Answer:
a) 81-6
b) 10.4
Step-by-step explanation:
a) assuming that the VAT is 20% of the 68 pounds,
you calculate 120% of 68 (convert percentage to decimal)
= 1,20 * 68 = 81.6 pounds
or
calculate 20% of 68 pounds and add the answer to 68 pounds:
(0.2 * 68) + 68 = 81.6 pounds
b) 20% of 52
first convert the percentage to decimals:
0.2 * 52 = 10.4 pounds
3. Rita is applying for a job as an engineer. Hier starting salary at Company will be $30,000 a $300 yearly
raise. Her starting salary at company will be $65.000 with a 5% increase sach year. If Rata is working at a
company for 5 years. Which company should she pick?
Answer:
The 65,000 salary
Step-by-step explanation:
Because the 30,000 salary after 5 years would be 31,500.
30,000+300=30,300
30,300+300=30,600
30,600+300=30,900
30,900+300=31,200
31,200+300=31,500
The 65,000 paying company
65,000x1.05=68,250
68,250x1.05=71.662.5
71,662.5x1.05=75,245.625
75,245.625x1.05=79,007.90625
79,007.90625x1.05=82,958.3015625
her salary after 5 years would be 82,958.3015625
-2/3a+5/6a-1/5a-1/6
Answer:
[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]
Step-by-step explanation:
This Venn diagram shows the pizza topping preferences for 9 students.
What elements are in A and B?
(Look at picture)
Answer:
I think the answer is C.
(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin
Answer:
A.
Step-by-step explanation:
85.9 > 85.31 > 85 > 84.52
Dallas, Fort Worth, San Antonio, Austin
What is the solution to this equation?
log_8 16 + 2log_8x =2
The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
Given the equation
[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2
We know that,
xlogb = log[tex]b^{x}[/tex]
So,
2[tex]log_{8}[/tex](x) = logx²
For the same base
logA + logB = log(AB)
So,
[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2
[tex]log_{8}[/tex](16x²) = 2
We know that
[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]
so,
[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²
x = 2 hence x = 2 will be correct answer.
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Check out this cube: 3 Find the surface area of the cube (above) using its net (below
Answer:
54
Step-by-step explanation:
Surface area of a cube = 6a²
Where,
a = edge = 3
Surface area of a cube = 6a²
= 6 * (3)²
= 6 * (3 * 3)
= 6 * 9
= 54
Therefore,
The Surface area of the cube = 54
please solve this please
Answer:
3
Step-by-step explanation:
The product of two algebraic expression is 4x²-9.If one of the expression is (2x+3),find the other expression
Answer:
Solution given:
we have formula
a²+b²=(a+b)(a-b)
now
4x²-9
(2x)²-3²
using formula
(2x+3)(2x-3)
other expression is 2x-3.
Answer:
( 2x - 3 )
Step-by-step explanation:
4x² - 9 is a perfect square meaning it can be factored into 2 expressions,
( 2x + 3 ) ( 2x - 3 )
how many metres are there in ½ of ⅕ km
Step-by-step explanation:
1/5=1/5×1000=200
1/2 of 200
1/2×200=100
What point lies on the line with point slope equation y-3=4(x+7)?
Answer:
(-7, 3)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify
y - 3 = 4(x + 7)
↓ Compare to Point-Slope Form
Point (-7, 3)
Slope m = 4
1. Determine the sum of the first 53 terms of the following series: 179+173+167+...
2. Determine the sum of the first 19 terms of the following series: 6−12+24−48+...
(1) This series consists of terms of an arithmetic sequence:
179 - 173 = 6
173 - 167 = 6
and so on, so that the n-th term in the series is (for n ≥ 1)
a(n) = 179 - 6 (n - 1) = 185 - 6n
Then the sum of the first 53 terms is
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}[/tex]
(2) This series has terms from a geometric sequence:
-12 / 6 = -2
24/(-12) = -2
-48/24 = -2
and so on. The n-th term is (again, for n ≥ 1)
a(n) = 6 (-2)ⁿ⁻¹
and the sum of the first 19 terms is
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)[/tex]
Multiply both sides by -2 :
[tex]\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)[/tex]
Subtracting this from the first sum gives
[tex]\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
and solving for the sum, you get
[tex]\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}[/tex]
Triangle ABC has vertices A(0, 2), B(5, 4), and C(5,0). Triangle A'B'C'has
corresponding vertices A'(-5, -1), B'(0, 1), and C'(0, -3). Which of the following
describes a translation that would produce triangle A'B'C' from the pre-image of
triangle ABC?
A) To the left five units, up three units.
B) To the left five units, down three units.
C) To the right five units, up three units.
D) To the right five units, down three units.
Answer:
B) To the left five units, down three units
Answer:
( B ) To the left five units, down three units.
On a Job application Doris gave her age as 32 years. Her actual age at the time was about 27. What is the relative error fo her age?
Answer:
Relative error = 0.19
Step-by-step explanation:
From the question given above, the following data were obtained:
Measured age = 32 years
Actual age = 27 years
Relative error =?
Next, we shall determine the absolute error. This can be obtained as follow:
Measured age = 32 years
Actual age = 27 years
Absolute error =?
Absolute error = | Measured – Actual |
Absolute error = | 32 – 27 |
Absolute error = 5 years
Finally, we shall determine the relative error. This can be obtained as follow:
Absolute error = 5 years
Actual age = 27 years
Relative error =?
Relative error = Absolute error / Actual years
Relative error = 5 / 27
Relative error = 0.19
b. Compare the similar triangle proof from question 3 with the inscribed square
proof. How are they different? Which method was easier for you to understand?
(1 point)
Answer:
i might be wrong but this is what i put
Step-by-step explanation:
In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.
Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)
Answer:
Choice C.
[tex]y + 1 = - 2(x - 2)[/tex]
Step-by-step explanation:
When converting to
[tex]y = mx + b[/tex]
We are left with:
[tex]y = - 2x + 3[/tex]
Which fits both the x-intercept and y-intercept.
Question 6 of 25
In APQR, m P= 60°, m_ Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.
Answer:
A, E, F
Step-by-step explanation:
From the angles given, we can infer that ΔPQR is a 30-60-90 special triangle. In a 30-60-90 triangle, the leg opposite the 30 degree angle is 1/2 the hypotenuse and the leg opposite the 60 degree angle is √3 times the one opposite the 30. Using this, we can say:
PR = 1/2 PQ which is just 2 PR = PQ(E)
PR √3 = QR (A)
We can substitute in PR from the first equation to the second to get:
√3/2 PQ = QR(F)
1 point (1) Three times a number minus two times a number* Your answer
Answer:
Three times a number minus two times a number
3x-2x
=x
Can someone please help
Answer:
[tex]162.07[/tex]
Step-by-step explanation:
An image that creates represents this situation has been attached to this answer. As one can see, the diagram models the situation, the angle of depression represents the angle between the horizon line and the line of sight. The horizon line and the tower form a right angle (a (90) degree angle). This means that the angle of depression is complementary to the angle of sight. Therefore, one can state the following:
[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]
Substitute,
[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]
[tex](m<ABD)+(m<DBC)=90[/tex]
[tex]42+(m<DBC)=90[/tex]
Inverse operations,
[tex]42+(m<DBC)=90[/tex]
[tex]m<DBC=48[/tex]
Now one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are a series of ratios that describe the relationship between the sides and angles in a right triangle. These ratios are as follows:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Bear in mind, the terms (opposite) and (adjacent) are subjective, and change depending on the reference angle. However, the term (hypotenuse) refers to the side opposite the right angle and is constant regardless of the reference angle.
In this case, one has found an angle in the triangle, one is given the measure of the side opposite this angle, and one is asked to find the side adjacent to this angle. Therefore, it would make the most sense to use the ratio tangent (tan).
[tex]tan(\theta)=\frac{opposite}{adjacnet}[/tex]
Substitute,
[tex]tan(48)=\frac{180}{adjacent}[/tex]
Inverse operations,
[tex]tan(48)=\frac{180}{adjacent}[/tex]
[tex]adjacent=\frac{180}{tan(48)}[/tex]
[tex]adjacent=162.07[/tex]
Solve for x. round to the nearest tenth, if necessary.
Answer:
29
Step-by-step explanation:
all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151
then 180-151=29
what is the volume of a cylinder, in cubic feet, with a height of 5 feet and a base diameter of 10 feet? Round to the nearest tenths place
Answer:
Volume of cylinder
= π r² h
3.14 × 5×5×5392.5= 392.9 ft³OAmalOHopeO
Answer:
The volume of the cylinder would be approximately 392.5 ft^3
Step-by-step explanation:
Just like the volume formulas for a cuboid, the formula for a cylinder is: Vol = (Circle Area)(Height). Since we already have the height value, let's move onto the circle area.
The formula for the area of a circle is: πr^2. The problem only gave us the value for the diameter (10), so to get the radius value, we just need to divide the diameter by 2, and we get a value of 5 ft as our radius. Next, we just need to square root it. So 5 x 5 = 25. Then, we multiply it by π. Because the problem is asking for an approximate answer, we can just assume that π is 3.14. And that gets us a value of 78.5 ft^2 for the area of the circle.
