The function f(t) = 6500(1.85)^365t represents the change in a quantity over t years. What does the constant 1.85 reveal about the rate of change of the quantity?
Here, we want to know what the constant reveal
The growth factor inside the bracket as can be seen is greater than 1
It can also be less than 1
When it is greater than 1, there is an indication of a positive change from year to year
1.85 is greater than 1 and as such, we have an indication for a positive change
That means, as the years roll by, there will be a greater value of the quantity
Hence, as t increases, f(t) increases
To find the percentage growth rate, we subtract 1 from the growth value which is (1.85-1) = 0.85
0.85 represents a percentage of 85%; and thus there is a growth rate of 85% per year
8th grade math
Subject in math: comparing ratios and graphs
The ratio of the graph X: Y is 1:9.
What is a straight-line graph?
The graph follows a straight-line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents the vertical line y-axis.
x represents the horizontal line x-axis.
m is the slope of the line
slope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)
Straight-line graphs show a linear relationship between the x and y values.
Calculation:-
The slope of X = 10/100 = 1/10
The slope of y = 90/100 = 9/10
Therefore the ratio of X: Y
= 1/10 × 10/9
= 1:9
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ASAP PLEASE
Mary buy a 5 kg jar of sweets for £25. Then Mary divide the sweets into 125 g packets and sell them for 99p each.
a. How many packets can Mary make?
b. How much profit will Mary make?
Write it Step by step.
Answer:
Step-by-step explanation:
a.
5kg = 5000 g
5000 ÷ 125 = 40
Mary can make 40 packets
b. 40 x 99 = 3960
3960 ÷ 100 = 39.60
39.6 - 25 = 14.6
Therefore, Mary makes a profit of £14.6
Kendall puts 1,000.00 into an account to use for school expenses the account earns 9% interest compounded monthly how much will be in the account after 9 years
To calculate the total amount accrued when you deposit the money in an account that earns compound interest you have to use the following formula
[tex]A=P(1+\frac{r}{n})^{tn}[/tex]A: amount accrued
P: principal amount
t: time, years
r: interest rate, expresed as a decimal value
n: number of coumpound periods
For this exericse
The principal amount is P=$1000
The time is t= 9 years
The interest rate is 9%/100=0.09
The compounding periods are 12/year (the interest is compounded monthly) so for the 9 year time period is 9*12=108
[tex]\begin{gathered} A=1000(1+\frac{0.09}{108})^{9\cdot108} \\ A=2247.15 \end{gathered}[/tex]Tell weather the ratios form proportion 3/11 and 17/6True or False
Answer:
False
They are not proportional
Writing a Works Cited Page
Short Writing Active
Prompt
Create a properly formatted works cited page for a research paper about the Little Rock Nine. Include at least five sources to
support the research paper. Use the provided list of sources.
Select the link below to view possible sources.
The Little Rock Nine were a group of African American students who were held by the National Guard on September 4, 1957, while attending class at Little Rock Central High School in Little Rock, Arkansas.
What is about Little Rock Nine?The Little Rock Nine were a group of African American students who were held by the National Guard on September 4, 1957, while attending class at Little Rock Central High School in Little Rock, Arkansas. This incident is regarded as one of the pivotal moments in American civil rights history.For many years, the educational system in the United States was segregated, with white students receiving a considerably better and more effective education. In Brown v. Board of Education, the Supreme Court of the United States unanimously ruled that segregation in public schools was unconstitutional.The Little Rock issue, which was heavily covered by the media, revealed how the nine black students who chose to attend courses were originally barred from doing so on the governor of Arkansas's (Orval Faubus) instruction.To learn more about Little Rock Nine refer to:
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If f(1) = 9 and f(n) = 5f(n − 1) then find the value of f(4).
The value of f(4) is 1125.
Here,
we have given the value of f(1)=9 and f(n)=5f(n-1) and we have to find out the value of f(4).
From the above equation of f(n), it is clear that for finding value of f(4) we have to find value of f(3).
And for f(3) we have to find out the value of f(2)
So,
first, we will find out value of f(2) and then eventually value of f(3) and f(4) by using the given formula of f(n)
The given formula for f(n) is
f(n)=5f(n-1)
So,
f(2)=5f(2-1)
f(2)=5f(1)
f(2)=5×9
f(2)=45
Now,
f(3)=5f(3-1)
f(3)=5f(2)
f(3)=5×45
f(3)=225
And,
f(4)=5f(4-1)
f(4)=5f(3)
f(4)=5×225
f(4)=1125
Hence, we got
The value of f(4) is 1125.
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Math COLL, help me plis
Using trigonometric functions, the value of cos O in simplest terms is 5/17.
What are trigonometric functions?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (CSC).So, we know that: cos α = Adjacent Side/Hypotenuse
We have,
adjacent side = 5hypotenuse = 17OM = 17 and ON =5As we know,
cos O = Adjacent Side/HypotenuseWe obtain:
cos O = ON/OMcos O = 5/17Therefore, using trigonometric functions, the value of cos O in simplest terms is 5/17.
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Angles. Solve for Vaule of D
Divide. Reduce the answer to lowest terms. 5 2/3÷ 3 1/9 28/51 1 23/28 1 3/476 17 17/27 PWEASE HELP
The correct mixed fraction is 2) 1 [tex]\frac{23}{28}[/tex]
What is mixed fraction and improper function ?
A mixed fraction is one that has both a whole number portion and a proper fraction, and whose value is always larger than 1. A mixed number is, for instance, 3[tex]\frac{2}{5}[/tex]. A fraction is deemed inappropriate if the numerator is consistently greater than or equal to the denominator. 4/3, 7/3, 11/5, etc. are a few instances of incorrect fractions.
Here the given division is,
=> 5 [tex]\frac{2}{3}[/tex] ÷ 3 [tex]\frac{1}{9}[/tex]
=> [tex]\frac{15+2}{3}[/tex] ÷ [tex]\frac{27+1}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] ÷ [tex]\frac{28}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] * [tex]\frac{9}{28}[/tex]
=> [tex]\frac{51}{28}[/tex]
=> 1 [tex]\frac{23}{28}[/tex]
Hence the correct option is 2) 1 [tex]\frac{23}{28}[/tex]
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Solve for the unknown 8k-2k=42
ANSWER
k = 7
EXPLANATION
The unknown variable in this equation is k,
[tex]8k-2k=42[/tex]To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,
[tex]\begin{gathered} (8-2)k=42 \\ \\ 6k=42 \end{gathered}[/tex]And then, divide both sides by 6,
[tex]\begin{gathered} \frac{6k}{6}=\frac{42}{6} \\ \\ k=7 \end{gathered}[/tex]Hence, the value of k is 7.
solve each equation by Elimination:-6x-2y=22-12x+10y=-26
Answer: x = -2 and y = -5
We are given two system of equations
-6x - 2y = 22 ---------------- equation 1
-12x + 10y = - 26------------- equation 2
These two system of equations can be solve simultaneously using elimination method
Before we can apply elimination method, we need to make one of the variables equal in both equations
Let us eliminate x
To make the co -efficient of x equal in both equations, Multiply equation 1 by 2 and equation 2 by 1
-6x - 2y = 22 * 2
-12x + 10y = -26 * 1
This becomes
-6x * 2 - 2y* 2 = 22*2
-12x*1 + 10y *1 = -26 * 1
-12x - 4y = 44------------------- equation 3
-12x + 10y = -26 --------------- equation 4
To eliminate x, substract equation 4 from equation 3
-12x - (-12x) - 4y - (10y) = 44 - (-26)
-12x + 12x -4y -10y = 44 + 26
0 - 14y = 70
-14y = 70
Divide both sides by -14
[tex]\begin{gathered} \frac{-14y}{-14}\text{ = }\frac{70}{-14} \\ y\text{ = }\frac{70}{-14} \\ y\text{ = -5} \end{gathered}[/tex]To find x, substitute the value of y = -5 into equation 1
-6x - 2y = 22
-6x - 2(-5) = 22
-6x + 10 = 22
-6x = 22 - 10
-6x = 12
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}\text{ = }\frac{12}{-6} \\ x\text{ = }\frac{12}{-6} \\ x\text{ = -2} \end{gathered}[/tex]Hence, x = -2, and y = -5 : (-2, -5)
Which ordered pairs are in the solution set of 8x + 16y > 32? (select two ordered pairs).
The ordered pair which is solution of 8x+16y > 32 is (-3,5) , the correct option is (b) .
In the question ,
it is given that ,
the linear inequality is 8x+16y > 32 .
to find the solution set ,
we substitute the options that are given
Option(a)
Substituting (0,2) in 8x+16y > 32 ,
we get ,
8(0) + 16(2) > 32
32 > 32 ,
false , hence it is not a solution .
Option(b)
Substituting (-3,5) in 8x+16y > 32 ,
we get ,
8(-3) + 16(5) > 32
-24 + 80 > 32
56 > 32
true , yes it is the solution .
Option(c)
Substituting (-1,1) in 8x+16y > 32 ,
we get ,
8(-1) + 16(1) > 32
-8 + 16 > 32
8 > 32
False , hence it is not a solution .
Option(d)
Substituting (4,0) in 8x+16y > 32 ,
we get ,
8(4) + 16(0) > 32
32 + 0 > 32
32 > 32
False , hence it is not a solution .
The only solution that satisfy the inequality is (-3,5) .
Therefore , The ordered pair which is solution of 8x+16y > 32 is (-3,5) .
The given question is incomplete , the complete question is
Which ordered pair is in the solution set of 8x+16y > 32 ?
(a) (0,2)
(b) (-3,5)
(c) (-1,1)
(d) (4,0)
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Hi I’m confused on this question an I need help.
PLS
A gaming system costs $600 and is on sale for 25% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
O $450.00
O $472.50
O $150.00
O $157.50
Answer:
b) $472.50
Step-by-step explanation:
The sale price will be,
→ (600/100) × (100 - 25)
→ 6 × 75
→ $450
Now the final price will be,
→ 450 + ((450/100) × 5)
→ 450 + (4.5 × 5)
→ 450 + 22.5
→ $472.50
Hence, the price of $472.50.
The final price of the gaming system is $472.50, which is the correct answer would be option (B).
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
A gaming system costs $600 and is on sale for 25% off. After the discount, there is a 5% tax.
To determine the final price of the gaming system, we need to first calculate the discount and then add the tax.
The discount is 25% of the original price, or 25% x $600 = $150.00.
So the price after the discount is $600 - $150 = $450.00.
The tax is 5% of the price after the discount, or 5% x $450 = $22.50.
Therefore, the final price of the gaming system is $450 + $22.50 = $472.50.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
The possible length of segment AB is 27 < AB < 81
From the question, we have
In triangle ABC
AC = 27
CB = 54
Using Pythagoras theorem,
AC² = AB² + CB²
54² = AB² + 27²
AB = 47
The possible length of segment AB is 27 < AB < 81
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
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Simplify the fraction:
18
90
Answer: 1/5 would be your answer!
Divide them both by 18 and you get 1/5
hope this helps :)
4) Which is the best deal?OA) $56 for 25 gallonsB) $32.05 for 15 gallonsO C) $51.29 for 23 gallonsOD) $22.50 for 10 gallons
To know the best deal, we have to know which one gives us the least cost per gallon.
To do that we divide the price by the quantity or volume.
A) $56 for 25 gallons
[tex]\frac{56\text{ \$}}{25\text{ gal}}=2.24\text{ \$/gal}[/tex]B) $32.05 for 15 gallons
[tex]\frac{32.05\text{ \$}}{15\text{ gal}}\approx2.14\text{ \$/gal}[/tex]C) $51.29 for 23 gallons
[tex]\frac{51.29\text{ \$}}{23\text{ gal}}=2.23\text{ \$/gal}[/tex]D) $22.50 for 10 gallons
[tex]\frac{22.50\text{ \$}}{10\text{ gal}}=2.25\text{ \$/gal}[/tex]The best deal is B: $32.05 for 15 gallons, because it offers a price per gallon that is lower than the others.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
6 13/36 simplify and write it as a mixed number
what value is equivalent to the expression 5-2(3+9)+4?a= -15b= -23c= 33d= 40
5- 2(3+9) +4
Apply PEMDAS
First solve parentheses: (3+9) = 12
5- 2 (12) + 4
Then, the multiplication:
5- 24 + 4
Add and subtract
-15
a=-15
Reggie carves and sells wooden sculptures online. He uses the function f(x) = 15x + 60 to determine the selling price, f(x), for a sculptures that took him x hours to make. Which statement explains the meaning of the value of f(75)
Given data:
The given selling price funnction is f(x)=15x+60.
SUbstitute 75 for x in the given expression.
ff(75)=15(75)+60
=1125+60
=1185
So, the selling price obtained after 75 hours is 1,185.
Divide using synthetic division (x^3 - 4x + 6) ÷ (x+3) =
Answer:
Quotient = x² - 3x + 5
Remainder = 9
Explanation:
To make the synthetic division, we need to rewrite the dividend with all the degrees of the exponents, so:
x³ - 4x + 6 = x³ + 0x² - 4x + 6
Then, we will use the coefficient of each term: 1, 0, -4 and 6
On the other hand, the divisor should have the form (x - a), so:
x + 3 = x - (-3)
Therefore, a = -3, and we will use this number for the synthetic division.
Finally, the synthetic division is:
Where the first number goes down, then the blue -3 is calculated as the number as 1 x -3, and the yellow -3 is equal to the sum of the number numbers 0 and -3, so: 0 + (-3) = -3
In the same way, 9 = -3 x -3 and 5 = -4 + 9
Finally, -15 = 5 x -3 and -9 = 6 - 15
Now, the coefficients 1, -3, and 5 give us the quotient of the division, and -9 is the remainder. So, the solution of the division is:
[tex]\begin{gathered} quotient=x^2-3x+5 \\ \text{remainder}=-9 \end{gathered}[/tex]i need help understand exponential functions
Given:
Exponential function
Required:
To define the exponential function.
