The proportional relationship is represented by the formula, y = kx, which demonstrates that y increases at the same rate as x does
Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.The ratio of the constant values of two proportional quantities is known as the proportionality constant.When either the ratio or product of two changing values results in a constant, that pair of values is said to be in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.The direct proportionality formula, y = kx, demonstrates that y increases at the same rate as x does. The cost per item (y), which is inversely proportional to the number of things purchased (x), is represented by the symbol y x.By using the indirect proportionality formula, y = k/x, it can be seen that when y rises, x falls, and vice versa.Therefore the proportional relationship is represented by the formula,
y = kx .
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What is the measure
Here, we want to get the measure of the angle marked A
We are going to use the sides given
The trigonometric ratio that links the adjacent to the hypotenuse is the cosine
The cosine is the ratio of the adjacent to the hypotenuse
Mathematically;
[tex]\begin{gathered} \cos \text{ m}\angle CAB\text{ = }\frac{12}{15} \\ \\ m\angle CAB\text{ = }\cos ^{-1}(\frac{12}{15}) \\ \\ m\angle CAB\text{ = 36.87} \end{gathered}[/tex]Divide using synthetic division. Write down the answer as a polynomial.x^3-5x^2-2x+24=0; (x+2)
we are given the following polynomial:
[tex]x^3-5x^2-2x+24=0[/tex]we are asked to use synthetic division by:
[tex]x+2[/tex]first we need to find the root of "x + 2":
[tex]\begin{gathered} x+2=0 \\ x=-2 \end{gathered}[/tex]Now we do the synthetic division using the following array:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we lower the first coefficient and multiply it by -2 and add that to the second coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {\square} \\ {1} & {-7} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. We multiply -7 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. we multiply 12 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {-24} & {} & {} \\ {0} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]The last number we got is the residue of the division, in this case, it is 0. Now we rewrite the polynomial but we subtract 1 to the order of the polynomial:
[tex]\frac{x^3-5x^2-2x+24}{x+2}=x^2-7x+12[/tex]A and B are sets of real numbers defined as follows.A = {x|x≤ 2}XB = {x|x < 7}Write A UB and An B using interval notation.If the set is empty, write 0.
The given sets are
[tex]\begin{gathered} A=\lbrace x:x,x\leq2\rbrace \\ \\ B=\lbrace x:x,x<7\rbrace \end{gathered}[/tex]That means A is all real numbers from 2 to negative infinity, and B is all real numbers between 7 and positive infinity
[tex]\begin{gathered} A=(-\infty,2] \\ \\ B=(7,\infty) \end{gathered}[/tex]Then we can find the union and intersection
[tex]\begin{gathered} A\cup B=(-\infty,2]\cup(7,\infty) \\ OR \\ A\cup B=(-\infty,\infty)-(2,7] \end{gathered}[/tex]I will draw a sketch to show you the intersection
We can see that there is NO intersection between A and B, then
[tex]\begin{gathered} A\cap B=\lbrace\rbrace \\ A\cap B=0 \end{gathered}[/tex]Given that Kelsey has already made 10 pendants how many additional pendants must she make and sell to make a profit of 50 dollars?
Part a: Kelsey should make 36 pendants
Part b: Kelsey needs to make 26 more pendants
Rent of the booth at the craft fair = $200
The material cost of each pendant = is $7.80
The selling cost of each pendant = is $13.50
Let Kelsey make x number of pendants
Formulating the inequality equation we get:
Selling cost of each pendant*Number of pendants >= Rent of the booth + Material cost of each pendant*Number of pendants
= 13.50x >= 200 + 7.80x
Solving the inequality we get:
13.50x >=200+7.80x
5.70x >= 200
x >= 35.08
So, she should make a total of 36 pendants
Considering that she has already made 10 pendants. She needs 26 more pendants.
Although a part of your question is missing, you might refer to this full question: Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A: Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B: Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit?
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what is the reciprocal for the fraction 5/7 ?
we know that
The reciprocal of a number is: 1 divided by the number
If you multiply a number by the reciprocal, the result is 1
so
we have
5/7
so
the reciprocal is 7/5
Verify
(5/7)(7/5)=1 -----> is ok
The temperature in the morning was –2º F. The temperature in the evening was 9º F higher than it was in the morning. What was the temperature in the evening?
Answer:
Step-by-step explanation:
-2f
David has a coin collection. He keeps 9 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?
Work Shown:
x = total number of coins
2% of x = 0.02x = 9 coins in the box
0.02x = 9
x = 9/0.02
x = 450 coins total
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
?
Answer:
it's wh question I think
the probability of a 4 child family having 4 girls is 0.5. is it true or false
Consider the phase space that consists of elements of the form (boy, boy, boy, boy), (girl, boy, boy, boy),...,(girl, girl, girl, girl).
There is a total of 2*2*2*2=2^4=16 possible combinations and each of them has the same probability to happen. Only one element is the case we are interested in (girl, girl, girl, girl).
Therefore, the probability of a family having 4 girls is
[tex]P(girl,girl,girl,girl)=\frac{1}{16}=0.0625[/tex]
The answer is false, the probability is 0.0625
CRITICAL THINKING Find the values of a, b, and c so that the linear system shown has (---1. 2. --3) as its only solution. Explain your reasoning. x + 2y - Bra -r-y +z = b 2x + 3y - 2z=c enter your answer as follows: a=_,b=_,c=__without any spaces. Show Your Work
1) Let's set the system of linear equations:
x +2y -3z = a
-x -y +z = b
2x +3y -2z =c
2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:
x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4
-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0
2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2
3) Hence, a = 4 b = 0 and c = -2
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 70
grams of an alloy that contains 12% copper with 90 grams of pure copper.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?
a)There is 160 grams of copper are in the resulting mixture
b) There is 61.5% percentage of the resulting mixture is copper.
What are mathematics operations?
• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.
• The operation's arity is determined by the number of operands.
• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.
• A zero-arity operation, also known as a nullary operation, is a constant.
• The mixed product is an example of an arity 3 operation, also known as a ternary operation
From the question:
a) Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams
b) 70 grams of an alloy that contains 12% copper = 70 × 12%
= 70 grams × 0.12
= 8.4 grams
The number of grams of copper in the resulting mixture = 160 grams
The percentage of the resulting mixture that is copper is
=( 8.4 grams + 90 grams of pure copper/160) × 100
= 98.4/160 × 100
= 61.5%
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The measure of two complementary angles are in ratio 2:3. What is the measure of the smaller angle
ANSWER
36°
EXPLANATION
Let a and b be the measures of the two angles. We know that they are complementary, so their measures add up to 90°. Also, we know that the quotient between their measures is 2/3,
[tex]\begin{gathered} a+b=90 \\ \frac{a}{b}=\frac{2}{3} \end{gathered}[/tex]Solve the second equation for a,
[tex]a=\frac{2}{3}b[/tex]Replace a with this expression in the first equation,
[tex]\frac{2}{3}b+b=90[/tex]Add like terms,
[tex]\frac{5}{3}b=90[/tex]Solving for b,
[tex]b=90\cdot\frac{3}{5}=54[/tex]So the other angle is,
[tex]a=\frac{2}{3}b=\frac{2}{3}\cdot54=36[/tex]Hence, the measure of the smaller angle is 36°.
Which relation IS a function?
Answer: B.
Step-by-step explanation: A function relates an input to an output.
The relation which is a function is: function 1.
Option A is correct.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
A relation is a function when each input have only one output.
Function 1 have one output to each corresponding output.
Function 2 have two output for input x= 2.
Function 3 have two output for input x= 3.
Function 4 have two output for input x= 1.
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solve for the following right triangle upper a and h
we have that
[tex]undefined[/tex]Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)a. -33b. -36c. -63d. -69
Given:
[tex]a_n=3-6(n-1)[/tex]Find-: 12th term of the sequence is
Sol:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} n=\text{ term.} \\ \\ n=12 \end{gathered}[/tex]Put the value then:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \\ n=12 \\ \\ a_{12}=3-6(12-1) \\ \\ a_{12}=3-6(11) \\ \\ a_{12}=3-(6\times11) \\ \\ a_{12}=3-66 \\ \\ a_{12}=-63 \end{gathered}[/tex]So 12th term is -63
Answer:
-63
Step-by-step explanation:
Does our data provide enough evidence to prove that New York police are racially biased (in terms of use of force)? Why or why not?
We want to proof for this case if there is enough evidence to conclude that the New York police are racially biased in terms of force
From the info given is possible to see that the proportion with High level of force used is higher for Black people compared to White people. A difference of 6.3-5.8% = 0.5%.
In the other hand, we can see that for the Hands up force level, there is a significant difference between the two proportions, higher for Black compared to White with a difference of 15.1-9.7%= 5.4%
And finally when we analyze the case for No force used, we can see that there is a higher percentage for White (84.4%) compared to Black (78.7%) with a difference of 5.7%.
