The equation of the line is y = (2/3)x + 2, having a y intercept of 2 and slope of 2
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
The equation of a line with slope m passing through (x₁, y₁) is:
y - y₁ = m(x - x₁)
The line that passes through (0, 2) and has a slope of 2/3, hence:
y - 2 = (2/3)(x - 0)
y = (2/3)x + 2
The equation of the line is y = (2/3)x + 2
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When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, start text, space, m, L, end text of chocolate syrup for every 90\,\text{mL}90mL90, start text, m, L, end text of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, start text, space, m, L, end text of chocolate syrup for every 180\,\text{mL}180mL180, start text, m, L, end text ounces of hot water.
Which hot cocoa is more chocolatey?
Choose 1 answer:
(Choice A)
A
Arjun's hot cocoa
(Choice B)
B
Eli's hot cocoa
(Choice C)
C
The two cocoas are equally chocolatey
On solving the provided question, we can say that from percentage Eli's hot cocoa has more chocolate flavor because his chocolate percentage is higher.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
proportion of chocolate in Arjun's beverage == 20 X 100/90 = 22.22%
Eli's beverage contains the following amount of chocolate:= 45/180 X 100 = 25
Eli's hot cocoa has more chocolate flavor because his chocolate percentage is higher.
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to the nearest second, what is the first time between 4:00 and 5:00 that the minute and hour hands of the clock are perpendicular to each other?
So the first time between 4:00 and 5:00 that the minute and hour hands of the clock are perpendicular to each other to the nearest second is 4:06.
The minute hand of a clock moves 360 degrees in 60 minutes, or 6 degrees per minute.
The hour hand moves 360 degrees in 12 hours, or 30 degrees in 1 hour, or 30 degrees in 60 minutes, or 0.5 degrees per minute.
At 4:00, the minute hand is pointing straight up (12 o'clock), and the hour hand is pointing at 4 o'clock.
To find the first time that the hands are perpendicular, we need to find the first time that the difference between the angle of the minute hand and the angle of the hour hand is 90 degrees.
We know that the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, so for every minute that passes, the angle between the hands increases by 5.5 degrees.
Each consecutive hour has 30 degrees in between, so angle between 12 and 4 is
4×30 = 120°
So,
At 4:00 the angle between the hands is
120°
At x minutes after 4, the angle is
120 - 5.5x
So to solve for x when angle is 90°
120 - 5.5x = 90
x = 30/ 5.5
x = 5.45 minutes
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for each picture there is a 1/4 chance of everyone looking at the camera. how many pictures do i need to take for at least a 4/5 pprobability of everyone looking at the camera
Answer: (My view) 6.
Step-by-step explanation: Letting "n" be the number of pictures taken. The probability of no one look at the camera for n photos is of (3/4)^n.
Hence, the probability of at least one photo be the picture craven is of:
(1 - (3/4)^n), and since the likelihood of that being equal to 4/5, it's feasible to assume that (1 - (3/4)^n) = 4/5, solving for that would give:
(3/4)^n = 1/5. Notice that the proposal can also be interpreted as "The number of pictures needed such that the probability of a picture NOT including one with everyone looking at the camera is at most 1/5",
Therefore, (3/4)^n < 1/5;
To solve for that:
n = 1:
3/4 > 1/5,
n = 2:
9/16 > 1/5
n = 3
27/64 > 1/5
n = 4
81/256 > 1/5
n = 5
243/1024 > 1/5
But finally:
n = 6
729/4096 < 1/5
For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.
Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,
= 1 - (1 - p)ⁿ ≥ P
= (1 - p)ⁿ ≤ 1 - P
= n ≥ ln(1-P)/ln(1-p)
= n ≥ ln (0.2) / ln (0.75)
=5.6
Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.
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How to put this in vertex form?
The vertex form of equation is discussed below,
What is Vertex form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants. of the parabola is at (h, k).
As, A parabola has a lowest point if it opens upward.
Additionally, a parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Now, the parent function f(x) = x² has its vertex at the origin.
Also, The vertex form of a quadratic function is
f(x) = a(x – h)² + k, where a, h, and k are constants.
For example, The parent function f(x) = x² is vertically stretched by a
factor of 4/3 and then translated 2 units left and 5 units down.
So, the vertex form : g(x) = 4/3 (x+2)² - 5.
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Amy works for a company that produces plastic lids and cups for restaurants. She wants to use a one-sample zzz interval to estimate what proportion of lids produced in a day have a defect that makes them not fit the cups. She takes a random sample of 100100100 lids from the more than 1{,}0001,0001, comma, 000 total lids produced that day and finds 555 lids in the sample with this defect.
