Times taken to complete a task
A
Here is a histogram showing
the times taken to complete
a task.
40-
Estimate the percentage of 35-
people who took less than
30 seconds to complete
the task.
30-
25-
Give your answer to
L
1 decimal place.
20-
Frequency
Density 15-
10-
5-
0+
0 5 10 15 20 25 30 35 40 45 50
Time (seconds)

The volume of the sphere is 39 cubic yards

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

The figure

Also, we have

a = 2.1 yards

Using the above as a guide, we have the following:

Volume = 4/3πa³

substitute the known values in the above equation, so, we have the following representation

Volume = 4/3 * π * 2.1³

Evaluate

Volume = 39

Hence, the volume is 39cubiv yard

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Answer: 2,220 cabinets

Step-by-step explanation:

The break-even point is the point where the total revenue equals the total cost. In this case, the total cost is the sum of the fixed cost and the variable cost, and the total revenue is the product of the selling price and the number of cabinets sold. So, we can set up the following equation:

118x = 111,300 + 65x

Where x is the number of cabinets sold.

Simplifying and solving for x, we get:

53x = 111,300

x = 2,100

Rounding to the nearest unit, we get:

x ≈ 2,220

Therefore, Nanno Metal Products must sell approximately 2,220 filing cabinets to break even.

Circumference of a circle = 2πr

So,

\(circumference = 2\pi \: r \\ = > circumference = 2 \times \frac{22}{7} \times \frac{63 \: cm}{2} \\ = > circumference = 2 \times \frac{11}{7} \times 63 \: cm \\ = > circumference = 2 \times 11 \times 9 \: cm \\ = > circumference = 198 \: cm\)

Answer: Therefore, the circumference of circle is 198 cm.

Step-by-step explanation:

diameter = 63 cm

radius = 63/2 = 31.5 cm

circumference = ?

circumference or perimeter of circle = 2*pi*r

= 2*(22/7)*31.5

= (44/7)*31.5

= 198 cm

As per the question, 33 boys tried the track and 87 boys didn't, whereas 12 girls tried the track and 68 girls didn't.

Total number of boys = 120

Total number of girls = 80

Students who tried out for track = 45

Students that were girls = 45

If 12 were girls, therefore,

Total number of boys -

= 45 - 12

= 33

This means that 33 boys tried the track

Now, since 12 girls tried the track

Boys who did not try the track -

= 120 - 33

= 87

Girls who did not try the track -

= 80 - 12

= 68

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To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:

    x - 4

____________

To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:

markdown

Copy code

    x - 4

____________

x + 8 | x^2 + 4x - 32

- (x^2 + 8x)

____________

-4x - 32

- ( -4x - 32 )

____________

0

Therefore, the quotient is x - 4.

Answer:

A circle of radius = 7 or diameter = 14 or circumference = 43.98 kilometers has an area of: 153.9 square kilometers (km²) 1.539 × 10 8 square meters (m²)

Step-by-step explanation:

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

B

10

Step-by-step explanation:

go up 7 then over 3, add them together and you got 10

Answer:

B. 7 = n + 4

Step-by-step explanation:

7 dogs

4 doberman

n Non doberman

7 - 4 = n

so B.  7 = n + 4

Answer:

\(10^{-3}\)

Step-by-step explanation:

Answer:

https://tex.z-dn.net/?f=10%5E%7B-3%7D

Step-by-step explanation:

The IQR for the males' data is 12.

The median would be a better measure of center for females' data.

The mean would be a better measure of center for males' data.

A possible reason for the outlier in the data set could be over sampling.

Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of male = Q₃ - Q₁

Interquartile range (IQR) of male = 15 - 3

Interquartile range (IQR) of male = 12.

For the difference between the median values of each data set, we have the following:

Median difference of male and female data = 10 - 6

Median difference of male and female data = 4.

The female's data has an outlier while the male's data does not have any outlier. Therefore, the median would a better measure of center for the female's data while the mean is a better measure of center for the male's data.

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Answer:

A would be at (-2,5) if reflected across the y axis

Answer:

(-2,5)

Step-by-step explanation:

Reflecting a point across the y axis mirrors it.

An expression is defined as a set of numbers, variables, and mathematical operations. The statements that are true are 1, 3, and 5.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

For the given expression 4x + 9 - y(6x + 7), the following things are can be written,

Thus, the statements that are true are:

Hence, the statements that are true are 1, 3, and 5.

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Answer:

A. (8, -2)

Step-by-step explanation:

Midpoint Formula: \((\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\)

We are given midpoint and 1 endpoint, so simply set the equation and solve:

1 = (-6 + x)/2

2 = -6 + x

x = 8

2 = (6 + y)/2

4 = 6 + y

y = -2

Answer:

no because the decimal doesn't have a % sign its 147.5

Answer: I do not understand

Step-by-step explanation:

Total volume is 45 unit³

We have given that the composite figure consists of two rectangular pyramids.

Suppose they are joined together to form the given figure, stacked to each other on their base.

\(Volume of pyramid=\frac{L\times w\times h}{3}\)

Bye using the formula we get

\(=\frac{9\times 1.5\times 5}{3}\\ =\frac{45}{2}\)

now, Since there are two pyramids in the figure on same base and height,

their volume will be equal

So area of composite figure

\(=\frac{45}{2}\times2\)

Therefore, the volume of the given figure = 45 units³

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Answer:

\(\boxed{440 km}\)

Step-by-step explanation:

→ Work out time between New Delhi and Lucknow

12:00 - 4:00 = 8:00

→ State the speed formula

Speed = Distance ÷ Time

→ Rearrange to make distance the subject

Distance = Speed × Time

→ Substitute in the values

55 × 8 = 440 km

Answer:

31764 is the answer ....

Hope it helps!!!

Answer: 12,600 + 31,764

Step-by-step explanation:

The required value of x is 6 / 7.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx     —-- 1

Now, find constant of proportion for given x = 2 and y = 7, we need to put these values in equation 1, i.e.

7 = k(2)

k = 7 / 2

Further calculate x for given y = 3 i.e.

3 = (7 / 2)x

x = 6 / 7

Hence, the required value of x is 6 / 7.

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Answer:

The answer is $2.14 per pound of apples.

Step-by-step explanation:

7.29/3.4= roughly 2.14.

Answer:

is 24.786

Step-by-step explanation:

multiply the numbers and that's how you get your answer and I use my calculator so I know the answer is 24.786

The Matlab code to approximate the derivative of sin(x) at x=0.5 using numerical differentiation is as follows:

```matlab

x = 0.5; % value of x

h = 1; % initial step size

for i = 1:20

   derivative = (sin(x + h) - sin(x)) / h; % forward difference approximation

   disp(derivative); % print the derivative

   h = h / 10; % divide h by 10 for the next iteration

end

```

The code provided implements the numerical differentiation technique to approximate the derivative of sin(x) at x=0.5. It starts with an initial step size of h=1 and iteratively divides h by 10 at each step until twenty approximations are computed.

The derivative is approximated using the forward difference formula, which calculates the difference quotient. By taking the difference of the function values at x+h and x, divided by h, we obtain an approximation of the derivative. In this case, we evaluate the sin function at x+h and x to estimate the derivative at x=0.5.

As the code runs, it prints all twenty approximations of the derivative to the screen. The initial approximations are computed with a relatively large step size, and as the step size decreases, the approximations become more accurate. This is because a smaller step size leads to a better estimation of the slope of the curve at the given point.

Interpretation:

The printed results show how the approximations of the derivative evolve as the step size decreases. Initially, with a larger step size of 1, the approximations may not be very accurate. However, as the step size decreases by a factor of 10 in each iteration, the approximations improve and become more precise.

This behavior can be explained by considering the concept of local linearity. Numerical differentiation approximates the derivative by calculating the slope of a secant line between two points on the curve. As the step size decreases, the secant line approaches the tangent line, resulting in a more accurate estimation of the derivative.

The printed approximations reflect this convergence towards the true value of the derivative at x=0.5. The earlier values may deviate from the true derivative, but as the step size gets smaller, the approximations become closer to the expected value.

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Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Answer:

The answer is C

Step-by-step explanation:

(a) The set W of vectors in R³ whose components form Pythagorean triples is not a subspace of the vector space.

(b) The set of 2x2 matrices whose trace is nonzero is a subspace of the vector space.

(a) To determine whether W is a subspace of the vector space, we need to check if it satisfies the three conditions of the subspace test. The first condition is that W must contain the zero vector. In this case, the zero vector is (0, 0, 0). However, this vector does not satisfy the Pythagorean triples condition, as a² + b² + c² ≠ 0. Therefore, W fails the first condition and is not a subspace.

(b) To determine whether the set of 2x2 matrices whose trace is nonzero is a subspace, we need to verify the three conditions of the subspace test. The first condition is satisfied since the zero matrix, which has a trace of zero, is not included in the set. The second condition is that the set must be closed under addition. Let A and B be two matrices in the set with traces a and b, respectively. The sum of A and B will have a trace of a + b, which is nonzero since a and b are both nonzero. Hence, the set is closed under addition. The third condition, closure under scalar multiplication, is also satisfied as multiplying a matrix by a nonzero scalar does not change the trace. Therefore, the set of 2x2 matrices whose trace is nonzero is a subspace of the vector space.

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The function is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|. The correct option is B.

The absolute value or modulus of a real number x, denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically,|x|=x.

In the given image the function is represented by the equation y = | x - 2 |. Now the similar function which is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|.

Therefore, the correct option for the function is B.

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The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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