The percentage of your savings that I use is 60%
This shows that the amount of money the organization will raise in total is $25,000.
1) Given
Total amount saved = $4500
Amount used = $2,700
Percentage of money used = Amount used/Total amount saved × 100%
[tex]Percentage \ of \ money \ used = \frac{2700}{4500} \times 100\\Percentage \ of \ money = \frac{27}{45} \times 100\\Percentage \ of \ money \ used = \frac{2700}{45} \\Percentage \ of \ money \ used = 60 \%[/tex]
Hence the percentage of your savings that I use is 60%
2) Let the amount of money the organization will raise in total be x
Since the 45% of the money they raise represents $11,250, hence:
[tex]45\% \ of \ x = \$11,250\\0.45x = 11,250\\x = \frac{11250}{0.45}\\ x = 25,000[/tex]
This shows that the amount of money the organization will raise in total is $25,000
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20 kg potatoes are sold at $12.80 each.If you have only $48, how many 20kg bags can you buy
.......... is a factor of every even number.
Answer:
2 is the factor of every even number hope this help you
if the area of the triangle is 5cm^2. find the angle.
9514 1404 393
Answer:
the angle is 30°
Step-by-step explanation:
The area of a triangle given two sides and the included angle is ...
A = 1/2ab·sin(C)
5 cm² = 1/2(4 cm)(5 cm)sin(θ)
0.5 = sin(θ) . . . . . . divide by 10 cm²
θ = arcsin(.5) ≈ 30°
_____
Additional comment
An obtuse angle of 150° in that location will give a triangle with the same area.
Given that V=4/3πrcube , make r the subject of formula
Answer:
[tex]V = \frac{4}{3} \pi {r}^{3} \\ \\ 3V = 4\pi {r}^{3} \\ {r}^{3} = \frac{3V}{4\pi} \\ \\ r = \sqrt[3]{ \frac{3V}{4\pi} } [/tex]
The ratio of red beads to blue beads on a necklace is 4:7. If there are 16 red beads, how many blue ones are there?
Answer:
There are 28 beads
Step-by-step explanation:
Total ratio:
[tex]{ \sf{ (4 + 7) = 11}}[/tex]
let total beads be x:
[tex]{ \sf{ \frac{4}{11} \times x = 16 }} \\ \\ { \sf{x = \frac{11 \times 16}{4} }} \\ x = 44 \: beads[/tex]
Blue beads:
[tex] = 44 - 16 \\ = 28 \: \: beads[/tex]
solve the inequality y-6>/2y-4
Answer:
Step-by-step explanation:
Let's solve your inequality step-by-step.
y - 6 > 2y - 4
y - 2y > -4 + 6
-y > 2
now divide by -1 and inequality sign changes
-y/-1 < 2/-1
y < -2
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3
You're looking for a solution of the form
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]
Differentiating twice yields
[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]
[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]
Substitute these series into the DE:
[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:
[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]
which indicates that the coefficients in the series solution are governed by the recurrence,
[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]
Use the recurrence to get the first few coefficients:
[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]
You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,
-7 = -7/0!
-7/2 = -7/2!
-7/6 = -7/3!
and so on, with only the coefficient in the n = 1 position being the odd one out. So we have
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]
which looks a lot like the power series expansion for -7eˣ.
Fortunately, we can rewrite the linear term as
3x = 10x - 7x = 10x - 7/1! x
and in doing so, we can condense this solution to
[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]
Just to confirm this solution is valid: we have
y = 10x - 7eˣ ==> y (0) = 0 - 7 = -7
y' = 10 - 7eˣ ==> y' (0) = 10 - 7 = 3
y'' = -7eˣ
and substituting into the DE gives
-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0
as required.
Evaluate the following expression
The length of a rectangle is three times its width. If the area of the rectangle is 300 in squared”, find its perimeter.
Can someone please help me solve the equation?
Answer:
(0,0) is the x and y intercept of the function
Step-by-step explanation:
The parabola touches the x and y axis at 0
The x intercept is (0,0) and the y intercept is (0,0)
Answer:
(0, 0) is the x and y intercepts
Step-by-step explanation:
intercepts are where the curve of the equation contacts an axis
The equation is y = x²
Can someone help me simplify this?
Answer:
See attached
Step-by-step explanation:
Which of the following is a solution of y> Ix| - 5?
O (-4,1)
O (-1,-4)
O (4, -1)
Hurry plz
Answer:
O (-4,1)
I hope I helped you^_^
Write in a shorter form:7m -7 +7m +7
Answer:
14m
Step-by-step explanation:
[tex]7m-7+7m-7\\[/tex]
First, we need to eliminate the like term and collect the like term.
[tex]-7+-7=0[/tex]
Now, we have 7m +7m, sum them up and you will get the answer.[tex]7m+7m=14m[/tex]
So, the answer is 14m.
Answer:
14m
Step-by-step explanation:
7m -7 +7m +7
7m + 7m - 7 + 7
14m
Integrate[Exp[Power[sinx,2]]sin2x,x]
Answer:
e^{sin²x}+c
Step-by-step explanation:
[tex]\int e^{sin^2x} sin 2x dx=?[/tex]
is this statement?
if so
then
[tex]put~sin^2x=t\\differentiate\\2 sin ~x~cos~x~dx=dt\\sin~2x ~dx=dt\\\int e^t~dt=e^t+c\\=e^{sin^2x}+c[/tex]
c program to generate prime numbers from 1 to 100.Also count prime numbers.
Answer:
Step-by-step explanation:
#include <stdio.h>
int main()
{
int num1, num2, flag_var, i, j;
/* Ask user to input the from/to range
* like 1 to 100, 10 to 1000 etc.
*/
printf("Enter two range(input integer numbers only):");
//Store the range in variables using scanf
scanf("%d %d", &num1, &num2);
//Display prime numbers for input range
printf("Prime numbers from %d and %d are:\n", num1, num2);
for(i=num1+1; i<num2; ++i)
{
flag_var=0;
for(j=2; j<=i/2; ++j)
{
if(i%j==0)
{
flag_var=1;
break;
}
}
if(flag_var==0)
printf("%d\n",i);
}
return 0;
}
A right triangle has side 14 and hypotenuse 50. Use the Pythagorean Theorem to find the length of the third side.
Answer:
48
Step-by-step explanation:
Pythagorean Theorem = h^2=p^2+b^2
We have,
(Hypotenuse)h=50
Let 14 be p, i.e (Perpendicular ,Known side)p=14
(Remaining side ,base)b=?(
Now,
h^2=p^2+b^2
or, 50^2=14^2+b^2
or, 2500-196=b^2
or, √2304=b
b=48
2. Mandla spent one quarter of his pocket money on sweets. a. What fraction does he have left? b. If he had R40 pocket money, how much did he spend?
Answer:
a. 3/4 of pocket money left
b. R10
Step-by-step explanation:
a. 4/4 - 1/4 = 3/4
b. 40/4 = 10 = 1/4 of pocket money
(a). The fraction of pocket money left is 3/4
(b). If he had R40 pocket money, he spend R10.
What is the Ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
Mandla spent one-quarter of his pocket money on sweets
Let x be the total amount of pocket money Mandla had originally
Solution of (a).
⇒ x - (1/4)x
⇒ (3/4)x
The fraction of pocket money left = 3/4
Solution of (b).
1/4 of pocket money
⇒ (1/4)x
⇒ (1/4)40
⇒ 10
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Find the zeros of the function in the interval (-2 pie, 2 pie). f(x) = 3 cos x
Answer:
Roots are -π/2 and π/2
Step-by-step explanation:
[tex]{ \bf{f(x) = 3 \cos(x) }}[/tex]
when x is -2π:
[tex]{ \sf{f( - 2\pi) = 3 \cos( - 2\pi) }} \\ { \sf{ = 3}}[/tex]
hence -2π is not a zero of the function
when x is 2π:
[tex]{ \sf{f(2\pi) = 3 \cos(2\pi) }} \\ { \sf{ = 3}}[/tex]
hence 2π is not a zero of the function
when x is π/2:
[tex]{ \sf{f( \frac{\pi}{2}) = 3 \cos( \frac{\pi}{2} ) }} \\ { \sf{ = 0}}[/tex]
Hence ±π/2 is the zero of the function.
What is the value of the logarithm below? (Round your answer to two decimal
places.)
log4 12
Answer:
1.68
Step-by-step explanation:
log(4)12=log(48)
log(48)=1.6812... or rounded, 1.68
Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?
a. 1/8
b. 64
c. 16
d. 8
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
16
Step-by-step explanation:
Inverse variation is of the form
xy = k where k is a constant
x=4 and y = 32
4*32 = k
128 = k
xy = 128
Let x = 8
8y = 128
Divide each side by 8
8y/8 = 128/8
y =16
A triangle has side lengths of (4.6x-4.4y)(4.6x−4.4y) centimeters, (7.5x-8.8z)(7.5x−8.8z) centimeters, and (7.7z-9.2y)(7.7z−9.2y) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The expression that represents the perimeter, in centimeters, of the triangle is [tex]77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters
From the question, the side lengths are
(4.6x-4.4y)(4.6x−4.4y) cm, (7.5x-8.8z)(7.5x−8.8z) cm, and (7.7z-9.2y)(7.7z−9.2y) cm.
First, we will clear the brackets one after the other
For (4.6x-4.4y)(4.6x−4.4y) cm
[tex]4.6x(4.6x-4.4y) -4.4y(4.6x-4.4y)[/tex]
[tex]21.16x^{2} -20.24xy -20.24xy+19.36y^{2}[/tex]
[tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex]
∴ (4.6x-4.4y)(4.6x−4.4y) cm = [tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex] cm
For (7.5x-8.8z)(7.5x−8.8z) cm
[tex]7.5x(7.5x-8.8z) -8.8z(7.5x-8.8z)[/tex]
[tex]56.25x^{2} - 66xz -66xz + 77.44z^{2}[/tex]
[tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex]
∴ (7.5x-8.8z)(7.5x−8.8z) cm = [tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex] cm
For (7.7z-9.2y)(7.7z−9.2y) cm
[tex]7.7z(7.7z-9.2y)-9.2y(7.7z-9.2y)[/tex]
[tex]59.29z^{2} - 70.84yz-70.84yz+84.64y^{2}[/tex]
[tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex]
∴ (7.7z-9.2y)(7.7z−9.2y) cm = [tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex] cm
Now, for the expression that represents the perimeter of the triangle,
Perimeter of a triangle can be calculated by determining the sum of all its sides
That is,
Perimeter of the triangle = [tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex] cm + [tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex] cm + [tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex] cm
[tex]=21.16x^{2} -40.48xy+19.36y^{2} + 56.25x^{2} - 132xz + 77.44z^{2} + 59.29z^{2} - 141.64yz+84.64y^{2}[/tex]
Collect like terms
[tex]= 21.16x^{2}+ 56.25x^{2} -40.48xy+19.36y^{2}+84.64y^{2} - 132xz + 77.44z^{2} + 59.29z^{2} - 141.64yz[/tex]
[tex]= 77.41x^{2} -40.48xy+104y^{2} - 132xz + 136.73z^{2} - 141.64yz[/tex]
[tex]= 77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm
Hence, the expression that represents the perimeter, in centimeters, of the triangle is [tex]77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters
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The percent of data between z=0.23 and z = 1.27 is
(Round to two decimal places as needed.)
Answer:
0.40905 - 0.10204 = .30701 = 30.7 %
Step-by-step explanation:
0.23 0.40905
1.27 0.10204
a bag contains 7 red chips and 11 blue chips. two chips are selected randomly without replacement from the bag. what is the probability that the two chips are NOT the same coler
Answer:
77/306 or around 25.2%
Step-by-step explanation:
[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement
just solve and you get 77/306
use quadratic formula to solve the following equation
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Answer:
x = 2 or x = 9
Step-by-step explanation:
To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).
2(3) +4(3(x -3)) = (x +4)(x -3)
6 +12x -36 = x² +x -12
x² -11x +18 = 0
Using the quadratic formula to find the solutions, we have ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]
The solutions are x=2 and x=9.
time in months it would take for a $1500 dollar investment in a TFSA to grow to $1545 if the simple interest at a rate paid was 2% per annum.
It would take 17 months and 14 days for the investment to grow to $1545.
To determine the time in months it would take for a $ 1500 dollar investment in a TFSA to grow to $ 1545 if the simple interest at a rate paid was 2% per annum, the following calculation must be performed:
First, you must obtain 2% of 1545 to determine the interest generated per year.
1545 x 2/100 = X 30.9 = XThen, a cross multiplication must be carried out considering the number of months it took to generate said interest, and compare it with the interest that arises from the subtraction of 1545 - 1500, that is, 45.
30.9 = 1245 = X45 x 12 / 30.9 = X540 / 30.9 = X17.47 = X 1 = 300.47 = X14 = XTherefore, it would take 17 months and 14 days for a $ 1500 dollar investment in a TFSA to grow to $ 1545.
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You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number
Solve the formula for t
V = 4(3.14)ct + 6(3.14)c^2
9514 1404 393
Answer:
t = (V -6(3.14)c^2)/(4(3.14)c)
Step-by-step explanation:
Isolate the term containing t, then divide by the coefficient of t
[tex]V=4(3.14)ct+6(3.14)c^2\\\\V-6(3.14)c^2=t(4(3.14)c)\\\\\boxed{t=\dfrac{V-6(3.14)c^2}{4(3.14)c}}[/tex]
If there are 43,560 square feet in an acre, and there are 7.5 gallons in a cubic foot, calculate gallons of irrigation water per square foot?
The gallons of irrigation water is 326,700 gallons per square foot
Given:
area of the land, A = 43,560 ft²/acre
7.5 gallons = 1 ft³
To find:
number of gallons per square foot
Note:
1 acre = 43,560 ft²1 acre-foot = 43,560 ft³The number of gallons per square foot is calculated as;
[tex]= \frac{43,560 \ acre}{ft^2} \times \ foot\times \frac{7.5 \ gallons}{ft^3} \\\\= \frac{43,560 \ acre-ft}{ft^2} \times \frac{7.5 \ gallons}{ft^3} \\\\= \frac{43,560 \ ft^3}{ft^2} \times \frac{7.5 \ gallons}{ft^3}\\\\= \frac{43,560 \ ft^3}{ft^3} \times \frac{7.5 \ gallons}{ft^2}\\\\=(43,560\times 7.5) \frac{gallons}{ft^2} \\\\= 326,700 \ \frac{gallons}{ft^2}[/tex]
Therefore, the gallons of irrigation water per square foot is 326,700 gallons per square foot.
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Can someone work out this problem for me because I do not get it and it is due tomorrow for homework? 83.971 + 10.9 PLSS HELPPPP MEE!!!!
9514 1404 393
Answer:
94.9
Step-by-step explanation:
It is straightforward addition to find the sum of the two numbers to be 94.871. Perhaps you're interested in rounding to the appropriate precision.
Here, the number with the fewest digits right of the decimal point is 10.9. In order to round the addition result appropriately, that "exact" result must be rounded so it has this same number of digits to the right of the decimal point (1 digit).
94.871 ≈ 94.9
_____
Additional comment
When you're asked to round a sum (or difference) to the appropriate precision, always first compute the exact result using the full precision of all contributors. Then determine the contributor with the least precision (least significant digit is farthest to the left), and round the result to that same precision.
What is the value of X? HELP
with no further informations, just go by looking at it.
it's 90°, all other options are too far off
