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2 years ago

Whats the area of the trapezoid

Mathematics

2 answers:

Lelu [443]2 years ago

6 0

Step-by-step explanation:

the area of a trapezoid is

(b1 + b2)/2 × h = (10 + 5)/2 × 4 = 15 × 2 = 30 in²

Harrizon [31]2 years ago

3 0

Answer: 30 square inches

This is the same as writing $30 \text{ in}^2$

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

Reason:

You could use the shortcut formula the other person mentioned.

Or you could break the figure into two triangles and a rectangle between them.

A = area of the triangle on the left

A = base*height/2

A = 3*4/2

A = 6

B = area of the rectangle in the middle

B = base*height

B = 5*4

B = 20

C = area of the triangle on the right side

C = base*height/2

C = 2*4/2

C = 4

Add up those sub-areas to get the grand total area

A+B+C = 6+20+4 = 30 square inches

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The Bilbo Company plans to manufacture decals for children's lunchboxes. Each decal

Gwar [14]

Answer: 1 -2ax²+2x-ax

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Area of a rectangle: length x width

Replacing with the values given:

A = (2x+1) (1-ax)

A = [2x(1)] + [2x(-ax)] +[ 1(1)]+ [1 (-ax)]

A = 2x- 2ax² +1- ax

A = 1 -2ax²+2x-ax

In conclusion, the correct option is 1 -2ax²+2x-ax

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

Please simplify the answer!

frutty [35]

Answer:

y = 9

Step-by-step explanation:

Given

4 + $\frac{y}{3}$ = 7

Isolate the term in y by subtracting 4 from both sides

$\frac{y}{3}$ = 3 ( multiply both sides by 3 )

y = 3 × 3 = 9

7 0

3 years ago

How can exponents help you find the area of a rectangle if each side length is multiplied by x?

NeX [460]

Exponents can make the problem smaller and look less confusing. If you see a problem with 5*5*5*5*5*5*5*5 then you're going to eventually loose count and will have to keep repeating. But if you put 5 to the 8th power then you know right away just to multiply 5, (8) times,

4 0

3 years ago

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliv

Vaselesa [24]

Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

Hope this Helps!!!

4 0

3 years ago

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. t

zhuklara [117]

Answer:

a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.

b) By the Central Limit Theorem, approximately normal.

c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean monthly fee is $142 and the standard deviation is $29.

This means that $\mu = 142, \sigma = 29$

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Sample of 1500(larger than 30).

By the Central Limit Theorem

The mean is $142

The standard deviation is $s = \frac{29}{\sqrt{1500}} = 0.7488$

Part b: what is the shape of the sampling distribution of x hat justify your answer.

By the Central Limit Theorem, approximately normal.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

This is 1 subtracted by the pvalue of Z when X = 143. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{143 - 142}{0.7488}$

$Z = 1.34$

$Z = 1.34$ has a pvalue of 0.9099

1 - 0.9099 = 0.0901

0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

4 0

3 years ago