I dug a hole that was 16 feet deep. My dog came and put 8 feet of dirt back into the hole but then my husband put 5 feet of dirt back into the hole. What integer represents the depth of the hole?

Answer:

18 1/4

Step-by-step explanation:

To find how long it took Amy to run her fastest and slowest mile combined, we add the two values.

9\dfrac{2}{4}\text{ min} + 8\dfrac{3}{4}\text{ min}9

4

2

​

min+8

4

3

​

min9, start fraction, 2, divided by, 4, end fraction, start text, space, m, i, n, end text, plus, 8, start fraction, 3, divided by, 4, end fraction, start text, space, m, i, n, end text

Hint #44 / 5

\begin{aligned} 9\dfrac24+8\dfrac34&=(8+9)+\left(\dfrac{2}{4}+\dfrac{3}{4} \right)\\\\ &= 17+\dfrac{5}{4}\\\\ &=17+1\dfrac{1}{4}\\\\ &=18\dfrac{1}{4} \end{aligned}

9

4

2

​

+8

4

3

​

​

=(8+9)+(

4

2

​

+

4

3

​

)

=17+

4

5

​

=17+1

4

1

​

=18

4

1

​

​

Hint #55 / 5

It took Amy 18\dfrac1418

4

1

​

18, start fraction, 1, divided by, 4, end fraction minutes to run her fastest and slowest mile combined.

Disclaimer: The given question was incomplete, with the data missing. The complete question can be seen in the picture attached.

Analyzing and interpreting the given data, we can say that Amy took 18 1/4 minutes in total to run her slowest and fastest mile combined.

The process of attributing meaning to the acquired data and deciding the conclusions, relevance, and consequences of the results is known as data analysis and interpretation.

We are given a data set, representing the time taken by Amy to run each mile while running 8 miles, nearest to 1/4th of a minute.

We are asked to find how long did it take Amy to run her slowest and fastest mile combined.

Analyzing the data, we can say that her slowest mile will be the one for which she took the maximum time, that is, 9 2/4 minutes. Whereas her fastest mile will be the one with the minimum time, that is, 8 3/4 minutes.

We are asked to tell the combined time for her slowest and the fastest mile, so we add times for both, to get

Combined time = 9 2/4 + 8 3/4

or, Combined time = 38/4 + 35/4

or, Combined time = 73/4

or, Combined time = 18 1/4.

∴ Analyzing and interpreting the given data, we can say that Amy took 18 1/4 minutes in total to run her slowest and fastest mile combined.

Learn more about data analysis and interpretation at

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Answer:

[tex]R = \frac{1}{6}[/tex]

Step-by-step explanation:

Given that she sold half the paintings and gives out one-third

Required

Determine the fraction left with her

The relationship between the paintings is as follows;

Sold Paintings + Giveaway Paintings + Remaining Paintings = 1

From the question;

Sold Paintings = 1/2

Giveaway = 1/3

Represent Remaining Paintings with R

Substitute these values in the above formula

[tex]\frac{1}{3} + \frac{1}{2} + R = 1[/tex]

Take LCM

[tex]\frac{2+3}{6} + R = 1[/tex]

[tex]\frac{5}{6} + R = 1[/tex]

Make R the subject of formula

[tex]R = 1 - \frac{5}{6}[/tex]

Take LCM

[tex]R = \frac{6-5}{6}[/tex]

[tex]R = \frac{1}{6}[/tex]

Hence, the fraction of the paintings left with her is [tex]\frac{1}{6}[/tex]

Answer:

[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]

Step-by-step explanation:

If you look at the objects thrown as garbage, it's a two- or three-dimensional item that takes up space and also has mass and this is a solid waste.

And the landfill that dumps such garbage is also three-dimensional.

Hence, the volume module, if the object inside is a solid, either would be

[tex]m^3,cm^4,Km^3[/tex]

As household numbers rise, landfill space increases.

