Using proportions, Nelly's total pay for last week was of £220.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From Monday to Friday, she worked 17 hours, hence:
For 15 hours, she was paid £8 per hour.For the last 2 hours, she was paid £10 per hour.On Saturday, she worked 5 hours, and was paid £16 per hour.
Hence her total payment is found as follows:
15 x 8 + 2 x 10 + 5 x 16 = £220.
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what is Rational Number
Answer:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.
1) A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4sqrt(7) - f feet high, how far away from the base of the building is the bottom of the ladder located? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the exact answer
Answer:
12√2.
Step-by-step explanation:
You can do this by the Pythagoras theorem:
20^2 = x^2 + (4sqrt7)^2 where x is the distance required.
x^2 = 20^2 - (4sqrt7)^2
= 400 - 112
= 288
x = √288
= √144 *√2
= 12√2.
Solve the equation 3x² = 108.
Answer:
x = 6
Step-by-step explanation:
First we divide both sides by 3 :
x² = 108 ÷ 3
x² = 36
Now we square root both sides :
x = √36
x = 6
Hope this helped and have a good day
Answer:
x = ± 6
Step-by-step explanation:
Quick steps
[tex]3x^{2} =108[/tex]
[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]
[tex]x=[/tex] ±6
A (positive) number has two square roots; one positive and one negative
Hope this helps
The logarithmic functions, f(x) and g(x), are shown on the graph.
What is the equation that represents g(x)? Explain your reasoning.
Answer:
g(x) = log(x + 1) + 4
Step-by-step explanation:
The graph of g(x) is shifted 1 unit left and 4 units right from its parent function.
Solve the system of equations for x. The value of x is ____. 3x + 4y = −16 x = 4y
Taking into account the definition of a system of linear equations, the value of x is -4.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
This caseIn this case, the system of equations to be solved is
[tex]\left \{ {{3x+4y=-16} \atop {x=4y}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
3×4y +4y= -16
Solving:
12y +4y= -16
16y= -16
y= (-16)÷ 16
y= -1
Remembering that x=4y, then x= 4×(-1)= -4.
Finally, the value of x is -4.
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When Kenny's electricity went out one night, his clock stopped at 8:39 p.m. when Kenny woke up the next morning his power was back on and his clock read 5:34 a.m. When he called the time services, the time was actually 7:11 a.m. How long was his electricity off?
Answer:
Step-by-step explanation:
Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM. 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM. 60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.
Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.
r(x) = a sinx
what is the value of a
Help me with this problem, random answer will be reported and you won’t get points
Answer:
A = 49B = 41 C = 90 a = 17.255526 (approximate)b = 15c = 22.863796 (approximate)Round the decimal values however needed.
Step-by-step explanation:
The uppercase letters represent the angles, while the lowercase counterparts are the side lengths opposite said angle. For example, side b is opposite angle B.
Angle B is 41 and angle C is 90 because of the square marker. The remaining angle A is...
A+B+C = 180
A+41+90 = 180
A+131 = 180
A = 180-131
A = 49
Or note that
A = 90 - B = 90 - 41 = 49
This shortcut works since we have a right triangle.
---------
That takes care of the angles. Now onto the sides.
We'll need to use trig ratios to determine the missing sides. There are a few approaches, but this is one you could take
tan(angle) = opposite/adjacent
tan(A) = a/b
tan(49) = a/15
a = 15*tan(49)
a = 17.255526 approximately
Furthermore,
sin(angle) = opposite/hypotenuse
sin(B) = b/c
sin(41) = 15/c
c*sin(41) = 15
c = 15/sin(41)
c = 22.863796 approximately
There is another trig function (cosine) that you could use. Also, you could use the pythagorean theorem once you know two sides of the right triangle.
The pythagorean theorem is a^2+b^2 = c^2
The answers have been confirmed with GeoGebra which is a useful geometry app.
Myra is 555 years younger than her sister Talat. Myra wants to write an equation for her own age (m)(m)left parenthesis, m, right parenthesis given Talat's age (t)(t)left parenthesis, t, right parenthesis.
The equation that represents the Myra's age given Talat age is as follows:
t = m + 5
How to represent an equation?Myra is 5 years younger than her sister Talat
Myra age is represented by m while Talat age is represented by t.
Hence,
m = age of Myra
t = age of Talat
Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.
Therefore, the equation that represents the Myra's age given Talat age is as follows:
t = m + 5
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Answer:
[tex]m=t-5[/tex]Step-by-step explanation:
give me brainiest if I'm correctWhen the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the function representing the number of people, f(x), at the fair x hours after the gates open.
The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x
What is the function that represent the number of people at the fair?
The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.
Linear functions can be represented by : y = mx + c
Where:
y = dependent variable c = constantf(x) = 68 + (1.5x)
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Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.
Answer:
When the eqn cuts the x-axis , y=0
3x=12
x=12/3
x=4
So,at x=4 is the point at which the linear equation cuts the x-axis
Answer:
collect like terms
12xy=12
xy=1
PLS HELP OR ILL FAIL MY CLASSES I RLLY NEED HELP PLEASE + 30 POINTS + BRAINLIST
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I’ll appreciate it so much please don’t skip and read this please
Answer:
See the attached picture.
Step-by-step explanation:
103h=7(
7
2
−
7
3
h)−103
Answer:
I think its -10 or -8
Step-by-step explanation:
The table lists the speeds of the fastest roller coasters in North America and Asia.
Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .
The difference of the means of the two data sets is = 4.57
The mean absolute deviation of the roller coaster speeds in North America is 13.3
The mean absolute deviation of the roller coaster speeds in Asia is 16.8
How to solve for the meansFirst we have to start with the data for North America
128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77
To get the mean you have to sum up the values and divide through by the total number 10
937.8/10
Mean = 93.78
Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10
133.32/10 = 13.3
For Asia, we have the data as
149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4
Mean for Asia = 892.1/10
= 89.21
Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10
= 168.32/10
16.8
The difference in the means = 93.78 -89.21
= 4.57
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escribe la ecuacion de la circunferencia que tiene como diametro AB donde A(3,-4) y B(-2,-4
La ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².
¿Cómo derivar la ecuación estándar de la circunferencia?
En este problema debemos derivar la ecuación estándar de la circunferencia, cuyo diámetro está comprendido por el segmento de recta entre los puntos A(x, y) = (3, - 4) y B(x, y) = (- 2, - 4). La ecuación estándar de la circunferencia se presenta a continuación:
(x - h)² + (y - k)² = r² (1)
Donde:
(h, k) - Coordenadas del centro.r - Radio de la circunferencia.El centro de la circunferencia es el punto medio del segmento de recta AB:
(h, k) = 0.5 · (3, - 4) + 0.5 · (- 2, 4)
(h, k) = (1.5, - 2) + (- 1, 2)
(h, k) = (0.5, 0)
Y el radio de la circunferencia es la mitad de la longitud del segmento de recta AB:
[tex]r = \frac{1}{2}\cdot \sqrt{(-2 - 3)^{2}+[-4 - (-4)]^{2}}[/tex]
r = 2.5
Por tanto, la ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².
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Simplify these expressions
4. 9a+7-2a+13=
5. 21-3b+5b-7=
6.3c squared + 8c squared - 15=
Answer:
4) 7a+20
5) 14+2b
6) 25c² - 15
Step-by-step explanation:
4) 9a+7-2a+13= 9a-2a+7+13 = 7a+20
5) 21-3b+5b-7= 21-7+5b-3b = 14+2b
6) (3c)² + (8c)² - 15 = 9c² + 16c² - 15 = 25c² - 15
thu gọn biểu thức : (x-5)(x+5)-(x+1)^2
[tex](x-5)(x+5)-(x+1)^2\\=x^2 -25-(x^2+2x +1)\\=x^2 -25-x^2-2x -1\\=-2x-26[/tex]
ANSWER: -2x -26
Ok done. Thank to me :3
please help i need
this asap!! drag each measure to the correct location on the table classify each measure as a measure of center or a measure or variation
The measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
what is measure centre and measure of variation?A measure of central tendency (measure of centre) is a value that attempts to describe a set of data by identifying the central position of the data set.
The measure of central tendency includes the mean, median and mode.
The measure of variation describes the amount of variability or spread in a set of data.
The common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.
Therefore, the measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
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Find the area of the base of a drum if it needs 88 m long rope to tie twice it around.
solve with full solutions!
Answer:
[tex]154 $\ m^2[/tex]
Step-by-step explanation:
If 88 m of long rope is wrapped twice around the base of the drum, the circumference of the drum is 44m. We can use this information to find the radius of the base.
Find the RadiusThe equation for circumference is [tex]C=2\pi r[/tex]. We can substitute the value we found for circumference into the equation:
[tex]44=2\pi r[/tex]
Divide both sides by 2
[tex]22=\pi r[/tex]
Divide both sides by π
[tex]r=\frac{22}{\pi}[/tex]
Use the Radius to find the AreaThe area of a circle is [tex]A=\pi r^2[/tex]. We can substitute the value we found for the radius into the equation:
[tex]A=\pi (\frac{22}{\pi})^2\\[/tex]
[tex]A=\pi (\frac{22}{\pi})(\frac{22}{\pi})[/tex]
[tex]A=22*\frac{22}{\pi}[/tex]
[tex]A=\frac{484}{\pi}[/tex]
[tex]A\approx154[/tex]
does someone mind helping me with this question? thank you!
Answer:
100
Step-by-step explanation:
to turn whole numbers to a fraction it is whatever numbers out of 100
Answer:
99
Step-by-step explanation:
2. G.CO.9 Look at the diagram below showing two parallel lines being cut
by two transversals. If m24 = 70 and m412 = 130, which of the following
statements are true? SELECT ALL THAT APPLY.
The statements that are true regarding the angles formed by the transversal and parallel lines are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
How to Find the Angles Formed by a Transversal and Parallel Lines?Given the following angle measures formed when two parallel lines ( being cut by two transversals:
m∠4 = 70° m∠12 = 130°Using relevant theorems, let's determine which of the statements are true:
Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.
m∠4 = m∠1
m∠1 = 70°.
m∠2 = 180 - m∠4 [linear angles theorem]
m∠2 = 180 - 70
m∠2 = 110°
m∠6 = m∠4 [base on the alternate interior angles theorem]
m∠6 = 70°.
m∠9 = 180 - m∠12 [based on the linear angles theorem]
m∠9 = 180 - 130
m∠9 = 50°
m∠16 = m∠12 [based on the corresponding angles theorem]
m∠16 = 130°
The statements that are true are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
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"if i purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would i owe after the 8.75% tax is applied?" employee: "your total would be __________."
Answer:$96.98
Step-by-step explanation: all you just do is to add it all up to the total amount.
Answer: $105.47
I hope you get the job!!!!!
Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?
Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
What was the relationship between the lines with equations 4x − 8y = 9 and 8x − 7y = 9?Given: 4x - 8y = 9 ............(1)
8x - 7y = 9 ............(2)
To be the same line, the equations have to be multiples of each other.
Multiplying (1) by 2, we get
2(4x - 8y = 9) = 8x - 16y = 18
From (1) solve the value of y, we get
4x - 8y = 9 ............(1)
-8y = -4x + 9
The value of y = (1/2)x - 9/8
From (2),
8x - 7y = 9
solve the value of y, we get
-7y = -8x + 9
The value of y = (8/7)x - 9/7
To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
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Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x<110)? (The greater than sign is actually greater than or equal to)
A. 0.975
B. 0.025
C. 0.16
D. 0.84
Using the normal distribution, the probability that x is less than 110 is:
A. 0.975.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 98, \sigma = 6[/tex]
The probability is the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 98}{6}[/tex]
Z = 2
Z = 2 has a p-value of 0.975.
Hence option A is correct.
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Write the first five terms of the sequence with the given nth term. an = cos n 2
The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
For given question,
We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]
We need to find the first five terms of the sequence.
For n = 1
[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]
For n = 2,
[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]
For n = 3,
[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]
For n = 4,
[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]
For n = 5,
[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]
Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
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What is the sum in simplest form?
4 1/2 + 1 3/5=
6 1/10
5 1/10
6 1/5
5 4/7
Answer:
6 1/10
Step-by-step explanation:
In order to add fractions, we have to make the denominators equal. we can multiply 1/2 by 5/5 and get 5/10, and multiply 3/5 by 2/2 and get 6/10, to make the denominator equal. Now we add the fractions. 4 5/10 + 1 6/10 = 5 11/10 = 6 1/10
Use the figure to the right to list all of the pairs of angles that fit each description.
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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find the maximum value of c=4x+2y subject to the fallowing constraints x≥0 y≥0 2x+2y≤10 3x+y≤9
The maximum value of c=4x+2y subject to the constraints is 14
How to determine the maximum value?The objective function is given as:
c = 4x+2y
The constraints are given as:
x≥0 y≥0
2x+2y≤10
3x+y≤9
Rewrite 2x+2y≤10 and 3x+y≤9 as equations
2x+2y = 10
3x+y = 9
Divide 2x+2y = 10 through by 2
x+y = 5
Subtract x+y = 5 from 3x+y = 9
3x - x + y - y = 9 - 5
Evaluate the difference
2x = 4
Divide by 2
x = 2
Substitute x = 2 in x+y = 5
2+y = 5
Solve for y
y = 3
So, we have
(x, y) = (2, 3)
Substitute (x, y) = (2, 3) in c = 4x+2y
c = 4 * 2 + 2 * 3
Evaluate
c = 14
Hence, the maximum value of c=4x+2y subject to the constraints is 14
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A weaver bought a bundle of grass of 50.00 dollars from which he made 8 mats if each mats was sold for 15.00 dollars find the percentage profit
The percentage profit is 140%
What is percentage?
Percentage can be described as the expression of a number in hundredth.
The formula for calculating percentage profit is
profit/cost price × 100
cost price= $50
selling price= $15
number of mats produced= 8
selling price of the mat= 15 × 8
= 120
Profit= selling price-cost price
= 120-50
$70
Therefore the percentage profit can be calculated as follows
= 70/50 × 100
= 1.4 ×100
= 140
Thus, the percentage profit is 140%
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PLEASE HELP ITS MATH
Answer:
y = 4x + 3
Step-by-step explanation:
as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:
to calculate for the y intercept, it is best to express the equation in slope intercept form:
y = mx + b
in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).
y = 4x + b
what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.
Using this information, we can replace x and y in the equation:
-5 = 4(-2) + b
with consideration to the order of operations, it is important to solve the brackets first
-5 = -8 + b
now to get b by itself add 8 to both sides of the equation:
-5 + 8 = -8 + 8 + b
3 = b
now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.
y = 4x + b
replace b with the number we solved for (3).
y = 4x + 3
this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)
hope this helps :)