Mr. Smith was so pleased with the amount of
homework his students completed that he bought
sandwiches, fries, and drinks for the whole class. The total
cost was $100. The sodas and fries cost $73.27.

If the sandwiches cost $0.99 each, how many sandwiches did he
buy?

(111)₂ = (12)₅

The base of a number system refers to the total number of digits that are actually used in the given number system. The number system that has the base 'b' consists of its digits in the [0, b-1] range. This base of the number system is also known as the radix of a number system.

Given,

number 111 with base 2

To convert it into base 5 number we need to first convert it into decimal

(111)₂ = 1×2²+1×2¹+1×2⁰

(111)₂ = 4+2+1

(111)₂ = (7)₁₀

Now converting decimal to base 5, converting decimal numbers to base 5 is nearly as simple: just divide by 5.

(111)₂ = (12)₅

Hence, the number becomes (12)₅.

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63.64% is the percentage of the area of the square.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

The radius of the circle r =  1 in.

The area of the circle = π r² = π (1)² = π = 22/7 inch.

Also the area of square = 1/2 x (diameter)²

The diameter of the square = 2r = 2

Area = 1/2(2)² = 2 square in.

The required percentage = (2 / (22/7)) x 100 = (7 / 11) x 100 = 700 / 11 = 63.6363.

The percentage of the area of the square is 63.64%.

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Answer:

Step-by-step explanation:

is that the question? what do you mean by 3

Answer:

998

Step-by-step explanation:

The Percentage of error of the measurement is 5.1 %

The formula of percentage of error

[tex]\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%[/tex]

where

[tex]\delta[/tex] is the percent error

Va is the actual value observed

Ve is the expected value of the measurement

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error or expected error is multiplied by 100 to calculate the percent error.

the percent error is

((Estimated Number - Actual Number)/ Actual number) x 100 equals percentage error.

[tex]\delta = \left| \frac{4.1- 3.9}{3.9} \right| \cdot 100\%[/tex]

=> 0.2 / 3.9 x 100

=> 0.0512 x 100

=> 5.12%

The percentage error in the measurement is 5.1%

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The percent error of the measurement is 5.1%, to the nearest tenth of a percent.

To calculate the percent error of the measurement, the formula is:

(|Actual Value - Measured Value|/Actual Value) * 100 = Percent Error

In this case, the actual value is 4.1 inches and the measured value is 3.9 inches. So the calculation is:

(|4.1 - 3.9|/4.1) * 100 = 5.1%

Therefore, the percent error of the measurement is 5.1%, to the nearest tenth of a percent.

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Based on the given function, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is 57.797°. (Option B)

The temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). Hence, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is given by:

1/((6-3)) ∫_3^6▒〖(65-8 sin⁡(πt/12)dt〗

65/3 t+  32/π  cos⁡(πt/12)

(65π-16√2)/π

57.797

Note: The question is incomplete. The complete question probably is: On a certain day, the temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). What is the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit? A) 57.609° B) 57.797° C) 58.172° D) 59.907°.

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The perimeter and area of the image:

(a)  3/2cm²

(b)  2/3cm²

(c)  3/8cm²

What is the perimeter of a trapezoid?

A trapezoid's perimeter is determined by adding the lengths of its four sides. The sum of the lengths of a trapezoid's four sides serves as the formula for the shape's perimeter.

Here,

We have to find the perimeter and area of the image when the trapezoid is dilated by a scale factor of (a) 2, (b) 3, and (c) 4.

(a)  Ratio 2: 1 of length

Perimeter = (2 + 5 + 3 +6)/2 = 8cm

Area = (1/2)×3×(6+2)/2×(1/2)² = 3/2cm²

(b) Ratio 3:1

Perimeter = (2 + 5 + 3 +6)/3 = 16/3cm

Area = (1/2)×3×(6+2)/2×(1/3)² = 2/3cm²

(c) Ratio 4:1

Perimeter = (2 + 5 + 3 +6)/4 = 4cm

Area = (1/2)×3×(6+2)/2×(1/4)² = 3/8cm²

Hence, The perimeter and area of the image: (a)  3/2cm², (b)  2/3cm², and (c)  3/8cm²

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This statement is not always true. It's only true if f(x) and g(x) are both non-decreasing functions.

If f(x) and g(x) are non-decreasing functions, the inequality f(x) ≥ g(x) for a < x < b holds, meaning that the values of f(x) are always greater than or equal to the values of g(x) for x within the interval [a,b]. Since the derivative of a non-decreasing function is non-negative, it follows that f'(x) ≥ 0 and g'(x) ≥ 0 for all x in the interval [a,b], which implies f '(x) ≥ g'(x) for a < x < b.

However, if f(x) and g(x) are not non-decreasing functions, this statement is not true. The inequality f(x) ≥ g(x) for a < x < b does not necessarily imply that the derivatives f '(x) and g'(x) will also be greater than or equal for all x in the interval [a,b].

Therefore, This statement is not always true. It's only true if f(x) and g(x) are both non-decreasing functions.

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Answer:

6^-14

Step-by-step explanation:

Using laws of indices you'll add the denominators power to account for multiplication

then substract it from the numerators power to get an answer which is 6×10^-14

Answer:

10.41

Step-by-step explanation:

Given ,

To Find : Number of Fuel used

Let us take the Number of fuel used as 'x'

13.01 = x + 2.60

x = 13.01 - 2.60

x = 10.41

Hence, the fuel used by Lashonda is 10.41

10,000 records have 30 predictor variables, each with 5% of the values missing, resulting in 15,000 missing values. The predictive model drops any row with even a single missing value, so 5,000 records would be dropped from the analysis.

1. There are 30 predictor variables.

2. Each variable has 5% of the values missing.

3. 5% of 10,000 records = 500 records.

4. 30 variables x 500 records = 15,000 missing values.

5. 10,000 records - 15,000 missing values = 5,000 records dropped from the analysis.

The data set has 10,000 records and 30 predictor variables. Each variable has 5% of the values missing, so 500 records are missing for each variable. This results in 15,000 missing values spread randomly and independently throughout the data set. The analyst uses a predictive model that drops any row (record) with even a single missing value, so 5,000 records would be dropped from the analysis.

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The requried simplified value of the given expression is,
(A) 4
(B) No solution,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Simplifying the expression, in order to get the solution,

(A)
[tex]= log_3(81)\\=log_3(3)^4\\= 4log_33 \ \ \ \ \ \ \ \{log_ee = 1}\\=4\times 1\\= 4[/tex]

(B)

[tex]2^x = 1/32x\\2^x\times 32 = x\\x = 2^x \times 2^5\\x = 2^{x + 5}\\[/tex]
A solution for this equation is not possible,

Thus, the requried simplified value of the given expression is,
(A) 4
(B) No solution,

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Wendel has left 144 nickels and 48 dimes to pay for a bus ticket back home.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of nickels and y represent the number of dimes.

Each nickel is 5 cents (0.05) and each dime is 10 cents (0.1). Hence:

Wendell has $12 in nickels and dimes, hence:

0.05x + 0.1y = 12  

0.1y = 12 - 0.05x

y = 120 - 0.5x    (1)

Wendell has 3 times as many nickels as dimes, hence:

x = 3y   (2)

Using substitution method:

Substituting y = 120 - 0.5x in eqn 2 gives:

x = 3(120 - 0.5x)

x = 360 - 1.5x

x = 144

y = 120 - 0.5(144) = 48

Wendel has 144 nickels and 48 dimes.

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Answer:

18 pieces

Step-by-step explanation:

78 pieces to start with and she kept 24 to herself which means that she has 54 pieces of candy remaining. Assuming she gave an equal amount to each friend, the answer would be 54/3=18. So she gave 18 pieces to each friend.

Answer:

[tex]1.\ (x - 1)^2 + (y + 4)^2 = 4\\2.\ (x + 2)^2 + (y -5)^2 = 36[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{-4}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-(-4) ~~ )^2~~ = ~~2^2\implies {\large \begin{array}{llll} (x-1)^2+(y+4)^2=4 \end{array}}[/tex]

now as for the 2nd one, we know the center and a point on it, well, what's the radius?  well, recall that for a circle the radius is simply the distance from the center to the circle in proper, so the distance between those two points is the radius

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad P(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CP=\sqrt{(~~-2 - (-2)~~)^2 + (~~-1 - 5~~)^2} \implies CP=\sqrt{(-2 +2)^2 + (-1 -5)^2} \\\\\\ CP=\sqrt{( 0 )^2 + ( -6 )^2} \implies CP=\sqrt{ 0 + 36 } \implies CP=\sqrt{ 36 }\implies \stackrel{radius}{CP=6}[/tex]

so we're really looking for the equation of a circle with a center at (-2 , 5) with a radius of 6

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{6}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-5 ~~ )^2~~ = ~~6^2\implies {\large \begin{array}{llll} (x+2)^2+(y-5)^2=36 \end{array}}[/tex]

we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.

1. f = 300s/200

2. f = 300 * 500/200 = 750 grams

1. To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.

2. To find out how many grams of flour we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.

To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.

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Answer:
750

Equation:
f = 3/2s

The angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.

What are parallel lines ?

parallel lines can be defined as the lines which are equi distant from each other and these lines never interest to each other.

Given ,

from the figure

the parallel lines are l and m.

the angles ∠1,∠2,∠3,∠4,∠5,∠6,∠7,∠8.

∠1,∠2,∠3,∠4. are in one plane

and ∠5,∠6,∠7,∠8. are in another plane.

so the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.

Hence ,  the angle which corresponds the ∠8 is ∠4 as ∠8 and ∠4 are parallel to each other.

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By algebra properties, the integer 975 is equivalent to rational expression 650 / (2 / 3).

Rational numbers are real numbers of the form m / n, where m and n are integers and n is a non-zero integer. In this problem we find a rational expression of the form (a / b) / (c / d), where a, b, c, d are also integers and b and d are non-zero integers.

This expression must be simplified into a rational number of the form m / n, this can be done by the following algebra property:

(a / b) / (c / d) = (a · d) / (b · c)

If we know that a = 6, b = 1, c = 2 and d = 3, then the resulting expression is:

650 / (2 / 3) = (650 / 1) / (2 / 3) = (650 ÷ 1) / (2 ÷ 3) = (650 × 3) / (1 × 2) = 1950 / 2 = 975 / 1 = 975

The rational expression 650 / (2 / 3) is equivalent to integer 975.

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The possibility of three people being chosen to give a random presentation as calculated from the given data is 1 / 12.

There are 10 possibilities of selecting the required  3 people.

Using combination we can find the required probability as ,

10c3

= 10 ! / 7! x 3 !

= 10 x 9 x 8 / 3 x 2

= 120

Thus, the probability is equal to 10 / 120 = 1 / 12 .

Combination is a way of combining things in the desired manner . Other than probability we also have permutation which tells about the possibility.

Probability refers to the possibility of occurrence of an event. It is used in industries such as weather forecast.

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Answer:

Step-by-step explanation:

lol

Answer:

Step-by-step explanation:

x = 16

Answer:

x = 16

Step-by-step explanation:

If 3 · 16 = 48 Then x = 16

The end behavior of each function is defined as follows:

1. [tex]\sqrt{6x}[/tex]: as x -> ∞, f(x) -> ∞.

2. [tex]\sqrt{x - 5} - 6[/tex]: as x -> ∞, f(x) -> ∞.

3. [tex]-3\sqrt{x + 3} + 7[/tex]: as x -> ∞, f(x) -> -∞.

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The functions in this problem are all variations of the square root function, which is defined only for non-negative numbers, and thus only the limit when x goes to infinity has to be considered.

As x goes to infinity, the square root goes to infinity, which already define the end behavior for items 1 and 2.

For item 3, the negative leading coefficient means that the function is reflected over the x-axis, assuming a negative value, and thus the end behavior is that the function goes to negative infinity.

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Answer:

B

D

E

The first choice A appears to be a typo, so I can't comment on that

Step-by-step explanation:

Substitute x = 4 in each of the polynomials and see which ones end up with a value of 0. Since each of the polynomials is a multiplicative of expressions if any one of the individual expressions is 0 then the whole expression becomes 0

A. Unknown

B. 2x - 8 = 2 · 4 - 8 = 8 - 8 = 0. So this has a zero at (4,0)

C None of the individual expressions will result in  0. So not a correct choice

D x - 4 = 4 - 4 = 0 So this is a correct choice

E. In this case we have a 4-x term which is 4- 4 = 0; so correct choice

The amount of rotation that is required to bring one side of an angle to the same position as the other is what is referred to as the measure of an angle. Degrees (°) are used as the unit of measurement for angles. One complete turn encompasses all 360 possible degrees.

There are several ways to find the measure of an angle in 8th grade geometry:

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The value of  f(a+2) = (5 + a) / (a - 1). so the correct option is B.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Now we directly substitute the a + 2 to the all the x's in the function such that,

f(a + 2) = (3 + a + 2) / (a + 2 - 3)

Then Simplifying the function generated above,

f(a + 2) = (5 + a) / (a - 1)

The correct option is B.

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Answer:

I'd say A, Adjacent

Step-by-step explanation:

I think its A because adjacent means together/along with, and these angles are next to each other.

The total members of the chess club at the school, given the number of teachers, can be found to be 25 students.

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

The number of chess club students is therefore :

= Number of people counted by Alan - Number of teachers

= 31 - 6

= 25 members

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The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1.  5x – 7 = 4x + 3.

To solve for x, we can add 7 to both sides of the equation and subtract 4x from both sides:

5x - 7 + 7 = 4x + 3 + 7

5x = 4x + 10

x = 10

2.  6 + 2x = 7x - 9

To solve for x, we can add 9 to both sides of the equation, subtract 6 from both sides and divide both sides by -1:

6 + 2x + 9 = 7x - 9 + 9

2x = -3

x = -3/2

3. 8x + 1 = -8 - x

To solve for x, we can add x to both sides of the equation and add 8 to both sides:

8x + 1 + x = -8 - x + x + 8

9x + 1 = 0

x = -1/9

4. -5 + 12x = 18x + 7

To solve for x, we can subtract 12x from both sides of the equation and add 5 to both sides:

-5 + 12x - 12x = 18x + 7 - 12x

-5 = 6x + 7

x = -6

5.  -4x + 3 = 5x - 13 - x

To solve for x, we can add x to both sides of the equation, subtract 3 from both sides and divide both sides by -1:

-4x + 3 + x = 5x - 13 - x + x + 3

-3x = -10

x = 10/3

The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3

That gives you the letters "joke"

Therefore, The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1.  5x – 7 = 4x + 3.

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Answer:

i don't know

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles.

<3  = <1 + <2

5x+4 = x+1   + 39

Combine like terms

5x+4=x+40

Subtract x from each side

5x-x+4=x-x+40

4x+4 = 40

Subtract 4 from each side

4x+4-4 = 40-4

4x = 36

Divide by 4

4x/4 = 36/4

x = 9

Answer:

x = 12

Step-by-step explanation:

We know that,

The exterior angle of a triangle equals to the sum of opposite interior angles.

Accordingly,

[tex] \angle \: 1 + \angle \: 2 = \angle \:3[/tex]

That is,

x + 13 + 39 = 5x + 4

Combine like terms.

x + 52 = 5x + 4

Subtract x from both sides.

52 = 5x - x + 4

52 = 4x + 4

Subtract 4 from both sides.

52 - 4 = 4x

48 = 4x

Divide both sides by 4.

12 = x