So,

[tex]household\ number = Proportionality\times landfill\ space[/tex]

If H represents the number of household keeps,  then it will be a sufficient unit for the purpose of Sophia that is

[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]

Answer:

For a given length l and width w, the new perimeter is....

2(l + w) + 8

Step-by-step explanation:

Currently, the rectangle's perimeter is 2(l + w). You knew that.

Now, the question asked you to change l into l + 7, and w into w - 3. Substitute them, so we get

Perimeter New = 2(l + 7 w - 3) = 2 (l + w + 4)

Then, I chose to "pull out" + 4, so I multiply it with the 2. Hence, we get

Perimeter New = 2 (l + w) + 8

Answer:

-15 = v

Step-by-step explanation:

-8=v/3-3

Add 3 to each side

-8+3=v/3-3+3

-5 = v/3

Multiply each side by 3

-15 = v

Answer: v=-15

Step-by-step explanation:

Given

-8=v/3-3

Add 3 on both sides (addition property of equality)

-5=v/3

Multiply 3 on both sides (multiplication property of equality)

v=-15

Hope this helps!! :)

Please let me know if you have any question

Answer:

x=9

Step-by-step explanation:

combine like terms

[tex]4+6x+5=7x[/tex]

4+5=9

9+6x=7x

to get 6x with 7x subtract 6x from both sides as its positive

6x-6x=0

7x-6x=x

9=x

x=9

Answer:

-11xy\26x\2y\6

Step-by-step explanation:

Answer:

Still (0,6)

Step-by-step explanation:

The point is actually on the y-axis.  It can't change in a y-axis reflection, only in an x-axis reflection.

Answer:

4 eggs

Step-by-step explanation:

40 divided by 10 = 4

Answer:

4

Step-by-step explanation:

40/10=4

Answer:

Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123  

2

1

​  

3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231  

2

1

​  

31, start fraction, 1, divided by, 2, end fraction minutes long.

Step-by-step explanation:

Answer:

Second choice

Step-by-step explanation:

f(x) = (1/4)(x + 4)^2 - 9

f(x) = (1/4)(x^2 + 8x + 16) - 9

f(x) = (1/4)x^2 + 2x + 4 - 9

f(x) = (1/4)x^2 + 2x - 5

(1/4)x^2 + 2x - 5 =

= (1/2 x + 5)(1/2 x - 1)

Answer: Second choice

Answer:

21.5

Step-by-step explanation:

Counting the full squares: 16

Counting the squares that are more than 1/2:  6

The best estimate would be 21.5

Answer:

6

Step-by-step explanation:

log ₐ (aˣ) = x

3 log ₂ (4)

3 log ₂ (2²)

3 * 2

6

Answer:

Step-by-step explanation:

In this problem we are expected to sum up the number of lines recorded during all court sessions for the day.

Also we know that the court report, reported for two (2) court session for that day.

Hence all the number of line is going to be from the 2 court sessions she reported

in the first court session we wrote 47 lines

in the second court session we reported 33 line

the total lines in all is 47+33= 80 lines

The total line recorded for the day is 80 lines

Answer:

Domain: (-5, 6]

Range: [-3, 6]

Step-by-step explanation:

Domain is all x-values that can be inputted into function f(x).

Range is all the y-values outputted by function f(x) when we plug in x.

We see that our x-values span from -5 to 6. Since -5 is a open dot, we cannot input -5. Therefore, we have:

Domain: (-5, 6]

Parenthesis on -5 shows that it is not included and bracket on 6 shows it is included.

We see that our y-values span from -3 to 6. Since both points are closed dots, we can include both. Therefore, we have:

Range: [-3, 6]

Brackets on both numbers signify that both values are included in the graph.

Step-by-step explanation:

Using distance formula:

√(5 - 9)² + (-3 - 2)²

√(-4)² + (-5)²

√16+25

√41

Answer:

a) (-3, 4) and radius = 2.

b) 7 cms.

Step-by-step explanation:

x^2+ y^2 + 6x - 8y + 21 = 0

x^2 + 6x + y^2 - 8y = -21

Completing the square on the x and y terms:

(x + 3)^2 - 9 + (y - 4)^2 - 16 = -21

(x + 3)^2 + (y - 4)^2  = -21 + 9 + 16 = 4

a) So the center is (-3, 4) and the radius = sqrt4 = 2.

Ill come back to you later with the second part.

(b) For the point P to be a maximum distance from the origin the line must pass through the center of the circle:

Distance of the center from origin:

= √(-3 - 0)^2 + (4 -0)^2)

= 5.

So the dsitance of P from  the origin is  5 + radius

= 7 cm.

Answer:

1) [tex]\huge\boxed{ 250\°}[/tex]

2) [tex]\huge\boxed{75\° + 25\°t }[/tex]

Step-by-step explanation:

Initial Temperature = 75°

Per minute Increase = 25°

After 7 minutes:

=> 75 + 25 ( 7 )

=> 75 + 175

=> 250°

After t minutes:

=> 75 + 25 (t)

=> 75° + 25°t

Answer:

[tex]\Large \boxed{\mathrm{a) \ 250\° \ \ \ b) \ 75\° +25\°t}}[/tex]

Step-by-step explanation:

Before baking, Joshua preheats the oven at an initial temperature of 75°. The temperature increases at a rate of 25° per minute.

Temperatute after 7 minutes,

[tex]75 \° + 25 \°(7)=75\° +175 \° =250 \°[/tex]

Tempertaure after t minutes,

[tex]75 \° +25 \° t[/tex]

Answer:

no because it has 2 of the same x-intercepts.

Step-by-step explanation:

If two angles are complementary, then the

sum of their measures is 90 degrees.

We can find the m<B by taking 90 minus the measure of <A.

So here, we have 90 - 15 which is 75.

So m<A is 75 degrees.

Answer:

4 and 5, closer to 4

Step-by-step explanation:

From the diagram above,

length of the diagonal = √18

√18 = 4.2426406871192

√18 is between 4 and 5

√18 is more than 4 by .2426406871192 but not up to 5

Rounding up 4.2426406871192 to an 1 significant figure,

We have 4

This means, the length of the diagonal, √18 is between 4 and 5 but it is closer to 4

Answer:

4 and 5, closer to 4

Step-by-ste

[tex]\sqrt18=4.24\\[/tex]

4.24 is closer to 4 than to 5

Answer:

we know that,

y-y1=m(x-x1)

or, y-1=-3(x-5)

or, y-1=15-3x

or 3x+y-16=0 is the required equation

The graph of the line with slope -3 passing through the point (5,1) is attached.

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.

The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.

The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.

The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).

We are asked to graph a line with a slope = -3, passing through the point (5, 1).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

y - 1 = -3(x - 5)

or, y = -3x + 15 + 1

or, y = -3x + 16.

or, 3x + y = 16

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.

Learn more about the graphing of a line at

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Answer:

Assume you meant: [tex]g(x) = 3x^{2}+3[/tex]

Answer is 3

Step-by-step explanation:

Replace x with 0:

[tex]g(0) = 3(0)^{2} +3[/tex] zero squared is zero

[tex]g(0) = 3(0) + 3[/tex]

[tex]g(0) = 0 + 3[/tex]

[tex]g(0) = 3[/tex]

Step-by-step explanation:

[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]

we have

[tex]g(x) = {3x}^{2} + 3[/tex]

in this we have x = 0

[tex]g(0) = 3( {0})^{2} + 3[/tex]

[tex]g(0) = 0 + 3[/tex]

[tex]g(0) = 3[/tex]

so we have x =3

Hope it helps

Answer:

Null hypothesis : top speed = height

Alternative hypothesis : top speed ≠ height

Dependent variable : speed

Independent variable : Height

Step-by-step explanation: The experiment aims to determine the relationship between the height of ramp and the top speed reached by her skateboard.

The Null hypothesis: top speed = height

while the alternative hypothesis will negate the Null.

