this is a binomial problem: p = 0.7 and q = 0.3
a) (0.7)^6
b) (6C4)(0.7)^4(0.3)^2
c) Pr ( at least 4) = Pr(4) + Pr(5) + Pr(6) = (6C5)(0.7)^5(0.3) + (0.7)^6
d) Pr (no more than 4) = 1 - Pr(at least 4) = 1 - (answer from c)
The question requires understanding of binomial probability. The probability of all 6 serves, exactly 4 serves, at least 4 serves, and no more than 4 serves can be calculated using binomial distribution when each serve is an independent event.
Explanation:The subject of this question relates to probability involved in binomial distribution. Binomial distribution applies when there is a fixed number of independent trials, each with a constant probability of success. Here, a tennis player making a successful serve can be considered a success, with a probability of 0.70.
For all 6 serves in, the calculation is simply the product of the successful probability raised to the power of 6, which is (0.70)^6.For exactly 4 serves in, the calculation uses a binomial probability formula P(x=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the total number of trials, k is the desired number of successes, and p is the probability of a single success. Here, C(6,4) * (0.70^4) * (0.30^2).For at least 4 serves in, it's the sum of the probabilities of getting exactly 4, 5, and 6 serves in.For no more than 4 serves in, it's the sum of the probabilities of getting exactly 0, 1, 2, 3, and 4 serves in.Learn more about Binomial Probability here:https://brainly.com/question/39666605
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Solve for t.
-5 − 2t = 3t
First, we have to isolate the t, or keep it by itself, to solve. To do that, we need to move everything with t in it to on side.
-5 - 2t + 2t = 3t + 2t
The -2t and + 2t cross out, leaving us with t on one side, which is exactly what we want!
-5 = 5t
But t isn't alone yet. We need to get rid of its five. To do that, we need to use the same process: use the opposite symbol. In 5t, 5 is being multiplied by t. To get rid of, we need to divide 5. BUT the mega rule in algebra... what you do to one side you must do to the other, or else the equation would not be true anymore, so...
-5/5 = 5t/5
-1 = t
There's your answer! Hope this helps!
how do i turn 1 and 1 fith in a decimal
Answer:
The answer is 1.2
Step-by-step explanation:
1/5 it basicly stands for 1 ÷ 5
1 ÷ 5 = 0.2
plus the one you already have
1 + 0.2 = 1.2
1.2
Hope this helped!
~Lunar Rose. Moon
Answer:
1.2
Step-by-step explanation:
Take 1/5, or make it larger into 2/10 and divide those.
2/10 is obviously .2, while 1/5 is also .2.
now take the .2+ the 1 we had and you get 1.2
I need help please.
Answer:
No
Step-by-step explanation:
No it is not the correct answer.
2y-9x= 14 what’s y??
Answer:
the answer is y= 9/2 x+7
Did you mean the interception or solve for? Anyway I'll do both.
Solve for y:
[tex]
2y-9x=14\Longrightarrow 2y=14+9x \\
2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}
[/tex]
Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]
Question 4
Use the figure below to find the value of x and y
Answer:
[tex]x=4, y=8[/tex]
Step-by-step explanation:
step 1
Find the value of y
we know that
In the right triangle of the figure
[tex]cos(30\°)=\frac{4\sqrt{3}}{y}[/tex]
Remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
so
[tex]\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{y}[/tex]
Simplify
[tex]y=8\ units[/tex]
step 2
Find the value of x
In the right triangle of the figure
[tex]sin(30\°)=\frac{x}{8}[/tex]
Remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
so
[tex]\frac{1}{2}=\frac{x}{8}[/tex]
[tex]x=4\ units[/tex]
A gas at 89°C occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?
Answer:
V1 / T1 = V2 / T2
0.67 / (273 + 89) = 1.12 / (273 + t )
t = 332 °C
Given values:
Volume,
[tex]V_1 = 0.67 \ L[/tex][tex]V_2 = 1.12 \ L[/tex]Temperature,
[tex]T_1 = 89^{\circ} C \ or \ 362 \ K[/tex][tex]T_2 = \ ?[/tex]We know the relation,
→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]
By substituting the values, we get
→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]
→ [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]
[tex]= 332^{\circ} C[/tex]
Thus the answer above is right.
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Whats is the equation of the following line?
D. Y= - 4/3 x Rise over run
The equation of the line is:
C. [tex]y=\dfrac{-3}{4}x[/tex]
Step-by-step explanation:The line passes through the point (0,0) and (4,-3).
By using the two point formula to find the equation of the line.
i.e. any line passing through two points (a,b) and (c,d) is calculated by using the formula:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(0,0) and (c,d)=(4,-3)
Hence, the equation of line is calculated as follows:
[tex]y-0=\dfrac{-3-0}{4-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-3}{4}\times x\\\\i.e.\\\\y=\dfrac{-3}{4}x[/tex]
Hence, the correct answer is: Option: C
factor completely x^3 + 1/8
Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
[tex]x^3+\dfrac{1}{8}=\\ \\ =x^3+2^{-3} = \\ \\ =x^3+(2^{-1})^3 =\\ \\ = (x+2^{-1})(x^2-2^{-1}x+2^{-2}) = \\ \\ = \Big(x+\dfrac{1}{2}\Big)\Big(x^2-\dfrac{x}{2}+\dfrac{1}{4}\Big)\\ \\ \\ \boxed{a^3+b^3 = (a+b)(a^2-ab+b^2)}[/tex]
Witch expression is equivalent to (cd)5?
