3 questions 40 points

We are given

edge of cube =x

we know that formula for volume of cube

[tex]V=x^3[/tex]

we are given

[tex]V=\frac{1}{8} cm^3[/tex]

we can plug value

[tex]x^3=\frac{1}{8} cm^3[/tex]

now, we can solve for x

[tex]\sqrt[3]{x^3} =\sqrt[3]{\frac{1}{8} cm^3 }[/tex]

[tex]x=\frac{1}{2} cm[/tex]............Answer

Answer:

1/2 cm

Step-by-step explanation:

First of all, we need to do the expression in parenthesis first.

(4% - 2.25%) = 1.75%

Now, we convert the percent into an integer.

1.75% = 0.0175

Then, we multiply 44.5 by 0.0175

and we get 0.77875.

We have to round the number to the nearest cent.

0.77875 is roughly 0.78

So the answer is $0.78.

Answer: [tex]\frac{7}{18}[/tex] = 7:18

Step-by-step explanation:

[tex]\frac{35(mangos)}{13(papayas)+23(stares)+35(mangos)+19(strawberries)} = \frac{35(mangos)}{90(total fruit)}[/tex]

[tex]\frac{35}{90}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{7}{18}[/tex]

Answer:

Domain ={0,infinity)

Range = (-infinity, 4]

Step-by-step explanation:

Given a graph with curve which has y intercept 4.

It passes x axis at 4 and extends fully

The domain is the set of values x can take

In the graph horizontal axis is x axis.

Hence from the graph we see that x can take values from 4 including 4 upto infinity.

Hence domain is x>=4

For range, we consider the values of y as per graph.

WE find that y is not taking values >4

Hence Range = (-infty, 4]

Answer:

[tex]Domain=[0,\infty)[/tex]

[tex]Range=(-\infty,4][/tex]

Step-by-step explanation:

We need to find the domain and range of the function.

Domain : It is the set of input values or x values. In a graph, domain of the function represented by the x-axis.

Range : It is the set of output values or y values. In a graph, range of the function represented by the y-axis.

From the given graph it is clear that it is defined for [tex]0\le x<\infty[/tex] and [tex]-\infty <y\le 4[/tex].

We have closed circle at (0,4). It means, 0 is included in the domain and 4 is included in the range.

[tex]Domain=[0,\infty)[/tex]

[tex]Range=(-\infty,4][/tex]

Therefore, [tex]Domain=[0,\infty)[/tex] and [tex]Range=(-\infty,4][/tex].

(C) is correct answer. The values in the table assign to each x only one y value.

Answer:

c is the best answer for the question

Step-by-step explanation:

The easiest way to do this is to start with the power of 5 that is just under 219.

125 would be the closest power of  5

Now subtract 125 from 219 = 94

=====================

The highest power of 5 closest to 94 is 25. You have to multiply 25 * 3 to get a number close enough to 94 that leaves a remainder under 25

94 - 75 = 19

=======================

19 - 3 * 5 = 4 Same argument as above.

Answer

219_10 = 1334_5

Answer:

1334/5

Step-by-step explanation:

Hello!

When multiply binomials together, we should use the FOIL method.

The FOIL method is an acronym for First, Outer, Inner, and Last.

First, let's set up the expression.

(7x - 1)(3x - 2)

Now, we can multiply in accordance with the FOIL method.

First: 7x · 3x = 21x²

Outer: 7x · -2 = -14x

Inner: -1 · 3x = -3x

Last: -1 · -2 = 2

Now, we simplify the inner terms.

21x² - 14x - 3x + 2

21x² - 17x + 2

Therefore, the area of the rectangle is 21x² - 17x + 2.

The area of the rectangle is (21x² - 17x + 2) units².

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Given the length of the rectangle is (7x-1) units, while its breadth is (3x-2) units. Therefore, the area of the rectangle is,

Area of rectangle = (7x-1) units × (3x-2) units

= 21x² - 14x - 3x + 2

= 21x² - 17x + 2 units²

Hence, the area of the rectangle is (21x² - 17x + 2) units².

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Answer:

The correct option will be:   b. One lap around the mall is equal to about 2,425 steps.

Step-by-step explanation:

Here, we will just find the slope of the line representing Debi’s data. For that, we will take any two data from the table in form of point like [tex](x,y)[/tex]

Lets take two points as  [tex](0, 1875)[/tex] and  [tex](2, 6725)[/tex]

Formula for finding the slope is:  [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] are two given points.

