Answer:
The difference between the bonus is £2.6
Step-by-step explanation:
First, you have to calculate the amount that Tom get for his bonus. So you have to multiply 30% to £96 :
[tex] \frac{30}{100} \times 96 = 28.8[/tex]
Next, you have to subtract Tom's amount from Sally's amount because Sally has the higher amount of bonus than Tom :
[tex]31.4 - 28.8 = 2.6[/tex]
Direct Variation: If y = 9, when x = -3, find x when y = -27. a.9 b.27 c.-27 d,-9
Answer:
a. 9
Step-by-step explanation:
[tex]k = \frac{9}{-3} = -3\\y = -3x\\-27 = -3x\\\frac{-27}{-3} = \frac{-3x}{-3} \\9 = x[/tex]
Answer:
a. 9
Step-by-step explanation:
because the orginal number was 9 and the newer one is -27 we can determine that y was multiplied by -3 so you would apply the same rule to -3 or x and you would get a product of 9 because two negatives equals a postive
A car was marked $25,000. Ms. Eve bought it at a discount of
18%. In addition, she had to pay 7% tax. If Ms. Eve had to put
14% of what she had to pay as down payment, how much
money did she have to pay for the down payment?
4
Answer:
$3,745
Step-by-step explanation:
First, you have to calculate the price after the discount is applied:
Price of the car: $25,000
Discount: 18%
$25,000*18%= $4,500
$25,000-$4,500= $20,500
Second, you have to calculate the total amount she has to pay including the 7% tax:
$25,000*7%= $1,750
$25,000+$1,750= $26,750
Third, as the statement indicates that Ms. Eve had to put 14% of what she had to pay as down payment, you have to calculate the 14% of $26,750:
$26,750*14%= $3,745
According to this, Ms. Eve has to pay $3,745 for the down payment.
Find the slope of the line y
The base of this solid crate has an area of 6 square meters. The height of the crate is 4 meters. What is the volume of the crate?
Answer: 24 m^3
Step-by-step explanation:
Given that you have a base with an area of 6 square meters, it has already calculated the product of length and width. In the Volume Formula Length x Width x Height, you're pretty much multiplying that given area by a height of 4, since you already have that length and width in the form of 6 square meters. The result you'll have is 24 Meters Cubed.
How many cubes with a side length of 1/2 unit would it take to fill a rectangular prism with a volume of 2 cubic units?
Answer:
16
Step-by-step explanation:
1/2*1/2*1/2 = 1/8 cubic units
2/(1/8) = 16
Answer:
16
Step-by-step explanation:
[tex](\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\\\frac{2}{\frac{1}{8}} = 2 \cdot 8 = 16[/tex]
What change(s) should Sylvia make to the equation to find the value of t in the above scenario?
Answer:
Option (D).
Step-by-step explanation:
Initial population of the deer [tex]P_{0}[/tex] = 4800
Decrease in the population of the deer after every 8 years = [tex]\frac{1}{2}\times (\text{Initial population})[/tex]
Decrease in population is an exponential process, so the expression representing population will be,
[tex]P_{t}=P_{0}(1-r)^x[/tex]
Where [tex]P_{t}[/tex] is the population after 'x' slots of 8 years.
r = fraction of decrease in the population
x = [tex]\frac{\text{Number of years}}{8}[/tex]
By substituting the values of r and x in the expression,
[tex]P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}[/tex]
[tex]P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}[/tex]
Therefore, Sylvia should do few corrections in her expression.
(8) should be replaced by ([tex]\frac{1}{2}[/tex]) and [tex]\frac{t}{2}[/tex] should be replaced by [tex]\frac{t}{8}[/tex].
Option D. will be the answer.
The length of a field in yards is a function f( n ) of the the length in n feet. Write a function rule for this situation.
Answer:
[tex]f(n)=\frac{1}{3}n[/tex]
Step-by-step explanation:
To convert from feet to yards, divide by the value 3.
