5000kg------->5%

x------------------>100%

Using Cross-multiplication:

5000/x=5/100

Solving for x:

x=(100*5000)/5 =100000kg

You can verify the answer:

100000kg *5% =100000*0.05= 5000kg

Neville purchases a guitar for $78.44. He has a coupon for 20% off the price. How much does Neville pay for the guitar after using the coupon?

**Answer: 62.752**

**Step-by-step explanation: 78.44$ - 20% = 62.752**

Nelson has half of his investments in stock paying a 6% dividend and the other half in a stock paying 9% interest. if his total annual interest is $660 how much does he have invested?

Given:

percent of dividend = 6%

percent of interest = 9%

Total annual interest = $ 660

Let the amount invested in both stocks be x and y.

Annual interest on 6% dividend gives:

[tex]\begin{gathered} =\text{ }\frac{6}{100}\text{ }\times\text{ x} \\ =\text{ 0.06x} \end{gathered}[/tex]Annual interest on 9% interest rate:

[tex]\begin{gathered} =\text{ }\frac{9}{100\text{ }}\times\text{ y} \\ =\text{ 0.09y} \end{gathered}[/tex]The total annual interest is $ 660. We can write:

[tex]0.06x\text{ + 0.09y =660}[/tex]We are given that Nelson divided his investment in half. This implies:

[tex]x\text{ = y}[/tex]Substituting, we have:

[tex]\begin{gathered} 0.06x\text{ + 0.09x = 660} \\ 0.15x\text{ = 660} \end{gathered}[/tex]Divide both sides by 0.15:

[tex]\begin{gathered} \frac{0.15x}{0.15}\text{ = }\frac{660}{0.15} \\ x\text{ = 4400} \end{gathered}[/tex]Hence, **the amount Nelson has invested:**

**Answer: **

**Nelson has $4400 invested in each investment**

I NEED HELP WITH MY HOMEWORK

**Chester** made 9 sales and **Vickie** made 16 sales this week

Base **salary** of Vickie = $70

Vickie's commission per sale = $24

Base salary of Chester = $142

Chester's commission per sale = $9

Both people earned the same amount this week. Let x represent the number of **sales** made by Vickie, then sales made by Chester is x+7

Formulating the equation we get:

Base salary of Vickie + Vickie's commission per sale***Number** of sales = Base salary of Chester + Chester's commission per sale*Number of sales

= 70 + 24x = 142 + 9(x+7)

70+24x = 142+9x+63

70+24x = 205+9x

15x = 135

x = 9

Chester sales = 9

Vickies sales = 9+7 = 16

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Write an equation of the parabola shown. (0,4) (-5, 1.5)

the general formula of a parabola is

[tex]y=ax^2+bx+c[/tex]we can replace the the points to find a,b and c

First (0,4)

[tex]\begin{gathered} 4=a(0)^2+b(0)+c \\ 4=0+0+c \\ c=4 \end{gathered}[/tex]Then (-5,1.5) and c=4

[tex]1.5=a(-5)^2+b(-5)+4[/tex]-15 = -3/4w solve for w and simplify your answer as much as possible

**Answer:**

w = 20

**Step-by-step explanation:**

a) Flip the equation.

-3/4 w = -15

b) Multiply both sides by 4/(-3).

(4/-3) * (-3/4 w) = (4/-3) * (-15)

**w = 20**

-26, 174, 374, 574, …

Find the explicit and recursive formula.

The** explicit **formula and the** recursive **formula are aₙ₋₁ + 200 and the rest is mentioned below.

A formula can be either recursive or explicit. The main difference between **Recursive** and** Explicit** is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.

Given : a₁ = -26, a₂ = 174, a₃ = 374, a₄= 574

The** common difference** that is d can be found out by

thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200

And this is same for all the numbers of this particular sequence.

Thus aₙ = aₙ₋₁ + d

= aₙ₋₁ + 200

Recursive formula : aₙ₋₁ + d

That is the following **sequence **will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .

774 , 974 ... etc

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Compare, choose , or = 20% of 25 25% of 16

**Answer: 20% of 25 is more than 25% of 16 if that is the question**

**I hope that is the question-**

20% of 25 > 25% of 16

Solve the inequality. Graph the solution. |8x−8|≤24

The **solution **of the given inequality would be x = 4. the **graph **of the given **inequality **is attached below.

If the **equation **or inequality contains variable terms, then there might be some values of those **variables **for which that equation or inequality might be true. Such values are called **solution **to that equation or **inequality**. Set of such values is called solution set to the considered equation or inequality.

Given the **inequality **as |8x−8|≤24.

For solving the given **expression**,

|8x−8|≤24

We can **consider **the expression as;

8x−8 = 24

8x = 24 + 8

8x = 32

x = 32/8

x = 4

Hence, the **solution **of the given inequality would be x = 4.

