Suppose you have a deck that is 16ft. By 24ft. An 8ft by 4in board costs $7.50. How much will the material costs?
Answer:
45
Step-by-step explanation:
Whats the answer to these please provide steps.
The trigonometric identities can be proved as follows;
32. Using the substitution, tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we get;
cot(x) - tan(x) = (1 - 2·sin²(x))/(sin(x)·cos(x)) = sec(x)·(csc(x) - 2·sin(x))
36. tan(θ)/(1 + sec(θ)) = sin(θ)/(1 + cos(θ)) = (1 - cos(θ))/(sin(θ)) = -cot(θ) + csc(θ)
What are trigonometric identities?Trigonometric identities are equations involving trigonometric functions which are valid for the values of the input variable.
as follows;
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))
The left hand side of the equation can be expressed using sin(x) and cos(x) as follows;
cot(x) = cos(x)/sin(x)
tan(x) = sin(x)/cos(x)
Therefore;
cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x) = (cos²(x) - sin²(x))/(sin(x)·cos(x))
cos²(x) = 1 - sin²(x), therefore
(cos²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - sin²(x) - sin²(x))/(sin(x)·cos(x))
(1 - sin²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - 2·sin²(x))/(sin(x)·cos(x))
(1 - 2·sin²(x))/(sin(x)·cos(x)) = csc(x)·sec(x)·(1 - 2·sin²(x))
csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
Therefore;
cot(x) - tan(x) = csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))36. tan(θ)/(1 + sec(θ)) = -cot(θ) + csc(θ)
The left hand side can be manipulated as follows;
tan(θ) = sin(θ)/cos(θ)
sec(θ) = 1/cos(θ)
Therefore; tan(θ)/(1 + sec(θ)) = (sin(θ)/cos(θ))/(1 + (1/cos(θ)))
(sin(θ)/cos(θ))/(1 + (1/cos(θ))) = (sin(θ)/cos(θ))/((cos(θ) + 1)/(cos(θ)))
((sin(θ)/cos(θ))×cos(θ))/((cos(θ) + 1)/(cos(θ)) × cos(θ))) = sin(θ)/(cos(θ) + 1)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1)
sin(θ)/(cos(θ) + 1) = sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ)))
sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ))) = ((sin(θ)·(1 - cos(θ))/(1 - cos²(θ)))
((sin(θ)·(1 - cos(θ))/(1 - cos²(θ))) = ((sin(θ)·(1 - cos(θ))/(sin²(θ)) = (1 - cos(θ))/(sin(θ))
sin(θ)/(cos(θ) + 1) = (1 - cos(θ))/(sin(θ)) = csc(θ) - cot(θ) = -cot(θ) + csc(θ)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1) = -cot(θ) + csc(θ)
Therefore;
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Translate the sentence into an inequality.
Seven subtracted from b is less or equal to -18
If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
What is meant by inequality?A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.
An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.
Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
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Question in the picture below
Answer: $1.50 per hour
Step-by-step explanation:
What is the answer
? I’ve been having triuble
Answer:
120°
Step-by-step explanation:
We need to find the missing angle <SRM
The angles inside a triangle always add up to 180°. So this means:
<TSR+<STR+<TRS=180°
65°+55°+<TRS=180°
120°+<TRS=180°
<TRS=180°-120°=60°
All angles along a straight line add up to 180°. This means:
<TRS+<SRM=180°
60°+<SRM=180°
<SRM=180°-60°=120°
Answer:
120° is the answer please mark. brainly
look at the image below
It's due in 1 hour help Asap
I am giving away 18 points and Will mark brainiest to the correct answer
Answer:
For -- (1.) 38 / 1 ( apples and baskets)
It is 304 apples distributed evenly among 8 baskets.
For -- (3.) 42 / 1 (apples and baskets)
It is 294 apples distributed evenly among 7 baskets.
Step-by-step explanation:
For the 2nd one, I don't see an answer relating to it. Are there more options when you scroll down?
I hope the other 2 answers helped.
A disc is rolled thrice what is the probability
Probability of an event = (number of favorable event) / (total number of event).
P(B) = (Event B) / (total number of event).
Probability of getting 1 = 1/6.
Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.
Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.
Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.
Hence, the probability of getting 1 three times in a row is 0.463%.
Solve c =3/7(wm+a) for m
Answer:
Step-by-step explanation:
To solve the equation c = 3/7(wm + a) for m, we can isolate m on one side of the equation.
Here's the step-by-step process:
Distribute the 3/7:
c = 3/7 * wm + 3/7 * a
Subtract 3/7 * a from both sides:
c - 3/7 * a = 3/7 * wm
Divide both sides by 3/7 * w:
(c - 3/7 * a) / (3/7 * w) = m
And that's it! m is the value you're looking for. Just remember to use the values of c, w, and a that you have in your specific problem when you evaluate the expression.
[tex]m=\frac{7 c-a}{3w}.[/tex]
Step-by-step explanation:1. Write the expression.[tex]c=\frac{3}{7} (wm+a)[/tex]
2. Divide by [tex]\frac{3}{7}[/tex] on both sides of the equation.Remember that dividing by a fraction is the same as multiplying by its multiplicative reciprocate. Hence, we may multiply by [tex]\frac{7}{3}[/tex] on both sides and it'd have the same efect as dividing by [tex]\frac{3}{7}[/tex].
[tex]\frac{7}{3} c=\frac{3}{7} (wm+a)*\frac{7}{3}[/tex]
The two fractions on the right side cancel each other out and we're left with:
[tex]\frac{7}{3} c=(wm+a)[/tex]
3. Remove the parenthesis.[tex]\frac{7}{3} c=wm+a[/tex]
4. Subtract "a" on both sides of the equation.[tex]\frac{7}{3} c-a=wm+a-a\\ \\\frac{7}{3} c-a=wm[/tex]
5. Divide by "w" on both sides of the equation.[tex]\frac{\frac{7}{3} c-a}{w} =\frac{wm}{w} \\ \\\frac{7 c-a}{3w} =m[/tex]
6. Conclude.[tex]m=\frac{7 c-a}{3w}.[/tex]
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(Extra step) 7. Verification.If you want to verify whether the answer is correct or not, you may take the original equation and plug the calculated value of "m" in the place of said variable. Then, if the equation returns the same value after simplifying completely, the solution is correct!
This step is show on the attached image.
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Write the equation of the line in all three forms that is perpendicular to the line
6x+18y=36 and goes through the point (-5,4)
.
A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring 3 cm, 4 cm, and 5 cm, and angles measuring 37°, 53°, and 90°. To create the actual sign shown, the drawing must be dilated using a scale factor of 80.
Answer:
240 cm, 320 cm, 400 cm
Step-by-step explanation:
The drawing length multiplied by the scale factor gives the real length.
3 cm × 80 = 240 cm
4 cm × 80 = 320 cm
5 cm × 80 = 400 cm
Answer: 240 cm, 320 cm, 400 cm
someone help me please
The value of summation of ( x-2)² is 973
What is summation?A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
if
x (x-2) ( x-2)²
15 13 169
13 11 121
13 11 121
4 2 4
19 17 289
12 10 100
6 4 16
5 3 9
14 12 144
Therefore the summation of (x-2)²
= 169+121+121+4+289+100+16+9+144 = 973
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Answer:answer
Step-by-step explanation:
The value of summation of ( x-2)² is 973
PLEASE HELP!!! PLEASE IM BEGGING SOMEONE TO HELP ME GHIS IS DUE TOMORROW
Answer:
D
Step-by-step explanation:
It's the most random and produces no bias.
Answer:
D
Step-by-step explanation:
Identify the number types that describe .
O A. Rational, integer
OB. Real, rational
O C. Real, integer
OD. Real, irrational
The type of number types that are being described are A. Rational, integer.
What is a Rational Number?A rational number in mathematics is one that can be stated as the quotient or fraction of two integers, p and q, with p being the numerator and q being the denominator, respectively.
Therefore, whole numbers are the numbers 0, 1, 2, 3, 4 and so on and negative numbers are not considered whole numbers.
natural numbers are called the counting numbers that are the numbers 1, 2, 3, 4, and so on. they are positive numbers and zero is not considered a natural number as you can see.
integers are all the whole numbers and their opposite (negative) but negative numbers are NOT whole or natural numbers. fractions and decimals are not integers.
irrational numbers are an infinite number of digits to the right of the decimal point, without repeating.
Thus, option A is the answer
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Classify the real number. (Choose all that apply). –9 A.) Rational B.) Whole C.) Irrational D.) Natural E.) Integer
For a survey based on 2,700 adults, what is the approximate margin of error? (round your answer to the nearest thousandth.)
The approximate margin of error for a survey based on 2,700 adults, when rounded to nearest thousand is 0.021.
In statistical surveys, the margin of error is a measure of the expected amount of random sampling error that is present in a survey's results. It is a range of values that is likely to contain the true value of the population parameter being estimated, with a certain degree of confidence.
In other words, the margin of error is the amount by which the sample estimate may differ from the true value of the population parameter.
The margin of error is affected by several factors, such as the size of the sample and the level of confidence. A larger sample size typically results in a smaller margin of error because larger samples provide more accurate estimates of the population parameter.
Similarly, a higher level of confidence requires a larger margin of error, since the interval of values that could contain the true population parameter becomes wider as the level of confidence increases.
Assuming a 95% level of confidence, the formula for calculating the margin of error is:
Margin of error = z * sqrt(p * (1 - p) / n)
where:
z is the z-score for the desired level of confidence (1.96 for 95%)
p is the sample proportion, which is the proportion of the sample that exhibits a particular characteristic of interest (e.g., the proportion of respondents who support a certain political candidate)
n is the sample size, which is the number of observations in the sample.
If the sample proportion is not known, it is common to use a value of 0.5, which corresponds to the maximum possible margin of error for a given sample size. This is because the maximum sampling error occurs when the sample proportion is closest to 0.5, which gives the least amount of information about the true population parameter.
To calculate the margin of error for a survey of 2,700 adults, we can assume a sample proportion of 0.5 and a 95% level of confidence. Plugging these values into the formula, we get:
Margin of error = 1.96 * sqrt(0.5 * (1 - 0.5) / 2700)
= 1.96 * sqrt(0.25 / 2700)
= 1.96 * 0.008
= 0.016
Rounding to the nearest thousandth, the approximate margin of error is 0.021. This means that we can expect the survey results to be within plus or minus 2.1 percentage points of the true population parameter, with a 95% level of confidence.
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PLEASE HELP ASAP IF YOU HELP I WILL GIVE BRANLIST AND BUT ONLY IF YOUR RIGHT BUT ONLY IF YOUR RIGHT. A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.
OPTIONS
1/3
2/3
2/6
4/9
Answer:
im pretty sure it is 4/9
Step-by-step explanation:
From the question, we are to determine the probability of selecting two cards with D and D
From the formula for probability, we have that
P(D) = Number of favorable outcomes to D / Total number of possible outcomes
From the given information,
Number of favorable outcomes to D = 2
Number of possible outcomes = 3
Thus,
P(D) = 2/3
Then,
The probability of selecting two cards that have D and D with replacement is
P(D, D) = P(D) × P(D)
P(D, D) = 2/3 × 2/3
P(D, D) = 4/9
Hence, the probability is 4/9.
Janelle has set up bird feeders around the pond behind her house. Each feeder can hold 1/2 a cup of bird food. After measuring, Janelle finds that she has 3 cups of bird food. How many feeders can she fill?
Answer: Janelle can fill 6 feeders.
Step-by-step explanation:
To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.
First, let's convert the total amount of bird food from cups to half-cups:
3 cups / 2 = 6 half-cups
So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.
Therefore, she can fill:
6 half-cups / 1 half-cup per feeder = 6 feeders.
So, Janelle can fill 6 feeders.
Graph y=0.5(2)^x on the domain -1 ≤ x ≤ 4
What is the range of this function?
The graph of the exponential function y = 0.5(2)^x on the domain -1 ≤ x ≤ 4 is given by the image presented at the end of the answer.
The range is given as follows:
0.25 ≤ y ≤ 8.
How to graph the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change, the value by which y is multiplied when x is increased by one.The parameters for the function in this problem are given as follows:
a = 0.5, b = 2.
The numeric values are given as follows:
x = -1, y = 0.25.x = 0, y = 0.5 -> x increases by one, y multiplies by 2.x = 1, y = 1.x = 2, y = 2.x = 3, y = 4.x = 4, y = 8.More can be learned about exponential functions at https://brainly.com/question/30113628
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Which of the following strategies will help you gain instructional control? Behavior tech
Gaining instructional control is an important aspect of teaching and behavior management.
What is instructional control?Instructional control is a term used in behavior analysis to describe a situation in which a teacher or other instructional agent has established the conditions necessary for effective teaching to occur.
Here are some strategies that can help you gain instructional control:
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the preimter of a rectangel measures 78 centimterers the measure of the with is 15 cenimeters what is the area of the rectangel
Answer:
360 cm^2
Step-by-step explanation:
The length of the rectangle can be found using the formula for perimeter:
Perimeter = 2 * (length + width)
Rearranging the equation, we can solve for the length:
length = (Perimeter - 2 * width) / 2
Plugging in the given values:
length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm
Next, the area of the rectangle can be found using the formula:
Area = length * width
Plugging in the given values:
Area = 24 * 15 = 360 cm^2
Which form or system of government gives the most power to the people of the nation?
Unitary
Autocracy
Democracy
Oligarchy
Question 3(Multiple Choice Worth 3 points)
The Leswaygo Times is a newspaper in the imaginary country Leswaygo. You read in one of its online articles that the people are unhappy with their new king. He is making changes to make Leswaygo more modern. He believes this will benefit the country, but the people do not agree. They are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to
communism
democracy
autocracy
socialism
Question 4(Multiple Choice Worth 3 points)
Which list shows forms or systems of government from the least power for the people to the most?
Oligarchy, autocracy, republic
Autocracy, oligarchy, democracy
Democracy, unitary, parliamentary
Federation, republic, unitary
Question 5(Multiple Choice Worth 3 points)
You read in the newspaper about a country that just held elections. The people voted for new representatives in their lawmaking branch of government. The members of this branch are busy meeting to discuss who will be the new prime minister. Only they, and not the voters, have a say in who will have this position. The new prime minister is part of the lawmaking branch and answers to it.
Which system of government does this represent?
Unitary
Federation
Parliamentary
Confederation
Question 6(Multiple Choice Worth 3 points)
In the early days of the United States, the central government was weak compared to the state governments. The leaders recognized there were problems with this arrangement. When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws.
Which system of government does the United States have?
Unitary
Federation
Parliamentary
Confederation
Question 7(Multiple Choice Worth 3 points)
Which of the following statements could appear in the sections labeled “B” and “D”?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
The use of force is unnecessary.
The people’s wishes are not always considered.
Local issues are heard and addressed.
Voters have a say in making decisions.
Question 8(Multiple Choice Worth 3 points)
Which of the following phrases belongs in the section labeled “A”?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
Decisions made quickly
Overlap in government services
Less waste of tax dollars
Single political party has control
Question 9(Multiple Choice Worth 3 points)
“Members can maintain power while working together on specific, shared concerns.” In which section would you place this statement?
Form or System Advantages Disadvantages
Unitary
A
Strong unity
B
Confederation
C
D
Central goverment may be too weak
Federation
E
Local governments can address local issues
F
D
B
E
C
Question 10(Multiple Choice Worth 3 points)
“Decisions take much longer because the people have a say in them.” In which section of the chart would you place this statement?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
E
F
A
B
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The answers include the following:
The form or system of government which gives the most power to the people of the nation is Democracy.The new prime minister is part of the lawmaking branch and answers to it which means that the system of government is parliamentary.When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws which depicts Confederation.“Decisions take much longer because the people have a say in them therefore the section of the chart which you would place this statement is Democracy.What is Democracy?
This is referred to as a system of government where the citizens of a state exercise power to rule the state, either directly or through electing representatives.
Decisions take much longer because the people have a say in them through the process of voting and is therefore the reason why it was chosen as the correct choice.
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Answer:
Step-by-step explanation:The form or system of government which gives the most power to the people of the nation is Democracy.
The new prime minister is part of the lawmaking branch and answers to it which means that the system of government is parliamentary.
When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws which depicts Confederation.
“Decisions take much longer because the people have a say in them therefore the section of the chart which you would place this statement is Democracy.
The height of a triangle is 8 m more than twice the length of the base. The area of the triangle is 21 m². Find the height of the triangle.
Answer:
The height of the triangle is 14 m,
Step-by-step explanation:
Let the base be x, then the height is:
2x + 8The area is half the product of base and height.
Set up equation and solve for x:
x(2x + 8)/2 = 21x(x + 4) = 21x² + 4x = 21x² + 4x - 21 = 0x² + 7x - 3x - 21 = 0x(x + 7) - 3(x + 7) = 0(x + 7)(x - 3) = 0x = - 7 or x = 3The first root is discarded as negative. The second root is the answer.
The base is 3 m, so the height is:
2*3 + 8 = 14 mAnswer:
The height of the triangle is 14 m.
Step-by-step explanation:
The area of a triangle can be found by using the following formula:
[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]
where:
b is the base of the triangle.h is the height of the triangle.If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:
[tex]h = 2b + 8[/tex]
Rewrite this equation to make b the subject:
[tex]\implies 2b=h-8[/tex]
[tex]\implies b=\dfrac{1}{2}h-4[/tex]
Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:
[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]
To find the height of the triangle, solve the equation for h.
[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]
[tex]\implies h^2-8h=84[/tex]
[tex]\implies h^2-8h-84=0[/tex]
[tex]\implies h^2-14h+6h-84=0[/tex]
[tex]\implies h(h-14)+6(h-14)=0[/tex]
[tex]\implies (h+6)(h-14)=0[/tex]
Apply the zero-product property:
[tex]h+6=0 \implies h=-6[/tex]
[tex]h-14=0 \implies h=14[/tex]
As length cannot be negative, the height of the triangle is 14 m.
I need help answering this
The domain of the function for this situation is given as follows:
B. All whole numbers greater than or equal to 0 and less than or equal to 7.
How to obtain the domain of a function?The domain of a function is the set that contains all the values assumed by the input of the function.
Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.
The values that compose the domain of the graph are given as follows:
0, 1, 2, 3, 4, 5, 6 and 7.
Which is best described by option B.
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The given tessellation formed by two or more regular polygons is shown.
Square , triangle and hexagon are the type of regular polygons that surround each vertex.
The angles are 60° , 90° , 90° , 120° .
From the given figure , it can be concluded that ,Square , triangle and hexagon are the type of regular polygons that surround each vertex.
Since , at each vertex they are one triangle , two squares and one hexagon therefore we can say that
The number of angles are 60° , 90° , 90° and 120°.
The tessellation is possible because the sum of measures of all angles that come together at the vertex is 360°
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Say that a certain stadium for professional football has 70,000 seats. What is the shape of the
supply curve for tickets to football games at that stadium? Explain.
Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.
The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.
However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.
Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.
Step-by-step explanation:
the instructions to mix a cool drink is to use concentrate and water in a ratio 2:9 how much water should be added to 500ml of concentrate
Answer:
2250ml
Step-by-step explanation:
The concentrate-to-water ratio is 2:9. This means 2ml of concentrate requires 9ml of water. We have 500ml of concentrate, which is 250 times more than 2ml, so to find the amount of water, we also multiply 9ml by 250:
2ml concentrate : 9ml water
(Multiply both sides by 250)
500ml concentrate : 2250ml water
Greta’s family drinks 3. 1/4 quarts of milk and 1 5/6 quarts of juice in one week. About how much more milk than juice does Greta’s family drink in one week?
Answer:1 5/12 or written the other way 17/12
Step-by-step explanation:
Write System of Equations from Context
Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than
pennies. Write a system of equations that could be used to determine the number of
pennies and the number of nickels that Kennedy has. Define the variables that you
use to write the system.
Let __=_________
Let__=___________
System of Equations:
_________________
_________________
13. Interpret the IQR and median in the context of the data set.
The interquartile range is 4 and the median is 27.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.
Interquartile range = 28 - 24 =4
Median is the central value of a data set. On a box plot, the median is the second line on the box.
The median is 27.
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Mrs Chong paid for a frying pan that cost $64 with some $10, $5 and $2 notes .If she used a total of 15 notes,how many $5 notes did she use?
Required process!
Thank you
For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
What is Inequalities?
Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.
Let's call the number of $10 notes Mrs. Chong used as "x".
We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:
10x + 5y + 2z = 64
Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).
We can substitute x = 15 - y - z into the first equation:
10(15 - y - z) + 5y + 2z = 64
Expanding the equation:
150 - 10y - 10z + 5y + 2z = 64
Combining like terms:
150 - 5y + 3z = 64
Subtracting 150 from both sides:
-5y + 3z = -86
Dividing both sides by -5:
y - (3/5)z = 17.2
So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
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Two angles are supplementary angles if the sum of their measures is 180°.
Find two supplementary angles such that the measure of the first angle is 26° less than
three times the measure of the second.
The measure of the first angle is____ft.
The measure of the first angle is 128. 5 degrees
How to determine the angleFrom the information given, we have that;
The two angles are supplementaryThe sum up to 180 degreesThe first angle is 3x - 26Let the second angle be x
We have the representation as;
3x - 26 + x = 180
collect the like terms, we get;
3x + x = 180 + 26
Add or subtract the like terms
4x = 206
Make 'x' the subject of formula by dividing by the coefficient of x, we get;
x = 206/4
divide the values
x = 51.5 degrees
Then, the angle is 128 .5 degrees
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