In the figure below, angle 1=(x+42)° and angle 2=2x° Find the angle measures.

Answer:

A number is odd

Step-by-step explanation:

Odd numbers are not completely divisible by 2.

The importance of knowing divisibility rules is that we can determine whether a number is divisible by certain numbers generally from 1 to 20 or not without actually dividing.

A number is divisible by 2 if it's unit digit is divisible by 2.

A number is divisible by 3 if the sum of the digits is divisible by 3.

A number is divisible by 4 if the last two digits is divisible by 4.

A number is divisible by 5 if its unit digit is 5 or 0.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if its unit digit is 0.

Given, If a number is odd, then it has a remainder of 1 when divided by 2.

So the numbers which are not completely divisible by 2 have a remainder and are odd numbers and numbers which are completely divisible by 2 with no remainder are even numbers.

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Answer:

x-525000+0

Step-by-step explanation:

Answer:

W > 2

Step-by-step explanation:

-2W + 17 < 13

-2W < -4

W > 2

The answer is x = 3 y=3. This can be solved by reorganising the equation 2x + 3y = 15, x-y=0.

This property is true for all real numbers, including integers, fractions, decimals, and any other real number. The Multiplication Zero Property states that the product of any number and zero is equal to zero.

Reorganising the equation:

2x + 3y = 15

x-y=0

To find the solution, multiply both parts of the equation by a multiplier, as in 2x+3y=15.

2(x-y)=0 x 2

Utilize the multiplicative distributional rule.

2x+3y=15

2x-2y=0 x 2

Application of the Multiplication Zero Property

2x+3y=15

2x-2y=0

Separate the two formulas: 2x+3y-(2x-2y)=15-0

2x+3y-2x+2y=15

Take the parentheses off

3+2=15

Expressions combined: 5y=5

Multiply both sides of the equation by the value of the variable: y = 15/5

Take out the joining piece. y=3

Substitute 0 for 2x-2x-2x in one of the computations.

2x-6=0 is used to determine the product.

In the calculation, 6 should be shifted to the left: 2x=6

Add the variable's value to both ends of the equation, then subtract it:

x = 6/2

Take out the intermediary: 2 = 3

The  answer is x = 3 y=3.

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The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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Answer:

$18.40

Step-by-step explanation:

To find 8% of $230, we first have to find 1% of $230.

230 ÷ 100 = 2.30

Because 1% of $230 is $2.30, to find 8% we multiply $2.30 by 8

2.30 x 8 = 18.4

8% of $230 is $18.40

Answer:

8377.6 yards

Step-by-step explanation:

The formula for the volume of a cone is V=1/3hπr²

then ->

\( \frac{1}{3} \times 20 \times \pi \times {20}^{2} = \frac{8000}{3} \pi = 8377.58041 \: yards\)

Answer:

Plz as i have exams

Step-by-step explanation:

Oh Almighty save me

Answer:

11x+6

Step-by-step explanation:

Using FOIL

(x+1)-(-2x-5)-original

F-first=(x+2x)=3x

O-outside=(x+5)=5x

I-inside=(1+2x)=3x

L-last=(1+5)=6

11x+6

Answer:

\(z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17\)  

The p value for this case would be given by:

\(p_v =P(z>3.17)=0.00076\)  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

\(\hat p=\frac{59}{400}=0.1475\) estimated proportion of defectives from the company B  

\(p_o=0.1\) is the value to verify

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:\(p \leq 0.1\)  

Alternative hypothesis:\(p > 0.1\)  

The statistic would be given by:

\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)  

Replacing the info given we got:

\(z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17\)  

The p value for this case would be given by:

\(p_v =P(z>3.17)=0.00076\)  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Answer: 158 feet

Step-by-step explanation: I’ve gotten this question right on a test.

The approximate perimeter of the pool will be 157.36 feet.

The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The perimeter of the shape is a combination of the perimeter of two small quarter circles, one big circle, and the sides of a rectangle. Then the perimeter is calculated as,

P = πr + 2L + w + πR

P = 3.14 x 9 + 2 x 35 + 12 + 3.14 x 15

P = 157.36 feet

The approximate perimeter of the pool will be 157.36 feet.

