Which expressions(s) is equivalent to

(7^2)^5 • 7^4?


A. 7^2•^5+^4
B. 7^3(^5+^4)
C. 7^2+^5+^4
D. 7^2+^5•7^4

Answer:

x= 12.714°

Step-by-step explanation:

<AEB + <CED = 90°

4x+1+3x = 90°

7x+1= 90°

7x=89

x= 12.714°

In the grating equation nλ=d sin θ, the quantity θ will be determined in the lab by using meter sticks and geometry/trigonometry

The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign

Here we have given that the grating equation nλ=d sin θ, the quantity θ will be determined in the lab.

The term grating equation in math states that d = 1/N where N is the grating constant, and it is the number of lines per unit length and n is the order of grating, which is a positive integer, representing the repetition of the spectrum.

And the term trigonometry is defined as a branch of mathematics concerned with relationships between angles and ratios of lengths.

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On solving the provide outlier question, we can say that The difference between the upper and lower fourth makes up the fourth outlier (h) = 73.7 - 22.2 = 51.5

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller range than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.

Here,

a) The data values should now be sorted from smallest to largest:

22.2 40.4 16.4 73.7 36.6 109.9

b) The sorted data set's median is its middle value. The median is the sixth data value in the sorted data set because there are 11 data values total:

m = 36.6

c) The median of the data values below the median, or at 25% of the data, is in the lower fourth.

The lower fourth is the third data value because there are 5 data values below the median.

d) The data value 6 + 3 = 9 represents the third quartile.

Q{3} 73.7

The difference between the upper and lower fourth makes up the fourth outlier (h):

73.7 - 22.2

51.5

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Answer:

24-6v-24x

Step-by-step explanation:

(-4 +v + 4x) × (-6)

Apply the Distributive Property:

- (-6) × 4+ (-6) × v + (-6) × 4x

Determine the sign:

6 × 4 - 6v - 6 × 4x

Calculate the product or quotient:

24 - 6v -6 × 4x

Multiply the monomials:

24 - 6v - 24x

Hope this helps you :)

Answer:

24-6v-24

Step-by-step explanation:

first distribute -6 to all other numbers as shown below.

(-4 . -6)+(v . -6)+(4x . -6)

then we will get 24-6v-24x

If henry can  70 words in 5 minutes and that in 8 minutes he can type 112 words the rate of change is 14.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Henry can type 70 words in 5 minutes and that in 8 minutes he can type 112 words.

m=112-70/8-5

=42/3

=14

Hence, the rate of change is 14.

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Therefore ,as a result, 42/5 is the value of the first term in the equation for the arithmetic mean.

The arithmetic average or means of the group is calculated as the sum of each value in a list divided by the total number of things in that list. The progression in mathematics is the same as this. The average of the integers 5, 7, and 9 is 4, as shown by the equation 5 + 7 + 9 being equal to 21, and 21 divided by 3 (there are actually three numbers) being equal to 7.

Here,

Given :

5 a + 10 d = 70 in the first five terms (1)

The first ten terms add up to 10 a + 45 d = 210. (2)

This means that in order to solve the system for a, multiply equation (1) by 2, then subtract it from equation (2):

=> 10a - 10a + 45d - 20d = 210-140

=> 25d = 70

=> d = 70/25

=> d = 14/5

A value then becomes:

5a + 10*14/5 = 70;

5a = 70-140/5;

5a = 350-140/5;

a = 42/5.

42/5 is the response.

As a result, 42/5 is the value of the first term in the equation for the arithmetic mean.

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The amount of  energy must be removed from the drink for it to reach this temperature is 35.5kJ

Here we have given that a 12oz can of soft drink at 25c is placed in a freezer where the temperature is -12c.

As we all know that the equation of the given measurement is written as,

=> Q1=m.c.AT

From the given, now we have to know that the mass "m" = 340gm

And the value of C= 4.18 J/g°C

Then at 25°C it will at the temperature of

=> Q1340g x 4.18 x 25

=> Q1 = 35, 5300J or 35.5kJ

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Answer:

5/4 should be the answer.

