To calculate the amount of steel needed to construct the oil tank, we need to find the surface area of the cylinder. A cylinder's surface area is composed of two parts: the area of its circular top and bottom (which are identical), and the area of its side.
Let's start by calculating the area of the two circular ends of the cylinder.
1. The area of one circle (either the top or the bottom) is given by the formula:
\[ A_{\text{circle}} = \pi r^2 \]
where \( r \) is the radius of the circle.
Since the diameter is twice the radius, we have:
\[ d = 12 \ \text{ft} \]
\[ r = \frac{d}{2} = \frac{12 \ \text{ft}}{2} = 6 \ \text{ft} \]
Now, we calculate the area of one circle:
\[ A_{\text{circle}} = \pi (6 \ \text{ft})^2 = \pi \times 36 \ \text{ft}^2 \]
\[ A_{\text{circle}} = 36\pi \ \text{ft}^2 \]
Since there are two circles (top and bottom), we double this area:
\[ A_{\text{circles}} = 2 \times 36\pi \ \text{ft}^2 \]
\[ A_{\text{circles}} = 72\pi \ \text{ft}^2 \]
2. Next, we calculate the area of the side of the cylinder. The side is essentially a rectangle that is wrapped around the circular ends. The width of this rectangle is the height of the cylinder, and the length is the circumference of the circle.
The circumference of the base circle is given by:
\[ C = 2\pi r \]
Using the radius we found before:
\[ C = 2\pi \times 6 \ \text{ft} = 12\pi \ \text{ft} \]
The area of the side is then:
\[ A_{\text{side}} = C \times \text{height} \]
\[ A_{\text{side}} = 12\pi \ \text{ft} \times 18 \ \text{ft} \]
\[ A_{\text{side}} = 216\pi \ \text{ft}^2 \]
3. The total surface area of the steel needed to make the tank is the sum of the areas of the circular ends and the side:
\[ A_{\text{total}} = A_{\text{circles}} + A_{\text{side}} \]
Substitute the values found above:
\[ A_{\text{total}} = 72\pi \ \text{ft}^2 + 216\pi \ \text{ft}^2 \]
\[ A_{\text{total}} = 288\pi \ \text{ft}^2 \]
To find a numerical value, we use the approximation \( \pi \approx 3.14159 \) (you can use a more precise value based on your requirements):
\[ A_{\text{total}} \approx 288 \times 3.14159 \ \text{ft}^2 \]
\[ A_{\text{total}} \approx 904.77792 \ \text{ft}^2 \]
So approximately 904.78 square feet of steel are needed to make the tank.
Which of the following is a solution to 4sin2x − 1 = 0?
x=0.12634012+
[tex]\\\pi144445618[/tex]
Answer:
A. 30
Step-by-step explanation:
The correct form is:
4sin^2 x − 1 = 0
First step is add 1 to both sides:
4sin^2 x-1+1=0+1
4sin^2 x=1
Now to eliminate 4 divide both sides by 4
4sin^2 x/4=1/4
sin^2 x=1/4
Take square root at both sides
√sin^2 x = √1/4
sinx = 1/2
Thus the correct option is 30° ....
find all zeros: f(x)=x^3-2x^2-4x+8
To find all zeros of f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. The only rational root is x = 2. The complex roots can be found by dividing the equation by (x - 2) and solving the resulting quadratic equation.
Explanation:To find all zeros of the equation f(x) = x^3 - 2x^2 - 4x + 8, we can use the Rational Root Theorem to test possible rational roots. By factorizing the constant term, 8, and the leading coefficient, 1, we find that the possible rational roots are ±1, ±2, ±4, ±8. By testing these values in the equation, we can find that the only rational root is x = 2. To find the complex roots, we can use polynomial long division or synthetic division to divide the original equation by (x - 2) and solve the resulting quadratic equation.
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The figure below is a net for a triangular prism. Side a = 22 feet, side b = 14 feet, side c = 13 feet, side d = 13 feet, and side e = 19 feet. What is the surface area of this figure?
