60 minutes is 20% of
minutes.

Answer:

obtuse

Step-by-step explanation:

A triangle with sides of 3,4and6 is NOT a Right triangle.

Answer:

Given

Step-by-step explanation:

When the base is same but the exponents are different, the rule is that a^m/a^n

= a^m-n

So in this case let a be 5, m be 3 and n be 7

5^3/5^7

= 5^3-7

= 5^-4

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

We have,

To write the function represented by the graph in intercept form, we need to find the x and y intercepts and write the function as a product of linear factors.

From the graph and the given points, we can see that the function has

4 x-intercepts at -5, -2, 1, and 4.

We can also see that the function has 3 turning points at (-3.8, 95), (-1.4, 35), and (2.5, 40).

To find the y-intercept, we can use the point (-5.8, -160), which the curve emerges from.

This means that the function can be written in the form:

f(x) = a(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

where a is a constant to be determined.

To find the value of a, we can use any of the given points that lie on the curve. Let's use the point (-3.8, 95):

95 = a(-3.8 + 5.8)(-3.8 + 5)(-3.8 + 2)(-3.8 - 1)(-3.8 - 4)

Simplifying and solving for a, we get:

a = -95/((5.8)(3)(0.8)(4.8)(7.8)) ≈ -0.00038

Therefore,

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

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Answer: Choice B)   sin (33) = x/14

This is because the sine of an angle is equal to the opposite side over the hypotenuse

sin(angle) = opposite/hypotenuse

sin(33) = x/14

We can't use cosine because we don't have a variable for the adjacent side.

Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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Answer:

|x+3|>8

Step-by-step explanation:

x is positive, so remove the absolute value signs. Adding a number greater than 5 to 3 will result in a number greater than 8.

The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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Given matrices are u=6 −3 6 and v= −4 −2 3. u•v=0u2 =81v2 =29u v2 =0

When multiplying two matrices, it is important to verify that the inner dimensions match. If you try to multiply two matrices that don't have compatible inner dimensions, you will get the following error message:

"Error using * Inner matrix dimensions must agree.

"The product of matrices AB is defined if the number of columns of A is equal to the number of rows of B.The product matrix AB is defined as follows:

If A is an m x n matrix and B is an n x p matrix then AB is an m x p matrix u•v Calculation:6 −3 6 • −4 −2 3= (6)(-4)+(-3)(-2)+(6)(3)=-24+6+18=0So, u•v=0u2

Calculation:u2 =u•u= 6 −3 6 •6 −3 6= (6)(6)+(-3)(-3)+(6)(6)=36+9+36=81

Therefore, u2 =81v2 Calculation:v2 =v•v= −4 −2 3 • −4 −2 3=(−4)(−4)+(−2)(−2)+(3)(3)=16+4+9=29Therefore, v2 =29u v2 Calculation:u v2 =u•v•v= (6 −3 6 )• ( −4 −2 3 )2u v2 =0•(−4 −2 3 )=0Therefore, u v2 =0.

Summary:Given matrices are u=6 −3 6 and v= −4 −2 3. u•v=0u2 =81v2 =29u v2 =0

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Answer:

11 is your answer.

Step-by-step explanation:

We have the equation: n + 2x^2

We know that n = 3 and x = -2

Substitute the variables for their values.

3 + 2(-2)^2 = ?

Then just solve to get 11.

