Answer:
A
Step-by-step explanation:
You take the number of shirts you have and are focusing on. In this case concert (12) and divide it by the total number of shirts to get the expected.
You can use the fact when random picking of t shirts happen, the probability of picking the Concert shirt can be taken by number of concert t shirts in total number of shirt since there is no bias towards a particular t shirt except their frequency.
The frequency of concert shirts obtained out of selected shirts compare to the expected frequency of the concert shirt as:
Option A: The frequency is 1 fewer that expected.
How to get the expected frequency of the object from the whole group?Suppose there are 100 fruits and 50 of them are apples and 50 other are mangoes. Then we can say that each one of the two fruit is apple and other one is mango. This 1 apple per 2 fruit is telling frequency of apples in selected 2 fruits.
Frequency is number of amount that item is present in the selected group.
The expected frequency can be obtained by seeing how many such objects are available to how many total objects.
You can think of expected frequency as how many of the considered object we expect to be present in the total amount of objects.
Thus, we have:
Expected frequency for concert shirt is 12 per 30 shirts or 4 per 10( i divided by 3) shirts or 2 per 5 shirts ( divided by 2). You can convert this to percent or probability too or ratio too like
2:5 = 2/5 = 0.4 = 40% (all four represent how many of the concert shirts are expected to be present out of amount of total shirts selected).
The frequency obtained from the selection contains 3 concert shirts out of 10 selected shirts.
Since the expected frequency of the concert shirts per 10 shirts selected is 4, and the frequency we obtained is 3, thus. the frequency obtained is 1 fewer than the expected.
Thus,
Option A: The frequency obtained is 1 fewer than expected.
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A paint store offers 15 different shades of blue. how many different ways could you purchase 3 shades of blue
Answer:
3.9230231e+12
Step-by-step explanation:
15! is 15 times 14 times 13 times 12 times 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 then times 3 because 3 shades of blue.
The number of different ways to purchase 3 shades of blue from 15 options is 455 different ways.
The question is asking about the number of combinations of 3 shades of blue that can be chosen from a total of 15 different shades. To calculate this, we use the formula for combinations without repetition, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, n is 15 and k is 3.
First, we calculate the factorial of n, which is 15! (15 factorial), then the factorial of k, which is 3!, and finally the factorial of n - k, which is 12!. Putting these into the formula gives us:
C(15, 3) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455
Therefore, there are 455 different ways to choose 3 shades of blue from 15 different shades.
2(x + 7) + 3x = 12
What is the first step in solving this equation for x?
A) 2x + 14 + 3x = 12
B) 2x + 7 + 3x = 12
C) 2x + 14 = 9
Eliminate
D) 5x = -2
A would be the very first step in solving the equation for x
You have to distribute 2 to x and 7.
2(x + 7) + 3x = 12
2x + 14 +3x = 12
Answer:
A) 2x + 14 + 3x = 12
Step-by-step explanation:
The first step is to distribute the 2
2(x + 7) + 3x = 12
2x+14 +3x =12
Then we combine like terms
5x+14 =12
Subtract 14 from each side
5x+14-14=12-14
5x = -2
Then divide each side by 5
5x/4 = -2/5
x = -2/5
use de moivres theorem to write the complex number in trigonometric form.
[sqrt(2)(cos(10)+isin(10)]^6
By DeMoivre's theorem,
[tex](\sqrt2(\cos10^\circ+i\sin10^\circ))^6=(\sqrt2)^6(\cos60^\circ+i\sin60^\circ)[/tex]
[tex]=8(\cos60^\circ+i\sin60^\circ)[/tex]
The answer is 8(cos60° +isin 60°)
Demoivre's theorem:, De Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it holds that (cosx + i sinx)^n= cosnx + i sinnx.
where i is the imaginary unit (i2 = −1).
By DeMoivre's theorem:
[sqrt(2)(cos(10)+isin(10)]^6
(√2 (cos 1o° + isin 10°))^6 = (√2)^6(cos 60° + isin 60°)
=8(cos60° +isin 60°)
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Select ALL the correct answers.!!!!
Observe the expression below and select the true statement(s)
3y(7 + 2x) + 9xy - 10
1. The "(7 + 2x)" in the first term is a factor.
2. The "9" in the second term is a coefficient,
3. The "3" in the first term is a factor
4.The "10" in the third term is a coefficient
5. The "2" in the first term is a constant,
6. The "x in the second term is an exponent
Answer: The true statements are:
The "(7 + 2x)" in the first term is a factor.
