Answer:
[tex]A_{5} = 1875[/tex]
Step-by-step explanation:
The geometric sequence is represented by
[tex]A_{n} = 5 \times A_{n - 1}[/tex] .......... (1) and [tex]A_{1} = 3[/tex]
So, [tex]A_{2} = 5 \times A_{2 - 1} = 5 \times A_{1} = 5 \times 3 = 15[/tex]
{Putting n = 2}
Again, putting n = 3 in equation (1), we get
[tex]A_{3} = 5 \times A_{2} = 5 \times 15 = 75[/tex]
Again, putting n = 4 in equation (1), we get
[tex]A_{4} = 5 \times A_{3} = 5 \times 75 = 375[/tex]
Again, putting n = 5 in equation (1), we get
[tex]A_{5} = 5 \times A_{4} = 5 \times 375 = 1875[/tex] (Answer)
x/-9 ≥ 3 find x one step inequalities
Answer:
[tex]x\leq -27[/tex]
Step-by-step explanation:
Given:
[tex]\frac{x}{-9}\geq 3[/tex]
Multiplying both sides by -9, we get
[tex]-9\times \frac{x}{-9}\leq -9\times 3\\x\leq -27[/tex]
On multiplying both sides of an inequality by a negative number, the sign of the inequality changes as evident in the above equation.
So, the value of [tex]x[/tex] varies as:
[tex]x\leq -27[/tex]
Find the x-and y-intercepts of the graph of each equation
8. x+y=9
Answer:
see explanation
Step-by-step explanation:
To find the x- intercept let y = 0 in the equation and solve for x
x + 0 = 9
x = 9 ← x- intercept ⇒ (9, 0 )
To find the y- intercept let x = 0 in the equation and solve for y
0 + y = 9
y = 9 ← y- intercept ⇒ (0, 9 )
What is the volume of a cone with diameter 12 centimeters and height 4 centimeters?
Answer:
48pi or about 150.8 cm^3
Step-by-step explanation:
volume of cone = 1/3 * pi * r^2 * h
r = 12/2 = 6
1/3 (6^2) (4) pi = 48pi
48pi ~= 150.8 cm^3
Answer: 150.8 cm^3
Step-by-step explanation: The volume formula is V=πr^2(h/3). Once you plug in the radius (half the diameter) and the height, you solve the equation and get the answer of 150.8 cm^3
La empresa González se dedica a la fabricación y venta de mesas para jugar domino. Luego de un estudio, determinaron que el costo variable por fabricar una mesa es de $6 y los costos fijos de fabricación son de $524.
-Presumiendo que el costo total de fabricar una mesa presenta un modelo lineal, determinar el costo total C por fabricar x mesas al día.
-que significa la pendiente?
-cual es el costo total para la empresa González por fabricar 345 mesas?
Answer:
Total cost/Costo total: [tex]TC=524+6x[/tex]Slope/pendiente: change in total cost when we produce an additional unit /cambio en el costo total cuando se incrementa la produccion en una unidad.Total cost if 345 tables are made/costo total por elaborar 345 mesas: [tex]TC=524+6\times{345}=2594[/tex].Step-by-step explanation:
Total cost/Costo total: [tex]524+6x[/tex]. Total amount of money spent when producing x amount of tables, equals a fixed amount that must be paid and an extra of $6 for every additional table produced./ Cantidad de dinero gastado cuando se produce una cantidad x de mesas, es equivalente a $524 de costos fijos mas $6 adicionales por cada mesa producida.Slope/pendiente: change in total cost when we produce an additional unit. It is the coefficient that is linkes the extra amount of money spent when producing an extra unit of x (tables). /Cambio en el costo total cuando se incrementa la produccion en una unidad. El el coeficiente que vincula el cambio en el costo total con el cambio en las cantidades producidas.Total cost if 345 tables are made/costo total por elaborar 345 mesas: [tex]TC=524+6\times{345}=2594[/tex]. (Is the result of replacing in the equation x=345, which means to evaluate the total costo when we produce 345 tables/Es el resultado de remplazar en la ecuacion x=345, lo que resulta en saber el costo total de producir 345 mesas).Three math questions
Answer:
1. A is d=1.75
Step-by-step explanation:
Answer:
1a) 10.50=6d
1b) d= 1.75
2a) w is less than or equal to 35
2b) It would not make sense to have a bag that weighed zero or below.
3a) The tree grows 15 ft for every since it was planted.
3b) h(t)=70+15x
Going to the movies cost $9.50 per person. What is the slope of the line that models this situation, if x represents number of people and t represents total cost?
