From the statement of the problem, we know that the organizer has the following guests:
• 12 cousins,
,• 6 aunts,
,• 4 brothers,
,• 2 sisters.
The total number of guests is 12 + 6 + 4 + 2 = 24. A 25% of the total number of guests is 0.25*24 = 6 guests. Because the group of aunts has 6 members, that group represent 25% of her guest.
Answer
The group of 6 aunts represents 25% of her guests.
Ms. Chen can run 5 miles in 2 hours andMs. Assis can run 6.3 miles in 3 hours.Who can run faster? Explain.
Ms. Assis
1) The way to find out who's faster, is to find their unit rates.
2) So, assuming their speed was at a constant rate, throughout the track we can write:
Chen hours
5 miles ------------------2
1 -------------------x
Cross Multiplying those ratios:
5x = 2 Divide both sides by 5
x=2/5
x=0.4 miles per hour
Assis
miles hours
6.3 ----------------- 3
1 -------------------- y
3 =6.3y Divide both sides by 6.3
y=0.47 miles per hour
3) Comparing those unit rates as
0.47 > 0.4
Then we can say that Ms. Assis runs faster than Ms. Chen
Find the area of the semicircle. Round to the nearest tenih. Use 3.14 for 3.8 yda. 22.7 yd²b. 23.9 yd²c. 45.3 yd²d. 11.9 yd²
Answer:
[tex]A[/tex]Explanation:
Here, we want to calculate the area of the semi-circle
To get this, we have to calculate the area of the circle and divide by 2
Mathematically, we have that as follows:
[tex]A\text{ = }\frac{\pi r^2}{2}[/tex]where pi is 3.14 and r which is the radius of the circle is 3.8 yd
Mathematically, we calculate the area as follows:
[tex]A\text{ = }\frac{3.14\times3.8^2}{2}\text{ = 22.7 yd}^2[/tex]I need help with a math assignment i linked the picture below with the question
Answer:
[tex]P\text{ = 29x+5}[/tex]Explanation:
Here, we want to get the perimeter of the rectangle
Mathematically, that is:
[tex]P\text{ = 2(L + B)}[/tex]Where L is the length of the rectangle, given as 6.5x + 9 ft and B is the width of the rectangle which is 8x-6.5
Substituting these values into the formula, we have the perimeter of the rectangle as follows:
[tex]\begin{gathered} P=2(6.5x\text{ + 9 +8x-6.5)} \\ P\text{ = 2(14.5x+2.5)} \\ P\text{ = 29x+5} \end{gathered}[/tex]Sally invested $1,200 in an account where interest compounded quarterly. After two years, she had $1,351.79 in her account. What was her interest rate?
use the formula
[tex]A=P(1+\frac{r}{t})^{n\cdot t}[/tex]clear the formula for the rate
[tex]A=P(1+\frac{r}{t})^{n\cdot t}[/tex].
An ordinary ( fair) die is a cube with the numbers. 1 through 6 on the sides ( represented by painted spots.) imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events.Event A: The sum is greater than 7 Event B: The sum is an even numberWrite your answer as fractions
EVENT A.
We have to count in how many possible ways does the sum of the two rolls of the die add up to more than 7. The possibilities are:
6+2
6+3
6+4
6+5
6+6
5+3
5+4
5+5
5+6
4+4
4+5
4+6
3+5
3+6
2+6
Then, there is 15 ways that the sum os greater than 7. Now we have to calculate how many combinations there is in total, which is 6 possible outcomes for the first roll and other 6 for the second roll, then there is 6x6=36 possible outcomes.
The probability for event A is then 15/36 or 5/12
EVENT B:
In a similar way, we have to count how many ways there is such that the sum is even:
1+1
1+3
1+5
2+2
2+4
2+6
3+1
3+3
3+5
....
We notice that there is 3 ways for each number from the first roll. Then the total is 6*3=18 ways such that the sum is even. The total possible outomes is 6x6=36.
Hence the probability for Evenet B is 18/36 or 1/2
Can you please me with the question on the picture
Solution
[tex]\begin{gathered} \text{Total marbles= 6+}5+4_{} \\ \text{Total marbles =15 marbles} \end{gathered}[/tex]6blue marbles
5 red marbles
4 white marbles
Part A
Formula
Not white means it blue or 5 = 11
[tex]P(\text{Blue given not white)}=\frac{P(B\text{ n W)}}{P(W)}=\frac{\frac{6}{15}\times\frac{6}{15}}{\frac{11}{15}}=\frac{6}{15}[/tex]Part B
If possible, find the area of the triangle defined by the following: a = 7, b = 4, y = 43°9.5 square units19.3 square units14 square units16.8 square units
So C = 180 - 23.7 - 35
= 121.3°
[tex]\begin{gathered} \text{ }\frac{C\text{ }}{\sin\text{ C}}\text{ = }\frac{B}{\sin \text{ B}} \\ \frac{C}{\sin\text{ 121.3}}\text{ = }\frac{100}{\sin \text{ 35}} \\ \text{ C = }\frac{100\sin \text{ 121.3}}{\sin \text{ 35}} \\ C\text{ = }\frac{85.44}{0.57} \\ C\text{ = 150 mi} \end{gathered}[/tex]Use the specified row transformation to change the given matrix.6R_1+R_2
ANSWER:
[tex]6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}[/tex]STEP-BY-STEP EXPLANATION:
We have the following matrix:
[tex]\begin{bmatrix}{1} & 5 & {4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{cases}R_1 \\ R_2 \\ R_3\end{cases}[/tex]Now, we apply the following changes
[tex]\begin{gathered} 6\cdot R_1+R_2 \\ 6\cdot R_1=\begin{bmatrix}{6\cdot1} & 6\cdot5 & 6\cdot{4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{6} & 30 & {24} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{6+(-6)} & 30+9 & {24+(-1)} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \end{gathered}[/tex]Write an inequality for each of the following Mrs. Champlin needs to make at least 28 costumes for the school play
ok
x = number of costumes
The inequality is:
[tex]\text{ x }\ge\text{ 28}[/tex]where "x" is the number of costumes
In the sentence given, they use the terms "at least", that means that the number must be equal or greater than 28.
In maths, there are five symbol that we can use in inequalities.
= means equal
< means less than
> means greater than
[tex]\begin{gathered} \ge\text{ means greater or equal than} \\ \leq\text{ means less or equal than} \end{gathered}[/tex]
In the sentence given, as they use at least, we must use greater or equal, it means it could be 28 or a greater number.
i need some help on this word problem please do it for me (12)
The first thing we need to do is identify the important values, our variables, and our equations that model or describe our problem.
• A total of 560 tickets were sold.
• Tickets can be ,A,dult or ,S,tudent
[tex]A+S=560\to(1)[/tex]• The total of tickets sold $3166
,• The value of the Adult ticket is $8
,• The value of the Student ticket is $3.5
[tex]8A+3.5S=3166\to(2)[/tex]We can see that A and S correspond to the number of Adult or Student tickets sold. We solve the equations to find our numbers.
[tex]A=560-S\to\text{(1)}[/tex][tex]\begin{gathered} 8(560-S)+3.5S=3166 \\ 8\times560-8S+3.5S=3166 \\ S(3.5-8)=3166-4480 \\ -4.5S=-1314 \\ S=\frac{-1314}{-4.5} \\ S=292 \end{gathered}[/tex][tex]\begin{gathered} A=560-292 \\ A=268 \end{gathered}[/tex]In total, 292 Student tickets and 268 Adult tickets were sold.P(E') = P(F) = 0.6 and P(E n F) = 0.24:a. Write down P(E).b. Explain how you know E and F:i are independentii are not mutually exclusivec Find P(E u F').
Answer:
Explanations:
Given the following probability values:
P(E') = 0.6
P(F) = 0.6
P(E n F) = 0.24
a) The probability of E [P(E)] is expressed according to the formula;
[tex]\begin{gathered} P(E)=1-P(E^{\prime}) \\ P(E)=1-0.6 \\ P(E)=0.4 \end{gathered}[/tex]b) For the events E and F to be independent, the product of their individual proban
Back | Next Question 2 Indicate the answer choice that best completes the statement or answers the question. Determine if the two figures are congruent by using transformations. Explain your reasonin a. congruent; a rotation followed by a reflection Ob. congruent; a reflection followed by another reflection Oc. congruent; a reflection followed by translation O d. not congruent
b. congruent; a reflection followed by another reflection
If grey shape is reflected across the x-axis and then the y-axis, or viceversa, white shape is obtained.
Which expression is equivalent to 9(7 +5) by the Distributive Property?
we have
9(7 +5)
apply distributive property
9*(7)+9*(5)
63+45
combine like terms
108
What is the volume of the solid?8 cm12 cm12 cm16 cm2 cmWe talenteΟ Α112 cubic cmОв192 cubic cmОс224 cubic cmOD304 cubic cm
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram:
solid
Step 02:
geometry:
volume:
we must analyze the figure to find the solution.
volume solid 1:
rectangle:
V = l * w * h
V1 = 12 cm * (16 cm - 12 cm) * 2 cm = 12 cm * 4 cm * 2 cm = 96 cm³
volume solid 2:
rectangle:
V = l * w * h
V2 = 12 cm * 2 cm * (16 cm - 8 cm) = 12 cm * 2 cm * 8 cm = 192 cm³
Total volume:
VT = V1 + V2 = "96 cm + ³192 cm = ³
Use substitution to solve.Solve the first equation for y and substitute it into the second equation. The resulting equati
The first equation is given as,
[tex]\begin{gathered} 2X^2\text{ = 5 +Y} \\ Y\text{ = }2X^2\text{ - 5\_\_\_\_\_\_\_(1)} \end{gathered}[/tex]The second equation is given as,
[tex]4Y\text{ = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ \_\_\_\_\_\_\_\_\_(2)}[/tex]Substituting equation ( 1 ) in equation (2),
[tex]4(\text{ }2X^2\text{ - 5) = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ }[/tex]Simplifying further,
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]Thus the required answer is
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]bailey buys new winter clothes for $136 she has to pay 8.25% sales tax on her purchase. how much is the sales tax for her new clothes?
Given :
The cost of the new winter clothes = $136
The sales tax = 8.25%
So, the sales tax = 8.25% of 136 =
[tex]\frac{8.25}{100}\cdot136=11.22[/tex]So, the answer is : the sales tax = $11.22
 Exponential Transformations: Identify if they represent growth or decay, range, horizontal move, vertical move, flip, stretch or shrink Y = 3(1/2) ^x+3 Y = 4^x-3 + 6Y = -2^x - 5 Y = (2/3)^x-2 +1
If b > 1 then it's an exponential growth
If b < 1 then it's an exponential decay
Y = 3(1/2)^(x+3) decay
Y = 4^(x-3) + 6 growth
Y = -2^x - 5 decay
Y = (2/3)^(x-2) +1 decay
The y-intercept is found replacing x = 0 into the equation.
Y = 3(1/2)^(0+3)
Y = 3(1/2)^3
Y = 3(1/8)
Y = 3/8
Y = 4^(0-3) + 6
Y = 4^(-3) + 6
Y = 1/64 + 6
Y = 385/64
Y = -2^0 - 5
Y = -1 - 5
Y = -6
Y = (2/3)^(0-2) +1
Y = (2/3)^(-2) +1
Y = (3/2)^(2) +1
Y = 9/4 +1
Y = 13/4
The vertical movement is found identifying k in the equations.
Y = 3(1/2)^(x+3) k = 0 no vertical move
Y = 4^(x-3) + 6 k = 6 vertical move 6 units up
Y = -2^x - 5 k = -5 vertical move 5 units down
Y = (2/3)^(x-2) +1 k = 1 vertical move 1 unit up
If the equation is flipped or not is seen in the a parameter. If a < 0, it's flipped, if a > 0, it isn't flipped
Y = 3(1/2)^(x+3) a > 0 not flipped
Y = 4^(x-3) + 6 a > 0 not flipped
Y = -2^x - 5 a < 0 flipped
Y = (2/3)^(x-2) +1 a > 0 not flipped
The range is found with help of the vertical move and the flip
Y = 3(1/2)^(x+3) no vertical move, not flipped range: [0, ∞]
Y = 4^(x-3) + 6 vertical move 6 units up, not flipped range: [6, ∞]
Y = -2^x - 5 vertical move 5 units down range: [-5, -∞]
Y = (2/3)^(x-2) +1 vertical move 1 unit up, not flipped range: [1, ∞]
The horizontal movement is found identifying h in the equations.
Y = 3(1/2)^(x+3) h = 3 horizontal move 3 units left
Y = 4^(x-3) + 6 h = -3 horizontal move 3 units right
Y = -2^x - 5 h = 0 no vertical move
Y = (2/3)^(x-2) +1 h = -2 horizontal move 2 units right
If the equation is stretched or shrunk is seen in the a parameter. If a > 1, the function stretches, if 0 < a < 1, 1, the function shrinks
Y = 3(1/2)^(x+3) a = 3 stretches
Y = 4^(x-3) + 6 a = 1 doesn't stretch nor shrink
Y = -2^x - 5 a = -1 doesn't stretch nor shrink
Y = (2/3)^(x-2) +1 a = 2/3 shrinks
a recent poll contacted 230 people who own a car and live in the California and asked whether or not they were a homeowner. Idenify the population of this poll
Population in statistics is the total collection of data being considered.
