The equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
The inspector at a bottling plant checks 25 bottles, and two bottles do not pass inspection.
To find the amount of sports drinks in milliliters that pass inspection, we can subtract the amount in the two bottles that do not pass inspection from the total amount in all 25 bottles.
Let x be the amount of sports drinks in milliliters in each bottle.
The expression for the milliliters of sports drink that pass inspection is = 25x - 2x
Now, simplifying the expression, we get,
25x - 2x = (25-2)x = 23x
Hence, the equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
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The complete question is -
The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drinks. Write an expression for the milliliters of sports drink that pass inspection. Then simplify it to create an equivalent expression.
For the translation below, give the vertices of ABC
Answer:
see explanation
Step-by-step explanation:
A translation of [tex]T_{(5,2)}[/tex] means
add 5 to the original x- coordinate and add 2 to the original y- coordinate.
A (1, - 2 ) → A' (1 + 5, - 2 + 2 ) → A' (6, 0 )
B (- 3, - 3 ) → B' (- 3 + 5, - 3 + 2 ) → B' (2, - 1 )
C (3, 5 ) → C' (3 + 5, 5 + 2 ) → C' (8, 7 )
The statement, 81:135 = 36:60 is a proportion.
If a and b are non-zero numbers and c = 0, then a/c = b/c is a proportion.
State whether the following statements are proportions or not. If it is a proportion, then prove by the definition of proportion. If not, then solve the correct value of x. Be sure to show the complete steps in solving for x.
a) The value of x from the proportion is x = 2/5
b) The value of x from the proportion is x = 8
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
a)
3 / ( x + 2 ) = ( 5 / 4 ) be equation (1)
On simplifying the equation , we get
Multiply by ( x + 4 ) on both sides of the equation , we get
( 5/4 ) ( x + 2 ) = 3
Multiply by 4 on both sides of the equation , we get
5 ( x + 2 ) = 12
On further simplification , we get
5x + 10 = 12
Subtracting 10 on both sides of the equation , we get
5x = 2
Divide by 5 on both sides of the equation , we get
x = 2/5
Therefore , the value of x is 2/5
b)
( x + 2 ) / 5 = ( x - 2 ) / 3 be equation (2)
On simplifying the equation , we get
Multiply by 5 on both sides of the equation , we get
( x + 2 ) = 5( x - 2 ) / 3
Multiply by 3 on both sides of the equation , we get
3 ( x + 2 ) = 5 ( x - 2 )
On further simplification , we get
3x + 6 = 5x - 10
Subtracting 3x on both sides of the equation , we get
2x - 10 = 6
Adding 10 on both sides of the equation , we get
2x = 16
Divide by 2 on both sides of the equation , we get
x = 8
Therefore , the value of x is 8
Hence , the proportion is solved
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E is the encoding matrix.
Use E to decode the coded message matrix.
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
What is an encoding matrix?It should be noted that a type of code, that is extremely difficult to break, and one which makes use of a large matrix to encode a message is the encoding matrix.
Here, the receiver of the message decodes it by using the inverse of the matrix. In their case, the first matrix is the encoding matrix and the inverse is the decoding matrix.
To decode the message, we simony have to take the string of coded numbers and then multiply it by the inverse of the matrix in order to get the original string of numbers.
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
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the difference between the squares of two positive integers is 2009. what is the maximum possible difference between these two integers?
Answer:
Step-by-step explanation:
i dont knpw
Javier is ordering a sandwich from a deli. There are 3 types of meat to choose from and 4 cheeses, and Javier must pick one of each. How many different sandwiches can Javier order?
The number of different sandwiches that Javier can order, given the number of types of meat and cheeses, is 12 sandwiches.
How to find the number of sandwiches ?Javier has 3 choices for the type of meat and 4 choices for the cheese, so the total number of different sandwiches he can order is the product of the number of choices for each ingredient.
To find the total number of different sandwiches, you can multiply the number of meat choices by 4 the number of cheese choices.
The number of sandwiches Javier can order are:
= 3 x 4
= 12 sandwiches
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a. Are the integers closed under addition and subtraction? In other words, when you add or subtract two integers, is the result always an integer? Justify your response.
b. Give a counterexample to show that the whole numbers are not closed under subtraction.
Answer:
a. The result is always an integer because integers are not fractions or decimals.
b. Sorry I don't have an answer for b i don;t know what that means. :(
a basket holds at most 14 pounds of apple and oranges. there are atleast 3 pounds of apples in the basket
The point (4, 3) is a viable solution.
What are systems of inequalities?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
Given:
A basket holds at most 14 pounds of apples and oranges.
There are at least 3 pounds of apples in the basket.
This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.
That means, we have the system of inequalities,
x + y ≤ 14,
x ≥ 3
Option B and C are discarded.
And y ≥ 0.
Option A is also discarded.
Substituting (4, 3),
x + y ≤ 14,
7 ≤ 14.
Therefore, (4, 3) is a solution.
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The complete question:
A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?
Round 0.814 to the nearest hundredth.
Answer: 0.81
Step-by-step explanation:
We will look at the thousands place to round to the hundredth. If the thousands place is at or above 5, we will round up. If it is 4 or below, we will round down.
[tex]\displaystyle 0.814\\0.81\boxed{4}\\\\4 < 5\\\\0.81[/tex]
expresa con una fracción cada situacion. a) la temperatura ambiente es un tercio bajo cero
Answer:
a) La temperatura ambiente es -1/3.
A small town has two local high schools. High School A currently has 800 students
and is projected to grow by 35 students each year. High School B currently has 550
students and is projected to grow by 85 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine the interval of years, t, for which High School A will have more
students than High School B.
Answer:
T < 5
Step-by-step explanation:
High School A: A(t) = 800 + 35t
High School B: B(t) = 550 + 85t
To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).
So, we need to solve the inequality A(t) > B(t)
800 + 35t > 550 + 85t
250 > 50t
t < 5
Therefore, High School A will have more students than High School B for the first five years.
The interval of years, t, for which High School A will have more students than High School B is t < 5
4X+3 2x+9 linear pairs of angles
Answer:
x = 28°
Step-by-step explanation:
4x+3 and 2x+9 are on a straight line, so the sum is 180°, we solve with an equation
4x + 3 + 2x + 9 = 180°
6x + 12 = 180
6x = 180 - 12
6x = 168
x = 168 : 6
x = 28°
-------------------------------
check4 × 28 + 3 + 2 × 28 + 9 = 180 (remember PEMDAS)
112 + 3 + 56 + 9 = 180
180 = 180
Substitute each variable to determine whether the inequality statement is true or false j/6 >3 if j =24
The inequality statement j/6 > 3 is true when j = 24.
How to Determine if an Inequality Statement is True?To substitute the value of j into the inequality statement, you will replace j with 24 and then simplify the expression.
j / 6 > 3
24 / 6 > 3
Simplifying, we get
4 > 3
Since 4 is greater than 3, the inequality statement is true.
You can also check by multiplying both sides of inequality by 6
j > 18
24 > 18
This is true because 24 is greater than 18. Therefore, the inequality statement j/6 >3 if j =24 is true.
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Learning Task 1: Solve for n. Write your answer in your notebook.
1. 7. 26 x 0. 22 =n
2. 17. 92 x 0. 64 = n
3. 7. 65 x 0. 85 =n
4. 36. 20 x 0. 05 = n
5. 31. 85 x 0. 91 = n
The solutions of each expression for n are given as follows:
1. n = 1.5972.
2. n = 11.4688.
3. n = 6.5025.
4. n = 1.81.
5. n = 28.9835.
How to solve the expressions?
All the five expressions in this problem are multiplication operations involving two decimal numbers.
Hence, to obtain the solution for n of each expression, we must simply apply the multiplication operation of the two decimals, using a calculator.
The result of each expression is given at the beginning of the answer.
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how many different batting orders can a baseball coach create from a team of 15 players, if there are nice positions to fill?
15 x 14 x 13 x ... x 3 x 2 x 1 is the possible batting orders.
A baseball coach can create 15! (15 factorial) different batting orders for a team of 15 players if there are nine positions to fill in the lineup. This is because, for the first spot in the lineup, there are 15 options, for the second spot there are 14 options, and so on, leading to 15 x 14 x 13 x ... x 3 x 2 x 1 possible batting orders.
The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
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a cat's heart beats approximately 45 times and 15 seconds. at this rate how many times does the cat's heartbeat per second?
help.
Answer:
Step-by-step explanation:
For the cat's heart to beat 45 times in 15 seconds
for 1 second, we must divide 45 by 15
the answer will be 3 beats per second
The length of Ms. Sheahan's office is
3x yards and the width is x + 4 yards.
Write a polynomial that represents the
area. Find the area if x = 1 yd.
Answer:
see explanation
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
= 3x(x + 4) ← distribute parenthesis by 3x
A = 3x² + 12x
when x = 1 , then
A = 3(1)² + 12(1) = 3 + 12 = 15 yd²
you go out to eat with your family. the subtotal on your bill is $45.50 you must pay a 8% sales tax. what is your bill INCLUDING sales tax? please help
an online company sells and ships T-shirts. The company has to pay extra to ship a package that weighs over 13 oz. Before putting any T-shirts in the box, the package weighs 1.5 oz. Each shirt weighs 5 oz. Which number line best represents the possible number of shirts the company can ship in a package without playing extra for shipping?
The number line inequality that best represents the possible number of shirts the company can ship in a package without playing extra for shipping is given by the image presented at the end of the answer.
How to solve the inequality?Before putting any T-shirts in the box, the package weighs 1.5 oz. Each shirt weighs 5 oz, hence the total weight function for x shirts is given as follows:
y = 1.5 + 5x.
The maximum weight without needing to pay extra is of 13 ounces, hence the inequality is given as follows:
5x + 1.5 <= 13
x <= 11.5/5
x <= 2.3.
Which can be simplified as:
x <= 2.
(as the number of shirts is a countable amount).
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Eva deposited $50 in an account earning 10% cents interest compounded annually. to the nearest cent, how much interest will she earn in 2 years
Eva will earn $10.50 interest.
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
Eva deposited $50 in an account earning 10% interest compounded annually.
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 50.00(1 + 0.1/1[tex])^{2}[/tex]
A = $60.50
Therefore, she will earn $10.50 of interest.
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a square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. what is the smallest possible value of the length of the side of the original square?
Answer: I need help with this what is the answer
Step-by-step explanation:
(-xy)^2 * (2x^9y^5)^4
please show me the steps on how to get the answer
Answer: 16x^38y^22
Step-by-step explanation:
Re-order terms so constants are on the left
(−xy)2(2x9y5)4(−)2(295)4
Distribute exponent
(−xy)2(2x9y5)4(−)2(295)4
Evaluate the exponent
(−1)2(xy)2⋅(2x9y5)4(−1)2()2⋅(295)4
Please help please help
For geometric shape no.4,∠1=26°,∠2=154°,∠3=26°,∠4=26°,
∠5=154°,∠6=154°,∠7=26°.
What are geometric shapes?
In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.
In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.
Now,
∠1+154°=180° -->∠1=26° (supplementary angles)
∠1=∠3 (opposite angles) -->∠3=26°
∠2+∠3=180°
∠2=154°
∠1=∠7 --->∠7=26°
∠7+∠6=180° (supplementary angles)
∠6=154°
∠5+∠7=180° (supplementary angles)
∠5=154°
∠4+∠5=180° (supplementary angles)
∠4=26°
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Formative REDO
1. Find the slope and y-intercept from the equation: y = -2x + 7
b=_
m=
2. Find the slope and y-intercept from the graph:
b=
m=
The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: y = mx + b
What is meant by slope?
Slope is a numerical representation of how inclined a line is with respect to the horizontal. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment.A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.The foundation of differential calculus is the idea of a slope. The rate of change for non-linear functions varies along the curve.Both the slope and the y intercept can have a positive or negative value. Slope is defined as the y-axis divided by the x-axis.The slope-intercept form of a linear equation is: y = mx + b
Where m is the slope and b is the y-intercept value.
Therefore, for this equation y = -2x - 7
The Slope is: m = -2
The Y=Intercept is b = -7 (or)
slope and y-intercept from the graph: (0, -7)
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Question
True or False... (8, -7) is a solution to the inequality y<12x−9
The statement is true, the point (8, 7) is a solution to the inequality.
Is the statement true or false?Here we have the following statement:
"(8, -7) is a solution to the inequality y < 12x − 9"
To check if that is true, we just need to replace the values of the point on the inequality and check if the ienquaity becomes true.
We will get:
-7 < 12*8 - 9
-7 < 87
This is true, 87 is a number larger than -7, then the statement is true, (8, -7) is a solution of the inequality.
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
2x+4y=16
Answer:
Step-by-step explanation: I do these in 2 steps:
1. isolate the y term ----- 4y = -2x + 16
2. divide each term by the coefficient of the y-term
y = (-2/4)x + 4
y = (-1/2)x + 4
Paul won a race with a time of 71. 3 seconds.
This time, t, is to the nearest tenth of a second.
Complete the error interval due to rounding.
____________________ ≤ t < ____________________
The error interval due to rounding:
71.25 ≤ t < 71.35
Now, According to the question:
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
"Information available from the question"
Paul won a race with a time of 71. 3 seconds.
The time, t, is to the nearest tenth of a second.
So, Rounding off to nearest tenth
Rounded to the nearest 0.1 or the Tenths Place will be
The error interval due to rounding:
So, 71.25 ≤ t < 71.35
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Use Similar Polygons to Find x
Answer:
x = 8--------------------------
We know that corresponding sides of similar figures are proportional.
Thus we have equal ratios:
7x/9x = (8x - 1)/(10x + 1)Solve it for x:
7x/9x = (8x - 1)/(10x + 1) Cancel x on the left side as x ≠ 07/9 = (8x - 1)/(10x + 1) Cross- multiply7(10x + 1) = 9(8x - 1) Distribute70x + 7 = 72x - 9 Collect like terms72x - 70x = 7 + 9 Simplify2x = 16 Divide by 2x = 8 AnswerCody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days?
The correct explaination to calculate the total number of miles that Cody hiked in two days is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
First of all, we must know the formula of average speed. The formula is as follows -
Average speed = distance ÷ time
Using this formula, we can calculate distance for Saturday and Sunday and subsequently add the distance to find the number of miles that Cody hiked in two days.
For Saturday -
Distance = 1 × 5
Performing multiplication
Distance = 5 miles
For Sunday -
Distance = 3 × 2
Performing multiplication
Distance = 6 miles
Total distance hiked = 5 + 6
Performing addition
Total distance hiked = 11 miles
Thus, the correct explaination is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
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The complete question is -
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days? Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Subtract the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products. Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Add the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Subtract the two products.
Find two other points on the line passing through (1,5) and (3,-1)
Answer:
We can find two other points on the line passing through (1,5) and (3,-1) by using the slope-intercept form of a line: y = mx + b where m is the slope of the line, and b is the y-intercept.
To find the slope (m) of the line, we can use the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two given points: m = (-1 - 5) / (3 - 1) = -6 / 2 = -3
To find the y-intercept (b) of the line, we can use one of the given points and substitute the values of x, y and m into the equation y = mx + b.
Plugging in the coordinates of the point (1,5) and the value of m: 5 = -3(1) + b, b = 8
So the equation of the line is y = -3x + 8
We can use this equation and any x value to find two other points on the line. For example, if we choose x = -2, we get y = -3(-2) + 8 = 2
so the point (-2,2) is on the line.
If we choose x = 0, we get y = -3(0) + 8 = 8
so the point (0,8) is on the line.
So two other points on the line passing through (1,5) and (3,-1) are (-2,2) and (0,8)
If I helped you, could you please make my answer best?
Answer:
x + y = 4
m = -1
Step-by-step explanation:
(3 - 5) / (1 - (-1))
m = -2/2
(y - 5) = -1 × (x - (-1))
y - 5 = - x - 1 = 0
Please help I need the answers ASAP.
Answer:
Refer to the step-by-step
Step-by-step explanation:
∠1 and ∠2 lie in the alternate interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal angles.