A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 22 inches and a height of 66 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 44 inches. What will the height of the new cones be?
Final answer:
The height of the new cones will be 16.5 inches.
Explanation:
To find the height of the new cones, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
Let's denote the radius of the new cones as r2 and the height of the new cones as h2. We know that the volume of the new cones will be the same as the volume of the existing cones:
(1/3)π(r2)^2h2 = (1/3)π(r1)^2h1
Substituting the given values, r1 = 22 inches (radius of existing cones) and h1 = 66 inches (height of existing cones), we can solve for h2:
(1/3)π(44)^2h2 = (1/3)π(22)^2(66)
Dividing both sides by (1/3)π(44)^2, we get:
h2 = h1(r1/r2)^2
Plugging in the values, h1 = 66 inches and r1 = 22 inches, and r2 = 44 inches, we can calculate:
h2 = 66(22/44)^2
h2 = 66(1/2)^2
h2 = 66(1/4)
h2 = 66/4
h2 = 16.5 inches
A video streaming service offers unlimited movies for 15 dollars a month or 1.99 per movie. Which offer is better
Answer:15 dollar a month movie offer is
Use the following function rule to find h(2y+6). Simplify your answer.
h(u)=
-
9u–3
h(2y+6)=
Answer:
Value of h(2y+6) = -18y -57
Step-by-step explanation:
Given the function rule:
h(u) = -9u -3 ......[1]
To find h(2y+6)
Substitute u = 2y + 6 in [1] we get;
h(2y+6) = -9(2y+6) - 3
Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
h(2y+6) = - 18y - 54 - 3 = -18y - 57
Therefore, the value of [tex]h(2y+6) = -18y - 57[/tex]
Bryan started to evaluate a decimal expression. 2.5(42 ÷ 3.2 – 10(0.2) + 3)– 5.2 2.5(16 ÷ 3.2 – 10(0.2) + 3) – 5.2
Bryan's next step should look like: [tex]\[37.3 - 5.2\][/tex].
To evaluate the given expression, Bryan should follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
Start with what's inside the parentheses:
[tex]\(42 / 3.2 = 13.125\)[/tex], and [tex]\(10(0.2) = 2\)[/tex]. So, inside the parentheses, we have: [tex]\(16 - 2 + 3 = 17\)[/tex].
Multiply and divide from left to right:
[tex]\(2.5 \times 17 = 42.5\).[/tex]
Substitute back into the expression:
[tex]\(42.5 - 5.2\).[/tex]
Complete the subtraction:
[tex]\(42.5 - 5.2 = 37.3\).[/tex]
Therefore, Bryan's next step should look like:
[tex]\[37.3 - 5.2\][/tex]
After this step, Bryan would perform the subtraction to find the final result. Following PEMDAS ensures that each operation is carried out correctly, leading to the accurate evaluation of the expression.
What is the recursive rule for this geometric sequence?
1, 3, 9, 27, ...
Enter your answers in the boxes.
A recursive rule for a geometric sequence:
[tex]a_1\\a_n=r\cdot a_{n-1}[/tex]
[tex]a_1=1,\ a_2=3,\ a_3=9,\ a_4=27\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\to r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=3\\\\\boxed{a_1=1,\qquad a_n=3\cdot a_{n-1}}[/tex]
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answer:
Option A is correct.
Value of [tex]S_{22} = 15.4[/tex]
Step-by-step explanation:
Given: [tex]a_{12} = 2.4[/tex] and common difference(d) = 3.4
A sequence of numbers is arithmetic i.e, it increases or decreases by a constant amount each term.
The sum of the nth term of a arithmetic sequence is given by;
[tex]S_n =\frac{n}{2}(2a+(n-1)d)[/tex], where n is the number of terms, a is the first term and d is the common difference.
