The possible outcomes are the sample space of the game
The number of possible outcomes in the game is 3
Now, According to the question:
In the domain of Statistics, the number of possible outcomes for a given event help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.
How to determine the possible outcomes
The number of games is given as:
n = 2 i.e. 2 games to finish the season
In each game, the soccer team can either win, lose or tie.
So, we have the outcome of each game to be:
Outcome = {Win, Lose, Tie}
Count the outcomes
Count = 3
Hence, the number of possible outcomes in the game is 3.
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The given question is incomplete , complete question is:
Assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is in the game ____
Can you please help me with this question. The question is on the image
Total VAT imposed on the Hungarian Secret boxes by Hungarian Government during time of purchase is 6480 Hungarian Forint
What is VAT ?A consumption tax known as value-added tax (VAT) is imposed on products and services at every step in the supply chain where value is added, from the point of initial production to the point of sale.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
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.
The total cost of the Secret Boxes is 30480.
The VAT is 27 %
So, the price of the Secret Boxes without Taxex is x
Therefore ,
x + 27% of x = 30480
⇒ x + 27x/100 = 30480
⇒ 127x/100 = 30480
⇒ x = 24000
Total VAT imposed on the boxes = 30480 - 24000 = 6480
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dopamine 4 mcg/kg/min by continuous iv infusion for a client who weighs 64 kg. available is dopamine 400 mg in 250 ml of d5w. determine how many ml/hr to administer. round to the nearest tenth.
We should administer 2.05 ml/hr.
A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.
To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:
dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)
dose (mg/kg/min) = 0.004 mg/kg/min
Next, we need to calculate the total dose in mg/min. We can use the following formula:
dose (mg/min) = dose (mg/kg/min) x weight (kg)
dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min
Now we need to convert the dose from mg/min to ml/hr, using the following formula:
ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr
ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr
ml/hr = 2.048 ml/hr
To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.
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159.12 divided by 6.8 give evidence.
The value of the mathematical statement 159.12 divided by 6.8 is 23.4
How to determine the value of the statementfrom the question, we have the following parameters that can be used in our computation:
159.12 divided by 6.8
When represented using numbers and expressions, we have
159.12/6.8
Using a calculator, the value of the quotient is
23.4
Hence, the solution is 23.4
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a school group sells gift cards and gift wrap for a fundraiser. twenty cards and forty gift wraps sell for $160. ten cards and thirty gift wraps sell for $110. how much does each gift wrap cost
The problem has no solution, because gift card will have negative price .
Define the term "system of equations" ?A system of equations is a set of multiple equations with multiple variables, where the goal is to find the values of the variables that satisfy all the equations simultaneously. It can be solved using different methods such as substitution, elimination and graphing.
This problem can be solved by setting up a system of equations and solving for the variables.
Let x be the cost of each gift card and y be the cost of each gift wrap.
According to the problem statement, we know that:
20x + 40y = $160 (where 20 gift cards and 40 gift wraps sell for $160)
10x + 30y = $110 (where 10 gift cards and 30 gift wraps sell for $110)
We can use these equations to find the value of x and y. To solve the system of equations, we can use the method of substitution.
We can solve the first equation for x:
x = ($160 - 40y) / 20
Now we can substitute this expression for x into the second equation:
10(($160 - 40y) / 20) + 30y = $110
Simplifying this equation:
8y = $50
then we can divide both sides by 8 to get:
y = $6.25
So each gift wrap costs $6.25
We can check our answer by substituting it back into the first equation to make sure it is consistent with the given information.
20x + 40($6.25) = $160
20x + $250 = $160
20x = -$90
x = -$4.5
We can see that x is negative, which is not a possible solution.
Therefore, the problem has no solution, because it is not possible to have negative prices for the gift cards.
