Solving a Real-World Inequality
Samuel is running a 3-mile race. He would like to finish the race in under 33 minutes. He has already run for 10.5
minutes. The inequality 10.5 +X< 33 represents the situation.
Solve the inequality. How is the solution interpreted in the context of the problem?
O x< 22.5; Sam hasa maximum of 22.5 minutes left to finish running.
Ox<22.5; Sam has fewer than 22.5 minutes left to finish running.
O x>43.5; Sam has at least 43.5 minutes left to finish running.
O x<43.5; Sam has no more than 43.5 minutes left to finish running.​

Answer:

these are my answers:

8-5=3

2÷6=3

5-2=3

2+1=3

3÷9=3

Answer:

  9 +6 +1 -8 -5 = 3

Step-by-step explanation:

There are numerous possibilities. Among them are ...

  9 +6 +1 -8 -5 = 3

  (9-5)·1·6/8 = 3

  (9·8)/(6·(5-1)) = 3

Answer:

Step-by-step explanation:

Hello!

This is an example of an ANOVA hypothesis test, where you'll compare the population means of the number of broken Mimbres in three different excavation sites.

The variable of interest is

Y: Number of broken pieces of prehistoric Native American clay vessels, called Mimbres in an excavation site.

Factor: Site

Treatments: 1, 2, 3

You are asked to identify the level of significance of the test. This value is the probability of committing Type I error, that is, when you fail to reject a false null hypothesis and is always represented with the Greek letter alpha "α"

This level is determined by the researcher when he is designing the experiment and statistical analysis. Normally you'd want this level to be as small as possible to be sure you didn't commit any mistake when deciding over the hypotheses.

The mos common values are 0.01, 0.05 or 0.1 and it can also be expressed as percentages 1%, 5% or 10%. Having a probability of making a mistake greater than 10% is too high so normally you would not encounter significance levels greater than 10%

With this in mind options b. 1% and c. 5% are valid values for α.

Have a nice day!

Next time check that all the information is copied!

Answer:

A

Step-by-step explanation:

First, find the y-intercept by seeing where the line goes through the y-axis

This is at (0, -2) so the y-intercept is -2.

Then, use rise over run to find the slope.

The slope is -3

Answer:

A. Slope -3, y- intercept -2

Step-by-step explanation:

Well the line passes through the point (0,-2) and from there if you draw a line 1 to the left (run) and then up 3(rise) you connect with the line, so the slope is -3(rise over run)

Hope this helps,

plx give brainliest

Answer:

[tex]V=\frac{1}{3}(2.5)(6)=5 \ in^{3}[/tex]

The volume of the pyramid is 5 cubic inches.

Step-by-step explanation:

Assuming that the triangle base dimensions are 1 inche and 5 inches, and the height of the pyramid is 6 inches, the volume would be

[tex]V=\frac{1}{3}Bh[/tex]

Where B is the area of the base (triangle) and h is the height.

[tex]B=\frac{1}{2}bh =\frac{1}{2}(1)(5)=2.5 \ in^{2}[/tex]

Then,

[tex]V=\frac{1}{3}(2.5)(6)=5 \ in^{3}[/tex]

Here is the right and correct question:

The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2,

[tex]y_2 = y_1 (x) \int\limits \dfrac{e ^{-\int\limits P(x) dx} }{y^2_1 (x)} dx \ \ \ \ \ (5)[/tex]

as instructed, to find a second solution [tex]y_2(x)[/tex]

[tex](1-2x-x^2)y''+2(1+x)y' -2y =0; \ \ \ y_1=x+1[/tex]

Answer:

[tex]y_2 = -2-x^2-x[/tex]

Step-by-step explanation:

Let take a look at the differential equation:

[tex](1-2x-x^2)y''+2(1+x)y' -2y =0[/tex]

So; [tex]y''+ \dfrac{2(1+x)}{(1-2x-x^2)}y' - \dfrac{2}{(1-2x-x^2)}y =0[/tex]

where;

[tex]P(x) = \dfrac{2(1+x)}{(1-2x-x^2)}[/tex]     ;

Also:

[tex]Q(x) = \dfrac{-2}{(1-2x-x^2)}[/tex]

The task is to find the value of [tex]y_2(x)[/tex] by using the reduction formula [tex]y_2 = y_1 (x) \int\limits \dfrac{e^{-\int\limits P(x) dx }}{y_1^2(x)}dx[/tex]  such that [tex]y_1(x) =x+1[/tex]

simplifying [tex]y_2 = y_1 (x) \int\limits \dfrac{e^{-\int\limits P(x) dx }}{y_1^2(x)}dx[/tex] ;we have:

[tex]y_2 =(x+1) \int\limits \dfrac{e ^{-\int\limits \frac{2(1+x)}{(1-2x-x^2)}}}{(x+1)^2} \ \ dx[/tex]

[tex]y_2 =(x+1) \int\limits \dfrac{e ^{\int\limits \frac{-2(1+x)}{(1-2x-x^2)}}}{(x+1)^2} \ \ dx[/tex]

[tex]y_2 =(x+1) \int\limits \dfrac{e^{In(1-2x-x^2)}}{(x+1)^2}\ \ dx[/tex]

[tex]y_2 =(x+1) \int\limits \dfrac{(1-2x-x^2)}{(x+1)^2} \ \ dx[/tex]

[tex]y_2 =(x+1) \int\limits \dfrac{1}{(x+1)^2}-\dfrac{2x}{(x+1)^2}- \dfrac{x^2}{(x+1)^2} \ \ dx[/tex]

Let assume that [tex]I_1[/tex] = [tex]\int\limits \dfrac{-2x}{(x+1)^2} \ \ dx[/tex]

[tex]= \int\limits \dfrac{-(2x+2-2) }{(x+1)^2} \ \ dx[/tex]

[tex]= \int\limits \dfrac{-(2x+2) }{(x+1)^2} + \dfrac{2}{(x+1)^2} \ \ dx[/tex]

[tex]=- In(x+1)^2 - \dfrac{2}{(x+1)}[/tex]

Also : Let [tex]I_2 = \int\limits \dfrac{x^2}{(x+1)^2} \ \ dx[/tex]

[tex]= \int\limits \dfrac{(x+1-1)^2}{(x+1)^2} \ \ dx[/tex]

[tex]= \int\limits \dfrac{(x+1)^2+1-2(x+1)}{(x+1)^2} \ \ dx[/tex]

[tex]= \int\limits \ 1 + \dfrac{1}{(x+1)^2}- \dfrac{2}{(x+1)} \ \ dx[/tex]

[tex]= x - \dfrac{1}{(x+1)}- 2 \ In (x+1)[/tex]

Replacing the value of [tex]I_1[/tex] and [tex]I_2[/tex] in the  equation

[tex]y_2 =(x+1) \int\limits \dfrac{1}{(x+1)^2}-\dfrac{2x}{(x+1)^2}- \dfrac{x^2}{(x+1)^2} \ \ dx[/tex]

[tex]y_2 =(x+1) [ \ \int\limits \dfrac{-1}{(x+1)}+ (-In(x+1)^2-\dfrac{2}{(x+1)})-(x-\dfrac{1}{(x+1)}-2 In(x+1))][/tex]

[tex]y_2 =(x+1) [ \ \int\limits \dfrac{-1}{(x+1)}- In(x+1)^2-\dfrac{2}{(x+1)}-x+\dfrac{1}{(x+1)}+2 In(x+1))][/tex]

[tex]y_2 =(x+1) [ \ \int\limits \dfrac{-1}{(x+1)}- 2In(x+1) -\dfrac{2}{(x+1)}-x + \dfrac{1}{(x+1)} +2 In(x+1)][/tex]

