The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
What is a triangle?A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.
We can use the Law οf Cοsines tο find the length οf side QR:
[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)
where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:
[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]
[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]
Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:
PQ/sin(30°) = QR/sin(P)
PQ = QR(sin(30°)/sin(P))
Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:
[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]
Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:
[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]
Using the quadratic fοrmula, we find that:
QR ≈ 7.466 cm οr QR ≈ 3.866 cm
Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:
[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]
[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]
[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]
Since cοs(R) ≤ 1, we have:
[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]
Sοlving fοr PQ using the quadratic fοrmula, we get:
PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm
Since PQ < PR, the οnly valid sοlutiοn is:
PQ ≈ 5.474 cm
Nοw we can use the Law οf Cοsines again tο find ∠R:
[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]
[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]
cοs(R) ≈ 0.828
R ≈ 33.6° οr R ≈ 326.4°
Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
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a local bakery sells the freshest bread in town. in fact, 65% of customers who come into this store buy bread. what is the probability that at least 3 customers out of the first 6 will buy bread?
The probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.
The formula used is :
P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
65% of customers who come into this store buy bread, hence p = 0.65.
A sample of 6 customers is taken, hence n = 6.
The probability that at least 3 customers out of the first 6 will buy bread is given by:
P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)
In which
P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]
P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355
P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328
P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437
P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754
Then,
P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)
= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826
The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.
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Complete question;
A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?
23.5%
88.3%
11.7%
76.5%
how can the idea of a sinusoidal function be used to help us model real-world things, or to help us solve real-world problems?
Sinusoidal functions can model natural phenomena and periodic patterns in data, aiding in better understanding and more accurate predictions, while also solving real-world problems.
The idea of a sinusoidal function can be used to model real-world phenomena or solve real-world problems. Many natural phenomena can be modeled using sinusoidal functions, including tides, sound waves, and electromagnetic waves.
In addition, sinusoidal functions can be used to model periodic patterns in data, such as seasonal trends or cyclical patterns in financial data. By using sinusoidal functions to model these phenomena, we can gain a better understanding of their behavior and make more accurate predictions about their future behavior.
Sinusoidal functions can also be used to solve real-world problems, such as calculating the amplitude, frequency, or period of a wave or predicting the behavior of a system that exhibits periodic patterns.
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suppose 6.0 mol pf h2 reacted with suffient nitrogen (n2). how many moles of ammonia would be produced
Thus, 4.0 moles of NH3 would be produced when 6.0 moles of H2 react with sufficient N2.
Suppose 6.0 mol of H2 reacts with sufficient N2 to produce ammonia, NH3. We can determine the number of moles of NH3 produced using stoichiometry.The balanced chemical equation for the reaction is:[tex]3H2(g) + N2(g) → 2NH3(g)[/tex]
From the equation, we can see that 3 moles of H2 react with 1 mole of N2 to produce 2 moles of NH3.
Therefore, using the mole ratio from the balanced equation, we can calculate the number of moles of NH3 that would be produced when 6.0 mol of H2 reacts with [tex]N2:6.0 mol H2 × (2 mol NH3/3 mol H2) = 4.0 mol NH3[/tex]
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PLEASEE HELP
A teacher wants to select two students at random to read two chapters aloud from a book
Which statement describes a random selection of two students?
A. The teacher selects the first two students who arrive to class.
• B. The teacher selects the first two students who raise their hand.
C. The teacher sees two students in the hall and asks them to do the reading.
• D. The teacher puts the student names on individual pieces of paper and draws two names.
Answer: D
Step-by-step explanation:
Its the fairest way to pick a random person
A race is 3/10 kilometers long. Alan ran 6 of these races. How far did he run altogether
Answer:
1.8 kilometers
hope this helped
Answer:
1 8/10 kilometers
Step-by-step explanation:
u keep on adding 3 on to 3/10th 6 times then u get a improper fraction and turn that into a fraction and u get ur answer
hope it helps
true of false: dispersion models are selected based on the phase of the material being modeled in a release scenario
The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.
Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.
Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.
Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.
For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.
Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.