Here,  [tex]x_{1}= 0 , y_{1}= 1875 , x_{2}=2 , y_{2}=6725[/tex]

So, plugging these values into the above formula, we will get......

[tex]m= \frac{6725-1875}{2-0}=\frac{4850}{2}=2425[/tex]

That means, one lap around the mall is equal to about 2,425 steps.

Answer:

One lap around the mall is equal to about 2,425 steps.

Step-by-step explanation:

Answer:

Gregory will catch up Efren after 26 minutes 40 seconds.

Explanation:

 Distance traveled = Speed x Time

 Speed of Efren = 4 mi/h

 Speed of Gregory = 8.5 mi/h

 Let the time of catch up be t hours.

 Time of journey of Efren before catch up = (t+0.5)hours, since he starts before half hour.

 Distance traveled by Efren = 4 x (t+0.5) miles

 Time of journey of Gregory before catch up = t hours.

 Distance traveled by Gregory = 8.5 x t miles

If they catch up the distance traveled by them is same, so equating both distances.

4 x (t+0.5) = 8.5 x t

4.5t = 2

t = 0.44 hours =26.67 minutes = 26 minutes 40 seconds.

So Gregory will catch up Efren after 26 minutes 40 seconds.

Gregory will catch up to Efren approximately at 9:56am.

To find out when Gregory will catch up to Efren, we need to set up an equation based on their speeds and the time they travel.

Calculate the head start distance: Efren leaves at 9am and walks at 4 miles per hour.

Determine their relative speed: Gregory runs at 8.5 miles per hour while Efren walks at 4 miles per hour.

Calculate the time for Gregory to catch up: We need to divide the head start distance by their relative speed.

Find the catch-up time: Gregory leaves at 9:30am, so add the catch-up time to this.

Therefore, Gregory will catch up to Efren at approximately 9:56am.

We are given

initial population is 5891

so, [tex]P_i=5891[/tex]

Population after 50 years is 5178

so, [tex]P_f=5178[/tex]

now, we can find percent error

so, we can use formula

[tex]error=\frac{P_i-P_f}{P_i}\times 100[/tex]

now, we can plug values

[tex]error=\frac{5891-5178}{5891}\times 100[/tex]

now, we can simplify it

so, we get

The percent decrease is 12.1032%.........Answer

First: work out the difference (decrease) between the two numbers you are comparing by the formula

Decrease = Original Number - New Number

In your case,

[tex]\text{Decrease}=5891-5178=713.[/tex]

Second: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

In your case,

[tex]\%\text{Decrease}=\dfrac{713}{5891}\cdot 100\%=12.1\%.[/tex]

Answer: The percent decrease is approximately  12.1%.

we are given

[tex]\frac{2x^5-x^4+3x^2-x+5}{x-1}[/tex]

Here , we have

[tex]dividend=2x^5-x^4+3x^2-x+5[/tex]

[tex]divisor=x-1[/tex]

now, we can use synthetic division

so, we get

[tex]Quotient=2x^4+x^3+x^2+4x+3[/tex]

[tex]Remainder=8[/tex]

now, we can write in fraction form

[tex]\frac{2x^5+x^4+3x^2-x+5}{x-1}=(2x^4+x^3+x^2+4x+3)+\frac{8}{x-1}[/tex]............Answer

To divide using synthetic division, arrange the polynomial in descending order, set up the synthetic division table, find the root of the divisor, perform the synthetic division, and read the coefficients of the quotient. In this case, the quotient is 2x^3 + x^2 + 4x + 3 with a remainder of -1.

To divide using synthetic division, you need to follow these steps:

In this case, the polynomial is 2x5 - x4 + 3x2 - x + 5, and the divisor is x - 1. Using synthetic division, we divide the coefficients:

The coefficients in the bottom row of the synthetic division table are 2, 1, 4, 3. Therefore, the quotient is 2x3 + x2 + 4x + 3, and the remainder is -1.

we can see that

zeros are at x=-3 , x=2 , x=3

now, we can set up function

[tex]f(x)=a(x+3)(x-2)(x-3)[/tex]

now, we can select any one point and then we can find 'a'

(0,36)

x=0 and f(x)=36

we can plug it and then we can find 'a'

[tex]36=a(0+3)(0-2)(0-3)[/tex]

[tex]a=2[/tex]

now, we can plug it back

and we get

[tex]f(x)=2(x+3)(x-2)(x-3)[/tex]

now, we can multiply it

we get

[tex]f(x)=2x^3-4x^2-18x+36[/tex]............Answer

Answer: 12.6

Step-by-step explanation:

  (0 + 11 + 13 + 2 + 20 + 3 + 40 + 4 + 40 + 5 + 13 + 6 + 7)/13

= 164/13

= 12.6

Answer:

Jenni spent 44

Step-by-step explanation:

Let the amount spent by Jenni be x

Let the amount spent by Sara be  2x which also equals 88

2x = 88

x = ?

