Kala bad 109 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left

Answer:

36 trust me I'm good at math

Step-by-step explanation:

add 19 and 17

Answer:

67.5 in^3

Step-by-step explanation:

just calculate the volume

= 5 x 4.5 x 3

= 67.5 in^3

Answer:

The answer is option A.

Step-by-step explanation:

A. y = 8/7x +5

In this problem, we are given vectors and asked to find the angle between them or calculate the dot product of linear combinations of the vectors. The angle between vectors can be determined using the dot product formula, and the dot product of linear combinations can be found by applying the properties of dot products and the given values of dot products between the vectors.

To find the angle θ between vectors u and v, we can use the formula: θ = cos^(-1)((u . v) / (||u|| ||v||)), where u . v represents the dot product of u and v, and ||u|| and ||v|| represent the magnitudes (or lengths) of u and v, respectively. By substituting the given values, we can calculate the angle θ in radians.

For the dot product of linear combinations (2u - 3v) . (3u - 2v), we can expand the expression and use the properties of dot products to simplify it. By substituting the given values of dot products between u and v, we can evaluate the expression and obtain the result.

By applying the appropriate formulas and calculations, we can find the angle θ between the vectors and calculate the dot product of linear combinations of the vectors.

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Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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Answer:

volume of the cylinder = 18,480

Step-by-step explanation:

volume of a cylinder =

\(v = \pi {r}^{2} h\)

where radius = 14cm

height = 30cm

therefore the volume

\(v = \frac{22}{7} \times {14}^{2} \times 30 \\ v = 22 \times 14 \times 2 \times 30 \\ v = 18480\)

Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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a private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks, and we need to determine whether the hypothesis test is two-tailed, right-tailed, or left-tailed and the given values. The required sample size is 1068.

Given that a private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks, and we need to determine whether the hypothesis test is two-tailed, right-tailed, or left-tailed and the given values are

Hop = 0.83

H1p ≠ 0.83

The given hypothesis test is two-tailed because of the ≠ sign.

To solve for the required sample size when a proportion will not differ from the true proportion by more than 3, we use the following formula:

n = (Z/ε)² * p(1-p)

where,

Z = 1.96 for a 95% confidence level

ε = 0.03

p = 0.5

(since we do not have any information about the population proportion)

Now, substituting the values, we get

n = (1.96/0.03)² * 0.5 * 0.5

n ≈ 1067.11

≈ 1068

Therefore, the required sample size is 1068.

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Answer:

the inclination of the line will decrease

Step-by-step explanation:

If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease

The proof of the given statement "there do not exist positive integers a and n such that a^2 3 = 3^n" is stated below.

Taking the square root of both sides gives:

a = 3^(m - 1/2)

Since m is a positive integer, (m - 1/2) is not an integer. Therefore, a cannot be an integer, which contradicts our assumption. Hence, there do not exist positive integers a and n such that a^2 * 3 = 3^n.

To prove that there do not exist positive integers a and n such that a^2 * 3 = 3^n, we will use proof by contradiction.

Assume that there exist positive integers a and n such that a^2 * 3 = 3^n. Then we can write:

a^2 = 3^(n-1)

Since 3 is a prime number, we know that any power of 3 is not a perfect square, except for 3^0 = 1. Thus, the equation above implies that a^2 is a power of 3 minus 1.

We can then write a^2 + 1 = 3^(n-1) + 1. Since a^2 is not divisible by 3, a^2 + 1 is not divisible by 3 either. Therefore, n must be even, so we can write n = 2m for some positive integer m.

Now, we have:

a^2 = 3^(2m - 1)

Taking the square root of both sides gives:

a = 3^(m - 1/2)

Since m is a positive integer, (m - 1/2) is not an integer.

Therefore, a cannot be an integer, which contradicts our assumption. Hence, there do not exist positive integers a and n such that a^2 * 3 = 3^n.

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Answer:

-1/2 and 1/3

Step-by-step explanation:

hope this helps?:)

Answer:

-½ and ⅓

Step-by-step explanation:

6x²+ x - 1 = 0

6x²+3x -2x - 1 = 0

3x(2x + 1) -1(2x + 1) = 0

(3x-1)(2x + 1) = 0

3x-1 = 0 and 2x + 1 = 0

3x = 1 2x = -1

x = ⅓ x = -½

Answer:

7abc

24h

63gh

28fg

27deyz

Step-by-step explanation:

7∙a∙b∙c = 7abc

3h ∙ 8 = 3  ∙ 8 ∙ h = 24h

7g ∙ 9h = 7 ∙ 9 ∙ g ∙ h = 63gh

4f ∙ 7g = 4 ∙ 7 ∙ f ∙ g = 28fg

3de ∙ 9yz = 3 ∙ d ∙ e ∙ 9 ∙ y ∙ z = 3 ∙ 9 ∙ d ∙ e ∙ y ∙ z = 27deyz

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

The second term of an infinite geometric series can be determined using the formula for the sum of an infinite geometric series.



In this case, the sum of the series is given as 200 and the common ratio is 0.15. We can use this information to find the second term of the series.

The formula for the sum of an infinite geometric series is S = a / (1 - r), where S is the sum of the series, a is the first term, and r is the common ratio. We are given that the sum of the series is 200 and the common ratio is 0.15.

Substituting these values into the formula, we have 200 = a / (1 - 0.15). Simplifying, we get 200 = a / 0.85. Multiplying both sides by 0.85, we find that a = 170. Therefore, the first term of the series is 170. Since the common ratio is 0.15, the second term of the series can be calculated by multiplying the first term by the common ratio: 170 * 0.15 = 25.5. Hence, the second term of the series is 25.5.

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Answer: >500

Step-by-step explanation:

Following is a description of the proportionate relationship in the table:

The number of hours spent exercising determines the quantity of calories expended. 190 calories are burned after a one-hour workout, and 380 calories are burned during a two-hour workout.

The definition of a proportionate relationship is as follows:

y = kx.

where k is the proportionality constant.

The following are the factors for this issue:

Number of hours to enter.

Calorie burned as an output.

Because of this, the constant is stated as k = 570/3 = 380/2 = 190/1 = 190 calories burned per hour.

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The complete question is:

The table shows a proportional relationship.

Workout (hours) 1 2 3

Calories Burned 190 380 570

Create a description in words for the table.

The number of calories burned is dependent on the number of hours working out. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.

The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.

The number of hours working out is dependent on the number of calories burned. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.

The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there

In one-year, the promised yields have risen to 7%, then the 1-year holding-period return was : (a) 0.61%.

The "Par-value" of the bond (face value) is = $1,000;

Coupon rate = 6% (annual payment coupon)

Yield at purchasing time is = 6%

Yield after 1 year = 7%

Step 1: Calculate the present value of the redeemable value:

We know that PVIF at 7% for 7 years is 0.623,

So, Present value of redeemable value = (Par value) × PVIF = $1,000 × 0.623 = $622.75,

Step 2: Calculate the present value of coupon payments:

Coupon payment = (Coupon rate)×(Par value) = 6% × $1,000 = $60,

We know that PVAF at 7% for 7 years is 5.389,

So, Present value of coupon payments = (Coupon payment) × (PVAF) = $60 × 5.389 = $323.36,

Step 3: Calculate the price of bond after 1 year:

Price of bond = Present value of redeemable value + Present value of coupon payments,

Substituting the values,

We get,

Price of bond = $622.75 + $323.36 = $946.11

Step 4: Calculate the 1-year holding-period return:

Holding return = (Price in next year + Coupon interest - Price in current year) / Price in current year,

Holding return = ($946.11 + $60 - $1,000) / $1,000

Holding return = $6.11 / $1,000

Holding return = 0.00611 = 0.61%.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

You buy an 8-year $1,000 par value bond today that has a 6% yield and a 6% annual payment coupon. In 1 year promised yields have risen to 7%. Your 1-year holding-period return was

(a) 0.61%

(b) -5.39%

(c) 1.28%

(d) -3.25%

The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.

acceleration = change in velocity / Time taken

a = 0 - 15.6 / 4.2

= -15.6 / 4.2

=  -3.71

The average acceleration is -3.71m/s²

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Given:

The inequality is

\(2n+8>12\)

To find:

The solution of the given inequality.

