Okay, here we have this:
Considering the provided function, we are going to calculate the requested roots, so we obtain the following:
[tex]\begin{gathered} x^2-12x+32=0 \\ x_{1,2}=\frac{-(-12)\pm\sqrt{(-12^2)-4(1)(32)}}{2(1)} \\ x_{1,2}=\frac{12\pm\sqrt{144-128}}{2} \\ x_{1,2}=\frac{12\pm\sqrt{16}}{2} \\ x_{1,2}=\frac{12\pm4}{2} \\ x_{1,2}=6\pm2 \\ x_1=6+2,x_2=6-2 \\ x_1=8,x_2=4 \end{gathered}[/tex]Finally we obtain that the roots of the function are x=8 and x=4.
Solve the following system for y: 2x+y=43x−12y=−4
On solving the equation 2x+y=-4 and 43x-12y=-4 for y we get the value of y=-164/67 as the definition of solution of equation says "A solution to an equation is a number that can be plugged in for the variable to make a true number statement".
What is system of equation?A group of equations involving one or more variables is known as a system of equations. The variable mappings that cause all component equations to be satisfied or intersected are the solutions to systems of equations.
Here,
2x+y=-4
43x-12y=-4
43(2x+y=-4)
2(43x-12y=-4)
86x+43y=-172
86x-24y=-8
subtracting equation,
67y=-164
y=-164/67
As stated in the definition of equation solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," we arrive at the value of y=-164/67 after solving the equations 2x+y=-4 and 43x-12y=-4 for y.
To know more about system of equation,
https://brainly.com/question/24065247?referrer=searchResults
#SPJ1
The length of a rectangle is 3 more than twice the width. Which of the following represents the length of the rectangle if the perimeter is 42 inches? 2(x) +2(2x+3)=42
Answer:
Step-by-step explanation: if the width is x then the length is 2x+3
The perimeter is 2x+2(2x+3)=42
then 6x+6=42
6x=36
x=6
Then the length is 2*6+3=15
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet. Which model shows how much money Ilya has all together?
The model is a linear function that shows $3.25 money that Ilya has all together
What is meant by a linear function?The phrase linear function relates to two distinct but related concepts in mathematics:
Some authors use the term "linear function" only for linear mappings that accept values in the scalar field; these are more frequently known as linear forms.
Calculus' "linear functions" qualify as "linear mappings" when (and only when) f(0,..., 0) = 0, or, equivalently, when the aforementioned constant b equals zero.
A linear function in calculus and related fields is one whose graph is a straight line, that is, a polynomial function of degree zero or one. The word affine function is commonly used to distinguish such a linear function from the other idea.
A linear function is also known as a linear map in linear algebra, mathematical analysis, and functional analysis.
Given,
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet.
Total money=$1.40+$1.85
=$3.25
The model is a linear function that shows $3.25 money that Ilya has all together.
To know more about linear function, visit:
https://brainly.com/question/20286983
#SPJ1
Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, with a replacement.
Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.
The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is
[tex]\frac{4}{52}=\frac{1}{13}[/tex]Since the cards are replaced, it is the same probability of getting an Ace on each draw.
Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is
[tex]\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}=\frac{1}{13^4}=\frac{1}{28561}=0.00003501277\ldots[/tex]Can someone help? :)
The slope of the given line is 2
What is slope of a line?
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]
The given line passes through ( 0, 5) and (-2, 1) .
Slope of the line =
[tex]\frac{1-5}{-2-0}\\\\\frac{-4}{-2}\\\\2[/tex]
To learn more about slope, refer to the link:
https://brainly.com/question/3493733
#SPJ1
Zachary is paying his dad back for the money he borrowed to pay for a car repair. The amount that he owes his dad is shown in the graph
Answer:
so you need to divide this and turn it into a coefficient for the answer
Step-by-step explanation:
What is the value of x?
30 points if answered
Answer: 20
Step-by-step explanation: They are both equal to each other, so 3x+50=6x-10. Then just solve for x by canceling out both sides.
Suppose cone a is similar to cone b and the scale factor between the solids is 3:2, respectively. If the height of cone a is 15 inches, determine the height of cone b.
The height of cone is 10 inches.
What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.
What is the formula for finding the height of a cone?
