A Basic Cellular Package Costs $20/month For 60 Minutes Of Calling With An Additional Charge Of $0.20/minute (2024)

If the price changes from $105,300 to $104,399, It means that there is a decrease in price.

Decrease = 105,300 - 104,399 = $901

The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes

[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]

By rounding up to the nearest whole number, it becomes 1%

The percent decrease is 1%

x = 0,1 are the real solutions of the equation .

What are real solutions in math?

Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.

4x³ - 8x² + 4x = 0

x( 4x² - 8x + 4 ) = 0

x( 4x² - 4x - 4x + 4 ) = 0

x ( 4x ( x - 1) -4 ( x - 1 )) = 0

x ( ( 4x - 4 ) ( x - 1 ) ) = 0

x = 0

4x - 4 = 0 ⇒ x = 1

x - 1 = 0 ⇒ x = 1

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According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.

Hence, the answer is D.

Probability that Deandre missed at least 1 day is;

[tex]Pr(x\ge1)=Pr(1)+Pr(2)+Pr(3)+Pr(4)+Pr(5)[/tex]

Write out the values of each probability and sum them

[tex]\begin{gathered} Pr(x\ge1)=0.25+0.18+0.34+0.12+0.04 \\ =0.93 \end{gathered}[/tex]

Hence,

The probability that Deandre missed at least 1 day is 0.93

Given the situation to model the arithmetic and the geometric sequences.

Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.

Option 1: She would give you $1000.50 a year until you are twenty-one.

This option represents the arithmetic sequence

The first term = a = 1000.50

The common difference = d = 1000.50

The general formula will be as follows:

[tex]\begin{gathered} a_n=a+d(n-1) \\ a_n=1000.50+1000.50(n-1) \\ \end{gathered}[/tex]

Simplify the expression:

[tex]a_n=1000.50n[/tex]

Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.

This option represents the geometric sequence

The first term = a = 1

The common ratio = r = 2/1 = 2

The general formula will be as follows:

[tex]\begin{gathered} a_n=a\cdot r^{n-1} \\ a_n=1\cdot2^{n-1} \end{gathered}[/tex]

Now, we will compare the options:

The first term of both options is when you are four years old that n = 1

you only received money for ten years so, n = 10

So, substitute with n = 10 into both formulas:

[tex]\begin{gathered} Option1\rightarrow a_{10}=1000.50(10)=10005 \\ Option2\rightarrow a_{10}=1\cdot2^{10-1}=2^9=512 \end{gathered}[/tex]

So, the answer will be:

For ten years, the option that gives the most money = Option 1

The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.

In this case:

[tex]\begin{gathered} 10(8y+5) \\ \text{open the bracket} \\ 80y+50 \end{gathered}[/tex]

Note you have to use the value outside the bracket to multiply the inner value.

Answer:

3y=6-x

Explanation:

The slope-intercept form of a line is y=mx+b.

First, we determine the slope(m) of the line.

[tex]\begin{gathered} m=\frac{2-0}{0-6} \\ =-\frac{2}{6} \\ m=-\frac{1}{3} \end{gathered}[/tex]

Since the y-intercept, b=2

The equation of the line is:

[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ y=\frac{-x+6}{3} \\ 3y=6-x \end{gathered}[/tex]

SOLUTION

Mean=54.11, standard deviation = 12.59

X=48

Using the z formula

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting values gives

[tex]z=\frac{48-54.11}{12.59}[/tex]

Solve for z

[tex]z=-0.4853[/tex]

This shows that the result shows that the value x=48 is 0.4853 standard deviation to the left of the mean.

Let 'x' represents the missing number

a) x % of 136 = 17

[tex]\begin{gathered} \text{where, }x\text{ \% =}\frac{\text{x}}{100} \\ \frac{x}{100}of136=17 \\ \frac{x}{100}\times136=17 \\ \frac{136x}{100}=17 \\ 1.36x=17 \end{gathered}[/tex]

Divide both sides by 1.36

[tex]\begin{gathered} \frac{1.36x}{1.36}=\frac{17}{1.36} \\ x=\frac{25}{2}=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]

Hence, 17 is 12.5% of 136.

b) x% of 352 = 44

[tex]\begin{gathered} \text{where, x\%=}\frac{\text{x}}{100} \\ \frac{x}{100}\times352=44 \\ \frac{352x}{100}=44 \\ 3.52x=44 \end{gathered}[/tex]

Divide both sides by 3.52

[tex]\begin{gathered} \frac{3.52x}{3.52}=\frac{44}{3.52} \\ x=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]

Hence, 44 is 12.5% of 352.

We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay

[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]

So the answer is: b.140 greater than sign M greater than sign 150.

Consider that the intercept form of equation of a line whose x-intercept is (a,0) and y-intercept is (0,b), is given by,

[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]

The equation of the line is given as,

[tex]5x+3y=15[/tex]

Convert this equation into intercept form,

[tex]\begin{gathered} \frac{5x}{15}+\frac{3y}{15}=1 \\ \frac{x}{3}+\frac{y}{5}=1 \end{gathered}[/tex]

Comparing with the standard equation,

[tex]\begin{gathered} a=3 \\ b=5 \end{gathered}[/tex]

Thus, the x-intercept and y-intercept of the equation, respectively, are,

[tex](3,5)\text{ and }(0,5)[/tex]

We know that two lines are parallel if they have the same slope. So we first find the slope of the given line. One way to do this is to rewrite the equation in its slope-intercept form, solving for y:

[tex]\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]

Then, we have:

[tex]\begin{gathered} 4x-5y=5 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=5-4x \\ -5y=5-4x \\ \text{ Divide by -5 from both sides} \\ \frac{-5y}{-5}=\frac{5-4x}{-5} \\ y=\frac{5}{-5}-\frac{4x}{-5} \\ y=-1+\frac{4x}{5} \\ y=\frac{4x}{5}-1 \\ y=\frac{4}{5}x-1 \end{gathered}[/tex]

Now, we have the slope and a point through which the line passes:

[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex]

Then, we can use the point-slope formula:

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{4}{5}(x-(-5)_{}) \\ y-2=\frac{4}{5}(x+5_{}) \end{gathered}[/tex]

The above equation is the equation of the line in its point-slope form. However, we can also rewrite the equation of the line in its standard form by solving for the constant:

[tex]ax+by=c\Rightarrow\text{ Standard form}[/tex][tex]\begin{gathered} y-2=\frac{4}{5}(x+5_{}) \\ \text{ Multiply by 5 from both sides of the equation} \\ 5(y-2)=5\cdot\frac{4}{5}(x+5_{}) \\ 5(y-2)=4(x+5_{}) \\ \text{ Apply the distributive property} \\ 5\cdot y-5\cdot2=4\cdot x+4\cdot5 \\ 5y-10=4x+20 \\ \text{ Subtract 5y from both sides} \\ 5y-10-5y=4x+20-5y \\ -10=4x+20-5y \\ \text{Subtract 20 from both sides } \\ -10-20=4x+20-5y-20 \\ -30=4x-5y \end{gathered}[/tex]

Therefore, an equation of the line that passes through the point (-5,2) and is parallel to the line 4x - 5y = 5 is

[tex]\boldsymbol{4x-5y=-30}[/tex]

Solution:

Given the endpoints of the line;

[tex](0,5),(6,4)[/tex]

The slope, m of the line is;

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ Where }x_1=0,y_1=5,x_2=6,y_2=4 \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} m=\frac{4-5}{6-6} \\ \\ m=-\frac{1}{6} \end{gathered}[/tex]

CORRECT ANSWER:

[tex]-\frac{1}{6}[/tex]

From the problem, we have an inequality of :

[tex]5x+9\le24[/tex]

Subtract 9 to both sides of the inequality :

[tex]\begin{gathered} 5x+9-9\le24-9 \\ 5x\le15 \end{gathered}[/tex]

Divide both sides by 5 :

[tex]\begin{gathered} \frac{5x}{5}\le\frac{15}{5} \\ x\le3 \end{gathered}[/tex]

The answer is x ≤ 3

[tex]\begin{gathered} \frac{5}{8}x=\frac{1}{2} \\ x=\frac{1}{2}\times\frac{8}{5}=\frac{4}{5} \end{gathered}[/tex]

So 4/5 times 5/8 is 1/2.

Answer:

Step-by-step explanation:

18098

We can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).

What exactly are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

So, the ordered pair of the equation 3x + y = 12:

(A) When (2,5):

3x + y = 123(2) + 5 = 126 + 5 = 1211 ≠ 12

(B) When (4,0):

3x + y = 123(4) + 0 = 1212 + 0 = 1212 = 12

(C) When (0,6):

3x + y = 123(0) + 6 = 120 + 6 = 126 ≠ 12

Therefore, we can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).

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The required change in the percentage is 20%.

Given that,
clarissa's division test was 60% in the first six weeks and 72% in the second six weeks. To determine the percent change.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
According to the question,
The change in the percentage = (72 - 60) / 60 × 100
The change in the percentage = 20%

Thus, the required change in the percentage is 20%.

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Ok, so:

We're going to factor this expression:

3a² - 24a + 48

First of all, we multiply and divide by 3 all the expression, like this:

3(3a² - 24a + 48) / 3

Now, we can rewrite this to a new form:

( (3a)² - 24(3a) + 144) / 3

Then, we have to find two numbers, whose sum is equal to -24 and its multiplication is 144.

And also we distribute:

((3a - 12 ) ( 3a - 12 )) / 3

Notice that the numbers we're going to find should be inside the brackets.

So, these numbers are -12 and -12.

Now, we factor the number 3 in the expression:

(3(a-4)*3(a-4))/3

And we can cancel one "3".

Therefore, the factored form will be: 3 (a - 4) (a - 4)

So, the answer is B.

Given:

a. The amount of flour that the bakery used this month was a 50% increase relative to last month.

So, we will draw a diagram that represents the situation

As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%

this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase

b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.

As shown, for last month, we have drawn a rectangle with four equal areas

75% decrease, so, we have to remove 3 areas to make the remaining = 25%

So, the difference will give a 75% decrease

Answer:

Odd, Even, Even, Neither

=========================

The difference between odd and even functions is that:

f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.

Let's test this property for the given functions.

Function f(x)

f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd function

Function g(x)

g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even function

Function j(x)

j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even function

Function k(x)

k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even function

we know that

the circumference of a circle is giving by

[tex]C=2\pi r[/tex]

we have

C=30pi

substitute

[tex]\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=\frac{30}{2} \\ r=15\text{ units} \end{gathered}[/tex]

Find the area of the circle

[tex]A=\pi r^2[/tex]

substitute the value of r

[tex]\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}[/tex]the area is 225π square units

Question:

Find the slope of

[tex]y=-5x+2[/tex]

Answer:

Remember that when we have the equation of a line in the form

[tex]y=mx+b[/tex]

The slope of the line is the number that accompanies x (A.K.A Coefficient)

Therefore, the slope of the line is -5

The linear function is given by 5200+350x = 750x

What is linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

Amount spent to obtain merchandise = $5,200

Cost of general expenses = $350

Earnings from sales per week = $750

Now,

Let 'x' be the number of weeks taken to make profit

thus,

Total cost involved = $5,200 + ( $350 × x )

Total profit from sales = $750 × x

Now, the number of weeks after that the cost and earning will be equal, will be given by

5200+350x = 750x

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GIVEN

The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.

QUESTION A

Let the number of items that can be gotten before the store closes be N.

The number of items can be calculated using the formula:

[tex]N=\text{ number of hours left}\div\text{ number of hours used to find one item}[/tex]

Therefore, the equation to get the number of items will be:

[tex]N=\frac{3}{4}\div\frac{1}{8}[/tex]

QUESTION B

The solution can be obtained by division.

Apply the fraction rule:

[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

Hence, the solution will be:

[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\times\frac{8}{1} \\ \Rightarrow\frac{3\times\:2}{1\times\:1}=6 \end{gathered}[/tex]

The answer is 6.

QUESTION C

Jane can find 6 items before the store closes.

56÷1/3

We have to model a problem where the solution is 56÷1/3.

So, we take something that is 56 and we have to divide it by 1/3rd.

So, we can say:

George had 56 large cakes.

Giving 1/3rd of each cake to each person is enough.

If George used all of the cake, how many person could he feed?

For the given right cylinder:

Radius = r = 4 in

Height = h = 12 in

The volume of the cylinder =

[tex]\pi\cdot r^2\cdot h=\pi\cdot4^2\cdot12=192\pi[/tex]

So, the answer will be the volume is 192π in^3

Answer;[tex]f(x)=(x+3)(x+2)(x-3)(x-4)[/tex]

Explanations:

A polynomial function is in standard form when the terms in its formula are ordered from highest to lowest degree.

The factored form of a polynomial function as a function of "x" is expressed as:

[tex]f(x)=(x-a)(x-b)(x-c)(x-d)[/tex]

where a, b, c, and d are the x-intercepts or zeros of the polynomial function.

From the given graph, the zeros of the polynomial graph are the point where the curve cuts the x-axis. The zeros of the polynomial are at x = -3, -2, 3 and 4

The factors of the polynomial function will be (x+3)(x+2)(x-3)(x-4)

The formula (in factored form) for a polynomial of least degree will be:

[tex]\begin{gathered} f(x)=(x-(-3))(x-(-2))(x-3)(x-4) \\ f(x)=(x+3)(x+2)(x-3)(x-4) \end{gathered}[/tex]

The median of the given data set will be 35.

What do we mean by media?In statistics and probability theory, the median is the number that separates the upper and lower half of a population, a probability distribution, or a sample of data. For a data set, it might be referred to as "the middle" value.

So, The variability metrics for each class are listed below:

The further classifications: Class A; Class B;

Range: 30 Range: 30IQR: 12.5 IQR: 20.5MAD: 7.2 MAD: 9.2

Greater variability in the data set is suggested by class B's wider interquartile range and mean absolute deviations.

Set A's median will be:

median = (20 + 32+ 36+ 37 + 50) / 5median = 175 / 5median = 35

Therefore, the median of the given data set will be 35.

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