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Write the equation of a line that goes through point (4, 0) and has an undefined slope

**Answer:**

x = 4

**Step-by-step explanation:**

You want the **equation of a line** that goes through **point (4, 0)** and has an **undefined slope**.

The slope of a line is the ratio of "rise" to "run." When the "run" is zero, the ratio involves division by zero, which results in the value "undefined." That is, a line with undefined slope has a "run" of zero, meaning it is a vertical line.

The equation for a vertical line is ...

x = c . . . . . where c is some constant

We want the line to go through a point that has x-coordinate = 4, so that constant must be 4.

**The equation is x = 4**.

The ordered pair (a,b) satisfies the inequality y

A. If you subtract 6 from b, it will be less than or equal to a.

B. If you add 6 to a, it will be greater than b.

C. a is greater than b.

D. If you add 6 to a, it will be less than b.

The **false **statement about the statement is (a) If you **subtract **6 from b, it will be less than or equal to a.

From the question, the **inequality **is given as

y > x - 6

The **ordered pair **is given as

(a, b)

The above ordered pair implies that

(x, y) = (a, b)

So, we have

x = a and y = b

This means that

b > a - 6

**Subtract **6 from both sides

b - 6 > a - 6 - 6

Evaluate

b - 6 > a - 12

Using the above as a guide, we cannot determine the **direct relationship **between variables a and b.

However, it is **false **that b is less than a

Hence, the **false **statement is (a)

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**Complete question**

The ordered pair (a,b) satisfies the inequality y > x - 6

Which statement is NOT true?

A. If you subtract 6 from b, it will be less than or equal to a.

B. If you add 6 to a, it will be greater than b.

C. a is greater than b.

D. If you add 6 to a, it will be less than b.

9+3.5g=11-0.5g is what

G is equal to 1 half (1/2)

What is the degree of the polynomial 12x^2+8x-9

**Answer:f(x)=x8−8x6+19x4−12x3+14x2−8x+9=x8−8x6+16x4+3x4−12x3+12x2+2x2−8x+8+1**

**which allows us to rewrite f(x) as**

**f(x)=x4(x2−4)2+3x2(x−2)2+2(x−2)2+1**

**The first three terms are clearly non-negative, and each reaches their minimum of 0 at x=2 (the first term also has a minimum at x=−2). Thus, the minimum of f(x) must be 1.**

**This can't really be generalized. (I mean, you can apply the approach generally, but it won't generally give you such a convenient result.) I'm not sure I would have looked for this decomposition of f(x) except for the presence of the question.**

**Step-by-step explanation:**

standard to intercept form

Answer in photo y = -2x/3 + 9

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 8x + 12y = 108[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 108 - 8x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{108}{12} - \frac{8}{12} x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]

That's the required equation, with slope (m) = -2/3 and y - intercept = 9

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The angle a lies between 0° and 90° and is such that

2 tan²a + sec²a = 5-4 tana

Show that

3 tan²a +4 tana -4 = 0

and hence find the exact value of tan a

Good.

Now we know this property

Sec^2 A = 1 + tan^2 A

Now lets replace the sec square term with this in the given question

We get,

3tan^2(A) + 1 = 5 - 4tanA

Hence 3tan^2A + 4tanA - 4 =0

Hence proved

Lets take tanA as a value x.

Thus 3x2+4x-4=0

=> 3x2 + 6x - 2x - 4 =0

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

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

x=2/3 or x=-2

But tanA cant have a negative value as 0Thus tanA=x= 2/3

Now we know this property

Sec^2 A = 1 + tan^2 A

Now lets replace the sec square term with this in the given question

We get,

3tan^2(A) + 1 = 5 - 4tanA

Hence 3tan^2A + 4tanA - 4 =0

Hence proved

Lets take tanA as a value x.

Thus 3x2+4x-4=0

=> 3x2 + 6x - 2x - 4 =0

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

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

x=2/3 or x=-2

But tanA cant have a negative value as 0Thus tanA=x= 2/3

What is the diameter of a circle whose area is 28.3 cm^2

I don't understand this question can someone help me with the answer

The approximate **diameter **of the **circle **is 5.77 cm

Given that :

area of circle = 28.3 cm²

**How is Area of circle is calculated ?**

**Area **of circle is calculated using formula :

A= πr²

where "π" represents 3.14 and r is **radius**. So now, according to given information,

Where Pi = 3.14

Hence,

A= πr²

**Substitution **the value of A in above formula :

28.3 = πr²

28.3 = 3.14r²

r² =28.3/3.14

r² =8.323

√r²=√8.323

r = 2.885

r = 2.885 cm Approximately.

d = 2r

**d = 5.77 Approximately.**

Therefore, the **diameter **of the **circle **is 5.77 cm

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he value of a baseball player's rookie card began to increase once the player retired. When he retired in 1999 his card was worth $7.81. The value has increased by $1.28 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2005? Question content area bottom Part 1 Express the relationship with an equation.

