An exponential function f ( x ) = a b x f ( x ) = a b x passes through the points (0, 10000) and (3, 2160). What are the values of a and b ?

Answer:

61 principals

Step-by-step explanation:

189 total - 128 teachers = 61 principals

Step-by-step explanation:

It has

two sides 8x12

two sides 12x4

two sides 4x8           total 352 in^2

The exact value of the cosine of θ is given as follows:

a) 3/5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

Applying the Pythagorean Theorem, the hypotenuse length is given as follows:

x² = 6² + (-8)²

x² = 100

x = 10.

As the x-coordinate is used for the cosine, the cosine is given as follows:

cos(θ) = 6/10

cos(θ) = 3/5.

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a ) The given expression from Sofia and Ella represents two different values.

b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.

To determine the surface area of a rectangle prism, the formula that should be used would be given below:

That is;

Surface area of rectangular prism;

= 2(wl+hl+hw)

when the formula is multiplied out the following is gotten;

= 2wl + 2hl + 2hw

From Ella's expression,

2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²

From Sofia's expression,

(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.

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Answer:

The two numbers are -10 and 4

Step-by-step explanation:

[tex]x+y=-6\\y=14+x\\\\x+(14+x)=-6\\2x+14=-6\\2x=-20\\x=-10\\\\x+y=-6\\-10+y=-6\\y=4[/tex]

Answer:

-----------------

Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:

So, there are 36 different shirts available from this company.

There are 36 different types of shirt available for this company.

Given that;

Number of design Company has = 3

Number of color pattern available = 6

Types of shirt (short or long sleeves) = 2

Now, We need to find the number of different types of shirts are available from this company.

Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).

Hence, By framing in equation form we get;

the number of different types of shirts is,

⇒ 3 × 6 × 2

⇒ 36

Therefore, We get;

There are 36 different types of shirt available for this company.

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The volume of the cone is 301. 44mm³

First, we need to know the formula

the formula that is used for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters are;

Substitute the values, we have;

Volume = 3.14 × 6² × 8/3

Multiply the values, we have;

Volume = 904.32/3

Divide the values

Volume = 301. 44mm³

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Yes, the given triangle is a right triangle.

We have,

This can be determined by applying the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Now,

In this case, the squares of the side lengths are:

3² = 9

4² = 16

6² = 36

If the sum of the squares of the two shorter sides (9 + 16 = 25) is equal to the square of the longest side (36), then the triangle is a right triangle.

Thus,

In this case, since 25 is indeed equal to 36, the triangle with side lengths 3 miles, 4 miles, and 6 miles is a right triangle.

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Answer:

  53%

Step-by-step explanation:

You want to know the depreciation of car value after 5 years if it is 14% per year.

The multiplier of value each year is ...

  1 + growth rate = 1 + (-14%) = 0.86

When the value has been multiplied by that 5 times, it has been multiplied by ...

  0.86^5 ≈ 0.4704

This represents a change in value from the original value of ...

  0.4704 -1 = -0.5296 = -52.96% ≈ -53%

Zara's car has depreciated by 53% after 5 years.

<95141404393>

The  times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:

[tex]4e^{(-3t)[/tex] sin(2πt) = 0

Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:

4[tex]e^{(-3t)[/tex] = 0

This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.

sin(2πt) = 0

The sine function is zero at integer multiples of π.

So, we can set 2πt equal to integer multiples of π:

2πt = 0, π, 2π, 3π, ...

Solving for t in each case, we get:

t = 0, 1/2, 1, 3/2, ...

Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

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The product of matrices A and B are:

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

The product of matrices A and B are:

AB = A * B

[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(-3 * 6) + (-8 * 4) = -50

(-3 * 3) + (-8 * (-2)) = 7

(2 * 6) + (8 * 4) = 44

(2 * 3) + (8 * (-2)) = -10

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

BA =  B * A

[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(6 * (-3)) + (3 * 2) = -12

(6 * (-8)) + (3 * 8) = -30

(4 * (-3)) + ((-2) * 2) = -16

(4 * (-8)) + ((-2) * 8) = -48

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

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The surface area of the dilated solid is 2,880 square units

Multiply each side of the shape by 4

Surface area of a rectangular prism = 2(LH + LW + WH)

Where,

Length, L = 8 × 4 = 32 units

Width, W = 6 × 4 = 24 units

Height, H = 3 × 4 = 12 units

Surface area of a rectangular prism = 2(LH + LW + WH)

= 2(32×12 + 32×24 + 24×12)

= 2(384 + 768 + 288)

= 2(1,440)

= 2,880 square units

Therefore, 2,880 square units is the surface area of the solid.

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Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)

The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.

For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.

Number of patients that are over 60 years and are for regular cleaning = 10

Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42

Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)

                                                                = (5/21)

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The variable that is contained in the given expression is y. Therefore, option C is the correct answer.

The given expression is 7y+2y² +3.

In the given expression there are 3 terms, so it is called trinomial.

In the term 7y, y is the coefficient of 7.

In the term 2y², y² is the coefficient of 2.

3 is the constant term.

Therefore, option C is the correct answer.

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The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.

The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.

In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.

Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.

To simplify the answer, we can state that there are 8 possible different routes for the driver.

In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

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The solution is:  the measure of angles 2, 3, and 4 are:

m∠2 = 95°

m∠3 = 85°

m∠4 = 95°

Vertical Angle Theorem:

When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.

Therefore,

m∠3 = 85°

m∠2 = m∠4

Linear pair:

Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.

Therefore,

85° + m∠2 = 180°

m∠3 + m∠4 = 180°

If  85° + m∠2 = 180°

⇒ m∠2 = 180° - 85°

⇒ m∠2 = 95°

As  m∠2 = m∠4  then  m∠4 = 95°

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complete question:

Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready

please help i missed a day of class i cant figure this out

Answer:

To make a box-and-whisker plot, we first need to order the data from smallest to largest:

4, 5, 6, 10, 15, 16, 21

Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.

Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:

4, 5, 6, 10 and 15, 16, 21

The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.

Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:

Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)

Plugging in the values, we get:

Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25

Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.

Therefore, the box-and-whisker plot for the given data is:

            |       4

     ___|___

    |              |

    |              |

    |        5.5 |-----  

    |              |      |

    |              |      |

    |------------|  10 |  

    |              |       |

    |      15.5 |------

    |       |      |

     ___|___

            |       21

The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.

Hope this helps!

Answer:

450°

Step-by-step explanation:

52)  The midpoint of the line segment is (-0.5, 9).

53) The midpoint of the line segment is (3, -8.5).

52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.

For the x-coordinate:

(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5

For the y-coordinate:

(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9

Therefore, the midpoint of the line segment is (-0.5, 9).

53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.

For the x-coordinate:

(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3

For the y-coordinate:

(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5

Hence, the midpoint of the line segment is (3, -8.5).

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To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.

To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).

To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).

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The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.

To calculate vertical asymptote,

Putting the denominator equal to zero,

x²+2x+3 = 0

Using Quadratic formulae,

b² - 4ac

where,

b = 2

a = 1

c = 3

putting value,

4-12 = -8<0

therefore, the solution is negative

Hence, no vertical asymptote of the given equation exists,

To calculate the horizontal asymptote,

the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.

The coefficient of x² in the numerator is 1

Hence, the horizontal asymptote is y = 1.

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[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]

By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.

In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:

Now we proceed to present the complete procedure:

f(11) = 11 / (11 + 1) - 1

f(11) = 11 / 12 - 1

f(11) = 11 / 12 - 12 / 12

f(11) = (11 - 12) / 12

f(11) = - 1 / 12

f(- 2) = (- 2) / (- 2 + 1) - 1

f(- 2) = - 2 / (- 1) - 1

f(- 2) = 2 - 1

f(- 2) = 1

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The values of

1. cosθ = √3/2

2. sinθ = √3/2

3. tanθ = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

cosθ = adj/hyp

sinθ = opp/hyp

tanθ = opp/adj

sec θ = 1/cosθ

cosec θ = 1/sinθ

cot θ = 1/tanθ

We need to find the hypotenuse of the triangle

x² = 3² +3²

x = √9+9

x = √18

x = 2√3

cosθ = 3/2√3 = 6√3/12

= √3/2

2. sinθ = 3/2√3 = √3/2

3. tanθ = 3/3 = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

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Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

Answer:

Step-by-step explanation:

x+y+z=27

x+y=17

z=?

since x+y=17

then

17+z=27

z=27-17

z=10

Answer:

(a) 34 cm

Step-by-step explanation:

The formula for perimeter of a rectangle is

P = 2l + 2w, where

Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:

P = 2(12) + 2(5)

P = 24 + 10

P = 34

Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.