A company is developing packaging for a new product as shown below.
Choose all of the expressions that can be used to find the volume of the packaging.

Packaging is made up of 2 cuboids. First cuboid has length as 2 m, height as 9 m and width as 4 m. Second cuboid has length as 2 m, height as 3 m and width as 4 m.
A. (2 × 3 × 4) + (2 × 9 × 2)
B. (2 × 4 × 3) + (2 × 9 × 4)
C. (2 × 4 × 3) + (4 × 9 × 4)
D. (3 × 4 × 4) + (2 × 9 × 2)
E. (3 × 4 × 4) + (6 × 4 × 2)

9514 1404 393

Answer:

Step-by-step explanation:

1. The desired angle is given on the diagram as 125°.

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For the rest of these problems, the Law of Sines applies. A side can be found from ...

  a = b(sin(A)/sin(B))

and an angle can be found from ...

  A = arcsin(a/b·sin(B))

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2. Y = arcsin(y/z·sin(Z)) = arcsin(5/11·sin(88°))

  ∠Y = 27°

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3. DF = (11 km)·sin(32°)/sin(103°)

  DF = 5.98 km ≈ 6 km

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4. b = c·sin(B)/sin(C) = (13 ft)·sin(65°)/sin(180° -65° -37°)

  b = 12 ft

Answer:

#1: The measure of m<B is 125°.

#2: M<Y is equal a 27°.

#3: So the length of DF is 5.99 km.

#4: the side length AC is 13.1 feet.

Explanation:

# 1: The following given,

c = AB = 17 cm

a = BC = unknown

b = CA = 44 cm

Ø = 125

M<B means it is the angle at vertex B of the triangle, it is also the only angle given in thbe figure.

Therefore, The measure of m<B is 125°.

#2: We can calculate the value of the angles by means of the law of sine which is the following:

[tex] \frac{yz}{sin \: x} = \frac{xz}{sin \: y} = \frac{xy}{sin \: z} [/tex]

We need you know the Y value, therefore we replace and solve for Y

[tex] \frac{xz}{sin \: y} = \frac{xy}{sin \: z} \\ \frac{5}{sin \: y} = \frac{11}{sin \: 88} \\ 5 \: . \: sin \: 88 = 11 \: . \: sin \: y \\ sin \: y = \frac{5 \: . \: sin \: 88}{11} \\ sin \: y = 0.45426 \\ y = {sin}^{ - 1} (0.45426) \\ y = 27[/tex]

#3: In order to find the length of Df, we can use the law of sines in this triangle:

[tex] \frac{11}{sin \: (103)} = \frac{df}{sin \: (32)} \\ \frac{11}{0.974} = \frac{df}{0.53} \\ df = \frac{11.0.53}{0.974} \\ df = 5.99[/tex]

So the length of DF is 5.99 km.

#4: We are given two two angles and one side length.

<A = 37°

<B = 65°

AB = 13 ft

We are asked to find side length AC

We can use the "law of sines" to find the side length AC

[tex] \frac{sin \: c}{ab} = \frac{sin \: b}{ac} [/tex]

Let us first find the angle <C

Recall that the sum of all three interior angles of a triangle must be equal to 180°

[tex] < a + < b + < c = 180 \\ 37 + 65 + < c = 180 \\ 102 + < c = 180 \\ < c = 180 - 102 \\ < c = 78[/tex]

So, the angle <C is 78°

Now let us substitute all the known values into the law of sines formula and solve for AC

[tex] \frac{sin \: c}{ab} = \frac{sin \: b}{ac} \\ \frac{sin \: 75}{13} = \frac{sin \: 65}{ac} \\ ac = \frac{sin \: 65 \: . \: 13}{sin \: 75} \\ ac = \frac{9.06 \: . \: 13}{0.899} \\ ac = 13.1ft[/tex]

Therefore, the side length AC is 13.1 feet.

Answer:

attachment plz

Step-by-step explanation:

nothing is being seen

Answer:

Step-by-step explanation:

Triangle PQR is in a coordinate plane. The triangle is reflected across the y–axis and

then translated 11 units left to form Triangle P'Q'R'. Determine which of the following statements must be true regarding this transformation. Select True or False for each statement.

Angle P has the same measure as angle P'. T or F

Angle Q has the same measure as angle R'. T or F

Angle R has the same measure as angle R'. T or F

Answer:

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

Step-by-step explanation:

The kittens are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.

This means that [tex]N = 8 + 10 = 18[/tex]

We want 3 boys, so [tex]k = 8[/tex]

The director is going to choose 8 of these kittens at random to be in the commercial.

This means that [tex]n = 8[/tex]

What is the probability that the director chooses 3 boy kittens and 5 girl kittens?

This is P(X = 3).

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,18,8,8) = \frac{C_{8,3}*C_{10,5}}{C_{18,8}} = 0.323[/tex]

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

Answer:

Step-by-step explanation:

original quantity = 10 mL

new quantity = 22 mL

amount of change = 22 - 10 = 12 mL

(12 mL)/(10 mL) = 1.20 = 120%

Answer:

472×82=38704

Step-by-step explanation:

Prime factorization:

2^4×41×59

Answer:

The answer would be letter D. Valuable.

Answer:

B and C

Step-by-step explanation:

A statistical question has more than one answer therefore multiple people could have different number of pets or different favorite flavor of ice cream.

