Answer:
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
Step-by-step explanation:
In order to calculate the amount of each ingredient they need for 6 liters of punch we can first create fractions for each ingredient based on the proportions we were given. This is shown bellow:
2 litters lemonade + 1 litter pineapple juice + 1 litter ginger ale = 4 litters punch
Then we have:
lemonade = 2/4
pineaple juice = 1/4
ginger ale = 1/4
If we want to make 6 liters of punch we can just apply this fractions to know how much of each we need:
lemonade = 6*(2/4) = 12/4 = 3 litters
pineaple juice = 6*(1/4) = 1.5 litters
ginger ale = 6*(1/4) = 1.5 litters
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
What are the similarities between the sine, cosine,
and tangent ratios? What are the differences?
Answer:
Similarities: All the trigonometric functions are periodic functions. All these trigonometric function values can be found by using special right triangles from the unit circle. Diffferences: The tangent has different domain and range values from sine and cosine. The tangent function is not a continuous function, unlike sine and cosine.
Step-by-step explanation:
The similarities and differences between the sine, cosine, and tangent ratios are given.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The sine, cosine, and tangent are three trigonometric ratios used in geometry to relate the angles of a right triangle to the lengths of its sides.
Similarities:
All three ratios involve comparing two sides of a right triangle to each other.
They are all functions of an angle and are dependent on the measure of the angle and not the size of the triangle.
They are all defined as ratios of two sides of a right triangle, and the values of these ratios depend on the angle in question.
Differences:
The sine and cosine ratios are periodic functions with a period of 2π, while the tangent ratio is not periodic, and its graph has vertical asymptotes.
The sine and cosine ratios are always between -1 and 1, while the tangent ratio can take any value, positive or negative.
The cosine of an angle is equal to the sine of its complement, while the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.
Hence, the similarities and differences between the sine, cosine, and tangent ratios are given.
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A sporting goods company has observed a decline in sales following the end of each of its advertising campaigns. The decline in
sales follows the formula S=42e -0.16t, where is the monthly sales in millions of dollars and is the number of months after the end
of the advertising campaign. What will the monthly sales be three months after the end of the current campaign, rounded to the
nearest hundred thousand dollars?
Answer:
$26.0 million
Step-by-step explanation:
Use t=3 and do the arithmetic.
S = 42e^(-0.16·3) = 42e^-0.48 ≈ 26.0
Three months after the end of the campaign, monthly sales are predicted to be $26.0 million.
Answer:
$26.0 million
Step-by-step explanation:
Seraphina says that △KLM is a right
triangle. Is she correct? Explain.
J K
N M 16 cm L
Without additional details about the triangle's angles or side lengths, it cannot be determined whether △KLM is a right triangle.
Explanation:Based on the information given in your question, it is impossible to definitively state whether Seraphina is correct in her assertion that △KLM is a right triangle. Checking if a triangle is a right triangle typically involves measuring its angles or applying the Pythagorean theorem to its sides. However, there is insufficient information in your question to do either. For instance, you mentioned a '16 cm' measurement but did not specify to which side it corresponds. Similarly, no angles are provided. Thus, without additional information, the claim that △KLM is a right triangle cannot be confirmed or refuted.
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HELP QUICK PLEASE!!
A cell phone costs $168, a battery charger costs $10, and batteries cost $5. What is the sales tax and total price for purchasing these items if the sales tax rate is 6%?
Whats the total sales tax?
Answer: $193.98
Step-by-step explanation:
$168 + $10 + $5 = $183
$183 x 6% = $10.98
$183 + $10.98 = $193.98
To find the sales tax and total price for purchasing these items, calculate the sales tax by multiplying the total cost of the items by the sales tax rate, and then add the sales tax to the total cost of the items.
Explanation:To find the sales tax and total price for purchasing these items, we need to calculate the amount of sales tax and then add it to the total cost of the items.
First, calculate the sales tax by multiplying the total cost of the items ($168 + $10 + $5 = $183) by the sales tax rate (6% or 0.06): $183 * 0.06 = $11. Therefore, the sales tax is $11.To find the total price, add the sales tax to the total cost of the items: $183 + $11 = $194.Therefore, the sales tax is $11 and the total price for purchasing these items is $194.
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Plot the coordinates
A (1, 2), B (4, 5), C (4, –3), and D (1, –1).
If the points are connected, what polygon is formed?
Triangle
Quadrilateral
Pentagon
Hexagon
Answer:
Quadrilateral
Explanation:
there are only for points,
triangle= three points
hexagon= 6 points
pentagon= 5 points
The A(1, 2), B(4, 5), C(4, -3), and D(1, -1) forms a quadrilateral.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
The points A (1, 2), B (4, 5), C (4, -3), and D (1, -1) form a quadrilateral
as all four points are noncolinear.
