9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.
Step-by-step explanation:
The given is,
Type A is 10 feet tall and grows at a rate of 21 inches per year
Type B is 7 feet tall and grows at a rate of 25 inches per year
Step:1
Convert the rate of grows of tree inch to feet,
For Tree A,
Rate of grow, A = 21 inches per year
= 21 × 0.0833333 ( 1 inch = 0.0833333 feet)
= 1.75 feet per year
For Tree B,
Rate of grow, B = 25 inches per year
= 25 × 0.0833333 ( 1 inch = 0.0833333 feet)
= 2.08333 feet per year
Step:2
Difference in the tall of Tree A & B,
= 10 - 7
= 3 feet
Difference in the rate of grow of tree A & B,
= 2.08333 - 1.75
= 0.3333325 feet per year
Step:3
Year take to both trees are same height,
[tex]= \frac{Difference in the height of tree A & B}{Difference in the rate of grows of A & B}[/tex]
[tex]= \frac{3}{0.3333325}[/tex]
[tex]= 9.00[/tex]
= 9 years
Step:4
Check for solution,
Height of tree = Height of Tree + (Rate of grow × Years)
For A,
= 10 + ( 1.75 × 9 )
= 25.75 feet.........................................(1)
For B,
= 7 + ( 2.08333 × 9 )
= 25.74999
≅ 25.75 feet.....................................(2)
From Equation (1) and (2),
25.75 feet = 25.75 feet
Result:
9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.
What is the area of the trapezoid? [A = 1/2(b1 + b2)h]
A) 1249.5 sq cm
B) 162.75 sq cm
C) 105 sq cm
D) 38.75 sq cm
We can see that b1 = 18, b2 = 24, and h = 5
So, we can just substitute these in.
A = 1/2(18 + 24)5
A = 1/2 * 42 * 5
A = 21 * 5
A = 105
So, the answer is C. 105 sq cm
Answer:
105
Step-by-step explanation:
you just have to plug in your variables
The diagonal of a square measures 16 inches. What is the length of the sides?
Answer:
The length of the sides is 8[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Since the diagonal divide a square into 2 45-45-90 triangles:
The diagonal is the hypotenuse of the triangle
Divide 16 by [tex]\sqrt{2}[/tex] and you will get 8[tex]\sqrt{2}[/tex].
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5p coins weigh approximatly 3g wat would be the weight of £5 worth of 5p coins
Answer:
3g
Step-by-step explanation:
Since 5p=3g
5p=x
So let's solve by cross multiplying
5px=3g×5p
5px=15gp
Divide both sides by 5p
x=3g
Therefore the final answer is 3g
You work 40 hours a week at a factory and make $2.00 per piece you create. It takes you
1 hour to create 5 pieces, how much money do you make per week?
I have to show work for the problem.
Answer:
400
Step-by-step explanation:
1 hour = 5 pieces • $2
1 hour = $10 bcas each piece you make is $2
40 hours = $400 because you get $10 per week
You earn $400 per week
Answer:
$400
Step-by-step explanation:
S x H = (1 x 5 x 2) x 40
S x H = (1 x 10) x 40
S x H = 10 x 40
S = 400
S = $400 H = 40
What is the total area of the following composite figure? Please answer ASAP for #34points
54.28 ft 2
73.12 ft 2
60.56 ft 2
98.24 ft 2
60.56 square feet, the area of the semicircles equates to 12.56 and the rectangle area is 48 so all you have to do is add them
Answer:
It is 60.56 ft2
Step-by-step explanation:
Hope this helps
What is the first step in evaluating the expression 3 × (5 + 4) – 27 ÷ 9?
Step-by-step explanation:
According to BODMAS
the first way to evaluate the expression is starting from brackets.,
=3 * 9 -27 / 9
= 3 * 9 - 3
= 27- 3
=24
Answer:
Parenthesis.
Step-by-step explanation:
Parenthesis
Exponent
Multiply or
Divide
Add or
Subtract
PEMDAS is the order to solve expressions like so.
