Notice the following pattern in the given sequence:
[tex]\begin{gathered} 11=4\cdot2\text{ +3,} \\ 25=11\cdot2+3, \\ 53=25\cdot2+3, \\ 109=53\cdot2+3. \end{gathered}[/tex]Therefore, the n-term of the sequence has the following form:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Answer:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]A jar contains 10 purple marbles, 2 red marbles, and 5 blue marbles. What is the probability thatrandomly chosen marble is purple? Round the answer to the nearest hundredth of a percent.
EXPLANATION
Let's see the facts:
purple marbles = 10
red marbles = 2
blue marbles = 5
The probability formula is:
[tex]P(X)\text{ = }\frac{n\nu mber\text{ of favourable outcomes}}{\text{Total number of outcomes}}[/tex]The totl number of outcomes is 10+2+5 = 17 marbles
The number of favourable outcomes is equal to 10 because there are 10 purple marbles.
Then, the probability would be:
[tex]P(X)=\frac{10}{17}=\text{ 0.59}[/tex]Probability is 0.5882352941-->0.59 Rounded to the nearest hunderdth--------------->59%.
Answer: The probability is 59% (Rounded to the nearest hunderdth).
Find three consecutive odd integers that add to - 99
We will investigate how three consecutive odd numbers add up to a certain value.
We will assign a variable to the first odd number as follows:
[tex]1st\text{ : x}[/tex]The next consecutive odd number will occur two integers ahead or two integers before the first odd number. We can choose either ( ahead or before ) and express second consecutive odd number in terms of first odd number as follows:
[tex]2nd\colon\text{ ( x + 2 ) OR ( x - 2 )}[/tex]Similarly, the next consecutive odd number will occcur two integers ahead or two integer before the second odd number OR four integers ahead of for integers before the first odd number. We can choose either ( ahead or before ) and express the third consecutive odd number in terms of first or second odd number as follows:
[tex]3rd\colon\text{ ( x + 4 ) OR ( x - 4 )}[/tex]We will now sum up all three consecutive odd numbers and equate the result to ( -99 ) as follows:
[tex]\begin{gathered} (\text{ x ) + ( x + 2 ) + ( x + 4 ) = -99} \\ OR \\ (\text{ x ) + ( x - 2 ) + ( x - 4 ) = -99} \end{gathered}[/tex]Then we will solve both possibilities step by step.
[tex]\begin{gathered} 3x\text{ + 6 = -99} \\ OR \\ 3x\text{ - 6 = -99} \\ \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3x\text{ = -105} \\ OR \\ 3x\text{ = -93} \end{gathered}[/tex]Next,
[tex]\begin{gathered} x\text{ = }\frac{-105}{3}\text{ = -35} \\ \\ OR \\ \\ x\text{ = }\frac{-93}{3}\text{ = -31 } \end{gathered}[/tex]For each possibilitiy the three consecutive odd numbers would be:
[tex]\begin{gathered} x\text{ = -35 , x + 2 = -33 , x + 4 = -31} \\ OR \\ x\text{ = -31 , x - 2 = -33 , x - 4 = -35} \end{gathered}[/tex]We see that both possibilities result in identical three consecutive odd numbers that would add up to a total of ( -99 ). Therefore, the three consecutive odd numbers are:
[tex]-31\text{ , -33 , -35 }\ldots\text{ Answer}[/tex]
in this work today in my class want to know if am right 5w+2p for w=6 and p=2 evaluate this
Solution
For this case we have the following expression given:
5w +2p
And we have that w= 6 and p= 2
And replacing we got:
5*6 + 2*2
30 + 4= 34
Seven years ago, Tom bought a house for $80,000, whichappreciated in value at 9% per year due to inflation. If Tomhas 48 more monthly payments of $500 to make to the bankon his 12% mortgage, find his present equity in the house.
The equity will be the value of the house today minus the present value of the remaining mortgage payments.
We can start with the value of the house. If the house was originally valued in $80,000 and appreciated at 9% per year during 7 seven years, we can calculate the present value as:
[tex]\begin{gathered} PV=80000\cdot(1+0.09)^7 \\ PV=80000\cdot1.09^7 \\ PV\approx80000\cdot1.828 \\ PV\approx146243.13 \end{gathered}[/tex]Now we can calculate the present value of the mortgage payments as an annuity.
The payments are monthly (m = 12), with an annual rate of 12% (r = 0.12). The amount paid monthly is $500 and there are 48 remaining payments (m*t = 48), so we can calculate the annuity as:
[tex]\begin{gathered} PV=M\cdot\frac{1-(1+\frac{r}{m})^{-m\cdot t}}{\frac{r}{m}} \\ PV=500\cdot\frac{1-(1+\frac{0.12}{12})^{-48}}{\frac{0.12}{12}} \\ PV=500\cdot\frac{1-(1.01)^{-48}}{0.01} \\ PV\approx500\cdot\frac{1-0.62026}{0.01} \\ PV\approx500\cdot\frac{0.37974}{0.01} \\ PV\approx500\cdot37.974 \\ PV\approx18986.98 \end{gathered}[/tex]Then, if we substract the mortgage present value from the present value of the house, we get the equity:
[tex]\begin{gathered} E=PV_{h\text{ouse}}-PV_{\text{mortgage}} \\ E=146243.13-18986.98 \\ E=127256.15 \end{gathered}[/tex]Answer: the present equity in the house is $127,256.15
what is 2*2?i dont know i in pweschool
2 x 2 is two times two
answer: 4
You put $400 in an account. The account earns $32 simple interest in 2 years what is the annual interest rate?
Answer
4 %
Explanation
Given:
Principal, P = $400
Interest, I = $32
Time,T = 2 years
What to find:
Annual interest rate, R
Step-by step solution:
The simple interest formula is given by:
[tex]I=\frac{\text{PRT}}{100}[/tex]Substituting P = 400, I = 32, and T = 2 into the formula:
[tex]\begin{gathered} 32=\frac{400\times R\times2}{100} \\ 800R=3200 \\ R=\frac{3200}{800} \\ R=4\text{ \%} \end{gathered}[/tex]u want to construct an open-top box that is 6 inches deep, with a square base. it must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.
Let's analyse each sentence:
A)
This sentence is true, because the volume of the box is given and it is 864 in³.
B)
This sentence is false, because the height of the box is given and it is 6 inches.
C)
Let's calculate the sides of the base, knowing that the length and width are the same:
[tex]\begin{gathered} V=\text{lwh} \\ 864=l\cdot l\cdot6 \\ l^2=\frac{864}{6} \\ l^2=144 \\ l=^{}12 \end{gathered}[/tex]The side of the cardboard will include the length of the base and two times the height, since it will be folded later on, so we have:
[tex]\text{cardboard side}=l+2h=12+6\cdot2=24[/tex]So the side of the cardboard needs to be 24 inches, so this sentence is false.
D)
This sentence is false, because the height is not equal the length and width.
E)
This sentence is true, because using the variable x to represent the side of the square base (that is, the length and the width), we have:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ V=6x^2=864 \end{gathered}[/tex]So the correct statements are A and E.
Find the unknown value in the proportion. Round to the nearest tenth if needed. 4/3=12/?
Starting with the proportion:
[tex]\frac{12}{?}[/tex]Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
[tex]\frac{12}{?}=\frac{12\div3}{?\div3}=\frac{4}{?\div3}=\frac{4}{3}[/tex]Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
Therefore, ?=9.
Translate the word sentence into a number sentence5. One thousand is less than a number6. A number is greater than four-fifths7. Five and nine tenths is greater than or equal to a number8. A number is not equal to twelve hundredths 9. Eight plus four is not equal to eleven10. The sum of twelve and five is greater than a number
To translate "One thousand is less than a number" into a number, we can divide the sentence in three parts.
One thousand is less than a number
a b c
Let's translate each part:
(a) One thousand
We have to write the equivalent number: 1000.
