Antoine purchased 1.8 kilograms of apples and 315 dekagrams of oranges. This was 1,350 grams more than the weight of bananas he purchased. What was the weight of the bananas Antoine purchased in grams?

1) We need to find out a pattern for the powers that have a base 2:

Note that from 4 to 4 powers the last digit starts to repeat itself.

2) So, let's proceed with this dividing the exponent 2058 by 4:

Now, note that the remainder is 2, therefore we can state that:

If we have the function

Then

This also can be written in the form

We see that both answer are the same, like it should be.

Answer:

Step-by-step explanation:

The base of the rectangle and triangle is same.

Triangle area formula:

Substitute the values:

Answer is 14 ft.

Triangle Area Use Formula.

A = 28 ft2

H = 4 ft

B Value.

28 = 4b/2

28 = (4/2)b

28 = 2b

b = 28/2

b = 14

_____________________

Class: Middle School

Lesson: Triangle

[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]

The number of cups of lemonade sold in each hour is 32.4.

The number of cups of lemonade in each hour is the rate of selling. The rate of selling will be calculated by the formula : number of cups ÷ time.

Keep the values in formula to find the number of cups of lemonade sold each hour

Number of cups of lemonade sold each hour = 162 ÷ 5

Performing division to find the number of cups sold each hour

Number of cups of lemonade sold each hour = 32.4

Thus, each hour, 32.4 cups of lemonade are sold.

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Answer:

a

Step-by-step explanation:

to rotate 180 degrees, simply invert both signs

Resolviendo una ecuación lineal veremos que el número es 76, y la mitad de ese número es 38.

Definamos la variable "x" como el número de la ecuación.

Tenemos la oración matematica:

"La cuarta parte de un número, disminuida en 17, es igual a 4"

Esto se puede escribir como la ecuacion:

(1/4)*x - 17 = 4

Esto es una ecuación lineal que puede ser resuelta para x.

(1/4)*x - 17 = 4

(1/4)*x = 4 + 17 = 19

x = 4*19 = 76

Entonces la mitad del número es:

x/2 = 76/2 = 38

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ANSWER :

f(x) = (3x-2)(x-3)(x-4)(x-2)^3

EXPLANATION :

A polynomial with a degree of 6 has 6 factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.

But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).

From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.

So we can rewrite this as :

Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0

Substitute 0 to the function.

Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.

We need to find the factors of 64,

64 = 8 x 4 x 3 x 2/3

And we can rewrite the equation as :

From here, we can observe that,

a^3 = 8 ⇒ a = 2

b = 4

c = 3

d = 2/3

So the function will be :

Explanation in 2/3

Since we only need 4 distinct factors of 64.

8 x 4 x 3 x 2/3

8 x 4 = 32

The product of the 3rd and 4th factor should be 2, in order to get 64.

Since from the first

The distance between home plate and first base is -1 feet

what is distance ?

Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.

How to determine the number

From the information given, we have that;

The expression for the number of feet between home plate and first base is given as;

√81-√100

Where;

√81 is the number of feet at home plate

√100 is the number of feet at the first base

To determine the distance, we take find the square root of the numbers and substitute, we have;

9 - 10 Find the difference

-1 feet

Thus, the distance between home plate and first base is -1 feet

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The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

The general equation of a straight line is of the form -

y = mx + c

where -

[m] is slope of line

[c] is y - intercept

Given is a equation of a straight line and a graph of a straight line.

We have the following equation -

y = 3x - 6

For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.

Now, the equation of the line plotted on graph -

m = (4 - 0)/(0 + 1.3)

m = 3.07

m = 3 (approx.)

Its y - intercept [c] = 4

Therefore, the equation of the plotted line -

y = 3x + 4

Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.

Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

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[The complete question needs the plotted graph. It is attached at the end  of the answer]

Solution

- The question would like us to determine the difference expression that corresponds to the following logarithm

- In order to solve this question, we should apply the Law of Logarithm which states that:

- Applying this law, we have:

Final Answer

The answer to the question is

The radius is 1.13 inches and the height of the cylinder is 4.52 inches.

