A 5-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (5 − x) ft. Find the length of the longer rope piece x (in ft)

The area of this compound figure is 85 cm².

The area of the compound figure given is calculated by subtracting the small area of the  figure from the big figure.

A (total) = 9 cm x 15 cm

A (total) = 135 cm²

The area of the small figure is calculated as follows;

A (small) = ( 9 cm - 4 cm ) x ( 15 cm - 5 cm )

A (small) = ( 5 cm ) x ( 10 cm )

A (small) = 50 cm²

The area of this compound figure = ( 135 cm² - 50 cm² ) = 85 cm²

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The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}

The event A has data - A = {6, 8, 10}

The event B has data - B = {5, 6, 9, 12}

The event C has data - C = {1, 3, 7}

The probability formula is -

Probability = No. of outcomes that is favorable / Total number of outcomes

The value for A∪B is -

A∪B = 3/4

The value of A∪B in data set is the values that are present in U data set and in A and B data set.

So, the value is - {5, 6, 8}

Therefore, the value is 3/4 or {5, 6, 8}.

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The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.

To begin, let's figure out how much each haircut will cost overall:

2 haircuts at $12.00 each = $24.00

3 haircuts at $15.00 each = $45.00

1 haircut at $25.00 = $25.00

Total cost = $24.00 + $45.00 + $25.00 = $94.00

Next, We must determine the total number of cuts:

2 haircuts + 3 haircuts + 1 haircut = 6 haircuts

Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:

The weighted mean cost of a haircut = Total cost / Total number of haircuts

= $94.00 / 6 haircuts

= $15.67 per haircut (rounded to the nearest cent)

Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

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The kilograms of compost in the barrel is 5.6 kg

From the question, we have the following parameters that can be used in our computation:

Amount filled on day 1 = 1/4

Remaining space = 4200 grams

The number of kilograms in the barrel is calculated as

Remaining space = (1 - 1/4) * Original space

Substitute the known values in the above equation, so, we have the following representation

(1 - 1/4) * Original space = 4200 grams

Convert to kg

(1 - 1/4) * Original space = 4.2 kg

So, we have

Original space = 4.2 kg/(1 - 1/4)

Evaluate

Original space = 5.6 kg

Hence, the original space is 5.6 kg

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The absolute value function on the graph is:

f(x) = -|x + 4| - 5

Remember that an absolute value function that has a vertex at (a, b) will be written as:

f(x) = |x - a| + b

Here the vertex is at (-4, -5), replacing that in the general formula we will get:

f(x) = |x + 4| - 5

And we also can see that the absolute value function opens downwards with slopes of 1, then there must be a leading coefficient of -1, the actual function is:

f(x) = -|x + 4| - 5

That is the graphed function.

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Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation: Because 1+1=2

2+2=4 therefore 2*2 also equal 4 and 2^2= 4

Anwer: EG=EF+EG => 6x+12+48=144

6x=144-12-48

6x=84

x=14

d)x=14

The original price of the table was $200 before the 64% discount was applied.

What is the percentage?

Percentage is a way of expressing a fraction or proportion out of 100. It is commonly used to compare two quantities, indicate the change or growth of a quantity over time, or express the probability or chance of an event occurring.

If you received a 64% discount on the sale price of a table, and the sale price is $72, we can calculate the original price of the table as follows:

Determine the percentage of the original price that corresponds to the sale price after the discount:

If the sale price is 100% - 64% = 36% of the original price, after the 64% discount.

Use the percentage found in step 1 to calculate the original price:

Let x be the original price

x * 36% = $72

0.36x = $72

x = $72 / 0.36

x = $200

Therefore, the original price of the table was $200 before the 64% discount was applied.

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A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

To estimate the sample size, we can use the following formula:

n = (Z^2 * p * (1-p)) / E^2

where:

n = sample size

Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)

p = the proportion in the pilot sample (0.641)

E = the maximum allowed error of estimation (0.047)

Plugging in the values, we get:

n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2

n = (5.3929 * 0.359) / 0.00222009

n = 1.928 / 0.00222009

n = 869.75

Since the sample size must be a whole number, we round up to the nearest whole number.

n = 870

Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

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Answer:

Option C

Step-by-step explanation:

2*-1 = -2

2*0 = 0

The area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.

What is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. In a trapezoid, the parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases.

There are several types of trapezoids, including isosceles trapezoids, where the legs are of equal length, and right trapezoids, where one leg is perpendicular to both bases. Trapezoids are commonly used in geometry and can be used to find the area of various shapes, such as triangles and rectangles.

To find the area of the trapezoid, we can use the formula:

Area = (1/2) x (sum of bases) x height

Since the trapezoid is isosceles, the length of the two parallel sides are the same. Let's call that length "x". We can use this information to set up an equation:

3 + 4 + 7 + x = 2x

Simplifying, we get:

14 + x = 2x

x = 14

So the length of both parallel sides is 14 meters.

Now we can plug in the values into the area formula:

Area = (1/2) x (3 + 14) x 5

Area = 8.5 x 5

Area = 42.5

Therefore, the area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.

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Answer: B 38m squared.

Step-by-step explanation:

I took the test and got this question correct.

At the end, Ann saves a total amount of 3 dollars according to the money she spent and on allowance according to the percentages.

Total Allowance of Ann = 15 dollars

Spent on food by Ann = [tex]\frac{15}{100}[/tex]*50

On food = 50 × [tex]\frac{15}{100}[/tex] = 7.5 dollars

Spent on stationary = 30% of Allowance

On stationary = 30 X[tex]\frac{15}{100}[/tex] = 4.5 dollars

Therefore, Money saved by Ann = Total Allowance - Money spent

Money saved = 15 dollars - 7.5 dollars - 4.5 dollars = 15-(7.5+4.5) dollars

Money saved = 3 dollars

Therefore, money saved by Ann is 3 dollars.

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Step-by-step explanation:

solution

let first part be 5x and second part be 9x

so ,

5x = 35

x = 35\5

x = 7

Now 9x = 9*7 = 63

this might help you thank you

Answer:

68

Step-by-step explanation:

-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3]  Start in the center and work your way out.

-2[-4 + 3(2 - 32 + 8 -3) - 3]

-2[-4 + 3(-30 + 8 - 3) -3]

-2[-4 + 3(-22 -3) -3]

-2[-4 + 3(-25)-3]

-2[-4 -27 -3}

-2[-31 - 3]

-2(-34)

68

The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.

Note that triangle ABC and triangle FBE are similar,(by AAA)

As [tex]\angle B[/tex] is common in both, and [tex]\angle F= \angle A[/tex] as they both are 90°

so, the [tex]\angle C[/tex] will also be equal to [tex]\angle E[/tex]

so [tex]\frac{BF}{FR} = \frac{AB}{AC}[/tex]

This can be written as [tex]\frac{4-x}{x} = \frac{4}{3}[/tex]

solving: 12 - 3x = 4x

7x = 12 or x = 12/7

Similarly, triangle A'B'C' and triangle RB'Q are similar,

so RB' = [tex]\frac{4}{3}y[/tex] and C'S= [tex]\frac{3}{4}y[/tex]

Thus, C'B' = C'S+ SR+ RB'

or  [tex]\frac{4}{3}y + y + \frac{3}{4} = 5[/tex]

solving y = 60/37

Now, x/y = [tex]\frac{12}{7} \times \frac{37}{60}[/tex] = 37/35

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The length of the radius of the sphere is 15 in.

It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.

We have,

Volume of the sphere = 14130 in³

So,

4/3πr³ = 14130 _____(1)

Solve for r.

4/3 x 3.14 x r³ = 14130

keep r on one side and the rest on the other side.

r³ = 14130 x 3 / 4 x 3.14

Cube root on both sides.

r³ = 3375

∛r³ = ∛3375

[ 15 x 15 x 15 = 3375 ]

So,

r = 15

Thus,

The radius of the sphere is 15 in.

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Answer:

19 miles

Step-by-step explanation:

hope this helps!!

As per the volume, we need to to purchase 4 containers of punch.

To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:

Total volume of punch = number of students * volume of punch per student

= 25 * 8 fluid ounces

= 200 fluid ounces

Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:

Number of containers of punch = Total volume of punch / Volume of punch per container

= 200 / 64

= 3.125

Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.

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Answer:

C

Step-by-step explanation:

The spaces go F A C E. The note shown is C.

The hourly change in temperature is -1.5

Fahreheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.

The 18th- cenetury German physicist Daniel Gabreil Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.

Given:

The temperature underwent a change of -18°F between noon and midnight.

To find:

The hourly change (h) in temperature

There are 12 hours between noon and midnight

So,

According to Question

Equation:

12h = -18

h = -18/12

h =-3/2

h = -1.5

The hourly change in temperature is -1.5

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The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight, then the hourly change in temperature is -1.5.

What is Fahrenheit?

Fahrenheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.

The 18th-century German physicist Daniel Gabriel Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.

Given:

The temperature underwent a change of -18°F between noon and midnight.

To find:

The hourly change (h) in temperature

There are 12 hours between noon and midnight

So,

According to Question

Equation:

12h = -18

h = -18/12

h =-3/2

h = -1.5

Therefore, The hourly change in temperature is -1.5

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The equation y < - 4 · x - 1 represents the inequality seen in the figure.

According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:

y < m · x - b

m = Δx / Δb

Where:

We know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:

m = (- 1 - 3) / [0 - (- 1)]

m = - 4

b = - 1

y < - 4 · x - 1

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In this solution, each molecule of (NH₄)₃PO₄ dissociates into three ammonium ions (NH₄₊) and one phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. Hence, the Van 't Hoff factor for this solution is 4.

The Van 't Hoff factor (i) is a measure of the degree to which a substance ionizes in a solution, and is defined as the ratio of the number of ions formed to the number of molecules (or formula units) dissolved. For the case of a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4. The Van 't Hoff factor is a measure of the extent to which an ionic substance dissociates into individual ions when dissolved in water. It is defined as the ratio of the number of ions formed to the number of formula units or molecules of the substance that are dissolved. For a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4 because each molecule dissociates into 3 ammonium ions (NH₄₊) and 1 phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. The Van 't Hoff factor is important in determining the colligative properties of solutions, such as boiling point elevation and freezing point depression.

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Answer:

  see below for a graph

  (-8, 4) is in the solution set

Step-by-step explanation:

You want the graph and a solution point for the inequalities y ≤ -6/5x -4 and y ≥ 2/5x +4.

The solid boundary line of the first inequality will cross the y-axis at -4, and will have a "rise" of -6 units for each "run" of 5 units. Shading is below this boundary line.

The solid boundary line of the second inequality will cross the y-axis at +4 and will have a "rise" of 2 units for each "run" of 5 units. Shading is above this boundary line.

The boundary lines make an X shape on the graph, crossing at the point (-5, 2). The solution set is in the left quadrant.

Point (-5, 2) is in the solution set, as are points in the doubly-shaded space to its left. (-8, 4) is one of those.

__

Additional comment

The boundary lines are solid because the "or equal to" case is included in each.

The ≤ symbol tells you y-values that satisfy the first inequality will be less than (or equal to) those on the boundary line.

The ≥ symbol tells you y-values that satisfy the second inequality will be greater than (or equal to) those on the boundary line.

Fοr distributions with a nοrmal shape or symmetry, the mean and standard deviation are emplοyed; for asymmetrical distributiοns, the median and interquartile range are used.

Because it is unaffected by οutliers, the IQR is frequently regarded as a mοre accurate measure of spread than the range. The variance and standard deviatiοn are indicators of hοw widely the data are dispersed from the mean. Each οbserved data value's prοximity to the mean is summarised.

The strοngest indicator of variability in data sets with οutliers or skewed distributions is the interquartile range. It's unlikely to be impacted by οutliers because it's based οn numbers that come frοm the centre half of the distribution.

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According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:

[tex]P = P_0 * 2^{t/t_d)}[/tex]

where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.

To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:

[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]

Dividing both sides by [tex]P_0[/tex] gives:

[tex]3 = 2^{t/t_d}[/tex]

Taking the logarithm of both sides (using any base) gives:

[tex]log(3) = log(2^{t/t_d} )[/tex]

Using the logarithmic identity

[tex]log(a^b) = b*log(a),[/tex]

we can rewrite this as:

[tex]log(3) = (t/t_d)*log(2)[/tex]

Solving for t, we get:

[tex]t = t_d * (log(3)/log(2))[/tex]

Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:

[tex]t = 6 * (log(3)/log(2)) hours[/tex]

Simplifying using the change of base formula

[tex](log(a)/log(b) = log_b(a))[/tex], we get:

[tex]t = 6 * log_2(3)[/tex] hours

Therefore, the answer is (f) None of the above.

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Correct question should be

Click on image for question

The rate at which the people are moving apart 15 minutes after person B starts walking is √2660 feet per second. To the nearest tenth of a foot per second, this is 51.3 feet per second.

Let's call the rate at which the people are moving apart "d".

15 minutes after person B starts walking, person A has been walking for 15 + 5 = 20 minutes, for a total distance of 20 * 4 = 80 feet north from point P.

At the same time, person B has been walking for 15 minutes, for a total distance of 15 * 5 = 75 feet south from point 500 feet due east of P.

The distance between the two people is the square root of the sum of the squares of their north-south and east-west separations, or:

d = √(80^2 + (500)^2) = √(80^2 + 250000) = √250100 = 500

Since the rate at which they are moving apart is the derivative of their separation with respect to time, we can find it by taking the derivative of the above equation with respect to time:

d/dt = √(2 * 80 * 4dt / dt + 2 * 500 * 5dt / dt) = √(160 + 2500) = √2660

To the nearest tenth of a foot per second, this is 51.3 feet per second.

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The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.

The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:

Kinetic Energy = (1/2) * mass * velocity^2

In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:

Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]

Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]

Kinetic Energy = 6 J

So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.

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Answer:

287 miles

Step-by-step explanation:

20.95+ .80x =250.55

250.55-20.95=229.6

.80x=229.6

229.6/.80=x

x=287 miles