Step-by-step explanation:

2 divided by 8/5 = 5/4

Answer:

Step-by-step explanation:

x is 5/4

8x/5=2

8x=10

x=5/4

The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).

This gradient is a vector pointing in the direction of the function f(x, y, z) = log(x2 + y2 + z2 )'s rate of growth. Calculating the function's partial derivatives with respect to x, y, and z is necessary to assess this gradient.

The function's partial derivative with regard to x is (2x / (x2 + y2 + z2) This becomes 2/1 when x is 1. The partial derivative with regard to z is (2z / (x2 + y2 + z2)), which becomes 2/1 when z is 1, and the partial derivative with respect to y is 0, and the partial derivative with respect to z is 0, respectively. Therefore, at (1, 0, 1), the gradient of f(x, y, z) = log(x2 + y2 + z2) is (2/1, 0, 2/1).

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Answer:

the solution is u5/2

Using the central limit theorem to find the mean is 5.4 and the standard error of the mean of the indicated sampling distribution is 0.6.

We must utilize the central limit theorem to determine the mean and standard error of the mean of the sample distribution in the given query.

Considering the posed query,

The company has a mean age of 5.4 years and is normally distributed.

2.1 years of standard deviation.

The population is sampled at random with an n = 12 size, and the mean of each sample is calculated.

The mean is determined using the central limit theorem.

μ(x) = μ = 5.4

The standard error of the mean of the indicated sampling distribution is:

σ(x) = σ/√n

σ(x) = 2.1/√12

σ(x) = 2.1/3.5

σ(x) = 0.6

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Answer: $23,800

Step-by-step explanation:

It was worth $37,000 at first and now it's worth $1800.

So we have 37,000 - 1800 = $35,200 that left away.

And we know that 8 years passed away.

So we have 35,200/8 = $4400 each year.

We are looking for 3 years later.

So we have 440*8 = $13,200 that left after 3 years.

And lastly, it's worth 37,000 - 13200 = $23,800 3 years later.

To find the general solution of the given differential equation x dy/ dx − y = x^2 sin x, we must use a series of calculations.

First, we need to separate the variables, so y can be expressed as a function of x. To do this, we divide both sides of the equation by x, giving us the equation dy/dx = x sin x + y/x.

Next, we will need to use integration to find the general solution. To integrate, we need to find an antiderivative of the equation dy/dx = x sin x + y/x. To do this, we can use the formula ∫xdx = 1/2 x^2 + c. Using this formula, we can integrate both sides of the equation to get 1/2 x^2 + c = x sin x + ∫ y/x dx.

We can then solve for the antiderivative of y/x, which is ln|y| + c. Therefore, the general solution of the equation is 1/2 x^2 + ln|y| + c = x sin x + c.

Finally, we can solve for y in terms of x to get y = x^2 sin x + c'e^(1/2 x^2), where c' is the integration constant. This is the general solution of the given differential equation.

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The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%. Multiply the result by 100 to get the annual yield in percentage: 0.0415 x 100 = 4.15%

Annual dividend per share: $3.60

Annual yield: 4.15%

1. To find the annual dividend per share, divide the increase in shares (1.6) by the number of shares owned before the reinvestment (400).

1.6/400 = 0.004

2. Multiply the result by the current share price of XOM ($86.40):

0.004 x 86.40 = $3.60

3. To find the annual yield, divide the annual dividend per share by the current share price of XOM ($86.40):

3.60/86.40 = 0.0415

4. Multiply the result by 100 to get the annual yield in percentage:

0.0415 x 100 = 4.15%

The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%.

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A stratified sample size is a method of sampling where the population is divided into homogeneous subsets and a sample is taken from each subset.

A stratified sample is a method of sampling where the population is divided into distinct subgroups, or strata, based on specific characteristics. This method of sampling ensures that each stratum is represented in the sample in the same proportion as it is in the population. This ensures that the sample is representative of the population. Stratified sampling is useful when the population is heterogeneous, which means that it is composed of subgroups that vary significantly in size or composition. By stratifying the population, it is possible to ensure that each subgroup is adequately represented in the sample. This method also helps to reduce sampling errors, which can occur if the sample is not representative of the population. Stratified sampling is a useful tool for researchers who want to accurately represent the population in their sample.

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Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.

It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.

The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.

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So,

The skateboard cost $67.

The protective helmet cost $25.

To find the percent that the price of the skateboard was out of the total amount, add 67 and 25 and divide 67 by the result.

Step 1:

67 + 25 = 92

Step 2:

67/92 = 0.728 or 72.8%.

The correct option is B.

Answer:200

Step-by-step explanation: when you multiply 81.7x2.68 it equals to 218.948 which to the nearest hundreth is 200

So, on solving the provided question we can say that the probability P(study) = 1/1-a

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

subjects selected  = a

not selected = 1-a

P(study) = 1/1-a

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Answer:

y=200/9. x= 329/9

Step-by-step explanation:

3x=-43-3y; x=-43/3-y. 5(43/3-y)-8y=5; y=200/9. x= 329/9

After completing the full turn around the circle by 42 participants as per given condition and number showing on the calculator the sum ends up with 0.

As given in the question,

Total number of participants = 42

Number of calculator = 3

Calculator that reads 1 dean pressed cube button

1³ = 1

Calculator that reads 0 dean pressed square button

0² = 0

Calculator that reads -1 dean pressed negation button

-(-1) = 1

Same activity repeated 42 times in the circle at the end number showed on the calculator are

Calculator reads 1 show 1

Calculator reads 0 show 0

Calculator reads -1 show -1

Sum of the three numbers are

= 1 + 0 + (-1)

= 0

Therefore, sum of the three numbers showing at the end on the calculator is equal to 0.

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The mechanical energy of the Jada and Aalisha systems at this point will be 2548 joules and 2205 joules respectively.

It is the sum of potential and kinetic energy. The mechanical energy is given as,

ME = mhg + 1/2 mv²

Jada and Aalisha are rock climbing, each moving up with a constant velocity of 1.0- Jada has a mass of 65 kg, and Aalisha has a mass of 75 kg. At one point, Jada is 4.0 m above the ground, and Aalisha is 3.0 m higher than Jada.

The mechanical energy of Jada is calculated as,

ME = 65 x 9.8 x 4

ME = 2548 joule

The mechanical energy of Aalisha is calculated as,

ME = 75 x 9.8 x 3

ME = 2205 joule

The mechanical energy of the Jada and Aalisha systems at this point will be 2548 joules and 2205 joules respectively.

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The best course of action would be to politely decline the offer and explain to your friend that you still have to finish the assignment.

Minutes is a record of the proceedings of a meeting or other event. It is typically written by the secretary of the meeting and contains a summary of the main points discussed, decisions taken, and any action points arising from the meeting. Minutes are an important part of any organization as they provide a record of the decisions taken and an opportunity for review. Minutes can also help to keep everyone on track and ensure that everyone is aware of their responsibilities.

Even though your friend may be disappointed, they will understand. It is important to prioritize your school work and stay on top of assignments, so you should continue to work on the task at hand.

If you find yourself struggling to stay focused, it can help to break down the assignment into manageable chunks and set a timer for each chunk. This can also help you stay on track with the time limit that your professor gave you. Additionally, taking a few minutes to get up and stretch or grab a snack can help you stay energized and productive.

If you need additional help, reach out to your professor or a tutor. You can also ask a classmate for help or advice. Your professor likely will not mind if you ask for an extension on the assignment, as long as it is reasonable and you provide a valid reason.

Remember, it is important to prioritize your school work and stay on top of assignments. It is ok to take breaks and accept help, but be sure to stay focused on the task at hand.

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Answer: The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass.

If the initial mass is 185 grams, after the first half-life, the mass will be reduced to 185/2 = 92.5 grams

After the second half-life, the mass will be reduced to 92.5/2 = 46.25 grams

After the third half-life, the mass will be reduced to 46.25/2 = 23.125 grams

So, after three half-lives, there will be 23.125 grams of the isotope left.

It's important to note that the half-life of the isotope is a constant value and it doesn't depend on the initial mass.

Step-by-step explanation:

Answer:

Step-by-step explanation:

83

To find the number of females who are not enrolled in Composition I, we can look at the table and find the total number of females and subtract the number of females who are enrolled in Composition I.

