Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.
It pays 2% per annum simple interest.
She puts £1500 into the account.
She does not make any deposits or withdrawals.
How much interest will the charity have received after 3 years?

If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

The quantity of fuel releases from the container = 5 gallon per second

Consider the fuel remaining in the container = y

Consider the number of seconds that have passed since the fuel started dispensing = x

Then x and y satisfy a linear relationship

The quantity of fuel in the tank at the beginning = 103 gallon

Time taken = 2 seconds

Then the equation will be

y = 103 - 5x

Time taken is x = 2

y = 103 - 5× 2

y = 103 - 10

y = 93 gallon

Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

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Standard deviation - The value of x is 1.96.

What is standard normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.

Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.

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Answer:

x = 4

Step-by-step Explanation:

[tex]\triangle LMO \sim \triangle NMO \ \rm{(AA \ Similarity)} \\ \\ \rm \implies 12x - 5 = 43 \\ \\ \rm \implies 12x = 43 + 5 \\ \\ \rm \implies 12x = 48 \\ \\ \rm \implies x = \frac{48}{12} \\ \\ \rm \implies x = 4[/tex]

Answer: USE the forumla

Step-by-step explanation:

Consider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H + h'. Its volume (V) can be calculated by using: V = πh/3 [ (R3 - r3) / r ] (OR) V = πH/3 (R2 + Rr + r2)

Answer:

Step-by-step explanation:

formula of a linear line - y=mx+c

so y=

m= gradient x =x coodinate c=y-intercept

c= -3

m = 0

which is y=-3

pls give me brainliest

pls:(

Answer:

Step-by-step explanation:

Points given:

This is a horizontal line with constant y - value of - 3.

So it equation is y = - 3.

Answer: 5^13

Step-by-step explanation:

1. The Exponent out of the parenthesis would be multiplied by the exponent in the parenthesis

(5^2)^4*5^5

5^8*5^5

2. Since the exponents have the same base, when they are multiplied you will keep the same base, and the exponents will add up

5^8*5^5=5^13

Answer:

49.7

Step-by-step explanation:

FORMULA : A = (b1 + b2)h/2

base 1 = 4.2

base 2 = 10

4.2 + 10 = 14.2

height = 7

14.2 x 7 = 99.4

99.4/2 = 49.7

Answer:

i can't see the pic

Step-by-step explanation:

Answer:

Desmos is a free graphing and teaching tool for math available on the web as well as on iOS and Android. In addition to plotting equations, classroom activities are available to help students learn about a variety of math concepts.

A definition of Desmos has been given below

What is Desmos?
Desmos can be applied in a variety of contexts. Students can avoid spending $100 on a graphing calculator by using it for free. It can be used by teachers to create stunning images for tests and presentations. But Desmos really shines in the classroom exercises. Teachers can use Desmos to assist students in making the connection between mathematical concepts and actual, concrete shapes and images. It's simple to begin an activity with your students: Just instruct the children to enter the website's activity code. Try the student preview of an activity before assigning it. In the teacher moves section at the bottom of each activity, you can find specific ways to guide your children while they work. The teacher dashboard allows for the tracking of progress.

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Answer:

Step-by-step explanation:

The equation would be y=25x+ 50 which is linear. Radical expressions have a number under the radical sign which this equation doesn't. Rational expressions have fractions containing polynomials in the numerator and denominator and exponential equations have 'x' as the exponent in a function.

The square of a number is increased by 5 times the number [tex]6x^{2} +5x-4=0[/tex]

What is quadratic equation?
A quadratic equation is a second order equation written as a[tex]x^{2}[/tex] + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Product of 6 and the square of a number is increased by 5 times the number, he result is 4.

Consider x as the number,

The question can be written as:

[tex]6(x^{2} )+5(x)=4[/tex]

[tex]6(x^{2} )+5(x)-4=0[/tex]

Hence, the answer for the given question is [tex]6x^{2} +5x-4=0[/tex].

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Answer: 9x + 16

Simplify the expression

The value of f is 19 and the value of g is 10.5 after solving the simultaneous equation, f-2g+3=2f-39+2=1 ​.

According to the question,

We have the following equation:

f-2g+3=2f-39+2=1 ​

Now, we will equate both these equations to 1:

f-2g+3 = 1

Subtracting 3 from both sides:

f-2g = 1-3

f-2g = -2 ..(1)

2f-39+2 = 1

2f -37 = 1

Adding 37 to both sides:

2f = 1+37

2f = 38

Dividing by 2 on both sides:

f = 38/2

f = 19

Putting this value of f in equation 1:

f-2g = -2

19-2g = -2

-2g = -2-19

-2g = -21

g = 21/2

g = 10.5

Hence, the value of f is 19 and the value of g is 10.5 after solving the simultaneous equation, f-2g+3=2f-39+2=1​.

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Order for the given exponential numbers will be:

5.48 x [tex]10^{9}[/tex]

3.24 x 10^{9}

1.2 x 10^{7}

8.34 x 10^{-2}

4.68 x 10^{-6}

What are the exponential functions?

A mathematical function called an exponential function is employed frequently in everyday life. It is primarily used to compute investments, model populations, find exponential decay or exponential growth, and so forth. You will discover the formulas, guidelines, characteristics, graphs, derivatives, exponential series, and examples of exponential functions in this article. The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be greater than 0. The transcendental number e, or roughly 2.71828, is the most frequently used exponential function base.

With the highest power in exponential function,

function will be more greater if the numbers multiplied by exponential function are in same order of decimal number.

In given Que,

numbers multiplied are all of 2 decimal number.

So, we can directly compare the values x in e^{x}

i.e. 9 > 7 > -2 > -6

for same value of x: compare value of number multiplied.

Hence, we found out the correct answer.
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Answer:

2 hours

Step-by-step explanation:

time it took on the first day = x

speed = d/t

time it took on second day = x + 1

75 = d/x

50 = d/x + 1

75x = d

50 = 75x/(x + 1)

50(x + 1) = 75x

50x + 50 = 75x

50 = 25x

x = 50/25

x = 2

The value of the car to be, to the nearest cent, after 11 years is $7641.

Given data;

A brand-new car is bought for $20300. The car's value decreases by 9.5% annually.

To know the value of the car to be, to the nearest cent, after 11 years;

[tex]S(t) = 20300*(0.915)^t[/tex]

[tex]S(11) = 20300*(0.915)^1^1[/tex]

[tex]S(11) = 20300*0.376[/tex]

[tex]S(11) = 7640.61[/tex]

Hence, the value of the car after 11 years is $7641.

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Answer:

======================

Number of eggs purchased:

Cost of eggs:

Number of eggs sold:

Money made:

Profit or loss?

Percent loss:

3 pounds 9 ounces of rutabagas would cost $2.28

The question is a percentage problem

The trim loss percent for rutabagas is 19%

= 19 percent

= 19 / 100

= 0.19

trim loss factor = 1 - 0.19 = 0.81

selling price of rutabagas  = $0.79 * 0.81 = 0.6399

converting all the unit in pounds

3 pounds 9 ounces: if 1 pound is 16 ounces then 9 ounces will be

3 pounds 9 ounces: 9/16 ounces = 0.5625

therefore we have 3.5625 pounds of rutabagas

3.5625 pounds of rutabagas will cost

= 3.5625 * 0.6399

= $2.28

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Answer: t=1

Step-by-step explanation:

1. Distribute the -3

-18t=-3t-15

2. Move the -3t to the other side

-15t=-15

3. Divide by -15 to solve for t

t=1

The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable. the correct option is (A).

Given that,

The projected amount of time spent with family for someone who spent 36 minutes playing video games is 81.54 minutes, according to the line of best fit.

To find :

Is it appropriate to make the aforementioned forecast using this line of best fit

According to the  "line of best fit" it is that along which the sum of squares of deviation is minimum. This means the line of best fit minimizes the deviation or we can say error due to which it gives better estimate than other method.so, the predicted number of minutes spent with family is both reliable and reasonable.

Therefore, the estimate, a predicted time of 81.54 minutes, is both reliable and reasonable

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The question was incomplete. Check below the complete question.

is it reasonable to use this line of best fit to make the above prediction? select the correct answer below:

a. 81.54minutes

b. 50.25minutes

c. 23minutes

d. 36minutes

Answer:

(-2.-3)

Step-by-step explanation:    

(-2.-3)

The volume of the cube A is 8 cm³ and the volume of the cube B is 64 cm³

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, and 4 on the sides faces.

We have been given that Two larger cubes are made out of unit cubes. Cuba A is 2 by 2 by 2. Cube B is 4 by 4 by 4. then the side length of Cube B is twice that of Cube A.

Then the surface area of Cube B = 6a²

Cube B = 6 x 4² = 96

Surface area of Cube A = 6 x 2² = 24

The volume of the cube A = a³ = 2³ = 8 cm³

The volume of the cube B = a³ = 4³ = 64 cm³

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The probability of choosing the biased coin if you win a prize is 0.3056

To answer this query, we employ the conditional probability formula. It is, where

P(B|A) is the likelihood that event B will occur in the absence of event A.

is the likelihood that both A and B will occur.

P(A) denotes the likelihood that A will occur.

The following probability applies:

50% chance of winning a prize with the fair coin.

There is a 100-78 = 22% chance of winning a reward with the biased coin.

50% chance of selecting each coin.

What is the likelihood that you would choose the biased coin if you were to win a prize?

Event A: Receiving the award

Choosing the skewed coin is event B.

the likelihood of selecting the skewed coin and obtaining the reward.

p(A∩B) = 0.5 * 0.22 = 0.11

probability of winning the prize:

p(A) = 0.5*0.22 + 0.5 *0.5 = 0.36

conditional probability:

p(B/A) = 0.11/0.36= 0.3056

the probability of choosing the biased coin if you win a prize is 0.3056

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The volume of the model of the air balloon is 1000m³.

So, the volume of the model:

So, calculate the volume of the model as follows:

Therefore, the volume of the model of the air balloon is 1000m³.

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The rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.

What is rate in mathematics?

A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).

The rate can be configured as.

Rate = [tex]\frac{1/3}{5/6}[/tex]

Rate = [tex]\frac{2}{5}[/tex]

Hence, the rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.

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For the given function 4xy-4x+4y³ = -36 , value of dy/dt for the condition dx/dt = -16 , x= 4, y= -1 is equal to dy/dt = -32/7.

As given in the question,

Given function is equal to :

4xy-4x+4y³ = -36

Let us consider x and y are function of t.

Now , evaluate the derivative of function with respect to t we get,

4x(dy/dt) + 4y(dx/dt) -4(dx/dt) + 12y²(dy/dt) = 0

⇒( 4x + 12y² ) (dy/dt) + ( 4y -4 ) (dx/dt) = 0

Substitute the value of dx/dt = -16, x = 4 , y = -1 we get,

[ 4(4) + 12(-1)² ](dy/dt) + [ 4(-1) - 4 ] (-16) =0

⇒(16 +12) (dy/dt) + (-8)(-16) = 0

⇒ dy/dt = - ( 8× 16)/ 28

⇒ dy/dt = -32/7

Therefore, for the given function 4xy-4x+4y³ = -36 , value of dy/dt for the condition dx/dt = -16 , x= 4, y= -1 is equal to dy/dt = -32/7.

The complete question is:

Assume x and y are functions of t. Evaluate dy/dt , for 4xy-4x+4y³ = -36, with the conditions dx/dt = -16 , x = 4 , y = -1.

(Type an exact answer in simplified form.)

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The DE is the ray with end point E and the ray GA and ray DF will not intersect

From the given diagram

Consider the ray DE,

The starting point of the ray DE = D

Then the end point of the ray DE = E

The D is the starting point and E is the end point of the ray DE

Therefore DE is the ray with end point E

Consider the ray GA and DF, those rays are not in contact and going opposite direction, therefore it will not intersect

The GA and DF will not intersect

Hence, the DE is the ray with end point E and the ray GA and ray DF will not intersect

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The students' Landry and Erika was the name used and the image is attached

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

y = output variable

m = slope

x = input variable

c = y intercept

The two graphs shown the first from the left represents a positive slope while the second is a negative slope

Cole and Erika are both positive slopes while Landry has a negative slope. This makes Landry to be sure of the second graph

Considering c (y intercept)

In Cole's equation c = -1 and in Erika's equation c = +4

Erika's equation coincides with the graph with positive slope and Landry matches with second graph.

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