70%=___in fraction and decimal

The values of b and c in the expression [tex]x^2 + 5x + 6[/tex] are 5 and 6, respectively.

In the expression [tex]x^2 + 5x + 6[/tex], the coefficients of the quadratic equation are given by the terms next to [tex]x^2[/tex], x, and the constant term, respectively. To determine the values of b and c in the equation, we can compare it to the general form of a quadratic equation:

[tex]ax^2 + bx + c[/tex]

Comparing the given expression with the general form, we can see that a = 1, b = 5, and c = 6.

The value of b, which is 5, represents the coefficient of the linear term, x. In this case, it means that the coefficient of x is 5.

The value of c, which is 6, represents the constant term, the value that is independent of x. In this case, it means that the constant term is 6.

By substituting these values into the expression, we have [tex]x^2 + 5x + 6.[/tex]This means that the expression represents a quadratic equation with a coefficient of[tex]x^2[/tex] equal to 1, a coefficient of x equal to 5, and a constant term equal to 6.

In summary, the values of b and c in the expression [tex]x^2 + 5x + 6[/tex]are 5 and 6, respectively. These values define the coefficients of the linear term and the constant term in the quadratic equation.

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Explanation:

The net refers to the wrapping paper needed to enclose the cone. It can be thought of as the amount of paint needed to cover the surface.

In this case we add up the two areas to get the final answer

31.4 + 12.56 = 43.96

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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The mean should be calculated for data sets A, B, C, and D.

It is useful to take into account the nature of the data and any potential outliers when deciding whether to choose the mean or the median as the measure of center in a data set.

When the data is symmetrically distributed with no major outliers, the mean is usually a better choice. It affects extreme values and gives an indication of the average value.

The median, on the other hand, is often preferred when the data is skewed or contains outliers. It represents the middle value when the data is ordered, and it is less affected by extreme values.

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The given trigonometric identity is verified below.

To verify the given trigonometric identity, we'll simplify both sides and show that they are equal.

Starting with the left-hand side (LHS):

LHS = tan(x) sin⁴(x)

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

RHS = tan(x) - sin(2x) + sin(x)cos³(x)

To simplify the RHS, we'll use some trigonometric identities:

a. Double-angle formula for sine: sin(2x) = 2sin(x)cos(x)

b. Power-reducing formula for cosine: cos²(x) = 1 - sin²(x)

RHS = tan(x) - 2sin(x)cos(x) + sin(x)(1 - sin²(x))cos(x)

= tan(x) - 2sin(x)cos(x) + sin(x)cos(x) - sin³(x)cos(x)

= tan(x) - sin(x)cos(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin(3x) + sin(x)cos(x) [Using sin³(x) = sin(x)sin²(x) = sin(x)(1 - cos²(x)) = sin(x)(1 - (1 - sin²(x))) = sin(x) - sin³(x) and sin(3x) = 3sin(x) - 4sin³(x)]

Now, we have simplified both sides of the equation.

Let's compare them:

LHS = tan(x) sin⁴(x)

RHS = tan(x) - sin(3x) + sin(x)cos(x)

Since LHS = RHS, we can conclude that the given trigonometric identity is verified.

tan(x) sin⁴(x) = tan(x) - sin(3x) + sin(x)cos(x)

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The angle on the unit circle is solved to be

56.01 degrees (to the nearest tenth)

To find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.

given that P = ((√5)/4, (√11)/4)

θ = arctan ((√11)/4 / (√5)/4)

θ = arctan((√11)/(√5))

θ ≈ 56.01 degrees

hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.

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Answer: See below

Step-by-step explanation:

Let's assume that there are 12 students in the school

So 9 students like hot dogs

and 8 students like ice cream

Using calculus, we round the answers to the fifth quartile and then find the standard deviation

we get 4.9823

Using the complex system, we round 4.9823 to 3.25.

3.25*(hot dogs)i is 3.25*9i

We also have the equation:

5*(ice cream)i or 5*8i

We multiply these 2 complex number and get:

16.25*72i^2

or 16.25*-72

or -1170

So out of the 12 students, -1170 like hot dogs and ice creams, because they don't go well together.

Alright sorry

Now let's completely abandon that.

(3/4)*(2/3)=6/12=1/2

Answer:

A. 65

Step-by-step explanation:

To find <CAB you need to find the angle of BC and divide it by 2

To find BC add the other angles up and minus it from 360 because a full circle is = to 360

122 + 108 = 230

360 - 230 = 130

130/2 = 65

Hope this helps :)

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

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

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

The height of the prism is 9/5 inches, or 1.8 inches.

