the ladder reach 14.13 feet high up the wall.
Anelys leans a 16-foot ladder against a wall so that it forms an angle of 61° with the ground.
We have to calculate how high up the wall does the ladder reach.
Solution
We have to calculate how high up the wall does the ladder reach.
Let's assume that the height of the wall is h, and the distance between the ladder's foot and the wall is d.
The hypotenuse of the right-angled triangle (the ladder) is 16 feet.
The angle formed by the ladder and the wall is 61°.
We know that sine function of an angle is the ratio of the opposite side to the hypotenuse:
Therefore: Now we can calculate the height of the wall:
We get that the ladder reaches 14.13 feet up the wall (rounded to the nearest hundredth of a foot).
So, the answer is 14.13 feet.
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HELP PLEASE MATH IS HARD
The box plot displays the number of flowers planted in a town last summer. A box plot uses a number line from 6 to 21 with tick marks every one-half unit. The box extends from 10 to 15 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 20. The graph is titled Flowers Planted In Town, and the line is labeled Number of Flowers. Which of the following is the best measure of center for the data shown, and what is that value? The mean is the best measure of center and equals 11. The mean is the best measure of center and equals 12. The median is the best measure of center and equals 11. The median is the best measure of center and equals 12.
After answering the presented question, we can conclude that thus, the equation correct answer is: The median, which equals 11, is the best measure of center.
What box plot represent?The box plot depicts the distribution of the quantity of flowers planted in a town last summer based on the information provided. The box spans the number line from 10 to 15, with a line at 11 inside the box and lines outside the box ending at 7 and 20.
The median is depicted by the line in the box, which is positioned at 11 in the box plot. As a result, the median is the best measure of center for the data provided, and its value is 11.
Thus, the correct answer is: The median, which equals 11, is the best measure of center.
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Jackie purchases a monthly pass to see movies at the theater in order to buy each movie ticket at a discounted rate. The graph shows the costs for different numbers of movie tickets. Find the slope and y-intercept and their meaning.
Fill the blanks.
(A) The slope is $____________ and means that________________
(B) The y-intercept is $________ and means that________________
(A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
What is slope?
Slope is a measure of the steepness of a line. It describes the rate at which the line rises or falls as it moves horizontally, and it is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Mathematically, slope can be represented as:
Slope = (change in y-coordinates) / (change in x-coordinates)
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1,30) and (3,40) to find the slope:
m = (40 - 30) / (3 - 1) = 10 / 2 = 5
Now we can use any of the given points and the slope to find the y-intercept. Let's use the point (1,30):
y = mx + b
30 = 5(1) + b
30 = 5 + b
b = 30 - 5
b = 25
So the equation of the line passing through the points (1,30), (3,40), (5,50), and (7,60) is:
y = 5x + 25
Therefore, (A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
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bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
What is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?
a) 0.17583334
b) 0.00000026
c) 0.00000214
d) 0.00000029
e) 0.00000016
The probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards is option (c) 0.00000214.
The probability of selecting exactly 3 hearts if 7 cards are chosen from a well-shuffled deck of 52 playing cards can be calculated using the hypergeometric distribution.
The total number of ways to choose 7 cards from 52 is given by the combination C(52,7), which is the total number of possible outcomes.
The number of ways to choose 3 hearts and 4 non-hearts is given by the product of the number of ways to choose 3 hearts from 13 and the number of ways to choose 4 non-hearts from 39. That is:
C(13,3) [tex]\times[/tex] C(39,4)
Therefore, the probability of selecting exactly 3 hearts is:
P(3 hearts) = [C(13,3) [tex]\times[/tex] C(39,4)] / C(52,7)
Calculating this probability gives:
P(3 hearts) ≈ 0.00000214
Therefore, the correct answer is option (c).