The "9" in the second term is a coefficient.
The "3y" in the first term is a factor.
Step-by-step explanation:
Answer:
Option 1 and 2.
Step-by-step explanation:
Given : Expression [tex]3y(7 + 2x) + 9xy - 10[/tex]
To find : Observe the expression below and select the true statement(s)?
Solution :
Using definition mentioned below :
Term is defined as a single numbers, variables, or the product of a number and variable. Factor is defined as one part of a product.Coefficient is defined as a number multiplied by a variable.Constant is defined as the term without variable.Exponent is defined as the power.We can say that statements which are true are
1) The "(7 + 2x)" in the first term is a factor.
2) The "9" in the second term is a coefficient.
Rest are false.
Therefore, option 1 and 2 is correct.
A town doubles its size every 30 years. If the population is currently 10,000, what will the population be in 60 years?
Answer: 20,000
Step-by-step explanation:
every 30 years 10,000 adds to the population
30 years=10,000 people
60 years=20,000 people
The result of multiplying two or more numbers is called
The numbers you are multiplying are called the factors the result is called the product.
Answer: Product?
Step-by-step explanation:
Adding: Sum
Subtracting: Difference
Dividing: Quotient
Multiplying: Product
Hope this helps
The times it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours and a standard deviation of 1.1 hours.
What is the time for a runner with a z-score of −1.2 ?
Enter your answer, rounded to the nearest hundredth, in the box.
The Answer will be 3.28 h
hope this will Help:)
Answer:
3.28
Step-by-step explanation:
z score is:
z = (x - μ) / σ
For z = -1.2, μ = 4.6, and σ = 1.1:
-1.2 = (x - 4.6) / 1.1
x = 3.28
Which system of equations does this graph represent?
A. y = x^2 − 6
y = −x − 4
B. y = x^2 + 6
y = x + 4
C. y = x^2 + 4
y = −x + 4
D. y = x^2 − 6
y = x − 4
Answer:
Option D
y = x^2 − 6
y = x − 4
Step-by-step explanation:
we know that
The y-intercept of the quadratic equation is the point (0,-6) (see the graph)
Could be option A or option D
The y-intercept of the linear equation is the point (0,-4) and the x-intercept is the point (4,0)
Could be option D
therefore
The system of equations is the option D
Verify
[tex]y=x^{2}-6[/tex]
[tex]y=x-4[/tex]
using a graphing tool
see the attached figure
The system of equations is the option D
Answer:
5
Step-by-step explanation:
.
.
.
Find the volume of the cone shown below.
Answer:
D
Step-by-step explanation:
The formula for volume of cone is [tex]V=\frac{1}{3}\pi r^2 h[/tex]
Where
V is the volume
r is the radius of the circular base
h is the height of the cone
In the diagram shown, we can clearly see that height is 12, radius is 9. We can simply plug them into the formula and get our exact answer (leaving pi as pi):
[tex]V=\frac{1}{3}\pi (9)^2(12)\\=324 \pi[/tex]
correct answer is D
Express 4.54545454545... as a rational number, in the form pq where p and q are positive integers with no common factors.
Answer:
the final answer is 50/11
Step-by-step explanation:
Here let's regard the first number of this geometric series as 0.54, holding the 4 to include later. The next is 0.0054, the next 0.000054, and so on.
Thus, the common ratio is 1/100. Then the sum of the infinite series, not including that 4, is
a 0.54 0.54
-------- = ------------ = ------------
1 - r 1 - 1/100 99/100
54
Multiplying both 0.54 and 99/100 by 100 results in ------- and this
99 0.545454....
Now add the 4 back in, obtaining 4 54/99, or (396 + 54) / 99.
This is the same as 450 / 99. You can readily check with a calculator to see whether this is equivalent to the given 4.54545454545...
Note that 450/99 is in the form p/q (not pq), where p and q are positive integers. But also note that 450/99 can be reduced to 150/33, or
50/11. A calculator will show you that 50/11 is equivalent to the given 4.54545454545...
Hence, the final answer is 50/11 (in the form p/q, NOT pq).
The number 4.54545454545... can be expressed as a rational number in the form of p/q as 50/11.
Explanation:To express the given number 4.54545454545... as a rational number in the form p/q, we need to use the concept of repeating decimals.
Let x = 4.54545... We can then write 100x = 454.54545... Subtracting the first equation from the second, we get 99x = 450. Solving for x gives us x = 450/99.
This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor. In this case, 450 and 99 share a common factor of 9. Dividing both numbers by 9 gives us 50/11, which is the simplest form of this fraction.
Therefore, 4.54545454545... as a rational number in the form p/q is 50/11.
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Match each curve to the area under it on the interval [-1, 5]. y = x2 + 16 42 square units y = -x2 + 7x 72 square units y = 4x + 26 204 square units y = -0.5x + 13 138 square units
Answer:
1. [tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]
2. [tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]
3. [tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]
4.[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]
Step-by-step explanation:
1. The first curve is [tex]y=x^2+16[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {x^2+16} \, dx[/tex]
We integrate to obtain:
[tex]\frac{1}{3}x^3+16x|_{-1}^5[/tex]
We evaluate to obtain:
[tex]\frac{1}{3}(5)^3+16(5)-(\frac{1}{3}(-1)^3+16(-1))=138sq.\:units[/tex]
[tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]
2. The second curve is [tex]y=-x^2+7x[/tex].
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {-x^2+7x} \, dx[/tex]
We integrate this function to obtain:
[tex]-\frac{1}{3}x^3+\frac{7}{2}x^2|_{-1}^5[/tex]
This evaluates to
[tex]-\frac{1}{3}(5)^3+\frac{7}{2}(5)^2-(-\frac{1}{3}(-1)^3+\frac{7}{2}(-1)^2)=42[/tex] square units.
[tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]
3. The third curve is [tex]y=4x+26[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {4x+26} \, dx[/tex]
We integrate this function to obtain:
[tex]2x^2+26x|_{-1}^5[/tex]
We evaluate the limits of integration to obtain:
[tex]2(5)^2+26(5)-(2(5)^2+26(5))=204sq.\:units[/tex]
[tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]
4. The fourth curve is [tex]y=-0.5x+13[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {-0,5x+13} \, dx[/tex]
We integrate this function to obtain:
[tex]-0.25x^2+13x|_{-1}^5[/tex]
We evaluate the limits of integration to obtain:
[tex]-0.25(5)^2+13(5)-(-0.25(-15)^2+13(-1))=72sq.\:units[/tex]
[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]
Which situation can be modeled by the inequality 50−12x≥8?
The situation that can be modeled by the given inequality is required.
Option D. is correct.
Let [tex]x[/tex] be the number of T shirts bought
The initial amount of money is $50
The savings should be at least $8 so more than or equal to $8.
The required inequality is [tex]50-12x\geq 8[/tex]
The inequalities of the other options that are not correct are
C. [tex]50-12x<8[/tex]
Here, [tex]x[/tex] is number of weeks
B. [tex]50-12x\geq 8[/tex]
Here [tex]x[/tex] is the number of packages bought.
So, [tex]12x[/tex] will be the total number of pretezels[/tex]
A. [tex]50-8x<12[/tex]
Here [tex]x[/tex] is the number of weeks.
So, option D. is correct.
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At a festival 2/7 of number of girls was equal to 3:5 of the number of boys. There were 165 fewer boys than girls, how many children were at the festival in all.
Answer:
[tex]\boxed{365}[/tex]
Step-by-step explanation:
Let g = number of girls
and b = number of boys
We have conditions (1) and (2):
[tex]\begin{array}{lrcll}(1) &\frac{2}{7}g & = & \frac{3}{5}b & \\(2) & g - b & = & 165 &\\(3) & 10g & = & 21b & \text{Multiplied each side of (1) by lcm of denominators}\\(4)& g & = & 165 + b &\text{Added b to each side of (2)}\\ & 10(165 + b) & = & 21b & \text{Substituted 4 into (3)} \\\end{array}[/tex]
[tex]\begin{array}{lrcll} & 1650 + 10b & = & 21b & \text{Distributed the 10} \\ & 1650 & = & 11b & \text{Subtracted 10b from each side} \\ (5) & b & = & 150 &\text{Divided each side by 11} \\ & g - 150 & = & 165 & \text{Substituted (5) into (2)} \\ & g & = & 215 &\text{Added 150 to each side} \\\\ & g + b & = & 365 &\text{Added girls and boys} \\\end{array}[/tex]
[tex]\text{The number of children at the festival was \boxed{\textbf{365}}}[/tex]
Check:
[tex]\begin{array}{rlcrl}\frac{2}{7}\times315& = \frac{3}{5} \times150 & \qquad & 315 - 160 & =165\\90 & = 90& \qquad & 165 & = 165\end{array}[/tex]
The graph of this system of equations is used to solve 4x2-3+6=2x4-9x3+2x What represents the solution set?
y intercepts of the graph
x intercepts of the graph
y coordinates of the intersection points
x coordinates of the intersection points
ANSWER
x coordinates of the intersection points
EXPLANATION
The given system of equations is:
[tex]y = 4 {x}^{2} - 3x + 6[/tex]
[tex]y = 2 {x}^{4} - 9 {x}^{3} + 2x[/tex]
We want to use the graph of these functions to solve
[tex] 4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]
The point of the intersection of the graph gives the solution to the simultaneous equation above.
