The **simplified expressions** for each case are given as follows:

1 - a) 11g.

1 - b) 3m.

1 - c) -k².

2 - a) 8x + 11y.

2 - b) 2a + b - 2c.

3 - a) 5q + 7.

3 - b) 6r + 3s + 7t.

How to simplify an expression?An expression is simplified **combining **the like terms, that is, adding or subtracting, depending on the signal, the terms that have the same variable and the same exponent.

For **item 1**, the variables are common for all terms, hence we just **add **the terms keeping the variable, hence:

For** item 2,** there are **multiple **variables, hence we combine the terms of each variable(we cannot add terms with x and y, for example), as follows:

**Item 3** works similarly to item 2, as there are multiple variables, hence we **combine **the terms with each variable(or with the constant = no variable), as follows:

The questions are missing and are given by the **image **at the end of the answer.

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Use a model to divide. 2/5÷4 Express the answer in simplest terms.

so the equation si:

[tex]\frac{\frac{2}{5}}{4}[/tex]This is equal to:

[tex]\frac{2}{20}=\frac{1}{10}[/tex]Finally:

[tex]\frac{1}{10}=0.1[/tex]The table graph shows the population of Oregon Mule Deer between 1980 and 2018,

84 - 250

94 - 237.50

04 - 245

14 - 230.50

18 - 173.50

What was the average population decline between 1984 and 2018?

B. The average rate of population decline between 2004 and 2014 is 1.45 thousand deer per year. If the population continued to decline at this rate, between which 2 year period would the population have reached 225 thousand deer? Explain reasoning.

C. Calculate and compare the average rate of change of the population from 1994 to 2004 to that from 2004 to 2014. Explain what this means in terms of the population of deer.

Using the **average rate of change**, it is found that:

**A. **The average population decline between 1984 and 2018 was of 2.25 thousand deer a year.

**B. **The population would have reached 225 thousand deer between 2017 and 2018.

**C.**

The **rates **are as follows:

Meaning that between 1994 and 2004 there was a increase in the population of deer, and from 2004 to 2014 there was a decrease.

What is the average rate of change of a function?The average rate of change of a function is given by the change in the **output divided** by the change in the **input**. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For** 1984 and 2018**, we have that:

Hence the **rate **is:

r = (173.50 - 250)/(2018 - 1984) = -2.25 thousand deer a year.

For **item b,** the situation is modeled by a **linear function, **as follows:

D(t) = 230.50 - 1.45t.

The **population **would be of 225 thousand deer **when **D(t) = 225, hence:

230.50 - 1.45t = 225

1.45t = 5.5

t = 5.5/1.45

t = 3.79.

Hence between the **years **of 2017 and 2018.

For **item c**, the **rates **are as follows:

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The sum is the measure of three angles of a triangle is 180 degrees. In a triangle, the measures of an angle are x,x+12 and x-48. What is the measure of each angle?

**Answer:**

24° , 72° , 84°

**Step-by-step explanation:**

sum the 3 angles and equate to 180 , that is

x + x + 12 + x - 48 = 180

3x - 36 = 180 ( add 36 to both sides )

3x = 216 ( divide both sides by 3 )

x = 72

Then the measure of the 3 angles are

x = 72°

x + 12 = 72 + 12 = 84°

x - 48 = 72 - 48 = 24°

A table is on sale for 38% off. The sale price is $527.00.What is the regular price?

**Given:**

A table is on sale for 38% off, The sale price of table is $527.00.

**To find:**

The regular price of the table.

**Step by step solution:**

To solve this problem, we need to use the basic formula of sales price and discount:

Sale price = $527.00

Discount percentage= 38%

[tex]\begin{gathered} \text{sale price = cost price - discount }\times\text{ \lparen cost price \rparen} \\ \\ 527=cp-\frac{38}{100}(cp) \\ \\ 527=\frac{62}{100}(cp) \\ \\ cp=\frac{52,700}{62} \\ \\ cp=850 \end{gathered}[/tex]**From here we can say that the Cost-price / Regular price of the table is equal to $850. **

Please help me solve and show the steps so I could understand

**Given polygon with sides 8 and radius 10yd.**

**Formula for area of ploygon**

So, solving further

[tex]\begin{gathered} =8\times10^2\times tan(\frac{\pi}{8}) \\ =800\times0.414 \\ =331.37 \end{gathered}[/tex]**Hence, 331.37 yd square is the area of polygon.**

The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:98.9 96.6 98.6 99.7 97 97.4 99.4Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidenceinterval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.98% C.I. -

Given the data temperatures to be;

[tex]98.9,96.6,98.6,99.7,97,97.4,99.4[/tex]We would require the following to get the 98% confidence interval of the mean body temperature.

**Mean, Standard deviation, sample size, Probability of a confidence interval of 98%.**

**Using a calculator, we can get the mean to be**

**The standard deviation would be derived to be;**

**The sample size can be gotten from the question to be;**

**The probability value of a 98% confidence interval is given to be 2.33**

**We can then derive the answer using the formula below;**

We would substitute into the formula

[tex]\begin{gathered} \mu\pm z^x(\frac{\sigma}{\sqrt[]{n}}) \\ =98.2285+2.33(\frac{1.2230}{\sqrt[]{7}}) \\ =98.2285\pm1.0770 \\ =(97.152,99.306) \end{gathered}[/tex]**ANSWER:**

help meeeeeee pleaseee !!!!

The **linear function** that passes through the two points (-6, -2) and (-9, -1) is defined by the **rule**:

y = -(1/3)*x - 4

The general **linear function **in the **slope-intercept form:**

y = m*x + k

Where m is the **slope **(also called rate of change)** **and k is the **intercept of the y-axis.**

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

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

So with only two points, we can find the **slope**.

In this case, the **line **passes through the points (-6, -2) and (-9, -1) , then the **slope **is:

m = (-1 +2)/(-9 + 6) = 1/-3 = -1/3

Then the **slope **is m = -1/3

So the **linear function **is something like:

y = (-1/3)*x + k

To find the value of k i will use the pint (-9, -1), replacing these values we get:

-1 = -(1/3)*-9 + k

-1 = 3 + k

-1 - 3 = k

-4 = k

So the** linear function **that passes through these points is:

y = -(1/3)*x - 4

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The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle

The **area** of the **triangle** with base 12 units, and height of 3 units is: B. 18.

To find the **area** of a **triangle**, find the height, which is the distance from its base to its highest point, and also find the length of the base of the **triangle**, then apply the formula below:

**Area** of **triangle** = 1/2 × base × height

From the information given, the following are the parameters we will need to work with:

Base of the **triangle** = QR = 12 units

Height of the **triangle** = PH = 3 units

Plug in the values

**Area** of **triangle** = 1/2 × 12 × 3

**Area** of **triangle** = 36/3

**Area** of **triangle** = 18 units

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A package of 3 pairs of insulated socks costs $15.87. What is the unit price of the pairs of socks?

The unit price is $

per pair of socks.

A package of 3 pairs of insulated socks costs $15.87, thus the **unit price** of the pair of socks can be calculated as $5.29 via the **unitary method.**

A **unit price** is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities.

Selling more than one unit of the same product at a discount from its unit price is known as **multiple pricing. **

A price stated in terms of a certain amount per predetermined or standard unit of good or service agreed to purchase the gravel for 50 cents per yard.

Frequently a price that is quoted that includes both the **base unit** of the good or service and any additional costs (such as shipment or installation).

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Ratios equivalent to 13:14

**Equivalent fractions** are those that, despite their visual differences, reflect the same value. For instance, if you take a cake and cut it into two equal pieces, you will have consumed half of the cake.

