Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle 18 units units 36 units units

The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

According to the statement

we have given the statement and we have to show that the statement is a true or false after analyzing.

So, to analyse the statement

Context diagrams show the interactions between a system and other actors (external factors) with which the system is designed to interface. System context diagrams can be helpful in understanding the context .

But we know that the standardized names is not used within each set of symbols. so, this is used in a randomly sets.

that's why the given statement is not true in the case of the standardized names.

So, The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

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Rewrite the second expression as

[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]

and the third expression as

[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]

so the fractions all have the same denominator.

Then combining the fractions gives the desired result,

[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]

The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)

In accordance with space geometry, the lateral areas of the cone and cylinder are described by the following equations:

Cone

[tex]A_{l} = \pi \cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]     (1)

Cylinder

[tex]A_{l} = 2\pi\cdot r\cdot h[/tex]     (2)

If we divide (2) by (1), then we have the following ratio:

[tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]

The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)

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The simplification of the expression (2x - 3)(5x⁴ - 7x³ + 6x² - 9) is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

(2x - 3)(5x⁴ - 7x³ + 6x² - 9)

= 10x^5 - 14x⁴ + 12x³ - 18x - 15x⁴ + 21x³ - 18x² + 27

= 10x^5 - 14x⁴ - 15x⁴ + 12x³ + 21x³ - 18x² - 18x + 27

= 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

The simplified expression is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (f + g)(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(x) + g(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]

Using the t-distribution, it is found that there is not enough evidence that the diet is helping people lose weight.

At the null hypothesis, it is tested if the mean hasn't decreased, that is:

[tex]H_0: \mu_B \leq \mu_A[/tex]

[tex]H_0: \mu_B - \mu_A \leq 0[qtex]

At the alternative hypothesis, it is tested if the mean has decreased, that is:

[tex]H_1: \mu_B - \mu_A > 0[qtex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are:

The test statistic is:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{9.88 - 0}{11.66}[/tex]

t = 0.85.

Considering a right-tailed test with 9 + 9 - 2 = 16 df, with a standard significance level of 0.05, the critical value is t = 1.7459. Since t = 0.85 < 0.85, there is not enough evidence that the diet is helping people lose weight.

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Answer:

1083 seats

Step-by-step explanation:

this is an arithmetic sequence :

an = an-1 + c

in our case

a1 = 10 (10 seats in the first row)

a2 = a1 + 1 = 10 + 1 = 11

a3 = a2 + 1 = a1 + 1 + 1 = 10 + 1 + 1 = 12

an = an-1 + 1 = a1 + (n-1)×1 = a1 + n - 1 = 10 + n - 1 = 9 + n

a38 = a1 + 37 = 10 + 37 = 47 seats.

altogether this means the sum of the arithmetic sequence of a1 to a38.

the general sum of an arithmetic sequence from a1 to an is

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

Answer:

(-4, -2).

(0, 0).

Step-by-step explanation:

Both coordinates will be negative or (0.0).

It's these followings:

□(-4,-2)

□(0,0)

Hope this helps!

Answer:

41 years old

Step-by-step explanation:

2050-2022=28 years

13years old +28years = 41 years old (sorry if wrong)

Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).

Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).

The speed is:

S = 742.5ft

The distance that the parachutist falls in 5 seconds is:

D = 742.5ft

We know that the speed in free fall is:

S = 45 m/s.

We know that:

1 m = 3.3ft

Then we can rewrite the speed as:

S = 45 m/s = 45 *(3.28ft)/s = 148.5 ft/s

Then, the distance that the parachutist falls during 5 seconds is:

D = S*5s = (148.5 ft/s)*5s = 742.5ft

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The double number line which shows the other values of fat and protein is: option B.

A number line is a type of graph with a graduated straight line which contain numerical values that are placed at equal intervals along its length.

For the fat component, we have:

Fat = 2n = 0, 2, 4, 6, 8.

For the protein component, we have:

Protein = 11n = 0, 11, 22, 33, 44.

Note: n represent integers such as 0, 1, 2, 3 and 4.

In conclusion, the double number line which represent the other values of fat and protein is shown in the image attached below.

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Complete Question:

One serving of beef je-rky contains 2 grams of fat and 11 grams of protein. Complete the double number line to show the other values of fat and protein.

The solution to the expression [tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex] is [tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]

The expression is given as:

[tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex]

Take the LCM of the expression

[tex]\frac{8x^3 * 27x^3 - 4x * 27x^3 + 2 * 9x^2 - 1}{27x^3}[/tex]

Evaluate the products

[tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]

Hence, the solution to the expression [tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex] is [tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]

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Answer:

f(4) = 5

Step-by-step explanation:

Think about it this way

a point with an x value of 4,

this x value is put into the function,

then the function outputted a y value (or value) of 5.

So, we can name this function f(x)

Then,  we let x = 4,

then the output for f(4) = 5

Answer: f(4) = 5

Step-by-step explanation:

      If the point (4, 5) is on the graph of a function, this means that when you input 4 you get an output of 5.

      Inputs are usually shown with the x-coordinate, and outputs are usually shown with the y-coordinate.

      This means that (4, 5) is an input of 4 for an output of 5.

Similarities and differences between solving an absolute value equation and solving an absolute value inequality are shown below.

Similarities and differences between solving an absolute value equation and solving an absolute value inequality:

1) The absolute value equation of a number is simply the number's distance from zero.

2) Absolute value inequalities and linear inequalities share the fact that they both have two variables and so require a second equation to obtain the variables.

Therefore, the similarities and differences between solving an absolute value equation and solving an absolute value inequality are shown.

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Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.

Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).

Some Key features of systemic chemotherapy are-

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Answer: There were 78 bags of chips.

The group that have the longer average forearm length is group Y, because six children have a forearm length longer than 12 inches.

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

In group X, the highest arm length is 12 while in group Y, it is 13. This means that group Y would have longer arm lengths.

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Answer:

5.

Step-by-step explanation:

f(x)=x^4+12x^3+30x^2−12x+70

The remainder theorem says that f(a)  is the value of f(x) when f(x) is divided by (x - a).

So when a = -5 f(a) will be 5.

Answer is 5.

The statement which is true about the translation is; The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Since it follows from the task content that the function g(x) represents a 6 units vertical shift downward, it can then be concluded in the same regard that The asymptote of g(x) is the asymptote of f(x) shifted six units down.

Therefore, the true statement is; the asymptote of g(x) is the asymptote of f(x) shifted six units down.

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The expression which represents the given conditional statement in shorthand is: S → W.

A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

If Megan is swimming = S

It is warm outside = W

Therefore, if Megan is swimming, then it is warm outside is represented by S → W.

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The length of the rectangle is 26ft.

What is the perimeter of a rectangle?

The perimeter of a rectangle is, P = 96 ft.

The width of the rectangle is, w = 22ft.

As we know the perimeter P of a rectangle is given by the formula, P=2l+2w

Therefore, substituting the values in the equation we get,

P = 2l + 2w

96 = 2l + 2*22

96 = 2l + 44

2l = 96 - 44

2l = 52

l = 52/2

l = 26

Hence, the length of the rectangle is 26ft.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

There are two hemispheres in there with radius 3 cm, so we can consider it as a whole one. and the other shape in between is Cylinder with radius 3 cm and height 4 cm.

Volume of whole ahape = volume of Cylinder + volume of sphere ~

Volume of sphere :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \pi {r}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \sdot3.14 \sdot {(3)}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 )\sdot(3.14) \sdot(9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of Cylinder :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} h[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \cdot(3) {}^{2} \sdot4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \sdot(9) \sdot(4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of whole shape :

[tex]\qquad \sf  \dashrightarrow \: 113.04 + 113.04 = 226.08 \: \: cm {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 226.08 \: \: cm {}^{3}[/tex]

Following are the dependent variables:

1. The amount of water that each orchard receives.

2. The species of trees in the orchard.

Reason:

The exercise scientist is looking for the effects of a chemical between an apple crop to which it is administered and another to which it is not, 4 options are presented, of which it is essential to count as a variable the amount of water each Orchard and tree species in the orchard, since they can generate alterations in the results, the other two variables of the exercise such as number of apples and size of the orchards are not significant and their variations do not affect the scientist's objective.

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Answer:

Q₂ = 10

Step-by-step explanation:

Given data set:  3, 9, 12, 4, 6, 40, 25, 14, 10

Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.

Order the values in the data set:

3, 4, 6, 9, 10, 12, 14, 25, 40

As the number of values is odd, the middle value is the 5th value.

Therefore, the median (Q₂) of the given data set is 10.

If the number of data values is even, and therefore there are two middle values, the median is halfway between them.

The value of x from the given expression is 23

Given the following equation

√3x+12 = 9

Square both sides

√3x+12)² = 9²

3x + 12. = 81

Subtract 12 from both sides

3x + 12 - 12 = 81- 12

3x = 69

x = 23

Hence the value of x from the given expression is 23

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The measure of the acute angles are 62° and 28° .

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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