Electron rescued 5 dogs and 3 cats this week.
If this happens every week for 6 weeks, how many animals
will Electron rescue?

Answer:

1  5/8

Step-by-step explanation:

3/4 -  -7/8

3/4 + 7/8

6/8 + 7/8

13/8 = 1  5/8

Answer:

1 5/8 or 13/8

Step-by-step explanation:

Remove parentheses.

\(\frac{3}{4}+\frac{7}{8}\)

Find the Least Common Denominator (LCD) of \(\frac{3}{4},\frac{7}{8}\) . In other words, find the Least Common Multiple (LCM) of 4,8.

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 4 : 4, 8, ...

Multiples of 8 : 8, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 8

Method 2: By Prime Factors

List the prime factors of each number

Prime Factors of 4 : 2, 2

Prime Factors of 8 : 2, 2, 2

Find the union of these primes.

2, 2, 2

Multiply these numbers: 2 * 2 * 2 = 8 ---> This is the LCM.

LCM = 8

---> LCD = 8

Make the denominators the same as the LCD.

\(\frac{3\times 2}{4\times 2}+\frac{7}{8}\)

Simplify. Denominators are now the same.

\(\frac{6}{8}+\frac{7}{8}\)

Join the denominators.

\(\frac{6+7}{8}\)

Simplify.

\(\frac{13}{8}\)

Convert to mixed fraction.

\(1\frac{5}{8}\)

Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Answer:

where is the question . ..... we are ready to help you

Answer:

please frame the question well if there is a picture help us with it,so that you can receive the exact answer

Answer:

22/3, or 7.3333

Step-by-step explanation:

the area of a rectangle is base x height, or length x width.

the area is 22m^2, so you must divide that by 3 (the width) to get the length.

therefore the length is 22/3, or 7.3333

Answer:

2.50x+80>4.00

Step-by-step explanation:

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Answer:

675

Step-by-step explanation:

Answer:

675

Step-by-step explanation:

Given :-

To find:-

Answer :-

We are here given two points (0,5) and (3,0) and we are interested in finding the equation of the passing through the given points. Firstly let's find out the slope as ,

\(\implies m =\dfrac{y_2-y_1}{x_2-x_1}\\\)

and here ,

substitute the respective values in the formula of slope stated above as ,

\(\implies m =\dfrac{ 0-5}{3-0} \\\)

\(\implies\underline{\underline{ m = \dfrac{-5}{3}}} \\\)

Now we can use the point slope form of the line to find out the equation of the given line . The point slope form of the line is ,

\(\implies y - y_1 = m(x - x_1) \dots(i) \\\)

Slope intercept form of the line is \( y = mx + c \) , where \( m\) is the slope of the line and \(c\) is y intercept.

Take any point out of the given two , say (3,0) . So here,

substitute the respective values in (i) as ,

\(\implies y -0 = \dfrac{-5}{3}( x -3)\\\)

\(\implies y = \dfrac{-5}{3}x + \dfrac{-5}{3}\times -3 \\\)

\(\implies \underline{\underline{ y =\dfrac{-5}{3}x + 5}} \\\)

This is our required equation in the slope intercept form.

And we are done!

v = 2√2 (i + j) in component form.

Given:

v lies in the first quadrant and makes an angle of π/4 with the positive x-axis, and |v| = 4.

To Find:

Find v in component form.

Components of a vector are given by:

x = |v| cos θ,

y = |v| sin θ,

where θ is the angle that the vector makes with the positive x-axis.

We are given that |v| = 4 and θ = π/4 (because the vector makes an angle of π/4 with the positive x-axis).

Components of v will be:

v = (|v| cos θ)i + (|v| sin θ)j

  = (4 cos π/4)i + (4 sin π/4)j

  = (4/√2)i + (4/√2)j

  = 2√2 i + 2√2 j

  = 2√2 (i + j)

Hence, v = 2√2 (i + j) in component form.

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Answer:

q= -4

Step-by-step explanation:

\(5q + 6 = 2 q- 2 + q\)

Collect like terms and simplify

\(5q - 2q - q = - 2 - 6 \\ 2q = - 8\)

Divide both sides of the equation by 2

\( \frac{2q}{2} = \frac{ - 8}{2} \\ \)

Simplify

\(q = - 4\)

The requried solution to the equation 5q + 6 = 2q - 2 + q is q = -4.

To solve the equation 5q + 6 = 2q - 2 + q, we need to simplify and combine like terms. Let's proceed step by step:

First, let's combine the q terms on the right side of the equation:

5q + 6 = 2q - 2 + q

Combining the q terms on the right side, we have:

5q + 6 = 3q - 2

Next, let's isolate the q term by moving all other terms to the opposite side:

To move the 3q term to the left side, we subtract 3q from both sides:

5q - 3q + 6 = -2

Simplifying the left side:

2q + 6 = -2

Next, let's isolate the constant term by moving 6 to the right side:

Subtracting 6 from both sides:

2q = -2 - 6

2q = -8

Finally, to solve for q, divide both sides by 2:

q = -8/2

q = -4

Therefore, the solution to the equation 5q + 6 = 2q - 2 + q is q = -4.

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Answer:

1430

Step-by-step explanation:

have a great day!

Given: A 180 degree rotation of a vertical angle will always map to the other vertical angle

To Determine: The prove that the vertical angles are congruent

Draw and label to vertical lines with an angle

The 180 degree rotation of the vertical angle BOC would give:

Note that the other vertical would be AOD

The students should respond that

Hence, the 180 degree rotation of a vertical angle will always map to the other vertical angle which are congruent to each other because:

The vertical angles are vertically opposite to each other

The surface area of the square pyramid with a side length of 6 cm and a slant height of 7 cm is 120 square cm.

To find the surface area of a square pyramid, we need to add up the areas of all its faces. A square pyramid has a square base and four triangular faces. We can use the side length of the square base and the slant height of the triangular faces to calculate the surface area.

First, let's find the area of the square base:

Area of square base = (side length)\(^2\)

Area of square base =\(6^2\)

Area of square base = 36 square cm

Next, let's find the area of one of the triangular faces. Since the pyramid is a square pyramid, all the triangular faces are congruent.

To find the area of a triangular face, we need to use the formula:

Area of one triangular face = (1/2) x base x height

Area of one triangular face = (1/2) x 6 x 7

Area of one triangular face = 21 square cm

Finally, we can calculate the surface area of the pyramid by adding the area of the square base and the total area of the triangular faces:

Surface area of square pyramid = area of square base + total area of triangular faces

Surface area of square pyramid = 36 + 84

Surface area of square pyramid = 120 square cm

Therefore, the surface area of the square pyramid with a side length of 6 cm and a slant height of 7 cm is 120 square cm.

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Answer: To fill the whole bucket, it will take 64 seconds so the remaining time is 40 seconds

Step-by-step explanation: As we are given 3/8 th part of the bucket is filled in 24 seconds. So by simply applying the unitary method we can say -

3/8 th part -----> 24 seconds

To fill the whole bucket multiply both sides by 8/3 in order to make the 1 unit of the bucket on the L.H.S, we get

1 bucket ----> 64 seconds.

The remaining times as it already passes 24 seconds and 3/8 th part of the bucket is filled, 64-24 seconds i.e 40 seconds is remaining in which bucket is full.

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The change in the price level from the first to the second month is 106.4

Price index: Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places.

A college student purchases 4 movie tickets for $7 each, 2 CDs for $13 each, and 20 gallons of gasoline at $2 a gallon during the base period.

Gas will cost $2.25 per gallon in the upcoming month, CDs will cost $12.50 each, and cinema tickets will cost $7.50

The price index

=(price in current year/price in last year) x 100

=100/94 x 100

=106.38 or 106.4

The change in the price level from the first to the second month is 106.4

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Answer:

acute and obtuse angles .

The angle hat has a measure of 46° is angle RWS (∠RWS)

From the question, we are to determine the angle that has the given measure.

From the given information,

The given measure is 46°.

Now, we will determine the angle that has a measure of 46°

From the vertical angles theorem, we know that

"A pair of vertically opposite angles are always equal to each other"

When two lines intersect each other, the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In the given diagram, angle NWP and angle RWS are vertical angles.

Thus,

m ∠NWP = m ∠RWS

From the given information

m ∠NWP = 46°

Therefore,

m ∠RWS = 46°

Hence,

∠RWS has a measure of 46°

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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Answer:

y=3/4 x- 1/2

Step-by-step explanation:

McCandless’s original plan was to hike westward to the Bering Sea, but he sheltered in an abandoned bus on the little-traveled trail. He lived by killing small animals (and one moose) and gathering roots and berries.

On April 25, 1992, McCandless hitchhiked through Canada to get to Fairbanks via the Alaska Highway. Three days later, he found another ride to the Stampede Trail in the southwest.

McCandless was only carrying around 10 pounds (4.5 kg) of rice and a few books, which the driver believed was inadequate for a lengthy stay in the jungle.

In addition, his 0.22 rifles were usually regarded as lacking enough power for big-game hunting or bear defense, and he lacked a reliable map.

Thus, McCandless’s original plan was to hike westward to the Bering Sea, but he sheltered in an abandoned bus on the little-traveled trail. He lived by killing small animals (and one moose) and gathering roots and berries.

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As per the theory, McCandless's Original plan was  to hike westward to the Bering Sea, but he ended up sheltering in an abandoned bus on the little-traveled trail.

According to the theory called "Into the wild", here his graduation ceremony in May 1990, the person called McCandless told his parents he was going to take a road trip during the summer, and he was also saying that "I think I'm going to disappear for a while."

At the time his parents realized that they had no way of contacting him, then here some three months later, where their son had disappeared and unbeknownst to them, then he had chosen a new name that is Alexander Supertramp.

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Answer: 1.465 : 1

Step-by-step explanation:

Slope of the line segment:

m = (5 - 3)/(4 - (-2)) = 2/6 = 1/3

The equation of the line which the line segment lies on is found by:

(y - 3)/(x - (-2)) = 1/3

(y - 3)/(x + 2) = 1/3

(y - 3)/(x + 2) * (x + 2) = 1/3 * (x + 2)

y - 3 = (x + 2)/3 = 1/3 x + 2/3

y = 1/3 x + 11/3

The equation of the line given:

4x + 5y = 21

5y = -4x + 21

y = -4/5 * x + 21/5

Set them equal to each other and solve for x to find their intersection:

1/3 x + 11/3 = -4/5 * x + 21/5

15(1/3 x + 11/3) = 15(-4/5 * x + 21/5)

5 x + 55 = -12 x + 63

17x = 8

x = 8/17

y = 1/3 (8/17) + 11/3 = 8/51 + 181/51 = 189/51

Point (8/17, 189/51)

Distance from right end of segment to intersection:

s = SQRT((4 - 8/17)^2 + (5 - 189/51)^2) = SQRT((60/17)^2 + (66/51)^2) = 3.759

length of segment = SQRT((5–3)^2 + (4 - (-2))^2) = SQRT(4 + 36) = SQRT(40) = 6.324

Distance from the left end to interseciton:

6.324 - 3.759 = 2.555

Ratio of right end to left end:

3.759/2.565 = 1.465

Ann will have approximately $24,388.43 in her savings account at the end of the tenth year.

By depositing $2000 in the account at the beginning of each year for ten years, Ann will have a total investment of $20,000 ($2000 x 10). Since the savings account pays 3% interest per year compounded annually, we can calculate the final amount using the compound interest formula.

To calculate compound interest, we use the formula:

A = P(1 + r/n)ⁿ

Where:

A = the final amount (including principal and interest)

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

In this case, P = $20,000, r = 3% (0.03 as a decimal), n = 1 (compounded annually), and t = 10 (number of years).

Plugging these values into the formula, we get:

A = $20,000(1 + 0.03/1)¹⁰

A = $20,000(1.03)¹⁰

A ≈ $24,388.43

Therefore, at the end of the tenth year, Ann will have approximately $24,388.43 in her savings account.

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The factors of the polynomial x^3-9x^2+27x-27 are (x -3), (x - 3) and (x - 3)

The polynomial you provided is x^3-9x^2+27x-27. If you know one of the factors of this polynomial, we can use that to find the remaining factors.

One factor of this polynomial is (x-3) as it gives remainder zero when divided by (x-3)

quotient is  x² - 6x + 9

remainder is zero

So the remaining factors are (x-3) and x² - 6x + 9

Alternatively, we can factor the remaining quadratic polynomial  x² - 6x + 9

by using Factor theorem or by using difference of squares

x² - 6x + 9 = (x - 3)²

So the remaining factors are (x-3) and (x - 3)

So the original polynomial can be factored as (x-3)(x-3)(x-3) = (x-3)³

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The probability that exactly 17 households own a DVD player is 0.0124.

Given:

The probability that a house hold in centercity owns a DVD player is = 53%.

So, p = 0.53

The probability that a house hold in centercity does not own a DVD player is = 100% - 53% = 47%

So, q = 0.47

The sample size is 22 households in the city.

So, n = 22

We have to calculate the probability that exactly 17 households own a DVD player.

So, r = 17

The formula to be used in binomial experiment is:

P (r) = \(\frac{n!}{r! (n -r)!}\) × \(p^{r}\) ×\(q^{n-r}\)

The probability that exactly 17 households own a DVD player will be,

= \(\frac{22!}{17! (22 - 17)!}\) × \(0.53^{17}\) ×\(0.43^{22-17}\)

= \(\frac{22!}{17! (5)!}\)× \(0.53^{17}\) ×\(0.43^{5}\)

= 0.0124

Therefore, the probability that exactly 17 households own a DVD player is 0.0124.

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Answer:

I think it's B not sure though.

The graphical representation that would be best to display the data is given as follows:

Histogram.

An histogram is a graph that shows the number of times each element of x was observed.

The four types of products are given as follows:

Each of these item would represent a bin, and the values of each bin are given as follows:

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Answer: 48 is the smaller integer

Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.