From the information, it's important to use the volume of a cylinder to illustrate the information.

Use the volume of a cylinder.

V = πr²h

V = volume.

r = radius

h = height

where:

V = 18

h = 2(2r) = 4r

Plug in the values into the equation and solve for r.

18 = πr²(4r)

18 = 4πr³

Divide both sides of the equation by 4π.

9 / (2π) = r³

r³ = 1.43

r = 1.13 inches.

Finally, multiply the radius by 4 to get the height. This will be:

= 4 × 1.13

= 4.52 inches.

In conclusion, the height is 4.52 inches.

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Using a linear function, it is found that:

a) The table is completed in the first image at the end of the answer.

b) The function is: s(w) = 125 - 10.50w.

c) The graph of the function is given by the second image at the end of the answer.

The slope-intercept representation of a linear function is shown by the rule presented below:

y = mx + b

The coefficients of the function are presented as follows:

In the context of this problem, the slope and the intercept are given as follows:

Hence the function is given as follows:

s(w) = 125 - 10.50w.

The numeric values to complete the table are given as follows:

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Answer:

B

I hope that this helps

Let's express the mixed fraction in decimal.

Then, from least to greatest, the numbers are

Answer is option A

Because the other side (AB) is 15 and the other rectangle (JM) is 10, so the realation between them is 15/10 = 3/2

But, since DC and ML relation is NOT 3/2, then the rectanlges are not similar

The sample space is the set of all different outcomes that can show up from the experiment.

Flipping a coin has two possible outcomes: heads or tails.

Spinning the spinner has three possible outcomes: A, B or C.

Draw a tree diagram to represent the sample space:

If we represent results using ordered pairs, the sample space is:

Where H stands for heads and T stands for tails.

Answer: We need to find the expression p(x) for profit.

Therefore the first option represents the profit of the company.

As we can see from the given data, that, it gives some informtaion about, an on going process, that is almost in rythm.

So, from that we can see that, Mile had increased the running time in a particular pattern, at first he had increased the time by 2, then by 3, then by 4, and so on.

So to find the running time for sunday, we can solve this problem by analysing this pattern.

Therefore the answer is (D): looking for patterns.

Answer:

$435,400

Step-by-step explanation:

Price of one ticket: $311,000/5,000

Price of one ticket: $62.20

Price of 7000 tickets: $62.20 x 7000

Price of 7000 tickets: $435,400

Using elimination method, we get the result  630 + 630 + 35 = n

What is elimination method?

The elimination method involves removing one of the variables from a system of linear equations by adding or subtracting from the system and multiplying or dividing the variable coefficients.

You need an equation that can determine n, 630's total, and 35 more than 630.

More

The value "35 more in June than in May" refers to the value "35 more than 630." That value is represented by the sum (630 +35).

Total two months

In total, there will be two months' worth of delivered papers.

May deliveries + June deliveries = n

630 + (630 +35) = n

Eliminating parentheses, this expression is ...

630 + 630 + 35 = n

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Given a normal distribution with m = 100 and s = 10, the probabilities are;

a) X > 75 = 0.0062

b) X < 70 = 0.00135

c) X < 80 or X > 110 = 0.053954

We are given;

Population mean; m = 100

standard deviation; s = 10

The z-score is gotten from the formula;

z = (X - m)/s

Thus;

1) Probability that X > 75 is;

z = (75 - 100)/10

z = -2.5

From online p-value from z-score calculator, we have;

probability = 0.0062

2) Probability that X < 70 is;

z = (70 - 100)/10

z = -3

From online p-value from z-score calculator, we have;

probability = 0.00135

3) Probability that X < 80 is;

z = (80 - 100)/10

z = -2

From online p-value from z-score calculator, we have;

probability = 0.02275.

Probability that X > 110 is;

z = (110 - 100)/10

z = -1

From online p-value from z-score calculator, we have;

probability = 0.158655

Thus, P(0.02275 < x < 0.158655) = 0.053954

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The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2

The vertex is given as

(h, k) = (-1,-2)

The point is also given as

(x, y) = (3, -10)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

Substitute (h, k) = (-1,-2)  in y = a(x - h)^2 + k

y = a(x + 1)^2 - 2

Substitute (x, y) = (3, -10)

-10 = a(3 + 1)^2 - 2

So, we have

-10 = a(4)^2 - 2

Add 2 to all sides

-8 = a(16)

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x + 1)^2 - 2

y = -1/2(x + 1)^2 - 2

Hence, the equation is y = -1/2(x + 1)^2 - 2

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The type of function we are going to work with here is an exponential function. These functions are given by equations like:

Where x is the variable and a, b and c fixed parameters. In this case c=0, a=1 and b=13/4. This number b, i.e. the one affected by the exponent is called the base so I'm going to refer to it with that word.

All exponential functions have similar graphs, they pass from being very close, almost pararel to the x-axis and then they begin to rapidly increase toward infinite y values. In the following picture you can see the graph of two exponential functions:

The red graph tends to zero for positive x values, this means that its equation has a negative sign in the exponent:

The blue graph on the other hand tends to zero for negative x values which means that there's no negative sign in the exponent. This is the case of our function r(x) so we can discard the upper left option.

Another thing to take into account is the offset of the function, that number that I labeled as "c" in the first equation. This offset translates the graph upwards or downwards depending on its sign.

For example, in this image the graphs decrease for negative x values which means their exponents don't have a negative sign but they all tend to different values which means their offsets are different. Blue's offset is 0 since it tends to 0 while gray's offset is 1 because it tends to 1. The same way you can deduce that the orange graph has an offset of -2. In the case of our problem, function r(x) doesn't have an offset which means that in one direction it has to tend to 0. This means we can discard the lower rigth option.

We have already discarded two options, if we discard one more we have the answer.

Now let's take r(x) and evaluate it in x=0:

You don't need a calculator for this because any number raised to 0 lays 1. This means that at x=0 ,i.e. the y-intercept of the graph, the function has y=1.

Lower left graph intercepts the y-axis in 1 while the upper right does it closer to 0 so we can discard this last option.

In summary, we have only one possible option left, the one in the lower left. This is the correct option.

Answer:

6

Step-by-step explanation:

Using the intersecting chords theorem,

[tex]x^2=36 \\ \\ x=6 (x>0)[/tex]

Explanation

The quotient is the number obtained by dividing one number by another

for example:

the quotient of a and b is

so

Step 1

Let

number 1=23x

number 2=15 t

so, the quotient would be

therefore, the answer is C:

I hope this helps you

We are asked to evaluate the mathematical expression below;

To do this we would use "PEMDAS". PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction.

Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third, and so on, until the calculation is complete.

We will then proceed to solve the expression according to PEMDAS.

Answer: 28

The price the supermarket can charge per egg that is between the prices of per egg for the two different-sized cartons is $0.245 per egg.

According to the question,

We have the following information:

Cost of 12 eggs in a carton = $3.00

Cost of 18 eggs in another carton = $4.32

Now, to find the charge per egg that is between the prices of per egg for these different-sized cartons, we will first find the charge per egg of both of them.

We know that to find the cost of 1 product we divide the given cost by the number of products.

Cost of 12 eggs in a carton = $3.00

Cost of 1 egg = $ (3.00/12)

Cost of 1 egg = $0.25

Cost of 18 eggs in another carton = $4.32

Cost of 1 egg = $(4.32/18)

Cost of 1 egg = $0.24

Now, we have to find the price of egg between 0.24 and 0.25.

Note the difference between these two charges is 0.01.

We will divide it by 2 to find the exact middle charge:

0.01/2 = 0.005

We can add this in $0.24 or subtract it from$ 0.25.

$0.24 + $0.005 = $0.245

Hence, price the supermarket can charge per egg is $0.245.

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Given:

f(x)=6x+3

Required:

To calculate the average rate

Explanation:

Required answer:

30

Answer:

Step-by-step explanation:

z 3 = 0.64 Take the specified root of both sides of the equation to eliminate the exponent on the left side. z = 3 √ 0.64 The result can be shown in multiple forms. Exact Form: z = 3 √ 0.64 Decimal Form: z = 0.86177387