Answer:
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~
( 3 , 4 )
( 1 , - 7 )
m = [tex]\frac{-7-4}{1-3}[/tex] = [tex]\frac{-11}{-2}[/tex] = [tex]\frac{11}{2}[/tex]
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
Please help with this problem my son is having problems showing his work an understanding how. Solve x2 – 6x = 16 using the quadratic formula method. Show your work. Then describe the solution.
Solution
We are given the quadratic equation
[tex]x^2-6x=16[/tex]We want to solve by using the quadratic formula method
Note: Given a quadratic equation
[tex]ax^2+bx+c=0[/tex]The formula method is given
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From
[tex]\begin{gathered} x^2-6x=16 \\ x^2-6x-16=0 \\ \text{Comparing with the general form of a quadratic equation} \\ a=1 \\ b=-6 \\ c=-16 \end{gathered}[/tex]Substituting the parameters intot the quadratic formula
and
Therefore,
[tex]x=8,-2[/tex](2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
Answer:
n = 6
Step-by-step explanation:
(2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
First lets solve the parentheses:
(2.4 × 1000) × ( 3 × 10^n) = (7.2 × 1000000000)
2.4 × 1000 = 2400 so...
2400 × (3 × 10^n ) = 7200000000
Next lets divide:
7200000000/2400 = 3000000
So now we have...
(3 × 10^n ) = 3000000
Even though we just divided we have to divide again so...
3000000/3 = 1000000
then to get the answer of n we have to figure out how many times to the power of 10 do we get 1000000.
one easy but time consuming way is
dividing it by ten till you get to one and you would get the same answer. You choose to do that way then that works for your.
There are also other way to figure that out but your teacher teaches you an easier way to figure it out.
Graph the following equation:(y + 4) = 2(x - 2)Step 1 of 3: Find a point on the line and the slope of the line.
Given:
The equation of line is,
[tex]y+4=2(x-2)[/tex]Find the slope of equation,
[tex]\begin{gathered} y+4=2(x-2) \\ y+4=2x-4 \\ y=2x-8 \\ \text{slope= 2} \end{gathered}[/tex]Find the points on line,
[tex]\begin{gathered} \text{For x=0,} \\ y=2x-8 \\ y=-8 \\ (x,y)=(0,-8) \\ \text{for x=4,} \\ y=2x-8 \\ y=2(4)-8 \\ y=0 \\ (x,y)=(4,0) \\ \text{For x=2} \\ y=2x-8 \\ y=2(2)-8=-4 \\ (x,y)=(2,-4) \\ \text{For }x=5 \\ y=2x-8 \\ y=2(5)-8=2 \\ (x,y)=(5,2) \end{gathered}[/tex]The graph of equation of line is,
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
By evaluating the equation in x = 2040, we can estimate the price to be $1507.7.
How to evaluate the equation?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Given that,
We know that the equation:
y = 1.83*x - 2225.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2040
we will get
y = 1.83*2040 - 2225.5 = 1507.7
Hence, The price will be 1507.7, in dollars, of a game in the year 2040.
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Where do the graph shifted if the function changes from Y=x^2 to Y=(x+h)^2
The independent variable x is shifted (x + h). This is a value of h units to the right since it is the sum to the variable x.
So, the graph to find where the graph shift, we need to find the difference between these two values:
[tex](x+h)^2-x^2=x^2+2hx+h^2-x^2=2hx+h^2[/tex]Then, the graph is shifted
[tex]2hx+h^2[/tex]$11,335 is invested, part at 9% and the rest at 6%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $865.35, how much is invested at each rate?
The amount that was invested at 9% is $10303 , and at 6% is $1032 .
In the question ,
it is given that
total amount invested is $11335 .
let the amount invested at 9% be "x" .
so , the interest earned from 9% part is 0.09x
and let the amount invested at 6% be "y" .
the interest earned from 6% part is 0.06y
So , the equation is x + y = 11335 .
x = 11335 - y
Also given that interest earned from 9% amount exceeds the interest earned from 6% by $865.35 .
So , according to the question
0.09x = 0.06y + 865.35
On substituting x = 11335 - y in the above equation , we get
0.09(11335 - y) = 0.06y + 865.35
1020.15 - 0.09y = 0.06y + 865.35
0.09y + 0.06y = 1020.15 - 865.35
0.15y = 154.8
y = 154.8/0.15
y = 1032
and x = 11335 - 1032
x = 10303
Therefore , The amount that was invested at 9% is $10303 , and at 6% is $1032 .
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66. WORKER EFFICIENCY An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled f(x) = -x³ + 6x² + 15x television sets x hours later. How many sets will such a worker have assembled by 10:00 A.M.? [Hint: At 10:00 A.M., x = 2.] b. Ilow many sets will such a worker assemble between 9:00 and 10:00 A.M.?
Step-by-step explanation:
use differential calculus
9×2=2×9 what is the property of this problem?
The property involved is called "commutative property of product"
SInce we are flipping the oerder of the factors and arrive at the same result.
The "flipping is called "commuting" in Math terms.
will give brainlist
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 320 640 960
Create a description in words for the table.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The description for the table in word will be A. The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
What is a proportional relationship?Proportional connections are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
In this case, the table shows a proportional relationship between workout and calories burned. In 1 hour, 320 calories are burned.
In conclusion, the correct option is A.
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Please help me solve. I also need help on what ratios to put in the two boxes before the answer. Do I just choose any of them?
Explanation
By metric conversion
[tex]\begin{gathered} 1\text{ mile =}1.61km \\ 1\text{ hour = 60 mins} \end{gathered}[/tex]Therefore;
[tex]\frac{57mi}{1hr}\times\frac{1.61}{1}\times\frac{1}{60}=1.5295\frac{km}{\min }[/tex]Answer:
[tex]\begin{gathered} \text{Box 1= }\frac{\text{1.61}}{1} \\ \text{Box 2=}\frac{1}{60} \\ \text{Box 3=}1.53 \end{gathered}[/tex]Which of the following choices are correct ways to name the line in the figure below?
line VK and line TV
Explanation:
To name the lines, we pick the points on the line.
The points on the line: K, T, and V
We can name the line towars the right or towards the left.
The lines using the points:
line KV or line VK
line TV or line VT
line KT or line TK
The line with two arrows at the end represent a line.
The line with one arrow represent a ray
from the options, the correct ways to name the line in the figure below:
line VK and line TV
KV is a ray not a line
Therefore, the correct ways to name the line in the figure below : line VK and line TV
9b 9a) Use the slope formula to determine the rate of change eq y- and find the y-intercept "5" by substituting the x and y values into y=mx + b
A) We need to find the rate of change of the function first.
The rate of change or slope of the line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Where x and y are the coordinates of a point in line.
In order to calculate the slope we can take the poinst:
x1 = -6, y1 = 4
x2 = -2, y2= 1
Using the formula of above we find that the slope is:
[tex]m=\frac{1-4}{-2-(-6)}=-\frac{3}{4}[/tex]Now, in order to find the value of y-intercept of the line we can use formula:
[tex]y=m\cdot x+b[/tex]Which is the function of the line. From the formula of above we don't know the value of b (the y-intercept).
But we know that the formula must be valid for a point in the line. We can find the value of b replacing the coordinates of a point in the line, let's choose: x = -6 and y = 4, so:
[tex]4=\text{ m}\cdot(-6)+b[/tex]Now we use the value of m of above:
[tex]4=(-\frac{3}{4})\cdot(-6)+b[/tex]And from the last equation we can see that:
[tex]b=4-\frac{3}{4}\cdot6=4-\frac{9}{2}=\frac{8}{2}-\frac{9}{2}=-\frac{1}{2}[/tex]So, the equation of the line is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]And the y-intercept is obtain replacing x = 0, so the y-intercept is: y = -1/2
b) From the stepts of above we already know an equation that represents the function! It is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]c) Now, we need to use the last equation to find y = n in the table. We know from the table that the value x for that value of y is x = 3, so we replace that value in the equation of the line:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot3-\frac{1}{2}=-\frac{9}{4}-\frac{1}{2}=-\frac{9}{4}-\frac{2}{4}=-\frac{11}{4}[/tex]So the value of n is:
[tex]n\text{ = -}\frac{\text{11}}{4}[/tex]At a coffee shop, there is a pot that has a volume of 5.4 L. Find how many cubic centimeters of coffee will completely fill the pot
Given:
Total volume = 5.4 L.
We know that 1 L is equivalent to 1000 cubic centimetres; hence:
[tex]5.4L\times\frac{1000cm^3}{1L}[/tex]ANSWER
5400 cm³ of coffee will completely fill the pot
the figure shows a net for a three-dimensional figure. the net includes three squares.a) what is the three dimension figure. b) what is the surface area of the digure.
(b).
The area of the figure is equal to the sum of the area of the three squares and 2 triangles.
The area of the square is
[tex]2\operatorname{cm}\times2\operatorname{cm}=4\operatorname{cm}^2[/tex]The area of the triangle is
[tex]\frac{1}{2}\times1.7\operatorname{cm}\times2\operatorname{cm}=1.7\operatorname{cm}^2[/tex]Hence, two triangles and three squares have a total area of
[tex](4\operatorname{cm}\times3)+(2\times1.7cm)=15.4\operatorname{cm}^2[/tex]Given that A = {1, 2,2 3} and B = {4, 6}, then find B×A
The solution for set B × A is {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Given,
The sets,
A = {1, 2, 3}
B = {4, 6}
We have to find B × A.
Here,
Consider the Cartesian product:
The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B is referred to as the Cartesian Product of sets A and B in mathematics. For instance, the Cartesian Product of A and B is (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), and (2, 5) if A = [1, 2] and B = [3, 4, 5].
The Cartesian product of B × A = {(b, a) | b € B, a € A}
So,
B × A = {4, 6} × {1, 2, 3}
B × A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
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23. At a company employing 140 people, 40% of the employees took the bus to work,and 5 % lived close enough to walk. The others drove cars. How many employeesdrive cars to work?Answer
Since the total percent of the employees is 100%
Since 40% of them took the bus
Since 5% walk
Add them and subtract the sum from 100% to get the percentage of who take the car
[tex]\begin{gathered} 40+5=45 \\ 100-45=55 \end{gathered}[/tex]Then 55% of the employees use cars
Since the total number of employees is 140, then
Let us find 55% of 140
Change 55% to a number by divide it by 100, then multiply it by 140
[tex]\begin{gathered} N=\frac{55}{100}\times140 \\ N=77 \end{gathered}[/tex]There are 77 employees who use cars
For Hox)=2x– 9 and 96 = ; « +9), find (10 g)(x) and (gof)(x). Then determine whether (f = 9/8)= (4 * H(X).What is (fog)x)?(10 g)x)=0
Given the functions;
[tex]\begin{gathered} f(x)=2x-9 \\ g(x)=\frac{1}{2}(x+9) \end{gathered}[/tex]We want to find the composite functions;
[tex]undefined[/tex]LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
Consider the right triangle shown below where a=8.09, b=9.4, and c=12.4. Note that θ and ϕ are measured in radians.What is the value of cos(θ)?cos(θ)= What is the value of sin(θ)?sin(θ)=What is the value of tan(θ)?tan(θ)= What is the value of θ?θ=
By definition
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hipotenuse}}[/tex]From the picture
[tex]\begin{gathered} \cos (\theta)=\frac{a}{c} \\ \cos (\theta)=\frac{8.09}{12.4} \\ \cos (\theta)=0.65 \end{gathered}[/tex]By definition
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hipotenuse}}[/tex]From the picture:
[tex]\begin{gathered} \sin (\theta)=\frac{b}{c} \\ \sin (\theta)=\frac{9.4}{12.4} \\ \sin (\theta)=0.76 \end{gathered}[/tex]By definition
[tex]\tan (angle)=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]From the picture
[tex]\begin{gathered} \tan (\theta)=\frac{b}{a} \\ \tan (\theta)=\frac{9.4}{8.09} \\ \tan (\theta)=1.16 \end{gathered}[/tex]Isolating θ from the previous equations:
[tex]\begin{gathered} \theta=\arccos (0.65)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arcsin (0.76)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arctan (1.16)=49.24\text{ \degree}\approx49\text{ \degree} \end{gathered}[/tex](The difference between the values is caused by rounding errors)
Evaluate the expression.If x=12, y=8, and z=3x3 + y + z3
We need to find the value of
[tex]x^3+y+z^3[/tex]Where x = 12, y = 8, and z = 3
Substitute these values in the expression above
[tex](12)^3+8+(3)^3[/tex]12^3 = 1728
3^3 = 27
Then
[tex]1728\text{ + 8 + 27 = 1763}[/tex]The value of the given expression is 1763
an object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) =
GIVEN
The function of the object's velocity is given as follows:
[tex]v(t)=-2\sin t[/tex]Also given:
[tex]s(0)=0[/tex]SOLUTION
To get the position's function (s(t)), the velocity function needs to be integrated:
[tex]s(t)=\int v(t)dt[/tex]Therefore:
[tex]\begin{gathered} s(t)=\int(-2\sin t)dt \\ \mathrm{Take\:the\:constant\:out}: \\ s(t)=-2\cdot\int\sin\left(t\right)dt \\ \mathrm{Use\:the\:common\:integral}:\quad \int \sin \left(t\right)dt=-\cos \left(t\right) \\ s(t)=-2\left(-\cos\left(t\right)\right) \\ \mathrm{Simplify}\text{ and add a constant to the solution} \\ s(t)=2\cos\left(t\right)+C \end{gathered}[/tex]Recall that s(0) = 0. Therefore:
[tex]\begin{gathered} s(0)=2\cos(0)+C=0 \\ \therefore \\ C=-2 \end{gathered}[/tex]Hence, the position function is:
[tex]s(t)=2\cos t-2[/tex]The THIRD OPTION is correct.
