Given the equation:
[tex]y-7.8=5.5[/tex]You need to solve for "y" in order to find its value. In this case, you need to apply the Addition Property of Equality, which states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]Therefore, you need to add 7.8 to both sides of the equation in order to solve for "y":
[tex]\begin{gathered} y-7.8+(7.8)=5.5+(7.8) \\ y=13.3 \end{gathered}[/tex]Hence, the answer is:
[tex]y=13.3[/tex]Use the Distributive Property to rewrite each product below. Simplify your answer.
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
As per the concept of distributive property, the values of
A.) 28 · 63 = 1768
B.) 17 (59) = 1003
C.) 458 (15) = 6870
Distributive property:
Distributive property states that, " multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together."
It can be written as expression like the following,
A( B + C) = AB + AC
Given,
Here we have the expressions,
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
Now, we have to find the solution for this by using the distributive property.
Now, we have to expand the given expressions by using the distributive property then we get,
A) 28. ( 60 + 3) = (28 x 63) + (28 x 3)
=> 1680 + 84
=> 1768
Similarly, we have simplify the next expression as,
B) 17 (59) = 17 x (50 + 9)
As per the distributive property,
17 x (50 + 9) = (17 x 50) + (17 x 9)
=> 850 + 153
=> 1003
Finally, applying the distributive law, we get,
C) 458 (15) = (450 + 8) x 15
=> (450 x 15) + (8 x 15)
=> 6750 + 120
=> 6870
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How many values does the expression 6+(x+3)^2 have?
The solution of a quadratic equation is imaginary.
What are the solutions of a quadratic function?
A quadratic equation with real or complex coefficients has two solutions, called roots.
These two solutions may or may not be distinct, and they may or may not be real.
The solution of the given quadratic function is calculated as follows;
6 + (x + 3)² = 0
subtract 6 from both sides of the equation;
6 + (x + 3)² - 6 = 0 - 6
(x + 3)² = - 6
take square root of both sides
x + 3 = √-6
x + 3 = 6i
x = 6i - 3
Thus, the solution of a quadratic equation can be determined solving for the value of unknown in the equation.
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The table of values represents a quadratic function.What is the average rate of change for f(x) from x=−10 to x = 0?Please help me with this problem so that my son can understand better. Enter your answer in the box.xf(x)−10184−5390−654910204
We are given a quadratic function and the rather than the equation for this function we already have the outputs at each given input as shown in the table provided. This means, for example, for the function given, when the input is -10, the output is 184. Thus the table includes among other values;
[tex]x=-10|f(x)=184[/tex]To calculate the average rate of change we shall apply the formula for the slope (which is also the average rate of change). This is given below;
[tex]\text{Aerage Rate of Change}=\frac{f(b)-f(a)}{b-a}[/tex]Note that the variables are;
[tex]\begin{gathered} f(a)=\text{first input value} \\ f(b)=\text{second input value} \end{gathered}[/tex]The first input value is -10 and the function at that value is 184
The second input value is 0 and the function at that value is -6
We now have;
[tex]\begin{gathered} a=-10,f(a)=184 \\ b=0,f(b)=-6 \end{gathered}[/tex]We can now substitute these into the formula shown nearlier and we'll have;
[tex]\begin{gathered} \text{Ave Rate Of Change}=\frac{f(b)-f(a)}{b-a} \\ =\frac{-6-184}{0-\lbrack-10\rbrack} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-190}{0+10} \\ \end{gathered}[/tex][tex]=\frac{-190}{10}[/tex][tex]\text{Average Rate of Change}=-19[/tex]ANSWER:
The average rate of change over the given interval is -19
In statistics, how do I find the p-value? I understand how to get the z-value. Please help! I am so confused. Thank you in advance!
SOLUTION:
Step 1:
In this question, we are meant to discuss the p-value.
1. The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test).
2.
3. What is the p-value in statistics?
The p-value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true. P-values are used in hypothesis testing to help decide whether to reject the null hypothesis.
4. How do I know when the test is left-tailed, right-tailed, or two-tailed?
Left-tailed test: The critical region is in the extreme left region (tail) under the curve.
Right-tailed test: The critical region is in the extreme right region (tail) under the curve.
5. How do you know when to use a one - tailed or two - tailed test?
This is because a two-tailed test uses both the positive and negative tails of the distribution.
In other words, it tests for the possibility of positive or negative differences. A one-tailed test is appropriate if you only want to determine if there is a difference between groups in a specific direction.
6. The formulae that involves z-score:
7. The formulae that involves p -value and standard deviation:
what is the slope of (12 -18) (-15 -18)
Answer:
m = 0
Step-by-step explanation:
[tex]m=\frac{-18-(-18)}{-15-12)} \\m=\frac{0}{-27} \\m= 0/-27 = 0\\m=0[/tex]
The height of a pole is 15 feet. A line with banners is connected to the top of the poleto a point that is 8 feet from the base of the pole on the ground. How long would theline with banners need to be in order for the pole to be at a 90° angle with the ground?Explain your reasoning.
In order to have a 90º angle (right angle) the length of the line with banners needs to fullfit the Pythagorean theorem: In a right triangle the squared hypotenuse is equal to the sum of the legs squared:
[tex]h^2=l^2+l^2[/tex]In the given situation the hypotenusa is the line with banners, and the legs are the pole and the 8ft ground from the base of the pole to the end of the line with banners:
h= x
l= 15ft
l= 8ft
[tex]x^2=(15ft)^2+(8ft)^2[/tex]Solve the equation to find the value of x:
[tex]\begin{gathered} x^2=225ft^2+64ft^2 \\ x^2=289ft^2 \\ x=\sqrt[]{289ft^2} \\ x=17ft \end{gathered}[/tex]Then, to make a right triangle the length of the line witg banners need to be 17ftcell phone company A charges a fee of $50 per month plus an additional $0.10 for every minute talked. cell phone company B computes its monthly charge by using the equation y=$0.05 + $75 where y is the total cost and X is the number of minutes talked.
We will first write A equation
Let x be the number of minutes
y = 0.10x + 50
Comparing the above with y=mx + b where m is the rate of change
m = 0.10
Company B
y = 0.05x + 75
comparing with y =mx + b
rate of change (m) = 0.05
Hence, company A has a higher rate of change at $0.10
Go on the head 120 eggs delivered to her bakery she used to 98 eggs to bake cakes which equation can she use find the number of eggs r she has left
Yolanda has 120 eggs, but she used 98 eggs
r represents the equation for the number of eggs that she left:
To find this, subtract the total of eggs by the eggs used
Then, r = 120 - 98
Paola says that when you apply the Distributive Property to multiply (3j+6) and (-5j), the result will have two terms. Is she correct?
Explain.
Choose the correct answer below.
A. No, because there will be one j-term
B. Yes, because there will be a j-term and a j²-term
C. Yes, because there will be a j-term and a numeric term
D. No, because there will be one j2-term
The Distributive Property to multiply (3j+6) and (-5j), the result will have two terms because there is a j-term and a j²-term.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
(3j+6) and (-5j)
and it is to multiply using Distributive Property of multiplication :
now, applying that ;
(3j+6) x (-5j)
= 3j x (-5j) + 6 x (-5j)
= -15j² - 30j
It is seen from the above expression that the Distributive Property to multiply (3j+6) and (-5j), the result will have two terms because there is a j-term and a j²-term.
Therefore, option B is the correct answer.
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Solve the system of two linear inequalities graphically.Sy < -2x + 3y > 6x – 9Step 1 of 3: Graph the solution set of the first linear inequality.
The red graph represents y < -2x + 3
The blue graph represents y > 6x - 9
The solutions of the system of inequalities lie on the red-blue shaded
The part which has two colors
Since the first inequality is y < -2x + 3, the shaded is under the line
Since the second inequality is y > 6x - 9, the shaded is over the line
The common shaded of the two colors represents the area of the solutions of the 2 inequalities
The type of boundary lines is dashed
The points on the boundary lines are
For the red line (0, 3) and (4, 0)
For the blue line (0, -9) and (1, -3)
There is a common point on the two lines (1.5, 0)
Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer.
1. angle j and k.
Due to the Converse of Corresponding Angles Postulate, j || k.
2. Angles 2 and 5 are the alternating inner angles of the lines j and k. Given that angle 2 = angle 5,
The Converse of Alternate Interior Angles Theorem states that j || k.
J || K converse alternative interior angles.
what are parallel angles?similarly
3. angle 3 = angle 10 The exterior angles of the lines l and m, respectively, are angle 3 and angle 10. Since the Converse of Alternate Exterior Angles Theorem states that angle 3= angle 10, l || m.
converse alternative exterior angles l || m.
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What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.
The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.
To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:
Houston:
[tex]2.3\cdot10^6[/tex]This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:
[tex]2.3\cdot10^6=2300000[/tex]San Antonio:
[tex]1.5\cdot10^6[/tex]The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:
[tex]1.5\cdot10^6=1500000[/tex]El Paso:
This population is already given in the standard form
[tex]680000[/tex]Corpus Christi:
[tex]3.2\cdot10^5[/tex]This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:
[tex]3.2\cdot10^5=320000[/tex]Now that all values are expressed in the standard form you can add them:
[tex]2300000+1500000+680000+320000=4800000[/tex]In the standard form, the total population of the four cities is 4,800,000 people
To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.
When you use scientific notation you have to write only the digits that are different than zero.
There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:
[tex]4.8\cdot10^6\text{people}[/tex]Please help with this question
The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.
How to find the average velocity and the instantaneous velocity of a stone
The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.
a) Then, the average velocities are determined below:
Case i)
u = [f(1.05) - f(1)] / (1.05 - 1)
u = (18.748 - 18.1) / 0.05
u = 12.96 m / s
Case ii)
u = [f(1.01) - f(1)] / (1.01 - 1)
u = (18.232 - 18.1) / 0.01
u = 13.20 m / s
Case iii)
u = [f(1.005) - f(1)] / (1.005 - 1)
u = (18.166 - 18.1) / 0.005
u = 13.20 m / s
Case iv)
u = [f(1.001) - f(1)] / (1.001 - 1)
u = (18.113 - 18.1) / 0.001
u = 13 m / s
The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.
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Solve the system. Is the answer (3,0) or (0, -1) or no solution or infinitely many solutions?
Given:
[tex]\begin{gathered} \frac{1}{3}x+y=1\ldots..(1) \\ 2x+6y=6\ldots\text{.}(2) \end{gathered}[/tex]Solve the system of equations.
Equation (2) can be simplified as,
[tex]\begin{gathered} 2x+6y=6 \\ \text{Divide by 6 on both sides} \\ \frac{2x}{6}+\frac{6y}{6}=\frac{6}{6} \\ \frac{1}{3}x+y=1\text{ which represents the equation (1)} \end{gathered}[/tex]Moreover, the slope and y-intercept of both the equation of lines are the same.
It shows that the lines are coincident.
The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.
a quadratic function has its vertex at the point (4,6) the function passes through the point (-5,-2) find the quadratic and linear coefficients and the constant term of the function The quadratic coefficient is_____The linear coefficient is_______the constant term is_____
We have to find the equation of the quadratic function.
We know the vertex, located in (4,6), and one point (-5,-2).
The x-coordinate of the vertex (4) is equal to -b/2a, being a the quadratic coefficient and b the linear coefficient.
Now, we have 2 points to define the 3 parameters, so one of the parameters is undefined.
[tex]y=ax^2+bx+c[/tex]We start with the vertex, that we know that is:
[tex]\begin{gathered} x=-\frac{b}{2a}=4 \\ -b=4\cdot2a=8a \\ b=-8a \end{gathered}[/tex]Then, we can write the equation as:
[tex]y=ax^2-8ax+c=a(x^2-8x)+c[/tex]If we replace the point (-5,-2) in the equation, we get:
[tex]\begin{gathered} -2=a((-5)^2-8\cdot(-5))+c \\ -2=a(25+40)+c \\ -2=65a+c \\ c=-2-65a \end{gathered}[/tex]We replace the vertex coordinates and get:
[tex]\begin{gathered} 6=a(4^2-8\cdot4)+c \\ 6=a(16-32)+(-2-65a) \\ 6=-16a-2-65a \\ 6=-81a-2 \\ 81a=-2-6 \\ a=-\frac{8}{81}\approx-0.01 \end{gathered}[/tex]Then, the linear coefficient b is:
[tex]b=-8a=-8\cdot(-\frac{8}{81})=\frac{64}{81}\approx0.79[/tex]And the constant term is:
[tex]c=-2-65a=-2-65\cdot(-\frac{8}{81})=-2+\frac{520}{81}=\frac{-162+520}{81}=\frac{358}{81}\approx4.42[/tex]The quadratic coefficient is a=-0.01
The linear coefficient is b=0.79
the constant term is c=4.42
1 3/8 × 3 2/3=answer must be in simplest fraction form
EXPLANATION
Given the fractions 1 3/8 and 3 2/3
First we need to turn both fractions into improper ones
[tex]1\frac{3}{8}=\frac{11}{8}[/tex][tex]3\frac{2}{3}=\frac{11}{3}[/tex]Now, multiplying both fractions:
[tex]\frac{11}{8}\cdot\frac{11}{3}=\frac{121}{24}[/tex]The answer is 121/24
n a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood
Total
Total
Question content area bottom
Part 1
(a) What is the probability that a randomly selected individual is years of age, given the individual is to buy a product emphasized as "Made in our country"?
The probability is approximately
0.134.
(Round to three decimal places as needed.)
Part 2
(b) What is the probability that a randomly selected individual is to buy a product emphasized as "Made in our country," given the individual is years of age?
The probability is approximately
a) The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy is 0.206
b) The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age is 0.309
c) 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
A random sample is one that is drawn at random from the population, meaning that every member of the population has an equal chance of being picked for the sample. The probability sampling approach is the practice of choosing people at random.
a. Total number of individuals that are neither more nor less likely to purchase = 786
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy =
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals more or less likely to purchase.
= 162/786
= 0.206
b. Total number of individuals 45-54 years of age = 524
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals 45-54 years of age.
= 162/524
= 0.309
c. The number of 18-34 year old individuals more likely to buy = 204
The total number of 18-34 year old individuals = 523
The proportion of 18-34 year old individuals more likely to buy = 204/523
= 0.390
= 39%
The total number of individuals more likely to buy = 1266
The total number of all individuals in the survey = 2123
The proportion of individuals, in general, more likely to buy = 1266/2123
= 0.596
= 59.6%
Therefore, 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
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Your question is incomplete. Please find the missing content below.
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood 18-34 35-44 45-54 55 and over Total
More likely 204 318 334 410 1266
Less likely 27 5 28 11 71
Neither more nor less 292 210 162 122 786
Total 523 533 524 543 2123
a) What is the probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy a product emphasized as "Made in our country"? The probability is approximately _____. (round to three decimal places)
b) What is the probability that a randomly selected individual is neither more nor less likely to buy a product emphasized as "Made in our country", given the individual is 45-54 years of age? The probability is approximately _____. (round to three decimal places)
c) Are 18-34-year-olds more likely to buy a product emphasized as "Made in our country" than individuals in general? Yes or no
What are the values of n in the following equation? Select all that apply. 4n + 2 = 34
The given equation is
[tex]4x+2=34[/tex]First, we subtract 2 from each side
[tex]\begin{gathered} 4x+2-2=34-2 \\ 4x=32 \end{gathered}[/tex]Then, we divide the equation by 4
[tex]\begin{gathered} \frac{4x}{4}=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Hence, the answer is x = 8.If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).
Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.
[tex]\begin{gathered} \sin A=\frac{3}{5},\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=\frac{4}{5} \\ \cos B=\frac{20}{29},\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=\frac{21}{29} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=\frac{\sin A}{\cos A},\tan B=\frac{\sin B}{\cos B} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\frac{\frac{3}{5}}{\frac{4}{5}}+\frac{\frac{21}{29}}{\frac{20}{29}}}{1-\frac{\frac{3}{5}}{\frac{4}{5}}\times\frac{\frac{21}{29}}{\frac{20}{29}}}=\frac{\frac{3}{4}+\frac{21}{20}}{1-\frac{3}{4}\times\frac{21}{20}}=\frac{\frac{9}{5}}{1-\frac{63}{80}}=\frac{\frac{9}{5}}{\frac{17}{80}} \\ \tan (A+B)=8.47 \end{gathered}[/tex]tan (A+B) = 8.47
$85000 is invested at 7.5% per annum simple interest for 5 years. Calculate the simple interest.
From the statement of the problem we know that:
• the principal amount of money invested is P = $85000,
,• the rate per year is 7.5%, in decimals r = 0.075,
,• the time is t = 5 years.
The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:
[tex]I=A-P=P(1+r\cdot t)-P=P\cdot r\cdot t.[/tex]Replacing by the data of the problem we find that the simple interest is:
[tex]I=85000\cdot0.075\cdot5=31875.[/tex]Answer
The simple interest is $31875.
Harriet found the number of At-Bats (AB) using the formula below
Here, we want to get what should have been written as step 1
As we can see from what is presented, she went directly to step 2 without writing out the individual product and summing them
So, we have the step 1 correctly written as;
[tex]0.520\text{ = }\frac{(28)\text{ + (94) +(3) + 240}}{AB}[/tex]The volume of a square-based rectangular cardboard box needs to be at least 1000cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces. Assume that there will be no waste material. The Machinery available cannot fabricate material smaller than 2 cm in length.
We have to find the dimensions of a box with a volume that is at least 1000 cm³.
We have to find the dimensions that require the minimum amount of material.
We can draw the box as:
The volume can be expressed as:
[tex]V=L\cdot W\cdot H\ge1000cm^3[/tex]The material will be the sum of the areas:
[tex]A=2LW+2LH+2WH[/tex]Since the box is square-based, the width and length are equal and we can write:
[tex]L=W[/tex]Then, we can re-write the area as:
[tex]\begin{gathered} A=2L^2+2LH+2LH \\ A=2L^2+4LH \end{gathered}[/tex]Now, we have the area expressed in function of L and H.
We can use the volume equation to express the height H in function of L:
[tex]\begin{gathered} V=1000 \\ L\cdot W\cdot H=1000 \\ L^2\cdot H=1000 \\ H=\frac{1000}{L^2} \end{gathered}[/tex]We replace H in the expression for the area:
[tex]\begin{gathered} A=2L^2+4LH \\ A=2L^2+4L\cdot\frac{1000}{L^2} \\ A=2L^2+\frac{4000}{L} \end{gathered}[/tex]We can now optimize the area by differentiating A and then equal the result to 0:
[tex]\begin{gathered} \frac{dA}{dL}=2\frac{d(L^2)}{dL}+4000\cdot\frac{d(L^{-1})}{dL} \\ \frac{dA}{dL}=4L+4000(-1)L^{-2} \\ \frac{dA}{dL}=4L-\frac{4000}{L^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{dA}{dL}=0 \\ 4L-\frac{4000}{L^2}=0 \\ 4L=\frac{4000}{L^2} \\ L\cdot L^2=\frac{4000}{4} \\ L^3=1000 \\ L=\sqrt[3]{1000} \\ L=10 \end{gathered}[/tex]We now can calculate the other dimensions as:
[tex]W=L=10[/tex][tex]H=\frac{1000}{L^2}=\frac{1000}{10^2}=\frac{1000}{100}=10[/tex]Then, the dimensions that minimize the surface area for a fixed volume of 1000 cm³ is the length, width and height of 10 cm, which correspond to a cube (all 3 dimensions are the same).
Answer: the dimensions are length = 10 cm, width = 10 cm and height = 10 cm.
Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.5,−2,45,...5,−2, 54 ,...Sum of a finite geometric series:Sum of a finite geometric series:Sn=a1−a1rn1−rS n = 1−ra 1 −a 1 r n
Solution:
Given:
[tex]5,-2,\frac{4}{5},\ldots[/tex]To get the sum of the first 7 terms, the formula below is used;
[tex]S_n=\frac{a_1-a_1r^n}{1-r}[/tex]where;
[tex]\begin{gathered} n=7 \\ a_1\text{ is the first term = 5} \\ r\text{ is the co}mmon\text{ ratio=}\frac{-2}{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} S_n=\frac{a_1-a_1r^n}{1-r} \\ S_7=\frac{5-5(-\frac{2}{5})^7}{1-(-\frac{2}{5})} \\ S_7=\frac{5-5(-0.4)^7}{1+\frac{2}{5}} \\ S_7=\frac{5-5(-0.0016384)}{1+0.4} \\ S_7=\frac{5+0.008192}{1.4} \\ S_7=\frac{5.008192}{1.4} \\ S_7=3.57728 \end{gathered}[/tex]Therefore, the sum of the first 7 terms is 3.57728
4x+10=30
solve it please
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30 ( subtract 10 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30
Step 1:
30 - 10 = 4x
20 = 4x
Step 2:
20/4
x=5
Step 3: Prove your answer correct
4(5) + 10 = 30
20 + 10 = 30
x = 5
Kuta Software - Infinite Precalculus Angles and Angle Measure Find the measure of each angle.
Explanation:
We are to draw the angle that is equivalent to 5pi/4
First we need to convert the radian value to degree
Since pi rad = 180degrees
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x = 5/4 * 180
x = 5 * 45
x = 225 degrees
This can also be written as 225 = 180 + 45
225degrees = 180 + pi/4
Note that 180degrees is an angle on a straight line. Find the digaram attached
The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x =
The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.9 in 2011 and 233.2 in 2016. Let x=11 correspond to the year 2011 and estimate the CPI in 2013 and 2014. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is____ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)
The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]can you explain what the 8th question is asking then answer it please
Answer:
Options A and C
Explanation:
We want to find out which arithmetic sequence(s) contain the term 34.
For an arithmetic sequence to contain the term, 34, the corresponding n-value must be an integer.
Option A
Set tn = 34
[tex]\begin{gathered} t_n=6+(n-1)4 \\ 34=6+(n-1)4 \end{gathered}[/tex]Solve for n:
[tex]\begin{gathered} 34-6=4n-4 \\ 28=4(n-1) \\ n-1=\frac{28}{4}=7 \\ n-1=7 \\ n=7+1 \\ n=8 \end{gathered}[/tex]The 8th term of this sequence is 34.
Option B
[tex]\begin{gathered} t_n=3n-1 \\ 34=3n-1 \\ 34+1=3n \\ 35=3n \\ n=\frac{35}{3}=11\frac{2}{3} \end{gathered}[/tex]A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.
Option C
T1 = 12, d=5.5
[tex]\begin{gathered} 12+5.5(n-1)=34 \\ 5.5(n-1)=34-12 \\ 5.5(n-1)=22 \\ n-1=\frac{22}{5.5} \\ n=4+1 \\ n=5 \end{gathered}[/tex]The 5th term of this sequence is 34, therefore, it contains the term 34.
Option D
3,7,11,...
[tex]\begin{gathered} t_1=3 \\ d=7-3=4 \end{gathered}[/tex]Using the nth term of an arithmetic sequence formula:
[tex]\begin{gathered} t_n=t_1+(n-1)d \\ 34=3+4(n-1) \\ 34-3=4(n-1) \\ 31=4(n-1) \\ n-1=\frac{31}{4} \\ n-1=7\frac{3}{4} \\ n=8\frac{3}{4} \end{gathered}[/tex]A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.
The sequences in Options A and C contain the term 34.
how much is 2 gallons in quarts
how much is 2 gallons in quarts
Answer:
8 quarts
Carrie sold 112 boxes of cookies, Megan sold 126 boxes of cookies, Julie sold 202 boxes of cookies, and Ashton sold 176 boxes of cookies. what was the average number of boxes of cookies sold by each individual
Answer:
154 boxes.
Explanation:
To calculate the average number of boxes of cookies sold by each individual, we use the formula:
[tex]\text{Average=}\frac{\text{Sum of all boxes sold}}{\text{Number of individuals}}[/tex]This gives:
[tex]\begin{gathered} \text{Average}=\frac{112+126+202+176}{4} \\ =\frac{616}{4} \\ =154\text{ boxes} \end{gathered}[/tex]The average number of boxes of cookies sold by each individual was 154 boxes.
Rosa receives money from her relatives every year on her birthday. Last year, she received a total of $350. This year, she received $441. What is the percent of increase in Rosa’s annual birthday money?
Answer:
26%
Step-by-step explanation:
use a online percentage calculator
