The number of ways I have ice cream if the goal is at least 4 flavors is 32192.
We know that from combination formula, C(n ,r) = n!/(r!(n - r)!)
Total number flavors ice cream vendor sells is = 15.
Number of ways I have 4 flavors = C(15, 4)
Number of ways I have 5 flavors = C(15, 5)
Number of ways I have 6 flavors = C(15, 6)
Number of ways I have 7 flavors = C(15, 7)
Number of ways I have 8 flavors = C(15, 8)
Number of ways I have 9 flavors = C(15, 9)
Number of ways I have 10 flavors = C(15, 10)
Number of ways I have 11 flavors = C(15, 11)
Number of ways I have 12 flavors = C(15, 12)
Number of ways I have 13 flavors = C(15, 13)
Number of ways I have 14 flavors = C(15, 14)
Number of ways I have 15 flavors = C(15, 15)
Thus the number of ways I have ice cream if the goal is at least 4 flavors is given by,
= C(15, 4) + C(15, 5) + C(15, 6) + C(15, 7) + C(15, 8) + C(15, 9) + C(15, 10) + C(15, 11) + C(15, 12) + C(15, 13) + C(15, 14) + C(15, 15)
= 32192
Hence the number of ways I have ice cream if the goal is at least 4 flavors is 32192.
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Which expression renames 3/4−7/10 using common denominators?
3/4 and 9/10 using the least common denominator is 15/20 and 18/20.
What is LCM?LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.
Given, are two fractions 3/4 and 7/10 we know the LCM of 4 and 10 is 20.
∴ (3×5)/(4×5) and (7×2)/(10×2).
(we have to multiply same constant to the fraction to retain it's original value).
So, 3/4 and 4/10 using the least common denominator is 15/20 and 14/20.
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The sum of two numbers is 27. The difference between the two numbers is 5. What are the two numbers?
Answer:
x = 16
y = 11
Step-by-step explanation:
x+y = 27
x-y = 5
__________
2x = 27+5
2x = 32 /:2
x = 16
16+y = 27
y = 27-16
y = 11
Write an equation of the line that passes through the given point and is parallel to the given line
The equation of the line that is parallel to 3y - x = - 12 and passes through (18, 2) will be 3y - x + 12 = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation is given below.
3y - x = - 12
The equation of the line that is parallel to the given line is given as,
3y - x + d = 0
The equation that passes through (18, 2) will be given as,
3(2) - 18 + d = 0
6 - 18 + d = 0
d = 18 - 6
d = 12
Then the equation of the parallel line will be 3y - x + 12 = 0.
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Eric ran 3 kilometers in 20 minutes.
Taylor ran 2,550 meters in 17 minutes. Was one person faster than the other or were they running at the same rate?
Answer:It is not possible to answer this question without knowing the rate at which the other person was running.
Step-by-step explanation:
An electric car battery, when fully charged, can travel 520 miles. As the car travels, the charge decreases at a rate of 89 miles every 1 hour.
Enter an equation in slope-intercept form or y = mx + b that shows the amount of battery charge y, in miles, after traveling for x hours.
Answer:
The car can only last for 5 hours.
That's the answer I got.
5.84269662
Step-by-step explanation:
Alright so say I was driving for 2 hours I would have,
342 miles left.
If I were driving for 3 hours I would have,
253 miles left.
If I were driving for 4 hours I would have,
164 miles left.
Now if I were driving for 5 hours I would have,
75 miles left.
Solve for x round to the nearest tenth 33 27
help me its due today
Answer:
(1,-1)
Step-by-step explanation:
my guy, are you good? dude this question is so easy l m a o
anyways, heres the explanation
where there is an "x," replace it with a 1
so: -4-9y = 5
-9y = 9
y = -1
and the question already gives you what x is so:
(x,y)
(1,-1)
1. Which of the following is 60% in fraction form?A. 25B. 35C. 45
Answer:
I think 35
Step-by-step explanation:
A club bought 6 equally priced pizzas and a large $15
bag of chips for a party. They spent a total of $ 69.
Write an equation modeling this, then solve.
I need an answer asappp
(THIS IS DUE TMRW!!)
Explain how to get the Unit Rate for Amount of Miles Ran per Minute for #18. Jaime ran 6 miles in 60 minutes. How far does Jaime run (in miles) per minute? Show all work and then write an explanation.
