SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the formula for the area of the triangle
[tex]Area=\frac{1}{2}\times base\times height[/tex]STEP 2: Represent the statements to get an equation
[tex]\begin{gathered} width=base \\ From\text{ the statement,} \\ six\text{ times of the width}=6w \\ four\text{ less than six times the width }=6w-4 \\ \therefore height=6w-4 \end{gathered}[/tex]STEP 3: Substitute into the formula in step 1
[tex]\begin{gathered} height=6w-4,width=base=w,Area=40in^2 \\ Area=\frac{1}{2}\times w\times(6w-4) \\ Area=\frac{w(6w-4)}{2}=\frac{6w^2-4w}{2}=40 \end{gathered}[/tex]STEP 4: Cross multiply
[tex]\begin{gathered} 6w^2-4w=40\times2 \\ 6w^2-4w=80 \\ Subtract\text{ 80 from both sides} \\ 6w^2-4w-80=80-80 \\ 6w^2-4w-80=0 \\ Divide\text{ through by 2, we have:} \\ 3w^2-2w-40=0 \\ By\text{ factorization;} \\ 3w^2-12w+10w-40=0 \\ 3w(w-4)+10(w-4)=0 \\ (w-4)(3w+10)=0 \end{gathered}[/tex]STEP 5: Find the values of w
[tex]\begin{gathered} w-4=0,w=0+4,w=4 \\ 3w+10=0,3w=0-10,3w=-10,w=\frac{-10}{3} \\ \\ Since\text{ the width cannot be negative, width=4 inches} \end{gathered}[/tex]STEP 6: Find the height
[tex]\begin{gathered} Recall\text{ from step 2:} \\ h=6w-4 \\ Substitute\text{ 4 for w} \\ h=6(4)-4=24-4=20in \end{gathered}[/tex]Hence,
width = 4 inches
height = 20 inches
Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.
EXPLANATION:
Given;
We are given two ice cream cups in the shapes of a cone and a cylinder.
The dimensions are;
[tex]\begin{gathered} Cone: \\ Radius=4in \\ \\ Height=6in \\ \\ Cylinder: \\ Radius=3in \\ \\ Height=2in \end{gathered}[/tex]Required;
We are required to determine which of the two cups will hold the most ice cream.
Step-by-step solution;
Take note that the radius of the cylinder was derived as follows;
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \\ radius=\frac{6}{2}=3 \end{gathered}[/tex]The volume of the cone is given by the formula;
[tex]\begin{gathered} Volume=\frac{1}{3}\pi r^2h \\ \\ Therefore: \\ Volume=\frac{1}{3}\times3.14\times4^2\times6 \\ \\ Volume=\frac{3.14\times16\times6}{3} \\ \\ Volume=100.48 \end{gathered}[/tex]Rounded to the nearest tenth, the volume that the cone can hold will be;
[tex]Vol_{cone}=100.5in^3[/tex]Also, the volume of the cylinder is given by the formula;
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=3.14\times3^2\times2 \\ \\ Volume=3.14\times9\times2 \\ \\ Volume=56.52 \end{gathered}[/tex]Rounded to the nearest tenth, the volume will be;
[tex]Vol_{cylinder}=56.5in^3[/tex]ANSWER:
Therefore, the results show that the CONE will hold the most ice cream.
Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10
Given:
[tex]\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}[/tex]Now, let's find (-1/2)A.
Each term of the matrix A is multiplied by -1/2.
[tex]\begin{gathered} \frac{-1}{2}A=\frac{-1}{2}\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-12}{2}} & {\frac{-4}{2}} & {} \\ {\frac{4}{2}} & {\frac{10}{2}} & {} \\ {\frac{6}{2}} & {-\frac{12}{2}} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}[/tex]Now let's find (-1/2)A+B.
To find (-1/2)A+B, the corresponding terms of the matrices are added together.
[tex]\begin{gathered} \frac{-1}{2}A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}[/tex]Therefore,
[tex]undefined[/tex]Line segments, AB,BC,CD,DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 BC: y = -3x + 11
The equations of the line segments are,
[tex]\begin{gathered} AB\colon y=\frac{1}{3}x+1 \\ BC\colon y=-3x+11 \end{gathered}[/tex]Calculate the equations of CD and AD.
The equation of line Cd is,
[tex]\begin{gathered} (y-(-3))=\frac{-1+3}{4+2}(x+2) \\ y+3=\frac{1}{3}(x+2) \\ 3y=x-7 \end{gathered}[/tex]The equation of the line AD is,
[tex]\begin{gathered} y-0=\frac{-3-0}{-2+3}(x+3) \\ y=-3x-9 \end{gathered}[/tex]1)If two lines are parallel slope will be equal and perpendicular product of slope will be -1.
From the equation, the slope of AB is 1/3
From the equation, the slope of Cd is 1/3.
So, they are parallel.
2)The slope of AB is 1/3.
The slope of BC is -3.
The product of two slopes is -1. Therefore, AB is perpendicular to BC.
3) The slope of AB is 1/3 and slope of AD is -3. Since, the product is -1, they are perpendicular.
Another pair of line segments that are perpendicular to each other is AB and AD.
Interpreting the whale population on the graph. I think (A).
The y-intercept is the value in the vertical axis (y-value) when the value on the horizontal axis is zero (x = 0).
Looking at the horizontal axis, the value of x indicates the generation since 2007.
That means x = 0 indicates the generation in year 2007.
The value of y for x = 0 is 240, so the population in year 2007 is 240.
Correct option: A
Austin walks 3.5km every day. How far does he walk in 7 days?Write your answer in meters.
Answer:
24,500 meters
Step-by-step explanation:
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?
Given that initial time for jogging is,
[tex]a_{_1}=14[/tex]After each week the time is increased by
[tex]d=7[/tex]This gives an arithmetic sequence.
To find n such that,
[tex]a_n=70[/tex]Therefore,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]So,
[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]Therefore, 9 weeks before you are up to jogging 70 minutes.
A play court on the school playground is shaped like a square joined by a semicircle. The perimeteraround the entire play court is 182.8 ft., and 62.8 ft. of the total perimeter comes from the semicircle.aWhat is the radius of the semicircle? Use 3.14 for atb.The school wants to cover the play court with sports court flooring. Using 3.14 for, how manysquare feet of flooring does the school need to purchase to cover the play court?
The total perimeter of the court is 182.8 ft, of this, 62.8ft represents the perimeter of the semicircle.
a)
The perimeter of the semicircle is calculated as the circumference of half the circle:
[tex]P=r(\pi+2)[/tex]Now write it for r
[tex]\begin{gathered} \frac{P}{r}=\pi \\ r=\frac{P}{\pi} \end{gathered}[/tex]Knowing that P=62.8 and for pi we have to use 3.14
[tex]\begin{gathered} r=\frac{62.8}{3.14} \\ r=20ft \end{gathered}[/tex]The radius of the semicircle is r=20 ft
b.
To solve this exercise you have to calculate the area of the whole figure.
The figure can be decomposed in a rectangle and a semicircle, calculate the area of both figures and add them to have the total area of the ground.
Semicircle
The area of the semicircle (SC) can be calculated as
[tex]A_{SC}=\frac{\pi r^2}{2}[/tex]We already know that our semicircla has a radius of 10ft so its area is:
[tex]A_{SC}=\frac{3.14\cdot20^2}{2}=628ft^2[/tex]Rectangle
To calculate the area of the rectangle (R) you have to calculate its lenght first.
We know that the total perimeter of the court is 182.8ft, from this 62.8ft corresponds to the semicircle, and the rest corresponds to the rectangle, so that:
[tex]\begin{gathered} P_T=P_R+P_{SC} \\ P_R=P_T-P_{SC} \\ P_R=182.8-62.8=120ft \end{gathered}[/tex]The perimeter of the rectangle can be calculated as
[tex]P_R=2w+2l[/tex]The width of the rectangle has the same length as the diameter of the circle.
So it is
[tex]w=2r=2\cdot20=40ft[/tex]Now we can calculate the length of the rectangle
[tex]\begin{gathered} P_R=2w+2l \\ P_R-2w=2l \\ l=\frac{P_R-2w}{2} \end{gathered}[/tex]For P=120ft and w=40ft
[tex]\begin{gathered} l=\frac{120-2\cdot40}{2} \\ l=20ft \end{gathered}[/tex]Now calculate the area of the rectangle
[tex]\begin{gathered} A_R=w\cdot l \\ A_R=40\cdot20 \\ A_R=800ft^2 \end{gathered}[/tex]Finally add the areas to determine the total area of the court
[tex]\begin{gathered} A_T=A_{SC}+A_R=628ft^2+800ft^2 \\ A_T=1428ft^2 \end{gathered}[/tex]A dilation with a scale factor of 4 is applied to the 3 line segment show on the resulting image are P'Q', A'B', And M'N'. Drag and drop the measures to correctly match the lengths of The images
Given:
Scale factor = 4 (Dilation)
PQ = 2 cm
AB = 1.5 cm
MN = 3 cm
Find-:
[tex]P^{\prime}Q^{\prime},A^{\prime}B^{\prime}\text{ and }M^{\prime}N^{\prime}[/tex]Explanation-:
Scale factor = 4
So,
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ A^{\prime}B^{\prime}=4AB \\ \\ M^{\prime}N^{\prime}=4MN \end{gathered}[/tex]So the value is:
[tex]\begin{gathered} P^{\prime}Q^{\prime}=4PQ \\ \\ P^{\prime}Q^{\prime}=4\times2 \\ \\ P^{\prime}Q^{\prime}=8\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} A^{\prime}B^{\prime}=4AB \\ \\ A^{\prime}B^{\prime}=4\times1.5 \\ \\ A^{\prime}B^{\prime}=6\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} M^{\prime}N^{\prime}=4MN \\ \\ M^{\prime}N^{\prime}=4\times3 \\ \\ M^{\prime}N^{\prime}=12\text{ cm} \end{gathered}[/tex]The endpoints CD are given. Find the coordinates of the midpoint m. 24. C (-4, 7) and D(0,-3)
To find the coordinates of the midpoint
We will use the formula;
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2})[/tex]x₁ = -4 y₁=7 x₂ = 0 y₂=-3
substituting into the formula
Xm = x₁+x₂ /2
=-4+0 /2
=-2
Ym= y₁+ y₂ /2
=7-3 /2
=4/2
=2
The coordinates of the midpoint m are (-2, 2)
What is the value of the expression below when y=9 and z=6?
The numerical value of the expression 9y - 10z when y = 9 and z = 6 is 21.
This question is incomplete, the complete question is;
What is the value of the expression below when y = 9 and z = 6?
9y - 10z
What is the numerical value of the given expression?An algebraic expression is simply an expression that is made up of constants and variables, including algebraic operations such as subtraction, addition, division, multiplication, et cetera.
Given the data in the question;
9y - 10zy = 9z = 6Numerical value of the expression = ?To determine the numerical value of the expression, replace plug y = 9 and z = 6 into the expression and simplify.
9y - 10z
9( 9 ) - 10z
9( 9 ) - 10( 6 )
Multiply 9 and 9
81 - 10( 6 )
Multiply 10 and 6
81 - 60
Subtract 60 from 81
21
Therefore, the numerical value of the expression is 21.
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help me please i'm stuck Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Myra owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests. The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests. How many guests does each size of tier serve? A small tier will serve ? guests and a large tier will serve ? guests.
the number of guests a small tier can serve is 22
the number of guest a large tier serves is 40
Explanation
Step 1
Set the equations
a) let
x represents the number of guest one small tier serves
y represents the number of guests one large tier serves
b) translate into math term
i)The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests,so
[tex]3x+4y=226\Rightarrow equation(1)[/tex]ii) The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests,so
[tex]x+y=62\Rightarrow equation(2)[/tex]Step 2
solve the equations:
[tex]\begin{gathered} 3x+4y=226\Rightarrow equation(1) \\ x+y=62\operatorname{\Rightarrow}equat\imaginaryI on(2) \end{gathered}[/tex]a) isolate the x value in equation (2) and replace in equatino (1) to solve for y
[tex]\begin{gathered} x+y=62\Rightarrow equation(2) \\ subtract\text{ y in both sides} \\ x=62-y \end{gathered}[/tex]replace into equation(1) and solve for y
[tex]\begin{gathered} 3x+4y=226\Rightarrow equation(1) \\ 3(62-y)+4y=226 \\ 186-3y+4y=226 \\ add\text{ like terms} \\ 186+y=226 \\ subtrac\text{ 186 in both sides} \\ 186+y-186=226-186 \\ y=40 \end{gathered}[/tex]so, the number of guest a large tier serves is 40
b)now, replace the y value into equation (2) and solve for x
[tex]\begin{gathered} x+y=62\Rightarrow equation(2) \\ x+40=62 \\ subtract\text{ 40 in both sides} \\ x+40-40=62-40 \\ x=22 \end{gathered}[/tex]so, the number of guests a small tier can serve is 22the number of guests a small tier can serve is 22
I hope this helps you
Simplify the expression (6^2)^46^?
The given expression is
[tex](6^2)^4[/tex]We would apply the rule of indices or exponent which is expressed as
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]If f(x) = x + 1, find f(x + 7). Hint: Replace x in the formula by x+7.f(x + 7) =
The original function is:
[tex]f(x)\text{ = x+1}[/tex]We want to find the value of the function when the input is "x + 7". So in the place of the original "x" we will add "x+7".
[tex]\begin{gathered} f(x+7)\text{ = (x+7)+1} \\ f(x+7)\text{ = x+7+1} \\ f(x+7)\text{ = x+8} \end{gathered}[/tex]The value of the expression is "x + 8"
a store donated 2 and 1/4 cases of cranes to a daycare center each case holds 24 boxes of crayons each box holds 8 crayons how many crayons did the center receive
Answer:
The center recieved 432 crayons
Explanation:
Given the following information:
There are 2 and 1/4 cases
Each case holds 24 boxes of crayons
Each box holds 8 crayons.
The number of crayons the center receive is:
8 * 24 * (2 + 1/4)
= 8 * 24 * (8/4 + 1/4)
= 192 * (9/4)
= 1728/4
= 432
Simplify the expression leave expression in exact form with coefficient a and b so we have a✔️b.
coefficient of a = 2x
Explanation:[tex]\text{The expression: 2}\sqrt[]{x^2y}[/tex]Simplifying:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = x} \\ 2\sqrt[]{x^2\times y}\text{ = 2x}\sqrt[]{y} \end{gathered}[/tex]Since we are told the coefficient of a can be the product of a number and variable:
[tex]\begin{gathered} 2x\sqrt[]{y}\text{ is in the form a}\sqrt[]{b} \\ a\text{ = 2x},\text{ b = y} \\ 2\text{ = number, x = variable} \\ 2x\text{ = product of number and variable} \\ \text{coefficient of }a\text{ = 2x} \end{gathered}[/tex]Solve for x:
A
+79
X
Answer: -11
Step-by-step explanation: 66+46=112
180-112=68
79+?=68
79+-11=68
The schedule for summer classes is available and Calculus and Introduction to Psychology are scheduled at the same time, so it is impossible for a student to schedule for both courses. The probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. What is the probability a student registers for Calculus or psychology?
Explanation
The given is that the probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. Since it impossible for a student to schedule for both courses, we will have
[tex]\begin{gathered} Pr(Psychology\text{ or calculus\rparen=Pr\lparen P\rparen+Pr\lparen C\rparen-Pr\lparen P}\cap C) \\ =0.05+0.62-0 \\ =0.67 \end{gathered}[/tex]Answer: 0.67
What does "equidistant” mean in relation to parallel lines?O The two lines lie in the same plane.The two lines have the same distance between them.The two lines go infinitely.The two lines have an infinite number of points.
we have that
parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
therefore
the answer is
The two lines have the same distance between them.given the residual plot below, which of the following statements is correct?
Let me explain this question with the following picture:
We can recognize a linear structure when all the points have a pattern that seems like a straight line as you can see above for example.
In the graph of your question, we can see that the points don't have a definited pattern and that's clearly not seemed like a straight line.
Therefore, the answer is option B:
There is not a pattern, so the data is not linear.
f(x)=1-x when f(x)=2
By solving the equation, we know that f(x) = 1 - x is - 1 when f(x) = 2.
What are equations?In mathematical equations, the equals sign is used to show that two expressions are equal.An equation is a mathematical statement that uses the word "equal to" in between two expressions of the same value.As an illustration, 3x + 5 equals 15.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary types of linear equations are slope-intercept, standard, and point-slope equations.So, f(x) = 1 - x when f(x)= 2:
Solve for f(x) as follows:
f(x) = 1 - xf(x) = 1 - 2f(x) = - 1Therefore, by solving the equation, we know that f(x) = 1 - x is - 1 when f(x) = 2.
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The perimeter of a rectangular room is 80 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Write the equation that could model this situation.
Answer:
2x+2y=80
Step-by-step explanation:
a rectangles perimeter has the formula of width+width+length+length
we can combine like terms so we get 2x+2y and according to the problem this rectangle has the perimeter of 80
if a driver drive at aconstant rate of 38 miles per hour how long would it take the driver to drive 209 mile
In order to calculate how long would it take to drive 209 miles, we just need to divide this total amount of miles by the speed of the driver.
So we have:
[tex]\text{time}=\frac{209}{38}=5.5[/tex]So it would take 5.5 hours (5 hours and 30 minutes).
Find functions f and g such that (f o g)(x) = [tex] \sqrt{2x} + 19[/tex]
We have the expression:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]So:
[tex]g(x)=2x[/tex][tex]f(x)=\sqrt[]{x}+19[/tex]***
Since we want to get the function g composed in the function f, and the result of this is:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]When we replace g in f, we have to get as answer the previous expression. And by looking at it the only place where we will be able to replace values is where the variable x is located. The function f will have the "skeleton" or shape of the overall function and g will be injected in it.
From this, we can have that f might be x + 19 and g might be sqrt(2x), but the only options that are given such that when we replace g in x of f, are f = sqrt(x) + 19 and g = 2x.
Let be two sets E and F such that:E = {x € R: -4 ≤ x ≤ 4}F = {x € R: | x | = x}What is the Cartesian product of the complement of E × F =?
Given:
[tex]\begin{gathered} E=\mleft\lbrace x\in\mathfrak{\Re }\colon-4\leq x\leq4\mright\rbrace \\ F=\mleft\lbrace x\in\mathfrak{\Re }\colon\lvert x\rvert=x\mright\rbrace \end{gathered}[/tex]If |x|=x that mean here x is grater then zero.
E is move -4 to 4 and F is grater then zero that mean multiplication of the function is obtaine all real value:
[tex]E\times F=\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace[/tex]Find the solution of the system by graphing.-x - 4y=4y=1/4x-3Part B: The solution to the system,as an ordered pair,is
Solution
-x -4y = 4
y= 1/4 x -3
Replacing the second equation in the first one we got:
-x -4(1/4x -3) =4
-x -x +12= 4
-2x = 4-12
-2x = -8
x= 4
And the value of y would be:
y= 1/4* 4 -3= 1 -3= - 2
And the solution would be ( 4,-2)
a) Consider an arithmetic series 4+2+0+(-2)+.....i) What is the first term? And find the common difference d.ii) Find the sum of the first 10 terms S(10).b) Solve [tex] {2}^{x - 3} = 7[/tex]
Answer:
Explanation:
Here, we want to work with an arithmetic series
a) First term
The first term (a) of the arithmetic is the first number on the left
From the question, we can see that this is 4
Hence, 4 is the first term
To find the common difference, we have this as the difference between twwo subsequent terms, going from left to right
We have this as:
[tex]2-4\text{ = 0-2 = -2-0 = -2}[/tex]The common difference d is -2
ii) We want to calculate the sum of the first 10 terms
The formula for this is:
[tex]S(n)\text{ = }\frac{n}{2}(2a\text{ + (n-1)d)}[/tex]Where S(n) is the sum of n terms
n is the number of terms which is 10
a is the first term of the series which is 4
d is the common difference which is -2
Substituting these values, we have it that:
[tex]\begin{gathered} S(10)\text{ = }\frac{10}{2}(2(4)\text{ + (10-1)-2)} \\ \\ S(10)\text{ = 5(8+ (9)(-2))} \\ S(10)\text{ = 5(8-18)} \\ S(10)\text{ = 5(-10)} \\ S(10)\text{ = -50} \end{gathered}[/tex]The circumference of a circle is 18pi meters. What is the radius?Give the exact answer in simplest form. ____ meters. (pi, fraction)
Given:
The circumference of a circle, C=18π m.
The expression for the circumference of a circle is given by,
[tex]C=2\pi r[/tex]Put the value of C in the above equation to find the radius.
[tex]\begin{gathered} 18\pi=2\pi r \\ r=\frac{18\pi}{2\pi} \\ r=9\text{ m} \end{gathered}[/tex]Therefore, the radius of the circle is 9 m.
We have a deck of 10 cards numbered from 1-10. Some are grey and some are white. The cards numbered are 1,2,3,5,6,8 and 9 are grey. The cards numbered 4,7, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.
Given:
The cards numbered are, 1,2,3,5,6,8, and 9 are grey.
The cards numbered 4,7 and 10 are white.
The total number of cards =10.
Let X be the event that the drawn card is grey.
P(X) be the probability of X.
Required:
We need to find P(X) and P(not X).
Explanation:
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 1,2,3,5,6,8, and 9 for event X.
The favourable outcomes = 1,2,3,5,6,8, and 9
[tex]n(X)=7[/tex]Since X be the event that the drawn card is grey.
The probability of X is
[tex]P(X)=\frac{n(X)}{n(S)}=\frac{7}{10}[/tex]Let not X be the event that the drawn card is not grey,
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 4,7, and 10 for event not X.
The favourable outcomes = 4,7, and 10
[tex]n(not\text{ }X)=3[/tex]Since not X be the event that the drawn card is whic is not grey.
The probability of not X is
[tex]P(not\text{ }X)=\frac{n(not\text{ }X)}{n(S)}=\frac{3}{10}[/tex]Consider the equation.
[tex]1-P(not\text{ X\rparen}[/tex][tex]Substitute\text{ }P(not\text{ }X)=\frac{3}{10}\text{ in the equation.}[/tex][tex]1-P(not\text{ X\rparen=1-}\frac{3}{10}[/tex][tex]1-P(not\text{ X\rparen=1}\times\frac{10}{10}\text{-}\frac{3}{10}=\frac{10-3}{10}=\frac{7}{10}[/tex][tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]Final answer:
[tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]
What function makes the HIV virus unique?
The function which makes the HIV virus unique is: B. It has viral DNA that is transmitted through indirect contact with infected persons.
HIV is an acronym or abbreviation for human immunodeficiency virus and it refers to a type of venereal disease that destabilizes and destroys the immune system of an infected person, thereby, making it impossible for antigens to effectively fight pathogens.
Generally, the high mutation or replication rate of the human immunodeficiency virus (HIV) owing to its enormous genetic diversity (deoxyribonucleic acid - DNA) makes it easily transmittable from an infected person to another.
This ultimately implies that, the HIV virus is unique among other viruses because it can be transmitted without having a direct contact with an infected person such as:
Sharing a hair clipper with him or her.
Using an object that has been infected by a HIV patient.
Additionally, it is extremely difficult to develop an effective and accurate vaccine against the HIV virus because it possesses a high error rate.
20) Determine if the number is rational (R) or irrational (I)
EXPLANATION:
Given;
Consider the number below;
[tex]97.33997[/tex]Required;
We are required to determine if the number is rational or irrational.
Solution;
A number can be split into the whole and the decimal. The decimal part of it can be a recurring decimal or terminating decimal. A recurring decimal has its decimal digits continuing into infinity, whereas a terminating decimal has a specified number of decimal digits.
The decimal digits for this number can be expressed in fraction as;
[tex]Fraction=\frac{33997}{100000}[/tex]In other words, the number can also be expressed as;
[tex]97\frac{33997}{100000}[/tex]Therefore,
ANSWER: This is a RATIONAL number