Alternative hypothesis : top speed ≠ height

The dependent variable in the experiment will be her top speed, because it is the variable we want to evaluate. We want to determine if thwre will be a change in the top speed of the skateboard if there is change in another variable 'height' of ramp. The variable which might cause a change in value of our dependent variable is called the independent or predictor variable, which in this case is the height variable.

Answer:

Yes! It can

[tex]Fraction=4\frac{7}{10}[/tex]

Decimals can convert into fractions!

4 is the whole number

.70 is

70 out hundredths

7/10 or 7/100

So the fraction would be

[tex]4\frac{7}{10}[/tex]

Hope this helps!

[tex]Fishylikeswater[/tex]

Answer: 4 and 7/10

Step-by-step explanation: Using the place value chart below,

we can see that 4.7 means four and seven tenths.

This can be written as the mixed number 4 and 7/10.

Answer:

2. Kayla's opportunity cost to go to the movie is $9.50

4. Tara's total cost of attending the movie is $50.5

Step-by-step explanation:

Complete question below:

Tara earns $8.50 an hour (after taxes) at the pizza place. She is scheduled to work four hours this afternoon. However, her friend Kayla called and asked her if she wants to go to the movie. A ticket to the movie costs $9.50. In addition, she always spends about $7 on snacks.

Which of the following statement are true? Select all that apply.

1. Tara's opportunity cost if she goes to work instead of the movie is $34.

2. Kayla's opportunity cost to go to the movie is $9.50.

3. There is no opportunity cost for Tara to go to the movie.

4. Tara's total cost of attending the movie is $50.5

5. Tara's opportunity cost if she goes to the movie instead of working is $34

Solution

Tara earns $8.50 per hour

She is scheduled to work for 4 hours

Total earnings=$8.50 × 4

=$34

Tara's opportunity cost of attending the movie instead of working is $34

Since, a ticket cost $9.50

And she always spend about $7 on snacks

Tara's total cost of going to the movies = opportunity cost of attending the movie + cost of tickets + cost of snacks

=$34 + $9.50 + $7

=$50.5

Opportunity cost refers to the cost of satisfying a want at the expense of another want. It can also be called REAL COST or TRUE COST.

Therefore,

2. Kayla's opportunity cost to go to the movie is $9.50

4. Tara's total cost of attending the movie is $50.5

2 and 4 are the answers

Answer:

Below.

Step-by-step explanation:

A measure of variation is an estimate of the spread of the numbers.

For example the set of numbers 1 2 3 19 78 has a greater measure of variation than the set 1 2 3 5 9.

The interquartile range and the mean absolute deviation are measures of variation.

3 6 8 15 21 22 23

The median of the data is the middle number 15..

The lower quartile is 6 and the higher quartile is  22

The interquartile range is 22 - 6 = 16.

The mean absolute deviation (M.A.D.) is calculated as follows:

Mean = (3+6+8+15+21+22+23) / 7 = 98/7

= 14.

List the absolute differences from the mean

14 - 3 = 11

14-6 = 8

15-14 = 1

21-14= 7

22-14 = 8

23-14 = 9   ( all these have to be positive)

The sum of the differences is 11+8+1+7+8+9 = 44

So the MAD = 44/7 = 6.3 to nearest tenth.

Answer:

Hector's kite is 61.84 feet from the ground.

Step-by-step explanation:

The angle of elevation of the kite is 42°15’30” when converted to decimals, it is [tex]42.258333^{0}[/tex] ≅ [tex]42.26^{0}[/tex]

Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,

Sin θ = [tex]\frac{opposite}{hypotenus}[/tex]

Sin [tex]42.26^{0}[/tex] = [tex]\frac{x}{86}[/tex]

⇒ x = 86 x Sin [tex]42.26^{0}[/tex]

      = 86 x 0.6725

     = 57.835

x ≅ 57.84 feet

The height of Hector's kite from the ground = x + 4

                                    = 57.84 + 4

                                   = 61.84 feet