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f(x) = x + 6 g(x) = 5x Work out the value of gf(3)
Answer:
45
Step-by-step explanation:
[tex]g(f(x))=5(x+6)[/tex]
[tex]g(f(3))=5(3+6)\\[/tex]
[tex]g(f(3))=5(9)\\[/tex]
[tex]g(f(3))=45[/tex]
Answer:
f(x) =x + 6g(x) =5x =
Calculate the formula weights:
mass of mole of
F(x) = x + 6g (x) = 5x = 19g
What is one barrier that can affect the assessment phase of financial planning?
Clients may project their anxiety onto the financial counselor, causing them to make accusations and instigate conflicts
O Clients may have too much to assess at one given time, which can make developing a financial plan difficult and tedious.
O Clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information
Clients may ask if the financial counselor could help another family member or friend free of charge while they are in the process of helping
the initial client
This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves methods for summarizing and describing data, making inferences and predictions about a population based on a sample, testing hypotheses, and identifying patterns and relationships within data. Statistics can be applied in a wide range of fields, including business, finance, social sciences, engineering, medicine, and more. It provides a framework for making informed decisions based on empirical evidence, and plays a crucial role in scientific research and data-driven decision making.
The barrier that can affect the assessment phase of financial planning is when clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information. This can lead to incomplete or inaccurate financial plans, which can ultimately harm the client's financial well-being. It is important for financial counselors to establish trust and create a comfortable environment for clients to feel safe sharing their financial information. This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
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What fraction of 1/2 square centimeter 1/2 centimeter square?
1/4 square centimeter is therefore equal to 1/2 square centimeter.
In math, what is a fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears inside the numerator and denominator of a complex fraction. The numerator of a proper fraction has a smaller denominator.
While "1/2-centimeter square" refers to a square having the side length of half a centimeter, the marking "1/2 square centimeter" typically refers to an area equal half a square centimeter. Even though these aren't the same object, we can still calculate the ratio of one to the other.
The area of such a square of side length 1/2 centimeter is:
(1/2 cm) x (1/2 cm) = 1/4 square centimeter
We may divide 1/4 by 1/2 to determine the percentage of 1/2 square centimeter that corresponds to 1/4 square centimeter:
(1/4 square cm) ÷ (1/2 square cm) = (1/4) x (2/1) = 1/2
Hence, 1/4 square centimeter is equal to 1/2 square centimeter in size.
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find the area of the image below
You made $25,000 last year and spend 20% of your money on food. How much money did you spend on food?
Answer:
$5,000 was spent on food.Step-by-step explanation:
To find:-
Money spent on food .Answer:-
We are here given that, out of the total money made 20% was spent on food .
To calculate the money spent on food we need to find out 20% of $25,00 .
So that,
==> 20% of $25,000
==> 20/100 * $25,000
==> 0.2 * $25,000
==> $5,000
Hence the total money spent on food was $5,000 .
[Questions in image]
Answer:
tesla electric company:
hours :cost
0:$50
1:$ 75
2: $100
3: $125
4: $150
Ac-Ad electric
hours: cost
0: $0
1: $50
2: $100
3: $150
4: $200
if f(x)=1-2x then what is 2f(x)
functions
The given function is f(x) = 1 - 2x.
To find 2f(x), we simply multiply the function f(x) by 2:
2f(x) = 2(1 - 2x)
Distributing the 2 across the expression, we get:
2f(x) = 2 - 4x
Therefore, 2f(x) = 2 - 4x.
what is the probability of being delt 4 hearts from a standard 52 card deck if only 4 cards are to be delt
The probability of being dealt 4 hearts from a standard 52 card deck if only 4 cards are to be dealt is 0.0026.
There are 52 cards in a standard deck, 13 of which are hearts.
We want to find the probability of getting dealt four hearts out of a four-card hand.
Since order doesn't matter, we will use combinations to calculate this probability.
P(A) = number of favorable outcomes / total number of possible outcomes.
There are 13 choose 4 ways to choose four hearts from the deck, and there are 52 choose 4 ways to choose any four cards from the deck.
So the probability of being dealt four hearts from a standard 52 card deck if only 4 cards are to be dealt is:
P(A) = (13 choose 4) / (52 choose 4)P(A)
= (715) / (270725)P(A)
= 0.002641056.
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paint samples are often sold by the pint; a pint of paint will cover 50 square feet. if the dimensions of a room are 138 inches by 117 inches, how many pints of paint would you need to purchase to paint the ceiling of this room?
To paint the ceiling of a room that is 138 inches by 117 inches, you would need to purchase 3 pints of paint.
To find out how many pints of paint are needed to paint the room's ceiling, we must first convert its dimensions from inches to feet:138 inches is equivalent to 11.5 feet (138 ÷ 12 = 11.5)117 inches is equivalent to 9.75 feet (117 ÷ 12 = 9.75)To determine the total square footage of the room, multiply the room's length and width:11.5 feet × 9.75 feet = 112.125 square feet
To calculate the amount of paint needed, divide the total square footage by the number of square feet that one pint of paint will cover:112.125 square feet ÷ 50 square feet per pint = 2.24 pints
Therefore, you would need to purchase approximately 2.24 pints of paint to paint the ceiling of a room that is 138 inches by 117 inches. However, since paint is often sold in whole pints, you would need to purchase 3 pints of paint.
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The temperature at 8 P.M. was - 6.8 degrees Celsius. • Between 8 P.M. and 10 P.M., the temperature change was -3.9 degrees Celsius. • The temperature change was -4.4 degrees Celsius between 10 P.m. and midnight. What was the temperature at midnight?
Using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we can solve for the temperature as follows:
8 pm = -6.8
8 - 10 pm = -6.8 -3.9 = -10.7
10 - 12 midnight = -10.7 -4.4 = -15.1°C
Therefore, using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
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in a sample of 500 customers, 140 say that service is poor. you select two customers without replacement to get more information on their satisfaction. what is the probability that both say service is poor?
The probability that both customers say that the service is poor is 0.0588 or 5.88%.
To determine the probability that both customers say the service is poor, use the binomial distribution and the following formula:P(X = k) = (nCk) * p^k * (1 - p)^(n - k)Where:P(X = k) represents the probability that k successes occurn is the sample sizep is the probability of successk is the number of successes requested(1 - p) represents the probability of failure.Substitute the given values and calculate:P(X = 2) = (2C2) * (140/500)^2 * (1 - 140/500)^(2 - 2) = 0.0588 or 5.88%
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The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α
= 0.01 is:
A) 2.33
B) 2.96
C) 2.05
D) 2.575
The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α = 0.01 is 2.575. The right option is (D).
What is a hypothesis test?In statistics, a hypothesis test is an examination of a particular hypothesis regarding a population parameter with the help of data from a sample. Hypothesis testing is a statistical method used to make decisions about a population based on a sample's data.
The following are the four stages of hypothesis testing:
1. Formulation of Hypothesis
2. Selection of a Significance Level
3. Calculation of Test Statistics
4. Acceptance or Rejection of the Null Hypothesis
The critical value for a two-tail hypothesis test is 2.575 when the sample size is greater than or equal to 30, the population standard deviation is known, and the significance level is α=0.01.
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Find the nth term of 23,17,11,5
Answer:
Find the nth term of 23,17,11,5:
23,17,11,5,-1,-7,-13...
If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A'(0,5)
A'(2,5)
A'(5,2)
A'(-5, -2)
The coordinate A when the triangle is reflected over the y-axis is (2, 5)
Reflecting the triangle over the y-axisFrom the triangle, we have
A = (-2, 5)
Reflecting a point over the x-axis is a type of transformation that involves flipping the point across the x-axis.
The reflection involves keeping the y-coordinate of the point the same, but changing the sign of the x-coordinate.
In this case, the original point is (-2, 5). To reflect this point over the y-axis, we keep the y-coordinate (5) the same, but change the sign of the x-coordinate to positive,
Resulting in the reflected point (2, 5).
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119. What is the linear equation for the pricing formula for Logan's Paint? One gallon cost $11 (1,11) and 5 gallons cost $35 (5, 35).
The linear equation is y = 6x + 5
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
To find the equation for the pricing formula, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the cost, x is the number of gallons, m is the slope (i.e., the rate of change of the cost per gallon), and b is the y-intercept (i.e., the cost when x = 0).
Using the given information, we can calculate the slope:
m = (35 - 11) / (5 - 1) = 24 / 4 = 6
The y-intercept can be found by plugging in one of the points:
11 = 6(1) + b
b = 5
Therefore, the linear equation for the pricing formula for Logan's Paint is:
y = 6x + 5
where y is the cost in dollars and x is the number of gallons.
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What is the answer in the photo
The sale price of the reusable water bottle is $18.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating these symbols. It is a broad area that includes various subfields such as elementary algebra, abstract algebra, and linear algebra, among others.
In elementary algebra, the focus is on the basic rules and operations involving variables, numbers, and equations. These concepts are used to solve problems in a wide range of fields, such as science, engineering, and finance. Abstract algebra, on the other hand, deals with the study of algebraic structures such as groups, rings, and fields. Linear algebra is the study of vector spaces and linear transformations, and is used extensively in fields such as computer science, physics, and engineering.
The discount on the reusable water bottles is 10%, which means that the customer pays only 90% of the regular price. To find the sale price, we can multiply the regular price by 90% or 0.9.
Sale price = Regular price x (1 - Discount rate)
Sale price = $20 x (1 - 0.1)
Sale price = $20 x 0.9
Sale price = $18
Therefore, the sale price of the reusable water bottle is $18.
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2,188,180 rounded to nearest tenth
Answer:
2,188,180
Step-by-step explanation:
since 0 can't give anything to 8 the number would stay the same
Question
Julio buys a salad and a container of yogurt. These bills and coins represent the cost of each item.
How much did Julio spend in all?
The total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
To determine how much Julio spent while buying a salad and a container of yogurt, we have to multiply the value of each notes into their quantity then add all of them.
Number of 25 cents coins = 4
⇒ 4×0.25 = 1.00
Number of 5 dollar note = 1
⇒ 1×5 = 5.00
Number of 10 cents coins = 3
⇒ 3×0.10=0.30
Number of 1 cents = 3
⇒ 3×0.01=0.03
Number of 5 cents = 1
⇒ 1×0.05=0.05
Julio spent = 1.00 + 5.00 + 0.30 + 0.03 + 0.05
= $6.38
Therefore, the total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
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The complete question is :
Julio buys a salad and a container of yogurt. These bills and coins shown in attached image represent the cost of each item. How much did Julio spend in all?
a company plans to manufacture a rectangular box with a square base, an open top, and a volume of 246 in.3. the cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch. determine the dimensions of the box that will minimize the cost of manufacturing it. what is the minimum cost?
The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in
And the minimum cost is 32.65 cents
Let us assume that x represents the base side of the box, and y represents the height of the box.
The volume of the box would be:
V = x²y
246 = x²y ........(1)
The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.
Since this box has 4 sides and 1 base, the total cost would be,
C = (0.2 × x² × 1) + (0.3 × 4 × xy)
C = 0.2x² + 1.2x(246x⁻²) (from (1) y = 246x⁻²)
C = 0.2x² + 295.2 x⁻¹
Consider derivative with respect to x,
dC/dx = 0.4x - 295.2 x⁻²
Consider dC/dx = 0
So, 0.4x - 295.2 x⁻² = 0
0.4x³ = 295.2
x³ = 738
So, x = 9.04
So, the value of y would be:
y = 246 x⁻²
y = 246 × (9.04)⁻²
y = 3.01
So, the minimum cost would be:
C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)
C = 32.65
Therefore, the minimum cost is: 32.65 cents
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Bob's dog, Buster, is a finicky eater. Bob is trying to determine which of two brands of
canned cat food Buster prefers, Busted Nuggets or Busted Tenders. For two months, he
flips a coin each day to decide which of the two foods to feed Buster, and weighs how
much Buster eats (in grams). Here are the data:
Dog Food
n X
S
Busted Nuggets 31 152.6 4.45
Busted Tenders 31 163.7 5.75
Construct and interpret a 98% confidence interval for the difference in mean amount of
food Buster eats when he is offered Busted Nuggets and when he is offered Busted
Tenders.
We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams
Hοw tο cοnstruct cοnfidence interval?Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.
The sample mean difference is:
X1 - X2 = 152.6 - 163.7 = -11.1 grams.
The standard errοr οf the difference can be calculated as fοllοws:
SE = √(S1²/n1 + S2²/n2)
where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.
Substituting the values, we get:
SE = √(4.45²/31 + 5.75²/31) = 1.463
ME = t x (SE) = 2.365 x 1.463 = 3.466
Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:
-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466
-14.566 < µ1 - µ2 < -7.634
Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.
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On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of his family were on their way. His wife sue had baked a cake. They'd all eat it by the lake. After the party the grandkids would play with all of the dogs then roll in the hay. He'd look out the window and what would he see? EIGHTY-FOUR legs and heads THIRTY-THREE!! grandpa Bill's question for you is not very hard. How many dogs and grandchildren will be in the yard?
Answer:
187
Step-by-step explanation:
If 70th after he see 84 and legs 33 so the answer is 70+84+33=187
in how many ways can we list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions?
There are 144 ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions.
We have to list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions. We can use the knowledge of permutations and combinations to solve this problem. We can start by selecting the positions for the distinct digits, i.e., (3, 4, 5). There are 3 distinct digits, so there are 3! = 6 ways to arrange them.
Once we have placed the distinct digits, we can place the two 1's and two 2's in the remaining positions such that no two identical digits are in consecutive positions. To do this, we can use the following approach:
We can start by placing one of the 1's. There are 4 positions available for the first 1.
We can then place one of the 2's. There are 3 positions available for the first 2.
We can then place the second 1. There are 2 positions available for the second 1.
We can then place the second 2. There are 1 positions available for the second 2.
Therefore, the total number of ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions is:
6 (arrangements of distinct digits) x 4 x 3 x 2 x 1 = 144.
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Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. How much interest will he have earned after 3 years?
Answer:
$45
Step-by-step explanation:
Interest earned in a year
5/100x300= $15
Interest earned in 3 years
=$15x3
=$45
Does anyone know how to answer this?
The probability that Esteban wins the game is 29/49.
What does probability mean?Probability is a concept that refers to the likelihood of a particular event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's consider an example: Esteban is playing a matching card game where he wins if the cards are identical. To calculate the probability of winning, we can use the following formula:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
If we assume that the deck of cards contains seven crosses and seven stars, the probability of getting a cross on both cards is:
2/7 x 2/7 = 4/49
The probability of getting a star on both cards is:
5/7 x 5/7 = 25/49
To calculate the overall probability of winning the game, we add the probabilities of getting a cross on both cards and getting a star on both cards:
4/49 + 25/49 = 29/49
Therefore, the probability that Esteban will win the game is 29/49.
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Complete the statements. Keith's strategy for finding the product is select and the product of 21. 5 and 5. 3 is select
When multiplying 31. 5 by 5. 3, Keith found the product using the following steps. (31 + 6. 5)(5 + 6. 3) = (35 * 5) + (5. 5 * 5. 3) = 155 + 5. 15
Keith found that the product of 31.5 and 5.3 is 160.15
Keith's strategy for finding the product is breaking the numbers into parts and then adding the results.
The product of 21.5 and 5.3 is
(20 + 1 + 0.5) × (5 + 0.3) = (20 × 5) + (20 × 0.3) + (1 × 5) + (1 × 0.3) + (0.5 × 5) + (0.5 × 0.3) = 100 + 6 + 5 + 0.3 + 2.5 + 0.15 = 114.95
When multiplying 31.5 by 5.3, Keith used a similar approach, breaking the numbers into parts and then adding the results. Specifically, he expanded the terms as (31 + 0.5)(5 + 0.3), added the partial products, and then rounded the result to two decimal places.
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2.8 is what percent of 2.24
Find the exact side length of a square with an area of 9/49 square meters.
Answer:
3/7 meters
Step-by-step explanation:
[tex] \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]