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I NEED HELP ASAP!!! 15 POINTS
The results of the multiplications are: 1) x²+6x-16 (2) x²+8x+15 (3) x²-2x-63 (4) 6x+x-15 (5) 4x²-17x-15 (5) x²+13x+42
How to multiply the brackets?The given equations are
1) (x+8)(x-2)
Opening the brackets to have and collecting like terms to have
x²-2x+8x-16
x²+6x-16
2) (x+5)(x+3)
Opening the brackets to have and collecting like terms to have
= x²+3x+5x+15
x²+8x+15
3) (x+7)(x-9)
Opening the brackets to have and collecting like terms to have
x²9x+7x-63
x²-2x-63
4) (2x-3)(3x+5)
Opening the brackets to have and collecting like terms to have
6x²+10x-9x-15
6x²+x-15
5) (4x+3)(x-5)
Opening the brackets to have and collecting like terms to have
4x²-20x+3x-15
4x²-17x-15
6) (x+7)(x+6)
Opening the brackets to have and collecting like terms to have
x²+6x+7x+42
x²+13x+42
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(Simple)......Classify the transformation pls
The transformation represented by the figure is (c) translation
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have the following
A figure and its translated image
When a shape is translated to form another, then the transformation is a translation
Hence, the transformation is translation
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A quantity with an initial value of 980 decays exponentially at a rate of 1% every 2 days. What is the value of the quantity after 5 weeks, to the nearest hundredth?
Answer:
An exponential decay function has the form y = a*b^(-kt) where a is the initial value, b is the base of the exponential function (in this case, 1 - the decay rate as a decimal), k is the decay rate and t is the time.
Given that the initial value is 980, the decay rate is 1% every 2 days and the time is 5 weeks. The first step is to convert the time to the same unit of time as the decay rate, in this case, days: 5 weeks * 7 days/week = 35 days.
The decay rate per day is 1/100 because 1% as a decimal is 0.01, so the decay rate per day is 0.01/2 = 0.005
Now we can plug in the values in the function:
y = 980 * (1 - 0.005)^(-0.005*35)
y = 980 * 0.995^(-17.5)
y ≈ 574.64
So, the value of the quantity after 5 weeks to the nearest hundredth is 574.64
It's worth noting that in this case, the base (1 - decay rate) is less than 1, which implies that the value of the quantity decreases over time.
I got this problem in edmentum, and i have no idea what i should be looking for. I answered 5 as a guess. i had no idea if i should be looking for an average or something else
The box plot given by the number of students read 8 books is the centre quartile which is 5.
Define the term quartile of the data?Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each. One kind of quantile is a quantile.
Q1, or the lower quartile, is another name for the first quartile. The number that falls in the middle of the lowest and middle numbers is this one.Second quartile: Also referred to as the median or Q2. This value sits in the middle, midway between the lowest and greatest numbers.Third quartile, or the upper quartile, is also referred to as Q3. The number that falls in the middle of the middle and highest numbers is this one.Thus, for the stated question.
The box plot given by the number of students read 8 books is the centre quartile which is 5.
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if you take an intelligence test three times within a week and get scores of 100, 75, and 125, the iq test is probably not:
If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not reliable. So the option 4 is correct.
A set of standardized tests or subtests created to measure human intellect result in a total score known as an intelligence quotient (IQ). When an intelligence test was given, a person's mental age score was calculated. This score was then divided by their chronological age, which was also expressed in years and months. The resulting fraction (quotient), which yielded the IQ score, was multiplied by 100.
Test results that measure intelligence are estimates of intelligence.
A vast range of item material can be found on the many distinct IQ test types. There are both verbal and visual test items. Test questions can range from being grounded on abstract reasoning issues to focusing on math, language, or general knowledge.
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If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not:
1. powerful.
2. accurate.
3. valid.
4. reliable.
10v + 11v I NEED HELP PLSSS
Answer:
21v
Step-by-step explanation:
Since it is the same variable you would just add them!!
10+11=21
10v+11v+21v
Rick paddles a kayak 20 miles upstream in 4 hours. The return trip downstream takes him 2. 5 hours. What is the rate that Rick paddles in still water? What is the rate of the current?
For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.
Let us consider 'x' be the rate at which Rick paddles in still water
'y' be the rate of the current
Distance covered while going in upstream = 20 miles
Time taken while going 20 miles upstream = 4 hours
Rate of upstream = 20 / 4
⇒ x - y = 5 miles /hours ___(1)
Distance covered while going in downstream = 20 miles
Time taken while going 20 miles downstream = 2.5hours
Rate of downstream = 20 / 2.5
⇒ x + y = 8 miles /hours ___(2)
Solve (1) and (2) we get,
x - y = 5
x + y = 8
2x = 13
⇒ x = 6.5miles per hour
y = x - 5
⇒ y = 1.5 miles per hour
Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.
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For each of the following research questions, determine whether an observational study, an experiment, or neither should be used to answer the question. Note - each term on the right may be used more than once or not at all. [Choose] chose What proportion of all college students in the United States have taken classes at a community college? Does an accelerated math program increase the success rates in transfer-level math? [Choose [Choose Are pregnant women who do not visit the doctor in the first trimester of their pregnancy more likely to have a low weight baby? Does oxidation of LDL cholesterol restrict the development of new neurons in the brain?
a. The first mentioned case is an Observational study, b. The second one is an Experiment, c. The same goes for the third case it is an observational study, d. And the fourth case is an Experiment.
In observational studies, researchers observe and record information about outcomes of interest without interfering with or controlling variables. Data on the proportion of community college students who successfully complete transfer-level English courses can be gathered and the data can be analyzed to provide answers to specific research questions.
The researcher must do this by contrasting her two sets of explanatory variables to see if there is a correlation between the explanatory and response variables.
If there is a causal relationship between two variables, researchers can observe plants and animals in new habitats and contrast them with their native habitats.
The relationship between consumption and LDL cholesterol oxidation is unclear, and experiments are required to determine whether eating simple carbohydrates increases LDL cholesterol oxidation.
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The question is -
For each of the following research questions, determine whether an observational study, an experiment, or neither should be used to answer the question. Note - each term on the right may be used more than once or not at all. Observational study What proportion of community college students successfully complete a transfer-level English course?
Experiment are non-elite soccer players less likely to develop arthritis of the hip or knee than elite soccer players. This is a question about the population of soccer players. The words "less likely in this research question require researchers to compare two groups of the explanatory variable to determine whether an association exists between the explanatory and response variables The researchers will then generalize the results to the population Observational study Does shifting flora and fauna to new habitats lead to the extinction of some species?
The word "lead" requires researchers to compare two groups of the explanatory variable to determine whether a cause-and-effect relationship exists between the explanatory variable and the response variables. Experiment Does the consumption of simple carbohydrates increase the oxidation of LDL cholesterol?
geometry i suck please help me please
Find m
The measure of ∠G is 48°.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure,
∠G and 48° are alternate exterior angles.
Alternate exterior angles are equal.
So,
∠G = 48°
Thus,
∠G = 48°
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How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
We assume that we have a plot given like the graph attached.
We have n points and we need to find How many of the 9 people listed in the scatterplot have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
So for this case we need to have the predicted value y^ and the real value y. We are going to put these two values and the difference
yi yi^ |yi - yi^|
157 161.5 4.5
163 163.1 0.1
175 167 8.0
171 170.5 0.5
173 172.5 0.5
173 174.3 1.3
172 176 4.0
183 178 5.0
178 180 2.0
So as we can see we have 4 points out of the 9 who satisfy the condition
|yi - yi^| >= 3.
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Janine sold 428 tickets for the school play. Student tickets were $3 and adult tickets were $5.
Janine’s total ticket sales were $1674. How many student tickets and how many adult tickets were sold ?
Solve this problem using a system of linear equations. Make sure you introduce the two variables
used and explain what they represent, write two equations using the two variables you have chosen,
solve the linear system using substitution OR elimination method, showing ALL steps, and write a
concluding statement in words.
The system of the equation is written as
x + y = 428
5x + 3y = 1674
the solution:
adult tickets is 195
students tickets is 233
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Janine sold 428 tickets for the school play
let the adult ticket be x and student ticket be yx + y = 428
Janine’s total ticket sales were $1674
Student tickets were $3 and adult tickets were $5
5x + 3y = 1674
The simultaneous equation
x + y = 428
5x + 3y = 1674
solving the equation by elimination method
x + y = 428 * 3
3x + 3y = 1284
5x + 3y = 1674
subtraction gives
-2x = -390
x = 195
substitute x = 195 into x + y = 428
195 + y = 428
y = 428 - 195
y = 233
hence adult tickets is 195, while students tickets is 233
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(10n^3*18n^2-2n-10)/(n+1) Synthetic Division
The expression for the synthetic division is 10n³ + 8n² -10 - 0
What is synthetic division?Synthetic division can be defined as a mathematical way to divide a polynomial by a given binomial x - c
Given that, c is a constant.
The steps to take in synthetic division;
Set up the synthetic divisionBring down the leading coefficient to the bottom rowMultiply c by the value just written on the bottom row Add the column created in step 3Repeat until doneGiven the polynomial;
(10n^3*18n^2-2n-10)/(n+1)
[tex]\sqrt[n + 1]{10n^3 + 18n^2 -2n - 10}[/tex]
- 1 coefficient of dividend
10 18 -2 -10
____-10_-8__10_________
10 8 -10 0
The quotient becomes;
10n³ + 8n² -10 - 0
Hence, the expression is 10n³ + 8n² -10 - 0
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The values in the table represent function A and B. Which statement about the 2 functions is true?
The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is presented as follows;
The y-intercept of the graph of A is equal to the y-intercept of the graph of BWhat is a linear relationship?
A linear relationship is a relationship that when plotted on the coordinate plane, produces a linear graph.
The first difference of the y-values in the data contained in the table for Function A are the same and equal to 6, therefore, the data for Function A is a linear relationship.
The slope of the graph of the values in Function A, [tex]m_A[/tex] is found as follows;
Slope of Function A, [tex]m_A[/tex] = (18 - 12)/(3 - 2) = 6
The slope of the graph of A is 6
The equation representing the relationship in function A in point-slope form is therefore;
y - 12 = 6·(x - 2)
y - 12 = 6·x - 12
y = 6·x - 12 + 12 = 6·x
The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x
The value c in the equation is 0 (c = 0). The y-intercept intercept of the graph of Function A is therefore, c = 0
The y-intercept of the graph of Function A is 0
The first difference of the data in the table of Function B is also a constant
The slope of Function B, [tex]m_B[/tex] = (5 - 1)/(1 - 0) = 4
The slope of the graph of B is 4
From the values in the table, the y-value at the y-intercept, which is the point where x = 0, is y = 1
The y-intercept of the graph of Function B is 1
The true statement is therefore;
The y-intercept of the graph of A is less than the y-intercept of the graph of B
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Janie wants to save 125,000 dollars over the next 8 years how much would she need to save each month to reach that goal?
Answer: 1,302$ per month.
Step-by-step explanation: 125,000 divided by 8 = 15,625. 15,625 divided by 12 = 1302
(I'M SO SORRY FOR GETTING IT WRONG THE FIRST TIME, I FORGOT TO DIVIDE BY 12)
HELP…………………………………………..
Answer:
24
Step-by-step explanation:
12*8*5 =480 current surface
double = 960
so make the 12 into 24 height.
done
asserion: 997 is the largest 3 digit prime number
reason: a positive integer n is a prime number if no positive integer less than or equal to √n divides n
The assertion that 997 is the largest 3-digit prime number is correct.
What is a prime number?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. In other words, it is a number that is divisible by only 1 and itself. To determine if a number is prime, one common method is to check if any positive integer less than or equal to the square root of the number divides the number.
In the case of the assertion that 997 is the largest 3-digit prime number, we know that 997 is a 3-digit number (999 being the largest) and we can check if any positive integer less than or equal to the square root of 997 divides 997. Since 997 is a prime number, it is not divisible by any positive integer less than or equal to 31 (the square root of 997). Therefore, we can conclude that 997 is a prime number and the largest 3-digit prime number.
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IM8~6. 2. 6 HOMEWORK
6-108. SEQUENCES OF TRANSFORMATIONS
a. A figure is rotated and reflected. What can you say about the new figure in relation to the
original figure?
b. A figure is translated, reflected, and then dilated. What can you say about the new figure in relation to the original figure?
When a figure is rotated and reflected, the new figure will be congruent to the original one, but different coordinate axis. When a figure is translated, reflected and dilated the image will be similar, but the scales will be different.
The original figure we transform is the pre-image and after transformation it is called image. Rotation is the transformation of an image when it is rotated through the Centre of axis. Reflection creates a mirror image of the original figure/ pre-image. Translation means the image is moved to a certain distance in the coordinate axis. Dilation is making an image bigger or smaller, the sides will be in ratio and thee will be a scale factor.
So if a image is rotated, reflected and translated, there will be changes in the coordinate plane, but no change in the size of the image. During dilation the size is varied.
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the perimeter of parallelogram is150cm if one of the sides is twice the other find the measure of all the sides of the parallelogram.
Answer: 25, 25, 50, 50
Step-by-step explanation: Hello! Because it is a parallelogram, there are two pairs of congruent sides. This means that if one of the sides is twice the size of the other, then the side congruent to the side that is twice the size of the smaller side is also twice the size of the smaller side.
Let's represent a as the two smaller sides and b as the two larger sides
2a = b, 2a + 2a = b + b, 1/2(b) = a
Since the parallelogram is 150 cm, you know that 100 + 50 = 150.
50 is half the quantity of 100 and both add up to 150.
You now know that a + a = 50 and b + b = 100
a = a and b = b.
Divide 50 and 100 by two to find the length of each side.
50/2 = 25, 100/2 = 50.
The lengths of each side of the parallelogram are: 25, 25, 50, 50.
How can I set up an equation to help solve this problem?
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{h}{2}=\cfrac{8}{h}\implies h^2=16\implies h=\sqrt{16}\implies h=4[/tex]
State the possible rational zeros for each function.
Then find all rational zeros.
ƒ(x) = 3x³ + 22x² +28x - 35
Answer:
no
Step-by-step explanation:
The possible rational zeros of ƒ(x) = 3x³ + 22x² +28x - 35 are the factors of -35 divided by the factors of 3. These are:
-35/1 = -35, -35/-1 = 35
-35/3 = -5, -35/-3 = 5
Using the Rational Root Theorem, we can now test these values to see if they are zeros of the function:
-35: 3(-35)³ + 22(-35)² + 28(-35) - 35 = -8,925 + 30,950 + -980 - 35 = -9,880 which is not a zero
35: 3(35)³ + 22(35)² + 28(35) - 35 = 42,875 + 30,950 + 980 - 35 = 74,770 which is not a zero
-5: 3(-5)³ + 22(-5)² + 28(-5) - 35 = -125 + -100 + -140 - 35 = -400 which is not a zero
5: 3(5)³ + 22(5)² + 28(5) - 35 = 125 + 100 + 140 - 35 = 330 which is not a zero
So the function ƒ(x) = 3x³ + 22x² +28x - 35 has no rational zeros.
С
Find the measure of angles 1 and 2.
Explain your reasoning as to how you determined the measurements of angles 1 and 2.
Answer:
m<1 = 135°
m<2 = 135°
Step-by-step explanation:
When solving for angles we know that the horizontal lines are both parallel. This means that 135° is equal to number 1.
For angle 2 we know that angles opposite are equal to the angle already given. This means that angle 2 is equal to angle 1.
The image I gave should help you understand this.
A recipe for punch requires 2 cups water to 5 cups juice. If
a total of 28 cups of punch were made, how many cups of juice were used
Answer:
2 cups of punch = 5 cups of juice
28cups of punch = 28/2 × 5
= 85 cups of juice
-3 1/2 = 1 1/4b
Solve for b
To solve for b, we need to get b on one side of the equation and all the other numbers on the other side. To do this, we can start by adding 3 1/2 to both sides of the equation:
-3 1/2 + 3 1/2 = 1 1/4b + 3 1/2
This simplifies to:
0 = 1 1/4b + 3 1/2
Now we can subtract 3 1/2 from both sides of the equation:
0 - 3 1/2 = 1 1/4b
This gives us:
-3 1/2 = 1 1/4b
To solve for b, we can divide both sides of the equation by 1 1/4. To do this, we need to convert the mixed number to an improper fraction:
-14/2 = 1 1/4b
Now we can divide both sides of the equation by 1 1/4:
-14/2 ÷ 1 1/4 = b
This simplifies to:
-7/1 = b
So the value of b is -7
It is worth noting that the solution for b is a negative number, it is possible that the original problem is not well defined and it might not have a solution.
Answer:
b = -2 4/5
Step-by-step explanation:
-3 1/2 = 1 1/4 b
-7/2 = 5/4 b
b = -7/2 × 4/5
b = -28/10
b = -14/5
b = -2 4/5
Lamar bought 2 CDs that were each the same price. Including sales tax, he paid a total of$23.80 . Of that total, $2.40 was tax. What was the price of each CD before tax?
ITS 7TH GRADE MATH
Answer:
the price of each CD before tax is $10.70
Step-by-step explanation:
We can start by using algebra to set up an equation to represent the situation. Let x be the price of each CD before tax.
We know that:
The total price of the CDs before tax is 2x (because he bought 2 CDs that were the same price)
The total price of the CDs including tax is $23.80 (because that's what he paid)
The amount of tax is $2.40 (because that's what is stated in the problem)
So we can set up the equation as:
2x + 2.40 = 23.80
To find the price of each CD before tax, we can subtract the amount of tax from both sides of the equation:
2x = 21.40
And then divide both sides by 2:
x = 10.70
So the price of each CD before tax is $10.70
which of these statements most closely describes the population of florida? answer choices for the above question a. the population of florida fluctuates wildly year to year. b. more people reside in northern florida than southern florida. c. florida boasts one of the youngest populations on average in the entire country. d. a majority of the residents of florida were born elsewhere.
The population of florida is d) a majority of the residents of florida were born elsewhere.
What is majority ?
A majority refers to a number or group that is greater than half of the total number or group. In a group of 10 people, a majority would be 6 or more people. In an election, a candidate who receives more than 50% of the vote is said to have won by a majority. In a legislative body, a majority vote is one where more than half of the members vote in favor of a motion or bill.
This statement is closest to describing the population of Florida. Florida is a popular destination for retirees and tourists, and many people move to Florida from other states and countries. According to the U.S. Census Bureau, Florida has the highest net in-migration of any state in the country, and as of 2020, about 57% of the state's population was born in another state or country.
The population of florida is d) a majority of the residents of florida were born elsewhere.
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If an imaginary line segment is drawn between the centers of the earth and the moon, then the net gravitational force F acting on an object situated on this line segment is F = −K x2 + 0.012K (239 − x)2 where K > 0 is a constant and x is the distance of the object from the center of the earth, measured in thousands of miles. How far from the center of the earth is the "dead spot" where no net gravitational force acts upon the object? (Express your answer to the nearest thousand miles. Hint: The distance from the earth to the moon is approximately 239 thousand miles.)
The "dead spot" is 19.04 thousand miles from the center of the earth
How find the dead spot?To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.
We know that F = −K x2 + 0.012K (239 − x)2
So, we set F equal to 0 and solve for x:
0 = −K x2 + 0.012K (239 − x)2
0 = −K x2 + 0.012K (239 − x)2
K x2 = 0.012K (239 − x)2
x2 = 0.012 (239 − x)2
x2 = 2.888 (239 − x)2
x2 = 2.888 (239 − x)2
x2 = 2.888 x2 - 676.8 x + 568.976
x2 - 2.888 x2 = 676.8 x - 568.976
-1.888 x2 = 676.8 x - 568.976
x2 = 361.6 x - 303.504
x = √(361.6 x - 303.504)
x = √(361.6 x - 303.504)
x = 19.04
So the "dead spot" is 19.04 thousand miles from the center of the earth
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