The number of ways in which the prizes are allocated is 67,525.
Combinations are the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given that
Number of customers = 75
Number of prizes = 3
And, the value of the gift card = $10
Based on the above information,
The number of ways in which the prizes are allocated is shown below:
=⁷⁵C₃
=[tex]\frac{75!}{(3!*(75-3)!}[/tex]
After solving this the number of ways that came is 67,525
Hence, the number of ways in which the prizes are allocated is 67,525
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a sample of 137cs (half-life = 30.1 years) decays at a rate of 10^10 decays per second. how long (in years) will it take the decay rate to decrease to 10^7 decays per second?
It will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.
The decay rate of 137Cs is given by the formula:
A = A0 * e^(-λt)
Where A is the decay rate, A0 is the initial decay rate (10^10 decays per second), λ is the decay constant (ln(2)/30.1 years) and t is the time in years.
To calculate the time, t, required for the decay rate to decrease to 10^7 decays per second, we solve for t and substitute the given values into the equation:
[tex]t = (ln(A0/A))/λ\\t = (ln(10^10/10^7))/(ln(2)/30.1)\\t = 19.44 years[/tex]
Therefore, it will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.
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PLEASE HELP SOLVE THIS SLOPE
Answer:
D
Step-by-step explanation:
1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?
2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)
B:
X: 0 - 4 = -4
Y: 4 - 0 = 4
4/-4 = -1
D:
X: 0 - -4 = 4
Y: 4 - 0 = 4
4/4 = 1
given rectangular prism ABCD
choose all of the terms that best describe each of the sets of lines or points.
points E, H, and J
[] non-coplanar
[] coplanar
[] equidistant
[] non- collinear
[] collinear
The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.
What are collinear points?An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.
Let A, B, C, and D be the collinear points. Then the condition of the collinear will be
AB + BC + CD = AD
The collinear points lie in the same plane. Then the points are coplanar too.
From the graph, the distance between points E, H, and J will be the same.
The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.
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What do you mean by data type?
Answer:
A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value
Step-by-step explanation:
Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.
Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.
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The image below shows that angles formed by two intersecting lines. What are the correct pairs of vertical angles?
View the image for the answers
By vertical angles theorem, ∠1≅∠3 and ∠2≅∠4. Therefore, option B is the correct answer.
What is vertical angle theorem?Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
From the given figure,
By vertical angles theorem, we have
Angle 1 and angle 3 are congruent.
Angle 2 and angle 4 are congruent
Therefore, option B is the correct answer.
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find the average value of the following function on the given interval. draw a graph of the function and indicate the average value. f(x); [0,1] for any integer n greater than 1
The average value is the intersection point between the function and the line, which is at (0,1+C).
The average value of a function on an interval can be calculated using the following formula: Average Value = (1/b-a)∫a b f(x)dx. In this case, the function is f(x) and the interval is [0,1]. To calculate the average value, we must first calculate the integral of the function on the given interval. The integral of f(x) is nx^n-1 + C, where C is a constant. Using the fundamental theorem of calculus, we can evaluate the integral from 0 to 1 to be 1 + C.
The average value of the function on the given interval is then (1/1-0)∫0 1 (1+C)dx, which simplifies to 1+C. Therefore, the average value of the function on the given interval is 1 + C.
Graphically, the average value of the function on the given interval can be seen by plotting the graph of the function, which is a parabola with a vertex at (0,0), and a line at y=1+C. The average value is the intersection point between the function and the line, which is at (0,1+C).
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Georgia loves to drop water balloons from her third-floor balcony into a dumpster located on the street below. Her brother filmed one balloon falling. He measured the height of the balcony rail. Then he used the video camera's time feature to figure out how far the balloon had traveled from Georgia's hand after each quarter of a second. He listed the times and distances in a table: Time 0.255 Distance 0.3 m 1.2 m 0.55 0.75 s 2.8 m 4.9 m 1.08 1.25 s 7.7 m 11.0 m 1.5 a . graph the distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected.
The distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected is attached below.
What is Distance -time Graph?A distance-time graph, also known as a displacement-time graph or position-time graph, is a graphical representation that shows the relationship between the distance traveled by an object and the time it takes to travel that distance.
Using the information gathered by Georgia's brother, we can plot the points on a coordinate plane to graph the distance the water balloon travelled during a period of 1.5 seconds.
