Carl ran the experiment and here are the results:17 times on letter A8 times on letter B5 times on letter CWhat is the EXPERIMENTAL probability of landing on B?5/308/308/178/13
Answers
Step 1: Calculate the total number times the experiment was carried out
[tex]\begin{gathered} A\Rightarrow17\text{ times} \\ B\Rightarrow8\text{ times} \\ C\Rightarrow5\text{ times} \\ \text{Total number of times =17+8+5=30} \end{gathered}[/tex]Step 2: Write out the formula for probability of an event to occur
[tex]\begin{gathered} Pr(B)=\frac{n(B)}{n(T)} \\ Pr(B)\Rightarrow\text{ probability that B shows up} \\ n(B)\Rightarrow\text{ number of times of B} \\ n(T)\Rightarrow\text{ Total number of times the experiment was carried out} \end{gathered}[/tex]Step 3: Find the experimental probability of landing on B
[tex]\begin{gathered} n(B)=8,n(T)=30 \\ Pr(B)=\frac{8}{30} \end{gathered}[/tex]Hence, the experimental probability of landing on B is 8/30
Related Questions
solve the following equation for G. be sure to take into account whether a letter is capitalized or not .H-3q=qr
Answers
H - 3q = gr
make g the subject of the relation.
H - 3q = gr
divide through by r
[tex]\begin{gathered} H\text{ - 3q = gr} \\ \frac{H}{r}\text{ - }\frac{3q}{r}\text{ = g} \end{gathered}[/tex]Final answer
[tex]g\text{ = }\frac{H}{r}\text{ - }\frac{3q}{r}\text{ or g = }\frac{H\text{ - 3q}}{r}[/tex]In ADEF, the measure of ZF=90°, DE = 52 feet, and FD = 14 feet. Find the measure of D to the nearest degree.
Answers
EXPLANATION
In order to find the measure of
[tex]\cos x=\frac{adjacent\text{ cathetus}}{\text{Hypotenuse}}[/tex][tex]x=\cos ^{-1}(\frac{14}{52})[/tex][tex]x=74.38^o\approx74^o[/tex]The answer is 74 degrees.
Label the median on the trapezoid.Then fill in the in the list
Answers
Given:
The trapezoid ABCD is given.
To find:
Label the median and fill in the blanks.
Explanation:
Let us label the median first.
Here, a line EF is a median.
It connects the midpoint of the legs. (It bisects each leg).
It is always parallel to both BC, and AD.
It is the average of the two parallel legs.
Find the area of a sector with a central angle of 170° and a radius of 17 millimeters. Round to the nearest tenth. 1) 857.5 mm22) 100.9 mm23) 428.7 mm24) 25.2 mm2
Answers
Problem statement: we have been given a task to find the area of the sector.
We are given some parameters:
[tex]\begin{gathered} \text{central angle=170}^0 \\ \text{radius}=17\operatorname{mm} \\ \end{gathered}[/tex]Method: We will apply the formula:
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \text{where} \\ \theta=\text{ central angle} \\ r=17\operatorname{mm} \\ A=\text{Area of the sector} \\ \pi=\frac{22}{7} \end{gathered}[/tex]Thus, applying the formula
[tex]A=\frac{170}{360}\times\frac{22}{7}\times17^2[/tex][tex]A=428.7\operatorname{mm}^2[/tex]The area of the sector is 428.7mm²
The answer is option 3
Draw slope triangles on the graph and create a table showing the price in dollars for pizzas that have between 0 and 3 toppings
Answers
Given
Table and data
Procedure
a. Draw the slope and create a table showing the price
Table
________________
Toppings ! Price
------------------------------
0 ! $7.00
1 ! $7.50
2 ! $8.00
3 ! $8.50
b. What is the y-intercept of the graph and what does it represent?
The y-intercept is (0, $7.00)
The y-intercept means that zero toppings cost $7.00
c. On the table you created, show the first differentiate from both
Inputs difference
1 - 0 = 1
Outputs difference
7.50 - 7.00 = 0.50
I need help asap I took a picture of my question.
