"The variable y varies directly as x."
For this type of condition, we can just interpret this as getting the missing value through ratios and proportions.
We get,
\(\text{ 20 : 12 = 15 : y}\)\(\text{ 20 : 12 = 15 : y }\rightarrow\text{ }\frac{\text{ 20}}{\text{ 12}}\text{ = }\frac{\text{ 15}}{\text{ y}}\)\(\text{ (20)(y) = (15)(12)}\)\(\text{ 20y = 180}\)\(\text{ }\frac{\text{20y}}{20}\text{ = }\frac{\text{180}}{20}\)\(\text{ y = 9}\)Therefore, at x = 15, y = 9.
The answer is letter B.
There are 2 boys for every 3 girls in Sappy Sunshine Childcare center. If there are a total of 171 girls at the center, how many boys are there? (do not include units in your answer, just the number)
Answer:
114 boys
Step-by-step explanation:
This question can be solved using a rule of three.
For each 2 boys, there are 3 girls on the center. So, how many boys will be there when there are 171 girls?
2 boys - 3 girls
x boys - 171 girls
\(3x = 2*171\)
Simplifying both sides by 3
\(x = 2*57 = 114\)
There are 114 boys there
He is pulling 400 feet over level ground by exerting a constant 25-pound force on the bar that makes an angle of 30° with the ground.
How much work is Thomas doing to pull the wagon?
10,000 foot-pounds
8,660 foot-pounds
7,070 foot-pounds
5,000 foot-pounds
Answer:
It’s b
Step-by-step explanation:
Answer:
B on edge
Step-by-step explanation:
I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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SOMEONE HELP PLEASE!!!
Find P(C|Y) from the information in the table.
To the nearest tenth, what is the value of P(C|Y)?
A. 0.4
B. 0.5
C. 0.7
D. 0.8
Answer:
The answer to your problem is, B, 0.5
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
As we know that the conditional probability formula of P(A/B) is given by:
P(A/B) = \(\frac{P(AnB)}{P(b)}\)
P(C/Y) = \(\frac{P(CnY)}{P(Y)}\)
P ( Y ) = \(\frac{30}{146}\) and P(CnY) = \(\frac{15}{146}\) [ because of the third column shown ]
Thus, the answer is, B. 0.5
Feel free to ask any questions down below \/ !
Please help me thank you
the answer should be "Y less than or equal to 4" if I'm correct
You find one quarter, two dimes, and two nickels.
a. Write the dollar amount as a decimal.
Answer:
$0.55
Step-by-step explanation:
1 quarter is 25 cents
2 dimes is a total of 20 cents
2 nickels is a total of 10 cents
if you add all of it up 25+20+10 you get 55 cents but u need it in dollar amount so it would but $0.55 since u have less than a dollar.
Solve 2^x-2=8^4 but not solving for x
Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.
To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.
First, let's simplify the equation:
2^x - 2 = 8^4
We know that 8 can be expressed as 2^3, so we can rewrite the equation as:
2^x - 2 = (2^3)^4
Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:
2^x - 2 = 2^(34)
Simplifying the right side of the equation:
2^x - 2 = 2^12
Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:
x = 12
Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.
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Pls help math easy will give brainlest
Answer(s)
Problem 9: 138.53
Problem 10: Function
Problem 11: Not A Function (Not Sure)
Edit; Problem 9 should've been right, I have no idea then.
Multiply 0.035 times a power of ten so that the product is greater than 1, but less than 100. Write the expression.
Answer:
0.035 x 2^10
Step-by-step explanation:
(0.035). * (2^10) = (0.035) * (1,024) = 35.84
triangle JKL is congruent with triangle \GHI Complete the congruence statement.angle J is congruent with angle _
From the picture, the congruent angles are:
∠K ≅ ∠H
∠J ≅ ∠G
∠L ≅ ∠I
use the formula A=P(1+rt) and elementary algebra to find the missing quantity. A= $2,242r = 6% t = 3 years P= $ _____ (simplify the answer)
Given the formula
\(A=P(1+rt)\)We want to find the 'P' value given the following information:
\(\begin{gathered} A=2242 \\ r=0.06 \\ t=3 \end{gathered}\)To find 'P', we just need to make the substitutions in the right places. Change 'A' in the equation for our A value(2242), and do the same with the other parameters.
\(A=P(1+rt)\Leftrightarrow2242=P(1+0.06\cdot3)\)Now, we just need to do the calculations
\(\begin{gathered} 2242=P(1+0.06\cdot3) \\ 2242=P(1+0.18) \\ 2242=P\cdot1.18 \\ P=\frac{2242}{1.18}=1900 \end{gathered}\)Our P value is P = $1900.
which number produces a rational nunber when multiplied by 0.5?
Answer:
2.22
Step-by-step explanation:
it is 2.22 because 111/100 gives a rational number
and it is a rational number because it has no repeating decimal
Answer:
10
Step-by-step explanation:
just try 10 i think thats the answer
PLEASE HELP!! 35 POINTS!!!
ignore my writing if it’s wrong
Answer: sin(x)=5/11
Step-by-step explanation:
For #7, the hypotenuse is always the longest side of a triangle and in right triangles it's always the side that's opposite the right angle. MO, the side thats 11, is the hypotenuse in this triangle and not the adjacent side which would be NM. Therefore, you need to use sin=opp/hyp and get sin(x)=5/11
Which of the following sets of ordered pairs represents a function? PLEASE HELP
The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.
A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).
{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}
In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}
In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.
{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}
In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}
In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.
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Using log evaluate 3^x=10
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
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The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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g (x)=√-3x+6
Look at photo please
Answer:
\((-\infty,2)\)
Step-by-step explanation:
Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).
Solve for y.
3(y-2) = y +4-2(-5y-2)
Simplify your answer as much as possible.
Answer:
y = -7/4
Step-by-step explanation:
What is the value of S4 for
♾️. n-1
Σ 1/4(-1/3)
The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.
The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.
To find the value of S4, we substitute n = 4 into the expression and evaluate it.
♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)
Simplifying, we get:
♾️. 3 Σ 1/4(-1/3)
Since the term 1/4(-1/3) is constant, we can pull it out of the summation:
1/4(-1/3) ♾️. 3
Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:
1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12
Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.
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The probable question could be:
What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?
A) 1/9
B) 7/54
C) 5/27
D) 10/27
Prius bought these items at the grocery store. Find each unit price.
A. 12 eggs for $3 how much is the cost per egg ?
Answer:
your answer would be 0.25 cents per egg
Step-by-step explanation:
the product of 0.8 and a number is 12represent the statement as an equation determine the solution set using the replacement set 0 8 1 7 15
Answer:
The product of 0.8 and a number is 12, so the equation representing this statement is: 0.8 * x = 12.
To solve this equation, we need to find the value of x that makes the equation true. We can do this by using the replacement set {0, 8, 1, 7, 15}.
If we substitute 0 for x in the equation, we get: 0.8 * 0 = 12. This equation is not true, so 0 is not a solution.
If we substitute 8 for x in the equation, we get: 0.8 * 8 = 12. This equation is not true, so 8 is not a solution.
If we substitute 1 for x in the equation, we get: 0.8 * 1 = 12. This equation is not true, so 1 is not a solution.
If we substitute 7 for x in the equation, we get: 0.8 * 7 = 12. This equation is not true, so 7 is not a solution.
Finally, if we substitute 15 for x in the equation, we get: 0.8 * 15 = 12. This equation is true, so 15 is a solution.
Therefore, the solution set for this equation is {15}.
Answer: 0.8x=12
x=15
Step-by-step explanation:
0.8x=12
x=15
15*0.8=12
I need help ASAP! Please
Answer:
\(ce = cd\)
ce = cd
write six multiples of 2/5
find the population variance and standard deviation 10 13 17 19 21
The population variance σ² = 16.
The standard deviation, σ = 4.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Given:
A population sample,
10, 13, 17, 19, 21.
The mean μ = 16.
The sum of squares SS = 80
Now, the standard deviation,
σ = √80/5 = 4
The population variance σ² = 16.
Hence, σ = 4, and σ² = 16.
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Venessa bought 80 apples for 4$.out of these apples 25 precent were rotten and had to be thrown away Vanessa sold the remaining apples at 6 cents per apple. What is the profit or loss percentage
The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.
Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.
Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.
Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.
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PLEASE HURRY ILL MARK AS BRAINLIEST!!!
Answer:
answer is 14 and it is a example of derivative
Step-by-step explanation:
6 tractors take 8 days to collect the harvest. how long will it take 18 tractors to do the same?
Answer:
2.25
Step-by-step explanation: If it takes 6 tractors in 8 days then u would have to divide 18 by 8 because its double the equitment.
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Two fractions between 2 and 2 1/2
What is the domain of the function represented by the graph?
Answer:
It's either A or D.......
IN CASE YOU ARE LOOKING FOR THE ANSWER
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. Earth has a radius of 3959 mi.
What is the climber's distance to the horizon?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: The answer is 171.2 Miles
Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.
Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.