a man spent one-eighth of his spare change for a package of cigarettes, three times as much for a meal, and then had eighty cents left. how much money did he have at first?

Answer:

Mario's heart beats 112 times per minute.

To find out, we can use the following equation:

Heart rate = number of beats / time

Since we're given that Mario's heart beats 28 times in 1/4 minute, we can set up the equation like this:

Heart rate = 28 / 1/4

To divide by a fraction, we can multiply by its reciprocal:

Heart rate = 28 x 4/1

Heart rate = 112

Therefore, Mario's heart rate is 112 beats per minute.

The value of x must be x = 18, assuming that K is a point on the segment JL.

Here we have a segment JL, such that K is a point between J and L.

Here we know that the lengths are:

JK = x + 7

KL = 3x + 25

JL = 7x - 22

We know that the sum of the two first ones should be equal to the total segment:

JK + KL = JL

Then we can write the equation:

x+ 7 + 3x + 25 = 7x - 22

Solving this for x.

4x + 32 = 7x - 22

32 + 22 = 7x - 4x

54 = 3x

54/3 = x = 18

that is the value of x.

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Answer:

2)

3x + 13 = 16

3x + 13 + (-13) = 16 + (-13)

3x = 3

3x / 3 = 3 / 3

x = 1

3)

2x / 2 = 20 / 2

x = 10

Activity 3:

1) x = 13, m‹O = 137°

2) x = 5, PG = 18

Step-by-step explanation:

Answer:

3.06 cm^2/sec

Step-by-step explanation:

Since the shape is a cube, all sides have equal lengths, 6 cm  The rate of increase of 0.025cm/s [Note: I assume the unit should be cm/s, not cms'].

See the attached spreadsheet calculation.  Starting at time = 0 sec, the initial area is 36 cm^2.  Each second adds 0.025 cm to each side length,.

We can express this change in length as an equation:

Initial Length (6cm) + (x seconds)*(0.025 cm/s)

So for 10 second, l = 6 cm + 0.25cm or 6.25cm

--

The area is also changing with time.  At 0 seconds, the area is (6cm)^2 or 36 cm^2.  At 10 seconds, the area is (6.25cm)*(6.25cm) or 39.06 cm^2.

The area increased from 36 cm^2 to 39.06 cm^2 in 10 seconds.  That is a change rate of ((39.06 - 36 cm^2)/(10 sec):

 ((39.06 - 36 cm^2)/(10 sec)

 ((3.06 cm^2)/(10 sec)

3.06 cm^2/sec

Using the surface area, the cost value for metal is obtained as $8,707.68.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

To find the surface area of the tank, we need to find the area of the circular top and bottom, and the area of the cylinder.

The area of a circle is given by: A = πr², where r is the radius.

Since the diameter is given as 14 feet, the radius is 7 feet.

So, the area of the top and bottom circles is: A1 = π(7²) = 153.94 square feet (rounded to two decimal places).

The circumference of the circular base is given by: C = πd, where d is the diameter.

So, the circumference is: C = π(14) = 43.98 feet.

The height of the cylinder is given as 2 feet, and the circumference of the base is 43.98 feet.

So, the area of the curved surface of the cylinder is -

A2 = C × h

A2 = 43.98 × 2

A2 = 87.96 square feet (rounded to two decimal places).

Therefore, the total surface area of the tank is -

A = 2A1 + A2

A = 2(153.94) + 87.96

A = 395.84 square feet (rounded to two decimal places).

The cost of the metal per square foot is given as $22.

So, the total cost of the metal is -

Cost = Area × Cost per square foot

Cost = 395.84 × 22

Cost = $8,707.68.

Therefore, the metal will cost $8,707.68 in total.

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Answer:

69.56 meters

Step-by-step explanation:

Let's call the distance between the two people "y" and the length of the bridge "x". Using trigonometry, we can set up two equations:

tan(72.2°) = y / 25

tan(90° - 72.2°) = y / x

We can simplify the second equation to:

tan(17.8°) = y / x

Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the unknowns.

First, let's solve for y in the first equation:

tan(72.2°) = y / 25

y = 25 * tan(72.2°)

y ≈ 69.56 meters

Now we can substitute this value of y into the second equation:

tan(17.8°) = y / x

tan(17.8°) = 69.56 / x

x = 69.56 / tan(17.8°)

x ≈ 202.11 meters

Therefore, the length of the bridge is approximately 202.11 meters and the distance between the two people is approximately 69.56 meters.

The present ages of the child and woman are 4 and 16, respectively.

A quadratic equation is a polynomial equation of second degree in one variable. It has the structure:

ax² + bx + c = 0

where the variable x and the constants a, b, and c. There may be one, two real solutions to a quadratic equation or two complex solutions. They are helpful in finding the roots of polynomials and other parabolic shape-related problems, such as projectile motion. Quadratic equations can be solved using a variety of strategies, including factoring, completing the square, and the quadratic formula.

Let us suppose the current age of the child = x.

The current age of the woman is 4x.

5 years ago, the age of the child = x - 5.

The age of the woman was 4x - 5.

Thus,

(x - 5)(4x - 5) = 175

4x² - 25x + 20 = 0

4x² - 25x + 20 = 0

(4x - 5)(x - 4) = 0

x = 5/4 or x = 4.

We can discard the first solution, as it implies a negative age for the woman.

Therefore, the present ages of the child and woman are 4 and 16, respectively.

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f and g are inverse functions

17. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.

So, f(g(x)) = f(4x+9) = 4(4x+9)−9 = 16x+4−9 = 16x−5 = x.

Similarly, g(f(x)) = g(4x−9) = 4(4x−9)+9 = 16x−5+9 = 16x+4 = x.

Therefore, f and g are inverse functions.

18. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.

So, f(g(x)) = f(−2x+8/3) = −3/2(−2x+8/3)−4 = 6x−4−4 = 6x−8 = x.

Similarly, g(f(x)) = g(−3/2x−4) = −2(−3/2x−4)+8/3 = 3x−2+8/3 = 3x+8/3 = x.

Therefore, f and g are inverse functions.

19. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.

So, f(g(x)) = f(x3/4) = x3/44 = x3/256 = x.

Similarly, g(f(x)) = g(x4) = x4/4 = x3/4 = x.

Therefore, f and g are inverse functions.

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Mei needs to score at least 94 on her next history exam to have an average of at least 82.

Let's call the score that Mei needs on her next exam "x".

To find her average score, we need to add up all four scores (including the score she hasn't taken yet) and divide by 4:

(76 + 80 + 78 + x) / 4

Now, we want this expression to be greater than or equal to 82, so we can write the following inequality:

(76 + 80 + 78 + x) / 4 ≥ 82

Multiplying both sides by 4 to eliminate the fraction, we get:

76 + 80 + 78 + x ≥ 328

Simplifying the left side, we get:

234 + x ≥ 328

Subtracting 234 from both sides, we get:

x ≥ 328 - 234

x ≥ 94

Therefore, the least score neeeded on her next history exam is 94.

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The equation p = 8.50h allows us to calculate Eric's pay for any number of hours worked.

An equation is a mathematical statement that shows the equality of two expressions or quantities. It typically contains variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations are often used to solve problems and find unknown values.

Here,

Eric's pay is $8.50 per hour, so we can write:

p = 8.50h

where p is his pay and h is the number of hours worked.

Let's take an example, if Eric works for 20 hours, we can substitute h = 20 into the equation to find his pay:

p = 8.50(20)

p = 170

So Eric's pay for working 20 hours is $170.

Similarly, if Eric works for 40 hours, we can substitute h = 40 into the equation:

p = 8.50(40)

p = 340

So Eric's pay for working 40 hours is $340.

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The rate of return that Elaine needs on her account is of 22.16% to reach her goal of $4,000 in 4 years.

To calculate the rate of return for a savings account, you can use the formula:

Rate of return = [tex](Ending balance / Beginning balance)^{(1/n) - 1}[/tex]

where n is the number of years.

In Elaine’s case, she needs to save up $4,000 in 4 years. If she can set aside $50 per month, she will have saved $2,400 in 4 years. To calculate the rate of return she needs on her account, we can use the formula above.

To calculate the rate of return she needs on her account, we can use the formula above.

Let’s assume that she has $0 in her account at the beginning of the 4 years and $2,400 at the end of the 4 years.

Rate of return = [tex](2400 / 0)^{(1/4) - 1}[/tex]

= [tex](2400)^{(1/4) - 1}[/tex]

= 0.2216 or 22.16%

Therefore, Elaine needs a rate of return of 22.16% on her account to reach her goal of $4,000 in 4 years.

Keep in mind that this is a very high rate of return and may not be achievable with a savings account.

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Complete question is:

Elaine needs to save up $4,000 in 4 years. If she can set aside $50 per month, what rate of return does she need on her account?

The probability that Mark selects a car key or door key is 0.3

Mark has a total of 10 keys, and he is equally likely to select any one of them. Out of these 10 keys, there are 2 car keys and 1 door key. Therefore, the probability that he selects a car key or door key is the sum of the probabilities of selecting a car key and a door key.

The probability of selecting a car key is 2/10 or 1/5, since there are 2 car keys out of 10 keys.

Similarly, the probability of selecting a door key is 1/10, since there is only one door key out of 10 keys.

Therefore, the probability of selecting a car key or door key is:

P(car key or door key) = P(car key) + P(door key)

= 1/5 + 1/10

= 3/10

= 0.3

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The zeros and their multiplicities of the function are 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3 and 1,1,1,1.

The value which satisfy the polynomial. that is on substituting the value in the polynomial will give 0.

To find the zeros of the function, we need to solve the equation f(x) = 0. We can do this by factoring the polynomial using the difference of squares formula:

[tex]\begin{aligned} f(x)&=9 x^{4}-82 x^{2}+9 \ &= (3x^2 - 1)(3x^2 - 9) \ &= 3(x-\frac{1}{\sqrt{3}})(x+\frac{1}{\sqrt{3}})(x-3)(x+3) \end{aligned}[/tex]

From this factorization, we can see that the zeros of the function are:

x = 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3

Therefore, the zero of f is (1/3, -1/3, 3, -3). To determine the multiplicities of each zero, we can look at the degree of each factor.

For the factors (x - 3) and (x + 3), we have a degree of 1, which means that each of these zeros has multiplicity 1.

For the factor (x - 1/√3), we have a degree of 1 as well, which means that this zero also has multiplicity 1.

For the factor (x + 1/√3), we have a degree of 1, which means that this zero also has multiplicity 1.

Therefore, the zeros and their multiplicities of the function are 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3 and 1,1,1,1.

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The answer to this question is:

01. (+11)

02. (-33)

The positive integers are added directly to the positive integers as in 01 solutions 3+8 gives 11

where else in the 02 solutions both the integers are negative and when negative integers are added to each other it is added but the sign remains negative (-20)+(-13) gives (-33).

The other formulas are:

(+) × (+) = +;   (+) ÷ (+) = +

(-) × (-) = +;   (-) ÷ (-) = +

(+) × (-) = -;   (+) ÷ (-) = -

(-) × (+) = -;   (-) ÷ (+) = -

Answer:

[tex]01.(+3) + (+8) = +11)[/tex]

[tex]02.(-20) + (-13) = (-33)[/tex]

The algebraic property that can be used to rewrite 3x ⋅ (7y ⋅ 4) as (3x ⋅ 7y) ⋅ 4 is the associative property of multiplication.

The associative property of multiplication states that the grouping of factors in a multiplication expression does not affect the result. In other words, the order in which the multiplication operations are performed does not change the final answer. Thus, we can rearrange the multiplication expression by grouping 3x and 7y together using the associative property and then multiply the product by 4 to get the same result. This property is very useful in simplifying and solving multiplication expressions with multiple factors.

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RT is equal to 46 and angle ∠VUT is 26°.

A quadrilateral is a fοur-sided pοlygοn with fοur edges and fοur cοrners in geοmetry. The name cοmes frοm the Latin wοrds quadri, a variatiοn οf fοur, and latus, which means "side."

Tο find x nοte that the diagοnals οf a rectangle are cοngruent. This means that RT = SU.

So,  3x + 8 = 6x - 7

8 + 7 = 6x - 3x

3x = 15

x = 15/3

x = 5

RT = 2RV

= 2(3x + 8)

= 2(3(5) + 8)

= 2(15+ 8)

= 2(23)

= 46

Thus, RT is equal to 46

For  m∠VUT,

Given ∠VRU = 64°

Using complementary angles

64° + ∠VRS = 90°

∠VRS = 90° - 64°

∠VRS = 26°

Now, using alternate angle theory as RT is a transverse

∠VRS = ∠VTU = 26°

Now, as the diagonals are congruent ∠VTU = ∠VUT

∠VUT = 26°

Thus, RT is equal to 46 and angle ∠VUT is 26°.

