Answer: 4.01% interest rate
This value is approximate. It is rounded to the nearest hundredth of a percent.
============================================
Work Shown:
A = P*e^(r*t)
1833 = 1500*e^(r*5)
1833/1500 = e^(5r)
1.222 = e^(5r)
e^(5r) = 1.222
5r = Ln(1.222)
5r = 0.2004888607494
r = 0.2004888607494/5
r = 0.04009777214989
r = 0.0401
r = 4.01%
Write an explicit formula for the sequence -13, -6, 1, 8, ...
a) an = -13n+7
b) an = -13+(n+7)
c) an = -13+7(n-1)
d) an = -13n+7
Answer:
c) an = -13+7(n-1)
Step-by-step explanation:
We can use the formula for arithmetic sequences
an =a1+d(n-1)
where a1 is the first term in the sequence
d is the common difference
and n is the term number
a1 is -13
d is found by taking the second term and subtracting the first term
d = -6--13
= -6+13
d=7
We are adding 7 each time
Substituting what we know,
an = -13 + 7(n-1)
The answer is:
c) [tex]a_{n}=-13+7(n-1)[/tex]Scenario: If the distance from person to the base of tree is 70 ft and the tree is 115 ft tall, how much does the person look up to see the top of the tree (i.e. Find the angle of elevation)? Note: you need to draw the triangle to figure out the layout on your own for this problem.
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
This is a right angle triangle.
Suppose the angle from person to top of the tree is x
Using SOH CAH TOA
Tan x = [tex]\frac{opposite}{adjacent}[/tex]
Tan x = [tex]\frac{115}{70}[/tex]
Tan x = 1.6428
taking tan inverse
x = 58.67 degrees
Means the person need to look up 58.67 degrees. : Answer
Hope it will help :)
Given h(x)=5(x-6)^2+2 what transformations were done compared to the parent function f(x)=x^2?
Answer:
1. Translation 6 units to the right.
2. Stretch by a factor 5.
3. Translation 2 units up.
Step-by-step explanation:
Consider parent function [tex]f(x)=x^2.[/tex]
1. Translate the graph of the function 6 units to the right. Then you get the function [tex]f_1(x)=(x-6)^2.[/tex]
2. Stretch the graph of the function [tex]f_1(x)=(x-6)^2[/tex] by a factor 5 and get the function [tex]f_2(x)=5(x-6)^2.[/tex]
3. Translate the graph of the function [tex]f_2(x)=5(x-6)^2[/tex] 2 units up to fet the function [tex]h(x)=5(x-6)^2+2.[/tex]
Kristy asks Lonnie to think of a number, and 3 to it, multiply the sum by 2, and then subtract 6. Let n stand for Lonnie's starting numbers. Which expression represents Lonnie's final number?
Answer:
2(n + 3) - 6 is the expression that represents the final number.
Step-by-step explanation:
-Given the number Lonnie thinks of at the beginning is 'n'-
1) adding 3 to n
sum = n + 3
2) multiply the sum by 2
sum = 2(n + 3)
3) subtract 6
sum = 2(n + 3) - 6.
Answer: 2(n + 3) - 6
Step-by-step explanation:
The bus comes at 6:55. It takes meg 19 minutes to get to the bus stop. What time would she have to leave at to catch the bus?
Answer:
6 hrs 36 mins
Step-by-step explanation:
Bus at 6:55
Minutes to get to the bus 19.
deduct 19 Minutes from 6:55 = 6 hrs 36 mins
Which is the graph of the line with equation:
y + 4 = 2(x−1)
Answer:
The graph in the first picture which intercepts the y-axis at (0,-6) and has a positive slope of 2.
Step-by-step explanation:
We can write the linear equation into slope-intercept form. We do this by simplifying and isolating y.
y+4=2(x-1)
y+4=2(x)-2(1)
y+4=2x-2
y+4-4=2x-2-4
y=2x-6
In y=mx +b form, we can connect the equation to the graph. This equation has b=-6 or (0,-6) for the y-intercept. It also has m=2 for the slope. This is the first graph.
Please help Mrs.Johnson spend $611 buying lunch for 78 students. If all lunches cost the same, about how much did she spend on each lunch
Answer:
$35.96 to 2.d.p. or 36 to 2.s.f.
Step-by-step explanation:
We can show this by:
611 = 78x
x being the 78 students
To find 1x which is the price of one student, or one lunch, we can simply divide both sides by 78:
[tex]\frac{611}{78} = \frac{78x}{78}[/tex]
Or:
35.95 = 1x
So each lunch cost 35.96 to 2.d.p. or 36 to 2.s.f.
PLEASE HELP. WILL GIVE BRAINIEST AND 60 POINTS if you show work so I can understand these.
1. Find the slope of the line that passes through the
points (-1, 2), (0, 5).
2. Suppose y varies directly with x, and y = 15 and x = 5.
Write a direct variation equation that relates x and y.
What is the value of y when x = 9?
3. Write an equation in slope-intercept form of the line
that passed through (-3, 4) and (1. 4).
4. Use point-slope form to write the equation of a line
that has a slope of 2/3
and passes through (-3, -1).
Write your final equation in slope-intercept form.
5. Write the equation in standard form using integers
(no fractions or decimals): = −2/3 − 1
6. Write an equation of the line that passes through
(2, -1) and is parallel to the graph of y = 5x – 2. Write
your final equation in slope-intercept form.
7. Write an equation of
1) use change in y/change in x to find the slope from two points:
change in y: 5-2=3
change in x: 0-(-1)=1
3/1=3 is your slope
2) if it is a direct variation, you know as x increases, y increases, both at constant rates
since y is 10 more than x in the example, it will always be 10 more than x
y=x+10 is your equation.
when x=9, y=19
now they could not be reffering to their difference in addition, but their difference in multiplication. In that case, y is 3 times x in the example, so it will always be 3 times x
y=3x is your equation
when x=9, y=27
3) the slope of this line is determined by change in y over change in x:
change in y: 4-4=0
you don't need to calculate the change in x because 0 divided by anything is 0, so that is your slope.
y=0x+b
4=0(1)+b
4=0+b
4=b
y=4 is your equation because 0 times x is zero. this means that it is a horizontal line with a constant y value of 4
4)
y - value of y in a point =slope (x - value of x in a point)
y-(-1)=2/3 * (x-(-3))
y+1=2/3x+2/3(3)
y+1= 2/3x+2
y=2/3x+1
from solving point slope form, you can get to slope intercept form
5) not sure what this question is asking for
- a line?
- an expression equivalent to -1 and 2/3?
both of those aren't possible with the information given
6) parallel means same slope different y intercept
y=5x+b
-1=5(2)+b
-1=10+b
-11=b
y=5x-11
What type of exponential equation is shown?
y = C(1 - r)t
Exponential growth
Compound interest
Exponential decay
Quadratic
Answer:
Exponential Decay or Growth
Step-by-step explanation:
[tex]y=C(1-r)^t[/tex] represents an exponential.
When r is greater than 0 but less than 1, the function decays by decreasing the values through the rate.
When r is less than 0 or negative, the function grows by increasing the values through the rate.
I rent a gym for $150.00 for 30 students. Another time I rent the gym for $270.00 for 70 students. I need to find a fixed rate.
(y= mx+b)
Answer: y = 3x + 60
Step-by-step explanation:
Set up two equations and solve the system:
270 = 70x + b
- (150 = 30x + b)
120 = 40x
3 = x
Input "x" into one of the equations and solve for "b":
150 = 30x + b
150 = 30(3) + b
150 = 90 + b
60 = b
Equation: y = 3x + 60
This means that there is a flat fee of $60 plus a rate of $3 per student
The fixed rate of gym fee of $60 plus a rate of $3 per student.
The fixed-rate is;
[tex]\rm y=3x+60[/tex]
Given
I rent a gym for $150.00 for 30 students.
Another time I rent the gym for $270.00 for 70 students.
Linear function;A linear function is a function that forms a straight line in a graph.
Let x be the number of students and y be the total cost of renting the gym.
To find the fixed-rate let us write the equation of line representing the total cost of renting a gym for x students.
The equation representing a fixed rate is;
[tex]\rm y = mx+b[/tex]
I rent a gym for $150.00 for 30 students.
[tex]\rm 150 = 30x + b[/tex]
Another time I rent the gym for $270.00 for 70 students.