When two fractions are expressed in their simplest form, they are said to be equivalent. When broken down into its simplest components, the fraction 26/28 equals 13/14. You only need to multiply the numerator and denominator of the reduced fraction (13/14) by the same natural number, i.e., multiply by 2, 3, 4, 5, 6 to get analogous fractions.

13 and 14 in decimal form.In decimal form, 13/14 is 0.92857142857143.

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An oil slick is expanding as a circle. The radius of the circle is currently 2 inches and is increasing at a rate of 5 inches per hour. Express the area of the circle, as a function of ℎ, the number of hours elapsed. ( Answer should be (ℎ)= some function of ℎ, enter as pi )

**Answer: f(h) = (2 pi (5x + 2)^2)**

**Step-by-step explanation:**

**1) Set the area of the circle in an equation**

**f(h) = pi r ^2**

**2) Set r to the rate that the circle is growing**

The rate is 5x +2 because its starting value is two, and the 5x because it is growing 5 inches per hour.

**f(h) = (2 pi (5x + 2)^2)**

"demonstrate that the functions are cumulative or not cumulative show all work"f(x)=1/4x+5 g(x)=4x-20

Given the functions:

f(x)=1/4x+5

g(x)=4x-20

The functions g and f are said to commute with each other if g ∘ f = f ∘ g.

Let's check the functions if they are commutative.

a.) **f ∘ g =** **f(g(x))**

b.) **g ∘ f = g(f(x))**

**Conclusion:**

**g ∘ f = f ∘ g**

Therefore, **the functions are commutative**.

If f(x) = 5x + 40, what is f(x) when x = -5?

we have the following:

[tex]f\mleft(x\mright)=5x+40[/tex]replacing, x = -5

[tex]\begin{gathered} f(-5)=5\cdot-5+40 \\ =-25+40 \\ =15 \end{gathered}[/tex]The answer is 15

3,000 is 1/10 of?-30030,000300,000

Let X be the number, then we know that

[tex]\frac{X}{10}=3,000[/tex]If we isolate X by moving 10 to the right hand side, we obtain

[tex]\begin{gathered} X=10\cdot3,000 \\ X=30,000 \end{gathered}[/tex]**that is, the answer is 30,000**

Christina made 4 three-point shots and 5 two-point shots in her basketball game. How many points (p) did she score?

The total points Christina made is as follows:

[tex]T=4\cdot3+5\cdot2=12+10=22[/tex]Then, **Christina scored 22 points.**

you and three friends share a sushi boat at House of Kobe the cost of the boat is $50 you each also pay for a soft drink that is $2.39 what is the total cost of the meal after you pay 6% tax

**ANSWER**

$63.13

**EXPLANATION**

We have that the cost of the boat is $50.

Each of you and your friends **(that is four of you**) will pay for a soft drink that cost $2.39 each.

The** cost of the soft drinks** will therefore be:

4 * 2.39 = $9.56

Adding the cost of the boat, total cost will be:

$9.56 + $50 =** $59.56**

Now, we have to add a tax of 6%, so we** find 6% of total cost:**

Finally, **add the tax to the cost**:

$59.56 + $3.57

= **$63.13**

**You pay a total of $63.13 (**including tax**)**

PLEASE HELP ME PLEASE I WILL GET A 0 ON THIS PLEASE HELP PLEASE

**Answer:**

[tex]58.29[/tex] cm

**Step-by-step explanation:**

So the area of a trapezium follows this equation/formula: [tex]\frac{a+b}{2} h[/tex]

So we pretty much just substitute the numbers given into this equation

[tex]\frac{a+b}{2} h[/tex]

[tex](\frac{7+10.4}{2} )6.7[/tex]

[tex](\frac{17.4}{2} )6.7[/tex]

[tex](8.7) 6.7[/tex]

[tex]58.29[/tex] cm

P(6, -3); y = x + 2

Write an equation for the line in point-slope form.

The equation of the line by using **slope **value is: y = x -9

**What is slope of a line?**

The **slope **of a **line **explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the **slope **value, it is classified as whether lines are parallel or perpendicular.

