What is the distance between (-5, 2) and (4,-9)?
Use the distance formula, d = √ (x2 − X1)² + (Y2 − Y1)².
OA. 8.23
O B. 11.05
O C. 14.21
O D. 16.27

Answer:

Plot the points on the graphing calculator. Then generate an exponential regression model.

y = 14,220.322(.838^x)

After 10 years:

y = 14,220.322(.838^10) = 2,428.56

After 10 years, the value of the car is $2,428.56.

To find the test statistic, we need to use the formula:

z = (p - P) / sqrt[(P * (1 - P)) / n]

where:

p = sample proportion = 15/20 = 0.75

P = hypothesized population proportion = 0.42

n = sample size = 20

Plugging in the values, we get:

z = (0.75 - 0.42) / sqrt[(0.42 * 0.58) / 20]

z = 2.11

Therefore, the test statistic is 2.11.

One possible rational function with the given characteristics is r(x) = 4 + (x + 9)(x + 2)(x - 4) / [(x - 3)(x + 5)].

In general, a function is a mathematical concept that defines a relationship between an input (or set of inputs) and an output (or set of outputs). It is a rule that takes an input value and produces a corresponding output value.

One possible rational function with the given characteristics is:

r(x) = 4 + (x + 9)(x + 2)(x - 4) / [(x - 3)(x + 5)]

Explanation:

The factor (x + 9) in the numerator makes the function cross the x-axis at x = -9.

The factor (x - 4) in the numerator makes the function touch the x-axis at x = 4.

The factors (x - 3) and (x + 5) in the denominator create vertical asymptotes at x = 3 and x = -5, respectively.

The factor (x + 2) in the numerator creates a hole at x = -2, since it cancels out the factor (x + 2) in the denominator.

Finally, the constant term 4 in the numerator and the absence of any higher degree terms in the numerator or denominator create a horizontal asymptote at y = 4.

Note that there may be other rational functions with the same characteristics, but this is one possible solution.

Therefore, One possible rational function with the given characteristics is r(x) = 4 + (x + 9)(x + 2)(x - 4) / [(x - 3)(x + 5)].

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 12000\\ P=\textit{original amount deposited}\dotfill & \$80000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 12000 = (80000)(\frac{r}{100})(1) \implies \cfrac{12000}{80000}=\cfrac{r}{100} \\\\\\ \cfrac{3}{20}=\cfrac{r}{100}\implies \cfrac{300}{20}=r\implies \stackrel{ \% }{15}=r[/tex]

The probability that Herman selects a fiction book is given as follows:

P(fiction) = 0.4.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The and/or probabilities are related as follows:

P(A and B) = P(A) + P(B) - P(A or B).

In the context of this problem, we have that:

P(hardcover and fiction) = P(hardcover) + P(fiction) - P(hardcover or fiction).

Hence the probability of selecting a fiction book is obtained as follows:

0.2 = 0.6 + P(fiction) - 0.8

P(fiction) = 0.4.

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The value of the given expression is 16.

The expression we are interested in is:

logₐ  ((x²y)/(z³))

To simplify this expression, we can use the properties of logarithms. In particular, we can use the fact that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. Similarly, the logarithm of a power is equal to the product of the logarithm of the base and the exponent.

Using these properties, we can rewrite the expression as follows:

log ₐ ((x²y)/(z³)) = log ₐ (x²) + log ₐ (y) - log ₐ (z³)

Now, we can substitute the given values of the logarithms of x, y, and z:

log ₐ (x²) = 2 log ₐ (x) = 2 * 5 = 10 log ₐ (y) = 3 log ₐ (z³) = 3 log ₐ (z) = 3 * (-1) = -3

Substituting these values back into the expression, we get:

log ₐ ((x²y)/(z³)) = 10 + 3 - (-3) = 16

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In the given graphs, the first and third graphs are connected graphs.

A connected graph is a collection of vertices, or points, and edges, or lines, such that there is a path between every pair of vertices.

This means that it is not possible to find any isolated vertices or disjoint subsets of vertices, and every vertex is connected to at least one other vertex.

The edges of a connected graph represent the relationships or connections between the vertices.

Here we have 3 graphs

In the first graph, every vertex is connected to other vertices and we can go from one node to another node

Hence, The first graph is a connected graph

In the second graph, there are two graphs that are not connected to other. Hence, The Second graph is not a connected graph

In the third graph, every node is connected

Hence, The third graph is a connected graph.  

Therefore,

In the given graphs, the first and third graphs are connected graphs.

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The calculated value of the area of the shape is 84.78 square units

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

The three quarter circle

The area of the shape is then calculated as

Area = 3/4 * πr²

Where

Radius, r = 6 ( from the diagram)

substitute the known values in the above equation, so, we have the following representation

Area = 3/4 * 3.14 * 6²

Evaluate

Area = 84.78

Hence, the area is 84.78 square units

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The exact values of sin(x/2), cos(x/2), and tan(x/2) are:

Sin (x/2) = √ [ 2 - √2)/4 ]

cos (x/2) = √[ (2 + √2)/4 ]

Tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

The tangent of an angle can be expressed in terms of the sine and cosine of the same angle using the identity: tan(x) = sin(x) / cos(x)

Here we have

tan x = 1

If tan(x) = 1, we can determine the values of sin(x) and cos(x) using the identity:

=> tan² (x) + 1 = sec² (x)

Substituting tan(x) = 1, we get:

1 + 1 = sec²(x)

2 = sec²(x)

sec(x) = √2

As we know sec(x) = 1/cos(x), so:

=> cos(x) = 1/sec(x) = 1/√2 = √2/2

Similarly, sin(x) = tan(x) × cos(x) = 1 × √2/2 = √2/2

Use the half-angle identities to find sin(x/2), cos(x/2), and tan(x/2):

=> sin(x/2) = ±√[(1 - cos(x))/2 ]

= ± √[(1 - √2/2)/2]

= ± √ [ 2 - √2)/4 ]

Since tan(x) = 1 is positive, we know that x is in the first quadrant, which means x/2 is also in the first quadrant.

Therefore, sin(x/2) is positive, so:

sin(x/2) = √ [ 2 - √2)/4 ]

cos(x/2) = ±√[ (1 + cos(x))/2]

= ±√ [ (1 + √2 /2)/2]  

= ± √[ (2 + √2)/4 ]

Since x/2 is in the first quadrant, cos(x/2) is also positive, so:

cos(x/2) = √[ (2 + √2)/4 ]

Finally, we can find tan(x/2) using the identity:

tan(x/2) = sin(x/2) / cos(x/2)

tan(x/2) = √[ (2 + √2)/4 ]/ √[ (2 + √2)/4 ]

tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

Therefore,

The exact values of sin(x/2), cos(x/2), and tan(x/2) are:

Sin (x/2) = √ [ 2 - √2)/4 ]

cos (x/2) = √[ (2 + √2)/4 ]

Tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

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The total surface area of the rectangular prism is 144 square inches.

To find the total surface area of the rectangular prism, we need to find the area of all six faces and then add them together. We are given the dimensions of three of the rectangular faces, and we can assume that the other three faces have the same dimensions as the ones given.

The area of a rectangular face can be found by multiplying the length and width. Using the dimensions given in the net, we can find the area of each face:

The top and bottom faces both have dimensions of 8 inches by 3 inches, so their areas are:

A = 8 x 3 = 24 square inches (each)

The left and right faces both have dimensions of 6 inches by 4 inches, so their areas are:

A = 6 x 4 = 24 square inches (each)

The front and back faces both have dimensions of 8 inches by 6 inches, so their areas are:

A = 8 x 6 = 48 square inches (each)

To find the total surface area, we add up the areas of all six faces:

Total surface area = 2(24) + 2(48) + 2(24) = 144 square inches

Therefore, the total surface area of the rectangular prism is 144 square inches.

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The new profit-sharing ratio is as follows:

Mazibuko's share: Vogel's share = 5: 8

Let's begin by determining the share of profits that each member of the original partnership—Vogel and Mazibuko—receives :

Vogel's share 1/(1+3) = 1/4

Share of Mazibuko: 3/(1+3) = 3/4

Let's now evaluate the new alliance with Malikane. The remaining 5/6 of the profits are divided between Vogel and Mazibuko in accordance with their prior profit-sharing ratio because Malikane receives a 1/6 part of the profits.

As a result, Vogel and Mazibuko share in the following profits from the new partnership:

Share for Vogel: (1/4) * (5/6) = 5/24

Share for Mazibuko: (3/4) * (5/6) = 15/24 = 5/8

The new profit-sharing ratio is as follows:

Mazibuko's share: Vogel's share = 5: 8

So, Vogel obtains 5 of the profits from the new partnership's 13 shares, whereas Mazibuko receives 8 of the income from the 13 shares.

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The volume of the family value box increases by approximately 44% compared to the regular box.

The volume of a rectangular box can be calculated as the product of its length, width, and height.

Let's assume the dimensions of the regular box are L, W, and H, and the dimensions of the family value box are 1.25L, W, and 1.15H, respectively.

The volume of the regular box is LWH, and the volume of the family value box is

(1.25L)(W)(1.15H) = 1.4375LWH.

To find the percentage increase in volume from the regular box to the family value box, we can use the following formula:

Percentage increase = (New value - Old value) ÷ Old value x 100%

In this case, the old value is the volume of the regular box, and the new value is the volume of the family value box. Therefore, the percentage increase in volume is:

(1.4375LWH - LWH) ÷ LWH x 100% ≈ 44%

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The correct question is:

A food company sells its cornflakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 25% the height has been increased by 15% and the width remains the same. By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.

Answer: D

Step-by-step explanation: Cuz i just know

Answer:

(x - 3)^2 = 8

x - 3 = + 2√2

x = 3 + 2√2

The values of x when the equation (x-3)² = 8 was solved is 3±2√2.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

solve  the equation means to find the value of x in the equation (x-3)² = 8.

To find the value of x, we following the steps below

Given equation = (x-3)² = 8.

Step 1:

Note: square root and square will cancel out.

Step 2

Hence, the values of x is 3±2√2.

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The simplest form of the radical expression (√2 + √3) / (√2 - √3) is -5 - 2√6.

Given the radical expression in the question;

(√2 + √3) / (√2 - √3)

To simplify the expression, we need to eliminate the radical in the denominator.

We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is (√2 + √3):

[(√2 + √3) / (√2 - √3)] × [ (√2 + √3) / (√2 + √3) ]

= (2 + √6 + √6 + 3) / (2 - √9)

= (5 + 2√6) / (2 - 3)

= (5 + 2√6) / (-1)

= -5 - 2√6

Therefore, the simplified form is -5 - 2√6.

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Answer:  The answer is 21 because for X: 23 + 2 = 25, 25 + 3 = 28, 28 + 4 = 32 

Step-by-step explanation: Please give Brainlist.

Hope this helps.

I can answer more questions for brainlists.

Answer:

$585/month

Step-by-step explanation:

To determine how much money Mr. Smith has left over monthly to put into savings, we need to first calculate his monthly income and his monthly expenses, including taxes.

Mr. Smith's hourly rate is $20, and he works full time, which is typically 40 hours per week. Therefore, his weekly income is:

$20/hour x 40 hours/week = $800/week

To find his monthly income, we multiply his weekly income by the number of weeks in a month:

$800/week x 4 weeks/month = $3,200/month

To find his monthly expenses, we add up the amounts for his household and automobile expenses:

$1,410/month (household) + $405/month (automobile) = $1,815/month

Since Mr. Smith gets about 25% of his income taken out for taxes, we need to calculate the amount of taxes he pays each month:

$3,200/month x 0.25 = $800/month (taxes)

Now we can subtract his monthly expenses and taxes from his monthly income to find out how much money he has left over to put into savings:

$3,200/month - $1,815/month - $800/month = $585/month

Therefore, Mr. Smith has $585/month left over to put into savings after paying his expenses and taxes.

Im diying:(

dont be mean man

A nurse is caring for a pediatric patient weighing 8.250 kilograms.

We will solve the problem of unit conversion. This time we will convert grams to kilograms as;

Recall that

[tex]{ \ 1 \ kilogram = 1,000 \ grams \ }[/tex]

8,250 grams = n kilograms

[tex]= 8,250 \grams \times \frac{1 \ kilogram}{1,000 \ grams} \ }\\= 8,250 \times 1 \ kilogram \\= 8.250 \ kilograms \ }}[/tex]

Thus, after the conversion process, the patient weight is 8.250 kilograms.

