Considering the given stem-and-leaf plot, the quartiles are given as follows:
The first quartile is of 67.5.The second quartile, which is the median, is of 84.5.The third quartile is of 91.5.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:
Me = (83 + 86)/2 = 84.5.
The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:
Q1 = (67 + 68)/2 = 67.5.
The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:
Q3 = (91 + 92)/2 = 91.5.
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Volume and surface area
By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.
How to determine the volume of a composite figure
The volume of the composite figure is the sum of the volumes of the two figures: (i) a cone, (ii) a hemisphere. The volume formula of the figure is shown below:
[tex]V = \frac{2\pi}{3} \cdot r^{3} + \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]
If we know that r = 5.3 cm and h = 8.4 cm, then the volume of the composite figure is:
V = (2π/3) · (5.3 cm)³ + (π/3) · (5.3 cm)² · (8.4 cm)
V ≈ 558.900 cm³
By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.
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Andrew has a new job at the local pizza store as a delivery boy
The distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 blocks away.
Distancea. The entire trip based on the given graph is 15 minutes.
b. Distance:
Distance=10-1
Distance=9 block away
c. Andrew stopped for 3 minutes for 1 minutes between third minutes and fourth minutes.
d. Distance:
Distance=10-2
Distance=8
Distance=15-8
Distance=7 minutes
Distance=5-1
Distance=4 minutes
Therefore the distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 minutes.
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Consider the problem: Jasmine wants to buy a brand new pair of headphones that cost $99. While she already has $40 saved up, she is planning on working at a local grocery store for $8 an hour to make up the extra cash. Which of the following inequalities will help her determine values of h, the number of hours that Jasmine can work so she can afford the new headphones?
The number of hours that Jasmine can work so she can afford the new headphones x = 6 weeks.
let x represent the number of weeks it will take to save enough money.
If she saves $11 each week, then in x weeks she will save 11x dollars.
Add this to the 107 she has already saved, and at the end of 11 weeks she will have
11x + 107 dollars.
We want the amount saved to be equal to the price of the bike, so our equation is
11x + 107 = 173
In a word problem, writing the equation is usually the hardest part. Now we solve the equation.
Subtract 107 from both sides to get
11x = 66
Divide both sides by 11 to get
x = 6 weeks.
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Please help! The graph of a linear function passes through the points (-2,-5) and (1,-3).
Find the slope of this function.
Answer:
m=2/3
Step-by-step explanation:
[tex]m=\dfrac{\delta y}{\delta x} \\\\=\dfrac{-5-(-3)}{(-2)-1}\\ \\\dfrac{2}{3}[/tex]
Longhorn Corporation provides low-cost food delivery services to senior citizens. At the end of the year on December 31, 2021, the company reports the following amounts:
Cash $ 1,300 Service revenue $ 65,700
Equipment 27,000 Cost of goods sold (food expense) 53,000
Accounts payable 4,000 Buildings 36,000
Delivery expense 2,200 Supplies 3,000
Salaries expense 5,100 Salaries payable 900
In addition, the company had common stock of $36,000 at the beginning of the year and issued an additional $3,600 during the year. The company also had retained earnings of $17,400 at the beginning of the year.
Required:
Prepare the income statement for Longhorn Corporation.
The preparation of the income statement for Longhorn Corporation for the year ended December 31, 2021, is as follows:
Longhorn Corporation
Income StatementFor the year ended December 31, 2021
Service revenue $ 65,700
Cost of goods sold (food expense) 53,000
Gross profit $12,700
Delivery expense $2,200
Salaries expense 5,100 $7,300
Net Income $5,400
What is the income statement?The income statement also called income summary is a financial statement that shows the financial performance of a business for a defined financial period.
Thus, from the income statement, the net income and the gross profit, which represent the gains achieved by the entity, are derived.
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Please solve this for me thank you!
