Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.

Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.

The range would be all real numbers such that 0 ≤ y ≤ 40.

The complete question is

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40\

A function is an algebraic expression which relates an independent variable with a dependent variable.

It always comes with a defined range and domain.

Draining rate is at 1.5 gallons per minute

That would be y = 1.5x +c

at x = 0 , y = 40

Therefore the equation is y = 1.5x + 40

and from the data

It can be interpreted that as the time increases the water is draining

The range would be all real numbers such that 0 ≤ y ≤ 40.

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C would be the correct answer, I just did the test and got the answer correct.

Answer: 75

Step-by-step explanation:

For the lines to be parallel, this means the given angles have to be congruent (because then the lines will be parallel by the converse of the corresponding angles theorem)

Step-by-step explanation:

there must be no confusion just put x= 0 u get y=0.5 which is true according to graph and also put x=2 you get y = 1.5 which is again satisfy by the graph so it is 1/2x+0.5

Answer:

y = 1/2 x + 1/2

Step-by-step explanation:

I think your answer is not wrong but if the math program won't accept it, check these two things:

Make sure the x is beside the 1/2 and is not interpreting it as the x on the bottom with the 2 which is wrong.

Also, usually we don't put a mix of decimals and fractions. So change that .5 to a 1/2. I know what you have is equivalent, but just the norms dictate how to write it. Maybe it is just some tiny detail as these two details. Please don't be confused, you aren't wrong.

The Z- score representing the 99th percentile is given by 2.33

Problems of commonly distributed samples can be solved using the z-score formula.

For a set with a standard deviation, the z-score scale X is provided by:

Z = ( x- mean )/ standard deviation

Z-score measures how many standard deviations are derived from the description. 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 scale is less than X, that is, the X percentage. Subtract 1 with p-value, we get the chance that the average value is greater than X.

To Find the z-result corresponding to P99, 99 percent of the normal distribution curve.

This is the Z value where X has a p-value of 0.99. This is between 2.32 and 2.33, so the answer is Z = 2.33

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Answer:  31.792.5 cu. ft.   (choice B)

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

Work Shown:

[tex]V = \pi*r^2*h\\\\V \approx 3.14*15^2*45\\\\V \approx 31,792.5 \text{ cubic feet}\\\\[/tex]

The result is approximate since [tex]\pi \approx 3.14[/tex] is approximate.

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

Radius (r) = 15 feet

Height (h) = 45 feet

Volume = ?

Taking π ≈ 3.14..

V = 3.14 × 15² × 45

V = 31,792.5 cu. feet

So, the cylindrical tank can hold upto 31,792.5 cu. feet of water..

Answer:

180 cm squared

Step-by-step explanation:

Area Of A Rectangle is Length times Width, so 20 times 9, which equals 180.

The expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

The most fundamental of curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. From a geometric perspective, it may be compared to a prism with a circle as its basis.

Given the volume of a cylinder is given by the formula V = 3.14r^2h, where r is the radius of the cylinder and h is the height and suppose a cylindrical cane has radius (x+8) and height (2x+3)

We have to find expression which represents the volume of the cane

So as per given,

r = x+8

h = 2x + 3

v = πr²h

v = π(x+8)²(2x+3)

v = π(x²+64+16x)(2x+3)

v = π(2x³+128x+32x²+3x²+192+48x)

v = π(2x³+35x²+176x+192)

v = π2x³+π35x²+π176x+π192

Hence the expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

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Answer:

-26

Step-by-step explanation:

Multiply -4 by 7

1-20-7

Subtract 20 from 1

-19-7

Subtract 7 from -19

-26

Answer:

A. negative

Step-by-step explanation:

It is clear from the accompanying graph that the value of y decreases as the value of x grows. The line has a negative slope, and the right answer is C, as shown by the inverse connection between the values of x and y.

Reasoning for other incorrect options:

Answer:

C

Step-by-step explanation:

The slope of a horizontal line, such as that of y= 3, is equal to 0.

This can be proved using the slope formula.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Let's choose 2 points on the line y= 3:

(0, 3) and (2, 3)

Slope

[tex] = \frac{3 - 3}{2 - 0} [/tex]

[tex] = \frac{0}{2} [/tex]

= 0

Thus, the line has a slope of zero.

On the other hand, vertical lines have an undefined slope.

Additional:

To learn more about horizontal lines and their slopes, do check out the following!

Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.

The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.

Frequency tells the number of waves that  pass a fixed location in a specific time frame.

Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.

Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.

Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.

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Answer:

16 : 19

Step-by-step explanation:

Given weights of the two castings : 32 lbs and 38 lbs respectively.

Now,

Ratio of the weights of the two castings ;

= 32 : 38

= 16 : 19

32:38

16:19

Answer:

this is my answer

Answer:

x is approximately 20.89

Step-by-step explanation:

cos(40°) = 16/x

x cos(40°) = 16

x = 16 / cos(40°) = 16/.766 = 20.89

The approximate value of x in the diagram is,

⇒ x = 20.77

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We can formulate by the given figure;

⇒ sin 50° = 16 / x

⇒ 0.77 = 16 / x

⇒ x = 16 / 0.77

⇒ x = 20.77

Thus, The approximate value of x in the diagram is,

⇒ x = 20.77

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Answer:

The condantrnirte will be 3x if x is 0 (underfined)

Step-by-step explanation:

Answer:

domain is all reals

Step-by-step explanation:

sorry I couldn't find the range

Answer:

D

Step-by-step explanation:

Passes through the x-axis at r and k

Answer:

CI = (71.41%, 78.99%)

Step-by-step explanation:

[tex] \frac{376}{500} - 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500} )}{500} } = 71.415\%[/tex]

[tex] \frac{376}{500} + 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500}) }{500} } = 78.985\%[/tex]

If 500 high school students, 376 said they would prefer to have computers in every classroom then the confidence interval at 95% is (71.41%,78.99%)  Since option (a) is correct.

Given x= 376, n = 500

The (71.41%,78.99%)  

[tex]\hat{p}=\frac{x}{n}\\ =\frac{376}{500} \\=0.752[/tex]

Critical values

Using the z-table the z-critical value at the given significance level at α=0.05 is,[tex]z_{a/2} =1.96[/tex]

Construct a 95% confidence interval

That is,

[tex]\hat{p}= z_{a/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]

  [tex]=0.752\pm 1.96\sqrt{\frac{0.752(1-0.752)}{500} }[/tex]

  [tex]=0.752\pm 0.0379[/tex]

  = (71.41%,78.99%)  

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Answer:

449 units

Step-by-step explanation:

Perimeter of a rectangle = 2(a+b)

= 2(223+3/2)

=449 units

The correct option will be Option D:      [tex]P_{10} =30000(1+0.079)^{10[/tex]

The compounds interest can be estimated by using the following formula

[tex]A =P(1+r/n)^{nt[/tex]

where

A: the final amount

P: the initial investment

r: the interest rate (in decimal)

n: the number of times the interest will be compounded per year

t: the time (in year)

Given in the problem that

the initial investment is $30,000 and the time period is 10 years,

so P=30000 and

t=10  

As we know The interest will be compounded one time per year

n=1.

now for converting the interest rate into decimal form, we will divide the rate of interest by 100.

r=7.9/100

⇒r=0.079

putting above values in the above formula

[tex]A =P(1+r/n)^{nt[/tex]

⇒ [tex]A =30000(1+0.079/1)^{(1)(10)[/tex]

⇒  [tex]A =30000(1+0.079)^{10[/tex]

⇒[tex]P_{10} =30000(1+0.079)^{10[/tex]

Therefore correct option is Option D:  [tex]P_{10} =30000(1+0.079)^{10[/tex]

By completing the above equation to find the total amount

[tex]P_{10} =30000(1+0.079)^{10[/tex]

⇒[tex]P_{10} =30000(1.079)^{10[/tex]

⇒[tex]P_{10} =64170.54[/tex]

Yolanda will have to pay $64,170.54 in her account after ten years.

