Caroline saved $3. 84 on a discounted item that was marked down 15% off of the

original price of the item. What was the original price of the item before the discount?

A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.

The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.

To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.

The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.

After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.

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if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

No, it is not possible to make two triangles that are not congruent and have three pairs of congruent angles. This is because if two angles of a triangle are congruent, then the third angle must also be congruent by the Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. If two triangles have three pairs of congruent angles, then all three angles in each triangle are congruent, meaning they have the same measure. However, this does not guarantee that the sides of the triangles are congruent. In order for two triangles to be congruent, they must have the same angle measures as well as the same side lengths. Therefore, if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

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Answer:

77=c=8

Step-by-step explanation:

The dimension of the column space of a matrix is equal to the rank of the matrix as well , Dim Col A is also 2.

The maximum number of rows or columns in a matrix that are linearly independent is the matrix's rank.

Given that the null space of a 7 x 5 matrix is 3-dimensional, we can conclude that the rank of the matrix is:

Rank(A) equals the number of columns minus the size of the null space

= 5 - 3

= 2

So, Rank A is 2.

The dimension of the row space of a matrix is equal to the rank of the matrix. Dim Row A is therefore also 2.

A matrix's rank and the dimension of its column space are both the same.

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Answer:

$289

Step-by-step explanation:

If you know the cost of one of the two items, you can subtract that item from the total in order to find the price of the second item

So:   total price - computer price = printer cost

So:   $1039- $750 = $289

The printer is $289

Answer:

14 cm per day

Step-by-step explanation:

To find the water level increase rate in cm per day, divide 84 by 6, since it increased by 84 cm in 6 days:

84/6

= 14

So, the water level increase rate in 14 cm per day

Step-by-step explanation:

7/10 - 1/2 = 7/10 - 5/10 = 2/10

Answer:

4/4

Step-by-step explanation:

When one point of the diameter touches the circle at (-3,1) and the other point touches the circle at (3,-7) that is these are endpoints of diameter. Then the radius of this circle is equals to the 5 units.

Radius of a circle is defined as the distance from the center of the circle to any arbitrary point on it's circumference. It is generally represented by symbol 'R' or 'r'. When the diameter of a circle is known, the formula for Radius, R= Diameter/2. We have specified two endpoints, i.e., (-3,1),(3,-7) of a diameter of a circle. Let the radius of circle be 'r '. We have to determine the value of r that is radius of circle. From the above definition we can say that radius is half of length of diameter. So, first we calculate the length of diameter of circle. Using the distance formula, the distance between two points is written as, \(d = \sqrt{(x_2-x_1)²+(y_2-y_1)²}\)

So, the distance between two points (-3,1),(3,-7) is \(d = \sqrt{ ( 3-(-3))²+(-7 -1)²}\)

=> \(d = \sqrt{6²+8²} =\sqrt{ 36 + 64}\)

=> d = 10 units

so, length of diameter of circle is 10 units. Now, by definition of radius, the radius of circle is half of diameter. Thus, the required value of radius, r is 5 units (10/2).

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The annual rate of return on the $1,000 investment, which grows to $2,400 in eight years, is approximately 11.48%.

To calculate the annual rate of return, we can use the compound interest formula:

Future Value = Present Value * (1 + Rate)^Time

Where:

Future Value = $2,400

Present Value = $1,000

Time = 8 years

Plugging in the given values, we have:

$2,400 = $1,000 * (1 + Rate)^8

To isolate the rate, we can rearrange the equation:

(1 + Rate)^8 = $2,400 / $1,000

(1 + Rate)^8 = 2.4

Taking the eighth root of both sides:

1 + Rate = (2.4)^(1/8)

Rate = (2.4)^(1/8) - 1

Using a calculator, we find:

Rate ≈ 0.1148

Rounding the result to 2 decimal places, the annual rate of return is approximately 11.48%.

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The number of karats in the bracelets which is 42% gold is equal to 10 karats ( round to the nearest whole number ).

As given in the question,

Number of karats represents pure gold is equal to 24 karats

Percentage form of pure gold = 100%

Proportion representation of pure gold to karat is given by:

24 karats is equal to 100% pure gold

100% gold = 24 karats

⇒ 1% gold = ( 24 / 100 ) karats

⇒ 42% gold = ( 24 × 42 )  / 100 karats

⇒ 42% gold = 10.08 karats

                    = 10 karats ( round to the nearest whole number )

Therefore, number of karats in the bracelets which is 42% gold is equal to 10 karats ( round to the nearest whole number ).

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Answer: x=4.7°

Step-by-step explanation:

\(m\angle PQS=119^0\\\angle PQR+\angle RQS=\angle PQS\\72^0+(10x)^0=119^0\\72^0+(10x)^0-72^0=119^0-72^0\\10(x^0)=47^0\\\)

Divide both parts of the equation by 10:

\(x=4.7^0\)

Answer:

-2

Step-by-step explanation:

you would solve the parentheses first and get -9 it is being multiplied by a negative so switch it to a positive to get 9 add 6,3,2 together but their all negative so add a mince there to get -11 then add nine to get -2

Answer:

109

Step-by-step explanation:

the sum of 37 and 72 is equal to x

proof:  

37+72 = 109

three angles of a triangle form 180 degree

to find the angle which is not given,

180 - 109  = 71

as you can see, angle with the measure 71 degree and angle x form a straight line, which means their sum is 180

so,

x = 180 - 71

x = 109

that means ,

=>    37+72 = x

=>    109 = 109            [ 37+72 = 109, x = 109]

hope this helps :)

Answer:

Step-by-step explanation:

Find the value of x in this triangle .

We know that sum of all the interior angles of triangle is equal to 180° . Then ,

Therefore , Angle y = 71° .

Now , We know that Angle 3 and Angle 4 is equal to 180° because they are Linear pair . So ,

Therefore , value of Angle x is 109° .

Answer:

\(\$2229.4\)

Step-by-step explanation:

Cost of 1 door = \(\$185.95\)

Total number of doors = 4

Cost of 4 doors = \(\$185.95\times 4=\$743.8\)

Cost of 1 window = \(\$148.56\)

Total number of windows = 10

Cost of 10 windows = \(\$148.56\times 10=\$1485.6\)

Total price of the doors and windows that needs to be purchased is \(\$743.8+\$1485.6=\$2229.4\).

Answer:

1x + 15?

Step-by-step explanation:

Answer:The graphed function has a higher minimum.Both functions have an axis of symmetry of x = 1.The function f(x) = x2 − 2x − 3 has a greater range.Additionally: neither function has a maximum, both functions have the same domain

Step-by-step explanation: just did it

Answer:

x ≈ 14.3 cm

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector, that is

It divides the isosceles triangle into 2 right triangles, with base \(\frac{1}{2}\) x

Using the tangent ratio on the left, right triangle, then

tan35° = \(\frac{opposite}{adjacent}\) = \(\frac{5}{\frac{1}{2}x }\) = \(\frac{10}{x}\) ( multiply both sides by x )

x × tan35° = 10 ( divide both sides by tan35° )

x = \(\frac{10}{tan35}\) ≈ 14.3 cm ( to 1 dec. place )

To satisfy the condition of the line d intersecting the graph at two distinct points with coordinates greater than 3, we can choose any nonzero value for m.

To find the value of m for the line d: mx + 3 that intersects the graph of the function\(y = x^3 - 3x + 2\) at two distinct points with coordinates greater than 3, we need to analyze the behavior of the function and the line.

The graph of the function\(y = x^3 - 3x + 2\) is a cubic curve.

By observing the shape of the graph, we can see that it has two local minima and one local maximum.

Since we are looking for two distinct points of intersection with coordinates greater than 3, we need to find the slope of the line d such that it intersects the function at these points.

To determine the slope of the line d, we need to find the derivative of the function\(y = x^3 - 3x + 2.\)

Taking the derivative, we get \(y' = 3x^2 - 3.\)

Since the line d intersects the graph at two distinct points, it must be a secant line rather than a tangent line.

This means that the slope of the line should be different from the slope of the tangent line at any point on the curve.

To find the slopes of the tangent lines, we set y' = 0 and solve for \(x: 3x^2 - 3 = 0.\)

Simplifying, we find \(x^2 - 1 = 0,\) which gives us x = ±1.

Therefore, the tangent lines at x = -1 and x = 1 have slopes of \(3(-1)^2 - 3 = 0\) and \(3(1)^2 - 3 = 0,\) respectively.

To find the slope of the line d that intersects the graph at two distinct points with coordinates greater than 3, we need a slope that is different from 0.

Thus, we can choose any value of m ≠ 0.

In summary, to satisfy the condition of the line d intersecting the graph at two distinct points with coordinates greater than 3, we can choose any nonzero value for m.

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The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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Answer:

An arithmetic sequence has a constant difference between each term.

A geometric sequence has a constant ratio.

Answer:

x = 7; y = 11

Step-by-step explanation:

AB = x

AB = CD

CD = 7 so....

x = 7

AD = y + x

AD = BC

BC = 18 so...

y + x = 18    

y + 7 = 18                        subtract 7 from 18

y = 11

Answer:

x = 7

y = 11

Step-by-step explanation:

Do you see those little arrow marks? Those indicate that if a side has those marks, they have the same length. If a side with one arrow is 7 units long, then it means that x = 7, because the side with x also has one arrow. Then, just plug in 7 into the y+x equation, and set it equal to the other side. (18).

y + 7 = 18; subtract 7 from both sides, to get x = 7; y = 11.

Hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day, and good luck on your assignment. :)

Answer:

D = 55 feet

Step-by-step explanation:

Let below sea level is negative direction and above sea level is positive direction.

A deep sea diver is at 45 feet below sea level = -45 feet

A helicopter is at 100 feet above sea level = +100 feet

We need to find the distance between the helicopter and deep sea diver. It can be calculated by simply adding the above data as follows:

D = -45 +100

= 55 feet

Hence, the distance between the helicopter and deep sea diver is 55 feet.

The most appropriate choice for volume of cuboid and cylinder will be given by-

Total mass of sculpture is 10.0464 tonnes

What is volume of cuboid and cylinder?

Cuboid is a three dimensional figure that has 6 faces, 12 edges and 8 vertices.

Volume of cuboid is given by the formula length \(\times\) breadth \(\times\) height

Cylinder is a three dimensional round figure that has two circular bases at the end

If r is the radius of the cylinder and h is the height of the cylinder, volume of the cylinder is given by the formula

V = \(\pi \times r^2 \times h\)

Here,

Radius of cylinder = 40 cm

Height of cylinder = 70 cm

Volume of cylinder = \(\pi \times r^2 \times h\)

                                = \(\frac{22}{7} \times (40)^2 \times 70\\\)

                                = 352000 \(cm^3\)

Length of cuboid = 80 cm

Breadth of cuboid = 80 cm

Height of cuboid = 140 m

Volume of cuboid = \(80 \times 80 \times 140\)

                              = 896000 \(cm^3\)

Total volume of sculpture = (352000 + 896000) \(cm^3\)

                                           = 1248000 \(cm^3\)

Density of sculpture = 8.05 \(g / cm^3\)

Mass of sculpture  = \(1248000 \times 8.05\)

                               = 10046400 g

                               = 10046.4 kg

                                = 10.0464 tonnes

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A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.

Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.

Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.

Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.

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To estimate the frequency spectrum of the signal {1, 9, 0, 1, 4, 9} using the FFT, we apply the FFT algorithm to the signal. The FFT decomposes the signal into its constituent frequencies and provides the corresponding magnitude and phase responses.

(a) By applying the FFT to the given signal, we obtain the frequency spectrum. The magnitude spectrum represents the amplitudes of different frequency components in the signal, while the phase spectrum represents the phase shifts of those components.

(b) To plot the magnitude and phase response of the calculated spectrum, we would need to compute the magnitude and phase values for each frequency component obtained from the FFT.

The magnitude values can be plotted on a graph as a function of frequency, representing the strength of each frequency component. Similarly, the phase values can be plotted as a function of frequency, showing the phase shifts at different frequencies.

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At least 11 students must take the quiz to assure that at least two have exactly the same answers to all five questions.

Determining the minimum number of students required to guarantee that at least two students have the same answers to all five questions on a multiple choice quiz. Under the area of probability and combinatorics.

There are 4 possible answers for each of the 5 questions, so there are a total of \(4^5 = 1024\) possible sets of answers.

Let's consider the opposite scenario where no two students have exactly the same answers to all five questions. In this case, the first student can choose any of the 1024 possible sets of answers. The second student must choose a different set of answers from the first student, so there are 1023 possible sets of answers for the second student. Similarly, the third student must choose a different set of answers from the first two students, so there are 1022 possible sets of answers for the third student. Continuing in this way, the nth student has 1025-n possible sets of answers to choose from.

Therefore, the total number of possible sets of answers for n students is the product of the number of possible sets of answers for each student:

1024 × 1023 × 1022 × ... × (1025-n)

We want to find the minimum value of n such that this product is less than 1024, because that is the maximum number of sets of answers possible. That is, we want to solve the inequality:

1024 × 1023 × 1022 × ... × (1025-n) < 1024

To simplify this expression, notice that each term in the product is very close to 1024, which suggests that we can approximate the product as \(1024^n\). This approximation is valid when n is much smaller than 1024, which is the case here.

Using this approximation, we can rewrite the inequality as:

\(1024^n\)< 1024

Taking the logarithm base 2 of both sides, we get:

n < log2(1024) = 10

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Answer:

H is E

Step-by-step explanation:

In the formula of the energy of photons "h" signifies Planck's constant.

The Planck constant, often known as Planck's constant, is a crucial physical constant in quantum physics. The mass-energy equivalency establishes the relationship between mass and frequency, and the constant establishes the relationship between a photon's energy and frequency.

In the equation energy E = h X v. The "h" there signifies Planck's constant

Planck's constant is a value, that shows the rate at which the energy of a photon increases/decreases, as the frequency of its electromagnetic wave changes.

Therefore,  in the formula of the energy of photons "h" signifies Planck's constant.

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