A mile is 5,280 feet long and an hour is 3,600 seconds long, thus 60 miles per hour is 60 x 5,280 / 3,600 = 88 feet per second.
What is the unit rate formula?How Do I Determine the Unit Rate? The denominator of a unit rate is always 1. To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.
Miles per hour is a relatively typical example of a unit rate that we face on a daily basis. This rate is a unit rate since it describes the number of miles in one hour.
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The balance on a credit card, that charges a 10.5% APR interest rate, over a 1 month period is given in the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily balance, for this card over this 1 month period?
finance charge = $[?]
Round to the nearest hundredth.
The finance charge on the average daily balance for the one month is $2.07.
What is the finance charge?The finance charge is the interest and other fees charged on a credit facility.
To compute the finance charge, we apply the annual percentage rate (APR) on the Average Daily Balance, multiplied by the number of days in the billing cycle, and divided by 365.
Days 1-3: $200 (initial balance) $600 ($200 x 3)
Days 4-20: $300 ($100 purchase) $5,100 ($300 x 17)
Days 21-30: $150 ($150 payment) $1,500 ($150 x 10)
Total = $7,200
Average Daily Balance = $240 ($7,200/30)
APR interest rate = 10.5%
MPR interest rate = 0.875% (10.5%/12)
Finance Charge = $2.07 ($240 x 10.5% x 30/365)
Or $ ($240 x 0.875%)
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Answer: It is C I got it right on the exam
Step-by-step explanation:
2) A normal distribution has mean 700 and standard deviation 50. The probability is 0.6 that a randomly
selected term from this distribution is above x. What is x?
According to the normal distribution data given the value for x is obtained as 687.5.
What is normal distribution?
One of the families of continuous distributions, the standard normal distribution has a mean of zero and a standard deviation of one. Since most observations are grouped around the mean and mean=median=mode, the distribution is symmetric at the mean zero.
The value for mean is μ = 700.
The value for standard deviation is σ = 50.
The probability value is 0.6.
Use z score formula to solve for value of x -
P (X>x) = 0.6
0.6 = 1 - P (X>x)
0.4 = P[{(X-μ)/σ} ≤ {(x-700)/50}]
z0.4 = (x-700)/50
-0.25 = (x-700)/50
x = (-0.25 × 50) + 700
x = -12.5 + 700
x = 687.5
Therefore, the value for x is 687.5.
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Find the volume of a pyramid with a square base, where the side length of the base is 19. 3\text{ ft}19. 3 ft and the height of the pyramid is 16. 2\text{ ft}16. 2 ft. Round your answer to the nearest tenth of a cubic foot.
The volume of the square pyramid is 2011.4 ft². The result is obtained by multiplying the area of base by height of the pyramid, then dividing it by 3.
What is the volume of a pyramid?
A pyramid is a polyhedron that has one base and lateral faces with the vertex at the top of the pyramid. The shape of lateral faces is always a triangle. While, the shape of the base varies and is used to name the pyramid.
The volume of the pyramid can be expressed as
V = ⅓ Bh
Where
B = area of baseh = height of a pyramidA pyramid with a square base has the side length of base of 19.3 ft. The height of the pyramid is 16.2 ft. Find the volume of the pyramid!
The area of base is
B = s²
B = 19.3 × 19.3
B = 372.49 ft²
The volume of the pyramid is
V = ⅓ Bh
V = ⅓ (372.49 ft²) (16.2 ft)
V = ⅓ (6034.338) ft²
V = 2011.446 ft²
V ≈ 2011.4 ft²
Hence, the volume of the pyramid with a square base is 2011.4 ft².
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Draw a rectangle with 45 square units
Answer:
See below
Step-by-step explanation:
Here is one possibility:
Answer:easy
Step-by-step explanation:
what is the slope of the graph?
The slope of the line is -4.
What is slope?A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites. A line's steepness is indicated by its slope. The slope's steepness increases with its size. The slope flattens out as it grows smaller. Slope also reveals whether a line is horizontal or vertical, or if it is going up or down. The slope in mathematics is a measure of how steep a line is. The gradient is another name for it. The slope equations.Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
From the diagram, the graph passes through point ( 0,2) and (1,-2)
Point 1( 0.2 )
x₁ = 0
y₁ = 2
Point 2( 1,-2 )
x₂ = 1
y₂ = -2
To determine the slope of the line, plug the coordinates into the above slope formula.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( -2 - 2 )/( 1 - 0 )
Slope m = ( -4 )/( 1 )
Slope m = -4/1
Slope m = -4
Therefore, the slope of the line is -4.
Option A is the correct answer.
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SOMEONE HELP ME PLEASE DUE TONIGHT
HI is 7 because all sides are equal. K is 100 because J is 40 and L is also 40 because they are equal. All triangles are equal to 180. 40+40+100=180
Reflect (0, -2) in the x-axis followed by the y-axis.
(0, -2) reflected in the x-axis followed by the y-axis is (,).
Therefore , the solution to the given problem of equation comes out to be The coordinates for the picture that is mirrored in the y-axis
are (-3, -2)
Define equationA formula for a mathematical equation combines two statements by using the equal sign (=) to denote equivalence. An equation in algebra is a statement proving the equality of two mathematical equations. For instance, the two numbers are connected by the equation 5x + 5 = 14. A mathematical relationship is built between the sentences on either side of a letter. Usually, the symbol serves as the only variable and the only factor. For instance, 8x - 4 = 2.
Here,
the specified point's coordinates are (3, -2).
Now,
(I) The image's coordinates that are reflected in the x-axis are (3, 2)
(ii) The coordinates for the picture that is mirrored in the y-axis are (-3, -2)
(iii) The point's coordinates for the x-axis reflection and the y-axis reflection will indeed be (-3, 2).
(iv) The point's coordinates that are reflected inside the source would be (-3, 2).
Therefore , the solution to the given problem of equation comes out to be The coordinates for the picture that is mirrored in the y-axis
are (-3, -2)
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Statistics not sure if I did it right and I don’t understand the blank ones can someone please help?
A 95% confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
Does confidence interval mean probability?[tex]$p=\frac{17}{125}=.130$[/tex]
[tex]$2=\frac{.136-.15}{.03^2}$[/tex]
[tex]$(-4 a,=0.44)$[/tex]
This is the range of values that, with a certain degree of confidence, you would anticipate your estimate to fall within if you repeated your test. Another approach to describe probability in statistics is confidence. An interval of confidence shows the likelihood that a parameter will fall between two values close to the mean.
Measured by confidence intervals, the level of a sampling technique's uncertainty or certainty. Both regression analysis and hypothesis testing make use of them. As a typical method for estimating intervals, confidence intervals are frequently utilized. It's possible that if you've ever used this method, you've run into the following statement: For a 90% confidence interval, there is a 90% possibility that a real parameter resides within that interval.
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Simplify: a) (−2)5x(−2)-3
2×2
Answer:
20x -64
Step-by-step explanation:
(−2)5x(−2)-3 2×2
2x5x x2-32x2
20x-32 x 2
20x -64
Select the correct answer!!!
A computer coast $800 it loses 1/5 of its value every year after it’s purchased complete the table after how many years will the computer be worth less than $100 _____ years write an equation representing the value v of the computer t years after it was purchased
On solving the provided question, we can say that equation for the question will be (n - 1) x 3/4
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
equation for the question will be
(n - 1) x 3/4
Value of the computer
at time 0 = $800
at time 1 = $800 x (3/4) x 1 = $600
at time 2 = $600 x 3/4 = $450
Value of the computer at time 3 = $450 x 3/4 = $337.50
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Select all the equations that are equivalent to y - 4 = (x - 1).
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
How to determine the equivalent equation?
To determine if two equations are equivalent, you can check if they represent the same line in the cartesian plane. The following methods can be used to determine equivalent equations:
Graph the equations: You can graph the equations on the same coordinate plane and see if they produce the same line. If they do, the equations are equivalent.Check for the same slope and y-intercept: You can check if the equations have the same slope and y-intercept. If they do, the equations are equivalent.Solving for y: You can put the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, if the slope and y-intercept are the same for both equations, the equations are equivalent.The following equations are equivalent to y - 4 = (x - 1):
y = x - 1 + 4
y = x + 3
y - 4 = x - 1 + 4
y - 4 = x + 3 - 4
(y - 4) + 4 = (x - 1) + 4
y = x - 1 + 4
All of the above equations have the same slope and y-intercept, which means they represent the same line in the cartesian plane.
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
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PLEASE HELP
calculate (30m) (2.01m). Use the correct number of significant digits in the answer
The expression 30m × 2.01m will be 60.3m²
How to illustrate the expression?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of the expression will be:
= 30m × 2.01m
= 60.3m²
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Help Please! I need to find the value of x in the quadrilateral
I know the sum of the exterior angles and interior angles is 360 and I know I need to do something with substitution but I have no idea where to start. Please explain it step by step so I understand.
The value of x in the quadrilateral is 23.
How to find the angles of a quadrilateral?A quadrilateral is a polygon with 4 sides. The sum of interior angles in a quadrilateral is 360 degrees.
The sum of exterior angles in a quadrilateral is 360 degrees.
Therefore, let's find the value of x in the quadrilateral.
Hence,
6x + 5x + x + 16 + 3x - 1 = 360
combine like terms
6x + 5x + x + 3x + 16 - 1 = 360
15x + 15 = 360
subtract 15 from both sides of the equation
15x = 360 - 15
15x = 345
divide both sides by 15
x = 345 / 15
x = 23
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Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
We cannot construct a triangle with side lengths 3.5 cm, 9.2 cm and 5.3 cm. So it is not possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm. This is because these lengths does not follow triangle inequality theorem.
It is not possible to construct a triangle using the given side lengths of 3.5 cm, 9.2 cm, and 5.3 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we take 3.5 cm and 5.3 cm as two sides, the sum of their lengths is 8.8 cm. But the length of the third side (9.2 cm) is greater than 8.8 cm, so these three side lengths cannot form a triangle.
It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle.
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By which postulate or theorem is ∠3 ≅ ∠6?
Answer:
B) Alternate Interior Angles Theorem
Step-by-step explanation:
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. In the above diagram, m∠3 ≅ m∠6
Hi, please help with this circle geometry question (image attached)! It would be helpful if you show your working out/proof. You also need to use tangent properties of circles.
Thank you!
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
what is triangle ?Since a triangle has three parts and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one triangle that has vertex shader A, B, and C. When the three principles are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the sides meet are known as the triangle's corners.
given
To find : radius 'r' of the incircle.
ABC is a right angled triangle
=100
⇒ BC= 100 =10cm
Since area of right anged triangle = 1/2×base×height
⇒ Area of △ABC= 1/2×6×8
=3×8=24cm 2
⇒ Area of △ABC=24cm 2 ....(1)
Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA
= 1/2 ×r×8+ 1/2 ×r×10+ 1/2 ×6×r= 1/2* r(8+10+6)= 1/2r(24)=12r....(2)
Equating (1) and (2) 12r=24
⇒ r= 12/24 =2cm
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
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The complete question :- In fig. 4 triangle ABC is a right triangle with AB=6 cm, AC=8 cm and ∠A=90∘ . A circle with center O is inscribed inside the triangle. Find the radius 'r'
Which graph represents the inequality y is less than negative one-third times x plus 1?
A graph which represents the inequality y is less than negative one-third times x plus 1 is shown in the image below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).How to determine the graph which represents the inequality?In order to determine and plot the graph which represents the inequality, we would first of all translate the word problem into an algebraic equation as follows;
y is less than or equal to one-third times x plus 1 ⇒ y < x/3 + 1.
Next, we would use an online graphing calculator to graphically solve the given inequality.
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Answer:
B
Step-by-step explanation:
The graph shows the answer accurately
What is an exponential function called?
An exponential function is a function in which the variable appears in an exponent.
The most common form of an exponential function is f(x) = aˣ, where a is a positive constant, known as the base of the function, and x is the variable. The variable x is called the exponent of the function.
The base, a, determines the growth rate of the function. If the base is greater than 1, the function will increase rapidly as x increases. If the base is between 0 and 1, the function will decrease rapidly as x increases.
Exponential functions can also be written in the form y = a×bˣ, where a and b are constants, b is the base and x is the exponent. In this form, a represents the y-intercept of the function, which is the point where the function crosses the y-axis.
An exponential function can be recognize by the presence of the variable in an exponent and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
In conclusion, an exponential function is a function in which the variable appears in an exponent and is defined as f(x) = aˣ or y = a×bˣ, where a is the base of the function and x is the exponent.
The base determines the growth rate of the function and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
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