Wendy is taking a cab ride. The ride costs $1.20 for the first 0.5 km, and $0.90 for each additional 0.5 km. If the trip costs $12.00, how many kilometres was the cab ride?

Answer:

The probability the student studies Art and Biology is 0.2143.

Step-by-step explanation:

Denote the events as follows:

A = a students studies Art

B = a students studies Biology

The information provided is:

N = 42

n (A ∩ B) = 9

n (A' ∩ B) = 10

n (A' ∩ B') = 7

Then the number of students who study Art but not Biology is:

n (A ∩ B') = N - n (A ∩ B) - n (A' ∩ B) - n (A' ∩ B')

               [tex]=42-10-7-9\\\\=16[/tex]

The number of students who study Art but not Biology is 16.

Compute the probability the student studies Art and Biology as follows:

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

               [tex]=\frac{9}{42}\\\\=\frac{3}{14}\\\\=0.2143[/tex]

Thus, the probability the student studies Art and Biology is 0.2143.

Answer:

motorcycle A: 180 km/h

motorcycle B: 200 km/h

Step-by-step explanation:

To solve this question we need to write a system of equations for A and B, using the equation:

distance = speed * time

The speed of A is 20 less than the speed of B, so:

speedA = speedB - 20

And the time A traveled is 3 minutes (0.05 hours) more than B's time, so:

timeA = timeB + 0.05

Then, using the distance equation, we have that:

distanceB = speedB * timeB

90 = speedB * timeB

distanceA = speedA * timeA

90 = (speedB - 20) * (timeB + 0.05)

90 = speedB * timeB + 0.05 * speedB - 20*timeB - 1

90 = 90 + 0.05 * speedB - 20*timeB - 1

20*timeB = 0.05 * speedB - 1

timeB = (speedB - 20)/400

using this timeB in the distance equation, we have:

90 = speedB * (speedB - 20)/400

90 * 400 = speedB^2 - 20*speedB

speedB^2 - 20*speedB - 36000 = 0

Solving this quadratic equation, we have speedB = 200 km/h

And the speedA is:

speedA = speedB - 20 = 200 - 20 = 180 km/h

Answer:

50

Step-by-step explanation:

f(x) = 8x² - 14x - 10

f(-2) = 8(-2)² - 14(-2) -10

f(-2) 8*4 + 28 - 10

f(-2) = 32 + 28 - 10 = 50

14.  Each leg is   [tex]21\sqrt{2}[/tex]  units long.

15 (a). The longer leg is [tex]7\sqrt{3}[/tex]  units long

15 (b). The hypotenuse is [tex]14[/tex] units long

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

Explanations:

For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say

[tex]y = x\sqrt{2}[/tex] where x is the leg and y is the hypotenuse

Let's solve for x

[tex]y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\[/tex]

Now plug in the given hypotenuse y = 42, this leads to,

[tex]x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\[/tex]

---------------------------

For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.

The longer leg is equal to sqrt(3) times the short leg. The longer leg is [tex]7\sqrt{3}[/tex]

Answer:

(-2,0.5)

Step-by-step explanation:

1st set of Point=(-5,-2)

2nd set  of Point=(1,3)

Midpoint=(X1+X2/2 , Y1+Y2/2)

=(-5+1/2 , -2+3/2)

=(-2,0.5)

Answer:

10

Step-by-step explanation:

(8-5)2 + 4, let's start with the first step, the parentheses.

(8-5)=3 , then we multiply by 2, so (3)*2 which equals 6. 6+4=10!

Hope this helps! :)

Answer: the answer is 19

Step-by-step explanation:

i just got this question and got it right!

Answer:

30

Step-by-step explanation:

3*10 = 30

Answer:

30

Step-by-step explanation:

PEMDAS says you do (8+2) first, which equals 10, then you multiply 3 by 10, which equals 30.

Answer:

Adding 13 to both sides we get x = 8.

Answer:

x = 8

Step-by-step explanation:

x - 13 = -5

x = 8

Answer: Because all individuals in the sample have the same job, so the sample is biased.

Step-by-step explanation:

Ignoring the fact that 30 is a small sample for a large city, we already know that all the people in the sample has the same profession.

Now, we can expect that two dentists win have around the same income, but not all the residents in the city are dentists

A lot of them work in fast food, others may be lawyers, others may be freelancers.

We have a lot of jobs where the income does not coincide with the average income of a dentist, so with the sample of 30 dentists we are not actually representing all the other possible jobs that there are in the city.

If we want a sample that represents the income of all the residents, we should have a random sample (so the sample is not biased, like in this case).

Answer:

5/18

Step-by-step explanation:

5/9 times 1/2

5/18

I may be wrong sorry

Answer: It’s C i got it right on the test

Step-by-step explanation:

RC’ ,180 o r m

Answer:

It's C I got a 100 on the test

Step-by-step explanation:

A and B have to be wrong because there is no 90° rotation and D isn't right because it's backwards

Answer:

tan 41 = 0.87

sin 63 = 0.89

cos 14 = 0.97

Step-by-step explanation:

No explanation since the question states to use the ALEKS calculator so you just make sure the calculator is in degrees then simply press tan 41 etc.

Answer:

[tex]p = 43 \: \: \: degrees[/tex]

Answer A is correct

Step-by-step explanation:

[tex]90 + p = 133[/tex]

the sum of the exterior angles in a triangle is equal to the sum of opposite interior angles.

[tex]p = 133 - 90 \\ p =4 3 \: \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

x-3

Step-by-step explanation:

f(x) = 3x-2

g(x) = 2x + 1

(f-g)(x) = 3x-2 - (2x+1)

Distribute the minus sign

          =3x-2-2x-1

Combine like terms

        = 3x-2x-2-1

        =x-3

Answer:

4 years old

Step-by-step explanation:

Harry = H

Brother = B

Aunty = A

Dad = B

H = ½ B

B = A - 28

A = D + 5

D = 31

A = 31 + 5 = 36

B = 36 -28 = 8 years old

H = ½ . 8 = 4 years old

Answer:

Step-by-step explanation:

Let's call the first number x.

We can write an equation representing the problem using x:

x+x+20=200 (because the second number is 20 more than the first, or x)

Combine like terms: 2x+20=200

Subtract 20 from each side of the equation: 2x=180

Divide by 2: x=90

The first number is 90, the second number is 110.

Hope this helps!

Answer

y=45

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

6.4 × 3 =19.2

44.4 - 19.2 =2.8y

25.2=2.8y

25.2/2.8=y

y=9

Answer:  d) DF ≅ JH

Step-by-step explanation:

Side-Side-Side Congruency Theorem states that triangles are congruent if and only if their corresponding side lengths are congruent.

Given: EF ≅HI

Given: DE ≅IJ

Missing: DF ≅ JH

Answer:

x = -7/2, y=2

Step-by-step explanation:

2x + 5y = 3

-2x - y = 5​

Add the two equations together to eliminate x

2x + 5y = 3

-2x - y = 5​

------------------------

     4y = 8

Divide each side by 4

4y/4 = 8/4

y =2

Now find x

2x +5y =3

2x +5(2) =3

2x+10 =3

Subtract 10

2x = -7

Divide by 2

2x/2 = -7/2

x = -7/2

Answer:

The answer is 6.

Step-by-step explanation:

To find this answer, divide 24 by 3 and you get 8. 8 minus 2 is 6.

Answer: proptional

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The slope is one half, because every time x increases by 1, y increases by 1/2. You can find the slope using the rise over run strategy. You choose a point, and you also choose the point to the right of the point you first chose. You then count how many units up and to the right the right point is.

Its Up/Right.

This version of rise over run however only works when the line is going up.

Answer:

False

Step-by-step explanation:

Let us check using Pythagorean Theorem

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

Where c is the hypotenuse (14), a is the base (13) and b is the perpendicular (5)

Putting in the above formula

[tex]14^2 = 13^2 + 5^2[/tex]

196 = 169+25

196 ≠ 194

So, It is not a right angled triangle

Answer:

1,3,5,7,9....up to soon are odd numbers

Step-by-step explanation:

they are not divided by 2

Answer:

1,3,5,7,9

Step-by-step explanation:

Answer:

1372

Step-by-step explanation:

4x7x7x7=1372:v=4/3 pi r^3

Therefore, 1372 is the value that should be multiplied by Pi in the numerator to correctly show the volume of the sphere.

please mark me brainliest :)

Answer:

y=7*3^x

Step-by-step explanation:

y=ab^x

(0,7) ⇒ 7=ab^0 ⇒ 7=a

(5, 1701) ⇒ 1701= 7b^5 ⇒ b^5=243 ⇒ b^5= 3^5 ⇒ b=3

y=7*3^x

Answer:

b. 75%

Step-by-step explanation:

Here are all the outcomes of three coin tosses:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

There are a total of 8 possible outcomes.

1 outcome is all heads.

1 outcome is all tails.

6 outcomes have at least one heads and 1 tails

p(at least 1 heads and at least 1 tails) = 6/8 = 3/4 = 75%

Step-by-step explanation:

b can be used to check her score

Answer:

Step-by-step explanation: