Hiroshi picked 25 apples and gave away 17. Hiroshi divided the rest equally among 2 friends. How many did each friend have?

Answer:

D. (–3, –6) and (5, 10)

Step-by-step explanation:

The system has equations:

[tex]y=2x[/tex]...(1)

and

[tex]y=x^2-15[/tex]...(2)

Equate both equations;

[tex]x^2-15=2x[/tex]

Rewrite in standard form:

[tex]x^2-2x-15=0[/tex]

We factor to obtain:

[tex](x+3)(x-5)=0[/tex]

By the zero product principle;

[tex](x+3)=0,(x-5)=0[/tex]

[tex]\implies x=-3,x=5[/tex]

When x=-3, y=2(-3)=-6

This yields the ordered pair (-3,-6).

When x=5, y=2(5)=10

This yields the ordered pair (5,10).

The correct choice is D.

Answer:

Step-by-step explanation:

5

The average yield per plant is 4.00 pints, and the standard deviation is approximately 0.35 pints.

To calculate the average yield per plant:

1. Add up all the yields: 4 + 3.5 + 4.5 + 4.2 + 3.8 = 19.0 pints.

2. Divide the total yield by the number of plants (5): 19.0 / 5 = 3.8 pints per plant.

To calculate the standard deviation:

1. Find the mean (average) yield per plant, which we already calculated as 3.8 pints.

2. Calculate the squared differences from the mean for each yield:

  - Plant 1: [tex](4 - 3.8)^2[/tex] = 0.04

  - Plant 2:[tex](3.5 - 3.8)^2[/tex] = 0.09

  - Plant 3: [tex](4.5 - 3.8)^2[/tex] = 0.49

  - Plant 4:[tex](4.2 - 3.8)^2[/tex] = 0.16

  - Plant 5:[tex](3.8 - 3.8)^2[/tex] = 0

3. Calculate the average of these squared differences: (0.04 + 0.09 + 0.49 + 0.16 + 0) / 5 = 0.156.

4. Take the square root of the variance to get the standard deviation: √0.156 ≈ 0.35 pints.

The average yield per plant provides a measure of the central tendency of the data set, indicating the typical yield for one plant.

The standard deviation measures the spread or variability of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates more variability. In this case, the standard deviation of approximately 0.35 pints suggests that the yields are relatively close to the average of 3.8 pints per plant, with minimal variability.

Complete question

A homeowner has 5 cherry tomato plants in her garden. Over the course of the season the yields (in pints of tomatoes per plant) are: Plant 1 2 3 4 5 Yield 4 3.5 4.5 4.2 3.8 What is the average yield per plant, and what is the standard deviation (to two decimal places)?

Answer:

Step-by-step explanation:

A parameter describes a population, and a statistic describes a sample.

The first one is a statistic.  A sample was surveyed.

The second one is a parameter.  It describes the entire soccer team.

The third one is a statistic.  A sample was surveyed.

The fourth one is a parameter.  It describes the entire golf team.

Answer:

[tex]\large\boxed{2\sqrt7}[/tex]

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]

We have

[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]

Substitute:

[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex]           cross multiply

[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]

Answer:

$219.6

Step-by-step explanation:

we know that

The sell price is equal to the cost price plus the profit

Let

C ----> the cost price

S----> the sell price

P ----> the profit

so

S=C+P

we have

C=$180

Find the profit

22%=22/100=0.22

P=0.22*(180)=$39.6

Find the sell price

S=$180+$39.6=$219.6

These 5 numbers can be written as [tex]x,x+2,x+4,x+6,x+8[/tex], so their sum is

[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=310[/tex]

[tex]\implies5x=290[/tex]

[tex]\implies x=58[/tex]

Then the numbers are 58, 60, 62, 64, and 66.

Answer:

3 3/4

Step-by-step explanation:

I've no idea if this is right, but this is how I'd do it:

For 2 batches you need 2 1/2 cups of blueberry

So, half of that is 1 and 1/4

So the total is 3 3/4

Answer:

The answer is 3 3/4

Step-by-step explanation:

I got it right on my test.

Answer:

18 Quarts

Step-by-step explanation:

there are 4 quarts per gallon

I multiplied 4 x 5 = 20 then subtracted the 2 quarts left which comes out to 18 quarts used.

Rewriting [tex]z[/tex] in polar form makes this trivial.

[tex]z=|z|e^{i\mathrm{arg}(z)}[/tex]

We have

[tex]|z|=\sqrt{(-1)^2+(-\sqrt3)^2}=2[/tex]

[tex]\mathrm{arg}(z)=\tan^{-1}(-1,-\sqrt3)=-\dfrac{2\pi}3[/tex]

(not to be confused with the standard inverse tangent function [tex]\tan^{-1}x[/tex]. Here [tex]\tan^{-1}(x,y)[/tex] is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)

So we have

[tex]z=-1-\sqrt3\,i=2e^{-2\pi/3\,i}[/tex]

Then

[tex]z^6=2^6\left(e^{-2\pi/3\,i}\right)^6=64e^{-4\pi\,i}=64[/tex]

so that [tex]a=64[/tex] and [tex]b=0[/tex].

Answer:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Step-by-step explanation:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Answer:  The fifth partial sum = 2210

The fifth partial sum represent the sum of the first 5 terms in the sequence.

Step-by-step explanation:

We know that he partial sum of a sequence gives the sum of the first n terms in the sequence.

Thus, the fifth partial sum represent the sum of the first 5 terms in the sequence.

The given geometric sequence : $400, $420, $441, $463, and $486.

Now, the fifth partial sum of the above sequence will be :

[tex]S_5=\$400+ \$420+ \$441+ \$463+\$486=\$2210[/tex]

Step-by-step explanation:

h = -490t² + 1470t

When h = 980:

980 = -490t² + 1470t

Simplifying:

0 = -490t² + 1470t - 980

0 = t² - 3t + 2

Factoring:

0 = (t - 1) (t - 2)

t = 1, 2

There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.

The rocket reaches a height of 980 cm at 1 second and 2 seconds. The equation is factored to find these solutions, symbolizing the ascent and descent of the rocket.

To find when the height of the rocket is 980 cm, we set the height formula equal to 980 cm:

h = -490t² + 1470t = 980.

We then solve the equation by factoring:

-490t² + 1470t - 980 = 0
Divide by -10:
t²- 3t + 2 = 0
Factor:
(t - 1)(t - 2) = 0

Setting each factor to zero gives us the solutions:

t = 1 second

t = 2 seconds

There are two solutions because the rocket reaches 980 cm twice: once on its way up and once on its way down. This is demonstrated by the positive and negative components of the parabolic trajectory represented by the quadratic equation.

Answer:

D. 158

Step-by-step explanation:

Fill in the x's with a 15:

[tex]y=-2(15)^2+40(15)+8[/tex]

so y = 158

The best prediction for the number of new cases in year 15 is 158.

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation.

Here, Given quadratic equation

                 y = -2x² + 40x + 8

 at put the value of x = 15, we get

               y(15) = -2 X (15)² + 40 X 15 + 8

               y(15) = -2 X 225 + 600 + 8

               y(15) = -450 + 600 + 8

              y(15) = 150 + 8

              y(15) = 158

Thus, the best prediction for the number of new cases in year 15 is 158.

Learn more about Quadratic Equation from:

https://brainly.com/question/17177510

#SPJ2

Answer:

The box of 32oz is cheaper by 2 cents per ounce.

Step-by-step explanation:

1. 3.84/24 ($0.16/oz)

2. 4.48/32 ($0.14/oz)

___

Hope this helps you! :)

Using technology, the regression equation is

y=9.08292(1.09965)ˣ. 

The number of recommendations after 60 days is 2113.277 ≈ 2113.

Explanation

I used Desmos to graph the points, then entered the expression y₁~a*bˣ to calculate the regression.

I then substituted 60 in for x in the regression equation to get the answer of 2113.

Answer:

(x + 5)² + (y + 8)² = 49

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 5, - 8), so

(x - (-5))² + (y - (- 8))² = r², that is

(x + 5)² + (y + 8)² = r²

The radius is the distance from the centre to a point on the circle

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (2, - 8)

r = [tex]\sqrt{(2+5)^2+(-8+8)^2}[/tex] = [tex]\sqrt{7^2+0^2}[/tex] = [tex]\sqrt{49}[/tex] = 7

r = 7 ⇒ r² = 7² = 49

Hence

(x +5)² + (y + 8)² = 49 ← equation of circle

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

They tell us that:

[tex]d = \frac {35} {2}\\\pi = \frac {22} {7}[/tex]

Substituting:

[tex]C = \frac {22} {7} * \frac {35} {2}\\C = \frac {770} {14}\\C = 55 \ cm[/tex]

Thus, the circumference of the circle is 55 centimeters.

Answer:

Option B

Answer:

55 im not sure

Step-by-step explanation:

You are given h(t) = 64–16t^2.

You need to find h(1.25).

Set up:

h(1.25) = 64 - 16(1.25)^2

Take it from here.

Answer:

Step-by-step explanation:

Given the height of a beach ball rolling off a cliff as a function of time

h = 64 — 16t²

We want to find the average change in height when t = 1.25s

The rate of change of height is the differentiation of the height I.e

∆h/∆t → dh/dt

Therefore

h = 64 — 16t².

Therefore

Differential of a constant is zero

dh/dt = —32t

At t = 1.25s

dh/dt = —32(1.25)

dh/dt = —40 ft/s

So, the height is reducing at a rate of 40ft in every seconds.

Answer:

B

Step-by-step explanation:

2 || 1   -   4     6    -   4

              2    -4       4

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

     1       -2    2

x^2 - 2x + 2 with no remainder.

Looks like the answer is B

Note: Note that the two in x - 2 changes sign. That always happens when using synthetic division as long the number in front of the x is positive.

Answer:

$48

Step-by-step explanation:

we know that

$80 represent 100%

so

using proportion

Find how much is 60%

80/100=x/60

x=80*60/100

x=$48

Answer:

  6

Step-by-step explanation:

In order for 132* to be a multiple of 2, the digit * must be even.

In order for 132* to be a multiple of 3, the sum of all digits must be a multiple of 3. That is (1 +3 +2 + *) = 6+* is a multiple of 3. Since 6 is already a multiple of 3, then * must be a multiple of 3.

Single-digit values of * that are both even and a multiple of 3 are 0 and 6. We know that any number ending in 0 will be a multiple of 5, so we cannot use that digit.

The only possible digit that makes 132* a multiple of 2 and 3, but not 5, is 6.

Answer:

Correct: A, D, F

Step-by-step explanation:

Consider right triangle EFG.

By the definition of the cosine function,

[tex]\cos \angle E=\dfrac{EG}{EF}\\ \\\cos 30^{\circ}=\dfrac{EG}{EF}\\ \\\dfrac{\sqrt{3}}{2}=\dfrac{EG}{EF}\\ \\EG=\dfrac{\sqrt{3}}{2}EF[/tex]

Option F is correct.

By the definition of the sine function,

[tex]\sin \angle E=\dfrac{FG}{EF}\\ \\\sin 30^{\circ}=\dfrac{GF}{EF}\\ \\\dfrac{1}{2}=\dfrac{GF}{EF}\\ \\GF=\dfrac{1}{2}EF\\ \\EF=2FG[/tex]

Option D is correct.

By the definition of tangence,

[tex]\tan \angle E=\dfrac{FG}{EG}\\ \\\tan 30^{\circ}=\dfrac{GF}{EGF}\\ \\\dfrac{1}{\sqrt{3}}=\dfrac{GF}{EG}\\ \\GF=\dfrac{1}{\sqrt{3}}EGF\\ \\EG=\sqrt{3}FG[/tex]

Option A is correct

Answer:

112560

Step-by-step explanation:

The total profit is the sale price of the helmet is $ 60 is:

                        $ 27,600

p denote the total profit and s denote the sale price.

The total profit in terms of the sale price is given by the function :

        [tex]p(s)=-24s^2+2200s-18000[/tex]

Now we are asked to find the value of p when the s=60

when s=60 we have:

[tex]p(60)=-24\times (60)^2+2200\times 60-18000\\\\\\p(60)=-24\times 3600+132000-18000\\\\\\p(60)=-86400+132000-18000\\\\\\p(60)=27600[/tex]

          Hence, the total profit when sale price is $ 60 is:

                              $ 27,600

Answer:

(x - 4)² + (y + 7)² = 53

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (4, - 7), so

(x - 4)² + (y + 7)² = r²

The radius is the distance from the centre to a point on the circle.

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)

r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]

  = [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]

Hence r² = ([tex]\sqrt{53}[/tex] )² = 53

(x - 4)² + (y + 7)² = 53 ← equation of circle

The option that shows a two-way conditional frequency table is option B as shown in the image attached.

A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:

Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.

The correct option is option B because it meets the following requirements:

Learn more about variables in: https://brainly.com/question/787279

Answer:

Do you prefer dancing or playing sports?

 Playing sports Dancing Row totals

Male students 0.48 0.52 1

Female students 0.35 0.65 1

Step-by-step explanation:

This is the answer

Answer:

they both have the equilateral lines on each side

Step-by-step explanation:

Answer:

The measure of angle 6 is m∠6=50°

Step-by-step explanation:

we know that

m∠3+m∠6=180° ----> supplementary angles (interior consecutive angles)

so

we have

m∠3=130°

substitute

130°+m∠6=180°

m∠6=180°-130°=50°

Answer:

B. Multiply 5 times 3. Multiply 5 times 4. Add the two products

Step-by-step explanation:

Right from the start the question is only asking for squash plants so the other two rows don't need to be counted.

7-2 = 5

In each row there's 3 yellow squash = 5*3 = 15

And 4 green squash = 5*4 = 20

which means there's 35 squash total in the garden.

Answer:

i am assuming 2 and 5 because they are the only ones that are not like the others

Step-by-step explanation:

Answer:

Angles 2 and 5

Step-by-step explanation:

Supplement angles are the angles which up to 180 degrees.

And all the angles shown are Vertically opposite angles and these angles are always the same.

Vertically opposite angles:

Angles  2 and 5

Angles 1 and 3

Angles 6 and 4

As shown in the picture, Angle 2 is 90 degrees and angle 5 being a vertically opposite angle, angle 5 is 90 degrees too.

90 + 90 = 180 degrees.

1.63

4.89 divided by 3 = 1.63

1.63 just divided the total by 3

Answer:

The product is equal to [tex]3\sqrt{15}[/tex]

Step-by-step explanation:

Ok,

First, you have

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

We must follow the rule for multiplying radicals, in this case:

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

Note that the types of root, n, have to match, in this case is 2 for each root

Then, we know that two negative numbers multiplied give a positive number, in this case

[tex](3\sqrt[2]{-3} )(\sqrt[2]{-5})=(3\sqrt[2]{(-3)(-5)})=(3\sqrt[2]{(15)})[/tex]

So, the correct answer is [tex](3\sqrt{-3})(\sqrt{-5} )=3\sqrt{15}[/tex]