Dexter is curious as to whether there is a relationship between a person’s height and thumb length. Fourteen of his classmates volunteered to be measured. He listed his data in a table.

Examine the data set and other information to describe the relationship, if any, between height and thumb length.

Hello there

This is a simple algebra problem, that we will be solving...

First let's use \(PEMDAS\), and \(DISTRIBUTIVE\:PROPERTY\)

______________

\({\huge{\boxed{\mathbb{PEMDAS}}}\)

______________

\({\huge{\boxed{\mathbb{DISTRIBUTIVE\:PROPERTY}}\)

Definition- Distribute Property - The distributive property is one of the most frequently used properties in math. In general, this term refers to the distributive property of multiplication which states that the Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

______________

\(4(1.75y-3.5)+1.25y\), first distribute...

\(7y-14+1.25y\), combine like terms, and we get \(8.25y-14\) as our answer

Answer:

This is not a function

Step-by-step explanation:

Assuming that the line in question is parallel with the y axis, by using the line test we can see that the line is not a function. The line test is where you draw straight lines going vertically over the graph and if the lines touch the figure in question more than once that means it's not a function.

This can also be proved by imagining there are 2 different points on the line in question. Since the line is straight vertically that means that the points will share the same x value for different y values, which makes it not a function

Answer:

This is not a function.

Step-by-step explanation:

The questioned parallel line within the y-axis does not meet the requirements to be a function. The line test, as the other person stated, is a test where lines are drawn over the points to determine if the graph / model is, or is not a function. Doing so in this process, if the lines touch the same point more than once, that means the graph is not a function.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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The ordered pair that  represents the halfway point between Mary's home and the grocery store is (1, 4)

The midpoint (a, b) between two linear points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:

\(a=\frac{x_1+x_2}{2} \\\\b=\frac{y_1+y_2}{2}\)

On a map, Mary's house is located at (−3, 1) and the grocery store is located at (5, 7).

\(x_1=-3, y_1=1, x_2=5, y_2=7\)

Substitute these values into the mid-point formulae

\(a=\frac{-3+5}{2} \\\\a=\frac{2}{2}\\\\a=1\)

\(b=\frac{1+7}{2} \\\\b=\frac{8}{2}\\\\b=4\)

The ordered pair that  represents the halfway point between Mary's home and the grocery store is (1, 4)

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Answer:

3

Step-by-step explanation:

We know that the sum of the angles of a triangle is 180

Assume that the angles are equal

x+x+x = 180

3x= 180

x = 180/3 =60

All three angles are less than 90 which makes them acute so we know that we can have 3 acute angles

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean grade for written test

x2 = sample mean grade for oral test

s1 = sample standard deviation for written

s2 = sample standard deviation for oral test

n1 = number of students for written test

n1 = number of students for oral test

For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28

z = 2.467

x1 - x2 = 1.523 - 4.166 = - 2.643

Margin of error = z√(s1²/n1 + s2²/n2) = 2.467√(1.530²/15 + 2.047²/15) = 2.467√0.43540726667

= 1.036

The 98% confidence interval is -2.643 ± 1.036

Answer:

  n = 27

  m = 36

Step-by-step explanation:

The isosceles triangle with n° as its base angle will have a sum of angles that is 180°.

  2n° +126° = 180°

  n +63 = 90 . . . . . . divide by 2°

  n = 27 . . . . . . . . . subtract 63

__

The external angle 126° is the sum of the remote interior angles m° and 90°.

  m° +90° = 126°

  m = 36 . . . . . . . . . . divide by °, subtract 90

Step-by-step explanation:

-7x²(3x² - 10x)

= -21x⁴ + 70x³

The number of local guests that visited the zoo on Saturday is given as follows:

600 local guests.

The number of guests is obtained applying the proportions in the context of the problem.

20% of the guests traveled from out of town, hence the percentage of local guests is given as follows:

100 - 20 = 80%.

Out of a total of 750 visitors, the number of local guests that visited the zoo on Saturday is obtained as follows:

0.8 x 750 = 600 local guests.

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Answer:

0.045

Step-by-step explanation:

4+2p=10(53p-2)

open the bracket

4+2p=530p-20

collecting like terms we have

4+20=530p-2p

24=528p

24/528=528p/528

p=0.04545

p=0.045

Hope it helps, please rate 5 and love

for more explanation, ask in the comment section

Step-by-step explanation:

p=22.

4+2p=10(53p-2)

4+2p=530p-20

4+20=530p-2p

24=528p

p= 22

Answer:

3+12i

Step-by-step explanation:

The difference of 5+3i and 2 + 1999 can be calculated as follows

= 5+3i - 2+9i

Collect the like terms

= 5-2+3i+9i

= 3+12i

Hence the difference of 5+3i and 2+9i is 3+12i

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

u need to tell me how many cups of grapes are used for 4 servings for me to be able to answer this

Step-by-step explanation:

\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

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The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Here you go.

The answer is A
II Only

Answer:

B

Step-by-step explanation:

2.

what is the middle between 2 numbers (any numbers, really) ?

you add both numbers and divide the result by 2.

the same here :

(-3 + 24) / 2 = 21/2 = 10 1/2

proof :

what is the distance from -3 to 10 1/2 ? it is 10 1/2 from 0 to 10 1/2 plus 3 from -3 to 0 = 10 1/2 + 3 = 13 1/2.

what is the distance from 10 1/2 to 24 ? it is 13 from 11 to 24, and another half from 10 1/2 to 11. so, in total 13 1/2.

both distances are equal, so it is proven for 10 1/2 to be the midpoint.

The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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hey I got a question what grade that math from

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:

G

f is 6/8=3/4 = 75%

h is 9/12=3/4 = 75%

I is 3/4 = 75%

so the answer is G