The cone height formula calculates the height of the cone. The height of the cone using cone height formulas are, h = 3V/πr 2 and h = √l2 - r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.We know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let x----> the height of cone B
using proportionality
3/2 = 15/x
x = 2 * 15/3
x = 10 inches
To know more about cone check the below link:
https://brainly.com/question/1082469
#SPJ4
Which ordered pair is a solution for this system of linear inequalities?
2x + 3y < 12
3x - 2y ≥ 18
A. (5,0)
B. (3,-1)
C. (-1,3)
D. (4,-9)
The ordered pair that is a solution for the inequality 2x + 3y < 12 and
3x - 2y ≥ 18 is
D. (4,-9)How to find the solutionThe solution is sought by substituting to each of the pair to the equation and comparing the answers
for D. (4,-9)
2 * 4 + 3 * -9 < 12
-19 < 12 correct
3x - 2y ≥ 18
3 * 4 - 2 * -9 ≥ 18
30 ≥ 18 correct
This proves that option D is the correct option
trying for A. (5,0)
2 * 5 + 3 * 5 < 12
25 < 12 incorrect
3x - 2y ≥ 18
3 * 5 - 2 * 0 ≥ 18
15 ≥ 18 incorrect
trying for B. (3,-1)
2 * 3 + 3 * -1 < 12
3 < 12 correct
3x - 2y ≥ 18
3 * 3 - 2 * -1 ≥ 18
11 ≥ 18 incorrect
When any part is incorrect the pair is not a solution
trying for C. (-1,3)
2 * -1 + 3 * 3 < 12
7 < 12 correct
3x - 2y ≥ 18
3 * -1 - 2 * 3 ≥ 18
-9 ≥ 18 incorrect
Learn more about inequality:
https://brainly.com/question/29244324
#SPJ1
Lu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.
$556.35
$648.35
$660.32
$721.31
Answer:
The total deposit is $721.31.
Step-by-step explanation:
6) How long will it take for an investment to double in value if it earns 4.75% compoundedcontinuously?A) 14.593 yearsB) 15.711 years C) 23.129 years D) 7.296 years
A quantity that is compounded continuously follows the next equation:
[tex]A=Pe^{rt}[/tex]Where:
[tex]\begin{gathered} A=\text{ amount in time ''t''} \\ P=\text{ initial amount} \\ r=\text{ rate of interest in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Now, the interest rate in decimal notation is determined by dividing the percentage by 100:
[tex]r=\frac{4.75}{100}=0.0475[/tex]Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:
[tex]A=2P[/tex]Substituting in the formula we get:
[tex]2P=Pe^{rt}[/tex]Now, we can cancel out the "P":
[tex]2=e^{rt}[/tex]Now, we solve for "t". First, we take the natural logarithm to both sides:
[tex]ln2=lne^{rt}[/tex]Now, we use the following property of logarithms:
[tex]lnx{}^y=ylnx[/tex]Applying the property we get:
[tex]ln2=rtlne[/tex]We have that:
[tex]lne=1[/tex]Therefore:
[tex]ln2=rt[/tex]Now, we divide both sides by "r":
[tex]\frac{ln2}{r}=t[/tex]Now, we substitute the value of "r":
[tex]\frac{ln2}{0.0475}=t[/tex]Solving the operations:
[tex]14.593=t[/tex]Therefore, the right option is A.
Bill flip a coin and roll a dice independent or dependent
Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.
Independent Events which we learn about here.
Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.
AnswerIndependent
Which figures can have two sides of the same length, but are not parallelograms?quadrilateralrectanglesquareisosceles trapezoid
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.
We have special types of quadrilaterals which are,
1) Rectangle
2) Square
3) Rhombus
4) Parallelogram
5) Trapezium
6) Kite
Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.
An isosceles trapezoid has left and right sides of equal length that join to the base at equal angles.
Below is the diagram of an Isosceles trapezoid
55 POINTS!!!
1. Identify the set of ordered pairs that represents y as a function of x.
Responses
{(−1, 0), (−1, 1), (−2, 2), (0, 3)}
{(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
{(0, 0), (1, 1), (2, 2), (3, 3)}
{(0, 0), (1, 0), (2, 4), (2, 3)}
2. Which table represents y as a function of x?
Responses
x y
0 1
0 2
1 3
2 3
x y
1 0
2 0
3 1
3 2
x y
−1 −1
0 −1
2 0
3 2
x y
−1 −1
−1 0
0 2
2 3
Answer:
1) B, 2) C
===========
As per definition, functions have only one y-value per x-value.
Let's test it with given sets and tables.
Part 1A) {(−1, 0), (−1, 1), (−2, 2), (0, 3)} - Not a function x = - 1 repeatedB) {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} - Not a function x = - 3 repeatedC) {(0, 0), (1, 1), (2, 2), (3, 3)} - FunctionD) {(0, 0), (1, 0), (2, 4), (2, 3)} - Not a function x = 2 repeatedPart 2A)
x y
0 1
0 2
1 3
2 3
Not a function, x = 0 is repeatedB)
x y
1 0
2 0
3 1
3 2
Not a function, x = 3 is repeatedC)
x y
−1 −1
0 −1
2 0
3 2
FunctionD)
x y
−1 −1
−1 0
0 2
2 3
Not a function, x = - 1 repeated1) The set of ordered pairs that represents y as a function of x is;
B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
2) The table that represents y as a function of x is; Table 3
How to Interpret Ordered Pairs?An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.
1) The first function given as {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.
The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.
The third function {(0, 0), (1, 1), (2, 2), (3, 3)}; This is a function because each input has unique output values.
The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ; This cannot be regraded as a function because the input x = 2 is repeated with different output values.
2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.
Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.
Table 3 is a Function because each input has unique output values.
Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.
Read more about Ordered pairs at; https://brainly.com/question/1528681
#SPJ1
To rent a moving truck for the day, it costs $75 plus $1.50 for each mile, m, driven. Which expression represents the cost, in dollars, to rent the moving truck?
The expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to represent the total cost will be:
The truck costs $75.And an extra $1.50 for every mile.The expression that gives the total cost.
Let, the number of miles are 'n' and the total cost be 'C'.
Now,
1.50n + 75 = C
Therefore, the expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
Know more about expressions here:
https://brainly.com/question/28934492
#SPJ1
Can you please help me out
ANSWER:
A. 2.2%
STEP-BY-STEP EXPLANATION:
We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:
[tex]\begin{gathered} p=\frac{A_c}{A_r} \\ A_c=\pi\cdot r^2 \\ A_r=l\cdot w \end{gathered}[/tex]In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.
Therefore we replace and we have:
[tex]\begin{gathered} A_c=3.14\cdot6^2=113.04 \\ A_r=84\cdot60=5040 \\ p=\frac{113.04}{5040}=0.022=2.2\text{\%} \end{gathered}[/tex]To save money for her son's college tuition, Mary invests $98 every month in an annuity that pays 6.1% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 21 years.
Given
Monthly deposit = $98
Rate = 6.1%
Number of years = 21
Find
Total value of the annuity in 21 years.
Explanation
Total value of annuity is given by
[tex]FV=A[\frac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}][/tex]where FV is a future value
so ,
[tex]\begin{gathered} FV=98[\frac{(1+\frac{0.061}{12})^{12\times21}-1}{\frac{0.061}{12}}] \\ \\ \end{gathered}[/tex]now solve this to obtain the future value .
[tex]\begin{gathered} FV=98\times509.227229162 \\ FV=49904.26 \end{gathered}[/tex]Final Answer
Therefore , the future value is $49904.27
The first puzzle includes a treasure map. The treasure map is an xy coordinate grid with the origin markingthe center of the room as shown below. Two lines intersect to show the location of the next clue. The linesmust be added to the treasure map.The first line is represented by the equation y = 3x - 16.The graph of the second line passes through the points (1,7) and (4,1).North6s411WestEast112South4. What is the equation of the second line? Show how you found the equation.(Replace this text with your equation)(Replace this text with your work).
Given
(1,7) and (4,1)
[tex]\begin{gathered} M=\frac{y_2-y_1}{x_2-x_1} \\ M=\text{ }\frac{1-7}{4-1} \\ M=-\frac{6}{3} \\ M=-2 \\ \\ y-y_1=m\mleft(x-x_1\mright) \\ y-7=-2(x-1) \\ y-7=-2x+2 \\ y=-2x+2+7 \\ y=-2x+9 \end{gathered}[/tex]y=-2x+9
[If f(x) = x and g(x) = 1/2 f(x) , how does the graph of g compare to the graph of f?]
We can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.So, the difference in the graph of the given functions:
f(x) = x g(x) = 1/2 f(x)Plot on the graph as follows:
(Refer to the graph attached below)
Therefore, we can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.