XYZ is an isosceles triangle inscribed I a circle, center O. XY=XZ= 20 and YZ=18. Calculate to 3.s.f.
a) the altitude of ∆XYZ
b) the diameter of the circle
Answer: 17.9
Step-by-step explanation:
Using Heron's formula:
Area of a triangle is given by:
√s(s-a)(s-b)(s-c)
Where a, b and c ara sides of the triangle and
S = (a+b+c) / 2
In the question above sides are :
XY=XZ= 20 and YZ=18
S = (20 + 20 + 18) / 2 = 58/2 = 29
Area = √29(29-20)(29-20)(29-18)
Area = √29(9)(9)(11)
Area = √25839
Area = 160.74513
Altitude = height(h)
Area = 0.5 × base × height
Base = yz = 18
160.74513 = 0.5 × 18 × h
160.74513 = 9 × h
h = 160.74513 / 9
h = 17.9 (3 s.f)
A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.
A. Find the original perimeter and area of the garden
B. Find the perimeter and area of the garden with a 20% increase in each dimension.
C. By what percent will the perimeter increase? By what percent will the area increase?
D. Explain why the area and perimeter will not increase by the same percentage.
Answer:
w=12 ft
l= 20 ft
A.
P= 2(12+20)= 64 ft
A= 12*20= 240 ft²
B.
P=2(12*1.2+20*1.2)= 76.8 ft
A= 12*1.2*20*1.2= 345.6 ft²
C.
(76.8-64)/64*100%= 20%
(345.6- 240)/240*100%= 44%
D.
perimeter increase is linear function of one dimension increase
area increase is function of 2 dimensions increase
The output or possible values you could get as a result from
an expression or equation.
Answer:
The Solution Set
Step-by-step explanation:
Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.
[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\S=\{3,4\}[/tex]
Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.
[tex](3)^{2}-7(3)+12=0\\-12+12=0\\0=0[/tex]
The output or possible values you could get as a result from an expression or equation is the solution set of the equation
Take for instance, we have the following equation
[tex]x^2 = 4[/tex]
When solved, the equation becomes
[tex]x = \pm 2[/tex]
This can be rewritten as:
[tex]x = \{-2,2\}[/tex]
This means that -2 and are the solution set of the equation [tex]x^2 = 4[/tex]
Hence, the output or possible values are called solution set
Read more about equations at:
https://brainly.com/question/14323743
help me for brainetest pls answer on paper on a number line
Answer:
10 5/8
Step-by-step explanation:
What is the answer to this, I need an explanation please ASAP
Answer:
323 ft^2
Step-by-step explanation:
Separate the figure on the left into two figures, a trapezoid and a square
The area of a trapezoid is
A = 1/2 (b1+b2)h
A = 1/2 (12+15)*7
= 1/2 (28)7
98 ft^2
The area of a square is
A = s^2
= 15^2
= 225 ft^2
Add the areas together
A total = 98+225 =323 ft^2
1
The measure of Z1 =
Answer:
∠1 = 90°
Step-by-step explanation:
The angle inscribed in a semicircle is always 90°
∠1 = 90°
What percent of a is b?
Please put your answer in percent.
Answer:
If you know two number a and b and need find, b is what percentage of a, P=b
- 100%
a
I need help with this problem.
Answer:
D
Step-by-step explanation:
[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]
Therefore, the correct answer is choice D. Hope this helps!
find the value of trig function indicated, use Pythagorean theorem to find the third side if you need it. Part 4
Answer:
[tex]\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}[/tex]
Step-by-step explanation:
A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)
According to the trigonometric properties:
[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]
[tex]cos(theta) = \frac{adjacent}{hypotenuse}[/tex]
[tex]tan(theta) = \frac{opposite}{adjacent}[/tex]
[tex](adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}[/tex]
[tex](adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}[/tex]
[tex](opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}[/tex]
Use the above formulas with corresponding sides:
[tex]13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83[/tex]
[tex]14) sin(theta) = \frac{\sqrt{5^{2}-3^{2} } }{5} = \frac{4}{5} = 0.8[/tex]
[tex]15) sin(theta) = \frac{9}{\sqrt{(8\sqrt{7}) ^{2} + 9^{2} } } = 0.391[/tex]
[tex]16) tan(theta) = \frac{3}{4} = 0.75[/tex]
Hope this helps!
