Answer:
there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
Step-by-step explanation:
First, we need to find the number of different combinations of a starter dish and a main dish. This is simply the number of combinations of 2 items from 8 starters and 15 main dishes, which can be calculated using the formula for combinations:
C(8 + 15, 2) = C(23, 2) = (23 * 22) / (2 * 1) = 276
Similarly, the number of different combinations of a main dish and a dessert dish is:
C(15 + 9, 2) = C(24, 2) = (24 * 23) / (2 * 1) = 276
Finally, the number of different combinations of a starter dish, a main dish, and a dessert dish is:
C(8 + 15 + 9, 3) = C(32, 3) = (32 * 31 * 30) / (3 * 2 * 1) = 5680
In total, there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
A tower with a wire that extends from the top of the tower to the ground is shown below. 55 ft. 68 ft. X 40 ft. Which of the following ratios could be used to find the measurement of angle æ, in degrees?
The ratio used to find the measurement of angle x is given as follows:
cos(x) = 40/68.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For angle x, we have that:
The adjacent side is of 40 ft.The hypotenuse is of 68 ft.Hence the ratio is given as follows:
cos(x) = 40/68.
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Richard can type 60 words per minute. At this rate, how low will it take him to type 720 words?
Answer:
It will take Richard 12 minutes to type 720 words.
Step-by-step explanation:
720 ÷ 60 = 12
A factory has two smokestacks. The rate of particle pollution produced is 12 kg / h
for the first smokestack and 32 kg / h
for the second. The manufacturing process requires that the first smokestack operates 2
hours longer than 1. 5
times as long as the second. A local pollution control board has ordered that the factory produce no more than 374 kg
of particle pollution per day. What is the maximum number of hours per day that each smokestack can operate?
Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.
According to the question a factory has two smokestacks:
Let first smokestack take x number of hours per day
and second smokestack take y number of hours per day
The rate of particle pollution produced is 12 kg/h for the first smokestack
and rate of particle pollution produced is 32 kg/h for the second.
A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.
so, equation becomes 12x + 32y = 374
also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.
so, x = 2 + 1.5y
putting value of x in other equation
12(2 + 1.5y) + 32y = 374
24 + 18y + 32y = 374
50y = 350
y = 7 hours
x = 2 + 1.5(7) = 12.5 hours
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Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plan in still air.
The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.
What is a linear equation?
This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.
Let the plane speed be 'P' and the wind speed be 'W'.
We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.
So, we get an equation as
P + W = 158 ...(1)
Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.
So, we get another equation as
P - W = 112 ...(2)
Now, on adding the equations we get,
⇒P + W + P - W = 158 + 112
⇒2P = 270
⇒P = 135
Now substituting the value into either equation, we get
⇒P + W = 158
⇒135 + W = 158
⇒W = 23
Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.
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E) Find the area of a rectangular field measuring 27.04 m by 20.21 m.
i) How much would it cost to spray insecticide on the field if the rate is $0.70 per square metre? Give your answer to the nearest dollar.
which rule best represents the dilation that was aplied to figure p to created figure q
The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).
The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.
When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒ (x + a, y + b).
The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.
Therefore, the correct transformation used is (b) (x, y) → (x+5, y+3).
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The given question is incomplete , the complete question is
A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?
(a) (x, y) → (x-5, y-3)
(b) (x, y) → (x+5, y+3)
(c) (x, y) → (x-3, y-5)
(d) (x, y) → (x+3, y+5)
1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.
A.) QIV
B.)QII
C.)QI
D.)QIII
Answer:
D.) QIII
Step-by-step explanation:
Because 1.2 radians is in between 7π/6 and 5π/4
Use the figure to find the measures of the numbered angles.
4
The value of ∠4 in the given transversal line image is; 85°
How to find the corresponding angles?Corresponding angles are defined as the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
In this question, we see that ∠3 is a corresponding angle to 95°. Thus;
∠3 = 95°
Now, ∠4 forms a straight line with ∠3 and as such they will sum up to 180 degrees as sum if angles on a straight line sums up to 180 degrees. Thus;
∠4 = 180 - 95
∠4 = 85°
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Jorge's printer can print 24 pages in 15 minutes. How many pages can it print in 3/4
hour. How many pages can he print in 1 hour?
Answer:
3/4 hour-72
1 hour- 92
Step-by-step explanation:
3/4-
24 x 3= 72
1-
24 x 4 =92
I neeeeeeeeeeedddddd help pls!!!!! What is 45 x 23
The multiply of 45 and 23 is = 1035 we calculate this by simple multiplication method.
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
And here we have 2 number 1st is 45 and 2nd is 23 so here we will multiply
4 5
x 2 3
----------------
1 3 5
9 0 x
---------------
1 0 3 5
--------------
final ans is 1035
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a person eating at a cafeteria must choose 3 of 19 vegetable on offer. calculate the number of elements in the sample space for this experiment
The number of elements in the sample space for this experiment is 969.
If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:
nCr = n! / [r!(n - r)!]
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:
19C3 = 19! / [3!(19 - 3)!]
= 19! / (3!)(16!)
= 969
Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.
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The Screaming Salamanders, a new rock band, released their new music video early for subscribers of their fan page. When the video was released to the public, it already had 2,642 views. One day later, the number of views increased to 3,963, and the band expects that the number of views will continue to grow each day. Write an exponential equation in the form y=a(b)x that can model the total number of views, y, x days after the music video was released to the public. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation is y=2,642(2.5)ˣ. x represents the number of days.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
Given that a video was released to the public, it already had 2,642 views.
One day later, the number of views increased to 3,963.
The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605
Assume that the exponential function y = a(b)ˣ represents the number of viewers. x represents the number of days.
Putting x = 0 and y = 2,642 in y = a(b)ˣ:
2,642 = a(b)⁰
a = 2,642
Putting x = 1 and y = 6,605 in y = a(b)ˣ:
6,605 = a(b)¹
Putting a = 2,642:
6,605 = 2,642(b)¹
b = 6,605/2,642
b = 2.5
Therefore, an exponential equation is y=2,642(2.5)ˣ.
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Please! I really need help.
The answers are given as follows:
2
a)
A = 8
b = 10
x = 118°
y = 62°
b)
a = 8
b = 15
y = 50
x = 100°
3)
(a)
∠2 = 25°
∠3 = 65°
∠4 = 65°
∠5 = 90°
(b)
since SL = 10,
i) LT 10
ii) TM = 10
iii) SM = 10
4)
a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°
If FA = 27, then LO = 13.5
The above are resolved using the properties of Parallelograms; Rhombus, and Rectangle
Since the above answers are justified by the qualities or properties of :
Parallelograms; Rhombus, and Rectangle, lets look at them one by one.
2
a)
A = 8 - opposite sides of a parallelogram are equal in length
b = 10 -opposite sides of a parallelogram are equal in length
y = 62° - opposite angles of a parallelogram are of equal measure.
x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2
= 118°
3)
(a) Here we have a Rhombus.
∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2
∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]
(b)
since SL = 10,
i) LT 10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal
iii) SM = 10 - All sides of a Rhombus are equal
4) Here we have a Rectangle.
a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ = 90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)
If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,
LO = FA/2
LO = 27/2
LO = 13.5
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How to solve this question ??
The number in question is the magic sum of the square. The outcome is the same as if you multiply the three integers in each column together and then add the three products: 8, times 3, 4, 1, 5, 6, 7, and 2 equals 225. This quantity is known as the magic square product.
What is an integers?The term "integer" refers to any number that is not zero, a positive natural number, or a negative integer denoted by a minus sign. Because they are diametrically opposed to their positive counterparts, negative integers are additive.
When representing a group of numbers in mathematical notation, the blackboard bold mathbb Z or boldface Z are frequently used. The word "integer" is pronounced "IN-tuh-jer" and refers to a whole number that can be positive, negative, or zero.
A few examples of integers are -5, 1, 5, 8, 97, and 3,043. Non-integer numbers include the figures -1.43, 1 3/4, and 3.14.
The integers are a collection of all whole numbers and their antipodes. Decimal points and fractions are not included in the set of integers. The numbers 2, 5, 0, 12, 244, 15, and 8 are examples.
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Solve for x *
04
45
O x = 50
Ox=8
x = 48.2
x = 40.5
20
S
18
R
Answer:
x = 40.5
Step-by-step explanation:
SQ is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is
[tex]\frac{PS}{RS}[/tex] = [tex]\frac{PQ}{RQ}[/tex] ( substitute values )
[tex]\frac{20}{18}[/tex] = [tex]\frac{45}{x}[/tex] ( cross- multiply )
20x = 18 × 45 = 810 ( divide both sides by 20 )
x = 40.5
Y is directly proportional to x when y=30 x=6. Work out an equation connectng y and x
The equation connecting y and x when y is directly proportional to x and y = 30 when x = 6 is y = 5x.
If y is directly proportional to x, we can write the equation in the form:
y = kx
where k is the constant of proportionality.
To find k, we can use the values of y and x given:
y = 30, x = 6
When we enter these values into the formula above, we obtain:
30 = k * 6
Solving for k, we get:
k = 30/6 = 5
Therefore, the equation connecting y and x when y is directly proportional to x is:
y = 5x
When two variables are directly proportional, it means that when one variable increases or decreases, the other variable changes in the same proportion. In this scenario, we are given that y is directly proportional to x and we are also given a specific point on the line, (6, 30). Using this information, we can solve for the constant of proportionality k and write the equation connecting y and x as y = kx, where k is 5.
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What was the CPI for 2020 if 2019 was the base year?
A. 120
B. 125
C. 130
D. 135
What was the CPI for 2021 if 2019 was the base year?
A. 145
B. 150
C. 155
D. 160
Answer: D and C
Step-by-step explanation:
To get the value of a market basket you would add up the cost of each year so
2019 market basket = 2.50 + 1.00 + 3.75 = 7.25
2020 market basket = 2.25 + 3.00 + 4.50 = 9.75
2021 market basket = 3.00 + 3.25 + 5.00 = 11.25
now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135
CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155
Suman found a great sale on bracelets. With the money in her pocket, she can buy 5 bracelets and have $3 left or she could by 2 bracelets and have $9 left. Write and solve an equation to find out how much each bracelet costs.
Step-by-step explanation:
9-3 =6
So we have 6 dollars for 3 bracelets
Which means each bracelet costs 2 dollar each
So 9x-3x=6x
Find the distance between the points L(7,−1) and M(−2, 4).
The exact distance between the two points is
Answer:
[tex]\sqrt{106}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]
how to use the five number summary to give the smallest intervat that we know contains the 30th percentile
The five number summary is the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and the maximum.
To give the smallest interval that we know contains the 30th percentile, we would take the 25th percentile and the 30th percentile. So, the smallest interval that we know contains the 30th percentile would be [25th percentile, 30th percentile].
The smallest interval that contains the 30th percentile is [25th percentile, 30th percentile], which is found using the five number summary (minimum, first quartile, median, third quartile, and maximum).
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Question 12(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Which point is a solution of the system of linear equations?
x - 3y = 4
y = -3x + 2
The solution of the given system of linear equations is (1, -1)
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given is a system of linear equations, x - 3y = 4 and y = -3x + 2, we need to find the point which is the solution of the system,
The linear equations are :-
x-3y = 4...(i)
y = -3x+2....(ii)
Put eq(ii) in eq(i)
x-3(-3x+2) = 4
x+9x-6 = 4
10x = 10
x = 1
Put x = 1 in eq(ii)
y = -3+2
y = -1
Therefore, the solution point is (1, -1)
We can find the solution point by graphing method also, we will plot the graph of the lines and the line where intersects is the solution point is (1, -1) [attached]
Hence, the solution of the given system of linear equations is (1, -1)
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The complete question is (Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Which point is a solution of the system of linear equations?
x - 3y = 4
y = -3x + 2
A) (9,0)
B) (-5, 8)
C) (1, 1)
D (1, -1)
Henry has 30 coins. He has 1 fewer pennies than dimes. he has 2 fewer nickels than dimes. how many dimes does Henry have?
A : 3
B: 9
C: 11
D: 27
Answer:
C 11
Step-by-step explanation:
you have 1 less penny than dimes which is 10 pennies
you have 2 less nickels than dimes which is 9
11+10+9=30
Please help ASAP
PLEAAEE PUT ONLY CORRECT ANSWERS THIS IS EXTRA CREDIT AND I NEED MY GRADE TO GO UP PLEASE ANYONE HELP
Answer:
Step-by-step explanation:
... good luck
-2x + 3y = -5
3x - 4y = 6.
Anshumann wants to paint the wall shown in the diagram below. In order to buy the paint, he will need to know the area of the wall. What is the area of the wall?
1 point
Answer: 240 ft²
Step-by-step explanation:
Break the diagram into a rectangle and triangle:
Area of Rectangle + Area of Triangle = Total area of Wall
(20x10) + 1/2(20 x 4) = Area of wall
200 + 40 = Area of wall
240 ft² = Area of wall
Hare Krishna :)
a statistical method for identifying cost behavior is the:A. Scatter diagram methodB. High-low methodC. Composite methodD. CVP charting methodE. Least-squares regression method
The statistical method that is used for identifying the cost behavior is (e) Least Squares regression method .
The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .
This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.
The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.
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The given question is incomplete , the complete question is
A statistical method for identifying cost behavior is the:
(a) Scatter diagram method
(b) High low method
(c) Composite method
(d) CVP charting method
(e) Least Squares regression method
Determine, by inspection, which of the following products are multiples of 30. 22 x 3 x 5 2 x 3² x 5 22 × 53 23 x 3² x 5²
By inspection, the following products which are multiples of 30 are:
2² x 3 x 52 x 3² x 52³ x 3² x 5²What is a Multiple?This is referred to as a number that may be divided by another a certain number of times without a remainder.
The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D were chosen as the correct choice.
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Need answersjjsjsjdjejejsjs
What is the average rate of change of the function -4≤x≤-3
Answer:
Step-by-step explanation:
The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.
If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:
Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))
So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
180
180
How far would Rahul drive in 180 minutes?
The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
What is meant by the speed of an object?
A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.
The formula of speed = Distance covered /Time taken
Given,
Distance travelled = 10 miles
Time taken to travel 10 miles = 20 minutes
Speed = Distance/ time = 10/20 = 0.5miles/min
Now given the speed remains constant throughout the journey.
So the distance travelled in 3 hours = 3 * 60 = 180 minutes
Distance = speed * time = 0.5 * 180 = 90 miles.
Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
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