Amy can use a one-sample z-interval to estimate the true proportion of lids in the population of 1,000,000 that have the defect.
What is sample?Sample can refer to an example of a particular item or type of thing. It can also refer to a section of a population that is chosen in order to represent the whole group. When used in research, samples are used to make conclusions about a population as a whole. Samples are also often used to test products or services in order to assess their quality or performance.
First, she will calculate the sample proportion of lids with the defect by dividing the number of lids in the sample with the defect (555) by the total number of lids in the sample (100,000). This sample proportion is 0.00555.
Next, Amy will calculate the standard error of the sample proportion. This is calculated by taking the square root of the sample proportion multiplied by (1 - sample proportion) divided by the sample size. The standard error for this sample is 0.00023.
Finally, Amy can calculate the one-sample z-interval. This is done by subtracting the standard error from the sample proportion and adding it to the sample proportion. This gives a one-sample z-interval of 0.0053 to 0.0058.
This one-sample z-interval tells Amy that she can be 95% confident that the true proportion of lids with the defect in the population of 1,000,000 is between 0.0053 and 0.0058.
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For the equation: 2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7 , the right side of the equation can be simplified by combining like terms.
Simplify 9 - 3x + 6 + 8 + 3x + 7 :
2(x - 5) can be simplified using the Distributive Property.
Simplify 2(x - 5):
The value of the equation is x=20.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is
=> 2(x-5)=9-3x+6+8+3x+7
Now simplify the equation for x then
=> 2x-10 = 30-3x+3x
=> 2x-10=30
=> 2x=30+10
=> 2x=40
=> x=20
Hence the value of the equation is x=20.
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Given that QM = 15 units, SM = 10 units, and RM = 18 units, what is the length of segment PM?
R
18
M
10
15
Q
OA 13 units
OB.
7 units
Ос.
8 units
OD
12 units
The length of segment PM would be 12 units
I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.
We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.
Our equation QM = (SM)(RM) (PM)
We now enter the information and resolve: (10)(18) = (15)(x) (x)
(10)(18) = 180
(15)(x) = 15x
180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x
x = 12
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Answer:
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Step-by-step explanationThe theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.:
Answer:
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
Step-by-step explanation:
Since the 4 sections are equal, theoretical probability is given by:
p = 1/4
Out of 20 trials, 4 resulted in pink, hence experimental probability is given by:
p = 4/20 = 0.2 = 20%.
Hence,
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
What is the measure of angle x?
Answer: 112 degrees
Step-by-step explanation:
Since the two lines are parallel and the line that intersects them is a transversal, 180 - 68 = x
Solving 180 - 68,
you can find that x = 112 degrees :>
Answer: a measure of an x angle is the longest line on the graph so that how u know
Step-by-step explanation:
A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. What overall dimensions will minimize the amount of paper used?
A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. the dimensions that will minimize the amount of paper used is that should be 12 inches wide by 6 inches tall.
The margins are 2 inches at the top and bottom and 3 inches at each side. The margins are then added to the two 150s, making a total width of 12 inches and a total height of 6 inches. This is the minimum amount of paper that can be used for the poster. In order to minimize the amount of paper used, it is important to consider the size of the margins.
The margins should be kept as small as possible in order to maximize the amount of space available for the printed material. Generally speaking, a margin of 1 inch is sufficient for most printed materials. If a larger margin is necessary, then the overall dimensions of the poster should be adjusted accordingly.
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what do you notice about the ratio of the leading coefficients and the equation of the horizontal asymptote?
The ratio of the leading coefficients and the equation of the horizontal asymptote is degree of numerator and denominator is equal.
The term coefficients in math is defined as the coefficient of the term of highest degree in a polynomial.
Here we have given that the ratio of the leading coefficients and the equation of the horizontal asymptote.
The term horizontal asymptote is known as a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
As we all know that if the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote is equal to the ratio of the leading coefficients.
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Height in meters 15 30 45 60 75 90 105 Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598 1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.
1. a function that could be used to model the data in the table. Make sure to use h for height and d for distance is d = -0.425h + 39.25
2. If the balloon is 800 meters high, the farthest distance that you would be able to see is 48 km
3. at the height of 67 does the balloon have to rise for the building to be visible.
The table in the question shows a relationship between the height of a balloon and the distance away from the balloon that can be seen. Using this data, a linear function can be determined that models this relationship. The function is d = -0.425h + 39.25, where h is the height of the balloon in meters and d is the distance in kilometers. Using this function, if the balloon is 800 meters high, the farthest distance that can be seen is 48 km, which is the y-intercept of the equation.
Inversely, if a building is 16 km away from the balloon, the height the balloon must rise for the building to be visible is 67 m. This can be determined by substituting 16 for d in the equation and solving for h. Overall, the linear function d = -0.425h + 39.25 models the relationship between the height of the balloon and the distance away from the balloon that can be seen. The equation can be used to determine the height of the balloon needed to see a certain distance or the distance away from the balloon that can be seen when the balloon is at a certain height.
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Height in meters 15 30 45 60 75 90 105 , Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round the answer to the nearest whole number
3. Round answer to the nearest whole number A building is 16 km away. What height does the balloon have to rise for the building to be visible?
6x-2y=26 -y+3=x Solve the system by substitution
Step-by-step explanation:
6x-2y = 26 ---(1)
x+y = 3 -------(2)
so, (y = 3-x)
put in equation 1st.,
6x-2(3-x) = 26
6x-6+2x = 26
8x = 32
(x = 4)
so, put x value in equation 2nd,
4+y = 3
(y = -1 ) Answer
Answer:
x = 4
y = -1
Step-by-step explanation:
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Given:
6x-2y=26
-y+3=x
Flip the equation around:
x = 3 - y
6(3-y) - 2y = 26 << Distribute property
18 -6y -2y = 26 << Add liked term
18 -8y = 26
-8y/-8 = 8/-8 << Divide both sides by -8
y = -1
Now, substitute y into the equation also known as -1.
6x - 2(-1) = 26
6x + 2 = 26 << Subtract 2 from 2 and 26 from 2
6x = 24
6x/6 = 24/6 << Divide both sides by 6.
x = 4
Hence, x = 4 and y = -1.
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3 semicircles are connected to 3 sides of a square. Each side of the square measures 4 centimeters. What is the area of the composite figure?
The area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
What is the area of the semicircle?The area of the semicircle is the space occupied by it. It can be given as,
[tex]A_{s} = \frac{d^{2} }{8} \pi[/tex]
Here, (d) is the diameter of the semicircle.
Each side of the square measures 4 centimeters. The area of the square is square of its side. Thus,
Area of the square, [tex]A_{s}[/tex] = 4² = 16cm²
3 semicircles are connected to 3 sides of a square. Thus, the diameter of the semicircle is equal to 4 cm. The area of 3 semicircles is,
[tex]A_{sc} = 3 *\frac{4^{2} }{8} \pi\\A_{sc} = 6\pi[/tex]
The area of the composite figure is,
[tex]A = A_{s} + A_{sc} \\A = (6\pi + 16) cm^{2}[/tex]
Thus, the area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
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-1/2x-2y=4
Solve for X and y pls
Answer:
The image attached
Step-by-step explanation:
Put the equation into slope-intercept form
[tex]y=mx+b[/tex]
The equation should look like this
[tex]y=-\frac{1}{4}x-2[/tex]
Graph the equation with the slope being [tex]-\frac{1}{4}[/tex] and [tex]-2[/tex] being the y-intercept.
What is 30x30 Divided by 0
Answer: Undefined
Step-by-step explanation: any number divided by 0 gives no solution and therefore it is undefined, if u need more explanation then comment
Answer:
Undefined
Step-by-step explanation:
Triangle ABC is congruent to Triangle PDF. Side AC corresponds to what side in Triangle PDF?
Answer:
the angle that corresponds to AC IS PF
Circle $A$ is in the interior of circle $B$. The diameter of circle $B$ is 16 cm. What is the diameter of circle $A$ for which the ratio of the shaded area to the area of circle $A$ is 3:1
As per the given ratio, the diameter for the circle A is 8 cm.
The term diameter in math is defined as a straight line that goes from one side to the other side of a circle, passing through the center
Here we have given that Circle A is in the interior of circle B. The diameter of circle B is 16 cm.
And we need to find the diameter of circle A in which the ratio of the shaded area to the area of circle A is 3:1.
While we looking into the given diagram, here we know that the area of the shaded region plus the area of circle A equals the Area of Circle B.
As we know that since the shaded area of the circle, 3:1,
And here we also have
=> 3x + x = 64π
When we simplify this one then we get,
=> 4x = 64π,
Then the value of x = 16π.
Here we have to directly we get
=> π x p² = 16π,
Then the value of
=> r² = 16
=> r = 4.
Here we must know that length can't be negative!
Therefore the diameter of circle A is
=> 4* 2 = 8 cm.
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a youth indoor soccer team has 6 starting players. the starting players must consist of 3 boys and 3 girls. there are 7 boys and 6 girls on the team. each player can play each position. in how many ways can the coach select players to start the game?
The coach can select the 6 starting players in 20 different ways, as probability are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position. To calculate this, the formula 6! / (3! * 3!) is used.
1. Calculate 6 factorial (6!) which is 6*5*4*3*2*1 = 720
2. Calculate 3 factorial (3!) which is 3*2*1 = 6
3. Calculate 3 factorial (3!) again which is also 6
4. Divide 6! by (3! * 3!) which is 720 / (6 * 6) = 20
When selecting a starting lineup for an indoor soccer team consisting of 6 players who must be 3 boys and 3 girls, there are 20 possible combinations. To calculate this, the coach must use the formula 6! / (3! * 3!). This formula is used to calculate the number of possible combinations when selecting a certain number of items from a set of items, where all items are unique. 6! is 6 factorial, which is calculated by multiplying the numbers from 6 down to 1 (6*5*4*3*2*1). 3! is 3 factorial, which is calculated by multiplying the numbers from 3 down to 1 (3*2*1). When 6! is divided by the product of 3! multiplied by 3!, the result is 20. This shows that the coach can select the 6 starting players in 20 different ways, as there are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position.
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How do you graph absolute value equations on a coordinate plane?
To graph an absolute value function, choose several values of x and find some ordered pairs. Plot the points on a coordinate plane and connect them.
Absolute value equations are the equations in which the absolute value operator is used.
To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.
If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.
Suppose we have an expression: |x+1|
If (x+1) is positive or equal to 0, then |x+1| =x+1
However, if (x+1) is negative, then |x+1| =-(x+1)=-x-1.
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1. why do financiers need hypothesis testing? data sets do not cover every instance of an event or measurement. so they can predict within a degree of certainty where stock prices will go in the future. stock and bond pricing data is difficult to obtain and impossible to predict. the normal distribution does not give them enough information to make sound decisions. 2. what method would you use to gather a data set on voter preferences? hypothesizing sampling distributing engineering 3. the null hypothesis represents . no idea at all, a placeholder the new idea that you wish to prove the old idea that you wish to disprove a third idea that is completely neutral 4. the alternative hypothesis represents . no idea at all, a placeholder the new idea that you wish to prove the old idea that you wish to disprove a third idea that is completely neutral 5. the result of any hypothesis test is . we reject or fail to reject the null hypothesis we accept or fail to accept the alternative hypothesis we accept or fail to accept the null hypothesis
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.
The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
Such data may come from a larger population, or from a data-generating process.
1 The correct option is B.
As the hypothesis testing helps to predict when certain certainty within which range the stock value will fluctuate.
The sampling is used to gather data from the population.
The sampling can be either random or systematic. The correct option is B.
2 The correct option is C
as the null hypothesis represents the current and present claim or knowledge.
The Alternate hypothesis is the assumption about the parameter need to be checked against the null hypothesis that is it is a new assumption to be proven. So the correct option is B.
3 The correct option is A.
As either there can be sufficient evidence to reject the null hypothesis or insufficient evidence to reject the null hypothesis.
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Name the property of real numbers illustrated by the equation.
-2(x+4)=2x-8
A. Associative property of multiplication
B. Commutative property of addition
C. Distributive property
D. Associative property of addition
The property of real numbers illustrated by the equation -2(x+4)=-2x-8 is option C: Distributive property.
What is Distributive property?
The distributive law of multiplication and addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed.
The given equation is -2(x+4)=-2x-8.
According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC.
In the equation it can be clearly seen that the form is distributive form as -
A = -2
B = x
C = 4
Therefore, the equation uses distributive property.
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A system of linear equations is shown in the graph. How many solutions does the system have?
a coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 4 and another line that passes through the points 0 comma negative 2 and 3 comma negative 1
No solution
One solution at (0, 3)
One solution at (−2, 0)
Infinitely many solutions
The number of solutions which the system of equations has is: A. no solution.
How to determine the number of solutions?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (0, 3), a linear equation of the first line can be calculated in slope-intercept form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (4 - 3)/(3 - 0)(x - 0)
y = 1/3(x - 0) + 3
y = x/3 + 3
For the second line, we have:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y + 2 = (-1 + 2)/(3 - 0)(x - 0)
y + 2 = x/3
y = x/3 - 2
In conclusion, we can logically deduce that the given system of linear equations has no solution because it represents parallel lines.
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I NEED HELP ASAP!!!! PLS HELP!!!!
