Given △ FDR≅△ TGH, what is the value of x? Please make sure to show all your work.

(please help me)

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

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Answer:

P = 48°

Step-by-step explanation:

Its an isosceles triangle so angle M and angle N are the same since they are the opposite angles to the sides that have the same measurement. so it would

180 - (66)2 = angle P

Sorry if you dont understand what i mean

Answer:

We can use the Pythagorean theorem to solve this problem. Let's assume that Cari's house is at point A, the airport is at point B, and her grandparents' house is at point C. We know that the distance from A to B is 45 miles and the distance from A to C is 45 miles. We want to find the distance from B to C, which we can call x.

We can form a right triangle with sides AB, AC, and BC. The distance we want to find, x, is the length of the hypotenuse of this triangle (side BC).

Using the Pythagorean theorem, we know that:

AB^2 + AC^2 = BC^2

Substituting in the values we know:

45^2 + 45^2 = x^2

Simplifying:

2025 + 2025 = x^2

4050 = x^2

Taking the square root of both sides:

x = sqrt(4050)

x is approximately equal to 63.64 miles (rounded to two decimal places).

Therefore, the direct distance from the airport to Cari's grandparents' house is approximately 63.64 miles.

r=I × 100÷pxt

8200×100÷ 11406×4

820000÷. 45624

17.97

make me brainliest .

The general solution to the differential equation is:
x/y^5 - 2y^3 - (1/6)x/y^3 + C = 0

To find the general solution of the given differential equation:

y dx − 6(x + y^8) dy = 0

First, we need to check if the equation is exact. To do this, we find the partial derivatives of the function with respect to x and y:

∂/∂y (y) = 1
∂/∂x (-6(x + y^8)) = -6

Since these partial derivatives are not equal, the equation is not exact.

Next, we need to find an integrating factor, denoted by μ, to make the equation exact. We can do this by multiplying both sides of the equation by μ:

μy dx − 6μ(x + y^8) dy = 0

To make the equation exact, we need to find μ such that:

∂/∂y (μy) = ∂/∂x (-6μ(x + y^8))

Expanding these partial derivatives and simplifying, we get:

μ = e^(int(-6/(y),dy))

Integrating with respect to y, we get:

μ = e^(-6ln|y|) = 1/y^6

Multiplying both sides of the original equation by μ, we get:

y^-5 dx - 6(x/y^6 + y^2) dy = 0

This equation is exact, so we can find the solution by integrating:

f(x,y) = ∫(y^-5)dx = x/y^5 + g(y)

Taking the partial derivative of f with respect to y and setting it equal to the remaining term in the equation:

∂/∂y (x/y^5 + g(y)) = -6y^2

-5x/y^6 + g'(y) = -6y^2

g'(y) = -6y^2 + 5x/y^6

Integrating both sides with respect to y, we get:

g(y) = -2y^3 + (-1/6)x/y^3 + C

where C is the constant of integration.

Thus, the general solution to the differential equation is:

x/y^5 - 2y^3 - (1/6)x/y^3 + C = 0

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Answer:

there are 13 newspapers per pile

Step-by-step explanation:

to find newspapers per pile we divide 39/ 3

39/3= 13

Answer:

29/56

Step-by-step explanation:

Here we're combining two fractions of different denominators, 7 and 8.  The LCD is the product of 7 and 8:  56.

1/7 is rewritten as 8/56 and 3/8 as 21/56.

Summing these up, we get 29/56

The number of groups formed is 10 if we consider 5 cars in groups of 3.

Given, 5 cars in groups of 3, we can use the formula,

(5 3) = 5! / 3! × 2!

= 10

Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.

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Possible translations such that the graph passes through the point (1,2) are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Two possible translations for the function to pass through the point (1,2) are given as follows:

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The statements that describe a triangular prism are:

A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.

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The area bounded by the graphs of y = x² + 17 and y = 0 over the interval -3 ≤ x ≤ 3 is 120 square units.

To find the area bounded by the two graphs, we need to calculate the definite integral of the difference between the upper function (y = x² + 17) and the lower function (y = 0) over the given interval.

Integrating the difference of the two functions, we have:

∫[from -3 to 3] (x² + 17 - 0) dx

Simplifying, the integral becomes:

∫[from -3 to 3] (x² + 17) dx

To evaluate this integral, we can use the power rule of integration. Integrating x² gives us (1/3)x³, and integrating the constant term 17 gives us 17x.

Applying the limits of integration, the integral becomes:

[(1/3)x³ + 17x] from -3 to 3

Evaluating the expression at the upper limit (x = 3) and subtracting the expression at the lower limit (x = -3), we get:

[(1/3)(3)³ + 17(3)] - [(1/3)(-3)³ + 17(-3)]

Simplifying further:

[(1/3)(27) + 51] - [(1/3)(-27) - 51]

= [9 + 51] - [-9 - 51]

= 60 + 60

= 120

Therefore, the area bounded by the two graphs is 120 square units.

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Using the piece-wise function f(-1) = 1

A piece-wise function is a function that is defined on a sequence of intervals.

Given the piece wise function defined by

f(x) = x + 2 if x < 2 and x + 1 if x ≥ 2. We desire to find f(-1). We proceed as follows.

To find f(-1), since -1 is in the interval x < 2, we use the value of the function f(x) = x + 2

So, substituting x = -1 into the equation, we have that

f(x) = x + 2

f(-1) = -1 + 2

= 1

So, f(-1) = 1

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Answer:

10

Step-by-step explanation:

The measure of an angle∠I  is 10 degrees between the 450 cm and 640 cm sides.

The Law of Cosines (also called the Cosine Rule) is defined as it relates all three sides of a triangle with an angle of a triangle.

c² = a² + b² − 2ab cos(C)

The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. it relates the lengths of the sides of a triangle to the cosine of one of its angles.

In the given triangle ΔHIJ,

Sides:

h = 450 m

i = 210 m

j = 640 m

The angle of ∠I  is 10 degrees between the 450 cm and 640 cm sides.

According to the cosine rule,

j² = h² + i² − 2ab cos(I)

Substitute the values in the Cosine Rule,

450² = 210² + 640² - 2(210)(640)cos(I)

After solving we get the value of  angle ∠I :

∠I = 9.56038°

Rounded to the nearest degree.

∠I = 10°

Thus, the measure of an angle∠I  is 10 degrees.

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The inequality solved by Aaron is (a) |x + 2| < 3

The attached graph represents the missing piece in the question.

From the graph, we can see that:

The value of x starts from -5 and ends at 1

Calculate the mean of these values

Mean = (1 - 5)/2 = -2

Calculate half the difference of these values

Difference = (1 + 5)/2 = 3

The inequality is then represented as:

|x - Mean| < Difference

This gives

|x + 2| < 3

Hence, the inequality solved by Aaron is (a) |x + 2| < 3

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Answer:

answer us the first option just took test

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

According to the rules of the distributive property, you have to multiply the term outside of the parentheses with the terms inside the parentheses first.

1. 2(-5)=-10    

2. 2(3)=6

The terms that we have are now -10 and 6. Add them together to get the final answer.

-10+6=-4

Answer:

is there any more information

The data set represents the time in minutes that takes 8 students of the class to get to school in the morning.

1) To calculate the mean of the data set you have to add all observations and divide it by the number of observations, following the formula:

X[bar] is the mean

xi represents the i-observation

n is the total observations

The mean value of the data set is 10.75 minutes, this means that the average commute time to school for the students of Mts Evans class is 10.8 minutes.

2) The median is the value of the sample that divides it into two halves. To determine the median of the data set, the first step is to calculate its position. To calculate the position of the median for n even sample you have to use the following formula:

Our sample size is n=8, so the position of the median is:

This value indicates that the median is the 4th observation of the data set.

The next step is to order the data set from least to greatest and then localize the fourth observation:

Counting from the left, the 4th observation is 10 minutes.

So the median of the data set is Me=10 minutes

As per the given distance, he surrounded around 20 miles

Here we have given that Pete drives from his house to the store and then to the fair.

While we have given the distance covered by the Pete driver as,

=> 6, 5, 4, 3, 2

Then the total travelling distance is calculated by sum up all the details,

Then  we get,

=> 6 + 5 + 4 + 3 + 2

=> 20 units.

Here we have also given that 1 unit is equal to 1 miles.

Therefore, the resulting distance is 20 miles.

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The piecewise function that gives his velocity is graphed at the end of the answer.

A piecewise function is a function that has different definitions, depending on the input.

Between 0 and 5 minutes, the velocity increases steadily, from 0 to 35 mph, hence the function is:

v = (35/5)t

v = 7t, 0 ≤ t ≤ 5.

Between 5 and 10 minutes, the velocity remains constant at 35 mph, hence:

v = 35, 5 ≤ t ≤ 10.

At the 10 minute mark, his speed decreases to 20 mph for 2.5 minutes, hence:

m = (20 - 35)/2.5

m = -6.

v = 35 - 6(t - 10), 10 ≤ t ≤ 12.5. (considering that the velocity was at 35 mph at t = 10s).

Between 12.5 and 17.5 minutes, the velocity remains constant at 20 mph, hence:

v = 20, 12.5 ≤ t ≤ 17.5.

After 17.5 minutes until 20 minutes, the velocity decays from 20 to 0, in 2.5 minutes, hence the slope is:

m = -20/2.5 = -8.

The function is:

v = 20 - 8(t - 17.5), 17.5 ≤ t ≤ 20.

Taking these different definitions, the graph of the function is given at the end of the answer.

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Step-by-step explanation:

since the arc angle VTW = 125°, and the line UTW is clearly a diameter through the circle T, then the arc angle UTV is the supplementary angle to VTW. that means they cover a half-circle and therefore 180°.

arc angle UTV = 180 - arc angle VTW =

= 180 - 125 = 55°

The price per pound of sand is 35 cents.

Given: 3 tons of sand cost $2,100.

To find the price per pound, we have to convert 3 tons to pounds.

We know that 1 ton is equal to 2000 pounds.

So, 3 tons = 3 x 2000 = 6000 pounds.

Now we can find the price per pound by dividing the total cost by the number of pounds.

We have,

Total Cost = $2,

100Number of Pounds = 6,000Price per Pound = ?

To find the price per pound, we will use the formula,

Cost per pound = Total cost / Number of pounds

Plugging in the given values,

Price per Pound = 2,100 / 6,000Price per Pound = 0.35 dollars.

Now we have to convert the price per pound into cents because 1 dollar equals 100 cents.

Therefore, the price per pound is 0.35 x 100 = 35 cents per pound.

Therefore, the price per pound of sand is 35 cents.

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Answer:

20m

Step-by-step explanation:

Given the formula that modelled the height given as;

h=30+40t-5t^2

At t = 4s

h=30+40(4)-5(4)^2

h = 30+160-80

h = 160-60

h = 110m

At t = 2s

h=30+40(2)-5(2)^2

h=30+80-20

h = 110-20

h= 90m

Difference in height = 110-90 = 20m

Hence the height is 20m higher above the ground at 4s than at 2s

Answer:

A and D

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

given 2 intersecting chords inside a circle then the product of the parts of one chord is equal to the product of the parts of the other chord , that is

16(5x - 11) = 38.4 × 10 = 384 ( divide both sides by 16 )

5x - 11 = 24 ( add 11 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

4.5 : i think thats the answer i don't know

No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.

The SSS congruence theorem  expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.

Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.

From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.

Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.

So, given triangle is proved to congruent by SAS congruency not by SSS congruency.

Hence, enough information is not given.

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To evaluate the integral ∫tan^4(x) cos^5(x) dx, we can use trigonometric identities to simplify the integrand.

We'll use the power-reducing formula for tan^4(x) and the power-reducing formula for cos^5(x) to simplify the integrand:

∫tan^4(x) * cos^5(x) dx

= ∫(tan^2(x))^2 * (cos^2(x))^2 * cos(x) * cos^2(x) dx

= ∫[(sec^2(x) - 1)^2] * [(1 - sin^2(x))^2] * cos(x) * cos^2(x) dx

Expanding the square terms, we get:

= ∫[(sec^4(x) - 2sec^2(x) + 1)] * [(1 - 2sin^2(x) + sin^4(x))] * cos(x) * cos^2(x) dx

Multiplying the terms together, we have:

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

Now, let's integrate each term separately:

∫sec^4(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 + u^2)^2 * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(1 + 2u^2 + u^4 - u^4 - u^6) du

= u + 2/3 u^3 + 1/5 u^5 - 1/7 u^7 + C

Substituting back u = sin(x), we have:

= sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x) + C

∫-2sec^2(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫-2(1 + u^2) * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(-2 + 2u^2 - 2u^2 + 2u^4) du

= -2u + 2/3 u^3 - 2/5 u^5 + 2/7 u^7 + C

Substituting back u = sin(x), we have:

= -2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x) + C

∫cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 - u^2) du

Integrating, we get:

= u - 1/3 u^3 + C

Substituting back u = sin(x), we have:

= sin(x) - 1/3 sin^3(x) + C

Putting it all together, the complete result of the integral is:

∫tan^4(x) * cos^5(x) dx

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

= ∫sec^4(x) *

cos^3(x) dx - 2∫sec^2(x) * cos^3(x) dx + ∫cos^3(x) dx

= (sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x)) - 2(-2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x)) + (sin(x) - 1/3 sin^3(x)) + C

= sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

Therefore, the final result is:

∫tan^4(x) * cos^5(x) dx = sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

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we have the expression

we have that

Using the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer.

so

We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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