Determine, which is the shorter path from A to B is: Around the two small semi circles or around the large semi-circle? Verify your answer by calculating the length of the path in each case.
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You decide to buy a car that costs $10,000. The normal depreciation for such a car is 5% per year. How much will the car be worth in 2 years?
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Answer:
11,000
Step-by-step explanation:
10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.
What is the remainder when f(x) = x³- 13x² + 40x + 18 is divided by x-7? Show your work.
Answers
Answer:
remainder = 4
Step-by-step explanation:
using the remainder theorem
when f(x) is divided by (x - a) then the remainder is f(a)
so when f(x) is divided by (x - 7) the remainder is f(7) , that is
f(7) = 7³ - 13(7)² + 40(7) + 18
= 343 - 13(49) + 280 + 18
= 343 - 637 + 298
= 4
Hence, the remainder is [tex]4[/tex].
What is the remainder value?
The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
Applying the remainder theorem
In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].
So, here when [tex]f(x)[/tex] is divided by [tex](x - 7)[/tex] the remainder is [tex]f(7)[/tex], that is
[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]
Hence, the remainder is [tex]4[/tex].
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Type the correct answer in each box. write each answer as a fraction, using / for the fraction bar. wesley draws a card at random from a well-shuffled deck of playing cards. the probability that wesley draws an ace or a jack is . the probability that wesley draws a number card or a black card is .
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The probability that Wesley draws an ace or a jack is 0.154 and the probability that Wesley draws a number card or a black card is 0.846
The probability of Ace or jackIn a standard deck of cards, we have:
Total = 52
Ace = 4
Jack = 4
Ace and Jack = 0
The probability is then calculated as:
P = P(Ace) +P(Jack) - P(Ace and Jack)
This gives
P = 4/52 + 4/52 - 0/52
Evaluate
P = 0.154
Hence, the probability that Wesley draws an ace or a jack is 0.154
The probability of Number card or black cardIn a standard deck of cards, we have:
Total = 52
Number card = 36
Black = 26
Number card and Black = 18
The probability is then calculated as:
P = P(Number card) +P(Black card) - P(Both)
This gives
P = 36/52 + 26/52 - 18/52
Evaluate
P = 0.846
Hence, the probability that Wesley draws a number card or a black card is 0.846
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Answer: my guess is 4/13 and 11/13
Step-by-step explanation:
sorry if im wrong
2. At the sale, Jessica bought 4 pairs
sunglasses. How much did she
of
spend?
8.78176.60
A $51.58
B $51.80
C$55.80
D$54.80
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27 Solve for x to the nearest tenth: x² + x - 5 = 0.
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Answer:
Step-by-step explanation:
We can use the quadratic formula to get the answer to this
Quadratic Formula: -b +- √b² - 4ac/2a
Once we input A, B, and C into this, and solve any multiplication, we get
x = -1 +- √1 + 20/2
We divide by 2a, which 2a = 2.
-0.5 +- 10.5.
these are the following values of x:
x = 10
x = 11
Pretty sure this is it, hope it helps!
Find the quotient of 1 4/5 and 1 1/5
Give your answer as a fraction in its simplest form
Answers
Answer: 1 1/2
Step-by-step explanation:
1 4/5 = 9/5
1 1/5 = 6/5
[tex]\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}[/tex]
I kinda need help with this
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Applying the leg rule, the value of x in the given right triangle is: A. 6.
What is the Leg Rule?The leg rule for solving a right triangle having an altitude is expressed as:
hypotenuse/leg = leg/part.
In the image given we have the following:
Hypotenuse = 4 + 5 = 9 units
Leg = x
Part = 4
Plug in the values into the leg rule formula:
9/x = x/4
(x)(x) = (9)(4)
x² = 36
x = √36
x = 6 units.
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37-(y-19)=2y this is a problom from rsm
Answers
Answer:
y = 56/3
Step-by-step explanation:
Distribute:
37 - (y - 19) = 2y
37 - y + 19 = 2y
Add the numbers:
37 - y + 19 = 2y
56 - y = 2y
Rearrange the terms:
56 - y = 2y
-y + 56 = 2y
Solution:
y = 56/3
Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 680 grams, how much of the element would remain after 19 years, to the nearest whole number?
Answers
Answer:
410 g
Step-by-step explanation:
Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).
y = a(1/2)^(t/h)
__
We can use this equation with the given values to find the amount remaining.
y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)
y ≈ 410 g
About 410 grams of element X will remain after 19 years.
A principal of $3900 is invested at 7.5% interest compounded annually how much will the investment be worth after 9 years
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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]
Lexi had 3/4 of an apple pie. She gave 1/4 of what she had to her friend Julie. What fraction of the whole pie did Julie get?
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Answer:
3/16 of the whole pie
Step-by-step explanation:
Lexi had 3/4 of an apple pie. She gave 1/4 of it to Julie. That means what Julie receives is the product of the whole and the portion.
==========================================================
Solving :
Therefore, the equation is :
⇒ 3/4 × 1/4
⇒ 3/16 of the whole pie
Factorise 2x^2 + x - 6
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[tex] \rm \: {2x}^{2} + x - 6[/tex]
[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]
[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]
[tex] \rm \: (x + 2) \times (2x - 3)[/tex]
if x=0 and y<0, where is the plot (x,y) located
Answers
Mark me the Brainliest!
Answer:
The point will be plotted on Y axis
One week, Genesis earned $367.40 at her job when she worked for 22 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $584.50?
Answers
Answer:
35 hrs
Step-by-step explanation:
Hope this helps! Have a great day!!
A rectangle is divided into exactly 20 congruent squares. Then these squares are lined up in a single row extending 36 inches (3 feet). What was the area of the rectangle?
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The area of the rectangle is 64.8 square .inch
What is a Rectangle ?A rectangle is a polygon with four sides , opposite sides are parallel and equal.
It is given that
A rectangle is divided into exactly 20 congruent squares
If they are lined up the Length is 36 inches
Therefore the length of each square or the side of the square = 36/20
= 1.8 inch
The area of the rectangle will be
20* Side of square * Side of square
=20*1.8*1.8
= 64.8 square inch
The area of the rectangle is 64.8 square .inch
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Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide. saif is building a second pen that is 75% the length of the original and 125% the width of the original. write an equation to determine the length of the second pen. what is the length of the second pen? . .
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The length of the second pen is 11.25 units.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposite sides are parallel and equal .
it is given in the question that
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide
length new = 75% length initial
Length new = (75/100) * 15
Length new = 0.75 * 15
Length new = 11.25 units
The length of the second pen is 11.25 units.
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PROVE :
sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4
Answers
Step-by-step explanation:
[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]
[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]
[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]
[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]
Express 34m 8cm 6mm in mm
Answers
Answer:
34086 mm
Step-by-step explanation:
34m = 34000 mm
8cm = 80 mm
6mm = 6mm
34000+80+6 = 34086 mm
Answer:
34086 mm
34m = 34000m
8cm = 80mm
There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?
Answers
Answer:
12.5% is the answer.
Step-by-step explanation:
the average of 5 girls is 6 yrs. the average of 4 of them is 16½. what is d age of d fifth gal
Answers
Answer:
This assumes the question should read:
"The average of 5 girls is 16 [not 6] yrs. the average of 4 of them is 16½. what is d age of d fifth gal
The age, d, is 14 years.
Step-by-step explanation:
When the girl with age d is not included, the average goes up to 16.5 years. Let's define GroupA as the sum of the ages of the 4 girls whose average age is 16.5 years. d is the age of the girl that is removed from the average.
We know that all the girls (GroupA + d) have an average age of 16 years:
(GroupA + d)/5 = 16 years [Add the ages for all the girls (GroupA and d) and divide by 5 to obtain the average age for the larger group].