We also know the nth tern sequence formula which is given by ;
[tex]a_n = a+(n-1)d[/tex] ......[2]
First find a.
it is given that [tex]a_{12} = 2.4[/tex]
Put n =12 and d=3.4 in equation [2] we have;
[tex]a_{12} = a+(12-1)(3.4)[/tex]
[tex]a_{12} = a+(11)(3.4)[/tex]
2.4 = a + 37.4
Simplify:
a = - 35
Now, to calculate [tex]S_{22}[/tex]
we use equation [1];
here, n =2 , a =-35 and d=3.4
[tex]S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))[/tex]
[tex]S_{22} = (11)(-70+21(3.4))[/tex]
[tex]S_{22} = (11)(-70+71.4)[/tex]
[tex]S_{22} = (11)(1.4)[/tex]
Simplify:
[tex]S_{22} = 15.4[/tex]
Therefore, the sum of sequence of 22nd term i.e, [tex]S_{22} = 15.4[/tex]
Answer:
A. 15.4
Step-by-step explanation:
factor 4x^2+81 over the set of complex numbers
Answer:(2x + 9i)(2x - 9i)
Step-by-step explanation:
a^2 - b^2 = (a+b)(a-b)
a^2 + b^2 = (a+bi)(a-bi) = a^2 + abi - abi - b^2 i^2
But -b^2 i^2 = +b^2
Answer:
[tex](4x+9i)(4x-9i)[/tex]
Step-by-step explanation:
Here, we have to apply this complex numbers property:
[tex]a^2 + b^2 = (a+bi)(a-bi)[/tex]
So, the given expression [tex]4x^2+81[/tex], can be rewrite as factor using the property:
[tex]4x^2+81=(4x+9i)(4x-9i)[/tex]
Because, if
[tex]a^2=x^2 \ and \ b^2=81\\\ then \ a=x \ and \ b=9[/tex]
Therefore, the factors are [tex](4x+9i)(4x-9i)[/tex]
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
0
2
1
cannot be determined
So to find the number of solutions this quadratic equation has without actually solving the equation, we are going to be using the discriminant formula. Plug in the numbers and solve:
[tex]D=5^2-4*1*7\\D=25-28\\D=-3[/tex]
Now, here are the rules with discriminants:
D > 0; there are 2 real solutions in the equationD = 0; there is 1 real solution in the equationD < 0; there are no real solutions in the equationAnswer:Since -3 is less than 0, this means that there are 0 real solutions in this equation.
Answer:
0 real solutions in this equation.
Can someone answer each step of this correctly?
About Slope - Intercept Form:
y = mx + bm is the slopeb is the y-interceptAbout Standard Form:
Ax + By = CA & B & C are integersA & B are both non-zeroThis form is good to use when wanting to find the x & y intercepts of a lineAbout Point - Slope Form:
Y - Y1 = m (x -X1)Y1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineOther Info:
Remember, y comes before the x An ordered pair from your problem: (-3,1), -3 is x & 1 is y & x is before the yAn ordered pair from your problem: (3,5), 3 is x & 5 is y & x is before the yFor the graph, the vertical line is yFor the graph, the horizontal line is xHope this information helps!!! :)
You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay model for the value of the stereo system in terms of the number of years since the purchase. b. What is the value of the system after 2 years? c. When will the stereo be worth half the original value?
Answer:
a. [tex]y=830*(0.87)^x[/tex]
b. The value of stereo system after 2 years will be $628.23.
c. After approximately 4.98 years the stereo will be worth half the original value.
Step-by-step explanation:
Let x be the number of years.
We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.
a. Since we know that an exponential function is in form: [tex]y=a*b^x[/tex], where,
a = Initial value,
b = For decay b is in form (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
[tex]13\%=\frac{13}{100}=0.13[/tex]
Upon substituting our given values in exponential decay function we will get
[tex]y=830*(1-0.13)^x[/tex]
[tex]y=830*(0.87)^x[/tex]
Therefore, the exponential model [tex]y=830*(0.87)^x[/tex] represents the value of the stereo system in terms of the number of years since the purchase.
b. To find the value of stereo system after 2 years we will substitute x=2 in our model.
[tex]y=830*(0.87)^2[/tex]
[tex]y=830*0.7569[/tex]
[tex]y=628.227\approx 628.23[/tex]
Therefore, the value of stereo system after 2 years will be $628.23.
c. The half of the original price will be [tex]\frac{830}{2}=415[/tex].
Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.
[tex]415=830*(0.87)^x[/tex]
Upon dividing both sides of our equation by 830 we will get,
[tex]\frac{415}{830}=\frac{830*(0.87)^x}{830}[/tex]
[tex]0.5=0.87^x[/tex]
Let us take natural log of both sides of our equation.
[tex]ln(0.5)=ln(0.87^x)[/tex]
Using natural log property [tex]ln(a^b)=b*ln(a)[/tex] we will get,
[tex]ln(0.5)=x*ln(0.87)[/tex]
[tex]\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}[/tex]
[tex]\frac{ln(0.5)}{ln(0.87)}=x[/tex]
[tex]\frac{-0.6931471805599}{-0.139262067}=x[/tex]
[tex]x=4.977286\approx 4.98[/tex]
Therefore, after approximately 4.98 years the stereo will be worth half the original value.
To find when a stereo system purchased for $830 and depreciating at 13% per year will be worth half of its value, use the exponential decay formula V(t) = [tex]P * (1 - r)^t[/tex]. After 2 years, the stereo is worth approximately $627.77, and it will be worth half its original value after about 5.42 years.
An exponential decay model can represent the value of an asset decreasing over time. For a stereo system purchased for $830 with a yearly depreciation of 13%, the model takes on the form of V(t) = [tex]P * (1 - r)^t[/tex], where:
V(t) is the value of the stereo system after t years.
P is the initial purchase price, which is $830.
r is the rate of decay per year, which is 13% or 0.13.
t is the number of years since the purchase.
The value of the stereo system after 2 years can be calculated using the above model:
[tex]V(2) = 830 * (1 - 0.13)^2 = 830 * 0.87^2[/tex]
= 830 * 0.7569
= $627.77 approximately.
To find when the stereo will be worth half the original value, we set [tex]V(t) = rac{P}{2}[/tex] and solve for t:
415 = [tex]830 * (1 - 0.13)^t[/tex]
[tex]0.5 = (1 - 0.13)^t[/tex]
[tex]Log_0.87(0.5) = t[/tex]
t
t = 5.42
The stereo will be worth half its original value after approximately 5.42 years.
Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° latitude. if the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [use π = 3.14, and round to the nearest mile.]
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
The distance between Seattle, WA, and San Francisco, CA, calculated using their latitudinal difference on a sphere with a radius of 4000 miles, is approximately 628 miles.
The question is asking for the distance between Seattle, WA and San Francisco, CA based on their respective latitudes and assuming they are on the same longitudinal line. To find the arc length and thus the distance between the two cities, you can use the formula for arc length on a sphere: [tex]\(Arc \ length = (\Delta Latitude \times \pi/180) \times \ Radius \ of\ Earth\)[/tex]. Here, [tex](\Delta Latitude\)[/tex] is the difference in latitude between the cities, which is [tex]\(47^\circ - 38^\circ = 9^\circ\)[/tex]. The radius of Earth is given as 4000 miles. Plugging these values into the formula, you get:
[tex]\(Arc \ length = (9 \times \pi/180) \times 4000\)[/tex]
[tex]\(Arc \ length = (9 \times 3.14/180) \times 4000\)\\\(Arc \ length = (0.157) \times 4000\)\\\(Arc \ length = 628 \ miles\)[/tex]
Therefore, the distance between Seattle and San Francisco, based on latitude and assuming they are directly north and south of each other, is approximately 628 miles.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
What is the value of x?
Answer: C
Step-by-step explanation:
[tex]\dfrac{x+2}{15} =\dfrac{x+1}{5}[/tex]
cross multiply: 5(x + 2) = 15(x + 1)
distribute: 5x + 10 = 15x + 15
-5x -5x
10 = 10x + 15
-15 -15
-5 = 10x
[tex]\dfrac{-5}{10}=\dfrac{10x}{10}[/tex]
[tex]-\dfrac{1}{2} =x[/tex]
classify the sequence arithmetic , geometric, or neither
Answer:
Geometric
Step-by-step explanation:
Given terms are {3, -1, 1/3, -1/9............}
If we have common difference between the terms then it is arithmetic
If we have common ratio between the terms then it is Geometric
Difference of 3 and -1 is 4
Difference of 1/3 and -1 is -4/3
Common difference it not same so it is not Arithmetic
Now we check common ratio
we divide second term by first term
first term is 3 and second term is -1
[tex]\frac{-1}{3}[/tex]
now we check with next two terms
[tex]\frac{\frac{1}{3}}{-1}=\frac{-1}{3}[/tex]
common ratio is -1/3
So this is Geometric
Answer:
B so geometric :)
Missy bought 3 umbrellas and 5 hats 27.00. Each umbrella coats the same amount. Each has costs the same amount. The price of a hat is $3.00. What is the cost of 1 umbrella?
34/99 as a decimal please help!
