Fill in the gap for the given equation to have:No solutionsOne solutionInfinitely many solutions

Answer: 2 feet tall

Step-by-step explanation: 5*6=30/60=2

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

You can prove that angle C is 30°. This is because we know that angle B is 120° also, and interior angles add to 180°, which makes angle BCF 60°. Then we can divide this by 2 as angle BCF is bisected by AC, so, therefore, angle ACF is 30° as 60 ÷ 2 = 30.

You can then prove angle A is 90°. First, we can find angle BAC because it is part of a triangle, and angles in a triangle add to 180°. This means we can do 30 + 120 = 150, and 180 - 150 = 30° which is angle BAC. Then we do 120 - 30 = 90, as the whole of angle BAF is 120°.

I hope this helps!

Answer:

-5x=-10

Step-by-step explanation:

Adding both equations will result in this

Answer:

A= 7

B= 8

C= 3

Step-by-step explanation:

For C: 9=C*C-->C=SQRT(9)=3

For B: Some number ending in 4 is equals to B*C, C being 3. Then, the first number that fits that criteria would be B=8, as B*C=8*3=24.

For C: Some number ending in 1 equals to A*C. Then, the first number that fits that criteria is A=7, as A*C=7*3=21.

If you now multiply ABC*ABC (783*783) you'll see that all the elements in the multiplication process as carried out in the pdf are non-zero, so our answer satisfies the conditions of the problem!

Answer:

4000

Step-by-step explanation:

140$ = 3.5 , divide by 3.5 on both sides

1% = 40$

100% = 4000$

Answer:

\(\huge\boxed{\$4,000}\)

Step-by-step explanation:

\(p\%=\dfrac{p}{100}\\\\3.5\%=\dfrac{3.5}{100}=0.035\\\\3.5\%\ \text{of}\ x\ \text{is}\ \$140\\\\0.035\cdot x=140\qquad\text{divide both sides by 0.035}\\\\\dfrac{0.035\cdot x}{0.035}=\dfrac{140}{0.035}\\\\x=4,000\)

(a) When measuring angle 9 and the lengths of AB and BC, one observation is required.

(b) The line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord, while the line drawn from the center of a circle to an endpoint of a chord bisects the chord.

a) In the given diagram, we have angle AOB (angle 9) and line segments AB and BC.

To measure angle 9, we use a protractor. We align the baseline of the protractor with the line segment OA, ensuring that the center point of the protractor coincides with the vertex O. Then, we read the degree measurement where the line segment OB intersects the protractor. Let's assume the measurement of angle 9 is x degrees.

To measure the length of line segments AB and BC, we use a ruler. We align the ruler with the line segments and read the length in units (e.g., centimeters or inches).

b) The statements to complete are:

(i) The line drawn from the center of a circle to the midpoint of a chord will be perpendicular to the chord.

(ii) The line drawn from the center of a circle to the endpoint of a chord will bisect the chord.

In a circle, the center of the circle lies on the perpendicular bisector of any chord. This means that if we draw a line from the center of the circle to the midpoint of a chord, it will be perpendicular to the chord (statement i). Similarly, if we draw a line from the center of the circle to one of the endpoints of the chord, it will bisect the chord into two equal parts (statement ii).

These properties hold true for any chord in a circle, and they are based on the geometric properties of circles and perpendicular bisectors.

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The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

no problem glad to help

Answer:

the answer is d :)

Step-by-step explanation:

Answer: (In order)

25/4 / 6 1/4 = 1

3 1/7 / 2/7 = 11

5/4 / 1/4 = 5

11 1/4 / 9/4 = 5

8 1/4 / 3/4 = 11

3 1/3 / 10/3 = 1

Step-by-step explanation:

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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Answer:

0 degrees

Step-by-step explanation: the temperature outside is 4 degrees, when the temperature drops by 4 degrees it will equal 0 degrees.

4 - 4

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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Answer:

conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.