These four points represent four vertices of a quadrilateral.
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Upper bound perimeter of rectangle 15.8 m x5.2 m
Answer:
82.16 m²
Step-by-step explanation:
15.8 m x 5.2 m
Which of the following is an irrational number? A. 16 B. 0.4 C. 4 D. 16
Please help me with this question.
Answer:
y = 6
Step-by-step explanation:
if the triangles are congruent then the corresponding sides are equal.
so
4x + 1 = 13
4x = 13 -1
4x = 12
Therefore x = 3
Now
8x - 2y = 2x + y
y + 2y = 8x - 2x
3y = 6x
3y = 6 * 3
3y =18
Therefore y = 6
Answer:
y = 6
Step-by-step explanation:
Since the triangles are congruent then corresponding sides are congruent
4x + 1 = 13 ( hypotenuse are congruent )
Subtract 1 from both sides
4x = 12 ( divide both sides by 4 )
x = 3
Thus
8x - 2y = 2x + y ( substitute x = 3 )
8(3) - 2y = 2(3) + y, that is
24 - 2y = 6 + y ( subtract y from both sides )
24 - 3y = 6 ( subtract 24 from both sides )
- 3y = - 18 ( divide both sides by - 3 )
y = 6
Match the formulas to the correct text. I. A equals the product of B or H, divided by 2. II. A equals the product of B times H, divided by 2. III. D equals P sub T plus the quantity 2 times T, divided by 3. IV. D equals P sub T times the quantity 2 times T, divided by 3. V. R sub T equals R sub 1 plus R sub 2. VI. R sub T equals R sub 1 plus the sum R sub 2.
The correct matches are as follows:
Formula | Text
I. A equals the product of B or H, divided by 2. | Incorrect
II. A equals the product of B times H, divided by 2. | Correct
III. D equals P sub T plus the quantity 2 times T, divided by 3. | Correct
IV. D equals P sub T times the quantity 2 times T, divided by 3. | Incorrect
V. R sub T equals R sub 1 plus R sub 2. | Correct
VI. R sub T equals R sub 1 plus the sum R sub 2. | Incorrect
Here is a more detailed explanation of each match:
II. A equals the product of B times H, divided by 2.
This formula is correct for the area of a triangle, where A is the area, B is the base, and H is the height.
III. D equals P sub T plus the quantity 2 times T, divided by 3.
This formula is correct for the average distance traveled, where D is the total distance traveled, P sub T is the starting point, and T is the time taken.
V. R sub T equals R sub 1 plus R sub 2.
This formula is correct for the total resistance in a parallel circuit, where R sub T is the total resistance, and R sub 1 and R sub 2 are the resistances of the two parallel resistors.
The other formulas are incorrect. For example, formula I states that A is equal to the product of B or H, divided by 2. This is not correct, because A cannot be equal to two different things at the same time. Formula IV is incorrect because it states that D is equal to P sub T times the quantity 2 times T, divided by 3.
This is not correct, because the average distance traveled cannot be equal to the starting point multiplied by the time taken. Formula VI is incorrect because it states that R sub T is equal to R sub 1 plus the sum R sub 2.
This is not correct, because the total resistance in a parallel circuit cannot be equal to the sum of the resistances of the two parallel resistors.
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Write the equation of a slope intercept form with a slope of 9 and a y-intercept of -3
Answer:
y = 9x-3
Step-by-step explanation:
since the slope intercept form is in the y=mx+b form, you just have to plug in the slope for m and the y-intercept for b.
Which expression is equivalent to x4 + 4x² – 45?
Answer:
Step-by-step explanation:
x4 + 4x² – 45 = x^4 + 4x^2 - 45. Use " ^ " to indicate exponentiation.
Temporarily substitute p for x^2. Then we have:
p^2 + 4p - 45, or
(p + 9)(p - 5)
But p = x^2.
Therefore, our expression becomes
(x^2 + 9)(x^2 - 5)
We could stop here or we could factor further.
Hint: x^2 - 5 = (x - √5)(x + √5); (x^2 + 9) factors into imaginary roots.
A water tank is in the shape of a cylinder with a diameter of 20 feet and a height of 20 feet. The tank is 70% full. About how many gallons of water are in the tank? Round your answer to the nearest whole number.
Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V = [tex]\pi r^2h[/tex]
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V = [tex]\pi * 10^2*20 = 6283.19 ft^3[/tex]
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:
[tex]\frac{70}{100} * 6283.19 = 4398.23 ft^3[/tex]
1 cubic foot ([tex]ft^3[/tex]) is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
32886.476 gal
Step-by-step explanation:
Given:
Diameter of tank 'd'= 20 ft
∴radius 'r'= d/2=> 20/2=> 10ft
Height 'h' = 20 ft
Volume of cylinder can be determined by
V= π r² h
Substituting the values in above equation
V= π (10)² (20) =>π(100)(20)
V=2000π ft³
When the tank is 70% full.
