The **interval notation** for the change in temperature are-

For the given function;

**Increasing **temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the **interval notations** are-

Increasing temperature; (1, 3) ∪ (6, 8).

Decreasing** temperature: **It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-

Decreasing** **temperature; (0, 1) ∪ (3, 6).

Thus, the interval notations for the** function **are found.

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A square napkin has sides of length 8 inches. To the nearest inch, what is the length of the diagonal of the (1

napkin?

O8 inches

09 inches

O11 inches

O16 inches

The length of the** diagonal **of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of **angle** formed by any two adjacent sides is also equal and 90°.

Thus, by using** Pythagoras theorem**, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the** length** of the diagonal of the napkin to the nearest inch comes out to be 11.

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A tank truck holds 35.3 kiloliters of oil. How many gallons does it hold?

The truck holds approximately _____ gallons of oil.

round to the nearest hundredth as needed

36 is the nearest hundredth

Full in the spaces to complete the equality:

5t^2 + 5t = 5t (t + 1).

If you take out a common factor of 5t from 5t^2 + 5t, you get

5t (t + 1).

To check this, distribute the 5t to the terms in the parentheses.

5t • t = 5t^2

5t • 1 = 5t

So, 5t^2 + 5t = 5t^2 + 5t

(which means it is equal!)

If you take out a common factor of 5t from 5t^2 + 5t, you get

5t (t + 1).

To check this, distribute the 5t to the terms in the parentheses.

5t • t = 5t^2

5t • 1 = 5t

So, 5t^2 + 5t = 5t^2 + 5t

(which means it is equal!)

How do I solve this?

**Answer: F**

**Step-by-step explanation:**

[tex]\sin(x+y)=\sin x \cos y+\cos x \sin y[/tex]

[tex]\tan x=2 \implies \sin x=\frac{2}{\sqrt{5}}, \cos x=\frac{1}{\sqrt{5}}\\\\\sin y=\frac{8}{17} \implies \cos y=-\frac{15}{17}\\\\\sin (x+y)=\left(\frac{2}{\sqrt{5}} \right) \left(-\frac{15}{17} \right)+\left(\frac{1}{\sqrt{5}} \right) \left(\frac{8}{17} \right)\\\\=-\frac{30}{17\sqrt{5}}+\frac{8}{17\sqrt{5}}\\\\=-\frac{22}{17\sqrt{5}}\\\\=-\frac{22\sqrt{5}}{85}[/tex]

A. 90 degrees clockwiseB. 180 clockwiseC. 90 degrees counter clockwise

**1**) What we have in the polygon P is at first a

90º Rotation Clockwise because it is in the direction of the clock.

**90º Rotation Clockwise**

Tracing a line inside the polygon P, we can count approximately 10 units to the right in the translation.

T

What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이

To complete the square, we want a number such that:

[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]because in this way we can writte the square as follows:

[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]**Hence the answer is the last option:**

Over the interval [0,2pi), what are the solutions to cos(2x)=cos(x)? Check all that apply.

**Answer:**

**x = 0 and 2pi/3**

**Explanation**

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

**Substituting into the equation given;**

cos(2x)=cos(x)

2xos^2x - 1 = cos x

**Rearrange**

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

**Factorize**

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

**Recall that** P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

**Hence the value of x that satisfies the equation is 0 ad 2pi/3**

I inserted a image of the question I’m very confused and need help with homework so I do good on test

To find the magnitude of a vector we use the following equation

[tex]\lvert\vec{v}\rvert=\sqrt[]{(v_x)^2+(v_y)^2}[/tex]This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:

In the case of your exercise, the values would be

[tex]\begin{gathered} v_x=x \\ v_y=y \\ \lvert\vec{v}\rvert=\sqrt[]{(x_{})^2+(y)^2} \end{gathered}[/tex]12. In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. If mZTVQ = 5x - 22 and mZTVQ = 3x + 10, for which value of x is PQ parallel to RS? P_ R W A. 6 B. 16 C. 24 D. 28

**ANSWER:**

The value of x is 16

**STEP-BY-STEP EXPLANATION:**

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

[tex]5x-22=3x+10[/tex]Solving for x:

[tex]\begin{gathered} 5x-3x=22+10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}[/tex]**Answer:**

16 is the answer

write the following in the form a+bi (2+5) - (-6 +bi)

The **complex expression **(2+5) - (-6 +bi) in the form a + bi is 13 - bi

The **expression **is given as

(2+5) - (-6 +bi)

The above expression is a **complex expression**

So, we have the following **expression**

(2+5) - (-6 +bi)

Remove the **brackets **in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the **like terms **in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the **complex expression **is 13 - bi

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I just need to make sure 1-9 are correct so if you could confirm please.9 b)

**Given:**

**To find:**

The roots.

**Explanation:**

Here,

[tex]\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}[/tex]Using the quadratic formula,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]On substitution we get,

[tex]\begin{gathered} x=\frac{-3\pm\sqrt{(3)^2-4(2)(9)}}{2(2)} \\ =\frac{-3\pm\sqrt{9-72}}{4} \\ =\frac{-3\pm\sqrt{-63}}{4} \\ =\frac{-3\pm3i\sqrt{7}}{4} \end{gathered}[/tex]Therefore, the solutions are,

[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]**Final answer:**

**The solutions are,**

Translate the sentence into an equation. Use the variable w for the unknown number.Two times the sum of a number and 7 equals 6.

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

2(w+7)=6ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4

**Answer:**

2^5m^15n^10

**Step-by-step explanation:**

**Answer:**

16m^12n^8t^4

**Step-by-step explanation:**

when raising exponents to another exponent you multiply the exponents

Find the simple interest on $50,000 for 2 years at 7%

**Answer:**

$7,000

**Explanation:**

To find the simple interest on any principal, we use the formula:

[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]From the given question:

• Principal = $50,000

,• Rate= 7%

,• Time = 2 years

Therefore:

[tex]\begin{gathered} \text{Interest}=\frac{50,000\times7\times2}{100} \\ =\$7,000 \end{gathered}[/tex]**The simple interest is $7,000.**

A coin has 2 sides: heads (H) and tails (T). A bag has 3 balls: 1 red (R), 1 green (G), and 1 blue (B). You toss a coin and randomly pick a ball. What is the sample space?

The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

The sum of two whole numbers is 63. The difference between the numbers is less than 10. Find as many solutions

**Answer:**

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

**Step-by-step explanation:**

That all I got....

According to medical data, the ages at which patients have their first hip replacement

surgery follows a normal distribution. The average age for a first hip replacement is 55

years of age, with a standard deviation of 8 years. Therefore, doctors can expect 95% of

their hip replacement surgery patients to be between what ages?

O 39-71

O 45-65

O 47-63

O 31-79

Question 4

2

**95% **of the people the doctor expects to have hip **replacement** **surgery** will be between the ages of **47 and 63.**

What exactly are the mean and standard deviation?

The **definition** of **average** is that it is the mean value, which is the ratio of the sum of the values in a particular set to all the values in the set.

The amount of variance from the mean is shown by the standard deviation.

Given that the** standard deviation** is 8 years and the average age is 55.

x=x0, where x0 and are the **mean** age and **standard deviation, **respectively, defines the relationship.

The standard deviation is 8 years, while the mean age is 55 years.

The answer is that 55+8=63 and 55-8=47.

Consequently, the age **range is 47 years to 63 years.**

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Eighth grade > T.14 Volume of spheres QX7 What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest hundredth. 18 cm cubic centimeters Submit Docs

hello

to solve this question, we need to use the formula for volume of a sphere

[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\text{volume} \\ r=\text{radius} \end{gathered}[/tex]from the image above, we can now find the radius of the sphere

[tex]\begin{gathered} radius=\frac{\text{diameter}}{2} \\ d=18\operatorname{cm} \\ r=9\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\frac{4}{3}\times3.14\times9^3 \\ v=3052.08\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the volume of the sphere is equal to 3052.08cm^3

Salaries of Business Graduates. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $45,000 and $60,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is a. $500? b. $200? c. $100? d. Would you recommend trying to obtain the $100 margin of error? Explain.

3750 is the planning value for the population **standard deviation**.

In the **sampling**, one should not recommend trying to obtain the $100 margin of error since the sample size is large.

Firstly, the **planning value** will be:

= (60000 - 45000) ÷ 4

= 3750

Then the number will be:

= 1.96 × (3750 ÷ 500)²

= 217

Also, for error 200, the desired **margin** will be:

= 1.96 × (3750 ÷ 100)²

= 5403.

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Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)

**Answer:**

slope would be 4/1

**Step-by-step explanation:**

its rise over run, so up 4 and out 1

have a good day!

help please

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample 50 of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

5 9 10 2 2 2 2 7 7 7 7 6 7

8 9 9 2 10 2 7 6 9 8 10 9 2

7 5 7 2 2 7 7 6 2 10 8 2 6

6 9 5 2 10 7 10 2 2 6 6

Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

Using the **t-distribution,** the **95% confidence interval** estimate of the population mean rating for Miami is of:

(4.29, 7.71).

What is a t-distribution confidence interval?The **bounds **of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the meaning of the **parameters **are:

Using a calculator from the 50 observations given in this problem, the **values **of the parameters are as follows:

[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]

The **critical value,** using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the **lower bound **of the interval is given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]

The **upper bound** of the interval is given by:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]

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a standard number cube number 1 through 6 on east side is rolled 3 times what is the probability of rolling a 2 on all three rolls express your answer as a fraction

the probability of getting a 2 tree times is

[tex]\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{216}[/tex]15

A principal needs to order 1,437 T-shirts for students at her school. She rounds to the nearest hundred

to estimate the number of T-shirts to order. Will there be enough T-shirts for all the students? Explain.

There will not be **enough T-shirts **for all the students

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal **approximates **the number of T-shirts to the **nearest hundred**

When the number of **T-shirts **is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400 is **less than** 1437

This means that the T-shirts will not be **enough**

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À La Mode Ice Cream Parlor uses the function f(x) to calculate its profits. When the parlor sells x cones, it makes f(x) dollars in profit.

What does f(50)=85 tell you?

Help please

**Answer: When the Ice Cream Parlor sells 50 ice cream cones, they make $85 dollars in profit.**

**Step-by-step explanation:**

x = cones

the function f tells us the profit for whatever x

The measure of USV is ________ degrees.The solution is _________________

Since ∠VST measures 90°, the measure of ∠RSV must also be 90° because the two angles are linear pair.

Since m∠RSU=51°, then the measure of ∠USV is as follows:

[tex]\begin{gathered} m\angle USV=m\angle RSV-m\angle RSU \\ m\angle USV=90\degree-51\degree \\ m\angle USV=39\degree \end{gathered}[/tex]I really don't know where to start on this problem and I would like it if some could help me please.

We can draw the following picture:

Since we have a right triangle with hypotenuse equal to 28ft, we can use the trigonometric function. That is, we can write the following relationships:

[tex]\begin{gathered} \sin 30=\frac{RG}{28} \\ \text{and } \\ \cos 60=\frac{RG}{28} \end{gathered}[/tex]both give the same result.

If we use the first one, we have

[tex]\begin{gathered} RG=28\cdot\sin 30 \\ \end{gathered}[/tex]since sin30=0.5, we have

[tex]\begin{gathered} RG=28\cdot(0.5) \\ RG=14 \end{gathered}[/tex]**that is, RG = 14 ft, which corresponds to the first option**

A cricket pitch measures $1$ chain by $10$ feet. What is the area of a cricket pitch in square feet?

(Useful information: there are $3$ feet in a yard, and there are $22$ yards in a chain.)

**Area** of the **cricket pitch** is 660 square feet

Given

1 **chain **is equal to 10 feet

There are 3 feet in a** yard**

And 22 yards in a chain

Hence it is evident that

**One chain **is equal to 22 x 3

1 chain = 66 Feet

**Area of a rectangle** is Length x Width

Length = 66

Width = 10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the **cricket pitch** is 660 square feet.

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Can someone help please

The **maximum** **displacement** of this cosine wave function is equal to 8 inches.

The **frequency** of this cosine wave function is equal to 1/8 Hertz.

The **time** (t) required for one cycle is equal to 8 seconds.

Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:

y = asinωt = asin2πft ......equation 1.

Where:

a represents the amplitude orFrom the information provided, the equation for this simple harmonic motion (SHM) is given by:

d = -8cos(π/4)t ......equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

**Maximum** **displacement **or amplitude, a = |-8|

Taking the absolute value of a, we have:

**Maximum** **displacement **or amplitude, a = 8

For the **frequency**, we have:

Angular velocity, ω = 2πf

Making **frequency **(f) the subject of formula, we have:

Frequency** **(f) = ω/2π

**Frequency **(f) = (π/4)/2π

**Frequency **(f) = π/8π

**Frequency **(f) = 1/8 Hertz.

Finally, we would calculate the amount of **time** (t) required for one cycle as follows:

Time (t) = 1/f

Time (t) = 1/(1/8)

**Time** (t) = 8 seconds.

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Complete Question:

An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:

maximum displacement

the frequency

the time required for one cycle.

help meeeeeee pleaseee !!!!

The **linear function** that passes through the points (-3, 18) and (2, -7) is defined by the **rule**:

y = -5*x + 3

We can find a general **linear function **in the **slope-intercept form **as:

y = m*x + k

Where m is the **slope **and k is the **intercept of the y-axis.**

If we know that the **line **passes through the points (a, b) and (c, d) then the **slope **of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the **slope **is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the** linear function** is:

y = -5*x + 3

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Multiply. Write your answer in scientific notation.

2.(4 × 10³)

The answer to the question is 4000

10x10x10=1000x4=4000

10x10x10=1000x4=4000

Here is the imagine of the triangle ABC and its dilations using center D and scale factor 2
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ASAP help with 8th grade math, 50 points