Cross multiplying gives:

x/2x × 88 = 44

Jenni therefore spent 44

Answer: 93 grams Zinc

Step-by-step explanation:

3 Zinc : 13 Copper

x 31       x 31            

93 Zinc,     403 Copper

or

set up a proportion, cross multiply, and solve for the variable:

[tex]\frac{Zinc}{Copper}: \frac{3}{13} = \frac{x}{403}[/tex]

3(403) = 13(x)

[tex]\frac{3(403)}{13} = x[/tex]

3(31) = x

93 = x

The amount of zinc in the chemical is determined by using the given ratio of zinc to copper and applying it to the given amount of copper. Step-by-step calculations reveal the quantity of zinc to be 93 grams.

The question is asking for the amount of zinc in a chemical where the ratio of zinc to copper is 3:13. To find out this, we need to solve for zinc in terms of the given amount of copper.

First, understand that the ratio means for every 3 grams of zinc, there are 13 grams of copper. Now, simply set up a proportion where 3/13 = x/403. Here x is the amount of zinc in grams we are trying to find. 3/13 is the zinc to copper ratio and 403 is the known amount of copper in grams.

When you cross multiply and solve for x, you'll find that x = 3 * 403 / 13 = 93 grams. This means, if there are 403 grams of copper, then there must be "93 grams of zinc".

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To divide the polynomial [tex]6x^2+11x-3[/tex] by the polynomial [tex]2x-1,[/tex] you have to do such steps:

1 step. Multiply the polynomial [tex]2x-1[/tex] by [tex]3x[/tex]. You get the polynomial [tex]6x^2-3x.[/tex]

2 step. Subtract the polynomial  [tex]6x^2-3x[/tex] fro mthe polynomial [tex]6x^2+11x-3:[/tex]

[tex]6x^2+11x-3-(6x^2-3x)=6x^2+11x-3-6x^2+3x=14x-3.[/tex]

Step 3. Multiply the polynomial [tex]2x-1[/tex] by [tex]7[/tex] to get the polynomial [tex]14x-7.[/tex]

Step 4. Subtract the polynomial  [tex]14x-7[/tex] from the polynomial [tex]14x-3:[/tex]

[tex]14x-3-(14x-7)=14x-3-14x+7=4.[/tex]

Step 5. Write the division result:

[tex]6x^2+11x-3=(2x-1)(3x+7)+4.[/tex]

Here the quotient is the polynomial [tex]3x+7[/tex] and the remainder is the polynomial [tex]4.[/tex]

Answer: the remainder is 4.

Answer:

-1

Step-by-step explanation:

Just took the test

<D = 360 - (80 + 115 + 100)

<D = 360 - 295

<D = 65

Answer

<D = 65°

Answer is: −4−7i−(5−6i) = −9−i

The given complex expression is (-4-7i) - (5-6i). The simplification would give −9−i.

Any complex number can be written as

z = a + ib

The given complex expression is

(-4-7i) - (5-6i)

The simplification will be

= −4−7i−(5−6i)

= −9−i

Therefore, The simplification would give −9−i.

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3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]

multiply each of the terms in the parenthesis by [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] (6e - 3f - [tex]\frac{3}{4}[/tex] )

= 3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]

Answer:

[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{1}{2}(6e-3f-\frac{3}{4})[/tex]

To find an equivalent expression, we need to use the distributive property, that is, we have to multiply [tex]\frac{1}{2}[/tex] with each term that's inside the parenthesis.

[tex]\frac{1}{2}(6e-3f-\frac{3}{4})\\\frac{6e}{2}-\frac{3f}{2}-\frac{3}{2(4)}\\ 3e-\frac{3}{2}f-\frac{3}{8}[/tex]

Therefore, the equivalent expression is

[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]

Remember that when we multiply fractions, we have to do it in a linear way, that is, numerators multiply each other, and denominators multiply each other. That means you CAN'T multiply a numerator with a denominator.

Answer:

Unfortunately, your answer is not right.

Step-by-step explanation:

The functions whose graphs do not have asymptotes are the power and the root.

The power function has no asymptote, its domain and rank are all the real.

To verify that the power function does not have an asymptote, let us make the following analysis:

The function [tex]y = x ^ n[/tex] , when x approaches infinity, where does y tend? Of course it tends to infinity as well, therefore it has no horizontal asymptotes (and neither vertical nor oblique)

With respect to the function [tex]y= \frac{1}{x}[/tex] we ​​can verify that if it has asymptote horizontal in y = 0. Since when x approaches infinity the function is closer to the value 0.

For example: 1/2 = 0.5;   1/1000 = 0.001;    1/100000 = 0.00001 and so on. As "x" grows "y" approaches zero

Also, when x approaches 0, the function approaches infinity, in other words, when x tends to 0 y tends to infinity. For example: 1 / 0.5 = 2; 1 / 0.1 = 10; 1 / 0.01 = 100 and so on. This means that the function also has an asymptote at x = 0

The question involves precalculus, a High School or College level Mathematics topic, focusing on the accuracy and reasonableness of answers related to engineering principles. Students must consider significant figures, units of measure, and logical consistency within their mathematical processes.

The student's question pertains to the subject of Mathematics, specifically within the realm of Precalculus, which is typically taught at the High School or College level. The inquiry involves reviewing the process of answering questions in mathematics and science as it relates to engineering. This includes checking whether an answer is reasonable in terms of units, magnitudes, and mathematical consistency. For instance, in the context of a precalculus class, students are expected to pay close attention to significant figures, units of measure, and ensuring answers are logically consistent with the problem presented.

The data set provided from Susan Dean's spring precalculus class can be used as an example for various statistical calculations. When dealing with such data, students need to organize it in a clear format, identify central tendencies (like mean, median, mode), and ensure that final answers are expressed with the proper significant figures and units. These practices are crucial for nd are rerced in a variety of STEM courses.

When it comes to the review questions mentioned, while specific questions are not provided, it is clear that students are encouraged to identify all correct answers to demonstrate their understanding of how mathematics and science connect with engineering. This holistic approach reflects real-world problem-solving where multiple solutions or considerations often exist.

3. AB≅CE

4.CE≅AC

5.transitive property of congruence

6. definition of a isosceles triangle

Answer: 4,398,200

Step-by-step explanation:

4, 398, 202    

the underlined 2 is in the 100's place.  look at the number to the right of it.  If that number is greater than or equal to 5, then the 2 is rounded up.  Otherwise, the 2 remains the same.

The number to the right of the underlined 2 is 0, so the 2 remains the same.  All digits to the right will become 0s.

Answer:

y = 44+22m

Step-by-step explanation:

Given that a taxi has a minimum charge of 44 dollar upto 1 mile and adds 22 for every additional 1 mile.

If a person travels 1 miles his charges are 44 dollar

If he travels >1 miles charges are 4 dollar +22(extra miles )

Let y be the charges and m be the no of miles.

Then the equation for y in terms of m would be

y =44+22m

is the correct answer.

TRUE

because if we substitute the value of x = 10 to the equation, then we have quotient with divide by zero!

[tex]y=\dfrac{1}{x-10}\to f(x)=\dfrac{1}{x-10}\\\\f(10)=\dfrac{1}{10-10}=\dfrac{1}{0}\ !!!![/tex]

The multiples of 8 are: 0, 8, 16, 24, 32, 40, 48, ...

The multiples of 10 are: 0, 10, 20, 30, 40, 50, ...

LCM(8, 10) = 40

LCM(x²y², x²y³) = x²y³

Therefore

The LCM of 8x²y² and 10x²y³ is Option A: 40x²y³.

Identify the LCM of the numerical coefficients.

For 8 and 10, the LCM =40.

Determine the highest power of each variable present in the terms,

For x2 from both terms, the highest power is [tex]x^2[/tex].

For y2 and y3, the highest power is [tex]y^3.[/tex]

Therefore, the LCM of [tex]8x^2y^2[/tex] and [tex]10x^2y^3[/tex]is [tex]40x^2y^3[/tex].

The correct answer is Option A: [tex]40x^2y^3.[/tex]

Answer:

502

Step-by-step explanation:

4560/x=100/11

(4560/x)*x=(100/11)*x       - we multiply both sides of the equation by x

4560=9.09*x       - we divide both sides of the equation by (9.09) to get x

4560/9.09=x

501.6=x

x=501.6

why hello there

Your answer is c i was gonna give a better answer but the other dude did it