Answer:
x = -22/3 and y = -1
Step-by-step explanation:
First, simplify the equation 12x + 20y = -108 by dividing both sides by 4:
3x + 5y = -27
now, you can subtract the two equations:
3x + 5y = -27
- (3x - 12y = -10)
17y = -17
y = -1
plug y = -1 into the equation 3x - 12y = -10
3x - 12 *(-1) = -10
3x + 12 = -10
3x = -22
x = -22/3
Answer:
-(22/3,-1)
Step-by-step explanation:
Mia is planting a flower garden.The table shows the type of flower bulbs planter.What is the ratio of daisy bulbs to total bulbs planted?help asap please!
Answer:
my answer is c
Step-by-step explanation:
the longest side of a triangle is 10 cm which group of the line segments could form the other two sides of the triangle
5 cm and 5 cm
7 cm and 8 cm
9 cm and 10 cm
4 cm and 4cm
Answer:
7 cm and 8 c
Step-by-step explanation:
7 cm and 8 cm. Why? Because both are shorter than the longest side (10 cm) but add up to more than 10 cm.
Esther has a budget of $800 to spend on a sofa and matching set of pillows. The sofa itself costs $720 and each matching pillow costs $16. If p represents the number of matching pillows purchased along with the sofa, which of these inequalities shows the values of p which fit within Esther's budget? p≥5 p≤5 p≥8 p≤8
Answer:
p<5
Step-by-step explanation:
To answer this question, we need to write an equation that represents the total cost of the sofa and the pillows in terms of p. The total cost is 720 + 16p, since the sofa costs $720 and each pillow costs $16. We want this total cost to be less than or equal to Esther’s budget of $800, so we have:
720 + 16p ≤ 800
To solve for p, we subtract 720 from both sides and get:
16p ≤ 80
Then we divide both sides by 16 and get:
p ≤ 5
So the correct inequality is p≤5.
hope this helped :)
For the third week of April, Patricia Thomas worked 53 hours. Patricia earns $11.90 an hour. Her employer pays overtime for all hours worked in excess of 40
hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the third week of April (round your responses to the nearest cent if necessary):
1. Regular pay amount
2. Overtime pay
3. Gross pay
Given statement solution is :- For the third week of April, Patricia's:
Regular pay amount is $476.
Overtime pay is $231.45.
Gross pay is $707.45.
To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.
Regular Pay:
Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:
Regular Pay = Regular Hours x Hourly Rate
Regular Pay = 40 hours x $11.90/hour
Regular Pay = $476
Overtime Pay:
Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.
Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)
Overtime Pay = 13 hours x ($11.90/hour x 1.5)
Overtime Pay = 13 hours x $17.85/hour
Overtime Pay = $231.45
Gross Pay:
Gross Pay is the sum of Regular Pay and Overtime Pay.
Gross Pay = Regular Pay + Overtime Pay
Gross Pay = $476 + $231.45
Gross Pay = $707.45
Therefore, for the third week of April, Patricia's:
Regular pay amount is $476.
Overtime pay is $231.45.
Gross pay is $707.45.
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Two trains leave two different stations 300 km apart; the first starts at noon and the second at 12 15 h. Travelling on parallel tracks, they meet each other at 15 00 h. Each train travels at a constant speed, the one leaving at 12 15 h moves at 15 km/h faster than the other. What are their speeds?
Answer:
See below
Step-by-step explanation:
From noon to 1500 is three hours
train A then travels 3x where x = speed in km/hr
train B only travels for 2.45 hours and covers
2.45 ( x + 15) where x + 15 is its speed in km/hr
these two values sum to the 300 km distance
3x + 2.45 ( x + 15) = 300
3x + 2.45 x + 36.75 = 300
x = 48.3 km/hr x+15= 63.3 km / hr
Solve for x
(8x-29)+(3x-1)+(6x-11)=180
Answer:
x= 13
Step-by-step explanation:
can i please get branlist? if not thats okay.
Please help!!!! 2(x + 4) > 2x +4 -2
Answer: 0>-6
Step-by-step explanation:
2x+8>2x+2 Distribute and subtract numbers.
2x+8-8 > 2x+2-8 Subtract eight from both sides.
2x > 2x-6 Then, simplify the expression. Subtract the numbers.
Answer: 0>-6
Hoping this helps!
Please help solve 3m/2/3 = 7
Answer:
the solution to the equation is m = 28/3, or approximately 9.3333
Step-by-step explanation:
To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:
3m/2/3 = 7
(2/3) * (3m/2/3) = (2/3) * 7
3m/2 = 7 * (2/3)
3m/2 = 14/3
Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:
(2) * (3m/2) = (2) * (14/3)
3m = 28/3
Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:
(3m) / 3 = (28/3) / 3
m = 28/3
Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.
Answer:
Maybe m = 14/9
Maybe m = 14
Step-by-step explanation:
It is not clear what you mean by the fraction on the left side.
Do you mean
3m/(2/3) = 7 ?
If so:
3m = 7 × 2/3
3m = 14/3
m = 14/9
Do you mean
(3m/2)/3 = 7 ?
If so:
3m/2 = 21
m = 21 × 2/3
m = 14
Do you mean something else?
HELP IS THIS A FUNCTION
Answer:
Its a function
Step-by-step explanation:
the 3 numbers share the same output.
Answer:
Yes it is a function
Step-by-step explanation:
Try using this formula supposing the week is"w"
and revenue is"r"
\(n = 13 + 7w\)
What is the missing length?
Answer:
h=7
Step-by-step explanation:
A=1/2bh
42=1/2(12)h
42=6h
42/6=7
h=7
i am confused on finding the answer i have tried a few times and i do not understand
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
Simplify the expression by removing symbols of grouping and combining like terms.
7(2s − 1) + s + 5
Answer:
=15s−2
Step-by-step explanation:
sorry if its not correct i tried
How many peaches will you get for $0.79 at Valley Market?
Answer:
1
Step-by-step explanation:
is the square root of 10 a rational number
Answer:
No
Step-by-step explanation
The square root of 10 is irrational because it isn't a fraction
For 5-7, use the given information to find the exact value of each expression.
sinθ = 3/5 in quadrant ll tan A = -√3 ,when 3π/2 < A < 2π
5.) cos(θ+A)
6.) tan2A
7.) sin θ/2
Answer:
\(x^{2} \geq 186\neq\)
Step-by-step explanation:
Neuroblastoma is a rare, serious, but treatable disease. A urine test, the VMA test, has been developed that gives a positive diagnosis in about 70% of cases of neuroblastoma. It has been proposed that this test be used for large-scale screening of children. Assume that 300,000 children are to be tested, of whom 8 have the disease. We are interested in whether or not the test detects the disease in the 8 children who have the disease. Find the probability that a) none will be missed. b) seven cases will be detected. c) two or more cases will be missed. d) exactly 75% will be detected. d) six or less cases will be detected.
Answer:
Part a) probability that none will be missed means none will have the disease= 0.058
Part b) probability that seven cases will be detected= 0.00122
Part c)probability that two or more cases will be missed.=0.744
Part d) ) probability that exactly 75% will be detected= 75% of 8= 6= 0.01000188
Part e) probability six or less cases will be detected = 0.171
Step-by-step explanation:
This is a binomial probability distribution . Here p= 0.7 and q= 1-0.7= 0.3 n= 8
Part a) none will be missed means none will have the disease
P (x= 0)= 8C0(0.7)^8 (0.3)^0
P (x= 0)=1*(0.7)^8 (0.3)^0=0.058
Part b) seven cases will be detected
P (x= 7)= 8C7(0.7)^1 (0.3)^7 = 0.00122
Part c) two or more cases will be missed.
1- P (x= 0)- P (x= 1)
1-0.058-0.198=0.744
Part d) ) exactly 75% will be detected= 75% of 8= 6
P (x= 6)= 8C6(0.7)^2 (0.3)^6=0.01000188
Part e) six or less cases will be detected.
1- P (x= 7)= 8C7(0.7)^1 (0.3)^7+P (x= 8)= 8C8(0.7)^0 (0.3)^8
1- 0.802+0.027=1- 0.829= 0.171
how to answer the (a) question?
help please
i believe its 4
Step-by-step explanation:
13 different cut flowers and I plan on using 7 of them. How many different selections of the 7 flowers are possible?
Answer:
7/13
Step-by-step explanation:
please help me answer this question thank you
Answer:
A
Step-by-step explanation:
Match each drawing on the left with its geometric notation on the right. Some of the answer choices on the right may not be used.
Answer:
Please attach a photo to this so I can better answer your question
The escape time (sec) for oil workers in a simulated exercise, gave the sample mean 370.69, sample standard deviation 24.36, and number of observations as n =26. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypothesis using a significance level of .05.
Answer:
Null hypothesis:\(\mu \leq 6\)
Alternative hypothesis:\(\mu > 6\)
The statistic is given by:
\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)
Replacing the info we got:
\(t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335\)
\(p_v =P(t_{25}>1.335)=0.097\)
And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes
Step-by-step explanation:
Information given
\(\bar X=370.69/60 =6.178\) represent the sample mean
\(s=24.36/36=0.68\) represent the standard deviation for the sample
\(n=26\) sample size
\(\mu_o =6\) represent the value to verify
\(\alpha=0.05\) represent the significance level
t would represent the statistic
\(p_v\) represent the p value
System of hypothesis
We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:
Null hypothesis:\(\mu \leq 6\)
Alternative hypothesis:\(\mu > 6\)
The statistic is given by:
\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)
Replacing the info we got:
\(t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335\)
The degrees of freedom are:
\(df=n-1=26-1=25\)
The p value would be given by:
\(p_v =P(t_{25}>1.335)=0.097\)
And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.
Hello! Please help me solve this Geometry question. Anything helps!
Answer:
\(x = 51\)
Step-by-step explanation:
\(the \: sum \: of \: the \: exterio \: angles\: a \\ \: polygon \: is \: 360. \\ \\ 64 + 60 + 69 + 42 + x + (x + 23) = 360 \\ 335 + 2x + 23 = 360 \\ x = \frac{360 - 258}{2} = 51\)
find the value of each variable. 3x 2y 34
X= 30
Y=28
Step-by-step explanation:
It's a right-angle triangle. So, 3 x 30 will give you a 90 degree angle.
180-90=90
That means the next 2 angles should add to 90.
2x28=56
56+34=90
Hope this helps!
2/9×45 what is the answer please
Answer: 10
Step-by-step explanation:
2*45=90
90/9=10
Answer:
10
Step-by-step explanation:
All you have to do is type the equation into a calculator and it will give you the answer.
Given the graph of f (x), determine the domain of f –1(x).
Radical function f of x that increases from the point negative 3 comma negative 2 and passes through the points 1 comma 0 and 6 comma 1
The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)
What is the inverse of a function?The inverse of a function that maps x into y, maps y into x.
The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)
To determine the domain of
\( {f}^{ - 1}( x)\)
The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x
The reflection of the point (x, y) across the line y = x, gives the point (y, x)
The points on the graph of the inverse of the function, f(x), \( {f}^{ - 1} (x)\) are therefore;
\(( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)\)
\(( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)\)
( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)
The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)
Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, \( {f}^{ - 1}( x)\), which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;
The domain of the inverse of the function, \( {f}^{ - 1}( x)\), using interval notation is; [-2, ∞)
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The length of a rectangle is 5ft more than double the width, and the area of the rectangle is 42ft^2. Find the dimensions of the rectangle
Answer: 54ft^6
Step-by-step explanation:
Because you add then divide 42 and 5
Angela has a collection of nickels and quarters worth $8.80. If she has 68 total nickels and quarters, how many quarters does she have?
The number of nickels are 41 and the number of quarters are 27.
Given that, Angela has a collection of nickels and quarters worth $8.80.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
We know that, a nickel is worth 5 cents and a quarter is worth 25 cents.
Let the number nickels be x and the number of quarters be y.
Now, 0.05x+0.25y=8.80 ----------(I)
x+y=68 ----------(II)
Substitute x=68-y in equation (I), we get
0.05(68-y)+0.25y=8.80
⇒ 3.4-0.05y+0.25y=8.80
⇒ 0.20y=8.80-3.4
⇒ 0.20y=5.4
⇒ y=5.4/0.20
⇒ y=27
Substitute y=27 in equation (II), we get
x=41
Therefore, the number of nickels are 41 and the number of quarters are 27.
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To number the pages of a book,2022 digits are used. How many pages are in the book?
Answer:
710
Step-by-step explanation:
Numeration of pages goes from 1.
9 pages with 1-digit numbers, from 1 to 9.
90 pages with 2-digit numbers, from 10 to 99.
So, 2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.
The rest of numbers are 3-digit.
2022-189/3 = 611 pages with 3-digit numbers.
Total pages = 9 + 90 + 611 = 710.
The number the pages of a book,2022 digits are used there are 8880 pages in the book.
Let's assume there are "x" pages in the book. Each page number requires a certain number of digits to represent. The number of digits required to represent a page number depends on the value of the page number itself.
For example:
Page numbers from 1 to 9 require 1 digit each.
Page numbers from 10 to 99 require 2 digits each.
Page numbers from 100 to 999 require 3 digits each.
And so on.
Since we're given that 2022 digits are used in total, we can set up an equation based on the above observations:
Number of 1-digit page numbers + Number of 2-digit page numbers + Number of 3-digit page numbers + ... = 2022
Now let's solve this equation to find the number of pages:
Number of 1-digit page numbers = 9 (from 1 to 9)
Number of 2-digit page numbers = 90 - 10 + 1 = 81 (from 10 to 99)
Number of 3-digit page numbers = 900 - 100 + 1 = 801 (from 100 to 999)
Substituting these values into the equation:
9 + 81 + 801 + ... = 2022
Now we need to find the number of terms in this sequence. Each term corresponds to a certain number of digits, and we want to find the smallest number of digits that will exceed 2022. We can try different numbers of digits until we find the correct one:
Number of 4-digit page numbers = 9000 - 1000 + 1 = 8001
Adding the terms up:
9 + 81 + 801 + 8001 = 8880
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Which of the following ordered pairs represents a solution to the equation graphed below?
A. (-2, -1)
B. (-1, -1)
C. (0, -4)
D. (1, -2)
E. (2, -6)
B. (-1,-1)
Reason:
Evidently shown in the graph.
Alina wants to make keepsake boxes for her two best friends. She doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material.
For Jen, Alina wants to make a box with a square base whose sides and base are made of wood and whose top is made of metal. The wood she wants to use costs 5 cents per square inch, while the material for the metal top costs 12 cents per square inch. What is the largest possible box (in terms of volume measured in cubic inches) that Alina can make for Jen if she only has $30.00 to spend on materials? (Round your answer to three decimal places.)
Answer:
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Step-by-step explanation:
Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.
The surface area of the box (excluding the top) is given by:
2(x^2) + 4(x^2) = 6(x^2)
The surface area of the metal top is:
x^2
The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:
6(x^2) + x^2 = 7(x^2)
The cost of the wood for the box is:
5 cents per square inch * 6(x^2) = 30x^2 cents
The cost of the metal for the top is:
12 cents per square inch * x^2 = 12x^2 cents
The total cost of the box is:
30x^2 + 12x^2 = 42x^2 cents
We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:
42x^2 = 3000
Solving for x, we get:
x^2 = 71.429
x ≈ 8.445
Therefore, the maximum volume of the box is:
V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.