In linear equation, 95 is Meghan's amount of money is changing .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Based on the given conditions, formulate ( 1100 - 720 ) ÷ 4
Calculate the sum or difference = 380/4
Cross out the common factor = 95
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A 64-foot piece of siding is cut into three pieces so that the second piece is three times as long as the first piece and the third piece is four times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
The length of the first, second, third pieces of sidings are 8 ft, 24ft and 32 ft respectively.
How to find the length of all the pieces?The 64 ft piece of siding is cut into three pieces so that the second piece is three times as long as the first piece and the third piece is four times as long as the first piece.
The length of the three pieces of siding can be found as follows:
x = length of the first piece
Therefore,
Second piece = 3x
Third piece = 4x
Hence,
x + 3x + 4x = 64
8x = 64
divide both sides by 8
x = 64 / 8
x = 8
Therefore, the length of all the pieces are as follows;
First piece = 8 ft
Second piece = 3(8) = 24 ft
Third piece = 4(8) = 32 ft
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Marla writes this problem
628 divided by 1300
Which expression represents Marla’s problem
Answer:
628/1300
Step-by-step explanation:
you originally had a six year loan. how long would it take you to pay off the remaining $12,825 if you paid $225 monthly
Answer:
57 Months
Step-by-step explanation:
Should take 57 months. Simple division, just divide 12,825 and 225 and you end up with 57 months. 4 years and 9 months simplified. Hope this helps.
Is y= 2/3 (x) a linear equation
Sean used ¾ cup of sugar to make a dozen brownies. How much sugar is in each brownie? How many cups ?
Based on the fact that Sean made a dozen brownies with 3/4 cups of sugar, the amount of sugar in each brownie is 1 / 16 cups of sugar
How to find the quantity of sugar?A dozen brownies were made with 3/4 cups of sugar. This means that 12 brownies were made by using 3/4 cups of sugar.
To find the amount of sugar used per brownie, the formula is:
= Number of cups of sugar / Number of brownies made
Solving for the cups of sugar per brownie gives:
= 3/4 ÷ 12
= 0.75 / 12
= 0.0625
= 1 / 16 cups of sugar
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Bob's Bagels sells 10 bagels for $11.00, and Donny's Bagels sells 4 bagels for $3.00. Which is the better deal? Answer the questions to find out.
What fractions do you compare to find the better deal
Answer:
11/10 and 3/4
Step-by-step explanation:
To find the better cost, you need to determine which options has a lower cost per bagel.
An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 miles per hour slower due to a headwind. Find the distance that the plane flies between the two cities. The distance that the plane flies between the two cities is ____ miles.
Use the equation distance=rate*time
The distance that the plane flies between the two cities is 2475 miles.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
Time taken = distance covered / velocity
In the first case ;
Time taken = 5 hour.
Velocity = V(Let's say)
Distance covered = x
So,
5 = x/V
x = 5V
Now,
In the second case ;
Velocity = V - 99 (99 slower to first)
Time taken = 6 hours and 15 minutes = 6.25 hour
Distance covered = x
So,
6.25 = x/(V - 99)
x = 6.25V - 618.75
By equating
6.25V - 618.75 = 5V
1.25V = 618.75
V = 495 miles / hour
Now,
x = 5(495) = 2475 miles.
Hence "The distance that the plane flies between the two cities is 2475 miles".
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pls help i will give brainliest if correct and u explain how to calculate it
In a picture we have a triangle with 3 sides. Sides are a,8 and 2. The side a=2[tex]\sqrt{15}[/tex].
Given that,
In a picture we have a triangle with 3 sides.
sides are a,8 and 2.
by using Pythagorean theorem
The Pythagorean Theorem, generally referred to as Pythagoras' Theorem, is a basic relationship between a right triangle's three sides. The Pythagorean theorem states that, given a right triangle, which is a triangle in which one of the angles is 90 degrees, the hypotenuse, the right triangle's longest side, forms a square whose area is equal to the sum of the areas of its other two sides.
In other words, given that the triangle's longest side, c, is also its hypotenuse and that sides a and b are its other two sides:
a² + b² = c²
a²+(2)²=8²
a²+4=64
a²=64-4
a²=60
Take root on both sides
[tex]\sqrt{a^{2} } =\sqrt{60}[/tex]
a=2[tex]\sqrt{15}[/tex]
Therefore, the side a=2[tex]\sqrt{15}[/tex].
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Suppose that f(0)=-1 and f′(x)≤6 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be.
The maximum value of f(4) will be 23.
What is Mean value theorem?
Mean value theorem states that if a function f is continuous on the closed interval [a ,b] and differentiable on the open interval (a ,b), then there exists a point c in the interval (a, b) such that f'(c) is equal to the function's average rate of change over [a, b].
That is; [tex]f'(c) = \frac{f((b) - f(a)}{b - a}[/tex]
Given that;
⇒ f(0) = -1 and f′(x) ≤ 6 for all values of x.
Now, According to Mean value theorem;
[tex]f'(x) = \frac{f(4) - f(0)}{4 - 0}[/tex]
Since, f′(x) ≤ 6
Hence,
[tex]f'(x) \leq 6\\\\ \frac{f(4) - f(0)}{4 - 0}\leq 6\\\\ f(4) -(-1) \leq 24\\\\f(4) \leq 23[/tex]
So, The maximum value of f(4) will be 23.
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On a test that has a normal distribution, a score of 45 falls two standard deviations above the mean, and a score of 30 falls three standard deviations below the mean. Determine the mean of this test.
The value of the mean is a 33.75 in the normal distribution.
According to the statement
We have to find that the students' favorite color was red.
So, For this purpose, we know that the
A mean is simply defined as the average of the given set of numbers.
From the given information:
On a test that has a normal distribution, a score of 45 falls two standard deviations above the mean, and a score of 30 falls three standard deviations below the mean.
Then
The interval for score = 45- 30= 15
If we divide it by the 4 standard deviations; the interval result into
= 15/4
= 3.75
Then, the standard deviation is 3.75, and
The mean = 30+ 3.75
The mean = 33.75
So, The value of the mean is a 33.75 in the normal distribution.
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One boxer weighs in at 91 kg. He is 100 dag heavier than his opponent. How much does his opponent weigh in kilograms ?
Answer:
unlimited is the weight
Step-by-step explanation:
Weight : 58283624946946784640469267619046404.4691649469464846404694956596894
If the probability of being hospitalized during a year is 0.25, find the probability that no one in a family of five will be
hospitalized in a year.
The probability that no one in a family of five will be hospitalized in a year 0.2373 .
Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with complete certainty. We can only predict the probability that an event will occur .Probabilities can range from 0 to 1. 0 means the event is not possible, 1 indicates the specific event. The formula for probability is given by P(E) + P'(E) = 1 ...(1) where P(E) is the event will happenLet P(E) denote the probability of being hospitalized during a year and P'(E) the probability of not being hospitalized during a year
Then , using equation (1) , we get
[tex]0.25+P'(E)=1\\P'(E)=1-0.25\\P'(E)=0.75[/tex]
The probability that no one in a family of five will be hospitalized in a year is equal to [tex](P'(E))^n[/tex] where n is the number of member .
[tex](P'(E))^n=(0.75)^5\\(P'(E))^n=0.2373[/tex]
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WHAT IS THE DOMAIN AND RANGE OF THE GRAPH SHOWN BELOW (please answer, be frl)
Write your answers as inequalities, using or as appropriate.
Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.
What is a function?A function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The independent variable = domain
The dependent variable = Range
We are given a graph where the x-axis contains the radius value and the y-axis contains the circumference value.
We can write the function as:
f(x) where x can be 4, 8, 12, 16, 20, 24, 28, 32, 36
f(0) = 0
f(4) = 22.5
f(8) = 52.5
f(12) = 75
f(16) = 105
f(20) = 127.5
f(24) = 150
The domain is between 0 to 150 and the range is between 0 and 28.
Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.
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In Exercises 1-3, use this fraction bar.
1 Shade two of the equal parts. What fraction does
the shaded portion model?
2 Split each equal part (each unit fraction) into two equal;
parts. What fraction does the shaded portion model now?
Step-by-step explanation:
Type 5 examples of terminating decimals..
1.21948
2.5345
4.305
5.94
9.1
Lesson 19: Solutions to Inequalities in One Variable
Here is an inequality: 7x +6/2 < 3x +2
The values that are a solution to the inequality are x<-1/4.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The inequality are
7x +6/2 < 3x +2
According to given question we have
The expression is :
7x +6/2 < 3x +2
compare like terms we get
7x +6/2 < 3x +2
7x-3x<2-3
4x<-1
Divide both sides by 4 we get,
x<-1/4
Hence, the values that are a solution to the inequality are x<-1/4.
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What is the following expression given in the function? F(3)=x²+7
The required solution of the given expression is F(3)=16.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
The given in the function
F(x)=x²+7
According to given question we have
The function
F(x)=x²+7
At x=3 we get
F(3)=3²+7
F(3)=9+7
F(3)=16
Therefore, the required solution of the given expression is F(3)=16.
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(-5,8)(9,29) find the slope
Answer:
3/2
Step-by-step explanation:
29-8=21
9-(-5)=14
21/14 =3/2
How do you know what number is missing in the
number sentence below?
24 321 = 20 000 +
+300+
+1
A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner. The missing numbers in the given number sentence are 4000 and 20.
What is Number system?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given number is
24321
This we can express in standard form as,
20000+4000+300+20+1.
The given expression is 20 000 +x+300+y+1.
If we compare the above expression with standard form of 24321 we get the values of x and y. so x is 4000 and y is 20.
The missing numbers in number sentence are 4000 and 20.
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Mika worked 10 hours more than Todd last month. If Mika worked 5 hours for every 3 hours that Todd
worked, how many hours did they each work?
(round answers to 1 decimal place)
Mika worked
Todd worked
hours
hours
Answer:
Mika worked for 25 hours.
Todd worked for 15 hours.
what's question 9? NEED ANSWER
Answer
I disagree
she said that the square root of 100 and of 121 is 4 and 5
the square root of 100 is 10 and the square root of 121 is 11.
I need help please quick
Answer:
Step-by-step explanation: These two angles are congruent because most of the points are opposite of each other. For example Angle R is congruent to Angle V and Angle T is congruent to Angle U. Another thing about vertical angles is that they must always equal each other.
The coordinates below represent rotations. Use what you’ve learned today to describe what type of rotation occurred
Type of rotation of Anticlockwise and clockwise .
A point in coordinate geometry can be rotated through 180 degrees around the origin by drawing an arc with a radius equal to the distance between the provided point's coordinates and the origin, and then extending an angle of 180 degrees at the origin.
The point must be rotated around the origin with regard to its location in the cartesian plane. It is nicely explained in the next part of the 180-degree rotation formula.
The formula for 180-degree rotation of a given value is as follows: if R(x, y) is a point that has to be rotated around the origin, then coordinates of R(x, y) .
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100 points.
A teacher is assessing the correlation between the number of hours spent studying and the average score on a music test. The table shows the data:
Number of hours spent studying
(x) (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4)
Score on music test
(y) (60, 62, 64, 66, 68, 70, 72, 74, 76)
Part A: Is there any correlation between the number of hours students spent studying and the score on the music test? Justify your answer.
Part B: Write a function that best fits the data.
Part C: What does the slope and y-intercept of the plot indicate?
Part A: Yes, there is a correlation between the number of hours students spent studying and the score on the music test because As we increase the hours of studying by 0.5 hours, then the music score increases by 2.
Part B: A function that best fits the data is; y = 60 + 4x
Part C: The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.
How to find the correlation of line of best fit?We have given the table below showing the data:
Number of hours spent studying (x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score on music test (y) 60 62 64 66 68 70 72 74 76
A) As we increase the hours of studying by 0.5 hours, then the music score increases by 2.
B) The function which best fits the data for the correlation from the above is; y = 60 + 4x
C) The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.
The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.
The y-intercept gives the music score when the number of hours spent on studying is zero.
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A garden table and a bench cost $863 combined. The garden table costs $87 less than the bench. What is the cost of the bench?
Answer:
The bench costs $388.
Step-by-step explanation:
Let the cost of the bench be x
The cost of the garden table = x + 87
x + (x + 87) = 863
2x + 87 = 863
2x = 776
x = 388
The bench costs $388 and the garden table costs 388 + 87 = $475
475 + 388 = 863
A cube with sides 11 inches long is covered with a coat of fiberglass 0.1 inch thick. Use differentials to estimate the volume of the fiberglass shell.
The volume of the fiberglass shell is approximately __ in^3.
The volume of the fiberglass shell is nearly = 508.2 in³
What exactly is volume?Volume is just a three-dimensional quantity used to determine a solid shape's capacity. It indicates that the volume of a closed figure decides how much of three-dimensional space it can occupy.
What is the definition of volume and an example?The capa.city of an object is measured by its volume. A cup's volume is 100 ml if it can carry 100 ml of water higher than or equal to the brim. A 3-dimensional object's volume can alternatively be described as the amount much space it takes up.
According to the given data:Cube side are 11 inches.
cube is covered with a coat of fiber glass 0.1 inch
need to find the volume of fiberglass.
area of cube = 6(11)²
= 6(121)
= 726 inch².
thickness of fiberglass = 0.7 inch.
dv ≅ ads
= 726(0.7)
= 508.2 in³
The volume of the fiberglass shell is nearly = 508.2 in³.
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-22 + (-10) + 15 I don’t know how to solve this problem
The answer is - 17
here, we have to apply BODMAS rule
given ,- 22 + (10) = 15
= - 22 - 10 + 15
= -32 + 15
= - 17
BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.
B=Brackets
O=Off
D=Division
M=Multiplication
A=Addition
S=Subtraction
Achilles is a mathematician who invented BODMAS. It is a mnemonic that helps us remember how to evaluate mathematical operators in a mathematical statement involving more than one mathematical operation.The four basic Mathematical rules are addition, subtraction, multiplication, and division.
Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.
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Can someone help with this problem?✨
The equation of a line that passes through the given point (4, 3) and is perpendicular to y = 2x + 2 is given by: y = -x/2 + 5.
What is a slope?The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represent the slope.c represent the intercept.y = mx + c ≡ y = 2x + 2
m₂ = 2
For perpendicularity, we have:
m₁ × m₂ = -1
m₁ × 2 = -1
m₁ = -1/2.
Next, we would use the point-slope form to write the equation of this line at point (4, 3):
y - y₁ = m(x - x₁)
y - 3 = -1/2(x - 4)
y - 3 = -x/2 + 2
y = -x/2 + 2 + 3
y = -x/2 + 5.
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Complete Question:
Write an equation for a line perpendicular to y = 2x + 2 and passing through the point (4, 3).
In the cost function below, C(x) is the cost of producing x items. Find the average cost per item when the required number of items is produced.
C(x)x
a. 200 items b. 2000 items c. 5000 items
Solve 8x − 2(x + 1) = 7x + 8 (4 points) x = 6 x = −6 x = 10 x = −10
Answer:
x = −10
Step-by-step explanation:
8x−2(x+1)=7x+8
Step 1: Simplify both sides of the equation.
8x−2(x+1)=7x+8
8x+(−2)(x)+(−2)(1)=7x+8(Distribute)
8x+−2x+−2=7x+8
(8x+−2x)+(−2)=7x+8(Combine Like Terms)
6x+−2=7x+8
6x−2=7x+8
Step 2: Subtract 7x from both sides.
6x−2−7x=7x+8−7x
−x−2=8
Step 3: Add 2 to both sides.
−x−2+2=8+2
−x=10
Step 4: Divide both sides by -1.
−x/−1 = 10/−1
x=−10