Solution:

We have,

\(2n+8>12\)

Subtract 8 from both sides.

\(2n+8-8>12-8\)

\(2n>4\)

Divide both sides by 2.

\(\dfrac{2n}{2}>\dfrac{4}{2}\)

\(n>2\)

It means, the value of n is greater than 2.

Therefore, the solution of given inequality is n > 2.

Here, the opposite angles of the triangle are equal. If 2 opp. angles in a triangle are equal, then the opposite sides will be equal as well.

So,

16 = x + 36

16 - 36 = x

-20 = x

______

Hope it helps ⚜

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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Answer:

The correct answer is: y=cosx + 2

Answer: Option B

Step-by-step explanation: To analyze the given graph let us,

compare the given to a known, standard function

take maxima and minima points from the graph and analyze them.

From the given graph we can pick the points which can tell us about the nature of the cosine function we took,

It is clear from the graph that the function plotted is 2 times greater than the standard function i.e. cos(x)

in cos(x) ⇒ we have minima at (-π, 1)

in the graph, ⇒ we have minima at  ( , -1)

By a factor of 2, there is a change in the graph with respect to the standard cosine graph.

hence, the graph given is cos(2x)  

we know that,

at (0,1) the cosine graph touches the y-axis.

in the given graph, the function has a maximum and touches the y-axis at (0,4)

therefore, 4× cos(2x) is the function represented in the graph.

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The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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The volume of a sphere is given by

where Pi=3.14 and r is the radius, which in our case is 5cm.

By substituting these values into the last formula, we get

which gives

then, by rounding to the nearest hundredth, the volume is 525.33 cm^3

The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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Answer:

70 miles

Step-by-step explanation:

If Nadia has a gas tank that can hold 14 gallons of gas and she uses a quarter of it, she has used 14 * 0.25 = 3.5 gallons of gas.

Since each gallon of gas can go 20 miles, Nadia has gone

3.5 * 20 = 70 miles

The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.

To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.

To explain this mathematically, we can use the formula:

where Inches/Foot = 12 and Feet/Yard = 3.

Plugging in the appropriate variables, we can calculate the number of inches in a football field as:

Inches = 120 x 3 x 12 = 4320 inches.

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Answer:

\(x_1=2; x_2=-1\)

Step-by-step explanation:

The square term is \(x^2\) so we expect the complete square to be of the form \((x-a) ^2=x^2+2ax+a^2\).

Let's compare the first degree terms now: we have \(2ax\) on one side and \(-1x\) on the other. That would make \(a=- \frac12\). At this point we have still the second squared term, so we add and subtract \(\frac14 = (\frac12)^2\)

Our equation becomes:

\(x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0\)

(the \(\frac94\) term comes from rewriting \(2= \frac84\) and adding the terms out of the bracket).

At this point it's just solving the equation:

\((x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1\)

The regular expression (xy | zy)* describes a language that consists of zero or more repetitions of either "x" followed by zero or more "y"s or "z" followed by one or more "y"s. "zyyxz" is part of the language generated by the given regular expression.

In the given string, "zyyxz", we can break it down into individual components based on the regular expression. The first "z" matches the pattern "z" followed by one or more "y"s. The "yyx" part matches the pattern "x*y", where "y" occurs zero or more times after "x". Finally, the "z" at the end also matches the pattern "z" followed by one or more "y"s.

Since all parts of the string "zyyxz" match the regular expression pattern, we can conclude that "zyyxz" indeed belongs to the language described by the regular expression (xy | zy)*.

Therefore, "zyyxz" is part of the language generated by the given regular expression.

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