Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -4.

we know that

Celia bought a bag of [tex]12[/tex] goldfish for [tex]\$3[/tex]

so

by proportion

Find the cost of [tex]1[/tex] goldfish

[tex]\frac{3}{12} \frac{\$}{goldfish} =\frac{x}{1} \frac{\$}{goldfish} \\ \\x=3/12 \\ \\x=\$0.25[/tex]

therefore

the answer is

The cost of one goldfish is [tex]\$0.25[/tex]

Celia will pay 0.25 dollars for 1 goldfish. The cost of 1 goldfish is $ 0.25

The Total number of goldfish purchased is 12.

Cost price for 12 goldfish is $ 3.

Let the price of 1 goldfish be x dollars.

Therefore,

[tex]\begin{aligned}x \times\$12&=\$3\\x&=\dfrac{3}{12}\\x&=0.25\end{aligned}[/tex]

Hence, the cost of 1 goldfish is 0.25 dollars.

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Answer:

y = sin 4x + 3

Step-by-step explanation:

A sine function is represented as y = a sin(bx + c) + d

Given values in the question are a = amplitude = 1

period = π/2 = 2π/b

Vertical shift d = 3 units up.

Horizontal shift c = 0

Since 2π/b = π/2

[tex]b=\frac{2\pi }{\frac{\pi }{2}} =\frac{4\pi }{\pi }=4[/tex]

Now the sinusoidal function will be

y = 1. sin( 4x ) + 3

y = sin 4x + 3

Hello!

1) 2.62

2) 4.8

3) 6.4

3) 2.25 hours

4) −406.25

5) X=19

I hope it helps!

Answer:

she sold 4 2/5 boxes of candy bars.

In total, she sold 88 bars.

:))

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

It has been given that Go has 3 orange pick for every 2 green.

Hence, the ratio of Go to Green is 3:2

Total number of picks = 25.

Number of picks of orange in 25 picks is given by

[tex]\frac{3}{3+2}\times25[/tex]

Simplifying, we get

[tex]=\frac{3}{5}\times25[/tex]

Multiply the numerator, we get

[tex]=\frac{75}{5}[/tex]

Dividing, we get

[tex]=15[/tex]

Hence, the number of picks of orange are 15.

Final answer:

To equally divide 12 cookies among 8 people, each person would receive 1 1/2 or 1.5 cookies, which is a fraction of 3/2 per person when simplified.

Explanation:

To divide 12 cookies equally among 8 people, we need to perform a simple division operation where 12 (total number of cookies) is divided by 8 (number of people). Mathematically, this can be represented as 12/8 which simplifies to 1 1/2 or 1.5 cookies per person. This means that each person would receive one and a half cookies.

If the problem requires the answer as a fraction, we can simplify 12/8 by dividing both numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, we get 12/8 = (12÷4) / (8÷4) = 3/2. Therefore, each person gets 3/2 or one and a half cookies.

The expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].

Given:

The given number is [tex]8.478[/tex].

To find:

The expanded form of the given number.

Explanation:

Write the given number as the sum of the place values of its all digits to find the expanded form of the given number.

[tex]8.478=8+0.4+0.07+0.008[/tex]

Therefore, the expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].

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Answer:

78 students chose lion.

Step-by-step explanation:

Let x students chose tiger.

Let y students chose bull dog.

Let z students chose lion.

Total students = 273

[tex]x+y+z=273[/tex]           ....(1)

Four times as many students chose Bulldog as chose Tiger.

[tex]y=4x[/tex]

Twice as many students chose Lion as chose Tiger.

[tex]z=2x[/tex]

Substituting the values of y and z in (1)

[tex]x+4x+2x=273[/tex]

=> [tex]7x=273[/tex]

x = 39   (students who chose tiger)

We have to find students who chose Lion or z (defined above)

[tex]z=2x[/tex]

[tex]z=2(39)[/tex]

So, z = 78

Therefore, 78 students chose lion.

Option 'C' is an example of an observational study because it involves recording data without manipulation from the researcher, fitting the definition of observing the natural state or habits of a situation over time.

You have correctly identified option 'C' as an example of an observational study. In an observational study, researchers merely observe and record data without manipulating or intervening in the study environment or subjects. Option 'C', which involves recording the daily output of a balloon factory for 6 months, fits this description as it simply measures and records data over time without any intervention from the researcher.

It is different from a controlled experiment where variables are manipulated to assess the effect of treatments, as in option 'B', which compares survival rates between different treatments for bone cancer. Similarly, options 'A' and 'D' involve asking for opinions, which might be part of a broader observational study but are not observational studies by themselves.

In summary, an observational study is characterized by the purposeful absence of manipulation by the researcher and is designed to observe the natural state or habits of the subject or situation being studied.

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.

Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.

10 to 0 =10

0 to -2 = 2

10+2 =12

 it changed by 12 degrees

Toby read 6 books during the first month by using the picture graph where each picture represents 2 books.

To determine how many books Toby read during month 1, follow these steps:

Toby read 6 books during the first month.