The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.
How to illustrate the information?From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.
The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:
35.50 + 5x < 50
Collect like terms
5x < 50 - 35.50
5x < 14.50
x < 14.50 / 5
x < 2.9
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an air conditioning and heating repair firm conducted a study to determine if the average outside temperature could be used to predict the cost of an electric bill for homes during the winter months in houston, texas. the resulting regression equation was: y
Finding the numeric value of the regression line, it is found that the electric bill in a month with temperature of 48 degrees is of $157.59.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
In the context of this problem, the function is given as follows:
y = 227.19 - 1.45x.
Which y giving the electric bill for a month of temperature x degrees.
The temperature is of 48 degrees, hence to find the electric bill, the lone instance of x in the function is replaced by 48, hence:
y = 227.19 - 1.45(48) = $157.59.
Hence the electric bill in a month with temperature of 48 degrees is of $157.59.
What is the missing information?The regression line is missing in this problem, as is defined as follows:
y = 227.19 - 1.45x.
In which:
y is the electric bill.x is the monthly temperature.The problem asks for the electric bill in a month with temperature of 48 degrees.
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8. Which best describes the relationship between the line that passes through (-1, -8) and (4,-4) and the line
that passes through (2, -9) and (7,-5)?
a. parallel
b. perpendicular
C.
same line
d. neither perpendicular nor parallel
Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Relationship between lines in this caseIn this case, you can calculated in this case:
Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:
m= (-4 - (-8))÷ (4 - (-1))
m= (-4 + 8)÷ (4 + 1)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-8= 4/5× (-1) + b
-8= -4/5 +b
-8 + 4/5= b
-36/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.
Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:
m= (-5 - (-9))÷ (7 - 2)
m= (-5 + 9)÷ (5)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-9= 4/5× (-2) + b
-9= -8/5 +b
-9 + 8/5= b
-37/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.
You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.
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1) The compound interest of a sum of money is Rs 13310 and in 4 years is Rs 14641. Find the rate of interest and sum.
The rate of interest is 10% and the sum is Rs 10,1000.
What is compound interest?The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.
The compound interest formula is given by
Compound Interest = Amount – Principal
Here, the amount is
[tex]A=P(1+\frac{r}{100} )^{n}[/tex] where,
A = amount
P = principal
r = rate of interest
n = time (in years)
Given:
C.I. of a sum of money in 3 years = Rs 13310
C.I. of a sum of money in 4 years = Rs 14641
Let the principal be P and the rate of interest be r%
Then, according to the question,
For 3 years:
[tex]13310=P(1+\frac{r}{100} )^{3}[/tex] ..... (1)
For 4 years:
[tex]14641=P(1+\frac{r}{100} )^{4}[/tex] ..... (2)
Dividing equation (2) by (1), we obtain
[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]
⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]
⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]
⇒[tex]r=\frac{100}{10}[/tex]
⇒ r = 10%
Now, substituting r in equation (1),
[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]
⇒[tex]13310=P(\frac{1331}{1000} )[/tex]
⇒P = Rs 10,000
Therefore, the rate of interest is 10% and the sum is Rs 10,1000.
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( Please help + Will mark brainliest )
Answer the question in photo.
Answer: 1/4
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that A'D'=2 and AD=8, so the scale factor is 2/8 = 1/4.
What is the relationship between multiplying and factoring? You multiply numbers or expressions to produce a (select). You factor a product into the numbers or(select)that were multiplied to produce it.
Answer:
Factoring polynomials is the inverse process of multiplying polynomials. After factoring a polynomial, if we divide the polynomial with the factors then the remainder will be zero.
How do you do question 7 and 8?
Answer:
7.
[tex]y = \frac{a - b \: x {}^{10} \times ln(x) }{x {}^{10} } [/tex]
8.
[tex]y = \frac{12x {}^{3} \times ln(x) - 2x {}^{4} + 1 + 4\pi {}^{2}x {}^{3} }{4x {}^{3} } [/tex]
I'd appreciate some help here
Answer:
6.6 is the correct number
Step-by-step explanation:
The base is 2.2 inches. The height is 3 inches. So the area is 2.2 × 3 = 6.6 square inches.
Ethan’s family used 16.8 gallons of gas to drive 428.4 miles .How many miles did they drive on each gallon of gas.
Answer: 25.5 miles per gallon. 16.8 gallons x 25.5 miles = 428.4 miles
help i don’t get it
answers pls
Answer: 13
Step-by-step explanation:
As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.
3x = 180 - 39 - 90 - 12
3x = 39
x = 13
1. An elevator in a tall building starts at a floor of the building that is 80 meters above the ground. The elevator descends2 meters every 0.5 seconds for 4 seconds. Identify the domain and range using the following formats and then graph.Inequality:Set Notation:
Let's begin by listing out the information given to us:
The elevator starts at 80 m
The elevator descends 2 meters every 0.5 seconds for 4 seconds
The inequality is given by:
[tex]\begin{gathered} y=80-2x \\ where\colon x=every\text{ 0.5}seconds \end{gathered}[/tex]The set notation is given by:
[tex]undefined[/tex]pls pls help whoever gets it right gets marked brainliest
Answer:
13 units
Step-by-step explanation:
[tex]d=√((x_2-x_1)²+(y_2-y_1)²) [/tex]
[tex] \sqrt{( - 2 - ( -14)^{2} } + ( - 4 - 1) {}^{2} [/tex]
[tex] \sqrt{12 {}^{2} } + ( - 5) {}^{2} [/tex]
[tex] \sqrt{169} [/tex]
= 13 UnitsIdentify the point corresponding to P.
P′ (−2, 0)
P′ (−4, 0)
P′ (−3, −1)
P′ (−5, −3)
Answer:
(-4,0)
ignore this line
. What values of x will make the absolute value equation, 2x - 4= 15, true?
After factorization, the absolute value of the variable 'x' is 9.
What is factorization method?
The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.
According to the question, the given linear equation is: |2x - 4| = 15
Now, to calculate the value of the variable 'x' by using factorization method. And to remove the bars which represent absolute value that means positive values
Required expression: |2x - 4| = 15
⇒ 2x = 15 + 4 = 19
⇒ x = 19/2 = 9.5
After factorization, the absolute value of the variable 'x' is 9.
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Identify all the sets which each number belongs. 15,-5.075,and π
The sets of numbers which each of the numbers given belong to as required in the task content is as follows;
15; Real, rational and Integers.-5.075; Real, rational and decimal.π; Real, Irrational and decimal.To what sets do all three numbers as given belong?As evident in the task content, the sets to which the three numbers belong is to be determined.
Hence, taking the numbers one after the other; we have;
15 => The number 15 belongs to the set of real numbers, rational numbers and most particularly, integers.
-5.075 => The number -5.075 belongs to the set of real numbers, rational numbers, and most particularly, decimals.
π => The number represented by π belongs to the set of real numbers, irrational numbers and it's numerical value is a non-terminal and non-repeating decimal.
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You purchase a home for $200,000 which appreciates at 2.5%. How much is it worth in 7 years?
Answer: The answer I came up with is: $237,737
Please help me please
please give answer fast and provide explanation so I know how to do it
Hey could you help me make sure these are right . Thanks so much they points are at 50 and I’ll mark brainliest
Step-by-step explanation:
your answers are right in my pov
Estimate the intercepts of the graph of the function
Answer:
x-intercept equals 5
y-intercept equals -10
Step-by-step explanation:
y-intercept: solve when x=0. y=-2|x-5|= -10
What is the smallest possible degree that the polynomial can have and why?
Check the picture below.
Use proof by contradiciton to prove that the sum of the squares of two odd integers cannot be a perfect square. HINT: you can use the fact that the sum of two odd numbers must be even without proof
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
What is a square?A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.
A square has four corners and is closed, two-dimensional (2D) object.
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.
Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.
Let, x=2m+1 and y=2n+1.
Hence,
[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]
=[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]
=[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]
=[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]
Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
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Write the definition as a biconditional statement:
An equilateral triangle is a triangle with three congruent sides.
The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.
A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.
This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.
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F(4) if f(x) = 3 x -1
Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;
A store sells small notebooks for $6 and large notebooks for $10. If a student buys 6 notebooks and spends $48, how many of each size did he buy?
They could buy 8 small notebooks or 3 large notebooks and 3 small notebooks.
Answer: just one way to do it. You can buy 3, large books and 3 small books
Step-by-step explanation:
10x3=30
48-30=18
18 divided by 3 = 6
for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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(ANSWER AT THE BOTTOM)A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.
How many rectangular containers will be necessary to package 6,400 candles?
How many cylindrical containers will be necessary to package 6,400 candles?
Which container should the company use to minimize costs? Explain.
143,157,the rectangular containers,because it will cost the company $67 more to use the cylinder containers.
The number of rectangular containers will be necessary to package 6,400 candles is 143
The number of cylindrical containers will be necessary to package 6,400 candles is 157.
The container that would minimise cost is the rectangular container because it would $67 less to use the rectangular container.
Which container minimises costs?The first step is to determine the total cost of packing 6400 candles using the rectangular container.
Total cost = number of containers needed x cost of one rectangular container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 45 = 142.22 = 143 rectangular containers
Total cost = $16 x 143 = $2,288
The next step is to determine the total cost of packing 6400 candles using the cylindrical container.
Total cost = number of containers needed x cost of one cylindrical container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 41 = 156.1 = 157 cylindrical containers
Total cost = $15 x 157 = $2,355
Difference in costs = $2,355 - $2,288 = $67
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How is the graph of each equation related to
standard form Ax + By = C?
Answer:
When A = 0 and y = 1 and C = 2
0x + 1y = 2
y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.
Step-by-step explanation:
Which expression is equivalent to t
3(x+24)?
A-2/3x+24
B-2/3x+16
C -2/3x-16
D 2/3x-16
0.3(6y + 15) = 1.8y + 4.5.
its hard
__________________________________________________________
Hello! In this question, we will be solving the given equation for the variable "y".
__________________________________________________________
Explanation:
In our question, we were given the following equation:
0.3(6y + 15) = 1.8y + 4.5To solve for our "y" variable, we will perform distributive property and simplify to get the value of "y".
__________________________________________________________
Solve:
[tex]0.3(6y + 15) = 1.8y + 4.5\\\\\text{Use the distributive property to distribute the "0.3"}\\\\1.8y+4.5=1.8y+4.5\\\\\text{Since both sides of the equal sign are equal, there will be infinite solutions}[/tex]
Proof:
[tex]\text{To prove that there are infinite solutions, we could continue to solve the}\\\text{equation:}\\\\1.8y+4.5 =1.8y+4.5 \\\\\text{Subtract 1.8y from both sides}\\\\4.5=4.5\\\\\text{Subtract 4.5 from both sides}\\\\0=0[/tex]
__________________________________________________________
Answer:
[tex]\boxed{\text{Infinite solutions}}[/tex]
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