For case (a), the person can hike up and down the mountain in 4 different ways. For case (b), the person can hike up and down the mountain in 15 different ways. For case (c), the person can hike up and down the mountain in 12 different ways.
In case (a), the person must take the same trail both ways, so there are only 4 different options available, one for each of the 4 trails.
In case (b), the person can take the same trail both ways if they choose, but they are not required to do so. This means that they have 4 different options for the trail they take on the way up, and then 4 different options for the trail they take on the way down. This results in a total of 4 x 4 = 16 different possibilities.
However, one of these possibilities is the case where the person takes the same trail both ways, which has already been counted in case (a), so we need to subtract this possibility to avoid double counting. This results in a total of 16 - 1 = 15 different possibilities.
In case (c), the person does not want to take the same trail both ways, so they have 4 different options for the trail they take on the way up, and then 3 different options for the trail they take on the way down (since they cannot take the same trail they took on the way up). This results in a total of 4 x 3 = 12 different possibilities.
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If ACDG~ AEDF, find the value of x.
F
2x + 7
48
D
5x2
40
E
G
The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF
What is meant by a triangle?Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. Since it was first described on the first page of Euclid's Elements, the vocabulary for classifying triangles is more than two thousand years old. Modern categorization names are either literal transliterations of Euclid's Greek or their Latin interpretations.
A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is used to signify a triangle in the previous illustration.
FD/DC=ED/DG
2x+7/48=5x-2/40
40(2x+7)=48(5x-2)
80x+280=240x-96
160x=376
x=2.35
Therefore, The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF
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it is known that pre-schoolers, on average, spend three hours a week on tablets. i believe that this is no longer true, and that the average time that pre-schoolers spend on tablets differs in either direction from the previously given average. i calculate a z-test statistic of 1.74. what is my statistical decision?
Retain the null because 1.74 is greater than 1.645.
What is z - test statistic?
Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.
Z-tests examine a distribution's mean.
Let X be the average time that prescholars spend on tablets.
X ~ N(μ, α^2)
To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.
The z - test statistic is obtained as 1.74.
Taking level of significance α = 0.05
Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]
Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],
so we retain the null hypothesis.
Hence, retain the null because 1.74 is greater than 1.645.
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Complete question:
Complete question is attached below.
Write to the equation y=mx+b in the terms of m?
Answers
M=y-b divided by x
M=X+b divided by y
M=y divided by X -b
M=xy-b
Which one?
The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
What is the isolation of a variable in an equation?
Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.
Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.
How to solve the question?
In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.
This means that we need to isolate the variable m, to get an expression equal to m.
The isolation of the variable m can be done as follows:
y = mx + b,
or, y - mx = mx + b - mx {Subtracting mx from both sides},
or, y - mx = b {Simplifying},
or, y - mx - y = b - y {Subtracting y from both sides},
or, -mx = b - y {Simplifying},
or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}
or, m = (y - b)/x {Simplifying}.
Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
What is the isolation of a variable in an equation?
Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.
Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.
How to solve the question?
In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.
This means that we need to isolate the variable m, to get an expression equal to m.
The isolation of the variable m can be done as follows:
y = mx + b,
or, y - mx = mx + b - mx {Subtracting mx from both sides},
or, y - mx = b {Simplifying},
or, y - mx - y = b - y {Subtracting y from both sides},
or, -mx = b - y {Simplifying},
or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}
or, m = (y - b)/x {Simplifying}.
Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.
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PLEASE HELP!!!!! I WILL MARK BRAINIEST
Answer:
Step-by-step explanation:
7/8
------
3/10
use the fraction rule: 7x10/8x3- 35/12
try that, im not sure if its fully correct
Solve by factoring
X^2+x=63
Answer:
x = 3[tex]\sqrt{7- x}[/tex]
Step-by-step explanation:
so what you do here is move the x to the other side.
X^2 = 63 - x
then you square root both sides
so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]
so you end up with
x = [tex]\sqrt{63 - x}[/tex]
so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with
x = 3[tex]\sqrt{7- x}[/tex]
have a good day :)
A shipping container will be used to transport several 50-kilogram
crates across the country by rail. The greatest weight that can be
loaded into the container is 27500 kilograms. Other shipments
weighing 9500 kilograms have already been loaded into the container.
Write and solve an inequality which can be used to determine x, the
number of 50-kilogram crates that can be loaded into the shipping
container.
Answer:
50x + 9500 ≤ 27500
x ≤ 360
Step-by-step explanation:
50x + 9500 ≤ 27500 Subtract 9500 from both sides
50x + 9500 - 9500 ≤ 27500 - 9500
50x ≤ 18000 Divide both sides by 50
[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]
x ≤ 360
y=a-bx^2 to make x the subject
Answer:
y=a -bx^2
-bx^2 = y-a
bx^2 = a-y
x^2 = (a-y)/b
x = + or - sqr[(a-y)/b]
50 POINTS!!! Which graph represents this system? y = 3. x + y = 4. Which graph represents this system? y = 3. x + y = 4. On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (3, 7). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (2, 6). On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (4, 0). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
For a system with equations y = f(x) and y = g(x), the graph of the system will be just a coordinate plane with the two functions graphed on it.
What is functions graphed?
What Does Graphing Functions Mean? Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function. As an illustration, the graph below depicts the linear function f(x) = -x+ 2.
From this, we can see that the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
Also a graph of the system can be seen at the end of this answer.
Here our system is:
y = 3
x + y = 4
The first one is a horizontal line at y = 3.
The second can be rewritten as:
y = -x + 4
So this is a line with a negative slope, that passes through the points (0, 4) (when you evaluate in x = 0, you get y = 4) and (4, 0) (when you evaluate in x = 4, you get y = 0)
Then the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
The graph can be seen below
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Consider the line -8x -6y = -4.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
What is the slope of a line?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.
y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.
where m is the slope and m = y/x
Take notice that tanФ = y/x.
This tanФ is often referred to as the line's slope.
Calculation:The given equation is of the form [tex]ax+by=c[/tex]
On comparing we can say that a is -8 and b is -6
So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]
The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]
Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
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Steven is a waiter. He earns $3.45 an hour plus 20% tips. One day he worked 7 hours and served meals costing $497 what were his earring? Round you answer to the nearest cent.
A cylindrical dog feeder is 18 inches tall and has a diameter of 8 inches if the feeder is currently half full, how much more food can be poured into the feeder? Use 22/7 for pie and round to the nearest cubic inch.
453 cubic units of food is poured to the cylindrical dog feeder of 18 inches tall and has a diameter of 8 inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the cylindrical dog feeder is 18 inches tall and has a diameter of 8 inches
height is 18 inches
Diameter=8 inches
Radius =4 inches
The feeder is currently half full, how much more food can be poured into the feeder.
We know that volume of a cylinder is V=πr²h
Substitute the values of r and h in the given formula.
V=22/7(4)²×18
=22×16×18/7
=6336/7
=905.142.
As the feeder is currently half full, so let divide the volume by 2.
905.142/2
=452.5
=453
Hence, 453 cubic units more food is need or poured into the feeder.
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A football team has four different jerseys that players wear throughout the season: school colors, white, throwback, and pink (for breast cancer awareness). The tree diagram shows the conditional probabilities of the outcome of their games when players wear each type of jersey.
For a randomly selected game, determine the probability that players wore their white jerseys, given that they won.
0.34
0.41
0.42
0.80
Answer:0.41
Step-by-step explanation:
4. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).
The proof that AB = CD in the concentric circles is shown below
How to prove the equation AB = CDFrom the question, we have the following parameters that can be used in our computation:
The concentric circles
This means that the circles have the same center
From the circles, we have the following congruent lines
AC = BD
Subtract BC from both sides of the equation
So, we have the following representation
AC - BC = BD - BC
Evaluate the difference
This gives
AB = CD
Hence, it is true that AB = CD
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Answer:
Hope it will help you...
consider the following: the mayor of a town has proposed a plan for the annexation of a new community. a political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 65%. what is the alternative hypothesis? group of answer choices
We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.
What do you mean by Annexation?
International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.
According to the question,
We have the given data:
A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.
The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.
This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.
Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.
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Write a paragraph that explains how you solved the equation 4(t + 25) = 4(t + 50) - 4(0.15t). You may include equations as part of your explanation, but be sure to use correct math terminology and write in complete sentences.
The equation 4(t + 25) = 4(t + 50) - 4(0.15t) can be solved as explained below to determine the value of t, which is t = 166.67.
How to Solve an Equation?If we are given the equation, 4(t + 25) = 4(t + 50) - 4(0.15t), to find the value of the variable t, follow the steps explained below.
4(t + 25) = 4(t + 50) - 4(0.15t) [given]
Open the parentheses by applying the distributive property:
4t + 100 = 4t + 200 - 0.6t
Combine like terms:
4t + 100 = 3.4t + 200
4t - 3.4t = -100 + 200
0.6t = 100
Divide both sides by 0.6
0.6t/0.6 = 100/0.6
t = 166.67
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what is the answer to this question?
−6(4y + 4y + (−4))
Answer:
-48y+24
Step-by-step explanation:
−6(4y + 4y + (−4))
=-6(8y+-4)
=-48y+24
Answer:
-48y + 24
Step-by-step explanation:
−6(4y + 4y + (−4)) =
= −6(8y - 4)
= -48y + 24
Number of nickels in $4.20
Answer:4
Step-by-step explanation:
(Find LCM of) :
ax² - (a² + ab)x+ a²b,
bx² - (b² + bc)x+ b²c and
cx² - (c² + ac)x + c²a
Answer:
Here is answer
Step-by-step explanation:
To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.
Let's start by factoring each of the given polynomials:
ax² - (a² + ab)x+ a²b = a(x - b)x
bx² - (b² + bc)x+ b²c = b(x - c)x
cx² - (c² + ac)x + c²a = c(x - a)x
The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.
Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.
according to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (n) and a 45% chance of experiencing decreased sexual drive (d). the information also states that there is a 14% chance of experiencing both side effects. what is the probability of experiencing only nausea?
The probability of experiencing only nausea is 0.06.
Using Venn Probabilities, it is found that there is a 0.45 = 45% probability of experiencing neither of the side effects.
What is a Venn probability?
In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
P(N∪D) = P(N) + P(D) - P(N∩D)
In this problem, the probabilities given are:
P(N)= 0.2 , P(D)= 0.45 , P(N∩D) = 0.14
The "at least one" probability is:
P(N∪D) = 0.20 + 0.45 - 0.14 = 0.51
Hence, the "neither" probability is:
1 - P(N∩D) = 1 - 0.51 = 0.49
The probability of experiencing only nausea = P(nausea) - P(both side effects)
=0.20 - 0.14
=0.06
0.49 = 49% probability of experiencing neither of the side effects.
The probability of experiencing only nausea is 0.06.
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due today pls help me
Answer: B
Step-by-step explanation:
A - Nope.
B - Possibility.
C. Nope. (2.23606797)
D. Nope.
When facing questions like this, it can be easier to use the process of elimination.
7. Olivia purchases gifts for her mom and
grandma
for Mother's Day. The first is a pair of
sunglasses for $16.35 and the second is a
bracelet. Her total is $39.75. How much did she
spend on the bracelet?
Answer: $23.40
Step-by-step explanation:
To find out how much Olivia spent on the bracelet, we need to subtract the cost of the sunglasses from the total amount spent. In this case, that would be $39.75 - $16.35 = $<<39.75-16.35=23.40>>23.40. Therefore, Olivia spent $23.40 on the bracelet.
Need help
What criteria are necessary to prove that two triangles are congruent to one another?
Answer:
SSS, SAS, ASA, AAS
Step-by-step explanation:
s = sides
a = angle
A tutor guarantees that 10% of her students will obtain A on every test they write. For the last test, the mean mark is 68 and the standard deviation is 6.
What mark is required to receive an A on the test?
The mark that is required to receive an A on the test is; 75.68
How to find sample mean?The formula for z-score here with the parameters given is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
p-value = 10% = 0.1
μ = 68
σ = 6
Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;
1.28 = (x' - 68)/6
x' = 68 + (1.28 * 6)
x' = 75.68
We conclude that this value is the mark required to receive an A on the test.
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Make b the subject of p=1/2ab^2
Answer:
b = [tex]\sqrt{2p/a}[/tex]
Step-by-step explanation:
The given equation is:
p=1/2ab^2
Multiply by 2 on both sides
2p = ab^2
Then divide by a on both sides,
b^2 = 2p/a
take square root on both sides, then we can get subject of b,
b = [tex]\sqrt{2p/a}[/tex]
Hence, the subject of the given equation make the value of b is b = [tex]\sqrt{2p/a}[/tex]
The subject of an equation is the value that is being solved for. An equation is a mathematical statement consisting of an equality sign (=) between two expressions that have the same value. The expression on the left side of the equality sign is called the left-hand side, while the expression on the right side of the equality sign is called the right-hand side. The left-hand side of the equation can be thought of as what is being solved for, while the right-hand side of the equation can be thought of as the clues or tools that are used to solve for the left-hand side. For example, in the equation 3x + 1 = 7, the subject of the equation is the variable x, which is the value that is being solved for.
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Select the correct answer.
Which graph represents function g?
g(x) = (-x)1/2
Answer:
Step-by-step explanation:
g(x) = (-x)1/2
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.
A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?
y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1
The system of inequalities that matches the graph is defined as follows:
y ≤ 3x.y > –2x – 1.How to define the system of inequalities?The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.
This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:
y ≤ 3x
he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.
When x increased by 3, y decayed by 6, hence the slope of the line is of:
m = -6/3 = -2.
Then:
y = -2x + b.
When x = 1, y = -3, then the intercept is given as follows:
-3 = -2 + b
b = -1.
Thus the constraint is of:
y > –2x – 1.
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What is the quotient of 535 ÷ 30? Enter your answer in the boxes.
what has the greatest value
Answer:
The greatest place value of a number is the first non-zero digit on the left in that number.
The original selling price was $171.59. The sale proteas $148.37. What is the first step in finding the percent markdown? Find the percent markdown
The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Original selling price = $171.59
Price during sales = $148.37
Then, the percentage markdown will be,
% markdown = (171.59 - 148.37)/171.59 × 100
= 23.22/171.59 × 100
% markdown = 13.53%
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closed-ended measures should provide response categories that are mutually exclusive and exhaustive. group of answer choices true false
It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.
It has been observed that when two occurrences are mutually exclusive, they cannot take place simultaneously. However, it need not entail that one of the two occurrences must take place. As a result, when two events are exhaustive of one another, one of them is said to occur.
It signifies that two occurrences cannot happen at the same moment if they are mutually exclusive. However, it doesn't entail that one of the two events must take place. If two occurrences are mutually exclusive, then one of them must take place.
The categories (answer possibilities) must, in the first place, be mutually exclusive, which means they cannot overlap. In order to give all alternatives that might make up a response list, survey answer options must be collectively thorough.
For instance, the act of flipping a coin is said to be both mutually exclusive and collectively exhaustive. Either heads or tails must result in this situation. These are variables, then.
Therefore,
It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.
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