the area of trapezoid $abcd$ is $80$. one base is $12$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.

With compound interest of 3.8% compounded annually it will take 7 years  for the value of the account to reach $6,880.

What is Compound interest?

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

Formula to find compound interest:

A=P(1+r/n)^nt

Where,

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time (in years)

Alternatively, we can write the formula as given below:

CI = A – P

Where CI=Compound Interest

Now,

As given

A=$6880

P=$5300

r=3.8%

n=1

t=?

Therefore,

The time it would take to become $6880 will be

6880=5300(1+3.8/100)^t

From here t=7 years

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Answer:

10.9%

Step-by-step explanation:

You want to do the number of ways that can happen, which is [tex]_8C_2 = 28[/tex] divided by the total number of possibilities which is [tex]2^8[/tex] to get 10.9%

Answer:

C

Step-by-step explanation:

(4+8x)/12 simplifies to (1+2x)/3x

The index form 4 ^–1  as a fraction or whole number without exponents is 1/4

The index form of a number described as the number that is written as an exponential expression

Index forms are also described as a single number that is raised to another number or variable.

The index or exponent of an exponential expression shows how many times to multiply the base by itself in the expression.

From the information given, we have the index form as;

4^-1

This is represented as a fraction;

1/4^1

Note that any number that is raised to 1 is equal to the number

1/4

Hence, the value is 1/4

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Answer:

The number is 20

Step-by-step explanation:

First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.

Answer:

20

Step-by-step explanation:

The value of x that will give a perimeter of 25 inches is 4 inches

The perimeter of a pentagon is the sum of the lengths of all its sides. The formula to calculate the perimeter of a pentagon is:

P = 5L

where is the side length

Initially, the sides of length, L is 1 inches

Now, we increase L by x and perimeter is 25 inches. Thus, can write:

25 = 5(1 + x)

25 = 5 + 5x

5x = 25 - 5

5x = 20

x = 20/5

x = 4 inches

Therefore, the value of x is 4 inches

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Answer:

C. Mara wished she could visit the stars: she often dreamed of it.

Answer:

Step-by-step explanation:

The selling price of a phone case with a 25% coupon is $56 and the original selling price of the phone case without any discount is $80.

What is the selling price?

The price at which an article is sold is known as the selling price of that article.

Given that you have a 25% off coupon and paid $42.00 for a phone case. The phone case was marked down 30%. So,

Let's consider that you use a 25% off coupon and then paid $42 for the phone case. The price of phone case including coupon is,

75 % of price  = $42.00

100% of price =

Answer: D

Step-by-step explanation: the amount per cashews (c) is $2.45. Therefore, its 2.45c

The amount per pounds of sugar is $0.61. Therefore, its 0.61s

And, since its "buying" (basically, adding), you gotta add them. So, the answer would be: 2.45c+0.61s

Answer: The explicit formula for a geometric sequence is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

Part A) In this sequence, the first term is 4, and the common ratio is 4/1 = 4.

So the explicit formula for this sequence is:

an = 4 * 4^(n-1)

To find the 8th term of this sequence, we can substitute n = 8 into the formula:

a8 = 4 * 4^(8-1)

a8 = 4 * 4^7

a8 = 4 * 16,384

a8 = 65,536

Therefore, the 8th term of this sequence is 65,536.

Step-by-step explanation:

The equation of the slope is y = -5x + 72.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Given that:

72 inches is the depth of the liquid level in water tank.

Water drains at a rate of 5 inches per minute.

Let y represent the tank's height, which is given as 72.

Let x be the total number of minutes, here x = 0.

Therefore, the slope's equation is the rate at which the water drains, that is:

m = -5

The equation of the line is given by the formula:

y = mx + c

Substitute the values:

72 = -5(0) + c

c = 72

And the equation is:

y = -5x + 72

Hence, the equation of the slope is y = -5x + 72.

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Answer:

Step-by-step explanation:

-2y=2-3x-5y=10-5x

-2y=10-5x

2-3x-5y-5x

(SIMPLIFY)

5x-2y=10

2x-5y=8

(MULTIPLY BOTH SIDES)

-25x-10y=-50

4x-10y=16

(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)

-21x=-34

(DIVIDE BOTH SIDES)

X=34/21

(SUBSTITUTE THE VALUE OF X)

2x34/21-5y=8

(SOLVE EQUATION)

Y=-20/21

(A POSSIBLE SOLUTION IS)

(X,Y)=(34/21 , -20/21)

(CHECK THE SOLUTION)

-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21

(SIMPLIFY)

40/21=40/21=40/21

(X,Y)= (34/21 , -20/21)

(SOLUTION)

Answer:

Step-by-step explanation:

Alright so let me try and explain this as best as I can:

So the graph isn't linear because the graph shows a parabola (a boomerang kind of shape that happens if you use an exponent somewhere in a y=mx+b formula if I remember correctly) and not a straight line. Linear graphs cannot curve, and this one does. Not sure why it it would be a function though. Assuming the answer chosen is correct, my best guess as to why it might be a function is because it continues to go in the same direction forever, there is a predictable amount of change between each point and you can follow a formula to find every point on the graph.

I really hope this helps a little!

1) The lower class limits: 100, 200, 300, 400, 500, 600 .

2) The upper class limits:  199, 299, 399, 499, 599, 699.

3) The class width: 100.

4) Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5, 649.5.

5) Class boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5.

6) The number of individuals included in the summary : 155

The lower class limit in each class: 0,100, 200, 300, 400, 500, 600.

The upper-class limit is the biggest value in each class.

so the upper-class limit is:  99, 199, 299, 399, 499, 599, 699.

As we know the class width is the difference between the lower limit of one class and the lower limit of the previous class.

For example, 300 is the lower limit of one class and the lower limit of the previous class is 200 , so 300 - 200 = 100.

We know that, the class midpoints are the average of the limits of a class.

So, using midpoint formula the class midpoints are:

[tex]\frac{100+199}{2} = 149.5\\\\\frac{200+299}{2} = 249.5\\\\\frac{300+3199}{2} = 349.5\\\\\frac{400+499}{2} = 449.5\\\\\frac{500+599}{2} = 549.5\\\\\frac{600+699}{2} = 649.5\\[/tex]

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries for the first class = (99.5, 199.5)

the class boundaries for the second class = (199.5, 299.5)

the class boundaries for the third class = (299.5, 399.5)

the class boundaries for the fourth class = (399.5, 499.5)

the class boundaries for the fifth class = (499.5, 599.5)

The total of individuals is equal to the sum of all the frequencies of each class: 3 + 54 + 76 + 21 + 0 + 0 + 1 = 155

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The complete question is:

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males ​(1000 ​cells/mu​L) Frequency 0​-99 3 100​-199 54 200​-299 76 300​-399 21 400​-499 0 500​-599 0 600​-699 1 Identify the lower class limits​ (in 1000 ​cells/mu​L).

Answer:

what grid

Step-by-step explanation:

c) both statements together are sufficient, but neither statement alone is sufficient.

According to the question

The query asks if statements (1) and (2) by themselves are sufficient to determine whether x is an even number. The answer is that neither assertion by itself is adequate to ascertain what x is worth. However, when both claims are taken into account, they are adequate to decide whether or not x is an even number. This is due to the fact that if xyz is even and yz is odd, x must be even. If x were odd, both xy xz and y xz would be strange as well. Due to this, the proper response is "c) neither statement is adequate when read alone, but both assertions taken together are sufficient."

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Answer:

The cost of the sneakers after the coupon is applied would be $46.99 - ($46.99 * 15%) = $39.94.

The total cost of the sneakers after 5% sales tax is included would be $39.94 + ($39.94 * 5%) = $41.94

Answer: $41.94

15% off means the sneakers are at 85% of it's original price.

85% = 0.85

$46.99 x 0.85

= $39.94 after 15% coupon

5% sales tax means you are adding 5% to the price.

105% = 1.05

$39.94 x 1.05

$41.94, after the coupon and sales tax.

No, the equation 2x + 2 = x + 1 has solution which is equal to x = -1.

Mia gave statement for the equation:

Left hand side is double the right hand side implies it has no solution.

2x + 2 = x + 1

Verification for the solution:

Simplify the above equation by subtracting  'x' both the sides we get,

⇒ 2x - x + 2 = x - x + 1

⇒ x + 2 = 1

Now subtract '2' from both the sides of the equations we get,

⇒ x + 2 - 2 = 1 - 2

⇒ x = -1

The above equation has no solution is incorrect statement.

Therefore, the equation 2x + 2 = x + 1 has no solution is wrong statement as the solution is given by x = -1.

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(i) 98³

(100-2)³

100³ + 2³ + 3(100*2)(100+2)

[by using the equation (a-b)3=a3+b3+3ab(a+b)]

1000000+8+(600*102)

The solution is 1000008+61200 1061208.

(ii) 188 × 212 = 39856

Given:

The ratio of 188 to 212

To locate

the importance of adopting a proper identity

Equation: (a + b) = (a2 - b2 ( a - b )

Solution:

Phase 1 of 2:

Note the supplied expression in writing.

The formula is 188 212. Step 2 of 2:

Find the expression's value.

188 × 212\s= ( 200 - 12 ) × ( 200 + 12 )

= ( 200 + 12 ) × ( 200 - 12 ) ( 200 - 12 )

= 200² - 12²

= 40000 - 144

= 39856

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Answer:

20

Step-by-step explanation:

(Hypotenuse)²=(Opposite)²+(Adjacent)²

(25)²=(15)²+(A)²

A²=625-225

A=✓400

A=20.00

The digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.7 will be 548

The 8 in our number, 2,980.7, is in the tens place and hence represents an 80.

The value of the digit 8 is equal to 1/10 of 10 divided by 1, which is 10 times greater than the value of the digit 888.

We need a number that contains an 8 and has a value that is 1/10 of the previous number, hence we need:

1/10*80 = 8

So, the number we're seeking has an 8 in the position of the one.

Option C: 548 would be this.

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The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

False. Using a systematic sample does not guarantee that members of each group within a population will be sampled. A systematic sample is a type of probability sampling in which a random starting point is chosen and then every nth item is selected from the population. This can lead to bias if the population contains patterns or cycles.

A true statement would be: "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled."

The given statement is False

The correct form is given below-

Using a random sample guarantees that members of each group within a population have an equal chance of being sampled.

Thus, The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

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The triangle pairs that can be mapped to one another using both a translation and a reflection across the line containing AB will be A based on the provided information. Triangles A B C and X Y Z are similar. Triangle A is created by reflecting triangle X, Y, and Z across a line. The correct option is A.

The first triangle pair is a pair that can be mapped to one another using both translation and reflection across a line containing AB.

The first figure is made up of the coordinates XYZ and ABC, which are translations and reflections of one another across the line AB.

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Answer: it is A

Step-by-step explanation: just took the test

Answer:

Independent variable.  cause the sales will be depending upon the weather.

Step-by-step explanation:

The decimal number and the fraction commonly used as approximations for pi are 3.142 and 22/7

from the question, we have the following parameters that can be used in our computation:

pi

The pi variable is a mathematical constant that has the following fractional value

pi = 22/7

When converted to decimal in 3 decimal places, we have

pi = 3.142

Hence, the representations are 22/7 and 3.142

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Answer:

B

Step-by-step explanation:

The decimal number less than 1.4 and greater than 1.35 is A = 1.39

The decimal numbers can only be expressed as fractions since they contain a fractional component. The accepted method for representing both integer and non-integer numbers is the decimal numeral system. There are 10 single-digit numbers in the decimal system:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. After the number 9, comes 10, then comes 11, then 12, and so on. Each time the digit to the right exceeds 9, the number on the left is increased by 1.

Given data ,

Let the decimal number be represented as A

Now , the value of A is

Let the first number be p = 1.4

Let the second number be q = 1.35

Now , q < A < p

The value of A is less than 1.4 and greater than 1.35

So , A = 1.39

Hence , the decimal number is A = 1.39

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The equations with the same y-intercept are y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Let's compare the given equations with y = mx+b:

y = 5x - 2,     y-intercept (b) = -2

y = 9x + 2,    y-intercept (b) = 2

y = 8x + 2,    y-intercept (b) = 2

y = 3x - 7,     y-intercept (b) = -7

y = 3x + 2,     y-intercept (b) = 2

y = 3x + 4,     y-intercept (b) = 4

y = (1/4)x + 2, y-intercept (b) = 2

Therefore, y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2 have the same y-intercept

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Answer:  13

Step-by-step explanation:

13+7= 20

Answer:

The number is 13.

Step-by-step explanation:

"A number" is a number we don't know to begin with. It should be represented by a variable. Let's use n. We'll probably be trying to find this number.

"increased by" usually means that there is adding going on here.

So far, we have:

n + 7

that is algebra for "A number increased by 7"

"gives 20" is a little strange wording, but it means yields or equals.

So now we have the whole equation:

n + 7 = 20

To solve, subtract 7 from both sides (of the equal sign)

n = 20 - 7

n = 13

The number is 13.

Check:

13 increased by 7 gives 20?

13 + 7 = 20 ?

20 = 20 ✔Yes! Done!