Hope that helped :)

Answer:

$72891.1094

Step-by-step explanation:

This method of saving is called sinking fund.

Future value (FV) =  A*([tex]\frac{[(1+r)^{n} - 1]}{r}[/tex])

Where A is the amortization, r is the rate and n the number of years.

A = $3000

r = 2% = 0.02

n = 20

FV = 3000 * [tex](\frac{[(1.02)^{20} - 1]}{0.02})[/tex]

     = 3000 * 24.2973698

     = 72891.1094

FV  = $ 72891.1094

The amount that would be in the account after 20 years is $72891.1094

Answer:

400ml of juice

Step-by-step explanation:

1 litre of water = 100ml of juice

4 litres of water =? ml of juice

to get from 1 litre to 4 litre of water you multiply by 4,so you do the same for the juice and multiply the juice by 4.

100×4=400

4 litres of water = 400ml of juice

Step-by-step explanation:

this is the cutest answer

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that [tex]\mu = 8, \sigma = 1.1[/tex]

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

[tex]n = 5[/tex] means that [tex]s = \frac{1.1}{\sqrt{5}} = 0.4919[/tex]

This probability is the pvalue of Z when X = 9.3. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{9.3 - 8}{0.4919}[/tex]

[tex]Z = 2.64[/tex]

[tex]Z = 2.64[/tex] has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

[tex]n = 6[/tex] means that [tex]s = \frac{1.1}{\sqrt{6}} = 0.4491[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 9. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{9 - 8}{0.4491}[/tex]

[tex]Z = 2.23[/tex]

[tex]Z = 2.23[/tex] has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Answer:

2 x 4.99 = 9.98

3/4 x 4.99 = 3.7425 round it to 3.74

9.98 + 3.74 = 13.73

Answer: $13.73

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

Given that,

Initial temperature of a piece of metal = 32°C

Final temperature of the piece of metal = 36°С

We need to find the percentage increase in the temperature of the piece of metal.​ The percentage increase in any value is given by the relation as follows :

[tex]\%=\dfrac{|\text{final value-initial value}|}{\text{initial value}}\times 100\\\\=\dfrac{36-32}{32}\times 100\\\\=12.5\%[/tex]

So, the required percentage increase in the temperature of the piece of metal is equal to 12.5%.

Answer:

$90.00

Step-by-step explanation:

Given

[tex]c = 45.00[/tex]--- base fee

[tex]m = 15.00[/tex] --- rate

[tex]x = 3[/tex] --- individuals

Required

Determine the total amount paid (y)

The relationship between the variables is:

[tex]Total = Base\ Fee + Rate * Individuals[/tex]

[tex]y = c + mx[/tex]

This gives:

[tex]y = 45.00 + 15.00 * 3[/tex]

[tex]y = 45.00 + 45.00[/tex]

[tex]y = 90.00[/tex]

Hence, the amount is $90.00

Answer:

62 cm

Step-by-step explanation:

It's basically just a rectangle, so area formula for rectangle is base x height

Answer:

29

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

anything for sangwoo

The numeric value of this expression is -6!

[tex] \large \sf f(x) = 12 - 2x {}^{2} [/tex]

[tex] \large \sf f(-3) = 12 - 2\cdot (-3){}^{2} [/tex]

[tex] \large \sf f(-3) = 12 - 2\cdot 9 [/tex]

[tex] \large \sf f(-3) = 12 - 18 [/tex]

[tex] \boxed{ \boxed{{ \large \sf f(-3)=-6}}}[/tex]

Therefore, the result of this expression is f(-3)=-6. ✅

Answer:

74

Step-by-step explanation:

If it is $10 for each GB, you would multiply the amount by 10.

You get $50.

Now you need to add the $24 to get $74 per month :)

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Work Shown:

3(m+2) + 4(6+m)

3m+6 + 24 + 4m

(3m+4m) + (6+24)

7m+30

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Explanation:

In the second step, I used the distribution rule a*(b+c) = a*b+a*c. We multiply the outer term by every term inside. So for instance 3(m+2) = 3*m+3*2 = 3m+6.  A similar situation applies to 4(6+m) as well. Afterward, I grouped and combined like terms.

We can think of 3m+4m = 7m as saying "I have 3 maps and someone gave me 4 more maps, so that means I have 3+4 = 7 maps now". The m is a place holder for any number.

Answer:

since all sides are equal 3x = 180

you find the 180÷3

which is 60

Answer:

Area = 80 units²

Step-by-step explanation:

Given that:

a = 19 units

b = 9 units

c = 97°

Find the area of the triangle!

Area = ab(sin(c))/2

Area = [19×9×(sin(97))]/2

Area = 84.86 units²

Area = 80 units² ✅

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#IndonesianPride

- kexcvi -

cancelStep-by-step explanation:

10) there are infinity values for k

4(k-8)=-32+4k

4k-32=-32+4k

these two equal each other so any value is equal to k

12) there are no values for b

-(3-6b)=6b+5

-3+6b=6b+5

the b's  out and you are left with -3=5 which is impossible

Hope that helps :)

Answer:

10 is k= -4           i dont know 12 though... u dont have to give brainly to me.

Step-by-step explanation:

Answer:

y=5/3x

Step-by-step explanation:

Answer:

x+y=3

Assuming that the option 1 and 2 dont mean anything