Confidence interval is written as
point estimate ± margin of error
In this case, the point estimate is the sample mean
the formula for calculating margin of error is expressed as
[tex]\text{margin of error = z }\times\frac{\sigma}{\sqrt[]{n}}[/tex]where
σ = population standard deviation
n = sample size
z is the z score corresponding to a 95% confidence level. From the standard normal distribution table, z = 1.96
From the information given,
σ = 15
n = 50
sample mean = 244
By substituting these values into the formula,
[tex]\text{margin of error = 1.96 }\times\frac{15}{\sqrt[]{50}}\text{ = 4.16}[/tex]Thus,
confidence interval = 244 ± 4.16
Lower limit of conidence interval = 244 - 4.16 = 239.84
Upper limit of conidence interval = 244 + 4.16 = 248.16
Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between 239.84 pounds and 248.16 pounds
The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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A company purchased 10,000 pairs of men'sslacks for $18.66 per pair and marked them up $22.93. What was the selling price of each pair of slacks? Use the formulaS=CMThe selling price of each pairs of slacks is ?
Given:
A company purchased slacks for $18.66 per pair.
Mark up= $22.93
[tex]\begin{gathered} \text{Selling price= cost price +mark up} \\ \text{Selling price=}18.66+22.93 \\ \text{Selling price= \$41.59} \end{gathered}[/tex]do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Write in terms of confunction of a complementary angle:tan 26°
ANSWER
The cofunction of tan 36 degrees is cot 54 degrees
STEP-BY-STEP EXPLANATION
Given information
[tex]\text{tan 26}\degree[/tex]Co function of tan can be written below as
[tex]\begin{gathered} \tan \text{ }(A)\text{ = cot (B)} \\ \text{if, A + B = 90} \end{gathered}[/tex][tex]\begin{gathered} \text{tan 36 = cot (90 - 36)} \\ \tan \text{ 36 = cot 54} \end{gathered}[/tex]Therefore,
tan 36 = 0.7265
cot 54 = 0.7265
Hence, the cofunction of tan 36 is cot 54
27–34: Describing Distributions. Consider the following distributions.-How many peaks would you expect the distribution to have? Explain.-Make a sketch of the distribution.-Would you expect the distribution to be symmetric, left-skewed, or right-skewed? Explain.-Would you expect the variation of the distribution to be small, moderate, or large? Explain.#29The annual snowfall amounts in 50 randomly selected American cities
Answer:
Step-by-step explanation:
1: Are the two slopes parallel.
perpendicular or neither?
The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.
P.S hopes this helps
What is the coefficient of the second term in this expression?-k + 10m² - 6 - n² ?
Given the expression:
[tex]-k+10m^2-6-n^{2^{}}[/tex]The second term in the expression means the 2nd term from left to right of an expression.
Here, the second term is 10m².
A coefficient is a number that is being multiplied by the variable.
Therefore, the coefficient of the term 10m² is 10.
Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning
Part 1
The labelled disgram is shown below.
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle ABE
Sin 60 = 10/BE
BE = 10/Sin60 = 11.55
tan60 =10/AE
AE = 10/tan60 = 5.77
Part 1
Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)
angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30
The sum of the angles in a triangle is 180 degrees. Thus,
angle DBC + angle DCB + angle BDC = 180
30 + 90 + angle BDC = 180
angle BDC = 180 = 180 - (30 + 90 = 180 - 120
angle BDC = 60
Sin 30 = CD/BD = 10/BD
BD = 10/Sin30
BD = 20
tan 30 = DC/BC = 10/BC
BC = 10/tan30
BC = 17.32
Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC
= BD + DC + BC
= 20 + 10 + 17.32
Perimeter = 47.32 feet
Can you help me with this problem? I will send a screenshot of the problem and the answer choices.
Given:
Distance of her beagle = 25/4 meters to the right
Distance of her labrador = 51/20 meters directly to her left.
Let's determine the expression which represents how far apart the two dogs are.
We have the following:
Since the beagle is to the right, the distance is = 25/4 meters
Since the labrador is to the left, the distance is = -51/20 meters.
