100 POINTS!! I need help with the explanation.

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

Learn more about ratios here:

https://brainly.com/question/19220252

#SPJ1

To obtain a smaller margin of error, choose a smaller confidence level.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error

z = found by using a z-score table

SD = sample standard deviation

n = sample size

Based on the formula, to reduce the margin of error, the z-score, z, must be small. In order to have a smaller value of z, the probability, p, should also be small. And to obtain a small probability, choose a smaller confidence level.

Hence, to reduce the margin of error, use a lower confidence level.

Learn more about margin of error here: brainly.com/question/10218601

#SPJ4

Answer:

6

Step-by-step explanation:

pizza has rotational symmetry of 60 degrees. Thus, the order of symmetry will be 6.

\(numerical \: coefficient \: = > 7 \\ \\ literal \: coefficient \: = > \: xy\)

hope that helps uh..☺

Answer:

10, 5, .75, π

Step-by-step explanation:

Answer:

10, 5, .75, π

Step-by-step explanation:

Therefore, the volume of a single Rh atom is approximately 1.011 × 10^(-29) m^3.

The diameter of a single Rh atom is given as 2.7 × 10^(-8) cm. The radius of the atom, which is half of the diameter, is therefore:

r = 2.7 × 10^(-8) cm / 2 = 1.35 × 10^(-8) cm

To find the volume of the sphere, we can use the formula:

V = (4/3)πr^3

where π is the constant pi.

Substituting the values, we get:

V = (4/3)π(1.35 × 10^(-8) cm)^3

= 1.011 × 10^(-23) cm^3

However, the answer is required in m^3, so we need to convert cm^3 to m^3. We know that:

1 cm = 0.01 m

Therefore:

(1 cm)^3 = (0.01 m)^3

1 cm^3 = 1 × 10^(-6) m^3

Substituting this conversion factor, we get:

V = 1.011 × 10^(-23) cm^3 × 1 × 10^(-6) m^3/cm^3

= 1.011 × 10^(-29) m^3

To know more about volume,

https://brainly.com/question/1565950

#SPJ11

The required number of revolution for small gear is 2

The given figure is a  circle,

Then,

Radius of big circle = 7

radius of small circle = 3

Since we know that perimeter of circle = 2πr

Therefore,

Perimeter of big circle = 2x7x(22/7)

                                     =  44 square units

Perimeter of small circle = 2x3x(22/7)

                                     =  18.84 square units

Now the umber of revolution for small gear to complete a single revolution of the larger gear = 44/18.84 = 2.33 ≈ 2

Hence, number of revolution = 2.

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

2×\(10^{8}\)

or

200000000

Step-by-step explanation:

\(\frac{6.28*10^{12} }{3.14*10^4}\)

2×\(10^{8}\)

or

200000000

First, we multiply the numbers : 10 x 5 = 50

Now, we multiply r squared to r^6. To do this, we add the index numbers together : r^2 x r^6 = r^(2+6) = r^8

So, the answer is 50r^8, or b.

The dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

What is the rectangular dimension?

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.

We have,

volume L* W * H = 512 cm³

sides of the box cost = 1 cent/cm²

top and bottom cost 2 cent/cm²

to find out

dimensions of the box that minimize the total cost of material use

we know here,

L* W * H = 512 cm³

where,

L is length and W is width and H is the height

so when we minimize the cost function

C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W

so put here H

substitute  \(H = \frac{512}{LW}\) we get,

C(L, W) = 512(\(\frac{1}{l}, \frac{1}{W}\)) + 2LW

so

minimum cost will be when the two partial derivatives is 0

dC/dL = 2W - 512/L² = 0

so

dC/dW = 2L - 512/W² = 0

L =  256/W²

so

by solving the above equation we get

L = W = (256)⁻³ = 16cm

and

H = 512/16 = 32

H =  32 cm

Hence, the dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

To learn more about the rectangular dimension visit,

https://brainly.com/question/27404871

#SPJ4

An irrational number is a real number that cannot be expressed as a ratio of integers. The decimal expansion of an irrational number is neither terminating nor recurring.

Let us check the options one at a time:

OPTION A: -√196

5 )

x^2 = 5^2 + 5^2

x^2 = 2 × 5^2

x = √( 2 × 5^2 )

x = 5√2 cm

_____________

6 )

x^2 = 30^2 + 40^2

x^2 = 900 + 1600

x^2 = 2500

x = √2500

x = 50 yards

The system of inequalities is y ≤ 32 - x and y ≥ (168 - 15x)/25.

Jordan is working for two summer jobs. The amount made per hour by walking dogs is $15. The amount made per hour by clearing tables is $25. Jordan can work for a maximum of 32 hours a week. He must earn at least $168.

The number of hours spent walking dogs is represented by "x". The number of hours spent clearing tables is represented by "y". The inequalities formed are :

x + y ≤ 32

15x + 25y ≥ 168

The graph of the common shaded region is attached below. The solutions lie in the first quadrant, where the region is shaded for both the inequalities.

To learn more about inequalities, visit :

https://brainly.com/question/28823603

#SPJ1

Answer:

slope = -  \(\frac{3}{2}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 7 ) and (x₂, y₂ ) = (- 7, 13 )

m = \(\frac{13-7}{-7-(-3)}\) = \(\frac{6}{-7+3}\) = \(\frac{6}{-4}\) = - \(\frac{3}{2}\)

Answer:

C) (1,0), and (-3,0)

Step-by-step explanation:

The parabola intercepts the x axis at points (1,0) and (-3,0).

your answer is

C) (1,0), and (-3,0)

have a good dayyy!

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653, which is equivalent to 65.3%.

It is important to note that this value is based on a random sample of respondents and may not necessarily represent the true proportion of the entire population of Vermont who exercise regularly.

To find the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week, follow these steps:

1. Convert the given percentage (65.3%) to a decimal by dividing by 100: 65.3 / 100 = 0.653
2. Multiply the decimal by the number of participants in the random sample (100 respondents): 0.653 * 100 = 65.3
3. Round the result to the nearest whole number to find the number of participants who exercised: 65.3 ≈ 65
4. Divide the number of participants who exercised (65) by the total number of participants in the random sample (100): 65 / 100 = 0.65

This means that out of the 100 participants sampled from Vermont, 65.3 of them answered "yes" to the question of whether they had exercised for more than 30 minutes a day for three days out of the week.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.65 or 65%.

Learn more about sample proportion here:

brainly.com/question/29912751

#SPJ11

Answer:

4 degrees per hour

Step-by-step explanation:

48 degrees per 12 hours = 48/12 degrees per hour = 4 degrees per hour

Answer: Choice B)   sin (33) = x/14

This is because the sine of an angle is equal to the opposite side over the hypotenuse

sin(angle) = opposite/hypotenuse

sin(33) = x/14

We can't use cosine because we don't have a variable for the adjacent side.

Answer:

32mm

Step-by-step explanation:

6 + 8 + 6 + 12 = 32mm

Answer:

Step-by-step explanation:

a = base

b = base

c = side

d = side

The given argument is " If x is a positive real number, then x² is a positive real number." is invalid. Because if a² is positive, it is not always true that a is a positive real number. The given argument is "  If x² ≠ 0, where x is a real number, then x ≠ 0. Let a be a real number with a² ≠ 0; then a ≠ 0." is valid argument. Because if a is real number so a² is also a real number.

If x is a positive real number, then x² is a positive real number. Therefore, if a² is positive, where a is a real number, then a is a positive real number. This is an invalid argument. The premise states that if x is a positive real number, then x² is a positive real number, which is true. However, the conclusion that if a² is positive, then a is a positive real number does not necessarily follow from the premise. For example, if a is -2, then a² is positive, but a is not a positive real number.

If x² ≠ 0, where x is a real number, then x ≠ 0. Let a be a real number with a² ≠ 0; then a ≠ 0. This is a valid argument. The premise states that if x² ≠ 0, then x ≠ 0, which is true since the only way for x² to be equal to zero is if x is equal to zero. The conclusion that if a² ≠ 0, then a ≠ 0 follows logically from the premise, since a is a real number and the same logic applies to a² as to x².

To know more about real number:

https://brainly.com/question/551408

#SPJ4

Answer:

19.995

Step-by-step explanation:

Answer:

-47

Step-by-step explanation:

-6(9) + 2(6) + 3 - 8

-54 + 12 + 3 - 8

-42 + 3 - 8

-39 - 8

-47

Answer:

A. √2 > 1

Step-by-step explanation:

A: The √2 is more than one but less than 2. It's approximated as 1.414. This answer choice is correct.

B: The √4 is 2, which is less than π. Pi is approximated as 3.141. Therefore, this answer choice is incorrect.

C: The √2 is less than pi but greater than one. It's approximated as 1.414. This answer choice is incorrect.

D: The √3 is less than 2 but greater than one. It's approximated as 1.732. Therefore, this is incorrect.

Therefore, the correct answer is A. √2 > 1.

Answer:

D.

Step-by-step explanation:

all numbers except d are pythagorean triples, hope this helps!!

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

Learn more about interest rate here:

https://brainly.com/question/14599912

#SPJ11

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

number = x = ?

Step 02:

x = number

5 * x + 8 = 10 + 3 * x

5x + 8 = 10 + 3x

5x - 3x = 10 - 8

2x = 2

x = 2 / 2 = 1

The answer is:

The number is 1

Answer:

(1/2)(4)(6)(12.5) = 12(12.5) = 150 ft²

To apply the Divergence Theorem, we need to first find the divergence of the vector field F:

div(F) = ∂/∂x(x²) + ∂/∂y(-y²) + ∂/∂z(z²)

= 2x - 2y + 2z

Next, we find the bounds for the region D by setting the two plane equations equal to each other and solving for z:

9 - x - y = 6 - x - y

z = 3

So the region D is bounded below by the xy-plane, above by the plane z = 3, and by the coordinate planes x = 0, y = 0, and z = 0. Therefore, we can set up the integral using the Divergence Theorem as follows:

∫∫F · dS = ∭div(F) dV

= ∭(2x - 2y + 2z) dV

= ∫₀³ ∫₀^(3-z) ∫₀^(3-x-y) (2x - 2y + 2z) dz dy dx

We can simplify this integral using the limits of integration to get:

∫∫F · dS = ∫₀³ ∫₀^(3-x) ∫₀^(3-x-y) (2x - 2y + 2z) dz dy dx

= ∫₀³ ∫₀^(3-x) [(2x - 2y)(3-x-y) + (2/3)(3-x-y)³] dy dx

= ∫₀³ [∫₀^(3-x) (2x - 2y)(3-x-y) dy + ∫₀^(3-x) (2/3)(3-x-y)³ dy] dx

Evaluating the two inner integrals, we get:

∫₀^(3-x) (2x - 2y)(3-x-y) dy = -x²(3-x) + (3/2)x(3-x)²

∫₀^(3-x) (2/3)(3-x-y)³ dy = (2/27)(3-x)⁴

Substituting these back into the integral and evaluating, we get:

∫∫F · dS = ∫₀³ [-x²(3-x) + (3/2)x(3-x)² + (2/27)(3-x)⁴] dx

= 9/5

Therefore, the net outward flux of the vector field F across the boundary of the region D is 9/5.

Learn more about  Divergence Theorem  from

https://brainly.com/question/17177764

#SPJ11