Based on this results we can conclude that in general the New York police is partially biased since is possible to see that for any level of force used the records are in favor of the White people.
Can Some one please help me match the congruence statements below!
1) Consider the ratio table below that compare hours worked to money earned for an employee at a pizza restaurant. Hours Worked 4 12 16 ? Money Earned 36 ? 76 108 144 270 a. How much money would an employee earn for working 8 hours? b. How many hours did a person work if they earned $270? c. Find the ratio associated with the table above (in simplest form). d. If you extend the ratio table, how much money will be earned if an employee works 24 hours? dollars they can amount of time
The ratio table can be used to find the amount earned and the number of hours worked based on the ratio of the values as follows;
a. A person that works for 8 hours earns $72
b. A person that earns $270 worked for 30 hours
c. The ratio is 9 : 1
d. The earnings of a person that works for 24 hours is $216
What is a ratio table?A ratio table is one that shows the constant relationship between the value pairs on the table.
The given ratio table is presented as follows;
Hours Worked; 4, 12, 16, ?
Money Earned; 36, 108, 144,
Required;
a. The amount a person will earn if he or she works for 8 hours
Solution;
Let x represent the hours worked, and let y represent the money earned
y = k•x
Therefore;
k = y/x
From the ratio table, we have;
k = 36/4 = 108/12 = 144/16 = 9
k = 9
y = 9•x
The amount earned, y for working 8 hours, x is therefore;
y = 9 × 8 = 72
The amount earned for working 8 hours is $72
b. The number of hours worked if a person earns $270
If a person earned $270, we have;
270 = 9 × x
x = 270/9 = 30
The number of hours worked if a person earned $270 is 30 hours
c. The ratio associated with the table in the simplest form is 36 : 4 = 9 : 1
d. The amount earned if a person worked 24 hours
Solution;
y = 9•x
Which gives;
y = 9 × 24 = 216
The amount earned if a person worked 24 hours is $216
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8 - 5(3 + 2x)I need help
8 - 5(3 + 2x)
open the parenthesis
8 - 15 - 10x
-7 -10x
27 is The same as the product of four and a number
Answer:
6.75
Step-by-step explanation:
6.75x4 = 27 so if this is what was meant by this then heres your answer
hope this helped
have a good day ^^
I really need help with number 5
Given:
Required:
To find the distance from point B to line AC.
Explanation:
The point B touches the line AC at P.
And it is perpendicular.
The length of BP is 4.3.
Therefore, the distance from point B to line AC is 4.3.
Final Answer:
The distance from point B to line AC is 4.3.
Can someone help with 16,17 and 18 ! thank you !
In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.
We can use the following relation to solve the problem:
[tex]tg(x)=\frac{\text{Opposite side}}{Adjacent\text{ side}}[/tex]16)
[tex]\begin{gathered} tg(x)=\frac{\text{1}7}{7}=2.4285 \\ tg(x)=2.4285 \\ x=tg^{-1}(2.4285) \\ x=68\degree \end{gathered}[/tex]17)
[tex]\begin{gathered} tg(x)=\frac{8}{10}=0.8 \\ x=tg^{-1}(0.8) \\ x=39\degree \end{gathered}[/tex]18)
[tex]\begin{gathered} tg(x)=\frac{\text{1}1}{8}=1.375 \\ x=tg^{-1}(1.375) \\ x=54\degree \end{gathered}[/tex]1/2 ^1/2 please show the steps
The value of [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex] is 0.707.
1÷2 = 0.5
Given, [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex]
Could be written like, [tex](0.5)^{0.5}[/tex] or √(1 ÷ 2) or √(0.5)
So the value of √(0.5) is 0.707.
Another way is to factorize each integer as the product of its primes using the square root prime factorization method. Follow these methods to find the square root of a certain number using prime factorization:
Step 1: Divide the supplied integer by its decimal equivalent.
Step 2: If the connected components are identical, a pair is generated.
Step 3: Choose one of the pair members for her.
Step 4: Multiply the prime numbers you got by picking one from each pair.
Step 5: This product is the square root of the specified number.
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.3 years, and standard deviation of 1.1 years.If you randomly purchase one item, what is the probability it will last longer than 10 years?Use the normal table and round answer to four decimal places
We want to find the following probability:
[tex]P(X>10)[/tex]where X is a normal random variable with mean 13.3 and standard deviation 1.1. To find this probability let's normalize the random variable; to do this we use the z-score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, in this case, we have:
[tex]P(X>10)=P(z>\frac{10-13.3}{1.1})=P(z>-3)[/tex]Using the standard normal table, we have:
[tex]P(X\gt10)=P(z\gt(10-13.3)\/1.1)=P(z\gt-3)=0.9987[/tex]Therefore, the probability of purchasing an item with a lifespan greater than 10 years is 0.9987
which situation can be represented by this inequality1.25x -6.50 > 50 A. Caleb has a balance of 6.50$ in his savings account and deposits 1.25$ each week. What is X the number of weeks must deposit 1.25$ in order to have a balance of more than 50$ in his savings account?B. Caleb earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of 6.50$. What is X the balance that Caleb must have in his checking account in order to have an ending balance greater than 50$ after interest and fees.C. Caleb charges 1.25$ for gasoline plus 6.50$ per hour for mowing lawns. What is X the number of hours he has to mow lawns to earn more than 50$D. Caleb spends 6.50$ on supplies for a lemonade stand and sells each cup of lemonade for 1.25$. what is X the number of cups of lemonade Caleb must sell to earn profit of more than 50$
We need to find a situation that can be represented by the inequality below:
[tex]1.25\cdot x-6.5>50[/tex]This means that there must be a variable for which each unit has a value of 1.25. There must be a fixed cost of 6.5, because we are subtracting that value and the end goal must be to have more than 50.
The only option for which this applies is the option D.
Caleb spent a fixed amount of 6.5, he earns 1.25 for each lemonade he sells and he wants to have a profit of more than 50.
Fin tends to exaggerate. He says if he stacked all the quarters he's ever spent on gumball machines, they would reach to the moon. The distance to the moon is about [tex]3.85 \times {10}^{8} [/tex]m and the width of a quarter is about[tex]1.75 \times {10}^{ - 3} [/tex]m. If Fin's claim were true, how many quarters has he spent on gumball machines?
For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.
In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:
[tex]\begin{gathered} n=\frac{3.85\cdot10^8}{1.75\cdot10^{-3}} \\ n=2.2\cdot10^{8-(-3)} \\ n=2.2\cdot10^{8+3} \\ b=2.2\cdot10^{11} \end{gathered}[/tex]If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.
A cooking for the nursing home is preparing 100 yeast rolls for dinner the dry ingredients needed include 14 1/8 cups of flour 6 3/8 cups of sugar and 3/8 cups of salt how many cups of dry ingredients are in this recipe
Given the following ingredients
Cups of flour = 14 1/8 = 113/8 cups
Cups of sugar = 6 3/8 cups = 51/8 cups
Cups of salts = 3/8 cups
Calculate the total cups of dry ingredients
[tex]Total\text{ cups}=\frac{113}{8}+\frac{51}{8}+\frac{3}{8}[/tex]Find the LCM
[tex]\begin{gathered} Total\text{ cups}=\frac{113+51+3}{8} \\ Total\text{ cups}=\frac{167}{8} \\ Total\text{ cups}=20\frac{7}{8}cups \\ Total\text{ cups}=19+1\frac{7}{8} \\ Total\text{ cups}=19+\frac{15}{8} \\ Total\text{ cups}=19\frac{15}{8}cups \end{gathered}[/tex]Therefore there are 19 15/8 cups of dry ingredients in this recipe
Write two numbers that multiply to the value on top and add to the value on bottom.
The values are -3 and -26
What is Multiplication?
A product is an expression that identifies the object to be multiplied, called the result of a multiplication, or coefficient. For example, 30 is the product of 6 and 5, and x\cdot is the product of x.
We have to find the number which is multiply to give the upper value and sum up to give the bottom value
So, the value of these numbers will be
-3 x -23 = 69
-3 + (-23) = -26
Hence the values are -3 and -23
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Complete the vertical algorithm to evaluate the product.Please see image below
Solution
Complete the vertical algorithm to evaluate the product:
Therefore the product of the expression is
[tex]4.09656[/tex]Write an equation to represent , the balance in an account after years, with an initial investment of $1,000 with an interest rate of 3%, compounded each year.
The balance in the account after years of compound interest arrangement can be represented by the equation; Balance = 1,000 (1.03)^n.
Which equation represents the balance in the account after years of compound interest?It follows from the task content that the equation which represents the balance in the account after years is required to be determined.
It follows that the principal amount is; $1,000 while the interest rate is; 3%.
This indicates that after each year, the new balance is 103% of the preceding balance.
Hence, the exponential equation which correctly represents the balance at any point in time is;
Balance = 1,000 (1.03)^n.
Where n = number of years after.
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