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According to the situation in the graph, the three inequalities will be: 7x + 2y < 40, y ≥ 4, x ≥ 2, where x is the wing packages and y is the hot dogs per pound.

Let x be the number of wing packages and y be the number of pounds of hot dogs.

Then the inequality equation is,

7x + 2y < 40

Inequality to represent at least 4 pounds of hot dogs,

y ≥ 4

Inequality to represent at least 2 packages of wings,

x ≥ 2

To graph it,

The graph will give the region that satisfies all the conditions and the shaded region represents the feasible region.

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Therefore, the greatest amount of money Hayley can collect by selling the bread made with 22 cups of sugar and 4 sticks of butter is $154.

In mathematics, an equation is a statement of equality between two expressions, which are composed of variables, numbers, and mathematical operations. An equation typically has one or more variables that can take different values, and the goal is often to find the values of the variables that make the equation true. Equations can be used to model a wide range of real-world situations, from simple problems like calculating the area of a rectangle, to complex systems like those found in physics and engineering. Solving equations is a fundamental skill in mathematics, and there are many techniques and strategies for finding solutions to different types of equations.

Here,

To find the maximum amount of money Hayley can collect by selling bread, we need to find the maximum number of loaves of each type of bread she can make with 22 cups of sugar and 4 sticks of butter.

Let's assume Hayley needs x cups of sugar and y sticks of butter to make one loaf of zucchini bread, and a cups of sugar and b sticks of butter to make one loaf of banana bread. We have the following system of equations:

x + a = 22 (total cups of sugar)

y + b = 4 (total sticks of butter)

To maximize the amount of money Hayley can collect, she should make as many loaves of zucchini bread as possible, since it sells for a higher price. Therefore, we want to maximize the value of x.

Solving the system of equations, we get:

x = 22 - a

y = 4 - b

To maximize x, we want to minimize a. Let's assume a = 0 (i.e., Hayley uses all 22 cups of sugar for zucchini bread), then we get:

x = 22

y = 4 - b

To make one loaf of banana bread, Hayley needs b sticks of butter. Since b is a positive integer, the maximum value of y is 3 (when b = 1). Therefore, Hayley can make 3 loaves of banana bread and 22 loaves of zucchini bread.

The total amount of money Hayley can collect is:

3($3) + 22($4) = $66 + $88

= $154

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Complete question:

She can sell zucchini bread for $4 and banana bread for $3. What is the greatest amount of money Hayley can collect by selling the bread made with 22 cups of sugar and 4 sticks of butter?

Answer:

Step-by-step explanation:

area of shaded region

[tex]=\pi r^2 \times\frac{121}{360} \\\\=\pi 8^2\times \frac{121}{360} \\=\frac{121 \pi }{45} \\\approx 8.447\\\approx 8.4~sq.~ft[/tex]

The components of each vector is :

u = (0,2)

v= (-4.9149, -3.4416)

Magnitude = 5.1

Direction = 196 deg

To find the magnitude and direction of the sum

.The magnitude and direction of the sum of two or more vectors can be calculated with vector addition.

To get the magnitude of the sum of two vectors (A and B), you can use the Pythagorean theorem: |C| = sqrt(A^2 + B^2 + 2ABcosθ).

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The total surface area of the cylinder is 62.8 ft². And the right option is D. 62.8.

A cylinder is a solid shape that is made up of a rolled surface with a circular top and a circular base.

To calculate the total surface area of the cylindrical drum, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence the total surface area is 62.8 ft².

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The transformation that produce function g(x) from f(x) is that g(x) = 4 f(x).

Given graphs of f(x) and g(x).3

Both are v shaped graphs, which is probably modulus functions.

For the graph of f(x),

Vertex = (0, 0)

Other points = (-1, 1) and (1, 1)

For the graph of g(x),

Vertex = (0, 0)

Other points = (-1, 4) and (1, 4)

Here the coordinates can be related as,

(x, f(x)) transformed to (x, 4f(x))

So g(x) = 4 f(x).

Hence the transformation is g(x) = 4 f(x).

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Using the simplification of an equation we can get the value of x to be,

x = 10 2/11.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.

Here in the question,

The given equation is:

(x-4 8/11) + 1 9/11= 7 3/11

Simplifying it, we get:

(x - 52/11) + 20/11 = 80/11

Subtracting 20/11 from both sides:

x - 52/11 = 60/11

Adding 52/11 on both side:

x = 112/11

x = 10 2/11

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Answer:

The surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Step-by-step explanation:

formulas:

Surface Area = 2B + Ph

Volume = Bh

where B is the area of the triangular base, P is the perimeter of the base, h is the height of the prism, and B and h are both in the same units (inches, feet, etc.).

Given:

Height of the triangular prism = 1 foot

Base of the triangular prism = 6 inches

Height of the triangular base = 4 inches

Length of the other two sides of the triangular base = 5 inches

First, we need to find the area of the triangular base (B):

B = (1/2) x base x height

B = (1/2) x 6 inches x 4 inches

B = 12 square inches

Next, we need to find the perimeter of the triangular base (P):

P = sum of all three sides

P = 6 inches + 5 inches + 5 inches

P = 16 inches

Now, we can use the formulas to find the surface area and volume:

Surface Area = 2B + Ph

Surface Area = 2(12 square inches) + (16 inches)(1 foot)

Surface Area = 24 square inches + 16 square feet

Surface Area = 16.222 square feet (rounded to three decimal places)

Volume = Bh

Volume = 12 square inches x 1 foot

Volume = 12 cubic feet

Therefore, the surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Answer:

87

Step-by-step explanation:

Step-by-step explanation:

4 ^x  = 1/64     take LOG of both sides

x log 4 =  log (1/64)

x = log(1/64) / log4  =  - 3

Answer:

$4.32

Step-by-step explanation:

Cost Price: $48

Selling Price: $52.32

tax = S.P - C.P

tax = $52.32 - $48 = $4.32

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Answer:

He can only wear 2 outfits because he only has 2 shirts.

Step-by-step explanation:

Hope it can help

Answer:

2 outfits because he only has 2 shirts

Step-by-step explanation:

The three cube roots of 4√3 + 4i are:

2(cos(π/18) + i sin(π/18))

2(cos(7π/18) + i sin(7π/18))

2(cos(11π/18) + i sin(11π/18))

To find the cube roots of a complex number, you can follow these steps:

Step 1: Write the complex number in polar form.

Step 2: Use the formula for finding the cube roots of a complex number in polar form. The formula for finding the cube roots of a complex number in polar form is:

        [tex]z^{\frac{1}{3}} = r^{\frac{1}{3} } [cos((\theta + 2k\pi)/3) + i sin((\theta + 2k\pi )/3)][/tex]

Step 3: Substitute the values into the formula.

Substitute the values for r and θ into the formula, and simplify.

Step 4: Calculate the cube roots.

Step 5: Write the cube roots in rectangular form.

Here we have 4√3 + 4i

The polar form of the complex number is

=> 4√3 + 4i = 8(cos(π/6) + i sin(π/6))

Using the formula, [tex]z^{\frac{1}{3}} = r^{\frac{1}{3} } [cos((\theta + 2k\pi)/3) + i sin((\theta + 2k\pi )/3)][/tex]

[tex]z^{\frac{1}{3}} = 8^{\frac{1}{3} } [cos((\pi /6 + 2k\pi)/3) + i sin((\pi/6 + 2k\pi )/3)][/tex]  

where k = 0, 1, 2.

Now, we can calculate the cube roots by substituting the values of k into the formula and simplifying. Here are the three cube roots:

Substituting k = 0, 1, 2 into the formula, we get:

k = 0: [tex]z^{1/3}[/tex] = 2(cos(π/18) + i sin(π/18))

k = 1:  [tex]z^{1/3}[/tex] = 2(cos(7π/18) + i sin(7π/18))

k = 2:  [tex]z^{1/3}[/tex]  = 2(cos(11π/18) + i sin(11π/18))

Therefore,

The three cube roots of 4√3 + 4i are:

2(cos(π/18) + i sin(π/18))

2(cos(7π/18) + i sin(7π/18))

2(cos(11π/18) + i sin(11π/18))

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