The first term is a=10.
The number of terms is n=44.
The common difference is d=4.
The formula for the sum of n terms is,
[tex]S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]Determine the sum of first 44 terms of the series.
[tex]\begin{gathered} S=\frac{44}{2}\lbrack2\cdot10+(44-1)4\rbrack \\ =22\cdot\lbrack20+172\rbrack \\ =22\cdot192 \\ =4224 \end{gathered}[/tex]So answer is 4224.
Use a graph to predict the value of jewelry in 7 years.
Solution:
Given that the initial cost price of the jewelry is $2,200.
The rate at which it decreases each year is 12%.
Thus, the exponential decay function is;
[tex]\begin{gathered} y(t)=2200(1-0.12)^t \\ \\ \text{ Where }t\text{ is the time in years.} \end{gathered}[/tex]The graph of the function is;
From the graph;
CORRECT OPTION:
[tex]\approx899.09[/tex]4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.
Based on the half-life, 35.36 mg will remain at 6:00P PM in the body
The amount of the medication that will remain at 6:00P PM?The details that complete the question are added as an attachment
From the question, we have
Initial dosage = 200 mg
This means that
M = 200
Also, we have
Initial time =1 : 00 pm
This means that the number of hours, is
n = 6pm - 1pm
n = 5
Recall that the function is given as
R = M(0.5)ⁿ/²
So, we have the following equation
R = 200 x (0.5)⁵/²
Evaluate the quotient of the exponents
So, we have the following equation
R = 200 x (0.5)².⁵
Evaluate the products
R = 35.36 mg
Using the above computation as a guide, we have the remaining amount to be 35.36 mg
Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg
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What is the solution to the equation below?A.x = -1B.x = 0C.x = -5D.x = 3
We must solve the following equation for x:
[tex]x+3=\sqrt{3-x}[/tex]We can square both sides of the equation so we can get rid of the radical:
[tex]\begin{gathered} (x+3)^2=(\sqrt{3-x})^2 \\ (x+3)^2=3-x \end{gathered}[/tex]We expand the squared binomial on the left:
[tex]\begin{gathered} (x+3)^2=x^2+6x+9=3-x \\ x^2+6x+9=3-x \end{gathered}[/tex]Then we substract (3-x) from both sides:
[tex]\begin{gathered} x^2+6x+9-(3-x)=x-3-(3-x) \\ x^2+6x+9+x-3=0 \\ x^2+7x+6=0 \end{gathered}[/tex]Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our case a=1, b=7 and c=6 so we get:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot6}}{2\cdot1}=\frac{-7\pm\sqrt{49-24}}{2}=\frac{-7\pm\sqrt{25}}{2}=\frac{-7\pm5}{2} \\ x=\frac{-7+5}{2}=-1\text{ and }x=\frac{-7-5}{2}=-6 \end{gathered}[/tex]So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:
[tex]\sqrt{3-x}[/tex]Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:
[tex]x+3\ge0\rightarrow x\ge-3[/tex]From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.
AnswerThen the answer is option A.
Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance
Given
n= 5
p = 0.7
Find:
a. mean
b. variance
sol:
Mean d
[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]Need answer if you could show work would be nice
In the Polynomial function f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]
So all the zeros of f(x) algebraically
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].
Step: 1
Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]
[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]
Step: 2
Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]
[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]
Step: 3
so for finding zeros of
[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]
[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]
Explanation: Please refer to solution in this step.
Answer:
So required zeros of
[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]
What is polynomial function?A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means term, and so when combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.
The polynomial function in standard form is:
f(x) = [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]
This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.
The three most common polynomials we usually encounter are
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Andrea invites 12 cousins 6 aunts 4 brothers 2 sisters what fraction of her party guests are cousins?
To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.
She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.
Then:
[tex]\frac{nº\text{cousins}}{\text{total guests}}=\frac{12}{24}[/tex]Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12
[tex]\frac{12\div12}{24\div12}=\frac{1}{2}[/tex]The fraction
In the figure below, ZYZA and _YZX are right angles and _XYZ and ZAYZ arecongruent. Which of the following can be concluded about the distance frompoint A from point Z using Thales's method?O A. The distance between points A and Z is the same as the distancebetween points X and Z.B. The distance between points A and Z is the same as the distancebetween points A and Y.O C. The distance between points A and Z is the same as the distancebetween points Yand Z.D. The distance between points A and Z is the same as the distancebetween points X and Y.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} \angle YZA=90^{\circ} \\ \angle YZX=90^{\circ} \\ \angle XYZ\cong\angle AYZ \end{gathered}[/tex]Thale's method shows that angles in a triangle opposite two sides of equal length are equal
[tex]undefined[/tex]As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)
A number cube is rolled once, {1,2,3,4,5,6)Determine the likelihood of each situation,Column AColumn B1.rolling an even numbera. unlikely2.rolling a 7b. impossible3.rolling a number greater than 0Ccertain4.rolling a number that is greater than 2d. likely5.rolling a 2 or 3e equally likely
The likelihood of the following situations:
1. rolling an even number is likely.
2. rolling a 7 is impossible.
3. rolling a number greater than 0 is certain.
4. rolling a number that is greater than 2 is likely.
5. rolling a 2 or 3 is equally likely
Tank A contains a mixture of 10 gallons of water and 5 gallons of pure alcohol tank b has 12 gallons of what and 3 gallons of alcohol how many gallons should be taken from each tank and combiend in order to obtain 8 gallons of a solution countaning 25% alcohol
The volume from tanks A and B are taken as 3 and 5 gallons respectively.
Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B = 1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40 + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3
Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.
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the lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams . how many calories would this be? if you don’t know , don’t respond
There would be 91.8 calories in 27 grams.
Define unitary method.The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.
Given,
Calories per serving = 25
Serving size = 85 grams
Calories per serving using unitary method:
Dividing,
[tex]\frac{85}{25}[/tex]
3.4
Calories per serving using unitary method is 3.4 calories.
Now, we have 27 grams,
Multiplying:
27 (3.4)
91.8
There would be 91.8 calories in 27 grams.
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of a sample of 200 students surveyed,38 students said the soccer was their favorite sport what percent of the students in the sample prefer soccer 19% 38%40%76%
Out of 200 students surveyed, 38 said that soccer was their favorite sport.
The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:
200 students____100%
38 students _____ x%
Both relationships are at the same ratio so that:
[tex]\frac{100}{200}=\frac{x}{38}[/tex]To determine the percentage multiply both sides by 38:
[tex]\begin{gathered} 38\cdot\frac{100}{200}=38\cdot\frac{x}{38} \\ 19=x \end{gathered}[/tex]The percentage of students surveyed that like soccer is 19%
Jenny wants to earn $1,300by the end of the summer. How much more will she need to earn to meet her goal?
The most appropriate choice for subtraction of natural numbers will be given by-
Jenny needs $1172.95 to earn her goal.
What is subtraction?
At first, it is important to know about natural numbers.
Natural numbers are integers which are greater than or equal to 1
One of the operations on natural number is subtraction
The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.
Amount of money Jennyy had before = $127.05
Amount of money Jenny wants to earn = $1300
Amount of money Jenny needs to earn her goal = $(1300 - 127.05)
= $1172.95
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Complete Question
Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?
(Jenny had $127.05 before.)
what is the approximation of 3√200
Given the expression:
[tex]\text{ }\sqrt[3]{200}[/tex]Let's simplify the expression and convert its decimal form to get its approximation.
We get,
[tex]\text{ }\sqrt[3]{200}\text{ = }\sqrt[3]{8\text{ x 25}}[/tex][tex]\text{ =2 }\sqrt[3]{25}[/tex]In decimal form:
[tex]\text{ 2 }\sqrt[3]{25}\text{ = 2 x 2.92401773821 = 5.84803547643 }\approx\text{ 5.8}[/tex]Therefore, the approximate equivalent of 3√200 is 5.8.
Given f(x)=3x+2 find f(-4)
Step-by-step explanation:
i think it will satisfied you
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Describe a situation that can be represented by the expression –15 + 8.
Answer:
-7
Step-by-step explanation:
Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).
can anyone help me?
solve using system of linear equations using elimination
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
The values of the variables are x = 2, y = -2 and z =0
How to solve the system of equations?From the question, the system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Subtract the second equation from the third
This action will eliminate (y)
So, we have
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
Evaluate
-x + z = -2
Make x the subject
x = z + 2
Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Evaluate
-2z - y = 2
-z + 3y = -6
Double -z + 3y = -6
-2z + 6y = -12
Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z
7y = -14
Divide
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the solution is x = 2, y = -2 and z =0
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ind the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
ANSWER
x = 10.2
EXPLANATION
In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.
With the given information, we can use the cosine of the angle to find the missing value,
[tex]\cos\theta=\frac{adjacent\text{ }leg}{hypotenuse}[/tex]In this problem,
[tex]\cos22\degree=\frac{x}{11}[/tex]Solving for x,
[tex]x=11\cdot\cos22\degree\approx10.2[/tex]Hence, the value of x is 10.2, rounded to the nearest tenth.
discriminant for 2n^2+8n+1=-7
The given equation is
[tex]\begin{gathered} 2n^2+8n+1=-7 \\ 2n^2+8n+1+7=0 \\ 2n^2+8n+8=0 \end{gathered}[/tex]Where a = 2, b = 8, and c = 8.
The discriminant formula is
[tex]D=b^2-4ac[/tex]Let's replace the values
[tex]D=(8)^2-4(2)(8)=64-64=0[/tex]The equation has one real solution.Reflect the following figure across the x-axis: S: (0, -3), T: (3, 1), U: (4, -3)
We are given the following coordinates.
[tex]\begin{gathered} S(0,-3) \\ T(3,1) \\ U(4,-3) \end{gathered}[/tex]We are asked to reflect them across the x-axis.
Recall that the rule for reflection across the x-axis is given by
[tex](x,y)\rightarrow(x,-y)[/tex]As you can see, the y-coordinate gets reversed.
Let us apply this rule on the given coordinates S, T, U
[tex]\begin{gathered} S(0,-3)\rightarrow U^{\prime}(0,3) \\ T(3,1)\rightarrow T^{\prime}(3,-1) \\ U(4,-3)\rightarrow U^{\prime}(4,3) \end{gathered}[/tex]Therefore, the above coordinates are reflected over the x-axis.
You need a quarter of a pumpkin
to make a pie. How many pies
can you make with three and a
half pumpkins?
Answer: 14
Step-by-step explanation:
1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.
1 pumpkin = 4/4
3.5 pumpkins = 14/4
If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.
I need help with my math homework question please. Plus it has a second part of the question
The given quadratic equation is
y = - x^2 + 25
a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.
Leading coefficient = - 1
Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is
Down
b) The standard form of a quadratic equation is
y = ax^2 + bx + c
By comparing both equations,
a = - 1
b = 0
c = 25
The formula for calculating the x coordinate of the vertex of the graph is
x = - b/2a
By substituting the given values,
x = - 0/2 * - 1 = 0
We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have
y = - 0^2 + 25
y = 25
The coordinate of the vertex is (0, 25)
c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have
- x^2 + 25 = 0
x^2 = 25
Taking the square root of both sides,
x = square root of 25
x = ± 5
Thus, the x intercepts are
(5, - 5)
d) The y intercept is the value of y when x = 0
Substituting x = 0 into the orignal equation,
y = - 0^2 + 25
y = 25
y intercept = (0, 25)
e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have
y = - (6)^2 + 25 = - 36 + 25
y = - 11
We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below
If lines L=4x and M=x are perpendicular, what is the value of x?
Those angles are complementary, therefore, we can conclude:
[tex]\begin{gathered} 4x+x=90 \\ add_{\text{ }}like_{\text{ }}terms: \\ 5x=90 \\ Solve_{\text{ }}for_{\text{ }}x: \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]Answer:
x = 18
2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?
Given a principal P, compounded anually at r% for t years. Then the
if an above ground graden is the shape of triangular pyramid measuring.the base is a right triangle with adjacent lengths measuring 5feet and 8feet. the height of the pyramid is 1.5feet. the organic soil cost $1.20 per cubic foot. how much will it cost to fill the graden fully
Solution
The volume for a triangular pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]And the Base is given by:
[tex]B=\frac{1}{2}(5)(8)[/tex]And since h= 1.5 ft we have this:
[tex]V=\frac{1}{6}(5\cdot8)\cdot1.5ft^3=10ft^3[/tex]And then we can find the total cost like this:
[tex]C=10ft^3\cdot\frac{1.2\text{ dollars}}{1ft^3}=12dollars[/tex]Then the final answer would be 12$
a storage container for oil is in the shape of a cylinder with a diameter of 10ft and a height of 17ft. what is the volume if the storage container in cubic feet?
To calculate the volume, w will use the formula:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question,
diameter = 10
This implies that; r=d/2 = 10/2 = 5
h = 17
susbtitute the values into the formula
[tex]V=\pi\times5^2\times17[/tex][tex]=425\pi\text{ cubic feet}[/tex]If we substitute the value of pie= 22/7
[tex]V=\frac{22}{7}\times425[/tex][tex]\approx1335.71\text{ cubic f}eet[/tex]Out of 3500 students at a college 1760 are enrolled in a computer class. What is the per cent of students taking the computer class?
Using percentages we can conclude that 50.2% of students are taking a computer class.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage of students taking computer classes:
The total number of students is 3500.The number of students enrolled in a computer class is 1760.Now, calculate as follows:
1760/3500 × 1000.502 × 10050.2Therefore, using percentages we can conclude that 50.2% of students are taking a computer class.
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Determine the shape when the following points are graphed one a coordinate plane. A(-3, 1), B(2, 1), C(2, 4), D(-3, 4)
The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).
The image below shows the figure formed by these points.
As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.
Therefore, the answer is "rectangle".I only need help for letter b, the question is on the picture
Part B
Remember that
z =(x - μ)/(σ/√n)
where
n=21
we have
μ=1,700
σ=200
For X=1,500
Find out the value of Z1
Z1=(1,500-1,700)/(200/√21)
Z1=-4.5826
For X=1,900
Z2=(1,900-1,700)//(200/√21)
Z2=4.5826
Using a z-score table value
P(1,500therefore
The answer is 21 out of 21
can you solve for x and y y=4x-11=x+13
x = 8, y = 21
Explanations:The given equation is:
y = 4x - 11 = x + 13
This can be splitted into two equations as:
y = 4x - 11..........(1)
y = x + 13..........(2)
Substitute equation (1) into equation (2)
4x - 11 = x + 13
4x - x = 13 + 11
3x = 24
x = 24/3
x = 8
Substitute the value of x into equation (1)
y = 4x - 11
y = 4(8) - 11
y = 32 - 11
y = 21
x = 8, y = 21
What would -5/6 be when turned into a decimal?
Answer:
answer is -0.8333
round about -0.834
Step-by-step explanation: I hope this helps.
Answer: