Therefore , the solution of the given problem of linear equation comes out to be y = 7.
The definition of a linear equation.A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Despite the fact because both y and x are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases. The equation for a simple linear equation is Y=mx+b, where m stands for the slope and b for the y-intercept. Y=mx+b, where m stands for slopes and b for the y-intercept, is how the equation is expressed.
Here,
Given :
=> 6y + 3 = 45
=> 6y = 45-3
=> 6y = 42
=> y = 42/6
=> y = 7
Therefore , the solution of the given problem of linear equation comes out to be y = 7.
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[tex]6y+3=45[/tex]
Subtract 3 from both sides:
[tex]6y+3-3=45-3[/tex]
[tex]6y=42[/tex]
Divide both sides by 7:
[tex]\dfrac{6y}{6} =\dfrac{42}{6}[/tex]
[tex]\fbox{y = 7}[/tex]
Kayla's towel is made of 2 3/4 yards of
fabric. If 1/3 of the towel is blue, how many
yards of blue fabric are in her fowel?
Kayla's towel is made of 2 3/4 yards of fabric. 3 1/12 yards of blue fabric are in her fowel.
How many yards of blue fabric are in her fowel?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
Kayla's towel is made of 2 3/4 yards of fabric.
If 1/3 of the towel is blue.
2 3/4 + 1/3 =
11/4 + 1/3=
33 + 4 / 12 = 37 / 12 = 3 1/12
3 1/12 yards of blue fabric are in her towel .
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A box of snack size
cracker packs weighs 28½ ounces. Each
snack pack weighs 4¾
ounces. How many snack packs are in the
box?
999999999999999999..j
Dorothy organises a charity raffle she sells 800 tickets for £2 each 4% of the tickets win a prize it cost £20 65% of the profit goes to charity A and the rest goes to charity be how much of the money does Dorothy raise for charity day
By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336
What is Percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.Total ticket sold = 800
Cost of each ticket is £ 2
Total fund raised (raw) = 2 * 800 = £1600
4% of the ticket won a prize of £20 each
so total number of tickets winning a prize = 4 % of 800 = 32
Total prize money distributed = 32 * 20 = £ 640
Total amount to distribute to charity = 1600 - 640 = £ 960
Total profit that goes to Charity A is = 65 % of 960 = £624
And rest to charity B is = £ 336
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Need Explanation on how to solve:
Please help
The denominator for the final answer for fraction in question 2 is 75 and the numerator for the final answer for the fraction in question 3 is 25.
How to evaluate for the denominator and numerator of the fractionsWe shall simplify the fractions to get the final answer for the denominators and numerators as follows:
5/9 + 1/3 = (15 + 1)/9 {simplifying to a single denominator}
5/9 + 1/3 = 16/9
(5/9 + 1/3) ÷ 25/3x = 16/9 × 3x/25 {changing division to multiplication}
(5/9 + 1/3) ÷ 25/3x = 16 × x/75
(5/9 + 1/3) ÷ 25/3x = 16x/75 {denominator 75}
4/5 - 16/(x + 2) = [4(x + 2) - 16(5)]/5(x + 2) {simplifying to a single denominator}
4/5 - 16/(x + 2) = (4x + 8 - 80)/5(x + 2)
4/5 - 16/(x + 2) = (4x -72)/5(x + 2)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) ÷ (4x -72)/5(x + 2)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) × 5(x + 2)/(4x -72) {changing division to multiplication}
(x + 2) will cancel out and 4 is factored out from (4x -72)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20 × 5/4(x -16)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 5 × 5/(x - 16)
[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 25/(x - 16) {numerator 25}
Therefore, the first fraction have 75 as its denominator and the second fraction have 25 as its numerator.
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HELP PLEASE
A particular hybrid car travels approximately168 miLe on 4 gal of gas. Find the amount of gas required for 714 -miLe trip.
The car needs____ gallons of gas for 714 -miLe trip.
(Type an integer or a decimal.)
The car needs 59.5 gallons of gas for 714 a mile trip.
What is an integer?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Given: A particular hybrid car travels approximately 168 miles on 4 gals of gas.
We have to find the amount of gas required for the 714 -mile trip.
168 × d = 14 × g
168/14d = 1 g
12d = 1 g
1 gallon will take you 12 miles.
If you are given gallons, use the first one. If you are given miles, use the second one. You are given miles, so
= 714 miles ×(1 gallon/ 12 miles)
= 59.5 gallons.
Hence, The car needs 59.5 gallons of gas for 714 a mile trip.
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A group of friends were working on a student film. They spent all their
budget on props and equipment. They spent $192 on props, and 68%
of the total budget on equipment. What was the total budget for their
student film?
The total budget for their student film is $1200
What is percentage ?A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it; There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage;
Given;
On a student movie, some pals were engaged.
On props and equipment, they used the entire budget.
A total of $24% of the budget was spent on equipment, or $912, on props.
Let the movie's overall budget be x;
Spent on the equipment= $870
The props budget = 24% of x.
Equipment costs plus prop costs equal the total budget;
x = 912 + 24% of x
x = 912 + 0.24x
x - 0.24x = 912
0.76x = 912
x= 912/0.76
x = 1200
Therefore, the student film's overall budget with 68 percent of the total budget on equipment will be $1200;
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Write an equation in point-slope form of the line that passes through (-3, -2) and (2, -1).
Please help me i do not know
The statements that are true for line 'n' are
a) The slope of line n is equal to BC/AC
d) The slope of line n is equal to DE/AE.
The slope of a line:A line's slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinate. And the formula for slope is given by
Slope (m) = (y₂ - y₁)/(x₂ - x₁)Here we have
A line 'n' passing diagonally through a coordinate plane
From the given figure,
The points that the line passes are (4, 3) and (-2, 0)
The slope of the line, 'm' = [-0 -3]/[-2 - 4] = 3/6 = 1/2
From the given figure,
BC = 1 unit and AC = 2 units
DE = 4 units and AE = 8 units
a) The slope of line n is equal to BC/AC = 1/2
d) The slope of line n is equal to DE/AE = 4/8 = 1/2
Therefore,
The statements that are true for line 'n' are
a) The slope of line n is equal to BC/AC
d) The slope of line n is equal to DE/AE.
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Complete Question:
Use the graph below to answer the question. Which statements about line n are true? n, Select all that apply.
Answer choices:
a) The slope of line n is equal to BC/AC.
b) The slope of line n is equal to AC/BC.
C) The slope of line n is equal to BC/DE.
d) The slope of line n is equal to DE/AE.
e) The slope of line n is equal to AE/DE.
f) The slope of line n is equal to AC/AE.
Luke invested $86,000 in an account paying an interest rate of 5 ⅛ % compounded
continuously. Alexander invested $86,000 in an account paying an interest rate of 5 ⅝ % compounded annually. After 8 years, how much more money would Alexander
have in his account than Luke, to the nearest dollar?
Therefore , the solution of the given problem of interest comes out to be
$4,962.93 money more made by Alexander.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
Luke :
Principal amount = $86,000
and rate of interest = 5 ⅛ % or 41/8% or 5.125%
Alexander :
Principal amount = $86,000
rate of interest = 5 ⅝ % or 45/8% or 5.625%
To find the amount of money after time =8 years.
So ,
using compound formula :
=> A = P[tex](1 + r/n)^{nt}[/tex]
For luke = P=86000[tex](1 + 41/8*1)^{1*8}[/tex] = $42,276.33
For Alexander = P=86000[tex](1 + 45/8*1)^{1*8}[/tex] = $47,239.26
The amount made by Alexander by luke
=> 47,239.26 - 42,276.33 = 4,962.93
Therefore , the solution of the given problem of interest comes out to be
$4,962.93 money more made by Alexander.