The data points provided are as follows:
Time (s) Distance (m)
0.25 0.3
0.5 1.2
0.75 2.8
1.0 4.9
1.25 7.7
1.5 11.0
Plotting these points on a graph with time on the x-axis and distance on the y-axis, we get the graph attached.
The water balloon's route over 1.5 seconds is depicted on a graph. As time increases, the distance traveled by the balloon also increases. The graph shows a curved line, indicating that the distance traveled is not constant but increases at a varying rate.
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a bag of fertilizer covers 3000 square feet of lawn. find how many bags of fertilizer should be purchased to cover a rectangular lawn 170 feet by 40 feet. round up to the nearest whole bag of fertilizer.
9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.
How to find the Calculation?The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.
When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.
Finding the location of the lawn is the first stage.
Area: 110 feet by 260 feet.
28600 square feet.
Calculating how many bags of fertilizer to purchase is the next step.
Bags = Area x 3,000 feet
Bags: 28600 feet / 3000 feet
9.53 bags total are in the bag.
Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.
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3/4(12a+8) =27.6
3/4 Multiplied by () + (multiply by 8) = ()
A =?
(Use the distributive property to solve, simplify your answers)
PLEASE HELP THIS IS MY LAST QUESTION!!!!!
3/4(12a+8) =27.6
3/4 Multiplied by () + (multiply by 8) = ()
A = 2.4
How did we get the value?Expanding the expression inside the parenthesis, we have:
3/4 (12a + 8) = 3/4 * 12a + 3/4 * 8 = 9a + 6
Setting this equal to 27.6 and solving for a:
9a + 6 = 27.6
9a = 21.6
a = 2.4
So, the value of a is 2.4
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(1/6+2 2/3)x(1 1/4-1/2)
Answer:2.12
Step-by-step explanation:
The following equation follows the commutative property of addition. Find the missing value.
39 + 67 = __ + 39
a, 42
b. 67
c. 39
d. 81
Using commutative property of addition, a + b = b + a, Therefore, 39 + 67 = 67 + 39, Hence the missing number is 67.
What is the commutative property of addition formula?The commutative property formula applies to addition and multiplication. The addition formula states that a+b=b+a, and the multiplication formula states that a×b=b×a.Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.We learned that the addition property of equality tells us that if we add the same quantity to both sides of an equation, then our equation remains the same. The formula is if a = b, then a + c = b + cThis law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answerTo learn more about commutative property refers to:
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A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 7 comma 4 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 6 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 5 and 8 comma 1
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 6 comma 4 and 7 comma 4
The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).
What is Graph?In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.
here, we have,
The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.
Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.
The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).
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I need a help on this one asap it can be without step by step just please asap for 25 points.
When the students select their random samples and plot the results on a dotplot, which of the following should they expect to see?
The dots, which represent the sample proportions obtained by the students,
A) will all be at the same number.
B) will be wildly unpredictable.
C) will be clustered around 0 and 1.
D) will be centered around p, the true population proportion.
The correct option is "will be centered around p, the true population proportion."
What are random sample?Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
Given that, the students select their random samples and plot the results on a dot plot, the dots, represent the sample proportions obtained by the students,
Since, the dots are representing the sample proportions, we know,
The population proportion is equal to the mean of the sampling distribution of the sample proportion.
Hence, the correct option is "will be centered around p, the true population proportion."
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consider the two functions shown below. assume the blue line represents a(x) and the pink line represents b(x). how do the second derivatives of the two functions with respect to x compare?
The second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
The second derivative of a function with respect to x is the rate of change of the first derivative with respect to x. The second derivative of a function measures the "curvature" of the graph. In the case of the two functions shown, the blue line represents a(x) and the pink line represents b(x). By looking at the graph, we can see that the first derivative of a(x) is steeper than that of b(x). Therefore, the second derivative of a(x) will be larger than the second derivative of b(x). This can be seen by looking at the graph and noting that the blue line has a greater curvature or "bend" than the pink line. In other words, the second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
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pls answer will buy you a reward or brainly premium after answer
The height of the tree is obtained as 27.7 m
What is the height of the light pole?We have to note that in the solution of the problem that the tangent of the angle is going to come in to play. The tangent if one of the trigonometric ratios and the other ratios are the cos and the sine.
