Answer:
The ninth term is -0.75.
Step-by-step explanation:
Let's write the actual formula for this arith. seq.
It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.
Here, a(n) = -2.75 + (n - 1)(0.25)
So the ninth term of this sequence is
a(9) = -2.75 + (9 - 1)(0.25
= -2.75 + 8(0.25)
= -2.75 + 2
= -0.75
The ninth term is -0.75.
Answer:
[tex]a_9=-0.75[/tex]
Step-by-step explanation:
The given sequence has the first term, [tex]a_1=-2.75[/tex] and d=0.25
The general formula for an arithmetic sequence is given by;
[tex]a_n=a_1+d(n-1)[/tex]
Since we want to find [tex]a_9[/tex], it means n=9
We substitute the given values into the formula to obtain;
[tex]a_9=-2.75+0.25(9-1)[/tex]
[tex]a_9=-2.75+0.25(8)=-0.75[/tex]
Hence, the 9th term is
[tex]a_9=-0.75[/tex]
bill and julio are selling wrapping paper for a school fundraiser. customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. bill sold 8 rolls of plain wrapping paper and 10 rolls of shiny wrapping paper for a total of $328. julio sold 9 rolls of plain wrapping paper and 2 rolls of shiny wrapping paper for a total of $184. find the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper
Answer:
Plain rolls: $16
Shinny rolls: $20
Step-by-step explanation:
So, we have 2 equations to start with, let p = plain rolls and s = shinny rolls:
1) 8p + 10s = 328
2) 9p + 2s = 184
We need to isolate one variable, usually I go for the one with the lowest multiplicative... so let's go for the '2s' and isolate the s from equation 2.
2s = 184 - 9p
3) s = (184 - 9p) / 2
And let's place that s equivalent into the first equation:
8p + 10 (184 - 9p)/2 = 328
8p + 5(184 - 9p) = 328
8p - 45p + 920 = 328
-37p = -592
p = 16
Then we go into any of the 3 equations to get the value of s. Let's take the 3rd equation, it will be simpler:
s = (184 - 9p) / 2 = (184 - 9*16) / 2
s = (184 - 144)/2 = 40/2 = 20
Then last step, we enter the values for s and p in one of the first equations to validate it. We haven't worked with first equation, so let's use that one:
8p + 10s = 328
8 (16) + 10 (20) = 328
128 + 200 = 328
328 = 328
Confirmed!
you have $47 to spend at the music store. Each cassette tape costs $5 and each CD cost $10. write a linear inequality that represent this situation. let x represent the number of tapes and y the number of CDs
Answer:
47 is greater than or equal to 5x+10y
Step-by-step explanation:
you can't spend more than $47 but you can spend less than or equal to that amount.
Answer:5x+10y=47
Step-by-step explanation:
Given
$47 money needed to spend
Each cassette tape cost $5
and each CD cost $10
Given no of cassette be x and no of CD be y
Thus cost of x cassette is 5x
cost of Y CD's 10y
Total cost=5x+10y
5x+10y=47
A rectangle's length and width are in a ratio of 5:2. The area is 160 square centimeters. What are the length and width?
If you could solve this please do so asap
Answer: The length and width are 20 square centimeters and 8 square centimeters
Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.
Answer:
length = 20 cm and width = 8 cmStep-by-step explanation:
l - length
w - width
length and width are in a ratio of 5:2
[tex]\dfrac{l}{w}=\dfrac{5}{2}[/tex] cross multiply
[tex]2l=5w[/tex] divide both sides by 2
[tex]l=\dfrac{5w}{2}[/tex]
the area is 160cm²
[tex]lw=160[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}l=\dfrac{5w}{2}&(1)\\lw=160&(2)\end{array}\right[/tex]
Substitute (1) to (2):
[tex]\left(\dfrac{5w}{2}\right)(w)=160\\\\\dfrac{5w^2}{2}=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=\sqrt{64}\\\\w=8[/tex]
Put the value of w to (1):
[tex]l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20[/tex]
Suppose that the local sales tax rate is 7% and you purchase a car for 11,100 how much tax is paid?
Answer:
11877
Step-by-step explanation:
11100 * 7% = 777
11100 + 777 = 11877
When you multiply by 7%, you get the amount of additional tax. You add this to the original amount to get the answer.
|5−4(x+2)| =3
PLZ ANSWER!