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The equation of the given line is
y = 2x + 4
By comparing both equations,
slope of the given line is 2
We would find a perpendicular line to this line passing through the given point. Recall, if two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through point K is - 1/2. We would find the y intercept by substituting x = 0, y = - 1 and m = - 1/2 into the slope intercept equation. We have
- 1 = - 1/2 * 0 + c
c = - 1
The equation of the perpendicular line is
y = - x/2 - 1
We would find the point of intersection by equating both lines. We have
2x + 4 = -x/2 - 1
Multiplying through by 2,
4x + 8 = - x - 2
4x + x = - 2 - 8
5x = - 10
x = - 10/5 = - 2
Substituting x = - 2 into the perpendicular line equation,
y = - - 2/2 - 1 = 1 - 1
y = 0
The point of intersection is (- 2, 0)
We would find the distance between K(0, - 1) and (- 2, 0) by applying the formula for finding the distance between two points which is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1\text{ = 0, y1 = -1} \\ x2\text{ = - 2, y2 = 0} \\ \text{Distance = }\sqrt[]{(-2-0)^2+(0-1)^2}\text{ = }\sqrt[]{4\text{ + 1}}\text{ = }\sqrt[]{5} \\ \text{Distance = 2.2}4 \end{gathered}[/tex]standard form to y intercept form x-y<=-2<= is less than or equal to
Answers
when you multiply an inequality with -1 to remove a negative sign, the inequality changes direction
So
[tex]\begin{gathered} -y(-1)\leq(-1)(-2-x) \\ y\ge2+x \end{gathered}[/tex]Translate the following into an inequality:What number divided by five, is less than 8?m ÷ 5 < 85 ÷ m ≤ 8m ÷ 5 > 85 ÷ m > 8
Answers
The phrase "number divided by five" can be expressed as
[tex]m\div5[/tex]"is less than 8" is expressed as
[tex]<8[/tex]Putting it together, the inequality is
[tex]m\div5<8[/tex]Evaluate the following expression.x² + 4x - 9 when x = 5
Answers
Okay, here we have this:
Considering the provided expression, we are going to evaluate it in the given value of x, so we obtain the following:
x² + 4x - 9 when x = 5
=(5)² + 4(5) - 9
=25 + 20 - 9
=36
Finally we obtain that x² + 4x - 9 when x = 5 is equal to 36.
A rectangle has an area of 16 ft?. The length is 2 ft longer than the width. Let w represent the width of the rectangle.Which equation can be used to find the dimensions of this rectangle?O A. W +2 = 16O B. 2w + 2 = 16OC. W2 + 2 = 16OD. W2 + 2w = 16
Answers
Given data:
The area of the rectangle is A=16 ft^2.
The expression for the length of the rectangle is l=w+2.
The expression for the area of the rectangle is,
[tex]A=l\times w[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 16=(w+2)w \\ w^2+2w=16 \\ w^2+2w=16 \end{gathered}[/tex]Thus, the option (D) is correct.
A witch brewed a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes. After drinking 1 milliliter of potion, the witch was invisible for 5 minutes. Write the equatio for the relationship between x and y. y
Answers
x represents the amount of portion in millimeters
y represents the time she was invisible
Write out an equation to show the variation relationship
Since the variation is direct
Then
[tex]\begin{gathered} x\propto y \\ x=k\times y \end{gathered}[/tex]To get the value of k
when x= 1 mm, y = 5 minutes
[tex]\begin{gathered} k\text{ = }\frac{x}{y} \\ =\frac{1}{5}\text{ mm/min} \end{gathered}[/tex]The relationship between x and y will be
[tex]\begin{gathered} \text{substitute k in x=}ky \\ x=\frac{1}{5}\times y \\ x=\frac{y}{5}\text{ (this is the relationship)} \end{gathered}[/tex]Find the simple interest rate due a dollars on a four months load of $875 if the monthly simple interest rate is 1.5%
Answers
1. Given :
• Loan = $875
,• Four months interest = 1.5%
2. Calculate simple interest:
Interest =( 875 *1.5* 4) /100
= 5250/100
= $52.5
• This means that simple interest due will be $52.5.
Complete the statements to describe the outcomes of operations with the following numbers. Q and b are non-zero rational numbers. x and y are Irrational numbers. Select the word that best completes each statement. To select a word, click the menu and then click the desired word. To choose a different word, click the menu and click the new word. a + b is-Select an Answer- rational. Xy is Select an Answer- Irrational. a + x is-Select an Answer- rational. b.xis -Select an Answer- Irrational.
Answers
a + b is ALWAYS rational
a + x is SOMETIMES rational
x.y is SOMETIMES irrational
b.x is ALWAYS irrational
The buses at the Zoomy Express Bus Company depart as scheduled 80% of the time. The buses depart and arrive as scheduled 68% of the time. What is the probability that a Zoomy Express bus arrive as scheduled given it departs as scheduled?
Answers
Probability = (0.80)(0.68)
= 0.544
The probability that Zoomy Express bus arrive as scheduled given it departs as scheduled is 0.544.
Suppose that the dollar value v(t) of a certain house that is t year's old is given by the following function.v(t)= 476,000 (1.01)t
Answers
Solution
We are given the function
[tex]\begin{gathered} v(t)=476,000(1.01)^t \\ \\ Initial\text{ Value}=476,000 \\ \\ We\text{ also have growth} \\ \\ The\text{ percentage growth }1\text{ \%} \end{gathered}[/tex]Find the greatest common factor of thefollowing monomials:6m3n2 m5 n52mn3
Answers
So we have the following set of terms:
[tex]6m^3n,2m^5n^5,2mn^3[/tex]The greatest common factor (from now on, GCF) is a term that meets the following:
- All the three terms are multiples of it.
