Mathematics High School

Each baby dinosaur made 15 paintings and each adult dinosaur made 7 paintings. The entire herd made 208 paintings in total, and there were 3 times as many baby dinosaurs as adult dinosaurs.

Answers

Answer 1

12 babies
4 adults.

Use the following system of equations:

x - 3y = 0
15x + 7y = 208

Answer 2

Answer:

Adult dinosaurs=4

Baby Dinosaurs=12

Step-by-step explanation:

You only have to put an X to a certain number, in this case it will be like this:

Adult dinosaurs=x

Baby Dinosaurs= 3x

So the equation will be:

15(3x)+7(x)=208

You multiply it and add it and it will end up like this:

52x=208

x=4

So there were 4 adult dinosaurs.

And baby dinosaurs there are 3x which equals 12.

Related Questions

Share 450 in the ratio of 4:5

Answers

Let's represent the ratio in variable form:
4n + 5n = 450
9n = 450
n = 50
Now we multiply into the ratio:
200:250
Or
200 and 250

4 : 5 → 4 + 5 = 9

450 : 9 = 50

4 · 50 = 200
5 · 50 = 250

Answer: 200 and 250.

Find the area of the following rectangle in square feet. 44 ft 2 11 ft 2 14.7 ft 2 132 ft 2

Answers

the picture in the attached figure

we know that
area of rectangle=base*height
in this problem
base is 22 ft
height is 2 yd

convert yd to ft
1 yd is equal to 3 ft
2 yd--------> 2*3-----> 6 ft

area of rectangle=22*6-----> 132 ft²

the answer is
132 ft²

Answer:

132

Step-by-step explanation:

Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.

Answers

Correlation is the measure of the type of association between two variables. There can be a positive, a negative or no association between two variables.

A correlation can be called association when it can be ascertained that the result in one variable is as a result of the result of the other variable. Though correlation is a condition for causation, but correlation does not imply causation.

Therefore, given that there were a strong correlation between the variables n and p, the true statement is "n may cause p".

What are the factors of x^2-64

Answers

Difference Of Two Squares
a^2 - b^2 = a^2 - b^2
so
x^2-64
=x^2 - 8^2
= (x + 8)(x - 8)

Final answer:

The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).

Explanation:

The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:

x^2 - 64 = (x - 8)(x + 8)

This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.

Given v=(6,3) and w=(1,-2), what is the result of v-w

Answers

Here, v - w would be (6-1, 3-[-2]), or (5, 5).
I don't believe you need the word "result" here. At first I thought you'd meant "resultant." Here you're finding the "difference" v less w.

Final answer:

The result of v - w is (5, 5).

Explanation:

To find the result of v - w, we need to subtract the corresponding components of the two vectors. Given v = (6, 3) and w = (1, -2), we subtract their x-components and their y-components separately.

v - w = (6 - 1, 3 - (-2))

Therefore, v - w = (5, 5).

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please help asap 50 pts

Answers

C. If you were to graph the parabola, you would find that the vertex is at (19,361). Therefore, the answer is C.

Your answer should be C.

[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]

What is the remainder when the positive integer n is divided by 12 ? (1) when n is divided by 6, the remainder is 1. (2) when n is divided by 12, the remainder is greater than 5?

Answers

The remainder is 7.

The number n would be 31. In this case you could divide it by 6 and get 5 with a 1 remainder and then divide it by 12 and get 2 with a 7 remainder.

multiply and simplify. 5x^2 / y^3 * 4y^2 / 10x

Answers

For this case we have the following expression:
[tex] \frac{5x^2}{y^3} * \frac{4y^2}{10x} [/tex]
Rewriting the expression we have:
[tex]\frac{20x^2y^2}{10xy^3} [/tex]
Then, simplifying and by properties of exponents we have:
[tex]{2x^{2-1}y^{2-3}} {2xy^{-1}}[/tex]
Rewriting we have::
[tex] \frac{2x}{y} [/tex]
Answer:
The simplified expression is given by:
[tex] \frac{2x}{y} [/tex]

What is sin (51)?
Answer Choices : 1.23 , 0.63 , 0.51 , 0.78

Answers

The correct answer is .78
Make sure your calculator is in degrre mode when doing these.