Explanation:
The exponential function is represented in the form of
[tex]y=a^x[/tex]Where a>1 and x represent the variable.
Here x is an independent variable and y is dependent, a is called the base. The value of the base is always constant.
The most important exponential function is
[tex]y=e^x[/tex]Where the value of e is 2.7182818.
Final Answer:
Explain in the explanation part.
if -(x-1)=4x-5-3x, then does x=3?
PROBLEMA 3 Con dos camiones cuyas capacidades de carga son respectivamente de 3 y 4 toneladas, se hicieron en total 23 viajes para transportar 80 toneladas de madera. ¿Cuantos viajes realizó cada camión?
El camión con capacidad de 3 toneladas viajó 12 veces y el camión con capacidad de 4 toneladas viajó 11 veces.
¿Cuántos viajes realiza cada camión?
En este problema encontramos dos camiones, uno de ellos con una capacidad de 3 toneladas y otro con capacidad de 4 toneladas, que desplazan 80 toneladas de madera en un total conjunto de 23 viajes. El total movido por cada camión es igual al producto del número de viajes y la capacidad de los camiones. Por tanto, el total desplazado de madera es igual a la siguiente ecuación:
3 · x + 4 · (23 - x) = 80
Donde x es la cantidad de viajes del camión de 3 toneladas de capacidad.
A continuación, despejamos la variable x:
3 · x + 4 · (23 - x) = 80
3 · x + 92 - 4 · x = 80
92 - x = 80
x = 92 - 80
x = 12
El primer camión viajó 12 veces y el segundo camión viajó 13 veces.
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Geometry Question: If the median to a side is a triangle is also an altitude to that side, then the triangle is isosceles. (#8 in picture)
8.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:
[tex]\begin{gathered} AM\cong MB \\ MC\cong CM_{\text{ }}Reflexive_{\text{ }}property \\ m\angle AMC\cong m\angle BMC_{\text{ }}Perpendicular_{\text{ }}bisector \end{gathered}[/tex]Therefore:
[tex]\Delta AMC\cong\Delta BMC_{\text{ }}SAS_{\text{ }}Theorem[/tex][tex]m\angle CAM\cong\angle CBM_{\text{ }}CPCTC[/tex]We can conclude that:
[tex]\Delta ABC[/tex]Is an isosceles triangle
Un equipo de fútbol asigna números de camiseta a sus jugadores usando la fórmula de 7y - 3x donde x e y se eligen al azar. ¿Qué número obtendrá un jugador si x=-2 y y = 4
Total number of players is 34.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.An algebraic expression is a mathematical phrase that includes variables, constants, coefficients, and algebraic operations.
Variables and constants can both be used in an algebraic expression.
It is given that a soccer team assigns jersey numbers to its players using the formula 7y - 3x where x and y are chosen at random.
Now, we have x = -2 and y = 4
Substitute these values in above expression we get,
7(4) - 3(-2) = 28 + 6 = 34
Therefore, total number of players is 34.
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For what value of x does 3²x _ g³x-4?
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
I believe your question is:
For what value of [tex]x[/tex] does [tex]3^{2x}=9^{3x-4}[/tex]?
—
First, rewrite [tex]9[/tex] as [tex]3^2[/tex]:
[tex]3^{2x}=(3^2)^{3x-4}[/tex]
Then, use exponentiation to apply the [tex](a^b)^c=a^{bc}[/tex] rule:
[tex]3^{2x}=3^{2(3x-4)}[/tex]
Rewrite the expression as a non-exponential one since the bases ([tex]3[/tex]) are equal on both sides:
[tex]2x=2(3x-4)[/tex]
Distribute the [tex]2[/tex]:
[tex]2x=6x-8[/tex]
Subtract [tex]6x[/tex] from both sides:
[tex]-4x=-8[/tex]
Divide both sides by [tex]-4[/tex]:
[tex]x=2[/tex]
1 What is the value of x? 45° m (2x - 5)° n
45, and
2x - 5
make up a straight angle pair.
So, they add up to 180 degrees.
Thus, we can write:
45 + 2x - 5 = 180
Now, we simply solve for x. Shown below:
[tex]\begin{gathered} 45+2x-5=180 \\ 2x+40=180 \\ 2x=180-40 \\ 2x=140 \\ x=\frac{140}{2} \\ x=70 \end{gathered}[/tex]find the slope of the line through each pair of points (2, -11), (7, -20)