wer:
My number is a 2-digit multiple of 9. The ratio of its units digit to its tens digit is 1:2.
What is my number?

Answer: The result when the number 45 is increased by 57% is approximately 70.65.

Step-by-step explanation:

To find the result when the number 45 is increased by 57%, we need to calculate 45 * (1 + 0.57), where 0.57 represents 57% as a decimal.

Performing the calculation, we get:

45 * (1 + 0.57) = 45 * 1.57 = 70.65

So, the result when the number 45 is increased by 57% is approximately 70.65.

Answer:

70.65

Step-by-step explanation:

The new value =

45 + The value of the percentage increase =

45 + (57% × 45) =

45 + 57% × 45 =

(1 + 57%) × 45 =

(100% + 57%) × 45 =

157% × 45 =

157 ÷ 100 × 45 =

157 × 45 ÷ 100 =

7,065 ÷ 100 =

70.65

Answer:

Step-by-step explanation:

Calculate the total hours used: We add up the hours used each year to find the total hours used:

2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500

Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:

$219,000 - $19,500 = $199,500

Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:

$199,500 / 6 = $33,250

Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:

$33,250 / 12,500 = $2.66

So the depreciation expense per hour is $2.66.

Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:

Year 1: 2,800 * $2.66 = $7,448

Year 2: 1,400 * $2.66 = $3,724

Year 3: 1,500 * $2.66 = $3,990

Year 4: 2,500 * $2.66 = $6,650

Year 5: 2,300 * $2.66 = $6,118

Year 6: 2,000 * $2.66 = $5,320

So the depreciation expense for each year is:

Year 1: $7,448

Year 2: $3,724

Year 3: $3,990

Year 4: $6,650

Year 5: $6,118

Year 6: $5,320

Answer:

It depends on the amount of slices.

Step-by-step explanation:

The diameter of the pie is 10 inches. Multiply this by π and we get approximately 31.4. Basically just divide it by the number of slices. For example, if there were six slices, 31.4/6=5.23, so that's the arc length of one slice.

The value of the expression is -11/15

It is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.

From the information given, we have that;

3 1/2x - 5 1/3x

turn into improper fractions

7x/2 - 16x/3

Now, let's determine the value by substituting the  value of x as 2/5 in the expression, we have;

7(2/5)/2 - 16(2/5)/3

Multiply the values

14/5/2 - 32/5 /3

Take inverse of the denominator

14/5 ×1/2 - 32/5 × 1/3

7/5 - 32/15

21 - 32/15

-11/5

Hence, the value is -11/15

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Answer:

41 inches

Step-by-step explanation:

to find the perimeter of any shape, add the length of all the sides together

Answer:

Step-by-step explanation:

I do not know bro. If I was a robot i'd know. I don't. I'm different.

Answer:

-30

Step-by-step explanation:

Answer:

1. 18 + 35

2. 6 * 50

3. b - 25

4. x / 4

5. t + 11

6. 100 - k

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:

     (1)

    /   \

 (H)     (T)

/   \   /   \

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

b) There are four stages in the tree diagram.

c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTTT

d) There are 2^4 = 16 outcomes in the sample space.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1)

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4)

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1).

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4).

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.

Approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

A logarithmic equation is an equation that involves a logarithmic function. A logarithmic function is the inverse of an exponential function, and it represents the exponent to which a given base must be raised to obtain a given number.

The formula that relates the energy released by an earthquake to its magnitude is given by:

logE = 5.24 + 1.44M

To find the amount of energy released by a magnitude 5 earthquake, we can substitute M = 5 into the formula and solve for E.

logE = 5.24 + 1.44(5)

logE = 5.24 + 7.2

logE = 12.44

Now we need to convert this logarithmic value to a regular value of E. We can do this by taking the antilogarithm (or exponentiating) both sides of the equation.

10⁽ˡᵒᵍᴱ⁾ = 10⁽¹²ॱ⁴⁴⁾

E = 2.51 x 10¹² joules

Therefore, approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

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The echelon form of the given augmented matrix with 1's on the diagonal is:

1 -1 0 1000

0 1 0 1100

0 0 1 300

To find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:

Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:

1 -1 2 400

0 1 -2 500

0 -2 5 -700

Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:

1 -1 2 400

0 1 -2 500

0 0 1 300

Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:

1 -1 0 1000

0 1 0 1100

0 0 1 300

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The perimeter of the trapezoid is 49.4.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

From the graph,

Height = 12 units

Parallel sides = 9 units and 15 units

Now,

Another side = x

Using Pythagorean theorem.

x² = 6² + 12²

x² = 36 + 144

x² = 180

x = √180

x = 13.42

Now,

The perimeter of the trapezoid.

= 12 + 13.42 + 9 + 15

= 49.42

= 49.4

Thus,

49.4 is the perimeter of the trapezoid.

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The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7.5/2

Constant of proportionality, k = $3.75.

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The probability of getting two twos is 0.003

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

probability = sample space/total outcome

probability of getting two = 1/6

probability of getting two twos = 1/36

getting two two can only 10times = 1/36 ÷ 10

= 10/36 = 0.003 (nearest thousandth)

therefore the probability of getting two twos in 20 rolls is 0.003( nearest thousandth)

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The leading coefficient of the expression is 1

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

4x² + x4 -8 -5

When written in standard form, we have

x^4 + 4x^2 - 8 - 5

Evaluate the like terms

x^4 + 4x^2 - 13

The leading coeffiicient is the coefficient of the term with highest power

In this case, it is

Coefficient = 1

Hence, the value is 1

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a. The number of pizzas the pizzeria must sell today for employees to receive the bonus will be 78 pizza.

b. The percent decrease in the number of pizzas sold today compared to yesterday is 7.69%.

a) To determine the number of pizzas the pizzeria must sell today for employees to receive the bonus, we need to calculate 20% of the 65 pizzas sold yesterday. 20% of 65 pizzas is 0.20 * 65 = 13. So, the pizzeria must sell 65 + 13 = 78 pizzas today for employees to receive the bonus.

b) To calculate the percent increase or decrease in the number of pizzas sold today compared to yesterday, we need to divide the difference between the two days' sales by the number of pizzas sold yesterday and multiply by 100.

((60 - 65) / 65) * 100

= (-5 / 65) * 100

= -7.69%

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Answer:

The correct answer is D. y = 3.35x + 73.96.

Step-by-step explanation:

D. y = 3.35x + 73.96

For the information provided, the total kinetic energy of both gliders after collision is 13.5 J. In an elastic collision, both momentum and kinetic energy are conserved.

The momentum conservation principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, we can write this as:

m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f

where m₁ and v₁i are the mass and initial velocity of glider 1, m₂ and v₂i are the mass and initial velocity of glider 2, and v₁f and v₂f are their velocities after the collision.

Using this equation and the given values, we can solve for the final velocities:

(7.0 kg)(2.0 m/s) + (4.0 kg)(-5.0 m/s) = (7.0 kg)v₁f + (4.0 kg)v₂f

14.0 kg·m/s - 20.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f

-6.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f ---(1)

The kinetic energy of an object is given by the equation:

KE = 1/2 mv²

Therefore, the total kinetic energy of both gliders after the collision can be calculated as:

KE_total = 1/2 m₁ v₁f² + 1/2 m₂ v₂f²

Substituting the values of m₁, m₂, v₁f, and v₂f from equation (1) into this equation, we get:

KE_total = 1/2 (7.0 kg) (0.86 m/s²) + 1/2 (4.0 kg) (5.14 m/s²)

KE_total = 13.5 J

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In  linear equation, 2 miles per hour is the rate in miles per hour .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Divide the distance by the time.

(1/5 miles) / (1/10 hour)

= 10(1/5) miles per hour

= 2 miles per hour

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The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;

A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.

The coordinates of the vertices of the triangle are;

X(0, 5), Y(10, 3), Z(4, -1)

The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;

The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;

Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))

The coordinates of the point Y(4, -1) following the composite transformation is therefore;

Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)

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now, we're making the assumption we're simply doing an identity proof, so

[tex]sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}[/tex]

The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.

It is important to understand the concept of interest beacause it is a part of our life and it hels us to understand the economic situation of ourselves.

It is the interest calculated on the principal at a given rate for a time period.

We have.

There are two types of interest commonly studied.

1)

Simple interest

2)

Compound interest

Now,

Simple interest is the interest calculated only on the principal year after year.

Whereas compound interest is the interest calculated on the principal as well as the interest after the first year.

Example:

Principal = $100

Rate = 10%

Time = 2 years

Simple interest after two years.

= 2 x (10% of 100)

= 2 x (1/10 x 100)

= 2 x 10

= $20

Compound interest after two years.

Ist year:

=  (10% of 100)

= (1/10 x 100)

= $10

2nd year:

= 10% of (100 + 10)

= 1/10 x 110

= $11

So,

= 10 + 11

= $21

Thus,

The concept of interest is given above.

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Answer:

Center = (-3, -3)

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]

[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]

Answer:

The answer

Step-by-step explanation:

Figure 1 figure

3/4

The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.

To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)

Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)

The number of monthly payments for the loan is plugged and computed as:

n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)

n = (-log(1 - 0.0208)) / log(1.0033)

n = (-log(0.9792)) / log(1.0033)

n = 21.8068 / 0.093984

n = 232.48 payment.

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You would earn $0.006 for recycling 24 iced tea cans.

To determine the amount earned from recycling 24 iced tea cans, we need to find the total weight of the aluminum used in those cans and then convert that weight to pounds.

The total weight of the aluminum used in 24 cans as follows:

24 cans * 0.01 ounce per square inch = 0.24 ounces

Converting ounces to pounds, using a conversion factor of 1/16:

0.24 ounces / 16 ounces per pound = 0.015 pounds

The total amount earned:, since each pound is $0.40

0.015 pounds * $0.40 per pound = $0.006

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Answer: the answer is C just did it

The store with the best deal is given as follows:

Store D.

The store with the best deal is obtained applying the proportions in the context of the problem.

The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.

Hence the hourly cost for each store is obtained as follows:

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