Now, to find how far apart the two dogs are, let's use the absolute value expression:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})|[/tex]Therefore, the expression which represents how far the two dogs are is:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]ANSWER:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]A linear equation written in the form y = mx + b is in ?
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
Error Analysis On a math test a student, Sarah, has to identify all the coefficients and constantsof the expression y +n + 2. Sarah says that 6 is a coefficient and 2 is a constant. Identify all thecoefficients and constants of the expression. What error might Sarah have made?The coefficient(s) of the expression is/are
the coefficients are the numbers that accompany a variable on this case we have 2 variables y and n so the numbers that accompany each one are 1 for y and 6 for n
so there area 2 coefficients 1 and 6
the constant are the numbers without a variable on this case only the 2
write the equation of the line passing through the given points write your awnser in slope intercept form Y=mx+b (5 1) and (-3 17)
The given points are (5, 1) and (-3, 17).
First, we have to find the slope using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=5 \\ x_2=-3 \\ y_1=1 \\ y_2=17 \end{gathered}[/tex]Let's use the coordinates above to find the slope.
[tex]m=\frac{17-1}{-3-5}=\frac{16}{-8}\Rightarrow m=-2[/tex]The slope is -2.
Now, we use the point-slope formula to find the equation.
[tex]y-y_1=m(x-x_1)[/tex]Let's use the same coordinates x_1 and y_1, and the slope m = -2.
[tex]y-1=-2(x-5)[/tex]Now, we solve for y to express the equation in slope-intercept form.
[tex]y-1=-2x+10\Rightarrow y=-2x+10+1\Rightarrow y=-2x+11[/tex]Therefore, the slope-intercept form of the equation is[tex]y=-2x+11[/tex]A pair of jeans is on sale for $30. If this price represents a 20% discount from the original price, what is the original price to the nearest cent ?
Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
Question 8 of 20If f(x) = 2x²+2 and g(x)=x2-1, find (f- g)(x).O A.3x²+3O B.x2²+1 O C.3x2² +1O D.x² +3
Solution
Step 1
Write the two functions:
[tex]f\mleft(x\mright)=2x²+2\text{ }and\text{ }g\left(x\right)=x2-1[/tex]Step 2
(f- g)(x) = f(g) - g(x)
[tex]\begin{gathered} \left(f-g\right)\left(x\right)=2x²+2\text{ - \lparen}x^2-1) \\ \\ (f-g)(x)=2x^2+\text{ 2 - x}^2\text{ + 1} \\ \\ (f-g)(x)=x^2+3 \end{gathered}[/tex]Final answer
D. x² +3
1. 3 In right AXYZ, the length of the hypotenuse YZ is 85 inches and tan Z= 3/4 What is the length, in inches, of the leg XY?
We have a right triangle XYZ.
The length of the hypotenuse is YZ=85.
We also know that the tangent of Z is 4.
We have to find the length of XY.
We can start by drawing the triangle and writing the data:
The tangent of an angle can be related with the sides by the following trigonometric ratio:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{XZ}=\frac{3}{4}[/tex]We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:
[tex]\begin{gathered} \frac{XY}{XZ}=\frac{3}{4} \\ XZ=\frac{4}{3}\cdot XY \end{gathered}[/tex]Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:
[tex]\begin{gathered} XY^2+XZ^2=YZ^2 \\ XY^2+(\frac{4}{3}XY)^2=YZ^2 \\ XY^2+\frac{16}{9}XY^2=YZ^2 \\ (\frac{16}{9}+1)XY^2=YZ^2 \\ \frac{16+9}{9}XY^2=YZ^2 \\ \frac{25}{9}XY^2=YZ^2 \\ XY^2=\frac{9}{25}YZ^2 \\ XY=\sqrt[]{\frac{9}{25}YZ^2} \\ XY=\frac{3}{5}YZ \\ XY=\frac{3}{5}\cdot85 \\ XY=51 \end{gathered}[/tex]Answer: the length of the leg XY is 51 inches.
I need help with my math
Answer:
Histogram Tells you how many pumpkins had mass below 6 kg
The box plot can be used to determine that the median was 8
Explanation:
A histogram is a chart the plots frequency of a certain quantity.
In our case, the histogram given tell us how many pumpkins fall within a certain mass range. Therefore, to find out how many pumpkins are below 6 kg, we use a histogram.
On the other hand, the box plot summarizes the numerical data. In our case, it can be used to find the median weight of the pumpkins by just reading off the position of the median line.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answer:
it would be the same since reflection doesn't change the andle
Answer:
A: It would have the same measure as the original angle.
Step-by-step explanation:
Well, reflecting is where you take the original image, which you see now, and flipping it like a mirror image. So, I think the answer would be: A It would have the same measure as the original angle. Because, it is literally the same thing, just in a mirror image. Like, if you look in the mirror, you see yourself, still the same.
Find the volume of a cylinder and cinema given the following dimensions
Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
Given the figure below, determine the angle that is a same side interior angle with respect to
We remember that two interior angles are those inside the are of the lines, Thus, the angles in the area:
Are interior. Now, we identify two sides, the right side, and the left side, which have been separated by the transversal line.
Thus, the angle that is is the same side as ∡3, and also that is interior is ∡5.
Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20
Solution
- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.
- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.
Statement 1:
- "1 tomato, 1 eggplant, 2 potatoes for $10"
- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).
- We are told that the total cost for this package is $10.
- Thus, the first equation must be:
[tex]a+b+2c=10[/tex]- We can interprete the other packages in a similar manner.
Statement 2:
"2 tomatoes, 1 eggplant, 3 potatoes for $14"
- This implies that the farmer would price the packages as follows:
2 tomatoes: 2(a)
1 eggplant: 1(b)
3 potatoes: 3(c)
- Since the total cost is $14, we can write the second equation as follows:
[tex]2a+b+3c=14[/tex]Statement 3:
"4 tomatoes, 3 eggplants, 5 potatoes for $20"
- This implies that the farmer would price the packages as follows:
4 tomatoes: 4(a)
3 eggplants: 3(b)
5 potatoes: 5(c)
- Since the total cost is $20, we can write the third equation as follows:
[tex]4a+3b+5c=20[/tex]Final Answer
The 3 equations are:
[tex]\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}[/tex]OPTION C
Help please not sure if I am right or wrong thank you
Given:
[tex]-1+\sqrt[]{-4}[/tex]To find the simplified complex number
[tex]\begin{gathered} -1+\sqrt[]{-4}=-1\pm2i \\ -1+\sqrt[]{-4}=-1+2i,-1-2i \end{gathered}[/tex]Ashley watches a giant that has 16 equally spread seats. Identify w.
The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]Determine the effect on the graph of the parent f(x)=x
To answer this question we first graph the parent function
Now we compare the two graphs. We notice that the graph shown is translated two units up.
To translate the graph of function we have to add the ammount we want to translate, then in this case
[tex]g(x)=f(x)+2[/tex]Therefore the answer is J.
Write a linear function f with f(0) = 3.75 and f(-6) =3.75
f(x) = ???
The linear function will be;
⇒ f (x) = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (0) = 3.75
And, f (-6) = 3.75
Now,
Let the linear function is,
f (x) = ax + b
Since, The values is given as;
f (0) = 3.75
And, f (-6) = 3.75
So, We can substitute the given values in the linear function, we get;
f (x) = ax + b
Substitute x = 0 we get;
f (0) = a × 0 + b
f (0) = b
3.75 = b
b = 3.75
And, We can substitute x = -6 and f(0) = 3.75 we get;
f (-6) = a × -6 + b
3.75 = -6a + 3.75
- 6a = 0
a = 0
So, Substitute a = 0 and b = 3.75 in linear function we get;
f (x) = ax + b
f (x) = a × 0 + 3.75
f (x) = 3.75
Therefore,
The linear function will be;
⇒ f (x) = 3.75
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What is the line of reflection for
SOLUTION:
Step 1:
In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:
Step 2:
The line of reflection for Triangle ABC and its image is:
[tex]\text{y = x --- OPTION D}[/tex]What’s eight less than four times a number in algebraic expression
Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
im having a hard time understanding this could you please help me
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9