Nina has $5 bills and $10 bills in her wallet. she has a total of 7 bills with a value of $55. how many of each type of bill does she have? show all work to justify your answer.

To determine the speeds, we set up relative speed equations and solve for 'x'. The cyclist's average speed is 15 km/h and the car's average speed is 45 km/h.

Let's denote the cyclist's speed as 'x' km/h and the car's speed as '3x' km/h (since it's three times the cyclist's speed).

Given that speed is distance over time, we can set up the following equations:

For the cyclist: 225km / x = time, and for the car: 225km / 3x = time - 5.

By equating these two expressions, we get: 225/x = 225/3x + 5.

Solving this equation for 'x', we get x = 15. Thus, the average speed of the cyclist is 15 km/h and the car (3x) is 45 km/h.

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Based on the mean score of the test, the percentage of students who scored above 85% in the test was 16%.

Based on the fact that this distribution is normally distributed, the percentage of students that scored higher or lower than 85% within 1 standard deviation is:

= 100% - 68%

= 32%

The number of students who scored above 85% would therefore be:

= 32% / 2

= 16%

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Final answer:

The third angle of the right triangle is calculated by subtracting the sum of the known right angle (90°) and the given angle (34°) from the total sum of angles in a triangle (180°), which equals 56°.

Explanation:

To find the measurement of the third angle in a right triangle where one of the angles is 34°, we use the fact that the sum of the angles in any triangle is 180°. Since one angle is 34° and another is by definition 90° in a right triangle, we can subtract these two angles from 180° to find the third angle:

Sum of angles in a triangle = 180°

Two known angles: 90° (right angle) + 34° = 124°

Third angle = 180° - 124° = 56°

Therefore, the measurement of the third angle is 56°.

Answer:

A.number of donuts delivered 2 hours from now.

2. Next=now +60+60

starting at 48                      because 2 hours meant  2*60 = 60+60

B. number of donuts delivered 7 hours from now C

3.Next= now +420

starting at 48                     because 7 hours meant  7*60 = 420 mn

C.number of donuts delivered n hours from now.

4. Next=now+60n

starting at 48            (this is obvious)

so finally,

D. number of donuts delivered 6 hours from now.

1. Next= now+ 6*60

starting at 48    

Step-by-step explanation:

Answer:

Option C. is the correct option.

Step-by-step explanation:

The given expression is [tex]log_{2}(x+11)=4[/tex]

We further solve this

[tex](x+11)=2^{4}=16[/tex]

[tex]x = 16-11=5[/tex]

Now we evaluate the options

A). [tex]log_{5}16\neq 2[/tex]

But the expression is given as [tex]log_{2}(x+11)=4[/tex]

Wrong expression so not correct.

B). [tex]log_{5}16\neq 4[/tex]

Wrong expression again so not correct

C). By putting x = 5 in the expression

[tex]log_{2}(x+11)=4[/tex]

[tex]log_{2}(5+11)=log_{2}(16)=log_{2}(2^{4})=4[/tex]

Therefore this option is the correct option.

D). By putting x = 5 in the expression

[tex]log_{4}(5+11)=log_{4}(16)=log_{4}(4^{2})=2[/tex]

But the expression is [tex]log_{2}(x+11)=4[/tex]

So this option is also not correct.

Answer:

c

Step-by-step explanation:

If you can't see the images here

36x2 − 4

Answer:

n=6

Step-by-step explanation:

Since, we know that  when two chords intersect each other inside a circle, the products of their segments are equal. Thus, using this property, we have

[tex](n+8)5=(n+4)7[/tex]

⇒[tex]5n+40=7n+28[/tex]

⇒[tex]40-28=7n-5n[/tex]

⇒[tex]12=2n[/tex]

⇒[tex]n=6[/tex]

Thus, the value of n is 6.

Answer:

[tex]n=6[/tex]

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the value of n.

We can see that two chords of our given circle are intersecting inside it, so we will use intersecting chords theorem to solve for n.

Intersecting chords theorem states that when two chords of a circle intersect inside the circle, then product of the segments of both chords is equal.

Using intersecting chords theorem we can set an equation as:

[tex]5(n+8)=7(n+4)[/tex]

Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]5*n+5*8=7*n+7*4[/tex]

[tex]5n+40=7n+28[/tex]

Subtracting 40 and 7n from both sides we will get,

[tex]5n-7n+40-40=7n-7n+28-40[/tex]

[tex]-2n=-12[/tex]

Dividing both sides by -2 we will get,

[tex]\frac{-2n}{-2}=\frac{-12}{-2}[/tex]

[tex]n=6[/tex]

Therefore, the value of n is 6.

Answer:

The answer is E

Step-by-step explanation:

The statements and reasons are m∠6 = m∠7 | Given, m∠7 = m∠8 | If alternate interior angles equal, then lines are parallel, m∠6 = m∠8, b||c | Substitution and a||b | If lines are parallel, corresponding angles are equal.

The reason for statement 1 is "Given" because it is given in the problem.

The reason for statement 2 is "If alternate interior angles equal, then lines are parallel." This is a theorem in geometry.

The reason for statement 3 is "Substitution" because we are substituting m∠7 for m∠8.

The reason for statement 4 is "If lines are parallel, corresponding angles are equal." This is also a theorem in geometry.

To learn more about statements here:

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Answer:

grams per mm

Step-by-step explanation:

Final answer:

To find the length of a side of the square, calculate the square root of the sum of the areas of the circle (36 cm²) and the additional 12 cm². This results in a square side length of approximately 6.93 cm.

Explanation:

We are given that the area of the circle is 36 cm², and we know that the area of a square is greater than the area of the circle by 12 cm², which means the area of the square is 36 cm² + 12 cm² = 48 cm².

The area of a square is given by A = a², where a is the length of the side of the square. So, we need to find the value of a that satisfies the equation a² = 48 cm².

By taking the square root of both sides of the equation, we get a = √(48 cm²). Simplifying the square root of 48 gives us a ≈ 6.93 cm. Therefore, the length of a side of the square is approximately 6.93 cm.

Answer with explanation:

A parabola is the locus of all the points such that distance from a fixed point called focus to distance from a fixed line is always constant equal to 1.

Let locus of all the point be (p,q).

 [tex]\rightarrow \sqrt{(p-4)^2+(q-0)^2}=p+4\\\\ \rightarrow \text{Squaring both sides}\\\\\rightarrow p^2+16-8 p+q^2=p^2+8 p+16\\\\\rightarrow q^2=8 p+8 p\\\\\rightarrow q^2=16 p\\\\\rightarrow y^2=16 x[/tex]

Required equation of Parabola:

    y²=16 x

Answer:

The measure of the ∠A is 59°.  

Step-by-step explanation:

It is given that a quadrilateral ABCD is inscribed in a circle, and from the properties of circle, we know that the sum of the opposite angles of the quadrilateral inscribed in the circle is equal to 180°.

Therefore, ∠A+∠C=180°

⇒[tex]A+121^{\circ}=180^{\circ}[/tex]

⇒[tex]A=180-121[/tex]

⇒[tex]A=59^{\circ}[/tex]

Therefore, the measure of the ∠A is 59°.

Apologies on this being 4 years late, but to anyone else who stumbles across this; answer is 59°

I had taken the test and got it correct

Good luck, and i hope this helps!! :]

The probability that Natalie got all four quiz questions correct after guessing would be 6. 25 %.

If Natalie guessed on the last four true or false questions, there are two possible outcomes for each question (correct or incorrect), and she has a 50% chance of guessing correctly for each question since there are only two options.

To find the probability that she got all four quiz questions correct, you can multiply the probabilities for each question:

Probability of guessing a question correctly = 0.5 (since there are 2 options, and she has a 50% chance of guessing correctly)

Probability of getting all four questions correct = (0.5) * (0.5) * (0.5) * (0.5)

= 0.0625

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