What did I do wrong tell me what I have to fix

The linear pair is the correct answer for a pair of adjacent angles whose opposite rays form their non-common sides.

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The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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1/2 (4a + 10b) = c

Remove the 1/2 by multiplying both sides by 2:

4a + 10b = 2c

Subtract 4a from both sides:

10b = 2c -4a

Divide both sides by 10:

b = (2c-4a)/10

SImplify by the fraction:

b = (c - 2a)/5

To find the area under the graph of the function y = x^3 over the interval [1,4], we need to evaluate the definite integral of the function within that interval and simplify the answer.

The area under the curve of a function can be found by evaluating the definite integral of the function over the given interval. In this case, we want to find the area under the curve y = \(x^3\) from x = 1 to x = 4.

The definite integral of the function y = \(x^3\)can be calculated as follows:

\(\[ \int_{1}^{4} x^3 \, dx \]\)

Evaluating this integral gives us:

\(\[ \left[ \frac{x^4}{4} \right]_1^4 \]\)

Plugging in the upper and lower limits of integration, we get:

\(\[ \left[ \frac{4^4}{4} - \frac{1^4}{4} \right] \]\)

Simplifying further:

\(\[ \left[ 64 - \frac{1}{4} \right] \]\)

The final result is:

\(\[ \frac{255}{4} \]\)

Therefore, the area under the graph of \(y = x^3\) over the interval [1,4] is\(\(\frac{255}{4}\)\)

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Finding the sample mean, deducting each value from the mean, squaring the differences, taking the average of these squared differences, and then taking the square root of the average are the steps required to determine the sample standard-deviation of a set of numbers.

In this case, the sample-mean is (1 + 3 + 5) / 3 = 9 / 3 = 3.

The differences between each value and the mean are:

(1 - 3) = -2

(3 - 3) = 0

(5 - 3) = 2

Then the squares of -2, 0 and 2:

(-2)² = 4

0² = 0

(2)² = 4

The average = (4 + 0 + 4) / 3 = 8 / 3 = 2.67.

Finally, the squareroot of the average is the sample standard deviation:

sample standard deviation = √(2.67)

Rounding to two decimal places, the sample standard deviation is approximately 1.63.

So, the closest answer is d. 1.67.

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Answer:

perimeter are the adding up of all side in a figure. Area is length times width and volume is length x width x height

Step-by-step explanation:

plz mark the brainliest

Answer:

Volume: The amount a container can hold.

Area: The space a flat shape covers.

Perimeter: The length around an object.

Step-by-step explanation:

The area of Triangle ABC is given by (1/2) times the product of the length of side BC (b) and the height (√2)

Area = (1/2) * b * √2

The area of Triangle ABC can be determined using the given information. Let's proceed with the calculations.

First, we need to find the length of side BC, denoted as b. We are given that the height to side BC is √2. In a right triangle, the height is perpendicular to the base, so side BC is the base of the triangle. Therefore, the length of side BC is equal to b.

Next, we can calculate the area of Triangle ABC using the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, the base is side BC (b) and the height is √2. Substituting these values into the formula, we have:

Area = (1/2) * b * √2

Therefore, the area of Triangle ABC is given by (1/2) times the product of the length of side BC (b) and the height (√2):

Area = (1/2) * b * √2

Now, let's summarize the findings:

The area of Triangle ABC is (1/2) * b * √2, where b represents the length of side BC.

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Answer:

62/51

Step-by-step explanation:

When dividing by a fraction, you multiply by the reciprocal instead. So, multiply 31/2 times 51/4 to get 62/51

Answer: Exponent is 4.

Step-by-step explanation: 4.12 x 10^4

We seek a number value between 1 and 10.

Moving the decimal point 4 units to the left yields the following: 4.12 x 10^4. As you can see, the exponent is 4.

No, Miguel is incorrect. "Grades" can be treated as categorical data because they represent distinct categories or groups, even though they are represented by numerical values.

Miguel's statement is not correct. While grades are represented by numerical values (9 through 12), they can still be treated as categorical data. Categorical data refers to variables that represent distinct categories or groups. In this case, the grades 9, 10, 11, and 12 represent distinct categories or groups of students.

Although the numerical values assigned to the grades can be ordered, the actual grades themselves are not continuous or quantitative measurements. Instead, they represent different levels or groups within the categorical variable "grade." Therefore, in the context of Miguel grouping athletes by grade, the variable "grade" can be considered categorical data, and the number of athletes in each grade can be treated as numerical data.

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Answer:

3mph

Step-by-step explanation:

Depending how far you're traveling and how fast you traveled. When doing speed you typically do it by hours and the unit will be miles per hour (mph).

1. 1.5 mi=0.5 hr

2. Multiple 0.5 by 2 to get one hour, and do the same to the other side

2(1.5)=2(0.5)

3. 3mi=1hr

4. The answer is 3mph

There are nine 3 number combinations that add up to 19

From the question, we have the following parameters that can be used in our computation:

Summation = 19

Combinations = 3

Using the above as a guide, we have the following:

The combinations of three numbers that add up to 19 are:

(1, 9, 9), (2, 6, 11), (3, 5, 11)

(3, 6, 10), (4, 4, 11), (4, 5, 10)

(5, 5, 9)

These are all the combinations of three positive integers that add up to 19.

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Using the definitions of the mean and of the standard deviation of a data-set, we have that:

When the measure of 84 is added to the data-set, we have that:

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You can use the following formula:

A = (b*h)/2

Where:

b = Base = 12cm

h = Height = 6cm

So:

A = (12*6)/2 = 72/2 = 36cm²7

The exact values of the six trigonometric functions of the angle (8, 18)

sin α = y/r = 18/√388, cos α = x/r = 8/√388, tan α = y/x = 18/ 8  

cot α = x/y = 8/18, secα = r/x =√388/8 & cosec α = r/y =√388/18

Trigonometric angles are angles given by the ratios of trigonometric functions. Trigonometry is the study of the relationship between the sides and angles of a triangle. Angle values ​​range from 0 to 360 degrees. Important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.

According too the Question:

If a point is given on one side of the endpoint of an angle, then:

Calculates the distance from the given point to the origin:

\(r =\sqrt{x^2+y^2}\)

Here it is:

\(r =\sqrt{8^2 +18^2}\)

  = \(\sqrt{64+324}\)

  = \(\sqrt{388} =19.69\)

Now,

we can calculate all 6 trigonometric functions:

sin α = y/r = 18/√388

cos α = x/r = 8/√388

tan α = y/x = 18/ 8

cot α = x/y = 8/18

secα = r/x =√388/8

cosec α = r/y =√388/18

Complete Question:

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

(?8, 18)

sinθ =?

cosθ =?

tanθ =?

cscθ =?

secθ =?

cotθ =?

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Answer:

  see attached

Step-by-step explanation:

The attachment is my effort to complete the proof. It appears to me the idea is to show that B=3+1 and that 1=3+C. Then you substitute (3+C) for 1 and you've got the proof you want.

_____

The given statements and reasons are intended to give you enough clues that you can figure out the logic that is being used. Once you have done that, you fill in the missing details.

10 * 11,026 = 110,260

But my question is why did you write a big paragraph of nonsense?!

Answer:

y=81x^4+648x^3+1944x^2+2592x+1289

Step-by-step explanation:

1. Interchange x and y.

2. Then solve x=\frac{\sqrt[4]{y+7}}{3}-2 for y.

3. y=81x^4+648x^3+1944x^2+2592x+1289

I hope this helps.

If the range of the matrix transformation t, denoted as R(T), is equal to \(R^n\), t is both onto and one-to-one (R(T) = \(R^n\) and nullity(T) = 0),  hence is one-to-one (injective).

To determine if the matrix transformation t is one-to-one, we need to consider the dimensionality of the range and null space of t. The range of t, R(T), represents the set of all possible outputs of t. If R(T) is equal to the entire n-dimensional space \(R^n\), it means that every possible vector in R^n can be achieved as an output of t.

For a transformation to be one-to-one, each input vector must have a unique output vector. In other words, different input vectors cannot map to the same output vector. If R(T) = \(R^n\), it implies that for every vector y in R^n, there exists an input vector x such that t(x) = y.

If the range of t covers the entire space R^n, it implies that t is onto (surjective). Since t is both onto and one-to-one (R(T) = \(R^n\) and nullity(T) = 0), t is invertible and has an inverse transformation. Therefore, if R(T) = \(R^n\), t is one-to-one.

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Answer:

-72p^7-64p^4

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

I can assume that as △ LMN has an inscribed circle, PQ & PS are perpendicular bisectors? If so then PQ & PS are also the radii of this inscribed circle since it is tangent to the points on △LMN...

PQ = PS,

-2y + 15 = 3y + 5,

10 = 5y,

y = 2

If y = 2, radius length = -2(2) + 15 = -4 + 15 = 11 units

The radius of the inscribed circle of △LMN is; 22 units

The image of the triangle △LMN is missing and so i have attached it.

Now, from the attached triangle, we can say that PQ = PS = PR because the distance to the centroid from the midpoint of any side of a triangle are always equal.

Thus;

-2y + 15 = 3y + 5

15 - 5 = 3y + 2y

10 = 5y

y = 10/5

y = 2

Thus; PQ = -2(2) + 15

PQ = 11

Since PQ = PS = PR, then;

PR = 11

Now, the radius of the circle will be;

PL = PM = PN.