:)
square roots of 263 by division method
Answer:
no whole number
Step-by-step explanation:
263 is a prime number, so it can be divided only by 1 and 263. So, no whole number will be square root for 263.
In the diagram above, <1 = 135º.
Find the measure of <3.
Answer:
The measurement of ∠3 is 135°
Step-by-step explanation:
In the problem, we are given a measurement. The measurement of ∠1 is 135°. We are asked to find the measurement of ∠3.
∠1 and ∠3 are corresponding angles. This means that they will have the same measurements.
So, if m∠1 is 135° then the m∠3 is also 135°
Answer:
m∠=135°
Step-by-step explanation:
These lines are parallel lines, which is indicated by the two arrows towards the right of the lines.
Since these lines are parallel, corresponding angles, such as ∠1 and ∠3 can exist.
Corresponding angles are congruent, which means they have the same measure.
∠1 and ∠3 are corresponding angles, therefore
∠1=∠3
We know that the measure of ∠1 is 135 degrees. Therefore, ∠3 will also have a measure of 135 degrees.
135=∠3
The measure of ∠3 is 135 degrees.
A : The distance around a closed figure B: The space within a closed figure C : Measure using the distance formula D : measure in units squared
Answer:
C : Measure using the distance formula
Step-by-step explanation:
A Venn diagram is a diagram which shows the relation of all different sets
Just like it is given in the attachment there is a relation between the perimeter and the area.
The distance formula is
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]
where,
[tex](x_1, y_1)[/tex] is the first point coordinates
[tex](x_2, y_2)[/tex] is the first point coordinates
By using the distance formula as discussed above shows the intersection of the Venn diagram
Hence, the correct option is C.
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 3) ← 2 points on the line
m = [tex]\frac{3-2}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]
-1/3 multiplied by 1/4
Answer:
[tex] - \frac{1}{12} \\ [/tex]
Step-by-step explanation:
[tex] - \frac{1}{3} \times \frac{1}{4} \\ \\ = - \frac{1}{12} [/tex]
Last question! I need help with showing my work! I already have the answer in the attached image below, thanks!
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\sqrt{\frac{4x^2}{3y} }[/tex]
= [tex]\frac{\sqrt{4x^2} }{\sqrt{3y} }[/tex]
= [tex]\frac{2x}{\sqrt{3y} }[/tex]
Rationalise the denominator by multiplying the numerator/ denominator by [tex]\sqrt{3y}[/tex]
Note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
= [tex]\frac{2x}{\sqrt{3y} }[/tex] × [tex]\frac{\sqrt{3y} }{\sqrt{3y} }[/tex]
= [tex]\frac{2x\sqrt{3y} }{3y}[/tex]
Find the measure of the arc.
146°E
mFD =
Answer:
124
Step-by-step explanation:
A circle is a curve sketched out by a point moving in a plane. The measure of the arc mFD is 124°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
As we know that the angle made at the center of the circle is 360°. And it is mentioned that the measure of mFE is 146°, while mED is 90°. Therefore, the sum of all angles can be written as,
[tex]\angle FOE + \angle EOD + \angle FOD = 360^o\\\\146^o + 90^o + \angle FOD = 360^o\\\\236^o +\angle FOD =360^o\\\\\angle FOD = 124^o[/tex]
Thus, the measure of the arc mFD is 124°.
Learn more about Circle:
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Use the equation e^x+e^-x/e^x-e^-x=t tosolve for x
Answer:
Solve the rational equation by combining expressions and isolating the variable
x = ln ( t − √ t ^2 + 4 )/2x = ln ( t +√ t ^2 + 4 )/2Answer:
Step-by-step explanation:
I assume that the equation is
[tex]e^x+\frac{e^{-x}}{e^x} -e^{-x}=t \\[/tex]
[tex]e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t[/tex]
[tex]e^{3x}+1-e^x=e^{2x}t[/tex]
[tex]e^{3x}-te^{2x}-e^x=-1[/tex]
Let u = e^x
[tex]u^3-tu^2-u=-1[/tex]
[tex]u(u^2-tu-1) = -1[/tex]
if u=1, then [tex]u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0[/tex]
then u = 0 (reject) or u = t
So far, we have u = 1 and u = t
if u =1, e^x =1 , then x = 0
if u = t, then e^x = t or x = lnt
Please help! Correct answer only!
Cooper and Alice made a list of 7 psychology experiments they want to try at home. Each experiment tackles one specific psychology topic. 5 of the experiments involve cats.
If Cooper and Alice randomly choose 4 experiments to try over the summer, what is the probability that all of them involve cats?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability = 0.2603
Step-by-step explanation:
Consider the steps below;
[tex]Probability of Experiment Involving Cats - 5 / 7,\\Probability That 4 Chosen Experiments Are All Involving Cats - ( 5 / 7 )^4,\\\\5 / 7 * 5 / 7 * 5 / 7 * 5 / 7 =\\\\Conclusion; Probability - 625 / 2401[/tex]
Solution; Probability = ( About ) 0.2603
CAN I HAVE AN ANSWER PLEASE?
Jasmine is traveling at 45 miles per hour. At that same rate, which of the following proportions could be used to find how long it will take her to travel 135 miles?
1. 45 miles / 1 hour = n hours/135 miles
2. 45 miles/n hours = 135 miles/1 hour
3. 45 miles /1 hour = n miles /135 hours
4. 45 miles/1 hour = 135 miles/n hours
Answer:
3 hours
Step-by-step explanation:
Jasmine's hourly distance covered (her rate of travel) is 45 mi / hr.
45 miles 135 miles
-------------- = ----------------
1 hour x
Cross-multiplying, we get 45x = 135, or x = 3 hours
What is the measure of the angle formed by a side of the given angle and the given angle's bisector? 30° 52° 172° 171°30'
Answer:
30°=15° 52°=26° 172°=86° 171'30°=85.75°
Step-by-step explanation:
okay so re-reading over the question, and analyzing what the question wants us to answer, you will then realize that the way to get the answer is to divide x by 2.
our x examples, in this case, would be 30°,52°,172°, and 171'30°.
and that's how you find the answer to this type of question. :)))
there are 48 cards in a pack and each card is either red or black.the ratio of the number of red cards to the number of black cards is 1:1.
8 red cards are removed from the pack
find the ratio of the number of red cards now in the pack to the number of black cards now in the pack
Answer:
2:3
Step-by-step explanation:
We know that there are 24 red and black cards in the 48 pack because their ratio is 1:1. When 8 red cards are removed we have 16 red and 24 black cards. The ratio of this is 16:24 which simplifies to 2:3.
The ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1
Calculation of ratioThe total amount of cards (red or black) in the pack is = 48
The ratio of the number of red cards to the number of black cards is = 1:1
The number of cards removed from the pack = 8
Therefore the total number of cards( red or black = 48 -8
= 40 cards
But to calculate the number of red card
= 1+1 = 2
40/2 = 20 red cards
The number of black cards
1+1 = 2
40/2 = 20 black cards
The ratio of red is to black cards = 20:20 or 20/20 = 1:1 or 1/1
Therefore the ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1
Learn more about ratio here:
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can sumone help with this pls
Answer:
D
Step-by-step explanation:
The range means the possible values of the y coordinate which is y ≥ 1 in this function
as an estimation 5 miles is 8km. convert 16km to miles
Answer:
if its 8 to 5 then 16 is 10
answer: 10 miles
Answer:
10 miles
Step-by-step explanation:
8 km = 5 miles
So, Let's use the unitary method
1 km = [tex]\frac{5}{8}[/tex] miles
Multiplying both sides by 16, we get
16 km = [tex]\frac{5}{8} * 16[/tex] miles
16 km = 5 × 2 miles
16 km = 10 miles