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Answer:

3x+4=79

Step-by-step explanation:

3x+4=79

3x=79-4

3x=75

Divide both sides by three

3x/3 = 75/3

x=25

Therefore the original number is 25.

Hope it helps.✨✨

The total price of the truck =$x + $ 0.13x

We have given that,

Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax.

We have to determine the expressions that could represent how much Camacho pays in total for the truck.

We will consider the price of the truck to be $x

And the amount of tax in the percentage would be 13%

13/100 = $ 0.13x (this is the actual amount of the tax)

Now we will calculate the total price of the truck =$x + $ 0.13x

= $ x(1 + 0.13)

If there is any confusion please leave a comment below.

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Answer:

Z = sin(xy)

[tex]\frac{1}{y} \times \frac{\partial Z}{\partial x} =\cos \left( xy\right) =\frac{1}{x} \times \frac{\partial Z}{\partial y}[/tex]

Option B is correct, the function f(x) = -7x² - x + 2  represents a quadratic function

A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to zero.

f(x) = -7x² - x + 2 is a quadratic function because it is of the required form.

Specifically, it has a quadratic term (-7x²), a linear term (-x), and a constant term (2).

The other three functions do not have a quadratic term and thus are not quadratic functions.

f(x) = 2x³ + 2x² - 4 is a cubic function because it has a cubic term (2x³).

f(x) = -3x + 2 is a linear function because it has only a linear term (-3x) and a constant term (2).

f(x) = 0x² + 3x - 3 is also a linear function because it has no quadratic term and only a linear term (3x) and a constant term (-3).

Hence, the function f(x) = -7x² - x + 2  represents a quadratic function

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The required probabilities are as follows:

a) P(X=5) = 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

Using a binomial random variable, the following is modeled:

There are always ten (10) persons that are being questioned.

From trial to trial, the likelihood of success (i.e., very little faith in newspapers) remains consistent (p=0.68).

The trials are impartial (a reasonable assumption, since the response of 1 of the people should not affect the response of any other)

There are just two possible results for each trial: low faith in newspapers or not.

X counts how many of the 10 trials were successful.

P(X=k) = is the probability mass function for the binomial random variable.

= [tex]^nC_k\times(p^k)\times(1-p)^{n-k}[/tex]

a) P(X=5) =[tex]^{10}C_5\times(0.68)^5\times(0.32)^5[/tex]≈ 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

These may all be calculated individually, then summed together.

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

the same concept as in (b) above.

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In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.

When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.

If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.

When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.

If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.

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Answer:

37.5

Step-by-step explanation:

37.5×144/100=54 the number is 37.5

Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.

We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).

Total miles driven is 10+50=60.

As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons

A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.

As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use

50/40=1.25 gallons;

So average miles per gallon equals to

[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]

Therefore option D is correct.

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Answer:

Option B :39 degrees is the correct.

The nearest degree is 39°

Step-by-step explanation:

Laws of cosines relates each side with its opposite angle.

Formula for this is :

[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]

[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]

[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]

in figure a=28

              b=18

              c=25

Here we have to find angle between a and c that is B

So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]

324 = 625 + 784 - 1400cosB

1400cosB =  625 + 784 - 324

1400cosB = 1085

cosB = 0.775

∠B = 39.195° ≈ 39°

The boat change 39°  when it made its first turn.

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Answer:

B 39 degrees

Step-by-step explanation:

The person above me is correct and I got proof for the people with trust issues. :  )

The total number of 512 portions will be made the recipe that contains 5 fluid ounces each.

The soup recipe gives 20 gallons.

As we know one gallon produces 128 fluid ounces.

There are 20 gallons produced.

So the number of fluid ounces produced will be 20*128= 2560

Given in the question each portion contains 5 fluid ounces.

Then there is a total of 2560 numbers of fluid ounces.

So the number of portions will be = number of fluid ounces/ number of fluid ounces in each portion=  2560/5= 512

Therefore the total number of 512 portions will be made the recipe that contains 5 fluid ounces each.

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y=[tex]\frac{1}{2}[/tex]x+0.5

Hope it helps!