Answer:
0.34
Step-by-step explanation:
I just used a calculator
What is the measure of YVZ
Answer:
D. 110 deg
Step-by-step explanation:
Angle YVZ and WVX are vertical angles.
A theorem states that vertical angles are congruent.
Angle YVZ is congruent to angle WVX.
m<YVZ = m<WVX = 110 deg
Answer:
110 degrees
Step-by-step explanation:
<YVZ is vertically opposite to a known angle <WVX
Vertically Opposite Angles are equal
<YVZ = WVX
<WVX = 110 degrees. Given
Therefore YVZ = 110 degrees. Property of Vertically opposite angles
Phil collected 60 eggs and sold 44 of them. Phil wrote that he sold 0.44 of the eggs he collected. Did Phil write the decimal correctly?
Which benefits do employers commonly offer to full-time employees?
Answer:
Employers offer bonuses ,health insurances, medical facilities ,residence facilities and other facilities to their full time employees.
Step-by-step explanation:
Employees play a vital role in progress of an organization.
they need inspiration to work better and to make company's rank better.
and for their inspiration and to enhance the relationship with employees, employers offer them bonuses,health insurances, medical facilities ,residence facilities and other facilities
Answer:
The common benefits of getting a full-time job are:
Health InsuranceSocial Security withholdings.Unemployment insurance.Periodic compensations.Remember that a full-time job has to have 40 hours per week. So, to compensate this amount of time spent in the company, they tend to "protect" their employees with better health insurance, their Social Security will give credits, which apply to retirement, and in case of accidents, their insurance will cover all costs.
All these variables make these jobs attractive in order to make people work even more.
After one week a music downloading site sold over 80,000 songs. After 4 weeks the music downloading site sold over 300,000 songs. Find the average rate of change of songs per week.
75,000 songs per week
80,000 songs per week
55,000 songs per week
73,334 songs per week
[tex]\bf \begin{array}{ccll} \stackrel{x}{weeks}&\stackrel{y}{songs}\\ \cline{1-2} 1&80000\\ 4&300000 \end{array}~\hspace{10em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{80000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{300000}) \\\\\\ \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{300000-80000}{4-1}\implies \cfrac{220000}{3}\quad \approx \quad 73333[/tex]
A dress is selling for $100 after a 20 percent discount. What was the original selling price?
SHOW ALL WORK
Answer:
$125
Step-by-step explanation:
original cost - discount = discounted price
discount = original cost * .2
original cost - original cost *.2 = 100
Factor out the original cost
original cost ( 1-.2) = 100
original cost *.8 = 100
Divide each side by .8
original cost *.8/.8 = 100/.8
original cost = 125
4. What is the rule of the nth term of the geometric sequence with [tex]a_{4}[/tex] = -18 and the common ratio r = 2?
a. [tex]a_{n}=2.25(2)^{n-1}[/tex]
b. [tex]a_{n}=2(2.25)^{n-1}[/tex]
c. [tex]a_{n}=2(2.25)^{n-1}[/tex]
d. [tex]a_{n}=-2.25(2)^{n-1}[/tex]
e. [tex]a_{n}=-2.25(-2)^{n-1}[/tex]
Answer:
[tex]\text{d.}\quad a_n=-2.25(2)^{n-1}[/tex]
Step-by-step explanation:
The common ratio is given as 2, so the base of any exponential must be 2 (not -2 or 2.25). The 4th term is negative, so the initial value must be negative (since the multiplying factor is positive). The only selection matching these requirements is d.
You know the general term is ...
... an = a1·r^(n-1)
so the 4th term is
... -18 = a1·2^(4-1) = 8·a1
Then the first term is ...
... a1 = -18/8 = -2.25 . . . . . confirms our choice of answer d.
Your gym teacher needs to put 96 students into 12 equal groups. Complete the equation to show which operation to use and how many students will be in each group.
Answer:
8
Step-by-step explanation:
We will use the math operation division to find the answer. Division takes a total and divides it into equal amounts. We have a total of 96 and need equal amounts in to each of the 12 groups.
96/12=8 students per group
Kenya jumped 7 and 1 sixth feet. Janet jumped 6 and 1 third feet. How much farther did Kenya jump?
Can anyone please tell me what I’m doing wrong. It’s not giving me the full marks. The marks for this question is 4 but I only got 1.
Answer:
33%
Step-by-step explanation:
The area of the entire circle:
The radius is 4+3+3 = 10
Area of a circle= pi * r^2
Area of largest circle = pi * 10^2 = 100 pi
Area of blue ring = Area of blue circle - area of inner white circle
The blue circle has a radius of (4+3) = 7
The inner white circle had a radius of 4
Substituting what we know
Area of blue ring = Area of blue circle - area of inner white circle
= pi * r^2 - pi*r^2
= pi * 7^2 - pi *4^2
= 49pi - 16pi
= 33 pi
The percentage of the logo that is blue is the blue ring/ area of largest circle
percentage = 33 pi/100 pi
Canceling pi
percentage = 33/100
= 33 %
what is the area of a rectangle with a length of 3.2 cm and a width of 6.8 cm?
Answer:
21.76 Centimeters
Step-by-step explanation:
Length - 3.2 Cm
Width - 6.8 Cm
Area = Width * Length (Or other way around)
Multiply:
3.2 * 6.8
= 21.76
- I.A -
A jewelry salesperson earns 6two fifths ?% commission on all sales. Today she sold ?$5 comma 570 in jewelry. What is her total commission? earned?
Answer:
$356.48
Step-by-step explanation:
We have been given that a jewelry salesperson earns [tex]6\frac{2}{5}[/tex]% commission on all sales. Today she sold $5,570 in jewelry.
To find the total commission earned by salesperson is same as finding the [tex]6\frac{2}{5}[/tex]% of 5,570.
Let us convert [tex]6\frac{2}{5}[/tex] in decimal form.
[tex]6\frac{2}{5}=6.4[/tex]
[tex]\text{Total commission earned by salesperson}=\frac{6.4}{100}\times 5,570[/tex]
[tex]\text{Total commission earned by salesperson}=0.064\times 5,570[/tex]
[tex]\text{Total commission earned by salesperson}=356.48[/tex]
Therefore, the total commission earned by salesperson is $356.48.
As a rule of thumb, people should drink 1/2 ounce of water for each pound of body weight per day. How much water should a 145-pound person drink per day?
Answer: 72.5 ounces per day
F(x) = x2 + 3x + 2 is shifted 2 units left, the result is g(x). What is g(x)?
Answer:
[tex]g(x)=x^2+7 x+12[/tex]
Step-by-step explanation:
since f(x)=[tex]x^{2}+3 x+2[/tex]
now we are given that this function f(X) is shifted 2 units to the left and we get a function g(x) this means
g(x)=f(x+2) since f(x+2) will shift the function f(x) 2 units to the left.
[tex]g(x)=(x+2)^{2}+3(x+2)+12[/tex]
g(x)=[tex]x^2+4+4 x+3 x+6+2[/tex]
hence, the function g(x)=[tex]x^2+7 x+12[/tex]
If Julie needs 3 and 1/4 cups of oatmeal how many 1/4 cups of oatmeal will she use
Answer:
She will use 13 quarter cups of oatmeal
Step-by-step explanation:
3 1/4 = 13/4
x/4 = 13/4
4(x/4) = 4(13/4)
x = 13
Find the values of x and y.
Answer:
[tex]x=3.5,y=24[/tex]
Step-by-step explanation:
The smaller triangle joining the midpoints of the bigger right angle triangle will also be a right angle triangle.
Midpoint Theorem-
According to this, the segment joining two sides of a triangle at the midpoints is half the length of the third side.
Applying this,
[tex]\Rightarrow x=\dfrac{1}{2}(4x-7)[/tex]
[tex]\Rightarrow 2x=4x-7[/tex]
[tex]\Rightarrow 4x-2x=7[/tex]
[tex]\Rightarrow 2x=7[/tex]
[tex]\Rightarrow x=\dfrac{7}{2}=3.5[/tex]
So, the hypotenuses of the bigger triangle will be,
[tex]=6(3.5)+4=25[/tex]
Applying the mid point theorem, the hypotenuses of the smaller triangle will be,
[tex]=\dfrac{1}{2}\times 25=12.5[/tex]
Applying Pythagoras theorem in the smaller triangle, the leg will be
[tex]=\sqrt{12.5^2-3.5^2}\\\\=\sqrt{156.25-12.25}\\\\=\sqrt{144}\\\\=12[/tex]
Again applying mid point theorem,
[tex]\Rightarrow y=2\times 12=24[/tex]