HELP.The grades students scored on the most recent math exam are shown on the histogram below. How many students took the exam? A. 100 B. 85 C. 95 D. 90
Help me please!!....
Answer:
J
Step-by-step explanation:
As you can see, the peak occurs at (2,6). That means that all values below 6 are in the range.
A town has a population of 17000 and grows at 3% every year. To the nearest year, how long will it be until the population will reach 20400
Answer:
The population will reach 20,400 after 6 years.
Step-by-step explanation:
Exponential function:
[tex]y(t)=y_0(1+r)^t[/tex]
y(t)= Population after t years
[tex]y_0[/tex] = initial population
r= rate of grow
t= time.
A town has a population of 17,000 and grows at a rate 3% every year.
y(t)= 20,400, [tex]y_0[/tex] = 17,000, r=3%=0.03, t=?
[tex]20,400=17,000(1+0.03)^t[/tex]
[tex]\Rightarrow \frac{20,400}{17,000}=(1.03)^t[/tex]
[tex]\Rightarrow \frac{102}{85}=(1.03)^t[/tex]
Taking ln function both sides
[tex]\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|[/tex]
[tex]\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|[/tex]
[tex]\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}[/tex]
⇒ t = 6 year.
The population will reach 20,400 after 6 years.
Answer:
6
Step-by-step explanation:
deltamath
Find the volume of a pyramid with a square base, where the side length of the base is
8.3 in and the height of the pyramid is 7.3 in. Round your answer to the nearest
tenth of a cubic inch.
The volume of the pyramid is 167.6 cube inch (approx).
Step-by-step explanation:
Given,
Each length (l) of the base of the pyramid = 8.3 in
Height(h) of the pyramid = 7.3 in
To find the volume of the pyramid.
Formula
Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height
Area of the base = l²
Now,
The volume of the pyramid = [tex]\frac{1}{3}[/tex]×l²×h
= [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)
The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.
Explanation:To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.
Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.
if 48 is 92 percent than what is 100 percent
Answer:
Approximately 53
Step-by-step explanation:
92% of 53 is 48.76, there is no way to use a whole number and get exactly 48, which is why it is approximately
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A ranch experienced growth of its gopher population at a 1.5% annual rate, compounded continuously. At the end of a 3 year period, the population had reached a size of 78 gophers. How many gophers were on the ranch at the beginning of the 3 years according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
Answer:
75 gophers (about)
Step-by-step explanation:
We will use continuous compounding interest formula:
[tex]P(t)=P_0e^{rt}[/tex]
Where
P(t) is final value (at time t)
P_0 is initial value
r is the compounding rate
t is the time period
Given:
P(t) = 78
r is 1.5% or 1.5/100 = 0.015
t is 3
We solve for P_0, what we want, using algebra as shown below:
[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]
So, the initial population was 75 gophers.
The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.
To solve this problem, we can use the following exponential growth function:
P(t) = P_0 * e^(rt)
where:
P(t) is the population at time t
P_0 is the initial population
r is the annual growth rate
t is the time in years
We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.
So, we can plug in the following values into the exponential growth function:
P(3) = 78 = P_0 * e^(0.015 * 3)
Dividing both sides by e^(0.015 * 3), we get:
P_0 = 78 / e^(0.015 * 3)
Using a calculator, we can evaluate P_0 to be approximately 75.0.
Rounding up to the nearest whole number, we get an initial population of 75 gophers.
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Use the distributive property to factor the expression below.
-15x²y² + 25xy²
[tex]-15x^2y^2+25xy^2=5xy^2(-3x+5)\:or\:-5xy^2(3x-5)[/tex]
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A trapezoid has vertices A(-5, 4), B(-3, 2), C(-7, -2).
and D(-7, 2). It is transformed according to the rule ry-axis o
T(-2.3).
What are the coordinates of C"?
(-9,5)
(-9, -1)
(5, 1)
(9, 1)
Answer:
d-(9,1)
Step-by-step explanation:
Answer:
(9,1)
Step-by-step explanation:
correct on edge
I need help plz only one question
What is the arclength of PQ
Given:
θ = 54°
Radius = 10 in
To find:
The arc length of PQ
Solution:
Arc length formula:
[tex]$\text{Arc length}=2 \pi r\left(\frac{\theta}{360^\circ}\right)[/tex]
[tex]$\text{Arc length}=2 \times 3.14 \times 10\left(\frac{54^\circ}{360^\circ}\right)[/tex]
= 9.42 in
The arc length of PQ is 9.42 inches.
What is the value of y? PLEASE HELP ASAP!
Answer:
y = 40 degrees can i have branliest
Step-by-step explanation:
All angles in a triangle add up to 180
180 - 50 = 130
3y + 10 = 130
3y = 120
y = 40
Answer:
c
Step-by-step explanation:
put the following equation of a line into slope-intercept form, simplifying all fractions. 4x + 3y = -3
The slope-intercept form of the equation 4x + 3y = -3 is y = -4/3x - 1. The slope of the line is -4/3 and the y-intercept is -1.
Explanation:The question asks to convert the equation 4x + 3y = -3 into slope-intercept form, and simplify all fractions. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
To transform the given equation into this form, we need to express it in terms of y. Here are the steps:
Subtract both sides of the equation by 4x, we get: 3y = -4x -3.Next, divide each term by 3 to isolate y: y = -4/3x - 1. Therefore, the slope-intercept form of the equation is y = -4/3x - 1.In this equation, the term -4/3 is the slope and the -1 is the y-intercept. That means the line decreases for every 4 units in the y-axis when it increases 3 units in the x-axis.
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The average price of a gallon of milk is $3.31. If the price increases .88% each year , how much will a gallon of milk cost in 20 years?
Answer:
$3.94
Step-by-step explanation:
You will need to use the compound interest formula for this.
[tex]P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
Your equation will look like this:
[tex]3.31(1+\frac{.0088}{1} )^{20}[/tex] = 3.94
15. f(x) = (x - 2)
Find f(-2)
Answer:
f (-2)=(-2)-2
= -4
By putting value of x= -2 in f (x)
The radius of a circle is 7m. Find the diameter. (Do not include unit)
Answer:
14
Step-by-step explanation:
The diameter of a circle is twice the radius
d = 2*r
d = 2*7
d =14 m
Answer:
diameter = 14
Step-by-step explanation:
given that the radius of a circle = 7m
diameter = ?
recall that the formulae for finding the diamer = 2 x radius
diameter = 2 x 7
diameter = 14
(x2 + 5x – 3) + (3x2 – 4x + 5)
(6x-3)+(7x-7)
Hope I helped :d
Answer:
[tex]4x^{2} +x+2[/tex]
Put all the division problems that have an estimated quotient of 12 into the box.
8/0.95
18/2.2
47.6/3.9
10.6/1.89
71.9/6.5
123.4/9.2
157.4/16.4
The division problems 123.4/9.2 and 71.9/6.5 have an estimated quotient of 12 by considering 123.4 as 120, 9.2 as 10, 71.9 as 70, and 6.5 as 6.
Explanation:The division problems with an estimated quotient of around 12 will be the ones where you divide a number close to 120 by 10. In this case, it comes to be 123.4/9.2 and 71.9/6.5. To estimate the quotient, you can consider 123.4 as approximately 120 and 9.2 as approximately 10. Similarly, 71.9 can be considered as approximately 70 and 6.5 as approximately 6. When you divide these estimate numbers, both quotients are close to 12.
Estimation is a useful skill in Mathematics that allows you to simplify complex problems and get close to the exact answer. It's particularly helpful in situations where you only need a rough estimate and not the exact figure.
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how do you write 2/16 as a percent?