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Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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Answer:

Step-by-step explanation:

3 (w - 2) ≥ 10

3w - 6 ≥ 10

3w ≥ 16

w ≥ 16/3

Answer:

a) Interest owed after 78 days = $110.01

b) Amount owed after 78 days = $14410.01

Explanation:

a) The formula for calculating simple interest is expressed as

I = PRT

Where

I represents the interest earned after T years

P represents the principal or initial amount

R represents the interest rate

T represents the time in years

From the information given,

R = 3.6% = 3.6/100 = 0.036

P = 14300

T = 78 x 1/365 = 78/365

By substituting these values into the formula,

I = 14300 x 0.036 x 78/365

I = 110.01

Interest owed after 78 days = $110.01

b) Amount owed after 78 days = principal + interest

Amount owed after 78 days = 14300 + 110.01 = 14410.01

Amount owed after 78 days = $14410.01

Answer:

c+2c+12=75

c = 21

Steps:

c+2c+12=75

Simplify both sides of the equation.

c+2c+12=75

(c+2c)+(12)=75(Combine Like Terms)

3c+12=75

3c+12=75

Subtract 12 from both sides.

3c+12−12=75−12

3c=63

Divide both sides by 3.

Answer:

225%

2*24=48, with 6 leftover. 6 is 25% of 24, so 200% (From when we multiplied 24 by 2) plus 25% (from the remainder) = 225%

Answer:

Step-by-step explanation:

area = Area of rectangle 1 + area of rectangle 2 + area of rectangle 3 + area of triangle

=5 * 12 + 5*5 + 2*3 + (1/2)* 4 * 3

= 60 + 25 + 6 +6

= 97

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

q=8/3

Step-by-step explanation:

First, add 5/6 to both sides to get rid of -5/6 to get q=16/6 then simplify to q=8/3.

Answer:

\(q=2\frac{2}{3}\)

Step-by-step explanation:

The given equation consists of a fraction and a mixed number.

First, convert the mixed number into an improper fraction by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

\(q-\dfrac{5}{6}=1 \frac{5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{1 \cdot 6+5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{11}{6}\)

Now, add 5/6 to both sides of the equation to isolate q:

\(q-\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{11}{6}+\dfrac{5}{6}\)

\(q=\dfrac{11}{6}+\dfrac{5}{6}\)

As the fractions have the same denominator, we can carry out the addition by simply adding the numerators:

\(q=\dfrac{11+5}{6}\)

\(q=\dfrac{16}{6}\)

Reduce the improper fraction to its simplest form by dividing the numerator and denominator by the greatest common factor (GCF).  

The GCF of 16 and 6 is 2, therefore:

\(q=\dfrac{16\div 2}{6 \div 2}\)

\(q=\dfrac{8}{3}\)

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

\(q=2 \; \textsf{remainder}\;2\)

The mixed number answer is the whole number and the remainder divided by the denominator:

\(q=2\frac{2}{3}\)

Answer: The flowchart is shown below.

Explanation:

Each box is a different statement. The reason for the statement is provided below the box. The arrows on the flowchart direct the flow of how the proof is laid out. Typically the flow is left to right, top to bottom, or a mix of both. This is to match the reading order of many western countries. Though I would imagine the flow is reversed for countries that read from right to left.

The structure of any type of proof is to start with what you are given. Then use the previously established, or previously proven, theorems to make your way to what you want to prove.

In this case, we start off with MN and KL being parallel line segments. This is shown by the arrows on MN and KL. Because the segments are parallel, we then can determine these two facts:

Both of those will have the reasoning of "corresponding angles theorem"

We have two pairs of angles which are congruent. This then directly leads to the triangles being similar. Refer to the AA (angle angle) similarity theorem for more information.

Feel free to use symbols in place of some words. For example, instead of saying something like "Triangle NMJ is similar to Triangle LKJ", you could write \(\triangle \text{NMJ} \sim \triangle \text{LKJ}\)

If you're curious what app I used to make the flowchart, the app is called "LucidChart". They have 3 options: 1 free and the other 2 are paid versions. I went with the free version and it worked just fine. But it's up to you which you prefer most.

Romania's imports Worth will be equal to $76.17 billion after calculation.

The relations between imports, exports, and tariffs can be described by ...

\(0.06E +0.21I = $18.9603 .\) . . . . . total tariff revenue

\(I -E = 26.76\). . . . . . . . . . . . . . . . trade deficit

Solving the second equation for E gives ...

\(E = I -26.76\)

Substituting into the first equation yields ...

\(0.06(I -26.76) +0.21I = 18.9603\)

\(0.27I = 18.9603 +1.6056 = 20.5659\). . . . add 1.6056 to both sides

\(I = 10.5659/0.27 = 76.17\)

Hence Romania's imports are worth about $76.17 billion.

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Answer:

c. $76.17 billion

Step-by-step explanation:

EDGE

Step-by-step explanation:

a reminder about a few things :

the sum of all angles in a triangle is always 180°.

the sum of all angles around a point on one side of a line is also always 180°.

similar shapes (like ABC and AEF) have the same angles.

they are similar, because all 3 sides from one triangle are parallel to their corresponding sides of the other triangle.

(b)

b + 5a - 40 = 180 (supplementary angles, b and 5a-40 are the complete set of angles around A on one side of BD).

b = 180 - 5a + 40 = 220 - 5a

80 + 2a + 220 - 5a = 180 (the sum of all angles)

-3a + 300 = 180

-3a = -120

3a = 120

a = 40

so, 2a = 2×40 = 80°, which is the same as the angle at F.

2 equal angles at both ends of a triangle side means that we have an isoceles triangle, and therefore A E = A F.

b = 220 - 5a = 220 - 5×40 = 220 - 200 = 20°

c = 2a = 80° (angles in similar shapes are the same).

d + 80 = 180

d = 100° (again supplementary angles this time around F)

e = 80 (again, angles in similar shapes are equal).

(c)

the angles between 2 intersecting lines are the same when one of these lines intersect with a line that is parallel to the other line.

because parallel lines simply imitate each other perfectly in all attributes except for the physical location. but slipped, angles are all the same.

also, the angles between 2 intersecting lines are the same on both sides of every one of the 2 lines, they are just left-right mirrored.

so,

x = 28°

as ED and EF are intersecting, CD (as parallel line to EF) intersects ED at the same angles.

28° is the angle on the "above" side of the intersection, and x is on the "under" side. because of the left-right mirroring between above and under sides, x = 28°.

x is part of the angle BDE, so the angle CDB is

160 - x = 160 - 28 = 132°

the angles CDB and ABD are together

132 + 48 = 180°

so, they are supplementary angles again, indicating they are again the sum of both angles around an intersection point of 2 lines (with the line BD). and that is only possible, if AB and CD are again parallel as before CD and EF.

9514 1404 393

Answer:

  £592 for 16 boxes

Step-by-step explanation:

The classroom floor area is ...

  A = LW = (8.8 m)(2.2 m) = 19.36 m²

The cupboard floor area is ...

  A = (2.3 m)(2.1 m) = 4.83 m²

Then the total area to be covered is ...

  19.36 m² +4.83 m² = 24.19 m²

At 1.6 m² per box, the number of boxes required is ...

  (24.19 m²)/(1.6 m²/box) = 15.12 boxes

If we assume we can only purchase whole boxes, we need to purchase 16 boxes to cover the floor. The cost will be ...

  (16 boxes)(£37/box) = £592 . . . . cost of laminate to replace the floor

Answer:

Hence the probability that the mean of their utility bills will be less than $75 = P(X < 75) is 0.9736.

Step-by-step explanation:

Now,  

Population mean electric bill, \(\mu =\)  $72  

Population standard deviation, \(\sigma =\)  $6  

Standard error of the mean\(= \sigma / \sqrt{n} = 6 / \sqrt{15} = 1.5492\)

The probability that the mean of their utility bills will be less than $75 = P(X < 75)

= P[Z < (75 - 72) / 1.5492]

= P[Z < 1.9365]

= 0.9736 (Using Z table)

The final cost of the items if the store bucks are applied before the 30% discount is 76 dollars.

Leah plans to purchase merchandise from a department store that is valued at $100. She will use $20 in-store bucks that she has earned plus a 30% discount coupon to reduce her final cost.

Therefore, the final cost of the items before tax can be calculated as follows:

The 20 dollars store bucks was applied before the discount.

Hence,

100 - 20 = 80 dollars

Let's apply the discount.

discount amount = 30% of 80

discount amount = 30 / 100 × 80

discount amount = 2400 / 100

discount amount = 24 dollars

Therefore,

final cost = 100 - 24 = 76 dollars

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