Answer:
$24,153
Step-by-step explanation:
Jan's monthly income from commissions is ...
4.15% × $48,500 = $2012.75
Multiplied by 12 months in the year, that is ...
$2012.75 × 12 = $24,153 . . . . gross annual income from commissions
Use the inverse properties of logarithms to simplify the expression.
10^ log 21
Answer:
21
Step-by-step explanation:
Rule of logs:
[tex] b^{\log_b x} = x [/tex]
Your problem:
[tex] 10^{\log_{10} 21} = 21 [/tex]
The value of the given logarithm expression will be 21.
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The expression is given below.
[tex]\rightarrow 10^{\log 21}[/tex]
We know that
[tex]\rm a ^{\log_ab} = b[/tex]
Then the expression will be
⇒ 21
More about the logarithm link is given below.
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The area of a parking lot is 1710 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. There can be at most 180 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many buses should be in the lot to maximize income? Please help :(
Answer:
To maximize the income should be 30 buses and 150 cars
Step-by-step explanation:
Let
x-----> the number of cars
y ----> the number of bus
we know that
[tex]5x+32y\leq1,710[/tex] ------> inequality A
[tex]x+y\leq 180[/tex] ----> inequality B
The function of the cost to maximize is equal to
[tex]C=2x+6y[/tex]
Solve the system of inequalities by graphing
The solution is the shaded area
see the attached figure
The vertices of the solution are
(0,0),(0,53),(150,30),(180,0)
Verify
(0,53) ---> [tex]C=2(0)+6(53)=\$318[/tex]
(150,30) ---> [tex]C=2(150)+6(30)=\$480[/tex]
therefore
To maximize the income should be 30 buses and 150 cars
Answer:
Givens
The area of the parking lot is 1710 square meters.A car requires 5 square meters.A bus requires 32 square meters.There can be a maximum of 180 vehicles.The cost for a car is $2.00.The cost for a bus is $6.00.To solve this problem we need to create a table to order all this information and express it as a system of inequations.
Car Bus Total Capcity
Sq. Meters 5c 32b 1710
N° vehicles c b 180
Therefore, the inequalities are
[tex]5c+32b\leq 1710\\c+b\leq 180[/tex]
The expresion which represents the income is
[tex]I=2c+6b[/tex], because a car is $2.00 and a bus is $6.00.
Now, we first need to find the critical points of the solution of the inequality system, which is attached. Observe that the only points that can be a solution is (150,30), because there can't be just car or just buses.
Then, we replace this point in the income expression
[tex]I=2c+6b\\I=2(150)+6(30)=300+180=480[/tex]
Therefore, in order to maximize incomes, we need to park 150 cars and 30 buses, to make $480 income.
A survey found that 78% of students do their homework before 10:00 P.M. Predict how many students out of 975 do their homework before 10:00 P.M.
a.
about 761
b.
about 78
c.
about 800
d.
about 13
Write the equation of a line that goes through point (0, −8) and has a slope of 0.
A.) x = -8
B.) x = 0
C.) y = - 8
D.) y = 0
Answer:
C.) y = - 8
Step-by-step explanation:
If the line has a slope of 0, it is a horizontal line. That means y= a value
Since we have the point (0,-8)
y = -8
Final answer:
The equation of a line that goes through point (0, -8) with a slope of 0 is y = -8.(Option c)
Explanation:
We need to find the equation of a line that goes through the point (0, -8) and has a slope of 0. The general equation for a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope (m) is 0, the line is horizontal.
A horizontal line has an equation of the form y = b, where b is the y-coordinate of every point on the line. As the line goes through (0, -8), we can see that the y-coordinate is -8 for all points on this line. Therefore, the equation of this line is C) y = -8.
what undefined term does a circle use
Answer:
The definition of a circle uses the undefined term Arc
Step-by-step explanation:
There are three terms generally considered to be undefined in geometry: point, line and plane. A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is plane.
A rectangles length is 1.5 times its width. The perimeter of the rectangle is four more than 3 times the length. What are the dimensions of the rectangle
Answer:
8 by 12 units
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is 1.5w. The perimeter is 4 more than 3 times this, so is (3(1.5w) +4) = 4.5w+4
The perimeter is given by the formula ...
P = 2(length + width)
Filling in the given values for the variables, we have ...
4.5w +4 = 2(w +1.5w)
4 = 0.5w . . . . . . subtract 4.5w and collect terms
8 = w . . . . . . . . . multiply by 2
length = 1.5×8 = 12
The rectangle is 8 units wide and 12 units long. The perimeter is 40 units.
Answer:
Step-by-step explanation:
8x12
PLS HELP WITH ALL QUESTIONS WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
THANK YOU IN ADVANCE.
Answer:
see explanation
Step-by-step explanation:
(a)
The opposite sides of a rectangle are congruent, hence
x + 1 = 5 ( subtract 1 from both sides )
x = 4
Or
x - 1 = 3 ( add 1 to both sides )
x = 4
(b)
The sum of the 3 angles in a triangle = 180°, hence
3y + 2y + y = 180
6y = 180 ( divide both sides by 6 )
y = 30
Answer:
PART A "4"
PART B "30"
Step-by-step explanation:
PART A
If you refer to my picture below, then you will know that the sides are equal.
The x-1 side is equal to 3 and the x+1 sign is equal to 5. So it best makes sense that 4 is equal to x. That's because x-1 is 3 and x+1 is 5.
PART B
This is tricky. As you know all sides of a triangle add up to 180 degrees. I would divide by 3, but that would be incorrect. Whenever you see these y's, you have to divide by that amount. The y's are there for a reason, so that some sides are bigger than the other. Divide 180 by 6(number of y's). That is 30. This gives you the solution to one y so if it asks you for 2y or 3y, then you would multiply. But it's not. 30 is the answer
On a coordinate grid Ming's house is located 2 blocks to the right and 5 blocks up from (0,0). Joe house is located 3 blocks to the right and 2 blocks down from Ming's house. What ordered pair describes the location of joe house?
Answer:
(5, 3)
Step-by-step explanation:
Conventionally, the ordered pairs are (right, up). Then ...
Ming's = (0, 0) + (2, 5) = (2, 5)
Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)
Joe's = (5, 3)
Answer:
( 5,3 )
Step-by-step explanation:
i am doing this test too
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
Answer:
1/64
Step-by-step explanation:
[tex]256^{-\frac{3}{4}}=2^{8(-\frac{3}{4})}=2^{-6}=\dfrac{1}{2^6}=\dfrac{1}{64}[/tex]
256^-3/4 can be converted into a positive fraction by interpreting the negative exponent as a reciprocal and the fractional exponent as a root. It simplifies to 1/(4th root of 256^3), which equals 1/64.
Explanation:To express the numeral 256^-3/4 in the form of a fraction, we first need to understand how negative and fractional exponents work. The number is in the form of a^(-m/n) which is equivalent to the nth root of a^-m or 1/(nth root of a^m). The negative sign in the exponent implies a reciprocal of the number and the fractional exponent denotes a root of the number.
Now applying this understanding to our number which is 256^-3/4. Here, the base a is 256 and the fractions -m/n is -3/4. Therefore, it is equivalent to the 4th root of 256^-3, which can also be written as 1/(4th root of 256^3).
The 4th root of 256 is 4. So, the expression now becomes 1/(4^3), which after simplifying gives us the result 1/64.
So, the expression 256^-3/4 written as a positive fraction is 1/64.
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Kim took out a $55,000 loan for college she is borrowing money from 2 banks bank a charges an interest rate of 8% and b charges an interest rate of 11% after one year Kim owes 5000 in interest how much money did she borrow from bank a.
Answer:
$35,000
Step-by-step explanation:
Let x represent the amount borrowed from Bank A. Then (55000-x) is the amount borrowed from Bank B. Kim's total 1-year interest is ...
0.08x + 0.11(55000 -x) = 5000
-0.03x + 6050 = 5000 . . . . . simplify
-0.03x = -1050 . . . . . . . . . . . . subtract 6050
x = 35,000 . . . . . . . . . . . . . . . divide by -0.03
Kim borrowed $35,000 from Bank A.
HELP awarding 60 points and brainliest answer!!!
Answer:
A
Step-by-step explanation:
Choice A is right because there is no dot above the two.
Choice B is not right because there is 2 dots above 1 and not 3.
Choice C is not right because the data doesn't go passed 5 to get to 8
Choice D is not right because it was 5 games because there is 5 dots above 3
The answer would be A. the team never scored exactly 2 goals in a single game
If you look at the number two on the dot plot you can see that there are NO dots above it. This means that the team never scored exactly 2 goals.
It can't be B. because they scored exactly 1 goal for 2 games NOT 3
It can't be C. because no where on the graph is the number 8. They never scored 8 goals. Five is actually the highest number of goals they ever scored.
It can't be D. because they scored 3 goals in a game for 5 games not for 4 games
Hope this helped!
~Just a girl in love with Shawn Mendes
Anzelm wants to burn 540 calories while jogging. Jogging burns about 12 calories per minute. When Anzelm goes jogging, he usually plans to stop and rest for about 5 minutes. Complete the equation below to find the total number of minutes (including rest) that Anzelm should plan to be out jogging. Use m to represent the total minutes ___( __–__) = ___
Answer:
12(m -5) = 540
Step-by-step explanation:
The left side of the equation is in the form of a product. A suitable product is ...
(calories/minute) × (minutes jogging) = (calories burned)
If m represent Anzelm's total minutes, then m-5 will represent the number of minutes actually jogging. This is what goes inside parentheses, so we have ...
(12 calories per minute) × ((m -5) minutes) = 540 calories
Leaving off the units, which we know are consistent, we have ...
12 (m -5) = 540
Answer:
12(m-5) = 540
Step-by-step explanation:
∵ The total calories have to burn = 540,
Also, here m represents the total time spent by Anzelm,
If he/she spent 5 minutes in rest,
Then the time he/she spent in jogging = (m - 5) minutes,
If the number of calories burnt in one minute = 12,
So, the number of calories burnt in (m-5) minutes = 12(m-5),
Therefore, for burning the whole calories,
Calories burnt by him/her = total calories
⇒ 12(m-5) = 540
Which is the required equation.
Becky is using the expression 2z + 3 to represent the number of chairs in her classroom. There are twice as many chairs as tables, and there are three extra chairs in the back. What does z represent?
The number of chairs.
The number of tables.
The number of chairs at tables.
The number of chairs and tables
Answer:
The number of tables
Step-by-step explanation:
Let
z ----> the number of tables
y-----> the number of chairs
we know that
[tex]y=2z+3[/tex]
therefore
z represent the number of tables
Answer:
the number of tables :]
Step-by-step explanation:
The product shown is a difference of squares. What is the missing constant term in the second factor?
(–5x – 3)(–5x +?
Answer:
[tex]\boxed{3)}[/tex]
Step-by-step explanation:
A difference of squares has the form (a - b)(a + b)
Your expression is (-5x - 3)(-5x + ?
Let's compare this with your expression.
[tex]\begin{array}{cclccl}(a & - & b) & (a & + & b)\\\downarrow & & \downarrow & \downarrow & & \downarrow \\(-5x & - & 3) & (-5x & + & \mathbf{3)} \\\end{array}\\\\\text{The missing term is }\boxed{\mathbf{3)}}[/tex]
Which two undefined geometric terms always describe figures with no beginning or end?
Answer:
lines, andplanes.Explanation:
In geometry, undefined terms refer to three entities: points, lines, and planes. They are considered undefined because they are rather described than formally defined.
