The probability of having two hearts in a randomly drawn hand of 5 cards is 0.2637
Number of cards are drawn from a standard deck = 5
The favorable outcomes = 2 hearts
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
Total number of cards = 52
Number of heart cards = 13
Number of remaining cards = 52 - 13
= 39
Then the probability of two hearts in five card hand = (5/2) × (13/52)^2 × (39/52)^3
= (5/2) × 1/16 × 27/64
= 0.2637
Therefore, the probability is 0.2637
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the probability of having two hearts in a randomly drawn hand of 5 cards?
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You have made 160 duct tape wallets to sell. If you sell 3 each day, write a function that represents this situation.
A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is
y = 160 - 3xHow to write the expression of the situationInformation from the problem
You have made 160 duct tape wallets to sell
If you sell 3 each day
From the information we can deduce that
assuming amount left is y and the number of days x the we have
y = 160 - 3x
Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is y = 160 - 3x
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f(x) = 8x4 - 2x3 + 5x² + 2x-11
Answer:
Add and subtract the second term to the expression and factor by grouping.
(2 x -1) ( x^2 + 4)
Hope this helps!
Are the ratios 3:4 and 11:20 equivalent
Answer:
nah
Step-by-step explanation:
the function c gives the temperature, in degrees celsius, that corresponds to a temperature of x degrees fahrenheit. if a temperature increased by 19.8 degrees fahrenheit, how much did the temperature increase in degrees celsius?
When the temperature increased by 19.8 degrees fahrenheit , the temperature in degrees Celsius got increased by 11 degree
The equation C that gives the temperature in degree Celsius is
C = [tex]\frac{5}{9}(x - 32)[/tex]
Where x denotes the degree Fahrenheit
According to the question,
Temperature has increased by 19.8 degree Fahrenheit
So, let the new temperature be " x' "
x' = x + 19.8
Therefore, For calculating temperature in degree Celsius
=> C' = 5/9 (x' - 32)
Substituting the value of x'
=> C' = 5/9 (x + 19.8 - 32)
=> C' = 5/9 ( x - 32) + 5×19.8/9
=> C' = C + 99/9
=> C' = C + 11
Hence , The temperature increased by 11 degree Celsius
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The perimeter of a square is 60 cm. Find the
area of the square.
Step-by-step explanation:
SOLUTIONSince a perimeter is a total distance around the figure.
And a square is a quadrilateral(with four sides) which are equal.To find the length of each side,divide the perimeter by 4.
60 cm÷4 = 15 cmSince,Area of square = side×side = 15cm×15cm = 225cm^2hope it helps you.
Answer:
Area of square = 225 cm²
Step-by-step explanation:
Perimeter of square formula,
→ P = 4 × side
→ P = 4a
Now the side of square will be,
→ P = 4a
→ 4a = 60
→ a = 60/4
→ [ a = 15 cm ]
Then the area of square will be,
→ (a)²
→ (15)²
→ 225 cm²
Hence, area of square is 225 cm².
First to compliment my hw gets 20 points and Brainly
Answer:
bro fr has the nicest notes not just for the points but like actually
What is 2/3 of 1 5/16
Answer:
7/8
Step-by-step explanation:
2/3 * 1 5/16 =
2/3 * (1 + 5/16)=
2/3 * (16/16 + 5/16)= -> common denominator numbers are easy to simplify
2/3 * (16+5)/16 =
2/3 * 21/16=
(2*21)/(3*16)=
42/48=
21/24=7/8
find the volume of the given solid. bounded by the cylinders z = 5x2, y = x2 and the planes z = 0, y = 4
1024/3 units³ is the required volume of the given solid using the triple integral theorem.
What is the triple integral formula?As the name implies, triple integrals are 3 sequential integrations, used to determine a volume or to integrate into a 4th dimension, over 3 other independent dimensions.
∭Ef(x,y,z)dV=∬D[∫u2(x,y)u1(x,y)f(x,y,z)dz]dA.
So, we must use the triple integral formula in rectangular coordinates to get the volume of the solid (v):
[tex]V=\iiint d y d x d z[/tex] ...(1)
The solid is restricted by the following intervals:
[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]
Then, this triple integral is now characterized as:
[tex]V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z[/tex]
Now we continue to integrate again to get the volume:
[tex]\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}[/tex]
Therefore, 1024/3 units³ is the required volume of the given solid using the triple integral theorem.
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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.
the base of a triangle is seven more than twice the height. the area of the triangle is 73.5 square feet. find the measures of the base and height of the triangle.
The base and height of the triangle are 21 and 7 respectively.
What is the base and height of a triangle?Area of the triangle = [tex]\frac{1}{2} bh[/tex]
= 73.5
Where, b is the base of a triangle
h is the height of the triangle
Let the base of the triangle = b
Here, b = 2h + 7
Area of the triangle = 1/2 (2h +7)h = 73.5
[tex]= > 2h^{2} +7h = 73.5*2 \\\\= > 2h^{2} +7h = 147\\\\= > 2h^{2} +7h -147 = 0\\\\= > h = 7[/tex]
Height of the triangle = h = 7
Base of the triangle = b = 2h + 7
= 2(7) +7
b = 21
The base and height of the triangle are 21 and 7 respectively.
