Answer:
Amount= $2933.2
Step-by-step explanation:
The interest of $2,500 principal earning with rate of 4%, compounded quarterly, after 4 years
A= p(1+r/n)^(nt)
P= $2500
r= 4/100= 0.04
t= 4
n = 4*4= 16
A= 2500(1+0.04/16)^(16*4)
A= 2500(1+0.0025)^(64)
A= 2500(1.0025)^64
A= 2500(1.17328)
A= 2933.2
Amount= $2933.2
first correct answer gets best marks
Answer:
x ≤5
Step-by-step explanation:
Pointing to the left means less than or less than or equal to
x ≤5
Answer:
[tex]\boxed{x \leq 5}[/tex]
Step-by-step explanation:
[tex]\sf Arrow \ pointing \ to \ the \ left \ on \ a \ number \ line \ means \ that[/tex]
[tex]\sf \ the \ value \ is \ either \ less \ than \ or \ less \ than \ or \ equal \ to.[/tex]
[tex]\sf{Graph}[/tex] [tex]x\leq 5[/tex] [tex]\sf{on \ the \ number \ line.}[/tex]
HELPPP PLZZZZZZZZZZZZZ
Two different sizes of square metal duct are joined by a piece that is a frustum of a pyramid. Find the lateral surface area, if the small end is square with one side of length 17 in. and the larger square end is of length 19 in. on one side with a slant height of 2 in.
Answer:
288 in²
Step-by-step explanation:
The formula used to solve this question is :
Lateral Surface Area = s( P1 + P2)
Where s = slant height = 2 inches
P1 and P2 = Perimeter of the bases
Perimeter of base 1 = 4 × length of the end of the small square
4 × 17 inches = 68 inches
Perimeter of base 2 = 4 × length of the end of the large square
4 × 19 inches = 76 inches
Lateral Surface Area = 2 × (68 + 76)
= 2 × 144
= 288 in²
Water drips from a faucet at a rate of 41 drops/minute. Assuming there are 15,000 drops in a gallon, how many minutes would it take for the dripping faucet to fill a 1‑gallon bucket? Round your answer to the nearest whole number.
Answer:
366 minutes
Step-by-step explanation:
divide 15000 by 41
Given that α and β are the roots of the quadratic equation [tex]2x^{2} +6x-7=p[/tex], and α=2β, a) find the value of p. b) form a quadratic equation with roots α+2 and β+2
Answer:
[tex]\large \boxed{\sf \ \ \ p=-11 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]\alpha \text{ and } \beta \text{ are the roots of the following equation}[/tex]
[tex]2x^2+6x-7=p[/tex]
It means that
[tex]2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\[/tex]
And we know that
[tex]\alpha= 2\cdot \beta[/tex]
So we got two equations
[tex]2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\<=>8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\<=>6\beta^2+6\beta =0\\\\<=>\beta(\beta+1)=0\\\\<=> \beta =0 \ or \ \beta=-1[/tex]
For [tex]\beta =0, \ \ \alpha =0, \ \ p = -7[/tex]
For [tex]\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11[/tex]
I assume that we are after two different roots so the solution for p is p=-11
b) [tex]\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1[/tex]
So a quadratic equation with the expected roots is
[tex]x(x-1)=x^2-x[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What number is 16% of 80?
Write and solve an equation to answer the question.
Answer:
The answer is 12
Step-by-step explanation:
Trust me, kay? Please mark Brainliest!!!!
Answer:
12.8
Step-by-step explanation:
16% of 80
[tex]\frac{16}{100}[/tex] × 80
[tex]\frac{16}{10}[/tex] × 8
[tex]\frac{16}{5}[/tex] × [tex]\frac{4}{1}[/tex]
16 × 4
5
12[tex]\frac{4}{5}[/tex] = 12.8
The length of the second side of a triangle is 2 inches less than the length of the first side.The length of the third side is 12 inches more than the length of the first side.the perimeter of the triangle is 73 inches.Find the length of each side of the triangle.
Answer:
The lenght of the tree sides of the triangle are:
first side: 21 inches
second side: 19 inches
third side: 33 inches
Step-by-step explanation:
a + b + c = 73
b = a - 2
c = a + 12
a = leght of the first side of the triangle
b = lenght of the second side of the triangle
c = lenght of the third side of the triangle
then:
a + (a-2) + (a+12) = 73
3a - 2 + 12 = 73
3a + 10 = 73
3a = 73 - 10
3a = 63
a = 63/3
a = 21 inches
b = a - 2
b = 21 - 2
b = 19 inches
c = a + 12
c = 21 + 12
c = 33 inches
Check:
21 + 19 + 33 = 73
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The length of the sides of the triangle are:
first side: 21 inchessecond side: 19 inchesthird side: 33 inchesWhat is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the sides of triangles be x, y, z.
