Answer:
Hey there! So the square root of 38 can be simplified by breaking it down into simpler parts. We can use a technique called prime factorization. We need to find the largest perfect square that is a factor of 38 and extract it from the square root. So, we can express 38 as 219 and that means we have 2^2=4 as the largest perfect square. Therefore, we can simplify the square root of 38 as 2sqrt(19).
It can't be simplified anymore, but it gives us a more manageable form. Let me know if you have any more questions, I'm happy to help!
________________________________________________________
How can you determine if a number is a perfect square?A perfect square is a number that can be written in the form of n^2 (n raised to the power of 2) for some whole number n. For example 4, 9, 16, 25 and 36 are perfect squares. A way to determine if a number is a perfect square is by taking the square root of that number, if the result is a whole number it's a perfect square. Also, you can check it by finding the prime factorization of the number, if each of the prime factors appears in even power, it's a perfect square.
Are there any shortcuts for simplifying square roots?There are a few techniques that can make simplifying square roots quicker and easier:
Recognizing perfect squares (as described above) and extracting them from the square root
Using prime factorization to simplify the square root
Recognizing when the square root can be written as a rational number (a fraction of two integers)
Another way to approach is to factorise the radicand and combine any pairs of identical factors out from the square root.
Please let me know if you have any other questions on this topic or any other topic I could help with.
√38 is the simplest representation of the square root of 38.
The square root of a number is a value that, when multiplied by itself, gives the original number.
In the case of √38, we are looking for a number that, when multiplied by itself, equals 38.
Since 6 multiplied by itself is 36 and 7 multiplied by itself is 49, we can conclude that the square root of 38 lies between 6 and 7.
We cannot find a whole number that satisfies the equation √38 = x, where x is an integer.
Therefore, we express the square root of 38 as an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal.
Hence, √38 is the simplest representation of the square root of 38.
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how do i do this qution
y = -1/2x is the equation of example of the direct variation.
What is polynomia?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
Given four linear equations in them we need to state which equation is an example of direct variation.
The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).
Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.
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Brie bought a rug for her bedroom. The area of the rug measures 25 square feet. Her bedroom is ten feet wide and twelve feet long. Using the given measurements, what is the amount of her bedroom NOT covered by the rug
The area of bedroom rug is 15 square feet. the longer side measures 5 feet. his living room rug is twice as long and twice as wide as the bedroom rug.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in cm², also known as square centimeters.To learn more about square centimeters refer to:
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Ash and her 2 friends went to dinner. If the bill was $124.72, and they left an 18% tip, how much did each person pay
Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
Which percentage is it?A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Amount of bill = $124.72
and tip they left = 18% of $124.72
total amount is =$124.72 + $124.72*18%=$147.1696
so, each person pay= $147.1696/3=$49.056
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Find the x and y Intercept of x + 2y = -14
Answer:
Y-intercept: (0, -7)
X-intercept: (-14,0)
Step-by-step explanation:
To find the y-intercept, we need to put 0 in for x
0 + 2y = -14
2y = -14
y = -7
So, the y-intercept is located at (0, -7)
To find the x-intercept, we need to put 0 in for y
x + 2(0) = -14
x = -14
So, the x-intercept is located at (-14,0)
Step-by-step explanation:
To find the y-intercep, we need to put 0 in for x
0 + 2y= -14
2y = -14
y = - 7
So, the y - intercept is located at ( 0, - 7)
does the order of the quantities in an inequality matter
The order of the quantities in an inequality matters. Therefore, it is true.
How to illustrate the inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.
Therefore, the order matters.
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how to solve x-y+x/2 (if x=10, y=1)
A rope is fixed between two trees that are 10 metres apart. When a child hangs on to the centre of the rope, it sags so that the centre is 2 metres below the level of the ends. Find the lenth of the rope.
The length of the rope is 2√29 meters.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Given that the distance between two trees is 2 meters. A boy hangs on a rope tied to the trees in the middle of the rope.
it sags so that the center is 2 meters below the level of the ends.
Thus it forms an isosceles triangle. △ACD and △BCD are two right triangles.
Since △ABD is isosceles triangle and AD = BD.
In △ACD, Hypotenouse = AD, Base = AC = 10/2 = 5 cm, Height = CD = 2 meters
Apply Pythagorean theorem on △ACD:
AD² = AC² + CD²
AD² = 5² + 2²
AD² = 29
AD = √29
Therefore, BD = √29
The length of the rope is AD + BD = 2√29 meters.
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I WILL MARK BRAINLYEST AND 40 POINTS
Describe a meal that you could put together that provides 4 servings of both a main course and a side dish. Explain how you know that it will not exceed the weight limit of the box
The total number of servings of chicken the food bank can provide is 70 servings.
What is per unit?Per-unit is a technique of expressing a quantity's value in terms of a base or reference quantity. Each system variable or quantity in a per-unit system is normalized in relation to its own base value.
Two chickens make up the main course of a plate of food, according to the table's content. Each chicken served by the food bank weighs 12.6 ounces. 110.9 pounds of chicken are available at the food bank (1,774.4 ounces of chicken)
Thus,
The mass of chicken per serving = 2 × 12.6 = 25.2 oz/serving
The total number of servings of chicken the food bank can provide = (The quantity of chicken the food bank has)/(The mass of chicken per serving)
∴ The total number of servings of chicken the food bank can provide = (1,774.4 oz)/(25.2 oz/serving) ≈ 70.413
Given that the servings are in whole numbers, we have;
therefore, To the nearest whole number, the food bank can offer a maximum of 70 servings of chicken.
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What is the plotting method?
Plotting method is the graphical representation of mathematical expression.
What is mean by plotting?A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.
What are the steps of plotting method?At first, we need to choose the coordinate system by which we plot the point.
suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.
besides, we need to determine the required value that will be plotted on the plan.
if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.
we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.
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Choose the best description of the data used to generate this histogram (note that the horizontal axis has no scale, so you will make your choice based solely upon the histogram's shape): OSAT Math scores of 1,000 future engineers and scientists. O Results of rolling a six-sided die 1,000 times. Cholesterol levels of 1,000 adults. O Shoe sizes of 1,000 men and women. O Prices of 1,000 California homes. * That is not quite right. The bulk of the SAT Math scores of engineers and scientists would be high scores, since people interested in those fields are usually good at math. So that distribution would be skewed left. Please try again.
On solving the provided question we can say that so the value of the data from histogram graphs will be x [tex]\alpha[/tex] 0.123 * 125 / 100 = 0.15375
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
the best way to describe the data that was used to create this histogram (keep in mind that there is no scale on the horizontal axis, so you must choose based simply on the appearance of the histogram graphs
so the value of the data from histogram graphs will be
z = 0.123
u = 100
x = 125
x [tex]\alpha[/tex] 0.123 * 125 / 100 = 0.15375
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Find the x-intercept and y-intercept
from the following linear equation:
12x + 30y = 180
x - intercept = ()
y - intercept ()_
Answer:
x - intercept = (15, 0)
y - intercept = (0, 6)
Step-by-step explanation:
x-int. is when y = 0
y-int. is when x=0
Plug in y = 0 and x = 0 to get intercepts.
FOR X-INT.:
12x + 30(0) = 180
12x = 180
x = 15
x-int. is (15, 0)
FOR Y-INT. :
12(0) + 30y = 180
30y = 180
y = 6
y-int. is (0, 6)
simplify square root of 3y^2 if y<0
Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3
What is the rationale for the above result?Note that we need to take a factor out of the square root: √(3y²) , where y<0.
The given expression is √(3y²)
Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,
√(3y²) = √3y²
⇒ √3 √y²
⇒ √3 (y²)[tex]^\frac{1}{2}[/tex]
⇒ √3 (y)[tex]^\frac{2}{2}[/tex]
= y √3
Thus, having simplified the expression √(3y²), the result is: y √3.
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PLEASE HELP ME
6.
Dom is selling pizza at Hoopfest to help him raise money to go on a road trip. He wants each topping to increase the total price at a rate of $1.25. When someone ordered a 3-topping pizza the price was $16.25. Write an equation to represent this data.
Answer : if each topping is 1.25 then multiply that by 3 because there's 3 toppings on the pizza and if the total was 16.25 the original price of the pizza is 12.5. I hope this was the answer you were looking for a good luck :)
Step-by-step explanation:
X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0. 1342. (a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places. ) at most 100 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places. ) (c) What is the value of the median distance? Hint: Find a such that P(X≤a)= 0. 50 (Round your answer to two decimal places. ) m
The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
What is Probability ?
probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.
We are given with an exponential distribution with
λ=0.01386.
The probability distribution function is:
F(x)=λ * e power (−λx)
Cumulative distribution function is
F(x) = 1- e power (−λx)
The mean of the exponential distribution function
E(X) = 1 / λ
= 1/0.01386
= 72.15
Hence, E(X) = 72.15
The variance of the exponential distribution function
V(X) = 1 / λ ^{2}
= 1/0.01386*0.01386
= 5205.63
V(X) = 5205.63
Probability that the distance is at most 100m
P(X <= 100 ) = F (100)
= 1- e power (−λx)
= 1 - e power (-0.01386*100)
= 1- e power (-1.386)
= 1-0.25007
= 0.749926
Therefore, P(X<=100) = 0.749926
probability that the distance is at most 200m
P ( X<= 200) = F(200)
=1-e power (−λx)
=1-e power (-0.01386*200)
= 1 - e power (-2.772)
= 1-0.06253
= 0.9375
P(X<= 200) = 0.9375
Probability that the distance is between 100 and 200m
P(100<= X <= 200) = F(200) - F(100)
= 0.9375-0.7499
=01876
P(100 <= X <= 200) = 0.1876
Probability that the distance exceeds the mean distance by more than 2 standard deviation.
P( X + P>μ+2σ) = P(X>72.15+2√5205.63)
= P(X > 72.15 +144.3)
P(X>216.45)
= 1-P(X<= 216.45)
1 - (1- e power (-0.01386*216.45)
= e power (-2.9999)
= 0.04979
P( X + P>μ+2σ) = 0.04979
Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
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The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:
For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v (t)=20,000 (0.86)'
Find the value of the car after 4 years and after 10 years.
Round your answers to the nearest dollar as necessary.
Value after 4 years:
Value after 10 years:
Answer:
4 years: $10,94010 years: $4,426Step-by-step explanation:
Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.
EvaluationPut the value of t in the formula where t is, and do the arithmetic.
The attached calculator output tells us ...
value after 4 years: $10,940
value after 10 years: $4,426
__
Additional comment
When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.
What type of line is Y 0?
If the value of y = 0, then it make the straight line on the graph.
The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.
Here we have the expression y = 0.
And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.
Therefore it represent the x-axis.
Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.
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Type the correct answer in each box. Sharon tracks the number of cupcakes she sells each day for a week. The numbers of cupcakes she sold are 23, 25, 32, 35, 36, 25, and 27. The mean of her sales over the week is , and the median is . Reset Next
The mean of her sales over the week is 29 and the median is 27.
What is mean?The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey. The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean.
Here,
To find the mean you need to sum all daily sales and then divided by the number of days. If we called daily sales as xi and the number of days evaluated as N, we have that the mean can be expressed as
mean = (∑xi)/N ⇒ media = (23 + 25 + 32 + 35 + 36 + 25 + 27 )/7
⇒mean = 29.
To find the mediana you have to put the number of sales in increasing orden and then look which is the number in the middle of the serie. So
23 - 25 - 25 - 27 - 32 - 35 - 36
⇒median = 27.
Summarizing, the mean of the sales is 29 and the median 27.
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Karina is designing a logo on a coordinate plane. The logo is a square whose area is 200200200 square units. She places a circle in the middle of the logo centered at (0,0)(0,0)(, 0, comma, 0, ). The circle passes through the point (6.3,1.6)(6.3,1.6)(, 6, point, 3, comma, 1, point, 6, ). Approximately what percentage of the logo does the circle cover
Approximately 66(2s f) percentage of the logo does the circle cover.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
To find the percentage we must first find the area of the circle:
We can find the radius of the circle using the distance formula;
⇒ [tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
⇒ [tex]r = \sqrt{(6.3-0)^2+(1.6-0)^2}[/tex]
⇒ r = 6.5
Now we calculate the area;
⇒ [tex]A = \pi r^2[/tex]
⇒ [tex]A = \pi (6.5)^2[/tex]
⇒ [tex]A = \frac{169}{4} \pi[/tex]
To get the percentage we divide the area of the circle by the square’s are and multiply by 100;
⇒ Percentage = [tex]\frac{42.25*\pi }{200}*100[/tex]
⇒ Percentage = 66(2s f)
Hence, approximately 66(2s f) percentage of the logo does the circle cover.
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If QS is the ANGLE bisector, solve for x
Question setup: x over 18 = 45 over 20
Solving for x in the angle bisector which resulted to the proportion x over 18 = 45 over 20 results to x = 40.5
What are angle bisectors as used in geometry?In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.
By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
The division from angle bisectors gave rise to the proportion which is given by
x / 18 = 45 / 20
cross multiplying
x = 18 * 45 / 20
x = 40.5
hence x is solved to get 40.5
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How to find a side length of a right triangle with an angle and a side?
Using trigonometric functions, we can find a side length of a right triangle with an angle and a side.
What is the trigonometric ratio?Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).
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PLEASE HELP!!! WILL AWARD BRAINLIEST!!!
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Top data set labeled males, minimum at 1, Q1 at 3, median at 11, Q3 at 14, maximum at 21, and an outlier at 30.
Bottom data set labeled females, minimum at 0, Q1 at 15, Median at 18, Q3 at 21.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions
The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.
What is median ?
The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.
When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.
A. IQR for male dataset
The IQR is calculated as follows:
IQR = Q3 - Q1
=
For the male's data:
IQR = Q3 - Q1
= 25 - 1
= 24
Hence, the IQR of the male dataset is 24.
B. Difference in median values
We have:
median = 20 ----- Male dataset
median = 6 ----- Female dataset
So, the difference (d) is:
d = 20 - 6
= 14
Hence, the difference in median of both dataset is 14.
C. Best measure of center
The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.
The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot
D. Reason for outlier
There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.
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20 workers can paint a building in 21 days. If work has to be finished in 15 days, find the number of extra workers required.
Step-by-step explanation:
20 workers finish work in 21 days.
the necessary work effort is 20×21 = 420 workdays.
the same effort is needed even if the overall time is shorter.
x workers in 15 days.
x × 15 = 420
x = 420/15 = 28 workers.
so, 28-20 = 8 additional workers are needed to finish the work in 15 days.
Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
i got 2/4 of the marks pls help
Answer:
Step-by-step explanation:
Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled
Calculate the size of angle ABC
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
Describe trigonometry.Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.
Here,
There are two potential solutions because the supplied angle is opposite the given side that is the shortest.
Using the sine law,
B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)
Angle B may take on the following values:
B is equal to arcsin(9/14) = 40.0°.
B = arcsin(9/14) - 180° = 140.0°
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
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A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a $\heartsuit$
The probability that the top card is a suit of heart as calculated from the data given is found to be 4 / 663.
We are given that ,
The number of cards in the deck = 52
Number of 3's in the deck = 4
Number of 8's in the deck = 4
As because all the card deck's have 4 cards of same number in different suits.
Probability is calculated as ,
P = required outcome / Total possible outcomes
Therefore, when we can choosing cards without replacing them we get,
P(top card is a 3) = 4 / 52
P(second being 8) = 4 / 51
P(top card is a 3 and second 8)
=4/52 x 4/51
= 16 / 2652
= 4 / 663.
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A spinner is divided into 7 equal regions, numbered 9 through 15. An arrow is spun and lands on one of the numbers. Which of the following best describes the probability of the arrow landing on a number that is greater than 13?
A.
0.143
B.
0.286
C.
0.429
D.
0.571
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
Define probability.Probability is the likelihood or potential for something to event. For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.
Here,
Given : S = {9,10,11,12,13,14,15}
If A is a subset of S, A could be {14,15}.
If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.
Thus,
To find the probability that it will land on number greater than 13
P = likelihood of event / total no of events
=> P = 2/7
=> P = 0.2857
=> P =0.286(approx)
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
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i don’t know this pls help
The perimeter of the right triangle is 228 inches
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.
Since it is a right triangle,
c² = 57² +76²
c² = 3249 + 5776
c² = 9025
c= √ 9025 = 95
Perimeter is the sum of all sides
Perimeter = 57+76+95 = 228 inches
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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.
The total surface area of the hemisphere is 108 pi cm^2.
Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.
The surface area of a sphere with the radius r is 4 pi r^2
The surface area of a hemisphere with the radius r = 2 pi r^2 + pi r^2
where pi r^2 represents the area of the circular base of the hemisphere of radius r.
The surface area of a hemisphere sphere with the radius r is 3 pi r^2
For radius r=6cm
TSA of the hemisphere is 3 pi (6x6) cm^2
TSA = 108 pi cm^2
108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.
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Solve the following equation. Then place the correct number in the box provided 7x-2<10
Answer:
[tex]\displaystyle x < \frac{12}{7}[/tex]
Step-by-step explanation:
This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:
[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]