Finally, we just need to multiply the area and the height of the cylinder. So 78.5 x 5 is approx. 392.5 ft^3. Since we don't need to round to the nearest tenths place, we can just leave it alone.
Since I didn't use the exact value of π, the real answer may be a little off of what we got, but if you want to extra precise, you can go ahead and use the actual value of π.
Solve the equation sine Ф=0.6792 for 0°≤Ф≤360
Answer:
42.78⁹, 137.22⁹.
Step-by-step explanation:
sine Ф=0.6792
Angle Ф in the first quadrant = 42.78 degrees.
The sine is also positive in the second quadrant so the second solutio is
180 - 42.78
= 137.33 degres.
Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4
What is the range of g ( x ) = 3x − 2, if the domain is { − 1, 0, 1, 2 }?
Answer:
range{-5,4)
Step-by-step explanation:
3(-1)-2= -5
3(2)-2=4
Mrs. Kennedy is teaching an 8th grade class. She is standing 7 meters in front of Catherine. Davis is sitting to Catherine’s left. If Davis and Mrs. Kennedy are 12 meters apart, how far apart are Davis and Catherine?
13.90 meters
5 meters
9.75 meters
4.36 meters
Answer:
9.75 meters
Step-by-step explanation:
Davis and Catherine are approximately 13.90 meters apart.
How to determine distance apartTo find the distance between Davis and Catherine, we can use the concept of right triangles and apply the Pythagorean theorem.
Let's consider a right triangle where the distance between Davis and Mrs. Kennedy is the base, the distance between Mrs. Kennedy and Catherine is the height, and the distance between Davis and Catherine is the hypotenuse.
According to the given information, Mrs. Kennedy is 7 meters in front of Catherine, and Davis and Mrs. Kennedy are 12 meters apart.
Using the Pythagorean theorem, we have:
(Base)² + (Height)² = (Hypotenuse)²
Substituting the given values:
(12)² + (7)² = (Hypotenuse)²
Simplifying the equation:
144 + 49 = (Hypotenuse)²
193 = (Hypotenuse)²
Taking the square root of both sides:
√193 ≈ 13.89 = 13.90
Therefore, Davis and Catherine are approximately 13.90 meters apart.
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WILL MARK BRAINLIEST
picture included^^^^
need help asap please n thank you!
^^^^
Answer:
14
Step-by-step explanation:
The a value is from the center to the maximum
We want from minimum to max so we need 2 times the amplitude
a = 7
2 *7 = 14
DB is a diagonal of parallelogram ABCD
What is the measurement of
Please help ASAP
Answer:
m∠DAB+m∠ADC=180
115+ 29 + m∠ADB=180
m∠ADB=180 - 115 -29
= 36°
The sum of three consecutive numbers is 117.what is the largest of the three numbers?write an equation to represent this scenario and solve for the variable
Answer:rrrrrrrr
rrrrrrrrrr
Step-by-step explanation:
rrrrrrrrrrrrrrr
The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the first number:
The other numbers are:
x+1, x+2
The sum of three consecutive numbers is 117:
x + x+1 + x+2 = 117
3x + 3 = 117
3x = 114
x = 38
x+ 1 = 38+1 = 39
x+2 = 38+2 = 40
Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
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NEED THIS ASAP :)
What is the length of the y-component of the vector plotted below?
A. 3
B. 4
C. 1
D. 2
Answer:
4
Step-by-step explanation:
Length of the y component is how far the vector reaches vertically, so in this case it's 4
Need help on this!!!
Answer:
7.8391
Step-by-step explanation:
Answer:
Step-by-step explanation:
The key to solving this equation is knowing how to "undo" a natural log. Just like square roots are "undone" by squaring, and cubing "undoes" a cubed root, raising a natural log to the base of e, Euler's number, undoes a natural log. Because this is an equation you have to raise both sides of it to the base of e:
[tex]e^{ln(x+3)}=e^5[/tex]
That leaves us on the left with simply
x + 3
On the right we have a constant. e is not a variable, it is a number. You can find its value on your calculator. Solving for x:
[tex]x=e^5-3[/tex] and
[tex]e^5=148.4131591[/tex], so
x = 148.4131591 - 3 and
x = 145.4132, the first choice listed.
An airplane from Singapore to Melbourne takes about 7 1/2 hours to cover a distance of 6057 km. What is the average speed of the airplane.
Answer: 13.46 km/h
Step-by-step explanation:
7 1/2 hr= 450 min
6057/450= 13.46
