Answer: Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Step-by-step explanation:
Since we have given that
Ari has 3 ounces of caramel for every 5 scoops of ice-cream .
Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice-cream.
According to Ari,
For every 5 scoops of ice-cream, he needs 3 ounces of caramel
For every 1 scoop of ice-cream, he needs
[tex]\frac{3}{5}\text{ ounces of caramel}[/tex]
For every 8 scoops of ice-cream, he needs
[tex]\frac{3}{5}\times 8=\frac{24}{5}=4.8\text{ ounces of caramel}[/tex]
So, Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Explanation:To determine what Ari will think about Freeze Zone's milkshakes, we need to compare the ratio of caramel to ice cream in Ari's perfect milkshake to the ratio in Freeze Zone's milkshakes.
Ari's perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream, so the ratio is 3:5.
Freeze Zone's milkshakes have 6 ounces of caramel for every 8 scoops of ice cream, so the ratio is 6:8.
To simplify both ratios, we can divide the numbers by their greatest common divisor. The GCD of 3 and 5 is 1, so the simplified ratio for Ari's perfect milkshake is 3:5. The GCD of 6 and 8 is 2, so the simplified ratio for Freeze Zone's milkshakes is 3:4.
Since both ratios are the same, we can conclude that Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
convert 3(3.14)/8 radians to degrees
How do you check your answer for volume of a cylinder? Desperate need of answering
please translate 2 minus the product of a number and 9 is 20.
The statement '2 minus the product of a number and 9 is 20' translates to the equation 2 - 9x = 20. Solving for x, we find the solution x = -2, meaning the number in question is -2.
The student is asking to translate the phrase '2 minus the product of a number and 9 is 20' into a mathematical equation. The 'product of a number and 9' can be represented as '9x' where 'x' is the unknown number. Therefore, translating the entire phrase, we end up with the equation: 2 - 9x = 20.
To solve for 'x', we first bring '9x' to the other side of the equation by adding '9x' to both sides, resulting in 2 = 9x + 20. Subsequently, we subtract 20 from both sides, yielding -18 = 9x, and then we divide both sides by 9 to find the value of 'x'. So, x = -18 / 9, which simplifies to x = -2.
The solution for the equation is x = -2, which means the number we were looking for is -2.
The set of points (2, 3), (9, 3), (9, –2), and (2, –2) identifies the vertices of a quadrilateral. Which is the most specific description to tell which figure the points form?
A parallelogram
B square
C rectangle
D trapezoid
Answer:
C rectangle
Step-by-step explanation:
All the coordinates of the setpoint are (x,y) so, you need to draw the axis and you'll found a rectangle (attached)
It is not a square because its side and height are not equal.
It is not a parallelogram because there are no diagonals.
It is not a trapezoid because it has parallels sides.
It's a rectangle because it has two pairs or parallels, one longer than the other.
Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.) Tiles area: 221.5584 square units area: 78.5 square units area: 452.16 square units area: 36.2984 square units area: 314 square units area: 886.2336 square units Pairs radius: 12 units arrowBoth diameter: 16.8 units arrowBoth radius: 3.4 units arrowBoth diameter: 10 units arrowBoth
find the volume of the cylinder 13mm and 16mm answer choices
A. 16,990
B. 8,491
C. 4,247
D. 2,369
The volume of the cylinder of a radius of 13mm and a height of 16mm
is, B. 8491 mm³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The cylinder has a radius of 13mm and a height of 16mm.
Therefore, The volume of this cylinder is,
= π×(13)²×16 mm³.
= 8,490.56 mm³.
Q. find the volume of the cylinder having a radius of 13mm and a height of 16mm answer choices.
A. 16,990
B. 8,491
C. 4,247
D. 2,369
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Find the value of the expression below.log5 2 + log5 10 - log5 4 A.0 B.1 C.3 D.2
The solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is calculated as:-
E = log₅ ( 2 )+ log₅( 10 ) - log₅( 4 )
Use Logarithmic property Loga(x / y ) = Loga(x) - Loga(y)
E = log₅ ( 2 ) + log₅( 10 / 4 )
Use Logarithmic property Loga(x y ) = Loga(x) + Loga(y)
E = log₅ [ 2 x ( 10 / 4 ) ]
E = log₅ ( 5 ) = 1
Therefore, the solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.
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Sara wrote 524 words in her journal. Then she crossed out 56 words and added 95 new words. How many words are written in her journal now?
find the values of x and y in the following equation. (x + yi) + (4 + 9) = 9 -4i
In this question we solve the given complex number equation. By comparing real and complex components on both sides of the equation, we find the values satisfying the equation are x = 5 and y=-13.
Explanation:In this complex number equation, we must solve for x and y: (x + yi) + (4 + 9) = 9 -4i. Begin by simplifying the left side of the equation, to give (x + 4 + yi +9i) = 9 - 4i. This further simplifies to (x + 4) + (y + 9)i = 9 -4i.
Now we can see that the real component of the equation (x + 4) must equal the real component on the other side of the equation (9), and the complex component of the equation (y + 9)i must equal the complex component -4i. Setting these equal gives x + 4 = 9 and y + 9 = -4.
Solving these gives x = 5 and y = -13, which are the values for x and y satisfying the equation.
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Write a number sentence that compares 3/5 and 5/6
5x−4y=−10
−4x+5y=8
Solve System of equations
For what interval is the function f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x}) continuous?
64 is 4 times the difference between Sarah's age a and 44 assume Sarah is older than 44 write an equation to determine Sarah's age a
Answer:
Sarah's age is 60.
Step-by-step explanation:
We have that Sarah's age is a.
The problem states that 64 is 4 times the difference between Sarah's age a and 44.
So
[tex]a - 44 = \frac{64}{4}[/tex]
[tex]a - 44 = 16[/tex]
[tex]a = 44 + 16[/tex]
[tex]a = 60[/tex].
Sarah's age is 60.
Olive wants to invite friends over for some ice cream. She has a total of 8 pints of ice cream in her freezer. If she splits each pint into 1/2 pint servings, how many servings of ice cream will olive have?
A tree on a hillside casts a shadow c = 235 ft down the hill. if the angle of inclination of the hillside is b = 16° to the horizontal and the angle of elevation of the sun is a = 46°, find the height of the tree. (round your answer to the nearest foot.)
Final answer:
By using the tangent function with the effective angle formed by the difference between the sun's elevation and the hill's incline, and the length of the shadow, we calculate the height of the tree to be approximately 136 feet.
Explanation:
To find the height of a tree on a hillside, we utilize the given angles and the length of the shadow it casts. The shadow is cast down the hill (c = 235 ft) with the hill inclining at an angle of 16° to the horizontal (b) and the sun's angle of elevation at 46° (a). To solve this, we can use trigonometry, specifically the concept of similar triangles and the tangent function, which relates the angle to the ratio of the opposite side over the adjacent side in a right triangle.
First, we find the effective angle Θ the sun's rays make with the hillside, which is the difference between the sun's elevation angle and the hill's inclination angle: Θ = 46° - 16° = 30°. Then, using the tangent function which involves the height of the tree (h) and the length of the shadow (c), we set up the equation tan(Θ) = h / c. Substituting the values gives tan(30°) = h / 235 ft.
Next, we solve for h: h = 235 ft x tan(30°). Calculating this, we find h is approximately 135.7 ft. Therefore, rounding to the nearest foot, the height of the tree is 136 feet.
which of the following values of x makes the rational expression below undefined? x-25/x+13
a. 13
b. 0
c. 25
d. -13
Answer:
Option D
Step-by-step explanation:
We will check each option for the given expression (x-25)/(x+13)
(A). for x = 13
[tex](\frac{x-25}{x+13})=\frac{13-25}{13+13} =\frac{-12}{26}[/tex]
So expression is defined.
(B). for x = 0
[tex]\frac{x-25}{x+13}=\frac{0-25}{0+13} =(\frac{-25}{13})[/tex]
So expression is defined.
(C). For x = 25
[tex](\frac{x-25}{x+13})=\frac{25-25}{25+13} =0[/tex]
So expression is defined
(D). For x = -13
[tex]\frac{x-25}{x+13}=\frac{-13-25}{-13+13}=( \frac{-38}{0})[/tex]
Function is not defined.
Option D is the answer.
A newborn child receives a $9,000 gift toward a college education from her grandparents. How much will the $9,000 be worth in 18 years if it is invested at 7.6% compounded quarterly? Round to the nearest cent.
what is the greatest common factor of 30 and 18
Hello there! :)
The GCF of 30 and 18 is 6.
STEPS:
List all the factors of 30 and 18:
18: 1, 2, 3, 6, 9, 18
30: 1, 2, 3, 5, 6, 10, 15, 30.
So the GCF is 6.
Hope this helps you!
~Just a felicitous girlie
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[tex]SilentNature :)[/tex]
The system of equations is graphed on the coordinate plane. y=−12x−1y=14x−4 A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3). Enter the coordinates of the solution to the system of equations in the boxes. ( , )
solve 3y − 7 = y + 5 and explain each step please so i understand
gabriel made 4 small meatloaves. he cut each meatloaf into fourths. how many 1/4 size pieces of meatloaf does gabriel have
The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .
Melissa bought a cake that cost $75. the sales-tax rate is 10 percent. what is the total amount she paid for the cake
Answer:
The total amount that Melissa paid for the cake is $82.5
Step-by-step explanation:
we know that
The total amount that Melissa paid for the cake is equal to the cost of the cake plus the sales tax
we have that
the cost is equal to $75
Find the sales tax
The sales tax is 10%, therefore find the 10% of the cost of the cake
10%=10/100=0.10
so
(0.10)*$75=$7.5
Adds the cost and the sales tax
$75+$7.5=$82.5
Solve 12 = x/4 algebraically. Then, check your answer.
what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x
3.1 Q15
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 70°, it's height, f(x), in feet, can be modeled by:
[tex]f(x)=-0.06x^2 + 2.7x + 5.9[/tex]
where x is the shot's horizontal distance, in feet, from its point of release.
What is the maximum height of the shot and how far from it's point of release does this occur?
The maximum height reached by the shot is 36.375 feet. This occurs at a horizontal distance of 22.5 feet from its point of release.
Explanation:This is a question about the maximum height of a shot put. The equation presented here is a quadratic function, and it has the form of a parabola. The maximum value of a parabola that opens downwards (as in this case, where the coefficient of x2 is negative) is given at its vertex.
To find the 'x' coordinate of the vertex, use the formula -b/2a, where 'a' is the coefficient of x2 and 'b' is the coefficient of 'x'. In this case, 'a' is -0.06, and 'b' is 2.7. -b/2a = -(2.7)/(2*-0.06) equals 22.5 feet. This is the horizontal distance from the point of release where the shot reaches the maximum height. To find the maximum height, substitute the value of 'x' into the equation, f(22.5) = -0.06*(22.5)2 + 2.7*22.5 + 5.9. This gives the maximum height as 36.375 feet.Learn more about Maximum Height of Shot here:
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A cake recipe suggests a cooking temperature of 325 °F if the batter is less than one inch thick and 350 °F if the batter is more than one inch thick. If the cake batter has a volume of 110 in3 and your cake pan is 9 inches by 11 inches, what does the oven need to be set at if the oven temperature settings are in degrees Celsius? (round to nearest whole number) A) 140 °C B) 163 °C C) 177 °C D) 190 °C
Answer C
the shape of cake pan is usually cuboid
volume of cuboid = length * breadth * height
110 = 9 *11 * height
height = 10/9 = 1.11 inches
so, the batter is more than 1 inch thick,
the temperature required is 350 degree F or 177 degree C
what is the square root of 64 multiplied by 72 divided by the sum of 43 plus 0
Can someone please help me with this ?
Answer:
E. 2i√5
Step-by-step explanation:
√-20 = (√-1)(√20) = i·(2√5) = 2i√5
what ia 10 + 10 -10 x 5932
Answer:
The answer would be 59,320
Step-by-step explanation:
10+10 is 20
20-10 is 10
10x5,932 is 59,320