- It's the greatest number with the greatest power of each variable that meets the condition above.
One way to find it is looking for the GCFs of the integers, the powers of m and the powers of n separately. For example, the integers present in the set of three terms are 6, 2 and 2. If we factor each of them we get:
[tex]2\cdot3,2,2[/tex]The only number that appears in the 3 factored numbers is 2 so the GCF of the integers is 2.
Then we have to find the GCF among the powers of m. When you look for the GCF of a set of powers of the same variable the result is the power with the smallest exponent so if the powers we have are:
[tex]m^3,m^5,m[/tex]Then the GCF is m because its exponent is 1 whereas the other two exponents 3 and 5 are greater.
If we do the same for the powers of n we have:
[tex]n,n^5,n^3[/tex]Again, the GCF is the power of n with the lowest exponent, in this case n.
Now that we have found the GCFs of the integers, the powers of m and the powers of n we can find the GCF of all the terms. This is given by the product of those 3. Then the answer is:
[tex]2mn[/tex]Katherine is a personal chef. She charges $100 per three-person meal. Her monthly expenses are $3,075. How many three-person meals must she sell in order to make a profit of at least $1,950?
Answers
Given,
Katherine charges for three-person meal is $100.
The monthly expenses of katherine is $3075.
The amount of profit she want is $1950 atleast.
The total amount she have to earned in the month is,
[tex]\begin{gathered} \text{Total earning amount = amount for expenses+amount of profit} \\ =3075+1950 \\ =\text{ \$ 5025 } \end{gathered}[/tex]The number of three-person meals must she sell in order to make a profit of at least $1,950,
[tex]\text{Number of meals = }\frac{total\text{ earning amount}}{\cos t\text{ of one three person meal}}[/tex]Substituting the values then,
[tex]\begin{gathered} \text{Number of meals = }\frac{5025}{100} \\ =50.25 \\ \approx51 \end{gathered}[/tex]Hence, she must sell 51 three person meal to get atleast profit of $1950.
given the function: f(x)=x^2-2x. how can you restrict the domain so that f(x) has an inverse? what is the equation of the inverse function?
Answers
Solution
We have the following equation given:
[tex]y=x^2-2x=x(x-2)[/tex]For this case we can do the following:
[tex]x=y^2-2y=y(y-2)[/tex]We can solve for the quadratic equation and we got:
[tex]y=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1\cdot-x)}}{2\cdot1}=\frac{2\pm\sqrt[]{4\cdot(1+x)}}{2}=1\pm\sqrt[]{1+x}[/tex]The two solutions are:
[tex]y_1=1-\sqrt[]{1+x},y_2=1+\sqrt[]{1+x}[/tex]Then the answer is:
Part 1
[tex]x\ge1[/tex]Part 2
[tex]f^{-1}(x)=1+\sqrt[]{1+x}[/tex]The quotient of two and the difference of four and a number
Answers
Let the number be represented a x
The difference of four and the number can be written mathematically as :
[tex]4\text{ - x}[/tex]The next step is to find the qoutient of two
Find the sum.(2x + 3y) + (4x + 9y)
Answers
Given the expression:
[tex](2x+3y)+(4x+9y)[/tex]To find the sum, we can group the similar terms and then do the addition:
[tex]\begin{gathered} (2x+3y)+(4x+9y)=2x+3y+4x+9y \\ =2x+4x+3y+9y=6x+12y \end{gathered}[/tex]therefore, the sum is 6x+12y
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $600 interest. The same amount invested in the other fund earns $800. Find the lower rate of interest (in percent). %
Answers
Given:
The first fund earns $600 and the second fund earns $800.
Let x% be the lower rate of interest.
And x+4% be the higher rate of interest.
The difference between the amounts is,
[tex]800-600=200[/tex]It means,
[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]Alternative way,
For the first fund. let a be the lower rate and a+4 be the higher rate.
[tex]ax=600[/tex]For second fund,
[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]So,
[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]Answer: The lower rate of interest is 12%
Which of the following statements are true about the graph of f(x) =1/4 cos(x+pi/3)-1 2 answers
Answers
The given function is written in the form of:
[tex]f(x)=a\cos (bx-c)+d[/tex]in which a = 1/4, b = 1, c = -π/3, and d = -1.
The amplitude of the function is A, hence, the amplitude is 1/4. Statement A is true.
In addition, the vertical shift of the function is D, hence, the vertical shift is 1 unit down since d is -1. Statement 2 is false.
In addition, the horizontal shift or phase shift of a cosine function is C. Therefore, the horizontal shift is -π/3 or π/3 to the left. Statement D is true.