As, perimeter of the triangle is 73 inches.
x+ y+ z= 73................(1)
and, length of the second side of a triangle is 2 inches less than the length of the first side.
y= x- 2
and, length of the third side is 12 inches more than the length of the first side.
z= x + 12
Substitute the values of y and z in equation (1)
x+ x-2 + x+ 12= 73
3x + 10 =73
3x= 63
x= 21
Then, First side= 21 inch
second side = 21 - 2 = 19 inch
third side= 21+ 12 = 33 inch
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Sally wants to save for a new cell phone. She opens a bank account with $60 and adds $10 each week. Which of the following equations can be used to determine how much she has after ‘w’ weeks? A : T = 70w B : T = 60 + 10 + w C : T = 60 + 10w D : T = 10 + 60w
Answer: C
Step-by-step explanation:
"w" represents the number of weeks. If she adds $10 per week, the equation will include 10w. Because she starts out with $60 already, the complete equation would be:
[tex]T=60+10w[/tex].
Hope this helps!
The equation that describes the amount she has after 'w' weeks is
C : T = 60 + 10w.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Sally wants to save for a new cell phone. She opens a bank account with $60 and adds $10 each week.
Assuming the total amount to be 'T' and no. of weeks to be 'w'.
∴ The equation that represents the amount of money she has is,
T = 60 + 10w.
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Rewrite the equation y= 4/5.x + 3 in general form Ax + By + C = O
Work Shown:
y = (4/5)x + 3
5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction
0 = 4x + 15 - 5y ... subtract 5y from both sides
4x-5y+15 = 0 .... rearrange terms
The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.
Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased
Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
Martin sent 3 emails on Wednesday 9 emails on Tuesday 27 emails on Friday 81 emails on Saturday 243 emails on Sunday. If the pattern continues how many emails will Martin sent on Monday...
Answer:
729 emails
Step-by-step explanation:
The pattern is to multiply by 3
3*3 = 9
9*3 = 27
27*3 = 81
81*3 = 243
If the pattern continues, Martin will sent on monday:
243*3 = 729
729 emails
Answer:
729
Step-by-step explanation:
Solve the proportion 26/z = 13/22
Answer:
z = 44
Step-by-step explanation:
26/z = 13/22
Using cross products
26 * 22 = 13*z
Divide each side by 13
26/13 * 22 = 13z/13
2 *22 =z
44 =z
Answer:
Z=44
To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.
A school recorded the number of times pupils were late each month. Colin says 'the number of lates in March was half that in January.' is he correct? Show how you know
Answer:
Colin is wrong
Step-by-step explanation:
The question is incomplete because the chart or the table which shows the data is not given. I have attached the full question at the bottom. Consult it for better understanding.
We can clearly see in the chart the number of lates in January is 30, while the number of lates in March is 20.
As the half of 30 is 15, not 20, we can say that the statement of Colin is wrong, because the number of lates in March should be 15 to prove his statement true
if an article is sold with 20% discount,there will be a profit of 15%.If it is sold at 10% discount, there will be a profit of Rs.200.Calculate the market price of an article
Answer:
The market price of the article is Rs. 978.72
Step-by-step explanation:
Let x represents the market price.
Let y represents the selling price.
Let z represents the cost price.
if an article is sold with 20% discount then there will be a profit of 15%.
SP = CP+Profit =z+0.15z=1.15z
ATQ
[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]
If it is sold at 10% discount then there will be a profit of Rs.200
ATQ
[tex]0.9x - z = 200[/tex]
Now we are supposed to find the market price of an article.
[tex]0.9x - z= 200[/tex]
Multiplying 1.15 both sides
[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]
We know that[tex]1.15z = 0.80x[/tex]
[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]
Hence The market price of the article is Rs. 978.72
One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) is 7 5 8 feet by 5 3 8 feet. Astronauts on the Apollo missions had a flag on a shoulder patch, use the scale factor 1/60 and find the union dimensions for the patch
Answer: 0.127 feet by 0.090 feet
Step-by-step explanation:
Given that :
The USA's flag dimension = 19feet by 10feet
Union's (blue rectangle in the top left corner) dimension = 7 5/8 feet by 5 3/8 feet.
Union dimension for the shoulder patch of the USA flag used by astronauts for the Apollo mission has a scale factor of 1/60
Therefore, dimension of the union patch ;
1/60 * ( 7 5/8 feet by 5 3/8 feet)
1/60 * (61 / 8 feet by 43/8 feet)
61/480 feet by 43/480 feet
0.127 feet by 0.0895 feet
0.127 feet by 0.090 feet
If cosθ = x, then ± √(1+x)/2 = _____.
cosθ/2
sinθ/2
cos2θ
sin2θ
Answer:
cos(theta/2) = sqrt((1+x)/2)
Step-by-step explanation:
From the double angle formula
cos^2(t)-sin^2(t) = cos(2t) ...................(1)
cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)
Add (1) and (2)
2cos^2(t) = 1+cos(2t)
cos^2(t) = (1+cos(2t))/2
cos(t) = sqrt((1+cos(2t))/2)
substitute t = theta/2
cos(theta/2) = sqrt((1+cos(theta))/2)
substitute cos(theta) = x
cos(theta/2) = sqrt((1+x)/2)
what is 35 - (0.35 x 100)
Answer:
0
Step-by-step explanation:
First let's solve for the value in the parentheses.
[tex]0.35 \cdot 100 = 35[/tex]
We know this is correct because if we multiply a value by 100, the decimal point is moved 2 places to the left.
35 - 35 = 0, so the value of this expression equals out to be 0.
Hope this helped!
What is P(A|B)?
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
What is P(A|B)? 
A.Not enough information
B.0.50 
C.0.10 
D.0.20
Answer:
50
Step-by-step explanation:
The value of P(A|B) = 0.50 which is correct option(B)
What is independent events?
Independent events is defined as an event that is not affected by other events.
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
Substitute the value of P(A) = 0.50,
P(A|B) = 0.50
Hence, the value of P(A|B) = 0.50
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Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.
Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g
I don't understand how to do this problem.
Answer:
First blank: 6a
Second blank: 2/3
Third blank: 21.6
Fourth blank: 3.9
Step-by-step explanation:
Basically, all you need to do is distribute the 2/3 to the stuff inside the parentheses. That means in the first blank, write 6a inside since you're multiplying 2/3 and 6a, and then in the second blank you write 2/3 since you're multiplying 2/3 and 9 together.
2/3*6a+2/3*9 = 21.6 is what you should have.
Now, just solve for a.
4a+6 = 21.6
4a=15.6
a=3.9
Answer:
2/3 * 6a+ 2/3 +9 = 21.6
a = 3.9
Step-by-step explanation:
2/3 ( 6a+9) = 21.6
Distribute
2/3 * 6a+ 2/3 +9 = 21.6
4a + 6 = 21.6
Subtract 6 from each side
4a = 15.6
Divide each side by 4
4a/4 = 15.6/4
a =3.9
Between which of the following pairs of numbers, can a rational number be found? (answer can be more than one pair)
PAIR 1: (-10) and (-9)
PAIR 2: 5.91 and 5.92
PAIR 3: 2/3 and 4/5
.
Answer:
Between all these pairs of numbers,a rational number can be found in all the 3 pairs
Step-by-step explanation:
PAIR1: -10 and -9
Rational numbers are: -10.5,-10.6,-10.1,etc (there are way more)
PAIR2: 5.91 and 5.92
Rational numbers:- 5.915,5.916,etc(there are way more)
PAIR3:2/3 and 4/5
LCM= 15
2/3=10/15
4/5=12/15 between these two (10/15 & 12/15)
Rational numbers: 11/15, 11.5/15(because it's result would be a recurring/repeating decimal),etc
What is answer for 26/25 × -16/63 Step by step no explanation I will make you as brainlist Please find out Thanks
Answer:
[tex] - \frac{416}{1575} [/tex]Step-by-step explanation:
[tex] \frac{26}{25} \times ( - \frac{16}{63} )[/tex]
Multiplying a positive and a negative equals a negative[tex]( + ) \times ( - ) = ( - )[/tex]
[tex] = - \frac{26}{25} \times \frac{16}{63} [/tex]
Multiply the fractions:
[tex] = - \frac{416}{1575} [/tex]
Hope this helps..
Best regards!!
What translation is made from f(x) = f(x) + 6?
Answer:
moves it up 6 units
Step-by-step explanation:
y = f(x) + C C > 0 moves it up
f(x) = f(x) + 6 moves it up 6 units
Answer:
Vertical shift, 6 up.
Step-by-step explanation:
The entire function f(x) has a value of six added to it. That means that regardless of where f(x) was plotted on the coordinate plane, after the translation f(x) + 6, every single point would increase its value by six. Since all points would increase their values by six, the entire function would shift 6 up.
Find the inverse of the function 3+4x/1-5x
Answer:
the inverse of the function f^-1(x)=(x-3)/(4+5x)
Step-by-step explanation:
( 3+4x)/(1-5x)
y=4x+3/1-5x swap the variables
x=4y+3/1-5y solve for y
y=x-3/4+5x
The inverse of a function is :y=x-3/4+5x
What is inverse of a function?
The inverse function returns the original value for which a function gave the output.
If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.
Steps are:
How do you solve inverse functions step by step?Finding the Inverse of a FunctionFirst, replace f(x) with y . Replace every x with a y and replace every y with an x .Solve the equation from Step 2 for y . Replace y with f−1(x) f − 1 ( x ) . Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.for example:
Suppose, f(x) = 2x + 3 is a function.