(b) is less than
The symbol that represents it is <.
(c) a number
Since we do not know this number, let's assume it is x.
Now, we can put the parts together and write the number sentence.
1000 < x.
Answer: One thousand is less than a number is the same as 1000 < x.
What is the slope of the line through (-1, -7) and (3,9)? Choose 1 answerA. -1/4B. -4C. 4D. 1/4
Answer:
C. 4
Explanation:
Given the line that passes through points (-1,-7) and (3,9):
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{9-(-7)}{3-(-1)} \\ =\frac{9+7}{3+1} \\ =\frac{16}{4} \\ =4 \end{gathered}[/tex]The slope of the line is 4.
The correct choice is C,
What is the range of the function on the graph?у5all real numbers32all real numbers greater than or equal to 0O all real numbers greater than or equal to 1all real numbers greater than or equal to 211-5 -4 -3 -2 -11 + 1 2 3 4 5 X-2--34+-3
Given:
The graph of the function is given.
The range of the function is all y-values or output
Answer:
The answer is D or "all real numbers greater than or equal to 2"
Edge 2023 ✅• The function (x) is a transformation of the square root parent function,f(x) = V. What function is h(x)?5nuA. h(x) = v=-4B. h(c) = V - 4O C. h(z) = y +4D. h(x) = 1 + 4
we are given the following function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of h(x) is the same graph translated 4 units to the left, therefore it must be:
[tex]h(x)=f(x+4)[/tex]Replacing x for x + 4 in f(x) we get:
[tex]h(x)=f(x+4)=\sqrt[]{x+4}[/tex]factor the expression 120 + 50 using gcf
The given expression is,
[tex]120+50[/tex]The factors of 120 are, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 50 are, 1, 2, 5, 10, 25, 50
From this, we can infer that, the greatest common factor of 120 and 50 is,
10.
Therefore, we can write,
[tex]120+50=(10\times12)+(10\times5)=10(12+5)=10\times17=170[/tex]In the gift shop of the History of Flight museum, Elisa bought a kit to make a model of a jet airplane. The actual plane is 18 feet long with a wingspan of 13.5 feet. If the finished model will be 10 inches long, what will the wingspan be?
3.75 in.
7.5 in.
24.3 in.
13.3 in.
Answer:
The answer is 24.3
Step-by-step explanation:
hope this helps you
The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans ofsoda cost $0.75 each. The department uses the algebraic expression 1.50x+0.75y to calculatecustomers' total expenses.a. What does the x variable represent?b. What does the y variable represent?c. A family buys 7 hot dogs and 4 sodas. What are their total expenses?
a) As the expression represents the total expense for a family, the term 1.50x represents how much the familiy spends in hot dogs.
This term is the product of the price (1.50) and the number of hot dogs purchased (x).
Then, x is the number of hot dogs bought by the familiy.
b) In the same way, 0.75y represent how much the family spends in soda: 0.75 is the price and y represents the number of soda cans purchased by the family.
c) If a family buys x=7 hot dogs and y=4 sodas, we can calculate the expenses as:
[tex]\begin{gathered} E=1.50x+0.75y \\ E=1.50\cdot7+0.75\cdot4 \\ E=10.5+3 \\ E=13.5 \end{gathered}[/tex]Their total expenses are $13.5.
Solve for X Geometry, Just need a quick over view!
The value of X = 11
Step - by - Step Explanation
What to find? The value of x
To find the value of X, take the ratio of the sides.
[tex]\frac{2x+6}{32}=\frac{52.5}{60}[/tex]Cross -multiply.
[tex]60(2x+6)=52.5(32)[/tex][tex]60(2x+6)=1680[/tex]Divide both-side of the equation by 60.
[tex]\frac{\cancel{60}(2x+6)}{\cancel{60}}=\frac{1680}{60}[/tex]2x + 6 = 28
Subtract 6 from both-side of the equation.
2x + 6 - 6 = 28 - 6
2x =22
Divide both-side of the equation by 2.
[tex]\frac{\cancel{2}x}{\cancel{2}}=\frac{22}{2}[/tex]x = 11
Hence, the value of X = 11
An empty tank is filled with water at a constant rate
Answer: D
Step-by-step explanation:
D is the answer because if you divide w by m, you get 16.5. Therefore 16.5 is the constant rate.
Bonnie is making a dipping sauce. She mixes 150 ml of soy sauce with 100 ml of vinegar.how much soy sauce does Bonnie mixed with every 1 milliliter of vinegar
The question is asking how much soy sauce Bonnie is mixing per every millilter of vinegar. To calculate this ratio, we simply divide the amount of soy sauce she mixed by the total amount of vinegar she used. This leads to
[tex]\frac{150\text{ (soy sauce)}}{100\text{ (vinegar)}}[/tex]which is equals to
[tex]\frac{150}{100}=\frac{30\cdot5}{20\cdot5}=\frac{30}{20}=\frac{3}{2}=1.5[/tex]so Bonnie uses 1.5 ml of soy sauce per every ml of vinegar
What is the product of the complex numbers below? (4-21)(1+7) O A. 18-301 O B. -10-301 ОО O C. -10 + 261 O D. 18 + 261
Given the complex product:
(4 - 2i)(1 + 7i) =
• First we multiply each parenthesis:
4 + 28i - 2i - 14i²
• Using i² = -1
4 + 28i - 2i + 14 =
18 + 26i
Karla says 4 and 4.7 would fall between V17 and 4O FactO Fib
First of all, we have to know the equivalent decimal number to each of them.
[tex]\begin{gathered} 4\frac{2}{3}=\frac{4\cdot3+2}{3}=\frac{12+2}{3}=\frac{14}{3}=4.66666\ldots \\ 4.7 \\ \sqrt[]{17}=4.12310\ldots \\ 4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{16+3}{4}=\frac{19}{4}=4.75 \end{gathered}[/tex]Notice that the interval is from 4.12310... to 4.75.
You can observe that 4.7 falls into this interval, and 4.666... also falls into this interval.
Therefore, the numbers Karla indicated fall into the interval she mentioned.The answer is Fact.The table shows the results of a survey of 100 people selected at randomat an airport. Find the experimental probability that a person selected atrandom is going to City C.AirportDestinationsNumber ofDestination ResponsesCity A24City B44City C12City D12NINISThe experimental probability that a person selected at random is going to City Cis.
we have that
the experimental probability is equal to
P=12/100
P=0.12 or P=12%Convert y+5=-(x+2) to the slope-Intercept (don’t put any spaces between numbers, variables, signs, or parentheses)
Given:
[tex]y+5=-(x+2)[/tex]Required:
To find the slope-Intercept form of the given equation.
Explanation:
We know that, the slope intercept form can be represented as
[tex]y=mx+b[/tex]Therefore, the given equation can be written as
[tex]\begin{gathered} y+5=-(x+2) \\ y+5=-x-2 \\ y=-x-2-5 \\ y=-x-7 \end{gathered}[/tex]Final Answer:
The slope-Intercept form of the given equation is
[tex]y=-x-7[/tex]The volume of the tent is 576 cubic feet and the area of the base is 36 square feet. what is the height of the tebt
The volume of a triangular prism is: B*h. Where B is the area and h is the height.
Replacing the values in the equation we have:
V = B*h
576 = (36)*h
576/36 = h (Dividing by 36 on both sides of the equation)
16 = h (Dividing)
The answer is 16 ft.
Use the vertex and intercept to sketch the graph of the quadratic function.
The expression we have is:
[tex]f(x)=9-(x+3)^2[/tex]We need to compare this expression with the Vertex form of the quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]Where the vertex is at (h,k).
We rewrite our expression as follows:
[tex]f(x)=-(x-(-3))^2+9[/tex]And we can see that h=-3, and k=9. Thus, the vertex of this quadratic function is at:
[tex](-3,9)[/tex]Also, since we have a negative sign along side the x, that means that the parabola opens down.
And the correct result is:
Option C
The perimeter of the rectangle blow is 70 units find the length of side PS
The perimeter of the given rectangle is 78 units.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Where w is the width and l is the length of the rectangle.
As you can see from the given figure,
w = 3z + 3
l = 4z + 1
We are asked to find the side length of side PS.
Substitute the given values into the above formula and solve for z.
[tex]\begin{gathered} P=2(w+l) \\ 78=2(3z+3+4z+1_{}) \\ 78=2(7z+4_{}) \\ \frac{78}{2}=(7z+4_{}) \\ 39=7z+4_{} \\ 39-4=7z \\ 35=7z \\ \frac{35}{7}=z \\ 5=z \end{gathered}[/tex]So, the value of z is 5
Finally, the length of side PS is
[tex]\begin{gathered} PS=4z+1 \\ PS=4(5)+1 \\ PS=20+1 \\ PS=21 \end{gathered}[/tex]Therefore, the length of the side PS is 21 units.
what isk + 6 greater than or equal to 19, if k = 11
what is
k + 6 greater than or equal to 19, if k = 11
we have
[tex]\begin{gathered} k+6\ge19 \\ k\ge19-6 \\ k\ge13 \end{gathered}[/tex]For k=11
we have
[tex]\begin{gathered} 11+6\ge19 \\ 17\ge19\text{ ----}\longrightarrow\text{ is not true} \\ \text{that means-}\longrightarrow\text{ the value of k is not a solution of the inequality} \end{gathered}[/tex]2 Which cookie is the better deal? Oreos $2.98 for 15.5 oz O $ Chips Ahoy $2.50 for 14oz 2b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0,43 or.43, if there is a dollar amount like 1.50, do not add zeros in front) Your answer
Chips ahoy $0.18 per oz.
1) Let's write it down, since the point here is what's the best deal we need to find out the unit rate for each one. Let's set a proportion:
$2.98 ----------- 15.5 oz
x -------------- 1 oz
Cross multiplying it:
15.5x = 2.98 * 1 Divide both sides by 15.5
x= 0.192
So $0.19 per oz.
Chips Ahoy:
$2.50------------14 oz
y --------------1
14y= 2.50
y=0.1785 rounding it to the nearest hundredth 0.18
Then $0.18 per oz
So the better deal, is buying Chips Ahoy.
2. What is the value of the expression (x - y) when x = 5and y=-1?F.7G.6H. 16K. 36
G.6
In this expression, let's plug it the values already informed to find the answer.
x=5
y= -1
(x-y)
(5-(-1)) = (5+1) =6
Remember that the minus changes the minus inside to plus.
AC = 12√3. Find BC and AB. Write answer in simplest form.
BC = a
AC = b= 12√3
AB =c
A= 30°
B=60°
C=90°
Using the sine rule
[tex]\frac{\sin\text{ A}}{a}=\frac{\sin B}{b}[/tex]substitute the values into the above
[tex]\frac{\sin30}{a}=\frac{\sin 60}{12\sqrt[]{3}}[/tex][tex]\frac{\frac{1}{2}}{a}=\frac{\frac{\sqrt[]{3}}{2}}{12\sqrt[]{3}}[/tex][tex]\frac{1}{2\times a}=\frac{\sqrt[]{3}}{2\times12\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{\sqrt[]{3}}{24\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{1}{24}[/tex]cross multiply
[tex]2a=\text{ 24}[/tex][tex]a=12[/tex]Therefore BC = 12
Let's proceed to find AB
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex][tex]\frac{\sin30}{12}=\frac{\sin 90}{c}[/tex][tex]\frac{\frac{1}{2}}{12}=\frac{1}{c}[/tex][tex]\frac{1}{2\times12}=\frac{1}{c}[/tex][tex]\frac{1}{24}=\frac{1}{c}[/tex]cross-multiply
[tex]c=24[/tex]
what is 1/5 turned into a percent