Answer:
620.14
Step-by-step explanation:
Original Equation:
[tex]\frac{4y}{1.025^4}+y-2y(1.05)^2=1500[/tex]
Calculate exponents
[tex]\frac{4y}{1.103812890625}+y-2y(1.1025)=1500\\[/tex]
Simplify:
[tex]3.6238025791990193084270042653997y + y - 2.205y = 1500[/tex]
Add like terms
[tex]2.4188025791990193084270042653997y \approx 1500[/tex]
Divide both sides by 7.012
[tex]y\approx 213.91[/tex][tex]y\approx620.14[/tex]
Answer:
y = $620.14 (nearest cent)
Step-by-step explanation:
Given equation:
[tex]\dfrac{4y}{1.025^4}+y-2y(1.05)^2=\$1,500[/tex]
Factor out y from the left side:
[tex]\implies y\left(\dfrac{4}{1.025^4}+1-2(1.05)^2\right)=\$1,500[/tex]
Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:
Calculate the exponents:
[tex]\implies y\left(\dfrac{4}{1.103812891...}+1-2(1.1025)\right)=\$1,500[/tex]
Carry out the multiplication and division from left to right:
[tex]\implies y\left(3.623802579...+1-2.205\right)=\$1,500[/tex]
Carry out the addition and subtraction from left to right:
[tex]\implies y\left(4.623802579...-2.205\right)=\$1,500[/tex]
[tex]\implies y\left(2.418802579...\right)=\$1,500[/tex]
Finally, divide both sides by the coefficient of y to isolate y:
[tex]\implies \dfrac{y\left(2.418802579...\right)}{2.418802579...}=\dfrac{\$1,500}{2.418802579...}[/tex]
[tex]\implies y=\$620.141558...[/tex]
Therefore, y = $620.14 (nearest cent)
Glenn, the owner of a hardware store, originally paid $54.60 for 15 tool sets. At his year-end clearance sale, he sold the last tool set for 24.00 How much money did he lose on the last tool set.
The amount of money he lose on the last tool set is: $30.60.
Amount loseUsing this formula
Amount lose=Original amount paid -Selling price
Where:
Original amount paid=$54.60
Selling price=$24.00
Let plug in the formula
Amount lose=$54.60-$24.00
Amount lose=$30.60
Therefore the amount of money he lose on the last tool set is: $30.60.
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The five evidence-based recommendations addressed in the practice guide include all of the following except:
A. Teach math using a developmental progression and monitor progress to ensure math instruction builds on what each child knows.
B. Teach children to view and describe their world mathematical and integrate math instruction throughout the school day.
C. Make sure you have strong curriculum so that all the math skills are addressed.
Answer:
I would say b since this defintally usally you aren't expeced to use math ouside of math class at school
Hope This Helps!!!
Answer:
The correct answer is C.
Step-by-step explanation:
What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 96 words per minute
Using the normal distribution, it is found that there is a 0.1029 = 10.29% probability that the sample mean is above 96.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching the problem on the internet, the parameters are given as follows:
[tex]\mu = 92, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623[/tex]
The probability that the sample mean is above 96 is one subtracted by the p-value of Z when X = 96, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{96 - 92}{3.1623}[/tex]
Z = 1.265
Z = 1.265 has a p-value of 0.8971.
1 - 0.8971 = 0.1029 = 10.29% probability that the sample mean is above 96.
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GIVING BRAINLIEST TO THE FIRST PERSON WHO CAN SOLVE THESE QUESTIONS. :)
Answer:
1) y = 2(x+3)^2 -4
2) x+6/x-4
3) 2x^2 + 6x +20 = 0
Step-by-step explanation:
4x=-3y+12 I don't know the answer to this please help.
Answer: y = -4x/3 + 4
Step-by-step explanation:
Assuming you want to solve for y:
4x = -3y + 12
-4x/3 = y - 4
y = -4x/3 + 4
Whats the correct answer answer asap for brainlist
What is the best approximation for the perimeter of polygon ABCDE? A. 11.0 units B. 17.0 units C. 24.3 units D. 22.1 units
TheThe best approximation for the perimeter of polygon ABCDE is: C. 24.3 units.
Perimeter of polygonCoordinate:
A=(-2,3)
B=(0,6)
C=(5,4)
D=(4,-1)
E=(-1,-2)
Distance AB=√(0+2)²+(6-3)²
Distance AB=√4+9
Distance AB=√13
Distance BC=√(5-0)²+(4-6)²
Distance BC=√25+4
Distance BC=√29
Distance CD=√(4-5)²+(-1-4)²
Distance CD=√1+25
Distance CD=√26
Distance DE=√(-1-4)²+(-2+1)²
Distance DE=√25+1
Distance DE=√26
Distance EA=√(-2+1)²+(3+2)²
Distance EA=√1+25
Distance EA=√26
Perimeter of pathogen ABCDE
=AB+BC+CD+DE+EA
=√13+√29+√26+√26+√26
=√13+√29+3√26
=24.2877 units
= 24.3 units (Approximately)
Therefore the correct option is C.
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Step-by-step explanation:
The population of Kenya is 50 000 000. The population of Pakistan is 4 times greater than the population of Kenya. What is the population of Pakistan?
Answer:
Step-by-step explanation:
Comment
I would think Pakistan should be more than just 4 times as large as Kenya. However if you are given that Kenya is 50 000 000 then Pakistan will be 4 times the size of Kenya.
Pakistan = 4 * Kenya
Pakistan = 4 * 50 000 000
Pakistan = 200 000 000
Answer: Pakistan = 200 000 000
A social security number is a sequence of nine digits. Determine the number of social security numbers that satisfy the following conditions:
a. There are no restrictions.
b. The digit 8 is never used.
c. The sequence does not begin or end with 8.
d. No digit is used more than once.
Answer:
765314290
Step-by-step explanation:
doesn’t use 8
Not start with 8
Digits used only 1’cd
The price p (in dollars) and the demand X for a particular clock radio are related by the equation X = 3000 -10p. Find and answer A - D
The price p based on the equation given is p = 3000 - 0.1x.
How to express the price?The equation given in the question is x = 3000 - 10p. The price(p) will be:
x = 3000 - 10p.
Make p the subject of the formula
x + 10p = 3000
10p = 3000 - x
p = (3000 - x)/10
p = 3000 - 0.1x
The revenue will be price multiplied by quantity. This will be:
= (3000 - 0.1x) × x
= 3000x - 0.1x²
The marginal revenue will be calculated after differentiating. This will be:
= 3000x - 0.1x²
= 3000 - 0.2x
The demand which is the quantity based on the information will be:
3000 - 0.2x = 0
0.2x = 3000
x = 1500
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How much interest will Brian earn on $875 in his savings account after 3 months if the annual interest rate is 5.5%?
The interest that Brain would receive is $12.03.
How much interest would Brain receive?The interest received is a function of the amount saved, interest time and the length of time the money was saved.
Interest = amount saved x number of months x (annual interest rate / 12)
$875 x 3 x (0.055 / 12) = $12.03
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Which rule describes the composition of transformations that maps figure PQRS to figure P"Q'R"S"?
The transformation is R₁R_Q ₁₈₀° option second is correct if the quadrilateral PQRS transformed into P"Q'R"S"
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a quadrilateral PQRS shown in the picture.
From the transformation:
The image of Q(x, y) = Q'(-x, -y) will be the highest and leftmost point following the rotation since Point S is the lowest and farthest point to the right of Point Q.
The same applies to points P P' and R R'.
Thus, the transformation is R₁R_Q ₁₈₀° option second is correct.
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Answer:
Option B is the correct answer
Find the area under the standard normal curve to the left of z=2.63. Round your answer to four decimal places, if necessary.
The area under the standard normal curve to the left of z = 2.63 is given by calculator will be 0.995.
What is a normal distribution?The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The area under the standard normal curve to the left of z = 2.63 is given by calculator will be
Area = 0.995
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Assuming you are a business owner with different shareholders. How may zero growth stock valuation and constant stock valuation affect your business operations?
