Answer:
a) Q = 0 or 9
b) Q = 5
c) Q = 7
d) Q = 8
Step-by-step explanation:
We assume the postal money order to be of the United State. A smudged digit is calculated using the following algorithm.
1. Add first 10 digits of 11-digit number.
2. Divide the sum of the 10 numbers by 9.
3.The remainder is the smudged digit.
4.The smudged digit is appended to the end of the ID number or anywhere in the number.
It is calculated as:
[tex]x_{11} = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} + x_{8} + x_{9} + x_{10} )mod 9[/tex]
a) 493212Q0688
[tex]8 = (4 + 9 + 3 + 2 + 1 + 2 + Q + 0 + 6 + 8) mod 9\\8 = (Q + 35) mod 9\\8 = Q mod 9 + 35 mod 9\\8 = Q mod 9 + 8\\Q mod 9 = 8 - 8\\Q mod 9 = 0\\Q = 0 or 9[/tex]
Therefore, Q is either 0 or 9.
b) 850Q9103858
[tex]8 = (8 + 5 + 0 + Q + 9 + 1 + 0 + 3 + 8 + 5) mod 9\\8 = (Q + 39) mod 9\\8 = Q mod 9 + 39 mod 9\\8 = Q mod 9 + 3\\Q mod 9 = 8 - 3\\Q mod 9 = 5\\Q = 5[/tex]
Therefore, Q is 5 because from Q mod 9 = 5, we have Q = 5 mod 9.
c) 2Q941007734
[tex]4 = (2 + Q + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3) mod 9\\4 = (Q + 33) mod 9\\4 = Q mod 9 + 33 mod 9\\4 = Q mod 9 + 6\\Q mod 9 = 4 - 6\\Q mod 9 = -2\\Q = -2 mod 9\\Q = 7[/tex]
Therefore, Q is 7 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -2 + 9 = 7.
d) 66687Q03201
[tex]1 = (6 + 6 + 6 + 8 + 7 + Q + 0 + 3 + 2 + 0) mod 9\\1 = (Q + 38) mod 9\\1 = Q mod 9 + 38 mod 9\\1 = Q mod 9 + 2\\Q mod 9 = 1 - 2\\Q mod 9 = -1\\Q = -1 mod 9\\Q = 8[/tex]
Therefore, Q is 8 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -1 + 9 = 8.
For the given postal money order scenarios, the smudged digit, Q, is determined as follows: Scenario a - either 0 or 9, Scenario b - 5, Scenario c - 5, and Scenario d - 3.
Let's analyze the given postal money order scenarios and determine the smudged digit, Q, using the provided algorithm:
Scenario a:
ID number: 493212Q0688
Sum of the first 10 digits: 4 + 9 + 3 + 2 + 1 + 2 + 0 + 6 + 8 + 8 = 43
43 divided by 9 equals 4 with a remainder of 7.
Therefore, the smudged digit, Q, is either 0 or 9.
Scenario b:
ID number: 850Q9103858
Sum of the first 10 digits: 8 + 5 + 0 + 9 + 1 + 0 + 3 + 8 + 5 + 8 = 47
47 divided by 9 equals 5 with a remainder of 2.
Therefore, the smudged digit, Q, is 5.
Scenario c:
ID number: 2Q941007734
Sum of the first 10 digits: 2 + 7 + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3 = 40
40 divided by 9 equals 4 with a remainder of 4.
To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -4 + 9 = 5.
Therefore, the smudged digit, Q, is 5.
Scenario d:
ID number: 66687Q03201
Sum of the first 10 digits: 6 + 6 + 6 + 8 + 7 + 0 + 3 + 2 + 0 + 1 = 33
33 divided by 9 equals 3 with a remainder of 6.
To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -6 + 9 = 3.
Therefore, the smudged digit, Q, is 3.
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A researcher conducts a related-sample study to evaluate two treatments with n = 16 participants and obtains a t statistic of t = 1.94. The treatment 2 is expected to have a greater sample mean than the treatment 1. What is the correct decision for a hypothesis test using α = .05?
