Consider the complex number z = -7 + 5i.

The real part of the complex number is _____.
(-2, 5i, 5, or 7)

The imaginary part of the complex number is _____.
(-2, 5i, 5, or 7)

Answer:

Same length

24 ÷ 2=12

There is 12 inches in a foot

1 + 1= 2 ft

24 inches = 2 feet

Answer:

The length of the shelf will be less than 24 in feet. It will be 2 feet long.

Step-by-step explanation:

Inches are a smaller unit than feet, meaning that when something is measured in inches, the numerical amount of inches will be higher than the numerical amount of feet. The ratio is 12 inches to 1 foot, meaning that even though the length may be the exact same, inches represents the length with a higher numerical value and feet represent the length with a lower numerical value.

Answer:

C. 270

Step-by-step explanation:

If there are 10 millimeters in 1 centimeter, that means there is 10 times the number of millimeters in a centimeter. So, we would multiply 27 centimeters by 10 to find the number of millimeters.

Answer:

Li Jing

Step-by-step explanation:

Given the sequence:

-5,-25,-125,-625,...

Mohamed's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n}}[/tex]

Using Mohamed's formula:

[tex]When\: n=1,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{1}=-25\\When\: n=2,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{2}=-125\\[/tex]

Li Jing's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n-1}}[/tex]

Using Mohamed's formula:

[tex]When\: n=1,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{1-1}=-5\\When\: n=2,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{\large{2-1}}=-25\\[/tex]

We can see that Li Jing's Formula produces the gien sequence.

Li Jing is Right.

Answer:

Only Li Jing

Step-by-step explanation:

This is because the formula −5 * 5 is worng as the first term is reapeated again so it is Li Jing

Answer:

0.18

Step-by-step explanation:

Answer:

9/50

Step-by-step explanation:

0.1 is the equivalent of 1/10

You multiply:

[tex]\frac{3}{7} *\frac{1}{10}[/tex]

= [tex]\frac{3}{70}[/tex]

[tex]\frac{3}{70}[/tex]÷[tex]\frac{5}{21}[/tex]  is the equivalent of

[tex]\frac{3}{70}* \frac{21}{5}[/tex]

which equals [tex]\frac{63}{350}[/tex], or [tex]\frac{9}{50}[/tex] simplified (divide both sides by 7)

To solve the problem, use the concept of differential equations and solve for the rate of water leakage. Then, find the time at which the tank will be half empty and the volume of water after 4 days.

To solve this problem, we can use the concept of differential equations. Let's denote the volume of water in the tank at any time t as V(t). We are given that the rate at which water leaks is proportional to the square root of the remaining volume, so we can write the differential equation:

dV/dt = k * sqrt(V)

Where k is the proportionality constant. We also know that during the first day, 20 liters leak out, so we can find k:

dV/dt = k * sqrt(350) = -20

Now, we can solve this differential equation to find the time at which the tank will be half empty, and the volume of water after 4 days.

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The tank will be half empty (175 liters remaining) after approximately 3.6 days, and there will be about 135 liters of water remaining after 4 days. The problem involves solving differential equations relating to the leak rate being proportional to the square root of the remaining volume.

This problem involves solving a differential equation based on the rate at which water leaks out of a cylindrical tank. The leak rate is proportional to the square root of the volume of water remaining in the tank.

Differential Equation and Initial Conditions

Given:

Where k is a constant. To find k, we use the initial conditions:

At t = 1 day,

V = 350 - 20

= 330 liters.

∫dV/√V = [tex]-k\int_{V_0(350)}^{V(330)} dt \quad \text{from} \quad t=0 \quad \text{to} \quad t=1[/tex]

[tex]2\sqrt{V}\Bigg|_{350}^{330} = -kt\Bigg|_{0}^{1}[/tex]

2(√330 - √350) = -k(1)

k ≈ 2(√350 - √330)

Finding When the Tank is Half Empty

Half of the initial volume is 350/2 = 175 liters.

We need to find t when V = 175.

[tex]2\left(\sqrt{V}\Bigg|_{350}^{175}\right)[/tex] = -kt

2(√350 - √175) = kt

Substituting k, we get t ≈ 3.6 days.

Volume After 4 Days

[tex]2\left(\sqrt{V}\Bigg|_{350}^{V}\right)[/tex] = -k(4)

2√V = 2√350 - 4k

Solving for V, we find V ≈ 135 liters.PJ11

Answer:

The solution for the system is the pair (6,1).

Step-by-step explanation:

The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:

2x-4y = 8

x + y = 7 *(-2)

2x - 4y = 8

-2x -2y = -14

We now sum boh equations:

2x -2x -4y -2y = 8 -14

-6y = -6

y = -6/-6 = 1

2x - 4(1) = 8

2x - 4 = 8

2x = 8 + 4

2x = 12

x = 12/2 = 6

The solution is the pair (6,1).

Answer:

The system has 2 solution .

Step-by-step explanation:

The equation is a simultaneous equation

2x - 4y=8 ............(i)

x + y=7................(ii)

make x the subject of the formula in equation (ii)

x = 7 - y

Substitute the value of x in equation(i)

2(7 - y) - 4y = 8

14 - 2y - 4y = 8

14 - 6y = 8

-6y =  8 - 14

-6y = -6

divide both sides by -6

y = 1

insert the value of  in equation (ii)

x + y = 7

x + 1 = 7

x = 7 - 1

x = 6

The system has 2 solution .

Answer:

19 meters

Step-by-step explanation:

The area of a circle is given as [tex]90.25\pi[/tex]

-A circle's area is calculated using the formula:

[tex]A=\pi r^2, r=0.5D, D=Diameter[/tex]

#We substitute for area in the equation and solve for D;

[tex]A=\pi (0.5D)^2\\\\90.25\pi=\pi (0.5D)^2\\\\\sqrt{90.25}=0.5D\\\\D=19[/tex]

Hence, the circle's diameter is 19 meters

Diameter of a circle = 19 meters

Circle is a rounded figure that consists of points that are equidistance from the center

Area of a circle is the area enclosed by the circle . The distance between the center to the circumference of circle is the radius.

Diameter is a straight line from one end of circle to the other end and it passes through the center of the circle

Given that area of the circle is 90.25 pi square meters

Area of the circle formula is

[tex]Area = \pi r^2\\90.25\pi =\pi r^2\\divide \; both \; sides \; by \; pi\\90.25=r^2\\take \; square \; root \; on \; both \; sides\\r=\sqrt{90.25}\\ r=9.5[/tex]

diameter of the circle = 2 times of the radius

Diameter = 2 times 9.5=19 meters

Diameter of a circle = 19 meters

Learn more information about 'Circle' here :

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Answer:

△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY ?

A.XY/TS

B.SY/RY

C.RX/XT

D.ST/YX

Step-by-step explanation:

Check attachment for solution

Answer:

D

Step-by-step explanation:

Steps to simplify:

2x - 1 / x

~Convert to fraction

2xx/x - 1/x

~Combine the fractions

2xx-1/x

~Simplify

2x²-1/x

Best of Luck!

Answer:

1 small bags and 5 large bags

Step-by-step explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: number of small bag

let y: number of large bag

So:

5 * x + 8 * y = 45

x + y = 6 => x = 6 - y

Replacing, we are left with that:

5 * ( 6 - y) + 8 * y = 45

30 - 5 * y + 8 * y = 45

- 5 * y + 8 * y = 45 - 30

3 * y = 15

y = 15/3

y = 5

Now to calculate x:

x = 6 - 5

x = 1

this means that 1 small bag and 5 large bags

Answer:

he bought 1 bag of small apple and 5 bags of Large apple

Step-by-step explanation: given that A small bag of apples = $5 and

A large bag = $8.

