A violin student records the number of hours she spends practicing during each of nine consecutive weeks:
6.2

5.0

4.3

7.4

5.8

7.2

8.4

1.2

6.3


What is the mean number of hours spent practicing per week during this period?

The value of the length of the shorter leg is 2.5 feet and the longer leg is 4.5 feet.

From the information, the following can be deduced:

This will be:

a = First leg = x

b = Second leg = x + 4

c = Hypothenuse = 7

This will then be:

a² + b² = c²

x² + (x + 4)² = 7²

x² + x² + 8x + + 16 = 49

2x² + 8x + 16 - 49

2x² + 8x - 33

The equation above will be calculated using the Almighty formula. This will give the value of x as 2.5.

Since the longer leg is x+4. This will be:

x + 4 = 2.5 + 4 = 6.5 feet.

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Answer:

c-43=47

Step-by-step explanation:

Well this is kinda obvious.

He already sold 43 cups of hot choclate and he needed 47 more.

So the total amount of cups is (c) so we can make an equation like this

c-43 (since theres total which is unknown so ”c” and then Theres the already sold 43 cups).

c-43=47 (the 47 is the amount he needs to sell)

So final equation to determine total cups needed

c-43=47

Solution

We are given

Distance = 5/2 miles

Time = 1/4 hours

Answer:

The speed would \(10~\text{mph}\).

Step-by-step explanation:

Step 1: State the formulas required

The formula for speed is:

\(\text{Speed}=\frac{\text{Distance}}{\text{Time}}\)

Step 2: Substitute the values into the formula

The distance is \(\frac{5}{2}~\text{miles}\) and the time is \(\frac{1}{4}~\text{hours}\).

Substitute these values into the formula:

\(\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\)

Step 3: Calculate

\(\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10\)

So, the speed is  \(10~\text{miles per hour}\)  or  \(10~\text{mph}\).

Answer:

20

Step-by-step explanation:

(2√5)²=

4*5=20

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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A line passes through point (1, 6) and has a slope is y=8x-14 We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope (8), we can immediately plug that into the equation

So far, the equation of the line is:

y=8x+b

Now we need to find b

The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b

Substitute 1 as x and -6 as y in the equation to solve for b

-6=8(1)+b

Multiply

-6=8+b

Subtract 8 from both sides

-14=b

Substitute -14 as b into the equation

y=8x-14

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Answer:

is this what you mean or something else?

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Answer:

Percent Increase in measure of the side of a square = 30%

Step-by-step explanation:

Let the measure of the side of a square = s

Area of the square = (Side)²

                                = s²

If the area of the square is increased by 69%

Area of the new square = s² + 69% of s²

                                        = s² + 0.69s²

                                        = 1.69s²

Therefore, measure of the side of the new square = √(Area of the square)

                                                                                    = √(1.69s²)

                                                                                    = 1.3s

Measure of side of the old square = s

Therefore, increase in measure of the square = 1.3s - s

                                                                            = 0.3s

Percent increase in the measure of the side of the square

= \(\frac{\text{Increase in measure}}{\text{Measure of the side of the original square}}\times 100\)

= \(\frac{0.3s}{s}\times 100\)

= 30%

Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.

When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.

The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.

Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.  

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Answer:

Step-by-step explanation:

The volume of a rectangular prism is

V=xyz, where x,y,z are the three dimensions, in this case

V=10(4.5)6.25

V=281.25 ft^3

Answer:

$3.72

Step-by-step explanation:

Divide $2.79 by 3

$0.93 is the price of one orange

$0.93 times 4 is $3.72

Hope this helps!

The situations does one quantity change at a constant rate per unit interval relative to another quantity are option A and option E

Here we have to find the situation that one quantity change at a constant rate per unit interval relative to another quantity

Part A

An employee earns $14 per hour.

The equation will be

y = 15x

Where y is the earning and x is the number of hours

It has constant rate per unit interval

Part B

An employee earns a 3% raise each year.

y = x + 0.03x

Where y is the earning and x is the number of years

It is not constant rate per unit interval

Part C

A gym charges a $50 down payment plus $30 per month.

y = 50 + 30x

Where y is the charges and x is the number of months

Its is not constant rate per unit interval

Part D

A piece of gym equipment decreases 8% in value every 6 months.

y = x - 0.08x

Where y is the total value and x is the number of 6 months

It is not constant rate per unit interval

Part E

A trainer charges $20 for every 30 minutes of training plus a $5 tip

y = 20x + 5

Where y is the charges and x is the number of 30 minutes times periods

It is constant rate per units

Therefore, option A and E are correct statement

I have answered the question in general, as the given question is incomplete

The complete question is:

For which situation does one quantity change at a constant rate per unit interval relative to another quantity?.

A. An employee earns $14 per hour.

B. An employee earns a 3% raise each year.

C. A gym charges a $50 down payment plus $30 per month.

D. A piece of gym equipment decreases 8% in value every 6 months.

E. A trainer charges $20 for every 30 minutes of training plus a $5 tip.

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John needs to make a 16 inches cut of the tiles along the median. The correct answer is option C. 16 inches.

When cutting the tile along the median, we need to find the length of the cut that divides the trapezoid into two equal areas.

The median of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides. In this case, the top base of the trapezoid is 13 inches and the bottom base is 19 inches.

To find the length of the cut, we can take the average of the lengths of the top and bottom bases. The average of 13 inches and 19 inches is (13 + 19) / 2 = 32 / 2 = 16 inches.

Therefore, John will need to make a 16-inch cut along the median to cut the tiles in half and create the desired pattern on his floor.

Option C, 16 inches, correctly represents the length of the cut required to cut the tiles along the median.

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Answer:

D.

Step-by-step explanation:

The solution has to be in the shaded area in order to be a solution. Only D. is in the shaded region, so that is your correct answer.

Answer:

Slope = 1/2

Step-by-step explanation:

Formula for getting slope using 2 points...

(y2 - y1) / (x2 - x1)

= (3 - 0) / (6 - 0)

= 3 / 6

= 1/2

So...

Slope is 1/2

Hope this helps :)

Let me know if there are any mistakes!!

Answer:  The slope is   1/2

Step-by-step explanation:

When a line passes through the origin the equation of the line will be represented in the form    y= kx   where k is the slope.

To to find k you will need to divide both sides by x.

y = kx

y/x = kx/x

  k = y/x  

This means that to find k, you will need to divide the y coordinate of the point by the x coordinate.  

  k = 3/6

K = 1/2

The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.

It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5

To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.

Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).

Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).

So, the p-value for the given test is 0.067 (rounded to two significant digits).

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

1196

Step-by-step explanation:

trust me i check the answer!

To show that the vectors ⎡⎣⎢121⎤⎦⎥, ⎡⎣⎢131⎤⎦⎥, ⎡⎣⎢141⎤⎦⎥ do not span R3, we need to find a vector that cannot be expressed as a linear combination of these vectors.

One way to do this is to set up a system of equations and see if there is a solution for the coefficients. For example, let's try to express the vector ⎡⎣⎢010⎤⎦⎥ as a linear combination of the given vectors:

a⎡⎣⎢121⎤⎦⎥ + b⎡⎣⎢131⎤⎦⎥ + c⎡⎣⎢141⎤⎦⎥ = ⎡⎣⎢010⎤⎦⎥

This gives us the following system of equations:

a + b + c = 0
2a + 3b + 4c = 1
a + b + c = 0

We can see that the first and third equations are the same, so we only have two independent equations. This means that we cannot solve for all three coefficients, and therefore the vector ⎡⎣⎢010⎤⎦⎥ cannot be expressed as a linear combination of the given vectors.

Therefore, the vectors ⎡⎣⎢121⎤⎦⎥, ⎡⎣⎢131⎤⎦⎥, ⎡⎣⎢141⎤⎦⎥ do not span R3, as there is at least one vector (⎡⎣⎢010⎤⎦⎥) that is not in their span.

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Answer: x = 15/8

Explanation: I used a calculator on a website.

Answer:

15/8

Step-by-step explanation:

Hope this helps: )

Answer:

none are parallel but A & D are perpendicular

Answer:

a and d are perpendicular

none r parallel

Step-by-step explanation:

The use of intersecting lines in a drawing to indicate areas of shadow and depth is called "cross-hatching."

Cross-hatching is a technique used in drawing and other visual arts to create the illusion of shadows, volume, and depth. It involves drawing a series of intersecting parallel lines or strokes in close proximity to one another. By varying the density, spacing, and direction of these lines, an artist can create areas of darker shading or indicate the contours and three-dimensional form of an object.

The intersecting lines create a pattern that visually simulates the effect of shadows and adds dimensionality to the artwork. Cross-hatching is a versatile and effective method to enhance the realism and visual impact of a drawing, and it is commonly employed in various art forms such as sketching, illustration, and pen-and-ink techniques.

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It can cause severe damage to cells and tissues, leading to various health risks such as cancer and radiation sickness. Proper shielding and protection measures are necessary when dealing with gamma radiation sources.

21: One of the three ways to protect yourself from radioactive exposure is:

Time: Minimize the time spent in proximity to the radioactive source. Limiting the exposure duration reduces the overall dose received.

Distance: Increase the distance between yourself and the radioactive source. Radiation intensity decreases with distance, so maintaining a safe distance helps reduce exposure.

Shielding: Use appropriate shielding materials to block or attenuate radiation. Different types of radiation require different types of shielding. For example, lead or concrete can be used to shield against gamma radiation, while plastic or aluminum can be effective against beta radiation.

22: The most dangerous type of radiation is:

d) Gamma

Gamma radiation consists of high-energy photons and can penetrate most materials, including the human body. It can cause severe damage to cells and tissues, leading to various health risks such as cancer and radiation sickness. Proper shielding and protection measures are necessary when dealing with gamma radiation sources.

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Answer:

p=0

Step-by-step explanation:

subtract 10p from both sides that leaves 8+p=12-4 12-8=4 p=4-4 p=0

Hi there!

$5.50=y

1 pound=x

4+1.50=5.50

The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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Answer: $36.45

Step-by-step explanation:

45(.25)=11.25

45-11.25=33.75

33.75(.08)=2.70

33.75+2.70=36.45

The appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

In a two-variable linear equation, x and y have a linear connection, meaning that the value of any one of the variables, y, relies upon that value of the other, x.

Cost for first mile of  taxi service  = $2.00

Additional cost = $1.20 per mile.

Peak distance = 25 miles.

a = number of miles traveled by taxi.

y = total cost of the taxi ride

The linear equation forms:

y = $1.20a + $2.00

When a = 0; y = $2.00

a = 25 ; y = $1.20*25 + $2.00 = 32

Thus, the appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

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