Answer:
Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim may be supported.
Step-by-step explanation:
Solution:-
- The sample size of two treatments, n = 16
- The mean of sample treatment 1, u1
- The mean of sample treatment 2 , u2
- The significance level, α = .05
- State the hypothesis:
Null hypothesis : u2 - u1 > 0
Alternate hypothesis : u2 - u1 ≤ 0
- The rejection region of the T- critical for lower tailed test.
significance level, α = .05
degree of freedom v = n - 1 = 16 - 1 = 15
T-critical = - 1.75
- The T-test value is compared with T-critical:
T-test = 1.94
T- critical = -1.75
T-test > T-critical .. ( Null not rejected )
- Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim maybe supported.
What is the value of x when x + 10 = 42
Answer: 32
Step-by-step explanation:
Use a fact family. 42 - 10 = 32.
You will get 32 as an answer.
So x = 32.
Answer:
32
Step-by-step explanation:
If x+10=42 then x=42-10 which makes x=32
Each blue cube represents one cubic unit of volume. What is the volume of the large box? A) 20 cubic units B) 48 cubic units C) 288 cubic units D) 384 cubic units
Answer:
The volume of the large box is 384 cubic units
Step-by-step explanation:
Here, we have;
The number of cubes along the base of the front of the large box (width) = 8 cubes
The number of cubes along the base of the side of the large box (length) = 8 cubes
The number of cubes along the right side of the front of the large box (the box height) = 6 cubes
The volume of the large box = Length × Width × Height
∴ The volume of the large box = 8 cubes × 8 cubes × 6 cubes = 384 cubic units.
The volume of the large box = 384 cubic units.
2.6-,2.061,2.601,2.34,2.7 order the following from least to greatest
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Hello!
This is a bit hard to explain! If you want me to try, just comment.
I have arranged the sequence in ascending order below:
[tex]2.061,\:2.34,\:2.6,\:2.601,\:2.7[/tex].
Hope this helps!
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Because the numbers all have a 2 in the ones place, you need to evaluate the numbers in the tenths place and the numbers with the lowest go first and so on :)
A kangaroo hooped 3,520 yards to the lake with her baby in her pouch. She hopped the remaining 5,280 yard without her baby in her pouch. How many miles did the Kangaroo hop to the lake?
Answer:
5 miles
Step-by-step explanation:
since she hopped in yards you must mulitiply both numbers 3520 and 5280 by 3 since there are three feet in a yard. then add together then divide the sum by 5280 since a mile is 5280 feet.
3520 X 3 = 10560
5280 X 3 = 15840
10560 + 15840 = 26400
26400/ 5280 = 5
An IQ test is designed so that the mean is 100 and the standard deviation is 1414 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 9090% confidence that the sample mean is within 66 IQ points of the true mean. Assume that sigmaσequals=1414 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
Answer:
37
Step-by-step explanation:
The first thing is to calculate critical z factor
the alpha and the critical z score for a confidence level of 90% is calculated as follows:
two sided alpha = (100% - 90%) / 200 = 0.05
critical z factor for two sided alpha of .05 is calculated as follows:
critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:
critical z factor = 2.58
Now we have the following formula:
ME = z * (sd / sqrt (N) ^ (1/2))
where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58
N the sample size and we want to know it, replacing:
6 = 2.58 * (14 / (N) ^ (1/2))
solving for N we have:
N = (2.58 * 14/6) ^ 2
N = 36.24
Which means that the sample size was 37.
Please help me with this question
Answer:
x = 55 degrees.
y = 49 degrees.
Step-by-step explanation:
AB = AD and BC = DC so we have 2 isosceles triangles here thus the base angles are equal.
Therefore m < y = (180 - 82)/2 = 98/2
= 49 degrees.
m < x = (180 - 2*35)/2 = 55 degrees.