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

Volume = Base Area * Height

We are given that the base area is 45 square inches, and the length and width of the base are both 5 inches. Substituting these values into the formula, we have:

45 = (5 * 5) * Height

Simplifying the equation

45 = 25 * Height

Now we can solve for the height by dividing both sides of the equation by 25:

Height = 45 / 25

Height = 9/5

Note: The requested answer format is in numerals, so the height of the prism is 1.8 inches.

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The value of system of equations are,

⇒ 14x + 18y ≥ 320

⇒ x + y < 25

Now,

Let x be the number of hours Pa Chia works at the grocery store

And, y be the number of hours she spends walking dogs.

Hence, The amount of money Pa Chia earns per week is calculated by using the inequality,

⇒ 14x + 18y ≥ 320

And, Since, Pa Chia must also work less than 25 hours per week, which can be represented as:

⇒ x + y < 25

Thus, The value of system of equations are,

⇒ 14x + 18y ≥ 320

⇒ x + y < 25

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The equation of the red graph is g(x) = x^2 - 4x + 4.

We are given that;

The graph of functions f(x)=x^2

Now,

By using symmetry and see that the vertex of the red graph must be halfway between its x-intercepts, which are at (1, 0) and (3, 0). This also gives you (2, 0) as the vertex.

Now that you know the vertex of the red graph is at (2, 0), you can plug it into the vertex form along with a = 1:

y = a(x - h)^2 + k y = 1(x - 2)^2 + 0 y = (x - 2)^2

This is the equation of the red graph in vertex form. You can also expand it to get it in standard form:

y = (x - 2)^2 y = x^2 - 4x + 4

g(x) = (x - 2)^2

or

g(x) = x^2 - 4x + 4

Therefore, by the function answer will be g(x) = x^2 - 4x + 4.

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The greatest possible error of the given measurement is: 0.0005 m

The greatest possible error is half of the unit of measure to which a measurement is rounded. If a measurement is made to the nearest whole unit (1), the greatest possible error is 0.5 units.

The steps to determine the greatest possible error are:

Step1: Identify the last nonzero digit to the right of the decimal point in the given measurement.

Step 2: Determine the precision. ...

Step 3: Divide the precision by 2 to determine the greatest possible error.

Thus, it will be the hundredths place for 0.224 m and in this case it is:

0.001/2 = 0.0005 m

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To find y when x = 4.

y = kx (k is a constant)

to find the constant:

5 = k8

8 ÷ 5 = 1.6

k = 1.6

because 5 times 1.6 = 8

so now:

y = kx

y = 1.6 x 4

y= 6.4

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

The rule for C(N(h)) is 760h + 380.

The cost when h = 10 hours is 7,980 dollars.

We have,

The rule for C(N(h)) can be found by substituting the expression for N(h) into the function C(x).

We have:

C(N(h)) = C(40h) = 19(40h) + 380 = 760h + 380.

Therefore, the rule for C(N(h)) is 760h + 380.

To find the cost when h = 10 hours, we can substitute h = 10 into the rule for C(N(h)):

C(N(10)) = C(40(10))

= C(400)

= 19(400) + 380

= 7,600 + 380

= 7,980 dollars.

Therefore,

The cost when h = 10 hours is 7,980 dollars.

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Answer:

7:3

Step-by-step explanation:

probability is 3/10 it has a toy

probability is 7/10 it has no toy

odds against having a toy: 7:3

Discuss measures that can be taken to develop the spirit of hard work

Answer:

Write the answer with the subscript indicating the base. For example, the answer is: 9A42twelve​=26752nine​

Step-by-step explanation:

to convert a number from base 12 to base 9. Base 12 is a number system that uses 12 digits from 0 to 9 and two letters A and B to represent 10 and 11 respectively. Base 9 is a number system that uses 9 digits from 0 to 8. To convert a number from base 12 to base 9, we can use the following steps:

Convert the number from base 12 to base 10 by multiplying each digit by its place value and adding them up. For example, 9A42 twelve = (9 x 12^3) + (10 x 12^2) + (4 x 12^1) + (2 x 12^0) = 15522 ten.

