The store has 16 board games
What are equivalent ratios?
The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.
Let x = number of legos
Let y = number of board games
Given ratio: 9:6= 9/6
x/y = 9/6
substitute x=24
24/y=9/6
Do cross multiplication
(6*24)/9=y
16=y
or
y=16
So, the store has 16 board games
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Pls list step by step : calculus : Use a linear approximation to estimate the value of √33. Express your answer as an exact rational number
Using linear approximation, the function y = √33 is approximated as 5.744
Linear ApproximationThe concept behind the linear approximation formula is the equation of a tangent line. We know that the slope of the tangent that is drawn to a curve y = f(x) at x = a is its derivative at that point. i.e., the slope of the tangent line is f'(a). Thus, the linear approximation formula is an application of derivatives. Let us learn more about this formula in the upcoming sections.
In equation y = √33
We can apply linear approximation to this
y = √33 = 5.744
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I need help with this one PLEASE
Answer: x = 14
Step-by-step explanation: Because these are vertical angles we know they are equal.
5x-10 = 60
Add 10 on both sides
5x = 70
Divide by 5 on both sides
x = 14
What is the greatest common factor of 306², 806², and 206³?
Answer:
4Step-by-step explanation:
Find the prime factors of each number:
206 = 2*103 ⇒ 206² = 2²*103²306 = 2*3²*17 ⇒ 306² = 2²*3⁴*17²806 = 2*13*31 ⇒ 806² = 2²*13²*31²The greatest common factor of the three numbers is:
2² = 4A stadium manager has signed five acts this year with a combined revenue projection of $1,000,050. The cost for these is expected to average $85,000 per act. How much profit margin does the stadium expect this last year?.
profit margin does the stadium anticipate for this year 575050
Given,
This year, a stadium manager has booked five performances with a projected aggregate revenue of $1,050,050.
Profit: 1000 - 425 (85 x 5) = 575
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i need help with this
The total 12 people answered the survey in total when in a survey, 7 people said that their favorite card game was patience.
Given that,
In a survey, 7 people said that their favorite card game was patience.
We have to find how may people answered the survey in total.
What is pie chart?Pie charts can be used to show percentages of a whole group and show percentages at a particular moment. In contrast to bar graphs and line graphs, pie charts do not show changes over time. The pages that follow provide a description of a pie chart's many elements.
We divide the patience by 7
210/7
30
So, For each person in patience we have 30°.
The total is
60°+30°+60°+210°
2+1+2+7
12
Therefore, The total 12 people answered the survey in total when in a survey, 7 people said that their favorite card game was patience.
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Question 3 of 5
What is the fractional equivalent of the repeating decimal 0.5?
A- 5/99
B- 5/9
C-5/11
D-1/2
Answer: A. 5/99
Step-by-step explanation: This is bc it is repeating and 5 is an odd number.
A $500 investment in a 12-month CD with an interest rate of 4.89% compounded monthly, earns $25.01 interest in
one year. What effective rate of interest does this investment earn?
Answer:
Step-by-step explanation:
Effective interest rate, r = [tex](1+\frac{i}{n} )^{n}-1[/tex]
Here,
r = effective annual rate
i = nominal rate
n = number of periods
r = [tex](1+\frac{0.0489}{12} )^{12}-1[/tex]
= 0.05001099558
= 5.001099558 %
Find the eighth term in the sequence and explain how you arrived at this answer.
4, 16, 36, 64, 100, ...
Answer: 144
Step-by-step explanation:
When we go from 4 to 16, we add 12. Then, to get to 36, we add 20. Then, we add 28 to get 64, and finally 36 to get 100. The pattern looks like we add by 8 more every time, so next number is 100 + (36 + 8) or 144.
The sequence of squares of even nos. so the 8th term would be the square of 16 which is 256.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
The given sequence is 4, 16, 36, 64, 100...
This is a sequence of squares of even nos.
The first term is the square of 2 and the second term is the square of 4 hence the 8th term would be the square of 16 which is 16² = 256.
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Shane bought a mid-level computer 10 years ago for $3800. Yesterday, Shane bought a mid-level computer for $1400.
What was the approximate percent of decrease in the cost of mid-level computers?
The percent of decrease is 63.16%
How to calculate the percentage of decrease?
First, we calculate the amount of decrease
= $3,800 - $1,400
= $2,400
Next we dividing the amount of decrease by original price (old price)
= $2,400 ÷ $3,800
= 0.6316
And then convert the result into a percentage by multiplying by 100%
= 0.6316 × 100%
= 63.16%
Thus, the percent of decrease is 63.16%
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If given that the area of a square is 121 cm², find the length of one side of the square.
A 30.25 cm
B 11 cm
C 60.5 cm
D 10 cm
write a linear function with the values f(0)=6 and f(7)=27
The equation of the linear function is f(x) = 3x + 6
Given,
In the question:
The values are given as:
f(0)=6 and f(7)=27
To write a linear function.
Now, According to the question:
Write the equation of linear function:
y = mx + b
Substitute (0,6) and (7, 27) into y = mx + b:
6 = m x 0 + b
27 = m x 7 + b
Solve the equation:
6 = b
27 = 7m + b
Swap the sides :
b = 6
27 =7m +b
Substitute into one equation:
27 = 7m + 6
7m = 27 - 6
7m = 21
m = 3
Substitute b = 6 , m = 3 into y = mx +b
f(x) = 3x + 6
Hence, The equation of the linear function is f(x) = 3x + 6
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Kristen is mixing sweet tea and lemonade to make her favorite beverage. She mixes 24 fluid ounces of sweet tea with 18 fluid ounces of lemonade. How many liters of the beverage did she mix? Round to the nearest hundredth.
Answer: The answer should be 1.24.
Step-by-step explanation:
1.24209 rounded to the nearest hunredth is 1.24.
Answer:
1.24
Step-by-step explanation:
there are 33.814 fluid ounces in one liter. But she mixes 24 + 18 = 42 fluid ounces which is 1.24209 liters rounded to the nearest hundredth is 1.24
y=x2-14x+1
y=-14x+17
Answer:
y-y=x2-14x+14x+1-17
x2-16=0
x2=16
x=4
Bob rides his bike with a constant speed of
16 km/h. How far can he travel in 2 hours
30 minutes?
Solve for z.
z + 1 is greater than it equal to 29
The solution of the inequality z + 1 ≥ 29 for z , is z ≥ 28 .
Inequality can be defined as a relationship between two expressions or values that are not equal to each other.
For Example : x > 3.
In the question ,
it is given that
the inequality is " z + 1 is greater than it equal to 29 ",
we have to solve this inequality for z ,
So inequality can be rewritten as
z + 1 ≥ 29
Subtracting 1 from both sides of the inequality , we get
z + 1 -1 ≥ 29 - 1
z ≥ 29 - 1
z ≥ 28 .
Therefore , The solution for z + 1 ≥ 29 , is z ≥ 28 .
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If f(x) = 2x - 9, which of the following are correct? Select all that apply. f(-1) = -11 f(2) = 5 f(3) = -3 f(0) = -9 f(-3) = 15
f(-1) = -11 and f(3) = -3 . these functions are true .
What does a math function mean?
A relationship between a group of inputs and one output each is referred to as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. f(x), where x is the input, is a common way to refer to a function.In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable).given function f(x) = 2x - 9
f(-1) = -11 ⇒ x = -1 put in function
f( -1 ) = 2 * -1 - 9 ⇒ - 11
f(2) = 5 ⇒ x = 2 put in function
f( 2 ) = 2 * 5 - 9 = 1
f(3) = -3 ⇒ x = 3 put in function
f ( 3 ) = 2 * 3 - 9 = -3
f(-3) = 15 ⇒ x = -3 put in function
f( -3) = 2 * -3 - 9 = - 15
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Mrs. Rowan allotted 30 minutes at the beginning of class for her students to complete an exam. The last student took 42 minutes to complete the exam. What is Mrs. Rowan's percent error
Mrs. Rowan's , percent error is 40% .
In the question ,
it is given that ,
the time allotted by Mrs. Rowan to complete the exam = 30 minutes
the time that the last student took to complete the exam = 42 minutes
the percent error can be calculated using the formula
percent error = (time student take - time allotted) / (time allotted) × 100
Substituting the values of allotted time and time taken by the student from above , we get
percent error = (42 - 30)/30 × 100
= 12/30 × 100
= 0.4 × 100
= 40%
Therefore , Mrs. Rowan's percent error is 40% .
The given question is incomplete , the complete question is
Mrs. Rowan allotted 30 minutes at the beginning of class for her students to complete an exam. The last student took 42 minutes to complete the exam. What is Mrs. Rowan's percent error ?
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Calculate
70
cos 20°
rounded to 1 d.p.
70
cos 20 is a faction btw
70 Cos 20° rounded up to 1d.p is 65.8 and as a fraction is 658/10.
What is a fraction?
This refers to the value that is part of a whole number. It has a numerator (upper part) and a denominator (lower part) eg.1/2.
What is Decimal point?
This refers to a dot that is used to demarcate a whole number from the fractional part of a number. eg. 12.6.
The number of points/ values after the decimal point is called the decimal place. Example: 3.7 ( 1 decimal place), 4.26 ( 2 decimal places).
From the question:
Calculate 70cos 20° rounded to 1 d.p.
=70 * 0.9397
=65.78
rounded to 1 d.p.
=65.8
As fraction:
65.8 =65.8/10
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PLEASE HELP 34 pointsssss
Answer:f(-10)= -60
Step-by-step explanation:
Answer:
f(- 10) = - 300
Step-by-step explanation:
substitute x = - 10 into f(x) , that is
f(- 10) = - 3(- 10)² = - 3(100) = - 300
A line with a slope of
4/7 passes through the points (h,10) and (–4,6). What is the value of h?
Answer:
h = 3
Step-by-step explanation:
y-6 = 4/7 (x-(-4)
y - 6 = 4/7 (x+4)
y - 6 = 4/7 x + 16/7
y = 4/7 x + 16/7 + 6
y = 4/7 x + (16+42)/7
y = 4/7 x + 58/7
10 = 4/7 x + 58/7
4/7 x = 10 - 58/7
4/7 x = (70-58)/7
4/7 x = 12/7
7/4 * 4/7 x = 12/7 * 7/4
x = 3
After 2/3 of a minute a turtle has moved just 3/7 of a foot. What is the turtle's speed in
feet per minute?
Pls help asap, 35 POINTS
The smaller triangle is dilated to create the larger triangle. The center of datio. Is plotted but not labeled.
Describe this dilation. Be sure to include all of the information someone would need to perform the dilation.
Answer: Wat is dat green unlined as
Step-by-step explanation:
based on the picture, would man a or man b have more gravity?
subject is science but it not there
Answer: what picture
Step-by-step explanation:
2. There were 198 men and 256 women at a party of the men and
One-fourth of women left early.how many people remained at the party?
Answer:1/4 ×256/1= 64 women that left party
256-64= 192 women who remained
192+198=390 men and women at the party
Step-by-step explanation:
five fair coins are tossed. what is the probability that five tails will show? express your answer as a common fraction.
The probability that five tails will show is 1/32.
Given that the 5 coins are tossed. The probability of getting the head or the tails is 1/2 for each toss.
This means, total number of observations = 2⁵ = 32.
Required outcome is → 5 Heads {H,H,H,H,H}
This can occur only ONCE! when all the coins show the heads.
Thus, required outcome = 1
so, the Probability (5 Heads) = 1/32.
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Relative maxima and relative minima of the function f(x) = x^5 - 4x^3 3x^2 - 8x - 6
The relative maxima and relative minima for f(x) = x⁵ - 4x³ + 3x² - 8x - 6 is is -1.871 and 1.518
The given function is f(x) = x⁵ - 4x³ + 3x² - 8x - 6 ,now differentiation function with respect to x we get
=5x⁴ - 12x² + 6x - 8
Now solving the given equation for the critical values are:
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
Now, taking derivative of the 5x⁴ - 12x² + 6x - 8 , with respect to x we get
= 20x³ - 24x + 6
now replacing the value of x by 1.58, we get
20 * 1.58³ - 24 * 1.58 + 6
= 46.966, which is positive so it is the minima
Again replacing the value of x by -1.871, we get
=>20 * -1.871³ - 24 * -1.871 + 6
=> -169.9, which is negative so it is the maxima
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11 times the product of 19 and a number g?
11 times the product of 19 and a number g?
11*(19g)
= 209g
please help asap
(possible answers are: 2,-5,1,-8)
The solution is y = -5
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Let the function be f ( x ) = y
And , y = x² + 2x - 8
So , f ( x ) = x² + 2x - 8
Substituting the value for x in the equation , we get
When x = -3
f ( -3 ) = ( -3 )² + 2( -3 ) - 8
= 9 - 6 - 8
= 9 - 14
f ( -3 ) = -5
When x = 1
f ( 1 ) = ( 1 )² + 2( 1 ) - 8
= 1 + 2 - 8
= 3 - 8
f ( 1 ) = -5
Hence , the value of y = -5
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Solve the following system of equations by linear combination: 2x + y = 8 x – y = 4
a. The solution is (5, –2).
b. The solution is (4, 0).
c. There is no solution.
d. There are an infinite number of solutions.
The solution to the equation by linear combination is (b) The solution is (4, 0).
How to determine the solution to the equation?From the question, we have the following system of equations
2x + y = 8
x – y = 4
By linear combination, we start by eliminating one of the variables
This is done by adding the equations
So, we have
2x + x - y + y = 8 + 4
Evaluate the like terms
3x = 12
Divide both sides
x = 4
Substitute x = 4 in x – y = 4
4 – y = 4
So, we have
y = 4 - 4
Divide
y = 0
Hence, the solution is (b) (4, 0)
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PLEASE HELP!
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model.
Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth.
What are the coordinates of the point that represents the weekly average per run for Week 7?
Answer: I think it (7,4.1)
Step-by-step explanation:
Answer:
7.3.0
Step-by-step explanation:
