The ratio of adults to children that came into the restaurant is 5:2. This means that for every 5 adults, there were 2 children who came into the restaurant.
To find the ratio of adults to children that came into the restaurant, we need to divide the number of adults by the number of children.
According to the given information, 12 children and 30 adults came into the restaurant over an hour.
Ratio = Number of Adults / Number of Children
Ratio = 30 adults / 12 children
To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor (GCD).
In this case, the GCD of 30 and 12 is 6.
Ratio = (30 / 6) adults / (12 / 6) children
Ratio = 5 adults / 2 children
So, the ratio of adults to children that came into the restaurant is 5:2.
This means that for every 5 adults, there were 2 children who came into the restaurant.
In conclusion, the ratio of adults to children that came into the restaurant is 5:2.
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how would you read the expression 54?
Answer:
Five to the fourth power
Answer:
Five to the fourth power
Step-by-step explanation:
THE PERSON WHO SOLVES THIS GETS A 50 POINTS AND BRAINLIEST!
Answer:
1/2
2
-1/2
-2
Step-by-step explanation:
ECHA
#1
(-2,2)(0,3)Slope:-
m=3-2/0+2=1/2E#2
(-1,-12)(1,-8)Slope
m=-8+12/1+1=4/2=2C#3
(2,-6)(-4,-3)Slope:-
m=-3+6/-4-2=3/-6=-1/2H#4
(0,3)(1,1)Slope:-
m=1-3/1-0=-2AThe code is
ECHAWork out an approximate solution to x^3+2x-1=0 use the iteration...... Help please!!!!?????
Approximate solutions are the estimate values of an equation
The approximate solution of the equation is x = 0.45
How to determine the approximate solutionThe equation is given as:
\(x^3 + 2x- 1= 0\)
The iteration is given as:
\(x_{n+1} = \frac{1}{x_n^2 + 2}\)
To start with, we have:
\(x_1 = 1\)
So, we have:
\(x_2 = \frac{1}{1^2 + 2} = \frac 13 =0.33333333\)
The next iteration is:
\(x_3 = \frac{1}{0.33333333^2 + 2} = 0.47368421102\)
The next iteration is:
\(x_4 = \frac{1}{0.47368421102^2 + 2} = 0.4495641344\)
The next iteration is:
\(x_5 = \frac{1}{0.4495641344^2 + 2} = 0.45411035264\)
The next iteration is:
\(x_6 = \frac{1}{0.45411035264^2 + 2} = 0.45326473189\)
Notice that:
x5 and x6 have the same value to 2 decimal places.
i.e. \(x_5 \approx x_6 = 0.45\)
Hence, the approximate solution of the equation is x = 0.45
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whats the scientific notation for 234,000,000
Answer:
scientific notation
= 2.34e8
scientific e notation
= 234 × 106
engineering notation
million; prefix mega- (M)
= 2.34 × 108
standard form
8
Order of Magnitude
for scientific and standard forms
= 234000000
(real number)
= two hundred thirty-four million
word form
Step-by-step explanation:
EX24) 29 du Use the chain rule to find the indicated derivative. og, where du g(u, v) = f(x(u, v),y(u, v)), f(x,y) = 7x³y³.x(u, v) = ucosv, y(u, v) = usiny = 56u² cos v sin³ v
∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).
To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:
Given:
g(u, v) = f(x(u, v), y(u, v))
f(x, y) = 7x³y³
x(u, v) = ucos(v)
y(u, v) = usin(v)
To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:
∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)
To find ∂f/∂x, we differentiate f(x, y) with respect to x:
∂f/∂x = 21x²y³
To find ∂x/∂u, we differentiate x(u, v) with respect to u:
∂x/∂u = cos(v)
To find ∂f/∂y, we differentiate f(x, y) with respect to y:
∂f/∂y = 21x³y²
To find ∂y/∂u, we differentiate y(u, v) with respect to u:
∂y/∂u = sin(v)
Now, we can substitute these partial derivatives into the equation for ∂g/∂u:
∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))
To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:
x(u, v) = ucos(v) = u * cos(v)
y(u, v) = usin(v) = u * sin(v)
∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))
Simplifying further, we get:
∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))
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Simplify the following expression by combining like terms:
36y - 8y + 15 - 13
Answer:
=28y+2
Step-by-step explanation:
36y-8y+15-13
=28y+15-13
=28y+2
Answer:
\( \huge{ \bold{ \boxed{ \text{28y + 2}}}}\)
Step-by-step explanation:
\( \text{36y - 8y + 15 - 13}\)
\( \text{Step \: 1 : Combine \: like \: terms} \: .\)
\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)
\( \text{↣ \: 28y + 15 - 13}\)
\( \text{Step \: 2 : Subtract \: 13 \: from \: 15}\)
\( \text{↣ \: 28y + 2}\)
\( \text{hope \: I \: helped}\)!
\( \text{Best \: regards}\)!
~\( \sf{TheAnimeGirl}\)
how do you write 4 x 4 x 4 x 5 x 5 in index notation
Answer:
4^3 x 5^2
Step-by-step explanation:
Use the distributive property to remove the parentheses -8(3v-w-4)
in how many ways can you split 8 people into two teams of 4? how about 9 people into 3 teams of 3? what about choosing 2 teams of 4 from 10 prospects? assume that teams are indistinguishable, e.g. choosing teams {c,d,a,b} first and {h,e,f,g} second is the same as choosing teams {h,e,f,g} first and {c,d,a,b} second.
There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.
To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.
To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.
To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.
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a car dealer so 32 cars their first month The next month they sell 54 cars What is the percentage of change in the number of sold cars
Answer:
68.75%
Step-by-step explanation:
First you do 54 - 32 to get 22.
Then you divide 22 by 32 to get the decimal 0.6875
Finally, you multiply 0.6875 by 100 to get 68.75% :D
Answer:
68.73% more cars were sold
Step-by-step explanation:
from 32 cars that represented 100% went to 54 so is a diference of 54-32=22
Now what percentage of 32 is 22?
32 is 100%
22 is x%
x=(22*100)/32=2200/32=68.73%
PLEASE HELP ME! THIS IS DUE TODAY, AND I WILL MARK BRAINLEST.
Answer:
The correct answer is B: XY=4 cm
Step-by-step explanation:
This is correct because the triangles are both leaning in the same direction so the sides are congruent as stated. Congruent, means that they are equal to each other in other words symmetrical. Because of this, they are the same triangle so where 4 is on the first triangle, it will appear on the same side on the other triangle. This means the answer is B. XY = 4 cm
Answer:
The second one
Step-by-step explanation:
It cant be the first because YZ=4cm
cant be the third because m∠Y= 50°
cant be the forth one because m∠Z= 70°
so, it has to be the second one because XY≅AB
so, if AB=4cm then XY=4cm
Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? check all that apply.
Letters x, y, and z are angle measures. The following equations would ensure that lines p and q are parallel: x = z ; x + y = 180°
A Equation is a numerical explanation that is comprised of two articulations associated by an equivalent sign. In its simplest form in algebra, an equation is a statement that demonstrates that two mathematical expressions are equal.
The image with the angles x, y, and z, as well as the lines p and q, can be found in the link at the answer's conclusion.
Using the image provided;
We can see that the two parallel lines p and q are divided by a transverse line. As a result,
We can say that because we can see that x and z are angles that correspond to one another; Second, we can see that y and z are supplementary angles due to the fact that they form a straight line and that the sum of straight angles is 180 degrees.
therefore; We can say that, using the negotiation property of equivalency, y + z = 180° because x = z.
x + y = 180°
Question:
Angle measures are represented by x, y, and z. Which conditions could ensure that lines p and q are equal? Select all relevant options.
x = z, x + y = 180°, x = y, and z = 180°
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Determine the unknown angle measures of △DEF. Round to the nearest degree.
m∠D =
°
m∠F =
°
m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.
Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:
m∠D + m∠F + m∠E = 180°
We can rearrange the equation to solve for m∠E:
m∠E = 180° - m∠D - m∠F
Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.
For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:
m∠E = 180° - 40° - 65° = 75°
Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
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Which rule must be used to find out the number of ways that two representatives can be picked so that one is a mathematics major and the other is a computer science major? (You must provide an answer before moving to the next part.) es Multiple Choice the division rule the subtraction rule the sum rule the product rule
The rule that must be used to find out the number of ways that two representatives can be picked, where one is a mathematics major and the other is a computer science major, is the product rule.
The product rule is a fundamental principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m * n ways to perform both tasks together. In this case, we can consider the selection of a mathematics major representative as one task and the selection of a computer science major representative as another task.
To apply the product rule, we need to determine the number of ways each task can be performed. Let's say there are k mathematics majors and j computer science majors available. To select one mathematics major representative, we have k choices, and for the computer science major representative, we have j choices. Therefore, according to the product rule, the total number of ways to pick one mathematics major and one computer science major representative is k * j.
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If Mark reads 18 pages less than originally planned, he will need 5 more days to complete the book. If he reads 24 pages less than originally planned, he will need 8 more days to finish. How many pages are in the book?
Answer: Let's denote the original number of pages Mark planned to read as "P".
From the first statement, we know that P - 18 pages will take 5 more days, which means P pages will take 5 days less, or 5 - 5 = 0 days.
From the second statement, we know that P - 24 pages will take 8 more days, which means P pages will take 8 days less, or 8 - 8 = 0 days.
So, we have two equations:
P - 18 = 5 * X
P - 24 = 8 * Y
Where X and Y are the number of pages Mark reads per day.
Since X and Y are equal, we can substitute one of them for the other:
P - 18 = 5 * (P - 24) / 8
Expanding the right side and solving for P, we find that P = 288 pages.
Step-by-step explanation:
time 0:08:39
There are only red, blue and green counters in a bag.
There are 6 red counters.
There are 4 blue counters.
There are 8 green counters.
Matt takes a counter at random from the bag.
a)
What is the probability that the counter is red?
Give your answer as a fraction.
b)
What is the probability that the counter is not blue?
Give
your answer as a fraction.
screen shot below evaluating functions please help
Answer: I believe the answer is 5.
Step-by-step explanation:
f(1) = -(-1)^2 -4(-1)
f(1) = 1^2 + 4
f(1) = 1 + 4
f(1) = 5
Hope this helps!
an item is regularly priced at $91 . it is on sale for 35% off the regular price. use the aleks calculator to find the sale price.
The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.
To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:
Step 1: Calculate the amount of discount = Regular Price × Discount rate
Discount rate = 35/100
Simplifying the value we have:
Discount rate = 0.35
Amount of discount = 91 × 0.35
Amount of discount = $31.85
Step 2: Calculate the sale price
Sale price = Regular price − Amount of discount
Sale price = $91 − $31.85
Sale price = $59.15
Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.
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The antiderivatives of many functions either cannot be expressed or cannot be expressed easily in closed form (that is, in terms of known functions). Consequently, rather than evaluate definite integrals of these functions directly, we resort to various techniques of _______________ integration to approximate their values.
The term which is to be filled in the sentence given in the question is numerical.
Given the antiderivatives of many ----------------- directly, we resort to various techniques of ________ integration to approximate their values.
We have to fill the blank in the sentence given with appropriate term.
Integration is a technique of finding a function from it's derivative.
Definite integral is the area under a curve between two limits. We have to find the answer by first putting upper limit and then lower limit. Then we have to subtract the answer from lower limit from the answer of upper limit.
In Indefinite integration we have not given any limits.
Numerical integration, a algorithm for calculating the numerical value of a definite integral.
Hence the term for the sentence is numerical integration.
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In a linear regression analysis with the usual assumptions, which one of the following quantities is the same for all individual units in the analysis?
a. Leverage hii b.s{Yi) c. S{ei) d. s{Yi}
A linear regression analysis involves the estimation of coefficients and the prediction of the dependent variable based on the independent variable.
In a linear regression analysis with the usual assumptions, s{ei} is the quantity that is the same for all individual units in the analysis. Let's explore each option in detail:a. Leverage hii: Leverage is the measure of an observation's influence on the estimation of coefficients. It helps in identifying the outlying observations that affect the estimates of the regression coefficients. Therefore, leverage values are different for different individual units.b. S{Yi}: It is the standard deviation of the dependent variable. The standard deviation is a measure of the spread of the data around the mean. Each individual unit has different values of Y, so the standard deviation of Y would also differ for different units.c. S{ei}: The standard error of the residuals, also known as the standard deviation of the residuals, measures the variability of the residuals around the regression line. This quantity is the same for all individual units in the analysis because the residuals are calculated as the difference between the actual and predicted values of Y, which is the same for all units.d. s{Yi}: This is the same as the standard deviation of Y, and it measures the spread of the dependent variable. Since the values of Y differ for different units, the standard deviation of Y would also differ for different units.Therefore, option c. S{ei} is the quantity that is the same for all individual units in the analysis. The other options differ for different units. A linear regression analysis involves the estimation of coefficients and the prediction of the dependent variable based on the independent variable. The usual assumptions of a linear regression model include linearity, independence, normality, and equal variance.
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0
2000
2%
2001 - 9000
5%
9001 and
up
5.4%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
The amount of state income tax owed on a $60,000 per year salary is $3,000.
What should we know about Progressive tax?A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.
We are given that the income is $60,000. The applicable Progressive tax for this income range is 5%.
The state income tax owed on a $60,000 per year salary goes as follows:
= $60,000 * 5%
= $3,000
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Calculate the following values
f(-1)
f(0)
f(2)
Use mathematical reasoning Two points have the same y-coordinate but different x-coordinates. Make a prediction about the slope of a line drawn through the points. Justify your prediction.
The slope of points with same y coordinate but a different x coordinate is 0
this is because change in y is zero
How to find the slope of the lineThe slope, m of the linear function is calculated using the formula
= change in y / change in x
This is represented mathematically as
m = (y₀ - y₁) / (x₀ - x₁)
In this case change in y is zero since it is same point
y₀ = y₁
And when a number in the numerator is zero the division will result to a quotient of zero and hence the line is a horizontal line
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What is an equation of the line that passes through the points (-3, -4) and
(-4, -6)?
\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}\)
In the diagram below, the cone has a radius of 9 centimeters and a slant height of 15 centimeters.
image 134fcf7d1dc04fbbb16d3bc2b8f9a75f
What is the volume of the cone?
Responses
324π cm3
324 π cm 3
405π cm3
405 π cm 3
972π cm3
972 π cm 3
1,215π cm3
Answer:
405π cm3
Step-by-step explanation:
Which expression describes the change (in dollars) from $100 after buying n books at $6 each?
Answer:
100 - 6n
Step-by-step explanation:
each book costs 6 and there are n books.
their total price is 6n
Round 0.9967 to 2 significant figures.
Answer:
1.00 significant figures
The required, 0.9967 rounded to 2 significant figures is approximately 1.0.
To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967
The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:
If the third digit is 5 or greater, round up the second digit.
If the third digit is less than 5, leave the second digit unchanged.
In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:
Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.
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can i have some help pls
The ratio of boys to girls in a class is 3:5. There are 40 students in the class. How many more girls than boys are there?
Answer:
3x+5x=40
=8x=40
=x=5
then no.of boys= 3×5 = 15
and no. of girls= 5×5=25
girls more than boys= 25-15=10
mark me brainliest
pls it takes too much time to solve this
Answer:
There will be 10 more girls than boys in the class.
Step-by-step explanation:
5x+3x=40
8x = 40
8x/8 = 40/8
x = 5
5*2 = 10
Question 6
Write the negation of the statement.
It is sunny.
O a It is rainy.
•b It is not sunny.
The correct negation of the statement "It is sunny" is "It is not sunny." This statement encompasses all possibilities of weather conditions other than sunny.
The negation of the statement "It is sunny" is "It is not sunny."
To understand why this is the case, let's explore the concept of negation in logic. In logic, the negation of a statement flips its truth value. If the original statement is true, then its negation is false, and vice versa.
In the given statement, "It is sunny," the proposition is that the weather condition is sunny.
If we want to negate this statement, we need to express the opposite condition, which is the absence of sun or the presence of non-sunny weather.
By stating "It is not sunny," we are explicitly saying that the weather is anything other than sunny. It could be rainy, cloudy, foggy, or any other condition except for sunny.
Using the other option, "It is rainy," would not be the correct negation in this case.
It would be an alternative statement that contradicts the original claim but does not represent the complete negation of "It is sunny."
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a family block of Chocolate is made up of 6o small squares
manica eats 10 square John eats 9 Squares and holly eats
5 squares what is the fraction of the block of chocolate
is left
Answer:
a family block of Chocolate is made up of 6o small squares
manica eats 10 square John eats 9 Squares and holly eats
5 squares what is the fraction of the block of chocolate
is left
Step-by-step explanation:
i think its answer is 36