ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex]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]
Which of the following is NOT a factor of x3 + x2 - 4x - 4?x + 1x + 2x - 1x - 2
Answer: (x - 1)
Explanation
Given:
[tex]x^3+x^2-4x-4[/tex]To factor a third-degree polynomial, we can do it by grouping:
[tex]=(x^3+x^2)+(-4x-4)[/tex]Then, we have to find the common factor between groups:
[tex]=x^2(x+1)-4(x+1)[/tex]Now, we can get the common factor of (x+1):
[tex]=(x^2-4)(x+1)[/tex]Finally, the differences of squares equal the following:
[tex](x^2-a^2)=(x-a)(x+a)[/tex]Then, applying this rule to our factor we get:
[tex]=(x+2)(x-2)(x+1)[/tex]Thus, the only factor that is not correct is (x - 1)
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).
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.
assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
Solve for x:
A
+79
X
Answer: -11
Step-by-step explanation: 66+46=112
180-112=68
79+?=68
79+-11=68
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.
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
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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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]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
Determine whether the sequence is geometric. 160, 40, 10,2.5, ...
Since the ratio is constant through the sequence, we conclude that it is geometric sequence.
Graph the line with slope -2 passing through the point (3,5)
To graph the line, you need to know at least two points of it.
Knowing its slope and one point you can determine the equation of the line by using the point-slope form:
[tex]y-y_1=m(x-x_1_{})[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
For m=-2 and (x₁,y₁)=(3,5) the equation of the line is:
[tex]y-5=-2(x-3)[/tex]Next, replace the equation for any value of x and solve for y, for example, use x=2
[tex]y-5=-2(2-3)[/tex]-Solve the difference within the parentheses then the multiplication
[tex]\begin{gathered} y-5=-2(-1) \\ y-5=2 \end{gathered}[/tex]-Add 5 to both sides of the equation
[tex]\begin{gathered} y-5+5=2+5 \\ y=7 \end{gathered}[/tex]The coordinates for the second point are (2,7)
Plot both points and link them with a line
Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=20, |w|=50, θ=80°
Vectors are represented by arrows, where the norm of a vector determinate its length.
Since θ = 80° is the angle between them, a sketch for our vectors is
The resultant of their sum is given by the parallelogram law. If we draw two vectors parallel to u and w, we're going to have a sketch of a parallelogram, and the diagonal connecting the angle between u and w to the opposite vertice represents the resultant.
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
which answer is the right one according to the image below
To do that, we have to do the following:
[tex]\begin{gathered} t(s(x))=t(x\text{ -}7) \\ =4(x\text{ - }7)^2\text{ - }(x\text{ - }7)+3 \\ \\ \end{gathered}[/tex]So, that would be the equivalent expression, because x is s(x), which is x - 7, so you have to replace every x value with (x - 7)
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)
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.
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)
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
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 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.
Make a tree diagramPlease be quick, I am in a hurry.
Explanation
The question wants us to obtain all the outcomes possible when a coin and a cube is tossed
A coin has two possible outcomes
[tex]\mleft\lbrace\text{Head, Tail}\mright\rbrace[/tex]A cube has 6 surfaces, so the outcomes are
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Thus, we can have the diagram showing the outcomes to be
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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Chloe deposits $2,000 in a money market account. The bank offers a simple interest rate of 1.2%. How much internet she earn in 10 years?
Given data:
deposits = $2,000
simple interest rate =1.2%
time =10 years
The formula to find the amount is,
[tex]A=\frac{\text{p}\cdot\text{n}\cdot\text{r}}{100}[/tex][tex]\begin{gathered} A=\frac{2000\cdot10\cdot1.2}{100} \\ A=\frac{24000}{100} \\ A=\text{ 240} \end{gathered}[/tex]The intrest she earn in 10 years is $240.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]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
solve the inequality for 5x + 9 ≤ 24
From the problem, we have an inequality of :
[tex]5x+9\le24[/tex]Subtract 9 to both sides of the inequality :
[tex]\begin{gathered} 5x+9-9\le24-9 \\ 5x\le15 \end{gathered}[/tex]Divide both sides by 5 :
[tex]\begin{gathered} \frac{5x}{5}\le\frac{15}{5} \\ x\le3 \end{gathered}[/tex]The answer is x ≤ 3
Kyzell is traveling 15 meters per second. Which expression could be used to convert this speed to kilometers per hour.
Given:
Kyzell is traveling 15 meters per second
we need to convert meters per second to kilometers per hours
As we know:
1 km = 1000 meters
So, 1 meters = 1/1000 kilometers
And, 1 Hour = 60 minutes = 3600 seconds
So, 1 seconds = 1/3600 Hours
So,
[tex]15\frac{meters}{\sec onds}=15\cdot\frac{1}{1000}\cdot3600\cdot\frac{kilometes}{\text{hours}}=54\frac{kilometrers}{hours}[/tex]So, the answer will be:
15 meters per second = 54 kilometers per hour