A total of
330
330 children and adults attended a school play. There were
21
21 times as many children in attendance as there were adults.



This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children.

Answer:

$121.95

Step-by-step explanation:

The cost of the same journey before midnight is,

⇒ $58

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

After midnight, the cost of any taxi journey increases by 45%.

And, One journey costs $84.10 after midnight.

Now, Let the cost of the same journey before midnight is x

Hence, WE can formulae;

x + 45% of x = 84.10

x + 0.45x = 84.10

1.45x = 84.10

x = $58

Thus, The cost of the same journey before midnight is,

⇒ $58

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Supplementary angles are angles that have a sum of 180 degrees.

Let the angle be x.

We're given:

Solve for x:

[tex]x=67.4+(180-x)\\x=67.4+180-x\\2x=247.4\\x=123.7[/tex]

Solve the the supplementary angle:

[tex]180-x\\= 180-123.7\\= 56.3[/tex]

The angle measures 123.7 degrees and its supplementary angle measures 56.3 degrees.

Answer:

Step-by-step explanation:

Rephrase it.

3(5) + 9² + (27 x 1/3) - (-10)

15 + 9x9 + 9 - (-10)

15 + 81 + 9 - (-10)

96 + 9 - (-10)

115

Answer:

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Step-by-step explanation:

To find the inverse of a function, we switch the x and y variables and solve for y. So, we start with:

y = 2x + 3

Switching x and y, we get:

x = 2y + 3

Now, we solve for y:

x - 3 = 2y

y = (x - 3) / 2

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Answer & Step-by-step explanation:

To determine f's inverse function (x)= 2x + 3, we can follow these steps:

Step 1: Replace f(x) with y: y = 2x + 3

Step 2: Solve for x in terms of y:

y = 2x + 3

y - 3 = 2x

x = (y - 3) / 2

Step 3: Replace x with f^(-1)(x):

f^(-1)(x) = (x - 3) / 2

Therefore, the inverse function of f(x) = 2x + 3 is f^(-1)(x) = (x - 3) / 2.

The area of the rose garden =129 square feet.

Consider the following diagram.

From the figure we can observe that the dimensions of the rectangular garden are: length = 15 ft and width = 9 ft

Let us assume that A₁ be the area of the rectangular garden.

Using the formula for the area of rectangle,

The area of the rectanguler garden would be,

A₁ = 15 × 9

A₁ = 135 ft²

Also, the dimensions of the rectangular patch of grass is 2 feet × 3 feet.

Let us assume that A₂ represents the area of the rectangular patch of grass.

Using the formula for area of rectangle, the area of rectangular patch of grass is:

A₂ = 2 × 3

A₂ = 6 ft²

Let a be the area of the rose garden.

So, the required area would be,

A = A₁ - A₂

A = 135 - 6

A = 129 ft²

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Find the complete question below.

Answer:

La respuesta de su problemamatemático es X= 6.63

Answer: e = 1/18

Step-by-step explanation:

e = 18/320

e = 1/18

Answer: 0.05625

Step-by-step explanation: So, you divide 18 by 320, and that gives you 0.05625, and you can double check by multiplying 0.05625 by 320, which gives you 18.

The number of table in the form of mixed number will be 4 ¹/₂ tables.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

27 children sit at table of 6, fillling where possible. Then the number of table is given as,

⇒ 27 / 6

⇒ 4 ³/₆

⇒ 4 ¹/₂ tables

The number of table in the form of mixed number will be 4 ¹/₂ tables.

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The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points on the function are given as follows:

(10, 110) and (20, 220).

The slope is given by the change in the output divided by the change in the input, hence:

m = (220 - 110)/10

m = 11.

Hence:

y = 11x + b.

When x = 10, y = 110, hence the intercept b is given as follows:

110 = 11(10) + b

b = 0.

Hence the function giving the cost for x people is of;

y = 11x.

The cost for 60 people would be of:

y = 11(60)

y = $660.

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Answer:

31.4 in^2

Step-by-step explanation:

Circumference formula: pi times 2 times radius

so equation would be 3.14 (pi value) times 2 times 5 and you get your answer

Answer:

B

Step-by-step explanation:

Use the distance formula.

Answer:

Step-by-step explanation:

-183

Answer:

Any negative minus a positive is a negative:

-183

Step-by-step explanation:

Hope it helps! =D

Answer:

Step-by-step explanation:

In "The Jungle" by Upton Sinclair, Jurgis is a character who starts out with a positive and optimistic outlook on life. He is full of hope and ambition when he arrives in America with his family, eager to make a better life for himself. However, after he is injured on the job and becomes unable to work, his attitude changes dramatically. He becomes disillusioned and bitter, losing his hope and faith in the American Dream.

In my opinion, Jurgis's response to his injury reflects the harsh realities of life for immigrants and the working class in America during that time. The injury not only physically incapacitates him, but it also robs him of his ability to provide for his family and live out his dreams. The experience shows the extent to which the system is stacked against those in Jurgis's position and serves as a powerful commentary on the injustices and inequalities of the time.

CP of 100 pencils = Rs.250

CP of 1 pencil = 250/100 = 2.5

SP of 1 dozen pencils = Rs.33

SP of 12 pencils = Rs.33

SP of 1 pencil = \frac{33}{12}=2.75

SP>CP

So, Profit% = SP - CP/ CP × 100 = 2.75 - 2.5/2.5 × 100 = 10 %

Hence The profit % is 10%

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600 élèves :

On sait que 7/30+1/6 ne font pas partie des 400 élèves qui possèdent téléphone portable et ordinateur . 7/30+1/6=12/30=2/5 mais parmi ces élèves figurent ceux qui n'ont ni l'un, ni l'autre. Ils font donc partie des 2/5 qui viennent d'être dénombrés

Il faut donc les retrancher, sinon ils seraient comptés deux fois

donc le nombre n'ayant ni l'un ni l'autre est : 2/5-1/15=5/15=1/3

Par conséquent 2/3 ont unt téléphone et un ordinateur

Comme ces 2/3 correspondent à 400 élèves, le nombre total d'élèves interrogés sera donc de 400*3/2=600 élèves.

The radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area is (18 × ✓π) / π

From the information, the triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3.

The area of a triangle will be;

A = 1/2 × a × b × sin C

= 1/2 × 12 × 12✓3 × sin 60

= 108

Area of sector = πr² / 360 × 60.

r² = (108/2) × 6 ) π

r² = 324 / π

r = 18✓π / π

The radius is 18✓π / π.

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Marta's rope is 10 inches shorter than three times the length of David's rope and they measure 120 inches long together , then Marta's rope is 77.5 inches long and David's rope is 32.5 inches long.

Let's call the length of David's rope x.

According to the problem, Marta's rope is 10 inches shorter than three times the length of David's rope, so we can write an equation for Marta's rope:

length of Marta's rope = 3 * x - 10

And the combined length of both of their ropes is 120 inches, so we can write another equation:

x + (3 * x - 10) = 120

Expanding the second equation and solving for x, we get:

4x - 10 = 120

Adding 10 to both sides:

4x = 130

Dividing both sides by 4:

x = 32.5

So, David's rope is 32.5 inches long.

We can use the first equation to find the length of Marta's rope:

length of Marta's rope = 3 * x - 10 = 3 * 32.5 - 10 = 87.5 - 10 = 77.5 inches

So, Marta's rope is 77.5 inches long.

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Answer:

No, it is not.

Step-by-step explanation:

remember PEMDAS (parenthesis, exponents, mult., etc)

use distributive property, but solve parenthesis first

3x(x+4)²

(x+4)(x+4) = x² + 8x + 16

3x(x² + 8x + 16) >>> 3x³ + 24x² + 48x

so the equation is not equal

Answer:

the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).

Step-by-step explanation:

To factorise the quadratic expression 14x^2 - x - 3, we can use the following steps:

So, the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).

Answer:

Step-by-step explanation:

14×14-×-3

196-×-3=196-3

=193

There are 6 cars that hold 3 people and 9 cars that hold 5 people.

Let's call the number of 3-passenger cars "x" and the number of 5-passenger cars "y".

We know the total number of cars is 15, so:

x + y = 15

We also know that the total number of passengers is 63, so:

3x + 5y = 63

Now we can use the first equation to solve for one of the variables in terms of the other:

y = 15 - x

Substitute this expression for y into the second equation:

3x + 5(15 - x) = 63

Expand

3x + 75 - 5x = 63

Evaluate like terms:

2x = 12

Divide both sides by 2:

x = 6

Recall that

y = 15 - x

So, we have

y = 15 - 9

y = 6

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Answer:

  4

Step-by-step explanation:

You want to know how many more questions Brian needed to answer correctly to get a passing grade of 60% on his 85-question test, given that he answered correctly 70% of the 20 arithmetic problems, 40% of the 30 algebra problems, and 60% of the 35 geometry problems.

The number of correct answers Brian supplied was ...

  0.70·20 +0.40·30 +0.60·35 = 14 +12 +21 = 47

The number of correct answers Brian needed for a passing grace was ...

  0.60·85 = 51

Brian needed to answer 51 -47 = 4 more questions correctly to earn a passing grade.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 1 } \implies 6[/tex]

[tex]\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}{1}=\stackrel{m}{ 6}(x-\stackrel{x_1}{1}) \\\\\\ y-1=6x-6\implies {\Large \begin{array}{llll} y=6x-5 \end{array}}[/tex]

(a) The sample size for the above sample is 15.

(b) The sample mean for these data is 3.8.

(c) The sample median is 3.6.

(d) To compute the 20% trimmed mean for the above data set is 3.7.

(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.

The following measurements were recorded for the drying time, in hours

3.4      2.5      4.8      2.9      3.6 is:

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

(a) We have to determine the sample size for the above sample.

The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.

Sample Size (n) = 15

(b) We have to calculate the sample mean for these data.

Sample Mean = Total Sum of data/Total Number

Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15

Sample Mean = 56.8/15

Sample Mean = 3.8

(c) We have to calculate the sample median.

To define the sample median we first represent the data in ascending order.

2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6

Sample Size(n) = 15

So Median = (n+1)/2th term

Median = (15 + 1)/2th term

Median = 16/2th term

Median = 8th term

So the 8th term in the given data is 3.6. So,

Median = 3.6

(d) We have to compute the 20% trimmed mean for the above data set.

To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.

New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8

New Mean = 33.3/9

New Mean = 3.7

(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.

The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.

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The complete question is:

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4      2.5      4.8      2.9      3.6

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

Assume that the measurements are a simple random

sample.

(a) What is the sample size for the above sample?

(b) Calculate the sample mean for these data.

(c) Calculate the sample median.

(d) Compute the 20% trimmed mean for the above data set.

(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

The skid marks be to the nearest foot is 913 ft.

The length of the skid marks can be calculated using the formula d = μV2/2gdf, where μ is the coefficient of static friction, V is the velocity, g is the acceleration due to gravity, and df is the drag factor. In this case, the coefficient of static friction can be assumed to be 0.9, the velocity is 35 mi/h, the acceleration due to gravity is 32.2 ft/s2, and the drag factor is 0.97. Plugging these values into the formula, we get [tex]d = 0.9(35 mi/h x 5280 ft/mi/h)2/2(32.2 ft/s2)(0.97) = 912.5 ft[/tex]. To the nearest foot, this is 913 ft.

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Answer: A = 30

Step-by-step explanation:

Hello, to find the area of a triangle, you first have to follow,

Step 1. The area of a triangle is A = 1/2 * b * h, so plug in the other numbers

Step 2. A = 1/2 * 6 * 10

Step 3. Get rid of the fraction by doing 10 * 1/2. A = 6 (10 * 1/2)

Step 4. A = 6 * 5

Step 5. A = 30

Answer:

6.3×10^6

Step-by-step explanation:

6.3×10^6

in standard form

Answer: x = 46°

Step-by-step explanation:

The total area of the composite figure is 484 square feet.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

A composite figure is shown.

To find the complete area:

Here, we have dissected three figures separately.

So, the complete area,

= The area of the triangle with a height 22 feet and base 8 feet +

the area of the rectangle with a length 16 feet and width 22 feet +

the area of the triangle with a height 4 feet and base 22 feet

=  (1/2 x 22 x 8) + (16 x 22) + (1/2 x 4 x 22)

= 88 + 44 + 352

= 484 square feet.

Hence, the area is 484 square feet.

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Option 234 cm is the correct option.

The measurement equivalent to 2.34 meters is: 234 cm

To convert meters to centimeters,

you multiply the number of meters by

100.

So, 2.34 meters multiplied by 100 is equal to 234 centimeters.

An object is only identified or classified using numbers on a nominal scale, which is a measuring scale. Only non-numeric (quantitative) factors or situations where numbers have no meaning are often addressed by this assessment.

By increasing the number of metres by 100, one may convert measurements from metres to centimetres. One metre equals one hundred centimetres, or 1 m = 100 cm, as is common knowledge.

Cm is used to represent it in writing. It may also be described as the unit of length in the current metric system, the International System of Units (SI). It is equal to one hundredth of a metre.

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