Write an equation of the line in point-slope form that passes through (7,5) and has a slope of m=4

Answer: -3

Step-by-step explanation: EDGE 2022

Answer:

yo

Step-by-step explanation:

its -3

EDGENUINITY 2023

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

Answer:

Step-by-step explanation:

40 crackers/5minutes=8 crackers per minute

To find out how many crackers the hamster eats in 1 minute at the given rate, we can set up a proportion using the information provided.

Let's assume that the number of crackers eaten in 1 minute is represented by "x".

We can set up the proportion:

40 crackers / 5 minutes = x crackers / 1 minute

To solve for "x", we can cross-multiply and then divide:

40 crackers * 1 minute = 5 minutes * x crackers

40 = 5x

Dividing both sides of the equation by 5:

40 / 5 = x

8 = x

Therefore, the hamster eats 8 crackers in 1 minute at the given rate.

After answering the provided question, we can conclude that the average (arithmetic mean) of 2x and 2y is 48.

The mean of a dataset is the sum of all values divided by the total number of values; this is also known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the total number of values in the dataset by the sum of those values yields this result. Calculations can be performed using both raw data and data that has been combined into frequency tables. The average of a number is referred to as its average. It is simple to calculate: Divide the total number of digits by the number of digits. the total divided by the count.

The average (arithmetic mean) of 2x and 2y is 48.

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Answer:

1/2 x base x height

Step-by-step explanation:

hope this helps!

The maximum prοfit that the cοmpany can make annuaIIy is 16 miIIiοn dοIIars when the price οf the app is $7.

AIgebraic expressiοn can be defined as cοmbinatiοn οf variabIe and cοnstants.

The given prοfit functiοn is:

P(x) = -2(x-3)(x-11)

where x is the price οf the mοbiIe app in dοIIars, and P(x) is the annuaI prοfit οf the cοmpany in miIIiοns οf dοIIars.

The functiοn is a quadratic functiοn in standard fοrm, where the cοefficient οf x² is negative, indicating that the functiοn has a maximum pοint.

Tο find the x-vaIue that gives the maximum prοfit, we can first find the x-vaIue οf the vertex οf the quadratic functiοn using the fοrmuIa:

x = -b/2a

where a = -2, b = (-2)(3+11) = -28

x = -(-28)/2(-2) = 7

Sο the maximum prοfit οccurs when the app is priced at $7.

Tο find the maximum prοfit, we can substitute x=7 intο the prοfit functiοn:

P(7) = -2(7-3)(7-11) = 16 miIIiοn dοIIars

Therefοre, the maximum prοfit that the cοmpany can make annuaIIy is 16 miIIiοn dοIIars when the price οf the app is $7.

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According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle.

In other words, \(a^2 + b^2 = c^2\) for the triangle depicted below.

The right triangle's legs, a and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.

Construction projects and almost anything involving right triangles, such as roofing for homes, are common uses for this application.

Hypotenuse² = Base² + Perpendicular²

The Pythagorean Theorem is used in a variety of computations. For instance, it may be used to determine the height and distance of straight and fallen trees, as well as the steepness of hills and mountains.

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Answer:

Using Piragorean Theorem:

\(x=\sqrt{7^2+10^2}=\sqrt{100+49}=\sqrt{149}\)

Answer:

\(\sqrt{149\)

Step-by-step explanation:

7² + 10² = 12.21²

49 + 100 = 149

In the multiple regression model with k regressors, the variance of the stochastic errors in the population can be estimated by the residual mean square (MSE).

         Multiple regression is a statistical tool that allows the researcher to estimate the relationship between multiple independent variables and a dependent variable. It measures the impact of a given independent variable on the dependent variable after controlling for the other independent variables.

        In simple linear regression, there is only one independent variable, whereas, in multiple linear regression, there is more than one independent variable.

         Residual mean square (MSE) is the variance of the error term (the difference between the predicted and observed values). It represents the average variance of the errors or the average deviation of the dependent variable from its predicted value.

         The MSE can be used to estimate the variance of the stochastic errors in the population. It is calculated by dividing the sum of squared residuals by the degrees of freedom (n-k-1)

           Where n is the sample size and k is the number of regressors.

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Answer: 6

Step-by-step explanation:

3

1

​

a−1−

2

1

​

b

=

3

1

​

⋅12−1−

2

1

​

⋅6 Replace a with 12 and b with 6.

=4−1−3

=0

​

Answer:

128 = 80 + 64 t - 16 t^2

8 = 5 + 4 t - t^2

3 = t (4 - t)

Inspection shows the equation is solved if

t = 1   and t = 3

Plug into original equation to check

Long answer: According to the International Telecommunication Union (ITU), there were an estimated 5 billion unique mobile phone users in the world as of January 2018. However, it is important to note that this number does not necessarily equate to the number of individual subscribers, as some people may have more than one mobile phone or SIM card. Additionally, the number of cell phone subscribers can vary by country and region. For example, according to Statista, the number of mobile phone users in the United States was approximately 266 million in 2018. Overall, while there is not a definitive global estimate for the number of cell phone subscribers in 2018, it is clear that mobile technology continues to have a significant impact on the way people communicate and access information worldwide.

The probability is given by:

Therefore:

- The probability of spinning blue is:

Favorable outcomes = 1 (blue color)

Total outcomes = 3 (red, blue, and yellow)

- The probability of flipping heads is:

Favorable outcomes = 1 (head)

Total outcomes = 2 (head and tail)

- The probability of spinning a one is:

Favorable outcomes = 1 (number 1)

Total outcomes = 3 (numbers 1, 2 and 3)

Next, the probability of the compound event:

Answer: the probability of the compound event is 1/18

Answer: x = 5

Step-by-step explanation:

10x and 130 degrees are supplementary, because they are interior angles and the lines are parallel.

10x + 130 = 180

10x = 50

x = 5

Answer:

See Explanation

Step-by-step explanation:

Let our quadratic polynomial function \(f(x)=x^2-7x+6\)

Let our linear binomial in the form (x − a)=x-1

Part 1: We use long division to divide the polynomial by the binomial.

\(\left|\begin{array}{c|c}&x-6\\-----&-----\\x-1&x^2-7x+6\\Subtract&-(x^2-x)\\&------\\&-6x+6\\Subtract&-6x+6\\&------\\&0\end{array}\right|\)

Therefore:\(\dfrac{x^2-7x+6}{x-1}=x-6\)

Part 2: In our chosen linear monomial x-1, a=1

\(f(a)=f(1)\\f(1)=1^2-7(1)+6=1-7+6=0\\f(a)=0\)

Part 3:

To determine whether a linear binomial is a factor of a polynomial function using the remainder theorem

9514 1404 393

Answer:

  (-3, 1.5)

Step-by-step explanation:

The circumcenter of a right triangle is the midpoint of the hypotenuse. Here, that is ...

  D = (A +C)/2 = ((-4, 5) +(-2, -2))/2 = (-6, 3)/2

  D = (-3, 1.5) . . . . the circumcenter

Answer:

81.859%

Step-by-step explanation:

We solve the question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 80 mph

σ is the population standard deviation = 7 mph

For x = 66 mph

z = 66 - 80/7

z = -2

Probability value from Z-Table:

P(x = 66) = 0.02275

For x = 87 mph

z = 87 - 80/7

z = 1

Probabilith value from Z-Table:

P(x = 87) = 0.84134

The probability of the trials will give the DeLorean a speed between 66 mph and 87 mph is calculated as:

P(x = 87 mph) - P(x = 66 mph)

0.84134 - 0.02275

= 0.81859

The percentage of the trials will give the DeLorean a speed between 66 mph and 87 mph?

100 × 0.81859

81.859%

Answer:

Step-by-step explanation:

\(\dfrac x4\div24=21\\^{\quad\ \ \times24\quad\times24}\\\\\dfrac x4=504\\^{\ \ \times4\quad\times4}\\\\x=2016\)

For the given scattered plot a- independent variable is mother and dependent variable is father, height of daughter is 60inches, predicted height of the daughter is 60.08 inches.

What is scatter plot?

A scatter plot is a type of data visualization that displays the relationship between two variables. It is commonly used to analyze and identify patterns or trends in a dataset.

In a scatter plot, each data point is represented by a dot or marker on a Cartesian coordinate system. The x-axis represents one variable, and the y-axis represents the other variable. The position of each dot on the plot corresponds to the values of the two variables for that particular data point.

a)As per the equation Daughter = 22.35 + 0.686 Mother, the independent variable is the "Mother" and the dependent variable is the "Daughter."

b) Based on the graph, the approximate predicted height of the daughter of a mother who is 55 inches tall is around 60 inches, determined by the position on the graph.

c) By substituting the value of the mother's height (55 inches) into the equation, the predicted height of the daughter is calculated as 60.08 inches.

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the complete question is:

The heights of mothers and daughters are displayed in the scatterplot. sections (a) through (e) in full

Daughter 22.35+0.888 Mother

A- What independent and dependent variables are shown on the data graph?

b) By looking at the graph, you can estimate the predicted height of the daughter of a mother who is 55 inches (4 feet 7 inches) tall.

c) Using the equation provided, you can determine the predicted height of the daughter when the mother's height is 55 inches.

A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Answer:

10t2+ 2

Step-by-step explanation:

9t^{2} x (t^{2} + 2) add 9t2, and t2 to get 10t2 + 2

Answer:

R325

Step-by-step explanation:

Cost to buy shoes (x)

x = 175 * 50

x = 8750

At this point they've lost R8750 (-8750)

7500 = -8750 + 16250

To make an overall profit of R7500 they would need to sell the shoes at

16250 / 50 = R325

Answer:

Y=2x- 5

       -----

          2

Step-by-step explanation:

Answer:

u = 6.82m

Step-by-step explanation:

tan θ = \(\frac{Perpendicular}{Base}\)

therefore, according to the fig

tan 37° = P/5.92

0.75 × 5.92m  =  P

         4.44m    =    P

and from fig it is clear that

u = p + 2.38m

u = 4.44+ 2.38

u = 6.82m answer

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Option B is Correct. Determine the number of solutions to a quadratic equation using the discriminant, b^2-4ac. We utilise the condition as follows for a quadratic equation of the form ax^2+bx+c=0.a=0. There is only one solution to the equation if b^2 - 4ac = 0.

Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic problem.

There are two solutions if the discriminant is bigger than zero. The square root's input (i.e., its contents), which is the phrase b^2 = 4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.

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The equation of the tangent line to h(x) = (x + 1)⁴ at x = 1 is y = 32x - 16.

To find the equation of the tangent line to the function f(x) = 2tan(7x) at x = 1, we need to find the derivative of f(x) and evaluate it at x = 1.

f'(x) = 2sec²(7x) * 7

Substituting x = 1 into f'(x), we have

f'(1) = 2sec²(7) * 7

To find the equation of the tangent line, we need the slope and a point on the line. The slope is given by f'(1), and the point is (1, f(1)).

The point (1, f(1)) is (1, 2tan(7)).

Therefore, the equation of the tangent line to f(x) at x = 1 is

y - 2tan(7) = 2sec²(7) * 7(x - 1)

For the function h(x) = (x + 1)⁴, we need to find the derivative h'(x) and evaluate it at x = 1.

h'(x) = 4(x + 1)³

h'(1) = 4(1 + 1)³ = 4(2)³ = 4 * 8 = 32

To find the equation of the tangent line to h(x) at x = 1, we use the slope h'(1) and the point (1, h(1)).

The point (1, h(1)) is (1, (1 + 1)⁴) = (1, 2⁴) = (1, 16).

Therefore, the equation of the tangent line to h(x) at x = 1 is:

y - 16 = 32(x - 1)

Simplifying, we get:

y = 32x - 16

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Answer:

The average speed on the return trip is 2.44 miles/h.                  

Step-by-step explanation:

To find the average speed we need to use the following equation:

\( \overline{v} = \frac{d}{t} \)

Where:

d: is the distance

t: is the time

Since the question is to find the average speed on the return trip, we will take the data of the time and speed of only the return trip.

\(\overline{v} = \frac{d}{t} = \frac{5 + 1/2}{2 + 1/4} = 2.44 miles/h\)                

Therefore, the average speed on the return trip is 2.44 miles/h.

I hope it helps you!

The pH of a 0.10M Tris-acid solution is 4.65.

pH: The pH of a solution is the negative logarithm (base 10) of the hydrogen ion concentration in moles per liter. In other words, it is a measure of the acidity or basicity of a solution. The pH scale ranges from 0 to 14, where 7 is neutral, less than 7 is acidic, and greater than 7 is basic or alkaline.What is the pH of a 0.10 M Tris-base solution? (pH 10.65)For the reaction, Tris-base + H₂O ↔ Tris-acid + OH⁻, the pKb of Tris-base can be computed as: pKb + pKa = 14pKb = 14 - pKa = 14 - 8.30 = 5.7Thus, Kb = antilog (-5.7) = 1.995 x 10⁻⁶, which is the equilibrium constant for the reaction Tris-base + H₂O ↔ Tris-acid + OH⁻[OH⁻] = Kb x [Tris-base] / [H₂O] = 1.995 x 10⁻⁶ x 0.10 / 1000 = 1.995 x 10⁻⁷pH = 14 - pOH = 14 - (-log[OH⁻]) = 14 - (-log(1.995 x 10⁻⁷)) = 10.65Therefore, the pH of a 0.10M Tris-base solution is 10.65.What is the pH of the solution after mixing 35.0 mL0.10M Tris-base with 2.50 mL of 1.00 M HCl. The pKa of Tris-acid is 8.30 at 25°C. (pH7.90)The balanced chemical equation is Tris-base + HCl ↔ Tris-acid + Cl⁻Initial concentration of Tris-base = (35.0 / 37.50) x 0.10 = 0.0933 MInitial concentration of HCl = (2.50 / 37.50) x 1.00 = 0.0667 MInitially, the mixture was a buffer solution with a pH of:pH = pKa + log([A⁻] / [HA])pH = 8.30 + log(0.0933 / 0.00667) = 9.35The number of moles of Tris-base and HCl can be calculated as follows:Number of moles of Tris-base = 35.0 / 1000 L x 0.10 mol / L = 0.0035 molNumber of moles of HCl = 2.50 / 1000 L x 1.00 mol / L = 0.0025 mol

The limiting reagent in the reaction is HCl, and all of it will be used up. Tris-base will be converted to Tris-acid. Therefore, the number of moles of Tris-base remaining will be:Number of moles of Tris-base remaining = 0.0035 mol - 0.0025 mol = 0.0010 molSince the volume of the mixture is 37.5 mL, the concentration of Tris-acid is 0.0010 mol / 0.0375 L = 0.0267 M.The concentration of Cl⁻ in the mixture is 0.0667 M, and the concentration of Tris-base remaining is 0.0010 M. Therefore, the concentration of OH⁻ can be calculated as follows:[OH⁻] = Kw / [H⁺] = 1.0 x 10⁻¹⁴ / 0.0667 = 1.50 x 10⁻¹³The pH of the mixture is:pH = pKa + log([A⁻] / [HA])pH = 8.30 + log(0.0010 / 0.0267) = 7.90Therefore, the pH of the solution after mixing 35.0 mL0.10M Tris-base with 2.50 mL of 1.00 M HCl is 7.90.What is the pH of a 0.10M Tris-acid solution? (pH 4.65)The pKb of Tris-acid can be calculated as:pKb + pKa = 14pKb = 14 - pKa = 14 - 8.30 = 5.7Kb = antilog (-5.7) = 1.995 x 10⁻⁶The Kb for Tris-acid can be used to calculate the concentration of OH⁻:[OH⁻] = Kb x [HA] / [H₂O] = 1.995 x 10⁻⁶ x 0.10 / 1000 = 1.995 x 10⁻⁷The pH of the solution can be calculated as:pH = 14 - pOH = 14 - (-log[OH⁻]) = 14 - (-log(1.995 x 10⁻⁷)) = 4.65Therefore, the pH of a 0.10M Tris-acid solution is 4.65.

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