We know that when d is removed, the average for the 4 remaining girls (GroupA) is 16.5 years:
(GroupA)/4 = 16.5 years
This tells us the sum of the ages for GroupA:
GroupA = 4*(16.5)
GroupA total = 66 years
From above: (GroupA + d)/5 = 16 years
Since GroupA = 66 years, (66 years + d)/5 = 16 years
(66 years + d) = 90 years
d = 14 years
A pennant in the shape of a right triangle has a base of 48 inches and a height of 14 inches what is the hypotenuse of the pennant?
Answers
Answer:
50 inches
Step-by-step explanation:
48^2 + 14^2 = h^2
Answer is 50 inches if you solve...
A rental car company charges $63.41 per day to rent a car and $0.05 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 275 miles. She has at most $200 to spend. What is the maximum number of days that Ella can rent the car while staying within her budget?
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Answer:
2 days
Step-by-step explanation:
275 miles times 0.05 = $13.75 for mileage
200-13.75=186.25 left
186.25/63.41(daily fee)= 2.93
She can rent it for 2 days
What is the difference of a surface area and a volume
Answers
Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.
For example:
A cube has a length,breadth and height of 5cm,find:
a) surface area of the cube;
b) and the volume of the cube.
a) area of one side of the cube = 5 x 5
= 25cm²
Total surface area = 25cm x 6 (a cube has 6 sides)
= 150cm²
b) volume of cube = length x breadth x height
= 5 x 5 x 5
= 125cm³
Hope this helps you :]
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Consider triangle ABC. What is b?
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Explanation:
for what value of x is the rational expression below equal to zero?
3x+15
———
6-x
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[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]
Answer:
the answer= -5
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.
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Answer:15
Step-by-step explanation:
A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.
Let the distance of the ladder from the wall be x
The length of the ladder = x+3
The ladder touches the wall at a vertical height of 9 feet.
(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem
x^2 + 6x+ 9 = x^2 + 81
x^2- x^2 +6x = 81-9
6x= 72
x= 12
Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.
Is 3²+3³ equal to 3⁵?
( yes, no ) the expressions (are, are not ) equal
Answers
Answer: No the expressions are not equal
Work Shown:
3² = 3*3 = 9
3³ = 3*3*3 = 27
3²+3³ = 9+27 = 36
3⁵ = 3*3*3*3*3 = 243
The 3²+3³ = 36 doesn't match up with 3⁵ = 243
Therefore, the two expressions are not equal.
Answer:
Step-by-step explanation:
No, the expressions are not equal.
3^2 + 3^3 = 9 + 27 = 36
3^2 * 3^3 = 3^5
keep the base the same and add the exponents
Select the correct answer from each drop-down menu.
This graph shows the relationship between demand and price for goods sold at a shop. Anna plots the data on a scatter plot and draws a line of best fit to represent the relationship as shown.
This is not the line of best fit because the line . Anna could get a better fit by the y-intercept and the slope.
Answers
This is not the line of best fit because the line is not through the middle of the data points.
What is line of best fit?
The line of best fit is a line through a scatter plot of data points that best expresses the relationship between those points.
In this case, this is not the line of best fit because the line is not through the middle of the data points.
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10
Select the correct answer.
Which equation is equivalent to the given equation?
- 4(x - 5) + 8x = 91 - 3
OA -5x = 2
OB. 5 = 17
OC. -5x = -23
OD. 5x = -12
Recet
Next
Answers
The equation that is equivalent to the given equation is 4x = 68. No answer is correct
Equations and expressionsEquations are two expressions equated to each other. Given the equation below;
- 4(x - 5) + 8x = 91 - 3
Expand
-4x + 20. + 8x = 88
Collect the like terms
4x + 20 = 88
4x = 88 - 20
4x = 68
Hence the equation that is equivalent to the given equation is 4x = 68
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what’s the surface area Due by tomorrow!!!
Answers
Answer: The surface area = 2040.
Step-by-step explanation: Have a great day!