If you bought 6 bags and spent $45,

Let number of small apple be S

And large Apple be L

L + S = 6 ....... (1) ×8

8L + 5S = 45 .......(2)

Solve equation 1 and 2 simultaneously

8L + 8S = 48

8L + 5S = 45

Eliminate L

3S = 3

S = 1

Substitute S in equation 1

L = 6 - 1 = 5

Therefore, he bought 1 bag of small apple and 5 bags of Large apple

Answer:

The height of Sydney opera house in the model is 2.13 feet.

Step-by-step explanation:

We are given the following in the question:

Height of Sydney opera house = 213 feet

Height in model =

[tex]\dfrac{1}{100}\text{ of the actual height}[/tex]

We have to evaluate the height of Sydney opera house in model.

Height in model =

[tex]=\dfrac{1}{100}\times 213\\\\=2.13\text{ feet}[/tex]

Thus, the height of Sydney opera house in the model is 2.13 feet.

12 bottles of paint does she need to paint 70 ornaments. Hence 12 is correct answer.

1. Calculate the surface area of one cone:
The surface area of a cone is the sum of the area of the base (a circle) and the lateral surface area. Since the cone is cut in half vertically, we only need to consider half of the base and lateral surface area.
Base area: The base is a circle with radius r. The area of a circle is πr². Since the cone is cut in half, the base area is πr² / 2.
Lateral surface area: The lateral surface area is a sector of a circle with radius r and arc length equal to the circumference of the base. The circumference of the base is 2πr. The area of a sector is (arc length × radius) / 2. In this case, area of sector is (2πr×r) / 2 = πr^2.
Therefore, total surface area of one cone is (πr²/ 2) + πr² = 3πr² / 2.
2. Calculate the surface area of one ornament:
Since each ornament is made up of two identical cones, the surface area of one ornament is twice the surface area of one cone. Therefore, the surface area of one ornament is 2×(3πr² / 2) = 3πr^2.
3. Calculate the total surface area of all ornaments:
If Donna needs to paint 70 ornaments, the total surface area she needs to cover is 70×3πr² = 210πr².
4. Convert the surface area to square meters:
However, if you provide the radius in meters, you can multiply the surface area you calculated in 3 by 1 to convert it to square meters.
5. Estimate the number of bottles of paint needed:
The total surface area in square meters, you can estimate the number of bottles of paint Donna needs by dividing the surface area by the coverage area of one bottle of paint. This information is typically available on the paint bottle itself. For example, if one bottle of paint covers 10 square meters, and the total surface area of the ornaments is 210 square meters, Donna would need approximately 210 square meters / 10 square meters/bottle = 21 bottles of paint.

Answer:

The answer to your question is 4 times bigger.

Step-by-step explanation:

Data

radius = 5 cm

height = 16 cm

Cylinder 2, 4 times taller the radius is the same

Process

1.- Calculate the volume of the first cylinder

Volume 1 = πr²h

-Substitution

Volume = π(5)²(16)

-Simplification

Volume = 400π cm³

2.- Calculate the volume of the second cylinder

height = 4(16)

           = 64

-Substitution

Volume = π(5)²(64)

-Simplification

Volume 2 = 1600π cm³

3.- Find the relationship between the volume

Volume 2 / volume 1 = 1600π / 400π

                                   = 4

4.- The second cylinder is 4 times bigger than the first cylinder

Answer:

m=8

Step-by-step explanation:

-40 divided by -5

Your answer is 8

Answer:

8m would be the answer

Step-by-step explanation:

-5m/-5  = -40/5 = positive 8

Answer:

Null hypothesis: [tex] p_1 = p_2[/tex]

Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]

So we need to conduct a:

D. A two-sample z-test for a difference in population proportions

Because the idea is to check if the population proportions in the states are similar or not.

Step-by-step explanation:

For this case they are trying two proof if there is a significant difference between two states in the percents of high school students who order yearbooks, and we chan check this with the difference of proportions.

Lets say that [tex]p_1,p_2[/tex] are the two proportions of interest and we want to check the following hypothesis:

We have the following info given:

[tex]\hat p_1 = \frac{70}{150}= 0.47[/tex] proportion of students that had ordered a yearbook from one state

[tex]\hat p_2= \frac{65}{100}= 0.65[/tex] proportion of students that had ordered a yearbook from another state

[tex]n_1 = 150[/tex] sample size from one state

[tex]n_2=100[/tex] sample size from another state

Null hypothesis: [tex] p_1 = p_2[/tex]

Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]

So we need to conduct a:

D. A two-sample z-test for a difference in population proportions

Because the idea is to check if the population proportions in the states are similar or not.

Answer:

320,000 people / km²

Step-by-step explanation:

We need to find the area of the city first.

The area of a triangle is: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.

Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:

[tex]A=\frac{1}{2} bh[/tex]

[tex]A=\frac{1}{2} *25*25=312.5[/tex] km²

Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:

100,000,000 ÷ 312.5 = 320,000 people / km²

Answer:

320,000 people per km²

Step-by-step explanation:

Since two angles are equal, their opposite lengths are also equal

Assuming it's a right ankle triangle,

Area = ½ × 25 × 25 = 312.5 km²

Population density:

100,000,000/312.5

320,000

To calculate the difference in area between two circular pizzas, first compute the area of each using the formula A = πr². After finding the areas, subtract the smaller area from the larger one to find the difference. The result is approximately 201 square inches.

The question involves calculating the area of two circles and finding the difference between the two. First, we need to find the radius of each pizza. Since the diameter is twice the radius, the large pizza has a radius of 10 inches (20 inches divided by 2), and the small pizza has a radius of 6 inches (12 inches divided by 2). The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159, and r is the radius.

The area of the large pizza is A = π(10 inches)² = π * 100 inches² = 314.16 inches² (rounded to two decimal places). The area of the small pizza is A = π(6 inches)² = π * 36 inches² = 113.10 inches² (rounded to two decimal places). To find the difference, we subtract the area of the small pizza from the area of the large pizza, which gives us 314.16 inches² - 113.10 inches² = 201.06 inches², which is closest to 201 inches².

Answer:

16

Step-by-step explanation:

a coin is 2 sided thus has 2 out comes so doing it 8 times = 16 outcomes

Answer:

It is the first choice. (A)

Step-by-step explanation:

Red line: y = 2x + 1

Blue line: y = -4x + 7

Answer:

C

Step-by-step explanation:

Since this is an indererminate form, use L'Hopital

d(sint)/dt = cos(t)

d[ln(2e^t) - 1] = (2e^t)/[2e^t - 1]

As t --> 0,

cos(0) = 1

(2e^t)/[2e^t - 1] = 2

1/2 is the limit

Answer:

0.083 is the required probability.

Step-by-step explanation:

We are given the following in the question:

Probability of captain hitting pirate's ship =

[tex]P(A) = \dfrac{1}{2}[/tex]

Probability of pirate hitting the captain's ship =

[tex]P(B) = \dfrac{1}{6}[/tex]

Probability that both the pirate and the Captain hit each other's ships:

[tex]P(A\cap B) = P(A)\times P(B)[/tex]

Putting values, we get,

[tex]P(A\cap B) =\dfrac{1}{2}\times \dfrac{1}{6} = \dfrac{1}{12} \\\\P(A\cap B) = 0 .083[/tex]

0.083 is the probability that both the pirate and the Captain hit each other's ships.

Answer:

The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.

Step-by-step explanation:

The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.

The company wants to test the claim.

Let the mean amount of liquid that the bottles are said to hold be, μ₀.

The hypothesis for this test can be defined as follows:

H₀: The mean amount of liquid that the bottles can hold is μ₀, i.e. μ = μ₀.

Hₐ: The mean amount of liquid that the bottles can hold is less than  μ₀, i.e. μ < μ₀.

The p-value of the test is, p = 0.054.

Decision rule:

The null hypothesis will be rejected if the p-value of the test is less than the significance level. And vice-versa.

