Your cousin’s birthday is this weekend. You want to buy a CD that costs $12.99 and a birthday card that costs $2.50. You have saved $25. Write an inequality to find the most money you have for other spending.

It took Paul a total of 12 hours and 40 minutes to complete all three parts of the Ironman triathlon.

Paul’s time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for biking was 5 hours longer than her swimming time, so her biking time was (1 hour + 5 hours) = 6 hours 25 minutes. She ran for 4 hours 50 minutes. The total time it took her to complete all three parts of the race is (1 hour 25 minutes) + (6 hours 25 minutes) + (4 hours 50 minutes) = 12 hours 40 minutes.

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See below for the proof of the trigonometry identity

The identity is given as:

(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1

Start by expanding the numerator

(sin²(x) + cos²(x) + sin(2x)) / sin(2x)= csc (2x) + 1

Express sin²(x) + cos²(x) as 1

(1 + sin(2x)) / sin(2x)= csc (2x) + 1

Expand the fraction

1/sin(2x) + sin(2x)/sin(2x) = csc(2x) + 1

Evaluate the quotient

csc(2x) + 1 = csc(2x) + 1

Hence, the trigonometry identity has been proved

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The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.

What is Translation ?

Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.

That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,

So, the measurement of segment A'B' would be 2 unit.

Verification :

Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,

Also, the rule of translation 6 unit right is,

(x,y) → (x + 6, y)

By the distance formula,

The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²

Thus, if A'B' is the transformed segment of segment AB,

Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)

So, the measure of segment A'B' =

√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²

Hence, the measure of AB = measure of A'B'.

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Answer:

n,n

I think

Step-by-step explanation:

Answer:

n,n

Step-by-step explanation:

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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EXPLANATION

Since we have that Ed bikes 48.6 miles, dividing this number by the number of hours will give us the mean speed as shown as follows:

In conclusion, the mean speed is 18 miles/hour

Answer:

h(-2) = 13

h(5) = -1

Step-by-step explanation:

Given the function

h(x) = -2x + 9

Evaluating at x = -22

substitute x = -2

h(-2) = -2(-2) + 9

h(-2) = 4 + 9

h(-2) = 13

Therefore,

Evaluating at x = 5

Given the function

h(x) = -2x + 9

substitute x = 5

h(5) = -2(5) + 9

h(5) = -10 + 9

h(5) = -1

Therefore,

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Step-by-step explanation:

mean = sum of all data points / number of data points

(1.3+1.5+2.2+2.2+2.8)/5 = 10/5 = 2

median is the number where half of the other data points are smaller or equal, and the other half are larger or equal.

median = 2.2

mode is the data point occurring most often = 2.2

range is the difference between largest and smallest data point : 2.8 - 1.3 = 1.5

It's important to note that the logarithm function is defined only for positive values of x.  f(10) = log(10) ≈ 1.000.

To evaluate f(x) = log(x) at a given value of x, you need to input that value into your calculator and then apply the logarithm function to it. For example, let's say you want to evaluate f(x) = log(x) at x = 10. Here's how you would do it:

1. Input 10 into your calculator.
2. Press the "log" button to apply the logarithm function.
3. Your calculator should display the result, which is approximately 1.000 (rounded to three decimal places).

So, f(10) = log(10) ≈ 1.000.

It's important to note that the logarithm function is defined only for positive values of x. If you try to evaluate f(x) = log(x) at a negative value of x, your calculator will give you an error message.

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1/2 is the likelihood of rolling an odd or even number in probability.

What is probability and how is it calculated?

The event "rolling an odd number" contains three outcomes. There are 6 equally likely outcomes in the sample space. Divide to find the probability of the event.

  P(E) = 3/9 = 1/2

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Answer:

Step-by-step explanation:

f(x)=2x^2-9x-18

(2x+3)(x-6)

Answer:

Let's solve for x. x=2y

Step-by-step explanation:

Let's solve for x.

x−2y=0

Step 1: Add 2y to both sides.

x−2y+2y=0+2y

x=2y

Let's solve for y.

x−2y=0

Step 1: Add -x to both sides.

x−2y+−x=0+−x

−2y=−x

Step 2: Divide both sides by -2.

−2y/−2=−x/−2

y=1/2x

The statement that you assume direct variation unless stated otherwise is True.

The true statement is that we assume direct variation unless another relationship is stated. Direct variation is a form of mathematical rule in which variables change in a proportional manner. One of the variables changes in relation to the other.

This is the standard way of representing many mathematical equations. So, we assume direct variation unless another relationship between the variables is specified. The formula, y =ks can be used to represent direct variations, and the s in the equation signifies the constant.

Complete Question:

Do you assume direct variation, unless stated otherwise? True or False.

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We can write 2 equations from the information given.

Let the amount invested in CD be "x" and the amount invested in bond be "y".

The total amount invested is $600,000. Thus, we can write,

The CD pays 2% (0.02) and the bond pays 8.5% (0.085). Total interest needed is $27,000. Thus, we can craft another equation,

Solving the first equation for "x", we can substitute it into the second equation and solve for "y" first. The steps are shown below:

Now, we can find "x",

Rounded to the nearest dollar, we write our answer >>>

Answer:

I would have to say C.) VA

Step-by-step explanation:

i obviously can't sketch it out but in a triangle there is the hypotenuse, the opposite, and the adjacent. this is going by the right angle in the triangle.

ok the triangle we are working with is YAV. in this triangle, the segment VA is the shortest

Answer:

use the formula( I=PTR/100)

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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Answer:

I have no idea what it is sorry

The factorization  of the polynomial is:

(x - 4)*(x + i)*(x - i)

If (x - x₁) is a factor of a polynomial, then x₁ is a zero of the polynomial.

Now we can evaluate the polynomial in the values of the options and see which ones are zeros.

if x = 4

p(4) = 4³ - 4*4² + 4 - 4 = 0

So (x-  4) is a factor.

if x  = i

p(i)= i³ - 4*i² + i - 4

     = -i + 4 + i - 4  = 0

(x - i) is not a factor.

if x = -i

p(-i) = (-i)³ - 4*(-i)² - i - 4

        = i + 4 - i - 4 = 0

Then the factorization is:

(x - 4)*(x + i)*(x - i)

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Answer:

Step-by-step explanation:

Answer:

5x+4

Step-by-step explanation:

A double negative sign gives a positive sign

Answer: 20

Step-by-step explaination: -4 minus 5x=20 because 4x5=20+-x=20

Non-response could cause the results of the survey to be biased because those people who did not respond in the survey may differ from those who did respond.

In the question, we are given;

A total of 2,000 people on a survey

we are told 317 (sample)  people returned the survey

The data given in the question is a non-response bias, therefore;

We can say that, people who did not respond in the survey may differ from those who did respond to the survey

Usually, in non-response bias, the samples that are given or chosen by people, are not capable of participating in the survey.

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3.65 is less than \(3\frac{3}{4}\)

First, you must change the mixed number into a decimal so you can compare the two numbers.

\(3\frac{3}{4} = 3.75\)

Then, you must compare the terms.

3.65 < 3.75

3.65 is less than \(3\frac{3}{4}\)

The effective interest rate on the operating lease is 12.45%

Under the straight-line method of depreciation, the annual depreciation for the computers can be determined as follows:

Depreciation expense = (Cost - Residual value) / Useful life

Depreciation expense = ($120,000 - $0) / 6 years = $20,000 per year

Hence, semi-annual depreciation is $10,000 ($20,000 / 2) per payment.

The operating lease payments are $15,000 per semi-annual payment. The total amount of the lease payments for the 2-year term is $60,000 ($15,000 x 4).

Thus, the present value of the operating lease payments can be computed as follows:PV of lease payments = ($10,000 / 0.0609) x [1 - (1 / 1.0609^8)]PV of lease payments = $47,907.29

The implicit interest rate on the lease is 0.0609 or 6.09% (computed by dividing the lease interest by the present value of the lease payments).

The effective interest rate is 12.45% (computed by doubling the implicit interest rate).

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Answer:

4760

Step-by-step explanation:

Simple interest= principal× time ×rate/100

=3500×4×9/100

= 1260

Amount that will be in the bank after 4years= 3500+1260

=4760

Answer:

look at the picture i sent......

Answer:

$3

Step-by-step explanation:

8 + 7 = 15

15 - 12 = 3

Answer:

6 x 25 = 150-40=110

Step-by-step explanation:

It's right I promise you

Answer:

Terms: 4x, -\(\frac{x}{2}\)

Coefficients: 4, \(\frac{1}{2}\)

Step-by-step explanation:

The terms of an expression are the numbers and variables that are being added. In this expression 4x is being added to -\(\frac{x}{2}\). This means that they must be the terms. The coefficients are the constants that come before a variable. A variable is an unknown number represented by a letter, in this case, x. So the coefficients are 4 and \(\frac{1}{2}\) because both these numbers are being multiplied by a variable.