For the requirements of a report Suzy has to write for school, she has a choice of wide-rule or narrow-rule paper and three different pen colors in which to write the report. How many different possibilities does Suzy have to write the report? Enter a numerical answer only.

Answer:

5+5=10

Step-by-step explanation:

your welcome:)

Answer:

Step-by-step explanation:

Answer: Its answer A

Hope you feel soon better friend.

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The correct option is Option D: Yes, the graph passes the vertical line test.

The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.

The vertical line test states that

If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.

So here in this function shown in the graph.

If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.

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With what?

Where is the picture

Answer:

b

Step-by-step explanation:

i just answered the same thing earlier

Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

B. \(86\,\frac{m}{s^{2}}\)

Step-by-step explanation:

From Newton's Laws of Motion, the spring is compressed against effects of weight of the person and as sping force is a restitutive force, the net force experimented by person is different from zero. By applying Second Newton's Law, we get this equation of equilibrium on person:

\(\Sigma F = k\cdot \Delta x -m\cdot g = m\cdot a\) (Eq. 1)

Where:

\(k\) - Spring constant, measured in newtons per meter.

\(\Delta x\) - Change in the length of spring, measured in meters.

\(m\) - Mass of the person, measured in meters.

\(g\) - Gravitational acceleration, measured in meters per square second.

\(a\) - Net acceleration of the person, measured in meters per square second.

Now we proceed to clear net acceleration:

\(a = \frac{k}{m}\cdot \Delta x -g\)

If we know that \(k = 1.4\times 10^{4}\,\frac{N}{m}\), \(m = 60\,kg\), \(\Delta x = 0.41\,m\) and \(g = 9.807\,\frac{m}{s^{2}}\), the acceleration of the person when spring reaches its greatest compression at the bottom of their jump is:

\(a = \frac{1.4\times 10^{4}\,\frac{N}{m} }{60\,kg} \cdot (0.41\,m)-9.807\,\frac{m}{s^{2}}\)

\(a = 85.859\,\frac{m}{s^{2}}\)

Which corresponds to option B.

Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.

To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:

Help Center to Water Slide #1:

Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)

Toddler area to Concessions:

Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)

Gift Shop to Restrooms:

Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)

Security desk to Water Slide #2:

Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)

Lazy River to Large Whirlpool:

Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5

Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)

Presently, let's calculate the linear equations for each case:

Help Center to Water Slide #1:

The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.

Toddler area to Concessions:

The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:

-7.5 = (-1/3)(1.5) + b

-7.5 = -0.5 + b

b = -7

Gift Shop to Restrooms:

The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.

Security desk to Water Slide #2:

The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.

Lazy River to Large Whirlpool:

The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:

12 = (2/5)(-2) + b

12 = -4/5 + b

b = 61/5

The Linear equations for each case are as follows:

Help Center to Water Slide #1: y = 3

Toddler area to Concessions: y = (-1/3)x - 7

Gift Shop to Restrooms: y = -9

Security desk to Water Slide #2: y = 4

Lazy River to Large Whirlpool: y = (2/5)x + 61/5

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

the nominal interest rate is the periodic interest rate.

it  is the periodic interest rate times the number of periods per year.

then then then

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The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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We need to show that if we choose right triangle with the interior angle θ, the ratios of the sides will be the same as shown in below figure.

The mathematical subject of trigonometry is the study of the connections between the angles and sides of triangles. It entails investigating trigonometric functions like sine, cosine, and tangent, which examine the relationship between a triangle's sides' lengths and its angles.

Let's consider a right triangle with acute angles α and β, as shown below:

To relate the sides of this triangle, we can use the Pythagorean theorem:

a² + b² = c²

Now, let's define the six trigonometric functions in terms of the sides of the triangle:

Sin(θ) = a/c

Cos(θ) = b/c

tan(θ) = a/b

csc(θ) = c/a

sec(θ) = c/b

cot(θ) = b/a

We want to show that these functions are well-defined, i.e., they do not depend on the particular triangle we choose. To do this, we need to show that if we choose another right triangle with the same interior angle θ, the ratios of the sides will be the same.

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Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  standard deviation is  \(\sigma = 2.45\)  

Step-by-step explanation:

From the given data we can compute the expected mean for each random values as follows

          \(E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6\)

So  

          \(E(x) = 0 + 0.6 + 0.8 + 0.6\)

          \(E(x) = 2\)

The  

             \(E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6\)

So  

        \(E(X^2) = 0 + 1.2 + 3.2 + 3.6\)

        \(E(X^2) = 8\)

Now  the variance is  mathematically evaluated as

         \(Var (X) = E(X^2 ) -[E(X]^2\)

Substituting value  

        \(Var (X) = 8-4\)

        \(Var (X) = 6\)

The standard deviation is mathematically evaluated as

       \(\sigma = \sqrt{Var(x)}\)

      \(\sigma = \sqrt{4}\)

      \(\sigma = 2\)

Answer:  Choice A.   \(-x^2+2x+8\)

Work Shown:

\((f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\\)

which shows the answer is choice A.

Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.

Answer:

hope it helps u plz mark me brainliest mate

Step-by-step explanation:

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

this is the correct answer

Answer:

Completing the square

Step-by-step explanation:

Completing the square is just what took place between those 2 steps. ALSO A p e x

Answer:

add 7 to both sides which makes

6x=33

divide by 6

x=33/6 or 5.5

Step-by-step explanation:

Answer:

11/2 or 5.5

Step-by-step explanation:

Answer:

x + 4y = 13

x = -4y + 13....now we sub this into the first equation

2x - 3y = -29

2(-4y + 13) - 3y = -29 <=====

-8y + 26 - 3y = -29

-11y + 26 = -29

-11y = -29 - 26

-11y = -55

y = 55/11

y = 5

x = -4y + 13

x = -4(5) + 13

x = -20 + 13

x = -7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It’s not B, because it’s saying each pound is 1.25 multiplied by the cost. We are looking for the cost, not the amount of pounds.

it isn’t C, because the oranges are sold in 3 pound bags, and the equation is comparing the cost of a 3 pound bag to 1 pound of oranges.

And it isn’t D, because D does the same thing as B, but with The cost of a 3 pound bag.

An equation is formed of two equal expressions. The correct option is A, c=1.25p.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that the farm stand sells oranges in 3-lb bags for $3.75. Therefore, the cost of the oranges for a pound is,

Cost of a pound of oranges = $3.75 / 3

                                              = $1.25

Now, if the cost,c for p pounds of oranges is,

Cost, c = Cost of a pound of oranges × Number of pounds

            = $1.25 × p

      c = 1.25p

Hence, the correct option is A, c=1.25p.

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Answer:

1. d)

4.a)

2.a)

5.d)

Step-by-step explanation:

The value of x will be equal to 3 for the given expression.

The fraction is defined as the division of the whole part into an equal number of parts.

Given expression is solved as:-

\(\dfrac{\dfrac{3}{4} }{\dfrac{6}{x}} = \dfrac{3}{8}\)

\(\dfrac{3}{4}\times \dfrac{x}{6}=\dfrac{3}{8}\)

\(\dfrac{x}{8}=\dfrac{3}{8}\)

x = 3

The value of x will be equal to 3 for the given expression.

Therefore the value of x will be equal to 3 for the given expression.

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Answer:

(-3, 2)

Step-by-step explanation:

If we are dealing with vertical movement up/down, we manipulate the x-axis.

If we are dealing with horizontal movement left/right, we manipulate the y-axis.

We are trying to move the point right 4 units (horizontal movement) and down 4 units (vertical movement).

(1, -2) → (1 - 4, -2 + 4) → (-3, 2)

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer: It would be the first one (20 pens for 8$)

Step-by-step explanation: If you divide 20 by 8 then each pencil will be 2.50$. However if you divide 30 by 10 it will be 3 dollars for each pencil so the first deal will be better since you spend less money.

The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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