Solve the following problems. You can use your calculator..
1. How many cubic inches of metal are
contained in the hollow rectangular bar
below?
T
5 in.
3 in.
K
-4 in.
6 in.
10 in.
2. The
man
2 ft

the length of the hall is 35 m and the breadth of the hall is 160 m.

To find the length and breadth of the drawing, we need to use the scale given. We know that 1 cm represents 5 m, so we can use this proportion to find the actual dimensions of the school compound:

1 cm : 5 m = x cm : y m

To find the length of the drawing, we can use the given dimensions of the football field, which are 50 m by 30 m:

Length of the drawing = 50 m / 5 m per cm = 10 cm

Breadth of the drawing = 30 m / 5 m per cm = 6 cm

Therefore, the length of the drawing is 10 cm and the breadth of the drawing is 6 cm.

To find the actual length and breadth of the hall, we need to use the scale given. We know that 7 cm represents the length and 32 cm represents the breadth:

Length of the hall = 7 cm x 5 m per cm = 35 m

Breadth of the hall = 32 cm x 5 m per cm = 160 m

Therefore, the length of the hall is 35 m and the breadth of the hall is 160 m.

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The total unpainted surface area of these cubes is: 12cm

Therefore, the formula for the volume of a rectangular prism is, volume of a rectangular prism (V) = l × w × h, where. To find the volume of the rectangular prism, we multiply the length, width, and height, that is the area of the base is multiplied by the height.

The unpainted ones will be the ones in the middle of the prism

Let 3 be the height

There will be 2 × 6 × 5  =  60  painted cubes on the top and bottom

There will  2 × 6  +   2 × 3  =  18 more painted cubes "sandwiched" between the top and bottom surfaces

So...the total unpainted cubes  is  90  - 78   =   12

So their total surface area is just   [12 × 6 ] cm^2   =  72 cm^2

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The given question is incomplete, complete question is:

A rectangular prism 3cm by 5cm by 6cm is painted mauve and is then cut into 1 cm cubes what is the total unpainted surface area of these cubes

True. The alpha level for a hypothesis test defines the critical region.

A hypothesis test is a statistical technique that is used to test an assumption or hypothesis regarding a population parameter or distribution.

The critical region refers to the region of the sampling distribution that contains values that are unlikely to have occurred by chance if the null hypothesis is true.

The alpha level is the probability of committing a type I error, which is rejecting the null hypothesis when it is actually true.

The critical region is defined by the alpha level, which is the level of significance or the maximum probability of rejecting the null hypothesis when it is actually true. For example, if the alpha level is set at 0.05, the critical region will be the upper and lower 2.5% of the sampling distribution. If the test statistic falls within this region, the null hypothesis is rejected. On the other hand, if the test statistic falls outside this region, the null hypothesis is accepted.

Therefore, the alpha level plays a crucial role in determining the critical region and making decisions based on the results of the hypothesis test.

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Option B is best represents for the answer. A. 84.13%. B. 15.87%. 99.87%. D. 81.86%. To create the distribution curve, we can use the normal distribution formula:  [tex]f(x) = (1/σ√(2π)) * e^(-0.5((x-μ)/σ)^2)[/tex]

where:

f(x) = probability density function at value x

μ = mean = 16.2

σ = standard deviation = 0.3

Using this formula, we can calculate the probabilities for the given scenarios:

a. Probability of a coke having less than 16.5 ounces:

We need to find P(X < 16.5), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 16.5:

z = (16.5 - 16.2) / 0.3 = 1

P(Z < 1) = 0.8413

Therefore, the probability of a coke having less than 16.5 ounces is 84.13%.

b. Probability of a coke having less than 15.9 ounces:

We need to find P(X < 15.9), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.9:

z = (15.9 - 16.2) / 0.3 = -1

P(Z < -1) = 0.1587

Therefore, the probability of a coke having less than 15.9 ounces is 15.87%.

c. Probability of a coke having more than 15.3 ounces:

We need to find P(X > 15.3), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.3:

z = (15.3 - 16.2) / 0.3 = -3

P(Z > -3) = 0.9987

Therefore, the probability of a coke having more than 15.3 ounces is 99.87%.

d. Probability of a bag having between 15.9 and 16.8 ounces:

We need to find P(15.9 < X < 16.8), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the values of 15.9 and 16.8:

z1 = (15.9 - 16.2) / 0.3 = -1

z2 = (16.8 - 16.2) / 0.3 = 2

P(-1 < Z < 2) = 0.8186

Therefore, the probability of a coke having a volume between 15.9 and 16.8 ounces is 81.86%.

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Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.

Given the following data:

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

From the graph of the data, we have the following linear equation:

[tex]y=\dfrac{1}{2}x+18[/tex]

Substituting the value of x, we have:

[tex]y=(\dfrac{1}{2}\times40)+18[/tex]

[tex]y=20+18[/tex]

[tex]\bold{y = 38 \ inches.}[/tex]

The required quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

To express the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] in scientific notation, we can write:

[tex]$\frac{1.888 \times 10}{5.9 \times 10^6}$[/tex]

We can simplify the numerator by moving the decimal point one place to the left:

[tex]$\frac{0.1888 \times 10^1}{5.9 \times 10^6}$[/tex]

Now, we can divide the coefficients and subtract the exponents:

[tex]$\frac{0.1888}{5.9} \times 10^{2-6}$[/tex]

[tex]$= 0.031966 \times 10^{-4}$[/tex]

Finally, we can express the result in proper scientific notation by moving the decimal point one place to the right:

[tex]$= 3.1966 \times 10^{-6}$[/tex]

Therefore, the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

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Therefore, the coordinates of the image point B' are (3, -4) when a triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6).

To find the image of point B after performing the given transformations, we need to apply them in sequence.

Reflection over the y-axis:

This transformation will change the sign of the x-coordinate of point B, while leaving the y-coordinate unchanged. Therefore, the image of point B after reflection over the y-axis is (-(-3), 1), which simplifies to (3, 1).

Rotation 90° clockwise:

This transformation will swap the x and y-coordinates of the point and then change the sign of the new x-coordinate. Therefore, the image of point B after rotation 90° clockwise is (1, -3).

Translation (x + 2, y - 1):

This transformation will shift the image of point B two units to the right and one unit down. Therefore, the final image of point B after all three transformations is (1 + 2, -3 - 1), which simplifies to (3, -4).

Therefore, the coordinates of the image point B' are (3, -4).

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Hank can feed his dog for 40 days with one bag of dog food.

A fraction represents a part of a whole or a ratio between two quantities. It is a mathematical expression that consists of a numerator and a denominator separated by a horizontal line, also called a fraction bar or a vinculum.  

To solve the problem, we need to find how many scoops of dog food are in the bag and divide that by the number of scoops used per day:

Number of scoops in bag = 5 cups ÷ 1/8 cup/scoop = 40 scoops

Number of days he can feed his dog = 40 scoops ÷ 1 scoop/day = 40 days

Therefore, Hank can feed his dog for 40 days with one bag of dog food.

Statement: Hank can feed his dog for 40 days with one bag of dog food.

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2x^-4y=2(2)^-4.4

2\2^16

1\2^15

The answer is not in the options

Answer:

3588

Step-by-step explanation: prime factorize and find common factors, only count those once, take the rest and the common factors and multiply

The circumference of the outer circle is 72 and circumference of the inner circle is 66.Therefore, the circumference of the outer circle is 6ft greater than the circumference of the inner circle.

We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

Given that the circumference of the inner circle is 66ft, we can find its radius by dividing the circumference by 2π:

r = C/2π = 66/(2π) ≈ 10.52ft

The distance between the inner and outer circles is 3ft, so the radius of the outer circle is 3ft greater than the radius of the inner circle:

r_outer = r_inner + 3ft = 10.52ft + 3ft = 13.52ft

Now, we can find the circumference of the outer circle using the same formula as before:

C_outer = 2πr_outer ≈ 72ft

Finally, to find the difference between the circumference of the outer circle and the circumference of the inner circle, we subtract the circumference of the inner circle from the circumference of the outer circle:

C_difference = C_outer - C_inner ≈ 72ft - 66ft = 6ft

Therefore, the circumference of the outer circle is 6ft greater than the circumference of the inner circle.

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Answer: Well, there are 12 months in a year, so that's 12 people at least, and if we wanted to make sure that we had at least 4 people of the same month, we'd want 4 times 12, so 48 people is my guess

sorry if it's wrong. Hope this helps!

Step-by-step explanation:

One more than two-thirds of a number is no less than 25 is x = -30.

An equation is a mathematical expression that contains two algebraic expressions on either side of the "equals (=)" sign. It shows the equality between the words written to the left and the words written to the right. In all mathematics there is L.H.S = R.H.S (left side = right side). Equations can be solved to find the values ​​of unknown variables that represent unknown quantities or numbers. If there is no "equals" sign in the expression, it means it is not equal. It will be treated as a guide.

let the no. be x

According to the question:-

2/3 × x = 1/2× (x-5)

⇒ 2x/3 = x/2- 5

⇒ 2x/3 - x/2 = -5

⇒ (4x- 3x)/6 = -5

⇒ x/6  = -5

⇒ x = -30.

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(a) GI side of right triangle GHI is the hypotenuse.

(b) GI is the side which is opposite to ∠H

(c) GH is the side that is adjacent to ∠G.

A right-angled triangle is a type οf triangle that has οne οf its angles equal tο 90 degrees. The οther twο angles sum up tο 90 degrees. The sides that include the right angle are perpendicular and the base οf the triangle. The third side is called the hypοtenuse, which is the lοngest side οf all three sides.

(a) GI side of right triangle GHI is the hypotenuse.

(b) GI is the side which is opposite to ∠H

(c) GH is the side that is adjacent to ∠G.

(d) HI is  the side that is opposite to ∠G

(e) HI is the side that is adjacent to ∠I.

(f) GH is the side which is opposite to I.

(g) 5 : 12 is the numerical ratio of the length of the side opposite to G to the length of the side adjacent to ZG.

(h) 12 : 5 is the numerical ratio of the length of the side opposite to I to the length of the side adjacent to I.

(i) 5 : 13 is the numerical ratio of the length of the side opposite to G to the length of the hypotenuse.

(j) 12 : 13 is the numerical ratio of the length of the side adjacent to ZG to the length of the hypotenuse.

(k) 12 : 13 is the numerical ratio of the length of the side opposite to I to the length of the hypotenuse.

(H) 5 : 13 is the numerical ratio of the length of the side adjacent to I to the length of the hypotenuse.

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Answer:

The answer is 6

Answer: 2.5

Step-by-step explanation:

Given the equation: f = 2.5w

The constant of proportionality is 2.5.

This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5

Notes:

Hi,

I don't really know what you're asking, so if you could clarify, that would be great. Thanks!

(Do you want me to simplify the equation? Find out what x is?)

- 201600823

Answer:

none of the above

Step-by-step explanation:

3(x − 4)² +6 = 0

3(x − 4)² = -6 / : 3

(x − 4)² = -2

x² - 8x + 16 = -2

x² - 8x + 16 + 2 = 0

x² - 8x + 18 = 0

D = b² - 4ac = (-8)² - 4 * 1 * 18 = 64 - 72 = -8 < 0

Since the discriminant is less than zero, this quadratic equation has no solutions, the graph would not cross the x-axis and therefore have no zeros.

According to the given information, We will use a right-tailed test. The critical [tex]$z$[/tex]-value is [tex]$z_\alpha = 1.645$[/tex] and the test value is 1.77.

What is right-tailed test?

A right-tailed test, also known as a one-tailed test, is a statistical hypothesis test where the alternative hypothesis is directional and is expressed as an inequality with the greater-than symbol (>), indicating that the parameter being tested is expected to be larger than a specified value.

(a) The null hypothesis [tex]($H_0$)[/tex] and alternative hypothesis [tex]($H_a$)[/tex] are:

[tex]$H_0: \mu = 25$[/tex] (the addition of the mineral does not increase the number of pages read per day)

[tex]$H_a: \mu > 25$[/tex] (the addition of the mineral increases the number of pages read per day)

We will use a right-tailed test because the alternative hypothesis is one-sided (i.e., [tex]$\mu$[/tex] is greater than the hypothesized value).

(b) The critical [tex]$z$[/tex]-value for a one-tailed test with a 5% significance level and 29 degrees of freedom ([tex]df=n-1$, where $n=30$[/tex]) is:

[tex]$z_\alpha = 1.645$[/tex] (from the standard normal distribution table or calculator)

(c) The test value ([tex]$z$[/tex]-value) can be calculated as:

[tex]$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]

where [tex]$\bar{x}$[/tex] is the sample mean, [tex]$\mu$[/tex] is the hypothesized population mean, [tex]$\sigma$[/tex] is the population standard deviation, and [tex]$n$[/tex] is the sample size.

Plugging in the values, we get:

[tex]$z = \frac{25.5 - 25}{\frac{2.4}{\sqrt{30}}} \approx 1.77$$[/tex]

The test value (1.77) is greater than the critical [tex]$z$[/tex]-value (1.645), so we reject the null hypothesis and conclude that the addition of the mineral is effective in increasing the number of pages read per day.

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Answer:

Step-by-step explanation:

Strap in man I can only do so much with 5000 characters:

1) 8 outcomes

2) Fried rice - chicken adobo - pineapple juice

   Fried rice - pinakbet -  pineapple juice

   Steamed rice - chicken adobo - pineapple juice

   Steamed rice - pinakbet - pineapple juice

3) 4

4) 2

5) 2

6) 2

7) 4/8 or 1/2 or 50%

8) 2/8 or 1/4 or 25%

9) 2/8 or 1/4 or 25%

10)2/8 or 1/4 or 25%

That's it! I hope this helps you out. Got any questions. I'll uh...be here :)

Answer:  135 + x = 258; x = distance driven on second day (in km).

Step-by-step explanation: Another alternative way to write the equation could be "258 - 135 = x" where x = distance driven on second day (in km).

"x" itself in the case of these equations would be 123km.

The missing numbers 50% of 60 = 30

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.

Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.

The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

50*60/100

30

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Answer:

The angle measures from least to greatest are 30°, 30° and 120°.

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

Given the ratio of the interior angles of a triangle is 1 : 1 : 4 then:

x + x + 4x = 180°

Solve the equation for x:

⇒ 6x = 180°

⇒ x = 30°

Therefore, the angle measures are:

So the angle measures from least to greatest are 30°, 30° and 120°.

Answer:

30 , 30 , 120 .

Step-by-step explanation:

Given :

To find :

Solution :

As we know that the angle sum property is 180° , that is the sum of all the interior angles is 180° .

Let us take the given ratio to be 1x:1x:4x .

Sum of these= 1x + 1x + 4x = 6x .

So we can create a equation as ,

==> 6x = 180°

==> x = 180°/6

==> x = 30°

Now we can find the angles as ,

Hence the angles of the triangle are 30° , 30° and 120° .

The probability that at least two of the six members of a family are not born in the fall is approximately 0.66.

Since there are four seasons and each season has an equal probability of containing a randomly selected person's birthday, the probability that a person's birthday is not in the fall is 3/4. Therefore, the probability that all six family members are born in a season other than fall is (3/4)⁶, which is approximately 0.18.

The probability that only one family member is born in the fall is 6*(1/4)*(3/4)⁵, which is approximately 0.41. To find the probability that at least two family members are not born in the fall, we can subtract the probability that all six are born in the fall or only one is born in the fall from 1: 1 - 0.18 - 0.41 = 0.41.

In conclusion, the chance of having at least two out of the six family members not born in the fall is roughly 66%.

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We can estimate that approximately 14.17% of students in the district are interested in playing hockey.

Total interested students = 0.1417 x 4,000 = 567.

An average proportion is the sum of a set of proportions divided by the number of proportions.

It represents the average or typical value of the proportions in the set, and can be used to estimate the overall proportion or percentage of a larger population

To estimate the total number of students in the district who are interested in playing hockey, we can first find the proportion of students in each sample who said yes, and then use the average proportion across all four samples to estimate the proportion of students in the district who are interested.

Finally, we can multiply this proportion by the total number of students in the district to estimate the total number of interested students.

The proportion of students in each sample who said yes is:

Sample 1: 4/30 = 0.1333

Sample 2: 5/30 = 0.1667

Sample 3: 5/30 = 0.1667

Sample 4: 3/30 = 0.1000

The average proportion across all four samples is:

(0.1333 + 0.1667 + 0.1667 + 0.1000) / 4 = 0.1417

To estimate the total number of interested students, we can multiply this proportion by the total number of students in the district: Total interested students = 0.1417 x 4,000 = 567.

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Answer: Yes, they are similar

Step-by-step explanation: HAVE AN AMAZING DAY AND GOOD GRADES!!!!! :D

Answer: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (4 in 4xy)

Step-by-step explanation: the coefficient is the number or digit that is being multiplied and it is placed before a constant quantity

Answer:

A) 39

B) 900

C) 60%

A) proportion:

21.84 is 56% of x number

x number = 100%

If you want to calculate x you can use proportion. First of all make this kind of system..

x - 100%

21.84 - 56%

Then multiply numbers diagonally.

56x = 2184

Finally solve x

x = 2184/56

x = 39