70% of 2000π =>0.7 x 2000π
1400π ft³
As we know that, 1ft³ = 7.481 gal
1400π ft³= 1400π x 7.481 gal
1400π ft³= 32886.476 gal
Therefore, if the tank is 70% full then 32886.476 gallons of water are in the tank
Find the gradient of the line segment between the points (4,3) and (5,7)
Answer:
gradient = 4
Step-by-step explanation:
Calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (5, 7)
m = [tex]\frac{7-3}{5-4}[/tex] = 4
The gradient of the line segment between the points (4,3) and (5,7) is 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The gradient of the line is also called as slope of line
Gradient of the line segment between the points (4,3) and (5,7)
Gradient = 7-3/5-4
=4/1
Hence, the gradient of the line segment between the points (4,3) and (5,7) is 4
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Match the sequence (term) with the correct type of sequence (definition). (4 points) Group of answer choices 128, 32, 8, 2, ... 1, 3, 9, 27, ... 5, 10, 15, 20, ... 20, 17, 14, 11, …
Answer:
Step-by-step explanation:
In an arithmetic sequence, the consecutive terms differ by a common difference, d. Therefore,
d = Term 2 - Term 1 = Term 3 - Term 2
In an geometric sequence, the consecutive terms differ by a common difference, r. Therefore,
r = Term 2 /Term 1 = Term 3 / Term 2
1) 128, 32, 8, 2, .. Is a geometric sequence
r = 32/128 = 1/4
2) 1, 3, 9, 27, .. Is a geometric sequence
r = 3/1 = 3
3) 5, 10, 15, 20, ...is an arithmetic sequence
d = 10 - 5 = 5
4) 20, 17, 14, 11, … is an arithmetic sequence
d = 17 - 20 = - 3
Miss Penny inherits £910.
She decides to save some of the
money and spend the rest.
The ratio of savings to spending
money is 7:6
How much does she save and how
much does she spend?
Savings
£
[2]
Spending money £
[2]
Answer:
Sacing 490 spending 420
Step-by-step explanation:
If a is a fraction
Saving 7a Spending 6a
7a + 6a = 910
13a = 910
a = 910/13
a = 70
Saving 7×70 = 490
Spending 6×70 = 420
The sum is 490 + 420 is equal to 910
Item 4 Find the median, first quartile, third quartile, and interquartile range of the data. 132,127,106,140,158,135,129,138 median: first quartile: third quartile: interquartile range
The median of this data set is 133.5, the first quartile (Q₁) is 128, the third quartile (Q₃) is 139, and the interquartile range (IQR) is 11.
Explanation:First, arrange the data in ascending order: 106, 127, 129, 132, 135, 138, 140, 158.
Median: The median is the middle value of a data set. Since there are 8 numbers, the median is the average of the 4th and 5th values: (132+135) ÷ 2 = 133.5.
First Quartile (Q₁): This is the median of the lower half of the data. Here, it is the average of the 2nd and 3rd values: (127+129) ÷ 2 = 128.
Third Quartile (Q₃): This is the median of the upper half of the data, which is the average of the 6th and 7th values: (138+140) ÷ 2 = 139.
Interquartile Range (IQR): You find the IQR by subtracting Q₁ from Q₃, hence IQR = 139 - 128 = 11. The IQR represents the middle 50% of the values when ordered from lowest to highest.
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In order to answer the question correctly, please use the following image below:
Find the value of x.
X=(Blank)
Please show all the work on how you got your answer.
Answer:
106°
Step-by-step explanation:
(152 + 60)/2
212/2
106°
You are trying to improve communication with your staff by posting graphs of significant statistics on the employee bulletin board. You recently calculated the percentage of time employees spend on each of six major tasks. Because you would like the employees to appreciate each task as a percentage of their whole day, you will post these figures using a pie graph.
Answer:
Yes, the Pie Graph is the right choice.
Step-by-step explanation:
A Pie Graph, or Sector Graph is one of the good options to display, usually relative frequencies, proportionally.
In a Pie Graph the focus is to show the importance of each observation, or category in comparison with the whole.
You need to be careful with the angles, since 180º is equal to 50%, 90º to 25% and 360º is equal to 100% so each "slice" each portion must directly proportional to the angles of one circle.
Since the goal is to show the importance of each work to the whole team, definitely a Pie Graph is one the appropriate one to pick.
A bus travels 120 km in 2 hours. What is the speed of the bus?
Answer:
60 km/hour
Step-by-step explanation:
To find the speed, divide the number of kilometers by the number of hours
kilometers/hours
120 km/ 2 hours
120/2=60
60 km/hour
The speed of the bus is 60 kilometers per hour
Answer:
60km/hr
Step-by-step explanation:
120 divided by 2 equals 60
Simplify: (5mn3)3 • (5mn)3
Answer:
photomath said 375m³n³
Step-by-step explanation:
-use exponent rules 3×(5mn)³
- calculate the product 3×125m³n³
-Solution 375m³n³
simplify 5/12+-5/18-7/24
Answer:
-11/72
Step-by-step explanation:
5/12+-5/18-7/24
We need to get a common denominator of 72
5/12 *6/6 =30/72
5/18 * 4/4 = 20/72
7/24 *3/3 = 21/72
30/72 -20/72 - 21/72
10/72 -21/72
-11/72
Please help me out! And please show your work!!
|
|
|
v
Answer:
Ratio of perimeters = 5:2
Ratio of areas: 25:4
Step-by-step explanation:
20/8 = 5/2 (ratio of lengths is equal to ratio of perimeters)
[tex](5/4) ^{2}[/tex] = 25/4 (ratio of areas is the square of ratio of lengths)
A scale drawing of an office space uses a scale of 2 inches in 3 yards the scale drawing has an area of 16 in.² what is the area of the actual office space
Answer:
36 Square Yards
Step-by-step explanation:
The Scale Drawing uses a ratio
2 Inches : 3 Yards
Therefore,
1 Inch = 3/2 Yards
If the area of the scale drawing is 16 Inch²
To get the area of the actual office, we multiply by the square of the scale factor.
Scale Factor=3/2
Therefore:
The area of the actual office space
=16X(3/2)² Square Yards
=36 Square Yards
Answer:
36 square yards.
Step-by-step explanation:
This question is solved with rule of three and ratios
We know that 2 inches is equivalent to 3 yards, and the area in the drawing is 16 square inches.
so if
2 inches ---- 3 yards then 1 inch is 3/2 yards.
Let's say that the office is 8 inches x 2 inches = 16 squared inches
Then, if we convert it to yards,
8 inches would be: [tex]8(\frac{3}{2})=12[/tex] yards
and 2 inches would be: [tex]2(\frac{3}{2})=3[/tex] yards
Then, the area of the office would be 12 x 3 = 36 squared yards.
Name the relationship: complementary, or supplementary.
Answer:
See below.
Step-by-step explanation:
1. a and b are supplementary ( they add up to 180 degrees as they are on a straight line).
2,3 and 4 are complementary as in each case a + b = 90 degrees.
Answer:
Complementary angles are the angles which add up to 90°. example - 60° + 30° = 90° . Supplementary angles are those angles which add up to 180° . example - 110° + 70° = 180°.
Step-by-step explanation:
What is............What is 60% of 1200
Answer: [tex]720[/tex]
Multiply
60%×1200=720
Note: When finding the percent of a number always multiply the percent times the number.
Answer:
[tex]720[/tex]
Step-by-step explanation:
[tex]1200 \times \frac{60}{100} \\ = \frac{72000}{100} \\ = 720[/tex]
hope this helps you...
a bag contains 2 coins. some of them are 10 cents coins and all of the others a 5 cent coins.
i) if the number of 10 cent coins is x, write down an expression for the number of 5 cent coins
ii) write down a expression, in terms of x, for the total value, in cents of the 24 coins
Answer:
i) 24 - x
ii) 5x + 120
Step-by-step explanation:
i) There are a total of 24 coins. We see that x of these 24 are 10 cent coins. The rest must be 5 cent coins, so they must be all the 24 coins that are NOT included in the x: 24 - x
ii) We know that there are x 10 cent coins, which are each 10 cents. There are also (24 - x) 5 cent coins, which are each 5 cents. In order to find their total value, we need to multiply the value of the denomination by how many there are of each denomination. So:
10x + 5(24 - x) = 10x + 120 - 5x = 5x + 120
Hope this helps!
Which statements best describe the motion of Car A and Car B? Check all that apply.
Answer:
Car A and Car B are moving in opposite directions.
Car A is moving faster than Car B.
Car A and Car B pass each other at the crossover point on the graph.
Step-by-step explanation:
Hope that helps!
a line passes through the point (-9,7) and has a slope of -4/3 write an equation in point slope form for this line
Pleaseee, I really need help with this❤️
Answer:
(4x + 5)(4x - 3)
Step-by-step explanation:
Given
16x² + 8x - 15
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 16 × - 15 = - 240 and sum = + 8
The factors are + 20 and - 12
Use these factors to split the x- term
16x² + 20x - 12x - 15 ( factor the first/second and third/fourth terms )
= 4x(4x + 5) - 3(4x + 5) ← factor out (4x + 5) from each term
= (4x + 5)(4x - 3) ← in factored form
whcih point on the number line represents the problem. point a point b point c or point d
Answer:
its D 100%
Step-by-step explanation:
Answer:
d
Step-by-step explanation: