The expression represents the probability of getting exactly 3 heads is,
[tex]C(n,r)(0.5)^3(0.5)^6[/tex]
We have given
Aron flips a penny 9 times.
We have to determine
Which expression represents the probability of getting exactly 3 heads
What is binomial distribution?The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.
The binomial probability formula shown has variables that represent:
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).
r is the number we want to find (here, we want the probability of 3 heads, so r = 3).
p is the probability of success (here, success means getting heads.
So, in a coin flip the probability of heads is always 1/2, so p = 1/2).
Therefore, The expression represents the probability of getting exactly 3 heads is;
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]
Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].
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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,
Probability (x≥3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰
= 0.5
Probability (x≤3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵
= 0.8125
Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
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Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?
D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
[tex]\rm x^{2}+4y^{2}-2x+16y-19=0[/tex]
We can write the above equation as:
[tex]\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1[/tex]
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
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Use point-slope form − 1 = ( − 1) to find the equation of the line that passes through the point (−3,5) and has slope = −2 . Write the answer in slope-intercept form = + .
Answer:
y - 5 = -2(x + 3)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-3, 5)
slope (m): -2
The standard point-slope equation is
y - y₁ = m(x - x₁)
Plug in what you know.
y - (5) = -2(x - (-3))
Simplify.
y - 5 = -2(x + 3)
This is your equation.
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need to know asap
Which of the following best describes the correlation between two variables if the correlation coefficient is -0.544?
weak positive
weak negative
strong negative
strong positive
2. A line goes through the points (4, 8) and (-4, 6).
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.
Any body can help?
(a) [tex]\frac{6-8}{-4-4}=\frac{-2}{-8}=\boxed{1/4}[/tex]
(b) Using the point (4,8), we get [tex]\boxed{y-8=\frac{1}{4}(x-4)}[/tex]
(c) Rearranging into slope-intercept form,
[tex]y-8=\frac{1}{4}(x-4)\\\\y-8=\frac{1}{4}x-1\\\\\boxed{y=\frac{1}{4}x+7}[/tex]
PLEASE HELP ME WITH MY MATH
The definition for the graphed function is the one shown in option d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Which piecewise function coincides with the graph?Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).
Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.
With that we can conclude that the correct option is:
d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.
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What is the solution to the equation shown below?
-1/3(6x+6)+21=3y
Answer:
A or 19/5
Step-by-step explanation:
To solve first we isolate are variables so we distubte to get -2y-2+21=3y then we add 2y to the opposite side to get -2+21=5y. Then we add -2+21 to get 19 so are equation is 19=5y. Next we just divide 19 by 5 to get y=(19/5) or option A
[tex]\frac{5}{x+5}(2x-5(2))[/tex]
Answer: 10
Step-by-step explanation:
[tex]\frac{5}{x+5} (2x-5(2))\\\frac{5}{x+5} (2x-10)\\\frac{10x-50}{x+5}\\\frac{10(x+5)}{x+5} \\\frac{10}{1} \\10[/tex]
2x+3y=4 cual es la respuesta??
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
Voy a suponer que necesitas resolver para y.
2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
who is known as the father of computer
Answer:
Charles Babbage
Step-by-step explanation:
Answer: Hope this may help you
Charles Babbage, I think
Step-by-step explanation:
Charles Babbage is sometimes referred to as the father of computers.
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this?
12
4
77-7/22
12
12
3
12
03-1/2/
4
The proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex]
Given that there are 3 feet in 1 yard, which is equivalent to 12 feet in 4 yards.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
We need to determine the proportion that can be used to represent this.
Now, 1 yard = 3 feet implies 4 yards = 12 feet.
The required proportion can be written as [tex]\frac{3}{1} =\frac{12}{4}[/tex].
Therefore, the proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex].
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which is the most appropriate Venn diagram...
The most appropriate Venn diagram is known to be option b in the image shown.
What is a common multiple?A Common multiples are known to be the multiples that are said to be common to two or that have more numbers in them.
The Least Common Multiple ( LCM ) is known to be a term that connote the Lowest Common Multiple ( LCM ) and also that has the Least Common Divisor ( LCD).
From the image shown the lowest multiples are 5², 2⁶, 3 while the greatest common factor is 2⁶.
Option B is correct because the greatest common factor which is 2⁶ can only be found in the middle and this was gotten when you add:
2³ . 2³
Collect like terms
2 ³⁺³
2⁶
Therefore, the greatest common factor which is 2⁶
To get the Least Common Multiple, one need to add all the factors in the Venn diagram which are therefore:
5², 2³ . 2³, 3
=5², 2 ³⁺³, 3
=5², 2⁶, 3
Therefore, The most appropriate Venn diagram is known to be option b in the image shown.
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Drag each tile to the correect location on the table. Not all tiles will be used. Maych each quadratic function with the attributes of its graph.
Answer:
I believe you forgot to add a picture
Solve by applying the counting principle. James is choosing a Four-digit Passcode for his smartphone. How many different Passcodes are possible? There are Ten digits that James can choose from. Enter Solve by applying the counting principle . James is choosing a Four - digit Passcode for his smartphone . How many different Passcodes are possible ? There are Ten digits that James can choose from.
Answer:
10k.
Step-by-step explanation:
1) if for the 1st position can be used 0-9 digits (10 digits), for the 2d - 0-9 digits, for the 3d - 0-9 digits and for the 4th - 0-9 digits, then
2) the required number of pwd is: 10*10*10*10=10⁴=10000.
As an inventory manager, you must decide on the order quantity for an item. Its annual demand is 679 units. Ordering costs are $7 each time an order is placed, and the holding cost is 10% of the unit cost. Your supplier provided the following price schedule. Quantity Price per Unit 1 - 100 $5.65 101 - 350 $4.95 351 or more $4.55 What ordering-quantity policy do you recommend
The ordering-quantity that should be recommended will be 117 units.
How to calculate the order quantity?The following can be deduced from the information given:
Demand = 679
Ordering cost = 7
Holding cost = 10%
Ordering quantity will be:
= ✓(2 × Demand × Ordering cost / Holding cost)
= ✓(2 × 679 × 7/0.1)
= ✓13580
= 116.53
= 117
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Question 4 of 40
Which of these is a correct expansion of (3x-2)(2x2+5)?
OA. 3x 2x2 + 3x 5+2 2x² +2.5
B. 3x 2x2 + 3x.5+ (-2) 2x2 + (-2).5
O C. 3x 2x²+(-2) 2x² + 2x².5+ (-2).5
SUBMIT
Answer:
3x* 2x^2 +3x*5 -2 * 2x^2 -2 *5
Step-by-step explanation:
(3x-2)(2x^2+5)
We can FOIL to find the expansion
First 3x* 2x^2 = 6x^3
Outer 3x*5 = 15x
Inner -2 * 2x^2 = -4x^2
Last -2 *5 = -10
Add all the terms together
3x* 2x^2 +3x*5 -2 * 2x^2 -2 *5
Answer:
3x • 2x^2 + 3x • 5 + (–2) • 2x^2 + (–2) • 5
Step-by-step explanation:
other answer was right
The length of a rectangle is five more than the width. The area is 66 square meters. Find the length and width. =
Answer:
It doesn't say anything about "Length" and "Width".
Step-by-step explanation:
Brainlest . Just press the .
Answer: We can take 2 common we could also write this as 2 times X plus y.
Step-by-step explanation:
Please please help asap I’ll make I brainliest
Answer: [tex]x=5\sqrt{3}[/tex]
Step-by-step explanation:
As the triangle is equilateral, we know that all sides have a length of 10. Thus, if we consider either of the right triangles, we know they have legs of lengths 5 and x (since an altitude of an equilateral triangle bisects the side it is drawn to), and a hypotenuse of 10.
Thus, by the Pythagorean theorem,
[tex]5^{2}+x^{2}=10^{2}\\\\25+x^{2}=100\\\\x^{2}=75\\\\\boxed{x=5\sqrt{3}}[/tex]
The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.
Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
Which statement correctly compares the means of the data in the dot plots?
The correct statement compares the means of the data in the dot plots is option C; the mode is greater for Mrs. Ramos’s class.
What are the median and mode of the data?Median represents the middle value of the given data when arranged in a particular order.
Mode is that number that appears most frequently in the given set of data.
Given;
The Number of pets in Mr. McIntyre’s class ;
0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,
Median = 1
Mode = 0 and 1
The Number of pets in Mrs. Ramos’s Class;
0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3
Median = 3
Mode = 4 and 5
Hence, C; The mode is greater for Mrs. Ramos’s class.
The remaining part of the question is
"Which statement correctly compares the measures of center of the data in the dot plots?
The median is greater for Mr. McIntyre’s class.
The median is the same for both classes.
The mode is greater for Mrs. Ramos’s class.
The mode is the same for both classes."
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100 students take a test. The mean score of the results is 88% with a standard deviation of 4%. Considering that the results were normally distributed, what is the median of the graph, what scores are within 2 standard deviations away, and how many student's scores would be within 1 standard deviation from the mean?
Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.68 scores are within one standard deviation of the mean.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.88 + 2 x 4 = 96%.68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
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[Question 10]
Two banks calculate the yearly interest they pay customers.
Westminster Bank
4% of the total that you invest
For example: Invest £700
Interest = 4% of £700.
Ashna has £500 to invest for one year.
Work out which bank will pay her more interest.
State how much extra interest she will earn.
District Bank
(4 marks]
1% of the first £300 that you invest and
6% of the amounts over £300 that you invest.
For example: Invest £700
Interest 1% of £300 + 6% of £400,
Answer:
yes
Step-by-step explanation:
because bank
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid?
A. A cross section cut parallel with the bottom
B. A cut parallel to the vertical axis, but off the vertical axis
C. Cutting off one of the bottom corners
D. A cut parallel to the vertical axis, directly through the vertical axis
Brainliest to who answers :>
Answer:
L is not valid.
Step-by-step explanation:
For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.
Answer:
L
Step-by-step explanation:
to add to the previous basically correct answer :
for a triangle the sum of any 2 sides must be greater than the third side (not just legs and Hypotenuse).
for all other options any combination of sum of 2 sides being bigger than the third side works.
but for L
2 + 5 = 7, which is smaller than the third side (8). so, this cannot be a triangle.
The inverse of the function f(x) = x + 10 is shown.
==
h(x) = 2x-0
What is the missing value?
01
05
O 10
O 20
Answer:
So, the answer is 20
Step-by-step explanation:
[tex]f(x) = \frac{1}{2} x + 10 = = = > \\ f(x) - 10 = \frac{1}{2} x = = = > \\ 2f(x) - 20 = x = = = > \\ {f}^{ - 1} (y) = 2y - 20 = = = > {f}^{ - 1} (x) = 2x - 20[/tex]
The missing value of the inverse function is 20.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the inverse of a function, we usually replace f(x) with y, then solve for x in terms of y, and finally replace y with the inverse function notation h(x).
So let's do that with the given function:
f(x) = (1/2)x + 10
y = (1/2)x + 10
2y = x + 20 (multiply both sides by 2 to isolate x)
x = 2y - 20 (subtract 20 from both sides)
Now we can replace x with h(x) and y with x to get the inverse function:
h(x) = 2x - 20
Thus,
The missing value is 20.
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Choose the single logarithmic expression that is equivalent to the one shown. log6 25 − log6 5
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(25) - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) {}^{2} - log_{6}(5) [/tex]
[ property : x² = 2 log x ]
[tex]\qquad \tt \rightarrow \: 2 \: log_{6}(5) {}^{} - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
square root of the quantity x plus 7 end quantity minus 11 equals 2
An equation is formed when two equal expressions are equated together. The value of x in the equation [√(x+7)]-11=2 is 162.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for x in the equation [√(x+7)]-11=2 can be solved as,
[tex]\sqrt{x+7}-11=2\\[/tex]
Using the addition property of equality,
[tex]\sqrt{x+7} -11+11= 2+11\\\\\\\sqrt{x+7} = 13[/tex]
Squaring both the sides of the equation,
x + 7 = 169
Using the subtraction property of equality,
x + 7 - 7 = 169 - 7
x = 162
Hence, the value of x in the equation [√(x+7)]-11=2 is 162.
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Which of the following is the difference of two squares?
A. 100m^2+9n^2
B.9x^2-12y^2
C. 16g-49h
D. 25a^2-36b^6
The difference of two squares expression is (d) 25a^2-36b^6
How to determine the difference of two squares?The difference of two squares is represented as:
x^2 - y^2
Where x and y are perfect square expressions.
From the list of options, we have:
25a^2-36b^6
The terms of the above expression are perfect squares
i.e.
25a^2 = (5a)^2
36b^6 = (6b^3)^2
Hence, the difference of two squares expression is (d) 25a^2-36b^6
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Explain how to graph a scatterplot and its regression line using a regression calculator
Press the Linear Regression button to generate the regression line.
We have given that, regression line using a regression calculator
We have to determine how to graph a scatterplot and its regression line using a regression calculator.
Before entering data into the regression calculator, it is important to determine which variable should be associated with the x-axis and which with the y-axis.
What is the regression line?
Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.
Enter the data pairs.
Press the Linear Regression button to generate the regression line.
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If REX ~ ROB, find the value of a.
Answer: 8
Step-by-step explanation:
As corresponding sides of similar triangles are proportional,
[tex]\frac{RX}{RB}=\frac{XE}{BO}\\\\\frac{6}{15}=\frac{a}{20}\\\\a=20\left(\frac{6}{15} \right)=\boxed{8}[/tex]
Given the first degree function f(x) = 2x +3, what is the value of f(10)?
a) 23
b) 25
c) 30
d) 50
Answer:
a
Step-by-step explanation:
substitute x = 10 into f(x) , that is
f(10) = 2(10) + 3 = 20 + 3 = 23
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\boxed{\underline{\huge{\tt{\orange{\: \: a)23 \: \: }}}}}[/tex][tex]\large \bold {SOLUTION}[/tex]
Given the first-degree function:
[tex]\Large\begin{array}{c}\rm f(x)=2x+3\end{array}[/tex]
We were asked to determine the value of f(10), so, to find its value, just replace the 10 where there is x in the function, see:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(x)=2x+3\\\\ \rm f(10)=2\cdot 10+3\end{array}\end{gathered}[/tex]
You see, we put that dot there, which indicates multiplication, because when a number is next to a letter it indicates that it is multiplying, thus:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(10)=2\cdot 10+3\\\\ \rm f(10)=20+3\\\\ \red{\boxed{\rm f(10)=23}}\checkmark\end{array}\end{gathered}[/tex]
Hence, the value of f(10) in this function is equal to 23.
Enter the correct answer in the box.
Function g has the same a value as function f, but its vertex is 2 units below and 3 units to the left.
f(x) = x² - 4x - 32
Write the vertex form of the equation modeling function g.
The equation in the vertex form of g(x) is:
[tex]g(x) = (x + 1)^2 - 38[/tex]
How to get the equation of function g?
We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).
So first, let's rewrite f(x) to its vertex form:
[tex]f(x) = x^2 - 4x - 32[/tex]
The vertex is at:
[tex]x = -(-4)/2*1 = 2[/tex]
The y-value of the vertex is:
[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]
Then the vertex form of f(x) is:
[tex]f(x) = (x - 2)^2 - 36[/tex]
If we move this vertex 2 units below, and 3 units to the left, then we have:
[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]
That is the equation for g(x) in vertex form.
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