Answer:
9.5
Step-by-step explanation:
The cost of movie tickets is $9.50 per person.
Now, if the variable x represents the number of people and t represents a total cost in dollars, then we can write the equation that models the above situation as
t = 9.5x ......... (1)
From this above two-variable linear equation it is clear that the slope of the line is 9.5. And its unit is dollars per person. (Answer)
which expression is equal to 1/36? A 1/3 x 1/6 B 1/4 x (1/3)^2 C (1/2)^2 x (1/3) ^2 D 1/2 x 1/3 x 1/3 x 1/3
Answer:
B is the correct answer
Step-by-step explanation:
use your calculator and or in the problem and it should give you a decimal just go to math. and click 1 and click enter again and it should give you a fraction
15. Determine the future value of $4,000 deposited into an ordinary
annuity after each quarter for 3 years at 6% interest compounded
quarterly. (Lesson 5.8)
Answer:
The future value of investment at 6 % compounded quarterly is $ 4782.472
Step-by-step explanation:
Given as :
The principal amount = $ 4000
The rate of interest compounded quarterly = 6 %
The time period = 3 years
Let The future amount = A
From Compounded method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{4\times \textrm time}[/tex]
Or, Amount = 4000 × [tex](1+\dfrac{\textrm 6}{4\times 100})^{4\times \textrm 3}[/tex]
Or, Amount = 4000 × [tex](1.015)^{12}[/tex]
Or, Amount = 4000 × 1.195618
∴ Amount = $ 4782.472
Hence The future value of investment at 6 % compounded quarterly is $ 4782.472 Answer
All rocks are made of:
a. minerals
b. something that was once living
c. sand
Answer:
minerals
Step-by-step explanation:
Rocks are either SEDIMENTARY , IGNEOUS, or METAMORPHIC. Almost all rocks made of minerals, but different rocks contain different mixtures of minerals.
hope this helps :)
Answer:
sand
Step-by-step explanation:
sand because sand is made of different substance and for a lon
g time it starts to sit and without water its hard for them to sit, and sand has more similar substance between some that was one living and mineral.
Goran's gas tank is 1/3
full. After he buys 3 gallons of gas, it is 1/2
full. How many gallons can Goran's tank hold?
Answer: 6 gallons
Step-by-step explanation:
1/3 = 2/6. 1/2 = 3/6
2/6 already + 3/6 = 5/6, it
To determine the total capacity of Goran's gas tank, we set up and solved an algebraic equation, finding that the total capacity of the tank is 18 gallons.
The student's question is about figuring out the total capacity of Goran's gas tank based on the information given. To solve this problem, we can set up a simple algebraic equation based on the proportions of the tank's capacity that are filled. Since filling the tank with 3 gallons of gas takes it from being 1/3 full to 1/2 full, we know that these 3 gallons represent the difference between 1/3 and 1/2 of the tank's total capacity.
Let's denote the total capacity of the tank as 'T' gallons. According to the question:
1/3 of 'T' + 3 gallons = 1/2 of 'T'We can now set up the equation:
1/3 * T + 3 = 1/2 * T
To find 'T', we need to solve for T:
1/2 * T - 1/3 * T = 3
This simplifies to:
(3T - 2T) / 6 = 3
T/6 = 3
Now multiply both sides by 6 to solve for T:
T = 18
Therefore, the total capacity of Goran's gas tank is 18 gallons.
There are 1500 students in a school. 65% are girls. How many girls are there in the school?
Answer:
975 girls
Step-by-step explanation:
To find 65% of 1500, multiply 1500 by .65 (to convert percentages to decimals, just move a decimal point over two spaces).
1500*.65=975
You can check that this answer is right with logic. Most of the students will be girls (more than 50%) and 975 makes up most of 1500.
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Write the equation of each line using the given information.
a. The points (2,1.5) and (−5,36.5) both lie on the line.
b. m=4 and the point (3,15) lies on the line.
c. It has the same slope as y=1 and passes through (3,−8).
d.m=2and it has a y-intercept of (0,4).
Answer:
a. 10x + 2y = 23
b. 4x - y + 3 = 0
c. y + 8 = 0
d. 2x - y + 4 = 0
Step-by-step explanation:
a.
Slope of the line 'm' is [tex]\frac{36.5-1.5}{-5-2}[/tex] = [tex]\frac{35}{-7}[/tex] = -5
Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)
⇒y-1.5 = -5·(x-2)
⇒y = -5x + 10 + 1.5
⇒5x + y = 11.5 (or) 10x + 2y = 23
b.
Slope of the line 'm' = 4
Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)
⇒y-15 = 4·(x-3)
⇒y = 4x -12 + 15
⇒4x - y + 3 = 0
c.
Line is parallel to y = 1
Equations of parallel lines only differ by constant. So the required line equation has the form y = c where c is any real number.
But, it is given that the line passes through the point (3,-8)
⇒c=-8
⇒y = -8 (or) y + 8 = 0
d.
Equation of a line with slope 'm' and y-intercept of (0,c) is of the form y = mx + c
⇒y = 2x + 4
⇒2x - y + 4 = 0
what is this equal
how can I solve similar trigonometric integrals like this one
Answer:
ln|sec θ + tan θ| + C
Step-by-step explanation:
The integrals of basic trig functions are:
∫ sin θ dθ = -cos θ + C
∫ cos θ dθ = sin θ + C
∫ csc θ dθ = -ln|csc θ + cot θ| + C
∫ sec θ dθ = ln|sec θ + tan θ| + C
∫ tan θ dθ = -ln|cos θ| + C
∫ cot θ dθ = ln|sin θ| + C
The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.
∫ sec θ dθ
∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ
∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ
ln|sec θ + tan θ| + C
14. You start an investment account with $3000 and save $100 each month. Write a
rule to represent the total amount of money you invest into your account as an
arithmetic sequence. How much money will you have invested after 12 months?
Answer:
4200
Step-by-step explanation:
In an arithmetic sequence equation t=a + (n-1)d, a is the starting value. In this case, a=3000.
Although, since the initial investment is not considered the first month, the equation is t = a + dn.
d is the rate of change. In this case, the rate of change is 100 for every month, n.
Substitute these values from the problem to get an equation:
t = 3000 + 100n
t means the total amount of money we have for the amount of months (n) that passed.
Sub n for 12.
t = 3000 + 100n
t = 3000 + 100(12)
t = 4200
You will have $4200 after 12 months of investment.
What is the quotient?
-286 ) 457.6
-16
-1.6
1.6
16
Answer:
-1.6
Step-by-step explanation:
Simple division but with a negative number. Positive ÷ Negative = Negative and vice versa
Answer:
-1.6
Step-by-step explanation:
edge-
please solve with working much appreciated
Answer:
Length n = 5 cm
Step-by-step explanation:
Given:
Each angle measure is of 60° for the triangle given in the figure.
Equilateral Triangle:
If all the angles measure of the triangle is 60° then the triangle is said to be an Equilateral Triangle.
Therefore, the triangle given in the figure is an Equilateral Triangle.
Another property of an Equilateral Triangle is
All the Three sides of an equilateral triangles are equal.
Here,
measure of each angle is 60° ...... { Given}
length of one side = 5 cm ........{Given}
∴ Length n = 5 cm
11. A biologist tracked the growth of a strain of bacteria, as shown in
the graph.
a. Explain why the relationship represented by the graph is a
function.
There are no repeated
hamber
b. What If? Suppose there was the same number of bacteria for two consecutive hours. Would the graph still represent a Function? Explain...
In a function, each "x" can only have one "y" number. A relation can still be a function if a y-value has more than one x-value.
Answer:
11. a)
The relationship represented by the graph is a function because it passes the vertical line test (VLT). Any vertical line you pass through the graph, it only "hits" one spot on the graph. For a relation to be a function, each x-value can only have one y-value. This means no hour can have two different amounts of bacteria.
b)
If there were the same number of bacteria for two consecutive hours, the graph would still represent a function. In this case, two values for "y" will have more than one value for "x". Although, each x-value still only has one y-value, so it's still a function.
4. Which ratios form a proportion? Use cross products to test each pair.
A. 9/17 27/50
B. 12/35 24/75
C. 15/55 33/121
D. 12/35 20/70
The right answer is Option C.
Step-by-step explanation:
A. 9/17 and 27/50
Using cross product;
[tex]\frac{9}{17}=\frac{27}{50}\\9*50=17*27\\450=459[/tex]
The ratio does not form proportion.
B. 12/35 and 24/75
[tex]\frac{12}{35}=\frac{24}{75}\\12*75=24*35\\900=840[/tex]
The ratio does not form proportion.
C. 15/55 and 33/121
[tex]\frac{15}{55}=\frac{33}{121}\\15*121=33*55\\1815=1815[/tex]
The ratio form a proportion.
D. 12/35 and 20/70
[tex]\frac{12}{35}=\frac{20}{70}\\12*70=20*35\\840=700[/tex]
The ratio does not form proportion.
The right answer is Option C.
Keywords: ratio, proportion
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What is the value of (–7 + 3) - (2 – 6)?
Answer:
0
Step-by-step explanation:
-7+3= -42-6= -4(-4)-(-4)= -4+4-4+4=0Answer:
The answer would be 0
the local bakery uses 1.75 cups of flour in each batch of cookies. the bakery usee 5.25 cups of flour this morning. How many batches of cookies did the bakery make? if there are 5 dozon cookies in each batch, how many cookies did the bakery make?
The bakery made 3 batches of cookies and a total of 180 cookies.
To determine the number of batches of cookies the bakery made, we divide the total amount of flour used by the amount of flour used in each batch. The bakery used 5.25 cups of flour in total, and each batch requires 1.75 cups of flour. Therefore, the number of batches made is:
[tex]\[ \text{Number of batches} = \frac{\text{Total flour used}}{\text{Flour per batch}} = \frac{5.25}{1.75} \][/tex]
[tex]\[ \text{Number of batches} = 3 \][/tex]
Since there are 5 dozen cookies in each batch, we multiply the number of batches by the number of cookies per batch to find the total number of cookies made:
[tex]\[ \text{Total number of cookies} = \text{Number of batches} \times \text{Cookies per batch} \][/tex]
[tex]\[ \text{Total number of cookies} = 3 \times (5 \times 12) \][/tex]
[tex]\[ \text{Total number of cookies} = 3 \times 60 \][/tex]
[tex]\[ \text{Total number of cookies} = 180 \][/tex]
Thus, the bakery made 3 batches of cookies, resulting in a total of 180 cookies."
Reduce each fraction as much as possible
Ex) 10/40
CAN SOMEONE HELP ME WITH THIS QUESTION???? I NEED HELP QUICK!!!!!!!!!
1. r closest to 1: figure
2. No linear relationship: Figure 1
3. r equal to 1: Figure 3
Step-by-step explanation:
Correlation is the link between two variables or things"
When one quantity is increasing and the other is also increasing then the correlation co-efficient is positiveWhen one quantity is increasing and the other is decreasing then the correlation is negative.Now for the scatter plot of a correlation:
If the data points are close to a best fit line then the correlation is strongIf the data points follow a linear relationship i.e. a straight line then the correlation is 1 or -1 depending on the sign of correlationIf the data points are more scattered then they have least correlationCorrelation coefficient closest to 1:
We can see in figure 4 that the data points are gathered across a line but not a perfect line and both the quantities are increasing so the correlation coefficient is close to 1.
Least Evidence of linear relationship:
Figure 1 can be observed to conclude that the data points are scattered on whole scatter plot hence creating no relationship
Correlation coefficient equal to -1:
We can see in figure 3 that one quantity is increasing and the other is decreasing and the data points are forming a line so the correlation coefficient will be -1
Keywords: Correlation, Scatter plot
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Marco needs $57 to buy new basketball shoes. If Marco earns $3 per day working and already has $12 saved, which equation shows how many days Marco must work before he can afford the shoes?
Answer:
57=12+3d
d=number of days worked
Answer:
(57-12)3/x=15 days
x=57-12
The difference of 3 times a number and 15 is no less than the square of the number.
Select the inequality that represents this relationship.
A. 3x – 15 > 22
B. 34 < x2 + 15
c. 3x < 32 – 15
D. 3x + 15 > 22
Answer:
(B) The inequality that represents this relationship is [tex]3x < x^2 +15[/tex]
Step-by-step explanation:
Let us assume the given number = x
⇒ 3 times the given number = 3 (x) = 3x
Square of the given number = [tex](x)^2 = x^2[/tex]
Now, According to the question:
The difference of (3 x) and 15 is no less than [tex] x^2[/tex]
⇒ [tex]3x - 15 < x^2\\ \implies 3x < x^2 +15[/tex]
or, [tex]3x < x^2 +15[/tex]
Hence, the given inequality is represented as [tex]3x < x^2 +15[/tex]
Answer:
3x - 15 > [tex]x^{2}[/tex]
Step-by-step explanation:
Let the number be x
⇒3 times the number is 3x and square of the number is [tex]x^{2}[/tex]
Difference of 3 times a number and 15 is 3x -15
⇒This difference is no less than the square of the number
⇒The difference is greater than or equal to square of the number
⇒ 3x - 15 ≥ [tex]x^{2}[/tex]
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.
Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.
HL
SAS
SSS
ASA
AAS
Answer:
1. HL
2. SAS
3. SSS
Step-by-step explanation:
Triangles ABR and ACR share side AR (hypotenuse of two right triiangles).
Angles ABR and ACR are right angles.
Sides AB and AC are congruent.
Sides BR and CR are congruent.
1. You can use HL theorem, because two triangles have congruent pair of legs and congruent hypotenuses.
2. You can use SAS theorem, because two triangles have two pairs of congruent legs and a pair of included right angles between these legs.
3. You can use SSS theorem, because two triangles have two pairs of congruent legs and congruent hypotenuses.
Answer
1. HL
2. SAS
3. SSS
Step-by-step explanation:
just took the test aced it
y=-4x+2 y=6x-8 in substitution
Answer:
(1, - 2 )
Step-by-step explanation:
Given the 2 equations
y = - 4x + 2 → (1)
y = 6x - 8 → (2)
Substitute y = 6x - 8 into (1)
6x - 8 = - 4x + 2 ( add 4x to both sides )
10x - 8 = 2 ( add 8 to both sides )
10x = 10 ( divide both sides by 10 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = 6(1) - 8 = 6 - 8 = - 2
Solution is (1, - 2 )
What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0. Negative StartFraction 3 p Superscript 8 Baseline Over 4 q cubed EndFraction Negative StartFraction 3 Over 4 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction Negative StartFraction p Superscript 8 Baseline Over 5 q cubed EndFraction Negative StartFraction 1 Over 5 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
can be simplified to
[tex]-\frac{3p^8}{4q^3}[/tex]
Hopes this helps
if not then I'm sorrr
The quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\) is \(-\frac{3p^8}{4q^3}\). This is found by dividing the numerical coefficients and subtracting the exponents for variables of the same base (negative exponents indicate reciprocals).
Explanation:To find the quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\), we perform division of the coefficients (15 divided by -20) and subtraction of the exponents for variables with the same base (p's and q's exponents) according to the rules of exponents. First, simplify the numerical coefficients:
\(\frac{15}{-20} = -\frac{3}{4}\)
Now, subtract the exponents for p (applying the formula x^p \cdot x^q = x^{(p+q)}):
\(p^{-4} - p^{-12} = p^{-4 + 12} = p^8\)
Next, apply the same process to the exponents of q:
\(q^{-6} - q^{-3} = q^{-6 + 3} = q^{-3}\)
Combine the results to get the simplified quotient:
\(-\frac{3}{4} × p^8 × q^{-3}\)
Remember that a negative exponent indicates a reciprocal, so we can write \(q^{-3}\) as \(\frac{1}{q^3}\). Therefore, the final answer is:
\(-\frac{3p^8}{4q^3}\)
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A rectangle with a width of 9 ft. and a length of 13 ft. is the base of a 30 ft. tall pyramid. What
is the volume of the pyramid?
Answer:
1170
Step-by-step explanation:
In the figure shown, which composition of rigid motions will map one triangle onto the other?
Translation
Explanation:Rigid motion occurs when you move figures without affecting the size or shape in order for the figure to be congruent in a new location.
The types of rigid motions are:
ReflectionsTranslations (We will use it in this problem)RotationsIn this problem, you haven't provided any figure, but I've attached one below. As you can see, we have a triangle ΔABC that has been translated to a new location in order to match triangle ΔDEF. So any point (x, y) on the triangle is mapped following this rule:
[tex](x,y) \rightarrow (x+8,y+2)[/tex]
So the new vertices D,E,F will be:
[tex]A(-6,2) \rightarrow D(-6+8,2+2)=\boxed{D(2,4)} \\ \\ B(-6,6) \rightarrow E(-6+8,6+2)=\boxed{E(2,8)} \\ \\ C(-2,2) \rightarrow F(-2+8,2+2)=\boxed{F(6,4)}[/tex]
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scott is riding a bike course that is 50 miles long. So far, he has ridden 6 miles of the course. What percentage of the course has Scott ridden so far?
Scott has ridden 12% of the course.
Step-by-step explanation:
Length of bike course = 50 miles
Distance covered = 6 miles
Distance covered in percentage = [tex]\frac{Distance\ covered}{length\ of\ bike\ course}*100[/tex]
Distance covered in percentage = [tex]\frac{6}{50}*100\\[/tex]
Distance covered in percentage = [tex]\frac{600}{50}[/tex]
Distance covered in percentage = 12%
Scott has ridden 12% of the course.
Keywords: percentage, distance
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