A dump truck is filled with 82.16 pounds of gravel. It drops off 77.29 pounds of gravel at a construction site. How much gravel is left on the truck?

Answer:

34%

Step-by-step explanation:

Given that the distribution of daily light bulb request replacement is approximately bell shaped with ;

Mean , μ = 45 ; standard deviation, σ = 3

Using the empirical formula where ;

68% of the distribution is within 1 standard deviation from the mean ;

95% of the distribution is within 2 standard deviation from the mean

Lightbulb replacement numbering between ;

42 and 45

Number of standard deviations from the mean /

Z = (x - μ) / σ

(x - μ) / σ < Z < (x - μ) / σ

(42 - 45) / 3 = -1

This lies between - 1 standard deviation a d the mean :

Hence, the approximate percentage is : 68% / 2 = 34%

9514 1404 393

Answer:

  c.  1 : 1

Step-by-step explanation:

The total of exterior angles of any convex polygon is 360°. The total of interior angles of a quadrilateral is 360°. So, the ratio of interest is ...

  interior : exterior = 360° : 360° = 1 : 1

Step-by-step explanation:

here's the answer to your question

Answer:

length= 125

width= 100

Step-by-step explanation:

let width have a length of x m

therefore length= (x+25)m

perimeter=2(length +width)

p=2((x+25)+x)

p=4x+50

but we have perimeter to be 450,, we equate it to 4x+50 above,

450=4x+50

4x=400

x=100 m

length= 125

width= 100

Answer:

Part A)

About 0.51% per year.

Part B)

About 0.30% per year.

Part C)

About 28.26%.

Step-by-step explanation:

We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:

[tex]f(t) = 10.72(0.9t+10)^{0.3}\text{ where } 0 \leq t \leq 20[/tex]

Where t is measured in years with t = 0 being the year 2000.

Part A)

Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:

[tex]\displaystyle f'(t) = \frac{d}{dt} \left[ 10.72\left(0.9t+10\right)^{0.3}\right][/tex]

Rewrite:

[tex]\displaystyle f'(t) = 10.72\frac{d}{dt} \left[(0.9t+10)^{0.3}\right][/tex]

We can use the chain rule. Recall that:

[tex]\displaystyle \frac{d}{dx} [u(v(x))] = u'(v(x)) \cdot v'(x)[/tex]

Let:

[tex]\displaystyle u(t) = t^{0.3}\text{ and } v(t) = 0.9t+10 \text{ (so } u(v(t)) = (0.9t+10)^{0.3}\text{)}[/tex]

Then from the Power Rule:

[tex]\displaystyle u'(t) = 0.3t^{-0.7}\text{ and } v'(t) = 0.9[/tex]

Thus:

[tex]\displaystyle \frac{d}{dt}\left[(0.9t+10)^{0.3}\right]= 0.3(0.9t+10)^{-0.7}\cdot 0.9[/tex]

Substitute:

[tex]\displaystyle f'(t) = 10.72\left( 0.3(0.9t+10)^{-0.7}\cdot 0.9 \right)[/tex]

And simplify:

[tex]\displaystyle f'(t) = 2.8944(0.9t+10)^{-0.7}[/tex]

For 2002, t = 2. Then the rate at which the percentage is changing will be:

[tex]\displaystyle f'(2) = 2.8944(0.9(2)+10)^{-0.7} = 0.5143...\approx 0.51[/tex]

Contextually, this means the percentage is increasing by about 0.51% per year.

Part B)

Evaluate f'(t) when t = 17. This yields:

[tex]\displaystyle f'(17) = 2.8944(0.9(17)+10)^{-0.7} =0.3015...\approx 0.30[/tex]

Contextually, this means the percetange is increasing by about 0.30% per year.

Part C)

For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:

[tex]\displaystyle f(17) = 10.72(0.9(17)+10)^{0.3}=28.2573...\approx 28.26[/tex]

So, about 28.26% of the American population in 2017 are age 55 and older.

Answer:

2 with 3 left over

Step-by-step explanation:

17 divided by 2 is 14 with 3 remaining

Answer:

2 pies

Step-by-step explanation:

Answer:

10 2/3 or 32/ 3

Step-by-step explanation:

5 - x^2 - (2 - 2x) =

= -x^2 + 2x + 3

Integral of (-x^2 + 2x + 3)dx from -1 to 3 =

= -x^3/3 + 2x^2/2 + 3x from -1 to 3

= -x^3/3 + x^2 + 3x from -1 to 3

= -27/3 + 9 + 9 - (1/3 + 1 - 3)

= -9 + 9 + 9 - 1/3 - 1 + 3

= 11 - 1/3

= 10 2/3 = 32/3

Answer:

32/3

Step-by-step explanation:

Check the pdf :)

Answer:

Step-by-step explanation:

(n-1)1.1

Answer:

People prefer pop music to any other type of music.

The least favorite genre of music is blues.

Four times as many people prefer pop music to blues.

Answer:

B) People prefer pop music to any other type of music.

C) The least favorite genre of music is blues.

E) Four times as many people prefer pop music to blues.

Step-by-step explanation:

edge 2023

Answer:3 and 4

Step-by-step explanation:

Answer:

A. 89.84

Step-by-step explanation:

Weighed mean:

Sum of the multiplications of each value by its weight, divided by the sum of the weights.

Weights:

15 had an average of 90.

7 averaged 85.

10 averaged 93.

What is the weighted mean for the 32 students taking the exam?

[tex]M = \frac{15*90 + 7*85 + 10*93}{15 + 7 + 10} = 89.84[/tex]

Thus the correct answer is given by option A.

Answer:

use the formula y = a(x-h)^2 + k

the a stretches or flattens the parabola,

The h shifts left to right , and the k shifts up/down

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

From the picture attached,

m∠ABC = 40° [Given]

Since, measure of the intercepted arc is double of the measure of the inscribed angle.

Therefore, m(arc AC) = 2(m∠ABC)

m(arc AC) = 2(40°)

                 = 80°

m(arc FB) = 115° [Given]

By applying theorem of the angles formed by the chords inside a circle,

m∠2 = [tex]\frac{1}{2}(\text{arc}AC+\text{arc}FB)[/tex]

        = [tex]\frac{1}{2}(80^{\circ}+115^{\circ})[/tex]

        = 97.5°

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 + 97.5° = 180°

m∠1 = 180° - 97.5°

       = 82.5°

Option C is the answer.

Answer:

6x + 10y

Step-by-step explanation:

4x + 3y + 2x + 7y

=> (4x + 2x) + (3y + 7y)

=> 6x + 10y

Answer:

You should expect 5 days in July with daily rainfall of more than 11.5 mm.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm.

This means that [tex]\mu = 10, \sigma = 1.5[/tex]

Proportion of days with the daily rainfall above 11.5 mm.

1 subtracted by the p-value of Z when X = 11.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{11.5 - 10}{1.5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

1 - 0.84 = 0.16.

How many days in July would you expect the daily rainfall to be more than 11.5 mm?

July has 31 days, so this is 0.16 of 31.

0.16*31 = 4.96, rounding to the nearest whole number, 5.

You should expect 5 days in July with daily rainfall of more than 11.5 mm.

Step-by-step explanation:

Given:

[tex]A=1.5\:\text{cm}^2×\left(\frac{1\:\text{m}^2}{10^4\:\text{cm}^2}\right)=1.5×10^{-4}\:\text{m}^2[/tex]

[tex]d = 2.0\:\text{mm} = 2.0×10^{-3}\:\text{mm}[/tex]

The charge stored in a capacitor is given by [tex]Q = CV.[/tex] In the case of a parallel-plate capacitor, its capacitance C is given by

[tex]C = \epsilon_0\dfrac{A}{d}[/tex]

where [tex]\epsilon_0[/tex] = permittivity of free space. The amount of charge stored in the capacitor is then

[tex]Q = \left(\epsilon_0\dfrac{A}{d}\right)V[/tex]

[tex]\:\:\:\:\:=\left[\dfrac{(8.85×10^{-12}\:\text{F/m})(1.5×10^{-4}\:\text{m}^2)}{(2.0×10^{-3}\:\text{m})}\right](12\:\text{V})[/tex]

[tex]\:\:\:\:\:=8.0×10^{-12}\:\text{C}[/tex]

Answer:

24cm

Step-by-step explanation:

Question: Find the length of side OR.

Answer + explanation:

24cm

Since PQ = 24 cm, OR = 24 cm because they're paralleled and congruent!

Answer:

<O = 125

OR = 24

Step-by-step explanation:

consecutive angles are supplementary in a parallelogram

<R + <O = 180

55 + <O =180

<O = 180-55

< O = 125

opposite sides are congruent in a parallelogram

PQ = OR = 24

Answer:

A

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )

44 × tan12° = AC , then

AC ≈ 9.35 ( to 2 dec. places )

Answer:

Mean = Sum of all numbers divided by the amount of numbers

[tex]Mean/Average=\frac{3+1+1.5+1.25+2.25+4+1+2}{8} =\frac{16}{8} =2[/tex]

Median = the middle number when the ordered from least to greatest.

If there are two middle numbers, find the mean/average of those numbers:

[tex]\frac{1.5+2}{2} =\frac{3.5}{2} =1.75[/tex]

Therefore, the answer would be:

Answer:

A. 37.39 B. 37.41 C. 37.27

Answer:

x = -5

Step-by-step explanation:

4-2(x+7) = 3(x+5)

Distribute

4 - 2x-14 = 3x+15

Combine like terms

-2x-10 = 3x+15

Add 2x to each side

-2x-10 +2x =3x+2x+15

-10 = 5x+15

Subtract 15 from each side

-10-15 = 5x+15-15

-25 = 5x

Divide by 5

-25/5 = 5x/5

-5 =x

Answer:

2√15

Step-by-step explanation:

Use the Pythagorean theorem.

2² + x² = 8²

x² + 4 = 64

x² = 60

x² = 4 * 15

x = 2√15

Answer:

340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.

Step-by-step explanation:

Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:

480 x 20 = 9600

400 x 28 = 11200

350 x 33 = 11550

300 x 38 = 11400

310 x 37 = 11470

320 x 36 = 11520

330 x 35 = 11550

340 x 34 = 11560

Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.

Answer:

300

Step-by-step explanation:

A significant figure is the most important (largest) number you can round it to.

As it wants 1 significant figure, you count 1 to the left and round the 4 down.

Hope this helps :)

Let it be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{14}{7}[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{10}=2[/tex]

[tex]\\ \sf\longmapsto x=10(2)[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

The angles are 45 and 135

Step-by-step explanation:

The two angles form a straight line, which is 180 degrees

c+ 3c = 180

4c = 180

Divide by 4

4c/4 =180/4

c = 45

3c = 3(45) = 135

The angles are 45 and 135

Answer:

45 and 135 ...

Answer:

There are four ways to represent an inequality: Equation notation, set notation, interval notation, and solution graph.

Answer:

Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the submarine is located at the point (0, 0)

And the radar range has the equation:

2*x^2 + 2*y^2 = 128

You can see that this seems like a circle equation.

If we divide both sides by 2, we get:

x^2 + y^2 = 128/2

x^2 + y^2 = 64 = 8^2

This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.

The graph can be seen below, this is just a circle of radius 8.

We also want to see if the submarine's radar can detect a ship located in the point (6, 6)

In the graph, this point is graphed, and you can see that it is outside the circle.

This means that it is outside the range of the radar, thus the radar can not detect the ship.

Answer:

Hence the answer is TRUE.

Step-by-step explanation:

If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.  

Mathematically,  

P(A) + P(B) = 1.