Let f(x) = 2x+3 = y
y = 2x+3
x = (y-3)/2 = f-1(y)
This is the inverse of f(x).
Given function:
f(x)= ( 3+4x)/(1-5x)
now, swap the variables x and y.
y=4x+3/1-5x
Now solving for y
x=4y+3/1-5y
y=x-3/4+5x
Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).
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y=-2x-21 determine the intercepts of the line (,) (,) ASAPPPP
Answer:
x intercept (10.5,0)
y intercept (0, -21)
Step-by-step explanation:
y=-2x-21
there are two intercept for a line
x intercept, the point of given equation of line which lies on x axis.
For x intercept corodinate of y is o
Thus, value x intercept is form (x,0)
putting these value in y=-2x-21, we find x intercept
0=-2x-21
2x = 21
x = 21/2 = 10.5
Thus, x intercept (10.5,0)
Y intercept, the point of given equation of line which lies on y axis.
For Y intercept coordinate of x is o
Thus, value y intercept is form (0,y)
putting these value in y=-2x-21, we find y intercept
y = -2*0 -21
y = -21
Thus, y intercept (0, -21)
Bianca has a piece of rope that is 22 feet long. She cuts the rope into 3 pieces of equal length. Explain how to determine the length, in feet , of each piece of rope. What is the length, in feet, of each piece of rope written as a mixed numbers? Explain how to use a multiplication equation to check your answer.
Answer:
Hey there!
To solve this problem, you want to divide 22 by 3, which is about 7.33 feet.
We can check this by seeing 7.33 times 3=22
Hope this helps :)
Which equation can be used to find the volume of this solid? A triangular prism. The triangular base has a base of 11 inches and height of 7 inches. The height is 9 inches. V = 11 times 9 times 7 V = 11 + 9 + 7 V = StartFraction 7 + 9 over 2 EndFraction + 11 V = StartFraction 7 times 11 over 2 EndFraction times 9
Answer:
V=11*7*9=693
Step-by-step explanation:
V=Bh ( B is the base area ( base*height) , and h is the height of the prism)
find B=base*h
B=11*7=77 in²
V=B*h=77*9=693 in³
The volume of the triangular prism is 174.25 in³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the triangular base has a base of 11 inches and height of 7 inches.
The formula for finding the volume of a triangular prism is V = (base area x height) / 2.
In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.
In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.
Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.
Therefore, the volume of the triangular prism is 174.25 in³.
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If (a-bi)^2 = 13 - 12i, what is the product of a and b?
Answer:
[tex]\large \boxed{\sf \ \ \ a\cdot b= 6 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex](a-bi)^2 = 13 - 12i\\\\<=> a^2+(bi)^2-2abi = 13-12i\\\\<=>a^2-b^2-2abi=13-12i[/tex]
Imaginary term must be the same so
-2ab=-12
2ab = 12
ab = 12/2 = 6
So the product of a and b is 6
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Let's solve the given equation step by step to find the product of a and b. Initially,
let's expand the left side of the equation: [tex](a - bi)^2 = (a - bi)(a - bi) = a^2 - abi - abi + b^2i^2 = a^2 - 2abi + b^2(-1) = a^2 - 2abi - b^2[/tex] We are given that this result is equal to[tex]13 - 12[/tex]i, so we can set up the following equation: [tex]a^2 - 2abi - b^2 = 13 - 12i[/tex] By comparing the real and imaginary parts of both sides, we can form two equations:
Equation [tex]1: a^2 - b^2 = 13[/tex] (Equating real parts) Equation [tex]2: -2ab = -12[/tex](Equating imaginary parts) From Equation 2, we can deduce that ab = 6. To proceed further and find the product of a and b, we need more information. The current given equation has infinite possible solutions for a and b.
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Help me with this please. I typed it on my iPad
An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft.
Answer:
The distance between the plane and the observer is 16,659.18ft
Step-by-step explanation:
Complete question:
(An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft, what is the distance between the observer and the plane)
Hello,
The question above requires us to find the distance between an observer and a plane. This is very much easy because we are given the angle at which the observer makes with the plane. To solve this question correctly, we need a pictorial representation of the situation.
See attached document for better illustration
In the diagram, we need to find x.
Since the observer and the plane makes a right angled triangle with the distance apart them, we can use SOHCAHTOA
In this case, we have to use Tangent
Tanθ = opposite/ adjacent
θ = 42°
Opposite = 15,000
Adjacent = x
Tan42 = 15000 / x
x = 15000 / tan42
x = 15000 / 0.90
x = 16,659.18ft
The horizontal distance between the observer and the plane is 16,659.18ft
Answer:
I am not too sure but I know it is not 10,035, or 16,648, nor 20,188 because I put that and it wasn’t right so the last option would be.
22,417