In a restaurant 1/5 of the customers are vegetarian and 3/4 eat meat. The remainder of the customers are dairy intolerant. What fraction of the customers are dairy intolerant? Give your answer as a fraction in its lowest terms

The number of customers that were served per hour at this restaurant is 60 customers per hour

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

600 customers were served during a 10-hour period of time. Hence:

slope = 600 customers / 10 hours = 60 customers per hour.

The number of customers that were served per hour at this restaurant is 60 customers per hour

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The proportional relationship that represents the situation is:

y = 60x.

The graph is given at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

\(y = kx\)

In which k is the constant of proportionality.

In this problem, 600 customers were served during a 10-hour period of time, hence:

k = 600/10 = 60.

And the equation is:

\(y = 60x, 0 \leq x \leq 10\)

The graph is sketched at the end of this answer.

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Answer:

l think

y= x^2

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Answer:

3/5miles

Step-by-step explanation:

a person walks = 2/10 mile = 1/3 hour

number of miles = 1hour

1 × 2/10 = 1/3x

when x rep number of miles

x =2/10 ÷ 1/3

x = 2/10 × 3/1

x = 6/10

x=3/5miles

Answer:

It is A

Step-by-step explanation:

I cant explain step by step I am in a rush but it is A

The length from the top corner to the farthest bottom corner of the room is approximately 12.65 inches.

To find the length from the top corner to the farthest bottom corner of the room, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the top corner, bottom corner, and the length connecting them form a right-angled triangle.

Given the dimensions of the room as 4" by 12" by 18", we can use the length (18") as the hypotenuse and the other two dimensions as the other two sides.

Using the Pythagorean theorem:

Length^2 = Width^2 + Height^2

Length^2 = 4^2 + 12^2

Length^2 = 16 + 144

Length^2 = 160

Taking the square root of both sides:

Length = √160

Length ≈ 12.65 inches

Therefore, the length from the top corner to the farthest bottom corner of the room is approximately 12.65 inches.

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Work Shown:

T(2) = 20 means the second term is 20

T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.

Since a = 26 is the first term and d = -6 is the common difference, the nth term is

T(n) = a + d*(n-1)

T(n) = 26 + (-6)(n-1)

T(n) = 26 - 6n + 6

T(n) = -6n + 32

Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.

Plug in n = 10 to find the tenth term

T(n) = -6n + 32

T(10) = -6(10) + 32

T(10) = -60+32

T(10) = -28

Answer:

-28.

Step-by-step explanation:

T(1) = 20 + 6 = 26.

This is an arithmetic series  with:

nth term T(n) =  26 - 6(n - 1).

So T(10) = 26 - 6(10-1)

= 26 -54

= -28.

According to the question the width of the running track is 5 feet.

The boundary of a circle is measured by its circumference or perimeter, which determines the amount of space it occupies. The circumference of a circle is the length of the circle when it is "unrolled" and measured as a straight line, and it is typically measured in units such as centimeters or meters.

The circumference of a circle is given by the formula \(C = 2\pi r\), where r is the radius. Using this formula for the two circles, we have:

\(C_1 = 2\pi r_1\\C_2 = 2\pi r_2\)

The problem states that the circumferences of the two circles differ by \(10\pi\) feet, which can be written as:

\(C_1 - C_2 = 10\pi\)

Substituting the formulas for \(C_1\) and \(C_2\), we get:

\(2\pi r_1 - 2\pi r_2 = 10\pi\)

Simplifying, we get:

\(2\pi (r_1 - r_2) = 10\pi\\r_1 - r_2 = \frac{10\pi}{2\pi} = 5\)

Therefore, the width of the running track is 5feet.

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Answer:

90-27= 63°

the sum of the angles are 180°

Step-by-step explanation:

Answer is 63°

Answer:

A

Step-by-step explanation:

Because each time you add on It Increases what you adding by 2

So It started with 2

then it added 4 to the other making It add on another 2 so for the next one it will be 8

pattern 2 4 6 8

Answer:

the answer is D

Step-by-step explanation:

Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

Answer:

Step-by-step explanation:

A parallel line will have the same slope as the reference line.  In this case, I don't see the "given line" as promised in the question.  If it does appear, and it looks like y = 5x + 3, for example, the slope is 5 and the new line will have the same slope.

1) The property of equality that justifies the statement "If AB=CD, then CD=AB" is the symmetric property.

2) The correct pair of corresponding angles is <1 and <8.

3) The slope of the line passing through (2,3) and (-2,-5) is 4/(-4) = -1.

4) The value of x cannot be determined without additional information or context.

5) The scale factor of AABC to ALMN is 1/3.

6) In circle C, m = 180 - 2(72) = 36 degrees.

7) The sum of the measures of the interior angles of an 18-gon is (18-2) x 180 = 2880 degrees.

8) The height of the tree is approximately 86.4 ft.

9) m = 180 - (31+88) = 61 degrees.

10) The polygon has 5 sides (a pentagon).

Procedure Part . Explaining
1) The symmetric property of equality states that if a=b, then b=a. In the given statement, AB=CD and CD=AB are equivalent statements and can be interchanged using the symmetric property.
2) Corresponding angles are pairs of angles that are in the same position relative to the parallel lines and the transversal. In the given figure, angles 1 and 8 are on the same side of the transversal and in the same position relative to the parallel lines, making them corresponding angles.
3) The slope of a line passing through two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1). Applying this formula to the given points, we get the slope as (3-(-5))/(2-(-2)) = 8/4 = 2. However, the given answer choices do not include 2 as an option.
4) Without additional information or context, it is impossible to determine the value of x.
5) The scale factor of two similar figures is the ratio of their corresponding side lengths. In the given problem, AABC and ALMN are similar triangles, and the scale factor is given by AB/LN = 18/9 = 2 and BC/LM = 12/6 = 2. Since both ratios are equal, the scale factor is 1/3.
6) In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. In this case, the intercepted arc is 72 degrees, so the inscribed angle is 36 degrees.
7) The sum of the measures of the interior angles of a polygon with n sides is given by (n-2) x 180 degrees. Substituting n=18, we get (18-2) x 180 = 2880 degrees.
8) The height of the tree can be determined using similar triangles. The ratio of the height of the tree to its shadow is equal to the ratio of Nancy's height to her shadow, which is 5/9. Thus, the height of the tree is (5/9) x 48 = 26.67 ft. However, the given answer choices are not close to this value, so it is unclear how the problem is meant to be solved.
9) The sum of the measures of the angles in a triangle is 180 degrees. In the given triangle, angles m and n are given, so we can find angle A using A+m+n=180.
10) The measure of each interior angle in a regular polygon with n sides is given by (n-2) x 180 / n degrees. Setting this expression equal to 108 and solving for n, we get n=5. Thus, the polygon has 5 sides, which is a pentagon.

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Answer:

10

Step-by-step explanation:

sqrt. 100 = 10

because base x height = area

base and height must be same length in a square

Answer:

18

Step-by-step explanation:

x =27-9

=18

Answer:

3(5a + 4)

Step-by-step explanation:

Given expression: 15a + 12

The common factor for both is 3.

Factorize:

=> 3(5a) + 3(4)

Take out the common factor: (3)

=> 3(5a + 4)

Answer:

3(5a+4)

Step-by-step explanation:

Firstly, find the highest common factor between 15a and 12, which is 3 and write it in brackets, which is:

3(5a+4)

The brackets are 5a+4 because 3×5a=15a and 3×4=12, which gives you the algebraic expression 15a+12

Answer:

1,1,1,1

Step-by-step explanation:

I believe this is right

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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Answer:

6 i think.

Hope this helps!

Answer:

\(8^{-5}\)

Step-by-step explanation:

Anything raised to the power of 0 is 1. This means that we need to multiply 8^5 by something to make it into 8^0. When you multiply together two numbers with the same base, you can add the exponents together. For instance, in this case:

\(8^{-5}\cdot 8^5= \\\\8^{-5+5}= \\\\8^0=1\)

Hope this helps!

Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:

z = -0.52.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.

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The simplified exponential notation of the given expression is x⁸.

Given that, simplified exponential notation, x³·x⁵,

x³·x⁵ we need to simplify it,

We know that,

mᵃ × mᵇ = mᵃ⁺ᵇ

x³·x⁵ = x³⁺⁵

x³·x⁵ = x⁸

Hence, the simplified exponential notation of the given expression is x⁸.

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We can organise 21 different friend groups for you to bring to the show.

We can use the idea of combinations to resolve this issue.

You have a total of 7 pals, and you want to pick 2 of them to go to the concert.

This circumstance can be represented as a combination, which is denoted by the notation C(n, r), where n denotes the total number of items and r denotes the number of items you want to select.

Here, the number of friends is n = 7 and the number of friends to bring is r = 2.

Combinations are calculated using the following formula: C(n, r) = n! / (r!(n-r)!)

C(7, 2) in our case equals 7 / (2!(7-2)!)

The factorials are calculated as follows: 7! = 7 6 5 4 3 2 1 = 5,040 2! = 2 1 = 2 (7-2)!
Calculating the factorials:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
2! = 2 × 1 = 2
(7-2)! = 5! = 5 × 4 × 3 × 2 × 1 = 120
Now, we can substitute these values back into our formula:
C(7, 2) = 5,040 / (2 × 120)
C(7, 2) = 5,040 / 240
C(7, 2) = 21.

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Answer:

c = 5

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

\( m\angle ADB = m\angle CDB... (given) \\\\

\therefore m\angle ADM = m\angle CDM... (1)\\

(\because D-M-B) \\\\

In\: \triangle 's ADM \: \&\: CDM\\\\

\overline{AD} \cong\overline {CD} ... (given) \\\\

m\angle ADM = m\angle CDM.(From \:1)\\\\

\overline{DM} \cong\overline{DM} ... (given) \\\\

\therefore \triangle ADM \: \cong\: \triangle CDM\\.. (By \: SAS\: postulate) \\\\

\therefore \overline{AM} \cong\overline{CM}..(2)\\(by\: c. s. c. t.) \\\\

m\angle AMD = m\angle CMD..(3)\\(by\: c. a. c. t.)\\\\

\because m\angle AMD + m\angle CMD= 180\degree ..(4)\\

(Linear\: pair\: \angle 's)\\\\

\therefore m\angle AMD + m\angle AMD= 180\degree \\..(From \: 3 \: \& \: 4)\\\\

\therefore 2m\angle AMD = 180\degree\\\\

\therefore m\angle AMD = \frac{180\degree}{2}\\\\

\therefore m\angle AMD =90\degree \\\\

\red{\implies \overline{MD} \perp\overline{AM}} \\\\

\implies m\angle AMB=m\angle CMB= m\angle CMD = 90\degree.. (5)\\\\

In\: \triangle 's ABM \: \&\: CBM\\\\

\overline{AM} \cong\overline{CM}\\.(From \: 2)\\\\

m\angle AMB=m\angle CMB\\..(each\: 90\degree) \\\\

\overline{BM} \cong\overline{BM} ... (common) \\\\

\therefore \triangle ABM \: \cong\: \triangle CBM\\.. (By \: SAS\: postulate) \\\\

\therefore m\angle BAM = m\angle BCM\\(by\: cact) \\\\

\purple {\implies m\angle BAC = m\angle BCA} \\(\because A-M-C) \)

In Question 10, to determine the year when Ryan's salary was highest in real terms, we need to adjust his earnings for inflation using the Consumer Price Index (CPI). Given the CPI values for 1970, 1980, and 1990, we can calculate the real value of Ryan's salary for each year and compare them.

In Question 11, we are asked to identify which item will be included in GDP. GDP measures the value of goods and services produced within a country's borders during a specific time period. We need to determine if the given options represent items that contribute to GDP.

In Question 13, we are discussing the problems with CPI calculations. CPI is used to measure inflation and changes in the cost of living. We need to identify the specific issues associated with CPI calculations.

Question 10: To determine the highest real salary, we need to adjust Ryan's earnings for inflation. We can do this by dividing his earnings in each year by the respective CPI value and then comparing the real values. By performing the calculations, we find that Ryan's salary was highest in 1970 when adjusted for inflation.

Question 11: In this question, option a (vegetables produced in the backyard for self-consumption) is not included in GDP as it represents non-market production for personal use. Option b (jewelry set bought from an antique store) is included in GDP as it involves a market transaction. Option c (rental value of owner-occupied houses) is not included in GDP as it is imputed and not a market transaction. Option d (purchase of a pre-owned car) is included in GDP as it involves a market transaction.

Question 13: The problem with CPI calculations includes both the substitution bias and unmeasured quality change. The substitution bias arises because CPI assumes constant consumption patterns and does not account for consumers' ability to substitute cheaper goods for more expensive ones. Unmeasured quality change refers to the difficulty of accurately capturing changes in the quality of goods and services over time in the CPI calculation. Therefore, the correct answer is that both the substitution bias and unmeasured quality change are problems with CPI calculations.

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Answer:

Step-by-step explanation:

8x + 4 = 28

8x = 28 - 4

8x = 24

x = 24 / 8

x = 3

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