Answer:
[tex]a_n=7(2^{n-1})[/tex]Explanation:
Given the sequence with the recursive formula:
[tex]\begin{gathered} a_1=7 \\ a_n=2a_{n-1} \end{gathered}[/tex]First, we determine the first three terms in the sequence.
[tex]\begin{gathered} a_2=2a_{2-1}=2a_1=2\times7=14 \\ a_3=2a_{3-1}=2a_2=2\times14=28 \end{gathered}[/tex]Therefore, the first three terms of the sequence are: 7, 14 and 28.
This is a geometric sequence where:
• The first term, a=7
,• The common ratio, r =14/7 = 2
We use the formula for the nth term of a GP.
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7\times2^{n-1} \end{gathered}[/tex]The explicit formula for the sequence is:
[tex]a_n=7(2^{n-1})[/tex]PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answer:
look below
Step-by-step explanation:
Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?
Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91
organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98
(a) Complete the grouped frequency distribution for the data.
79 to 83 -> 3
84 to 88 -> 4
89 to 93 -> 6
94 to 98 -> 2
(b) Construct a histogram for the data.
the histogram can be constructed using the information obtained in point (a)
Juan earned 60% of the possible points on his first math test. His teacher offered to let him take another test to earn extra credit. Juan earned 80% of the possible points on the second test. Each test had the same number of possible points. If Juan earned 30 points on the first test, how many points did he earn on the second test?
Let:
x = Number of points Juan earned on the second text
n = Total number of points of each test
First, let's find the total number of points of each test using the information provided:
[tex]\begin{gathered} 0.6\cdot n=30 \\ so\colon \\ n=\frac{30}{0.6} \\ n=50 \end{gathered}[/tex]Now, we can find how many points Juan earned on the second test:
[tex]\begin{gathered} x=0.8\cdot n \\ x=0.8\cdot50 \\ x=40 \end{gathered}[/tex]Answer:
40 points
Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.
The area of the overlapping region is of: 6.25 units squared.
Area of a rectangleThe area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:
A = lw.
The dimensions of the right triangle as follows:
Leg x.Leg 2.Hence the remaining leg on the overlapping region is:
4 - x, as AD = 4.
By symmetry, the other dimension of the overlapping region is also of:
4 - x.
Being also the hypotenuse of the right triangles.
The value of x can be found applying the Pythagorean Theorem as follows:
x² + 2² = (4 - x)²
x² + 4 = 16 - 8x + x²
8x = 12
x = 1.5.
Then the two dimensions of the shaded region are:
4 - 1.5 = 2.5.
Meaning that the area is of:
A = 2.5 x 2.5 = 6.25 units squared.
Missing information
The figure is missing and is given by the image at the end of the answer.
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The chart below shows how many newspapers each person stacked. Which operation would be used to find the total number of newspapers Diane stacked?
Answer:
Where's the chart?
Step-by-step explanation:
tim wants to order pizza for 22 employees.Each employee should get 1/4 of a pizza.How many pizzas should tim order ?
Tim should order approximately 6 pizza.
Define division.Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction. Mathematicians use addition, subtraction, multiplication, and division as their four fundamental arithmetic operations. The division is one of these four operations that we employ most frequently in our daily work. It involves dividing a huge group into equally sized smaller units. Divide 25, for instance, by 5.
Given Data
Number of employees = 22
Slice of pizza one should get = 1/4
Dividing 22 by 1/4
[tex]\frac{22}{4}[/tex]
5 and [tex]\frac{1}{2}[/tex]
Tim should order approximately 6 pizza.
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Find the distance and the midpoint for each set of points given
Given,
The coordinates of the points are (2,6) and (7, 2).
Required:
The distance between the points and the midpoint of the points.
The distance between two points is calculated as,
[tex]\begin{gathered} Distance\text{ =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt{(7-2)^2+(2-6)^2} \\ =\sqrt{5^2+4^2} \\ =\sqrt{25+16} \\ =\sqrt{41} \\ =6.4 \end{gathered}[/tex]Hence, the distance between the points is 6.4
The midpoint is calculated as,
[tex]\begin{gathered} Midpoint=(\frac{2+7}{2},\frac{6+2}{2}) \\ =\frac{9}{2},\frac{8}{2} \\ =(4.5,4) \end{gathered}[/tex]Hence, the midpoint is (4.5,4).