Answer:
Step-by-step explanation:
the expression is equivalent to (cd)5 : c^5×d^5
A cake is shaped like a cylinder with a diameter of 9 in. The height of the cake is 6 in.
What is the exact volume of the cake?
Enter your answer in the box.
pi in^3
Answer: 121.5 pi in^3 or 381.7 in^3
Step-by-step explanation:
Volume of a cylinder = pi r^2(h)
Radius = 4.5 in, Height = 6 in
pi (4.5)^2(6)
pi(20.25)(6)
121.5 pi in^3 or 381.7 in^3
The exact volume of a cylindrical cake with a diameter of 9 inches and a height of 6 inches is 121.5π cubic inches.
The volume of a cylinder can be found using the formula V = πr^2h, where V stands for volume, r is the radius of the base of the cylinder, and h is the height of the cylinder. Given the diameter of the cake is 9 inches, the radius is half of that, which is 4.5 inches. Therefore, the exact volume of the cake is calculated as follows:
V = π × (4.5 )² ×2 × 6
Which simplifies to:
V = π × 20.25 ×2 × 6
So, the exact volume of the cake is:
V = 121.5π in^3
Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Answer:
Louise is missing the term [tex]30x^3[/tex]
Step-by-step explanation:
Remember that the formula for squaring a binomial is:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Where
[tex]a[/tex] is the first term of the binomial
[tex]b[/tex] is the second term of the binomial
Our binomial is [tex](5x^3+3)^2[/tex], so [tex]a=5x^3[/tex] and [tex]b=3[/tex].
Replacing values
[tex](5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2[/tex]
[tex](5x^3+3)^2=5^2x^6+6(5x^3)+9[/tex]
[tex](5x^3+3)^2=25x^6+30x^3+9[/tex]
Since Louise’s answer is [tex](5x^3+3)^2=25x^6+9[/tex], we can conclude that she is missing the term [tex]30x^3[/tex]
Answer:
Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Step-by-step explanation:
solve for x cos90=4/x
Final answer:
The equation cos(90°) = 4/x has no solution because cos(90°) is 0, and no value of x would satisfy the equation 0 = 4/x.
Explanation:
The student's equation is cos(90°) = 4/x. Knowing that the cosine of 90 degrees (or π/2 radians) is 0, we can substitute that into the equation, which simplifies to 0 = 4/x. This indicates that there is no value of x that would satisfy this equation, as no number multiplied by 0 can result in 4. Therefore, the solution is that there is no solution for x in this equation.
Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.
Find the mean, median, range, IQR, MAD for Derek's collection and Paul's collection.
Answer:
Derek:
Mean:1929
Median: 1930
range: 54
IQR: 48
MAD: 23.75
Paul:
Mean: 1929
Median: 1929.5
range: 15
IQR: 6
MAD: 3.5
Step-by-step explanation:
For the Derek's collection:
1. Mean = 1930.375
2. Median = 1930
For the Paul's collection:
1. Mean = 1929.75
2. Median = 1931
For Derek's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8
= 1930.375
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955
The median is the average of the middle two numbers, which are 1910 and 1950:
Median = (1910 + 1950) / 2
= 1930
For Paul's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8
= 1929.75
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935
The median is the average of the middle two numbers, which are 1930 and 1932:
Median = (1930 + 1932) / 2
= 1931
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You rent a bicycle for $20 plus $2 per hour
Answer:
It all depends on how long you have the bike for if you have it for only 1 hour it will be $22 dollars. If you have it for 2 hours it will be $24 dollars.
What’s this answer ?
Answer:
the radius is 13
the diameter is 40.82 inches squared
the area is 530.66
Step-by-step explanation:
well, the radius is 13
What is the measure of each angel of a rectangle ?
Answer:
All 4 four angles of the rectangle are 90°
Answer:
Opposite sides of a rectangle are the same length (congruent). The angles of a rectangle are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle." So, a rectangle has four right angles.
four- 90 degrees
A house worth $70,000 when purchased was worth $67,000 after the first year and $64,000 after the second year. If the economy does not improve and this trend continues, what will be the value of the house after 7 years? a) Write an explicit formula for the sequence. Explain where you found the numbers you are putting in the formula. b) Identify the value of n and explain where you found it. Use the explicit formula to solve the problem.
Answer:
a) The formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
b) [tex]a_7 = 49,000[/tex]
Step-by-step explanation:
Note that the difference between any two consecutive terms in the sequence is always equal to $3,000
[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]
Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.