Answer:11

Step-by-step explanation:

The fractions of the hole above that are the standard 4 patterns blocks are as follows:Standard pattern block hexagon: 1/1 or 1Trapezoid: 0/1 or 0Parallelogram: 0/1 or 0Rhombus: 0/1 or 0

To find the fractions of the hole above that are the standard 4 patterns blocks, we need to analyze the given figures. The figures are as follows:

Figure 1: The standard pattern block hexagon

Figure 2: A trapezoid

Figure 3: A parallelogram

Figure 4: A rhombus

Now, we need to identify which of these figures fit into the given hole. Looking at the hole, we can see that it is in the shape of a hexagon. Therefore, the only pattern block that can fit into this hole is the standard pattern block hexagon. Hence, the fraction of the hole above that is the standard pattern block hexagon is 1/1 or simply 1. No other pattern blocks fit into the given hole. Therefore, the fractions of the hole above that are the standard 4 patterns blocks are as follows:

Standard pattern block hexagon: 1/1 or 1

Trapezoid: 0/1 or 0

Parallelogram: 0/1 or 0

Rhombus: 0/1 or 0

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Answer:

p≤1 or p∠-2

Step-by-step explanation:

REMEMBER OUR GOAL IS TO LEAVE P ALONE!!

p≤1:

1. \(\frac{3p+5}{2}\geq 4\) Multiply by 2 to cancel out 1/2 which would give you \({3p+5}\geq 8\)

2. Then subtract 5 which would give you 3p≥3

3. Then divide by 3 which will FLIP the ≥ into ≤.

4. Therefore, it's p≤1.

p∠-2:

1. \(\frac{p-6}{4}\leq -2\) Multiply by 4 to cancel out the denominator which would give you \(p-6\)∠-8

2. Add 6 to both sides which results in p<-2

Answer:

Simplifying

4y + 3 = 5x + -7 + 3x + 17

Reorder the terms:

3 + 4y = 5x + -7 + 3x + 17

Reorder the terms:

3 + 4y = -7 + 17 + 5x + 3x

Combine like terms: -7 + 17 = 10

3 + 4y = 10 + 5x + 3x

Combine like terms: 5x + 3x = 8x

3 + 4y = 10 + 8x

Solving

3 + 4y = 10 + 8x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 4y = 10 + -3 + 8x

Combine like terms: 3 + -3 = 0

0 + 4y = 10 + -3 + 8x

4y = 10 + -3 + 8x

Combine like terms: 10 + -3 = 7

4y = 7 + 8x

Divide each side by '4'.

y = 1.75 + 2x

Simplifying

y = 1.75 + 2x

Answer:

Adrian's songs played on 9 commercials and 5 movies.

Step-by-step explanation:

Let x denotes number of commercials and y denotes number of movies.

Total number of commercials and movies = 14

So,

\(x+y=14\\x=14-y\,\,\,\,...(i)\)

Adrian will earn $40 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie

Total amount earned = $1010

\(40x+130y=1010\,\,\,...(ii)\)

Put \(x=14-y\) in (ii)

\(40(14-y)+130y=1010\\560-40y+130y=1010\\90y=1010-560\\90y=450\\y=\frac{450}{90}=5\)

Put \(y=5\) in \(x=14-y\)

\(x=14-5=9\)

Therefore, Adrian's songs played on 9 commercials and 5 movies.

Answer:

15.

Step-by-step explanation:

3.75 / 25 = 15.

a) From z-test, we have enough evidence to accept that the mean life is different from 350 hours .

b) Using p-value, the probability that the life of light bulbs less than 350 and greater than 350 is 0.9772

c) The 95% confidence interval for population mean is: (325.5, 374.5)

Let μ be the population mean .

By observing the given information, we have :-

H0 : μ = 375

Hα : μ ≠ 375

Since the alternative hypotheses is two tailed so the test is a two-tailed test.

We assume that the  life of a large shipment of light bulbs is normally distributed.

(a) Given : Sample size :  n=64 , since n > 30 so we use z-test.

Sample mean = 350

standard deviation = 100

z = (350 - 375) / (100/√64)

z = -2

The critical value (two-tailed) corresponds to the given significance level :- z_(α/2) = 1.96

Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.

Therefore, we conclude that we have enough evidence to accept that the mean life is different from 350 hours .

