Answer:
3/5
Step-by-step explanation:
There are 10 letters in the word "statistics".
Out of which, there are 3 s's and 3 t's.
So, the question asks what's the probability to get a S or a T out of 10 letters.
Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.
6/10 or if we simplify/reduce it... we get 3/5.
the correct answer is 3/5
The question is asking for the probability of selecting either an 's' or a 't' from the word 'statistics'. To solve this, we need to look at the total number of each letter and the total number of letters in the word. The word 'statistics' has 10 letters in total, with 3 's' letters and 3 't' letters.
To calculate the probability, we add the number of 's' letters to the number of 't' letters, which gives us 6. Then we divide this sum by the total number of letters in the word:
Probability('s' or 't') = (Number of 's' + Number of 't') / Total number of letters
Probability('s' or 't') = (3 + 3) / 10 = 6/10 = 3/5.
Thus, the correct answer is 3/5, meaning there is a 60% chance of picking either an 's' or a 't' from the word 'statistics'.
Solve for x.
1/10(x - 3) = -40
A) -403
B) -397
C) -7
D) -1
Answer:
-397Step-by-step explanation:
This may look daunting, but let us approach it step by step.
Step 1: Remove the Parenthesesmultiply 1/10 by x - 3
0.1x - 0.3 = -40
Step 2: Add 0.3In algebra, the goal is always to undo all the operations and get back to the original problem so that the mystery value can be determined. In this case since 0.3 was removed, we must add it back.
0.1x = -39.7
Step 3. Divide by 0.10.1x/0.1 = x
39.7/0.1 = -397
Step 4. Preliminary AnswerAnswer seems to be B. -397, but we should still check it.
Step 5: Check0.1(-397) - 0.3 = -40
-39.7 - 0.3 = -40
-40 = -40 Correct
If the answer was incorrect, this would show that there had been a flaw in our calculations. But everything checks out, so we are done!
Step 6: Final AnswerOur final answer is B. -397.
PLEASE MARK BRAINLIEST
Answer:
The answer is -397
Step-by-step explanation:
[Trigonometric Graphs]
Use the following information to write an equation of the graph described:
10. sin; Amp = 4, per = 2π/3; phase shift = right π/4; vertical shift = up 3; reflect over x-axis.
12. cos; Amp = 2, period of 10π/3, reflect over x-axis.
Explain.
Answer:
Here's what I get.
Step-by-step explanation:
Question 10
The general equation for a sine function is
y = a sin[b(x - h)] + k
Here's what the parameters control:
a = amplitude
k = vertical shift
b = the period (period = 2π/b; If period = 2π/3, b = 3)
h = horizontal shift
Reflect across y-axis (x ⟶ -x)
Your sine function will be:
[tex]\begin{array}{rllll}y = & a \text{ sin}[ & b(x- & h)] + & k)\\& \downarrow & \downarrow & \downarrow & \downarrow\\& 4 & 3 & \frac{\pi}{4} & 3\\\end{array}[/tex]
Here are the effects of each parameter.
(a) Amp = 4
Increases the amplitude by a factor of 4 (Fig. 1)
(b) Up 3
k = 3. The graph shifts up three units (Fig. 2).
(c) Period = 2π/3
Set k = 3. The period changes from 2π to 2π/3 (Fig. 3).
Notice that you now hav3 three waves between 0 and 2π, where originally you had one.
(d) Right π/4.
Set h = 4. The graph shifts right by π/4.
notice how the trough at ½π shifts to ¾π.
(e) Reflect about y-axis
Set x equal to -x. Notice how the trough at (¾π, -1) is transformed to the trough at (-¾π, -1) (Fig. 5).
Question 12
y = a cos[b(x - h)] + k
a = 2
Per = 10π/3 ⟶ b = 3/5
h = 0
k = 0
Reflect over x-axis: y ⟶ -y
(a) a = 2
The amplitude is doubled.
(b) Per = 10π/3 ⟶ b = 3/5
The period (peak-to-peak distance) lengthens to 10π/3.
(c) Reflect about x-axis (y ⟶ -y)
All peaks are transformed into troughs and vice-versa.
a cylindrical barrel has a height of 8 feet and a diameter of 6 feet. what is the volume of the barrel?
Answer: The volume is about 226 feet squared
Step-by-step explanation:
(10.02)
The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
Part 1) [tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
Part 2) [tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
Part 3) [tex]tan(\theta)=-1/3[/tex]
Step-by-step explanation:
we know that
The angle is in the second quadrant so the sine is positive, the cosine is negative and the tangent is negative
step 1
Find the radius r applying the Pythagoras theorem
[tex]r^{2}=x^{2} +y^{2}[/tex]
substitute the given values
[tex]r^{2}=(-3)^{2} +(1)^{2}[/tex]
[tex]r^{2}=10[/tex]
[tex]r=\sqrt{10}\ units[/tex]
step 2
Find the value of [tex]sin(\theta)[/tex]
[tex]sin(\theta)=y/r[/tex]
substitute values
[tex]sin(\theta)=1/\sqrt{10}[/tex]
Simplify
[tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
step 3
Find the value of [tex]cos(\theta)[/tex]
[tex]cos(\theta)=x/r[/tex]
substitute values
[tex]cos(\theta)=-3/\sqrt{10}[/tex]
Simplify
[tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
step 4
Find the value of [tex]tan(\theta)[/tex]
[tex]tan(\theta)=y/x[/tex]
substitute values
[tex]tan(\theta)=-1/3[/tex]
Hotdogs and corndogs were sold at last night’s football game. Use the information below to write equations to help you determine how many corndogs were sold.
The number of hotdogs sold was three fewer than twice the number of corndogs sold. Write an equation relating the number of hotdogs and corndogs. Let h represent the number of hotdogs and c represent the number of corndogs. A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write an equation to represent this information. How many corndogs were sold? Show how you calculated your answer.
Answer:
28
Step-by-step explanation:
If we set up our equation using the unknown number of hot dogs and corn dogs with their individual prices attached to them, we can set the sum of them equal to $201. We know that a hot dog costs $3, so we can represent hot dogs monetarily by attaching the cost of a single hot dog to the h. For example, if a hot dog costs $3, and we represent the expression as 3h, with h being the number of hot dogs sold, if we sell 4 hot dogs at $3 apiece, we make $12. If we sell 6 hot dogs we will make $18. The same goes for the corn dogs. We don't know how many corn dogs or hot dogs we sold, but we do know that the sales of both made $201. So our expression for that is
3h + 1.50c = 201
That's great, but we have too many unknowns, and that's a problem. So let's look back up to where we are told that the number of hot dogs is 3 less than 2 times the number of corn dogs. "3 less than" is -3 algebraically. "Twice the number" is 2times and the words "is" and "was" represent the = sign. So putting those words into an algebraic equation looks like this:
h = 2c - 3
That says "the number of hot dogs was twice the number of corn dogs less 3". Now that we have an expression for hot dogs we can sub it into our money equation in place of h:
3h + 1.5c = 201 becomes 3(2c - 3) + 1.5c = 201
Now we have an equation with only c's in it.
Distribute through the parenthesis to get
6c - 9 + 1.5c = 201
Simplify to 7.5c = 210
Now divide by 7.5 to get that c = 28.
Now that we know that, we go back with that number and sub it in for c in
h = 2c - 3 --> h = 2(28) - 3 gives us that the number of hot dogs sold was 53
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
let
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
Read more:
https://brainly.com/question/16450098
4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513
Fill in the blanks.
___/___
10.) Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.
What is the angle of inclination (angle of elevation) of the light beam?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
11.)
Suppose that a man standing at the edge of a cliff near the North Rim of the Grand Canyon is looking downward towards a campground inside the canyon. The elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The man's range finder indicates that his line of sight distance to the campground is 3044 ft.
What is the angle of depression of the man's line of sight to the campground?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
12.) What is the exact value of arcsin(0.5)?
Determine the value in degrees.
13.) Determine the exact value in degrees:
What is the exact value of arcsin−2√2
Answer:
Part 4) [tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10) The angle of elevation is [tex]40.36\°[/tex]
Part 11) The angle of depression is [tex]78.61\°[/tex]
Part 12) [tex]arcsin(0.5)=30\°[/tex] or [tex]arcsin(0.5)=150\°[/tex]
Part 13) [tex]-45\°[/tex] or [tex]225\°[/tex]
Step-by-step explanation:
Part 4) we have that
[tex]cos(\theta)=-\frac{5}{13}[/tex]
The angle theta lies in Quadrant II
so
The sine of angle theta is positive
Remember that
[tex]sin^{2}(\theta)+ cos^{2}(\theta)=1[/tex]
substitute the given value
[tex]sin^{2}(\theta)+(-\frac{5}{13})^{2}=1[/tex]
[tex]sin^{2}(\theta)+(\frac{25}{169})=1[/tex]
[tex]sin^{2}(\theta)=1-(\frac{25}{169})[/tex]
[tex]sin^{2}(\theta)=(\frac{144}{169})[/tex]
[tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10)
Let
[tex]\theta[/tex] ----> angle of elevation
we know that
[tex]tan(\theta)=\frac{85}{100}[/tex] ----> opposite side angle theta divided by adjacent side angle theta
[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]
Part 11)
Let
[tex]\theta[/tex] ----> angle of depression
we know that
[tex]sin(\theta)=\frac{5,389-2,405}{3,044}[/tex] ----> opposite side angle theta divided by hypotenuse
[tex]sin(\theta)=\frac{2,984}{3,044}[/tex]
[tex]\theta=arcsin(\frac{2,984}{3,044})=78.61\°[/tex]
Part 12) What is the exact value of arcsin(0.5)?
Remember that
[tex]sin(30\°)=0.5[/tex]
therefore
[tex]arcsin(0.5)[/tex] -----> has two solutions
[tex]arcsin(0.5)=30\°[/tex] ----> I Quadrant
or
[tex]arcsin(0.5)=180\°-30\°=150\°[/tex] ----> II Quadrant
Part 13) What is the exact value of [tex]arcsin(-\frac{\sqrt{2}}{2})[/tex]
The sine is negative
so
The angle lies in Quadrant III or Quadrant IV
Remember that
[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]
therefore
[tex]arcsin(-\frac{\sqrt{2}}{2})[/tex] ----> has two solutions
[tex]arcsin(-\frac{\sqrt{2}}{2})=-45\°[/tex] ----> IV Quadrant
or
[tex]arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°[/tex] ----> III Quadrant
Use this formula to find the value of a house with appreciation: A = V (1+r)Y
When Henry bought his house for $135,700, he was told that it would appreciate at a rate of five percent per year. If this remains true, how much will his house be worth in four years?
Answer:
[tex]A=\$164,944.20[/tex]
Step-by-step explanation:
we know that
[tex]A=V(1+r)^{Y}[/tex]
In this problem we have
[tex]r=5\%=0.05[/tex]
[tex]V=\$135,700[/tex]
[tex]Y=4\ years[/tex]
substitute in the formula and solve for A
[tex]A=\$135,700(1+0.05)^{4}=\$164,944.20[/tex]
Please please help me
Answer:
x = 8.3
Step-by-step explanation:
Given a tangent and 2 secants drawn to the circle from an external point then
The square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.
Using the secant with measure 4 + x, then
4(4 +x) = 7²
16 + 4x = 49 ( subtract 16 from both sides )
4x = 33 ( divide both sides by 4 )
x = 33 ÷ 4 = 8.25 ≈ 8.3 ( nearest tenth )
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
Answer:
3x^2+2x-1
Step-by-step explanation:
Start by plugging in the 2 equations into their assigned places then simplify.
Answer:14
Step-by-step explanation:( 3X2+1)-(1-X)
=3X2+1 -1+X
=3X2+X
ANY WHERE WE SEE X WE PLACE 2
=3(2)(2)+2
3*4+2
=12+2
14
Can someone find x (the height) for me please!!
Answer:
x = √5
Step-by-step explanation:
The Pythagorean theorem tells you the square of the diagonal is the sum of the squares of the two sides:
(√7)² = (√2)² + x²
7 = 2 + x² . . . . . . simplify
5 = x² . . . . . . . . . subtract 2
√5 = x . . . . . . . . . take the square root
A manufacturer makes closed cubic containers from sheet metal. How many square centimeters of sheet metal will a 27,000 cm 3 container need?
let's recall that a cube is just a rectangular prism with all equal sides, check picture below.
[tex]\bf \textit{volume of a cube}\\\\ V=s^3~~ \begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} V=&27000 \end{cases}\implies 27000=s^3\implies \sqrt[3]{27000}=s\implies 30=s \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cube}\\\\ SA=6s~~\begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} s=&30 \end{cases}\implies SA=6(30)\implies SA=180[/tex]
Please use the information below to complete this assignment.
y = 4
(1) What is the slope of this line?
(2) What is the x-intercept?
(3) What is the y-intercept?
Answer:
y = 4
That's a straight line.
The slope is 0.
There is no x-intercept.
The y-intercept is 4.
I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!
Answer:
the slope is 0
the x intercept is 0
the y intercept is 4
if UVWX is a parallelogram, what is the value of y?
Answer:
B. 60
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent.
This implies that:
|UV|=|XW|
From the diagram; |UV|=15
and [tex]|XW|=\frac{1}{4}y[/tex]
We equate the two side lengths to get:
[tex]15=\frac{1}{4}y[/tex]
We multiply both sides by 4 to obtain:
[tex]4\times 15=4\times \frac{1}{4}y[/tex]
This implies that:
y=60
Answer:
B!
Step-by-step explanation:
If the radius is 10 inches , in square inches, what is the circumference of the circle?
A. 15.7
B. 31.4
C. 47.1
D. 62.8
[tex]C=2\pi r =2\pi10=20\pi\approx\boxed{62.8}[/tex]
The answer is D.
The circumference of a circle with a radius of 10 inches is approximately 62.8 inches, calculated using the formula C = 2πr, resulting in the answer choice D. 62.8.
To calculate the circumference of a circle when the radius is given, we use the formula C = 2πr. Given that the radius (r) of the circle is 10 inches, we can calculate the diameter (d) as 2×10 inches, which equals 20 inches. Now, we multiply the diameter by π (approximately 3.1416) to find the circumference:
C = πd = 3.1416 × 20 inches = 62.832 inches.
Based on standard rounding rules, this is approximately 62.8 inches. Thus, the correct answer is D. 62.8 square inches.
Which members are in the sample
Answer:
20, 26, 35, 18
Step-by-step explanation:
So starting at row 129, we look at the sequence two-digits at a time without overlapping. If that number is between 01 and 43, then they get selected.
The first two digits are 20. That fits between 01 and 43, so that member gets selected.
Next, we have 26. That also fits.
After that we have 64. Nope, too high.
98 and 44 are also too high.
35 fits though. So does 18.
So the members that get selected are 20, 26, 35, 18.
If you have 14 1/2 dozen boxes of envelopes, and you order 3 1/4 dozen more, how many dozen boxes will you have in all?
The answere is 213 boxes
If you add 3 dozens to 14 dozens of boxes of envilopes , then you get 17 dozens of boxes of envilopes.Then of you sum up the 1/2 (2/4 ) with the 1/4.You get 3/4. Finally, you add 17 dozens to 3/4 of a dozen you get 17 3/4 dozens( wich is 213 boxes )
Can someone help me¿
Answer:
Step-by-step explanation:
number3
Please please help me out
Answer:
The measure of angle y is [tex]m\angle y=54\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle y=\frac{1}{2}(108\°)=54\°[/tex]
Anyone mind helping me out?:)
The answer is does matter.
At Eagle Rock High School, the probability that a student takes theatre and choir is 0.078. The probability that a student takes choir is 0.26. What is the probability that a student takes theatre given that the student is taking choir?
Final answer:
The probability that a student takes theatre given that the student is taking choir is found using conditional probability and is calculated to be 0.3, or 30%.
Explanation:
To find the probability that a student takes theatre given that the student is taking choir, we use the definition of conditional probability. In this scenario, the probability of a student taking theatre and choir (joint probability) is given as 0.078, and the probability of a student taking choir (marginal probability) is 0.26.
The formula for conditional probability is:
P(A | B) = P(A and B) / P(B)
Let A represent the event of a student taking theatre, and B represent the event of a student taking choir. Substituting the given values into the formula yields:
P(A | B) = 0.078 / 0.26
Performing the division gives us:
P(A | B) = 0.3
Therefore, the probability that a student takes theatre given that the student is taking choir is 0.3, or 30%.
Suppose that a coin is tossed 5 times. how many different outcomes include at least two heads
26 different outcomes include at least two heads.
There are [tex]26[/tex] different outcomes that include at least two heads when a coin is tossed [tex]5[/tex] times.
The total number of outcomes when a coin is tossed [tex]5[/tex] times is [tex]\(2^5 = 32\)[/tex], since each toss has [tex]2[/tex] possible outcomes (heads or tails).
To find the number of outcomes with at least two heads, we can find the total number of outcomes with exactly one head and no heads, and subtract that from the total number of outcomes.
1. Number of outcomes with no heads: There is only [tex]1[/tex] outcome with no heads ([tex]5[/tex] tails).
2. Number of outcomes with exactly one head: This can be calculated using combinations. There are [tex]5[/tex] ways to choose which toss will be heads, and for each of these, the remaining [tex]4[/tex] tosses must be tails. So, there are [tex]\(5 \times 1 = 5\)[/tex]outcomes with exactly one head.
Therefore, the number of outcomes with at least two heads is:
[tex]\[ 32 - 1 - 5 = 26 \][/tex]
simplify this expression
5*sqrt(x^22) where x<0
Answer:
[tex]\boxed{5x^{11}, x < 0}[/tex]
Step-by-step explanation:
[tex]5\sqrt{x^{22}}[/tex]
Remember that we evaluate the term under the radical first.
Even though x < 0, x²² > 0
So,
[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]
The simplified expression is
[tex]\boxed{5x^{11}, x < 0}[/tex]
Is the relationship shown by the data linear? If so, model the data with an equation. x y 1 5 5 10 9 15 13 20 The relationship is linear; y – 5 = (x – 1). The relationship is not linear. The relationship is linear; y – 5 = (x – 1).
Answer:
The relationship is linear; y – 5 = 5/4*(x – 1)
Step-by-step explanation:
We have been given the following data set;
x: 1, 5, 9, 13
y: 5, 10, 15, 20
The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.
The average rate of change is equivalent to the slope;
(change in y) / (change in x)
Using the first two pair of points we have;
(10-5) / ( 5-1) = 5/4
The point-slope form of equation of the line is thus;
y - 5 = 5/4 (x - 1)
Please help me out please
What we have here is called INTERSECTING CHORDS IN A CIRCLE.
The equation is:
10 times x = 7 times 7
10x = 49
x = 49/10
x = 4.9
answer 4.9cm
10times x=7times7(multiple it)
10x=49
x=49/10
x=4.9
Find the zeros of the function. Write the smaller solution first, and the larger solution second. G(x)=4x^2-484
Answer:
-11, 11
Step-by-step explanation:
You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11
Answer:
x = -11,11
Step-by-step explanation:
G(x)=4x^2-484
To find the zero's, set the function equal to zero
0 = 4x^2 - 484
Add 484 to each side
484 = 4x^2 -484+484
484 = 4x^2
Divide each side by 4
484/4 = 4x^2/4
121 = x^2
Take the square root of each side
sqrt(121) = sqrt(x^2)
±11 =x
x = -11,11
through (-1,2) parallel to y=-4x+3
Answer:
y = -4x - 2
Step-by-step explanation:
Parallel has same slope
so
y - 2 = -4(x + 1)
y - 2 = -4x - 4
y = -4x - 2
Equation
y = -4x - 2
HELP PLEASE!!
Question 1 (2 points)
Generalize the pattern by finding the nth term.
6, 10, 14, 18, 22,
A. 4n
B. 4n + 2
C. 4n + 10
D. 6n + 4
Answer:
B. 4n+2
Step-by-step explanation:
You are given the pattern 6, 10, 14, 18, 22
Rewrite it as
[tex]a_1=6\\ \\a_2=10\\ \\a_3=14\\ \\a_4=18\\ \\a_5=22[/tex]
Note that
[tex]a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=4[/tex]
This means that given pattern is a part of arithmetic sequence with
[tex]a_1=6\\ \\d=4[/tex]
So, the nth term of this arithmetic sequence is
[tex]a_n=a_1+(n-1)d\\ \\a_n=6+4(n-1)\\ \\a_n=6+4n-4\\ \\a_n=4n+2[/tex]
What should the balance be in Diane's register?
Will give BRAINLIEST
Answer:
The balance of Dianne's register should be $359.41
Step-by-step explanation:
We can begin at the ending balance on the bank statement at $578.30
Then a check is written for $219.25, so a debit
Next a deposit is made for $140.36, so a credit
Then a withdrawal is made for $140.00, so a debit
This means we can make the equation
[tex]578.30-219.25+140.36-140.00=359.41[/tex]
at certain time of day , a 30 meter high building cast a shadow that is 31 meters long . what is the angle of the elevation of the sun? round to the nearest degree.
A. 46 degree
B. 16 degree
C.44 degree
D.75 degree
Answer:
Option C. 44 degree
Step-by-step explanation:
Let
A-----> the angle of the elevation of the sun
we know that
The tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A
In this problem
The opposite side is 30 meters
The adjacent side is 31 meters
[tex]tan(A)=\frac{30}{31}[/tex]
[tex]A=arctan(\frac{30}{31})=44\°[/tex]
Please please help me
Answer:
(a)
Step-by-step explanation:
The line y = x + 1 has a solid circle at x = 2 indicating that x is valid for this value, thus
y = x + 1 for x ≤ 2
The line y = x + 2 has an open circle at x = 2 indicating that x = 2 is not part of the solution but that values greater than 2 are valid, that is
y = x + 2 for x > 2
The definition for the function is (a)