Answer:
5-4(x+2)=3
1(x+2)=3
1x+2=3
3-2=1
Step-by-step explanation:
x=1
Choose the linear inequality that describes the graph. The gray area represents the shaded region.
y > –5x – 3
y > –5x + 3
y > –3x + 5
y < –5x + 3
Answer:
y > –5x + 3
Step-by-step explanation:
we know that
1) The solution of the inequality is the shaded area above the dashed line
so
The linear inequality could be
y > –5x – 3
y > –5x + 3
y > –3x + 5
2) The slope of the dashed line is negative ----> the three options have slope negative
3) The y-intercept of the dashed line is (0,3)
therefore
The linear inequality is
y > –5x + 3
Answer:
[tex]y>-5x+3[/tex]
Step-by-step explanation:
To find the linear inequality , Let pick two points from the graph
Lets pick (0,3) and (1,-2)
Lets find out slope using the points
[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]slope =\frac{-2-3}{1-0}=-5[/tex]
Slope m= -5
y intercept b= 3
Equation of the line is y=mx+b
[tex]y=-5x+3[/tex]
Now we look at the shaded part. we use test point (0,0)
(0,0) is not in the shaded region
[tex]y=-5x+3[/tex]
[tex]0=-5(0)+3[/tex]
0 >3 is false
[tex]y>-5x+3[/tex]
In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.
What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
answer:The z-score for 2,500 g is –2.
According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.
5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.
Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.
The z-score for 2,500 g is –2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.
2.5% of babies weigh less than 2,500g.
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within 1 standard deviation from the mean, 95% of the values are within 2 standard deviation from the mean and 99.7% are within 3 standard deviation from the mean.
Given that mean (μ) = 3,500 g and a standard deviation of σ = 500 g.
95% of babies have a birth weight of between two standard deviation = 2,500 g and 4,500 gHence 2.5% of babies weigh less than 2,500g.
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You have violin lessons every fourth day and singing lessons every
fifth day. Today you have both lessons. In how many days will you
have both lessons on the same day again?
Answer:
Every 20 days.
Step-by-step explanation:
I just did 5 times 4 to get the answer
In 20 days there will be both lessons on the same day again.
What is combination?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given:
Violin class= 4th day
singing lesson= 5th day
So, the possible number of days on which we have both violin and singing class
=4 x 5
=20 days
Hence, 20 days there will be both lessons on the same day again.
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Find u•v when u= 12i+4j and v=15i-5j
Answer:
180i^2 - 20j^2
Step-by-step explanation:
u.v
(12i+4j) . (15i-5j)
12i(15i-5j) + 4j(15i-5j)
180i square -60ij + 60ij-20j square
180i^2 - 20j^2
The value of the dot product of the two vectors is u · v = -160.
What are vectors?The product of vectors can refer to several different operations, including the dot product, cross product, and scalar multiplication.
Dot Product:
The dot product of two vectors u and v is a scalar given by the formula:
u · v = ||u|| ||v|| cos θ
We have,
To find the dot product of two vectors, we need to multiply their corresponding components and add up the results:
u · v
= (12i + 4j) · (15i - 5j)
= 12i · 15i + 12i · (-5j) + 4j · 15i + 4j · (-5j)
= 180i^2 - 60ij + 60ij - 20j² [since i² = j² = -1]
= 180(-1) - 20(-1) [since ij = ji = 0]
= -160
Therefore,
The value of the dot product of the two vectors is u · v = -160.
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Gayle and Jerry had some money. After their mother gave each of them $20, Gayle had twice as much money as Jerry and Jerry had $50 less than Gayle. How much money did Gayle have at first?
Answer:
$100
Step-by-step explanation:
To find out how much money Gayle initially had, we solved the two equations provided by the problem: G + 20 = 2(J + 20) and J + 20 = G + 20 - 50. Solving these equations, it was found that Gayle initially had $90.
Explanation:The question is asking us to figure out how much money Gayle had before their mother gave them each $20. Let's denote the amount of money Jerry initially had as J and the amount of money Gayle initially had as G. According to the problem, after the mother gave them $20 each, Gayle had twice the amount of Jerry's, which mathematically translates to G + 20 = 2(J + 20). Likewise, Jerry had $50 less than Gayle, which can be written as J + 20 = G + 20 - 50. Thus we are given a system of two equations that we can solve simultaneously.
Both equations can be simplified to G = 2J + 20 and J = G - 50. By substituting J = G - 50 in the first equation, we can solve for G to get G = 2(G - 50) + 20 which further simplifies to G = $90. Thus, Gayle initially had $90.
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PLEASE HELP 14 POINTS
[tex] \frac{27}{30} \times 100\% \\ = 90\%[/tex]
Approximately 90 percent voted for her
If P (x,y) is the point on the unit circle defined by real number 0, then csc0=_.
Answer:
cscθ = [tex]\frac{1}{y}[/tex]
Step-by-step explanation:
cscθ = [tex]\frac{Hypotenuse}{opposite}[/tex]
For a unit circle, radius = 1
hence, hypotenuse = 1
opposite = y
cscθ = [tex]\frac{1}{y}[/tex]
What is the direct variation equation iffy varies directly with x and y = 12 when x= 6
Answer:
y = 2x
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 12 when x = 6
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence
y = 2x ← equation of variation
Can someone please help me
Answer:
Step-by-step explanation:
abs(x)>0
This statement is false because what happens when x = 0? For all other instances, the statement is true, but not for 0.
Zero is not greater than itself.
Please explain your answer as well. THX!!
Answer:
1
Step-by-step explanation:
sec(x)*cos(x) + cos(x)-1/(sec(x))
We know that sex(x) = 1/(cos(x))
substitute it in our expression.
1/(cos(x)) * cos(x) + cos(x) - 1/(1/cos(x)) = 1+cos(x) - cos (x)= 1
ANSWER
A. 1
EXPLANATION
The given trigonometric expression is
[tex] \sec(x) \cos(x) + \cos(x) - \frac{1}{ \sec(x) } [/tex]
Recall and use the following reciprocal identities.
[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]
and
[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]
When we apply these identities, we get
[tex] \frac{1}{ \cos(x) } \times \cos(x) + \cos(x) - \cos(x) [/tex]
This simplifies to:
[tex]1 + 0 = 1[/tex]
The correct choice is A
Analyze the diagram below and complete the in destructions that follow
Answer:
option D
8√2
Step-by-step explanation:
Given in the question a right angle triangle,
hypotenuse = x
height = 8
We can use trigonometry identity to solve x
we know that,
sinФ = opposite / hypotenuse
sin(45) = 8 / x
x = 8 / sin(45)
x = 8√2
twice the difference of a numbrr and 8 is equal to 2.twice the difference of a number and 8 is equal to 2
Answer:
2(x-8)=8
x=12
Step-by-step explanation:
The equation for the given statement is 2(x-8)=2.
The given statement "Twice the difference of a number and 8 is equal to 2
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, the difference between a number and 8 can then be written as 'x-8'. Twice that amount would be 2(x-8). If it's equal to 2, you can say 2(x-8)=2.
Therefore, the equation for the statement is 2(x-8)=2.
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Help please I can’t solve
Answer:
IT would be 6 because 10 X 6 = 60 just take away the 0
Step-by-step explanation:
find the sum of -6/ab + a^2/b^2
Answer:
[tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)
Step-by-step explanation:
[tex]\frac{-6}{ab} + \frac{a^{2} }{b^{2} }[/tex]
= [tex]\frac{-6b + a^{3} }{ab^{2} }[/tex]
= [tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)
I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make
Answer:
[tex]4\pi[/tex]
or
12.57
Step-by-step explanation:
I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make
Essentially, you are attempting to find the area of a circle with a radius of 2 meters.
The formula for an area of a circle is [tex]\pi r^2[/tex], or pi times radius squared.
Plugging in 2 meters as your radius, that gets your answer to be [tex]4\pi[/tex], or 12.57 in decimal.
Please answer photo below thank you :’)
Answer:x2_>16 B.
Step-by-step explanation:
For this case we will show that the correct option is option C.
[tex]x ^ 2 \leq16[/tex]
We find the value of the variable "x":
We apply root to both sides of the equation to eliminate the exponent:
[tex]x \leq \pm \sqrt {16}\\x \leq \pm4[/tex]
We found the first solution with the positive value:
[tex]x \leq4[/tex]
We use the negative value to find the other solution. Since it is an inequality, the sign of the inequality changes in the negative portion of the solution.
[tex]x \geq-4[/tex]
So, the roots are:
[tex]x_ {1} \geq-4\\x_ {2} \leq + 4[/tex]
The solution is given by the values of "x" greater than or equal to -4 and less than or equal to 4
Answer:
Option C
suppose that f(x) = x^2 and g(x) = 2/5 x^2 which statement best compares the graph of g(x) with the graph of f(x) A.the graph of g(x) is the graph of f(x) compressed vertically and flipped over the x-axis b.the graph of g(x) is the graph of f(x) compressed vertically c. the graph of g(x) is the graph of f(x) stretched vertically and flipped over the x-axis
Answer:
b.the graph of g(x) is the graph of f(x) compressed vertically
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
and
[tex]g(x)=\frac{2}{5}x^2[/tex]
This is a transformation in the form
[tex]y=a*f(x)[/tex] where [tex]a=\frac{2}{5}[/tex]
Since 0<a<1, the graph of f(x) is compressed vertically by a factor of
[tex]\frac{2}{5}[/tex]
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
When the graph of the two function f(x) and g(x) is plotted, then it can be observed that the graph of g(x) is the graph of f(x) compressed vertically.
Hence, the correct option is B.
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look at picture and plzz help me
Answer: A
Step-by-step explanation:
factor out the greatest perfect foot factorthe root of a product is equal to the product of the roots of eachotherreduce the index of the radical and exponet with 5For this case we must simplify the following expression:
[tex]\sqrt [5] {224x ^ {11} * y ^ 8}[/tex]
We follow the steps below:
We rewrite 224 as the product of: 32 * 7
[tex]\sqrt [5] {32 * 7 * x ^ {11} * y ^ 8} =[/tex]
We rewrite [tex]32\ as\ 2 ^ 5, x^{11}\ as\ x * x^{10}:[/tex]
[tex]\sqrt [5] {2 ^ 5 * 7 * x ^ {10} * x * y ^ 8} =[/tex]
We rewrite [tex]x^{10}[/tex] as [tex](x ^ 2) ^ 5,[/tex] we also rewrite [tex]y ^ 8[/tex] as [tex]y ^ 5 * y ^ 3:[/tex]
[tex]\sqrt [5] {2 ^ 5 * 7 * (x ^ 2) ^ 5 * x * y ^ 5 * y ^ 3} =[/tex]
We reorder:
[tex]\sqrt [5] {2 ^ 5 * (x ^ 2) ^ 5 * y ^ 5 * 7 * x * y ^ 3} =\\\sqrt [5] {(2 * x ^ 2 * y) ^ 5 * (7 * x * y ^ 3)} =[/tex]
We take the terms of the radical considering that: [tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
[tex]2 x ^ 2y \sqrt [5] {7 x y ^ 3}[/tex]
Answer:
Option A
PLEASE HELP BEEN HERE for 30 minutes. GET A EASY 30 POINTS!
Replace x with 3 and solve for Y.
If y equals 8 in both equations, then it is a solution.
y = -5(3) +1 = -15+1 = -14
-14 does not equal 8 , so it is not a solution.
No because -5• 3 +1 does not equal 8 makings it impossible for it to work for that equation. Then 3•3-2 doesn’t equal 8 either so (3,8) is not a solution for these equations
The weights of nine different cats in pounds were used to create the box plot above. Which of the following is the interquartile range of the set of weights?
A. 11
B. 3
C. 1.5
D. 7
Answer:
the answer is B: 3
Step-by-step explanation:
you look at the verticle line on the left side of the box which represents the lower quartile then to the right of the verticle line represents the upper quartile
To find the interquartile range, subtract the lower quartile, 9.5, from the upper quartile, 12.5
12.5 - 9.5 = 3
Please help please help
Answer:
D
Step-by-step explanation:
The tenth column value is the first after the decimal point, that is 3
To round the required value of 3
• If the value following 3 ≥ 5, round 3 up to 4
• If the value following 3 < 5 , then leave as 3
Here the value following 3 is 5 so round 3 up to 4
All other digits remain unchanged.
Thus
3, 295.351 ≈ 3, 295.4 → D
By visual inspection, determine the best-fitting regression model for the data plot below.
A) Exponential
B) No pattern
C) Linear decreasing
D) Linear increasing
Answer:
A) exponential
Step-by-step explanation:
It is in a curving pattern which indicates exponential. Linear is a straight line.
The best-fitting regression model for the considered data plot is given by: Option A: Exponential.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).
Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.
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Angelos pet rabbit weighs 1 pound less than twice the weight of Carmen’s pet rabbit.Angelos rabbit weighs 9 pounds. Write an equation that can be used to find w, the weight of Carmen’s pet rabbit. I need the answer plsss???!!!
The required weight of Carmen's rabbit is given as 5 pounds and the equation is given as 9 = 2x -1.
As mentioned in the question,
Angelos's pet rabbit weighs 1 pound less than twice the weight of Carmen’s pet rabbit. Angelos rabbit weighs 9 pounds.
The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the weight of the Carmen's be x,
According to the question,
Angelos pet rabbit weighs,
9 = 2x -1
x = 5
Thus, the required weight of Carmen's rabbit is given as 5 pounds.
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To find the weight of Carmen's pet rabbit, an equation is set up: 2w - 1 = 9, where w represents the unknown weight of Carmen's rabbit. Solving the equation, we find that Carmen's rabbit weighs 5 pounds.
Explanation:To find the weight of Carmen's pet rabbit, we first need to translate the given information into a mathematical equation. The problem states that Angelo's pet rabbit weighs 1 pound less than twice the weight of Carmen's pet rabbit and Angelo's rabbit weighs 9 pounds. Let's denote the weight of Carmen's rabbit as w. The relationship can be written as:
2w - 1 = 9
To solve for w, we add 1 to both sides of the equation:
2w - 1 + 1 = 9 + 1
2w = 10
Now, we divide both sides by 2 to get the weight of Carmen's rabbit:
2w / 2 = 10 / 2
w = 5
Therefore, Carmen's pet rabbit weighs 5 pounds.
Solve the follwoing questions: a. 17 x 10 = b. 24 x 100 = c. 6 x 1000 =
Answer:
a. 17 x 10 = 170
b. 24 x 100 = 2,400
c. 6 x 1000 = 6000
Step-by-step explanation:
Answer:
a. 170
b. 2,400
c. 6,000
Step-by-step explanation:
You need to make the multiplications that are indicated in each option:
Option a: you only need to multiply the first factor (17) by the digit that is not zero (1) of the second factor (10), and then write all the zeros that has the second factor:
[tex]17*10=170[/tex]
Option b: you need to multiply the first factor (24) by the digit that is not zero (1) of the second factor (100), and then write all the zeros that has the second factor:
[tex]24*100=2,400[/tex]
Option c: you have to multiply the the first factor (6) by digit that is not zero (1) of the second factor (1000), and then write all the zeros that has the second factor:
[tex]6*1,000=6,000[/tex]
Divide 4200 by a multiple of 10 so that the quotient is also a multiple of 10
Answer:
4200 divided by 10
Step-by-step explanation:
To make 4200 a multiple of ten after dividing it by a multiple of ten, we first find the number of 5's in 4200 to see how many 10's go into 4200. Since 4200 = 6*7*2*2*5*5, we see that there are 2 fives. This means that there are two tens too. Since we have to keep 4200 a multiple of ten after dividing it by another 10. So the only possible way to do that is dividing 4200 by 10.
Dividing 4200 by the power of 10, 100, results in the quotient 42, which is also a multiple of 10. This is achieved by moving the decimal point two places to the left in the number 4200 due to the two zeros in the power of 10.
Explanation:In this mathematics problem, you are asked to divide 4200 by a multiple of 10 such that the result, or quotient, is also a multiple of 10. The key to this problem lies in understanding the concept of dividing by powers of 10.
When you divide a number by a power of 10, you move the decimal point to the left by as many places as there are zeros in the power of 10. So if you wanted to divide 4200 by a multiple of 10 so that the result is also a multiple of 10, you might choose 100 (10^2) as your divisor. Why? Because there are two zeros in the power of 10, which means you move the decimal point two places to the left in the number 4200.
So when you divide 4200 by 100, you get 42 which is a multiple of 10. Therefore, 4200 divided by a multiple of 10 (100 in this case) gives a quotient (42) that is also a multiple of 10.
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