What is the area of a triangle?The total amount of space allotted to a triangle's three sides in a two-dimensional plane is known as the area of a triangle. Half of the product of a triangle's base and height is the basic formula for calculating its area. Whether it be a scalene triangle, isosceles triangle, or equilateral triangle, this formula works for all triangle kinds. You should keep in mind that a triangle's base and height are parallel to one another. The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another.To learn more about triangles, refer:
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3 letters are typed, with repetition allowed. what is the probability that all 3 will be vowels? write your answer as a percent. round to the nearest hundredth of a percent as needed.
The probability that all 3 will be vowels will be .01 to the nearest hundredth
Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.
There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.
First of all, we need to know the number of vowels in the 26 letters.
There are 5 vowels among the 26 letters,
probability (3 vowels of 3)
= (5/26)*(5/26)(5/26) multiplication of probability of each letters
=0.1923*0.1923*0.1923
≈0.0071
≈0.71%
or .01 to the nearest hundredth
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if f(x)=x²+9 and g(x)=x-9 find g(f(-2))
The value of composite function g(f(-2) is when f(x) = x^2+9 and g(x) = x-9 is 4
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
We are given two functions f(x) = x^2+9 and g(x) = x-9
and we are asked to find g(f(-2))
this term means we first substitute f(x) in the place of x in function g
We get
g(f(x))= f(x) - 9
Now substitute the value of f(x) in the above function
g(f(x))= x^2+9 -9
g(f(x))= x^2
g(f(-2))= (-2)^2
g(f(-2))= 4
Hence the value of the function if 4
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To test if x is a good predictor of y in Simple Linear Regression we need to determine whether:
A. the slope is significantly different from zero.
B. the intercept is significantly different from zero.
C. the response variable is significantly different from zero.
D. the predictor variable is significantly different from zero.
E. the error term is significantly different from zero.
F. the F test statistic is significantly different from zero
Option A is correct.
For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.
What is linear regression?
A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.
Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.
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5 1/5 - 1 3/4 what’s the answer
Answer: 69/20
Step-by-step explanation:
5 1/5 = 26/5
1 3/4 = 7/4
26/5 - 7/4
= 104/20 - 35/20
= 69/20
PLEASE HELP EASY EASY EASY
Answer:
12
Step-by-step explanation:
2 is 40 percent of 5
12 is 40 percent of 30
Answer:
15 people would be running out of 30
Step-by-step explanation:
30/2
The sides of two similar pentagons are in a ratio of 2:7. The area of the larger pentagon is 98 in². Find the
a of the larger pentagon.
Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .
What is pentagon?A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."
Why is pentagon so important?The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.
Similar figures' surfaces have an area that is proportional to the square of their sides.
The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.
Keep in mind that the ratio of the sides is squared because we are working with areas.
[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]
Let area a smaller pentagon is a
[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]
a=[tex]\frac{98*4}{49}[/tex]
a= 8 [tex]in^{2}[/tex]
So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]
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distance formula definition
The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)
The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.
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suppose a new production method will be implemented if a hypothesis test supports the conclusion that it reduces the mean operating cost per hour. (a) state the appropriate null and alternative hypotheses if the mean cost for the current production method is $280 per hour.
The null and alternative hypotheses are:
H₀ : µ ≥ 280
Hₐ : µ < 280
It would be claiming µ < 280 when the new method does not lower costs. This mistake could result in implementing the method when it would not lower costs.
It would be claiming µ ≥ 260 when the method really would lower costs. This mistake could result in not implementing a method that would lower costs.
We know that the type 1 occurs when we reject the null hypothesis when it is true and the type 11 error occurs when we do not reject the null hypothesis when it is not true. For the given scenario, the type 1 error is to reject the null and conclude that new method not lower costs, when actually it lowers.
Hence we get the required answer.
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5x - 4y= 10
10x - 8y = 20
Answer:
infinite number of solutions
Step-by-step explanation:
5x - 4y = 10 → (1)
10x - 8y = 20 → (2)
multiply (1) by - 2
- 10x + 8y = - 20 → (3)
ad (2) and (3) term by term
0 + 0 = 0
0 = 0 ← true statement
this indicates the system has an infinite number of solutions
Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.
y = (smaller slope)
y = (larger slope)
Answer:
y = -x - 1 ; y = 11x - 25
Step-by-step explanation:
y = x² + x
y-(-3) = m(x-2)
y = x²+x
y + 3 = mx - 2m
y = x² + x
y = mx - 2m - 3
x² + x = mx - 2m - 3
x² + x - mx + 2m + 3 = 0
x² + (1-m)x + 2m + 3 = 0
discriminant = m² + 1 - 2m -4 (2m + 3)
m² + 1 - 2m - 8m - 12
m² - 10m - 11
the line is tangent so the discriminant must be equal to 0
m² - 10m - 11 = 0
(m-11)(m+1) = 0
m = 11
m = -1
y + 3 = -(x-2)
y+ 3 = -x + 2
y = -x + 2 - 3
y = -x - 1
y + 3 = 11(x-2)
y + 3 = 11x - 22
y = 11x -22 - 3
y = 11x - 25
The value of the test statistic for the test H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9 is
The value of the test statistic for the test is 1.52
How to determine the value of the test statistic for the test?From the question, we have the following parameters that can be used in our computation:
H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9
The above parameters mean that
Sample mean = 3.8Number of samples = 52x = 4.2Standard deviation = 1.9The value of the test statistic for the test is calculated as
[tex]t = \frac{x - \mu_0}{s/\sqrt n}[/tex]
Substitute the known values in the above equation
[tex]t = \frac{4.2 - 3.8}{1.9/\sqrt {52}}[/tex]
Evaluate the equation
t = 1.52
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Write all classifications that apply to the real number −2.
A. natural number, terminating decimal
B. rational, integer, whole number
C. rational, integer, whole number, natural number, terminating decimal
D. terminating decimal, integer, rational
Answer: D
Step-by-step explanation:
-2 is not a repeating decimal.
It is not a fraction
And it is a rational number
Which figure is the Preimage?
Ben reads 6 pages of a book in 8 minutes, 9 pages in 12 minutes, and 30 pages in 40 minutes.
If m represents the number of minutes and p represents the number of pages, which equation represents the number of pages Ben reads per minute?
The equation that represents the number of pages Ben can read per minute is p = (3/4)m.
What is Direct Proportion:
The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.
If x and y are in direct proportion then
=> x ∝ y
=> x = ky [ where k is constant ]
Here we have,
Ben reads 6 pages in 8 minutes
9 pages can be read in 12 minutes
30 pages can be read in 40 minutes
And the number of minutes = m
Number of pages = p
If observe the given data,
When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages
=> p ∝ m
=> p = km --- (1)
[ where k is constant ]
From the given data,
At p = 6 pages, m = 8 minutes
=> 6 = k(8)
=> k = 6/8 = 3/4
From (1)
=> p = (3/4)m
Therefore,
The equation that represents the number of pages Ben can read per minute is p = (3/4)m
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Solve pls brainliest
Answer:
A, D, E, and F are all equivalent expressions.
Step-by-step explanation:
A. 1:
1 is already a simplified fraction, so there is nothing to do.D. 4:
4 is already a simplified fraction, so there is nothing to do.E. 1.
28.:
This expression is not a fraction, but rather a mixed number. To convert it to a fraction, we first need to rewrite it as an improper fraction. To do this, we take the whole number (1) and multiply it by the denominator (28), and then add the numerator (0):1.28 = 1 * 28 + 0 = 28Then we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:28/4 = 7F. 1
22:
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:1/22 = 1/22
I hope this helps! Let me know if you have any questions.
6² subtracted 4 divided 2
Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both
Step-by-step explanation:
problem a problem b
(6²-4)/2 or 6²-4/2
| |
[tex]6^2=36\\[/tex] [tex]6^2=36[/tex]
36-4=32 36-4/2
32/2=16 36-2=34
16 34
Find the common ratio of the geometric sequence
17, -34, -68, ...
The common ratio of the geometric sequence will be negative 2.
Given that:
Geometric sequence: 17, -34, -68, .....
A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The common ratio of the geometric sequence is calculated as,
r = (-34) / (17)
r = - 2
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I need help ! Solve for x.
The solution for x in the pentagon is 90
How to determine the solution for x?From the question, we have the following parameters that can be used in our computation:
Shape = pentagon
This means that
n = 5
The sum of the internal angles is calculated as
Angles = 180(n - 2)
Substitute the known values in the above equation, so, we have the following representation
Angles = 180(5 - 2)
So, we have
Angles = 540
This means that
x + 90 + 90 + 135 + 135 = 540
So, we have
x + 450 = 540
Evaluate
x = 90
Hence, the value of x is 90
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Can someone help me really quick
One would expect the foreword of a book to be found:
C. At the beginning of the book
What is the foreword in a book?The foreword in a book refers to the introductory part of the book that is written by an expert on the subject discussed by the book. The foreword of a book is located at the beginning part of the book and it provides reasons that readers should consider reading the book.
The foreword is not meant to dissuade the readers but to encourage them on the importance and content of the book. It is logical then to expect this feature of books to be located at the beginning of the book.
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Write each expression as a product.
(a+b)^2-(b+c)^2
The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.
What is the difference of two squaresConsidering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).
We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:
(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]
open brackets and simplify;
(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)
add and subtract like terms;
(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)
(a + b)² - (b + c)² = (a + 2b + c)(a - c)
In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.
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a range of values estimated to have a high probably of containing the population value is called:
A range of values estimated to have a high probably of containing the population value is called Confidence interval.
A confidence interval is a range of values that is likely to contain the true value of a population parameter, such as a mean or proportion. The degree of confidence associated with a confidence interval is the probability that the population parameter falls within the range of the confidence interval.
Population parameter : In statistics, a population parameter is a numerical measure of a population, such as its mean, variance, or proportion of a certain characteristic. It is usually estimated from a sample of the population and is usually not known precisely.
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