Solve for x in the diagram below.
x
2x
(x+10)

For the square on the diagram, we can see that:

Remember that all the sides of a square have the same length.

Here we know that AC, the diagonal of the square, has a measure of 20 cm.

Then the length of DE, which is half of the diagonal of the square, is half of that, then:

20cm/2 = 10cm

DE = 10cm

DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:

D = √2*S

Then the sidelength is:

S = D/√2

Here we know that the diagonal measures 20 cm, then:

DC = S = 20cm/√2 = 14.14 cm

DC = 14.14cm

Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.

Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°

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Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.

The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:

5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups

Now, we can find three-fourths (3/4) of 17/3:

(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups

Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

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Answer:

-9

Step-by-step explanation:

8(x - 1) = 5x - 35

8x - 8 = 5x - 35

8x - 5x = 8 - 35

3x = -27

x = -27/3

x = - 9

The probability that the person will be cured of back pain is 2/7.

The probability that a person will be cured of back pain after being given a sugar pill can be determined by using the given information in the question. According to the question, for every 2 patients cured by the sugar pill, 5 patients were not cured by the sugar pill. This means that out of a total of 2 + 5 = 7 patients given the sugar pill, only 2 were cured. Therefore, the probability of a patient being cured of back pain after being given a sugar pill is 2/7.

To calculate the probability, we can use the formula:

P(cured) = number of patients cured / total number of patients

Plugging in the given values, we get:

P(cured) = 2 / 7

Therefore, the probability that a patient will be cured of back pain after being given a sugar pill is 2/7.

In conclusion, according to the results of the study, if a patient is given a sugar pill, the probability that the person will be cured of back pain is 2/7.

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The questionnaire is indeed at the center of the research process, and the quality of the analysis directly affects the quality of the data collected. Therefore, the statement is true.

Here's a step-by-step explanation:

1. A questionnaire is a research instrument used to collect data from participants in a study. It typically consists of a series of questions that are designed to gather specific information.

2. The questionnaire plays a central role in the research process because it serves multiple functions. These include:
  - Collecting data: The questionnaire is used to gather information from participants, which can be in the form of responses to closed-ended questions (e.g., multiple-choice) or open-ended questions (e.g., essay-style answers).
  - Standardizing data collection: By using a questionnaire, researchers can ensure that all participants are asked the same questions in the same order. This helps to minimize bias and increase the reliability of the data collected.  
  - Obtaining quantitative and qualitative data: Depending on the design of the questionnaire, researchers can collect both quantitative data (numerical measurements or ratings) and qualitative data (descriptive or explanatory responses). This allows for a comprehensive analysis of the research topic.
  - Testing hypotheses: Researchers can include specific questions in the questionnaire to test hypotheses or explore relationships between variables. This helps to address the research objectives and answer the research questions.
 
3. The quality of the analysis directly affects the quality of the data collected. After the data is collected through the questionnaire, it needs to be analyzed to draw meaningful conclusions. If the analysis is not done properly, it can lead to incorrect or unreliable results. For example, if the researcher makes mistakes in data entry or fails to use appropriate statistical techniques, it can affect the accuracy and validity of the findings.

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The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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Answer:

Looks like true to me

Step-by-step explanation:

y = x +6

The exclusive right to distribute, exhibit, perform, or reproduce an original work in copies, as well as the right to create derivative works based on the original work, is known as copyright. This assertion is true.

A bundle of legal privileges known as copyrights automatically belongs to everyone who produces an original work of authorship, such as a piece of literature, film, music, or software. These privileges include the ability to copy, create derivative works from, distribute, perform, and show the work in public.

The following exclusive rights belong to copyright owners exclusively, according American copyright law: Create phonorecords or duplicates of the material. Make works based on the original work. distribute copies or phonorecords of the work to the public by selling, transferring ownership, leasing, renting, or borrowing.

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Answer:

Here you go, hope my handwriting is clear :D

X can either equal -5 or 3/2

Answer:

i believe its the rise and the run of the slope.

Step-by-step explanation:

i believe its something similar to this photo

We require 16 lbs of $2.95 coffee and 28 lbs of $3.30 coffee to produce 44 pounds of blended coffee.

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions, unique response, No remedy, and there are several options.

Let the coffee worth 2.95 pound = x.

Let the coffee worth 3.50 pound = y

The blend of 3.30 pound for 44 pounds is = 145.2.

Given that, coffee worth 2.95 a pound was mixed with coffee worth 3.50 a pound to produce a blend worth 3.30 a pound.

