
==>Perimeter of shape:
The perimeter of the shape is the sum of all the external sides of the 7 squares that form along the boundary of the shape. Check the attachment to see each side length that makes up the length of the entire boundary.
Perimeter of shape = 1 + 1 + 1 + ½ + ½ + 1 + 1 + ½ + 1½ + 1 + 4 + 1 = 14 units.
thirteen less than the total of a number and eleven. Translate into variable expression. And also simply.
Answer: Required variable expression. [tex]x-13=11[/tex]
The value of x is 24.
Step-by-step explanation:
Let x be the number.
Given statement: "thirteen less than the total of a number and eleven."
Expression for "thirteen less than the total of a number" = [tex]x-13[/tex]
Now , the complete expression will be : [tex]x-13=11[/tex]
To simplify, we add 13 on both the sides , we get
[tex]x-13+13=11+13\\\\\Rightarrow\ x= 24[/tex]
Hence, the value of x is 24.