The reason behind this lack of definition is that they are abstractions: you cannot touch or see a real point, line or plane.
A point represents a position in the plane or the space, and it is dimensionless. Yet it is used to define a line and a plane.
Among those three terms, only line and plane meet the feature of not having begin or end. That is so because lines and planes extend infinetly
LInes extend in two directions, in one dimension: for example, from left to right, or from east to west, or vertically.
Planes extend infinetly in two dimensions: they are flat infinite surfaces.
Which of the following statements are true?
Answer:
Both graphs have been shifted and flipped
Both graphs have exactly one asymptote
Step-by-step explanation:
Choice A is incorrect since both graphs are not logarithmic functions. The graph of f(x) appears to be an exponential function.
Choice B is also incorrect since both graphs are not exponential functions. The graph of g(x) does not belong to the exponential family since y can take on negative values.
When the graph of f(x) is shifted downwards and flipped, we can obtain the graph of g(x).
Both graphs have exactly one horizontal asymptote
The potential and kinetic energy of a rock thrown into the air and falling back is misunderstood in statement 1. Voting rates are lower in the United States compared to some other democratic countries, and according to Kepler's laws, a satellite speeds up as it approaches its parent body and slows down as it moves away.
Explanation:For the given set of statements:
The statement that 'If a rock is thrown into the air, the increase in the height would increase the rock's kinetic energy, and then the increase in the velocity as it falls to the ground would increase its potential energy.' is False. The potential energy increases with height, not kinetic energy, and when the rock falls, its velocity increases which in turn increases its kinetic energy, not potential energy.The statement that 'Voting rates are higher in the United States than in most democratic industrialized countries, including Sweden and South Korea' is False. These countries are known to have higher voter turnouts compared to the United States.The statement, 'According to Kepler's laws of planetary motion, a satellite increases its speed as it approaches its parent body and decreases its speed as it moves away from the parent body' is True. As a satellite approaches the parent body, gravitational force pulls it in, causing it to speed up and as it travels further from the parent body, it decelerates. Learn more about Physics Statements here:https://brainly.com/question/30255438
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Need help with a math question
Answer:
b = 17
Step-by-step explanation:
The angle bisector of the apex angle of an isosceles triangle is also a median and altitude. PS=RS=17
b = 17
Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three balls is equal to the height of the cylinder. and the diameter of one ball is equal to the diameter of the cylinder. The radius of one tennis ball is 1.3 inches. How much air space is in the cylinder around the tennis balls?
Answer:
about 13.8 in³
Step-by-step explanation:
The volume of air is the difference between the volume of the cylinder of radius 1.3 inches and height 7.8 inches, and that of three spheres, each with a radius of 1.3 inches.
The formula for the volume of a cylinder is ...
V = πr²h
The formula for the volume of a sphere is ...
V = (4/3)πr³
For h = 6r, the difference is ...
(cylinder volume) - 3×(sphere volume) = πr²·(6r) - 3×(4/3)πr³
= πr³(6 -4)
= 2πr³ = 2π(1.3 in)³ = 4.394π in³
≈ 13.8 in³ . . . . air space in the cylinder of tennis balls
Cylinder A has a volume of 100 cm and cylinder B has a height that two fifths of the height of cylinder A
You need more input here what even is the question
A student received a 75% on an exam. If there were 20 questions on the exam, which ratio would show the number of questions answered correctly to the total number of questions? A. 5:20 B. 15:20 C. 20:15 D. 20:5
Answer:
15:20
Step-by-step explanation:
15:20 = 15/20 = .75 = 75%
A bag contains 7 pieces of paper numbered 1 to 7. P(2)=. Is this an experimental or theoretical probability and why?
CAN YOU GUYS PLEASE HELP ME I NEED TO TURN THIS IN IN 30 MINUETS!!!!!
Answer:
theoretical probability
Step-by-step explanation:
This is theoretical probability. The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}. There is only one piece of paper marked 7. So the probability of drawing a 2 is 1/7.
i need help with area of a circle
A circular plate has a diameter of 6 inches.
What is the exact area of the plate?
A.3_ square inches
B.6_ square inches
C.36_ square inches
D.9_ square inches
Answer:
D.
Step-by-step explanation:
The area formula for a circle is [tex]A=\pi r^2[/tex].
If the diameter is given, we take half of it to find the radius measure. If d = 6, then r = 3. Therefore, our formula can be filled in as
[tex]A=\pi (3)^2[/tex] or [tex]A=9\pi[/tex]. That is the exact area. The approximate area is found by multiplying in 3.1415 as pi to give you that the area is approximately 28.27 square inches. I think you meant to put pi in those answer choices instead of an underscore, so it's my belief that D. is supposed to reflect the answer of [tex]9\pi[/tex] square inches. I'm going with D.
If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the canyon
Angle ACB = 50°
Angle ABC=100°
a=75 yds
What does C equal?
Answer:
Length of side [tex]c[/tex]:
[tex]c = \rm AB \approx 115\; yds[/tex].
The distance across the canyon is approximately
[tex]\rm 113\;yds[/tex].
Step-by-step explanation:
[tex]c[/tex] is the length of the side opposite to the angle [tex]\rm A\hat{C} B[/tex].[tex]a[/tex] is the length of the side opposite to the angle [tex]\rm B\hat{A}C[/tex].Apply the law of sine:
[tex]\displaystyle \frac{c}{\sin{\rm A\hat{C}B} = \frac{a}{\sin{\rm B\hat{A}C}}[/tex].
In other words,
[tex]\displaystyle c = \sin{\rm B\hat{A}C} \cdot \frac{a}{\sin{\rm A\hat{C} B}}[/tex].
However, the value of the angle [tex]\rm B\hat{A}C[/tex] isn't given. Don't panic. The three interior angles of a triangle shall add up to 180°. Two of the three angles are given. The value of the third angle is implied.
[tex]\rm B\hat{A}C = 180\textdegree{} - A\hat{C}B - A\hat{B}C = 30\textdegree{}[/tex].
Apply the law of sine to find [tex]c[/tex]:
[tex]\displaystyle \begin{aligned}c &= \sin{\rm A\hat{C}B} \cdot \frac{a}{\sin{\rm B\hat{A}C}}\\ &= \sin{50\textdegree{}}\cdot \frac{\rm 75\; yds}{\sin{30\textdegree{}}}\\ &\rm = 114.907\; yds\end{aligned}[/tex].
Refer to the diagram. The distance across the canyon will be
[tex]\rm AB \cdot \sin{A\hat{B}C} = 114.907\times \sin{100\textdegree{}} \approx 113\;yds[/tex].
Need help with math question
Answer:
center (1,-3) and radius is 5
Step-by-step explanation:
We have to use completing the square here:
x^2-2x + y^2+6y =15 (reorder some things and added 15 on both sides)
x^2-2x+(-2/2)^2 + y^2+6y+(6/2)^2 =15+(-2/2)^2+(6/2)^2 (whatever you add on one side you also do to the other side)
x^2-2x+(-1)^2 + y^2+6y+(3)^2=15+1+9
(x-1)^2 + (y+3)^2 =25
Center is (1,-3) and radius is 5
ANSWER
The center is (1,-3) and the radius is r=5 units.
EXPLANATION
The given equation is:
[tex] {x}^{2} + {y}^{2} - 2x + 6y - 15 = 0[/tex]
Let rearrange to get:
[tex]{x}^{2} - 2x + {y}^{2} + 6y=15[/tex]
We complete the square to get;
[tex]{x}^{2} - 2x + ( { - 1)}^{2} + {y}^{2} + 6y + {3}^{2} = 15+ ( { - 1)}^{2} + {3}^{2}[/tex]
[tex] ( {x - 1)}^{2} +( {y + 3)}^{2} = 15 + 1+ 9[/tex]
[tex] ( {x - 1)}^{2} +( {y + 3)}^{2} =25[/tex]
[tex]( {x - 1)}^{2} +( {y + 3)}^{2} = {5}^{2} [/tex]
Comparing to
[tex]( {x - h)}^{2} +( {y - h)}^{2} = {r}^{2} [/tex]
The center is (1,-3) and the radius is r=5 units.
