I need the first one

The first mistake in Ismail's proof is that (3) cos(90 - Ф) = AC/BC

The complete question is added as an attachment

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

The two column proof

In the two column proof, we have

cos(90 - Ф) = AC/BC

This equation is incorrect because by the definition of cosine, we have

cos(90 - Ф) = AB/BC

i.e. cos(x) = adjacent/hypotenuse

Hence, the mistake in his proof is cos(90 - Ф) = AC/BC

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Answer: a

Step-by-step explanation: it's increasing and it's a line

Answer:

This is not math...

Step-by-step explanation:

Using the system of equations, we found the number of adult tickets sold as 82 and the number of child tickets sold as 42.

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Given,

Number of tickets sold = 124

Cost of one adult ticket = $ 12.50

Cost of one child ticket = $ 6.50

Total money received = $ 1298

We can write a system of equations using the above information.

Number of adult tickets sold = x

Number of child tickets sold = y

x + y = 124

12.5x + 6.5y = 1298

Solving the above equations, we can find x and y.

Multiplying the first equation by 6.5

6.5x+ 6.5y = 806

12.5x + 6.5y = 1298

Subtracting the equations,

-6x = -492

x = 82

Substituting the above value in any one of the equation

82 + y = 124

y = 42

Therefore from the system of equations, the number of adult tickets sold is 82 and the number of child tickets sold is 42.

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Answer:

Step-by-step explanation:

12 x 3 =36

Answer:

Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:

Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.

Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.

Simplify the equation: On simplifying the equation, we get: y = 2x - 2.

Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.

Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.

Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.

That's it! You have successfully graphed the equation -3y + 6x = 6.

Answer:



Step-by-step explanation:

16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C

The given diagram is a triangle with the following sides

Hypotenuse = AC = 18

m<A = 68 Degrees

We need to determine the measure of a, b and m<C

Using the trigonometry identity

sin 68 = a/18

a = 18sin68

a = 16.7

Similarly;

cos68 = c/18

c = 18cos68

c = 6.7

Since the sum of angles in a triangle is 180 degrees, hence:

m<C = 90 - m<A

m<C = 90 - 68

m<C = 22 degrees

Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.

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Answer:

[tex]\frac{1}{22}[/tex]

Step-by-step explanation:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:

[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

[tex]\frac{1}{\sqrt{x}+11}[/tex]

and now we can directly plug in 121

[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]

The amount of federal state tax Selina owes if her gross pay for two weeks is $840 is  $14.11, which is closest to option A: $16.17. so the best answer is A as it is the closest.

To calculate Selina's federal tax contribution, we first need to determine her taxable income. From her gross pay of $840, we can subtract the biweekly standard deduction for a single person, which is $191.15 (based on the federal tax table provided). This gives us a taxable income of $648.85.

Using the federal tax table for biweekly earnings of a single person, we can see that the federal tax on this amount is $67.25.

Selina's state tax deduction is 21% of her federal tax contribution, which is 0.21 x $67.25 = $14.11.

Therefore, the amount of state tax Selina owes is $14.11, which is closest to option A: $16.17. However, none of the given options match the calculated amount exactly, so the best answer is A as it is the closest.

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Three possible rectangles of area 24 square inches are:

A rectangle with width 6 inches and length 4 inches

A rectangle with width 8 inches and length 3 inches

A rectangle with width 4 inches and length 6 inches

It should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.

In this case, W and L are variables and A is a constant.

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Answer:

So, the answer is (b) 320 feet.

Step-by-step explanation:

Let's call the length and width of the first playground "x".

The perimeter of the first playground is 160 feet, so 2 times the length plus 2 times the width is equal to 160:

2x + 2x = 160

Simplifying:

4x = 160

Dividing both sides by 4:

x = 40

So the length and width of the first playground are both 40 feet.

The second playground is twice as long and twice as wide as the first playground, so the length and width of the second playground would be 2 * 40 = 80 feet.

The perimeter of the second playground would then be 2 * 80 + 2 * 80 = 320 feet.

So, the answer is (b) 320 feet.

The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 75x + 0.55y = 125.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute x=0, 1, 2, 3, 4, 5,....

When x=0

75(0)+0.55y=125

0.55y=125

y=125/0.55

y=227

When x=1

75(1)+0.55y=125

0.55y=50

y=50/0.55

y=91

When x=2

75(2)+0.55y=125

0.55y=-25

y=-25/0.55

y=-45.45

Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

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The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Answer:

3/400 per min

Explanation:

Divide the rate at which he can walk by the number how mins he can walk at that rate

The evaluation of the function expressions gives:

(q + f)(5) = 1

(f - q)(2) = -2

(q f)(4) = 9

(f /q)(0) = 1

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

From the graph, when c = 5, q(5) = 0, f(5) = 1. Thus:

(q + f)(5) = 0 + 1 = 1

From the graph, when c = 2, f(2) = 0, q(2) = 2. Thus:

(f - q)(2) = 0 - 2 = -2

From the graph, when c = 4, q(4) = 3, f(4) = 3. Thus:

(q f)(4) = 3 * 3 = 9

From the graph, when c = 0, f(0) = 4, q(0) = 4. Thus:

(f /q)(0) = 4/4 = 1

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the displacement is 23.14m and the velocity is 21.28m/s

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation y  = 25t - 1.86t²

at t =  1

So the displacement y = 25-1.86 = 23.14

to find velocity dy/dt = 25- 2(1.86)t

v = 25 - 3.72 = 21.28m/s

Hence the displacement is 23.14m and velocity is 21.28m/s

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Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

Average = (Sum of all values) / (Number of values)

Average = ($19) / (7 days)

Average = ($19) / (7)

Average = $2.71

Sunday = ($2.71) x (7)

Sunday = $19.00 + $76.00

Sunday = $95.00

Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

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Answer:

$121.00

Step-by-step explanation:

y = 18.50x + 47.00

y = the total amount in the account

x = the number of weeks

y = 18.50(4) + 47.00

y = 74.00 + 47.00

y = 121

Answer:

2489

Step-by-step explanation:

it would be 30+ 1,000+29+30+400+1,000+ 2489

I really hope this helps

Proverbs 4:6-7

Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)

Answer:

2489

Step-by-step explanation:

19.375 pounds is the weight of bike.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that the  frame of a bike weighs16 pounds.

each tire weighs 9 ounces.

In a bike there are 2 tires, so total weight of tires is 2×9=18 ounces.

The seat weighs 12 ounces

The handlebars weigh 24 ounces.

Convert the ounces to pounds.

We know that 1 pound=16 ounces

So The total number of weight in ounces is 18+12+24=54 ounces

Divide by 16 to convert 54 ounces to pounds

54/16=3.375

Now total weight=16+3.375 pounds

=19.375

Hence, 19.375 pounds is the weight of bike.

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The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)

Thus, the required equation among the option is y = -3x + 2.

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The solution is, the equation of the line is y = 2x/3 + 2, that is, The correct option is A.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept(This is the point where the line cut across the y axis.

The first step is to find the slope. The formula is

Slope, m = (y2 - y1)/(x2 - x1)

From the given points on the graph,

when x1 = 0, y1 = 2

when x2 = 3, y2 = 4

m = (4 - 2)/(3 - 0)

m = 2/3

Looking at the graph, at the point where the line cuts the y axis, y = 2. Thus, c = 2

We would substitute m = 2/3 and c = 2 into the slope intercept equation. Thus, the equation of the line is

y = 2x/3 + 2

The correct option is A.

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The candidates received ;

Person A = 734 votes

Person B = 793 votes

Person C = 798 votes

From the information given, we have that;

Now, substitute the values

Person A + Person B + Person C = 2325

Person B - 59 + Person B + Person + B = 2325

Let Person B = x

x -59 + x + x + 5 = 2325

collect like terms

3x = 2325 +54

Add the like terms

3x = 2379

Make 'x' the subject of formula

x = 2379/3

x = 793 votes

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The probability that the sample proportion exceeds 0.12 is given as follows:

0.6103 = 61.03%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The parameters of the binomial distribution are given as follows:

n = 90, p = 0.13.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:

Z = (0.12 - 0.13)/0.0354

Z = -0.28

Z = -0.28 has a p-value of 0.3897.

Hence:

1 - 0.3897 = 0.6103.

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Answer:

1.8 quintillion or 1,800,000,000,000,000,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

the Answer is b

To the nearest tenth, 13.55% of people aged 29 have some form of cardiac disease.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

The function for the estimation of the percentage of heart disease is,

[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]

The percentage will be calculated as:-

[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]

[tex]P =\dfrac{ 120}{1+372e^{-0.133\times 29}}[/tex]

P= 120 / ( 1 +7.85)

P = 13.55%

Therefore, 13.55% of adults aged 29 have a heart condition, to the closest tenth.

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The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the probability of a tornado in any given year is 0.08,

the probability of no tornado in any given year is;:

=  1 - 0.08

= 0.92.

Let X be the number of tornadoes in a 22-year period.

X follows a binomial distribution with n = 22 and p = 0.08.

We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.

This can be written as:

P(X < 2) = P(X = 0) + P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038

P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214

So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.

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The distance between the line and the point is 2 units

A perpendicular line will give the shortest distance between a point and a line.

From the equation of the line y = x+1. Therefore the slope is 1

using the equation (y-y1) = m(x-x1)

equation of the line joining the point and the line

= y-(-6) = -1(x - (-5)

= y+6 = -x-5

y = -x-11

x-1 = -x-11

2x = -10

x = -5

y = -5+1

y = -4

(x,y) = (-5,-4)

d = √ -5-(-5)²+ -4-(-6)²

d = √ 0+ 4

d = √4

d = 2 unit

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The copy machine make 44 copies per minute.

The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;

We are given that Time copy machine take= 4min 15sec

Number of copies=187

Now, 1min=60sec

4min=240sec

Total time=240+15 =255sec

Therefore, 255sec=187copies

60sec= 187 x 60/255

=44

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