45% of all 1st graders at Sierra Elementary School are female students. This year there are 54 female 1st graders at Sierra Elementary School. How many 1st graders are there at Sierra Elementary School this year?

The derivative of y with respect to x is cos²x. To find the derivative of y = Sx⁴ 0 cos²θdθ, we need to apply the fundamental theorem of calculus and the chain rule of differentiation.

First, let's rewrite the integral in terms of x:

Sx⁴ 0 cos²θdθ = ∫₀ˣ cos²θ dθ

Now, we can use the fundamental theorem of calculus to find the derivative:

y = ∫₀ˣ cos²θ dθ

dy/dx = d/dx (∫₀ˣ cos²θ dθ)

By the chain rule, we have:

d/dx (∫₀ˣ cos²θ dθ) = d/dx (F(x)) = F'(x)

where F(x) = ∫₀ˣ cos²θ dθ

To find F'(x), we need to use the chain rule and the fundamental theorem of calculus again.

Let u = x, and let the integrand be f(θ) = cos²θ. Then, we have:

F(x) = ∫₀ˣ cos²θ dθ = ∫₀ᵡ f(θ) dθ

By the fundamental theorem of calculus, we know that:

d/dx (F(x)) = d/dx (∫₀ᵡ f(θ) dθ) = f(x) * dx/dx = f(x)

Using the chain rule, we have:

d/dx (F(x)) = d/dx (∫₀ᵡ f(θ) dθ) = f(x) * d/dx (x) = f(x)

Now, we need to find f(x), which is just cos²x.

Therefore, we have:

F'(x) = f(x) = cos²x

Finally, substituting F'(x) into the expression we obtained for y, we get:

dy/dx = F'(x) = cos²x

So the derivative of y with respect to x is cos²x.

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On that day, approximately 77.5% of the carpenters were at work.

To calculate the percentage of carpenters at work on a given day, we can use the following formula:

Percentage = (Number at Work / Total Number) * 100

Given:

Total number of carpenters = 40

Number of carpenters at work = 31

Using the formula:

Percentage = (31 / 40) * 100

Calculating the percentage:

Percentage = 0.775 * 100

Percentage = 77.5%

Therefore, on that day, approximately 77.5% of the carpenters were at work.

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Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

B. y = [x] + 7

Step-by-step explanation:

If you are going left on the x-axis your sign would be positive

Answer:

50 inches

Step-by-step explanation:

Given that

5 equal sized square shelves arranged in a column.

Total area of five shelves = 500 sq inches

To find:

Length of shelving unit = ?

Solution:

First of all, let us find the area of each shelving unit.

Area of each shelving unit = Total area of five shelved divided by 5

Area of each shelving unit = 500 \(\div\) 5 = 100 sq units.

Each shelving unit is of square shape and area of a square is given as:

Area = \(Side^2\)

100 = \(Side^2\)

So, side of shelve = 10 inches

Now, there are 5 squares in the shelving unit.

So, length of shelving unit = \(10 \times 5 = \bold{50 \ inches}\)

The denominator of the simplified expression will be (9n² + 4).

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given below.

[(2 / 6n + 4)] [(3n + 2) / (3n – 2)]

On multiplication, we have

(6n + 4) / (18n² + 8)

(3n + 2) / (9n² + 4)

The denominator of the simplified expression will be (9n² + 4).

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The conjecture is that Sage saw approximately 43 black-hooded parakeets on the eighteenth day.

Based on the scatter plot provided, we can see that the line drawn is a linear regression line that approximates the relationship between the number of days and the number of parakeets Sage sees. To write the equation of this line in slope-intercept form, we can use the slope formula:

slope = (change in y)/(change in x) = (y2-y1)/(x2-x1)

Using two points from the line (5, 17) and (12, 31), we get:

slope = (31-17)/(12-5) = 14/7 = 2

Now that we have the slope, we can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.

Using the point (5, 17), we get:

y - 17 = 2(x - 5)

Simplifying, we get:

y = 2x + 7

This is the equation of the line that approximates the relationship between the number of days and the number of parakeets Sage sees.

To make a conjecture about the number of parakeets she saw on the eighteenth day, we can simply plug in x=18 into the equation:

y = 2(18) + 7

y = 43

Therefore, our conjecture is that Sage saw approximately 43 black-hooded parakeets on the eighteenth day.

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The equation to find the entrance cost is 5(c + 3) = 85.

Given that 5 five friends made plan for trip, which will cost them a total of $85,

This includes a $3 fee added to each entrance ticket to cover the cost of a pair of grip socks.

We need to establish an equation to find c, the cost of an entrance ticket,

So,

The total cost of one entrance ticket = c + 3,

So, for 5 people = 5(c+3)

Now, this is equal to 85.

So the equation is = 5(c + 3) = 85.

Hence the equation to find the entrance cost is 5(c + 3) = 85.

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Answer:

26%

Step-by-step explanation:

10/39 + 100% = 25.64102%

nearest percent, 26%

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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False. We do not always evaluate just the specific result obtained in an experiment.

In scientific experiments, we do not just evaluate the specific result obtained in the experiment. Instead, we evaluate the entire experimental design, including the methods used, the sample size, and the statistical analysis.

For example, suppose a researcher conducts an experiment to test a new drug's effectiveness in treating a particular disease. If the result of the experiment shows that the drug is effective, the researcher cannot simply conclude that the drug works based on this one result. Instead, the researcher must evaluate the experimental design to ensure that the result is reliable and valid.

This evaluation includes examining the study's methods to determine if they are appropriate and if the sample size is large enough to produce meaningful results. It also involves statistical analysis to assess the strength of the relationship between the treatment and the outcome and to determine if the result is statistically significant.

Therefore, evaluating just the specific result obtained in an experiment is not sufficient. We must also consider the experimental design, methods used, sample size, and statistical analysis to draw valid and reliable conclusions from the experiment.

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By AA similarity Triangle ABC and DEF are similar.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

First in Triangle ABC

using Angle Sum Property

<C= 180 - <A - <B

<C = 180 - 77 - 48

<C = 55 degree

and, In Triangle DEF

using Angle Sum Property

ND= 180- <E- <F

<D = 180- 55 - 48

<D = 77

As, In both Triangle ABC and DEF all angles triangles are Equal.

<A = <D= 77

<B = <E = 48

<C = <F= 55

So, by AA similarity Triangle  ABC and DEF are similar.

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The mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y

The solution of the equation is given as

10x - 3y = 6

      +3y     +3y

----------------------------

10x = 3y + 6

-6           -6

----------------------------

(10x - 6)/3 = 3y/3

10x - 2 = y

In the above steps, we have the following equation

(10x - 6)/3 = 3y/3

When the above equation is expanded, we have

10x/3 - 6/3 = 3y/3

Evaluate the quotient in the above equation

So, we have

10x/3 - 2 = y

The abvoe equation is different from Mike's result

Hence, the mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y

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A planning phase for an engineering component generated 80 engineering drawings. The QA team randomly selected 8 drawings for inspection. This exercise can BEST be described as example of random sampling.

The exercise can be described as an example of random sampling, which is a statistical technique used to select a subset of individuals or items from a larger population, in a way that each member of the population has an equal chance of being selected. In this case, the 80 engineering drawings represent the population, and the QA team randomly selecting 8 of them for inspection is a form of random sampling.

By selecting the drawings randomly, the QA team can get an unbiased representation of the population and make inferences about the quality of the engineering component as a whole based on the inspection results of the selected subset.

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Answer: 1.25

Step-by-step explanation:

Answer:

-3h+8

Step-by-step explanation:

-5h+2h+8

-3h+8

Answer:

12

Step-by-step explanation:

Divide both sides by 6 to isolate x

Answer:12

Step-by-step explanation:

divide 6 from 72

Answer:

Yes

Step-by-step explanation:

For lines to be parallel alternate interior angles should be equal

Angle GHD=180-angle FHD

=180-115 = 65°

Therefore angle AGH = angle GHD

So lines are parallel

Step-by-step explanation:

\( \angle H = 115 \degree ... (vertical \: \angle s) \\ \angle H + 65 \degree \\ = 115 \degree + 65 \degree \\ = 180 \degree \\ \)

Therefore by interior angle test,

\(line \: AB || \: line \: CD\)

Answer:

56.7

Step-by-step explanation:

2.7 x 21 = 56.7

Answer:

32%

Step-by-step explanation:

50-34=16

16/50=0.32

0.32 x 100= 32

There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.

For d=7, we can see that:

3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.

For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.

In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.

However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.

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Step-by-step explanation:

the lengths OB, OC & BC together forms a isosceles triangle.

therefore,

OB=OC

3x+4=x+8

2x=4

x=2.

OB = 3x+4= 3.2+4=10cm.

OC= x+8= 2+8=10cm.

therefore, the diagonals are : 20cm each.

hope this helps you.

Answer:

18: x<32/5 19: c>-202

Step-by-step explanation:

\(x < \frac{32}{5}\\\)

\(c > -202\)

Solving \(x +\frac35 < 7\\\):

\(x +\frac35 < 7 \\ x +\frac35 -\frac35 < 7 -\frac35 \\ x < \frac{35}{5} -\frac35 \\ x < \frac{32}{5}\)

Solving for \(4 < 206 +c\):

\(4 < 206 +c \\ 206 +c > 4 \\ 206 +c -206 > 4 -206 \\ c > -202\)

Expected counts are calculated by the test of independence and also by using Homogeneity.

The main difference between a test of independence and a test of uniformity when analyzing voting results from a two-page table is how the expected count is calculated.

The test of independence calculates expected frequencies assuming no relationship between the two variables analyzed and is based on the marginal totals of the two-way table.

Independence tests are used to know whether there is a significant association between two variables or not.

Homogeneity tests, on the other hand, compute expected frequencies assuming that the two groups being compared have the same distribution for the variable being analyzed, based on the row sums of a two-way table.

Homogeneity tests are used to know whether there is a  difference in the distribution of a categorical variable between groups.

The number of columns and rows in the two-way table and the number of samples obtained are important factors to consider when performing both tests.

However, how the expected count is calculated is the main difference between the two tests. The degrees of freedom are also calculated differently for the two tests, but this is secondary. 

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Answer:

c is the correct answer

Step-by-step explanation:

Answer:

0.058

Step-by-step explanation:

Give an example of a proportion that uses the numbers 2, 3, 4 and 6.

2:3 is the same as 4:6

Proportion says that two ratios (or fractions) are equal.

Answer:

3 is the answer

hope this helps

have a good day :)

Step-by-step explanation: