Find the period, range, and amplitude of the cosine function.y = –3 cos 4x

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:$2.45

Step-by-step explanation:

the first thing you need to do is take your 7% and turn it to a decimal which is 0.07 then you multiply 0.07 by 34.99 that give you the answer of 2.4493 that you can round to $ 2.45

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Considering the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

The null and alternative hypotheses are as follows:

H o: p ≤ 0.23 (proportion of men who own cats is less than or equal to 23%)

H a: p > 0.23 (proportion of men who own cats is larger than 23%)

The test is right-tailed because the alternative hypothesis states that the proportion is larger than 23%.

Based on a sample of 40 people, with 15% of them owning cats, we can calculate the p-value.

To find the p-value, we need to use the binomial distribution and calculate the probability of observing a result as extreme or more extreme than the one obtained under the null hypothesis.

Let's calculate the p-value:

p = 0.15 (proportion of men in the sample who own cats)

n = 40 (sample size)

p-value = P(X ≥ 0.15 x 40) = P(X ≥ 6)

Using a binomial calculator or software, we can find that P(X ≥ 6) is approximately 0.162.

Since the p-value (0.162) is greater than the significance level of 0.10, we fail to reject the null hypothesis.

Therefore, based on the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Given:

Required: length?

the formula for the area of a rectangle :

let the length of the rectangle be l

Using the long division method

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

x = 12

Step-by-step explanation:

im 100% sure i hope this helps :)

Answer:

\(4x + 12 = 60 \\ 4x = 60 - 12 \\ 4x = 48 \\ x = \frac{48}{4} \\ x = 12\)

=> 12 IՏ Tᕼᗴ ᑕOᖇᖇᗴᑕT ᗩᑎՏᗯᗴᖇ.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

2/5 × 3/2

I hope this helps!

Answer:

The answer is: 1.2 + -0.4y

Answer: -0.4y + 1.2

Step-by-step explanation:

0.4(y) = 0.4y

0.4(3) = 1.2

0.4y + 1.2 - 0.8y

0.4y - 0.8y = -0.4y

-0.4y + 1.2

Answer:

−x+y+1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

You would replace the x with -2x so you would end up with -2×-2 and that is 4 then minus 2 is 2.

Answer:

\(h(t)\) is likely a quadratic function.

Based on values in the table, domain of \(h(t)\) : \(\lbrace 0,\, 1,\, 2,\, 3,\, 4,\, 5,\, 6,\, 7,\, 8\rbrace\); range of \(h(t)\!\): \(\lbrace 0,\, 35.1,\, 60.1\, 75.2,\, 80.3,\, 75.3,\, 60.2,\, 35.0 \rbrace\).

Step-by-step explanation:

By the power rule, \(h(t)\) is a quadratic function if and only if its first derivative, \(h^\prime(t)\), is linear.

In other words, \(h(t)\) is quadratic if and only if \(h^\prime(t)\) is of the form \(a\, x + b\) for some constants \(a\) and \(b\). Tables of differences of \(h(t)\!\) could help approximate  whether \(h^\prime(t)\!\) is indeed linear.

Make sure that values of \(t\) in the first row of the table are equally spaced. Calculate the change in \(h(t)\) over each interval:

Consecutive changes to the value of \(h(t)\) appears to resemble a line with slope \((-10)\) within a margin of \(0.2\). Hence, it is likely that \(h(t)\!\) is indeed a quadratic function of \(t\).

The domain of a function is the set of input values that it accepts. For the \(h(t)\) of this question, the domain of \(h(t)\!\) is the set of values that \(t\) could take. These are listed in the first row of this table.

On the other hand, the range of a function is the set of values that it outputs. For the \(h(t)\) of this question, these are the values in the second row of the table.

Since both the domain and range of a function are sets, their members are supposed to be unique. For example, the number "\(0\)" appears twice in the second row of this table: one for \(t = 0\) and the other for \(t = 8\). However, since the range of \(h(t)\) is a set, it should include the number \(0\!\) only once.

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

According to the table the probability of the team Q scored in the first five minutes of the game is 3.55%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

With the data given we have the probabilities of a particular soccer team scoring a goal within the first five minutes of the game:

(P, 2.34%)

(Q, 3.56%)

(R, 1.24%)

(S, 4.01%)

(T, 3.88%)

According to this we have:

The probability of a goal being scored in the first five minutes of the game, given that the team is team Q= 3.56%

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Answer:

9/25

Step-by-step explanation:

Don't worry, I just took this test and got it correct. Best of luck to you all!

Answer:

I think maybe associative property of addition?

Answer:3 lines could be used

Step-by-step explanation:

You need 2 points to draw a line. The order doesn't really matter. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we do the same to the others, we get the following pairs of points to draw lines.

AB , AC

BA , BC

CA , CB

which is only 3 lines

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

Option B.

Step-by-step explanation:

Let as consider the given equation:

\(2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30\)

It can be written as

\(2(\ln 2x)-(\ln 10x)=\ln 30\)         \([\because \ln e^a=a]\)

\(\ln (2x)^2-(\ln 10x)=\ln 30\)        \([\because \ln a^b=b\ln a]\)

\(\ln \dfrac{4x^2}{10x}=\ln 30\)        \([\because \ln \dfrac{a}{b}=\ln a-\ln b]\)

\(\ln \dfrac{2x}{5}=\ln 30\)

On comparing both sides, we get

\(\dfrac{2x}{5}=30\)

Multiply both sides by 5.

\(2x=150\)

Divide both sides by 2.

\(x=75\)

Therefore, the correct option is B.

Answer:

b x=75

Step-by-step explanation:

h: The domain

-5 ≤ x ≤ 5

Answer: 164

Step-by-step explanation: (16 X 8) + (6 X 5)+ (^^triang)+ 164

The required it will take 2 hours for the friends to put 7 km between them.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).

We can now set up an equation:

2x + 3(x-1) = 7

Expanding the second term:

2x + 3x - 3 = 7

Combining like terms:

5x - 3 = 7

Adding 3 to both sides:

5x = 10

Finally, dividing both sides by 5:

x = 2

So it will take 2 hours for the friends to put 7 km between them.

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A 98​% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments is

70.9 min < x-bar < 113.3 min

Yes, the result indicate that the treatment is​ effective

Confidence interval gives the probability that the unknown parameter will fall within a stated range

The confidence interval is constructed using the formula

confidence interval = x-bar ± z(s/√n)

Definition of variables

mean, x-bar = 92.1 min

standard deviation, s = 40.5 min

sample size, n = 23

confidence level = 98%

z score, z

For sample size less than 30, n < 30. t scores are used

degree of freedom, df = n - 1 = 23 - 1 =22

t score for 98% confidence level and dt of 22 = 2.509

substituting into the formula

= x-bar ± t(s/√n)

= 92.1 ± 2.509 (40.5 / √23)

= 92.1 ± 21.188

= 70.9112 < x-bar < 113.288  

Effectiveness of the treatment

when a test a test more than 2 standard deviations away from mean it is considered unusual. The usual range is

= 92.1 ± 2 * 40.5

= 11.5 < x-bar < 173.5

Hence the treatment is effective

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A budget of £ 105 can buy a total of 3 books.

In this problem we find the case of book that is sold with discount and we should determine how many books can be sold if there is a budget of £ 105 and a discount of 40 % per book. The price of a book with discount is determined by the following equation:

c' = c · (1 - r / 100)

Where:

And the number of books (n) that can be bought is:

n = C / c'

Where C is the budget, in sterling pounds.

If we know that c = 25, r = 40 and C = 105, then the number of books are:

c' = 25 · (1 + 40 / 100)

c' = 35

n = 105 / 35

n = 3

A number of 3 books can be bought with a budget of £ 105.

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Answer:

4 minutes per question

Step-by-step explanation:

3 hours = 180 mins

180/45 = 4

4 minutes per question

Answer:

an average of 4 minutes on each

Step-by-step explanation:

The author of the review is disappointed with the meatball sub casserole recipe posted on Recipe Masters, which did not turn out well despite following the recipe.

The author recommends that others should not attempt to make the recipe and believes that Recipe Masters should ensure that their posted recipes are reliable and thoroughly tested. The author also implies that the quality of the recipes on Recipe Masters is not as advertised, which could potentially lead subscribers to lose faith in the service and seek out free recipe sites instead.

Therefore, a suitable summary of the author's point of view would be: The author is dissatisfied with the meatball sub casserole recipe on Recipe Masters, which did not work out well and believes that Recipe Masters should provide reliable, thoroughly tested recipes as advertised.

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The equation and the graph that shows the yearly cost of downloading music with Music A and Music B are given below.

y = 10 + 1.25x

y = 14 + 0.75x

The blue line is for B music.

The red line is for A music.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Music A:

Music A charges $10 for a year membership plus $1.25 for every song download.

The yearly cost.

y = 10 + 1.25x

Where x is the number of songs downloaded

Music B:

Music B charges $14 for a year membership plus $0.75 for every song downloaded.

The yearly cost

y = 14 + 0.75x

Where x is the number of songs downloaded

Now,

The graph of (1) and (2) are given below.

Thus,

The graph that shows the yearly cost of downloading music with Music A and Music B is given below.

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