Answer:
[tex]\huge\boxed{\dfrac{2}{16}=12.5\%}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\dfrac{2}{16}=\dfrac{2:2}{16:2}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{8}\cdot100\%=\dfrac{100}{8}\%=12.5\%\\\\\text{Other method.}\\\\\dfrac{1}{8}=\dfrac{1\cdot125}{8\cdot125}=\dfrac{125}{1000}=\dfrac{125:10}{1000:10}=\dfrac{12.5}{100}=12.5\%[/tex]
Point A is at (-7,-7) and point M is at (-6,-1). Point M is the midpoint of point A and point B. What are the coordinates of point B?
Step-by-step explanation:
M is the mid point of AB
here given A ( - 7 , -7) and M ( -6 , -1) Let the coordinates of point B be ( x1, y1)
Now
( - 6 , -1 ) = {( x1 - 7)/ 2 , ( y1 - 7) / 2}
Equating
-6 = x1 -7 -1 = y1 - 7
2. 2
-12 = x1 - 7. -2 = y1 - 7
x1 = -12 +7. y1 = -2 +7
Therefore x1 = - 5. Therefore y1 = 5
Therefore the coordinates of B is ( -5 , 5)
Answer:
the coordinates of B is ( -5 , 5)
Step-by-step explanation:
What number makes the equation true? Enter the answer in the box.
24-
=4
suppose for everyone cup of rice I add 2 3/4 cups of water. If I add 2 1/2 cups of rice, how much cups of water do I add?
Answer:
6 7/8
Step-by-step explanation:
Since 1 cup of rice is added to 2 3/4 water
We are to determine the Amount of water to be to 2 1/2 cups of rice
Let the unknown number for water be x
So let's solve
1 cup of rice=11/4 water
5/2 cup of rice=x water
Cross multiply
x=5/2×11/4
x=55/8
X=6 7/8
Therefore,6 7/8 water is needed
The area of a circular window is 113.04 square inches. What is the diameter of the window? Use 3.14 for pi.
Answer: 12inches
Step-by-step explanation:
Area of a circle= 113.04square inches
Area of a circle =pir^2
Pi=3.14
R=?
So we are looking for the radius and from there we will get the diameter
Area=pir^2
113.04=3.14×r^2
R^2= 113.04/3.14
R^2=36
R=square root of 36
R= 6
Diameter =2r
Diameter = 2×6
Diameter = 12inches
Answer:
12 inches
Step-by-step explanation:
3.14 × r² = 113.04
r² = 36
r = 6
Diameter = 2r = 12
Solve the system of equations
5x + 3y = -2
3x + 2y = -1
Answer:
Step-by-step explanation:
Bob is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $76 and allows unlimited mileage.
Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
m = the number of miles driven
Company A cost = 76
[they charge $76 for unlimited mileage, so they don't charge by the miles driven]
Company B cost = 0.70m + 55
[they charge an initial fee of $55 plus $0.70 per mile(m)]
For what mileages will Company A charge less than Company B?
Company A cost < Company B cost -----> 76 < 0.70m + 55
To solve for m, isolate/get the variable "m" by itself in the inequality:
76 < 0.70m + 55 Subtract 55 on both sides
76 - 55 < 0.70m + 55 - 55
21 < 0.70m Divide 0.70 on both sides to get "m" by itself
[tex]\frac{21}{0.70} <\frac{0.70m}{0.70}[/tex]
30 < m [m is any number greater than 30]
Company A will charge less than Company B for mileages over/greater than 30.
Final answer:
Company A will charge less than Company B when more than 30 miles are driven; the inequality used to determine this is 76 < 55 + 0.70m, and after solving, it shows that m > 30.
Explanation:
To find out for what mileages Company A will charge less than Company B, we need to set up an inequality based on the given price structures for both companies:
Company A charges a flat rate of $76 per day, regardless of mileage.
Company B charges an initial fee of $55 plus $0.70 per mile driven.
The inequality to represent this scenario is:
76 < 55 + 0.70m
To solve for m (the number of miles driven), we subtract 55 from both sides:
21 < 0.70m
Then, divide both sides by 0.70 to isolate m:
m > 30
So, Company A will charge less than Company B when Bob drives more than 30 miles.