Hence the x-coordinates of the intersection points gives the solution set of
[tex]4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]
The last choice is correct.
Answer: It's D
Step-by-step explanation:
Vanessa bought a house for $268,500. She has a 30 year mortgage with a fixed rate of 6.25%. Vanessa’s monthly payments are $1,595.85. How much was Vanessa’s down payment? a. $9,314.45 b. $16,781.25 c. $40,275.00 d. $53,040.00
Answer:
Option a - $9,314.45
Step-by-step explanation:
Cost of the house = $268,500
Time of repayment = 30 years
Repayment is done monthly, so number of repayments = 30 X 12 = 360
Monthly Payment = $1595.85
Rate of interest per payment period = [tex]\frac{.0625}{12}[/tex]
So, Present value of monthly payments = 1595.85 X [tex]\frac{(1+\frac{.0625}{12})^{360}-1}{(1+\frac{.0625}{12})^{360}*(\frac{.0625}{12})}[/tex]
= $259,185.55
So, Vanessa's down payment = $268,500 - $259,185.55 = $9,314.45
Hope it helps.
Thank you !!
Answer:
Option a - $9,314.45
Step-by-step explanation:
e d g e
In the figure, m∠1 = m∠2 = 22 and m∠3 = m∠4 = 123. From this, you can conclude that m∠TKL = _____
a. 22.
b. . 57.
c. 35.
d. 47.
Answer:
57°
Step-by-step explanation:
Angle 3 is supplementary to angle TKL. That means they add up to 180°. Therefore, 180° - 123° = 57°
Answer:
57°
Step-by-step explanation:
You can notice that by putting ∠3 and ∠TKL together you have a flat angle.
A flat angle has 180 degrees.
so, you can say that m∠3 and m∠TKL add 180 degrees, then they are supplementary angles.
Remember: Two angles are supplementary if they add 180 degrees.
Then, as you know m∠3=123°:
m∠3 + m∠TKL=180°
123 + m∠TKL=180°
m∠TKL=180° - 123°
m∠TKL=57°
A cone has a volume of $12288\pi$ cubic inches and the vertex angle of the vertical cross section is 60 degrees. what is the height of the cone? express your answer as a decimal to the nearest tenth.
Answer:
The height of the cone is [tex]48\ in[/tex]
Step-by-step explanation:
step 1
Find the radius of the base of cone
we know that
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=12,288\pi\ in^{3}[/tex]
[tex]tan(30\°)=\frac{r}{h}[/tex] ---> remember that the vertex angle of the vertical cross section is 60 degrees
so
[tex]r=(h)tan(30\°)[/tex]
[tex]r=(h)\frac{\sqrt{3}}{3}[/tex]
substitute the values and solve for h
[tex]12,288\pi=\frac{1}{3}\pi ((h)\frac{\sqrt{3}}{3})^{2} h[/tex]
[tex]36,864=\frac{h^{3}}{3}[/tex]
[tex]h^{3}=110,592[/tex]
[tex]h=48\ in[/tex]
Find the equation of the cosine graphed.
Answer:
C) y = -cos(x) +2
Step-by-step explanation:
The centerline is 2, so 2 is added. That leaves out choices A and B.
There is a minimum (not a maximum) at x=0, so the multiplier is negative, eliminating choice D.
The correct equation is that of C: y = -cos(x) +2.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
If s(x) = 2x^2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =
Answer:
A) 2x³+11x²+8x-16
Step-by-step explanation:
When you multiply s(x) by t(x) you get something like this:
[tex]s(x) \times t(x) = (2 {x}^{2} + 3x - 4) \times (x + 4) \\ = 2 {x}^{3} + 3 {x}^{2} - 4x + 8 {x}^{2} + 12x - 16 \\ = 2 {x}^{3} + 11 {x}^{2} + 8x - 16[/tex]
Answer: A) 2x³ + 11x² + 8x - 16
Step-by-step explanation:
s(x) · t(x) = (x + 4)(2x² + 3x - 4)
= x(2x² + 3x - 4) + 4(2x² + 3x - 4)
= 2x³ + 3x² - 4x + 8x² + 12x - 16
= 2x³ + (3x² + 8x²) + (- 4x + 12x) - 16
= 2x³ + 11x² + 8x - 16
Please help me out !!!!!!
Answer:
101.956 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = 14.2 and h = 7.18, hence
A = 14.2 × 7.18 = 101.956 cm²
udy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. The cone has a height of 4.5 inches and a radius of 1.5 inches.
A) 7.1 cubic inches
B) 10.6 cubic inches
C) 14.1 cubic inches
D) 31.8 cubic inches
Answer:
B) 10.6 cubic inches
Step-by-step explanation:
Vol = (1/3) base area × hight = (1/3)π×1.5²×4.5
Nick buys 2 shirts and 4 hats for a total of 44.00.If the hats cost 5.00 each, how much does each shirt cost?
If he bought 4 hats for $5 each and he spent a total of $44, he spent $44 - $20 in shirts.
44 - 20 = 24
2 shirts for $24 is 1 for 12
$12 for each shirt
Hope it helps :)
Answer:
1 shirt= $12
Step-by-step explanation
we can make an equation where S= shirts, and H for hats. this would look like 2S+4H=44. now we get the info H=5(dollars). we plug it in to get 2S+4 x 5=44. now we simplify to get 2S+20=44. we subtract 20 from both sides to simplify further to get 2S=24. now we can divide this by 2 on each side to get S=11, and since S is the shirts, it says one shirt is =to 11, or 1 shirt= $12
In EFGH find the measure of GFH !!!! PLEASE HELP!!!!
Need to graduate.
A. 30
B. 120
C. 60
D. 90
Answer:
C
Step-by-step explanation:
Since EF and GH are parallel lines then
∠EGF = ∠GFH = 60° ( Alternate angles )
What is the value of (gof)(4)
F(x)=3-x; g(x)=4x+1
Answer:
-3
Step-by-step explanation:
[tex]f(x) = 3 - x[/tex]
[tex]g(x) = 4x + 1[/tex]
[tex]h(x) = (g \bullet f) (x) = g(f(x)) \\ = 4(3 - x) + 1 \\ = 13 - 4x[/tex]
then
[tex]h(4) = 13 - 4 \times 4 = - 3[/tex]
I need help with a pre-calc problem I really don't understand how to solve it
(the answer is: 101.496936 feet above the ground.)
And please explain how you got the answer step-by-step, thank you:))
Answer:
Step-by-step explanation:
We know a maximum point on the height vs. time curve is at t=16 seconds. Then the height function can be written by filling in the known values in ...
h(t) = (center height) + (wheel radius)·cos((frequency)·2π·(t -(time at max height)))
Since t is in seconds, we want the frequency in revolutions per second. That will be ...
(3.2 rev/min)·(1 min)/(60 sec) = 3.2/60 rev/sec = 4/75 rev/sec
Then our height function is ...
h(t) = 59 + 45·cos(8π/75·(t -16))
9 minutes is 9·60 sec = 540 sec, so we want to find the value of h(540).
h(540) = 59 + 45·cos(8π/75·(540 -16))
= 59 +45·cos(4192π/75)
≈ 59 + 45·0.944376 . . . . . calculator in radians mode
≈ 101.496937 . . . . feet
_____
The cosine function is a maximum when its argument is zero. We used the process of function translation to translate the maximum point to t=16 from t=0. That is, we replaced t in the usual cosine function with (t-16).
We can also evaluate the cosine function by subtracting multiples of 2π from the argument. When we do that, we find that Shirley's height at 9 minutes is the same as it is after 15 seconds. Some calculators evaluate smaller cosine arguments more accurately than they do larger argument values.
Is the square root of 5/8 rational or irrational? I think it's irrational, but I'm not sure because it's not a repeating decimal and it doesn't terminate, so I'm pretty sure it's irrational. Pls double check my thinking!
Your Right It Is Irrational
What is the phase shift of y = cos(3x - 3pi/4 )?
Use the form
a
cos
(
b
x
−
c
)
+
d
acos(bx-c)+d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
4
a=4
b
=
3
b=3
c
=
π
4
c=π4
d
=
0
d=0
Find the amplitude
|
a
|
|a|
.
Amplitude:
4
4
Find the period using the formula
2
π
|
b
|
2π|b|
.
Tap for more steps...
Period:
2
π
3
2π3
Find the phase shift using the formula
c
b
cb
.
Tap for more steps...
Phase Shift:
π
12
π12
Find the vertical shift
d
d
.
Vertical Shift:
0
0
List the properties of the trigonometric function.
Amplitude:
4
4
Period:
2
π
3
2π3
Phase Shift:
π
12
π12
(
π
12
π12
to the right)
Vertical Shift:
0
0
i think ;-;
Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
The standard form of the cosine function is
y = a cos(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = 3 and c = - [tex]\frac{3\pi }{4}[/tex], hence
phase shift = - [tex]\frac{-\frac{3\pi }{4} }{3}[/tex] = [tex]\frac{\pi }{4}[/tex]
Which choice is equivalent to the quotient shown here for acceptable values of x?
Answer: OPTION D
Step-by-step explanation:
You need to remember this property:
[tex]\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }[/tex]
And remember that:
[tex]\frac{a}{a}=1[/tex]
Then, the first step is rewrite the expression:
[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}[/tex] [tex]=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }[/tex]
Now, to find the corresponding equivalent expression, you need to simplify the expression.
Therefore, the equivalent expression is the following:
[tex]\sqrt{\frac{6}{(x-1)}} }[/tex]
Finally, you can observe that this matches with the option D.
Answer:
Choice D
Step-by-step explanation:
The division of the two radicals can be re-written in the following format;
[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }[/tex]
Using the properties of radicals division, the expression can further be written as;
[tex]\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }[/tex]
We simplify the terms under the radical sign to obtain;
[tex]\sqrt{\frac{6}{x-1} }[/tex]
Choice D is thus the correct solution
56% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.
(a) ≈ 0.202, (b) ≈ 0.878, (c) ≈ 0.376, calculated using binomial probability formula with 56% chance for baseball fans.
To solve this problem, we can use the binomial probability formula since we have a fixed number of trials (selecting 10 men) and each trial (man) has two possible outcomes (considering themselves a baseball fan or not).
The binomial probability formula is:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
- [tex]\( P(X = k) \)[/tex] is the probability of getting exactly \( k \) successes,
- [tex]\( n \)[/tex] is the number of trials (in this case, 10 men),
- [tex]\( k \)[/tex] is the number of successes we are interested in (number of men considering themselves baseball fans),
- [tex]\( p \)[/tex] is the probability of success on each trial (in this case, 56% or 0.56),
- [tex]\( \binom{n}{k} \)[/tex] is the binomial coefficient, representing the number of ways to choose [tex]\( k \)[/tex] successes from [tex]\( n \)[/tex] trials.
Let's solve each part of the problem:
(a) Finding the probability of exactly five men considering themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.56)^5 \times (1 - 0.56)^{10 - 5} \][/tex]
(b) Finding the probability of at least six men considering themselves baseball fans. This is the sum of probabilities of having 6, 7, 8, 9, or 10 successes:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
(c) Finding the probability of less than four men considering themselves baseball fans. This is the sum of probabilities of having 0, 1, 2, or 3 successes:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Let's calculate each part:
(a)
[tex]$\begin{aligned} & P(X=5)=\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(1-0.56)^{10-5} \\ & =\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(0.44)^5 \\ & \approx 0.202\end{aligned}$[/tex]
(b)
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \]\[ = \sum_{k=6}^{10} \binom{10}{k} \times (0.56)^k \times (0.44)^{10 - k} \]\[ \approx 0.878 \][/tex]
(c)
[tex]$\begin{aligned} & P(X < 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3) \\ & =\sum_{k=0}^3\left(\begin{array}{c}10 \\ k\end{array}\right) \times(0.56)^k \times(0.44)^{10-k} \\ & \approx 0.006+0.034+0.111+0.225 \\ & \approx 0.376\end{aligned}$[/tex]
So, the probabilities are:
(a) [tex]\( \approx 0.202 \)[/tex]
(b) [tex]\( \approx 0.878 \)[/tex]
(c) [tex]\( \approx 0.376 \)[/tex]
HELP WITH THIS QUESTION, PLEASE!!
Answer:
74°
Step-by-step explanation:
The given congruence relations mean ...
3x -7 = 6x -88
81 = 3x . . . . . . . add 88-3x
(3x -7)° = (81 -7)° = 74°
The measure of angle XMZ is 74°.