[tex]y_2 = -2-x(x+1)[/tex]

Therefore;

[tex]y_2 = -2-x^2-x[/tex]

Answer:

d) Z= -1.49

Step-by-step explanation:

sample #1   ----->              

first sample size,[tex]n_1= 85[/tex]

number of successes, sample 1 =   [tex]x_1= 17[/tex]

proportion success of sample 1 ,

[tex]\bar p_1= \frac{x_1}{n_1} = 0.2000000[/tex]                  

sample #2   ----->              

second sample size,

[tex]n_2 = 80[/tex]

number of successes, sample 2 = [tex]x_2 = 24[/tex]

proportion success of sample 1 ,

[tex]\bar p_2= \frac{x_2}{n_2} = 0.300000[/tex]            

difference in sample proportions,

[tex]\bar p_1 - \bar p_2 = 0.2000 - 0.3000 \\\\= -0.1000[/tex]

pooled proportion ,

[tex]p = \frac{ (x_1+x_2)}{(n_1+n_2)}\\\\= 0.2484848[/tex]

std error ,

   [tex]SE=\sqrt{p*(1-p)*(\frac{1}{n_1}+\frac{1}{n_2} )} \\\\=0.06731[/tex]

Z-statistic = [tex](\bar p_1 - \bar p_2)/SE = ( -0.100 / 0.0673 ) = -1.49[/tex]

how to read pathater in himdi

Answer:

The expression [tex]9.8x+11.3y+9.9z[/tex] represents the perimeter, in centimeters of the obtuse triangle.

Step-by-step explanation:

An obtuse triangle is a triangle where one of the internal angles is obtuse (greater than 90 degrees).

The perimeter of a triangle is the total distance around the outside of a triangle, which can be found by adding together the length of each side. Or as a formula:

                                                    [tex]P=a+b+c[/tex]

where:

a, b and c are the lengths of each side of the triangle.

We know that the triangle has side lengths of [tex]a = 5.5x + 6.2y[/tex], [tex]b= 4.3x + 8.3z[/tex] and [tex]c=1.6z + 5.1y[/tex] centimeters. Therefore, the perimeter is

[tex]P=a+b+c\\P=(5.5x + 6.2y)+(4.3x + 8.3z)+(1.6z + 5.1y)\\\\\mathrm{Group\:like\:terms}\\P=5.5x+4.3x+6.2y+5.1y+8.3z+1.6z\\\\\mathrm{Add\:similar\:elements:}\\P=9.8x+11.3y+9.9z[/tex]

Answer:

x^2 -2x = 4x+1

2x^2 +12x = 0

9x^2 +6x -3=0

Step-by-step explanation:

A quadratic equation has the highest power of x being squared

x^2 -2x = 4x+1

2x^2 +12x = 0

9x^2 +6x -3=0

These are all quadratic equations

Answer:

Gabriel has the highest proportion of wins, so he should start.

Step-by-step explanation:

He should start the quarterbacks with the highest proportion of wins.

The proportion of wins is the number of games won divided by the number of games played(wins + losses).

We have that:

Germaine has 8 wins in 8+5 = 13 games. So his proportion of wins is 8/13 = 0.6154.

Gabriel has 7 wins in 7+4 = 11 games. 7/11 = 0.6364

Gabriel has the highest proportion of wins, so he should start.

Answer:

Hypotenuse = 6

Step-by-step explanation:

Find attached diagram used in solving the question.

The triangle is a 45°-45°-90° triangle meaning it's two legs are equal. The opposite = adjacent

Since we are told to find hypotenuse, it means the length given = opposite = adjacent = 3√2

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse ² = (3√2)² + (3√2)²

Hypotenuse ² = 9(2)+9(2) = 18+18

Hypotenuse ² = 36

Hypotenuse = √36

Hypotenuse = 6

Answer:

  see below

Step-by-step explanation:

Multiply each of the coordinates by the dilation factor:

  A' = (1/2)A = 1/2(6, 4) = (3, 2)

Point A gets transformed to point A'(3, 2), matching choice B.

Answer:

John is traveling 5 mph

Trey is traveling 12 mph

Step-by-step explanation:

we will concept of speed distance and time where

distance = speed * time

Let the speed of john be x miles per hour

if, Trey travels 7 mph faster than John

then speed of trey = (x+7) miles per hour

Time of travel for both of them  = 5 hours

distance traveled by john in 5 hours =  x* 5 = 5x miles

distance traveled by john in 5 hours =  (x+7) * 5 = (5x + 35)miles

total distance covered by them = 5x miles + (5x + 35)miles = (10x+35) miles

it is given that after 5 hours they were 85 miles apart, thus the distance above calculated should be equal to 85 miles

10x+35 = 85

=>10x = 85 -35

=> 10x = 50

=> x = 50/10

=> x = 5

Thus, speed of john is 5 miles per hour

speed of Trey is: x+7= 5 + 7 = 12  miles per hour

Answer:

The expected value of the proposition is -$12.74.

Step-by-step explanation:

Expected value:

It is the multiplication of each outcome by it's probability.

For each free throw, there are only two possible outcomes. Either the player makes, or he does not. Each free throw is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 184 out of 329 free throws.

This means that [tex]p = \frac{184}{329} = 0.5593[/tex]

2 free throws:

This means that [tex]n = 2[/tex]

Probability of making two free throws.

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.5593)^{2}.(0.4407)^{0} = 0.3128[/tex]

Expected value:

If he makes both free throws, you earn $12. So 0.3128 probability of you earning $12.

Otherwise, you have to pay $24. 1 - 0.3128 = 0.6872 probability of you losing $24.

So

E = 0.3128*12 - 0.6872*24 = -12.74

The expected value of the proposition is -$12.74.

Answer:

-.74

Step-by-step explanation:

I just did the homework and this is the correct answer

Answer:

(a) t = 7 sec approximately; (b) t = 6 sec

Step-by-step explanation:

(a)  Set h(t)= -16(t-3)^2 + 288 = 0 and solve for t:

                     16(t-3)^2 = 288  

       After simplification, this becomes (t - 3)^2 = 18, or t - 3 = ±3√2.

        Because t can be only zero or positive, t = 3 + 3√2 = 7 seconds

(b) Solve h(t)= -16(t-3)^2 + 288 = 150:

                        -16(t-3)^2 = - 162

      or                (t - 3)^2 = 10.125, or

                            t - 3 =  ±3.18, or, finally, t = 6.18 sec (discard t = -0.18 sec)

Answer:I believe the answer is -1,-4 lies on the graph

Step-by-step explanation:

Answer:

  TP = 13

Step-by-step explanation:

The height of the trapezoid can be found from the area formula:

  A = (1/2)(b1 +b2)h

  h = 2A/(b1 +b2) = 2(100)/(32 +8)

  h = 5

The horizontal length of each triangular end of the trapezoid is ...

  (32 -8)/2 = 24/2 = 12

so the hypotenuse of the triangular end of the trapezoid is ...

  TP = √(12^2 +5^2) = √169

  TP = 13

The sides of the trapezoid have length 13 units.

Answer:

y= 3x+16

Step-by-step explanation:

y = 3x + 8 ║ y= mx +b

Since lines are parallel, m=3

y= 3x+b

(-3, 7) intersect

y= 3x+16

Answer:

= 5x-5y

Step-by-step explanation:

Multiply 5to x and y

Answer:

5x-5y

Step-by-step explanation:

multiply both the terms x and y by 5.

Answer: its A and D

Step-by-step explanation:

Ape x

The trigonometric identities are (csc x = 1/sinx ) and ( tan x = sin x/cos x ). Hence, option A and option D are correct.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

The trigonometric identities are ( csc x = 1/sinx ) and  ( tan x = sin x/cos x ). The other two options are incorrect. The correct values for the other two options are tan x = 1/cot x and sec x = 1/cos x.

Hence, option A and option D are correct.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ2

Answer:

241 minutes

Step-by-step explanation:

Given:

Height of cylinder, h = 15 ft

Radius, r = [tex] \frac{d}{2} = \frac{12}{2} = 6 [/tex] (both cylinder and cone have same radius)

Let's find the height of cone, since angle of inclination = 25°C.

[tex] tan25 = \frac{h}{r} [/tex]

[tex] h = r tan25 [/tex]

[tex] h = 6 tan25 = 2.8 [/tex]

Height of cone = 2.8 ft

Let's find colume of tower.

Volume = Volume of cone + volume of cylinder.

Formula for volume of cone = ⅓πr²h

Volume of cylinder = πr²h

Therefore,

V = ⅓πr²h + πr²h

V = ⅓π*6²*2.8 + π*6²*15

V = 105.558 + 1696.46

V = 1802.02 ft³

Since volume is 1802.02 ft³, and there are 7.48 gallons in a cubic ft, the total gallon =

1802.02 * 7.48 = 13479.11 gallons

Water is used at an average rate of 56 gallons per minute.

Amount if time to drain the water:

Total gallons / average rate

[tex] = \frac{13479.11}{56} = 240.698 [/tex]

≈ 241 minutes

Answer:

t = -1 or 5/2

Step-by-step explanation:

To find t; we equate H(t) = 0

-16t^2+24t+40.0= 0

dividing through by 8 we have ;

-16t^2 / 8+ 24t/8+40.0/8=0

-2t^2 + 3t + 5=0

-2t^2 + 5t -2t + 5=0

By factorisation;

t(-2t + 5) +1 (-2t + 5)=0

This means;

(t + 1)(-2t +5)= 0

t + 1 = 0 or -2t + 5 = 0;

t= -1 ; -2t = -5

2t = 5

t = 5/2;

Hence t = -1 or 5/2

Answer:

Step-by-step explanation:

Given the expression 18x²-8, the best method to factor this expression are Factor by grouping and by factoring out the greatest common factor.

Step 1: Factor by grouping

Factor by grouping is done by creating a smaller groups from each term in the expression as shown;

18x² = (2*3*3* x²)

8 =  2*2*2

18x²-8 = (2*3*3* x²) - (2*2*2)

Step 2: Then we will factor out the greatest common factor (GCF) in the expression. GCF is the value that is common to both terms of the expression. The only common term in this case is 2.

Answer:

Factor out the GCF, and Use the difference of squares rule.

Step-by-step explanation:

The terms in the expression have a common factor of 2, so the first step is to factor out the GCF:

2(9x2 − 4).

Then, factor the remaining expression using the difference of squares rule.

75g/400ml: Simplify per unit

÷ by bottom.

0.1875g/ml nearest hundredth

0.19g/ml

Answer:

V = 615.44 mm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2h

The diameter is 14 so the radius is 14/2 = 7

V = 3.14 ( 7)^2 4

V = 615.44 mm^3

Answer:

Answer:

V = 615.44 mm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2h

The diameter is 14 so the radius is 14/2 = 7

V = 3.14 ( 7)^2 4

V = 615.44 mm^3

Step-by-step explanation:

Answer:

{ 11 , 19 , 41 , 61 , 89 } is only the two digits number having both their non-prime.

Step-by-step explanation:

Answer:

If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).

Step-by-step explanation:

We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.

The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:

[tex]a^2+b^2=h^2[/tex]

Then, we can express one side in function of the other as:

[tex]a^2+b^2=h^2\\\\a^2=h^2-b^2\\\\a=\sqrt{h^2-b^2}=\sqrt{7.21-b^2}=\sqrt{52-b^2}[/tex]

Then, if we define b, we get the value of a that satisfies the equation.

A graph of values of a and b is attached.

If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).