This could be in a survey.
In our question we are told 230 people were contacted if they were homeowner.
SInce we are dealing with a particular sample of people, the population poll will be 230 people who own a car and live in the California
I need some help on finding the surface area. i don't know how to solve with a triangular base?
The surface area(A) of a triangular pyramid can be found using the formula:
[tex]A\text{ = }\frac{1}{2}\text{ }\times\text{ a }\times\text{ b + }\frac{3}{2}\text{ }\times b\text{ }\times\text{ s}[/tex]Given the triangular prism:
Hence, we have:
a = 3.5 m
b = 4m
s = 11.1 m
Substituting the values into the formula:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times3.5\text{ }\times4\text{ + }\frac{3}{2}\text{ }\times\text{ 4 }\times\text{ 11.1} \\ =\text{ 7 + 66.6} \\ =\text{ 73.6 m}^2 \end{gathered}[/tex]Hence, the surface area of the pyramid is 73.6 square meter
solve for the indicated Variable 5t+r=s for tt=
Given the following equation:
[tex]5t+r=s[/tex]You can solve for the variable "t" by following the steps shown below:
1. You can apply the Subtraction Property of Equality by subtracting "r" from both sides of the equation:
[tex]\begin{gathered} 5t+r-(r)=s-(r) \\ 5t=s-r \end{gathered}[/tex]2. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by 5. Then, you get:
[tex]\begin{gathered} \frac{5t}{5}=\frac{s-r}{5} \\ \\ t=\frac{s-r}{5} \end{gathered}[/tex]Therefore, the answer is:
[tex]t=\frac{s-r}{5}[/tex]Write the series using sigma notation to find the sum of the termsDrag the tiles to the correct location is not a tiles will be used
The number over the sigma sign is 5
Explanation:
5 represent the finale value
Find the greatest common factor of the following monomials46b^5 16b^3
Factors of 46: 1, 2, 23 and 46
Factors of 16: 1, 2, 4, 8 and 16.
With respect to variable b, the GCF has the variable raised to the lowest power of the monomials, which in this case is 3. Then, the greatest common factor of the given monomials is: 2b³
A If mzABD 61, and mzDBC = 59, then mABC = [ ?P
I need the answer as fast as you can give it to me
Explanation
Given
[tex](256x^{16})^{\frac{1}{4}}[/tex]We can simplify the expression below;
[tex]\begin{gathered} =256^{\frac{1}{4}}\times x^{16\times\frac{1}{4}} \\ =\sqrt[4]{256}\times x^{\frac{16}{4}} \\ =4x^4 \end{gathered}[/tex]Answer:
Write each ratio in simplest form1- 300:1082- 5280:8003- 42:1204- 20:965- 24:16
Given:
1) 300:108
[tex]\begin{gathered} \frac{300}{108} \\ \text{Greatest common factor of 300 and 108 is 12.} \\ \frac{300}{108}=\frac{25\cdot12}{9\cdot12}=\frac{25}{9}\Rightarrow25\colon9 \end{gathered}[/tex]2) 5280:800
[tex]\begin{gathered} \frac{5280}{800} \\ \text{Greatest common factor of 5280 and 800 is 160.} \\ \frac{5280}{800}=\frac{33\cdot160}{5\cdot160}=\frac{33}{5}\Rightarrow33\colon5 \end{gathered}[/tex]3) 42:120
[tex]\begin{gathered} \frac{42}{120} \\ \text{Greatest common factor of 42 and 120 is 6.} \\ \frac{42}{120}=\frac{7\cdot6}{20\cdot6}=\frac{7}{20}\Rightarrow7\colon20 \end{gathered}[/tex]4) 20:96
[tex]\begin{gathered} \frac{20}{96} \\ \text{Greatest common factor of 20 and 96 is 4.} \\ \frac{20}{96}=\frac{4\cdot5}{4\cdot24}=\frac{5}{24}\Rightarrow5\colon24 \end{gathered}[/tex]5)
[tex]\begin{gathered} \frac{24}{16} \\ \text{Greatest common factor of 24 and 16 is 8.} \\ \frac{24}{16}=\frac{3\cdot8}{2\cdot8}=\frac{3}{2}\Rightarrow3\colon2 \end{gathered}[/tex]LMNO is a rhombus find at 3s + 12 5x - 2y -6
In this case the answer is very simple. .
