A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.
B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.
What is an algebraic expression?An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.
While equations show the equality of expressions, algebraic expressions merely state values.
Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.
Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.
The total weight loss over time = 5¹/₂ pounds
The constant rate of weight loss = ¹/₂ pounds per week
The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).
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Which expression can be used to find the
surface area of the triangular prism?
4-2+3.2+5.2
2
2.3.4+4-2+3·2+5-2
1/2-3-4) -
2
+4-2+3.2+5.2
3.4+4-2+3-2+5-2
2
4 ft
4 ft
3 ft
3 ft
5 ft
2 ft
5 ft
2 ft
The expression used to find the surface area of the rectangular prism is given as follows:
S = 2 x (1/2 x 3 x 4) + 4 x 2 + 3 x 2 + 5 x 2.
How to obtain the surface area?
The prism is composed as follows:
The area of each component is given as follows:
Two right triangles of 4 ft and 3 ft: 2 x 0.5 x 4 x 3.One rectangle of dimensions 2 ft and 5 ft: 2 x 5One rectangle of dimensions 3 ft and 2 ft: 3 x 2.One rectangle of dimensions 3 ft and 4 ft: 3 x 4.The surface area is given by the addition of all these areas.
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6(2x²-5) = [?]
x = -3
Answer:
Below
Step-by-step explanation:
Put ' - 3' into the equation where 'x' is and compute
6 ( 2(-3)^2 -5) =
6 ( 2*9 -5)
6 ( 18-5)
6(13) = 78
Estimate the following difference by replacing each fraction with 0, 12
, or 1.
7/8−6/11
If we substitute so every tiny proportion with 0, 1, or 12, the approximate distinction among 7/8 and 6/11 is then equal to 0.
What is a difference example?the end result of subtracting two numbers. the difference between two numbers. Example: Subtract five to get the difference between eight and three.
We can substitute each percentage with either a 0, 1, or 12 to calculate the difference between 7/8 and 6/11.
We can round up to one because we know that 7/8 is larger than 1/2 but much less over 1.
For 6/11, we can round up to 1 since we know it is larger than 1/2 but a little less than 1.
As a result, we can calculate the difference as follows:
7/8 - 6/11
= 1 - 1
= 0
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Rhea wants to purchase a new home house. The house on main street requires a $10,000 down payment and will be a $900 a month on the loan. the other house she likes on Empire Road who has a $4000 down payment and is $1050 per month. Which house has a greater rate of change and what is it? Which house had a greater initial value and what is it?
Answer:
Step-by-step explanation:
First, we'll write the cost equations for each house, using the number of months since the initial purchase as the independent variable X:
For the house on Main Street:
Cost = 900X + 10,000
For the house on Empire Road:
Cost = 1050X + 4000
Next, we'll find the rate of change for each house by finding the slope of the respective cost equation:
The slope of the cost equation for the house on Main Street is 900. This means that for every month that passes, the cost of the house will increase by $900.
The slope of the cost equation for the house on Empire Road is 1050. This means that for every month that passes, the cost of the house will increase by $1050.
Now that we have found the rate of change for each house, we can compare them to determine which house has the greater rate of change:
Since the slope of the cost equation for the house on Empire Road is greater than the slope of the cost equation for the house on Main Street (1050 > 900), the house on Empire Road has a greater rate of change.
Finally, we can compare the initial values of each house by comparing the y-intercepts of the respective cost equations:
The y-intercept of the cost equation for the house on Main Street is 10,000, which means that the initial cost of the house is $10,000.
The y-intercept of the cost equation for the house on Empire Road is 4000, which means that the initial cost of the house is $4,000.
Since the y-intercept of the cost equation for the house on Main Street is greater than the y-intercept of the cost equation for the house on Empire Road (10,000 > 4,000), the house on Main Street has a greater initial value.
Justifying a Claim Based on a Confidence Interval for a Population Proportion
Based on the simulation, what proportion of the 95 percent confidence intervals capture the population proportion of 0.3? Explain how you determined your answer.
Based on the simulation, we can say that, 95% of proportion of the 95 percent confidence intervals capture the population proportion of 0.3.
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.
If we say that the confidence interval is A% for a certain parameter like proportion, mean, standard deviation, etc. to be fall within a range of x and y, then this can be interpreted as that we are A% confident that the parameters fall within x and y.
In other words, A% of the intervals capture the parameters.
Therefore, here, we can say that, 95% of the 95% confidence intervals will capture the population proportion of 0.3.
Hence 95% of proportion of the 95 percent confidence intervals capture the given proportion.
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A toy is in the form of a cone mounted on a hemisphere of the same diameter. the radius of the base is 5cm and height of the cone is 12cm
Answer:
Step-by-step explanation:
Given the radius of the base of the cone is 5 cm and the height of the cone is 12 cm, we can find the volume of the toy as follows:
Volume of the cone:
The volume of a cone can be found using the formula: V = (π * r^2 * h) / 3, where r is the radius and h is the height of the cone.
Plugging in the values, we get:
V = (π * 5^2 * 12) / 3 = 100π cm^3
Volume of the hemisphere:
The volume of a hemisphere can be found using the formula: V = (4/3) * π * r^3, where r is the radius of the hemisphere.
Plugging in the values, we get:
V = (4/3) * π * 5^3 = (4/3) * π * 125 = 500π / 3 cm^3
Total volume of the toy:
The total volume of the toy is equal to the sum of the volume of the cone and the volume of the hemisphere:
V = 100π + 500π / 3 = (100 + 500 / 3) * π = 600π / 3 cm^3
So, the total volume of the toy is 600π / 3 cubic centimeters.
please help!!!!!
6 wholes and 1/2—1 wholes and 1/3=
The value of 6½ - 1⅓ is 5 ⅙
What are fractions?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
To solve 6½ - 1⅓ ;
we make the mixed fraction improper fraction
= 13/2 - 4/3
= (39-8)/6
= 31/6
= 5 1/6
therefore The value of 6½ - 1⅓ = 5 1/6
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Step-by-step explanation:
[tex]6 \frac{1}{2} - 1\frac{1}{3} = 5 \frac{1}{6} [/tex]
The names of the months of the year are cut from a calendar and put into a bag. A month with more than 5 letters in its name is drawn. What is the probability of the complement of the event? Express your answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
There are 12 months in a year, and 7 of them have more than 5 letters in their names (July, August, September, October, November, December, and January).
The complement of the event is drawing a month with 5 or fewer letters in its name. There are 5 months with 5 letters in their names (May, March, April, June, and August), and 2 months with 4 letters in their names (July and June). Therefore, there are 7 months with 5 or fewer letters in their names.
The probability of drawing a month with 5 or fewer letters in its name is 7/12. The probability of the complement of the event (drawing a month with more than 5 letters in its name) is 1 - 7/12 = 5/12.
Therefore, the probability of the complement of the event is 5/12.
If yall ain't gotta show work just put 5/12 that's the answer the person with the long paragraph
The square footage and monthly rental of 10 rental of 10 similar one-bedroom apartments yield the linear regression y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. Grace can afford $1,500 per month rent. Using the equation, what size apartment should she expect to be able to rent for that price? Explain work in a sentence. :)
Answer:
Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.
Step-by-step explanation:
The given linear regression equation is y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. To find the size of the apartment Grace can expect to rent for $1,500 per month, we can substitute y with 1,500 in the equation and solve for x:
1,500 = 0.775x + 950.25
0.775x = 1,500 - 950.25
0.775x = 549.75
x = 710.32
Therefore, Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.
3x + 6 = 8x - 11, what is the value of 10x + 2
Answer:
36
Step-by-step explanation:
3x+6= 8x-11
3x-8x= -11-6
-5x= -17x
x= 3 2/5
10x+2= 10(3 2/5)+2
= 34+2
= 36
this is kinda complex ngl could any high schoolers help me? this is the problem.
Solve for
a
aa.
Give an exact answer.
3
+
0.5
(
4
a
+
8
)
=
9
−
2
a
3+0.5(4a+8)=9−2a. A= ?
Answer:
a = 1/2
Step-by-step explanation:
You want the solution to 3 +0.5(4a +8) = 9 −2a.
SolutionIt usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.
3 +0.5(4a) +0.5(8) = 9 -2a
3 + 2a +4 = 9 -2a
7 +4a = 9 . . . . . . . . . add 2a
4a = 2 . . . . . . . . . subtract 7
a = 0.5 . . . . . . divide by 4
The value of a is 1/2.
__
Additional comment
The attached calculator output shows this value of 'a' satisfies the equation.
How to calculate MLB magic number?
The formula to calculate the magic number in MLB is: Magic number = 163 - (number of wins by leading team) + (number of losses by trailing team) - 1.
The "magic number" in Major League Baseball (MLB) represents the combination of wins by the leading team and losses by the trailing team required for the leading team to clinch a playoff spot. To calculate the magic number, follow these steps:
1. Determine the total number of games in the season. In MLB, this is typically 162 games.
2. Subtract the number of games in the season from 163. For example, 163 - 162 = 1.
3. Subtract the number of wins by the leading team from 163. For example, if the leading team has 90 wins, 163 - 90 = 73.
4. Add the result from step 2 to the result from step 3. For example, 73 + 1 = 74.
5. Finally, subtract the number of losses by the trailing team from the result of step 4. For example, if the trailing team has 80 losses, 74 - 80 = -6. In this case, the magic number is zero, meaning that the leading team has already clinched a playoff spot.
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An art teacher enlarged the area of a copy of a painting by 49%. Let d represent the
area of the original painting. The expression d+ 0.49d is one way to represent the area of the new painting. Write two additional expressions that will give the area of the new
painting.
The required two other expression are d + 49d/100 and 149d/100.
What is percentage?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
According to question:We have;
An art teacher enlarged the area of a copy of a painting by 49%. and d represent the area of the original painting.
Given expression is d+ 0.49d
New expressions are
1) d+ 0.49d
= d + 49d/100
2) d+ 0.49d
= d + 49d/100
= 149d/100
Thus, required two other expression are d + 49d/100 and 149d/100.
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how to find the exact value of a trig function
The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.
How to find the exact value of a trig function?To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:
1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).
2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.
3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.
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five less than twice a number is a different number more than negative six in verbal phrase
The algebraic expression is 2x - 5 > 6
How to determine the expressionThe given equation can be written in a verbal phrase as:
"Twice a number, decreased by five, is equal to a number greater than negative six."
When represented as an expression, we have
Twice a number = 2xDecreased by 5 = 2x - 5 Number greater than 6 = 2x - 5 > 6Hence, the expression is 2x - 5 > 6
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y=x-6 and y=-x-2 graph the system then right a solution if there is one
Answer: To graph the system of linear equations, you can plot the two lines on the same coordinate plane and look for the point where they intersect. If they intersect, that point represents the solution to the system.
The equation y = x - 6 can be written in slope-intercept form, y = mx + b, where m = 1 and b = -6. The equation of the line will be y = x - 6.
The equation y = -x - 2 can be written in slope-intercept form, y = mx + b, where m = -1 and b = -2. The equation of the line will be y = -x - 2.
Plotting these two lines on the same coordinate plane, we can see that they intersect at the point (2, -4). This means that there is one solution to the system of equations: (2, -4).
Step-by-step explanation:
for every 10 clovers that lucy picked, 3 of them had four leaves, while the others only had three leaves. in total, lucy picked 100 clovers. if her pattern continued, how many three-leaf and four-leaf clovers would lucy have?
how many of each clover would she have if she picked 200 clovers?
I need help! first to answer and the best answer will get 100 point and get to get 5 more if it is the best
Answer:
100 = 30 (four-leaf) + 70 (three-leaf);200 = 60 (four-leaf) + 140 (three-leaf).--------------------------------------
Every 3 clovers out of 10 have four leaves and the rest 7 have three leaves.
This gives us the ratio of clovers with four leaves by the total number:
3/10 or 0.3If the total number is 100, then Lucy has:
100*3/10 = 30 four-leaf and 70 three-leaf cloversIf there are 200 clovers, then the number of four-leaf clovers is doubled:
30*2 = 60 and the number of three-leaf clovers is70*2 = 140What is the equation of the line with slope -5 and y-intercept 6 in slope-intercept form?
Answer:y=-5x+6
Step-by-step explanation:
1,530÷34 how to do it
Answer:It is 45
Step-by-step explanation:Take 1,530 and divid it by 34 using a calculator.
What is an entire group of objects from which data can be collected
Typically, the group of objects in which data is collected from is called the population
pls help i don’t understand how to graph
Answer:
Slope: [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]
y-intercept: [tex]\boxed{-1}[/tex]
Equation: [tex]\boxed{\bf{y=-\dfrac{1}{3}x - 1}}[/tex]
The two boxes at the bottom are asking you to repeat the above information:
the slope is [tex]\bf \boxed{-\dfrac{1}{3}}[/tex] the y-intercept is [tex]\boxed{-1}[/tex]
Step-by-step explanation:
Actually, you don't have to graph the equation since the graph is already provided
You have to answer the questions based on the provided graph
To find slope
1. Take any two well=defined points on the graph:
We can see that point (0, -1) which has x value at 0 and y-value 1 unit down is a distinguishable point. Let's call this point P1Another point is (3, -2). Let's call this point P22. Find the difference in y-values between P2 - P1. This called rise
rise = P2 v-value - P1 y-value = -2 - (-1) = -2 + 1 = - 1
3. Find the corresponding difference in x-values: P2 - P. This is called run
4. The slope is computed as rise/run = - 1/3
To find y-intercept
Just note where the line crosses the y-axis and the y-value corresponding to that would be the y-intercept
This is also the y-value at which x = 0
Looking at the graph we see that the line crosses(intercepts) the y-axis at y = - 1
So y-intercept = - 1
To write the equation
The equation of the line is
y = mx + b
where
m = slope
b = y-intercept
So the equation of this particular line is
[tex]\bf{-\dfrac{1}{3}x - 1}[/tex]
What are the first 10 Pythagorean triples?
The first 10 Pythagorean triples are: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65).
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The first 10 Pythagorean triples, listed in ascending order of their hypotenuse lengths, are (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65). There are infinitely many Pythagorean triples, and they have important applications in mathematics, physics, and engineering.
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Which expression can be used to find the value of the expression shown below?
1,284 ÷ 4
A (1,200 ÷ 4) × (84 ÷ 4)
B (1,200 ÷ 4) ÷ (84 ÷ 4)
C (1,200 ÷ 4) + (84 ÷ 4)
D (1,200 ÷ 4) - (84 ÷ 4)
Estelle has $300 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year?
$15 is the interest on the amount saved in a year
Calculating the simple interest on a sum of moneyThe formula for calculating simple interest is expressed according to the equation below:
I = PRT
where:
P is the principal = $300
R is the rate = 5% = 0.05
T is the time = 1 year
Substitute to have:
I = 300 * 0.05 * 1
I = $15
Hence the interest that she will earn in a year is $15
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Find the 59th term of the arithmetic sequence 26, 17, 8,
The 59th term of the given arithmetic sequence, is -496
What is an arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called the common difference of that arithmetic progression.
Given that, an arithmetic sequence 26, 17, 8, we are asked to find the 59th term,
nth term of an arithmetic sequence, is given by :-
aₙ = a₁+(n-1)d
Where n is the asked term, d is the common difference,
Here d = 17-26 = 8-17 = -9
Therefore,
a₅₉ = a₁+(59-1)(-9)
a₅₉ = 26+58×(-9)
a₅₉ = -496
Hence, the 59th term of the given arithmetic sequence, is -496
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[tex]456.232 ÷ 4[/tex]pls help me
Answer:
Step-by-step explanation:
$\frac{456.232}{4}$
Drag and drop numbers into the boxes to complete the expanded form of 916.408
The expanded form of 916.408 can be written as:
(9 x 100) + (1 x 10) + (6 x 1) + (4 x 0.1) + (8 x 0.01)
What is expanded form?Expanded form is a way of writing a number that shows the place value of each digit in the number. In expanded form, a number is expressed as the sum of individual terms, each representing a digit in the number multiplied by its place value.
For example, the number 356 can be written in expanded form as:
3 x 100 + 5 x 10 + 6 x 1
Expanded form can be used to better understand the structure of numbers and how place value works.
So, the numbers should be placed as follows:
(9 x 1,000) + (1 x 100) + (6 x 10) + (4 x 1) + (8 x 0.1)
Therefore, the correct order is:
1000, 100, 10, 1, 0.1
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 5 liters of synthetic oil. In order to make 855 liters
of Petrolyn oil, how many liters of natural oil are needed?
Using the concept of proportions and ratios, 684L of natural oil is required to produce 855L of Petrolyn oil.
What is ProportionsProportions are mathematical statements that express the equality of two ratios. A ratio is a comparison of two values, often written as a fraction. For example, if you have 5 apples and 2 bananas, the ratio of apples to bananas can be written as 5/2. A proportion is an equation that sets two ratios equal to each other, such as:
a/b = c/d
In this problem, we need to find the ratio or simply equate and calculate how many liters of natural oil are needed
4L of natural oil = 5L of synthetic oil
xL of natural oil = 855L
cross multiply both sides and solve for x
x = (855 * 4) / 5
x = 684L
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Which of the following is not a characteristic of the normal distribution?1.The total area under the curve is 1.02. The two tails of the curve extend indefinitely3. The value of the mean is always greater than the value of the standard deviation4.The curve is symmetric about the mean
" The value of the mean is always greater than the value of the standard deviation" is not a characteristic of the normal distribution
The curve of a normal distribution is known as the bell curve. The curve in statistical analysis represents the occurrence of some particular result as a product of the experiment. The normal curve is always symmetrical. This implies that the results of the trials will produce results near the mean value of the distribution.
Characteristics of a normal distribution involve:
1. The total area beneath the symmetric curve is 1: Since the area under the curve represents the chances of all the experiments; hence the summation must be 1.
2. The two tails of the curve extend indefinitely: The tails of the normal distribution never touch the horizontal axis; it is extended indefinitely.
4. The curve is symmetric about the mean: In a normal curve, the mean value of the distribution lies in the centre dividing the distribution curve into two symmetric parts.
Not a characteristic of a normal curve:
3. The value of the mean is always greater than the value of the standard deviation. The mean of the data can be negative as well as positive, but the value of the standard deviation is always positive. The small value of standard deviation implies the presence of more clustered data around the mean. The large value of the standard deviation indicates that the data is more spread out.
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PLEASE HELP ME!! I NEED THIS DONE FAST.
What is the common ratio of the following geometric sequence? 6, 4, 8/3, 16/9,...
a. r=2
b. r=2/3
c. r=3/2
d. r=-2
Answer:
b
Step-by-step explanation:
T2÷T1=r and T3÷T2=r and T4÷T3=r