how do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check
In polar coordinates, the x variable is given as
[tex]x=r\cos \theta[/tex]So, we have the equation
[tex]r\cos \theta=15[/tex]By dividing both sides by cosine of thetat, we get
[tex]r=\frac{15}{\cos \theta}[/tex]since
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]The above result is equivalent to:
[tex]r=15\sec \theta[/tex]Which expression represents the area of the rectangle below in square units
Area of rectangle is given by:-
[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]So the correct answer is
[tex]6x^2+4x[/tex]Tony will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60and costs an additional $0.50per mile driven
The second plan has noinitial fee and costs an additional $0.70per mile driven
E
For what amount of driving do the two plans cost the
Same
Plan 1:
Initial (fixed) fee: $60
Variable fee: $0.50 per mile
Plan 2:
Initial (fixed) fee: $0
Variable fee: $0.70 per mile
If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:
P1 = 60 + 0.5x
The cost of Plan 2 is:
P2 = 0.7x
It's required to find the number of miles Tony should drive for both plans to cost the same, that is:
60 + 0.5x = 0.7x
Subtracting 0.5x:
60 = 0.7x - 0.5x
Operating:
60 = 0.2x
Dividing by 0.2:
x = 60 / 0.2
x = 300
Tony should drive 300 miles for both plans to cost the same.
Under that condition, both plans cost the same. Plan 1 cost:
P1 = 60 + 0.5*300
P1 = 60 + 150
P1 = $210
Plan 2 cost:
P2 = 0.7*300
P2 = $210
Both costs are equal
Sx-3y =-3
(2x + 3y = -6
a. by graphing,
What are
y =
Y2=
Given,
x-3y=-3
2x+3y=-6
Plotting it in graph we have,
Since we have only one point of intersection so that would be only one solution.
The point of intersection is (-3,0)
Thus x=-3 and y=0
Find the values of sin 0, cos 0, and tan e for the given right triangle. Give the exact values.sin 0=cos 0=tan 0=87
We can use the definition:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]Looking at the figure we can see the values:
But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it
[tex]\begin{gathered} \text{hypotenuse = }\sqrt[]{7^2+8^2} \\ \\ \text{hypotenuse = }\sqrt[]{113} \end{gathered}[/tex]Now we have the hypotenuse we can find all values
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}}=\frac{8}{\sqrt[]{113}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}}=\frac{7}{\sqrt[]{113}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{7} \end{gathered}[/tex]please help this is very difficult
Answer:
x=-6. y=6. xy=-36
x=-2. y=-3. xy=6
x=1. y=2. xy=2
Given Hx)= vx and g(x) = \» ,which is the graph of (fºg)(x)?-2-222&DONE
Answer:
Step-by-step explanation:
A composite function is created when one functions is substituted into another function.
Given:
[tex]\begin{gathered} f(x)=\sqrt[]{x}\text{ and g(x)=}\lvert x\rvert \\ \text{Then, (f }\circ g)(x)\text{ would be f(g(x))} \end{gathered}[/tex]Therefore,
[tex](f\circ g)(x)=\sqrt[]{\lvert x\rvert}[/tex]Now, graphing this function...
Find the areas of the figures for parts (a) and (b) below.
SOLUTION:
Case: Area of plane shapes
Method:
a) Parallelogram
To find the area we need to find the perpendicular height (using Pythagoras theorem)
[tex]\begin{gathered} h^2+7^2=25^2 \\ h^2+49=625 \\ h^2=625-49 \\ h^2=576 \\ h=\sqrt{576} \\ h=24 \end{gathered}[/tex]The Area of a parallelogram is given as:
[tex]\begin{gathered} A=bh \\ A=23\times24 \\ A=552\text{ }ft^2 \end{gathered}[/tex]b) Triangle
To find the area of the triangle, we need to find the base first
First, lets find 'a'
[tex]\begin{gathered} a^2+60^2=70^2 \\ a^2+3600=4900 \\ a^2=4900-3600 \\ a^=\sqrt{1300} \\ a=36.06 \end{gathered}[/tex]The base, b
b= 2(a)
b= 2 (36.06)
b= 72.12
The area of the triangle is:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}\times72.12\times60 \\ A=2163.6 \end{gathered}[/tex]Final answer:
a) Parallelogram,
A= 552 square feet
b) Triangle
A= 2163.6 square feet
Write an equation of a line in slope-intercept form that has a slope of -3 and goes through the point (0, 3) O y = 3x - 1 O y = 3x + 2 O y = 3x O y = -3x + 3
ANSWER
y = -3x + 3
EXPLANATION
We want to write the equation in slope-intercept form, which is the form:
y = mx + c
where m = slope; c = intercept
To do that, we have to use the point-slope method:
y - y1 = m(x - x1)
where (x1, y1) = point the line goes through
From the question:
m = -3
(x1, y1) = (0, 3)
So, we have that:
y - 3 = -3(x - 0)
y - 3 = -3x
=> y = -3x + 3
That is the equation of the line in slope-intercept form.
Sara’s dogsMorning: 39, 21, 12, 27, 23, 19, 31, 36, 25Afternoon: 15, 51, 8, 16, 43, 34, 27, 11, 8, 39Comparing the morning and afternoon groups Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds.
Answer;
Medain for morning is 25
Median for evening is 21.5
Explanation;
Here, we want to create frequency tables for each of the given groups
We start with the morning group
The frequency table for it is as follows;
Now, we proceed to the afternoon group
We have this as follows;
Lastly, we will want to get the median value of both groups
To do this, we need to re-arrange the values in the data set in ascending or descending order
For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value
For the morning group, we have;
12, 19,21, 23,25,27,31,36,39
Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right
Thus, we have the median value as 25
The afternoon set, we have it as;
8,8,11,15,16,27,34,39,43,51
We proceed to choose the mid 5th values comig from both ends
We have this as;
We have these values as; 16 and 27
We add these and divide by 2
We have this as;
[tex]\frac{16+27}{2}\text{ = 21.5}[/tex]
Quadrilateral TUVW is a rhombus and m∠SVU=4z+56°. What is the value of z?WTUVS26°z=°Submit
From the question, we were told:
TUVW is a rhombus
Angle SUV = 4z + 56˚
We are asked to find the value of z.
From the diagram, we can see that angle SVU is 90˚
So, to get the value of z, we equate the value of SVU to 90˚
4z + 56˚ = 90˚
subtract 56˚ from both sides:
4z + 56 - 56 = 90 - 56
4z = 34
divide both sides by 4 to make z the subject of formula:
z = 34/4
z = 8.5
Are the triangles congruent using AAS?
True
False
a1. The amount of milk in a one-gallon milk container has a normal distribution with a meanof 1.07 gallons and a standard deviation of 0.12 gallons.Calculate and interpret the z-score for exactly one gallon of milk.
The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
How do the graphs of transformations compared to the graph of the parent function. Need the answer to this
• A ,Reflection
,• A ,Vertical Shift 4 units down
1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:
[tex]f(x)=x^4[/tex]2) Then we can state that this transformed function:
[tex]g(x)=-x^4-8[/tex]We can see the following transformations:
• A ,Reflection,, pointed out by the negative coefficient
,• A ,Vertical Shift 4 units down
As we can see below, to better grasp it:
How many fourteenths are there in 3/ 7 ?
2x 5x+6 please simplify
Answer:
Step-by-step explanation:
Maybe
2x times 11x
The length of a rectangle is 9 inches more than the width. The perimeter is 34 inches. Find the length I need both length and the width of the rectangle
The perimeter is the sum of the side lengths of a polygon. Now, let it be:
• l,: the length of the rectangle
,• w,: the width of the rectangle
Considering the information given and the previous definition, we can write and solve the following system of equations.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ l+w+l+w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]We can use the substitution method to solve the system of equations.
Step 1: We combine like terms in Equation 2.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ 2l+2w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]Step 2: We substitute the value of l from Equation 1 into Equation 2.
[tex]\begin{gathered} 2l+2w=34 \\ 2(9+w)+2w=34 \end{gathered}[/tex]Step 3: We solve for w the resulting equation.
[tex]\begin{gathered} \text{ Apply the distributive property on the left side} \\ 2\cdot9+2\cdot w+2w=34 \\ 18+2w+2w=34 \\ \text{ Add similar terms} \\ 18+4w=34 \\ \text{ Subtract 18 from both sides} \\ 18+4w-18=34-18 \\ 4w=16 \\ \text{ Divide by 4 from both sides} \\ \frac{4w}{4}=\frac{16}{4} \\ w=4 \end{gathered}[/tex]Step 4: We replace the value of w in Equation 1.
[tex]\begin{gathered} \begin{equation*} l=9+w \end{equation*} \\ l=9+4 \\ l=13 \end{gathered}[/tex]Thus, the solution of the system of equations is:
[tex]\begin{gathered} l=13 \\ w=4 \end{gathered}[/tex]AnswerThe length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.