Step-by-step explanation:

H0 : μ1 = μ2

H0 : μ1 ≠ μ2

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

(49.5 - 48.5) / √(1.1²/38) + (2.6²/33)

1 / √0.2366905

Test statistic = 2.055

Using the Pvalue from Tstatistic calculator :

df = (smaller sample - 1) = 33 - 1 = 32

Pvalue from Test score calculator = 0.048

Pvalue > α ; Fail to reject the null ;

Hence, conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.

Answer:

$1,954

Step-by-step explanation:

The answer is in the image below ↓

Hope this helps! :)

Answer:

A if I'm wrong I apologize

I hope this helps and sorry if it's wrong

Answer:

True

Step-by-step explanation:

Slope:

The slope of an equation represents how the y value changes as the x values changes, defined as: \(\frac{\text{change in y}}{\text{change in x}}\), so the slope of 60 can be represented as: \(\frac{60}{1}\), which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.

The value of a for the given expression will be -3.31.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a ​ −1.6. The value of a will be calculated as below,

3.6 = − a/0.8 − 1.6 − 0.8 a ​ −1.6

3.6 + 1.6 + 1.6 = -a / 0.8  - 0.8a

6.8 = ( -a - 0.64a ) / 0.8

5.44 = -1.64a

a = -3.31

Therefore, the value of a will be -3.31.

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Answer:

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

Step-by-step explanation: INCOMPLETE QUESTION.

As the problem statement establishes:  "Each crop requires labor, fertilizer, and insecticide"  and information about quantities and availability does not exist. To build a model and that such model would be feasible I copy from the internet the following data. We assume the problem is to maximize the number of acres to plant with a maximum of profit ( we will use as profit the numbers 550  ;  350 ; 450 for  acres of corn, peanuts, and cotton)

Then z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

                                            labor (h)      fertilizer ( tn)    Insecticide (Tn)

acres of corn         (x₁)               2                     4                        3

acres of peanut     (x₂)              3                     3                        2

acres of cotton      (x₃)              2                     1                         4

Availability         acres 40       120                120                      100

Constraints:

1) Size of the farm 120 acres

x₁  +  x₂   +   x₃   ≤   40

2) labor   120 h

2*x₁  +  3*x₂  +  2*x₃    ≤   120

3) Fertilizer  120 Tn

4*x₁  +  3*x₂  +  1*x₃      ≤   120

4) Insecticide 100 Tn

3*x₁   +  2*x₂  +  4*x₃     ≤  100

The Model is:

z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

Subject to:

x₁  +  x₂   +   x₃   ≤   40

2*x₁  +  3*x₂  +  2*x₃    ≤   120

4*x₁  +  3*x₂  +  1*x₃      ≤   120

3*x₁   +  2*x₂  +  4*x₃     ≤  100

x₁    ≥   0  ;   x₂   ≥   0  ;   x₃   ≥   0

After 3 iterations using an on-line solver optimal solution is:

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

Answer:  c. Level of Significance

This is the alpha value

alpha is a greek letter with the symbol \(\alpha\)

A type 1 error is when the researcher rejects the null, but the null was true (meaning the researcher shouldn't have rejected the null).

From the given question;

1 cup = 16 tablespoons.

To get the number of cups that are equivalent to 40 table spoon, we will say;

x cups = 40 tablespoons

1 cup = 16 tablespoons.

x cups = 40 tablespoons

Cross multiply;

x * 16 = 40

divide both sides by 16

16x/16 = 40/16

x = 40/16

x = 2.5

Hence 2 1/2 cups is equivalent to 40 tablespoon

These two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

The correct system of equations to model this scenario is:

x + y = 414 (Equation 1)

9x + 12y = 3780 (Equation 2)

In this system, x represents the number of children and y represents the number of adults who played that day.

Equation 1 represents the total number of customers, which is 414. It states that the sum of the number of children (x) and the number of adults (y) is equal to 414.

Equation 2 represents the total cost of the games played. Since the cost for a child's game is $9 and the cost for an adult's game is $12, we multiply the number of children (x) by $9 and the number of adults (y) by $12. The equation states that the total cost, which is $3780, is equal to the sum of these individual costs.

Together, these two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

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Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}\)