The four winning numbers are 24, 32, 27 and 37 respectively
How to determine the numbersIt is important to note the following;
A prime number is a number than is divisible by 1 and itselfA square root is defined as the factor of a number which when multiplied by itself would give back the original numberThe cube of a number is that number to the exponent or power of 3A multiple is defined as the product of an integer, element or quantityFrom the information given;
a. First number = square root of 576
This is represented as
First number = √576
First number = 24
b. Second number = multiple of 8 between 30 and 39
Second number = 32
c. Third number = cube of 3
This is represented as;
Third number = 3³
Third number = 37
d. largest prime number less than 40
Fourth number = 37
Hence, the numbers are 24, 32, 27 and 37
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What is A-1? A=[-2 -3 3 12] Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
In this Matrix A= [-2 -3
3 12]
the matrix of A - 1 is
[-4/5 -1/5
1/5 2/15]
According to the question, given that
[-2 -3
3 12 ] ^ -1
First, we find the determinant
-2 * 12 - (-3 *3) = -24 - (-9) = -24 +9 = -15
Multiply 1 over the determinant by The matrix with the -2 and 12 switched and negate the -3 and the 3
1/-15 [12 3
-3 -2 ]
after multiply by 1/ - 15, we get
[-4/5 -1/5
1/5 2/15]
Therefore, In given Matrix A, after solving we get the value A- 1 is
[-4/5 -1/5
1/5 2/15]
Matrix
If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,
Matrix. [ 5 6 3
-2 3 2 ]
is a 2 × 3 matrix. A square matrix of order n have n rows and n columns. Ordinary numbers can be thought of as 1 1 matrices, making the number 3 the matrix [3]A row vector is a matrix with one row and n columns, and a column vector is a matrix with one column and n rows.
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Station 5
The ratio of the number of dollars Jada has to the number of dollars Kelly has is 4:7. Kelly
gives Jada $6.00. The ratio of the number of dollars Jada has to the number of dollars Kelly
has changes to 6:5. How many dollars do Jada and Kelly each have now?
The number of dollars Jada and Kelly each have now is $18 and $15.
What are ratios?Mathematicians refer to a comparison of two or more integers as a "ratio."It acts as a measuring tool to demonstrate how large or small one amount is in contrast to another. In a ratio, two quantities are compared by utilizing division. The "antecedent" in this instance is the dividend, while the "consequent" is the divisor.Given:
Ratio of the number of dollars Jada has to the number of dollars Kelly has = 4:7
Changed ratio after Kelly gives Jada $6.00 = 6:5
Let the number of dollars Jada and Kelly have be 4x and 7x.
Kelly gives Jada $6.00,
So,
Number of dollars Jada has now is $(4x + 6).
Number of dollars Kelly has now is $(7x - 6).
The ratio of the number of dollars is changed to 6:5.
⇒ [tex]\frac{4x + 6}{7x -6} = \frac{6}{5}[/tex]
⇒ 5(4x + 6) = 6(7x - 6)
⇒ 20x + 30 = 42x - 36
⇒ 42x - 20x = 30 + 36
⇒ 22x = 66
⇒ x = 3
Number of dollars Jada has now = (4x + 6) = $18
Number of dollars Kelly has now = (7x - 6) = $15
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A quality assurance engineer randomly checks manufactured parts to ensure that they are within 0.002 mm of the desired specifications. If the desired length of the part is 3 mm, then the compound inequality
-0.002
Choose the absolute value inequality that represents the situation.
The value of absolute inequality will be given by 0.002 ≥ |x-3|.
Inequality may be defined as the expression which shows unequal behavior between two entities while absolute inequality expression includes inequality along with an absolute value. For example, |x| > 3, |x| <3, |x| ≤3 or |x| ≥3. Now, let us assume the length of the part in the question as x. Since, the desired length is given as 3mm and also the parts are within 0.002 mm of the desired specifications.
Therefore, the maximum length of the part can be = 3 + 0.002
and the minimum length of the part can be = 3 - 0.002
Therefore, we can write the inequality as
3 - 0.002 ≤ x ≤ 3 + 0.002
⇒ 3 - 0.002 ≤ x and x ≤ 3 + 0.002
⇒ -0.002 ≤ x-3 and x-3 ≤ 0.002
⇒ 0.002 ≥ -(x-3) and x-3 ≤ 0.002 (Because a > b ⇒ -a<-b)
⇒ 0.002 ≥ | x - 3 |
Thus, the required absolute inequality is 0.002 ≥ |x-3|.
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Answer:
A: |x - 3| ≤ 0.002
Step-by-step explanation:
The table shows the worldwide box office (in billions of
dollars) for the movie industry during the years shown.
Year
2001
2003
2005
2007
2009
Box office
(in billions of dollars)
17.1
18.2
19.3
21.5
23.7
a. Write this paired data as a set of ordered pairs of
the form (year, box office).
What is the ordered pair that corresponds to the first
row of data given in the table?
Answer:
193 is it I'm not lying
Step-by-step explanation:
A 22-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than four times the length of the first piece. Find the lengths of the pieces.
A 22-inch piece of steel is divided into three parts, the length of 1st 2nd and 3rd piece are 3 inch,6 inch and 13 inch.
Given that,
A 22-inch piece of steel is divided into three parts, the second of which is twice as long as the first and the third of which is one inch longer than the first.
We have to find the parts' lengths.
Let us take, the length of the first piece is x inch.
Then the length of the second piece is 2x.
Then the length of the third piece is 4x + 1 inch.
We know total length of the steel is 22 inch.
We can write as,
x + 2x + 4x + 1 = 22
7x = 21
x = 3.
Then, the length of the first piece is 3 inch.
Then the length of the second piece is 2×3=6 inch.
Then the length of the third piece is 4×3 + 1=12+1=13 inch.
Therefore, the length of 1st 2nd and 3rd piece are 3 inch,6inch and 13 inch.
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What is the domain of the exponential function shown below?
F(x)=2• (1/10)^x
O A. All real numbers except 2
о B. x>0
о C. x<0
O D. All real numbers
We can replace x with any real number, positive or negative. We can also plug in x = 0. There aren't any restrictions to worry about with the input.
Examples:
Plug in x = 2 to get f(2) = 2(1/10)^2 = 0.02
Plug in x = -2 to get f(-2) = 2(1/10)^(-2) = 200
Plug in x = 0 to get f(0) = 2(1/10)^(0) = 2
The domain of the given function is "All real numbers". So, option D is correct.
What is the domain of a function?The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.
here, we have,
Finding the domain of the given function:
The given function is f(x) = 2×
Since this function has the variable x in the exponent, this is an exponential function.
So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.
Thus, option D is true.
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If ΔEFG ~ ΔLMN with a ratio of 2:1, which of the following is true?
Step 1
Given;
Step 2
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
[tex]\begin{gathered} Triangle\text{ EFG}\approx\text{ Triangle LMN in the ratio 2:1} \\ Thus, \\ \frac{EF}{L\text{ M}}=\frac{FG}{MN}=\frac{EG}{LN}=\frac{2}{1} \end{gathered}[/tex]Thus, the answer is;
COMMER MATHEMATICSGross pay with commission and salaryColumbia Mirror and Glass pays Eric Lee a $1730 monthly salary plus a 12% commission on merchandise he sells each month. Assume Eric's sales were $87,400 for last month.Calculate the following amounts:1. Amount of Commission2. Gross Pay
Answer:Explanation:
(a)$10,488
(b)$12,218.
• ric;' Monthly Salary = $1,730
,• Percentage commision = 12%
Part A
f Eric 's sales were $87,400 for last month, his amount of commission will be:
[tex]\begin{gathered} Commision=12\%\text{ of Sales} \\ =\frac{12}{100}\times87400 \\ =\$10,488 \end{gathered}[/tex]Eric's amount of commission is $10,488.
art B
Eric's gross pay will be the sum of his monthly salary and commission.
[tex]\begin{gathered} \text{Gross Pay=Salary+Commission} \\ =1730+10488 \\ =\$12,218 \end{gathered}[/tex]Eric's gross pay is $12,218.
Xbxbxbdndbdndbdnsndnsnsnnssn
SOLUTION:
Case: Simple Interest
Method:
Simple Interest, I
[tex]\begin{gathered} I=PRT \\ Hence \\ T=\frac{I}{PR} \end{gathered}[/tex]Where
P= $500
R= 7.5% or 0.075
I= $225
Therefore, Time T
[tex]\begin{gathered} T=\frac{225}{500\times0.075} \\ T=6 \end{gathered}[/tex]Final answer:
6 years
if the temperature was -2 1/2 in the morning . by the afternoon the temperature was 0.2 what was the change between the morning and afternoon.
The change between the morning and afternoon temperature is 2.7.
What is temperature?It should be noted that temperature simply means the degree of hotness as well as the coldness that is in a particular body
In this case, the temperature was -2 1/2 in the morning . by the afternoon the temperature was 0.2.
The change between the temperature will be:
= 0.2 - (- 2 1/2)
= 0.2 + 2.5
= 2.7
The temperature change is 2.7.
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Write an expression for the amount of money (in nickels) in n dollars.
PLEASE HELP ITS DUE IN AN HOUR
Answer:
11 nickels . Are in a doldollar
Step-by-step explanation:
Solve the following inequalities,express the solution in interval notation and graph it 4.a)
The inequality is given to be:
[tex]\mleft|x-6\mright|\ge2[/tex]Recall the Absolute Rule:
[tex]\mathrm{If}\: |u|\: \ge\: a,\: a\: >\: 0\: \mathrm{then}\: u\: \le\: -a\: \quad \mathrm{or}\quad \: u\: \ge\: a[/tex]Applying this to the inequality, we have:
[tex]\begin{gathered} x-6\ge2 \\ x\ge2+6 \\ x\ge8 \end{gathered}[/tex]or
[tex]\begin{gathered} x-6\le-2 \\ x\le-2+6 \\ x\le4 \end{gathered}[/tex]Therefore, the solution to the inequality is:
[tex]x\le\: 4\quad \mathrm{or}\quad \: x\ge\: 8[/tex]A multivitamin tablet contains
10.5 mg of calcium how much calcium does a bottle of 40 tablets contain
The bottle of 40 tablets will contain 420 milligrams of tablets.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
Given that a multivitamin tablet contains 10.5 mg of calcium and there are 40 tablets in the bottle. The total amount of the tablets in the bottles will be calculated as:-
Total tablets = 10.5 mg x 40
Total tablets = 420 mg
Therefore, a bottle of 40 tablets will contain 420 milligrams of tablets.
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You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.
The number of weeks for your friend's savings to be same as your savings does not exist
How to determine the number of weeks?The given parameters are:
Your savings account
Initial amount = $100
Weekly savings = $40
Your friend's savings account
Initial amount = $80
Weekly savings = $10
The equation that represents the amount in the account after w weeks is represented as
Amount = Initial amount + Weekly savings x Number of weeks
This gives:
You: Amount = 100 + 40x
Your friend = 80 + 10x
The above equations are linear equations
When the amounts are equal, we have
100 + 40x = 80 + 10x
This gives
30x = -20
Divide
x = -2/3
The number of weeks cannot be negative
Hence, your friend's savings will never be up to your savings
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Possible question
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.
When will you and your friend have the same amount?
Two angles of a triangle have the same measure and the third one is 21 degrees greater than the measure of each of the other two. Find the
measure of the largest angle in the triangle.
Answer: The largest angle has a measure of
degrees
Answer:
Since two angles of the triangle have the same measure, the triangle is an isosceles triangle.
Let one angle be a variable (eg: x) so we can form expressions and solve.
Let the first and second angle be x°.
Form an expression for the third angle using the information given.
Third angle = (x + 21)°
Since sum of angles in a triangle is 180°, we can form an equation.
x + x + (x + 21) = 180
Simplify and solve for x.
3x + 21 = 180
3x = 159
x = 53
Largest angle is the third angle.
Substitute x into the expression to find the value.
Third angle = 53 + 21
= 74°
An operation has experienced total sales of $85,000, beverage costs of $16,230, food costs of $30,167, labor costs of $22,158, rent of $4,000, and insurance of $1,000.
What is its prime cost as a percentage of total sales?
O 86.6%
19.3 %
O 13.4%
O 80.7%
Answer: 80.7%
Step-by-step explanation: COGS (beverage and food costs) = $68,555
$68,555 is 80.6529412% of $85,000 rounded to the nearest tenth is 80.7%
The following account balances were taken from the adjusted trial balance for Urgent Messenger Service, a delivery service firm, for the fiscal year ended November 30, 20Y1:
If the account balances were taken from the adjusted trial balance for Urgent Messenger Service, a delivery service firm, for the fiscal year ended November 30, 20Y1: The income statement is $186,750.
What is income statement ?Income statement can be defined as the statement that help to shows the revenue and expenditure a company or an organization. When preparing income statement when the revenue amount is greater that the expenses the end result will be net income and in a situation were the expenses is higher than the revenue the end result will be net loss.
Now let prepare the income statement
Urgent Messenger Service Income Statement For the Year Ended November 30, 20Y1
Revenue:
Fees earned $724,500
Expenses:
Salaries expense $393,100
Rent expense $75,000
Utilities expense $41,200
Supplies expense $6,150
Insurance expense $5,000
Miscellaneous expense $6,650
Total expenses $537,750
Net income $186,750
($724,500 - $537,750 )
Therefore the income statement is the amount of $186,750.
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The complete question is:
The following account balances were taken from the adjusted trial balance for Urgent Messenger Service, a delivery service firm, for the fiscal year ended November 30, 20Y1:
Depreciation Expense $10,650
Fees Earned 724,500
Insurance Expense 5,000
Miscellaneous Expense 6,650
Rent Expense 75,000
Salaries Expense 393,100
Supplies Expense 6,150
Utilities Expense 41,200
Prepare an income statement.
A rabbit is moving in the positive x-direction at 1.50 m/s when it spots a predator and accelerates to a velocity of 12.1 m/s along the positive y-axis, all in 2.20 s. Determine the x-component and the y-component of the rabbit's acceleration. (Enter your answers in m/s2. Indicate the direction with the signs of your answers.)
Answer:
Step-by-step explanation:
First we have to consider the initial and final velocities to calculate the average acceleration:
v_i= - \Big[ 1.10\frac{m}{s}\Big]\widehat{i} \\ v_f= \Big[ 11.5\frac{m}{s}\Big]\widehat{j} \\ \implies \Delta v=v_f-v_i \\ \implies \Delta v= [ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j} \text{ in an average time } \Delta t=1.40\,s.v
i
=−[1.10
s
m
]
i
v
f
=[11.5
s
m
]
j
⟹Δv=v
f
−v
i
⟹Δv=[1.10
s
m
]
i
+[11.5
s
m
]
j
in an average time Δt=1.40s.
With the information we can calculate the average acceleration in terms of the x- and y-components:
a=\Delta v/\Delta t= \dfrac{[ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j}}{1.40\,s} \\ \text{ } \\ \implies a= \big[ 0.786\frac{m}{s^2}\big]\widehat{i} + \big[ 8.214\frac{m}{s^2} \big]\widehat{j}a=Δv/Δt=
1.40s
[1.10
s
m
]
i
+[11.5
s
m
]
j
⟹a=[0.786
s
2
m
]
i
+[8.214
s
2
m
]
j
3/4 + -3.9 =
I NEED HELP
Answer:
-3.15
Step-by-step explanation:
3/4 converted to a decimal is .75 so .75 + -3.9 is -3.15
Hope this helps! <3
I can send the other options? I just need this explained?
The standard equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
For:
[tex]\begin{gathered} (x+3)^2+(y+1)^2=16 \\ \end{gathered}[/tex]Rewrite the equation as:
[tex]\begin{gathered} (x-(-3))^2+(y-(-1))^2=4^2 \\ so\colon \\ h=-3 \\ k=-1 \\ r=4 \end{gathered}[/tex]We can conclude it is a circle with center at (-3,-1) and radius of 4
What is the area of this shape
Given a figure of a right trapezoid
The bases are the sides, 4 and 6
And the height = 4
The area of the trapezoid = 1/2(sum of the bases) times the height
So, the area =
[tex]\frac{1}{2}(4+6)\cdot4=\frac{1}{2}\cdot10\cdot4=20[/tex]So, the answer will be: Area = 20 unit²
how many 42’’ wide wall panels must be bolted together to create a 28’ wall?
From the question, we were asked that how many 42 inches wide panels must be bolted together to create a 28 feet wall.
First let's covert the two measurement to same unit.
So, lets convert 42 inches into feet.
Recall, 1 foot will give 12 inches
42 inches will be:
42/12 = 3.5 feet
Therefore, the wide wall that must be bolted together to create a 28 feet wall is:
= 28/3.5
= 8 feet.
Identify the domain and range of y = [x] + 2.
The most appropriate choice for function, domain and range of a function will be given by
Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers
Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.
What is Function, Domain and Range of a function?
Function
A function from A to B is a rule that assigns to each element of A a unique element of B
Domain of a function
Domain of a function is the set of values for which the function is defined.
Range of a function
The set of values obtained on putting the values of the domain is called the range of a function.
Here,
Domain of [tex]y = [x] + 2[/tex]
[tex][x][/tex] is defined for all [tex]x[/tex] ∈ [tex]\mathbb{R}[/tex], the set of real numbers
Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers
[tex][x][/tex] is the greatest integer not exceeding [tex]x[/tex]
So [tex][x][/tex] [tex]+ 2[/tex] gives only integer values
So Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.
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Solve the inequality.
a-6<8
no real solutions
O all real numbers
O 2
O a < 14
O a< -2 or a> 14
[tex]a < 8 -+ 6 \\ =a < 14[/tex]
The second option is the answer.
Dante rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 87 cents for each mile driven. Dante had to pay $218.22 when he returned the truck. For how many miles did he drive the truck?
Choose the expression that completes the equation. 30 ÷ 2 + 10 = ________ Question 4 options: 3(2 + 3) 7(2 + 1) 6(3 + 7) 5(4 +1).
Answer:
5(4 + 1).
Step-by-step explanation:
[tex]{ \rm{(30 \div 2) + 10 = 15 + 10}} \\ [/tex]
- Factorise out 5;
[tex]{ \tt{ = 5(3 + 2)}} \\ \\ = { \tt{5(4 + 1)}}[/tex]
Probability of dependent
Events
Dependent events: The likelihood of one event happening influences the likelihood of the other event happening.
What are dependent events?
When the result of one event affects the result of another, two events are said to be dependent events.
The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.
The likelihood of one event does influence the likelihood of the other happening.
For instance, the likelihood of drawing another King decreases if you remove a King from a deck of cards without replacing it.
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From the choices below, choose an expression that is equivalent to the expression:
22/-4
A. (-22|-4 )
B. 22|4
C. -(22|-4)
D. -(22|4)
Answer: b
Step-by-step explanation:
what is the prime fractorization of 42?
First I will define what prime factor means
Prime factors of 42 are the factors of 42 that are prime
Prime numbers are those numbers that have two factors; 1 and itself
Factors of 42 are those numbers that can go into 42 without remainder
So let's list out the factors of 42, they are;
Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42
Now among these factors, we will list out the ones that are prime, they are the prime factors
That is;
Prime factors of 42 = 2, 3, and 7
To express 42 as a product of it's prime factors, we have 2 ways of doing this
The first method is; To keep dividing 42 by the smallest prime factors
42 = 2 x 3 x 7
The second method is;
Therefore, the prime factorization of 42 = 2 x 3 x 7
The prime factorization of 42 is 2 × 3 × 7.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The positive pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).
The negative pair factors of 42 are (-1, -42), (-2, -21), (-3, -14), and (-6, -7).
The 42 factors that are prime are known as the prime factors of 42.
Prime numbers are those with just themselves and factor 1 as their factors.
The numbers that can round to 42 without leaving a remainder are known as 42 factors. Let's enumerate the 42 factors, which are as follows:
1, 2, 3, 6, 7, 14, 21, and 42 are factors of 42.
We shall now list the prime factors among them, they are the prime factors. which is;
42 has prime factors of 2, 3, and 7.
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Let x, y, z, and w represent the population in millions of four cities A, B, C, and D, respectively. Express the given statement as an equation in x, y, z, and w. If the equation is linear, express it in the standard form
ax + by + cz + dw = k.
(If the equation is not linear, enter NONLINEAR.)
City A has three times as many people as cities B and C combined
Answer:
x -3y -3z = 0
Step-by-step explanation:
You want to write "City A has three times as many people as cities B and C combined" as an equation in standard form, letting x, y, z, w represent the populations of cities A, B, C, D, respectively.
TranslationThe populations of cites B and C combined can be expressed by ...
y +z
Three times the combined population is then ...
3(y +z)
This is equal to the population of city A, so we can write ...
x = 3(y +z)
Standard formThis equation is in standard form when all of the variable terms are on one side of the equal sign, and the expression is simplified.
x -3(y +z) = 0 . . . . . . . subtract the right side expression
x -3y -3z = 0 . . . . . . . eliminate parentheses; standard form