Answer: $27,000
Step-by-step explanation:
In order to calculate what his salary is this year, you need to divide $3,600 / 12% since $3,600 equals 12%. $3,600 / .12 = $30,000. If his salary is $30,000 it was 3,000 less last year, or $27,000.
His salary last year was 27,000
Steps:
find what 3,600 is 12% of.
we do this by is over of equals percent over a hundred
this gives us 30,000 dollars
next we subtract the 3000 dollars more he earned
this gives us 27,000 dollars
What is the length of segment LM
Answer:
LM = 23 units
Step-by-step explanation:
triangle KLN and triangle MLN are congruent.
The segment LM is equal to segment LK.
Also, MN is same as KN, thus we can write:
[tex]MN=KN\\25=14x-3\\25+3=14x\\28=14x\\x=2[/tex]
Since, x = 2, we can get the side length LM:
[tex]LM=LK=9x+5\\LM=LK=9(2)+5\\LM=23[/tex]
Hence, LM = 23 units
Answer:
LM = 23 units
Step-by-step explanation:
From figure we can see an isosceles triangle KNM
KN = NM
NL is the perpendicular from N to KM,
Therefore KL = LM
To find the value of x
From figure we can write,
14x - 3 = 25
14x = 25 + 3 = 28
x = 28/14 = 2
To find LM
LM = KL
we have KL = 9x + 5
Therefore LM = 9x + 5 = (9 * 2) + 5 = 23 units
If sinx=1/9, x in quadrant 1, then find (without finding x):
Sin(2x)=
Cos(2x)=
Tan(2x)=?
Answer:
Part 1) [tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
Part 2) [tex]cos(2x)=\frac{79}{81}[/tex]
Part 3) [tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]
Step-by-step explanation:
Part 1) Find sin(2x)
we know that
[tex]sin(2x)=2sin(x)cos(x)[/tex]
we have
[tex]sin(x)=\frac{1}{9}[/tex]
Find cos(x)
Remember that
[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]
substitute
[tex](\frac{1}{9})^{2}+cos^{2}(x)=1[/tex]
[tex]cos^{2}(x)=1-(\frac{1}{9})^{2}[/tex]
[tex]cos^{2}(x)=1-(\frac{1}{81})[/tex]
[tex]cos^{2}(x)=\frac{80}{81}[/tex]
[tex]cos(x)=\frac{\sqrt{80}}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex] -----> is positive because angle x belong to the I quadrant
Find sin(2x)
we have
[tex]sin(x)=\frac{1}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]
so
[tex]sin(2x)=2sin(x)cos(x)[/tex]
[tex]sin(2x)=2(\frac{1}{9})(4\frac{\sqrt{5}}{9})[/tex]
[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
Part 2) Find cos(2x)
we know that
[tex]cos(2x)=cos^{2}(x)-sin^{2}(x)[/tex]
we have
[tex]sin(x)=\frac{1}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]
so
[tex]cos(2x)=(4\frac{\sqrt{5}}{9})^{2}-(\frac{1}{9})^{2}[/tex]
[tex]cos(2x)=\frac{80}{81}-\frac{1}{81}[/tex]
[tex]cos(2x)=\frac{79}{81}[/tex]
Part 3) Find tan(2x)
we know that
[tex]tan(2x)=\frac{sin(2x)}{cos(2x)}[/tex]
we have
[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
[tex]cos(2x)=\frac{79}{81}[/tex]
so
[tex]tan(2x)=\frac{8\frac{\sqrt{5}}{81}}{\frac{79}{81}}[/tex]
[tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]
Using trigonometric identity functions, when Sinx equals 1/9, Sin(2x) equals 2√80/729, Cos(2x) equals 79/81, and Tan(2x) equals 162√80/56831.
Explanation:The question asks for the values of Sin(2x), Cos(2x), and Tan(2x) when Sinx = 1/9 (x in Quadrant 1). To solve for these values, we can use the identity formulas. If given that sinx = 1/9, it follows that cosx = √(1 - sin²x) = √(1 - (1/81)) = √(80/81) because in quadrant 1, the cosine value is positive. Therefore:
Sin(2x) = 2sinxcosx = 2 * 1/9 * √80/81 = 2√80/729,Cos(2x) = cos²x - sin²x = (80/81 - 1/81) = 79/81,Tan(2x) = sin(2x)/cos(2x)= (2√80/729) / (79/81) = 162√80/56831Learn more about Trigonometry here:https://brainly.com/question/11016599
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What is the volume of this rectangular prism.
Answer:
Volume of Rectangular Prism:
V = lwh thus: V = 5 cm³
Step-by-step explanation:
Answer:
l = 2.5 cm
w = 4 cm
h = 0.5 cm
d = 4.74342 cm
S = 26.5 cm²
Agenda:
l = length
w = width
h = height
d = diagonal
S = surface area
V = volume
Answer:
The answer is 5 cm cubed.
Step-by-step explanation:
First, use the formula for solving rectangular prisms, l*w*h(length times width times height). If you do that, 4*1/2 is 2. 2*5/2 is 5. Thus, the answer is 5.
Hope this helps!
determine whether the question is a statistical question. If it is a statistical question, identify the units for the answer. “How tall is sam?”
Answer:
No
Step-by-step explanation:
Here we are taking only one measurement: the height of one person. Strictly speaking, this is NOT a statistical question.
"List the heights of a sample of 50 first-graders" would definitely be a stat. question.
The question 'How tall is Sam?' is not a statistical question. Statistical questions expect a variety of responses, not a singular answer. Height is typically measured in feet or centimeters.
Explanation:The question 'How tall is Sam?' is not considered a statistical question. A statistical question is one in which the answer varies and requires data collection for multiple items or individuals to answer. It is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you're interested in the distribution and tendency of those answers. For instance, 'How tall are the students in a class?' is a statistical question because it would result in a variety of answers and we could analyze that data set.
The unit for height in this context typically is measured in feet or centimeters.
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ave buys a book for $8.58 and she pays with a $10 bill. how much change will she get back?
Answer:
$1.42
Step-by-step explanation:
Change = Amount She Pays With - The Cost of the Book
y=10-8.58
y=$1.42
Answer:
First we must subtract 10 into 8.58, which will equal 1.42
so she will have $1.42 change back
Indicate in standard form the equation of the line passing through the given points. M(0, 6), N(6, 0)
ANSWER
[tex]x + y = 6[/tex]
EXPLANATION
Given the x- intercept: (a,0)
and the y-intercept : (0,b)
The equation in standard form is given by:
[tex] \frac{x}{a} + \frac{y}{b} = 1[/tex]
The given x-intercept is N(6,0) and y-intercept is M(0,6).
This implies that:
a=6, and b=6.
We substitute into the formula to obtain:
[tex]\frac{x}{6} + \frac{y}{6} = 1[/tex]
Multiply through by 6 to get the standard form of the equation as:
[tex]x + y = 6[/tex]
Lynn is a single mother with two children. She qualifies to file as head of household. Her total income before deductions was $38,900 last year. Her total deductions were $11,450. Her employer withheld $3,150 from her pay for tax. Use the tax table below. How much more will Lynn owe in taxes?
To calculate how much more Lynn owes in taxes, we need to subtract her deductions from her total income to find her taxable income, then apply the tax rate from the provided table (which is missing in this case) to determine her tax liability. Unfortunately, without the tax table, we cannot accurately compute her tax obligation or the additional amount owed beyond the $3,150 withheld.
Explanation:The question involves calculating how much more in taxes Lynn will owe after her deductions. Lynn's total income before deductions is $38,900. After subtracting her total deductions of $11,450, her taxable income becomes $27,450. Without the tax table provided in the question, we cannot determine the exact tax rate applicable to Lynn's taxable income nor can we calculate the precise amount of taxes she owes or how much more she will have to pay on top of the $3,150 already withheld by her employer. Typically, to find out how much more Lynn owes, we would apply the appropriate tax rate to her taxable income and then subtract the amount already withheld.
Without specific tax rates and brackets from the tax table, we can only outline the steps to calculate Lynn's tax liability. This scenario underlines the importance of having complete information to accurately determine tax obligations.
The amount Lynn owe in taxes is determined as $399. (Option D).
How to calculate the amount Lynn owe in taxes?
The amount Lynn owe in taxes is calculated by applying the following method as shown below.
Lynn income before tax = $38,900
the total deduction in Lynn income = $11,450
amount withheld for taxes = $3,150
Lynn total income after tax is calculated as;
total income after tax = $38,900 - $11,450
total income after tax = $27,450
From the tax table attached, the tax payable for a head of household earing an income between $27,450 and $27,500 is $3,549.
So if the employer withheld $3,150 for tax, the remaining amount to be paid for tax is;
remaining amount for be paid for tax is calculated as;
= total tax - amount withheld
= $3,549 - $3,150
= $399
Thus, the amount Lynn owe in taxes is $399.
The complete question is below:
Lynn is a single mother with two children. She qualifies to file as head of household. Her total income before deductions was $38,900 last year. Her total deductions were $11,450. Her employer withheld $3,150 from her pay for tax. Use the tax table below. How much more will Lynn owe in taxes?
A. $570
B. $563
C. $407
D. $399
Graph the equations to solve the system y=-2x-3 y=x+6
Answer:Simplifying
y = -2x + -3
Reorder the terms:
y = -3 + -2x
Solving
y = -3 + -2x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = -3 + -2x
Step-by-step explanation:Simplifying
y = x + 6
Reorder the terms:
y = 6 + x
Solving
y = 6 + x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = 6 + x
subtract -5x+7 from 3x-2 set up your expression show your work
3x-2
-(-5x+7)
☝️this is your equation
distribute your subtraction sign to -5x+7 and you get
3x-2
+5x-7
add everything together and you end up with
8x-9
Answer:
[tex]\large\boxed{(3x-2)-(-5x+7)=8x-9}[/tex]
Step-by-step explanation:
[tex](3x-2)-(-5x+7)\\\\=3x-2-(-5x)-7\\\\=3x-2+5x-7\qquad\text{combine like terms}\\\\=(3x+5x)+(-2-7)\\\\=8x-9[/tex]
Path a for every 36 meters of horizontal distance , the vertical change is 14 meters
Path B for every 4.27 meters of horizontal distance , the vertical change is 2 meters
The grade of path a is _%
The grade of path b is _ %
Answer:
The grade for path a is 257.1428571%
The grade for path b is 213.5%
Step-by-step explanation:
To find the grade of a slope, you take the rise over run then you multiply by 100.
Easy question :)
There are 3 orange markers and 15 red markers in a box. Write a ratio that is equivalent to 3/15.
The answer would be 1:5
1:5 is the correct answer
Jenna can paint the shed in 2 hours. Juan can paint it in 1.5 hours. • Jenna says is they work together the job will take 1/2+1/1.5=1^1/2 hours. • Juan says if they work together the job will take 2+1.5/2=1^3/4 hours. Determine if either Jenna or Juan is correct. Explain your reasoning with numbers and words.
Answer:
There is a formula for this:
[Worker 1 Time * Worker 2 Time] / [Worker 1 Time + Worker 2 Time]
[2 * 1.5] / [2 + 1.5] = 3.0 / 3.5
= 0.8571428571 Hours =
51.43 minutes
Both Jenna and Juan are INCORRECT.
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 job / 2 hours + 1 job / 1.5 hours = 1 job / x When they work together.
1/2 + 1/1.5 = 1/x Basic Equation. Change to decimal form
0.5 + 0.6666 = 1/x Add like terms on the left
1.1666666 = 1/x Multiply by x on both sides.
1.1666667 x = 1 Divide by 1.16666667
x = 1 / 1.166667 Do the division.
x = 0.8571428
x = 6/7 of an hour.
This kind of question will always produce an answer that is less than the smallest number.
So the answer must be smaller than 2 hours or 1.5 hours.
If a rectangular prism with a length of 12 feet and a width of 9 feet has a surface area of 930 square feet find its height
Answer:
The height is 17 ft
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(LW +WH + LH)
where L = length, W = width, and H = height
We know SA = 930, L = 12, and W = 9
930 = 2(12*9 +9H + 12H)
Divide each side by 2
930/2 = 2/2(12*9 +9H + 12H)
465 = (12*9 +9H + 12H)
Combine like terms
465 = 84+21H
Subtract 84 from each side
465-84 = 84-84+21H
357 = 21H
Divide by 21
357/21=21H/21
17 = H
The height is 17 ft
Answer:
Height is 17 ft.
Step-by-step explanation:
Given: Rectangular Prism is also called cuboid
Length, L = 12 ft. and width, W = 9 ft.
Surface Area of cuboid, SA = 930 ft.²
To find: height , H
The surface area of a rectangular prism or cuboid
SA = 2(LW +WH + LH)
930 = 2(12×9 +9H + 12H)
[tex]\frac{930}{2}=108 +9H + 12H[/tex]
465 = 108 + 9H + 12H
108 + 9H + 12H = 465
21H + 108 = 465
21H = 465 - 108
21H = 357
[tex]H=\farc{357}{21}[/tex]
H = 17
therefore, Height is 17 ft.
Your job is to sort and sack marbles for sale. A bag contains 90 marbles, some red and some blue. If there are 60 blue marbles, what is the ratio of blue to red marbles?
Answer:
2:1
Step-by-step explanation:
90-60 = 30 red marbles
blue:red → 60:30 → 2:1
The table shows the mean daily temperature in Idaho during a week in January. Which statement about the data is true?
Math item stem image
The lowest mean temperature was on Tuesday.
The lowest mean temperature was on Thursday.
The highest mean temperature was on Sunday.
The highest mean temperature was on Tuesday.
Answer:
The correct option is 1.
Step-by-step explanation:
The given table shows the mean daily temperature in Idaho during a week in January.
Sunday = 0.7°F
Monday = -1.2°F
Tuesday = -1.8°F
Wednesday = 1.1°F
Thursday = 0°F
Friday = 0.2°F
Saturday = -0.4°F
Arrange the temperature in ascending order.
-1.8°F, -1.2°F, -0.4°F, 0°F, 0.2°F, 0.7°F, 1.1°F
It means the lowest mean temperature was on Tuesday and the highest mean temperature was on Wednesday.
Therefore the correct option is 1.
Answer:
The lowest mean temperature was on Tuesday.
THIS IS THE EXACT ANSWER ON TTM
Step-by-step explanation:
what us a property of a base?
1)bitter taste
2)watery feel
3)strong color
4)unreactive
Bases have bitter taste. (1)
Answer:
Bitter taste would belong to a base
Step-by-step explanation:
Please give me the answer
Answer:
Could be (1,-1) or (1,3) depending where is UP
Best regards
three times the sum of a number and eight is forty-five. what equation represents this?
3(n+8)=45
3*n+8=45
24n=45
Answer:
3(n+8)=45
Step-by-step explanation:
Don't pick the 2nd one because that would have been PEMDAS
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Hope this helps!
Option (A) The correct equation that represents 'three times the sum of a number and eight is forty-five' is 3(n+8)=45.
The equation representing "three times the sum of a number and eight is forty-five" is 3(n+8)=45. This is derived by translating the sentence into a mathematical expression: 'three times' corresponds to multiplication by 3, 'the sum of a number and eight' translates to the expression (n+8), where 'n' is the unknown number. Lastly, 'is forty-five' establishes the equality to 45.
Simplify 32 • 35.
37
310
Answer:
Simplify 32 • 35.
37
310
Step-by-step explanation:
• = Multiplication
Also by the process of elimination, 32+35 is not 37
Answer:
32x35=1120
Step-by-step explanation:
Zev is planting a garden. The garden is 10 1/3 yards long and 8 yards wide. What is the area of the garden?
Answer: 82 2/3 yards squared
Step-by-step explanation: The formula for area is l × w = A. Because of this, you need to multiply the two numbers.
1. Make 10 1/3 into an improper fraction.
10 1/3 = 31/3
2. Multiply!
31/3 × 8/1 = 248/3
3. Simplify
3 goes into 248 82 times with 2 left over (82 2/3)
how many solutions does 9x+3=9x+5 have?
There is No Absolute Solution
9x+3 = 9x+5 has zero solutions.
How to find the solution to an equation?The solution of an equation can be found by finding the value of the variable in the equation.
We can find the solution of the given equation as follows:9x+3 = 9x+5
⇒ 3 = 9x - 9x + 5
⇒ 3 = 5
But 3 ≠ 5
The variables canceled each other out and we found that the given equation doesn't have a solution. Thus the equation has no solution.
Therefore, we have determined that the given equation 9x+3=9x+5 has zero equations.
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What I need to know from this equation is the answer and the way you got it
Answer:
see explanation
Step-by-step explanation:
given
2x² - 5x - 3 = 0 ← in standard form
To factor the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 3 = - 6 and sum = - 5
The factors are - 6 and + 1
Use these factors to split the x- term
2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 3) + 1(x - 3) = 0 ← factor out (x - 3)
(x - 3)(2x + 1) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
Javier has 30 year mortgage on his 120,000 home hid bank required a 20% down payment and initially offers him a rate of 5.75% but he chose to buy 2 points and lower his rate.His current mortgage is 55.698 Taken all this into consideration ,what is the total financed price he paid for his home ?
Answer:226,432.80
Step-by-step explanation:
Final answer:
Javier's total financed price for his home, excluding the longer-term interest but including the cost of buying points, is $97,920. This total includes the initial mortgage of $96,000 after a 20% down payment on a $120,000 home and the $1,920 spent on purchasing two points to reduce the interest rate.
Explanation:
Javier's home cost $120,000, and he was required to make a 20% down payment. Twenty percent of $120,000 is $24,000, which is the down payment amount. Therefore, the initial loan amount is $120,000 - $24,000 = $96,000.
Buying points typically costs 1% of the loan amount per point to lower the interest rate by a certain percentage. It is not specified how much the rate was lowered by purchasing 2 points, but we can calculate the cost. Two points on a $96,000 loan is 2% of $96,000, which equals $1,920.
Thus, the total financed price of the home, not counting interest payments over the term of the mortgage but including the cost of the points, is the initial loan amount plus the cost of the points: $96,000 initial loan + $1,920 for points = $97,920.
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1). If ΔDEF ∼ ΔABC and DE = 4AB, what is the length of EF? The answers are √10,√17,4√10,4√17
EF = 4BC
BC = sqrt ((3-(-1)^2 +(1-2)^2)
=》 BC = sqrt (4^2 +(-1)^2) = sqrt17
=》 EF = 4BC = 4(sqrt 17)
Answer:
D. 4√17
Step-by-step explanation:
A number from 1 to 100, inclusive, is selected at random. What is the probability that the
number selected—
a. is a prime number?
b. contains the digit 9?
c. is both prime and contains the digit 9?
Answer:i might be wrong but i believe its b
Step-by-step explanation:
Answer:
A : 1/4
B : 19/100
C : 3/50
Step-by-step explanation:
There are 25 prime numbers from 1 to 100.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
25/100 = 1/4
There are 19 numbers that contain 9.
9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99.
19/100
There are 6 numbers that are prime and contain 9.
19, 29, 59, 79, 89, 97.
6/100 = 3/50
Solve the following: 5x -1oy -6y +8x +4=
What is the slope line y=5x+4
Answer:
The slope is 5
Step-by-step explanation:
This equation is in slope intercept form
y = mx +b
where m is the slope and b is the y intercept
y = 5x+4
where 5 is the slope and 4 is the y intercept
Answer:
The slope = 5Step-by-step explanation:
The slope-intercept form of the equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the equation y = 5x + 4
Therefore the slope is m = 5
how can the probability of an event help make predictions?
Answer:
The probability of an event can help in determining that how much chance is there of the event to occur. The probability is between 0 to 1 always. Closer value to 1 means that the event has more chance of occurrence while a probability close to zero means the event is less likely to occur.
Step-by-step explanation:
what is the Interquartile Range (IQR) for 6.0,6.5,6.2,5.5,6.8,6.3,6.4,6.7,6.5,6.2
Answer:
The IQR is 0.2999999999999998
Step-by-step explanation:
You take the 3rd quartile and the 4th and you subtract them.
3rd-4th=IQR
Answer:
0.3
Step-by-step explanation:
5.5, 6.0, 6.2, 6.2, 6.3, 6.4, 6.5, 6.5, 6.8, 6.7
Median: 6.35
Lower quartile: 6.2
Upper quartile: 6.5
Interquartile range: 6.5 - 6.2 = 0.3
what is the sum of the sequence 152,138,124, ... if there are 24 terms?
Answer: -216
Step-by-step explanation:
To solve the exercise you must use the formula shown below:
[tex]Sn=\frac{(a_1+a_n)n}{2}[/tex]
Where:
[tex]a_1=152\\a_n=a_{24}[/tex]
You should find [tex]a_{24}[/tex]
The formula to find it is:
[tex]a_n=a_1+(n-1)d[/tex]
Where d is the difference between two consecutive terms.
[tex]d=138-152=-14[/tex]
Then:
[tex]a_{24}=152+(24-1)(14)=-170[/tex]
Substitute it into the first formula. Therefore, you obtain:
[tex]S_{24}=\frac{(152-170)(24)}{2}=-216[/tex]
Answer:
Sn = -216
Step-by-step explanation:
We are given the following sequence and we are to find the sum of the given sequence if there are 24 terms in it:
[tex] 152, 138, 124, ... [/tex]
We know that the formula of sum for an arithmetic sequence is given by:
[tex]S_n =\frac{n(a_1+a_n)}{2}[/tex]
where [tex]a_1[/tex] is the first term (124)and [tex]a_n[/tex] is the last term [tex]a_{24}[/tex].
To find [tex]a_1[/tex], we will use the following formual:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_24=152+(24-1)(-14)[/tex]
[tex]a_{24}=170[/tex]
Substituting the given values in the above formula to get the sum:
[tex]S_n =\frac{24(152-170)}{2}[/tex]
[tex]S_n=-216[/tex]