Answer:
0.1
Step-by-step explanation:
100 x 10 = 1000. Essentially, you just add a zero to 100. so you take a zero out of .01. SO your answer is 0.1.
Answer: 0.1 fluid ounce
explanation:
since 100 drops of a liquid have 0.01 fluid ounces
1 drop of a liquid has (0.01/100)× 1 fluid ounces = 0.0001 ounces
so 1000 drops of a liquid have (1000×0.0001)= 0.1 fluid ounce
Find SR in the triangle…………………………………..
The length of the segment QR, obtained using the angle bisector theorem is; SR ≈ 11.4 units
What is the angle bisector theorem?The angle bisector theorem states an angle bisector in a triangle, intersects opposite side, such that the ratio of the two segments formed by the point of intersection is the same as the ratio of the other two sides of the triangle.
The angle congruence marks at angle ∠Q, indicates that the angle ∠PQS and the angle ∠SRQ are congruent.
Therefore, the segment QS is an angle bisector of the angle ∠PQR.
The angle bisector theorem, indicates that we get;
30/12 = PS/SR
PS = PR - SR, therefore;
30/12 = 5/2 = (PR - SR)/SR
Plugging in the values, we get;
5/2 = (40 - SR)/SR
5 × SR = 2 × (40 - SR) = 80 - 2 × SR
5 × SR + 2 × SR = 80
7 × SR = 80
SR = 80/7 ≈ 11.4
The length of the segment SR is about 11.4 units
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15 The table shows values of s and t.
S
t
0.2
7.5
0.5
1.4
0.9
Is s inversely proportional to f? Explain why.
(2 marks)
Answer:
s is inversely proportional to t
Step-by-step explanation:
As s increases, t decreases. They are inversely proportioanl when that happens.
Which point lies on the circle represented by the equation (x − 3)2 + (y + 4)2 = 62?
Therefore, any of these two points lies on the circle represented by the equation. [tex](x - 3)^2 + (y+4)^2=6^2.[/tex]
What is circle?A circle is a geometric shape that consists of all the points that are a fixed distance, called the radius, from a given point, called the center. The distance from the center to any point on the circle is always the same. A circle can also be defined as the set of points in a plane that are equidistant from a given point, which is the center of the circle. Circles are often studied in geometry and have a number of important properties, such as their circumference, area, and diameter. They are also widely used in mathematics, physics, and engineering, and have many practical applications in fields such as architecture, art, and design.
by the question.
The equation of the circle in standard form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
Comparing this with the given equation:
[tex](x - 3)^2 + (y + 4)^2 = 6^2[/tex]
we can see that the center of the circle is at point (3, -4) and the radius is 6.
To find a point on the circle, we can substitute any value for x or y and solve for the other variable. For example, let's choose x = 0:
[tex](0 - 3)^2 + (y + 4)^2 = 6^2[/tex]
[tex]9 + (y + 4)^2 = 36[/tex]
[tex](y + 4)^2 = 27[/tex]
[tex]y + 4=±\sqrt{27}[/tex]
[tex]y = -4±\sqrt{27}[/tex]
So, the two points on the circle are:
(0, -4 + √27) and (0, -4 - √27)
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Question 3(Multiple Choice Worth 4 points)
(06.05 MC)
The way in which response options are presented in a question can affect a person's response. Two hundred randomly selected people were asked about their milk
chocolate or dark chocolate preference. One hundred of the participants were randomly given the option of milk chocolate first and the remaining 100 participants
were given the option of dark chocolate first. The results are given in the table.
Milk chocolate option first
Dark chocolate option first
Milk Chocolate Dark Chocolate
52
41
48
59
To conclude if the order in which options are presented in a question affects the answer, a two-proportion z-test was conducted. What is the correct p-value of the
test?
A. 0.0594
B. 0.1189
C. 0.3193
D. 0.4650
E. 0.5200
Answer: To calculate the p-value for a two-proportion z-test, we need to determine the test statistic, which is calculated as:
z = (p1 - p2) / SE
where p1 and p2 are the sample proportions for each group, and SE is the standard error of the difference between the two proportions.
The sample proportion for the group given the milk chocolate option first is:
p1 = (52 + 48) / 100 = 0.50
The sample proportion for the group given the dark chocolate option first is:
p2 = (41 + 59) / 100 = 0.60
The standard error of the difference between two proportions is:
SE = sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2)
where n1 and n2 are the sample sizes for each group.
SE = sqrt((0.50*(1-0.50))/100 + (0.60*(1-0.60))/100) = 0.0748
Substituting the values into the test statistic formula, we get:
z = (0.50 - 0.60) / 0.0748 = -1.338
Using a standard normal distribution table or calculator, we find the p-value for a two-tailed test to be approximately 0.1814.
However, since we are testing whether the order of the options affects the response, this is a one-tailed test. To find the one-tailed p-value, we divide the two-tailed p-value by 2, since the area of the distribution in one tail is half of the area in both tails.
p-value = 0.1814 / 2 = 0.0907
Therefore, the correct answer is A. 0.0594 (rounded to four decimal places).
Step-by-step explanation:
A researcher investigates whether or not a new cold medication disrupts mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with μ = 64 and σ = 8. A random sample of n = 16 subjects are given the drug and then tested. For this sample, the mean is M = 58, and the standard deviation is s = 7. (4 pts) Are the data sufficient to conclude that the medication affects performance? Test with α =. 1. Compute Cohen's d to measure the size of the treatment effect
The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.
To determine whether the medication affects performance, we can perform a one-sample t-test with the following hypotheses:
Null hypothesis: The mean score for the population (μ) is 64.
Alternative hypothesis: The mean score for the population (μ) is less than 64.
We will use a significance level of α = 0.1.
First, we need to compute the t-statistic:
t = (M - μ) / (s / sqrt(n))
t = (58 - 64) / (7 / sqrt(16))
t = -2.29
Next, we need to find the corresponding p-value for this t-value with 15 degrees of freedom (n-1=16-1=15). We can use a t-distribution table or calculator to find that the p-value is 0.017.
Since the p-value (0.017) is less than the significance level (0.1), we reject the null hypothesis and conclude that the medication affects performance.
To measure the size of the treatment effect, we can calculate Cohen's d, which is a standardized measure of effect size. Cohen's d is computed as the difference between the sample mean and population mean, divided by the sample standard deviation:
d = (M - μ) / s
d = (58 - 64) / 7
d = -0.86
The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.
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Where have i gone wrong?
I need an answer!
Answer:
a)6
b)15 and -15
Step-by-step explanation:
a)5*5*5*5*5*5 there is 6 5's so, we can show it as, [tex]5^{6}[/tex]
[tex]5^{6}[/tex]=[tex]5^{x}[/tex]
x=6
b) in this one you found one of the answers of y which is 15.
but [tex]15^{2}=-15^{2}\\so y=15\\and y=-15[/tex]
Answer:
The answer is down below
Step-by-step explanation:
a) 5×5×5×5×5×5=5^x
5×5×5×5×5×5=5⁶
b)y²=225
square both sides
√y²=√225
y=15
(3x) raised by 2x is equal to (9x raised by 2)raised by 2
we have shown that [tex](3x)^2x = (9x^2)^2,[/tex] which is the equation you provided. This is true for any value of x, so the equation is valid. The statement you have provided is a mathematical equation that involves exponentiation. To understand this equation, we need to know the rules of exponents.
The rule for exponentiation with the same base states that when we have a base raised to multiple exponents, we can simply multiply the exponents. In other words, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can simplify the right-hand side of the equation to [tex](9x^2)^2 = 81x^4.[/tex]
Now, let's look at the left-hand side of the equation:[tex](3x)^2x[/tex]. To simplify this expression, we can use the distributive property of exponents. That is, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can write[tex](3x)^2x as (3x^2)^x.[/tex]Then, using the rule for exponentiation with the same base, we can write this as [tex]3^(2x) * x^(2x).[/tex]
So now we have the equation [tex]3^(2x) * x^(2x) = 81x^4.[/tex]We can simplify this equation further by dividing both sides by[tex]x^(2x) to get 3^(2x) = 81x^(4-2x).[/tex] Simplifying the right-hand side, we get [tex]3^(2x) = 81x^(2(2-x)) = 81x^(4-2x).[/tex]
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Mabel has $30,000 in a savings account that earns 11% annually. The interest is not compounded. How much interest will she earn in 2 years?
please help :(
Step-by-step explanation:
If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.
The formula for calculating simple interest is:
Interest = (Principal x Rate x Time)
Where:
Principal = $30,000
Rate = 11% = 0.11 (as a decimal)
Time = 2 years
So, substituting the values in the formula, we get:
Interest = (30,000 x 0.11 x 2) = $6,600
Therefore, Mabel will earn $6,600 in interest over a period of 2 years.
A straight trail leads from the Alpine Hotel,
elevation 8000 feet, to a scenic overlook,
elevation 11,100 feet. The length of the trail is
14,100 feet. What is the inclination (grade) of
the trail?
The inclination or grade of the trail from the Alpine Hotel to the scenic overlook is 21.9%.
The inclination or grade of a trail is the ratio of the change in elevation to the length of the trail, expressed as a percentage. To find the inclination of the trail from the Alpine Hotel to the scenic overlook, we need to first calculate the change in elevation.
Change in elevation = 11,100 feet - 8,000 feet = 3,100 feet
Now we can calculate the inclination or grade of the trail as follows:
Grade = (change in elevation / length of trail) x 100%
Grade = (3,100 / 14,100) x 100%
Grade = 0.219 x 100%
Grade = 21.9%
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Suppose that 42% of a population has a virus. You repeatedly test members of this population until you find one who is infected. Find the probability that: Round to three decimals. a. The first positive test is person number 9 : b. The first positive test happens on or before person number 9 : c. You test more than 9 people before getting a positive test :
The probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).
What is probability ?
Probability is a measure of the likelihood or chance that a particular event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
Given that 42% of the population has a virus, the probability that any given person has the virus is 0.42. We can use this information to answer the following questions:
a. The probability that the first positive test is person number 9 can be calculated using the binomial distribution:
[tex]P(X = 1) = (9-1)C(1) * 0.42^{1} * (1 - 0.42)^{(9-1)} = 0.251[/tex]
Therefore, the probability that the first positive test is person number 9 is 0.251 (rounded to three decimals).
b. The probability that the first positive test happens on or before person number 9 can be calculated using the cumulative binomial distribution:
P(X <= 1) = P(X = 0) + P(X = 1) = 0.58
Therefore, the probability that the first positive test happens on or before person number 9 is 0.58 (rounded to three decimals).
c. The probability that you test more than 9 people before getting a positive test can be calculated using the complementary probability:
P(X > 1) = 1 - P(X <= 1) = 1 - 0.58 = 0.42
Therefore, the probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).
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how many solutions the linear system have
Answer:
It all depends on the linear system
Step-by-step explanation:
A system of linear equations usually has a single solution but sometimes it can have no solution (parrel lines) or infinite solutions (same line).
I hope this helped
The answer is Three.
One solution.
Infinitely many solutions.
No Solutions at all.
The midpoint M of bar (RS) has coordinates (10.5,9). Point R has coordinates (1,10). Find the coordinates of point S.
Step-by-step explanation:
the midpoint between 2 points A (xa, ya) and B (xb, yb) is
M ((xa + xb)/2, (ya + yb)/2)
(xa + xb)/2 = 10.5
(ya + yb)/2 = 9
let's say R = A
(1 + xb)/2 = 10.5
(10 + yb)/2 = 9
1 + xb = 21
xb = 20
10 + yb = 18
yb = 8
S = (20, 8)
Select the equation that is true.
A.
2
2
3
×
4
=
8
2
3
B.
2
2
3
×
5
8
=
1
2
3
C.
2
2
3
×
2
3
=
2
4
9
D.
2
2
3
×
4
3
5
=
8
6
15
Answer:
D is the only possible answer
1. Suppose that there is a forest with 10,000 rabbits. We randomly select 100 of them, place a nonremovable mark on them, and set them free in the forest. After a couple of days, the marked rabbits mixed well with other living ones in the forest, and we randomly catch 50 rabbits from the forest. Find the probability that the sample of 50 rabbits contains exactly 2 marked rabbits.
The probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
Explain about the hypergeometric distribution?When sampling from either a small population without replacement, the hypergeometric distribution consists of a discrete probability distribution which determines the likelihood that an event occurs k times in n trials.
The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution.As a result, it is frequently used in random sampling to ensure statistical quality. A straightforward, indication would be choosing team members at random from a population of males and girls.The given data:
Total market sample of rabbits = 100.
Randomly selected rabbits = 50.
Let the probability that the sample of 50 rabbits contains exactly 2 marked rabbits be P(E).
Then, using hypergeometric distribution;
P(E) = ⁵⁰C₂ / ¹⁰⁰C₂
Solve the probability using the combination.
P(E) = 25*49 / 50*49
P(E) = 25/50
P(E) = 1/2
Thus, the probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
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A circle has a radius of 5.4 cm. What is the exact length of an arc formed by a central angle measuring 45°?
The length of the arc with a central angle of 45° is 4.24 cm
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The length of an arc formed on a circle with a central angle Ф and radius r is:
Length of arc = (Ф/360) * 2πr
Given the circle radius is 5.4 cm and the central angle is 45°, hence:
Length of arc = (Ф/360) * 2πr = (45/360) * 2π(5.4) = 4.24 cm
The length of the arc is 4.24 cm
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Solve for X.
3x + 3 - x + (-7) > 6
A. x > (-5)
B. x > 5
C. x > 2.5
D. x < 5
Answer:
B
Step-by-step explanation:
3x + 3 - x + (-7) > 6
2x + 3 - 7 > 6
2x - 4 > 6
2x > 10
x > 5
Answer:
B. x > 5
Step-by-step explanation:
3x + 3 - x + (-7) > 6
3x - x + 3 - 7 > 6
2x + (-4) > 6
2x - 4 > 6
2x > 6 + 4
2x > 10
x > 10 / 2
x > 5
:D
Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
The scale that Wyatt used is 1 inch represents 0.36 yards
What is the scale?The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.
Scale of the drawing = original length / length of the drawing
84 / 231 = 0.36 yards
This means that 1 inch is represented by 0.36 yards
Alternatively, it can be written as 1 : 0.36 yards
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The profit made by a small ski resort, not surprisingly, depends largely on the seasonal
weather. In a season with more than 75 inches of snow, it makes an average of $250,000. If snowfall is between 40 and 75 inches, the average profit is $160,000, and if snowfall
is less than 40 inches, it loses $70,000. The resort gets over 75 inches of snow 40% of
years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years. Find
the resort’s expected yearly profit
If the resort gets over 75 inches of snow 40% of years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years the resort's expected yearly profit is $161,500.
To find the resort's expected yearly profit, we need to calculate the weighted average of its profits under different snowfall conditions, using the probabilities of each condition occurring as weights.
Let P1, P2, and P3 be the probabilities of snowfall being over 75 inches, between 40 and 75 inches, and less than 40 inches, respectively. We are given that P1 = 0.4, P2 = 0.45, and P3 = 0.15.
Let R1, R2, and R3 be the profits that the resort makes under each of these snowfall conditions. We are given that R1 = $250,000, R2 = $160,000, and R3 = -$70,000 (since the resort loses money if snowfall is less than 40 inches).
Then the expected yearly profit, E, is:
E = P1R1 + P2R2 + P3R3
= 0.4250,000 + 0.45160,000 + 0.15(-70,000)
= 100,000 + 72,000 - 10,500
= $161,500
This means that, on average, the resort can expect to make a profit of this amount each year, taking into account the varying probabilities of different snowfall conditions.
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Help plsss
Determine if it’s linear
The functions are classified as follows:
a) Linear.
b) Linear.
c) Linear.
d) Non-linear.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.Hence, from the definition, a function is classified as linear if the highest exponent of both x and y is of one.
A term x on the denominator has an exponent of -1, hence item d is not a linear function.
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The linear equations in the options are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
How to deterimine if it is linear?We say that an equation is linear if the dependence with the veriables is only of first degree.
For example, equations of the form:
a*x + b*y = c
Are linear, because the variables x and y have an exponent of 1.
Then, the options that show linear equations are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
The last option is non linear, because x is on the denominator.
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27/27x+18 rewrite expression
The expression 27/(27x + 18) can be rewritten as 3/(3x + 2).
What are common factors?
Common factors are factors that two or more numbers share. In other words, they are factors that divide into two or more numbers without leaving a remainder. For example, the common factors of 12 and 18 are 1, 2, 3, and 6. These are the numbers that divide evenly into both 12 and 18.
Finding common factors is useful in simplifying fractions and factoring expressions. When simplifying a fraction, you can divide both the numerator and denominator by a common factor to reduce the fraction to its simplest form. When factoring an expression, you can factor out a common factor to simplify the expression and make it easier to work with.
It's worth noting that the greatest common factor (GCF) is the largest common factor that two or more numbers share. For example, the GCF of 12 and 18 is 6, which is the largest number that divides evenly into both 12 and 18.
To rewrite the expression 27/(27x + 18), we can factor out the greatest common factor in the denominator, which is 9. This gives:
27 / (9 * (3x + 2))
We can simplify this expression further by dividing both the numerator and denominator by 9, which results in:
3 / (3x + 2)
Therefore, the expression 27/(27x + 18) can be rewritten as 3/(3x + 2).
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pls help meee 100 points
Explain why this comparison is either reasonable
3.4< 3.36
WHAT DO I PUT IN
100 points if you help mee
Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.
The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.
Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.
Step-by-step explanation:
Help meeeeeeeee pleaseee
The quadratic function represented by the given table is:
y = -1*(x - 2)^2 + 3
How to find the quadratic function?Here we have a table that defines a quadratic equation, remember a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)^2 + k
Here we can see that the vertex is (2, 3), then we can write:
y = a*(x - 2)^2 + 3
And we can see that it also passes through the point (0, -1), then:
-1 = a*(0 - 2)^2 + 3
-1 = a*4 + 3
-1 - 3 = a*4
-4 = a*4
-4/4 = a = -1
The quadratic function is:
y = -1*(x - 2)^2 + 3
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A persons lung capacity can be modeled by the function C(t) = 250sin(2x/5 * t) + 2450 where C(t) represents the volume in mL present in the lungs after t seconds. State the maximum value of this function over one full cycle and explain what this value represents
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath. The function C(t) = 250sin(2I/5(t))+2450.
It shows the capacity of the lung of a person at any point of time t in milliliters (mL).
We not only need to find the one full cycle but also determine the period of function and it is given by:
T = 2I/(2I/5)
T = 5 seconds.
This means that the function completes one full cycle every 5 seconds.
To find the maximum value of the function over one full cycle, we need to find the maximum value of sin(2π/5(t)). The maximum value of sin(2π/5t) is 1, this happens at 2π/5(t) = π/2 + nπ, and n is considered as an integer.
So, the maximum value of the function occurs when sin(2I/5(t)) = 1, Substituting this into the original function, we get maximum value, Cm:
Cm = 250(1) + 2450
= 2700 mL.
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath.
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in a reaction that is first order with respect to x and first order with respect to y, which of the following changes will have no effect overall on the rate? if the concentration of a reactant is tripled and the rate increases by a factor of nine, what is the order with respect to that reactant? (a) doubling [x] and doubling [y] (b) doubling [x] (c) quadrupling [y] (d) halving [x] and doubling [y] (e) halving [x] and halving [y]
In a reaction that is first order reaction with respect to x and first order with respect to y, the change will have no effect overall on the rate is doubling [x]. The answer is option (b).
If the reaction is first order with respect to x and first order with respect to y, then the rate equation is given by Rate = k [x]^1 [y]^1 = k [x][y].Option (a) Doubling [x] and doubling [y] will increase the rate by a factor of Option (c) Quadrupling [y] will increase the rate by a factor of 4 x 4 = 16.
Option (d) Halving [x] and doubling [y] will have no overall effect on the rate since rate will increase by a factor of 2/1 = 2 and then decrease by a factor of 1/2 = 0.5, for an overall effect of 1. Option (e) Halving [x] and halving [y] will decrease the rate by a factor of 2 x 2 = 4.
Thus, option (b) Doubling [x] is the correct answer. If the concentration of a reactant is tripled and the rate increases by a factor of nine, then we can write k [x][y] = 9 k [x (3)][y]k = 9 k / 3 = 3 k. Since the concentration of x is raised to the power of 1, the order with respect to that reactant is 1.
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help me with this please im stuck
Answer:
refer to the attachment
What would a suitable class width be if your highest observed value (i.e., H) is equal to 400, your lowest observed value (i.e., L) is equal to 50, and your number of observations (i.e., n) is equal to 100?
100
The suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to 100.What is a class width?The class width is the width of each interval in a frequency distribution. It is found by subtracting the smallest value from the largest value and then dividing by the number of classes.Class width = (highest value - lowest value) / number of classesWhere,H = highest observed value = 400L = lowest observed value = 50n = number of observations = 100Using the formula:Class width = (H - L) / nClass width = (400 - 50) / 100Class width = 350 / 100Class width = 3.5Thus, the suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to.
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determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. x 2 4 6 p(x) 15 15 15 select all that apply: the given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. the given distribution is a probability distribution, since the sum of probabilities is equal to 1. the given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. the given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1.
The given distribution is not a probability distribution.
The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. A probability distribution must satisfy two conditions: 1) the probabilities must lie inclusively between 0 and 1, and 2) the sum of probabilities must be equal to 1.
In this case, the sum of probabilities is 15+15+15 = 45, which is not equal to 1. Therefore, the given distribution is not a probability distribution. The other options are incorrect because they do not accurately describe the given distribution.
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Yolanda makes 6 goals and 2 penalties ending the game with 16 points and neel earns 4 goals and 2 penalties and ends the game with 6 points use x and y to represent the number
the number of goals Yolanda scores without penalties is x = 8, and the number of goals Neel scores without penalties is y = 0.
Let x be the number of goals Yolanda scores without penalties, and let y be the number of goals Neel scores without penalties.
According to the problem, Yolanda makes 6 goals and 2 penalties, so her total number of goals is:
x + 6
And her total number of points is:
(x + 6) + 2(1) = x + 8
Similarly, Neel scores 4 goals and 2 penalties, so his total number of goals is:
y + 4
And his total number of points is:
(y + 4) + 2(1) = y + 6
We know that Yolanda ends the game with 16 points, so we can write:
x + 8 = 16
Subtracting 8 from both sides, we get:
x = 8
We also know that Neel ends the game with 6 points, so we can write:
Y + 6 = 6
Subtracting 6 from both sides, we get:
y = 0
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Dos ingenieros deciden medir la altura de una montaña cercana a un pueblo que está a 1200 msnm. Miden la cima de la montaña desde el punto "A" señalado en el gráfico con un ángulo de elevación de 37°, luego avanzan hacia al punto "B" que dista 480 m del punto "A" y vuelven a medir la cima con un ángulo de elevación de 45°. ¿Cuál es la altura de la montaña respecto al nivel del mar?
The height of the mountain above sea level is 777.94 m.
The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.
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14x +5y = 31 slve for x
Answer: x = 31 over 14 − 5y over 14
Step-by-step explanation: Move all terms that don't contain x to the right side and solve.