Find the distance between the points 7,-1 and -2,4

Step-by-step explanation:

(x+1) + (2x-15) = 10

x + 1 + 2x - 15 = 10

3x - 14 = 10

3x = 14 + 10

3x = 24

x = 24/3

x = 8

Therefore,

Option B is correct ✔.

The total length of the line is 10.

The line is divided by 2 equations. Add the two equations together to equal the total length:

x + 1 + 2x -15 = 10

Combine like terms:

3x -14 = 10

Add 14 to both sides:

3x = 24

Divide both sides by 3:

x = 24/3

x = 8

The answer is B. 8

Answer:

Female: 93/328

Adult: 103/328

Baby: 61/328

Step-by-step explanation:

71 + 93 + 103 + 61 = 328

Male: 71/328

Female: 93/328

Adult: 103/328

Baby: 61/328

Answer:

PLS help,269 divided by 4​

Step-by-step explanation:

Heidi must drag stones into the box and place them end-to-end to create a path that is between 8 and 8.5 feet long in order to create a stone path that meets Heidi's requirements.

She can begin by counting the number of stones she must drag into the box by measuring the length of the path. She can drag the required number of stones into the box and arrange them end-to-end to construct a path of the appropriate length. In order to ensure that the stones fit together correctly and form a stable path, she may need to arrange them in a particular pattern or layout.

In addition, in order to guarantee that the stones remain in place and do not shift or move over time, she may need to incorporate some kind of stabilizing material, such as gravel or sand.

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Answer:

\(\textsf{A)} \quad \cos (2\theta)=-\dfrac{11}{25}\)

\(\textsf{B)} \quad \sin \left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{7}}{10}\)

Step-by-step explanation:

Given:

\(\sin \theta=\dfrac{3\sqrt{2}}{5}, \quad \quad \dfrac{\pi}{2} < \theta < \pi\)

\(\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\cos (2 \theta)=\cos^2 \theta - \sin^2 \theta\\\\\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}\)

Using the trigonometric identities, rewrite cos(2θ) using sinθ only:

\(\begin{aligned}\implies \cos (2 \theta) & =\cos^2 \theta - \sin^2 \theta\\&=1-\sin^2 \theta - \sin^2 \theta\\&=1 - 2 \sin^2 \theta\end{aligned}\)

Substitute the given value of sinθ into the rewritten cos double angle identity:

\(\begin{aligned}\implies \cos (2 \theta) & =1 - 2 \sin^2 \theta \\ & =1 - 2 \left(\dfrac{3\sqrt{2}}{5}\right)^2 \\& = 1-2\left(\dfrac{18}{25}\right)\\& = 1-\dfrac{36}{25}\\& = -\dfrac{11}{25}\end{aligned}\)

\(\boxed{\begin{minipage}{5.5cm}\underline{Trigonometric Identities}\\\\$ \sin \left(\dfrac{\theta}{2}\right)=\pm \sqrt{\dfrac{1-\cos \theta}{2}} $\\\\\sin^2 \theta + \cos^2 \theta=1\\\end{minipage}}\)

Rewrite the second identity to isolate cosθ:

\(\begin{aligned}\sin^2 \theta+\cos ^2 \theta & =1\\\cos ^2 \theta & =1-\sin^2 \theta\\\cos \theta & = \pm \sqrt{1-\sin^2 \theta}\end{aligned}\)

As θ is obtuse, cosθ < 0.  Therefore:

\(\begin{aligned}cos \theta & =- \sqrt{1-\sin^2 \theta}\\& =- \sqrt{1-\left(\dfrac{3\sqrt{2}}{5}\right)^2}\\& =- \sqrt{1-\left(\dfrac{18}{2}\right)}\\& =- \sqrt{\dfrac{7}{25}}\\& =- \dfrac{\sqrt{7}}{5}\end{aligned}\)

Substitute this into the Half Angle Identity, using the positive root as sinθ is positive:

\(\begin{aligned}\sin \left(\dfrac{\theta}{2}\right) & = \sqrt{\dfrac{1-\cos \theta}{2}}\\& = \sqrt{\dfrac{\dfrac{5+\sqrt{7}}{5}}{2}}\\& = \sqrt{\dfrac{5+\sqrt{7}}{10}}\\\end{aligned}\)

Answer:

254m

Step-by-step explanation:

The setup will be in form of a right triangle. Hence;

The angle of elevation = 64degrees

distance from herself to the base of the castle = 124 meters (Adjacent)

Required

Height of the castle (Opposite)

Using the SOH CAH TOA identity

Tan theta = opp/adj

Tan 64 = H/124

H = 124tan64

H = 124(2.05030)

H = 254.23

H ≈ 254m

Hence the height of the castle to the nearest whole meters is 254metres

The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.

The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.

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The probability of it landing heads up at least three times is 1/4.

According to the statement

We have a given that the coin is tossed 4 times And we have to find the probability of it landing heads up at least three times.

So, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

So, According to the statement

Coin is tossed 4 times and we have to probability of find heads three times it means n = 3.

To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin.

Thus there are only 4 outcomes which have three heads.

The probability is 4/16 = 1/4.

So, The probability of it landing heads up at least three times is 1/4.

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Answer:

its A

Step-by-step explanation:

i think

Answer:

16

Step-by-step explanation:

-4x-5=20 and 20-4=16

Answer:

500000000

Step-by-step explanation:

When you do the first one you get 0.000006 and then when you do the second one you get 3000 so when you divide them then it puts all the numbers together, therefore, you get your answer.

Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

To fidn the surface area of the grain tank you need to find the area of:

Cylinder (without one of the bases as there are just one base exposed), use the next formula:

You have for the given cylinder:

h=12ft

r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft

Cone (without the base as the base is not exposed), use the next formula:

You have for the given cone:

r= 4.2ft

s= 5.5ft

The entire exposed surface of the tank is:

Answer:

The statements about arcs and angles that are true in the figure are;

1) ∠EFD ≅ ∠EGD

2) \(\overline{ED}\cong \overline{FD}\)

3) mFD = 120°

Step-by-step explanation:

1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)

∠CEG = ∠CDG = 90° (Given)

∠GDE = 60° (Given)

∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)

∠ECD = 360° - (90° + 90° + 60°) = 120°

∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)

120° = 2 × ∠EFD

∠EFD = 120°/2 = 60°

∠EFD ≅ ∠EGD

∠ECD = 120°

∠EGD = 60°

∴∠EGD ≠ ∠ECD

2) Given that arc mEF ≅ arc mFD

Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF

∠ECF = mEF = mFD = ∠DCF (Given)

∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)

\(\\ \overline{EF}\cong \overline{FD}\) (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

∠FED ≅ ∠FDE (base angles of isosceles triangle)

∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)

∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°

∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)

2 × ∠FED  = 120°

∠FED = 120°/2 = 60° = ∠FDE

∴ ∠FED = ∠FDE = ∠EFD =  60°

ΔEFD  is an equilateral triangle as all interior angles are equal

\(\\ \overline{EF}\cong \overline{FD}\cong \overline{ED}\) (definition of equilateral triangle)

\(\overline{ED}\cong \overline{FD}\)

3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)

Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)

60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)

60° = 2 × ∠CFE

∠CFE =60°/2 = 30° = ∠CFD

\(\overline{CF}\cong \overline{CD}\) (radii of the same circle)

ΔFCD is an isosceles triangle (definition)

∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)

∠CFD + ∠CDF + ∠DCF = 180°

∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°

mFD = ∠DCF (definition)

mFD = 120°.

Answer:

1,3,5

Step-by-step explanation:

right on edge 2022

Answer:

yeet on them

Step-by-step explanation:

Answer:

  A = B = 45°

  x = 11√2

Step-by-step explanation:

The sides of the right triangle have equal lengths, so this is an isosceles right triangle. Its acute base angles are complementary and have the same measure: A = B = 45°.

You should know from memory that the hypotenuse of an isosceles right triangle is √2 times the side length, so would be x = 11√2. Even if you don't, you can figure it from the Pythagorean theorem:

  x² = 11² +11² = 11²·2

  x = 11√2 . . . . . take the square root

Answer: 2

Step-by-step explanation:

\((-3+5)^0=2\)

Answer:

D.

Step-by-step explanation:

4(5 + 8)

= 4*5 + 4*8

= 20 + 32

Answer:

can you click a full photo of this question.

The augmented matrix is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

We have given system of linear equation is,

\(x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.\)

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

\(1\ -1\ -4\ 5\)

the second row is

\(2\ 0\ 2\ 0\)

and the third row is

\(4\ 1\ 1\ 3\)

Therefore the augmented matrix for this linear system is,

\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)

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The augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.

The given equation has three variables so the matrix form will be of \(3\times3\)

The given linear equations are

\(x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3\)

From the above equations, we will make an augmented matrix.

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

The first equation will be followed by the first row of the matrix and the rest will be followed the same.

Thus the augmented matrix for the given linear equations will be constructed as follows

\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)

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The probability of guessing the winning number in the game "Pick Three V2" is 0.001.

The probability of guessing the winning number in the game "Pick Three V2" can be calculated by considering the number of favorable outcomes (winning combinations) divided by the total number of possible outcomes.

In this game, you select any three-digit number, and three digits are randomly drawn to create the winning number. To calculate the probability of guessing the winning number, we need to determine the number of favorable outcomes.

There are only three digits drawn to create the winning number, so the order of the digits does not matter. Therefore, the number of favorable outcomes is 1, as there is only one way to match all three digits.

Next, we need to calculate the total number of possible outcomes. Since you select any three-digit number, there are 10 choices for each digit (0-9). Therefore, the total number of possible outcomes is 10 x 10 x 10 = 1000.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1000

Probability = 0.001

Therefore, the probability of guessing the winning number in the game "Pick Three V2" is 0.001.

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Answer:

if you have about an 85 now than you shouldn’t go below a b

Step-by-step explanation:

Answer:

10x + 4

Step-by-step explanation:

10x + 4

There are two sides on each so 2(x+1) = 2x + 2 and 2(4x + 1) = 8x + 2. (8x+2) + (2x + 2) = 10x + 4

The profit-maximizing price for a bag of Brand X potato chips is approximately $3.35.

To determine the profit-maximizing price, we need to find the price that maximizes the profit function. The profit function can be expressed as follows:

Profit = Total Revenue - Total Cost

Total Revenue (TR) is calculated by multiplying the quantity sold (Qx) by the price (Px):

TR = Qx * Px

Total Cost (TC) includes the costs of advertising, plant lease, depreciation, employee payments, and the costs of raw materials:

TC = Advertising Cost + Plant Lease + Depreciation + Employee Payments + Raw Material Costs

Given the information provided, last year FoodMax sold 5 million bags of Brand X chips, spent $0.25 million on advertising, and incurred costs of $2.5 million for raw materials.

To find the profit-maximizing price, we differentiate the profit function with respect to Px and set it equal to zero:

d(Profit)/d(Px) = d(TR)/d(Px) - d(TC)/d(Px) = 0

The derivative of the total revenue with respect to the price is simply the quantity sold:

d(TR)/d(Px) = Qx

The derivative of the total cost with respect to the price is found by substituting the given demand equation into the cost equation and differentiating:

d(TC)/d(Px) = -3.2 * Qx

Setting these two derivatives equal to each other:

Qx = -3.2 * Qx

Simplifying the equation:

4.2 * Qx = 0

Since the quantity sold cannot be zero, we solve for Qx:

Qx = 0

This implies that the quantity sold, Qx, is zero when the price is zero. However, a price of zero would not maximize profit.

To find the profit-maximizing price, we substitute the given values into the demand equation:

5 million = 10.34 - 3.2 * Px + 4 * Py + 1.5 * 0.25

Simplifying the equation:

5 million = 10.34 - 3.2 * Px + 4 * Py + 0.375

Rearranging terms:

3.2 * Px = 14.34 - 4 * Py

Substituting the given value of Py as 0 (since no information is provided about the competitor's price):

3.2 * Px = 14.34 - 4 * 0

Simplifying:

3.2 * Px = 14.34

Dividing both sides by 3.2:

Px = 4.48

Thus, the profit-maximizing price for a bag of Brand X potato chips is approximately $4.48. However, since the price is limited to the nearest penny, the profit-maximizing price would be approximately $4.48 rounded to $4.47.

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The volume of the described solid is does not exist. The correct answer is B.

To use the method of cylindrical shells to find the volume of the solid of revolution, we need to express the function in terms of y instead of x, and then integrate over the range of y values.

Solving for x in the equation f(x) = 11(4 − x)^−1/3, we get:

x = 4 - (11/y^3)

So, the radius of a typical cylindrical shell at height y is given by r = x = 4 - (11/y^3), and its height is given by h = y.

The volume of the cylindrical shell is:

dV = 2πrh dy

dV = 2π(4 - (11/y^3))y dy

dV = 8πy dy - (22π/y^2) dy

Integrating this expression over the range of y = 0 to y = infinity gives an infinite volume, which means the solid of revolution does not exist.

Therefore, the answer is (B) The volume does not exist.

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The equation of the circle with center at (-1, 5) and passes through the point (2, 9) is equal to (x + 1)² + (y - 5)² = 25.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Next, we would determine the length of the radius (r) by using the distance formula. Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the given parameters into the formula, we have;

Radius = √[(2 - (-1))² + (9 - 5)²]

Radius = √[(2 + 1)² + (4)²]

Radius = √[3² + 4²]

Radius = √[9 + 16]

Radius = √25

Radius = 5 units.

For the equation of a circle, we have:

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 5)² = 25

(x + 1)² + (y - 5)² = 25

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Complete Question:

Write the equation of the circle with center at (-1, 5) and passes through the point (2, 9).

The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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The number of groups is 3, the number of participants is 36, and the f ratio is 5.5.

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

f(2, 33) = 5.5, p < 0.01

From the above details, we can find the number of groups:

5) Number of groups = df for groups + 1

Number of groups  = 2+ 1 = 3

Option (c) is correct.

6) Number of participants =2 + 33 + 1 = 36

Option (a) is correct.

7) f ratio = 5.5

Option (a) is correct.

8) True; as the p-value is less than the 0.01 level.

Thus, the number of groups is 3, the number of participants is 36, and the f ratio is 5.5.

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To calculate z table online we put Raw Score, Population Mean, Standard Deviation, σ   then calculator give us answer.

A z-table, also called a standard normal table or unit normal table, is a table of standardized values ​​used to determine the probability that a given statistic is below, above, or below the standard normal distribution. A z-score of 0 indicates that the given point is the same as the mean. Therefore, on the graph of the standard normal distribution, z = 0 is the midpoint of the curve. A positive Z value indicates that the point is to the right of the mean, and a negative Z value indicates that the point is to the left of the mean. There are several different types of Z-tables. The values ​​in the table below represent a range from z=0 to a specific z-score.

Z Means table (0 to Z)  

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