The total number of females is found in the "Column Totals" row, in the second column, and is 251.

The number of females enrolled in Composition I is found in the "Males" row, in the second column, and is 46.

So the number of females who are not enrolled in Composition I is:

251 (total number of females) - 46 (females enrolled in Composition I) = 205

Therefore, the answer is 83.

Answer:

91.1cm²

Step-by-step explanation:

since all of them are quarters of circles

area of figure 1 = (π(r.1)²)÷4 = (64π)÷4= 16π cm²

area of figure 2 = (π(r.2)²)÷4 = (25π)÷4= 6.25π cm²

area of figure 3 = (π(r.3)²)÷4 = (9π)÷4= 2.25π cm²

area of figure 4 = (π(r.4)²)÷4 = (4π)÷4= 4π cm²

area of figure 5 = (π(r.5)²)÷4 = (π)÷4 cm²

area of figure 6 = (π(r.6)²)÷4 = (π)÷4 cm²

the total area = 16π+6.25π+2.25π+4π+2(π÷4)=

28.5π+0.5π = 29π = 91.1cm²

The expression (-7*√3)*(11*√10) can be simplified to get:

-77*√30

Here we want to simplify the following expression:

(-7*√3)*(11*√10)

Remember that the square roots are distributive, this means that we can write:

√a*√b = √(a*b)

And also remember that we can perform a sequence of multiplications in any order we want, so we can reorder the factors of our expression

Now let's rewrite our expression:

(-7*√3)*(11*√10)

as:

(-7*11)*(√3*√10)

-77*√(3*10)

-77*√30

That is the expression simplified.

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Answer:

the angle that corresponds to AC IS PF

The probability is 7/72 that each of the final three rolls is at least as large as the roll preceding it.

Let [tex]N_{i}[/tex] represent the number appearing on die when die is rolled ith time,

i=1,2,3,4

Given that [tex]N_{1}[/tex]≤[tex]N_{2}[/tex]≤[tex]N_{3}[/tex]≤[tex]N_{4}[/tex]

Each time when a die is rolled, six options are there.

Let we have four equal sets

{1,2,3,4,5,6}, now we have to select four numbers such that, exactly one number is selected from each set

Case 1: All four are same

Number of ways:⁶C₁ =6

Case 2: Three are same but one is different

Number of ways: ⁶C₁ ⁵C₁ =30

Case 3: Two are same of one kind and two are same of second kind

Number of ways: [tex]\frac{1}{2}[/tex] ⁶C₁ ⁵C₁=15

Case 4: Two are same and two are different

Number of ways: ⁶C₁ ⁵C₂=60

Case 5: All four are different

Number of ways: ⁶C₄=15

Required probability:

=[tex]\frac{6+30+5+60+15}{6*6*6*6}[/tex]

=[tex]\frac{126}{36*36}[/tex]

=[tex]\frac{72}{7}[/tex]

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The reading of the angle sec θ in the second quadrant of the given problem is; Negative

There are 6 main trigonometric ratios and if we can use which are;

sin θ

cos θ

tan θ

secθ

cotan θ = sin θ/cosθ

cosec θ = 1/sin θ

sec θ = 1/cos θ

Now, we are told that sec θ is in the second quadrant and we know that in the second quadrant only sin θ and cosecθ are positive and as such  sec θ  will be negative.                                                        

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Step-by-step explanation:

y = 37 + x

the 4th angle (bottom right) is

360 - 90 - 90 - 125 = 55°

because the sum of all angles in any quadrilateral is 360°.

now we can assume a right-angled triangle on the right side of the trapezium.

one leg is 15 cm (like the left side), the other leg is x cm. and the right side of the trapezium is the Hypotenuse.

the bottom right angle is 55°.

the upper angle is 125 - 90 = 35°.

we can use the law of sine to get x.

the law of sine is

a/sin(A) = b/(sin(B) = c/sin(C)

with a, b, c being the sides of the triangle opposite of the corresponding angles A, B, C.

so,

15/sin(55) = x/sin(35)

x = 15×sin(35)/sin(55) = 10.50311307... cm

y = 37 + 10.50311307... = 47.50311307... ≈

≈ 47.5 cm