We know that from centroid theorem, the distance of the centroid to each vertex is 2/3 the length of each median.

Thus;

2PR = PL

Thus; PL = 2 × 11

PL = 22 Units

In conclusion, radius is 22 units.

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Answer:

i think its c

Step-by-step explanation:

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

\(\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C\)

(where \(a\) and \(b\) are the sides, and \(C\) is the included angle)

\(\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2\)

(where \(\theta\) is the angle in degrees and \(r\) is the radius)

Therefore, using the above formulas:

\(\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}\)

Given:

Substitute the given values into the formula and solve for r:

\(\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}\)

To find the equation of a line in slope-intercept form (y = mx + b) that passes through the points (-2, 2) and (7, -4), we first need to determine the slope (m) of the line.

The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (-2, 2) and (7, -4) into the formula, we get:

m = (-4 - 2) / (7 - (-2)) = -6 / 9 = -2/3

Now that we have the slope (m), we can use it along with one of the given points to find the y-intercept (b).

Let's use the point (-2, 2) and substitute the values into the slope-intercept form:

2 = (-2/3)(-2) + b

2 = 4/3 + b

b = 2 - 4/3

b = 2/3

Therefore, the equation of the line in slope-intercept form is:

y = (-2/3)x + 2/3

By using the formula for slope, we calculate the slope of the line passing through the given points. Substituting one of the points into the slope-intercept form equation, we solve for the y-intercept. Finally, we combine the slope and y-intercept to obtain the equation of the line in slope-intercept form, which is y = (-2/3)x + 2/3.

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Using Chebyshev's theorem, we can conclude that at least 56% of the gym members' ages fall between 26 and 70.

Chebyshev's theorem states that for any given dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations from the mean.

We can use Chebyshev's theorem to determine the percentage of gym members aged between 26 and 70. We need to determine how many standard deviations away from the mean these ages are.

To do this, we calculate the z-scores for both ages using the formula z = \((x - μ) / σ\), where x is the value (in this case, either 26 or 70), \(μ\) is the mean (48), and σ is the standard deviation (10). For x = 26: z = (26 - 48) / 10 = -2.2 For x = 70: z = (70 - 48) / 10 = 2.2

Both ages are 2.2 standard deviations away from the mean. Using Chebyshev's theorem, we know that at least 1 - 1/2.2² = 56% of the gym members' ages fall within this range.This is a lower bound - the actual percentage of gym members aged between 26 and 70 could be higher than 56%, as the distribution of ages may not be perfectly symmetrical or may have outliers.

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Answer:

the possible amounts that he will spend is $29-$15=$14

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

y = ⅔x - 5

Step-by-step explanation:

The line that is parallel to 2x - 3y = 24, would have the same slope as the line, 2x - 3y = 24.

Rewrite;

2x - 3y = 24

-3y = -2x + 24

Divide both sides by -3

y = ⅔x - 8

Thus, the slope of 2x - 3y = 24 is ⅔.

Therefore the line that is parallel to 2x - 3y = 24, will have a slope (m) of ⅔.

Using point-slope form, we can generate an equation that passes through (-3, -7) and is parallel to 2x - 3y = 24.

Thus, substitute (a, b) = (-3, -7) and m = ⅔ into y - b = m(x - a)

Therefore:

y - (-7) = ⅔(x - (-3))

y + 7 = ⅔(x + 3)

Rewrite in slope-intercept form.

Multiply both sides by 3

3(y + 7) = 2(x + 3)

3y + 21 = 2x + 6

3y = 2x + 6 - 21

3y = 2x - 15

Divide both sides by 3

y = ⅔x - 5

Use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.Therefore, the estimated amount of metal in the can is 0.001416.

To estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick, we can use differentials.

First, let's calculate the volume of the can. The volume of a cylinder is calculated by the formula

\(V = πr^{2} h,\)

where r is the radius of the cylinder, and h is its height.

In this case, the radius is 5 cm and the height is 15 cm, so the volume of the can is

\(V = π x (5 cm)^{2}  x 15 cm = 707.1 cm^{3}\)

Next, we need to calculate the volume of the metal. The volume of a rectangular prism is

V = l x w x h,

where l is the length, w is the width, and h is the height. In this case, the length and width are both 10 cm, and the height is 0.1 cm, so the volume of the metal is

\(V = 10 cm x 10 cm x 0.1 cm = 1 cm^{3}\)

Finally, we can calculate the amount of metal in the can by dividing the volume of the metal by the volume of the can:

\(1 cm^{3} / 707.1 cm^{3}  = 0.001416.\)

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