The **value** of the **card** in 2005 is $15.49.

A mathematical **equation** is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the **scenario**.

When he retired in 1999 his card was worth $7.81 but the **value** has increased by $1.28 each year since then.

Therefore, the value of the **card** in 2005 will be:

y = 7.81 + 1.28x

where x = number of years

From 1999 to 2005 is 6 years. This will be:

= 7.81 + 1.28x

= 7.81 + 1.28(6)

= 7.81 + 7.68

= 15.49

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a playground is rectangular and the length is 7/8 miles. if the area is 8/20 what is the width?

**Answer:**

so the width is 16/35 miles

**Step-by-step explanation:**

Length - 7/8 miles

Area - 8/20 miles

we know from the equation that area = Length x width

we need to rearrange so the width = Area ÷Length

width = 8/20 ÷ 7/8

= 8/20 × 8/7

= 16/35

The measure of an angle is four times the measure of its supplementary angle. What is the measure of each angle?

**Answer: 1 angle is 144° and the other angle is 36°**

**Step-by-step explanation: **

**To find the smaller angle you would do:**

**1. x+4x=180**

**2. 5x=180**

**3. x=36 **

**Then for the larger angle it would be 36×4=144**

44+400 divided by (4+62)-24

**Answer:**

185

**Step-by-step explanation:**

**Answer:**

18

**Step-by-step explanation:**

**250**

**244**

**18**

**10**

**are one of the answers**

**give this 5 stars if correct**

Consider these two graphs. Does each represent a function? Why or why not?

**Answer:**

The first one is a function but the second one is not.

**Step-by-step explanation:**

Using the vertical line test, we can check if the graphs are a function or not. Every vertical line can only touch a graph once in order for the function to pass the Vertical Line Test. If a graph passes the Vertical Line Test, it's the graph of a function. The first one has no points intersecting each other if you draw a vertical line for each point. However, if you draw vertical lines for the second graph, the points vertically intersect each other, making it not a function.

Divide.

3/4÷2 1/2

Responses

3/10

1 1/2

1 7/8

3 1/3

**The answer is 3/10**

**Explanation: **

**= 3/4 x 2/5**

**= 3/4 x 2/5**

**= 3/2 x 1/5**

**= 3 x 1 / 2 x 5**

**= 3 / 2 x 5**

**= 3/10**

suppose that an allergist wishes to test the hypothesis that at least 30% of the public is allergic to some cheese products. explain how the allergist could commit a. a type i error; b. a type ii error.

Through **hypothesis testing**, it can be explained that **Type I error **occurs when the allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%. Similarly, **Type II error** occurs when the allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%

There are two possible outcomes for hypothesis testing, which leads to two different sorts of **conclusion-related errors**. This is due to the possibility that the estimated value of the measure and the inference made about the population measure from the samples could diverge.

Let's say an allergist wants to investigate the claim that at least 30% of the population has a cheese allergy.

Let p represent the actual percentage of the population that were allergic to certain cheese products.

The following is how the **hypotheses** are put forth:

[tex]H_{0}:p < 0.3\\H_{a}:p\geq 0.3[/tex]

The **two types of errors** that can be committed by the allergist can be described as below:

**(a) Type I error:**

When the **null hypothesis** is assumed to be true when it is actually false, type I error arises.

When an allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%, type I mistake has been committed.

**(b) Type II error**:

When the **null hypothesis** is unsuccessfully rejected even when it is false, type II error has occurred.

When an allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%, type II error has occurred.

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11-(15g-13)=-6

what does G stand for

**Answer:**

g = 2

**Step-by-step explanation:**

11- (15g - 13) = - 6 ( subtract 11 from both sides )

- (15g - 13) = - 17 ( multiply both sides by - 1 )

15g - 13 = 17 ( add 13 to both sides )

15g = 30 ( divide both sides by 15 )

g = 2

A ball is thrown in the air the function H = 30t￼-5t^2 can be used to find the height (h) of the ball in meters after t seconds￼￼. how long does it take the ball to reach a height of 45 meters?￼

The most appropriate choice for **Distance** will be given by:

The ball takes [tex]3s[/tex] to reach a **height** of [tex]45[/tex] [tex]m[/tex].

**What is Distance?**

The **length** of the** path** an object takes without taking into account the **direction of motion** of the object is known as** distance**.

If [tex]s[/tex] is the **speed **of the object and [tex]t[/tex] is the **time**, then

**Distance** = [tex]s \times t[/tex]

Here,

[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds

For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]

Now putting [tex]H(t) = 45[/tex]

[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]

So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

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a perfect square is an integer that is the square of an integer. suppose that m and n are positive integers such that mn > 15. if 15mn is a perfect square, what is the least possible value of mn ?

Least** possible** **value of m and n** are 6 and 10.

Given a **perfect square** is an integer that is also **square of an integer.**

The given m and n are positive integers such that mn > 15.

To find out the least possible value of mn;

As given 15mn is a **perfect square**.

[tex]\sqrt{15mn}[/tex] is to be an integer.

[tex]\sqrt{15mn} = \sqrt{5*3*m*n}[/tex]

Now, insert m = 3, n = 5;

⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5^2* 3^2} = 15[/tex]

but it is mn < 15.

So, assume m = 3 * 2, n = 5 * 2;

⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5*3*3*2*5*2} = \sqrt{5^2*3^2*2^2} = 30[/tex]

30 it is an integer.

As we solved that the least **possible value of m and n** are 6 and 10.

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Rodney is flying on an airplane to puerto rico. his suitcase and the contents inside must weigh less than 50lbs. his suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds. if each of his shirts weighs 0.75 pounds, write an inequality to represent the number of shirts he needs to remove to meet the flight requirements.

The **inequality **that represents, the number of **shirts **he needs to remove to meet the **flight **requirements is 0.75p + 50ibs ≤ 49

If the **equation **or inequality contains variable **terms**, then there might be some values of those **variables **for which that equation or inequality might be true. Such values are called **solution **to that equation or **inequality**.

Let the weight of **Rodney **suitcase be p

First the contents **inside **must **weigh **less than 50lbs.

x < 50

The **suitcase **weighs 4 pounds and the **contents **he wants to pack weigh 49 pounds.

0.75p < 49

Therefore, 0.75p + 50ibs ≤ 49

The **inequality **that represents, the number of **shirts **he needs to remove to meet the **flight **requirements is 0.75p + 50ibs ≤ 49

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Joe mows a lawn, for which he charges $30, and does some one-time cleanup work, for which he is paid $60. How many times will he have to mow the law before he makes a total of $300

He has mowed the law before he makes a total of **Dollar** 300, The **number** of times he has to mow a lawn is 10

Joe mows a lawn, for which he charges = $ 30

Some one-time cleanup work, for which he is paid = $ 60

According to the question:

He has to mow the lawn before he makes a total of **Dollar**300

**Number **of times he has to mow a lawn = 300 / 30

The **number** of times he has to mow a lawn = is 10

He has mowed the law before he makes a total of **Dollar** 300, 10 times.

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chegg a spherical ball is measured to have a radius of 5 mm, with a possible measurement error of 0.1 mm. use the differential to estimate the possible change in volume (in mm3) resulting from the error in measuring the radius.

The possible **change** in **volume** that results from the error in measuring the radius is 32. 06 millimeters

It is important to note that the formula for **volume** of a** sphere** is expressed by;

Volume = 4/3 πr³

Given that;

r is the radius of the sphereπ has the value 3.14Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm

The original value of radius = 5mm

Radius after the measurement error = 5 + 0. 1 = 5. 01mm

Let's substitute the values into the formula

Volume = 4/ 3 (3.14)(5)³

We then expand the bracket

Volume = 4/ 3 (392.5)

Volume = 523. 3 cubic millimeters

For radius of the measurement error = 5.01mm

Volume = 4/ 3 (3.14)(5.1)³

Then, expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 cubic millimeters

Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters

Hence, the **change** in** volume** is given as 32. 06 cubic millimeters

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1.) Tony deposited $743.22 to his checking account on July 1st. He then wrote a

check for $312.29 and another check for $36.70. The bank charged a

monthly service of $6.26. He now has $410.98 in the bank. How much did

Tony have in the bank at the end of June?

34

A. $387.97

B. $23.01

C. $798.95

D. $394.23

**Answer:**

23.01

**Step-by-step explanation:**

743.22-312.29-36.7-6.26

=387.97

410.98-387.97

=23.01

When driving up a certain hill, you rise 15 feet for every 1000 feet you drive forward. What is the slope of the rode?

**slope **of the **rode **is 0.015.

**What is slope of line ? **

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

Here, it is given that :

When driving up a certain hill, we rise 15 feet for every 1000 feet that is :

for 15 **feet up **= 1000 **feet forward**

Now,

slope = upward distance / horizontal distance covered

slope = 15/1000

slope = 0.015

slope is a unitless quantity.

Therefore, **slope **of the **rode **is 0.015.

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Metric area unit conversion with decimal valuesA rectangular field is 0.35 kilometers long and 0.2 kilometerswide. What is the area of the field in square meters? Do notround your answer.mX 5 ?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm) = 100 meters (m)1 kilometer (km) = 1000 meters (m) I need help with this math problem.
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