The perimeter of a rectangle is 24 m. The length is 3 m more than two times the width. Find the
length and the width of the rectangle.

Answer:

Step-by-step explanation:

360° - the know angles

360 - 20 - 70 - 20 = 250°

Step-by-step explanation:

Well this is a full circle, and in a full circle, theres 360 degrees.

So if we add up 20, 70 and 20 degrees, it comes to a total of 110 degrees.

If we subtract 110 d from 360 d, we get 250 degrees. Therefore,

Hope this helped

The probability that a person chosen at random uses both internet connections is 1/9

Total number of people = 27

Number of people who use ADSL lines = 16

Number of people who use wireless internet = 15

Number of people who use neither of the two = 3

Let the number of people who use only ADSL lines and wireless internet be denoted by A and B respectively.

Then A + B + A∩B + 3 must be equal to 27

A + B + A∩B = 24

further, we can see that

(A + A∩B) = 16  

B + 16 = 24

B = 8

Also, (B + A∩B) = 15

8+ A∩B = 15

A∩B = 7

Thus, the number of people who use both internet connections = 7

Now, P(A∩B) = 7/27

= 1/9

Hence, probability that a person chosen at random uses both internet connections is 1/9.

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Cost of a bottle of juice is $ 1.62

Equation for determining the cost of juice is 1.56 + 20x = 33.96

Given,

The cost of a bag of chips = $ 1.56

Number of juice bottles bought by Sarah = 20 pack

Total cost before tax = $ 33.96

Cost of one bottle of juice = x

We have to find x:

Then the equation will be:

1.56 + 20x = 33.96

Add -1.56 to both sides:

1.56 + 20x - 1.56 = 33.96 - 1.56

We get,

20x = 32.4

Now find x,

x = 32.4 / 20

Then,

x = 1.62

That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.

The cost of one bottle of juice is $1,62

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Based on the fact that Mary's family goes every 14 days and Sally's family goes every 4 days, the method of solving this problem is the Least Common Multiple.

The Least Common Multiple is used to find out when two or more events will occur at the same time if those events occur at fixed intervals that are different from each other.

Sally's family goes to the beach every 4 days and Mary's family goes every 14 days.

You can therefore solve for the day that they will next meet on the beach using their Least Common Multiple which is 28. They will next be at the beach on the same day after 28 days.

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Answer:

y = - [tex]\frac{\sqrt{111} }{20}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle formed by the radius 1 and the given point, then

y² + (- [tex]\frac{17}{20}[/tex] )² = 1²

y² + [tex]\frac{289}{400}[/tex] = 1

y² = 1 - [tex]\frac{289}{400}[/tex] = [tex]\frac{111}{400}[/tex] ( take square root of both sides )

y = ± [tex]\sqrt{\frac{111}{400} }[/tex] = ± [tex]\frac{\sqrt{111} }{20}[/tex]

since the point is in the third quadrant then y < 0

y = - [tex]\frac{\sqrt{111} }{20}[/tex]

Using substitution method, the ground will be 96 feet far after 3 seconds.

Finding the value of any variable from one equation in terms of another variable is the first step in the substitution technique. For instance, if there are two equations, x+y=7 and x-y=8, we may deduce that x=7-y from the first equation. Applying the replacement approach begins with this.

240-16 t² {t = 3, Substitution method}

=240 - 16×32

=240 - 16x9

=240-144

= 96 feet

96 feet from the ground.

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Answer:

[tex]{ \tt{( \frac{ - 4}{9} \times \frac{63}{28}) - ( \frac{33}{66} \times \frac{ - 51}{17} ) + ( \frac{5}{8} \times \frac{4}{10)} }} \\ \\ = { \tt{( \frac{ - 4}{28} \times \frac{63}{9}) - ( \frac{1}{2} \times \frac{ - 3}{1} ) + ( \frac{5}{10} \times \frac{4}{8} )}} \\ \\ { \tt{ = ( - 1) - ( - \frac{3}{2} ) + ( \frac{1}{4}) }} \\ \\ = { \tt{ \frac{3}{4} }}[/tex]

Answer:

[tex]\sf \dfrac{3}{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\implies \sf \left(\dfrac{-4}{9} \times \dfrac{63}{28}\right)-\left(\dfrac{33}{66} \times \dfrac{-51}{17}\right)+\left(\dfrac{5}{8} \times \dfrac{4}{10}\right)[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{a \times b}{c \times d}:[/tex]

[tex]\implies \sf \left(\dfrac{-4\times63}{9\times28} \right)-\left(\dfrac{33 \times -51}{66 \times 17}\right)+\left(\dfrac{5\times4}{8\times10} \right)[/tex]

Multiply the numbers:

[tex]\implies \sf \left(\dfrac{-252}{252} \right)-\left(\dfrac{-1683}{1122}\right)+\left(\dfrac{20}{80} \right)[/tex]

Reduce the fractions:

[tex]\implies \sf -1-\left(\dfrac{-3}{2}\right)+\left(\dfrac{1}{4} \right)[/tex]

[tex]\textsf{Apply rule}\quad \:a-\left(-b\right)=a+b:[/tex]

[tex]\implies \sf -1+\dfrac{3}{2}+\dfrac{1}{4}[/tex]

Adjust the fractions based on the LCM of 4:

[tex]\implies \sf \dfrac{-4}{4}+\dfrac{6}{4}+\dfrac{1}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \sf\dfrac{-4+6+1}{4}[/tex]

Add the numbers in the numerator:

[tex]\implies \sf \dfrac{3}{4}[/tex]

Answer:

3

Step-by-step explanation:

3  seeing as most dogs (5 dogs) are at the age of 3

The point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

In this question we have been given a graph of Skateboards vs. Bikes.

We need to find the point that represents an INEFFICIENT point of production.

Inefficient production means the economy can be producing more goods without using any additional resources.

In given production possibility curve, an INEFFICIENT point of production is point A.

Therefore, the point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

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The term that explains the relationship between angles C and D is: A. Adjacent angles.

When two angles share a common vertex and a common side, the two angles are referred to as adjacent angles.

In the diagram given, lines JK and JM intersect at point J to form 4 angles of which angles C and D share a common side and a common vertex (point J).

Therefore, the term that explains the relationship between angles C and D is: A. Adjacent angles.

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Answer:

A

i took the test and got it right

Answer:

$2,482.94

Step-by-step explanation:

[tex]p {e}^{.09 \times 13} = 8000[/tex]

[tex]p = \frac{8000}{ {e}^{.09 \times 13} } = 2482.94[/tex]

Answer:

The circumference of a circle with diameter 9.36 is 29.41

Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius and therefore, 2×r being the diameter.

2×pi×r = 9.36 cm

2r = diameter = 9.36/pi = 2.979380535... ≈ 2.98 cm

The weight of apple that Sandy has left after one week is 2.1 pounds.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of apple remaining after x days. Sandy collected 10 pounds of apples at an apple orchard and eat 20% daily, hence:

y = 10(1 - 0.2)ˣ

y = 10(0.8)ˣ

After 1 week, x = 7:

y = 10(0.8)⁷ = 2.1 pounds

The weight of apple that Sandy has left after one week is 2.1 pounds.

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The percentage is 42.8571%.

Percentage, a relative value indicating hundredth parts of any quantity. One percent  is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given fraction:

3/7

To convert the fraction into percentage we have multiply 100

3/7*100

=300/7

= 42.8571%

Hence, the percentage of fraction 3/7 is 42.8571%.

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Answer: 1680

Step-by-step explanation:The answer is 1680 because 56 percent of 3000 is 1680 people and 44 percent of 3000 is 1320 people

Answer:

Step-by-step explanation:

0.195/12 = 0.0163 = 1.63%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

What is the periodic rate?

A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.

Lenders typically quote interest rates on an annual basis, but the interest compounds more frequently than annually in most cases.

Here given that,

Loan with an APR of [tex]19.5[/tex]%

So, [tex]19.5[/tex]% is

[tex]\frac{19.5}{100}=0.195[/tex]

Annual periodic rate means [tex]12[/tex] months.

then,

[tex]{0.195}{12}=0.0163\\[/tex]

[tex]=1.63[/tex]%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

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Answer:

The answer would be 14061.364 grams.

[tex]\frac{10.25}{100}[/tex]Answer:

Step-by-step explanation:

The formula for simple interest is: A= P(1+in)

The formula for compound interest is: A=P[tex](1+i)^{n}[/tex]

A= amount after added interest

P= initial amount invested

i= interest rate

n= number of periods (in this case its 7 years)

*REMEMBER THIS FORMULA

a) A=0

P=?

i=10,25

n=7

(simple interest)

a) A= 0 (1 +[tex]\frac{10.25}{100}[/tex] ×7)

=0

b) A=2 000 (1 + [tex]\frac{10.25}{100}[/tex] ×7)

A=3435

c) A= 3 000( 1 + [tex]\frac{10.25}{100}[/tex] ×7)

A= 5152.5

d) 5000(1 + [tex]\frac{10.25}{100}[/tex] ×7)

= 8587.5

It's just a matter of substitution. I hope this helped.

Answer:

(a) $668.39

(b) $634.93

(c) $618.20

(d) $584.74

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]

where:

Given:

Down payment = $0

⇒ P = $39,950

[tex]\implies \sf PMT=\dfrac{39950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 668.3892086[/tex]

Therefore, the monthly payment is $668.39.

Down payment = $2,000

⇒ P = $39,950 - $2,000 = $37,950

[tex]\implies \sf PMT=\dfrac{37950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 634.9279215[/tex]

Therefore, the monthly payment is $634.93.

Down payment = $3,000

⇒ P = $39,950 - $3,000 = $36,950

[tex]\implies \sf PMT=\dfrac{36950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 618.197278[/tex]

Therefore, the monthly payment is $618.20.

Down payment = $5,000

⇒ P = $39,950 - $5,000 = $34,950

[tex]\implies \sf PMT=\dfrac{34950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 584.735991[/tex]

Therefore, the monthly payment is $584.74.

Considering the definition of probability and its properties:

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)= number of favorable cases÷ number of total cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.

A complementary event, also called an opposite event, is made up of the inverse of the results of another event.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

The conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:

P(A|B) = P(A∩B)÷ P(B)

In first place, let's define the following events:

You know:

The probability that a student is a freshman or a mathematics mayor is:

P [(F∪M)']= 1- P(F∪M)

7/51= 1 - P(F∪M)

7/51 - 1= -P(F∪M)

-44/51= -P(F∪M)

44/51= P(F∪M)

So, the probability that the student is both a freshman and a mathematics major is calculated as:

P(F∪M)= P(F) + P(M) -P(F∩M)

44/51= 23/51 + 30/51 - P(F∩M)

44/51- 23/51 - 30/51= - P(F∩M)

-3/17= - P(F∩M)

3/17= P(F∩M)

Finally, the probability that the student is both a freshman and a mathematics major is 3/17.

The probability that a student is a mathematics major, knowing that he is also a freshman, is calculated as:

P(M|F) = P(M∩F)÷ P(M)

So:

P(M|F) = 3/17÷ 30/51

P(M|F) = 3/10

Finally, given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.

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The value of x from the given figure is 8/3

The sum of all the ides of the parallelogram is perimeter. According to the given figure;

2(3x-8)+2(16) = 32.2

Expand to have:

6x-16 + 32 = 32.2

6x + 16 = 32.2

Subtract 16 from both sides

6x = 16

x = 16/6

x = 8/3

Hence the value of x from the given figure is 8/3

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Answer:

Step-by-step explanation:

Let

[tex]S = \displaystyle \sum_{1\le j<k\le673} z_jz_k[/tex]

and

[tex]p_{\mu,\nu}(x) = (x-z_1)^\mu (x-z_2)^\mu \cdots (x-z_\nu)^\mu[/tex]

The [tex]z_jz_k[/tex] terms occur in the coefficient of the [tex]x^{\mu\nu-2}[/tex] term, given by

[tex]\displaystyle \left[x^{\mu\nu-2}\right] p_{\mu,\nu} = \binom\mu2 \sum_{r=j}^\nu z_j^2 + \mu^2 \sum_{1 \le j < k \le \nu} z_jz_k[/tex]

(essentially due to Vieta's formulas)

With [tex]\mu=3[/tex] and [tex]\nu=673[/tex], we have

[tex]\displaystyle \left[x^{2017}\right] p_{3,673} = \binom32 \sum_{j=1}^{673} z_j^2 + 3^2 S \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \sum_{j=1}^{673} z_j^2 \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \left(\left(\sum_{j=1}^{673} z_j\right)^2 - 2 S\right) \\\\ ~~~~ \implies S = \frac{19}3 - \left(\sum_{j=1}^{673} z_j\right)^2[/tex]

The remaining sum on the right is the sum of the roots of [tex]\sqrt[3]{p_{3,673}(x)} = p_{1,673}(x)[/tex].

Recall that the sum of the roots of a polynomial

[tex]P_n(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0[/tex]

is [tex]-\frac{a_{n-1}}{a_n}[/tex]. Then the sum of the roots of [tex]p_{3,673}(x)[/tex] is -20, which is 3 times the sum of the roots (counting multiplicity) of [tex]p_{1,673}[/tex], so

[tex]\displaystyle \sum_{j=1}^{673} z_j = -\dfrac{20}3 \\\\ ~~~~ \implies S = \frac{19}3 - \left(-\frac{20}3\right)^2 = -\frac{343}9 \\\\ ~~~~ \implies |S| = \frac{343}9, m=343, n=9 \implies m+n = \boxed{352}[/tex]

The terms in the expression x² + x + 7 + 22 are x², x, 7 and 22.

What is an expression?

The value of anything is represented by a group of numbers, symbols, and operators called an expression.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.

The terms in the given expression are x², x, 7 and 22.

The coefficient of x² is 1 and coefficient of x is also 1.

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Answer:

true for the first one and also true for the other one.

The amount of Alfalfa hay is 385.71 lbs

The amount of Clover is 572.45 lbs.

A percentage is a number or ratio that can be expressed as a fraction of 100.

We have,

Alfalfa hay = 18 % CP

Clover = 4% CP.

The total amount of ration is 600 lbs of a 13% CP.

Let x pounds of alfalfa hay have been used.

The amount of clover will be 600 - x lbs.

The CP amount in 600 lbs mixture will be equal to the sum of CP amounts in x lbs alfalfa and (600 - x) lbs clover.

13% of 600 = 18% of x + 4% of (600 - x)

We need to find x.

13/100 x 600 = 18/100 x (x) + 4/100 x (600 -x)

78 = 18x / 100 + 24 - 4x/100

78 - 24 = 18x/100 - 4x/100

54 = 14x / 100

14x = 54 x 100

x = 5400/14

x = 385.71 lbs

Thus,

The amount of Alfalfa hay= 385.71 lbs

The amount of Clover = 600 - 385.71 = 572.45 lbs.

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Answer:

m=33

Step-by-step explanation:

Step 1: Subtract 1 from both sides.

3m+1−1=100−1

3m=99

Step 2: Divide both sides by 3

m=33

Step-by-step explanation:

solve:

3m+1=100

3m=99

99/3=33

m=33

check:

m= 33

33*3=99

99+1=100

The expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. A mathematical expression shows the value of something by combining numbers, variables, and operators. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.

From the information, Maria bought 5 tickets for $20 each. Each ticket had a $2 fee.

The expression that can be used to illustrate this will be:

C = (5 × $20) + ($2 × 5)

where C = Total cost

C = $100 + $10

C = $110

Therefore the expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.

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The volume of the shed ordered by Lorie to hold her gardening supplies is (option a) 1423.5 cubic ft.

Given,

Lorie ordered a shed to hold her gardening supplies.

The length of the shed, l = 18.25 feet

The width of the shed, w = 15 feet

The height of the shed, h = 5 1/5 feet = 26/5 = 5.2 feet

We have to determine the volume of the shed:

From the given data we can assume that the shed is like a cuboid. So to determine the volume, we can use the cuboidal formula.

That is,

Volume = length × width × height

V = l × w × h

V = 18.25 × 15 × 5.2

V = 1423.5 feet

Therefore, the volume of the shed ordered by Lorie to hold her gardening supplies is 1423.5 feet.

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Answer:

$1.92

Step-by-step explanation:

The corresponding row to 6 ounces is this

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

Reason:

Let's go through the four answer choices to see which are true and which are false. We'll rule out the ones that are true.