2.95x + 3.50y = 145.2.......(1)

We need to produce 44 pounds of coffee.

x + y = 44...........(2)

The equation 2 can be written as:

y = 44 - x

Substitute the value of y in equation 1:

2.95x + 3.50(44 - x) = 145.2

2.95x + 15.4 - 3.50x = 145.2

6.45x = 145.2 - 15.4

x = 16

Substitute the value of x in equation 2:

16 + y = 44

y = 28

Hence, we require 16 lbs of $2.95 coffee and 28 lbs of $3.30 coffee to produce 44 pounds of blended coffee.

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Answer:

A≈78.54cm² Diamter= 10

Step-by-step explanation:

hope this helps

Answer:

A=78.54 cm sq

Step-by-step explanation:

Using the formulas

A=πr2

d=2r

Solving for A

A=1

4πd2=1

4·π·102≈78.53982cm²

Sally's friends took 105 marbles

A word problem  is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario. Solving word problem requires critical thinking.

Let x represents the total number of marble

Sue takes 1/3 of the marble = (1/3)x

remaining marble after sue = x-(1/3)x = (2/3)x

Bill takes 1/4 of the remainder =( 2/3)x × 1/4 =(1/6)x

the remaining marble after Bill is( ⅔-⅙)x = 5x/6

Brian takes 1/2 of the remainder 5x/6 ÷2 = 5x/12

The remainder after Brian = 5x/6-5x/12= 75

multiply through by 12

= 10x-5x = 900

5x = 900

divide both sides by 5

x = 900/5 = 180 marbles

This means the total marble is 180 after all Sally's friends have taken, 75 is left.

Therefore the number of marbles taken by Sally's friends is 180-75 = 105 marbles

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Answer:

21

Step-by-step explanation:

The median is the middle so you list them from least to greatest like so : 15, 16, 18, 19, 20, 20, 21, 21, 21, 22, 24, 27, 48. You then would find the middle number which is 21 in this particular situation.

Hope this helped

There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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The equation X^2 + Y^2 + Z^2 = 4 represents a sphere in Cartesian coordinates. In spherical coordinates, this equation can be expressed as ρ^2 = 4, where ρ is the radial distance from the origin.

The equation X^2 + Y^2 + Z^2 = 4 represents a sphere with a radius of 2 units in Cartesian coordinates. To express this equation in spherical coordinates, we need to convert the Cartesian variables (X, Y, Z) into spherical variables (ρ, θ, φ).

In spherical coordinates, ρ represents the radial distance from the origin, θ represents the azimuthal angle (measured from the positive x-axis), and φ represents the polar angle (measured from the positive z-axis).

To rewrite the equation X^2 + Y^2 + Z^2 = 4 in spherical coordinates, we replace X with ρ sin(φ) cos(θ), Y with ρ sin(φ) sin(θ), and Z with ρ cos(φ). Substituting these values, we obtain (ρ sin(φ) cos(θ))^2 + (ρ sin(φ) sin(θ))^2 + (ρ cos(φ))^2 = 4.

Simplifying this equation, we have ρ^2 sin^2(φ) (cos^2(θ) + sin^2(θ)) + ρ^2 cos^2(φ) = 4. Since cos^2(θ) + sin^2(θ) = 1, we can further simplify the equation to ρ^2 sin^2(φ) + ρ^2 cos^2(φ) = 4.

Finally, recognizing that sin^2(φ) + cos^2(φ) = 1, we arrive at the equation ρ^2 = 4, which represents a sphere with a radius of 2 units in spherical coordinates.

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angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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Answer:

True , null

Step-by-step explanation:

Mostly the true hypothesis is the null hypothesis .

We test the true hypothesis , the null hypothesis  against the claim provided which is named as alternate hypothesis.

When the false hypothesis is the null hypothesis , type II error is made.

Confounded in statistics means when the alternative explanations cannot be eliminated.But we have the alternate hypothesis in hypothesis testing.

So option 1 is correct

Answer:

\(x^{2} -xz-xy+yz\)

Step-by-step explanation:

To answer this question we have to multiply each value of a bracket by every value from the other bracket!

It is super important to make sure that we take in consideration the operations of each value

Firstly, we are going to multiply the x in the first bracket by every value in the other bracket...

Now we are going to multiply the \(-y\) by everything in the other bracket...

This leaves us with \(x^{2} -xz-xy+yz\)

Hope this helps, have a lovely day! :)

Given:

Face value = $101,000

Carrying value = $97,900

Bonds call price = $95,500

Find:

Gain or loss on retirement = ?

So, the formula to find the gain or loss on retirement is:

Carrying value – bonds call price

Substituting their values, we get:

$97,900 - $95,500

= $2,400

The journal entries are:

Dr Bonds payable $101,000

Dr Gain on retirement of bonds $1,200

Cr Cash $95,500

Therefore, you gained $2,400 on retirement.

To add, when a bond is retired at any time before its maturity date, it is said to be retired early.

Based on this model, we can say that accounting for bonds retired at maturity is pretty straight forward: the company pays out cash and removes the bond payable from its balance sheet.

The figure shown would represent a parallelogram if opposite sides are parallel and congruent

It is true that the figure is a parallelogram

The coordinates of the figure are given as:

O = (0,0)

P = (a,b)

S = (a + c,b)

T = (c,0)

Vertices O and T are on the same horizontal level, because they have the same y-coordinate

The above is also applicable to vertices P and S

By observation, we have the following distances:

PS = c

OT = c

This means that the opposite sides are parallel and congruent

Hence, the figure is a parallelogram

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The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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Answer: k=-4

Step-by-step explanation:

1/4k +3 =2

k+12=8

k=-4

In the equation:\( \frac{1}{4k} + 3 = 2\)

Collect like terms:

\( \frac{1}{4k} = 2 - 3 \\ \frac{1}{4k} = - 1\)

Cross Multiply

\( - 4k = 1\)

Divide both sides by \( - 4\)

\( \frac{ - 4k}{ - 4} = \frac{1}{ - 4} \)

Final answer: \(k = - \frac{ 1}{4} \)

The z-table based on the information is C. (0.09 0.16) ±1.96 √0.09(1-0.09) 250+0.16(1 0.16) 250

The confidence interval is CI = (p1 - p2) ± Z * ✓((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where:

p1 and p2 are the proportions of clothes that receive a rating of 7 or higher for detergent A and detergent B, respectively.

n1 and n2 are the sample sizes for detergent A and detergent B, respectively.

Z is the critical value from the z-table corresponding to the desired confidence level (90% in this case).

Therefore, the value will be:

= (0.912 - 0.84) + 1.645 ✓0.912(1 - 0.912)/250 + 0.84(1 - 0.84)/250

= (0.072, 0.148)

The correct option is C

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When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

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Answer: 24+12=36

Step-by-step explanation:

36= _+_

2x(2 times)

x

X+2x=36

3x=36

12

12+2(12)=36

12+24=36

Answer:

Step-by-step explanation:

From, the given word explanation try to create your own equation like

From, equation (1) solve for x

Substitute, equation (3) to equation (2).

Answer:

The answer is

Step-by-step explanation:

\( {3}^{x} = 5\)

Take logarithm of both sides of the equation

That's

\( log(3)^{x} = log(5) \)

Using the rules of logarithms

\( log(3)^{x} = x log(3) \)

So we have

\(xlog(3) = log(5) \)

Divide both sides by log 3

We have

\(x = \frac{ log(5) }{ log(3) } \)

We have the final answer as

1.46497

which is

1.46 to 2 decimal places

Hope this helps you

The number of weak compositions of 2n into 2k parts from which 2 are even and the others are all odd can be found by using the following formula:

C(2n - 2k + 2k - 2, 2k - 2) * C(2k - 2, 2)

Where C(n, k) is the binomial coefficient, which can be calculated as:

C(n, k) = n! / (k! * (n - k)!)

So, for the given example where n = 4 and k = 3, the number of weak compositions would be:

C(2 * 4 - 2 * 3 + 2 * 3 - 2, 2 * 3 - 2) * C(2 * 3 - 2, 2) = C(8, 4) * C(4, 2) = 70 * 6 = 420

Therefore, the number of weak compositions of 2n into 2k parts from which 2 are even and the others are all odd is 420.

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Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is \(0.78\).

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

For a family living in Southern Mississippi, the probability of owning a dog is \(0.4\), the probability of owning a cat is \(0.5\), and the probability of owning both a cat and a dog is \(0.12\).

Probability od owing a dog is

\(P(A)=0.4\)

Probability of owing a cat is

\(P(B)=0.5\)

Probability pf owing both a cat and a dog is

\(P(A\)∩\(B)=0.12\)

As we know,

\(P(A\)∪\(B)=P(A)+P(B)-P(A\)∩\(B)\)

\(P(A\)∪\(B)=0.4+0.5-0.12\)

\(P(A\)∪\(B)=0.78\)

Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is \(0.78\).

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