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if adding predictor variables to a regression model never reduces r2, why not just include all the available predictor variables in the model? also, remark on the meaning of r2 adj.
Answer: If adding predictor variables to a regression model never reduces r2, you can include all the available predictor variables in the model, as long as they have a significant correlation with the dependent variable. However, having too many variables in a model may lead to overfitting, resulting in poor model generalization. In addition, some predictor variables may not be useful, while others may be collinear. As a result, it is usually recommended to use a stepwise regression method, which selects the best subset of predictor variables that improve the model's performance, without including irrelevant or collinear variables.r2 adj: R2 adj is the adjusted R2 value of a regression model. R2 adj is a statistical measure of how well the regression model fits the observed data. It is similar to the R2 value, but takes into account the number of predictor variables in the model, in addition to the sample size. The adjusted R2 value increases when a new predictor variable improves the model's fit, but decreases when the new predictor variable does not improve the model's fit or is collinear with other predictor variables.
The adjusted R2 value ranges from 0 to 1, with higher values indicating better model fit.
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Use the equation 2,401 = 76 – 2x.
What power of 7 is 2,401?
Hi!
The power of 7 to make 2,401 is 4.
Written out ↓ ↓ ↓
7 x 7 = 49 (Thats the first 2 sevens)
49 x 7 = 343 (Three)
343 x 7 = 2,401 (Four)
= 7^4
Hope this helps!
~~PicklePoppers~~
Help Please! DUE SOON
how do i solve this question, explanation please
Answer:
Step-by-step explanation:
You can read the answers right off the graph.
a) When t=5: Find 5 on the x-axis (time (h)), go straight up vertically until you hit the line, then go straight to the left horizontally until you hit the y-axis (distance (km)); at that point d ≈ 14 km
b) When d=20: Find 20 on the y-axis (distance (km)), go straight to the right horizontally until you hit the line, then go straight down vertically until you hit the x-axis (time (h)); at that point t ≈ 7 hr
Complete the table below using what you know about trigonometric ratios for right triangles.
Write your ratios as fractions. A message will appear when you are correct.
(a) The ratio of sin A as a fraction is 63/65, cos A is 16/65 and the tan of angle A is 63/16.
(b) The ratio of sin B as a fraction is 16/65, cos B is 63/65 and the tan of angle B is 16/63.
What is the missing part of the right triangle?The missing parts of the right triangle is calculated using the trigonometry principle as shown below.
For angle A:
opposite side = 63
adjacent side = 16
hypothenuse side = 65
sin A = opp/hypo = 63 / 65
cos A = adj/hypo = 16 / 65
tan A = opp/adja = 63/16
For angle B:
opposite side = 16
adjacent side = 63
hypothenuse side = 65
sin B = opp/hypo = 16 / 65
cos B = adj/hypo = 63 / 65
tan A = opp/adja = 16/63
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4. Determine the length of supporting guy wires from the top of a 45 ft. tall cell
phone tower if they are secured to the ground 28 ft. horizontally from the base
of the tower.
Accοrding tο the Pythagοrean theοrem, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is 53 ft.
What is Pythagοrean theοrem?The Pythagοrean theοrem is a fundamental result in Euclidean geοmetry that describes the relatiοnship between the three sides οf a right-angled triangle.
In equatiοn fοrm, this can be written as:
c² = a² + b²
where c is the length οf the hypοtenuse, and a and b are the lengths οf the οther twο sides (alsο knοwn as the legs) οf the right-angled triangle.
In this case, the tοwer, the grοund, and the guy wire fοrm a right triangle. We knοw the height οf the tοwer is 45 ft, and the hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured tο the grοund is 28 ft. Let's call the length οf the guy wire c. Then, we have:
a = 28 ft (hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured)
b = 45 ft (height οf the tοwer)
c = length οf the guy wire (hypοtenuse)
Using the Pythagοrean theοrem, we can sοlve fοr c:
[tex]a^2 + b^2 = c^2[/tex]
[tex]28^2 + 45^2 = c^2[/tex]
[tex]784 + 2025 = c^2[/tex]
[tex]2809 = c^2[/tex]
[tex]c = \sqrt{(2809)[/tex]
c ≈ 53 ft
Therefοre, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is apprοximately 53 ft.
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To get ready for a pep rally, Mrs. McGee's class is making banners. They have a 3-foot piece of poster board and cut it into pieces that are 1 4 of a foot long. How many banners do they make?
Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.
The total length of the poster board is 3 feet, which is equivalent to 3 x 12 = 36 inches.
Each piece of poster board is 1/4 of a foot long, which is equivalent to 3 inches (since 1 foot is equal to 12 inches).
To find out how many banners can be made from the poster board, we need to divide the total length of the poster board by the length of each banner:
Number of banners = Total length of poster board / Length of each banner
Number of banners = 36 inches / 3 inches
Number of banners = 12 banners
Therefore, Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.
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The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What is the number?
The smaller number is 5.5 and the larger number is 15.5.
Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.
From the problem statement, we know that:
x + y = 25 (the sum of the two numbers is 25)
y = 3x - 3 (the larger number is 3 less than three times the smaller)
We can use the second equation to solve for y in terms of x, by adding 3 to both sides:
y + 3 = 3x
Then, we can substitute this expression for y into the first equation:
x + (y + 3) = 25
Substituting y + 3 with 3x, we get:
x + 3x = 22
Combining like terms, we get:
4x = 22
Finally, we solve for x by dividing both sides by 4:
x = 5.5
Now that we know x, we can use the equation y = 3x - 3 to find y:
y = 3(5.5) - 3 = 15.5
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Aria puts 0. 75 liters of apple juice and 0. 5 liter of cranberry juice in a pitcher that holds 2 liters of liquid. She fills the rest of the pitcher with orange juice. What fraction of the mixture is orange juice?
Answer:
Step-by-step explanation:
Your equation is 0.75L + 0.5L + x = 2L
x = Orange juice
0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L
[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex] simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,
the width of a rectangle is increasing at a rate, while the length increases at a rate. at what rate is the area increasing when
When the width of a rectangle is increasing at a rate, and the length increases at a rate, the rate at which the area increases can be determined by multiplying the rates of the width and the length.
When the width and length of a rectangle increase at certain rates, the area of the rectangle also changes at a specific rate. The rate of change of the area is determined by multiplying the rates of change of the width and length.
This is because the area of a rectangle is calculated by multiplying its width and length, and therefore any change in either dimension affects the overall area. The product of the rates of change of the width and length gives the overall rate of change of the area.
Therefore, the rate at which the area is increasing when the width of a rectangle is increasing at a rate, while the length increases at a rate can be calculated using the above formula.
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a jar contains 4 red, 5 white and 6 blue marbles. 3 marbles are selected at random. find the probability that you get one marble of each color using counting.
The probability of getting one marble of each color will be 0.044.
What is probability?The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
In this question,
Total number of balls=4+5+6=15
probability of red ball= 4/15
probability of white ball = 5/14 (Since the number of balls are decreasing
probability of blue ball= 6/13
probability of getting one marble of each color= 4/15×5/14×6/13
= 0.044
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ASAP FAST ANSWER NO TIMEEEEE
Answer:
C
Step-by-step explanation:
A (- 6, - 8 ) and C (9, - 8 )
since the y- coordinates of both points are equal, both - 8
then AC is a horizontal line
the distance AC can be calculated by calculating the absolute value of the x- coordinates, that is
AC = | 9 - (- 6) | = | 9 + 6 | = | 15 | = 15 units
or
AC = | - 6 - 9 | = | - 15 | = | 15 | = 15 units
given 1 unit = [tex]\frac{1}{2}[/tex] mile , then
AC = 15 units = 15 × [tex]\frac{1}{2}[/tex] = 7.5 miles
PLEASE PLEASE SOLVE NEED CORRECT ANSWER THANK YOU GUYS SEE the FILE PLS Thank u so much
The expected profit of Ayo is $ 79.95.
What is Probability:
The probability of an event happening can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Here in this problem, we use probability to calculate the total profit. Calculate the probability of winning 150 people so that we can calculate the total winning amount of 150 persons.