To find the solution to the exercise we'll have to carry out several steps.
(3x + 12) = (5x -2)
12 + 2 = 5x - 3x
14 = 2x
14 /2 = x
7 = x
The answer is:
x = 7
what is 6cos square theta+cos theta -2=0 what the theta in degrees
Given:
[tex]6\cos^2\theta+\cos\theta-2=0[/tex]Let
[tex]\cos\theta=t[/tex]Then
[tex]\begin{gathered} 6t^2+t-2=0 \\ (2t-1)(3t+2)=0 \\ 2t-1=0 \\ \Rightarrow t=\frac{1}{2} \\ \\ 3t+2=0 \\ \Rightarrow t=-\frac{2}{3} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \cos\theta=\frac{1}{2} \\ \\ \Rightarrow\theta=60^o \\ \\ \cos\theta=-\frac{2}{3} \\ \Rightarrow\theta=131.8^o \end{gathered}[/tex]For each ordered pair, determine whether it is a solution to the system of equations -5x+4y=2. 3x-5y=4 solution? (x, y) (6,8) it is a solution yes or no. (-4,-4) it is a solutions yes or no. (-7,0) it is a solution yes or no. (3,1) it is a solution yes or no
Check the solutions
(6,8)
(-4,-4)
(-7,0)
(3,1)
To check if the pair is a solution to teh system of equations you must replace x and y on both of the equations and see if the equation is fulfilled
(6,8) Is not a solution to the system of a solutions
[tex]\begin{gathered} \begin{aligned}-5(6)+4(8)=2 \\ 3(6)-5(8)=4\end{aligned} \\ \\ -30+32=2\longrightarrow2=2 \\ 18-40=4\longrightarrow-22\ne4 \end{gathered}[/tex](-4,-4) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-4)+4(-4)=2 \\ 3(-4)-5(-4)=4\end{aligned} \\ \\ 20-16=2\longrightarrow4\ne2 \\ -12+16=4\longrightarrow4=4 \end{gathered}[/tex](-7,0) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-7)+4(0)=2 \\ 3(-7)-5(0)=4\end{aligned} \\ \\ 35+0=2\longrightarrow35\ne2 \\ -21-0=4-21\ne4 \end{gathered}[/tex](3,1) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(3)+4(1)=2 \\ 3(3)-5(1)=4\end{aligned} \\ \\ -15+4=2\longrightarrow-11\ne2 \\ 9-5=4\longrightarrow4=4 \end{gathered}[/tex]When planning a cruise, you have a choice of 2 destinations: Cozumel (C) or Jamaica (J); a choice of 4 types of rooms: balcony (B), inside view (I), ocean view (O), or suite (S); and a choice of 2 types of excursions: water sports (W) or horseback riding (H). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.
Given
There are 2 options for a destination: Cozumel (C) or Jamaica (J)
There are 4 types of rooms : Balcony (B), Inside View (I), Ocean View (O), Suite (S)
There are two types of excursions : Water sports (W) or Horseback (H)
The sample space is a combination of all the available options and can be calculated using the formula:
[tex]\begin{gathered} Sample\text{ space = Number of options for A }\times\text{ Number of options for B }\times \\ Number\text{ of options C} \end{gathered}[/tex]Applying the formula:
[tex]\begin{gathered} Sample\text{ space = 2 }\times\text{ 4 }\times\text{ 2} \\ =\text{ 16 } \end{gathered}[/tex]The list of the combinations is shown below:
CBW, CBH, CIW, CIH , COW, COH, CSW, CSH, JBW, JBH, JIW, JIH, JOW, JOH, JSW, JSH
Please finish the following proof using the "prove steps" and write the two-column statements.
Based on the AAS congruence theorem, ΔADB ≅ ΔCDB. The two-column proof for this is explained below.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles are equal or congruent to each other if they have two pairs of congruent angles and a pair of non-included congruent sides.
We are given that ∠ADB and ∠CDB are right angles, therefore, they are congruent to each other. We are also given that ∠A ≅ ∠C.
Also, BD ≅ BD based on the reflexive property of congruency.
Therefore, according to the AAS congruence theorem, ΔADB ≅ ΔCDB.
The two-column proof would be stated as shown below:
Statement Reasons
1. ∠ADB and ∠CDB are right angles 1. Given
2. ∠A ≅ ∠C 2. Given
3. BD ≅ BD 3. Reflexive property
4. ΔADB ≅ ΔCDB 4. AAS congruence theorem
Learn more about the AAS congruence theorem on:
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