        The p-value = 0.054 > α = 0.01.

        The null hypothesis was failed to be rejected at 1% level of

        significance. Concluding that the mean amount of liquid that the

         bottles can hold is μ₀.

        The p-value = 0.054 > α = 0.05.

        The null hypothesis was failed to be rejected at 5% level of

        significance. Concluding that the mean amount of liquid that the

         bottles can hold is μ₀.

        The p-value = 0.054 < α = 0.10.

        The null hypothesis will be rejected at 10% level of

        significance. Concluding that the mean amount of liquid that the

         bottles can hold is less than μ₀.

Answer: ok so for 5 and 125 it is 65 and 25

for 1 and 9 it is 5 and 3 and for 4 and 9 it is 13/2 and 6

Answer:

-1.596

Step-by-step explanation:

4^(x + 3) = 7

log4 both sides

log4[4^(x + 3)] = log4(7)

(x + 3) × log4(4) = lg7/lg4

x + 3 = 1.403677461

x = -1.596322539

Answer:

Area= (3x+4)×(x+3)

Step-by-step explanation:

(3x^2+10x+12)feet

Answer:

3x² + 13x + 12 ft²

Step-by-step explanation:

To work out the area of a rectangle you have to multiply the length and width together. In this case the length is 3x + 4 and the width is x + 3

So

( 3x + 4 ) × ( x + 3 )

Remember FOIL when expanding brackets

F = First two so 3x × x = 3x²

O = Outer two so 3x × 3 = 9x

I = Inner two so 4 × x = 4x

L = Last two so 4 × 3 = 12

but we aren't finished

3x² + 9x + 4x + 12 = 3x² + 13x + 12

Don't forget unit! ft²

Answer:

Upper level = 2502 seats

Middle level = 5044 seats

Lower level = 7456 seats

Step-by-step explanation: given that

A baseball stadium holds 15,002 seats.

Let the Upper, middle and lower levels be represented as U, M and L respectively. And x = number of seat at the upper level

The lower level has 50 fewer than three times as many seats as the upper. That is

L = 3x - 50 .... (1)

The middle level has 40 more than twice as many seats as the upper level. That is

M = 2x + 40

Where L = x

x+ (2x + 40) + (3x - 50) = 15,002

You solved for x and found out the upper level has 2,502 seats . How many seats are in the lower level and how many seats are in the middle ?

That is x = 2502

Substitute x into equation 1

L = 3(2502) - 50

L = 7456 seats

Substitutes x into equation 2

M = 2(2502) + 40

M = 5044 seats

Answer:

212

Step-by-step explanation:

47 goes into 99 2 times

Bring down the 5

47 goes into 56 1 time

Bring the 9

47 goes into 94 2 times

Answer:

1

Step-by-step explanation:

he cant earn 400 dollars because 8*40 is 320. if he cant work more than eight hours, theres no possible way he can earn 400 dollars ('least in a math equation).

i love brainless tttree

Answer: 57 child tickets were sold that day.

Step-by-step explanation:

Let x represent the number of child tickets that were sold.

Let y represent the number of adult tickets that were sold.

on Friday, 155 tickets were sold. It means that

x + y = 155

At the city museum, child admission is $5.70 and adult admission is $9.50. The ticket sales totaled $1255.90 on that day. It means that

5.7x + 9.5y = 1255.9- - - - - - - - - 1

Substituting x = 155 - y into equation 1, it becomes

5.7(155 - y) + 9.5y = 1255.9

883.5 - 5.7y + 9.5y = 1255.9

- 5.7y + 9.5y = 1255.9 - 883.5

3.8y = 372.4

y = 372.4/3.8

y = 98

x = 155 - y = 155 - 98

x = 57

Answer:

the correct volume is 120in.3

Step-by-step explanation:

he did his math wrong, 20 x 6 is not 26.

V = 5 x 4 x 6 = 20 x 6 = 120

Answer:

He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.

Step-by-step explanation:

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