What is the y-intercept of the line that passes through the point (4,-9) with a slope of -1/2
Answer:
The y-intercept b for the derived equation is;
[tex]b=-7[/tex]Explanation:
Given that the line passes through the point (4,-9) and has a slope of -1/2;
[tex]\begin{gathered} \text{slope m=-}\frac{1}{2} \\ \text{ point (4,-9)} \end{gathered}[/tex]Applying the point-slope form of linear equation;
[tex]y-y_1=m(x-x_1)[/tex]substituting the slope and the given point;
[tex]\begin{gathered} y-(-9)=-\frac{1}{2}(x-4) \\ y+9=-\frac{1}{2}x+\frac{4}{2} \\ y+9=-\frac{x}{2}+2 \\ y=-\frac{x}{2}+2-9 \\ y=-\frac{x}{2}-7 \end{gathered}[/tex]Comparing it to the slope intercept form of linear equation;
[tex]y=mx+b[/tex]where;
m = slope
and b = y-intercept
Therefore, the y-intercept b for the derived equation is;
[tex]b=-7[/tex]Bentley has 32 biscuits left in his treat jar. If this represents 4/5 of what he orginally had in the jar, how may treats did he have in the beginning
he had 40 biscuits in the beginning
Explanation
to solve this we can use a rule of three
so
Step 1
let x represents the total treats he had in the beginning , so
[tex]\begin{gathered} if \\ 32\text{ biscuits}\rightarrow\frac{4}{5}of\text{ total } \\ then \\ x\text{ biscuits}\rightarrow total\text{ \lparen1\rparen} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{32}{\frac{4}{5}\text{ }}=\frac{x}{1} \\ \frac{160}{4}=x \\ x=40 \end{gathered}[/tex]therefore,
he had 40 biscuits in the beginning
I hope this helps you
A swim team consists of 5 boys and 5 girls. A relay team of 4 swimmers is chosen at random from the team members. What is the probability that 3 boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then
[tex]10\cdot9\cdot8\cdot7=5040[/tex]if the first member is a girl and the other three needs to be boys, the number of possibilities are
[tex]1\cdot5\cdot4\cdot3=60[/tex]then, divide in order to find the probability
[tex]\frac{60}{5040}=\frac{1}{84}[/tex]72bz +96b2h + 90xbz + 120xbh +
Factoring
Factor the expression:
[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]Divide the expression into two halves:
[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]Factor b^2 from the first group and xb from the second group:
[tex]b^2(72z+96h)+xb(90z+120h)[/tex]Now find the greatest common multiple of 72 and 96:
72= 2*2*2*3*3
96=2*2*2*2*2*2*3
Now we take the common factors with their least number of repetitions:
GCF=2*2*2*3=24
Now we find the GCF of 90 and 120:
90=2*3*3*5
120=2*2*2*3*5
GCF=2*3*5=30
Taking the GCF of each group:
[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]Now we finally take out 3z+4h from both groups:
[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]This last expression can be further factored by taking out 6b from both terms:
[tex]6b(3z+4h)(4b+5x)[/tex]This is the final expression factored as much as possible
Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%Round to two decimal places
Given:
The accumulated value of investment is A = 13,407.58.
The invested amount is P = 12,000.00.
The time period is 4 years and 6 months.
Explanation:
The formula for the accumulated value at r rate of interest is compounded semi-annually.
[tex]A=P(1+\frac{r}{200})^{2\cdot t}[/tex]Substitute the values in the formula to determine the value of r.
[tex]\begin{gathered} 13407.58=12000(1+\frac{r}{200})^{2\cdot4.5} \\ \frac{13407.58}{12000}=(1+\frac{r}{200})^9 \\ 1+\frac{r}{200}=(\frac{13407.58}{12000})^{\frac{1}{9}} \\ \frac{r}{200}=1.01239-1 \\ r=0.01239\cdot200 \\ =2.478 \\ \approx2.48 \end{gathered}[/tex]So the rate of interest is 2.48%.
1. Which of the following would be considered a statistical question? (1) Who was the highest paid athlete in 2020? (2) How much does a gallon of gasoline cost? (3) How many people voted for president in 2016?(4) What are the different types of maple trees?
Looking at the sentences, we have that (1), (2) and (3) are questions that require just one specific answer (For (1) it's a name of a person, for (2) it's a value and for (3) it's also a single value).
But in sentence (4), there are more than one type of maple tree, so we can answer with each type of maple tree, stating the percentage of each type for example.
So the sentence that would be considered a statistical question is (4).