Which aspect of electronic commerce does the FTC regulate?
A.
encryption and transfer of data
B.
disposing of credit reports
C.
network security
D.
antivirus software updates
Answer:
The correct answer option is A. encryption and transfer of data.
Step-by-step explanation:
The business activities that take place through internet as the medium are referred to as electronic commerce.
The Federal Trade Commission [FCT] is one of the main functional bodies responsible for regulating such electronic commerce activities which includes encryption and transfer of data.
The risk of data theft from encryption and transfer of data is really high so FTC makes sure to prevent theft from the transaction made through e-commerce.
Answer:
Which aspect of electronic commerce does the FTC regulate?
A.
encryption and transfer of data
B.
disposing of credit reports
C.
network security
D.
antivirus software updates
Step-by-step explanation:
#platofam
The vertices of a hyperbola are located at (−4, 1) and (4, 1). The foci of the same hyperbola are located at (−5, 1) and (5, 1). What is the equation of the hyperbola?
The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
How to determine the equation of the hyperbola?The vertices of the hyperbola are given as:
Vertices = (±4, 1)
The foci of the hyperbola are given as:
Foci = (±5, 1)
The coordinates of the vertices is represented as::
Vertices = (±a, n)
By comparing (±a, n) and (±4, 1), we have:
a = 4
n = 1
The coordinates of the foci is represented as::
Foci = (±c, n)
By comparing (±c, n) and (±5, n), we have:
c = 5
n = 1
Calculate b using:
b = √(c² - a²)
So, we have:
b = √(5² - 4²)
Evaluate
b = 3
The equation of a hyperbola is:
[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{4^2} - \frac{(y - 1)^2}{3^2} = 1[/tex]
Evaluate the exponent
[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
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Keshawn is asked to compare and contrast the domain and range for the two functions. f(x) = 5x g(x) = 5x Which statements could he include in his explanation? Check all that apply. The domain of both functions is all real numbers. The domain of f(x) is x > 5. The domain of g(x) is x > 5. The range of both functions is y > 5. The range of f(x) is y > 0. The range of g(x) is y > 0.
Answer:
"The domain of both functions is all real numbers."
Step-by-step explanation:
Given
[tex]f(x) = 5x\\and\\g(x) = 5x[/tex]
We can see that the function will have some value for any value of x and is not undefined on any value of x. So the domain of f(x) is all real numbers.
Similarly, g(x) is also not undefined on any value of x so it also has domain of all real numbers.
The range of f(x) and g(x) will be all real numbers as the functions do not produce infinity on any of the input.
Only the statement that
"The domain of both functions is all real numbers."
is true for the given functions ..
If you had a cube measuring 5 cm per side, what is its total surface area?
Answer:150 square cm
Step-by-step explanation:
Mr de guzman bought 7 1/2 of meat.He used 2 3/4 for afritada,3 1/8 kg for menudo and the rest for pochero.How many kilograms of meat did he used for pochero?
Answer:
hola puto
Step-by-step explanation:
bggyyhh yyesws kihtwrqas bts23e4gyhun
Need help with math question
Answer:
D
Step-by-step explanation:
This is a vertical opening parabola, since the focus is above the vertex on the axis of symmetry x = 2
The standard form of a vertically opening parabola is
(x - h)² = 4a(y - k)
where (h,k) are the coordinates of the vertex and a is the distance from the vertex to the focus.
here (h, k) = (2, - 1) and a = 4, hence
(x - 2)² = 16(x + 1) → D
Answer:
D
Step-by-step explanation: