Answer:
Step-by-step explanation:
The two equations that have the solution x = 2 when x is substituted for 2 are:
Equation 1: 2 + 3x = 10
2 + 3(2) = 10
2 + 6 = 10
8 = 10
Equation 2: 2x + 4 = 10
2(2) + 4 = 10
4 + 4 = 10
8 = 10
help please its very urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(Thank you!)
Answer:
4x+5 = 13
Step-by-step explanation:
2x-7= 5
Picture⬇️. Thank you!
Answer:
The bottom most option
Step-by-step explanation:
Lets divide 3 2/5 and 3 1/6
3 2/5 = 17/5 and 3 1/6 = 19/6
17/5/(19/6) = 17/5 x 6/19 = 102/95 = 1 7/95 or the last option.
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A, B & C form the vertices of a triangle.
CAB = 90°, ABC = 38° and AC = 9.1.
Calculate the length of BC rounded to 3 SF.
In given triangle ABC the length if BC is 7.1 .
What is trigonometric functions?
A subfield of mathematics called trigonometry is concerned with the study of triangles. It is frequently referred to as "trig" casually. In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.
Here in given triangle contains 90°, So it is right triangle.
Now using tangent function then
=> tan B = [tex]\frac{opposite}{adjacent}[/tex] then
=> tan 38° = [tex]\frac{AC}{BC}[/tex]
=> BC = tan 38° × AC
=> BC = tan 38° × 9.1
=> BC = 7.1
Hence the length of the side BC is 7.1.
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The length of BC in the triangle ABC is 7.109.
What is the length of side?Trigonometry is a branch of mathematics concerned with the study of triangles. It is commonly referred to as "trig" in a casual manner. Trigonometry examines how the sides and angles of triangles relate to one another.
Because the given triangle contains 90°, it is a right triangle.
Now, using the tangent function,
The tangent function is one of trigonometry's six primary functions.
Tan A = Opposite Side/Adjacent Side is the Tangent Formula. In terms of sine and cosine, tangent may be represented as: Tan A = Sin
then,
= tan B = opposite side / adjacent side
= tan 38° = AC/BC
= BC = 38° tan x AC
= BC = tan 38° × 9.1
= BC = 7.109
As a result, the length of the side BC is 7.109.
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A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the p-value of the test
The p-value is a probability and it should be between 0 and 1.
The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.
In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.
Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.
It is also important to note that the p-value is a probability and it should be between 0 and 1.
Therefore, The p-value is a probability and it should be between 0 and 1.
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I need help with thi
The length of each diagonal is of: 11 units.
How to obtain the length of each diagonal?The diagonal lengths are defined as follows:
WY = 6x - 7.XZ = 3x + 2.As the figure is a rectangle, the diagonal lengths are the same, and thus the value of x is obtained as follows:
WY = XZ
6x - 7 = 3x + 2
3x = 9
x = 9/3
x = 3.
Hence the diagonal length is given as follows:
XZ = 3(3) + 2 = 9 + 2 = 11 units.
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In a study; the sample is chosen by separating all cars by size, and selecting 10 of each size grouping What is the sampling method? Simple Random Systematic Stratified Cluster Convenience
Stratified sampling is used when the population is heterogeneous.
What is Stratified sampling?
A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub-populations) and random samples are drawn from each. This increases representativeness as a proportion of each population is represented.
The sampling method described in the study is a stratified sampling method.
In stratified sampling, the population is first divided into subgroups or strata based on some relevant characteristic, such as size in this case.
Then, a simple random sample is taken from each stratum.
In this study, the sample is chosen by separating all cars by size and selecting 10 of each size grouping, this is the definition of stratified sampling.
Stratified sampling is useful when the population is heterogeneous and you want to ensure that the sample is representative of specific subgroups within the population.
This method allows for a more precise estimation of population characteristics and can reduce sampling error.
Hence, Stratified sampling is used when the population is heterogeneous.
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For what values of x is the equation 34+x4=1 true?
Answer:
true
Step-by-step explanation:
i had the same question on a quiz.
The value of x for the equation 34+x4=1 is [tex]\frac{-33}{ 4}[/tex]
As we have [tex]34+4x=1[/tex]
Subtracting [tex]34[/tex] from both sides we get
[tex]4x=1-34[/tex]
[tex]4x=-33[/tex]
Dividing with [tex]4[/tex] both sides
we get the answer [tex]x=\frac{-33}{4}[/tex]
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allante pizza delivers pizzas throughout its local market area at no charge to the customer. however, customers often tip the driver. the owner is interested in estimating the mean tip income per delivery. to do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. these data are: $2.25 $2.50 $2.25 $2.00 $2.00 $1.50 $0.00 $2.00 $1.50 $2.00 $3.00 $1.50 suppose the owner is interested in developing a 90% confidence interval estimate. given the fact that the population standard deviation is unknown, what distribution will be used to obtain the critical value?
The distribution used to obtain the critical value in this situation is the Student's t-distribution.
What is critical value?Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.
The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.
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Solve for X, Leave in simplest radical
Answer:
32
Step-by-step explanation:
[tex]8\sqrt{3}[/tex] is opposite to the 60 degree angle
The side opposite to the 60 degree angle = [tex]\sqrt{3}[/tex] times the side opposite to the 30 degree angle.
Side opposite to the 30 degree angle = 8
Leg opposite to the 30 degree angle theorem states that the side opposite to the 30 degree angle is half of the hypotenuse.
Hypotenuse = 16
In the big triangle, 16 is the side opposite to the 30 degree angle, which means it is half of the hypotenuse (big triangle).
Hypotenuse of the big triangle = x = 32
Hope this helps :)
Have a great day!
Melanie babysits for $14 per hour.
If she earned $91 last week,
how many hours did she work?
Define the variable. Write and
solve the equation.
Answer:
Equation is 14h = 91
It solves to h = 6.5
===========================================
Work Shown:
h = number of hours worked
14h = amount earned at $14 per hour
14h = 91 is the equation
To solve this equation, divide both sides by 14.
14h = 91
14h/14 = 91/14
h = 6.5
She worked 6.5 hours last week.
How is shape d different from shapes a, b, and c?
it has 2 pairs of angles with the same
measure.
a
b
)
it has 2 acute angles and 2 obtuse
angles.
it has only 1 pair of parallel sides.
d
it has 0 pairs of perpendicular sides.
done
On solving the provided question, we can say that unlike other shapes, which all have parallel lines, only has one parallel side.
what is parallel lines?Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.
unlike other shapes, which all have parallel sides, only has one parallel side.
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B. Reviewing Key Terms
Complete each sentence by writing the correct term in the blank.
15. When a bank borrows money from another bank, the interest rate it pays is called the
16. Ownership of more than one bank constitutes a
17. When a bank customer writes a check, the check will go through the process of
M
18. A bank's total assets minus its total liabilities make up its
19. Banks repay loans from the Federal Reserve at a rate of interest called the
The correct term for each term is -
Federal Fund Rate
Bank holding company
Check clearing
Net worth
Discount rate
What is an account?
A certain kind of financial asset or debt that is kept and owned in your name.
When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.
Ownership of more than one bank constitutes a bank holding company.
When a bank customer writes a check, the check will go through the process of check clearing.
A bank's total assets minus its total liabilities make up its net worth.
Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.
Therefore, these are the key terms used in banking.
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I NEED HELP IMMEDIATELY!!
One shake and two taco supremes provide 2830 calories. Two shakes and one taco supreme provide 2540 calories. Find the caloric content of each item. One shake contains calories.
Answer:
We can set up a system of equations using the information given:
x + 2y = 2830 (equation 1)
2x + y = 2540 (equation 2)
where x is the number of calories in one shake and y is the number of calories in one taco supreme.
We can use either equation to solve for one of the variables and then substitute that into the other equation.
From equation (1), x = 2830 - 2y
And substituting this into equation (2) we get
2(2830-2y) + y = 2540
Now we can solve for y.
5,660 - 4y + y = 2540
-3y = -3120
y = 1040
So, one taco supreme contains 1040 calories.
And substituting this value of y back into equation (1) we can find the number of calories in one shake:
x + 2(1040) = 2830
x = 550
So, one shake contains 550 calories.
in a group of 10 people, each person shakes hands with everyone else once. how many handshakea re there
The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.
Number of people in the group = 10
Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂
where C denotes the combination , is represent an arrangement of objects in different ways without care of order.
Total number of handshakes = ¹⁰C₂
= 10!/2!(10 - 2)! = 10!/2!×8!
= 10×9×8!/(2×1)8!
= (10×9)/2
= 45 handshakes.
In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90
(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).
The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.
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The circle centered at (2, -1) and with radius 4 intersects the circle centered at (2, 5) and with radius sqrt10 at two points A and B. Find (AB)^2
The value of (AB)² is 15.
A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius. Two circles can be called congruent if they have the same radius. Equal chords are always equidistant from the center of the circle. The perpendicular bisector of a chord passes through the center of the circle. When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points. Tangents drawn at the endpoints of the diameter are parallel to each other.
Equation of first circle:
(x - 2)² + (y + 1)² = 4²
Equation of secnd circle:
(x - 2)² + (y - 5)² = (√10)²
Solve for (x - 2)² :
(x - 2)² + (y + 1)² = 4² ==> (x - 2)² = 16 - (y + 1)²
(x - 2)² + (y - 5)² = (√10)² ==> (x - 2)² = 10 - (y - 5)²
Then,
16 - (y + 1)² = 10 - (y - 5)²
16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)
15 - 2y - y ² = -15 + 10y - y ²
30 - 12y = 0
12y = 30
y = 30/12 = 5/2
Thus, the y coordinate of A and B is 5/2.
Then solve for x :
(x - 2)² = 16 - (5/2 + 1)²
(x - 2)² = 15/4
x - 2 = ± √(15/4) = ±√15/2
x = 2 ± √15/2
Thus, the x coordinates for either A or B are 2 +√15/2 or 2- √15/2.
The intersections points are A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). Thus, the squared distance between them:
(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²
(AB)² = (-√15)² + 0²
(AB)² = 15
Thus, the value of (AB)² is 15.
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Which number produces an irrational number when multiplied to 0.5?
Answer: Root 16 = 4, 4*1/2= 2
1/3*1/2= 1/6 r5/9*1/2= 5/18
Root 3 = 1.73205...*1/2= 0.866025...
Root 3 is the answer
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The Scott family takes a walk together every night after dinner. It takes them 5 minutes to walk 4 blocks.
Complete the table.
Minutes 5
30
Blocks walked 4 12 16
The solution to the equations are
The number of blocks walked in 5 minutes = 4 blocks
The number of blocks walked in 30 minutes = 24 blocks
The time taken to walk 4 blocks = 5 minutes
The time taken to walk 12 blocks = 15 minutes
The time taken to walk 16 blocks = 20 minutes
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The time taken for the Scott family to walk 4 blocks = 5 minutes
So , time taken for the Scott family to walk 12 blocks = 3 x time taken for the Scott family to walk 4 blocks
Substituting the values in the equation , we get
Time taken for the Scott family to walk 12 blocks = 3 x 5 = 15 minutes
And ,
Time taken for the Scott family to walk 16 blocks = 4 x time taken for the Scott family to walk 4 blocks
Substituting the values in the equation , we get
Time taken for the Scott family to walk 16 blocks = 4 x 5 = 20 minutes
Now ,
Number of blocks walked in 5 minutes = 4 blocks
So , the number of blocks walked in 30 minutes = 6 x Number of blocks walked in 5 minutes
Substituting the values in the equation , we get
The number of blocks walked in 30 minutes = 6 x 4 = 24 blocks
Hence , the equations are solved
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2. maria has 3 more than 4 times how much money josh has in savings. if josh has $505, how much does maria have?
Answer:
2023
Step-by-step explanation:
3 + 4x = y
y = 3 + 4(505)
y = 3 + 2020
y = 2023
"Please help me out with this one !!! Evaluate the integral.1∫0r3over⩗ 16 + r2dr
The provided integral may be expressed as follows using the following statement as a guide: 128/3 - 31 [tex]\sqrt{17}[/tex] /3
What is the definition of an integral?An integral in mathematics is either a number that depicts the area underneath the graph of a function over a specific period of time or a about before, the reversed of which includes the initial result (indefinite integral). To complete the whole, an essential component is required. The term crucial is a close synonym in this context. Integrals of functional and equations are a concept in mathematics. The word "aal" is derived from Middle English, which is derived from Latin Word integralis "thinking up unity," from Latin "with, entire."
To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]
Put [tex]$16+r^2=t^2$[/tex]
[tex]$2 r d r=2 t d t$[/tex]
[tex]$r d r=d t$[/tex]
[tex]$r=0 \Rightarrow t=4$[/tex]
[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} t d t$[/tex]
[tex]$=\left[\frac{t^3}{3}-16 t\right]_4^{\sqrt{7}}$[/tex]
[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]
[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
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On Monday,Jeffery drove 146.3 miles. On Tuesday, he drove 84.13 miles. On Wednesday, he drove 73.02 miles. How many miles did he drive overall?
Answer:
Jeffrey drove a total of 303.43 miles on Monday, Tuesday, and Wednesday.
Step-by-step explanation:
To find the total miles driven by Jeffrey on Monday, Tuesday, and Wednesday, we need to add up the total miles. The total miles driven are 146.3 + 84.13 + 73.02 = 303.43 miles.
What are the 2 types of system types?
There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range.
1. Discrete systems: A system with distinct, separate elements, such as a set of integers or a graph.
2. Continuous systems: A system with elements that are connected and can take on any value over a range, such as a line or a curve.
1. Discrete systems: A discrete system is a system with distinct, separate elements. Examples include a set of integers, a graph, or a network of nodes. Discrete systems are usually studied using discrete mathematics.
2. Continuous systems: A continuous system is a system with elements that are connected and can take on any value over a range. Examples include a line, a curve, a function, or a surface. Continuous systems are usually studied using calculus.
There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range. Discrete systems are studied using discrete mathematics, while continuous systems are studied using calculus.
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HELP FOR BRAINLIEST ANSWER
Answer:
(motorboat speed is 40 km/h)
(current speed) = 10 km/h
Step-by-step explanation:
Ok, let the speed of the water current be x and the speed of the motorboat be y. Then, the speed of the motorboat upstream
against the current is (x - y)
Putting it into the equation, we get,
5h (x - y) = 150 km or
(x - y) = 30 km/h - 1
Now, downstream speed is (x + y).
Again, forming it into equation, we get,
3(x + y) = 150
x + y = 50 km/h - 2
Adding both equations, we get,
2x = 80 km/h
x (motorboat speed is 40 km/h)
40 - y = 30 km/h
y(current speed) = 10 km/h
Answer:
still water (s): 40 mph
current rate (c): 10 mph
Step-by-step explanation:
We are given two things:
1) 5 hours to travel 150 mi upstream
2) return trip 3 hours downstream
Note that when the boat goes upstream, it must push against the current, versus when it goes downstream, the current helps the boat to move. Also keep in mind the trip is always 150 mi both ways.
With that said, lets set up the problem. First, let s be the rate of the boat in still water, and let c be the rate of the current. We must keep in mind that when the boat goes upstream, it impedes its overall speed. So our equation for that looks like:
5(s-c)=150 (use for upstream)
And downstream would look like:
3(s+c)=150 (use for downstream)
Now that we have both equations, the next step is to expand them. You should get the two following equations:
5s-5c=150 AND 3s+3c=150.
Essentially, we are going to need to solve a system of equations here. You must add them to solve. First, multiply the first equation above by 3 and get 15s-15c=450 and multiply the second one by 5 and get 15s+15c=750.
When we add them we will get the following equation as a result: 30s=1200. Now divide both sides by 30 revelaing s to be 40. Now substiute in:
3(40)+3c=150
120+3c=150
-120 -120
3c=30
c=10
The system of equations is now solved revelaing the speed of the boat in still water to be 40 and the current speed to be 10.
how many distinguishable ways are there to write $9$ as the sum of $1\text{'s},$ $2\text{'s},$ and $4\text{'s},$ where the order of the addends matters? for example, $4 4 1$ and $1 4 4$ are two different ways.
The required number of ways to write 9 as sum of 1, 2, 4 is 96 ways.
What is permutation?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.
According to question:Two fours and one one Three numbers must be added up. Any one of the three spaces will accept a one before fours are used to fill the remaining slots. There are thus 3 possible arrangements for these. Thus, there are
1 + 8 + 21 + 6 + 20 + 20 + 5 + 12 + 3 = 96 ways
Thus, there are 96 ways to write 9 as sum of 1, 2, 4.
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Solve for X, Leave in simplest radical form.
X=5times (root2)/2
Step-by-step explanation:
Sin45=x/5
x=5sin45
x=5 times root2/2
What is Sin45? In trigonometry, there are three primary ratios, Sine, Cosine and Tangent, which are used to find the angles and length of the right-angled triangle. Before discussing Sin 45 degrees, let us know the importance of Sine function in trigonometry. Sine function defines a relation between the acute angle of a right-angled triangle and the opposite side to the angle and hypotenuse. Or you can say, the Sine of angle α is equal to the ratio of the opposite side(perpendicular) and hypotenuse of a right-angled triangle. The trigonometry ratios sine, cosine and tangent for an angle α are the primary functions. The value for sin 45 degrees and other trigonometry ratios for all the degrees 0°, 30°, 60°, 90°,180° are generally used in trigonometry equations.to learn more about Tangent refer to:
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A number or algebraic expression is said to be in its simplest radical form and to be an nth root if it lacks any elements that are perfect nth powers under the radical.
What is meant by simplest radical form?The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to be in its simplest radical form and be an nth root.
When all of a radical expression's perfect squares, cubes, etc. are eliminated from the radical, the radical is in its simplest form. A radical is a phrase containing a root, most frequently a square or cube root.
Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
Sin45 = x/5
x = 5 sin 45
x = 5 × (√2)/2
Therefore, the value of x be x = 5 × (√2)/2
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What is answer to this very hard question
Check the picture below.
[tex]cos(Y )=\cfrac{\stackrel{adjacent}{6}}{\underset{hypotenuse}{15}}\implies cos(Y)=\cfrac{2}{5}\implies cos^{-1}[cos(Y)]=cos^{-1}\left( \cfrac{2}{5}\right) \\\\\\ Y=cos^{-1}\left( \cfrac{2}{5}\right) \implies Y\approx 66.4^o[/tex]
Make sure your calculator is in Degree mode.
Answer:
66.4
Step-by-step explanation:
Hope this helped!
one student made a purchase from three different online retailers, a, b, and c. she paid for next day shipping on each purchase. the probabilities of next day orders arriving on time for each retailer are 0.99, 0.97, and 0.96, respectively. if purchases from different retailers arrive on time independently of one another, what is the probability that none of the student's purchases arrive the next day?
the probability that none of the student's purchases arrive the next day
P( STUDENT) = 0.99 - 0.97 = 0.002
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
here,
the probabilities of next day orders arriving on time for each retailer are 0.99, 0.97, and 0.96,
the probability that none of the student's purchases arrive the next day
P( STUDENT) = 0.99 - 0.97 = 0.002
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Please answer within 10 min! The information is in the picture.
Answer:
CD = 3/√2 in
Step-by-step explanation:
You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.
Similar trianglesAll of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.
In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...
CD = BD = CB/√2
CD = 3/√2 in
__
Additional comment
Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...
CD = 3/√2 = (3/2)√2 = 1.5√2
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consider the following bet. you toss two coins. if both of them come up heads, you win and get $10. otherwise you lose and have to pay $2. would you take this bet?
I would recommend taking this bet, as the expected value of the bet is Positive.
The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is a good bet to take. It is more likely that you will gain money .
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Answer:
14.8%
Step-by-step explanation:
decrease = -100 * ((final - initial) / initial)
Answer:
14.8%
Step-by-step explanation:
Original fishing pole cost: $54
New fishing pole cost: $46
Using the percentage decrease formula:
[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex] ×100%
Substitute
[tex]\frac{54-46}{|46|}[/tex] ×100%
From this, you should get 14.814814814814814...
Round to nearest tenths.
Final answer: 14.8%
the australian official lottery has scratch-off instant lottery tickets that can be purchased for $1. the probability of winning a prize is 1 in 4. (a) mr. urban is feeling lucky one day and decides to purchase 100 of the scratch-off instant lottery tickets. find the probability that fewer than 20 tickets are winners.
In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.
The probability that k out of n trials will be successful is given by the binomial probability mass function:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.
To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.
P(x<20) = P(0) + P(1) + P(2) +...+ P(19)
using the above formula we can find the probability of getting k winning tickets
P(x<20) = P(0) + P(1) + P(2) +...+ P(19)
= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81
This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.
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