Now calculate the total amount gained by Ayo by costing each turn. Now subtract both values and will get the expected profit.
Here we have
Ayo runs fairground games
In each turn, a player rolls a fair dice numbered from 1 - 6 and a spin numbered 1 - 5
Every player can win £ 8 or £ 3
In total there are 150 to play
Here probability of winning £ 8 i.e rolling 2 and rolling 5
= [ 1/6 × 1/5 ] = 1/30
Probability of winning £ 3 i.e getting at least one 3 in roll or spin
Here we have taken 3 cases that are getting 3 in a roll but not in spin, getting 3 in a spin but not in roll, and getting 3 in both roll spin
= [ 1/6 × 4/5 ] + [5/6 × 1/5 ] + [ 1/6 × 1/5 ]
= 4/30 + 5/30 + 1/30 = 10/30 = 1/3
Hence, the expected amount in 1 a single game
= 8 × 1/30 + 3 1/3 = 8/30 + 1 = 0.267 + 1 = 1.267
There are 150 player
Total amount won by 150 = 150 (1.267) = $ 190.05
Here It cost a player 1.80 for every turn
Ayo will get for 150 players = 1.80 × 150 = $ 270
If 150 players won $ 190.05,
then the profit won by Ayo = 270 - 190.05 = 79.95
Therefore,
The expected profit of Ayo is $ 79.95.
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find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45
The probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is [tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]
The formula is [tex]P(X) = nCx (p)^x (1-p)^(n-x)[/tex], where n is the number of trials, x is the number of successes, and p is the probability of success for one trial. In this case, n represents the number of teenagers sampled, x represents the number of teenagers who own a smartphone, and p represents the probability that any one teenager owns a smartphone.
First, let us calculate p. The probability of success (owning a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the probability of success lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is p.
Next, let us calculate x. The number of successes (teenagers who own a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the number of successes lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is x.
Finally, we can calculate n. We know that the number of teenagers sampled is 100, so n = 100.
[tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]
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An athlete runs 1/3 of a mile every 1/20 hour. At this rate, how far does the athlete run per hour?
Answer: 20/3 mph or 6.667 mph.
Step-by-step explanation:
Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.
Write an equation to represent each relationship
This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.
However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]
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consider a 20-lb pink flamingo that stands 3 ft in height and has legs that are 2 ft in length. model the height and leg length of a 100-lb flamingo. what assumptions are necessary? are they reasonable assumptions?
The height of a 100-lb flamingo can be estimated by assuming that it would be proportional to the height of the 20-lb pink flamingo. Based on this assumption, the 100-lb flamingo would be 6 ft tall.
The leg length of a 100-lb flamingo can be estimated by assuming that it would also be proportional to the leg length of the 20-lb pink flamingo. Using this assumption, the 100-lb flamingo would have legs 4 ft in length.
These assumptions are reasonable given that the difference in size of the two flamingos is only a factor of 5. This means that the size difference between the two is not large enough to drastically change the proportions of their bodies. Thus, it is a fair assumption that the proportions of their height and leg length would remain roughly the same.
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Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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for a recent year, the monthly snowfall (in inches) for chicago, illinois, for november, december, january, and february was 2, 8.4, 11.2, and 7.9, respectively. how much snow would be necessary in march for chicago to exceed its monthly average snowfall of 7.28 in. for these five months?
6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.
The given data is as follows:
Snowfall months and their fallen depth is:
November = 2
December = 8.4
January = 11.2
February = 7.9
First, we need to first find out the total snowfall for the five months of November, December, January, February, and March.
Total snowfall = 2 + 8.4 + 11.2 + 7.9 + March
The average snowfall = 7.28 iches.
7.28 inches/month x 5 months = 36.4 inches
2 + 8.4 + 11.2 + 7.9 + March = 36.4
29.5 + March = 36.4
March = 36.4 - 29.5
March = 6.9 inches.
Therefore, we can conclude that more than 6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.
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A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation
The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25
Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.
The amount of medicine in the 10 grams of 15% solution is
0.15 × 10 = 1.5 grams
The amount of medicine in the 25 grams of 10% solution is
0.10 × 25 = 2.5 grams
So the total amount of medicine in the original mixture is,
1.5 + 2.5 = 4 grams
Now let x be the amount of pure medicine added.
The total amount of medicine in the final mixture is,
4 + x
The total amount of solution in the final mixture is,
10 + 25 + x
So the concentration of the final mixture is,
(4 + x) / (10 + 25 + x)
We know that this concentration is 25%, so we can write:
(4 + x) / (10 + 25 + x) = 0.25
This is the equation that represents the situation.
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The given question is incomplete, the complete question is:
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation
The sum of Joy's age and her brother's age is $24$ . Her brother's age is $3$ years older than twice Joy's age.
What is the difference, in years, between Joy's age and her brother's age?
Answer:
please give question properly
decide whether the events shown in the accompanying venn diagram are mutually exclusive. explain your reasoning.
Since there are students who play both sports, the events of playing basketball and playing soccer are not mutually exclusive.
What is venn diagram?A Venn diagram is a visual representation of sets or groups and their relationships to one another.
It consists of two or more circles or other shapes that overlap, with each shape representing a different set, and the overlap representing the elements that belong to both sets.
Looking at the diagram, we see that there is a region where the two circles overlap, which means there are elements (points) that are in both circles. Therefore, the events shown in the Venn diagram are not mutually exclusive.
In this particular case, the circles represent the events of students who play basketball and students who play soccer, respectively. The overlap represents students who play both basketball and soccer.
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The complete question is given below-
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15 box and whisker plot
The box and whisker plot can be created by :
Minimum value - 6
Maximum Value - 15
Median - 10
Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5
To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.
Minimum value: 6
Maximum value: 15
Median: To find the median, we need to first arrange the data set in ascending order:
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15
The median is the middle value in the data set, which is 10.
Quartiles: To find the quartiles, we need to divide the data set into four equal parts.
First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:
6,7,7,8,9,10
The median of this set is (7+8)/2 = 7.5.
Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.
Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:
10,10,10,10,13,13,14,14,15,15
The median of this set is (13+14)/2 = 13.5.
Now, we can use the above information to create the box and whisker plot.
The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).
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Customer three found a hair in their taco! To make up for it, you gave 40% off their order, but they still had to pay a 4.5% sales tax. What is the new cost of the order?
The new cost of the order is 62.7% of the original price where still 4.5% sales tax had to pay.
What is discount?A discount is a reduction in the price of an item or service, usually expressed as a percentage of the original price.
According to question:Let's assume the original cost of the order was $x.
After the 40% discount, the customer paid 60% of the original cost, which is 0.6x.Then, the 4.5% sales tax is applied to the discounted price of 0.6x, which is 0.045(0.6x) = 0.027x.So the final cost of the order is the discounted price plus the sales tax:0.6x + 0.027x = 0.627x
Therefore, the new cost of the order is 62.7% of the original price.
For example, if the original cost of the order was $20, then the discounted price is $12 (60% of $20), and the sales tax is $0.324 (4.5% of $12). The final cost of the order would be $12.324.
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assuming the rest of your diet remains constant, how many days will it take you to lose 10 pounds? you must burn an extra 3500 calories to lose 1 pound of body weight. express your answer using two significant figures.
The number of days that it would take to lose 10 pounds, given the calories in the morning latte is 97 days.
How to find the number of days ?Determine the total number of calories you need to burn to lose 8 pounds:
Calories to burn = Pounds to lose × Calories per pound
Calories to burn = 8 × 3,500 = 28,000
Calculate the number of calories you save per day by giving up your morning latte:
Daily calorie savings = Calories in latte
Daily calorie savings = 290
Determine how many days it would take to burn the total number of calories needed to lose 8 pounds:
Days to lose weight = Calories to burn / Daily calorie savings
Days to lose weight = 28,000 / 290 = 97 days
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Full question is:
Assuming the rest of your diet remains constant, how many days will it take you to lose 8 pounds? You must burn an extra 3500 Calories to lose 1 pound of body weight. (your daily latte contains 290 Calories. You want to lose weight by giving up your morning latte and drinking water instead.)