The explicit formula for an arithmetic sequence is:
[tex]a_n = a_1 +d(n-1)[/tex]
Where d is the common difference between the consecutive terms of the sequence
[tex]d = -3,000[/tex]
[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]
n represents the number of years since the house was purchased
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
a) Then the formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
---------------------------------------------------------------------------------------------
b) Now we can use the formula to find the price of the house after 7 years
[tex]a_7 = 67,000 -3,000(7-1)[/tex]
[tex]a_7 = 67,000 -3,000(6)[/tex]
[tex]a_7 = 49,000[/tex]
50 POINTS! HELP! A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
A) mean
B) median
C) mode
D) range
Answer:
The best possible answer for this would be: D. Mode.
This is because mode measures how many times each number appears.
Answer:
mine said c is the correct answer
Step-by-step explanation:
4x+24=5x+1 what pus it really need answer
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
Answer:
Step-by-step explanation:
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $192 in interest after 2 years. How much money should be deposit?
Answers:
A: $6,000
B: $600
C: $60
D: $3,072
B is correct. Hope I helped yah.
a building casts a shadow that is 348 meters long at the same time a person who is 2 meters tall casts a shadow that is 6 meters long how tall is the building A.) 1044m B.) 116m C.) 64 m D) 100n
Answer:
Option B. [tex]116\ m[/tex]
Step-by-step explanation:
Let
x------> the height of the building
we know that
using proportion
[tex]\frac{2}{6}=\frac{x}{348} \\ \\x=348*2/6\\ \\x=116\ m[/tex]
triangle ABC is congruent to triangle DEF
Answer:
m<A = m<D
Step-by-step explanation:
This is the correct answer to your question.
Hope this helps!!!
Kyle.
Simplify 2x+x+x+2y x 3y x y
Answer:
3x+6y^3
Step-by-step explanation:
-First you add all the Xs
2x+x+x
-Then you multiply all the Ys
2y * 3y * y
* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3
*the numbers are multiplied making it a 6
Together it forms 6y^3
-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3
The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of 2x+x+x+(2y × 3y × y) can be done as,
2x + x + x + (2y × 3y × y)
= 4x + (2y × 3y × y)
= 4x + 6y³
Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
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PLEASE ANSWERRRRRRR! THANKS!!!!!!!!!!!!!!!!!!!!!!
Solve for x.
57 = 3x + 12
57-12= 3x+12-12
45=3x
Divide by 3
x=15
Check answer
57= 3(15)+12
57=57
Answer is correct.
x= 15
In a bus there is, A pregnant lady 24 years old A security guard 37 years old A random woman 56 years old Driver 68 years old Who is the youngest?
Answer:
The baby
Step-by-step explanation:
If you count the baby inside the pregnant woman, then he is the youngest.
hahha funny the baby of course
In the diagram, rectangle ABCD is split in half by AC. What is the value of tan x?
A) 3/4
B) 4/5
C) 3/5
D) 5/4
E) 4/3
Random answers will be reported!
Answer:
Then tan(x) = 4/3
Step-by-step explanation:
Given that we have a rectangle ABCD, we can affirm the following:
AD = BC = 4
AB = DC = 3
Now, we now that tan = Opposite Side / Adjacent Side
Then the opposite side to the angle x is AB = 4, and the adjacent side to angle x is DC = 3.
Then tan(x) = Opposite Side / Adjacent Side = 4/3 = 1,3333.
Answer: E
Step-by-step explanation:
Which expression is equivalent to the algebraic expression below?
3(–2x – 1)
a x – 1
b –6x – 3
c x + 2
d –6x – 1
Answer:
b) -6x - 3
Step-by-step explanation:
3(-2x-1)=3*(-2x)+3*(-1)= -6x - 3
B. -6x - 3
Distribute the 3, or multiply it by everything in the parentheses.
You multiply 3 times -2x to get -6x, and you multiply 3 times -1 to get -3.
Put these together to get -6x-3.
Write the equation of the circle shown here.
Answer:
(x − 7)² + (y + 2)² = 52
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
We know that (h, k) = (7, -2). But we need to find the radius. To do that, find the distance from the center to a point on the edge:
r² = (x₁ − x₂)² + (y₁ − y₂)²
r² = (7 − 1)² + (-2 − -6)²
r² = 6² + 4²
r² = 36 + 16
r² = 52
So the equation of the circle is:
(x − 7)² + (y + 2)² = 52
The equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
Explanation:To write the equation of a circle, we need to know the center and the radius of the circle. We can see from the diagram that the center of the circle is the point (2, -3), and the radius is 5 units.
The equation of a circle is given by the formula (x-h)^2 + (y-k)^2 = r^2,
where (h, k) is the center and r is the radius. Therefore, the equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
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Use the properties of logarithms to expand log(zy8).
(By 8, they mean the exponent of 8, or the eighth power.)
Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
Answer:
log (y)+ 8 log (z)
Step-by-step explanation:
use the rules of logarithm
The expanded form of the given function is log (x)+ 8 log (y).
What is a logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Given;
[tex]log(xy^8)[/tex]
use the rules of the logarithm;
log (x)+ 8 log (y)
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I need help to solve this question.
Answer:
B
Step-by-step explanation: