Answer:
a = 4 first term, r = ?, T10 = 100.Tn = ar^n - 1 formula for g.pT10 = 4r^ 10 - 1100 = 4r^9Divide both side by 4100/4 = 4/4r^925 = r^9 take the 9th root of both side 9√25 = 9√r^9r = 9√25To find the nth term Since Tn = ar^n - 1
Use the drawing tool(s) to form the correct answer on the provided graph. Graph the solution to this system of inequalities in the coordinate plane. 3y> 2x+122x+y < -5
Thank you in advance!
The solution to the system of inequalities is (-3.375, 1.75)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x+12
2x+y < -5
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-3.375, 1.75)
Hence, the solution to the system of inequalities is (-3.375, 1.75)
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Shayla is 3 years older than Todd. If t represents Todd’s age, which expression represents Shayla’s age?
Answer:
t + 3
Step-by-step explanation:
adding 3 years onto t amount of years
NEED HELP!20 points find the area.
Answer:
80 square units
Step-by-step explanation:
These are rectangles and triangles.
The formula to get the area of a rectangle is its length multiplied by its width.
The formula to get the area triangle is its base multiplied by its height, then divided by 2.
Step 1: Rectangle areaThe 3 rectangles all share the width of 6 units, so we can combine the 3 rectangles and consider it as 1 large rectangle.
The lengths of the rectangles are 2, 8, and 2 units.
We can add them together to get a total height of 12 units.
So, the formula to get the area of this rectangle is:
[tex]6\times12= A[/tex]
By solving this, we get:
A = 72 square units
There are 4 triangles remaining.
The base and height of all the triangles are 2 units.
So, by plugging these values into the triangle area formula, as mentioned from the beginning, we get:
[tex](2\times2)\div2=A[/tex]
So, the area of 1 triangle is 2 square units.
But since there are 4 triangles with the same bases and heights, we will multiply the area of 1 triangle by 4.
So, [tex]4 \times 2 = A[/tex]
This means the area of all the triangles together is 8 square units.
Step 3: Total areaBy adding the area of the triangles and rectangles together, we will get the answer.
[tex]72+8 = A[/tex]
So, the total area of this box is 80 square units.
If f(x) = -4x-8 and g(x)=3x²+x, then f(-1)g(2) =
Answer:
b
Step-by-step explanation:
(-4(-1)-8)(3(2)^2+2=4-8×12+2
-4×14=-56
Find the area between the two functions
The area between the two functions is 0
How to determine the area?The functions are given as:
f₁(x)= 1
f₂(x) = |x - 2|
x ∈ [0, 4]
The area between the functions is
A = ∫[f₂(x) - f₁(x) ] dx
The above integral becomes
A = ∫|x - 2| - 1 dx (0 to 4)
When the above is integrated, we have:
A = [(|x - 2|(x - 2))/2 - x] (0 to 4)
Expand the above integral
A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]
This gives
A = [2 - 4] - [-2- 0]
Evaluate the expression
A = 0
Hence, the area between the two functions is 0
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Q3 The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:
3.2 1.9 2.7 2.4 2.8 2.9 3.8 3.0 2.5 3.3
1.8 2.5 3.7 2.8 2.0 3.2 2.3 2.1 2.5 1.9
a) Evaluate the Median of grade point
b) Calculate the highest marks of bottom 30% students
d) Calculate Q1 & Q3.
Answer:
Step-by-step explanation:
A) The median number is just the middle number so it should be 2.8
B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.
A room has a floor dimension of 30 feet by 50 feet. The height of the basement is 6 feet. What is the total area of all four walls?
Answer:
960 feet
Step-by-step explanation:
30×6=180
180×2=360
50×6=300
300×2=600
360+600=960
An individual is planning a trip to a baseball game for 15 people. Of the people planning to go to the baseball game, 10 can go on Saturday and 12 can go on Sunday, some of them can go on both days. How many people can only go to the game on Sunday?
The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.
Total number of people for a trip to a baseball game = 15
Number of people planning to go on Saturday = 10
Number of people planning to go Sunday = 12
Let x be the number of people who can go on both Saturday and Sunday.
Then, the number of people who can go only on Saturday is 10 - x.
And the number of people who can go only on Sunday is 12 - x.
Total of 15 people are going to the baseball game.
Using set theory we have,
Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15
Substitute the value we have,
⇒(10 - x) + (12 - x) + x = 15
Simplifying the above equation, we get,
⇒22 - x = 15
⇒ x = 7
The number of people who can only go to the game on Sunday is
= 12 - x
= 12 - 7
= 5
Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .
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Find the missing angle and side, A is 25 degrees, C is 90 degrees, and B is 16.
The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.
How to find all missing sides and angles of the triangle
In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:
B = 180° - A - C
B = 180° - 25° - 90°
B = 65°
a = 16 × (sin 25°/sin 65°)
a ≈ 7.461
c = 16 × (sin 25°/sin 90°)
c ≈ 6.762
The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.
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Determine the point where the lines x=4t+1,y=t-9,z=2t+1 and x=5s+1, y= -s, z= 5s -9 intersect.
(Write your answer in the form of a point, (*,*,*). Enter DNE if the lines do not intersect.)
By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
How to find the point of intersection between two lines in space
From statement we have two lines in space, whose vector forms are described below:
(x, y, z) = (1, - 9, 1) + t · (4, 1, 2) (1)
(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5) (2)
The point of intersection satisfies the following condition:
(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)
(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)
s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)
There is a point of intersection if the resulting system of linear equations has at least a solution:
5 · s - 4 · t = 0 (2)
- s - t = - 9 (3)
5 · s - 2 · t = - 8 (4)
By (2):
s = 4 · t/5
(2) in (3):
- 4 · t/5 - t = - 9
- 9 · t/5 = - 9
t/5 = 1
t = 5
(2) in (4):
5 · (4 · t/5) - 2 · t = - 8
4 · t - 2 · t = - 8
2 · t = - 8
t = - 4
By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
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Oliver and Layla each built a rectangular prism with centimeter cubes. Both prisms have a volume of 24 cubic centimeters but they do not look the same. Give possible dimensions for each prism.
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
How to find the dimensions of a rectangular Prism?We are told that volume of both rectangular prisms is; V = 24 cm³
Now, formula for Volume of a rectangular prism is;
V = lwh
where;
l is length
w is width
h is height
Thus, to solve this, we have to look for multiples of 24 which are;
1, 2, 3, 4, 6, 8, 12, 24.
Now, we must pick 3 numbers from the above in which their products will be equal to 24.
Thus;
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
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Complete the solution of the equation. Find
the value of y when x equals 4.
-3x + 9y = -57
Answer: -5
Step-by-step explanation:
-3x+9y=-57 x=4
-3(4)+9y=-57
-12+9y=-57
+12
9y=-45
9y
y=-5
PLEASE HELP WORTH 14 POINTS!
Answer:
180°
cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°
Burger Corp has $468,500 of assets, and it uses only common equity capital (zero debt). Its sales for the last year were $778,500, and its net income after taxes was $25,000. Stockholders recently voted in a new management team that has promised to lower costs and get the return on equity up to 15%. What profit margin would Burger need in order to achieve the 15% ROE, holding everything else constant?
Answer in % without units (i.e. 17.11% -> 17.1 )
ANSWER: 9.0
BUT I WANT TO KNOW HOW TO SOLVE
The profit margin required to achieve 15% targeted ROE is 9.0%
The ROE means return on equity, it is the return earned on shareholders fund or shareholders equity.
Based on the three-way DuPont approach to computing the ROE, the below formula is very relevant to this analysis:
ROE=net profit margin*assets turnover*equity multiplier
ROE=15%
net profit margin=the unknown now(assume it is X)
assets turnover=sales/total assets
assets turnover=$778,500/$468,500
assets turnover=1.6616862326574200
equity multiplier=total assets/total equity
Note the company is entirely financed by equity(zero debt) which means that total assets is the same as total equity
equity multiplier=$468,500 /$468,500
equity multiplier=1.00
15%=X*1.6616862326574200*1.00
15%=X*1.6616862326574200
X=15%/1.6616862326574200
X=9.0%
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I have tried finding the answer for this but 1.4 or anything like that is wrong and i dont know why, what is 2.1 / 1.488, and then rounded to the nearest tenth.
After rounding to the nearest tenth, we get:
[tex]\frac{2.1}{1.488} = 1.5[/tex]
How to get the quotient?We have the quotient:
[tex]\frac{2.1}{1.488}[/tex]
If you multiply the numerator and denominator by 1000, you will get the simpler quotient:
[tex]\frac{2100}{1488}[/tex]
It gives:
[tex]\frac{2100}{1488} = 1.45[/tex]
Now we want to round it to the nearest tenth, which is the first digit after the decimal point.
To do so, we need to look at the number at the right of it.
If is between 0 and 4, then we round down.If it is between 5 and 9, we round up.In this case, we can see a 5, so we should round up, then we have:
[tex]\frac{2100}{1488} = 1.5[/tex]
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Expand 4(6)to the 8th power
4(6)^8
The expanded form of the given exponential equation is 6718464
Exponential equationsExponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x
where
a is the base
x is the exponent
Given the expression below;
a = 4(6)^8
Expand to have:
a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6
a = 4 * 1679616
a = 6718464
Hence the expanded form of the given exponential equation is 6718464
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None of the pots in the kitchen have a lid.
For each statement below, determine whether it is a negation
All pots in the kitchen have a lid.
Not every pot in the kitchen has a lid.
At least one pot in the kitchen has a lid.
Some pots in the kitchen have a lid.
Yes
No
O
O
The first three statements are not a negation. Only the last statement is a negation.
What is negation?The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "P" is the statement's negation. The words negation is used to denote a statement's denial.
It's vital to know the opposite of a given mathematical statement from time to time in mathematics. This practice is known as "negating" a statement. Remember that if a statement is true, then its negation must be false (and if a statement is false, then its negation is true).
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It rains 4 days in a week and is dry for 3 days. What fraction of the week is dry?
Answer:3/7
Step-by-step explanation:There are total 7 days in a week. 3 days were dry so the fraction is 3/7 . The dry days over the total days of the week
4. G.CO.10 In the figure below, p ll q. What is the value of x? *
O A. 7
B. 68
C. 59
OD. 44
136
121
The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two lines that are parallel to each other or p ll q
The angle made by transversal t is 136 degrees
The measure of the other angle = 180 - 136 = 44 degrees
Draw a line parallel to p and q and passes through the intersection point of line t and v
The angle made by the transversal and the line drawn is the same as 44 degrees.
The measure of the other angle = 121 - 44 = 77 degrees
Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.
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Value of x after the statement "if P(x) then x 1" is executed where P(x): > 1
and x = 0 when the statement is reached:
The values of x after the statement are:
b) If x=1, then the statement P(1)="1>1" is false, and thus the value of x is equal to 1 after the statement "P(x) then x := 1".c) If x=2, then the statement P(2)="2>1" is true, and thus the value of x is equal to 1 after the statement "if P(x) then x := 1".What is Discrete Mathematics?This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.
Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false
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A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.75. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.25. How much does one ounce of peanuts and one ounce of cashews cost?
The cost of one ounce of peanuts is $0.20
The cost of one ounce of cashew is $0.35
What are the linear equations that represent the question?15p + 5c = 4.75 equation 1
5p + 15c = 6.25 equation 2
Where:
p = cost of one ounce of peanutsc = cost of one ounce of cashewWhat is the cost of one ounce of peanut and cashew?Multiply equation 2 by 3
15p + 45c = 18.75 equation 3
Subtract equation 1 from equation 3
40c = 14
c = 14/40
c = $0.35
Substitute for c in equation 1
15p + (5 x 0.35) = $4.75
15p + 1.75 = 4.75
15p = 4.75 - 1.75
15p = 3
p = 3/15
p = $0.20
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Find the measure of side a.
A = _ m
The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. What is the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be
(a) 15.1kg or less? (answer?)
(b) 15.1kg or more? (answer?)
Leave all answers to 4 decimal places.
The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.
Given Information:
Population mean, μ = 15.8 kg
Population standard deviation, σ = 4.2 kg
For finding the probability for the sample mean, we first need to find the standard score.
(a) For sample mean to be 15.1kg or less,
z = (x - μ) / (σ/√n)
Here, x = 15.1
⇒ z = (15.1 - 15.8) / (4.2/√49
z =-0.7 / (4.2/7)
z = -1.17
Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.
∴ P(x ≤ 15.1) = 0.121
(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.
⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)
P(x ≥ 15.1) = 1 - 0.121
P(x ≥ 15.1) = 0.879
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A teacher designs a test so that 93% of students who study will pass and 9% of students who don't study will pass. 88%
of students study for a test. What is the probability that a randomly selected student passes?
A. 1.057
B. 0.833
C. 0.084
D. 0
E. 0.829
Answer:
Step-by-step explanation:
First find the percentage of the ones that pass that study
.93 *(88)=88.84%
next find the ones that pass that did not study
.09*(100-88)=1.08
sum these to get the total passing percentage
88.84+1.08=82.92%
The probability is 82.9 per 100 or .8292 for student
E is the answer
Points A, B and C make the triangle triangle ABC and are at the coordinates A(- 4, 3) , B(- 48, 17) and C(22, - 53) . Point D is the midpoint of BC and AD is a median of triangle ABC . What is the equation of the median in standard form?
PLEASE HELP ASAP
The equation of the median in standard form is; 9y - 38x = 179.
What is the equation of the media in standard form?It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).
The equation of the median which is the line joining points A and D is therefore determined as follows;
Slope = (-35-3)/(-13-(-4)) = 38/9
38/9 = (y-3)/(x+4)
9y -27 = 38x + 152
9y - 38x = 179.
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Instructions: Given the vertex, fill in the vertex form of the quadratic function..
Vertex: (2,-6)
Answer:
[tex]\implies y=(x-2)^2-6[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where:
(h, k) is the vertexa is some constantGiven vertex: (2, -6)
⇒ h = 2 and k = -6
Substitute the values of h and k into the formula:
[tex]\implies y=a(x-2)^2+(-6)[/tex]
[tex]\implies y=a(x-2)^2-6[/tex]
As we have not been given a value for the constant [tex]a[/tex], assume this is 1.
Therefore, the vertex form of the quadratic function with vertex (2, -6) is:
[tex]y=(x-2)^2-6[/tex]
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Vertex form
y=a(x-h)²+ka=1
Put values
y=(x-2)²-6If y = square root 81, what is the value of y?
add the different of 9/16 and 5/4
Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].
How to estimate the sum of 9/16 and 5/4?Find the least common denominator or LCM of the two denominators:
LCM of 4 and 16 exist 16.
Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.
For the 1st fraction, since 16 × 1 = 16,
9/16 = (9 × 1) / (16 × 1) = 9/16
For the 2nd fraction, since 4 × 4 = 16,
5/4 = (5 × 4) / (4 × 4) = 20/16
Add the two like fractions, then we get
(20/16) + (9/16) = (20 + 9)/16 = 29/16
So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]
In mixed form: [tex]$1 \frac{13}{16}[/tex].
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Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
The energy is compared based on the information given below.
How to illustrate the energy?Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8
Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10
Therefore,
Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25
Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.
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The other part of the question:
Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8
Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10
From atop a 15 m lighthouse, a man spots a dolphin 50 m out to sea. Find the angle of depression from the man to the dolphin, to nearest degree.
Answer:
16.7 degrees
Step-by-step explanation: