Answer:
Step-by-step explanation:
here's a more detailed explanation:
The assistant received a raise of 10%, which means that their salary increased by 10% of the original salary. The new salary after the raise is given as 47,585.
To find the original salary before the raise, we need to reverse the effect of the raise. To do this, we divide the new salary by the factor that represents the increase, which is 1 plus the raise as a decimal.
The raise as a percentage is 10%, which is equivalent to 0.10 as a decimal. Therefore, the factor that represents the increase is 1 + 0.10 = 1.10.
We can now use this factor to find the original salary by dividing the new salary by the factor:
Original salary = New salary / (1 + Raise as a decimal)
Original salary = 47,585 / (1 + 0.10)
Original salary = 47,585 / 1.10
Original salary = 43,259.09
So the salary before the raise was 43,259.09.
Find the equation for the line through the point (7/5,1/12) that is perpendicular to the line 3x-4y=7. You may leave your answer in the point-slope form if you wish. If you use slope-intercept form, all fractions must be combined and reduced wherever possible.
The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
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Fine Angle R using law of cosines. Round to the nearest tenth
The measure of angle R from the triangle PQR is 15.31°.
What is cosine rule?In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
The formula for the cosine rule is c=√(a²+b²-2ab cosC)
In the given triangle PQR, PQ=9 units, PR=12 units and RQ=20 units
PQ²=PR²+RQ² -2×12×20cosR
9²=12²+20² -2×12×20cosR
81=144+400-480cosR
81=544-480cosR
81-544= -480cosR
-463= -480cosR
cosR= 463/480
cosR= 0.9645
∠R=15.31°
Therefore, the measure of angle R is 15.31°.
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question is in the picture
The formula of the area of the trapezium as subject to x is,
x = 2A/h - y.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The area of the trapezium,
A = (1/2)h(x + y)
To make x the subject of the equation:
2A/h = (x + y)
2A/h - y = x
x = 2A/h - y
Therefore, the formula is x = 2A/h - y.
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If n=540 and
(p-hat) = 0.64, construct a 90% confidence interval.
Give your answers to three decimals.
__ < p < __
Answer:
0.606 < p < 0.674
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.64\pm1.645\sqrt{\frac{0.64(1-0.64)}{540}}\\\\CI_{90\%}\approx0.64\pm0.034\\\\CI_{90\%}=\{0.606,0.674\}[/tex]
Thus, we are 90% confident that the true population proportion is between 0.606 and 0.674
Given below are descriptions of two lines.
Line 1: Goes through (-6,-3) and (0,5)
Line 2: Goes through (-6,-5) and (-3,-1)
The slope of Line 1 is m =
The slope of Line 2 is m =
Finally, which of the following is true?
O Line 1 is parallel to Line 2.
O Line 1 is perpendicular to Line 2
O Line 1 is neither parallel nor perpendicular to Line 2
Answer:
The slope of line 1 is -4/3.
The slope of line 2 is 2/3.
Line 1 is neither parallel nor perpendicular to line 2.
Step-by-step explanation:
firstly we find slope using two point formula .
The lines are said to be parallel when their slopes are equal.The lines are said to be perpendicular when the product of their slope is -1. Hence, line 1 is neither parallel nor perpendicular to line 2.
Solve for x:
-4x + 2(x+4)= -7x- (x + 1)
Answer: x = -3/2
Step-by-step explanation:
-4x + 2(x+4) = -7x - (x+1)
-4x + 2x+8 = -7x -x-1
-2x + 8 = -8x - 1
+2x +2x
8 = -6x - 1
+1 +1
9 = -6x
/-6 /-6
-9/6 = x
-3/2 = x
Find the variance for the given sample data, Round your answer to one more decimal place than the original data 7 725 1 A. 11. 8 B. 7. 8 22 C. 6. 2 D. 7. 7
The variance of the given frequency distribution is 60.92, and the standard deviation is option (b) 7.80.
To calculate the variance of a frequency distribution, we need to first find the mean or average of the data. The formula for calculating the mean is as follows:
mean (μ) = Σfx / Σf
where Σfx represents the sum of the products of each value and its corresponding frequency, and Σf is the sum of all the frequencies.
Using the given data, we can calculate the mean as follows:
μ = (43 + 85 + 119 + 175 + 204 + 243 + 32*1) / (3+5+9+5+4+3+1)
μ = 13.5
Next, we need to calculate the deviation of each data point from the mean. To do this, we subtract the mean from each value and square the result. The formula for this is:
(x - μ)²
Using this formula, we get the following deviations for each data point:
(4 - 13.5)² = 81.00
(8 - 13.5)² = 30.25
(11 - 13.5)² = 6.25
(17 - 13.5)² = 12.25
(20 - 13.5)² = 42.25
(24 - 13.5)² = 110.25
(32 - 13.5)² = 333.22
Next, we need to multiply each deviation by its corresponding frequency, and then sum up the results. The formula for this is:
Σf(x - μ)²
Using the above deviations and frequencies, we can calculate the sum of squares as follows:
Σf(x - μ)² = 381.00 + 530.25 + 96.25 + 512.25 + 442.25 + 3110.25 + 1 x 333.22
Σf(x - μ)² = 1827.48
Finally, we can calculate the variance by dividing the sum of squares by the total number of observations (Σf). The formula for variance is:
σ² = Σf(x - μ)² / Σf
Using the above values, we can calculate the variance as follows:
σ² = 1827.48 / 30
σ² = 60.92
The standard deviation is the square root of the variance. Therefore:
σ = √(60.92)
σ = 7.80
Therefore, the correction option is (b).
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Complete Question:
Find the variance and standard deviation of the following frequency distribution:
x 4 8 11 17 20 24 32
f 3 5 9 5 4 3 1
Help with question 6:
If the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other.
How are g.f' and f.g' related?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
If the quotient of two functions f(x) and g(x) is a constant k, meaning f(x)/g(x) = k for all x, then it follows that:
f(x) = k.g(x)
Taking the derivative of both sides with respect to x, we get:
f'(x) = k.g'(x) + g(x).d(k)/dx
Since the constant k is a constant and not a function of x, its derivative with respect to x is zero, so we can simplify the equation to:
f'(x) = k.g'(x)
Thus, we can see that if the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other, with the constant of proportionality equal to k.
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Find the perimeter of the figure.
Answer:
Step-by-step explanation:
its 11
ignore bllllllllllldjbjddddddddddddddddddddddddd
14. What is the equation of the line that passes through the
point (-3, -5) and has a slope of
-2/3
Answer:
y=-2/3x-0.5
Step-by-step explanation:
y=mx+b is the equation for slopes so I used it and all I needed to find was the y-intercept, which is -0.5
what mistake did he make help!!
Answer:
b
Step-by-step explanation:
Can't see the whole transaction because it is cutoff on the bottom but it looks like b
Graph y=0.5(2)^x on the domain -1 ≤ x ≤ 4
What is the range of this function?
The graph of the exponential function y = 0.5(2)^x on the domain -1 ≤ x ≤ 4 is given by the image presented at the end of the answer.
The range is given as follows:
0.25 ≤ y ≤ 8.
How to graph the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change, the value by which y is multiplied when x is increased by one.The parameters for the function in this problem are given as follows:
a = 0.5, b = 2.
The numeric values are given as follows:
x = -1, y = 0.25.x = 0, y = 0.5 -> x increases by one, y multiplies by 2.x = 1, y = 1.x = 2, y = 2.x = 3, y = 4.x = 4, y = 8.More can be learned about exponential functions at https://brainly.com/question/30113628
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Let h(x) = (gof)(x)=√x+3
Which of the following could be a possible decomposition of h(x)?
A. f(x)=√x; g(x)=x+3
B. f(x)=x; g(x)=x+3
c. f(x)=x+3; g(x)=√x
D. f(x)=3x; g(x)=√x
Answer:
the correct answer is letter A
3m^2 + 4m + 7
4m^2 - 3m + 2
Which of the following is the sum of the above two polynomials?
Answer: The sum of the two polynomials 3m^2 + 4m + 7 and 4m^2 - 3m + 2 is 7m^2 + m + 9.
Step-by-step explanation:
Let
U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
List all the members of the given set. (Enter your answers as a comma-separated list.)
A ∪ (B ∩ C)
On solving the provided question we can say that The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
what is set?A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,
The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
z(180) = (180-185)/4 = -1.25
P(x < 180) = P(z < -1.25)
3)28 C 5
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Math Essay on probability of the Ohio lottery
The Ohio Lottery has been based on the probability deriving with the correct derivation of the number with the highest chances.
What is probability?Probability has been defined as the mathematical description of learning the chances of an event to occur. The probability ranges from 0 to 1, with 1 being complete probability, and 0 means no chances of event to occur.
The Ohio lottery has been given as the game of lottery operated by the Ohio Lottery Commission. The purpose initiated by the Ohio Lottery has been to raise the funds for the education.
The lottery has been based on the probability of the common outcomes that delivers the formation of the numbers with the highest chances of getting resulted.
The games such as Bucket 5, Super Lotto, Ohio Lotto has been based on the probability of the drawing the numbers, and the correct probability won the lottery.
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Your question is probably incomplete, and most probably the complete question is:
Create a Math Essay on probability of the Ohio lottery.
The angle y° and 49° are complementary,find the value y
sum of two complementary angle is 180•
[tex]180 - 49 = y = 131[/tex]
am a 4-digit number. My thousands digit is greater than 6, but less than 8 My hundreds digits is the highest even number. and ones The sum of my tens cligit a digit is equal to my hundreds digit. My tens digit is 6. Who am I?
Answer:
From the given information, we know that:
The thousands digit is greater than 6 and less than 8, so it must be 7.
The hundreds digit is the highest even number, so it must be 8.
The tens digit is 6.
The sum of the tens and ones digit is equal to the hundreds digit, so 6 + ones digit = 8.
Solving for the ones digit, we get:
ones digit = 8 - 6 = 2
Putting the digits together, we get the number: 7862.
So, the 4-digit number that satisfies all the given conditions is 7862.
Step-by-step explanation:
Given the clues, the thousands digit is 7, the hundreds digit is 8, the tens digit is 6, and the ones digit is 2; therefore, the 4-digit number is 7862.
Explanation:Given the hints, we can infer that:
The thousands digit is greater than 6, but less than 8, so it can only be 7.The hundreds digit is the highest even number, which is 8.The tens digit was specifically said to be 6.The sum of the tens and ones digit is equal to the hundreds digit. The tens digit is 6 and the hundreds digit is 8, so the ones digit must be 2 because 6 + 2 = 8.Therefore, the 4-digit number is 7862.
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Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.
The ratio of the amounts of money that they each get:
1 : 3 : 3/2
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's represent the amount of money that Jan gets as x.
Then, the amount of money that Freda gets is 3x,
and the amount of money that Pieter gets is:
= (1/2) x 3x
= 3/2 x (x)
The ratio of the amounts of money that they each get can be written as:
⇒ x : 3x : 3/2 x (x)
⇒ 1 : 3 : 3/2
So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.
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A castle guard is standing on the opposite side of an 8-foot moat and wants to reach a window that is 15 feet above the ground. The guard props a ladder against the castle wall to form a right triangle as shown. Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot.
The length of the ladder needed to reach the window to the nearest tenth of a foot is option (a). 17.0 feet.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given,
Length of the moat = 8 feet
Height of the window from the ground = 15 feet
Using the concept of right triangle, from the figure, length of the moat is the base and height of the window is the altitude.
Length of the ladder is the hypotenuse.
By Pythagoras theorem,
Length of the ladder = [tex]\sqrt{8^{2}+15^2 }[/tex] = [tex]\sqrt{289}[/tex] = 17
Hence the length of the ladder is 17.0 feet to the nearest tenth of a foot.
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find the equation of a line passing through two points (1,-1, 2) and (0,2-3).
Answer: The equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is: y = 3x - 4.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the point-slope form of a line. The point-slope form of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.
Step 1: Find the slope of the line (m)
The slope of the line can be found using the two points:
m = (y2 - y1) / (x2 - x1)
Plug in the values of x1, x2, y1, and y2 from the two given points:
m = (2 - (-1)) / (0 - 1) = 3
Step 2: Write the equation using the point-slope form
Use the point-slope form and the slope from step 1, and one of the given points:
y - (-1) = 3(x - 1)
Step 3: Simplify the equation
y + 1 = 3x - 3
Step 4: Solve for y
y = 3x - 4
So, the equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is y = 3x - 4.
which answer choice is the correct one
5 Heena and Sudha share Profit & Loss equally. Their capitals were Rs.1,20,000 and Rs. 80,000 respectively. There was also a balance of Rs. 60,000 in General reserve and revaluation gain amounted to
Rs. 15,000. They admit friend Teena with 1/5 share. Teena brings Rs.90,000 as capital. Calculate the
amount of goodwill of the firm.
a) Rs.85,000
b) Rs.1,00,000
c) Rs.20,000
d) None of the above
On solving the provided question, we can say that by unitary method, Total capital of the firm = Rs. 85,000
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Heena and Sudha share profits and losses equally.
If the capital of Teena is 1/5 of the total capital which is equal to Rs. [tex]90,000[/tex] 1/5 of Total capital = Rs. [tex]90,000[/tex]
Total capital = Rs. 90,000 × 5 = 4,50,000, capital of all partners = Rs. [tex]1,20,000 + Rs. 80,000 + Rs. 90,000 + 60,000 + Rs. 15,000[/tex]
Total capital of all partners = Rs. [tex]3,65,000[/tex]
Total capital of the firm = Rs. [tex]85,000[/tex]
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7. The proof shows that opposite angles of a parallelogram are congruent.
Given: ABCD is a parallelogram with diagonal AC.
Prove: ZBAD ZDCB
Proof:
Statements
ABCD is a parallelogram with diagonal AC.
AB II CD and AD II BC
42 = 23
21 = 24
m22= m23 and m/1 =m24
D
mz1+m22=m24+ m22
m21+ m/2 = m24+ m23
mz1+mz2 = m/BAD
m23+ m24 = m/DCB
m/BAD = m/DCB
ZBAD LDCB
Reasons
Given
Definition of parallelogs
Alternate interior angl
are congruent.
Measures of congru
are equal.
Addition property
Angle addition
Substitution
Angles are c
their measu
What is the missing reason in this partial proof?
?
A. ASA
B. Substitution
C. Angle addition postulate
D. Alternate interior angles are congruent.
The completed two-column table that is used to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution. The correct option is option B
B. Substitution
What are congruent angles?
Congruent angles are angles that have the same measurement,
The two-column table is presented as follows;
[tex]{}[/tex] Statements Reasons
1. ABCD is a parallelogram with diagonal [tex]\overline{AC}[/tex] [tex]{}[/tex] Given
2. [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{AD}[/tex]║[tex]\overline{BC}[/tex] [tex]{}[/tex] Definition of a parallelogram
3. ∠2≅∠3, ∠1≅∠4 [tex]{}[/tex] Alt. int. ∠s are ≅
4. m∠2 = m∠3 and m∠1 = m∠4 [tex]{}[/tex] Measures of ≅ ∠s are =
5. m∠1 + m∠2 = m∠4 + m∠2 [tex]{}[/tex] Addition prop. of equality
6. m∠1 + m∠2 = m∠4 + m∠3[tex]{}[/tex] Substitution
7. m∠1 + m∠2 = m∠BAD [tex]{}[/tex] Angle addition property
m∠3 + m∠4 = m∠DCB
8. m∠BAD = m∠DCB [tex]{}[/tex] Substitution
9. ∠BAD ≅ ∠DCB [tex]{}[/tex] Angles are congruent if [tex]{}[/tex]
[tex]{}[/tex] their measures are the same
The missing reason in the partial proof is therefore; B. Substitution
The abbreviations in the table are expanded as follows;
Alt. int. ∠s are ≅; Alternate interior angles are congruent
Measures of ≅ ∠s are =; Measures of congruent angles are equivalent
Addition prop. of equality; Addition property of equality
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help help help help help help help help help help help help help help help help help help help help
Find the number of sides of a regular polygon in which each exterior angle has a measure of 6
Answer:
Below
Step-by-step explanation:
The exterior angles for any polygon sum to 360 °
so
6 * n = 360 ° <===== where 'n' is the number of sides
n = 60 sides
Please help me with the quwstion below
Answer:Steve
Step-by-step explanation:
Terms and expressions of nth term
Answer:
see explanation
Step-by-step explanation:
(a)
there is a common difference between consecutive terms, that is
10 - 12 = 8 - 10 = 6 - 8 = 4 - 6 = - 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 12 and d = - 2 , then
[tex]a_{n}[/tex] = 12 - 2(n - 1) = 12 - 2n + 2 = 14 - 2n
(b)
similarly this is an arithmetic sequence
with a₁ = 25 and d = 20 - 25 = 15 - 20 = 10 - 15 = 5 - 10 = - 5
[tex]a_{n}[/tex] = 25 - 5(n - 1) = 25 - 5n + 5 = 30 - 5n
I need help with this math problem please
The scale factor of dilation is 4/9
How to determine the scaled factorFrom the question, we have the following parameters that can be used in our computation:
The triangles
Given that the right is the scaled copy of the left
We have the following representation
Scaled factor = Right/Left
Substitute the known values in the above equation, so, we have the following representation
Scaled factor = 4/9
Hence, the scale factor is 4/9
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Does anyone know the answers for daffynition decoder solving proportions
To solve proportions in math, you can use the following steps:
Write the proportion as a fraction.Cross-multiply the fractions (multiply the numerator of one fraction by the denominator of the other fraction).Solve for the variable by isolating it on one side of the equation.Check your answer by plugging it back into the original proportion.What is daffynition decoder solving proportions?
"Daffynition decoder" is a word puzzle game in which a code is employed to represent words, phrases, or sentences. To solve the puzzle, use the provided code to decode the words or phrases.
"Daffynition decoder" is a word puzzle game where a code is used to represent words, phrases or sentences. To solve the puzzle, you need to use the provided code to decode the words or phrases.
To solve proportions in math, you can use the following steps:
Write the proportion as a fraction.Cross-multiply the fractions (multiply the numerator of one fraction by the denominator of the other fraction).Solve for the variable by isolating it on one side of the equation.Check your answer by plugging it back into the original proportion.To know more about daffynition decoder visit,
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A dolphin is at the surface of the ocean.What is the dolphin’s elevation?
Answer:
0
Step-by-step explanation:
surface of ocean = sea level = elevation of zero