The ways that zero growth stock valuation can affect business operations is that:
When zero-growth model states that the dividend is at the same rate, it shows that one has no measure of growth in terms of dividends. This therefore shows that stock price is equal to the annual dividends and divided also by the needed rate of return.What ways does constant stock valuation affect business operations?The Constant stock valuation is known to be a kind of share evaluation as it states that the dividends paid by a firm will consistently increase at a constant growth rate.
This will help one to know especially investors on how to set or know the fair price that one needs to pay for a stock on daily basis today by due to future dividend payments.
The overall statement is that stock value affect one's business operations as the company's stock price is one that shows an investor perception of their capability to get profit and also if they can grow their profits in terms of future times.
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At the beginning of the year (January 1), a company has $11,000 of common stock outstanding and retained earnings of $7,900. During the year, the company reports net income of $8,200 and pays dividends of $2,900. In addition, the company issues additional common stock for $7,700.
The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented below in the form of table.
How to find the stockholder's equity?The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented as:
Statement of stockholder's equity
Particulars Common stock Retained earnings Total stockholder
Equity
Beginning
balance $11,000 $7,900 $18,900
Add: Additional
common stock $7,700 $7,700
Add: Net income $8,200 $8,200
Less - dividend -$2,900 -$2,900
Ending balance $17,000 $5,300 $5,300
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Please help with these 2 questions. I got 73.0 for question 12
The height of the tower based on the angle of elevation given is
How to calculate the height?From the information given, the tower is 45m, the clinometer is set at 1.3m above the ground, and the angle of elevation is 32°.
This can be illustrated as:
tan 32° = (45 - 1.3)/x
tan 32° = 43.7/x
x = 43.7/tan 32°
x = 69.93m.
Also, for triangle ACD,
tan 47° = (43.7 + y)/x
x × tan 47° = 43.7 + y
74.49 = 43.7 + y
y = 31.29
The height of the tower will be:
= 43.7 + 31.29
= 74.99m
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The graph of f(x)=x2 is shown. Use the parabola tool to graph the function g(x)=(15x)2 . To graph a parabola, first plot the vertex then plot another point on the parabola
The graph of the parabola can be seen in the image below.
How to plot the parabola?Here we have the function:
g(x) = (15x)^2
Notice that this is a contraction of scale factor 15 of the function f(x) = x^2
To graph this, we can just evaluate the function in 3 points, the vertex and two other ones.
for x = 0.
g(0) = (15*0)^2 = 0
So we have the point (0, 0).
Evaluating in x = 1 and x = -1 (give the same value) we get:
g(±1) = (±15)^2 = 225
So we have the points (1, 225) and (-1, 225).
Now we can just connect these 3 points with a parabola. The graph can be seen below.
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triangle abc is equal to triangle pqr, angle p=8x+4, angle a=5x+16 , and angle q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d. 102
Answer: b.not enough info
Step-by-step explanation:
Corresponding angles of congruent triangles are congruent, so [tex]\angle A =\angle P[/tex]
However, we don't have all 3 interior angles of either triangle, so we cannot conclude anything.
If Jonathan has 2 times as many dimes as quarters and they have a combined value of 360 cents, how many of each coin does he have?
Answer:
16 dimes8 quartersStep-by-step explanation:
When ratios of quantities are given, it is often convenient to consider a group of objects in which the objects have that ratio.
How many groups?Here, we have 2 dimes for each quarter, so a group of 2 dimes and 1 quarter is a useful group for this problem. Its value is 2×$0.10 +0.25 = $0.45.
The total value of all of the groups is $3.60, so there must be ...
$3.60/($0.45/group) = 8 groups
The 8 groups of coins will have 16 dimes and 8 quarters.
yoo if you passed algebra one help me with these questions please should be pretty easy u dont have to explain or anything.
1) Find the domain of the function f ( x ) = 3 ( 3 ) x - 1
options: a. ( 0, ∞ ) b. ( − ∞, ∞ ) c. ( − ∞, 0 ) d. ( 0, 10 )
2) What is the range of the function f ( x ) = 2 x.
options: a.( 0, ∞ )b.( − ∞, 0 )c.( − ∞, ∞ )d.( − ∞, 1 ]
3) What is the range of the function f ( x ) = 2 x.
options: a. ( 0, ∞ ) b. ( − ∞, 0 ) c. ( − ∞, ∞ ) d. ( − ∞, 1 ]
4) What is the domain of the function f ( x ) = 2 x.
options: a. ( 0, ∞ ) b. ( − ∞, 0 ] c. ( − ∞, 0 ) d. ( − ∞, ∞ )
5) What is the range of the function f ( x ) = 2 x − 2.
options: a. [ 1, 5 ] b. ( − ∞, 0 ) c. ( − ∞, ∞ ) d. ( 0, ∞ )
6) What is the domain of the function f ( x ) = -2 x
options: a. ( − ∞, 0 ) b. [ − 1, 5 ] c. ( − ∞, ∞ ) d. ( 0, ∞ )
7) Find the range of the function f ( x ) = -.5 ( 3 ) x-1
options: a. ( 1, ∞ ) b. ( − ∞, 0) c. ( − ∞, ∞ ) d. ( − ∞, -1 )
thanks :)
See below for the domain and the range of the functions.
How to determine the domain and the range?As a general rule, all linear functions have a domain and a range of all set of real numbers i.e. (−∞, ∞)
The functions (2), (3), (4), (5) and (6) are linear functions.
So, their domain and range are (−∞,∞)
For function (1), we have:
f(x) = 3(3)^x - 1
The above is an exponential function.
The domain of an exponential function is all set of real numbers i.e. (−∞, ∞)
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In the year 1985, a house was valued at $106,000. By the year 2005, the value had appreciated to $146,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?
The value of the house in the year 2010 is 150056.47.
What is growth rate?The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year)
Value
v(t) = V0 ( 1 + r)^t
let V0 = 106, v(20) = 146
So,
146 = 110(1 + r )^20
146/110 = (1 + r )^20
1.327 = (1 + r )^20
1+ r = 1.014
r= 0.014
So, annual growth rate is 1.4%.
In the year 2010
v(t) = 106(1.014)^25
v(t) = 106(1.014)^25
v(t) - 150056.47
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length
AT=5,
3 In right triangle ABC shown below, point D is on
AB and point E is on CB such that AC || DE.
C
D
E
B
If AB= 15, BC = 12, and EC = 7, what is the
length of BD?
1) 8.75
2) 6.25
3) 5
4) 4
id or create
k as done
nments
Assi
to Susan Guha
Answer:
6.25
Step-by-step explanation:
BE = BC - EC = 12 - 7 = 5BE/BC = BD/AB
5/12 = BD/15
BD = 15(5/12) = 6.25
Otto has some whipping cream that is 30%, butterfat, and some milk that is 2%, butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.
What does point K represent in this context?
Answer:
CORRECT (SELECTED)
The mixture has the intended volume and has the intended percent of butterfat.
Explanation: Point K is on line b, so it represents a scenario where the mixture has a volume of 500 \,\text{mL}500mL500, start text, m, L, end text. Point KKK is on line aaa, so it represents a scenario where the mixture has 12\%12%12, percent butterfat.
The inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
How to illustrate the information?It should be noted that an inference simply means the conclusion that can be deduced based on the information given.
In this case, the inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
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Answer: It The mixture has less than the intended volume and has more than the intended percent of butterfat.
Step-by-step explanation:
With the aid of a power reducing formula, 14sin² acos² a = ?
The reduced form of the trig expression is 7/2sin²2a
Trigonometry identityTrigonometry identities are written in terms of sine, cosine and tangent. Given the trigonometry identity
14sin² acos² a
Since sin(a)cos(a) = sin2a/2, hence
14sin²acos²a = 14[sin(a)cos(a)]²
14sin²acos²a = 14(sin2a/2)²
14sin²acos²a = 14/4(sin²2a)
14sin²acos²a = 7/2sin²2a
Hence the reduced form of the trig expression is 7/2sin²2a
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