We know that the tangent of the angle is;
tan 36 = opposite/adjacent
Opposite of the angle = x + 5
(Where x is the height of the tree)
Adjacent of the angle = 45 m
We would then have that;
tan 36 = x + 5/45
45 tan 36 = x + 5
x = (45 tan 36) - 5
x = 27.7 m
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Real number system using the given theme and its description formulate three conditional statements not written in if then form and convert the three conditional statements into if - then form
Conditional statements using the theme of the real number system:
The product of two positive real numbers is positive.The sum of a positive real number and a negative real number is positive if the magnitude of the negative number is less than the positive number.The quotient of two real numbers is positive if the numerator is positive and the denominator is negative.Conditional statements in if-then form:
If x and y are positive real numbers, then xy is positive.If a is a positive real number and b is a negative real number with |b| < a, then a + b is positive.If x is a positive real number and y is a negative real number, then x/y is positive.Conditional statements are statements in logic and mathematics that assert the truth of a statement based on certain conditions. They are usually written in the form "if P, then Q", where P is a condition and Q is a conclusion that follows from P. Conditional statements are used to make decisions or test certain conditions in programming, mathematics, and everyday life.
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a scale of 1:900,000 is ________ a scale of 1:24,000
A scale of 1:900,000 is 36 times smaller than a scale of 1:24,000.
This can be expressed mathematically as a ratio: 1:900,000 = 1:24,000 / 36. To calculate the scale factor between two maps, divide the denominator of the larger scale by the denominator of the smaller scale. In this example, the scale factor is 36.
A scale of 1:900,000 means that one unit on the map represents 900,000 units of the same type in the real world. For example, one centimeter on the map could represent 900,000 centimeters in real life, or 9 kilometers. A scale of 1:24,000 would mean that one unit on the map represents 24,000 units of the same type in the real world. For example, one centimeter on the map could represent 24,000 centimeters in real life, or 0.24 kilometers.
The scale factor is the number that is used to compare the size of one map to another. In this example, a map with a scale of 1:900,000 is 36 times smaller than a map with a scale of 1:24,000. This means that the features on the 1:900,000 map are 36 times smaller than the same features on the 1:24,000 map. Therefore, the 1:900,000 map is not as detailed as the 1:24,000 map.
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find the volume of the solid obtained by rotating the region bounded by the curves y=1−x2 and y=0 about the x-axis.
The volume of the region will be 4/3 cubic unit with the help of integration.
What is integration?
Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in Mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables).
Definite Integral
An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.
A definite Integral is represented as:
∫f(x)dx from a to b.
Indefinite Integral
Indefinite integrals are defined without upper and lower limits. It is represented as:
∫f(x)dx = F(x) + C
Where C is any constant and the function f(x) is called the integrand.
Now,
For volume
Integrate y=1-x^2 for x=-1 to 1.
volume=1-x^2.dx
V=x-x^3/3
=1-1/3+1-1/3
=2-2/3
Hence,
Volume=4/3 cubic unit
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According to a recent article the average number of babie born with ignificant hearing lo (deafne) i approximately
two per 1,000 babie in a healthy baby nurery. The number climb to an average of 30 per 1,000 babie in an intenive care
nurery. Suppoe that 1,000 babie from healthy baby nurerie were randomly urveyed. Find the probability that exactly two babie
were born deaf
The probability of exactly two babies being born deaf is approximately 0.037, or 3.7%.
Calculating Deaf Birth ProbabilityThe probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries can be calculated using the binomial distribution.
The binomial distribution formula for finding the probability of exactly "k" successes in "n" trials with a probability of success "p" is:P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where "n choose k" is the number of combinations of "n" things taken "k" at a time, and can be calculated as:(n choose k) = n! / (k! * (n-k)!)
For this problem:
n = 1000 (number of babies surveyed)
k = 2 (number of deaf babies)
p = 2/1000 (probability of a baby being deaf in a healthy baby nursery)
Plugging these values into the formula:P(X = 2) = (1000 choose 2) * (2/1000)² * (998/1000)^998
P(X = 2) = 999000 * 4 * (998/1000)⁹⁹⁸
P(X = 2) = approximately 0.037
So the probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries is approximately 0.037, or 3.7%.
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X el largo de un escritorio es 6 pulgadas mas que su ancho. expresar el largo de la mesa en términos de su ancho W
The algebraic expression representing the length of the desk as a function of the width is given as follows:
L = W + 6.
How to obtain the algebraic expression?The two variables in the context of this problem are given as follows:
Length L.Width W.The length is 6 inches greater than the width of the desk, hence the algebraic expression representing the length of the desk as a function of the width is given as follows:L = W + 6.
TranslationThe problem asks for the algebraic expression representing the length of the desk as a function of the width.
