It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus. Every​ week, she must make at least 8 trips to the​ place, and she plans to spend no more than 9 hr in travel time. If a train trip costs ​$6 and a bus trip costs ​$5​, how many times per week should she ride each in order to minimize her​ cost?
She should ride the train for ___ trips and the bus for ___ trips in order to minimize her cost.

Answer:

-x^4, and (2√x)/x

Step-by-step explanation:

4. [tex]- \sqrt{ x^{8} } = - \sqrt{x^{4} *x^{4} } = -x^{4}[/tex]

x^8 = x*x*x*x*x*x*x*x = (x*x*x*x)(x*x*x*x) = (x^4)(x^4)

5.

[tex]\sqrt{\frac{4}{x} } = \frac{\sqrt{4} }{\sqrt{x} } = \frac{2}{\sqrt{x} } \\\\\\\frac{2}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } = \frac{2\sqrt{x} }{x}[/tex]

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

[tex]\angle A+40+100=180[/tex]

[tex]\angle A+140=180[/tex]

[tex]\angle A=180-140[/tex]

[tex]\angle A=40[/tex] degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

[tex]\implies BC=AC [/tex]

Now, Sine law

[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Using the sine law

[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]

[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]

[tex]BC=\frac{8\times sin40}{sin 100}[/tex]

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

(a) The area of the region would be given by the integral

[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]

(b) The area of the surface of revolution would be given by

[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]

Answer:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Step-by-step explanation:

We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]

We make the denominators of both fractions same. So,

[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]

and

[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]

The rational number are:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Answer:

n=-9,-8,-7

Step-by-step explanation:

n<100

but that is the positive square root

\(-10 n is between the negative and positive square root of 100

thus, n=-9,-8,-7

The solution of the inequality n² < 100 will be less than 10.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The inequality is given below.

n² < 100

Simplify the equation, then we have

n² < 100

n² < 10²

n < 10

The solution of the inequality n² < 100 will be less than 10.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]

Step-by-step explanation:

[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]

Answer:

-2, - 1, 0, 1, 2

Step-by-step explanation:

The greater than or equal to sign (≤) demonstrates that the unknown is equal to -2 and greater, but is less than 3, so the largest integer solution is 2, not 3

Answer:

62.5%

Step-by-step explanation:

Given that :

20 cup bowl of punch = 75% Juice

We can infer that :

The number of cups of JUICE is :

75% * 20 = 0.75 * 20 = 15 cups

Adding 4 cups of water to the 20 cups, we have = 24 cups

With 15 cups of JUICE ;

The percentage of the new punch that is juice will be x

x% of 24 cups = 15 cups

x/100 * 24 = 15

0.01x * 24 = 15

0.24x = 15

x = 15 / 0.24

x = 62.5

x = 62.5%

Answer:

It's C

62.5% btw

Step-by-step explanation:

Did the quiz lol

Answer: 113.01m - You are almost right

Step-by-step explanation:

Simply by using pir^2, you get the number you calculated, but it is asking for at least 2 decimal places. So it would be "113.01"

Answer:

y + 1 = 3(x+ 1)

Step-by-step explanation:

(2,3) , (0 ,-3)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]= \frac{-3-3}{0-2}\\\\=\frac{-6}{-2}\\\\= 3[/tex]

m = 3

Parallel lines have same slope.

m = 3; (-1 , -1)

y -y1 = m (x -x1)

y -[-1] = 3(x -[-1])

y + 1 = 3(x+ 1)

Answer:

D. y+1=3(x+1)

Answer:

a) 0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

b) 0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.

c) 0.1777 = 17.77% probability he or she is a registered Independent.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

57% of 46%(democrats)

38% of 42%(republicans)

76% of 12%(independents)

So

[tex]P = 0.57*0.46 + 0.38*0.42 + 0.76*0.12 = 0.513[/tex]

0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

Question b:

1 - 0.513 = 0.487

0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.

c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?

Event A: Supports the tax increase.

Event B: Is a independent.

0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

This means that [tex]P(A) = 0.513[/tex]

Probability it supports a tax increase and is a independent:

76% of 12%, so:

[tex]P(A \cap B) = 0.76*0.12[/tex]

Thus

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.76*0.12}{0.513} = 0.1777[/tex]

0.1777 = 17.77% probability he or she is a registered Independent.

Answer:

The answer is C

Step-by-step explanation:

The intersection of those figures results to a point

Answer:

=6

Step-by-step explanation:

(5×8)×(5-2)/(5×4)

Numerator =40×3

=120

Denominator = 5×4

=20

simplifying 120/20

=6

Answer:

6

follow the BDMAS rule

bracket ,division ,multiplication, addition and last subtraction

you won't get any maths problem wrong

The solution for set F(x) is -1

Step-by-step explanation:

THERE ARE TWO UNIQUE EQUATIONs

4x+3=2x+1

2x=-2

x=-1

(or)

4x+3= -(2x+1)

4x+3=-2x-1

6x=-4

x=-2/3

Answer:

Step-by-step explanation:

We will work in the y-dimension only here. What we need to remember is that acceleration in this dimension is -9.8 m/s/s and that when the projectile reaches its max height, it is here that the final velocity = 0. Another thing we have to remember is that an object reaches its max height exactly halfway through its travels. Putting all of that together, we will solve for t using the following equation.