What is the prime factorization of 740?
A)
[tex]2 \times 5 \times 37[/tex]
B)
[tex] {2}^{2} \times 5 \times 37[/tex]
C)
[tex] {2}^{2} \times {5}^{2} \times 37[/tex]
D)
[tex] {2}^{3} \times 5 \times 37[/tex]
Answer:
B) [tex]2^2 \times 5 \times 37[/tex]
Step-by-step explanation:
[tex]740=2 \times 370=2^2 \times 185=2^2 \times 5 \times 37[/tex]
A memberhip to Gym A cot $200 to ign up and $10 per month. Gym B’ memberhip cot $0 to ign up and $60 a month. Write an equation to find out how many month you can belong to each gym for it to cot the ame at both place
So, the equation to determine the number of months is 200 + 10x = 0 + 60x.
Let x be the number of months you can belong to each gym for it to cost the same at both places.
The equation to determine the number of months is:
200 + 10x = 0 + 60x
To solve for x, we can subtract 200 from both sides of the equation:
10x = -200
And finally, we divide both sides by 10:
x = -20
Therefore, you can belong to each gym for -20 months for it to cost the same at both places. But since month are positive numbers, x=-20 is not a solution. Therefore, the statement is not true, the cost will never be the same for both gyms.
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work out the value of r in the equation below
5.8/r=tan 19
give your answer in 1d.p.
Answer: 16.8
Step-by-step explanation:
[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]
find the difference (12m + 5) - (3m - 2) i nee help asap
Answer:
(12m + 5 ) - (3m - 2)
12m + 5 - 3m + 2
12m - 3m + 5 +2
9m + 7
Answer:
[tex] \sf \: 9m + 7 [/tex]
Step-by-step explanation:
Given expression,
→ (12m + 5) - (3m - 2)
Let's simplify the expression,
→ (12m + 5) - (3m - 2)
→ 12m + 5 - 3m + 2
→ (12m - 3m) + (5 + 2)
→ (9m) + (7)
→ 9m + 7
Hence, the answer is 9m + 7.
M and N are midpoints of opposites of square ABCD.
A point is selected at random in the square. Find the probability that it lies in:
a)∆ADM
b)∆ADM but not in ∆ADN.
c) neither in ∆ADM nor in ∆ADN
Answer:
Step-by-step explanation:
a) The probability that the point selected at random lies in ∆ADM is 1/4. This is because ∆ADM is one of the four equal parts of the square ABCD.
b) The probability that the point selected at random lies in ∆ADM but not in ∆ADN is 1/8. This is because ∆ADM and ∆ADN are two of the four equal parts of the square ABCD, and the union of these two parts forms one quarter of the square. Hence, the probability of the point lying in one of these parts but not in the other is 1/8.
c) The probability that the point selected at random lies neither in ∆ADM nor in ∆ADN is 3/4. This is because the union of ∆ADM and ∆ADN forms one quarter of the square ABCD, while the remaining three quarters of the square lie outside of both ∆ADM and ∆ADN. Hence, the probability that the point lies outside of both these parts is 3/4.
A cell phone company charges 50$ for a phone plus 25$ per month. You get a gift card for 100$. When does the total spent on your phone service exceed the amount on you gift card?
A) Write an inequality to represent the money spent on a phone plan
B) when doe the total spent on your phone service exceed the amount of your gift card
Answer:
A) The money spent on a phone plan can be represented by the inequality:
50 + 25x > 100
B) The total spent on the phone service exceeds the amount of the gift card after the 2nd month.
Step-by-step explanation:
A. The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.
The first part of the inequality, 50$, represents the initial cost of the phone.
The second part, 25x, represents the monthly cost of the service, 25$ per month.
So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.
50 + 25x > 100
It states that the total cost (50 + 25x) of the phone plan is greater than 100$.
It's the total cost you have to pay for the phone and the service.
It's used to know when the total cost exceeds 100$, which is the gift card's value.
B. To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.
50 + 25x > 100
x > (100-50)/25
x > 2
So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.
To know more about inequality refer:
https://brainly.com/question/25944814
Write the function of the graph in f(x)=a∙b^x form.
The exponential function graphed is given as follows:
y = 2^x.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the parameters are given as follows:
a is the initial value.b is the rate of change.When x increases by one, the output is multiplied by 2, hence the parameter b is given as follows:
b = 2.
The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:
a = 1.
Hence the function is defined as follows:
y = 2^x.
Missing InformationThe graph is given by the image presented at the end of the answer.
More can be learned about exponential functions at https://brainly.com/question/25537936
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