Will was scuba diving while his friend Sabrina was climbing a mountain. If Will was at an elevation of -75 feet, and Sabrina was at an elevation of 2,195 feet, what was the difference in elevation (in feet) between Will and Sabrina?

Answer:

C.No, the two triangles can only be proven congruent through SSS.

Answer:

2/15

Step-by-step explanation:

Take the fractions of the park for sports and multiply the fraction of the sports that is for soccer.  That will give the fraction of the park that is for soccer

1/3 * 2/5 = 2/15

Answer:

\(4(x+7)=3\)

Step-by-step explanation:

Since the sum is being multiplied 4 different times, it's best to write the equation of the sum and the number 4 being in the outside. and since it's saying it equals 3, just add the equal sign

Hope this helps!

- doomdabomb

The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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To find the equation of a line passing through two points, (-1, -5) and (5, 4), we can use the point-slope form of a linear equation.

The formula for the point-slope form is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.

First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, -5) and (x2, y2) = (5, 4).

m = (4 - (-5)) / (5 - (-1))

m = 9 / 6

m = 3/2

Now, we can choose one of the points, let's use (-1, -5), and substitute the values into the point-slope form:

y - y1 = m(x - x1)

y - (-5) = (3/2)(x - (-1))

y + 5 = (3/2)(x + 1)

To convert this equation to the standard form (Ax + By = C), we can multiply through by 2 to eliminate the fraction:

2(y + 5) = 3(x + 1)

2y + 10 = 3x + 3

3x - 2y = 7

So, the equation of the line passing through the points (-1, -5) and (5, 4) is 3x - 2y = 7.

For a, the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.

What is the percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

Examples of percentages are:

10% is equal to 1/10 fraction.

20% is equivalent to ⅕ fraction.

25% is equivalent to ¼ fraction.

Now,

Given angle=1.3°

Total rotation = 360°

So, percentage of given angle=1.3/360*100=0.36%

and 1.3° in radian=1.3*π/180=0.0072π

Hence,

            the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.

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Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.

Therefore option A is correct.

The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.

With reference to the table, the occupations that do not require a college degree are:

We were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.

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Step-by-step explanation:

We are here given that a point B is between A and C . Also ,

And we would like to calculate the length of BC . For figure refer to the attachment. From figure we can see that ,

\(\rm:\implies AC = AB + BC \)

Substitute the respective values,

\(\rm:\implies 21 = 2x + 3x + 1\)

Add like terms ,

\(\rm:\implies 21 = 5x +1 \)

Subtract 1 on both sides,

\(\rm:\implies 21-1 = 5x \)

Simplify,

\(\rm:\implies 20=5x \)

Divide both sides by 5,

\(\rm:\implies \blue{ x = 4}\)

Now consider ,

\(\rm:\implies BC = 3x+1 \)

Plug in the value of x found above ,

\(\rm:\implies BC= 3(4)+1\)

Simplify,

\(\rm:\implies BC = 12+1\)

Add,

\(\rm:\implies \underline{\boxed{\blue{\rm{ \quad BC \quad =\quad 13\quad }}}}\)

And we are done !

Answer:

+ BC = AC

x + 2x+1 = 22

3x +1 = 22

3x = 21

x = 7

AB = 7

BC = 2*7+1 = 14 + 1 = 15

15 - 2

13

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Given the function:

You can identify that its Leading Coefficient is:

And its degree is:

Because its highest exponent is 6.

By definition, when the Leading Coefficient is negative and the Degree of the function is Even, its end behavior is:

Therefore, both ends of the function go in the same direction (to negative infinite).

Hence, the answer is: Option D.

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

As given by the question

There are given that the 26 ft^2

Now,

To convert the ft^2 into yd^2, divide by 9 into the value of ft^2

So,

Hence, the value of yd^2 is 2.888

The  average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.

a. Average:

Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91

Average=70.35÷0.91

Average=77.31%

b. Average

Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91

Average=66.64÷0.91

Average=73.23%

Therefore the average for both a and b is 77.31% and 73.23%.

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Answer:

The pvalue of the test is 0.0178 < 0.1, which means that there is evidence at the .10 level to suggest that the mean IQ score for Lower Arlington residents differs from the national average

Step-by-step explanation:

Previous analyses have determined that national average adult IQ score is 100.

This means that the null hypothesis is: \(H_0: \mu = 100\)

Is there any evidence at the .10 level to suggest that the mean IQ score for Lower Arlington residents differs from the national average.

This means that the alternate hypothesis that will be tested is:

\(H_a: \mu \neq 100\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

100 is tested at the null hypothesis:

This means that \(\mu = 100\)

Standard deviation of 15.

This means that \(\sigma = 15\)

A random sample of 35 adults from Lower Arlington, yields an average score of 106.

This means that \(n = 35, X = 106\)

Value of the test-statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{106 - 100}{\frac{15}{\sqrt{35}}}\)

\(z = 2.37\)

Pvalue of the test:

Since z is positive, and we are testing if the mean is different from a value, the pvalue of the test is 2 multiplied by 1 subtracted by the pvalue of z = 2.37.

Looking at the z-table, z = 2.37 has a pvalue of 0.9911

1 - 0.9911 = 0.0089

2*0.0089 = 0.0178

Is there any evidence at the .10 level to suggest that the mean IQ score for Lower Arlington residents differs from the national average

The pvalue of the test is 0.0178 < 0.1, which means that there is evidence at the .10 level to suggest that the mean IQ score for Lower Arlington residents differs from the national average

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

A = 48

Step-by-step explanation:

In this equation, we can factor out the expression \((\frac{1}{7} )^x\). If we do so, the expression becomes:

\((\frac{1}{7})^x((\frac{1}{7})^{-2} - 1)\)

We can simplify to get:

\((\frac{1}{7} )^x(49 - 1)\)

and get:

\(48*(\frac{1}{7})^x\)

Therefore, A = 48

Answer:

5

Step-by-step explanation:

factors of 15: 1, 3, 5, 15

factors of 40: 1, 2, 4, 5, 8, 10, 40

factors of 20: 1, 2, 4, 5, 10, 20

hope this helped:)

The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

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Answer:

5 feet

Step-by-step explanation:

1 second =-3 inches what of

4 seconds=?

-3×4÷1=-12 inches

-12 inches =-1 foot

6 feet + (-1) foot= 5 feet

Answer: 57

Step-by-step explanation:

x² - 7

When x = 8

= x² - 7

= 8² - 7

= 64 - 7

= 57

jawabannya adalah 57

The range of a function is the set of all possible outputs.

When the quadratic functions are in standard form, they generally look like this:

\(f(x) = ax^{2} + bx + c\)

If a is positive, the function opens up; if it’s negative, the function opens down. In this form, the y-coordinate of the vertex is found by evaluating f(−\(\frac{b}{2a}\)). For example, consider this function:

f(x) = \(-2x^{2} + 8x -3\\\)

So we’re gonna do: −b/2a=−8/2(−2)=−8/−4=2

Then, we plug this in:

\(f(2) = -2(2)^{2} +8(2) -3 = 5\)

a is negative, so the range is all real numbers less than or equal to 5.

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Answer:

10%

Step-by-step explanation:

10% of the Male students have blonde hair

Answer:

You should be able to get your answer by

Step-by-step explanation:

For example let's sayAbout 33%. You divide 12 by 18 and get 0.6666666 and it goes on. So, rounded to the nearest percent, it is 67%. Then, you subtract it from 100 and get 33%. So the percent decrease is 33%.

Hope this helps

Answer:

\(3)\ x = 8\)

\(4)\ x = 12\)

Step-by-step explanation:

Given

The similar triangles

Required

Solve for x

TUV to TLM implies that, the corresponding sides are:

\(TU \to TL\)

\(TV \to TM\)

\(UV \to LM\)

To solve for x, we use the following equivalent ratios

\(TV : TM =TU:TL\)

This gives:

\(24 : x + 8=36 : 24\)

Express as fraction

\(\frac{24 }{ x + 8} =\frac{36 }{ 24}\)

Cross Multiply

\(36(x + 8) =576\)

Divide both sides by 36

\(x + 8 =16\)

Subtract 8 from both sides

\(x = 8\)

FGH to WVU implies that, the corresponding sides are:

\(FG \to WV\)

\(FH \to WU\)

\(GH \to VU\)

To solve for x, we use the following equivalent ratios

\(FH : WU =FG:WV\)

This gives:

\(x + 3 : 5 = 27 : 9\)

Express as fraction

\(\frac{x + 3 }{ 5 }= \frac{27 }{ 9}\)

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

Cross Multiply

\(x + 3 = 3 * 5\)

\(x + 3 = 15\)

Subtract 3 from both sides

\(x = 12\)

The absolute value of the elevation difference between the valley and sea level is 94 feet.

The absolute value of a number is the distance of that number from zero on the number line. It represents the magnitude or size of a quantity without considering its direction. In the given scenario, we are dealing with the elevation difference between a valley and sea level.

The valley is described as being 94 feet below sea level. To find the absolute value of the elevation difference, we need to ignore the negative sign and consider the magnitude of the difference.

In this case, since the valley is below sea level, the elevation difference is negative. However, when we take the absolute value, we disregard the negative sign and focus solely on the numerical value of the difference.

By applying the absolute value to the elevation difference of -94 feet, we remove the negative sign and consider only the magnitude. Thus, the absolute value of -94 is simply 94.

Therefore, the absolute value of the elevation difference between the valley and sea level is 94 feet. It indicates that the valley is 94 feet away from sea level in terms of elevation, regardless of the direction (above or below sea level). The absolute value provides a measure of the magnitude of the difference while disregarding the direction or sign associated with it.

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       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

0 cavities

minimum is 0 cavities. there are people having 0 cavities. see the graph.

hope it helps!

Answer:

0

Step-by-step explanation:

The minimum is the smallest value in the dataset. The smallest number of cavities is 0.

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