Using calculator I got 0.77714.....
so the answer is 0.78

using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. the telescope is positioned so that the line of sight to the eagle forms a 38 degree angle of elevation. the telescope sits 1.3 m above the ground and the base of the telescope is 116 m away from the base of the cliff. to the nearest tenth of a meter, how high above the ground is the eagle?

Answers

the correct answer is B 91.9 m

Am I correct in thinking that the answer to this derivative problem is B?

dy/dx = y/x^2

dy/y = dx/x^2

ln y * ln c = -1/x

cy = e^(-1/x)

y = ce^(-1/x)

Answers

y ' = x(1+y)
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1

Answer is actually choice C (not choice B)

note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative

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

Checking the answer:

y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression

x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before

So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.

Quick need the answer!

Answers

The answer is “c” x=90.y=45

suzie divided a 3-pound bag of apples into 2 equal piles. How many lbs of apples are in each pile

Answers

3/2 = 1.5 Lbs per pile.

3 pounds divided by 2 piles = 1.5 pounds per pile

Final answer:

Suzie's 3-pound bag of apples divided into two equal piles will result in each pile weighing 1.5 pounds. This is a basic arithmetic problem often referred to as equal distribution.

Explanation:

Suzie is dividing a 3-pound bag of apples into two equal piles. This is a simple division problem where the total weight of apples (3 pounds) is distributed equally into two piles. Therefore, we simply divide the total weight by the number of piles.

To calculate the weight of apples in each pile, we divide the total weight (which is 3 lbs) by the number of piles (which is 2). So, 3 lbs ÷ 2 = 1.5 lbs. Each pile would weigh 1.5 lbs.

This type of problem is often referred to as an equal distribution problem in mathematics. It falls under the category of basic arithmetic and is typically taught in lower grades.

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The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit

Answers

Hoi!

To calculate the area, multiply 15 and 6, then divide the product by 2.

15 × 6 = 90

90 ÷ 2 = 45

The area of this triangle is 45.

What is the area of a regular hexagon with a side length of 12 cm

Answers

The answer is about 374.
More exactly would be 374.12.
Hope this helps!

The answer is 72 cm. Because 12*6=72.

Bob can type 2 letters in 4 hours while Bill can do it in 6. How many hours would it take them, working together, to type six letters?

Answers

Bob's production rate is given by:
r1 = 2/4 = 1/2 letter / hour
The production rate of Bill is given by:
r2 = 2/6 = 1/3 letter / hour
Thus, the production rate of both is:
r1 + r2 = 1/2 + 1/3 = 5/6 letter / hour
Then, the production of 6 letters is given by:
rate * time = letters
(5/6) t = 6
t = (6/5) 6
t = 36/5 = 7 1/5 hours = 7hr 12 min
Answer:
it would take them, working together, to type six letters about:
7hr 12 min

Answer:

It would take them 7.2 hours.

The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form? Show your work.

8 square units
20 square units
24 square units
28 square units

Answers

see the picture with letters attached to better understand the problem

we know that
surface area=area A +area B+area C+area D+area E+area F

area A=area F
area B=area area D
area C=area E
so
surface area=[2*1]+[4*2]+[4*1]+[4*2]+[4*1]+[2*1]----> 28 units²

the answer is
28 units²

Answer:

the answer is d:)

Step-by-step explanation:

i took the quiz on edge and got 100:D

what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)

Answers

the answer in the attached figure

Answer:

[tex](30\sqrt{3}-21\sqrt{6})[/tex]

Step-by-step explanation:

We have to find the product of the expressions.

[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]

= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)

= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]

= [tex]15\sqrt{12}-21\sqrt{6}[/tex]

= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]

= [tex]30\sqrt{3}-21\sqrt{6}[/tex]

= [tex](30\sqrt{3}-21\sqrt{6})[/tex]

Maria works at a bookstore. On Wednesday, she sold three times as many books as she did on Tuesday. On Thursday, she sold 8 fewer books than she did on Wednesday. During the three days, Maria sold 20 books. Create an equation that can be used to find m, the number of books Maria sold on Tuesday.

Answers

To write an equation to show how many books Maria sold on Tuesday, you will write an equation for each day.

Tuesday - m
Wednesday - 3m
Thursday - 3m - 8

Show all of these in an addition problem with a total of 20 and simplify.

m + 3m + (3m - 8) = 20

7m - 8 = 20; You can solve this equation to find the number of books Maria read.

What is the area of the figure to the nearest tenth?

Answers

Area of circle = πr²

Area of the full circle = π (6)² = 36π

Area of the sector = 165/360 x 36π = 51.8 in²

Answer: 51.8 in²

area of full circle with a radius of 6 in = PI x 6^2

3.14 x 36 = 113.04 square inches

the shape is 165 degrees of a full circle which is 360 degrees

so area of the shape would be 165/360 x 113.04

= 51.8 square inches

Write the expression 5x+4x^2(2x+7)-6x^2-9x as a polynomial in standard form

Answers

5x + 4x²(2x + 7) - 6x² - 9x
5x + 8x³ + 28x² - 6x² - 9x

8x³ + 22x² - 4x

This can be simplified to:

2x(4x² + 11x - 2)

I don't know which of those answers you are looking for.

Answer:

8x^3 + 22x^2 - 4x

Step-by-step explanation:

5x+4x^2(2x+7)-6x^2-9x

Open the bracket

5x + 8x^3 + 28x^2 - 6x^2 - 9x

= 8x^3 + 28x^2 - 6x^2 - 9x + 5x

= 8x^3 + 22x^2 - 4x

In standard form, the polynomial 5x+4x^2(2x+7)-6x^2-9x is 8x^3 + 22x^2 - 4x

What is the measure of the angle?

Answers

Remember that the x-axis and the y-axis make an angle of 90° in the first quadrant. To find the measure of the angle we just need to add the smaller angle, 65°, and the right angle between the axis 90°:

Measure of the angle=65°+90°=155°

We can conclude that the measure of the bigger angle in the picture is 155°

The 65 degrees lies in the beginning of the 2nd quadrant where the second quadrant starts with 90 degrees.

So the angle is 90 degrees + 65 degrees = 155 degrees

The fourth one is the answer

Find the surface area of each right regular pyramid. a pentagonal pyramid with base sides 1.5 meters, base area 3.9 m2, and slant height 4 meters

Answers

The answer is 18.9, i think, because there is a formula for finding the total surface area of such pyramids, but i used the simpler way of finding all the separate areas of each face using this information:

since the base area is 3.9 m2, we could just add that to the total at the end.

since the base edge is 1.5 m and the height is 4m, we could find the area of the face by doing (1.5 times 4)/2 which would give us 3m2.

Since there are 5 faces(pentagonal), we would multiply 3 times 5, and would get 15m total for all the triangle faces.

so to get the total surface area, you would add 15 + 3.9 (which was the base area) and get 18.9m2....

....;);) hope this helps

A group of 12 people attend a meeting. Every pair of people shook hands with each other. How many handshakes were there?

Answers

There are 12 people handshakes

The first person will shake the hand whit the other 11 people, the second with 10 because he has already shook his hand with the first, and so on.
So there will be 11+10+9+8+7+6+5+4+3+2+1=66 handshakes.

Hope this helped!

Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.

Answers

The initial term of this geometric series is 4, and the common ratio is -1/2. The sum is given by

[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}\\\\S_{10}=4\cdot \dfrac{(-\frac{1}{2})^{10}-1}{-\frac{1}{2}-1}=4\cdot \dfrac{(\frac{1}{1024}-1)}{(-\frac{3}{2})}\\\\=\dfrac{8}{3}\cdot \dfrac{1023}{1024}=\dfrac{341}{128}[/tex]

The sum is approximately 2.66.

I WILL MARK BRAINLIEST TO A CORRECT AND EXPLAINED ANSWER!!!!
Look at points C and D on the graph:

What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.

A. 4.54 units
B. 5.00 units
C. 5.83 units
D. 34.00 units

Answers

C(-4;3)
D(1:0)

Image the right triangle between C, D and the point A(-4,0)

CA is 3-0=3; AD is 1-(-4)=1+4=5

CD is √3²+5²=√34=5.8309...

Answer:

Option C.

Step-by-step explanation:

Coordinates of the points C and D are (-4, 3) and (1, 0)

We have to find the distance CD.

Distance CD = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

CD = [tex]\sqrt{(1+4)^{2}+(0-3)^{2}}[/tex]

= [tex]\sqrt{25+9}[/tex]

= [tex]\sqrt{34}[/tex]

= 5.83 units

Therefore, Option C. distance CD = 5.83 units is the answer.

Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)

Answers

For this case we must find the set of ordered pairs that form an exponential function.

When observing, the last set of ordered pairs is an exponential function of the form:

[tex]y = 3 ^ x[/tex]

For x = 0:

[tex]y = 3 ^ 0 = 1[/tex]

We have the ordered pair:

[tex](x, y): (0, 1)[/tex]

For x = 1:

[tex]y = 3 ^ 1 = 3[/tex]

We have the ordered pair:

[tex](x, y): (1, 3)[/tex]

For x = 2:

[tex]y = 3 ^ 2 = 9[/tex]

We have the ordered pair:

[tex](x, y): (2, 9)[/tex]

For x = 3:

[tex]y = 3 ^ 3 = 27[/tex]

We have the ordered pair:

[tex](x, y): (3, 27)[/tex]

Answer:

The set of ordered pairs that form an exponential function is:

[tex](0, 1), (1, 3), (2, 9), (3, 27)[/tex]

Answer:

Step-by-step explanation:

Mind helping someone out?
I've kinda been stuck on this problem and it's my last math problem for the day.

Answers

[tex]\bf 2a^3b^2\sqrt[3]{12b}\implies 2a^3b^2\sqrt[3]{12b^1}\implies \sqrt[3]{(2)^3(a^3)^3(b^2)^3~~~~12b^1} \\\\\\ \sqrt[3]{2^3a^{3\cdot 3}b^{2\cdot 3}~~~~12b^1}\implies \sqrt[3]{8a^9b^6~~~~12b^1}\implies \sqrt[3]{(8)(12)a^9b^6b^1} \\\\\\ \sqrt[3]{96a^9b^{6+1}}\implies \sqrt[3]{96a^9b^7}[/tex]

A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease

A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?

Answers

A) You need to use the binomial distribution, for which the probability of an event X is given by:
[tex]P(X) = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of success we want
p = probability of success

Therefore, since the problem tells you that X is the number of subjects who test positive for the disease, you will have:

[tex]P(X) = \frac{30!}{0!(30-0)!} 0.02^{0} (1-0.02)^{30-0} [/tex]

= 1 · 1 · 0.98³⁰
= 0.5455

Hence, the probability of none of the 30 subjects testing positive to the desease is 54.55%

B) In a binomial distribution, the mean is given by the formula:
μ = n · p
   = 30 · 0.02
   = 0.6

And the standard deviation is given by the formula:
σ = √[n·p·(1-p)]
   = √[30·0.02·0.98]
   = √0.588
   = 0.77

Hence, the mean is 0.6 and the standard deviation is 0.77

C) This test is not very viable: 30 subjects are a sample too small compared to the population (millions of people who need to be tested), the probability of finding that all the 30 subjects are healty is only a little bit over 50%, the standard deviation is too high compared to the mean, and 2% of false positive is a percentage too high to consider the test viable.

Daniel’s tennis team made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64. What expression would model the amount of money each player would receive if the money is divided equally?

Answers

The answer would be

1. (582.85 - 64)/p Or D

And

2. 64.85 Or A

The expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).

What is division?

Division is a operation in mathematics which is used to divide a specific number into equal parts of specific magnitude.

Given is Daniel’s tennis team which made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64.

Assume that there are [x] players in the team.

Now, the money left after spending on food = 582.85 - 64 = 518.85

Each player, when divided equally, would receive = y = (518.85/x)

Therefore, the expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).

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