Find the area of the region enclosed by f(x) and the x axis for the given function over the specified u reevaluate f(x)=x^2+3x+4 x<3 f(x)=4x+10 x greater than or equal to 3 on -3,4
Answer:
A = 68 unit^2
Step-by-step explanation:
Given:-
The piece-wise function f(x) is defined over an interval as follows:
f(x) = { x^2+3x+4 , x < 3
f(x) = { x^2+3x+4 , x≥3
Domain : [ -3 , 4 ]
Find:-
Find the area of the region enclosed by f(x) and the x axis
Solution:-
- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.
- The first portion of function is valid over the interval [ -3 , 3 ]:
[tex]f(x) = x^2+3x+4[/tex]
- The area "A1" bounded by f(x) is given as:
[tex]A1 = \int\limits^a_b {f(x)} \, dx[/tex]
Where, The interval of the function { -3 , 3 ] = [ a , b ]:
[tex]A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2[/tex]
- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :
[tex]f(x) = 4x+10[/tex]
- The area "A2" bounded by f(x) is given as:
[tex]A2 = \int\limits^a_b {f(x)} \, dx[/tex]
Where, The interval of the function { 3 , 4 ] = [ a , b ]:
[tex]A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2[/tex]
- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:
A = A1 + A2
A = 42 + 26
A = 68 unit^2
To find the area enclosed by f(x) and the x-axis from x = -3 to x = 4 for the given piecewise function, calculate the integral of each piece separately and then sum the areas. The area is divided into two parts due to the function having different expressions before and after x = 3.
Explanation:The student is asking to find the area under the curve of a given piecewise function f(x) on the interval from x = -3 to x = 4. Since the function is defined differently for x < 3 and x ≥ 3, the area calculation involves two parts:
Calculating the area under [tex]f(x) = x^2 + 3x + 4[/tex] from x = -3 to x = 3.Calculating the area under [tex]f(x) = 4x + 10[/tex] from x = 3 to x = 4.The first part can be calculated using the integral of [tex]f(x) = x^2 + 3x + 4[/tex]from x = -3 to x = 3. The second part is the integral of [tex]f(x) = 4x + 10[/tex] from x = 3 to x = 4. The total area is the sum of these two areas. For this function, the areas are bounded above by the function and below by the x-axis, so all areas are considered positive.
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The first three terms of a geometric sequence are as follows.
-3, 6, -12
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answer:
24, -48
Step-by-step explanation:
In this geometric sequence, the previous number is being multiplyed by -2 each time
This said the next number is 24.
-12*-2=24
and the next one is -48.
24*-2=-48
Final answer:
The next two terms of the geometric sequence -3, 6, -12 are 24 and -48, found by repeatedly multiplying with the common ratio of -2.
Explanation:
The first three terms of the given geometric sequence are -3, 6, and -12. To find the next two terms in this sequence, we need to determine the common ratio between the terms. The common ratio (r) is the factor by which we multiply one term to get the next term. In this case, 6 divided by -3 equals -2, and similarly, -12 divided by 6 also equals -2. This confirms that our common ratio is -2.
Now, to find the fourth term of the sequence, we multiply the third term (-12) by the common ratio (-2):
-12 × -2 = 24
To find the fifth term, we multiply the fourth term (24) by the common ratio (-2):
24 × -2 = -48
Therefore, the fourth and fifth terms of the geometric sequence are 24 and -48, respectively.
State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situation. The cost of admission admission is $4848 for forfour pets pets and $9696 for eighteight pets pets. Determine the independent variable.
We have been given that the cost of admission is $48 for four pets and $96 for eight pets. We are asked to determine the independent variable and the dependent variable in the given linear relationship.
We can see that as the number of pets is increasing cost of admission is also increasing. This means that cost depends on number of pets.
Therefore, cost of admission is dependent variable and number of pets is independent variable.
To find rate of change, we will use slope formula.
We have been given two points on line that are (4,48) and (8,96).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Upon substituting the coordinates of our given points in slope formula, we will get:
[tex]m=\frac{96-48}{8-4}[/tex]
[tex]m=\frac{48}{4}[/tex]
[tex]m=12[/tex]
Therefore, the rate of change is $12 per pet.
what is the mean absolute deviation, round if needed.
78,93,84,97,100,77,94,96,93,92,90,89
Answer:
5.54
Step-by-step explanation:
5.54 is the (MAD)
Two less than the product of 3 and x
Answer:
3x-2
Step-by-step explanation:
Answer:
3x-2
Step-by-step explanation:
"Less than" makes the whole expression changed.
If the less than was not there, it would have been 2-3x.
"Product" is multiplication. So it would be 3x.
The "Less than" also has less in it which is subtraction.
You are wrapping a gift with the dimensions shown below. What is the least amount of wrapping paper you need?
Answer:2 identical side rectangle
2 identical end triangle
1 bottom rectangle
area of trialge=1/2bh
aera of rectangle=legnth tiems width
2 side rectangles are 5 by 10=50
times 2 since 2 of them 50*2=100
end triangles
1/2 times 8 times 3=12
2 of them
12 times 2=24
bottom
8 by 10
80
add everybody
100+24+80=204 in^2 i think this is how
Step-by-step explanation:
Answer:
2 identical side rectangle
2 identical end triangle
1 bottom rectangle
area of trialge=1/2bh
aera of rectangle=legnth tiems width
2 side rectangles are 5 by 10=50
times 2 since 2 of them 50*2=100
end triangles
1/2 times 8 times 3=12
2 of them
12 times 2=24
bottom
8 by 10
80
add everybody
100+24+80=204 in^2 i think this is how
Step-by-step explanation:
MaryJo is considering investing in 2 different mutual funds. Option A has an annual interest rate of 7% and requires a principal of $10,000 with monthly deposits of $200 for 10 years. Option B has an annual interest rate of 9% and requires a principal of $10,000 with monthly deposits of $200 for 5 years.
The option A mutual funds will be more effective.
Step-by-step explanation:
Option A:
Principal amount = $10000
Monthly deposit = $200
Time = 10 years
Rate of interest = 7%
Total deposit = (200 x 12 x 10) + 10000
= 24000 + 10000
= $34000
Interest = (34000 x 7 ) /100
= 340 x 7
= $2380
Total amount = 34000 + 2380
= $36380
Option B:
Principal amount = $10000
Monthly deposit = $200
Time = 5 years
Rate of interest = 9%
Total deposit = (200 x 12 x 5) + 10000
= 12000 + 10000
= $22000
Interest = (22000 x 9 ) /100
= $1980
Total amount = 22000+1980
= $23980
The option A mutual funds will be more effective.
Answer:
What is the difference in the final balances of the two mutual funds?
Step-by-step explanation:
The difference is $12,400.
Which of the following is correct about a probability distribution? Select one: a. The sum of all probabilities of possible outcomes must equal 1.0. b. The outcomes must be mutually exclusive. c. The probability of each outcome must be between 0.0 and 1.0 inclusive d. All of these answers are correct
Answer: All of the answers are correct.
Step-by-step explanation:
A probability distribution is the collection of probabilities which defines the likelihood of observing all the various outcomes of an experiment or event. A probability distribution has two main properties which are that:
• Each probability in the distribution consist of a value between 0 and 1.
• The sum of all probabilities in the distribution equals 1.
Also, in probability, an outcome is the possible result of an experiment and each possible outcome gotten is unique, therefore the different outcomes are mutually exclusive i.e. only one outcome can occur on each trial during the experiment.
The sum of all probabilities of possible outcomes in a probability distribution must equal 1.0, and the probability of each outcome must be between 0.0 and 1.0, inclusive.
A probability distribution is a function that assigns probabilities to all possible outcomes of an experiment. The correct statement about a probability distribution is that the sum of all probabilities of possible outcomes must equal 1.0. This is known as the axiom of probability. In addition, the probabilities of each outcome must be between 0.0 and 1.0, inclusive. This ensures that probabilities are valid and within the appropriate range. The outcomes themselves do not have to be mutually exclusive; they can overlap or have common elements.
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The population of the city of Miami is approximately 463,300 and is increasing at a rate of 3% each year. Use an exponential function to find the population of the city after 7 years. Round to the nearest whole number.
Step-by-step explanation:
The population of the city of Miami = 463,300
The rate of increase in population every year = 3%
The population of the city after 7 years = ?
By formula, [tex]P_{n} = P (1 +\frac{r}{100})^{n }[/tex]
Pn is the population after 7 years
P is the current population = 463,300
r = 3 %, n = 7
[tex]P_{7} = 463300 (1 +\frac{3}{100})^{7 }[/tex]
= 463300 (1.23)
= 569859
The population of the city after 7 years = 569,859
The travel time it takes elevator A to reach height in meters is 0.8h+16 seconds. The travel time it takes elevator B to reach height in meters is -0.8h+12 seconds. How long would it take each elevator to reach ground level?
Answer:
Time taken by A = 16 seconds
Time taken by B = 12 seconds
Step-by-step explanation:
Given:
Two elevator and their respective time to reach certain height.
Here time is function of height.
Time taken by elevator A = 0.8(h)+16
Time taken by elevator B = -0.8(h)+12
We have to find the time taken by the elevator to reach ground level.
Accordingly:
We know that ground level the height will be zero meaning that (h=0).
Plugging the h values in the equation we can find the time taken by both the elevators to reach zero height that is the ground level.
⇒ [tex]t_A=0.8h+16[/tex] ⇒ [tex]t_B=-0.8h+12[/tex]
⇒ [tex]t_A=0.8(0)+16[/tex] ⇒ [tex]t_B=-0.8(0)+12[/tex]
⇒ [tex]t_A=16[/tex] sec ⇒ [tex]t_B=12[/tex] sec
So,
Time taken by elevator A and elevator B to reach the ground is 16 seconds and 12 seconds respectively.
Tom gets $12 off a box of chocolates that had an original price of $48.What percentage is the discount
Answer:
25 percent
Step-by-step explanation:multiply 48 by .25 it will give you 12 which is the discount hope this helps god bless
Answer:
25%
Step-by-step explanation:
12/48=.25=25%
Haley bought a 3-pound bag of cat food. She feeds her cat 6 ounces of cat food each day. Will the bag of cat food be enough to feed her cat for 7 days? Use the drop-down menus to explain.
Answer:
a -pound bag of cat food can enough to feed her cat for 7 days
Step-by-step explanation:
Given:
3-pound bag of cat food6 ounces of cat used per dayNumber of cat food used in 7 days (in ounces): 7*6 = 42 ounces
As we know,1 pound (lb) is equal to 16 Ounces (oz)
<=> 42 ounces = 42 /16 = 2.625 pounds < 3-pound bag
So a -pound bag of cat food can enough to feed her cat for 7 days
Hope it will find you well.
Answer:
Yes it will
Step-by-step explanation:
Let's first work with a single unit so that our work will be a lot easier.
We are going to convert pounds to ounces and since 1 pound = 16 ounces, 3 pounds = 16 × 3 = 48 ounces of cat food.
And she feeds her cat 6 ounces of food each day,that means that in 7 days the cat will only be able to consume just 7 × 6 = 42 ounces,but remember that the amount of cat food bought is equal to 48 pounds.
This here means that the cat food will be enough to feed the cat for 7 days
Jacob wants to enlarge a triangle with sides 7, 12, and 12 inches to create a similar triangle. If the shortest side of the enlarged triangle is 24.5 inches, how long will each of the other two sides be?
Answer:
42
Step-by-step explanation:
If the shortest side is 7 and it is enlarged to be 24.5.
It is enlarged by a scale of 3.5.
so if you scale 12 by 3.5
then you get 42
Solve the equation
x-23=5(2x+3)-2
Answer:
x=4.4
Step-by-step explanation:
expand the brackets
10x+15
full equation now
=x-23=10x+15-2 this makes it more simpler to find like terms
+2 on both sides
=x-25=10x+15
=+25 on both sides
x=10x+40
= -x on both sides
=9x=40
40/9=x
x=4.4
Answer:
[tex]x = - 4[/tex]
Step-by-step explanation:
[tex]x - 23 = 5(2x + 3) - 2 \\ x - 23 = 10x + 15 - 2 \\ - 23 - 15 + 2 = 10x - x \\ - 36 = 9x \\ \frac{ - 36}{9} = \frac{9x}{9} \\ - 4 = x[/tex]
Write .00026 as a multiple of a power of 10
Step-by-step explanation:
[tex]0.00026 = 2.6 \times {10}^{ - 4} \\ [/tex]
students in art class make square tiles that are 5 inches long. They plan to make a row of tiles that is 4 feet 2 inches long. How many tiles will the students need to make?
The required students will need to make 10 tiles to create a row that is 4 feet 2 inches long.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To solve this problem, we first need to convert the length of the row from feet and inches to inches.
4 feet 2 inches is equal to (4 x 12) + 2 = 50 inches.
Next, we can divide the length of the row by the length of each tile to find the number of tiles needed:
Number of tiles = Length of row / Length of each tile
Number of tiles = 50 inches / 5 inches
Number of tiles = 10 tiles
Therefore, the students will need to make 10 tiles to create a row that is 4 feet 2 inches long.
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Iding a go-kart costs $10 on Saturday and Sunday and $5 on Monday through Friday. Is the cost a function of the activity type? Explain why or why not.
Answer:
Answer is No, ITS NOT.
Refer below.
Step-by-step explanation:
There are two different cost of the same activity i.e. $10 on Saturday and Sunday and $5 on Monday through Friday, So it wouldn't be a function.
Need help fast!!!!!!
Answer:
There is no answer to this, closest answer is the 1st choice
Step-by-step explanation:
The equation of a line is y=8x+2 and the point (3,q) lies on this line. What is the value of q?
Answer:
q = 26
Step-by-step explanation:
Given that (3, q ) lies on the line, then the coordinates of the point make the equation true.
Substitute x = 3, y = q into the equation
q = 8(3) + 2 = 24 + 2 = 26
Final answer:
To determine the value of q for the point (3, q) on the line y=8x+2, substitute x with 3 to get y=26. Hence, q is 26, and the point is (3, 26).
Explanation:
To find the value of q for the point (3, q) that lies on the line with the equation y=8x+2, we substitute the x-coordinate of the point, which is 3, into the equation and solve for y. This gives us:
y = 8(3) + 2
y = 24 + 2
y = 26
Therefore, the value of q is 26, and the point is (3, 26). This demonstrates how to use a line's equation to find a specific point on the line. The question illustrates the algebraic relationship between the coordinates of a point on a line and the equation of the line itself.
What is the value of x when solving the equation Negative 2 x + (negative 8) = 2 x + 8 using algebra tiles?
x = negative 4
x = negative 2
x = 2
x = 4
Answer:
the first option ...-4
Step-by-step explanation:
The solution is Option A.
The value of the equation is x = -4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = Negative 2 x + (negative 8) = 2 x + 8
Substituting the values in the equation , we get
( -2x ) + ( -8 ) = 2x + 8 be equation (1)
On simplifying the equation , we get
-2x - 8 = 2x + 8
Adding 8 on both sides of the equation , we get
2x + 16 = -2x
Adding 2x on both sides of the equation , we get
4x + 16 = 0
Subtracting 16 on both sides of the equation , we get
4x = -16
Divide by 4 on both sides of the equation , we get
x = -4
Therefore , the value of x is -4
Hence , the value of the equation is x = -4
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Vince worked 675 hours in 15 weeks. At what rate did he work in hours per week?
Answer:
45 hours a week
Step-by-step explanation:
Ok, so we know that he worked 675 hours in 15 weeks.
So all we need to do is divide the hours by the amount of weeks, which is 15:
675/15= 45
So he worked 45 hours a week!
select all of the ratios that are equivalent to 4 to 7.
5/8
12/10
8.14
5 to 10
16/28
9 to 16
Answer:
[tex]\frac{16}{28}[/tex]
Step-by-step explanation:
Question asked:
Select all of the ratios that are equivalent to 4 to 7.
1) 5/8
2) 12/10
3) 8.14
4) 5 to 10
5) 16/28
6) 9 to 16
Solution:
To know the ratios are equivalent to [tex]\frac{4}{7}[/tex] or not, we have to check each by cross multiplication:-
1) [tex]\frac{5}{8}[/tex]
[tex]\frac{4}{7} =\frac{5}{8} \\ \\[/tex]
By cross multiplication:
[tex]4\times8=5\times7\\ \\ 32=35[/tex]
Not equivalent.
2) [tex]\frac{12}{10}[/tex]
[tex]\frac{4}{7} =\frac{12}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=12\times7\\ \\ 40=84[/tex]
Not equivalent.
3) 8.14 = [tex]\frac{814}{100} \ eliminating\ decimal[/tex]
[tex]\frac{4}{7} =\frac{814}{100} \\ \\[/tex]
By cross multiplication:
[tex]4\times100=814\times7\\ \\ 400=5698[/tex]
Not equivalent.
4) [tex]\frac{5}{10}[/tex]
[tex]\frac{4}{7} =\frac{5}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=5\times7\\ \\ 40=35[/tex]
Not equivalent.
5)[tex]\frac{16}{28}[/tex]
[tex]\frac{4}{7} =\frac{16}{28} \\ \\[/tex]
By cross multiplication:
[tex]4\times28=16\times7\\ \\ 112=112[/tex]
Yes, this is equivalent.
6) [tex]\frac{9}{16}[/tex]
[tex]\frac{4}{7} =\frac{9}{16} \\ \\[/tex]
By cross multiplication:
[tex]4\times16=9\times7\\ \\ 64=63[/tex]
Not equivalent.
Thus, only [tex]\frac{16}{28}[/tex] is equivalent.
An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 4 cm.
Answer:
[tex]\frac{225}{16} cm/s[/tex]
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=25cm^3/s[/tex]
Side of base=4 cm
l=w=4 cm
Height,h=12 cm
We have to find the rate at which the water level rising when the water level is 4 cm.
Volume of pyramid=[tex]\frac{1}{3}lwh=\frac{1}{3}l^2h[/tex]
[tex]\frac{l}{h}=\frac{4}{12}=\frac{1}{3}[/tex]
[tex]l=\frac{1}{3}h[/tex]
Substitute the value
[tex]V=\frac{1}{27}h^3[/tex]
Differentiate w.r.t t
[tex]\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}[/tex]
Substitute the values
[tex]25=\frac{1}{9}(4^2)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s[/tex]
Final answer:
Using the volume of a pyramid and the concept of similar triangles, we set up a proportion to find the changing base area at a specific water level. Then, applying the product rule for differentiation, we relate the rate of volume change to the rate of height change, which allows us to solve for the water level rising rate when it is 4 cm.
Explanation:
To find the rate at which the water level is rising when the water level is 4 cm in an inverted pyramid being filled at a constant rate of 25 cubic centimeters per second, we can use the concept of similar triangles and the volume of a pyramid.
The volume V of a pyramid is given by V = (1/3)Bh, where B is the base area and h is the height. As the pyramid fills, the water forms a smaller, similar pyramid whose volume increases at a rate of 25 cm3/s.
Since the sides of the smaller pyramid are proportional to the height, we can set up a proportion using the side length s of the water level: s/4 = 4/12. Solving for s gives us s = 4 * (4/12) = 4/3 cm. The base area B of the water at this level is B = s2 = (4/3)2 cm2.
To find the rate of the rise of water dh/dt, we use the relation dV/dt = (1/3) * d(Bh)/dt. Since B is also changing with h, we have to use the product rule for differentiation: dV/dt = (1/3)(B(dh/dt) + h(dB/dt)). However, because B is a function of h2, dB/dt can be expressed as a function of dh/dt. This allows us to solve for dh/dt.