3. What is the slope and the y-intercept of
the line represented by equation:
2x + y = 1?
Explanation:

Answer:

3.2 x 10^12

Step-by-step explanation:

80000000/40000

Answer:

Answer:

3.2 x 10^12

Step-by-step explanation:

80000000/40000

Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4​ years.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 400 × 4.4/100 × 4

S.I = 400 × 0.044 × 4

S.I = $70.4.

Next, we would calculate the future value as follows;

S.I = A - P

Future value, A = S.I + P

Future value, A = $70.4 + $400

Future value, A = $470.4.

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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Answer:

La distancia desde el supermercado hasta la puerta del rascacielos es de 585,29 metros

Step-by-step explanation:

Dado que la altura del ático = 527 metros

El ángulo de elevación de la vista = 42 °

Tomamos la posición de la persona que ve el rascacielos en el supermercado, el ático del rascacielos y la base del rascacielos directamente frente a la persona, formando los vértices de un triángulo rectángulo ABC, respectivamente.

Por lo tanto;

AB = Línea de visión desde la persona hasta el ático.

BC = La altura del rascacielos = 527 metros

AC = La distancia desde el supermercado hasta la puerta del rascacielos.

De lo cual se nos da, ∠BAC = 42 °

Por lo tanto, ∠ACB = 90 ° y el ángulo de depresión desde el ático del rascacielos hasta la persona en el supermercado ∠ABC = 180 ° - 90 ° - 42 ° = 48 °

De la regla senoidal, tenemos;

\(\dfrac{BC}{sin(\angle BAC)} =\dfrac{527}{sin(42^{\circ})} = \dfrac{AC}{sin(\angle BAC))} = \dfrac{AC}{sin(48^{\circ})}\)

Lo que da;

\(AC = \dfrac{527 \times sin(48^{\circ}) }{sin(42^{\circ})}= 585.29 \ metros\)

Por lo tanto;

La distancia desde el supermercado hasta la puerta del rascacielos = 585,29 metros.

Answer:

multiply by 12 and would serve 18 people

Step-by-step explanation:

I did a test for it

Answer:

We multiplied the original recipe by 3/2 or 1 1/2, the new recipe will serve 18 people.

Step-by-step explanation:

to get 1 to 3 you multiply it by 3 and to get 4 to 8 you multiply it by 2 so you end up with 3/2 or 1 1/2

Answer:

11, 3, -1, -7

Step-by-step explanation:

y = -2x - 5

x = -7, -4, -2, 1

y = -2(-7) - 5

y = 14 - 5

y = 11

y = -2(-4) - 5

y = 8 - 5

y = 3

y = -2(-2) - 5

y = 4 - 5

y = -1

y = -2(1) - 5

y = -2 - 5

y = -7

By using combination, it can be obtained that

Number of simple random samples of size 3 that can be selected from a population of size 7 = 35

What is combination?

Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.

Here, concept of combination is used

Number of simple random samples of size 3 that can be selected from a population of size 7 = \({7 \choose 3}\) = 35

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2/4 pound

2 1/4 equals 9/4

1 3/4 equals 7/4

9 - 7 = 2/4

Answer:

Step-by-step explanation:

10

A sample size of 76 would be required to estimate the population mean with a margin of error of 4 and a 98% level of confidence.

To determine the sample size required to estimate the population mean with a specific margin of error and level of confidence, we can use the formula:

n = (Z * σ / E)²

where

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = standard deviation of the population

E = desired margin of error

here, we have that

the standard deviation (σ) is given as 15,

the margin of error (E) is 4 and

the level of confidence is 98% and For a 98% confidence level, the Z-score is approximately 2.33.

Plugging the values into the formula:

n = (2.33 * 15 / 4)²

n = (8.7375)²

n ≈ 76.34

n = 76

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Step-by-step explanation:

Simplify.

Include the exponent:

\( (x-3)(x-3)+ x(x + 9)={x}^{2} - 6x + 9 + x(x+9)\)

Use the Distributive Property:

\( {x}^{2} - 6x + 9 + {x}^{2} + 9x\)

Add and format the trinomial:

\(2{x}^{2} + 3x + 9\)

Answer:

\(2x^2 + 3x +9\)

Step-by-step explanation:

\((x-3)^2+x(x+9)\)

\((x-3)^2\) = \((x-3)(x-3)\)

\((x-3)(x-3)\)

\(x^2-3x-3x+9\)

\(x^2-6x+9\)

\(x(x+9)\)

\(x^2+9x\)

\(x^2-6x+9+x^2+9x\)

\((x^2+x^2)+(-6x+9x)+9\)

\(2x^2 + 3x +9\)

Hope this helps!

Answer:

the answer is -5

Step-by-step explanation:

1. identify the ordered pairs

2. write down the slope formula

3. replace the letters with their values

4. subtract

5. divide

Two different numbers that could be used to fill the blank in the sequence 1, 4, 7, 10 are 13 and 13.

To fill the blank in the sequence 1, 4, 7, 10 with two different numbers, we need to find values that maintain the pattern or rule of the sequence. Let's analyze the given sequence to identify the pattern:

Looking at the sequence, we can observe that each number is increasing by 3. So, to find two different numbers to fill the blank, we can continue this pattern by adding 3 to the last number in the sequence.

The last number in the sequence is 10. Adding 3 to it gives us:

10 + 3 = 13

Therefore, one possible number to fill the blank is 13. Now, let's find another number using a different approach.

Alternatively, we can see that each number in the sequence is 3 more than a multiple of 3. We can express this pattern as:

1 = 3(0) + 1

4 = 3(1) + 1

7 = 3(2) + 1

10 = 3(3) + 1

Following this pattern, the next number would be obtained by multiplying 3 by the next natural number (4) and adding 1:

3(4) + 1 = 13

So, another number to fill the blank is 13.

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Answer:

32°F

Step-by-step explanation:

Answer:

The probability that event B will occur is 0.45

Step-by-step explanation:

Given;

probability that event A occurs, P(A) = 0.4

the probability that events A and B both occur, P(A ∩ B) = 0.25

the probability that either event A or event B occurs, P(A ∪ B) = 0.6

To determine the probability that event B will occur, we use probability addition rule;

P(A) + P(B) = P(A ∩ B) + P(A ∪ B)

0.4 + P(B) = 0.25 + 0.6

0.4 + P(B) = 0.85

P(B) = 0.85 - 0.4

P(B) = 0.45

Therefore, the probability that event B will occur is 0.45

When Triangle GHJ is rotated 270° counterclockwise about the origin the points would be:

When a figure is rotated 270° counterclockwise about the origin, the vertices go from (x, y) to (y, -x).

This means that the vertices of the GHJ prime will be:

G = (2, -9)

G' = (-9, -2)

H = (3, 8)

H' = (8, -3)

J = (1, 6)

J' = (6, -1)

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The solution to the given equation is -25.

The given equation is:2x/(x+5) = (2x-5)/x

The above equation has a denominator x(x + 5)

So, the equation can be rewritten as follows:

2x(x) = (2x - 5)(x + 5)2x² = 2x² + 5x - 25x² - 5x = -25x²x(1 + 5x) = -25x²

Dividing by x as x ≠ 0 and x + 5 ≠ 0x = -25

Therefore, the solution to the given equation is: -25.

The solution to the given equation is -25.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Step-by-step explanation:

type the prove that you took in school because some of them you may not have been taught in your school

STATEMENT REASON

∠D and ∠B are right angles 1. Given

∠D = ∠B 2. If lines are parallel, then alternate interior angles are equal

∠D + ∠C + ∠B = 180° 3. Sum of angles in a triangle is 180°

∠D + ∠C + ∠B = 180° 4. Hypotenuse Angle Theorem

∠C = ∠C 5. Reflexive Property

△ADC ≅ △CBA 6. SAS Congruence Theorem

Answer:

Step-by-step explanation:

The parenthesis can cancel because the lack of anything you can do in them, so that will leave you with 7m + 3 + 7m + 6

Next step is to add like numbers, you should start by adding 7m + 7m, which would be 14m.

Next would be to add 3 + 6, which is nine.

To end this equation, simply put 14m + 9

There is no one-number answer because we do not know what m is. So the equation 14m + 9 is the final answer.

The probability of a rain-free weekend is 0.6962

The probability =  Number of favorable outcomes / Total number of outcomes

The probability of rain on Saturday = 62/100

= 31/50

The probability of rain on Sunday = 49 /100

The probability of rain on Saturday and Sunday = The probability of rain on Saturday × The probability of rain on Sunday

= (31/50) × (49/100)

= 0.3038

The probability of rain free weekend = 1 - The probability of rain on Saturday and Sunday

Substitute the values in the equation

The probability of rain free weekend = 1 - 0.3038

= 0.6962

Hence, the probability of a rain-free weekend is 0.6962

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Distance in BC can be calculated using the distance calculator available on the BC Government website. Simply enter the starting and ending locations, and the distance in kilometres will be calculated.

The BC government provides an online distance calculator which can be used to easily calculate the distance between two locations in the province. To use the calculator, simply enter the starting and ending locations, and the distance in kilometres between them will be calculated. This is a convenient and accurate way to calculate distances in British Columbia. The tool is easy to use and can save time and effort when trying to plan a route or determine how far apart two places are. Furthermore, the calculator is available for free, making it a great option for anyone who needs to quickly and accurately calculate the distance between two locations in BC.

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Step-by-step explanation:

since$420 is the original price then it's 100%

then to find the %decrease, $420-$280=$140

if, 100%=420

then x%=140

14000/420=x

x=33.3%

Answer:

B-

point s

Step-by-step explanation:

I just did the quiz, this is the correct answer

Point S is the endpoint of the rays.

Option B is the correct answer.

In geometry, a ray is a straight line that starts from a specific point (called the endpoint) and extends infinitely in one direction.

A ray can be thought of as a part of a line that has one endpoint and continues indefinitely in one direction.

We have,

A ray is a line that starts from a specific point and extends infinitely in one direction.

The starting point of the ray is called the endpoint, and the other end of the ray extends indefinitely.

Therefore, a ray does not have an endpoint in the direction it extends, but only at its starting point.

From the figure,

The ray SR, SU, and ST have one common starting point.

i.e Point S.

Thus,

Point S is the endpoint of the rays.

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Answer:

Your answer is 3/4  or  0.75

Step-by-step explanation:

4/5  /   16/15

4/5  *   15/16

Cross simplify.

The horizontal distance from Macy and Jeremy's sail boat to the base of the lighthouse is approximately 568 meters.

Let x be the horizontal distance from Macy and Jeremy's sail boat to the base of the lighthouse.

Then we can draw a right triangle with the lighthouse as the hypotenuse, the horizontal distance x as the adjacent side, and the vertical distance from the sail boat to the top of the lighthouse (511 meters) as the opposite side.
The angle of elevation from Macy to the top of the lighthouse is given as 42 degrees.

This means that the angle between the opposite side and the hypotenuse is also 42 degrees, since they are opposite angles in a parallelogram.
Now we can use the tangent function:
tan(42) = opposite / adjacent
We know that the opposite side is 511 meters and we want to find the adjacent side (x).

So we can rearrange the equation:
x = opposite / tan(42)
Plugging in the values, we get:
x = 511 / tan(42)
Using a calculator, we find that tan(42) is approximately 0.9. So:
x = 511 / 0.9
x ≈ 568 meters
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Answer:

480

please mark brainliest

The transformation of the rectangles ABCD and ABCD is for the 90-degree clockwise rotation about the origin and a translation of 7 units down.

Here the transformed rectangle is  the result of two steps, including the steps of  rotation and  translation from the x-y axis, near the origin.

Here change is in such a way that,  the first rotation is a 90 clockwise rotation about the origin, where the vertex c is near to the origin,  again there is a translation of 7 units down, considering the rotated rectangle As A'B'C'D'. here the proper explanation of the process is shown in the image attached.

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