[tex]v=v_0+at[/tex]

BUT we do not have the upwards velocity of the projectile, we only have the "blanket" velocity. Initial velocity is different in both the x and y dimension. We have formulas to find the initial velocity having been given the "blanket" (or generic) velocity and the angle of inclination. Since we are only working in the y dimension, the formula is

[tex]v_{0y}=V_0sin\theta[/tex] so solving for this initial velocity specific to the y dimension:

[tex]v_{0y}=35sin(35)[/tex] so

[tex]v_{0y}=[/tex] 2.0 × 10¹ m/s

NOW we can fill in our equation from above:

0 = 2.0 × 10¹ + (-9.8)t and

-2.0 × 10¹ = -9.8t so

t = 2.0 seconds

This is how long it takes for the projectile to reach its max height. It will then fall back down to the ground for a total time of 4.0 seconds.

Answer:

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

Step-by-step explanation:

Given

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2[/tex]

Required

Solve

Start with the bracket

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ (9.1)^2-(-1.4)^2[/tex]

Evaluate all exponents

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ 82.81-1.96[/tex]

Evaluate all products

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 2.4+ 82.81-1.96[/tex]

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

9514 1404 393

Answer:

  (c)  f(t)=21,000(0.85)^t

Step-by-step explanation:

Each year, the value is multiplied by 1-15% = 85% = 0.85. This is correctly shown in the function ...

  f(t)=21,000(0.85)^t

Answer:

5

Step-by-step explanation:

x² - 4x = 5

x² - 4x - 5 = 0

the solution of a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = -4

c = -5

x = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2

x1 = (4 + 6)/2 = 5

x2 = (4 - 6)/2 = -1

since we are looking only for a positive number, x=5 is the answer.

Answer:

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Step-by-step explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

[tex] {3}^{2} = 9[/tex]

8 is a multiple of 4, and 9 is more than 8.

[tex] {11}^{2} = 121[/tex]

120 is a multiple of 4 and 121 is one more than it.

[tex] {25}^{2} = 625[/tex]

624 is a multiple of 4 and 625 is one more than it.

[tex] {37}^{2} = 1369[/tex]

1368 is a multiple of 4 and 1369 is one more than 1368.

[tex] {131}^{2} = 17161[/tex]

17160 is a multiple of 4.

Answer:

it would be the last one.

Step-by-step explanation:

its looking for a right triangle, a right triangle has one 90 degree angle. all of the other triagles have acute angles making them smaller than 90 degrees

Triangle BGC is the right triangle, because BG is perpendicular to CC'.

The line passing through points E, F, and G in the image is now perpendicular to the lines is DF and CG.

So we know that our triangle will be made with some of these lines.

For example, the right triangles in the figure are:

BFD, BGC, B'FD', and B'GC'.

Then, the concluded statement is ΔBGC, because BG ⊥CC.

There says that "Triangle BGC is the Right because BG is perpendicular to CC.

Learn more about right triangle here:

brainly.com/question/2217700

#SPJ7

Answer:

C={n : n=i^2 where i belongs to Natural_numbers and 1 <= i <= 5}

Answer:

i put in 3 to make 23436 because 36 is divisible by 6

Answer:

0.6836

Step-by-step explanation:

(weight - mean weight) = 48

Variance, s² = 204,304

Sample size, n = 89

We need to obtain the Zscore :

Zscore = (X - mean) / standard Error

Zscore = (weight - mean weight ) / (s/√n)

s = √204304 = 452

The difference from the meanncoukdnbe either to the right or left :

Zscore = - 48 / (452/√89) OR 48 / (452/√89)

Zscore = - 48 / 47.911904 OR - 48 / 47.911904

Zscore = - 1.002 or 1.002

P(Z < - 1.002) = 0.1582 (using Z table)

P(Z < 1.002) = 0.8418

P(Z < 1.002) - P(Z < - 1.002)

0.8418 - 0.1582

= 0.6836

Answer:

function ar true in the mach on which

Answer:

i think three one is right answer...

Answer:

P( fraction) = 1/2

P ( percent) = 50%

P ( decimal) = .5

Step-by-step explanation:

The possible outcomes on  a six sided cube are 1,2,3,4,5,6

Multiples of 2 are  2,4,6

P( multiple of 2) = number of multiples of 2 / total outcomes

                           = 3/6 = 1/2

P( fraction) = 1/2

P ( percent) = 50%

P ( decimal) = .5

Answer:

[tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

F(x) = x² - 15

G(x) = 4 - x

Step 2: Find

Step 3: Evaluate

Answer:

3 x² y¹

Step-by-step explanation:

15 x²y³ = 3. 5. x². y³

-18x³yz = -2. 3². x³. y¹. z¹

so, the GCF = 3. x². y¹

Answer:

Solution given:

15x²y³=3*5*x*x*y*y*y

-18x³yz=-3*2*3*x*x*x*y*z

over here common is

3*x*x*y

so

greatest common factor is 3x²y¹

Answer:

last one

Step-by-step explanation:

x = width

x+6 = length

Area = length times width

x(x + 6) = [tex]x^{2}[/tex] + 6x

[tex]x^{2}[/tex] + 6x = 114   (subtract 114 from both sides)

[tex]x^{2}[/tex] + 6x -114 = 0