How to simplify 2a x a x 3a +b x4b
Answers
Answer
6a³ + 4b²
Step-by-step explanation
Given the expression:
[tex]2a\times a\times3a+b\times4b[/tex]Combining similar terms (terms with the same variable):
[tex]\begin{gathered} (2a\times a\times3a)+(b\times4b)= \\ =\lbrack(2\times3)(a\operatorname{\times}a\operatorname{\times}a)\rbrack+\lbrack4(b\operatorname{\times}b)\rbrack= \\ =6a^3+4b^2 \end{gathered}[/tex]What is the quotient? 71,760 divided by 100Round answer to four decimal places. If answer does not have four decimal placesthen use zeros so that it does.
Answers
The quotient is the answer obtained when we divide one number by another. For example, if we divide the number 6 by 3, we get the result as 2, which is the quotient.
We are to find the quotient when 71,760 is divided by 100. We can evaluate the answer by dividing:
[tex]71760\div100[/tex]When a number is divided by 100, the quotient is the number made by the digits, except the digits at one's and ten's places. The number formed by ten's and one's digit of the dividend number is the remainder.
Therefore, the whole number part of the division will be717 and 60 is the remainder.
Hence, the quotient is:
[tex]\Rightarrow717.6000[/tex]Write the first 5 terms of the arithmetic sequence. *a =-23 + 17(n + 1)
Answers
Let's determine the first 5 term under the arithmetic sequence formula:
A dentist gives each patient a toothbrush after his or her visit. The toothbrushes come in 5 differentcolors, and they are chosen at random to give to the patients. The chart shows the number of eachcolor toothbrush given to the last 50 patients to visit the dentist's office. Fill in the table with theprobability of each event occurring.Toothbrush ColorNumber of patientswho received itObserved ProbabilityRed9a.Blue7b.Green15c.Yellow11d.Orange8e.
Answers
Probability = required outcome/ all possible outcome
all possible outcome = 50
p(Red) = 9/50
p(blue) = 7/50
P(Green) = 15/50
p(yellow) =11/50
p(Orange) = 8/50 = 4/25
Which of the following functions has a vertical asymptote at x=3, a horizontal asymptote at f(x)=2, and a root at x=5?
Answers
To have a vertical asymptote, is the value in which the denominator is zero, therefore if vertical asymptote x=3, then the denominator must be x-3.
Then we find the root, which is the x-intercepts, let's find them:
[tex]\begin{gathered} \frac{-4}{x-3}+2=0 \\ \text{ }\frac{-4}{x\text{ - 3}}=\text{ - 2} \\ \text{ -4 = - 2\lparen x - 3\rparen} \\ \text{ }\frac{-4}{\text{ -2}}=\text{ x - 3 } \\ \\ 2=x\text{ - 3} \\ x=5 \end{gathered}[/tex]So, the function D has the requirements
Need help finding 2 more points on the line for question # 12(3,8) and (-4,8)Slope:8-8/-4-3 = 0/-7
Answers
ANSWER
The slope between the two points is 0
EXPLANATION
Given that;
(3, 8) and (-4, 8)
Slope is defined as the gradient of a line
The formula for determining slope is given below as
[tex]\text{ Slope = }\frac{\text{ rise}}{\text{ run}}[/tex]Where
rise = y2 - y1
run = x2 - x1
So, we have
[tex]\text{ Slope = }\frac{\text{ y}_2\text{ - y}_1}{\text{ x}_2\text{ - x}_1}[/tex]In the given point, let x1 = 3, y1 = 8, x2 = -4 and y2 = 8
[tex]\begin{gathered} \text{ slope = }\frac{\text{ 8 - 8}}{\text{ -4 - 3}} \\ \\ \text{ slope = }\frac{\text{ 0}}{\text{ -7 }} \\ \text{ slope = 0} \end{gathered}[/tex]Therefore, the slope between the two points is 0
quar OT rate in die table below Number of Pizzas 1 Number of Students 4. 8 12 16 2 3 4 Multiply the number of pizzas by 8 to find the number of students. Multiply the number of pizzas by 4 to find the number of students. Multiply the number of students by 4 to find the number of pizzas. Multiply the number of students by 8 to find the number of pizzas.
Answers
From the given table,
1 Pizza corresponds to 4 students
2 Pizza corresponds to 8 students
3 Pizza corresponds to 12 students
4 Pizza corresponds to 16 students
As you notice, for every pizza there are 4 students,
so the multiplier is 4.
2 pizza x 4 = 8 students
3 pizza x 4 = 12 students
4 pizza x 4 = 16 students
The answer is Option B. Multiply the number of pizza by 4 to find the number of students
use Euler circles to determine if the Argument is valid or invalid
Answers
Let's use Euler circles, to represent the argument.
As you can observe in the diagram above, the given argument is true because it's being proved that all P is R, basically because P is a subset of R.