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Ill give brainlyest for the answer
Step-by-step explanation:
it has answer is square because it has four sides
Maria has a cylindrical container that she uses to store craft supplies. The measurements of the container are shown.
She wants to cover the entire container with paper. Approximately how much paper will she need? Use 3.14 for π. PLEASE HELP TYYY DUE
A) 583cm squared
B) 704cm squared
C) 1.83cm squared
(D) 2, 210cm squared
Maria will need approximately 2209.6 square cm of paper to cover the entire container.
What is the surface area of a cylinder?The formula for the surface area of a cylinder is A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.
To find the surface area of the container, we can plug in the given values for r = 11 and h = 21:
A = 2π(11²) + 2π(11)(21)
A = 2π(121) + 2π(231)
A = 242π + 462π
A = 704π
We can approximate π as 3.14, then
A ≈ 704 × 3.14
Apply the multiplication operation, and we get
A = 2,210 square cm
Thus, the surface area of a cylinder is approximately 2,210 square cm.
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please help me now i need help
The equation that describes the diagram could be; 5 + 9 = 14
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Since Adding a negative number is the same as subtracting a positive number just as subtracting a negative number is the same as adding a positive.
The equation becomes as
5 + 9 = 14
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Find the discriminant of each quadratic equation
7k² + k + 7 = 0
a. Discriminant=
b. State the number of solutions(how many times the graph hits the x-axis):
(For example type: 1, 2, 0)
The discriminant of the given equation is -195 and the number of real solutions is 0.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
(a) Discriminant of a quadratic equation of the form ax² + b x + c = 0 is b² - 4ac.
Given quadratic equation is 7k² + k + 7 = 0.
Discriminant = 1² - (4 × 7 × 7) = 1 - 196 = -195
(b) Discriminant is negative.
So there are no real solutions for the given quadratic equation.
There are two complex solutions.
Hence the value of the discriminant is negative and there are no solutions.
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Pls Help…….Thank uuuu !!!!
Answer:
About 95% used
Step-by-step explanation:
78÷82=95.12200
Therefor, 78 is 95.12200% of 82
Problem No. 6 Tamsin is saving up for a smartwatch and puts all of her 50 cent and 20 cent coins in a jar each night. She thinks that she has saved enough and empties the 620 coins to count the money. 286 of the coins are 50 cent. If the cost of the smart watch is €230, how much more must she save to allow her buy the watch?
Answer: She must save €230 - €209.8 = €20.2 more to buy the watch.
Step-by-step explanation:
Tamsin has saved 286 * €0.50 = €143 from 50 cent coins.
The remaining coins are 620 - 286 = 334 which are 20 cent coins
So the total amount she has saved from 20 cent coins is 334 * €0.20 = €66.8
Therefore, the total amount she has saved is €143 + €66.8 = €209.8
So she must save €230 - €209.8 = €20.2 more to buy the watch.
PLEASE HELP!!! URGENT
Answer: It's the third option
Also could you mark my answer as brainliest? It helps and doesnt hurt a bit
Answer:
The third one(C)
Step-by-step explanation:
To find the answer you would divide 26 by 3, 65 by 5, etc. Then you take what you get when you divide those. Which would be 13 then you times it by 14, resulting in 182.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer: 36
Step-by-step explanation: The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
The standard form for finding the equation of a circle is expressed as;
(x-a)^2 + (y-b)^2 = b=r^2
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following
diameter = 12 units
radius = 12/2 = 6 units
If the centre lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)^2 + (y-3)^2 = 6^2 equivalent to x²+ (y-3)² = 36
Lynn is taking a trip in her car. She spent $387.00 on gasoline and snacks. Lynn spent $35.80 on snacks for the entire trip. Gasoline costs $2.54 per gallon.
How many gallons of gasoline did Lynn purchase on her trip?
Enter your answer in the box rounded to the nearest gallon.
Answer: she got 138 gallons of gas on her trip
Step-by-step explanation:
Warren wanted to save money to purchase a new car. He started by saving $1 on the first of January. On the first of February, he saved $4. On the first of March, he saved $16. So on the first day of each month, he wanted to save four times as much as he did on the first day of the previous month. If Warren continues his savings pattern, how much will he need to save on the first day of October?
If Warren keeps up his saving pace, he will need to have $262144 saved by October 1st.
What is an arithmetic sequence?
The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
given, Warren wanted to save money to purchase a new car. He started by saving $1 on the first of January. On the first of February, he saved $4. On the first of March, he saved $16
that means on the first day of each month he saves 4 times as much as he did on the first day of the previous month.
From the general formula of a geometric sequence
The nth term of a geometric sequence aₙ = arⁿ⁻¹
Where a = first term
r = ratio
in our case
a = 1
r = 4/1 = 4
Since October is the 10th month of the year
thus,
the money he will save in the month of October = ar⁹
the money he will save in the month of October = 1 * 4⁹
the money he will save in the month of October = 262144
Therefore, if Warren continues his savings pattern, he needs to save $262144 on the first day of October
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Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 09 in. Find P95. That is, find the hip breadth for men that separates the smallest 95% from the largest 5%.
Using standard normal distribution table, the hip breadth for men that separates the smallest 95% from the largest 5% is approximately 16.055 inches. This means that seats that are designed to be at least 16 inches wide will fit 95% of all males.
What is Normal DistributionNormal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that describes a continuous variable, such as a measurement or a test score, that is symmetric about the mean, with most of the observations clustering around the mean and fewer observations as we move away from the mean.
In the given question, to find the hip breadth that separates the smallest 95% from the largest 5% of men, we need to find the P95 value, which is also known as the 95th percentile.
Since the hip breadths of men are normally distributed with a mean of 14.8 inches and a standard deviation of 0.9 inches, we can use the standard normal distribution table (or a calculator with the inverse cumulative distribution function) to find the P95 value.
Using a standard normal distribution table or calculator, we find that P95 corresponds to a z-score of 1.65.
To find the P95 hip breadth, we can use the following formula:
P(95) = mean + (z-score * standard deviation)
P(95)= 14.8 + (1.65 * 0.9)
P(95) = 16.285 inches
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What is the new point after rotating the point (3,−5) 180° clockwise?
Since 180 is a straight line, it would be (-3,-5) because you would be going from (3,-5) around the origin twice (-3,-5)
what is order of rotation ?The most rotations that can be accommodated by a geometry are determined by its order of rotational symmetry. The degree of rotational symmetry is represented by the angle 360°A°, where A° is the lowest angle by which a figure may be rotated from its rotated shape to its original shape. (180 degrees) How many times a perfect circle can be rotated without losing its appearance tells us about a shape's degree of rotational symmetry. A full 360° revolution will only appear to be the same if a triangle is back in its initial starting position.
given
The new point (x′, y′) is defined by its coordinates as x′=xcos()ysin() and y′=xsin()+ycos()
when a point (x, y) is rotated counterclockwise by an angle about the origin (0, 0).
Since 180 is a straight line, it would be (-3,-5) because you would be going from (3,-5) around the origin twice (-3,-5) .
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Hello I need help with my math please help me thank you I need help with the first question
The first question have the unknown sides a = 12.29 and b = 275. 84 approximately to 2 decimal place using the trigonometric ratio of cosine the the angles 35° and 25° for the respective right triangles.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios are: sine cosine and tangent.
cos 35° = a/15 {adjacent/hypotenuse}
a = 15 × cos 35° {cross multiplication}
a = 12.2873
cos 25° = 250/b {adjacent/hypotenuse}
b = 250/cos 25° {cross multiplication}
b= 274.8445
Therefore, the unknown lengths a is equal to 12.29 and b is equal to 275.84 approximately to 2 decimal place for the respective right triangles using the trigonometric ratio of cosine for angles 35° and 25°.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The two options that represent the equation of the circle are:
x² + (y – 3)² = 36
x² + (y + 8)² = 36
Options A and E are the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
The equation of a circle is (x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius.
Now,
Diameter of the circle = 12 units
This means,
Radius = 12/2 units = 6 units
Now,
Center of the circle = y-axis.
This means,
x = 0,
y = a
Center = (0, a)
Now,
The equation of the circle.
(x - 0)² + (y - a) = 6²
x² + (y - a)² = 36
Where a can be any number.
Thus,
The equation of the circle can be:
x² + (y – 3)² = 36
x² + (y + 8)² = 36
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What is the value of f(x) = -x2 + 3 when x = 1? -2 -1 2 4
Answer:
f(x) = g(x)
3(2) - 4 = (2)² - 2
6 - 4 = 4 - 2
2 = 2
Step-by-step explanation:
I just substituted all the values in the domain to see which one would work. That's not really the quickest way but that's the only way I know
the answer is 4
Step-by-step explanation:
1²+ 3
1+3=4.
Evaluate the expression for x = -8.x = 16, and x = 4.
X ÷ 4
Answer:
-2, 4, 1
Step-by-step explanation:
Step 1: Substitute x for the values.
-8 / 4
16 / 4
4 / 4
Step 2: Solve
-8 / 4 = -2
16 / 4 = 4
4 / 4 = 1
Evaluate the expression below when x = 8 and y = 6.
The value of expression for x = 8 and y = 6 is,
⇒ 25
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (x² + y²) / 4
Here, We have;
⇒ x = 8 and y = 6
Substitute the value of x and y in above expression, we get;
⇒ (x² + y²) / 4
⇒ (8² + 6²) / 4
⇒ (64 + 36) / 4
⇒ (100) / 4
⇒ 25
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a point has a positive x coordinate and a positive y coordinate. What quadrant is it in
Which choice is equivalent to the quotient shown here when x ≥ 0?
√27 x + √48
O A. 3√x
OB.
V1 14
о с. 18x-32
O D. 3√x
8
Upon solving the root, the answer for given expression is option D: 3√x / 3.
What does "root" actually mean?In this case, the radical symbol for the number's root is "√". By multiplying the positive integer by itself, the square of the number is represented. By taking the square root of the square of a positive number, the original number can be found. For instance, 32 also equals 9, as does the square of 3 and the square root of 9.
How should the provided expression be calculated?This is the given expression:√27x + √48.
We will first simplify the square roots before simplifying the statement. √27 = 3 and √48 = 6.
Thus, the formula becomes 3√x + 6.
None of the suggested alternatives are equivalent to this statement. However, we can rephrase the expression in a way that is comparable to options A and D.
Let's multiply the expression's two sides by three.
The formula is now:√x + 2
Option D is represented by the formula 3√x/3 = √x + 2.
The solution is therefore option D: 3√x/3.
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Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you. Don’t understand how to work it out. Try to give me a good and simple step by of how to do this. Thanks .
Answer: Formulas for Solving Composite Figures
Step-by-step explanation:
The formula for finding the area of a rectangle is length x width.
The formula for finding the area of a square is side x side.
The formula for finding the area of a triangle is base x height/2.
The formula for finding the area of a circle is π x radius x radius
Hope this helps! :)
4.1 (Probability, Law of Large Numbers, Simulation)
1. The MARTA claims that their 5:30 am Red Line Train from Airport Station to College Park
Station has a probability of .95 of arriving on time. Assume for now that this claim is
true.
a. Explain what the probability .95 means in context.
b. If the 5:30a.m. train has arrived on time 6 days in a row, what is the probability
that it will arrive on time the next day? Why?
c. A student takes the 5:30am train to school 22 days in a month. They are
surprised when the train is late to Airport Station on 9 out of 22 days. Should
they be surprised? Describe how you would create a simulation that to estimate
the probability to see if their claim is true.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.
What is meant by Probability?The term "probability" is most commonly used to refer to the likelihood that a specific event (or group of events) will occur, either as a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
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