Know more about graphs here:
https://brainly.com/question/28953186
#SPJ1
What is the center and radius of -10x = -121 - y2 - x2 -22y
We need to find the center and the radius of
[tex]-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y[/tex]The general circle equation is the following
[tex](x-h)^2+(y-k)^2=r^2[/tex]where
(h,k) is the center and
r is the radius
1. rearrange the equation
[tex](x^2-10x)+(y^2+22y+121)=0[/tex]2. Add 25 on both sides
[tex](x^2-10x+25)+(y^2+22y+121)=25[/tex]3. Factor
[tex](x-5)^2+(y+11)^2=5^2[/tex]Now we have an equation that is very similar to the circle equation, so let's compare them
Center -> (h,k) = (5,-11)
radius -> r = 5
Select the correct answer.
Solve the system of equations.
y=x-5
y=x-5x+3
O A. (4,-3) and (2,-1)
О в.
(4,-1) and (2,-3)
O C.
(-4,-9) and (-2,-7)
O D.
(4,-9) and (2,-7)
The value of x is -2 and the value of y is -7. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equations are y = x - 5 and y = 5x + 3. The value of x and y will be calculated by solving the equations,
y=x-5
y=5x+3
x -5 = 5x + 3
-4x = 8
x = -2
The value of y will be calculated as,
y = x - 5
y = -2 - 5
y = -7
To know more about an expression follow
https://brainly.com/question/28196676
#SPJ1
mDE= ?Use O, A to find mDE , given that BF is a diameter of O. A.
STEP 1: Identify and Set Up
We are required to get the angle subtended by the arc DE.
We first acknowledge that it is part of the angles in a quadrant as this will help us find it.
STEP 2: Execute
First find angle DAE
[tex]\begin{gathered} Angle subtended by DE = 45 degreesWrite the system of linear equations represented by the augmented matrix. (Use variables x, y, and z, if applicable.)1 - 1 21-30 1 -1 50 0 1-5Use back-substitution to solve the system.(x, y, z) =
The augmented matrix represents the following system of linear equations:
[tex]\begin{gathered} x-y+2z=-3 \\ y-z=5 \\ z=-5 \end{gathered}[/tex]Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:
[tex]\begin{gathered} y-z=5 \\ y-(-5)=5 \\ y+5=5 \\ y=5-5 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} x-y+2z=-3 \\ x-0+2(-5)=-3 \\ x-10=-3 \\ x=-3+10 \\ x=7 \end{gathered}[/tex]The solution of the system is (x, y, z)=(7, 0, -5)
Solve each equation by graphing. Verify youranswer algebraically.
12. 5-8x=16- 8x
21. 12x +132 = 12x- 100
Answer:
12. 0 = 11
No Solution
21. 0 = -132
No Solution
Step-by-step explanation:
12.
5 - 8x = 16 - 8x
-8x + 5 = -8x + 16
- 5 = - 5
-8x = -8x + 11
-8x = -8x
0 = 11
No Solution
21.
12x + 32 = 12x - 100
- 32 - 32
12x = 12x - 132
-12x -12x
0 = -132
No Solution
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
16. Describe, step-by-step how to find the slope of a line through two points.
Answer:
1. find the 2 points and determine their coordinates.
2. determine the difference in the rise or y-coordinates.
3. determine the difference in the run or x-coordinates.
