The kilometres that she has cycled in total by the end of the 18th week is 105.
How to calculate the number of kilometers?Based on the information, this is an arithmetic sequence and the formula is illustrated as
= a + (n - 1)d
where a = first term = 20
d = common difference = 5
n = numbers = 18
Therefore, the 18th term will be:
= a + (n - 1)d
= 20 + (18 - 1)5
= 20 + (17 × 5)
= 20 + 85
= 105
The number of kilometers is 105 kilometers.
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5x^2-25=100 solve by taking square root
Answer:
x=5,−5
Step-by-step explanation:
Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
Which graph represents data used in a linear regression that produces a correlation coefficient closest to -1?
What does the letter "L" stand for in the simulation?
Answer: d
Step-by-step explanation: ion know man but i looked it up and got it right
Using the information found in these tables which of the following statements is true
Please helpppp
What’s the answer plss I really need help
Answer:
The answer is d) 22.4
Step-by-step explanation:
I attached a file below if you want to see the process!
draw a model to represent 2 1/4 and write it as an improrer frrcation
The improper fraction equivalent of the fraction 2 1/4 is 9/4.
Improper fraction:
Basically, the improper fraction is also the fraction where the numerator is greater than or equal to the denominator.
Given,
Here we have the mixed fraction 2 1/4.
And we have to convert this mixed fraction into improper fraction.
The conversion from mixed fraction to an improper fraction will follow the following formula,
numerator = (denominator × whole number) + numerator of mixed fraction
Based on the this rule, the numerator of the improper fraction is,
=> numerator = (4 x 2) + 1
=> numerator = 8 + 1
=> numerator = 9
The denominator will remain same.
Therefore, the resulting improper fraction is 9/4.
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A pet hotel charges $25 per night to keep a dog. When the dog arrives, there is a mandatory $15 examination fee. Part A: Write a function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days. Part B: How much would a 6 night stay cost? Part C: Does a 3 night stay cost half as much as a 6 day stay since it is half the time? Explain in detail!
A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15
B) The total cost to stay for 6 nights is; $165
C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.
How to solve algebra word problems?We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.
A) If the number of nights spent is n, then the function rule here for the total cost is;
T = 25n + 15
B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;
T(6) = 25(6) + 15
T(6) = $165
C) The cost of 3 nights would be;
T(3) = 25(3) + 15
T(3) = $90
This is more than half of the cost of 6 nights.
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Mason went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 15 grams of sugar. Mason purchased a total of 11 bottles of juice and soda which collectively contain 285 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system
The number of soda bottles = 4
The number of sugar bottles = 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
Let the number of soda bottle = x
And, The number of sugar bottle = y
Since, Total number of bottles = 11
So, We can formulate;
⇒ x + y = 11 .... (i)
And, Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
So, We can formulate;
⇒ 45x + 15y = 285 ... (ii)
Multiply by 15 in equation (i) and subtract from (ii), we get;
⇒ 45x + 15y - 15x - 15y = 285 - 165
⇒ 30x = 120
Divide by 30;
⇒ x = 4
Hence, x + y = 11
4 + y = 11
y = 11 - 4
y = 7
So, The number of soda bottles = 4
The number of sugar bottles = 7.
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.25 and the cost of a large greeting card is $4.50. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the Cost of the small greeting card = is $1.25 .
The Cost of the large greeting card =$4.50.
We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.
The Cost of 5 small greeting cards = 6.25
The Cost of 4 large greeting cards = 18
Then the Total cost = $6.25+ $18 =$24.25
Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.
Now, the total cost of x small and y large greeting cards will be;
Cost of x small greeting cards = 1.25x
Cost of y large greeting cards = 4.50y
Total cost = 1.25x + 4.50y
Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
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8/13 x 3 =
SHOW YOUR WORKl
8/13 x 3/1 = 24/13
24 - 13 =11
So, simplified answer is 1 11/13 or 24/13
Hope this helps!
Which of the following rational functions is graphed below?
Find the sum of the following infinite series.1/3−2/21+4/147−8/1029+···
Given:
The series is 1/3−2/21+4/147−8/1029+··
Explanation:
For the given series, the first term is,
[tex]a=\frac{1}{3}[/tex]The common ratio is,
[tex]\begin{gathered} r=\frac{-\frac{2}{21}}{\frac{1}{3}} \\ =-\frac{2}{21}\cdot\frac{3}{1} \\ =-\frac{2}{7} \end{gathered}[/tex]The formula for the sum of infinite series is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values in the formula to determine the sum of infinite series.
[tex]\begin{gathered} S_{\infty}=\frac{\frac{1}{3}}{1-(-\frac{2}{7})} \\ =\frac{\frac{1}{3}}{\frac{9}{7}} \\ =\frac{1}{3}\times\frac{7}{9} \\ =\frac{7}{27} \end{gathered}[/tex]Answer: 7/27
The gumball machine contains 9 red,7 white and 8 blue gumballs. find the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.
Given, gumball machine contains 9 red gumballs
7 white gumballs and
8 blue gumballs.
we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.
Hence 10 gumballs should be purchased.
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84 minutes for 32 songs = 42 minutes for _____
songs
Answer: 84 minutes for 32 songs= 42 minutes for 16 songs.
Step-by-step explanation: All I had to do was divide 84 by two and divide 32 by 2.
84/2=42
32/2= 16 songs.
Answer: 16 songs.
84 dived by 2 equals 42.
Do 32 divided by 2 and it gives us 16.
Solve the equation 5x = 85 for x.
−17
17
−90
80
x = 17
Step-by-step explanation:
5x = 85
x = 85/5
x = 17.
Hence, option (b) is correct answer
Answer: x=17 the answer is B
Hope this helped
Step-by-step explanation:
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The two equations that are true when x = -2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16.
We have given x = 2 and x = -2
Substitute the values in the given equations
Equation 1
x^2 - 4 = 0
Substitute x = 2 in LHS, we get
2^2-4 = 4 - 4 = 0 = RHS
Substitute x = -2 in LHS, we get
(-2)^2-4 = 4 - 4 = 0 = RHS
Equation 2
x^2 = -4
Substitute x = 2 in LHS, we get
2^2 = 4 ≠ RHS
Substitute x = -2 in LHS, we get
(-2)^2 = 4 ≠ RHS
Equation 3
3x^2 + 12 = 0
Substitute x = 2 in LHS, we get
3(2)^2 + 12 = 12 + 12 = 24 ≠ RHS
Substitute x = -2 in LHS, we get
3(-2)^2 + 12 = 12 + 12 = 24 ≠ RHS
Equation 4
4x^2 = 16
Substitute x = 2 in LHS, we get
4(2)^2 = 4(4) = 16 = RHS
Substitute x = -2 in LHS, we get
4(-2)^2 = 4(4) = 16 = RHS
Equation 5
2(x-2)2 = 0
Substitute x = 2 in LHS, we get
2(2-2)2 = 2(0)(2) = 0 = RHS
Substitute x = -2 in LHS, we get
2(-2-2)2 = 2(-4)(2) = 16
Hence, we find that Equation 1 and Equation 2 are true for x = 2 and x = -2
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sin(40 + 2°) csc(30 + 5°) = 1
sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
Given,
sin(40 + 2°) cosec(30 + 5°) = 1
To prove the trigonometry function equal to 1.
Now, According to the question:
We know that
Sin 42° = 0.66913061
Cosec 35° = 1.7434468
sin(40 + 2°) cosec(30 + 5°) = 1
sin 42° × cosec 35° = 1
Plug the values of sin and cosec in above function:
0.66913061 × 1.7434468
= 1.16659
But we take the before decimal value i.e., 1
Hence, sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
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For a particular rectangle, twice the width is 4 meters shorter than the length. The area of the rectangle is 126 square meters. What is the perimeter of the rectangle? ? meters
Let l be the length of the rectangle and w its width.
Then its area is given by:
a = l*w
Its perimeter is given by:
p = 2l + 2w
We also know that, for this specific triangle, we have:
2w = l - 4
l = 2w + 4
a = 126 m²
Applying this result in the area formula, we have:
w*l = 126
w(2w + 4) = 126
2w² +4w = 126
2w + 4w - 126 = 0
Therefore, w = 7 m and l = 2*7 + 4 = 10 m
Then, the perimeter is given by:
p = 2*18 + 2*7 = 36 + 14 = 50 m
Write the slope-intercept form of the equation of the line through the given points13) through: (5, 3) and (5, 4)14) through: (0, 4) and (2, 3)15) trough: (-1, 4) and (-4,-5)16) through: (-1, -2) and (-3,0)
The slope-intercept form of the linear equation is
y = m x + b, where
m is the slope
b is the y-intercept
If the x-coordinates of the two points are equal, that means the line is vertical
A vertical line has no slope
Its equation is x = a, where a is the x-coordinate of any point on the line
13) The two points are (5, 3) and (5, 4)
They have the same x-coordinates, then its equation is
x = 5
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line
The line passes through points (0, 4) and (2, 3)
x1 = 0 and y1 = 4
x2 = 2 and y2 = 3
Substitute them in the rule above to find m
[tex]m=\frac{3-4}{2-0}=-\frac{1}{2}[/tex]The equation is
[tex]y=-\frac{1}{2}x+b[/tex]b is the value of y at x = 0
at x = 0 y = 4
b = 4
The equation of the line is
[tex]y=-\frac{1}{2}x+4[/tex]
The price of an item has risen to $300 today. Yesterday it was $125. Find the percentage increase.
Answer:
140
Step-by-step explanation:
Use the table to answer the question. Number of cases ordered Number of rolls of paper towels 1 12 3 36 5 60 10 120 A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.
Given that,
There is a table.
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.
We have to find what ratio does the proportionality constant appear at in the data table.
The table is
Number of cases ordered | Number of rolls of paper towels
1 | 12
3 | 36
5 | 60
10 | 120
Therefore, 1:12 ratio does the proportionality constant appear at in the data table.
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A 21-foot beam is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If X represents represents the length of the first piece find the length of each piece.
The length of the first piece is 3 inches, and the second and third pieces are each 9 inches
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that a 21-foot beam is to be cut into three pieces so that the second and third pieces are each 3 times the length of the first piece.
We have to determine the length of each piece.
Let x represents the length of the first piece
As per the given condition,
x + 3x + 3x = 21
7x = 21
x = 21 / 7
x = 3
Thus, the first piece is 3 inch
So 2nd piece is 3×3 = 9 inches ( 3 times to first piece )
And 3rd piece is 3×3 = 9 inches ( 3 times to first piece )
Therefore, the length of the first piece is 3 inches, and the second and third pieces are each 9 inches
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A model car is a 1/40 if the length of the real car is 5.5 m what is the length of the model car
Answer:
0.14 meters, or 140 mm
Step-by-step explanation:
(1/40) means that the model car will have dimensions that are (1/40) the original car.
Real car = 5.5 meters.
Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm
HELP! WILL GIVE BRAINLIEST
Answer:
second answer
Step-by-step explanation:
How to solve? Please help i will give good rating.
Answer:
6. Draw a vertical line that goes though points (4,7) and (4,9). For a relation to be a function, each input has to have only one output. The input 4 cannot have the output of 7 and 9. This proves that this is not a function
7. The range is 91, 3, 6, 10 and 15)
Step-by-step explanation:
The range is the answer if you put in the x for range that they give you.
For example:
x ( x+ 1)/2 If I put in 1 for x, I will get
1(1+1)/2
2/2
1
When the input is 1, the output is one. You that for each of the domains given and you will find the ranges (outputs) that I have written above.
help!!
I'm not sure if i'm right...
are these the steps to solve for x?
-5 *4 +3 /2
Yes, you are right!
First of all, we will subtract [tex]5[/tex] from each side.
[tex]\frac{2x-3}{4}=5[/tex]Then we multiply both sides by [tex]4[/tex].
[tex]2x-3=20[/tex]Then add [tex]3[/tex] to each side.
[tex]2x=23[/tex]Finally, we divide each side by [tex]2[/tex].
[tex]x=\frac{23}{2}=11.5[/tex][tex]\boldsymbol{\sf{\cfrac{2x-3}{4}+5=10 }}[/tex]
Multiply the two sides of the equation by 4.
2x - 3+20 = 40
Add −3 and 20 to get 17.
2x+17 = 40
It remains 17 on both sides.
2x = 40−17
Subtract 17 of 40 to get 23.
2x = 23
Divide both sides by 2.
[tex]\boldsymbol{\sf{x=\dfrac{23}{2} \ \ \longmapsto \ Answer }}[/tex]
Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?
144 yards of string will need to use balloons for the party.
Given,
The length of balloon string Orlando wanted = 6 feet
Number of balloons = 72
We have to find the total length of strings wanted for 72 balloons in yards.
1 yard = 3 feet
Now,
Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet
Now convert 432 feet into yard
That is,
432 / 3 = 144 yards
So,
144 yards of string will need to use balloons for the party.
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in the presence of changing variability, the estimated standard errors of the ols estimators are inappropriate. what does this imply about using standard testing?
The error term, which refers to the sum of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.
What does OLS regression's error term mean?The error term, often referred to as the residual, disturbance, or remaining term, is denoted by the letters e,, or u in various ways in models.Use of an Error Term in a Formula : An error term basically denotes that the model is not entirely precise and yields varying outcomes when used in practical applications. Assume, for instance, that a multiple linear regression function has the following shape:Y=αX+βρ+ϵ
where:
α,β=Constant parameters
X,ρ=Independent variables
ϵ=Error term
During an empirical test, if the actual Y is different from the expected or projected Y in the model, the error term does not equal 0, indicating that other factors affect Y.The OLS estimators will continue to be linear, impartial, and consistent in the presence of autocorrelation. However, because to the absence of a minimal variance, the estimators will no longer be BLUE. It implies that the predictions made using the OLS estimators will be ineffective if the error terms are autocorrelated.To Learn more About error term refer to:
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Please show me how to factorize this
[tex]5x {}^{3} - 9x {}^{2} - 17x - 3[/tex]
Answer:
(x - 3) (5x + 1)(x + 1).
Step-by-step explanation:
5x^3 - 9x^2 - 17x - 3
As the first coefficient is 5 and the last -3, so product is -15, we could try if (x-3) is a factor:
By the Factor Theorem, if x-3 is a factor then f(3) = 0.
f(3) = 5(3)^3 - 9(3)^2 - 17(3) - 3
= 135 - 81 - 51 - 3 = 0
So, x - 3 is a factor.
Now divide:
x - 3)5x^3 - 9x^2 - 17x - 3(5x^2 + 6x + 1 <------- Quotient
5x^3 - 15x^2
6x^2 - 17x
6x^2 - 18x
x - 3
x - 3
.......
Factoring 5x^2 + 6x + 1:
= (5x + 1)(x + 1)
So, the answer is:
(x - 3) (5x + 1)(x + 1).
Divide. Enter the correct answer.
17+2=
