Without Computing, decide whether the value of each expression is much smaller than one, close to one, or much greater than one.​ 50 1/3 divided 50 1/4

Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.

The basic mathematical operations involve addition, subtraction, division, and multiplication.

These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.

In this situation, we employ division and multiplication operations to solve the requirement.

Loren and Julie's Total Income Table

Hours    2   4   6   8   10   12  14   16   18

Dollars 18 36 54 72 90 108    ?    ?  162

Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)

Hours     3  6   9    12  15    18  21    24    27

Dollars 36 ? 108 144 180 216    ?  288 324

Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)

Total hours worked = 16

Total earnings = $192 ($12 x 16)

Thus, when Julie works 16 hours, she earns $192.

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The inequality equations for the rides High-Bounce, Climb-A-Thon, and Twirl-O-Coaster are 55<h<7, h<60, and h>=58 respectively.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

Let the unknown height be h.

For the ride High-Bounce, the height requirement is between 55 and 72 inches tall.

This can be written in the inequality form as 55<h<72.

For the ride Climb-A-Thon, the height requirement is under 60 inches tall.

This can be written in the inequality form as h<60.

For the ride Twirl-O-Coaster, the height requirement is 58 inches minimum.

This can be written in the inequality form as h>=58.

The representations of these inequalities on number lines is given below.

Therefore, the inequalities are - 55<h<7, h<60, h>=58.

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The values of m in the graph of y = mx²-5x-2 have no x-intercepts are

m< 25/8.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

Given a function y = mx²-5x-2 for not having the x-intercepts means that at any value of m function can not have the value zero or in other words function would not have any roots.

Thus for not having any root b² - 4ac < 0

For our function

a = m

b = -5

c = -2

substituting the values in the general formula

(-5)² - 4 * m * -2 < 0

25 + 8m< 0

m < 25/ 8

Therefore, The values of m are m 25/8 on the graph of y = mx2-5x-2, which has no x-intercepts.

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Answer:

-5a

Step-by-step explanation:

Think of it as 5-10 since both of them have "a"

5-10=-5

-5a

Answer:

-5a

Step-by-step explanation:

Algebra are algebraic expressions that can be used as variables and is subjected to BODMAS rule just like numerical expressions.

Example: 5b + 9b = 14b

Given from the question:

5a - 10a = -5a

Answer:

Step-by-step explanation:

All triangle's angles have a sum of 180 degrees.

56 + 61 = 117

180 - 117 = 63

x = 63

The table for all missing values of s and d should be completed as follows;

Number of songs, s               Amount of money ($), d

2                                                           2.58

4                                                           5.16

7                                                           9.03

11                                                           14.19

17                                                           21.93

In order to have a proportional relationship and equivalent ratios, the variables s and d must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = d/s

Constant of proportionality (k) = 2.58/2

Constant of proportionality (k) = 1.29.

When the amount of money (d) is 5.16, the number of songs (s) is given by;

s = d/k

s = 5.16/1.29

s = 4 songs.

When the number of songs (s) is 7, the amount of money (d) is given by;

d = ks

d = 1.29(7)

d = $9.03.

When the number of songs (s) is 11, the amount of money (d) is given by;

d = ks

d = 1.29(11)

d = $14.19.

When the amount of money (d) is 21.93, the number of songs (s) is given by;

s = d/k

s = 21.93/1.29

s = 17 songs.

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Answer:

-0.04 = decrease of 4%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

Given interval:

Therefore:

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(1940)-f(1920)}{1940-1920}\\\\&=\dfrac{45.3-46.1}{1940-1920}\\\\&=\dfrac{-0.8}{20}\\\\&=-0.04\end{aligned}[/tex]

Therefore, the average rate of change was -0.04 which is a decrease of 4%.

As the p-value of the test, of 0.0002, is less than the significance level of 0.05, the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

At the null hypothesis, it is tested if the tablets are filled as advertised, that is, the mean is of 5 grains, hence:

[tex]H_0: \mu = 5[/tex]

At the alternative hypothesis, it is tested if the tablets are not filled as advertised, that is, if the mean is less than 5 grains, hence:

[tex]H_1: \mu < 5[/tex]

The equation for the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are given as follows:

The values of these parameters for this problem are given as follows:

[tex]\overline{x} = 4.87, \mu = 5, s = 0.35, n = 100[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{4.87 - 5}{\frac{0.35}{\sqrt{100}}}[/tex]

t = -3.71.

Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with 100 - 1 = 99 df, the p-value of the test is of:

0.0002.

Hence the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

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Answer: If you're on the test, the answer should be B

Step-by-step explanation:

Answer:

[tex]\left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]

Step-by-step explanation:

The [tex]x[/tex]-intercepts are when [tex]y=0[/tex].

[tex]0 \leq x \leq 2\pi \implies 0 \leq 2x \leq 4\pi \\ \\ \cos 2x=0 \implies 2x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2} \\ \\ \implies x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \\ \\ \therefore \left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]

Answer: The expression in simplified form is D. 3x³√15

To simplify the expression, we can first simplify the fractions.

2/1356 can be simplified to 12/225.

Then, we can use the distributive property to simplify the expression further.

12/225 - 3√156 = 12/225 - 18√15

The last step is to combine the terms,

12/225 - 18√15 = (-6/75) - (6√15) = -6/5 * (1/5 - √15) = -6 * (- √15/5) = 3 * √15 * 6

Therefore, the simplified form of the expression is D. 3x³√15

Step-by-step explanation:

Answer:

-31c + 20

Step-by-step explanation:

distribute

9c + -10 × 4c, -10 × -2

9c - 40c + 20

-31c + 20

Answer:

-31c+20

Step-by-step explanation:

You multiply the equation in the parenthesis by negative ten and then subtract it all from 9c

Answer: Less than

Step-by-step explanation:

The percent change is exactly what it sounds like, the percent that changed. and 1/9 is less that 4.5/9 (half of 9) so it is less than

Answer:

B. 3⁻⁴; E. 1/3⁴.

Step-by-step explanation:

1. rule is:

cᵃ:cᵇ=cᵃ⁻ᵇ;

2. according to the rule above:

3⁻⁸:3⁻⁴=3⁻⁸⁺⁴=3⁻⁴, then

3. correct answer is 'B'; 'E'.

Answer:

reciprocal

Step-by-step explanation:

Reciprocal just means to turn it upside down.

Answer: x = 0, 16

Step-by-step explanation:

First square both sides

(sqrt2x+4 - sqrtx)^2 = 4

now distribute the inside using the (a-b)^2 = a^2 -2ab + b^2 property to get

2x+4 - (2sqrt 2x^2 +4x) + X = 4

3x=2sqrt 2x^2 +4x

9x^2 = 4(2x^2+4x)

9x^2 = 8x^2+16x=0

x^2-16x=0

x(x-16)=0

x=0, 16

The sum of the sequence ∑₀⁵⁰⁰(2i - 312) is 94500

The sum of a sequence is the sum of terms of the sequence.

Given the sum ∑₀⁵⁰⁰(2i - 312).

To evaluate the sum, we expand the brackets.

So, we have that

∑₀⁵⁰⁰(2i - 312) = ∑₀⁵⁰⁰2i -  ∑₀⁵⁰⁰312

= 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

Now, ∑₀⁵⁰⁰i is the sum of natural numbers

So, ∑₀⁵⁰⁰i = n(n + 1)/2 where n = 500

Also, ∑₀⁵⁰⁰312 = 312n where n = 500

Thus substituting these into the equation for the sum, we have that

∑₀⁵⁰⁰(2i - 312) = 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

= 2n(n + 1)/2 - 312n

Given that n = 500, substituting n = 500 into the equation, we have that

∑₀⁵⁰⁰(2i - 312) = n(n + 1) - 312n

= 500(500 + 1) - 312 × 500

= 500(501) - 312 × 500

= 250500 - 156000

= 94500

So, the sum is 94500

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Answer:2

Step-by-step explanation:

N minus 3 equals negative 1

add 3 to both sides leaving the equation N = -1 +3 or N=3-1

3-1 equals 2

The equation of the variation is y =7x.

When we are discussing about the idea of variation then on specie is changing with respect to the other. If the change is such that the both variables are increasing at the same time then we could say that we have a direct variation.

Now, we know that;

y=8.4 when x=1.2

Given that;

y α x

If we add k;

y = kx

8.4 = k 1.2

x = 8.4/1.2

x = 7

Then the equation is;

y =7x

This is the equation that has been used to produce the graph in the image attached to the answer given here.

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a) The least squares estimate of the slope (b₁) can be calculated using the formula:

b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)

Where n is the number of observations, x and y are the explanatory and response variables, respectively.

b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8

b) The least squares estimate of the intercept (b₀) can be calculated using the formula:

b₀ = (∑y - b₁*(∑x))/n

b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4

c) The point estimate of y when x=2 can be calculated using the equation of the line:

y = b₀ + b₁x

y = 3.4 + 0.82 = 4.8

So the point estimate of y when x=2 is 4.8

In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.

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Answer:

Iniko's part is 4/15

Allea had the highest score

Step-by-step explanation:

Use the LCD 15 and convert the fractions:

Allea: 2/5 = 6/15

Loki:   1/3 = 5/15

Iniko score = 15/15 - 6/15 - 5/15 = 4/15

There is a percent decrease of about 43.75%

Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100. They are used like fractions and decimals i.e ways to describe parts of a whole.  While using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage

New Process = 45 mins

Old Process = 1 hour and 20 minutes (80mins)

Increase/Decrease = Old Process - New Process

Increase/Decrease = 80 - 45

Increase/Decrease = 35

Therefore there is reduction in the manufacturing process;

% decrease = (35/80) x 100

% decrease = 43.75%

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Answer:

6125555566/6661234567

a. The system of inequalities for this situation can be represented as:

x (number of snacks) ≥ 0

y (number of bottles of water) ≥ 0

2x + 2.25y ≤ 70 (total amount of money remaining)

y ≤ 4 (maximum number of bottles of water that can be carried on a tray)

7x + 7y ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

b. To graph the system, we can start by plotting the inequality 2x + 2.25y ≤ 70. This represents all the points that satisfy the inequality and forms a boundary line for the feasible region. The line will be a boundary line because it is less than or equal to 70.

We can plot the inequality y ≤ 4 as a horizontal line at y = 4. This represents the maximum number of bottles of water that can be carried.

Finally, we can plot the inequality 7x + 7y ≤ 70 as a boundary line. This represents the total cost of tickets and snacks/drinks that cannot exceed the amount given.

The feasible region will be the area between these lines, above the x-axis and y-axis, and below the line y=4.

The vertices of this feasible region will be the intersection points of the three lines, which are (10,0), (0,10) and (8,4)

c. The combinations of snacks and drinks that are possible are the ones that fall within the feasible region. Any point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

d. Every point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

e. One possible combination is (8,4) which is 8 snacks and 4 bottles of water, this combination is possible because it's within the feasible region and satisfies all the constraints. One combination that is not possible is (12,3), it's not possible because it's not within the feasible region and doesn't satisfy the constraint y ≤ 4.

f. To prove that the combination (8,4) is possible, we substitute these values into the system of inequalities:

2(8) + 2.25(4) = 35 ≤ 70 (total amount of money remaining)

4 ≤ 4 (maximum number of bottles of water that can be carried)

7(8) + 7(4) = 56 ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

To prove that the combination (12,3) is not possible, we substitute these values into the system of inequalities:

2(12) + 2.25(3) = 30.5 > 70 (total amount of money remaining)

3 > 4 (maximum number of bottles of water that can be carried)

7(12) + 7(3) = 63 > 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

As all the inequalities are not satisfied, the combination (12,3) is not possible.

A system of inequalities is a set of two or more inequalities that must be satisfied simultaneously. It is a way to represent a set of constraints using mathematical equations. These constraints can be related to a problem in a specific area, such as finance, engineering, or operations research. The solution set of a system of inequalities is the common set of solutions that satisfy all the inequalities in the system. The solutions can be represented graphically as a region in a coordinate plane called the feasible region, which is the set of all possible solutions.

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The solution to the expression -6.15/-8.2 is 0.75

From the question, we have the following parameters that can be used in our computation:

-6.15/-8.2

Next, we cancel out the negative sign

So, we have the following representation

-6.15/-8.2 = 6.15/8.2

Using a calculator, we have the following result

So, we have the following representation

-6.15/-8.2 = 0.75

Hence, the solution is 0.75

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Answer:

  B.  15, 20, ...

Step-by-step explanation:

You want to know which sequence of numbers has the steepest graph.

The slope (steepness) of the graph is the ratio of the change in y to the change in x. Here, we presume the x-values for each of these sets of points are 1, 2, 3, 4, ....

That means the slope will be the difference of adjacent y-values. Subtracting the first from the second, we get ...

  8 -4 = 4

  20 -15 = 5

  52 -50 = 2

  7 -4 = 3

The sequence in which the values differ by 5 has the largest difference, so will have the steepest graph:

  15, 20, 25, 30, ...

Answer:

12

Step-by-step explanation:

4 / 12   =  12 / 36      so answer : 12

That was just by looking.....here is mathematical way :

4/ x  = x/36       cross multiply

144 = x^2

x = 12

The probability that the student is absent is 3/20

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability that the student will be absent and it will be on Monday is 3 /100.

The probability that it will be Monday is 1/5

Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20

Since it is certain that it is Monday , the probability that it is Monday is 1.

Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20

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