(b) Now we find p value:

2p(z > -2) = 0.9772

This means that the probability that the life of light bulbs less than 350 and greater than 350 is 0.9772

(c) The 95% confidence interval for population mean would be:

= 350 ± (1.96)(100/√64)

= (350 - (1.96)(100/√64), 350 + (1.96)(100/√64))

= (325.5, 374.5)

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Given the following equation:

You know, based on the information given in the exercise, that it is a true equation. You can notice that the sum (the result of the Addition) of the terms on the left side of the equation, is:

Then, knowing the above and having the following expression:

You can substitute the sum of the equation into the expression:

Finally, adding the numbers, you get that the value of the expression is:

Answer: x ≈ 1.853 or \(log_{12}100\)

Step-by-step explanation:

      Given:

\(12^x=100\)

      Exponential form to logarithmic form:

\(log_{12}100=x\)

      Compute:

x ≈ 1.853

\(12^x=100\\x=\log_{12}100\)

If you want to use a scientific calculator to find the approximate value, you can express the solution using natural logarithm.

\(x=\dfrac{\log100}{\log12}\)

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Volumes.

Volume = base area * Height

hence, here,

base area = 1/2(3)(4)

base area = 6 sq. inches,

now volume = 6 * height

==> Volume = 6*11 = 66 cubic inches

====> hence the volume of the triangular prism is 66 cubic inches.

Actually Welcome to the Concept of the Volumes.

Volume = base area * Height

hence, here,

base area = 1/2(3)(4)

base area = 6 sq. inches,

now volume = 6 * height

==> Volume = 6*11 = 66 cubic inches

====> hence the volume of the triangular prism is 66 cubic inches.

Answer:

Length of diagonal in the first top figure is 13 yd

Okay for this one, the formula of a diagonal in a cuboid is the root of sum of squares

length, breadth and height

so

D = root of 12^2 + 4^2 + 3^2

D = root of 144 + 16 + 9

D = root 169

D = 13yd

Length of diagonal in the bottom figure is 10.77 which is 10.8m

For this one, you have to find the diameter of base first

Since radius of the base is 5 diameter = 10

Since its a right angled triangle, Hypotenuse square = sum of sides square

Diagonal^2 = 10^2 + 4^2

D^2 = 100 + 16

D^2 = 116

D = root 116

D = 10.77

D = 10.8 m

1. The fraction of full-time employees who work in the bank is 16/31.

2. The fraction of pieces that David need to fix to complete the puzzle is 9/27

3. The fraction of girls that wore red outfits is 1/2.

4. The fraction of books on the shelf that are in Spanish is 2/7.

1. Alocal community bank has 31 employees on it’s rolls. 15 employees work part-time at the bank. The fraction of full-time employees will be:

= (31 - 15) / 31

= 16/31

2. David was gifted a 28 piece puzzle by his aunt. He has fixed 19 pieces of the puzzle. The fraction of pieces that David need to fix will be:

= (28 - 19)/28

= 9/28

3. 20 girls were dressed in green outfits and 10 girls donned red outfits at a dance recital. The fraction of girls that wore red outfits will be:

= 10/20

= 1/2

4. A section of Tina’s bookshelf has 15 French books and 6 Spanish books. The fraction of books on the shelf that are in Spanish will be:

= Spanish books / Total books

= 6 / (15 + 6)

= 6/21

= 2/7

The above illustrate the fraction.

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The measure of the central angle is equal to the measure of the subtended arc and is given by

a) A = 100°

b) B = 170°

c) C = 60°

Given data ,

Let the circle be represented as A , B and C

where the measure of the subtended arc is given by

A = 100°

B = 170°

C = 60°

Now , The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

And , The measure of the central angle is equal to the measure of the subtended arc

So , the measure of angles are

a) A = 100°

b) B = 170°

c) C = 60°

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Answer:

\(y=-\frac{7}{1}x+2\)

Step-by-step explanation:

The slope of -7=

\(-\frac{7}{1}\)

so fractional slope is

\(y=mx+b\)

Substituting slope into a fraction,

\(y=-\frac{7}{1} x+b\)

Point is 0,2 so substitute in x and y.

\(2=-\frac{7}{1} (0)+b\)

Solve the equation.

\(b=2\)

So the equation for the line is

\(y=-\frac{7}{1}x+2\)

Hope this helps :D

Using section formula, the coordinates of M is (-2, 0)

To find the coordinates of point M, which partitions the line segment connecting L(-4, 2) and N(2, -4) in the ratio 1:2, we can use the concept of section formula.

We can use section formula here because the coordinates of point M can be determined if a line segment AB is divided at the point in the ratio m:n

M(x, y) = ((n * Ax) + (m * Bx)) / (m + n), ((n * Ay) + (m * By)) / (m + n)

In the given problem;

m = 1

n = 2

We may determine the coordinates of point M by substituting the coordinates of points L and N into the formula.

M(x, y) = ((2 * (-4)) + (1 * 2)) / (1 + 2), ((2 * 2) + (1 * (-4))) / (1 + 2)

Solving the problem;

Mx = (-8 + 2)/ 3

Mx = -2

My = (4 - 4) / 3

My = 0/3

My = 0

Putting the values together;

M(x, y) = -2, 0

Therefore, the coordinates of point M are (-2, 0).

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Complete question: Point M lies on the line segment connecting L(-4, 2) and N (2,-4). If M partitions the segment in the ratio 1:2, what are the coordinates of M?

The set of parameters that would give you the highest position within the class with a score of x = 75 is option (C) μ = 60 and σ = 5 is the correct answer.

In this question,

A z-score tells us how many standard deviations away a value is from the mean. A positive z-score indicates the raw score is higher than the mean average. A negative z-score reveals the raw score is below the mean average.

According to the Percentile to z-score calculator, the z-score that corresponds to the 90th percentile is 1.2816. Thus, any student who receives a z-score greater than 1.2816 would be considered a “good” z-score.

The z-score can be calculated as

z-score = \(\frac{x-\mu}{\sigma}\)

On substituting the above options of μ and σ with the score of x = 75,

a) μ = 70 and σ = 5,

z-score = \(\frac{75-70}{5}\)

⇒ \(\frac{5}{5}\) = 1

b) μ = 70 and σ = 10,

z-score = \(\frac{75-70}{10}\)

⇒ \(\frac{5}{10}\) = 0.5

c) μ = 60 and σ = 5,

z-score = \(\frac{75-60}{5}\)

⇒ \(\frac{15}{5}\) = 3

d) μ = 60 and σ = 10

z-score = \(\frac{75-60}{10}\)

⇒ \(\frac{15}{10}\) = 1.5

Thus the z-score 3, is the higher value. 99% have a z-score between -3 and 3. Therefore, the set of parameters that would give you the highest position within the class with a score of x = 75 is option (C) μ = 60 and σ = 5 is the correct answer.

The complete question is as follows,

If you have a score of x = 75 on an exam, which set of parameters would give you the highest position within the class?

The options for this question are a) μ = 70 and σ = 5, b) μ = 70 and σ = 10, c) μ = 60 and σ = 5, d) μ = 60 and σ = 10.

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Answer:

The pass costs $26.60, the souvenir costs $19.70, and the burger costs $2.45.

After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

So, -(8⁻²):

Now, evaluate -(8⁻²) as follows:

Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

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9514 1404 393

Answer:

  $12.07

Step-by-step explanation:

The cost is proportional to the weight, so we have ...

  dollars/pounds = c/4.2 = 8.62/3

Multiplying by 4.2 gives ...

  c = 4.2×8.62/3 = 12.068

The cost of 4.2 pounds of strawberries is $12.07.

Answer:

62

Step-by-step explanation:

38 + 48 ÷ 12 • 6

In an equation, we multiply and divide first, then add and subtract.

38 + 48 ÷ 12 • 6

= 38 + 4 · 6

= 38 + 24

= 62