According to the question, the given parameters for the line segment is as written below:

Equation of a line = x + 2 and the coordinate points = (6, -3): (x = 6; y = -3)

Now, by using standard equation for the line segment: y = mx + c

where, 'm' is the **slope**; c is the y-intercept; (x, y) are coordinates

Substituting given values that is **slope **and y-intercept in the standard equation, we get:

y = mx + c

⇒ -3 = (1)(6) + c

⇒ c = -3 - 6 = -9

Therefore, the value of the y-intercept is: c = (-9)

equation of the line by substituting the value of the y-intercept as well as **slope **value:

y = (1)x + (-9) = y = x -9

Hence, the equation of the line by using **slope **value is: y = x -9

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1. The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?

To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.

P = (8,533/68,811)* 100

P = 12.400, the nearest hundredth of a percent is 12.

11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus. so we need to find percentage 12 for 11690000.

(11690000* 12) / 100

1402800 is the number of people who would test positive for the virus

how to solve the problem “Compute 3'7 mod 7”

**Given**

**Find**

Compute the value of mod

**Explanation**

We have given

[tex]3^7mod\text{ }7[/tex]as we can rewrite it

[tex]\begin{gathered} 3^7mod\text{ 7} \\ 2187mod7 \\ \end{gathered}[/tex]here , we see dividend , a = 2187 and divisor , b = 7

we know ,

[tex]a\text{ mod b = a- \lparen int \lparen a/b\rparen}\times b\text{\rparen}[/tex]where int is a integer part of the value .

so ,

2187 mod 7 = 2187 -(Int (2187/7)*7)

2187 mod 7 = 2187 - 312 *7

2187 mod 7 = 2187 - 2184

2187 mod 7 = 3

**Final Answer**

Therefore , the value of **3^7 mod 7 = 3**

Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²

The given equation is:

[tex]y=\frac{5}{x^2}[/tex]**a. **Find the value of dy/dx when x=3

Start by finding the derivative:

[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):

[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:

[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:

[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:

[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]**b. **Estimate the value of 5/(2.98)^2:

After how many months of saving do Sam and Frank have thesame amount in their accounts? How much do they have in theiraccounts at this time? Use the graph to explain your answer.

Answer:

To find: After how many months of saving do Sam and Frank have the same amount in their accounts and how much do they have in their accounts at this time

From the graph,

x axis represents number of months,

axis represents Amount saved.

The red graph represents the amount saved by Sam over the number of months

The blue graph represents the amount saved by Frank over the number of months

To find the intersection point of the two graphs.

**The intersection point is (4,80)**

After 4 months Sam and Frank saved $80.

Hence we get that,

After 4 months, Sam and Frank have the same amount in their accounts. They have $80 in their accounts.

Answer is: After **4 months,**** **Sam and Frank have the same amount in their accounts. They have **$80** in their accounts.

Solve this inequality for the y variable: 6x-9y> 12 u y GON 4 3 2 4 O ya 3 2. 4 ys vs - 2 x + 2

We solve the inequality as follows:

[tex]6x-9y>12\Rightarrow-9y>-6x+12[/tex][tex]\Rightarrow y<\frac{2}{3}x-\frac{4}{3}[/tex](37) + (-2) + (-65) + (-8)

You have the following expression:

**(37) + (-2) + (-65) + (-8)**

eliminate parenthesis with the required change of signs:

**37 - 2 - 65 - 8**

sum negative numbers

**37 - 75**

simplify: rest the numbers and put the sign of the higher number:

**-38**

**Then, you have:**

**(37) + (-2) + (-65) + (-8) = -38**

A falling object travels a distance given by the formula d = 4t + 6t?, where d is measured in feet and t is measured in seconds.

How many seconds will it take for the object to travel 68 feet? Round the answer to 4 decimal places.

If a falling object travels a** distance** given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the **time taken** by the object to travel 68 feet is 3.0496 seconds

**The formula** of the object traveling a distance d = 4t + [tex]6t^{2}[/tex]

Where d is the distance traveled in feet

t is the time taken in seconds

Here

The distance traveled = 68 feet

Therefore the equation will be

68 = 4t + [tex]6t^{2}[/tex]

[tex]6t^{2} +4t-68=0[/tex]

We have to solve **quadratic equation** [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

a = 6

b = 4

c = -68

Substitute the values in the equation

= [tex]\frac{-4+/-\sqrt{4^2-(4)(6)(-68)} }{(2)(6)}[/tex]

= [tex]\frac{-4+/-\sqrt{1648} }{12}[/tex]

t = [tex]\frac{-1+/-\sqrt{103} }{3}[/tex]

We take only **positive value**

t = [tex]\frac{-1+\sqrt{103} }{3}[/tex]

t = 3.0496 seconds

Hence, if a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds

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I need help please 5. Find the distance between C (-5, 4) and Q (2,0). A. 22 B. 33 C. 53 D. 65

Given the two points:

C (-5, 4) and Q (2, 0)

To find the distance, use the distance formula below:

[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,

(x1, y1) = (-5, 4)

(x2, y2) = (2, 0)

Therefore, we have:

[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]Which fraction is the smallest?8/9, 9/10, 11/12, 12/13

Given:

[tex]\frac{8}{9},\frac{9}{10},\frac{11}{12},\frac{12}{13}[/tex][tex]\frac{8}{9}=0.8889[/tex][tex]\frac{9}{10}=0.9[/tex][tex]\frac{11}{12}=0.9167[/tex][tex]\frac{12}{13}=0.9231[/tex][tex]\frac{8}{9}\text{ is the smallest fraction.}[/tex]Explain how you can use an array to find partial products for 4x36.

**Answer:**

(4 x 30) +(4 x6)

120 + 24

144

**Step-by-step explanation:**

Let p: The shape is a rhombus.

Let q: The diagonals are perpendicular.

Let r: The sides are congruent.

Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

p ∧ (q ∧ r)

(p ∨ q) ∨ r

p ↔ (q ∧ r)

(p ∨ q) ↔ r

The **correct representation** of statement ''The shape is a rhombus **if and only if** the diagonals are perpendicular **and **the sides are congruent'' will be;

⇒ p ↔ (q ∧ r).

**What is Logic operators?**

A symbol or words to use to connect two or more expressions are called **Logic operators.**

Given that;

The **statement **is,

''The shape is a rhombus** if and only if **the diagonals are perpendicular **and **the sides are congruent''

Now,

Since, The word **''if and only if'' **is represent by using the **biconditional logic operator** (↔) and the word ''**and**'' is represented by using the logical **conjunction operator** (∧).

So, The logic representation of the statement;

"The shape is a rhombus **if and only if** the diagonals are perpendicular **and **the sides are congruent” will be;

⇒ p ↔ (q ∧ r).

Thus, The **correct representation** of statement ''The shape is a rhombus **if and only if** the diagonals are perpendicular **and **the sides are congruent'' will be;

⇒ p ↔ (q ∧ r).

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Which equation is the correct translation of the following statement?Four less than a number is nine.9 - x = 49 - 4 = xx - 4 = 94 - x = 9

Given

The statement,

Four less than a number is nine.

To find:

Which equation is the correct translation of the following statement?

Explanation:

Let x be the number.

Since four less than a number is nine.

Then,

[tex]x-4=9[/tex]**Hence, the correct statement is x-4=9.**

What does it mean for a strong base to be in equilibrium?The position of equilibrium lies far to the right, with products being favoredO The position of equilibrium bes far to the left, with products being favoredThere is a great deal of base and very few bns.There is an equal amount of reactants and products.
PLEASE HELP!! If there is an if number of water molecules inside and outside the cell, how will the water move?Out of the cell onlyIt will not moveInto the cell onlyInto and out of the cell in equal amounts
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