Which of the following tests should be administered to see if an experimental medicine lowers blood pressure among hypertensive patients? A. two-tailed test OB. right-tailed test OC. alternative test OD. left-tailed test
We have to select the appropiate test to see if an experimental medicine lowers blood pressure among hypertensive patients.
In this case, we want to test if the mean for the blood pressure after the treatment is significantly lower than the blood pressure mean without treatment.
Then, for the blood pressure to be significantly different it has to be to the left of a critical value.
Then, it is a left-tailed test.
Answer:
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark ( 1 ) for the fraction bar.
Consider that the coordinates of the mid-point of a line segment is given by the formula,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]The given diagram represents the line segment between the points (-3,4) and (-6,-1).
So the corresponding mid-point is given by,
[tex]\begin{gathered} x=\frac{-3+(-6)}{2}=\frac{-9}{2} \\ y=\frac{4+(-1)}{2}=\frac{3}{2} \end{gathered}[/tex]Thus, the mid-point of the given line segment is ( -9/2 , 3/2 ) .
Triangle ABC is inscribed in the circle with arcs shown. find X and the measures of angle A, angle B, Angle C
The total circumference of a circle = 360°
Therefore,
[tex]\text{arc AB + arc BC+ arc AC}=360^0[/tex]Where,
[tex]\begin{gathered} \text{arc AB=(6x+10)}^0 \\ \text{arc BC=(x+15)}^0 \\ \text{arc AC=((8x-40)}^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} (6x+10)^0+(x+15)^0+(8x-40)^0=360^0 \\ 6x^0+x^0+8x^0+10^0+15^0-40^0=360^0 \\ 15x^0-15^0=360^0 \\ 15x^0=360^0+15^0 \\ 15x^0=375^0 \\ \text{divide both sides by }15 \\ \frac{15x}{15}=\frac{375^0}{15} \\ x=25^0 \end{gathered}[/tex][tex]\begin{gathered} \text{arc AB=(6x+10)}^0=(6\times25+10)^0=150^0+10^0=160^0 \\ \text{arc BC=(x+15)}^0=(25^0+15^0)=40^0 \\ \text{arc AC=(8x-40)}^0=(8\times25^0-40^0)=200^0-40^0=160^0 \end{gathered}[/tex]To calculate
[tex]\begin{gathered} \angle A,B,\angle C \\ We\text{ will use the theorem,} \\ \text{The measure of an insribed angle in a circle equals half the measure of the intercepting arc} \\ \end{gathered}[/tex][tex]\begin{gathered} \angle A=\frac{arc\text{ BC}}{2} \\ \angle A=\frac{40^0}{2}=20^0 \end{gathered}[/tex][tex]\begin{gathered} \angle B=\frac{arc\text{ AC}}{2} \\ \angle B=\frac{160^0}{2}=80^0 \end{gathered}[/tex][tex]\begin{gathered} \angle C=\frac{arc\text{ AB}}{2} \\ \angle C=\frac{160^0}{2}=80^0 \end{gathered}[/tex]Hence,
x = 25°
∠ A=20°
∠ B=80°
∠ C=80°
find the slope of the line passing through the points (-5,4) and (3,-3)
P1 = (-5, 4)
P2 = (3, -3)
Formula
[tex]\text{slope = }\frac{(y2\text{ - y1)}}{(x2\text{ - x1)}}[/tex]Substitution
[tex]\begin{gathered} \text{ slope = }\frac{(-3-4)}{(3\text{ + 5)}} \\ \text{ slope = }\frac{-7}{8} \end{gathered}[/tex]Result
[tex]\text{ slope = }\frac{-7}{8}[/tex]Number of adult tickets sold = Number of child tickets sold =
Given:
Total ticket = 321
Total collection = $3535
Adult ticket price = $15
Child ticket price = $5
Find-:
(1)
Number of adult tickets sold
(2)
Number of child tickets sold
Explanation-:
Let the number of adult tickets = x
Let the number of child tickets = y
If the total ticket is 321 then,
[tex]x+y=321........................(1)[/tex]Price for adult ticket is:
[tex]=15x[/tex]The price for child ticket is:
[tex]=5y[/tex]total price is $3535 then,
[tex]15x+5y=3535...................(2)[/tex]From eq(1)
[tex]\begin{gathered} x+y=321 \\ \\ 5x+5y=1605..............(3) \end{gathered}[/tex]So eq(2) - eq(3) is:
[tex]\begin{gathered} (15x+5y)-(5x+5y)=3535-1605 \\ \\ 15x-5x+5y-5y=1930 \\ \\ 15x-5x=1930 \\ \\ 10x=1930 \\ \\ x=\frac{1930}{10} \\ \\ x=193 \end{gathered}[/tex]Put the value in eq(1) then,
[tex]\begin{gathered} x+y=321 \\ \\ 193+y=321 \\ \\ y=321-193 \\ \\ y=128 \end{gathered}[/tex]So,
Number of adult tickets = 193
Number of child tickets = 128
If you bought a stock last year for a price of $90 and it is gone down 13% since then how much is the stock worth now to the nearest cent
The stock worth is $78.3
Given,
Bought a stock last year for a price of $90
And, price gone down is 13%
To find how much is the stock worth?
No, According to the question
Firstly, find the 13% of 90 i.e.,
= 13/100 x90
= $11.7
Stock worth is
= 90 - 11.7
= 78.3
Hence, The stock worth is $78.3
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A French restaurant used 808,870 ounces of cream last year. This year, due to a menu update, it used 90% less. How much cream did the restaurant use this year?
Answer:
80,887
Step-by-step explanation:
808,870 x (1 - 0.9)
808,870 x 0.1
80,887
3. Given x=2 and y=-3, evaluate the expression given below 2x - 3xy - 2y? A) -28 B) 28 C) 8 D) 44
Given:-
x=2,y=-3
[tex]2x-3xy-2y\text{?}[/tex]To find evalute the given expression,
[tex]2x-3xy-2y[/tex]
Subtitute the x and y value in above equation,
[tex]\begin{gathered} 2(2)-3(2)(-3)-2(-3) \\ =4-(6\times-3)+6 \\ =4-(-18)+6_{} \\ =4+18+6 \\ =28 \end{gathered}[/tex]So the required value is 28.
So the correct option B.
A cookie jar contains 8 oatmeal, 7 peanut butter and 10 sugar cookies. What is theprobability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls asugar cookie from the jar?A. 17/49B.7/60C. 17/600D. 7/600
Answer:
B. 7/60
Explanation:
Given;
Number of oatmeal cookies = 8
Number of peanut butter cookies = 7
Number of sugar cookies = 10
Total number of cookies = 8 + 7 + 10 = 25
So the probability of Ivan pulling a peanut butter cookie from the jar can be determined as seen below;
[tex]\begin{gathered} P(\text{peanut butter cookie) }=\frac{\text{ number of peanut butter cookies}}{\text{Total number of cookies}} \\ P(\text{peanut butter cookie) }=\frac{7}{25} \end{gathered}[/tex]So if Ivan ate the peanut butter cookie he pulled (he did not replace it), it means that the total number of cookies will be 24, so the probability of pulling a sugar cookie from the jar will now be;
[tex]\begin{gathered} P(sugar\text{ cookie) }=\frac{\text{ number of sugar cookies}}{\text{Total number of cookies}} \\ P(sugar\text{ cookie) }=\frac{10}{24}=\frac{5}{12} \end{gathered}[/tex]So we can determine the probability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls a sugar cookie from the jar by multiplying the above probabilities;
[tex]P(peanut,sugar)=\frac{7}{25}\times\frac{5}{12}=\frac{7}{5}\times\frac{1}{12}=\frac{7}{60}[/tex]Therefore, the probability is 7/60