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what is the ratio of number 600g:4kg
Madelyn has a home-based business making and selling scented soaps. She initially spent $50 to purchase soap-making equipment, and the materials for each kilogram of soap cost $6. Madelyn sells the soap for $8 per kilogram. Eventually, she will sell enough soap to cover the cost of the equipment. Write a system of equations.
Answer:
25
Step-by-step explanation:
$50
Cost=$6
Selling price=$8
Profit=$8-$6=$2
50/2=25
To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.
Answer:
Factors
Step-by-step explanation:
To find the roots of a polynomial, [factors] help the process of finding them
Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
At what point do both teams earn the same amount of profit? How do you know and
how much profit is earned?
Team A needs to sell 255 bags of popcorn to reach their goal of $100.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Team A will sell the bags of popcorn for $0.50 each.
Team B will sell the cotton candy for $0.75 per stick.
Let the number of bags of popcorn sold by Team A be "x".
So, the total cost for the popcorn machine rental and supplies is
= $15 + 0.05x.
To reach their goal of $100
$100 = 0.5x - ($15 + 0.05x)
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45
x = 255 bags of popcorn
Thus, Team A needs to sell 255 bags of popcorn.
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11). Find the area of the enclosed figure below.
Total area of the enclosed figure is given as 66 sq. units.
What is Area of a figure ?The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm2 and m2 are used to measure area. A shape's area is a two-dimensional measurement.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The common ways to depict square units, which are the same as areas, are square inches, square feet, etc.
The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric forms.
In the shape there is 2 triangles and 3 rectangle
Area of the bottom triangle = 1/2 * 3*4 = 6 sq. units
Area of the top triangle = 1/2 * 4*2 = 4 sq. units
Area of the bottom rectangle = 8*3 = 24 sq. units
Area of the middle rectangle = 8*3 = 24 sq. units
Area of the top rectangle = 4*2 - 8 sq. units
Total area of the enclosed figure is given as 6+4+ 24+ 24+ 8 = 66 sq. units.
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In ΔABC, a= 270 inches, m∠C=164° and m∠A=8°. Find the length of c to the nearest 10th of an inch
Answer:
456.9 inches
Step-by-step explanation:
We can use the law of sines to find c:
c = (a / sin C) = (270 inches / sin 164°)
To find the sine of an angle in degrees, we can use a scientific calculator or a trigonometry table. Rounding to the nearest 10th of an inch, c = approximately 456.9 inches.
Answer: It's 534.7
Step-by-step explanation:
I sacrificed my chance of getting it right to see the answer. It's right That I guarantee. btw brainiest, please?
Investigation • Getting to the root
ASAP PLEASE!!!
The exponents of the values are;
1) 343
2) 9
3) 32
4) That the nth root of a and raise to the power of m
What are the laws of exponents?The laws of exponents are a set of rules for performing arithmetic operations with exponential expressions. They include:
Product rule: For any real numbers a, b and positive integers m, n, (am)(bn) = a^m * b^n.
Quotient rule: For any real numbers a, b and positive integers m, n, (a^m)/(a^n) = a^(m-n).
Power rule: For any real number a and positive integers m, n, (a^m)^n = a^(mn).
Zero exponent rule: For any real number a, a^0 = 1.
Negative exponent rule: For any real number a ≠ 0 and positive integer n, (1/a^n) = a^(-n).
Exponent of a power rule: For any real numbers a, b and positive integers m, n, (a^m)^n = (a^n)^m.
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Ernesto has 29 cups of water. Is this enough water to make 15 batches of green slime for a class project? Explain.
8. There are 16 tablespoons in 1 cup. How many tablespoons of cornstarch would Ernesto need to make 20 batches of green slime ?
help please???????????
Answer:240!
16 xs 15 = 240
Step-by-step explanation:
Answer: 240
Step-by-step explanation:
16 x 15 = 240 :)
Use algebra to solve these problems Question 1: Work out the sizes of the angles marked with letters. 68⁰ ( 83° 95° 32° d
The sizes of the angles are: a = 112, b = 97, c = 85, d = 148
How to calculate the sizes of the angles marked with lettersTo calculate the sizes of the angles, we substract the given value from 180 (sum of angles on a straight line)
For a = 180 - 68 = 112( sum of angles on a straight line)
b = 180 - 83 = 97( sum of angles on a straight line)
c = 180 - 95 = 85( sum of angles on a straight line)
d = 180 - 32 = 148( sum of angles on a straight line)
Hence, the sizes of the the angles a,b,c,d, are 112,97,85 and 148 respectively
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