A. 1,194 square feet
B. 908 square feet
C. 1,172 square feet
D. 1,216 square feet
Answer:
the answer is 1,194
Step-by-step explanation:
what you want to do is find the area of 2 triangles and 3 rectangles
area of 1st rectangle
1 = ae
=(22 ft) (19 ft)
=418 sq. ft.
area of 2nd rectangle
2 = ab
=(22 ft.) (14 ft.)
=308 sq. ft.
area of 3rd rectangle
3=ad
=(22 ft.) (13 ft.)
=286 sq. ft.
area of 1st triangle
Area of triangle = 1/2 cb
=1/2 (13ft) (14ft)
= 1/2 (182 sq. ft)
=91 sq. ft.
***this would be the same for 2nd triangle*** 91 sq ft.
Next add all areas together to get the total surface area
Total surface area = ae + ab + ad + 2 (1/2 cb)
= 418 sq. ft + 308 sq. ft. + 286 sq. ft. + 2(91 sq. ft)
=418 + 308 + 286 + 182
= 1,194 sq. ft.
lizzy gets her paycheck every 10 days. Her husband, Don gets a paycheck every 14 days. On July 3, they both get a paycheck. How many days will pass before they both get check on same day
5 weeks .... 35 days
Lizzy and Don will both receive their paychecks on the same day after 70 days, as 70 is the Least Common Multiple (LCM) of their paycheck intervals of 10 and 14 days.
Lizzy and Don are trying to find out when they will both receive their paychecks on the same day again. To solve this, we need to find the Least Common Multiple (LCM) of their paycheck intervals which are 10 days for Lizzy and 14 days for Don. The LCM of 10 and 14 is the smallest number that both 10 and 14 can divide into without leaving a remainder.
Let's list the multiples of each:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, ...
The smallest common multiple they share is 70. This means that after 70 days, both Lizzy and Don will receive their paychecks on the same day again.
For question 9 and 10 use the graph below
9. What is the x intercept
10.what is the y intercept
Answer:the x intercept is (0,-7) that is number 9 and number 10 is (0,2)
Step-by-step explanation:
PLEASE HELP I REALLY DONT UNDERSTAND WILL GIVE 100 POINTS
Show work!!!
Circle with tangent MN.
MSN = 60°; mQS = x; mQP = x + 40; m PN = 2x-16
Find X =
Angle 5 =
Angle 1 =
Angle 2 =
Angle 6 =
Angle 7 =
Angle 3 =
Angle 8 =
Angle 4 =
MPN =
Answer:
Part 1) The value of x is 69°
Part 2) Angle 1=64.5°
Part 3) Angle 2=84.5°
Part 4) Angle 3=31°
Part 5) Angle 4=84.5°
Part 6) Angle 5=95.5°
Part 7) Angle 6=95.5°
Part 8) Angle 7=54.5°
Part 9) Angle 8=30°
Step-by-step explanation:
Part 1) Find the value of x
we know that
arc SN+arc QS+arc QP+arc PN=360° -----> by complete circle
substitute the values
60°+x°+(x+40)°+(2x-16)°=360°
solve for x
84°+4x°=360°
4x=276°
x=69°
Part 2) Find the measure of angle 1
we know that
The inscribed angle is half that of the arc it comprises
so
m∠1=(1/2)[arc QSN]
arc QSN=arc QS+SN
arc QSN=x+60°=69°+60°=129°
substitute
m∠1=(1/2)[129°]=64.5°
Part 3) Find the measure of angle 2
we know that
The measure of the inner angle is the semi-sum of the arcs that comprise it and its opposite
m∠2=(1/2)[arc SN+arc QP]
substitute the values
m∠2=(1/2)[60°+(x+40)°]
m∠2=(1/2)[60°+(69+40)°]
m∠2=(1/2)[169°]=84.5°
Part 4) Find the measure of angle 3
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
m∠3=(1/2)[arc PN-arc SN]
substitute the values
m∠3=(1/2)[(2x-16)°-60°]
m∠3=(1/2)[(2(69)-16)°-60°]
m∠3=(1/2)[62°]=31°
Part 5) Find the measure of angle 4
we know that
m∠4=m∠2 -----> by vertical angles
so
m∠4=84.5°
Part 6) Find the measure of angle 5
we know that
m∠5+m∠2=180° -----> by supplementary angles
so
m∠5+84.5°=180°
m∠5=180°-84.5°=95.5°
Part 7) Find the measure of angle 6
we know that
m∠6=m∠5 -----> by vertical angles
so
m∠6=95.5°
Part 8) Find the measure of angle 7
we know that
The inscribed angle is half that of the arc it comprises
so
m∠7=(1/2)[arc QP]
arc QP=(x+40)°=(69+40)°=109°
substitute
m∠7=(1/2)[109°]=54.5°
Part 9) Find the measure of angle 8
we know that
The inscribed angle is half that of the arc it comprises
so
m∠8=(1/2)[arc SN]
arc SN=60°
substitute
m∠8=(1/2)[60°]=30°
Helpppppp plsssssssss
Answer:
C
Step-by-step explanation:
The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.
x is the hypotenuse (side opposite of 90 degree angle).
We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.
For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:
[tex]6^2 + 3^2 = x^2\\36 + 9 = x^2\\45 = x^2\\x=\sqrt{45}[/tex]
Now we can use property of radical [tex]\sqrt{x}\sqrt{y} =\sqrt{x*y}[/tex] to simplify:
[tex]x=\sqrt{45} \\x=\sqrt{5*9} \\x=\sqrt{5} \sqrt{9} \\x=3\sqrt{5}[/tex]
Correct answer is C
Answer:
The correct answer is option C. 3√5
Step-by-step explanation:
Points to remember
For a right angled triangle
Hypotenuse ² = Base² + Height²
From the attached figure we can see a square and a right angled triangle associated with the square.
Sides of square = 6
To find the value of x
Base = 3 and height = 6
Hypotenuse = x
x² = 3² + 6²
= 9 + 36 = 45
x = √45 = 3√5
Therefore the correct answer is option C. 3√5
PLEASE ANSWER RIGHT AEAY
Answer:
[tex]y=Sin(x-\frac{\pi}{4})[/tex]
Step-by-step explanation:
The basic graph of y = Sin(x), starts at x = 0.
Looking at the graph, the basic sin curve starts at x = π/4
So this function is the parent sin function shifted π/4 units to the right.
Note:
y = Sin(x-a) is the parent function ( y= Sinx) shifted a units right
y = Sin(x+a) is the parent function shifted a units left
Since this function is shifted π/4 units right, the equation would be:
y = Sin (x-π/4)
The third answer choice is right.
Describe the transformation that occurred on f(x) to create g(x).
Tranlslated:
A. 6 units to the right
B. 6 units to the left
C. 7 units to the right
D. 7 units to the left
and:
A: 6 units up
B. 6 units down
C. 7 units up
D. 7 units down
Reflection:
A. Did occur
B. Did not occur
C. Can't be determined
Answer:
f(x) translated 3 units to the left and 8 units down, there is no reflection occurred
Step-by-step explanation:
* Lets revise some transformation for the functions
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets study the problem
∵ g(x) = 2(x + 3)² - 8
# x + 3 ⇒ means f(x) translated 3 units to the left
# -8 ⇒ means f(x) translated 8 units down
# There is no reflection occurred
find 2 different ways to make the addition problem work. each letter stands for the same digit 0 to 9 whenever it is used
The addition problem can be solved in two ways: treating each column separately without carrying and writing down the sum of each column even if it is 10 or more. Examples demonstrate each method using single-digit addition without carrying and adjusting sums that exceed single digits.
Explanation:The question at hand involves solving a unique addition problem where each letter corresponds to a digit between 0 and 9. To find 2 different ways to make the addition problem work, we need to apply traditional addition rules along with the clues provided.
First, let's analyze the given examples:
42 + 59 equals 911 - This suggests that each digit is added independently, without carrying over to the next column. Adding 2 and 9 gives 11, placed in the units column. 4 and 5 give 9, placed in the tens column.23 + 54 equals 77 - This result follows the standard addition rules with carrying over.To construct two solutions, let's use the same principle:
For the first way, treat each column separately without carrying. For example, 35 + 46 would equal 711 (5+6 = 11 and 3+4 = 7).For the second way, consider a different interpretation where numbers in each column that add up to 10 or more result in just writing down the sum. For instance, 85 + 78 would equal 1513 (5+8 = 13, and 8+7 = 15).It's important to follow the instructions closely and understand that digits in these sum calculations are handled independently based on the context provided.
two lines are intersecting what is the value of x
Answer:
[tex]x=111[/tex]
Step-by-step explanation:
Since these angles are supplementary, they add up to 180°.
Let's make an equation.
[tex]360=(x+23)+(2x+4) \\ \\ 360=x+23+2x+4 \\ \\ 360=3x+27 \\ \\ 3x=333 \\ \\ x = 111[/tex]
Answer:
[tex]x=51[/tex]
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x.
We can see that both angles are supplementary, so we can set an equation as:
[tex]x+23+2x+4=180[/tex]
[tex]x+2x+4+23=180[/tex]
[tex]3x+27=180[/tex]
[tex]3x+27-27=180-27[/tex]
[tex]3x=153[/tex]
[tex]\frac{3x}{3}=\frac{153}{3}[/tex]
[tex]x=51[/tex]
Therefore, the value of x is 51.
Expand and simplify (2X-3)^2
Answer:
4x^2−12x+9
If you have another question ask
The solution of expression is,
⇒ 4x² + 9 - 12x
We have to given that,
An expression to solve,
⇒ (2x - 3)²
Now, We can used the formula,
⇒ (a - b)² = a² + b² - 2ab
Hence, We get;
⇒ (2x - 3)² = (2x)² + 3² - 2×2x×3
= 4x² + 9 - 12x
Therefore, The solution of expression is,
⇒ 4x² + 9 - 12x
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Riddle
"If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?"
Answer:
100 minutes?
lol
Answer:
5 minutes
Step-by-step explanation:
duh...
Carolyn averaged 10.4 miles per hour. At that rate, how far could she ride from 8:00 A.M. to 10:30 A.M.?
The answer is 26 miles.
Explanation:
10:30-8:00= 2:30.
10.4÷2=5.2
10.4 ×2÷ 20.8 +5.2= 26
In the triangle ABC , AB=17cm,BC=9cm and angle ACB=90°
Calculate AC
I believe the answer is 14.42
The length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°. This can be obtained by using Pythagoras' theorem.
What is Pythagoras' theorem?Pythagoras' theorem states that the sum of squares of the legs of a right triangle is equal to the square of the hypotenuse, that is,⇒ a² + b² = c²Calculate the side AC of ΔABC:Given that, AB=17cm, BC=9cm and angle ∠ACB=90°.
By using Pythagoras' theorem,
AB² = AC²+BC²
17² = AC²+9²
AC² = 17²-9² =289-81 = 208
AC = √208 =14.42
⇒AC = 14.42cm
Hence the length of AC is 14.42 in the triangle ΔABC where AB=17cm, BC=9cm and angle ∠ACB=90°.
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trigonometry help?
Answer:
x ≈ 6.7
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan40° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{8}[/tex]
Multiply both sides by 8
8 × tan40° = x, hence
x = 6.7 ( to 1 dec. place )
The inequality 2x - 3y ≥ 5 is satisfied by point (1/2,1/3 ). True False
For this case we evaluate the following inequality in the given point and verify if it is met:
[tex]2x-3y\geq 5[/tex]
[tex](x, y) = (\frac {1} {2}, \frac {1} {3})[/tex]
Substituting:
[tex]2 \frac {1} {2} -3 \frac {1} {3}\geq5[/tex]
[tex]1-1\geq 5\\0\geq 5[/tex]
It is not fulfilled!
The point does not satisfy the inequality
ANswer:
False
Answer:
False
Step-by-step explanation:
(1/2, 1/3) ⇒ x = 1/2 and y = 1/3
Substitute these values in the given equation;
2x - 3y ≥ 5
2(1/2) - 3(1/3) ≥ 5
[tex]\frac{2}{2}[/tex] - [tex]\frac{3}{3}[/tex]
= 1 - 1 = 0
Thus the inequality is not satisfied by the given points, since 0 < 5 and ≠ 5.
Find the length of the diameter of a circle that has a center at Point T (3, 1) and passes through the point (1, -6).
Answer:
[tex]D=14.56[/tex]
Step-by-step explanation:
We know that the diameter of a circle is twice the radius.
Calculate the radius of the circle with the formula for calculate the distance between two points:
[tex]d=r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where "r" is the radius.
Knowing that the center of the circle is at point (3, 1) and the circle passes through the point (1, -6), we can substitute values into the formula to find the radius:
[tex]r=\sqrt{(3-1)^2+(1-(-6))^2}=\sqrt{53}[/tex]
Then the diameter of the circle is:
[tex]D=2r\\D=2\sqrt{53}[/tex]
[tex]D=14.56[/tex]
Plz help me with this
It's the second option.
y = -2 sin x + 2
Tell me if I'm wrong :)
It looks spiker because my graph is more spread out with the intervals.
Answer: b) y = -2 sin x + 2
Step-by-step explanation:
The standard equation for a sine graph is: y = A sin (Bx - C) + D
[tex]\text{Amplitude (A) = }\dfrac{max-min}{2}=\dfrac{4-0}{2}=\dfrac{4}{2}=2\\\\\\\text{Vertical Shift (D) = max - amplitude = }4 - 2 = 2[/tex]
A sine graph starts at the origin and tends upward. The given graph stars at the origin and tends downward so it is a reflection → - sin x
⇒ y = -2 sin x + 2
Factor 140c+28-14a140c+28−14a140, c, plus, 28, minus, 14, a to identify the equivalent expressions. Choose 2 answers: Choose 2 answers:
The factored form of the given expression is 14(10c + 2 - a).
Given is an expression 140c + 28 - 14a, we need to factor it to simplify in equivalent expression.
We search for common term that can be eliminated in order to factor the expression 140c + 28 - 14a.
In this instance, we may factor the terms that share a common factor of 14 out.
The expression changes to:
140c + 28 - 14a
Let's now subtract 14:
14(10c + 2 - a)
Therefore, the expression's factored form is 14(10c + 2 - a).
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Plz help me with this
Answer: A) y = -5 cos(2x - π)
Step-by-step explanation:
[tex]\text{The standard form of a cosine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
A (amplitude) = 5Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg) = \dfrac{\pi}{2}[/tex] to the rightP (period) = π --> B = 2D (vertical shift) = 0There is also a reflection across the x-axis.[tex]\implies \large\boxed{y = -5cos(2x-\pi)}[/tex]
see graph below for verification
I need to find the scale factor
I did something wrong could you help?
Answer:
Slope = 1/2
y-intercept = 30
Equation : y = 1/2x + 30
D. 150 miles
Step-by-step explanation:
We can use the two visible points you marked on the graph.
They are (0,30) which is also the y-intercept and (20,40).
Calculate change of y over change of x.
10/20 or 1/2
So the slope is 1/2 and the y-intercept is 30.
Therefore, using y = mx + b form, the equation is y = 1/2x + 30
Then, to find how many miles you drove if the cost was $105, we can plug in 105 for y in the equation.
105 = 1/2x + 30
75 = 1/2x
x = 150
please help asap ( 10 points)
The estimate and the answer of the given real numbers are:
Estimate Answer
[tex]\dfrac{21}{4}[/tex] 5.25
[tex]\dfrac{4}{3}[/tex] 1.33
[tex]\dfrac{4}{1}[/tex] 4
Multiplication of real numbers.
The multiplication of real numbers (rational or irrational) can take different forms or processes. Here, we are to multiply the following numbers.
[tex]1\frac{3}{4} \times 3[/tex]
Let us convert the mixed fraction to an improper fraction to find the estimate.
[tex]\dfrac{7}{4} \times 3[/tex]
The estimate [tex]=\dfrac{21}{4}[/tex]
The answer [tex]\dfrac{21}{4} = 5.25[/tex]
The second question:
[tex]\dfrac{8}{9}\times 1\dfrac{1}{2}[/tex]
[tex]=\dfrac{8}{9}\times \dfrac{3}{2}[/tex]
[tex]=\dfrac{4}{3}\times \dfrac{1}{1}[/tex]
Estimate = [tex]\dfrac{4}{3}[/tex]
Answer = 1.33
The third question
[tex]3\dfrac{1}{2}\times 1\dfrac{1}{7}[/tex]
[tex]=\dfrac{7}{2}\times \dfrac{8}{7}[/tex]
[tex]=\dfrac{1}{1}\times \dfrac{4}{1}[/tex]
Estimate = [tex]\dfrac{4}{1}[/tex]
Answer = 4
PPPLLLSSS HELP ME!!!!
3 to the 4 power + 4 ⋅ 5 = ____. (Input only whole numbers.)
Answer:
101
Step-by-step explanation:
3 to the fourth power is 3*3*3*3 which is 81. 4*5=20. 81+20=101
Answer: 3^4 + 4 * 5 = 101
Step-by-step explanation:
You have to use the order of operations (PEMDAS)
3^4 is an exponent, so you simplify this first
3^4 = 81
4*5 is multiplication, so you do this next
4*5 = 20
81+20 = 101
Solve this system of linear equations. Separate the x- and y-values with a comma. -3x=42-16y 14x=76-16y
To solve the given system of linear equations -3x = 42-16y and 14x = 76-16y, use the method of elimination to find the solution (20-6y, y).
Explanation:To solve the system of linear equations -3x = 42-16y and 14x = 76-16y, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the first equation by 2 to make the coefficients of y in both equations equal. The equations become:
-6x = 84-32y and 14x = 76-16y
Add the two equations together:
-6x + 14x = 84-32y + 76-16y
Simplify:
8x = 160-48y
Rearrange the equation to solve for x:
x = (160-48y)/8
Simplify further:
x = 20-6y
The solution to the system of equations is x = 20-6y. To separate the x- and y-values, we write it as (20-6y, y).
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Annabelle measured her bedroom as 11 ft x 13 ft which is 143 square feet help me in this
Answer:
theres the answer I got it right
Step-by-step explanation:
There are 12 inches in every feet and the area will be increased by 144 factors.
How do convert feet into inches?Feet and inches are the units of length. One inch is equal to 1/12 times the feet.
The length and the breadth are given as 11 feet and 13 feet.
The area of the bedroom is 143 square feet.
We know that 1ft = 12 in
So, The length would become 11 feet to 132 inches.
The breadth would become 13 feet to 156 inches.
The area would become
The area of the rectangle = length × Width
= 132 × 156
= 20592 in .sq
The area of the bedroom increased by 144 factors.
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Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee. Which inequalities can represent this situation if m is the number of songs he can buy? Check all that apply.
Answer:
[tex]1.5m+1\leq 25[/tex]
Step-by-step explanation:
Given that Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee.
This activation fee is once for all and hence fixed independent of the number of songs.
Thus total amount available = 25 dollars
This should be spent for both activation fee and songs
Let number of songs = m
Total cost [tex]= 1.5m+1[/tex]
This cannot exceed 25 dollars
So the ineqality would be
[tex]1.5m+1\leq 25[/tex]
Opel runs a bakery, and it takes her 15 minutes to make a batch of cookie dough. What is Opel's rate per minute for making batches of cookie dough?
Answer:
ok so it can either be 0.07x or 1/15x (they are equal)
(both being 1/15th of a cookie per minute)
Opel's rate of making cookie dough is determined by recognizing that she makes one batch every 15 minutes. Therefore, per minute, she can make about 0.067 batches.
Explanation:In the context of this problem, we're examining Opel's productivity in creating batches of cookie dough. Specifically, Opel can make a batch of cookie dough in 15 minutes. Therefore, to find her rate per minute, we simply recognize that one task (making a batch of cookie dough) corresponds to 15 minutes. Thus, her rate is 1 batch per 15 minutes. But we want to express this in terms of batches per minute. To do this, we simply take the reciprocal of 15, which is approximately 0.067. So, Opel's rate of making cookie dough is roughly 0.067 batches per minute.
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I need help finding the sine of angle R
Answer:
the sine of angle R is 5/7.
Step-by-step explanation:
Recall that the sine function is defined as sin Ф = (opposite side) / hypotenuse.
The side opposite Angle R is √65 and the hypotenuse is √91.
Thus, the sine of angle R is sin R = √65 / √91, or 5/7.