The base of this right prism is a rectangle. What is the surface area of the prism? Height = 10 ft

Okay, here we have this:

Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:

According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:

Now let's solve for x in the second equation:

x+x+5=30

2x+5=30

2x=30-5

2x=25

x=25/2

x=12.5

Now from the value of x that we got, then we will plug it into the first equation to get the value of y:

Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.

Answer:

a) £960

b) £576

Step-by-step explanation:

Hi!

Ok so since the store has a 20% sale we multiply 0.2 to the original amount it would have costed without the sale:

a) [tex]1200*0.2 = 240[/tex]

Then we subtract the number we got from the price:

1200 - 240 = 960

Now we do the same thing but this time add since we are trying to find the price of the table before the sale:

b) [tex]480*0.2 = 96[/tex]

480 + 96 = 576

Please ask me if you have any more questions!

and Have a great day! :)

Answer:

(0,1) and (-10.-4)

Step-by-step explanation:

To find the solutions, find the points where both the curve and line intersect and read off the coordinates

The measure of angle 2 is 81° because angles 1 and 2 are corresponding angles.

Corresponding angles:

Corresponding angle means the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

Given,

Two electricity poles are built standing parallel to each other, as shown below. The measure of angle 1 is 81°.

Here we need to find the measure of the angle 2.

We know that,

If the lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet.

And as per the definition of corresponding angles, we know that, if any two lines are said to be parallel if the Corresponding angles so formed are equal.

Then the measure of the angle 2 is 81° because angle 1 and 2 are parallel.

Therefore, those angles are the corresponding angles also.

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Applying the law of indeces for the fraction with radicals, the value of A=3, b=14 and c=-5

In mathematics, the term radical expressions such that contain a square root. In this question, we have fractions at both sides of the equation with radicals.

To solve this question, let's see some laws below that will help us:

[tex] \sqrt[x]{a} = {a}^{ \frac{1}{x} } [/tex]

[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]

[tex] \frac{1}{ {a}^{x} } = {a}^{ - x} [/tex]

From the given equation; the left hand side will be simplified as follows;

[3^(1/7)]÷[3^(1/2)]=[3^[(2-7)/14]=3^(-5/14)

And the right hand side will be simplified as follows;

1÷[A^(c/b)]=A^-(c/b)

Hence, by comparing both sides of the equation after simplifying the fractional radicals, the value of A is 3, b is 14 and c is -5.

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The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).

Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.

The question gives the follow numbers

1. -8 8

2. -1 -11

3. -17 17

4. 31 -31

5. 11 1

The opposite for:

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Answer:

From the bit that you have given , we can say = 5a + ab = to the rest of the equation

ANSWER

EXPLANATION

For the first cylinder;

Recall, the formula for calculating the surface area of a cylinder is;

Now, substitute the values for the first cylinder;

The volume of the first cylinder is calculated using the formula;

Substitute the values of r and h for the first cylinder;

To get the surface area of the second cylinder, we need to calculate the height (h).

To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).

Hence;

Substitute the height to calculate the surface area is calculated thus;

The estimate of the impact that a successful preventive program might have can be derived from

attributable risk.

In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.

Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.

The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.

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The correct statement will be:

A. The rate of change is the number of inches grown per month, and the initial value is the starting height.

We can form the following equation from the given data:

H(m) = 13 + 41m,

Where H ( Height ) is a function of the number of months ( m ).

We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.

The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.

So, option A will be the ultimate explanation for the data given.

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Answer:

Step-by-step explanation:

This is a linear function of time, as mentioned.

A linear function is always in the form of:

[tex]y=mx+b[/tex]

The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.

The initial value is when [tex]x=0[/tex].

[tex]x=0[/tex] means at the very beginning.

At the very beginning, the height would be the starting height, so the initial value would be the starting height.

The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].

Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.

You could also write it as the number of inches grown per month.

The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).

No, Hannah is incorrect.

We are given the expression 42*19.

Hannah got the solution by multiplying 40*10 and 2*9 and then adding the values.

This can be done by using distributive property, which is given by:-

(a + b)(c + d) = ac + ad + bc + bd

We can write,

42*19 = (40 + 2)(10 + 9) = 40*10 + 40*9 + 2*10 + 2*9

Hence, the answer is not just 40*10 + 2*9 but 40*10 + 40*9 + 2*10 + 2*9.

Hannah did not add the remaining 40*9 + 2*10 to calculate the answer.

That is why Hannah was incorrect.

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Answer:

A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.

Answer:

The answers are (-10, -4) and (0, 1)

Step-by-step explanation:

The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.

Hope this helps!

The probability P(5 ≤ x ≤ 9) is 0.6847

Assume that x has a normal distribution

We have been the mean and standard deviation μ = 6; σ = 2.

To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.

z = (5 - 6)/2

  = -0.5

and z = (9 - 6)/2

         = 1.5

Then the probability is calculated as:

P(x ≤ 5) = 0.3085

P(x ≤ 9) = 0.9932

P(5 ≤ x ≤ 9) = 0.9932 - 0.3085

P(5 ≤ x ≤ 9) = 0.6847

Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847

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Probability that the man wins money from at least one of the sources, a lottery and a card game, is equal to  17/50.

Probability that he wins from first source = 1/100

Probability that he doesn’t wins from first source = 99/100

Probability that he wins from second source = 1/3

Probability that he doesn’t wins from second source  = 2/3

Probability that the man wins money from at least one of the sources = 1-(probability that the man wins no money from any of the sources)

[tex]=1-[(\frac{99}{100} )(\frac{2}{3} )] =1-(\frac{33}{50} )=\frac{17}{50}[/tex]

So, the required probability of winning the money by the man from at least one of the sources is 17/50.

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The equation is c = 31 + 0.13x and total cost on driving 180 miles is $54.4.

Firstly we will form the equation using one time charge and the product of number of miles and charge per mile. Then we will keep the value in equation to find the total cost.

Forming the equation -

c = 31 + 0.13x

Keep the value of x in formula for calculation of total cost.

c = 31 + 0.13×180

Performing multiplication on Right Hand Side of the equation

c = 31 + 23.4

Performing addition on Right Hand Side of the equation

c = $54.4

Thus, the equation for calculation of total cost is c = 31 + 0.13x and total cost is $54.4.

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The dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.

For the given question,

The perimeter of the triangle is 50 units.

The three sides of the triangle is given as;

The formula for finding the perimeter is;

Perimeter =  sum of all sides.

Let 'P' be the perimeter of the triangle. Then,

P = x-1 + 2x-3 + 3x - 6

Simplifying.

P = x + 2x + 3x - 1 - 3 - 6

50 = 6x - 10

6x = 60

x = 10

For the measure of the side length, put x = 10 in the sides.

Thus, the dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.

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The arc length is given by:

In this case the radius is 400 m and the angle is 36°, plugging these values we have:

Therefore, the part of the train track that runs through water world is approximately 250 meters.

Angle XBC is a corresponding angle to angle AXY.

The value of angle BXC is 30 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines and are cut by the transversal line AB and XC.

XBC forms an isosceles triangle.

∠AXY = 75 degrees.

∠XBC is a corresponding angle to ∠AXY.

Corresponding angles are congruent.

Therefore,

∠AXY = ∠XBC

Let's find the angle BXC.

The sum of angle in a triangle is 180 degrees.

The triangle BXC is an isosceles triangle. An isosceles triangle has base angles equal to each other.

Hence,

75 + 75 + ∠BXC = 180°

∠BXC = 180 - 150

∠BXC = 30°

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The corresponding element in the range when 6 is an element in the domain is f(6) = -4.

Given function f(x) = 8–2x.

6 is an element in the domain of this function.

To find the corresponding element in the range of the function,

Substitute x = 6 in the given function f(x).

So,

f(6) = 8 - 2(6)

f(6) = 8 -12

f(6) = -4

Hence, the corresponding element in the range when 6 is an element in the domain is -4.

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We can use the given points to find the slope

It means that every year, there are 1.4 million MORE households with personal computers

We have a loan of 65 days.

The principal is $1250 and the interest is $7.75.

We have to find the annual simple interest rate.

We can express the interest of a loan of this type as:

where r = annual interest rate, t = period of the loan in days, I = interest and P = principal.

Then, we can rearrange the equation and replace with the values:

Answer: the annual simple interest rate is 3.4%.

The equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a line that is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2),

The midpoint of line joining (-4,4) and (2,-2) will be -

x[m] = (- 4 + 2)/2 = -1

y[m] = (4 - 2)/2 = 1

Coordinates of the midpoint will be M(-1, 1)

Slope of the line joining (-4,4) and (2,-2) will be -

m = (- 2 - 4)/(2 + 4)

m = -6/6

m = - 1

Then, the slope of the line perpendicular to this line will be -

m[p] = -1/-1

m[p] = 1

Assume that the equation of the perpendicular line as -

y[p] = x + c

Since it passes though (-1, 1) so -

1 = -1 + c

c = 2

Therefore, the equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.

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Answer:

$2,000

Step-by-step explanation:

Amount invested in Fund A = 6000

Profit rate of return = 5%

Amount of profit = 6000 x 5% = 6000 x 0.05 = $300

Let amount invested in Fund B be $x

Profit amount = 0.01x

Total amount invested is 6000 + x

Total profit in $ = 300 + 0.01x

Total profit in percentage = Total Profit/Total investment x 100

= 4 %

So Total Profit/Total investment = 4/ 100 = 0.04

= (300 + 0.01x) / (6000 + x)  = 0.04

Multiply both sides by (6000 + x)

=> 300 + 0.01x = 0.04(6000 + x)

=> 300 + 0.01x = 240 + 0.04x

==> 300 - 240 = 0.04x - 0.01x

=> 60 = 0.03x

x = 60/0.03

x = $2,000

Amount invested in Fund B = $2,000

Step-by-step explanation:

Fund A

$6000 returned a 5% profit. that means it had at the end 105% of the original investment

the formally correct way

100% = 6000

1% = 100%/100 = 6000/100 = $60

5% = 1%×5 = 60×5 = $300

in short, if we knew what we are doing, we could have simply calculated 6000 × 0.05 = $300.

and by the way, 6000 × 1.05 = $6300. which is the current balance of the account (investment plus the returned profit). but we don't need this here. this is just FYI.

Fund B

x returned 1% profit.

Fund A + Fund B

6000 + x returned 4% profit.

so, we have

6000×0.05 + x×0.01 = (6000 + x)×0.04

300 + 0.01x = 240 + 0.04x

60 + 0.01x = 0.04x

60 = 0.03x

x = 60/0.03 = $2000

so, he invested $2000 into fund B.

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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Answer:

6,300 grams

Step-by-step explanation:

kg to g is multiply by 1,000

Answer:

Step-by-step explanation:

630%

Answer:

39% of 80 = 39.2

74% of 240 = 177.6

91% of 82 = 74.62

66% of 160 = 105.6

9% of 71 = 63.9

126% of 80 = 100.8

234% of 145 = 339.3

97.9% of 39 = 38.181

52% of 57.9 = 30.108

33% of 15.3 = 5.049

Step-by-step explanation:

In order to find the percentage of each equation, we will use the first one as an example. We take the 39%, and convert it to 0.39 and get rid of the %. Then, "of" means multiplication.

So, we have:

0.39 x 80 = 39.2

Answer:

$91.08

Step-by-step explanation:

Interest = $90 × .012 = $1.08

Total amount = $90 + $1.08 = $91.08

Answer:

To rewrite the given fraction with the least common denominator between them

The given fractions are,

we get, LCM of 3,10,30 is 30

The equivalent fractions for the above factions as common denominator 30 is as follows,

For 1/3,

Multiply and divide by 10, we get,

Using this we get,

For 5/10,

Multiply and divide by 3, we get,

Using this we get,

For 7/30,

Since the denominator 30, we get same fraction,

Answer is:

Answer: 26m

Step-by-step explanation:

The area is 36m^2, the possible measurement that could've worked is 4m for width and 9m for length (4x9=36). Now just do 4+4+9+9 = 26m.

Hope this helped