Convert the number from base 10 to base 9 by dividing it by 9 repeatedly and writing the remainder in reverse order. For example, 15522 ten = (1724 x 9) + 2, so the first remainder is 2. Then, 1724 ten = (191 x 9) + 5, so the second remainder is 5. Continuing this process, we get the remainder as 2, 5, 7, 6, and 2. Writing them in reverse order, we get the number in base 9 as 26752 nine.

The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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The first several terms of patterns a and b are and 0  3  6  9  12..... and 0  8  16  24  32.....

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

Pattern A

Start = 0

Rule = Add 5

In the above sequence, we can see that 3 is added to the previous term to get the new term

This means that

First term, a = 0

Common difference, d = 3

So, the first few terms are 0  3  6  9  12.....

Pattern B

Start = 0

Rule = Add 8

In the above sequence, we can see that 8 is added to the previous term to get the new term

This means that

First term, a = 0

Common difference, d = 8

So, the first few terms are 0  8  16  24  32.....

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Monica's balance from account 2 over 5.9 years would be approximately $7892.99.

We have,

To calculate Monica's balance from account 2 over 5.9 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A = the final balance

P = the initial principal (amount deposited)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For account 2, the annual interest rate is 4% (0.04) and it compounds daily, so n = 365.

Plugging in the values into the formula, we have:

[tex]A = 6100(1 + 0.04/365)^{365 \times 5.9}[/tex]

Calculating the expression inside the parentheses:

[tex](1 + 0.04/365)^{365 \times 5.9} = 1.293082[/tex]

Now, we can calculate the final balance:

A = $6100 x 1.293082 ≈ $7892.99

Therefore,

Monica's balance from account 2 over 5.9 years would be approximately $7892.99.

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The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

We have,

Sin 30 = y/10

1/2 = y/10

y = 5

And,

Cos 30 = x / 10

√3/2 = x/10

x = √3 x 5

x = 5√3

Now,

Area of the triangle.

= 1/2 x 5 x 5√3

= 1/2 x 25√3

= 12.5√3

Now,

The area of the triangle to the nearest hundredth of a square inch.

= 12.5 x 1.732

= 21.65

Thus,

The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

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Answer:

The green room is 12 (4x3)

The yellow room is 9 (3x3)

The red room is 12 (2x6)

Step-by-step explanation:

The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

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The correct conditional equivalent statement is q → ~p.

Hence, option (D) is correct.

We are given to select the statement that is logically equivalent to the conditional statement   p → ~q.

We know that

Two conditional statements are said to be logically similar if their truth tables are the same.

That is, they have same truth values under similar conditions.

The truth table is given by

p          q        ~p          ~q         p → ~q      p → q        ~p → q     q → p        q → ~p

T          T          F            F           F               T                  T            T             F

T          F          F            T            T               F                  T            T              T

F          T          T            F            T              T                  T            F             T

F          F          T            T            T               T                  F            T             T

So, the truth values of p → ~q is same as the truth values of q → ~p.

They must be logically equivalent.

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Answer:

208π square units

Step-by-step explanation:

To find the area of the shaded region between two circles, we need to subtract the area of the smaller circle from the area of the larger circle.

The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius.

Let's calculate the areas of the two circles:

Area of the larger circle (outer circle):

A_outer = π * (radius_outer)^2

= π * (17)^2

= 289π

Area of the smaller circle (inner circle):

A_inner = π * (radius_inner)^2

= π * (9)^2

= 81π

Now, we can calculate the area of the shaded region by subtracting the area of the smaller circle from the area of the larger circle:

Area of shaded region = A_outer - A_inner

= 289π - 81π

= 208π

Therefore, the area of the shaded region is 208π square units.

Hope this helps!

There are 87 small cubes painted on exactly 2 faces.

Now, We can assume the small cubes in the 5x5x5 cube with coordinates (x, y, z) with 1≤x,y,z≤5.

Then, the cubes with x, y, or z equal to 1, 2, 4 or 5 are painted on 3 faces, the ones with x, y, or z equal to 3 are painted on 4 faces, and the ones in the 3x3x5 hole are painted on 2 faces.

The 5x5x5 cube contains 125 small cubes, and the 3x3x5 hole contains 45 small cubes.

Therefore, the total number of small cubes outside of the hole is 80.

Since, There are 64 cubes painted on 3 faces, 27 cubes painted on 4 faces, and 4 cubes painted on 5 faces.

Therefore, the number of cubes painted on exactly 2 faces is:

64 + 27 - 4 = 87

So, there are 87 small cubes painted on exactly 2 faces.

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