[tex]\rm 270 = 70x + b[/tex]
Subtracting both the equations;
[tex]\rm 150-270=30x+b-70x-b\\\\-120=-40x\\\\120=4x\\\\x=\dfrac{120}{4}\\\\x=3[/tex]
Substitute the value of x in equation 1
[tex]\rm 150 = 30x + b\\\\150=30(3)+b\\\\150=90+b\\\\b=150-90\\\\b=60[/tex]
Therefore,
The fixed-rate is;
[tex]\rm y=mx+b\\\\y=3x+60[/tex]
Hence, the fixed rate of gym fee of $60 plus a rate of $3 per student.'
To know more about linear function click the link given below.
https://brainly.com/question/371915
Real estate values in a town are increasing at a rate of 7% per year. Ms. Keene purchased a building for $245,000 in 2015. How much can she expect to sell the building for in 2020, assuming this trend continues? Enter your answer in the box. Round to the nearest whole dollar.
This is an exponential growth problem.
The formula for this is:
y = a(1+rate)^time
a = the starting value = 245,000
Rate is the percent of increase written as a decimal = 7% = 0.07
Time would be the number of years from the starting year to the year you are trying to find: 2020 - 2015 = 5 years
Now you have y = 245000(1 + 0.07)^5
Simplify:
245000(1.07)^5
Calculate:
New value = $343,625
Please help ASAP!
What is the value of cosθ given that (−5, −4) is a point on the terminal side of θ ?
A). 5√41/41
B). −4√41/41
C). 4√41/41
D). −5√41/41
Answer:
D
Step-by-step explanation:
The value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
What are trigonometric expressions?
Trigonometric expressions are the ratios of the sides of a right triangle, which are always constant despite the increase or decrease in the size of its sides.
These are the trigonometric ratios:
sin θ = perpendicular/hypotenusecos θ = base/hypotenusetan θ = sin θ/cos θ = perpendicular/basecot θ = 1/tan θ = cos θ/sin θ = base/perpendicularsec θ = 1/cos θ = hypotenuse/basecosec θ = 1/sin θ = hypotenuse/perpendicular.How to solve the question?In the question, we are asked to find the value of cos θ, given that (-5, -4) is a point on the terminal side of θ.
This means that we; are in quadrant III. As we know, cos θ is negative in the 3rd quadrant.
The base is the distance of the x-coordinate from the origin, that is, 5 units.
The perpendicular is the distance of the y-coordinate from the origin, that is, 4 units.
By Pythagoras' Theorem,
Hypotenuse² = Base² + Perpendicular²,
or, Hypotenuse² = 5² + 4²,
or, Hypotenuse² = 25 + 16,
or, Hypotenuse = √41.
As we know, cos θ = Base/Hypotenuse = 5/√41 = 5√41/41.
Because of the 3rd quadrant, we will take, cos θ = - 5√41/41.
Thus, the value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
Learn more about trigonometric expressions at
https://brainly.com/question/19770283
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Sinea wants to spend money using the same ratios as on her last trip to the car nivel. If she spends $26 on games,how much will she spend on souvenirs? CHART Snacks Games Souvenirs Sinea $5 $8 $12 Ren. $10 $8 $20
Answer:
A. Sinea spends $26 on games, she wants to keep the same ratio, how much does she spend on souvenirs?
A- (snacks- 16.25) (games- 26) (souvenirs- 39)
B. Ren spends $5 on souvenirs, he wants to keep the same ratio, how much does he spend on snacks
B- (snacks- 2.5) (games- 2) (souvenirs- 5)
C. Both spend $40 on snacks, they want to keep their original ratio, who spends more on souvenirs?
C. Ratios
Sinea- (snacks- 40) (game- 64) (souvenirs- 96)
Ren- (snacks- 40) (game- 32) (souvenirs- 80)
Which person would be eligible to run for president of the United States in the Election of 2020?
A) Susan, born in 1988 in Texas, has lived in Georgia for 15 years
B)George, a naturalized citizen, has lived in New York for 20 years
C) Tiffany, born in 1973 in Nebraska, has lived in the U.S. for 45 years
D)John, a legal immigrant, has lived in the U.S. for 14 consecutive years
Answer:
C. Tiffany, born in 1973 in Nebraska, has lived in the U.S. for 45 years
Step-by-step explanation:
its right bro
heyyy help pls with pciutreeeee
Answer:
12 Fetches
Step-by-step explanation:
this one is easy but you probably overthought it,
since 2 is half of 4 then you would just multiply everything by 2
let's just say that didn't work right, for these types of problems you have to make a proportion so in this case it would be 2 minutes/6 fetches= 4 minutes/ x fetches. then you solve by cross multiplication.
Jina received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.51 per pound. After buying the coffee, she had $47.47 left on her card. How many pounds of coffee did she buy
Answer: 3 pounds
Step-by-step explanation:
The equation can be set up according to slope form: y=mx+b where x represents cost per round.
$70 = $7.51x + $47.47
Subtract 47.47 to both sides: $22.53 = $7.51x
Divide both sides by 7.51: 3 = x
Answer: 70 - 47.47 = 22.53. She spent $22.53. If one pound is $7.51. And she spent $22.53 = 3.
She bought 3 pounds of coffee. Brainliest is always appreciated. :)
The matrix shows the number of different basketball shots three players made in two minutes. These players want to double these results. Which matrix shows what the players want to do?
Answer:
B
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Answer:B. [10 2]
[6 4]
[8 4]
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Explanation:
As a general rule, to double, triple or as the case may be, the result of a matrix, we apply what is known in Maths as scalar multiplication.
Scalar multiplication seeks to multiply the entries in a matrix by a scalar. The resulting matrix is called the scalar product of the original matrix.
For instance:
Let matrix A = [a b] [c d] and k be a scalar.
The matrix kA is called a scalar product of the matrix, A and the constant, k is defined as:
kA = k [a b] [c d]
= [ka kb] [kc kd]
So, for the given question, the best option would be the matrix that depicts a scalar multiple of 2 of the original matrix entry. Option B.
I.e:
Javi = 2[5 1] = [2*5 2*1] = [10 2]
Victor= 2[3 2] = [2*3 2*2] = [6 4]
Chris = 2[4 2] = [2*4 2*2] = [8 4]
Caitlan went to the store to buyschool clothes . She has store credit from a previous return in the amount 39.58. If she bought 4 of the same style shirt in different colors and spent total of 52.22 after the store credit was taken off he total, what was the price of each shirt ahe bought? Write and solve and equation with integrr coefficients
Answer:
Each shirt costs $22.95
Step-by-step explanation:
39.58 + 52.22 = 91.80
91.80/4= 22.95
Final answer:
Caitlan bought 4 shirts for a total cost of $91.80. Therefore, the price of each shirt was $22.95.
Explanation:
To find the price of each shirt Caitlan bought, we can use the equation:
x - 39.58 = 52.22
where x represents the total cost of the shirts before the store credit is applied. To solve for x, we can add 39.58 to both sides of the equation:
x = 52.22 + 39.58 = 91.80
Since Caitlan bought 4 shirts, we can divide the total cost by 4 to find the price of each shirt:
91.80 / 4 = 22.95
Therefore, the price of each shirt Caitlan bought was $22.95.
please help me ill give brainliest
Answer:
The answer would be remove two negative tiles.
Step-by-step explanation:
-5-(-2) becomes -5+2, and since the latter aren't of the same sign, you'd subtract two negative tiles so that it gives you the answer, which would be -3.
How to:
-5-(-2)
-5+2
= -3
Answer:
B) Remove 2 negative tiles
Step-by-step explanation:
-5 - (-2)
-5 + 2 [-(-2) = +2]
= -3
Remove two negative tiles
Answer: Remove 2 negative tiles
Under a dilation, the point (2, 6) is moved to (6, 18).
What is the scale factor of the dilation?
Divide the new X value by the original x value:
6 / 2 = 3
Then check that with the Y value:
Original Y value = 6, 6 x 3 = 18, which is the new Y value.
This means the scale factor is 3.
A graph is translated according to the following rule. Describe the translation.
(x, y) → (x, y – 3)
The graph is translated three units to the right.
The graph is translated three units to the left.
The graph is translated three units down.
The graph is translated three units up.
Answer:
The graph is translated three units down.
Step-by-step explanation:
We know that, a 'Translation' is an transformation where the figure or graph is shifted in any direction.
According to our question (x,y) becomes (x, y-3) , this means that the graph value of 'x' co-ordinate remains same and the value of 'y' co-ordinate is decreased by 3 units.
So, the graph is shifted three units downwards i.e. it is translated three units down.
Which of the following is a root of the polynomial function F(x)=x^4+2x^3-3x^2-6x?
Answer: x = 0, √3, -√3, -2
Step-by-step explanation:
x⁴ + 2x³ - 3x² - 6x
= x (x³ + 2x² - 3x - 6)
= ↓ x²(x + 2) -3(x + 2)
= x (x² - 3)(x + 2)
= x(x - √3)(x + √3)(x + 2)
Set each factor equal to zero to find the roots:
x = 0 x - √3 = 0 x + √3 = 0 x + 2 = 0
x = √3 x = -√3 x = -2
Bernie's car used 100 cups of gasoline during a drive he paid 3.12 per gallon for gas how much does it gas cost
Answer:
19.50
Step-by-step explanation:
There are 16 cups in a gallon. Divide 100 into 16 to get 6.25. You now just multiply 3.12 by 6.25 to get 19.5. Your answer is $19.50.
I cell phone company charges $40 per month plus a $35 activation fee Write anExpression for the total cost for M months
Answer:
$35 + $40M
Step-by-step explanation:
A cell phone company charges per month fees = $40
and an activation fee = $35
Total cost = Activation fees + ($40 × total number of months)
So the expression for the total cost for M months will be
$35 + $40M
Please answer this question!! 41 points and brainliest!
Answer:
x > -3
Step-by-step explanation:
5x+ 7 > 2(x-1)
Distribute the 2 on each side
5x+7 > 2x -2*1
5x+7 > 2x-2
Subtract 2x from each side
5x-2x +7 > 2x-2x-2
3x + 7>-2
Subtract 7 from each side
3x+7-7>-2-7
3x>-9
Divide by 3 on each side
3x/3 >-9/3
x > -3
Answer:
[tex]x>-3[/tex]
Step-by-step explanation:
To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.
We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.
[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]
To graph, we draw a number line, draw an open circle at -3.
Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3
A square lawn is surrounded by a path 2.5 m wide . If the area of the path is 165 m sq, find the area of the lawn
Please answer quickly, more might be coming soon. 50 Points!
Answer:
2) ∠SDH and ∠SDT are right angles because SD ⊥ HT.
3) [tex]\bar{SH}\cong \bar{ST}[/tex] as it is given in the question.
4) [tex]\bar{SD}\cong \bar{SD}[/tex] is the reflexive property.
5) ΔSHD ≅ ΔSTD by RHS congruency.
Step-by-step explanation:
Given in the question:
[tex]\bar{SH}\cong \bar{ST}\\\bar{SD}\perp \bar{HT}[/tex]
In ΔSHD and ΔSTD
[tex]\bar{SH}\cong \bar{ST}[/tex] (Given)
[tex]\angle SDH\cong \angle SDT=90^o[/tex] (SD ⊥ HT)
[tex]\bar{SD}\cong \bar{SD}[/tex] (Common)
Therefore, [tex]\Delta SHD\cong \Delta STD[/tex] (By RHS rule)
Reflexive property of congruency is defined as the property in which something is equal to itself. Hence, the reflexive property of these two triangles is [tex]\bar{SD}\cong \bar{SD}[/tex]
Tommy notices that he reads 2/3 page in a minute. At the rate, how long will it take him to read 12 pages
Answer:
18 minutes
Step-by-step explanation:
To do this, you need to divide 12 by the two thirds to find out how many 2/3 there are in 12, giving the amount of minutes it takes:
12 ÷ 2/3 = 18
So it would take him 18 minutes!
Sara drives 425 miles in 6 hours and 45 minutes. What is her average rate of speed? Round your answer to the nearest whole number.
Answer: 63 miles per hour (mph)
6 hours + 45 minutes = 6 hrs + 0.75 hrs = 6.75 hrs
Divide the distance (425 miles) over the time (6.75 hours) to get the speed. You must convert the time value to a single unit rather than a mixed unit of hours and minutes. So we get 425/6.75 = 62.96926 which rounds to 63
Which equation is a quadratic model for the data set? Hint: Use a graphing calculator or a spreadsheet program.
Data table
Answer:
Equation for the quadratic model for the data set is;
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Step-by-step explanation:
A Quadratic regression is the process of finding the equation of the parabola that best fits the set of data.
An equation is in the form of: [tex]y=ax^2+bx+c[/tex] where a≠0.
You just enter the x-coordinates and y-coordinates in your graphing calculator and
then do a quadratic regression.
The equation of the parabola that best approximates the points is
:
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Now, plot the graph of the above equation as shown below in the figure.
Also you can see that the [tex]R^2[/tex] value for the above data is, 0.994