Solve the system of equations given below

Answer:

C.

Step-by-step explanation:

Answer:  c) 56 and 88

Step-by-step explanation:

95% is 2 standard deviations above and below the mean.

  72 ± 2(8)

= 72 ± 16

= 56 and 88

Answer:

341.3 g

Step-by-step explanation:

we know that

The density is equal to the ratio of the mass by the volume

D=m/V

Solve for the mass m

m=D*V

In this problem we have

D=22.6 g/cm³

V=15.1 cm³

substitute in the formula

m=22.6*(15.1)=341.26 g

Round to the nearest tenth of a gram

341.26 g=341.3 g

Answer:

They are all the same.

Step-by-step explanation:

The area of a parallelogram is computed by multiplying the base length by the height. All of these parallelograms will have an area of ...

  A = (6 units)(4 units) = 24 units²

You can draw any number of parallelograms with these dimensions, and they will all have the same area.

Answer:

The complex number in the form of a + b i is 3/2 + i √3/2

Step-by-step explanation:

* Lets revise the complex number in Cartesian form and polar form

- The complex number in the Cartesian form is a + bi

-The complex number in the polar form is r(cosФ + i sinФ)

* Lets revise how we can find one from the other

- r² = a² + b²

- tanФ = b/a

* Now lets solve the problem

∵ z = 3(cos 60° + i sin 60°)

∴ r = 3 and Ф = 60°

∵ cos 60° = 1/2

∵ sin 60 = √3/2

- Substitute these values in z

∴ z = 3(1/2 + i √3/2) ⇒ open the bracket

∴ z = 3/2 + i √3/2

* The complex number in the form of a + b i is 3/2 + i √3/2

Answer:

3/2 + (3sqrt(3))/2 i

Step-by-step explanation:

On the unit circle cosine and sine 60 degrees can be found in the first quadrant. With the correct measures. Once located, (1/2, sqrt(3)/2), multiply those numbers by 3. Don't forget to include i.

3(1/2 + sqrt(3)/2 * i)

= 3/2 + (3sqrt(3))/2 i

The answer is:

The height of the  lightning rod is 27.4 feet.

To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.

So, writing the equations we have:

We know that the angle of elevation from the base of the buildings is 36°

Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.

Using the information we have:

To the top of the building:

[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}[/tex]

To the top of the lightning rod:

[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}[/tex]

Now, isolating we have:

[tex]tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\DistanceToTheTopOfTheBuilding=tan(36\°)*BuildingBase \\\\DistanceToTheTopOfTheBuilding=tan(36\°)*500feet=363.27feet[/tex]

Also, we have that:

[tex]tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*BuildingBase\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*500feet=390.64feet[/tex]

Therefore, if we want to calculate the height of the lightning rod, we need to do the following:

Let "x" the distance to the top of the building and "y" the distance to the top of the lightning rod, so:

[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet[/tex]

Rounding to the nearest foot, we have:

[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet=27.4feet[/tex]

Hence, the answer is:

The height of the lightning rod is 27.4 feet.

Have a nice day!

To find the height of the lightning rod, create two right triangles using the tangent function and the given angles of elevation. Use the distance from the base to the location as the base of both triangles. Calculate the height of the building and the height of the lightning rod separately using trigonometry.

To find the height of the lightning rod, we can use the concept of trigonometry and create a right triangle with the base of the triangle as the distance from the base of the building to the location, the height of the building as the vertical side of the triangle, and the angle of elevation to the top of the building as one of the acute angles. Using the tangent function, we can calculate the height of the building to be approximately 287 feet. Next, we can create another right triangle with the same base the height of the lightning rod as the vertical side, and the angle of elevation to the top of the lightning rod as one of the acute angles. Again, using the tangent function, we can calculate the height of the lightning rod to be approximately 310 feet. Therefore, the height of the lightning rod is approximately 310 feet.

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Answer:

I think it is 285 bc 15*19 is 285

Answer: Here...

Step-by-step explanation:

Mean: The average of the numbers so add them up then divide by how many numbers you added

Median: The middle number of the numbers in numerical order

Mode: The number that is repeated the most often

Range: The smallest number subtracted from the larger number

Outlier: A data point or observation that is not with the others so basically the odd one out

Hope this helps Brainliest plz

Answer:

1.44π m²

Step-by-step explanation:

The area (A) of the circle is calculated as

A = πr² ← r is the radius

here the diameter is 2.4 and the radius is half the diameter, thus

r = 1.2, so

A = π × 1.2² = 1.44π m²

Answer:

The equation of this line is therefore    y = 2x + 3.

Step-by-step explanation:

this line passes thru the points (0, 3) and (3, 9).  As we move from  (0, 3) to (3, 9), x increases by 3 and y increases by 6.  Thus, the slope of this line is

m = rise / run = 6/3, or m = 2.  Inserting the known info (m = 2, x = 0, y = 3) into y = mx + b, we get:  3 = 2(0) + b, so we see that b = 3.

The equation of this line is therefore    y = 2x + 3.

Answer:330 degrees

Step-by-step explanation: It helps by drawing a picture, hope this helps

Answer: [tex]arc\ length=3[/tex]

Step-by-step explanation:

The formula for calculate the arc lenght is:

[tex]arc\ length=2\pi r(\frac{\theta}{360})[/tex]

Where "r" is the radius and "[tex]\theta[/tex]" is the central angle of the arc in degrees.

The formula used to find the circumference of a circle is:

 [tex]C=2\pi r[/tex]

Where "r" is the radius.

Then, we can observe that the formula for calculate the arc lenght can be rewritten in this form:

[tex]arc\ length=C(\frac{\theta}{360})[/tex]

Where "C" is the circumference of the circle.

Finally we need to substitute the central angle and the circumference into [tex]arc\ length=C(\frac{\theta}{360})[/tex]. Then the result is this:

[tex]arc\ length=36(\frac{30\°}{360})=3[/tex]

Answer:

If im correct from the way this is set up, I believe it is C

Step-by-step explanation:

Answer:

Your answer would be A) y=-x+1

Step-by-step explanation:

Looking at each value in the table you can take x, make it a negative, then add 1 for it to equal y. Hope this helped and have a wonderful day!

Answer:

121

Step-by-step explanation:

First, we find the z-score for 13 cm:

z = (x - μ) / σ

z = (13 - 11.2) / 2.1

z = 0.86

Next, we use a calculator or a z-score table to find P(x<0.857).

P(x<0.86) = 0.8051

So the number of green beans in a bag of 150 less than or equal to 13 cm is:

0.8051 * 150

121

The number of green beans that is 13 centimeters or shorter will be 121. Then the correct option is C.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The z-score is given as,

z = (13 - 11.2) / 2.1

z = 1.8 / 2.1

z = 0.587

The number of green beans that is 13 centimeters or shorter will be given as,

⇒ 150 x P(z ≤ 0.587)

⇒ 150 x 0.8023

⇒ 121

Thus, the correct option is C.

More about the z-score link is given below.

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The answer is given in the file attached

angle addition postulate:

m∠B = m∠1 + m∠3

m∠1 = m∠B - m∠3

Answer:

First choice V = 18,432π m^3; S = 2,304π m^2

Step-by-step explanation:

Start with the two formulas:

Volume of a circle:

[tex] V = \dfrac{4}{3} \pi r^3 [/tex]

Surface area of a circle:

[tex] S = 4 \pi r^2 [/tex]

Now use r = 24 m in each formula.

Volume:

[tex] V = \dfrac{4}{3} \pi (24~m)^3 [/tex]

[tex] V = \dfrac{4}{3} \pi (13,824~m^3) [/tex]

[tex] V = 18,432\pi~m^3 [/tex]

Surface area:

[tex] S = 4 \pi r^2 [/tex]

[tex] S = 4 \pi (24~m)^2 [/tex]

[tex] S = 4 \pi (576~m^2) [/tex]

[tex] S = 2,304\pi ~m^2 [/tex]

Answer: First choice V = 18,432π m^3; S = 2,304π m^2

Correct  Option 2: The volume of the sphere is 972π cm³ and its surface area is 324π cm²

To determine the volume and surface area of a sphere, we use the formulas:

Given the radius (r) of the sphere is 9 centimeters:

Hence, the volume of the sphere is 972π cm³ and the surface area is 324π cm².

Answer:

-35/7

3/-1

Step-by-step explanation:

If you divide a positive number by a positive number

the outcome will be positive

If you divide a positive number by a negative number the outcome will be negative

If you divide a negative number by a negative number the outcome will be positive

If you have any questions do not hesitate to ask

:)

3/-1 is also a solution

Answer:

Part 1) 0.669

Part 2) x=23.78 cm

Step-by-step explanation:

Part 1) we have

cos(48°)

Using a calculator

cos(48°)=0.66913

Round to the nearest thousandth

0.66913=0.669

Part 2) we know that

In the right triangle of the figure

The cosine of angle of 18 degrees is equal to divide the adjacent side to the angle of 18 degrees by the hypotenuse of the right triangle

so

cos(18°)=x/25

x=(25)cos(18°)=23.78 cm

Answer:

Use a calculator to find the cos 48° to the nearest thousandth: A. 0.669

Find the value of x in the triangle below to the nearest hundredth.: B. 23.78 cm

Step-by-step explanation:

I just did these questions and these were the answers that were right for me. Hope this helps!

Answer:

$27.99 interest.

Step-by-step explanation:

Use the formula for Compound interest = P(1 + r/n)^t  . Here n = 365 (number of days in a year), r = annual rate as a decimal and t = the number of days, P = 8000.

Amount after 15 days = 8,000(1 + 0.085/365)^15

= $8027.99.

Final answer:

Charlie will earn interest on his $8,000 investment at an 8.5% annual rate, compounded daily, for 15 days. The interest can be calculated using the formula for compound interest and will likely result in slightly more interest earned than if it was calculated using simple interest.

Explanation:

Charlie can invest $8,000 at 8.5% interest for 15 days. To calculate the interest earned with daily compounding, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($8,000), r is the annual interest rate (8.5%), n is the number of times that interest is compounded per year (365, since it's daily), and t is the time the money is invested in years (15/365, because here t is 15 days).

By substituting the values into the formula we get: A = $8,000(1 + 0.085/365)365*(15/365). After computing this, we find the new amount that Charlie will have after the 15 days are over. The interest earned is then found by subtracting the principal ($8,000) from this new amount.

Note that compound interest, especially when compounded frequently, can lead to greater earnings than simple interest. This difference is more pronounced with larger amounts and over longer periods, as shown by the reference provided where compound interest for a $100 investment over three years was $0.76 more than with simple interest.

Answer:

The selected answers are correct.

Step-by-step explanation:

The first step of the 3-step test for continuity is

The second step of the 3-step test for continuity is

The third step is

Answer:

The length of the diagonal of the cube = √(3 × 10²) = √300 cm

Step-by-step explanation:

* Lets revise the properties of the cube

- It has six equal faces all of them are squares

- It has 12 vertices

- The diagonal of the cube is the line joining two vertices in opposite

 faces (look to the attached figure)

- To find the length of the diagonal do that:

# Find the diagonal of the base using Pythagoras theorem

∵ The length of the side of the cube is L

∵ The base is a square

∴ The length of the diagonal d = √(L² + L²) = √(2L²)

- Now use the diagonal of the base and a side of a side face to find the

 diagonal of the cube by Pythagoras theorem

∵ d = √(2L²)

∵ The length of the side of the square = L

∴ The length of the diagonal of the cube = √[d² + L²]

∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root

∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)

* Now lets solve the problem

∵ The length of the side of the square = 10 cm

∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm

- Note: you can find the length of the diagonal of any cube using

 this rule Diagonal = √(3L²)

Answer:

its c on endeguity

Step-by-step explanation:

Answer:

B) 10.6 cubic inches

Step-by-step explanation:

Vol = (1/3) base area × hight = (1/3)π×1.5²×4.5

To be in the tallest 5% of adult males in Croatia, given a mean height of 180 cm and a standard deviation of 7 cm, the required height would be about 191.515 cm.

The question is related to the concept of normal distribution in statistics. Given that the heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm, we are asked to calculate the height a male would need to be in the tallest 5% of males.

We use the z-score to solve this. The z-score associated with the top 5% of a standard normal distribution is approximately 1.645 (you can find this in a standard z-table or through a statistical calculator).

To find the height associated with this z-score, we use the formula: X = μ + zσ, where X is the measurement we seek, μ is the mean, z is the z-score, and σ is the standard deviation. Substituting the given values, we get:

X = 180 cm + 1.645 * 7 cm

X = approximately 191.515 cm

So, to be in the tallest 5% of males in Croatia, an adult male would have to be about 191.515 cm or taller.

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An adult male in Croatia must be approximately 190.5 cm tall to be in the tallest 5% of the males.

To find out how tall an adult male in Croatia must be in order to be the tallest 5% of the males, we need to find the z-score corresponding to the upper 5% tail of the standard normal distribution.

Using the z-score formula, z = (x - mean) / standard deviation, we can solve for x.

Plugging in the values, we have z = (x - 180) / 7. Now, we can find the z-score corresponding to the upper 5% tail, which is approximately 1.645.

Substituting this value back into the z-score formula, we have 1.645 = (x - 180) / 7. Solving for x, we find that x is approximately 190.5 cm.

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Answer:

Step-by-step explanation:

Here the coefficients are a = 2, b = 3 and c = -7.

Thus, the discriminant b²-4ac is 3²-4(2)(-7), or 9 + 56 = 63.

Because the discriminant is positive, we know we have two real, different roots.  They are:

      -3 ± √63         -3 + 3√7                      -3 - 3√7

x = ---------------- = -----------------  and  x = -----------------

          2(2)                   4                                   4

If 5 equals 1

then 100 will equal 20

the shoes are 20 dollars

Answer:

$20.00 is the correct answer

Step-by-step explanation:

I promise this is correct

Answer:

sin 2Ф = -24/25

Step-by-step explanation:

* Lets revise the trigonometry functions in the four quadrants

# First quadrant the measure of all angles is between 0° and 90°  

∴ All the angles are acute  

∴ All the trigonometry functions of any angle are positive

# Second quadrant the measure of all angles is between 90° and 180°

∴ All the angles are obtuse

∴ The value of sin of any angle is positive (cos and tan are negative)

# Third quadrant the measure of all angles is between 180° and 270°

∴ All the angles are reflex

∴ The value of tan of any angle is positive (sin and cos are negative)

# Fourth quadrant the measure of all angles is between 270° and 360°  

∴ All the angles are reflex

∴ The value of cos any angle is positive ( sin and tan are negative)

* We will need to revise two identity to solve the question

# sin²Ф + cos²Ф = 1

# sin 2Ф = 2 sinФ cosФ

* Now lets solve the question

∵ cosФ = 3/5

∵ Ф is in the fourth quadrant

∴ The value of sinФ is negative

∵ sin²Ф + cos²Ф = 1

∴ sin²Ф + (3/5)² = 1

∴ sin²Ф + 9/25 = 1 ⇒ subtract 9/25 from both sides

∴ sin²Ф = 16/25 ⇒ take √ for both sides

∴ sinФ = ± 4/5

- We will chose the value -4/5 because Ф is in the fourth quadrant

∴ sinФ = -4/5

∵ sin 2Ф = 2 sinФ cosФ

∵ sinФ = -4/5 and cosФ = 3/5

∴ sin 2Ф = 2 (-4/5) (3/5) = -24/25

Answer:

259.8 cm²

Step-by-step explanation:

A regular hexagon can be cut into 6 equilateral triangles and an equilateral triangle can be divided into two 30°- 60°- 90° triangles

Note that the apothem (5[tex]\sqrt{3}[/tex]) divides the triangle into two equilateral triangles, thus

The apothem is the long leg (the x[tex]\sqrt{3}[/tex]) side of a 30- 60- 90 triangle, so

x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex] ⇒ x = 5

Thus the side length of the hexagon = 2 × 5 = 10

and the perimeter = 6 × 10 = 60

A = [tex]\frac{1}{2}[/tex] × perimeter × apothem

   = 0.5 × 60 × 5[tex]\sqrt{3}[/tex] = 150[tex]\sqrt{3}[/tex] ≈ 259.8 cm²

Answer:

1677

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) p=0.35 and q = 0.65

Std error =[tex]\sqrt{\frac{0.35*0.65}{n} }[/tex]

Margin of error = 2.58*std error = 3%

i.e. [tex]2.58*0.477/\sqrt{n}= 0.03\\n = 1683\\[/tex]

Approximately 1677

2) Same method as above

Margin of error = 1.645 * [tex]\sqrt{\frac{0.85(0.15)}{n} }[/tex]=0.02

Hence n = 863

3) Margin of error = 1.96*[tex]\sqrt{\frac{0.45(0.55)}{875} }[/tex]

=0.0329

=0.033

(option d)

Answer:

Option c.) the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Step-by-step explanation:

step 1

Find the volume of one ball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}[/tex]

therefore

The volume of two balls is

[tex](2)*14.13=28.26\ in^{3}[/tex]

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]h=1.5*4=6\ in[/tex]

substitute

[tex]V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}[/tex]

therefore

The wasted space with the cylinder is equal to

[tex]42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}[/tex]

step 3

Find the volume of the square prism

The volume of the square prism is equal to

[tex]V=b^{2}h[/tex]

we have

[tex]b=1.5*2=3\ in[/tex]

[tex]h=1.5*4=6\ in[/tex]

substitute

[tex]V=(3)^{2}(6)=54\ in^{3}[/tex]

therefore

The wasted space with the prism is equal to

[tex]54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}[/tex]

step 4

Find the difference of the wasted space

[tex]25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}[/tex]

Answer:

C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Step-by-step explanation:

if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.

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Answer:

The solution is  (2,6)

Step-by-step explanation:

Let

x-----> the number of hours to change a fuel injection unit

y-----> the number of hours to change a transmission

we know that

5x+10y=70 -----> equation A

8x+8y=64 -----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (2,6)

see the attached figure

Answer:

Step-by-step explanation:

[tex]\text{We have the recursive form of sequence:}\\\\a_1=50\\a_n=a_{n-1}+(-4)=a_{n-1}-4\\\\a_2=a_{2-1}-4=a_1-4\to a_2=50-4=46\\a_3=a_{3-1}-4=a_2-4\to a_3=46-4=42\\a_4=a_{4-1}-4=a_3-4\to a_4=42-4=38\\a_5=a_{5-1}-4=a_4-4\to a_5=38-4=34[/tex]