4. place the rise over the run and divide to find slope
A ship travels from Akron (A) on a bearing of 030° to Bellvilie (B),90km away. It then travels to Comptin (C) which is 310 km due east of Akron (A).Draw a diagram showing the movement of the ship indicate:a.)Northb.)the distances travelledc.)the know angles
Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)
To Determine: The distance travelled and the angles
Solution
The diagram of the journey can be represented as shown below
Let us solve for BC using cosine rule
[tex]\begin{gathered} BC^2=AB^2+AC^2-2(AB)(AC)cosA \\ BC^2=90^2+310^2-2(90)(310)(cos60^0) \\ BC^2=8100+96100-27900 \\ BC^2=76300 \\ BC=\sqrt{76300} \\ BC=276.22km \\ BC\approx276km \end{gathered}[/tex]The total distance travelled is
[tex]\begin{gathered} Total-distance=AB+BC+AC \\ =90km+276km+310km \\ =676km \end{gathered}[/tex]Using sine rule, we can determine the measure of angle C
[tex]\begin{gathered} \frac{AB}{sinC}=\frac{BC}{sinA}=\frac{AC}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0}=\frac{310}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0} \\ sinC=\frac{90(sin60^0)}{276} \\ sinC=\frac{155.88}{276} \\ sinC=0.5648 \\ C=sin^{-1}(0.5648) \\ C=34.39^0 \end{gathered}[/tex]Also know that the sum of angles in a triangle is 180 degree. Therefore
[tex]\begin{gathered} A+B+C=180^0 \\ 60^0+B+34.39^0=180^0 \\ B+94.39^0=180^0 \\ B=180^0-94.39^0 \\ B=85.61^0 \\ B\approx85.6^0 \end{gathered}[/tex]The bearing of Compton from Bellville(B) is
[tex]Bearing(C-from-B)=90^0+34.39^0=124.39^0\approx124.4^0[/tex]The bearring of Akron(A) from Compton(C) is
[tex]Bearing(A-from-C)=270^0+34.39^0=304.39^0\approx304.4^0[/tex]In summary
The total distance travelled is 676km
The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees
One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 5 or a Club. Note that the ace is considered a low card.The probability that the card selected is less than 5 or a club is.(Type an integer or a simplified fraction.)
The total number of cards in a deck of cards is: 52
The total number of club cards is: 13
The total number of cards that less than 5 is: 8.
The probability of selecting a club card is,
[tex]\begin{gathered} P(Club)=\frac{Total\text{ number of club cards}}{\text{Total number of cards}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of selecting a card that is less than five is,
[tex]\begin{gathered} P(card<5)=\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The total number of club card that is less than 5 is 3.
The probability of selecting a club card and a card that is less than 5 is,
[tex]P\text{ (club and less than 5)}=\frac{3}{52}[/tex]The probability of selecting a card that is a club or less than 5 is,
[tex]\begin{gathered} P\text{ (Club or less than5)}=P(Club)+P\text{(card less than 5)-P(Club and less than 5)} \\ =\frac{1}{4}+\frac{2}{13}-\frac{3}{52} \\ =\frac{21}{52}-\frac{3}{52} \\ =\frac{9}{26} \end{gathered}[/tex]Thus, the probability of selecting a club card or card that is less than 5 is 9/26.
Can anyone help with this? Thanks
The surface area of the prism is 1440 mm²
Given,
Triangular prism
Height of the prism = 32 mm
Base of the prism = 24 mm
Length of the prism = 7 mm
We have to find the surface area of the prism;
Surface area, SA = bh + (b₁ + b₂ + b₃) l
Here,
Base, b = 24 mm
Height, h = 32 mm
Length, l = 7 mm
b₁ = 24 mm
b₂ = 32 mm
b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm
Then,
Surface Area = bh + (b₁ + b₂ + b₃) l
SA = 24 x 32 + (24 + 32 + 40) 7
SA = 768 + 96 x 7
SA = 768 + 672
SA = 1440 mm²
That is,
The surface area of the prism is 1440 mm²
Learn more about surface area of prism here;
https://brainly.com/question/16765719
#SPJ1
A full-grown monarch caterpillar weights 0.75 grams, has a length of 5 centimeters, and is about 2.5 centimeters around. How can the surface area of the caterpillar be estimated?
A ___ can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of ___ square centimeters.
The choices for the first blank are:
*rectangular prism
*triangular prism
*sphere
*cylinder
The choices for the second blank are:
*13.5
*6.75
*49.1
*117.8
A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.3 cm²
A full-grown monarch caterpillar is of cylinder shape . so , the option 4th is correct for first blank.
Surface area of cylinder is 2πrh + 2πr²
where r is radius of circle and h is height of cylinder
here , length of caterpillar is 5cm and radius is 2.5cm
Surface area = 2πrh + 2πr²
= 2π(5)(2.5) + 2π(2.5)²
= 2π(12.5) + 2π(6.25)
putting π = 3.14
=78.5+39.25
=117.8 cm²
Rewriting the sentence
A cylinder can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of 117.8 square centimeters.
To know more about Surface Area of cylinder here
https://brainly.com/question/27847638
#SPJ1
Answer: A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.8 square centimeters
(if your on PLATO) if not then 117.8