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Answer:

The Area of the Triangle = 81.77

Step-by-step explanation:

Using the Formula for the Area of the Triangle given two sides and the included angle between them

Then the Area = [tex]\frac{1}{2} *13*15*sin(57)=81.77[/tex]

Hope it is Helpful

Li-ming's initial investment was $20,000, the interest rate was [tex]3.2[/tex]  % (or 0.032 as a decimal), and the total interest earned was $ [tex]2,240[/tex]  .

We can use the formula for simple interest to solve for the time:

Simple Interest [tex]= Principal \times Rate \times Time[/tex]

where Principal is the initial investment, Rate is the interest rate, and Time is the time period.

In this case, we know:

Principal = $[tex]20,000[/tex]

Rate =  [tex]3.2[/tex] %

Simple Interest = $ [tex]2,240[/tex]

Substituting these values into the formula, we get:

$ [tex]2,240 = $20,000 \times 0.032 \times Time[/tex]

Simplifying the equation, we get:

Time = $ [tex]2,240 / ($20,000 \times 0.032)[/tex]

Time  [tex]= 3.5[/tex] years (rounded to one decimal place)

Therefore, Li-ming's money was invested for 3.5 years to earn a simple interest of $  [tex]2,240[/tex] at a rate of  [tex]3.2[/tex] %.

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Answer:

1.     m∠1 = 60° because angle ∠1 and the 60° angle are vertical angles

2.    ∠1 and ∠2 are adjacent.

3.    m∠2 = 180° - 60°

Step-by-step explanation:

m∠2 is not equal to 60° because it is the complementary angle of the one labeled 60°. Therefore, m∠2 = 30°. m∠2 can be determined by the information given. m∠1 ≠ m∠2 because m∠1 = 60° and m∠2 = 30°

The equivalent expressions are:

(30/12)*k + (4/12)*k + 1-  3/4

(34/12)*k - 1/4

So here we have the expression:

(5/2)*k + 1 + (1/3)*k - 3/4

An equivalent expression is an expression that can be rewritten into this one.

If we simplify the expression we will get:

(5/2)*k + (1/3)*k + 1-  3/4

(15/6)*k + (2/6)*k + 1/4

(17/6)*k + 1/4

The equivalent expressions are then:

(30/12)*k + (4/12)*k + 1-  3/4  (this is like our second step).

(34/12)*k - 1/4 (just multiply the fraction by 2 in the denominator and numerator)

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The equivalent expressions of 5/2k + 1 + 1/3k - 3/4 are

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

5/2k + 1 + 1/3k - 3/4

Express the fractions to have equal denominators

So, we have

30/12k + 1 + 4/12k - 3/4 ---- this is represented by option (a)

Evaluate the like terms

34/12k + 1/4 ---- this is represented by option (d)

The above are the expressions equivalent to 5/2k + 1 + 1/3k - 3/4

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Answer:  Let's assume that the base of the rectangle is "x", and the height of the rectangle is "y". Let's also assume that the side length of the equilateral triangle is "t".

Then, we can write the perimeter of the window as:

p = x + 2y + 3t

We want to find the value of "x" that maximizes the area of the window. The area of the window can be expressed as:

A = xy + (1/2) * t * sqrt(3) * t

where the first term represents the area of the rectangle and the second term represents the area of the equilateral triangle.

To simplify the expression, we can use the perimeter equation to eliminate "y" and "t". Solving for "y", we get:

y = (1/2) * (p - x - 3t)

Solving for "t", we get:

t = (1/3) * (p - x - 2y)

Substituting these expressions into the area equation, we get:

A = x/2 * (p - x - 2y) + (1/6) * (p - x - 2y)^2 * sqrt(3)

Expanding this expression and simplifying, we get:

A = (1/12) * (p^2 - 2px + 3x^2) * sqrt(3) + (1/2) * px - (1/2) * x^2

To find the value of "x" that maximizes this expression, we can take the derivative of "A" with respect to "x" and set it equal to zero:

dA/dx = (1/12) * (6x - 2p) * sqrt(3) + (1/2) * p - x = 0

Simplifying this expression, we get:

x = (1/33) * (6 + sqrt(3)) * p

Therefore, in order to obtain a window of maximum area, the base of the rectangle should be equal to (1/33) * (6 + sqrt(3)) times the perimeter of the window.

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The surface area οf the cοne is 578.1 square feet.

An οbject's surface area is the tοtal area that all οf its surfaces οccupy. The fοrmulas we will learn in this pοst make it simple tο determine the variοus surface areas that variοus 3D shapes in geοmetry have. There are twο grοups fοr the surface area:

1. Surface area οf the lateral Surface that is curved.

2. Surface area οverall

In the questiοn,

We knοw that fοr a cοne οf radius R and slant height H the surface area is given by the fοrmula:

S = π×R^2 + π×R×(H)

with pi = 3.14

On the diagram we can see that H = 19.3ft, and the diameter οf the base is 14 ft, then the radius is:

R = 14ft/2

= 7ft

Replacing these values in the fοrmula abοve we will get:

S = 3.14×(7ft) ² + 3.14×7ft×(19.3ft)

= 578.1 ft²

Sο, the cοrrect οptiοn is the secοnd οne.

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The complete question is:

Which is closest to the surface area of the figure below? 1463.8 m2 1463.8 m squared 578.1 m2 578.1 m squared 923.2 m2 923.2 m squared 3692.6 m2

let's recall that Bearing is always a clockwise angle using the North Line, so  "of X from Y", means we draw a North line at Y and a line towards X, clockwise is our angle.  Check the picture below.

Answer: it represent the hours it took

Step-by-step explanation:

Answer:

Answer

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

M=4-3/6-8

=1/-2

=-0.5

midpoint=4+3/2=6+8/2

=7/2=14/2

=3.5=7

(7;3.5)

Answer:

It’s the last one 3/5

Step-by-step explanation:

because you just simplify 18/30 with 6, witch =3/5.

18/30 divided by 6 for each and get (=) 3/5

9 ounces are left in the bucket. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is asserted that the four basic operations, usually referred to as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that Gina and Lane share a 24-ounce bucket of clay.

Gina has used [tex]\frac{3}{8}[/tex] of the bucket of clay.

So, we get

[tex]\frac{3}{8}[/tex] of 24 = 9 ounces

Similarly, Lane has used [tex]\frac{1}{4}[/tex] of the bucket of clay.

So, we get

[tex]\frac{1}{4}[/tex] of 24 = 6 ounces

Using the addition operation, we get

Total clay used = 9 + 6 = 15 ounces

Now, using the subtraction operation, we get

Ounces left = 24 - 15 = 9 ounces

Hence, 9 ounces are left in the bucket.

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Question: Gina and Lane share a 24-ounce bucket of clay. By the end of the week, Gina has used 3/8 of the bucket, and Lane has used 1/4 of the bucket of clay. How many ounces are left in the bucket?

The answer of the given question based on the an upward-sloping normal yield curve the answer is there is a positive maturity risk premium.

In mathematics and geometry,  curve is  continuous and smooth line or path that can be described using the mathematical equations or functions. Curves can be of different shapes and sizes, like  straight lines, circles, ellipses, parabolas, hyperbolas, and more complex shapes.

Based on an upward-sloping normal yield curve, the correct statement would be: there is a positive maturity risk premium.

The maturity risk premium is the additional return that investors require to hold a longer-term bond instead of a shorter-term bond. In an upward-sloping normal yield curve, longer-term bonds have higher yields than shorter-term bonds, indicating that investors are demanding a higher return to hold longer-term bonds.

This additional return, or maturity risk premium, compensates investors for the risk that interest rates may rise in the future, which would cause the value of longer-term bonds to decline more than shorter-term bonds. Therefore, a positive maturity risk premium indicates that investors expect interest rates to rise in the future.

However, the shape of the yield curve alone does not provide information on future inflation expectations. Other factors such as economic growth, monetary policy, and geopolitical events can also influence interest rates and inflation expectations.

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Answer:

3y-16

y-5=x

4x-y+4

4(y-5)-y+4

4y-20-y+4

3y-16