The probability of selecting a custard-filled donut followed by a lemon-filled donut is:
P(custard, lemon) = P(custard) * P(lemon | custard)
P(custard, lemon) = (2/3) * (5/23)
P(custard, lemon) = 10
What is the probability?
Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.
We can find the probability of selecting a custard-filled donut followed by a lemon-filled donut by multiplying the probability of selecting the first donut by the probability of selecting the second donut, given that the first donut was selected.
The probability of selecting a custard-filled donut is:
P(custard) = number of custard-filled donuts / total number of donuts
P(custard) = 16 / 24
P(custard) = 2/3
Given that a custard-filled donut was selected, the probability of selecting a lemon-filled donut next is:
P(lemon | custard) = number of lemon-filled donuts / total number of donuts remaining
P(lemon | custard) = 5 / (24-1) = 5/23
The probability of selecting a custard-filled donut followed by a lemon-filled donut is:
P(custard, lemon) = P(custard) * P(lemon | custard)
P(custard, lemon) = (2/3) * (5/23)
P(custard, lemon) = 10
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Currently, the temperature of a bowl of ramen is 57°C above room temperature. The temperature of the ramen decreases based on the function f(t) = 57(0.89)t where t represents time elapsed in minutes. Where does the graph of f(t) cross the y-axis, and what does this represent in the context of the problem?
a
f(57) = 0; the time it takes for the above-room temperature to reach 0°C
b
f(0) = 57; the time it takes for the above-room temperature to reach 0°C
c
f(57) = 0; the above-room temperature of the ramen at time t = 0
d
f(0) = 57; the above-room temperature of the ramen at time t = 0
The solution is Option D.
The value of the equation f ( 0 ) = 57 ; the above-room temperature of the ramen at time t = 0
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( t ) = 57 ( 0.89 ) ^ t be equation (1)
Now , t represents time elapsed in minutes
Substituting the value of t = 0 , we get
The time elapsed be 0 minutes , the above room temperature will be
f ( t ) = 57 ( 0.89 ) ^ t
when t = 0
f ( 0 ) = 57 ( 0.89 )⁰
Any number raised to the power of 0 is 1
So , the value of the equation is
f ( 0 ) = 57
And , f ( 0 ) is the above room temperature at the time t = 0
Hence , the equation is solved
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Tickets for a reserved seat, r, for the basketball game cost $4 each and student tickets, s,
cost $3 each. There were 1,787 people who attended the basketball game and total of
$5,792 was earned in ticket sales.
14. Select the two equations that represent the situation.
A. r + s = = 5,792
B. r + s = 1,787
C.
3r + 4s = 1,787
D. 3r + 4s = 5,792
E.
4r + 3s = 5,792
The two equations that represent the situation are r+s= 1,787 and
4r+3s= 5,792. The solution is obtained using cost function.
What is Cost Function?
A mathematical formula known as a cost function is used to visualise how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
We are given that 'r' represent the number of reserve seats.
So, if 'r' number of reserve seats are sold, then '1,787-r' represents the number of student tickets sold.
Therefore, we get the equation as,
⇒ s= 1,787-r
⇒ r+s= 1,787
Also, we are given that tickets for a reserved seat, r, for the basketball game cost $4 each and student tickets, s, cost $3 each. Total $5,792 was earned in ticket sales.
Therefore, we get the equation as,
⇒ 4r+3s= 5,792
Hence, the two equations that represent the situation are r+s= 1,787 and
4r+3s= 5,792.
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Solve the following word problem by setting up systems of equations: Rob hosted a party last week. He purchased 24 pizzas and 24 sodas for $282.00. This week he purchased 15 pizzas and 8 sodas for $157.00. Determine the cost for each pizza and soda.
Answer:$2.75 for soda 9$ for pizza
Step-by-step explanation: Let p = pizza and s = soda. For the first week, we have the following:
24p+24s = 282
Now, for the next week, we have:
15p + 8s = 157.
We can multiply the equation 15p+8s=157 by -3 which ends up equaling
-45p -24s = -471
Now, we add them.
24p+24s = 282
-45p-24s = -471.
The s cancels out and we have -21p = -189. each pizza costs $9, so each soda costs (157-135)/8 which equals $2.75
in a certain state about 3/5 of registred voters particated in 2016 election what fraction of registred voters did not
The requried fraction of the registered voters who didn't vote is given as 2/5.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole. Fraction is generally denoted as a / b, where a = numerator and b = denominator.
In a certain state about 3/5 of registered voters participated in the 2016 election.
Let the fraction of registered voters to did not vote to be x,
So,
According to the question,
1 = 3/5 + x
x = 1 - 3/5
x = 2 / 5
Thus, the requried fraction of the registered voters who didn't vote is given as 2/5.
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Karen, Chau, and Goran sent a total of 112 text messages over their cell phones during the weekend. Chau sent 3 times as many messages as Goran. Goran sent 8 more messages than Karen. How many messages did they each send?
Karen sent 16, Chau sent 72 and Goran sent 24 messages over their phones during the weekend.
Finding Unknown quantity:Here we use the concept of Linear equation to find the Number of messages sent by each person. A linear Equation is a mathematical statement that is formed by constant and variable terms.
Given that
Karen, Chau, and Goran sent a total of 112 text messages over their cell phones during the weekend.
[Since we don't know the number of messages sent by each person take them as different variables. ]
Let x, y, and z be the number of messages that Karen, Chau, and Goran sent respectively
=> x + y + z = 112 ---- (1)
Given that
Chau sent 3 times as many messages as Goran.
=> y = 3z --- (2)
Goran sent 8 more messages than Karen.
=> z = x + 8
=> x = z - 8 --- (3)
From (1) (2) and (3)
=> z - 8 + 3z + z = 112
=> 5z = 120
=> z = 24
From (3)
=> x = 24 - 8 = 16
From (2)
=> y = 3(24) = 72
Therefore,
Karen sent 16, Chau sent 72 and Goran sent 24 messages over their phones during the weekend.
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Emily misses 25% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 20?
She misses 5 throws.
This problem can be solved by percentage:
25% of 20 throws
= 25/100 × 20
= 1/4 × 20
= 5
Thus, Emily misses 5 throws.
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The parade for Martin Luther king Day went in square around downtown.
If the band marched 1,872 yards before their first turn onto Market Street, how many feet was the entire parade route?
PLEASE SHOW FULL WORK AND EXPLAIN HOW YOU THE ANSWER
THANKS FOR YOUR TIME :)
Answer: To find the entire parade route, we need to know how many yards the band marched for each of the four sides of the square and then convert those yards to feet.
If the band marched 1,872 yards before their first turn onto Market Street, it means that they also marched 1,872 yards along each of the other three sides of the square.
So the total distance of the parade route in yards is:
1,872 yards + 1,872 yards + 1,872 yards + 1,872 yards = 7,488 yards
To convert that to feet we need to multiply it by 3, since 1 yard equals to 3 feet.
7,488 yards * 3 feet/yard = 22,464 feet
Therefore, the entire parade route was 22,464 feet long.
Step-by-step explanation:
If a 36-inch yardstick casts a 21-foot shadow, how tall is a building whose shadow is
168 feet? (Draw a picture with two similar polygons.)
The ratio of an object's original scale to that of a new, smaller representation is known as the scale factor.
What is meant by scale factor?A scale factor is defined as the ratio of an object's original scale to that of a new, smaller depiction of that object (bigger or smaller).
The scale factor is the amount that is multiplied by the original object to create a replica that is smaller but otherwise identical. The only difference between the copy and the original is its size. As though you had used a copy machine to increase or reduce the image or object, scale factor doubles it.
The ratio between the representation and the real thing is indicated by a scale factor. In order to reduce the actual thing's dimensions, a precise depiction of the object is called a scale drawing.
168 ÷ 21 = 8
The scale factor is 8
36 × 8 = 288
The building exists 288 inches.
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A mixture of alcohol and water contains a total of 52 oz of liquid. There are 13 oz of pure alcohol in the mixture. What percent of the mixture is water? What percent is alcohol?
The percent of water in the mixture is
The percent of water in the mixture is
p[tex]^{w}[/tex]=m[tex]^{w}[/tex]/m×100%=
52 oz/65oz×100%
=80%
What is mixture?A mixture is a compound made up of two or more chemical components that are not chemically linked. A mixture is a physical blend of two or more substances that preserve their identities and are blended in the form of solutions, suspensions, or colloids.A mixture is a material that is made up of two more chemical compounds or substances that do not combine together chemically. It is actually the physical combination of two or more substances that are able to retain their identities while they are mixed in form of solutions, suspensions, or colloids. You can separate them by physical methods. In any mixture, the various components do not form through any kind of chemical change. Therefore, the components’ individual properties remain intact.
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What color printer prints 11 pages in 6 minutes how many minutes does it take per page
Answer:
11/7 = 1.6
Step-by-step explanation:
11 pages divide 7 1.57 pages
____ = __________
7 minutes divide 7 1 minute
Solve the problem below:
(-10)+13-2=?
Answer:
1
Step-by-step explanation:
(-10)+13-2
-10+13-2
3-2
1
NEED HELP ASAP PLS AND THX Picture is attached
M<2 + M<3 = 180 degrees, as this is the sum of all angles in a triangle.
Right angle triangleA right angle triangle is a triangle with one angle will be 90 degrees. It is the most basic type of triangle and is often used in mathematics and geometry. The other two angles of a right angle triangle must be acute angles, meaning that their measure must be less than 90 degrees. The three sides of a right angle triangle are referred to as the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side of the triangle, the adjacent side is the side that is next to the right angle, and the opposite side is the side that is across from the right angle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right angle triangle is equal to the square of the hypotenuse. This theorem can be used to calculate the length of the sides of a right angle triangle if the lengths of two sides are known.To learn more about Right angle triangle refer to:
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Solve linear system by graphing
State if their is a solution or no solution
X+3y=6
3x+9y=18
The given linear system of equation has no solution.
What is no solution?In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x + 3y = 6 ........equation 1.
3x + 9y = 18 ........equation 2.
Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines are the same and lie on the same co-ordinate.
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The solution to an inequality is graphed on the number line. A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5. What is another way to represent this solution set? {x | x < 4. 5} {x | x ≤ 4. 5} {x | x > 4. 5} {x | x ≥ 4. 5}.
Another way to represent this solution set is to express it as a set notation, which is {x | x ≤ 4.5}. This notation represents all values of x that are less than or equal to 4.5.
What is inequality?Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.
To graph this set, a closed circle would be placed at the 4.5 mark on the number line, and the numbers to the left of the circle would be shaded. This would indicate that all of the numbers to the left of the 4.5 mark, including the 4.5 mark itself, are part of the solution set.
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Two contestants on Get Fit TV Show are Valerie and Oscar. Their weight loss progress is shown below.
Valerie's weight loss is shown by this function, where W is her weight in pounds and t is the time in weeks.
W=235−2.5t
Oscar's weight loss is tracked in the table below.
Weeks 0 2 5 6
Weight 247 243 237 235
True or False: Oscar is losing weight faster than Valerie
How cool is that! I love real-life problems, do you?
V = 236 - 2.5t
O = 0, 2, 5, 6
247, 243, 237, 235
So let's try substituting some numbers in for Valerie. Let's do 0, 2, 5 and 6 to compare them to Oscar.
V = 236 - 2.5(0)
V = 236
She started at a lesser weight than Oscar.
Week 2:
V = 236 - 2.5(2)
V = 236 - 5
V = 231
So already, at week 2, Valerie lost 5 pounds compared to her first weight. Oscar lost 4 pounds. Valerie is losing weight faster than Oscar.
Week 5:
V = 236 - 2.5(5)
V = 236 - 12.5
V = 223.5
From week 2, she lost 12.5 pounds. Oscar lost 6 pounds. Looks like Valerie is losing weight faster!
So now, week 6.
V = 236 - 2.5(6)
V = 236 - 15
V = 221
Valerie lost 2.5 pounds compared to week 5.
Oscar lost 2 pounds compared to week 5.
True or False: you decide! :)
11*90+5-20=?
I really don't know the answer to it and I'm not going to use a calculator on this
Show your work
Answer:
To solve this problem, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
First, we need to perform the multiplication.
11*90 = 990
Next, we add 5 to 990:
990+5 = 995
Finally, we subtract 20 from 995:
995-20 = 975
Therefore, the solution is 975
In summary, we first multiplied 11 and 90, then added 5 to the result, and finally subtracted 20. This is why the order of operations is important because it determines the order in which we perform the calculations in the equation.
The set of all numbers in the form a plus b i
is called the set of _______ numbers. If b not equals 0
,
then the number is also called a/an _______ number. If b equals 0
,
then the number is also called a/an _______ number.
The set of all numbers in the form a + bi is called the set of complex numbers. If b ≠ 0, then the number is also called a non-real number. If b = 0, then the number is also called a real number.
What is a complex number?Complex numbers are those expressed as a+ib, where a, b, and I are real numbers and I is an imaginary number. An iota complex number is a component of a number system that extends real numbers by a particular element denoted I also known as the imaginary unit.
Imaginary numbers are another name for non-real numbers. A negative number's square root (or any other even root) creates an imaginary component, which is a property of imaginary numbers. The letter i stands for imaginary components.
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Lila a réussi 19 services sur 34 et Milo 47 services sur 98.
Qui est le meilleur serveur en proportion?
[tex]\it \dfrac{34}{19}=1\dfrac{16}{19}\ \ pourcentage \ \ d'inefficacit\acute e\ \ pour \ \ Lila\\ \\ \\ \dfrac{98}{47}=2\dfrac{4}{98}\ \ pourcentage \ \ d'inefficacit\acute e\ \ pour \ \ Milo\\ \\ \\ Donc,\ \ Lila \ \ \acute etait \ \ plus\ \ efficace[/tex]
Une autre méthode:
[tex]\it \dfrac{19}{34} > \dfrac{47}{98}\ \Leftrightarrow\ 19\cdot98 > 34\cdot47 \Leftrightarrow 1862 > 1598\ \ (Vrai)[/tex]
What is the vertex form of f(x) = (x-2)(x+6)
Answer:
[tex]y=(x+2)^2-16[/tex]
Step-by-step explanation:
Without solving the quadratic equation 2x^2-10x+12=0, find the sum of the cubes of its roots
Answer: The sum of the cubes of the roots of a quadratic equation with coefficients a, b, and c can be found using the formula:
x³ + y³ = (x + y)(x² - xy + y²) = -b
Where x and y are the roots of the equation ax² + bx + c = 0.
In this case, the equation is 2x² - 10x + 12 = 0, so a = 2, b = -10, and c = 12.
So, the sum of the cubes of the roots is:
x³ + y³ = -b = -(-10) = 10
Therefore, the sum of the cubes of the roots of the equation 2x² - 10x + 12 = 0 is 10.
Step-by-step explanation:
12/1 divided by 1 1/5
263.76 to the nearest whole number
What percentage of the students in both grades prefer hot dogs for lunch?
what is the decimal that is 1/10 of 0.9
Answer:
1/10 x .9 = .09
Step-by-step explanation:
Divide using synthetic division
To divide a polynomial by a binomial of the form x - c using synthetic division.
What is synthetic division? In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.“Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1 and is generally used to find the zeroes of polynomials” This division method is performed manually with less effort of calculation than the long division method.Synthetic division is a shorthand method for dividing a polynomial by a linear factor such as x + 3, and it's much simpler and faster.
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Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes. Find the unit rate for each brand. Round to the nearest cent (hundredth).
Brand A costs
per ounce.
Brand B costs
per ounce.
Answer:
Brand A Costs 37.38 per ounce and Brand B cost 31.19 per ounce hope this helped ^-^
Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you.
5. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
lateral surface area of the
cylinder.
6.
The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.
The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base.
The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.
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Find y coordinate of y intercept of the polynomial f(x)=x(5x+6)
The y-coordinate of the y-intercept of the polynomial is 0
What are polynomials?Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
The polynomial function is given as;
f(x) = x(5x + 6)
At the y-intercept, the value of x is;
x = 0
Substitute x = 0 in f(x) = x(5x + 6)
f(0) = 0(5 * 0 + 6)
Evaluate;
f(0) = 0
Therefore, the answer of the polynomial function will be 0
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Can someone help? I’m stuck on these. I only need the ones on the left.
3x - 4y = -14
-3x + 2y = -2
--------------------Adding the two equation we solve for y:
-2y = -16
y = 16/2
y = 8
Now by back substitution, we get:
3x - 4y = -14
3x - 4(8) = -14
3x - 32 = -14
3x = -14 + 32
3x = 18
x = 18
x = 6
Therfore, x = 6 and y = 8
Thus the solution.
What is substitution?A substitute, or substitutable good, in economics and consumer theory refers to a product or service that consumers see as essentially the same or similar-enough to another product. Put simply, a substitute is a good that can be used in place of another.Substitutes play an important part in the marketplace and are considered a benefit for consumers. They provide more choices for consumers, who are then better able to satisfy their needs. Bills of materials often include alternate parts that can replace the standard part if it's destroyed.In economics, products are often substitutes if the demand for one product increases when the price of the other goes up.To learn more about consumers refer to:
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